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https://www.anl.gov/partnerships/case-study-economics-of-pollinator-habitats-at-solar-facilities
|
# Argonne National Laboratory
Science and Technology Partnerships and Outreach Directorate
# Case Study: Economics of Pollinator Habitats at Solar Facilities
### The Challenge
Insects such as bees and butterflies are at least partially responsible for pollinating nearly 75 percent of all crops consumed by humans. But as man-made environmental stressors – including pesticides and land development – have increased, insect pollinators have lost habitats and species have declined significantly.
### The Approach
A team of researchers from Argonne and the U.S. Department of Energy’s National Renewable Energy Laboratory examined the potential benefits of establishing pollinator habitats at utility-scale solar energy (USSE) facilities to conserve pollinators and restore the ecosystem they provide.
Looking at more than 2,800 existing and planned USSE facilities in the contiguous U.S., researchers found that the area around solar panels could provide an ideal location for the plants that attract pollinators. Often filled with gravel or turf grass, this land otherwise goes unused. The team concluded that establishing native plant species – such as prairie grass or wildflowers – around solar panels would encourage steady population growth in the insect pollinators.
### The Results
The researchers identified about 12 million hectors of land across the U.S. (more than 1,200 counties) that are suitable for pollinator habitat development.
The team found that by marrying solar installation with a pollinator habitat, we can increase the number of pollinators, which aids crop production in the vicinity. This also reduces maintenance costs for operators.
The researchers estimate that the value of pollinator habitats over 1.1 million hectors of such land to be between $1.5 billion and$3.2 billion to energy producers and farmers.
| 2023-02-08T11:41:07 |
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|
https://dlmf.nist.gov/10.32
|
# §10.32 Integral Representations
## §10.32(i) Integrals along the Real Line
10.32.1 $I_{0}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^{\pm z\cos\theta}\mathrm{d}% \theta=\frac{1}{\pi}\int_{0}^{\pi}\cosh\left(z\cos\theta\right)\mathrm{d}\theta.$
10.32.2 $I_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma\left% (\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{\pm z\cos\theta}(\sin\theta)^{2\nu}% \mathrm{d}\theta=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma\left(\nu+% \frac{1}{2}\right)}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{\pm zt}\mathrm{d% }t,$ $\Re\nu>-\tfrac{1}{2}$.
10.32.3 $I_{n}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^{z\cos\theta}\cos\left(n% \theta\right)\mathrm{d}\theta.$
10.32.4 $I_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^{z\cos\theta}\cos\left(\nu% \theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu\pi\right)}{\pi}\int_{0}^{% \infty}e^{-z\cosh t-\nu t}\mathrm{d}t,$ $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
10.32.5 $K_{0}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\pi}e^{\pm z\cos\theta}\left(% \gamma+\ln\left(2z(\sin\theta)^{2}\right)\right)\mathrm{d}\theta.$
10.32.6 $K_{0}\left(x\right)=\int_{0}^{\infty}\cos\left(x\sinh t\right)\mathrm{d}t=\int% _{0}^{\infty}\frac{\cos\left(xt\right)}{\sqrt{t^{2}+1}}\mathrm{d}t,$ $x>0$.
10.32.7 $K_{\nu}\left(x\right)=\sec\left(\tfrac{1}{2}\nu\pi\right)\int_{0}^{\infty}\cos% \left(x\sinh t\right)\cosh\left(\nu t\right)\mathrm{d}t=\csc\left(\tfrac{1}{2}% \nu\pi\right)\int_{0}^{\infty}\sin\left(x\sinh t\right)\sinh\left(\nu t\right)% \mathrm{d}t,$ $|\Re\nu|<1$, $x>0$.
10.32.8 $K_{\nu}\left(z\right)=\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\Gamma\left% (\nu+\frac{1}{2}\right)}\int_{0}^{\infty}e^{-z\cosh t}(\sinh t)^{2\nu}\mathrm{% d}t=\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\Gamma\left(\nu+\frac{1}{2}% \right)}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\mathrm{d}t,$ $\Re\nu>-\tfrac{1}{2}$, $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
10.32.9 $K_{\nu}\left(z\right)=\int_{0}^{\infty}e^{-z\cosh t}\cosh\left(\nu t\right)% \mathrm{d}t,$ $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
10.32.10 $K_{\nu}\left(z\right)=\tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp% \left(-t-\frac{z^{2}}{4t}\right)\frac{\mathrm{d}t}{t^{\nu+1}},$ $|\operatorname{ph}z|<\tfrac{1}{4}\pi$.
### Basset’s Integral
10.32.11 $K_{\nu}\left(xz\right)=\frac{\Gamma\left(\nu+\frac{1}{2}\right)(2z)^{\nu}}{\pi% ^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos\left(xt\right)\mathrm{d}t}{(% t^{2}+z^{2})^{\nu+\frac{1}{2}}},$ $\Re\nu>-\tfrac{1}{2}$, $x>0$, $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
## §10.32(ii) Contour Integrals
10.32.12 $I_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z% \cosh t-\nu t}\mathrm{d}t,$ $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
### Mellin–Barnes Type
10.32.13 $K_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i% \infty}\Gamma\left(t\right)\Gamma\left(t-\nu\right)(\tfrac{1}{2}z)^{-2t}% \mathrm{d}t,$ $c>\max(\Re\nu,0),|\operatorname{ph}z|<\frac{1}{2}\pi$. ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\mathrm{i}$: imaginary unit, $\int$: integral, $K_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Bessel function of the second kind, $\operatorname{ph}$: phase, $\Re$: real part, $z$: complex variable and $\nu$: complex parameter Keywords: Mellin transform Referenced by: Erratum (V1.0.11) for Equation (10.32.13) Permalink: http://dlmf.nist.gov/10.32.E13 Encodings: TeX, pMML, png Errata (effective with 1.0.11): Originally the constraint $|\operatorname{ph}z|<\frac{1}{2}\pi$ was written incorrectly as $|\operatorname{ph}z|<\pi$. Reported 2015-05-20 by Richard Paris See also: Annotations for §10.32(ii), §10.32(ii), §10.32 and Ch.10
10.32.14 $K_{\nu}\left(z\right)=\frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}% {2}}e^{-z}\cos\left(\nu\pi\right)\*\int_{-i\infty}^{i\infty}\Gamma\left(t% \right)\Gamma\left(\tfrac{1}{2}-t-\nu\right)\Gamma\left(\tfrac{1}{2}-t+\nu% \right)(2z)^{t}\mathrm{d}t,$ $\nu-\tfrac{1}{2}\notin\mathbb{Z},|\operatorname{ph}z|<\tfrac{3}{2}\pi$.
In (10.32.14) the integration contour separates the poles of $\Gamma\left(t\right)$ from the poles of $\Gamma\left(\frac{1}{2}-t-\nu\right)\Gamma\left(\frac{1}{2}-t+\nu\right)$.
## §10.32(iii) Products
10.32.15 $I_{\mu}\left(z\right)I_{\nu}\left(z\right)=\frac{2}{\pi}\int_{0}^{\frac{1}{2}% \pi}I_{\mu+\nu}\left(2z\cos\theta\right)\cos\left((\mu-\nu)\theta\right)% \mathrm{d}\theta,$ $\Re\left(\mu+\nu\right)>-1$.
10.32.16 $I_{\mu}\left(x\right)K_{\nu}\left(x\right)=\int_{0}^{\infty}J_{\mu\pm\nu}\left% (2x\sinh t\right)e^{(-\mu\pm\nu)t}\mathrm{d}t,$ $\Re\left(\mu\mp\nu\right)>-\tfrac{1}{2}$, $\Re\left(\mu\pm\nu\right)>-1$, $x>0$.
10.32.17 $K_{\mu}\left(z\right)K_{\nu}\left(z\right)=2\int_{0}^{\infty}K_{\mu\pm\nu}% \left(2z\cosh t\right)\cosh\left((\mu\mp\nu)t\right)\mathrm{d}t,$ $|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
10.32.18 $K_{\nu}\left(z\right)K_{\nu}\left(\zeta\right)=\frac{1}{2}\int_{0}^{\infty}% \exp\left(-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}\right)K_{\nu}\left(\frac{z% \zeta}{t}\right)\frac{\mathrm{d}t}{t},$ $|\operatorname{ph}z|<\pi$, $|\operatorname{ph}\zeta|<\pi$, $|\operatorname{ph}\left(z+\zeta\right)|<\tfrac{1}{4}\pi$.
### Mellin–Barnes Type
10.32.19 $K_{\mu}\left(z\right)K_{\nu}\left(z\right)=\frac{1}{8\pi i}\int_{c-i\infty}^{c% +i\infty}\frac{\Gamma\left(t+\frac{1}{2}\mu+\frac{1}{2}\nu\right)\Gamma\left(t% +\frac{1}{2}\mu-\frac{1}{2}\nu\right)\Gamma\left(t-\frac{1}{2}\mu+\frac{1}{2}% \nu\right)\Gamma\left(t-\frac{1}{2}\mu-\frac{1}{2}\nu\right)}{\Gamma\left(2t% \right)}(\tfrac{1}{2}z)^{-2t}\mathrm{d}t,$ $c>\tfrac{1}{2}(|\Re\mu|+|\Re\nu|),|\operatorname{ph}z|<\tfrac{1}{2}\pi$.
For similar integrals for $J_{\nu}\left(z\right)K_{\nu}\left(z\right)$ and $I_{\nu}\left(z\right)K_{\nu}\left(z\right)$ see Paris and Kaminski (2001, p. 116).
## §10.32(iv) Compendia
For collections of integral representations of modified Bessel functions, or products of modified Bessel functions, see Erdélyi et al. (1953b, §§7.3, 7.12, and 7.14.2), Erdélyi et al. (1954a, pp. 48–60, 105–115, 276–285, and 357–359), Gröbner and Hofreiter (1950, pp. 193–194), Magnus et al. (1966, §3.7), Marichev (1983, pp. 191–216), and Watson (1944, Chapters 6, 12, and 13).
| 2020-10-24T02:54:44 |
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https://www.usgs.gov/center-news/volcano-watch-m56-pahala-earthquake
|
# Volcano Watch — M5.6 Pahala earthquake
Release Date:
After an earthquake felt by residents of Hawaii County, we at the U S Geological Survey's Hawaiian Volcano Observatory are often asked what the earthquake means or indicates in terms of the volcano's behavior. It is beyond our ability to know the detailed implications of a single earthquake event for the complex and inter-related volcanic and tectonic processes that shape our island.
After an earthquake felt by residents of Hawaii County, we at the U S Geological Survey's Hawaiian Volcano Observatory are often asked what the earthquake means or indicates in terms of the volcano's behavior. It is beyond our ability to know the detailed implications of a single earthquake event for the complex and inter-related volcanic and tectonic processes that shape our island. In response to public inquiries about specific earthquakes, then, sometimes our best response is, "It's a gentle reminder that we live in a geologically active region and that we can expect, on occasion, larger and potentially damaging earthquakes in the future."
Unfortunately, our reminders are not always so gentle - like the M5.6 that occurred beneath Pahala at 2:56 p. m. on Friday, April 16. As described in newspaper and television reports, this earthquake destroyed homes and interrupted the delivery of power to the affected region. Elsewhere, there were reports of small landslides or rockfalls near steep cliffs.
Seismologically speaking, a M5.6 earthquake is not a large earthquake. It's not even large for Pahala, which lies where the Kaoiki and Hilea fault zones on Mauna Loa's southeast flank come together. In 1868, the strongest earthquake historically recorded in Hawaii, estimated to be M7.9, is thought to have originated near April 16's M5.6 epicenter. While the M5.6 caused damage restricted to the earthquake's epicentral region, larger earthquakes like the November 16, 1983, M6.6 Kaoiki earthquake, the November 29, 1975, M7.2 Kalapana earthquake, as well as the 1868 earthquake can cause widespread damage, possibly affecting all of Hawaii County.
Sometimes, our telephone conversations with the general public end with, "You'll let us know when the Big One is coming, won't you?" It would be terrific if we could. However, it has proven to be difficult, if not impossible, to correctly and consistently predict the times, locations, and magnitudes of earthquakes.
With the knowledge that we've had damaging—and devastating—earthquakes in the past, and our gentle and not-so-gentle reminders that the volcanoes and island continue to be very active geologically, we can reasonably expect that more Big Ones will come. So, what can we do to try to protect ourselves and our communities against future earthquakes?
If we choose to live with the hazards posed by damaging earthquakes, we ought to be prepared to experience them and be prepared to respond, if necessary, after they occur. There are numerous steps that we can take to mitigate against the hazards that we are exposed to and to minimize the hardships and costs of putting our homes and communities back together after a disaster. A great deal of information regarding personal earthquake safety is available from the Hawaii County Civil Defense Agency, the Center for the Study of Active Volcanoes at UH-Hilo, and public libraries, as well as the USGS.
Other important tools in earthquake hazards and risk management and post-disaster recovery relate to appropriate zoning, planning, and design. Currently, the building code for Hawaii County is based on the 1991 Uniform Building Code (UBC). In the 1997 edition of the UBC, the International Conference of Building Officials has upgraded its seismic zonation of Hawaii County from Seismic Zone 3, as in the 1991 UBC, to Seismic Zone 4. This determination was based in part on recent USGS studies of earthquake occurrence and how seismic energy propagates through the island, and it signifies that Hawaii lies in a region exposed to the highest seismic hazards considered in the UBC.
We expect that, later this spring, the Hawaii County Council will be looking into adopting parts of the 1997 UBC. These will relate to the 1997 UBC seismic provisions for earthquake-resistant design with Hawaii County included in Seismic Zone 4. As we examine the effects of April 16's earthquake and recall our experiences from other damaging earthquakes, it is essential that we use what we know to develop effective mitigation programs designed to prevent or minimize the casualties and losses that might result from future earthquakes that we know will occur.
### Volcano Activity Update
Lava continues to erupt from Puu Oo and flow through a network of tubes from the vent to the sea near Kamokuna, in Hawaii Volcanoes National Park. A lava flow that oozed from a tube on the coastal plain has remained active; although sluggish, it has advanced to about 500 m of the coastline. Lava flows are also commonly visible at the bench, where lava enters the sea. Explosive activity there has been less frequent than in previous weeks. The public is reminded that the ocean-entry area is extremely hazardous, with explosions accompanying unpredictable collapses of new land. The steam clouds are highly acidic and laced with glass particles.
There were numerous earthquake reports for the week ending on April 22. The April 16 magnitude-5.6 earthquake, which occurred at 2:56 p.m. 7 km (4 mi) north of Pahala, was felt islandwide. Consequently, there were many felt aftershocks of magnitude less than, or equal to, 3.5. On April 17 at 10:11 p.m., a magnitude-3.7 earthquake occurred near Pu`ulena Crater at a depth of 1.5 km (.9 mi) and was felt in lower Puna. On April 18 at 1:06 a.m., a magnitude-4.0 earthquake, which occurred beneath Hana at a depth of 16.7 km (10 mi), was felt in Olinda, Haiku, Kihei, and Hana, Maui. On April 19, a magnitude-3.1 earthquake 7 km northwest of Pahala, located at a depth of 10 km (6.2 mi), was felt in Pahala and Hilo.
| 2019-11-14T05:56:49 |
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https://weblink-public.wichitafallstx.gov/WebLink8_Pub/DocView.aspx?id=431950&dbid=0&repo=Wichita-Falls
|
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Ord 3687 6/24/1980 • ORDINANCE NO. 16'17 ORDINANCE CLOSING HEARING AND LEVING ASSESSMENTS FOR PART OF THE COST OF IMPROVING VARIOUS STREETS DESIGNATED AS THE 1980 COMMUNITY DEVELOPMENT PAV- ING PROGRAM IN THE CITY OF WICHITA FALLS, TEXAS FIXING CHARGES AND LIENS AGAINST ABUTTING PROPERTY THEREON, AND AGAINST THE OWNERS THEREOF; PROVIDING FOR THE COLLECTION OF SUCH ASSESSMENTS AND THE ISSU- ANCE OF ASSIGNABLE CERTIFICATIONS IN EVIDENCE THERE- OF; RESERVING UNTO THE BOARD OF ALDERMEN THE RIGHT TO ALLOW CREDITS REDUCING THE AMOUNT OF THE RESPECT- IVE ASSESSMENT TO THE EXTENT OF ANY CREDIT GRANTED; DIRECTING THE CITY CLERK TO ENGROSS AND ENROLL THE ORDINANCE BY COPYING THE CAPTION OF SAME IN THE MIN- UTES OF THE BOARD OF ALDERMEN OF WICHITA FALLS, TEXAS AND BY FILING THE ORDINANCE IN THE ORDINANCE RECORDS OF SAID CITY; PROVIDING AN EFFECTIVE DATE, PROVID- ING SUNDRY MATTERS INCIDENT THERETO, AND DECLARING AN EMERGENCY; WHEREAS, the City of Wichita Falls, Texas, has heretofore ordered that each of the hereinafter described portions of streets, avenues, and public places in the City of Wichita FAlls, Texas, be improved by raising, grading, or filling same and by constructing thereon, to-wit: Six (6) inches of hot mix asphaltic concrete surface and four (4) inches of sandstone sub-base or Six (6) inches of cement stablized base with one and one half (1-1/2) inches of hot mix asphaltic concrete surface. BE BE LANE: From the south property line of Beatrice Lane to the south property line of Harding Street. EAST SECOND From the east property line of East- STREET: side Drive to the east property line of Pine Street. FARRIS From the south property line of STREET: Seventh Street south 150 feet. LIVE OAK From the north property line of East STREET: Third Street to the south property line of East Second Street. MAPLE From the north property line of East STREET: Third Street to 350 feet north of the north property line of East Second Street. MILL From the north property line of Flood STREET: Street to northeast corner of Lot 4, Block 159, Original Townsite. NORTH BROOK From the north property line of Lincoln AVENUE: Street to the south property line of North Tenth Street. • 1980 C.D. NORTH TENTH From the east property line of STREET: North Broadway to the west property line of North Brook Avenue. PARK From the north property line of Flood STREET: Street to the south property line of Tulsa Street. PERIGO From the south property line of Ireland STREET: Street to the south property line of Hawthorne Street. REYNOLDS From 480 feet north of the north property LANE : line of Harding Street to the north property line of Hickory Lane. TEXAS From the north property line of East Scott AVENUE: Street to the south property line of Ft. Worth Street. TULSA From the east property line of Park Street STREET: to the east property line of Mill Street. WARREN STREET: From the east property line of North Brook STREET: Avenue to the west property line of North Burnett Street. WASHINGTON From the east property line of Calhoun STREET: Street to the west property line of Clay Street. WASHINGTON From the east property line of North STREET: Brook Avenue to the west property line of of North Lamar Street. C.A.C. PARKING LOT SUNSET ROAD EXTENSION INTO SPUDDER PARK PARKING LOT LUCY PARK. . JALONIC PARK PARKING . '?, NORTH TEXAS SKILL CENTER WILLIAMS PARK PARKINC T P4RKING LOT. LYNWGOD EAST PARK PAP'.' G LOT '1ARTIN LUTHER KING ;ENTER PARKI TENTH AND uH10 Pr,? It.'; JT, 'ThRKING LOT, The above, together w th corm :red concrete curbs ..,nd gutters on r'roper grade and l me where same are not alry so constructed, together with _ i.her necessary incident.,'s and ap'.,urtenan( • : all of : aid imps, vement to be constr t- ed a and where shown on the plans ar 1 strict accordance with ')e pl and specifications then 'or; and ontrac •k refor 'gas been mjJe and , itered into with Timmin',-Anderson Corporatior: , W' ' a Fal !; , Texas for such Improve nts the above s ' reet,; , a,enue', , and pub 1 7 races r ' • WHEREAS, estimates of the cost of the improvements of each such portion of streets, avenues, and public places were prepared and filed and approved and adopted by the Board of Aldermen of the City, and a time and place were fixed for a hearing and the proper notice of the time, place and purpose of said hearing was given and said hearing was held at the time and place fixed therefor, to-wit, on the _ 24th day of _June, 198CL , _, at 8:30 a.m. , in the Council Chamber in the City of Wichita Falls, Texas, and at such hearing the following protest and objections were made, to-wit: Nathan Brown, 900 Mill , PROTESTED THAT it would not enhance his property in the amount assessed. PROTESTED THAT Maurice McGinty, 1212 North 10th, PROTESTED THAT he would not object if he thought it would enhance the value of the property. . PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT PROTESTED THAT and said hearing was continued to the present time in order to more fully accomplish the purposes thereof, and all desiring to be heard were given full and fair opportunity to be heard, and the Board of Aldermen of the City having fully considered all proper matters, is of the opinion that the said hearing should be closed and assessments should be made and levied as herein ordered: NOW THEREFORE: BE IT ORDAINED BY THE BOARD OF ALDERMEN OF T{ CITY 07 WICHITA FALLS, TEXAS, THAT: I. Said hearing be, and the same is hereby, closed and the said protest and _ objections, and any and all other protests and objections, whether herein enumerat- ed or not, be and the same are hereby, overruled. II. The Board of Aldermen, from the evidence, finds that the assessments here- in levied should be made and levied against the respective parcels of property abutting upon the said portions of streets, avenues and public places and against the owners of such property, and that such assessments and charges are right and proper and are substantially in proportion to the benefits to the respective parcels of property by means of the improvements in the unit for which such assessments are levied, and establish substantial justice and equality and uni- formity between the respective owners of the respective properties, and between all parties concerned, considering the benefits received and burdens imposed, and further finds that in each case the abutting property assessed is specially bene- fited in enhanced value to the said property by means of the said improvements in the unit upon which the particular property abuts and for which assessment is levied and charge made, in a sum in excess of the said assessment and charge made against the same by this ordinance, and further finds that the apportion- ment of the cost of the improvements is in accordance with the law in force in this City, and the proceedings of the City heretofore had with reference to said improvements, and is in all respects valid and regular. III. There shall be, and is hereby, levied and assessed against the parcels of property listed in Exhibit "A", the Engineer's Rolls, attached hereto and made a part hereof for all purposes and against the real and true owners there- of (whether such owners be correctly named herein or not) the sums of money itemized in such exhibit opposite the description of the respective parcels of property and the several amounts assessed against the same, and the owners there- of, as far as such owners are known. IV. Where more than one person, firm or corporation awns an interest in any property above described, each said person, firm or corporation shall be personally liable only for its, her or his pro rata of the total assessment against such property in proportion as its, his or her respective interest bears to the total ownership of such property, and its, his or her respective interest in such property may be released from the assessment lien upon pay- ment of such proportionate sum. V. The several sums above mentioned and assessed against the said parcels of property, and the owners thereof, and interest thereon at the rate of eight per cent (8) per annum, together with reasonable attorney's fees and costs of collection, if incurred, are hereby declared to be and are made a lien upon the respective parcels of property against which the same are assessed, and a personal liability and charge against the real and true owners of ee h prop- erty, whether such owners be correctly named herein or not, and the said liens shall be and constitute the first enforceable lien and claim against the prop- erty on which such assessments are' levied, and shall be a first and paramount lien thereon, superior to all other liens and claims, except State, County, School District and City ad valorem taxes. • When the improvements are completed and accepted by the City on a par- ticular unit, the sums assessed against property abutting upon such completed and accepted unit shall be and become payable in 12 successive monthly install- ments , from the date of such completion and acceptance, and the assessments against the property abutting upon the remaining units shall be and become due and payable in such installments after the date of completion and acceptance of such respective unit. The entire amount assessed against the particular parcels of the improvements on the unit upon which the particular property abuts at the rate of eight (8q) per cent per annum, payable monthly except as to interest on the first installment, which shall be due and payable on the date said install- ment matures, provided that any owner shall have the right to pay any and all of such installments at any time before maturity by paying principal with interest accrued to the date of payment, and further provided if default be made in the payment of any installment promptly as the same matures, then at the option of the City of Wichita Falls , or its assigns, the entire amount of the assessment upon which such default is made shall be and become immediately due and pay- able; but it is specifically provided that no assessment shall in any case be made against any property or any owner thereof in excess of the special bene- fits to property in the enhanced value thereof by means of said improvements in the unit upon which the particular property abuts , as ascertained at the hearing provided by the law in force in the City, nor shall any assessment be. made in any case until after notice of hearing as provided by the law. Said assessments against the respective lots and parcels of property and owners thereof shall be evidenced by certificates of a special assessment which shall be executed in the name of the City of Wichita Falls, PROVIDED, that the City Tax Assessor- Collector is hereby empowered to authorize payments of said sums in lesser install- ments and over a longer period of time not to exceed 96 months, in cases in which the City Tax Assessor-Collector has determined that an extreme financial hardship upon the property owner will otherwise result. VI . If default shall be made in the payment of an assessment , collection thereof shall be enforced either by the sale of the property by the City as near as possible in the manner provided for the sale of property for the nonpayment of ad valorem taxes, or at the option of the City of Wichita Falls , or its assigns , payment of said sums shall be enforced by suit in any court of competent jurisdiction , or as provided in any mechanic's or materialman's contract and said City shall exercise all of its lawful powers to aid in the enforcement and collection of said assess- ments. VII:. The total amount assessed against the respective parcels of abutting property, and the owners thereof, is in accordance with the proceedings of the City relat- ing to said improvements and assessments thereof, and is less than the proportion of the cost allowed and permitted by the law in force in the City. VIII . Although the aforementioned charges have been fixed, levied, and assessed in the respective amounts hereinabove stated, the Board of Aldermen does hereby reserve unto itself the right to reduce the aforementioned assessments by allowing credits to certain property owners where deemed appropriate. Notwithstanding the Board of Aldermen has herein reserved the right to issue credits, it shall not be required to issue credits , and will not do so, if same would result in any inequity and/or unjust discrimination. The principal amount of each of the several assessment certificates to be issued the City of Wichita Falls , Texas, as hereinafter provided, shall be fixed and determined by deducting from the amount of any assessment hereinabove levied such amount or amounts, if any, as may hereafter be allowed by the Board of Aldermen as a credit against the respective assessments. IX. For the purpose of evidencing the several sums assessed against the respective parcels of abutting property and the owners thereof, and the time and terms of payment, and to aid in the enforcement and collection thereof, assignable certificates in the principal amount of the respective assessments less the amount of any respective credit allowed thereon, shall be issued by the City of Wichita Falls, Texas.„ upon completion and acceptance by the City of the improvements in each unit of improvement as the work in such unit is completed and accepted, which certificates shall be executed by the mayor in the name of the City and attested by the City Clerk with the corporate seal of the City impress thereon, and shall declare the said amounts, time and terms of payment, rate of interest, and the date of the completion and acceptance of the improvements abutting upon such prop- erty for which the certificate is issued, and shall contain the name of the owner or owners, if known, description of the property by lot and block number, or front feet thereon, or such other description as may otherwise identify the same; and if the said property shall be owned by an estate, then the description of same as so owned shall be sufficient and no error or mistake in describing any property, or in giving the name of the owner, shall invalidate or in anywise impair such certificate, to the assessments levied. The certificates shall provide substantially that if same shall not be paid promptly upon maturity, then they shall be collectable, with reasonable attorney's fees and costs of collection, if incurred, and shall provide substan- tially that the amounts evidenced thereby shall be paid to the Tax Assessor and Collector of the City of Wichita Falls, Texas, who shall issue his receipt there- for, which shall be evidence of such payment on any demand for the same, and the Tax Assessor and Collector shall deposit the sums so received with the Director of Finance to be kept and held in a separate fund, and when any payment shall be made in the City, the Tax Assessor and Collector upon such certificate shall upon presentation to him of the certificate by the holder thereof, endorse said payment thereon. If such certificate be assigned, then the holder thereof shall be entitled to receive from the Director of Finance the amount paid upon the presentation to him of such certificate so endoresed and credited; and such en dorsement and credit shall be the Director of Finance's authority for making such payment. Such payments by the Director of Finance shall be receipted for the holder of such certificate in writing and by surrender thereof when the principal, together with accrued interest and all costs of collection and reasonable attorney's fees, if incurred , have been paid in full. Said certificates shall further recite substantially that the proceed- ings with reference to making the improvements have been regularly had in com- pliance with the law, and that all prerequisites to the fixing of the assessment lien against the property described in such certificate and the personal liability of the owners thereof have been performed, and such recitals shall be prima facie evidence of all the matters recited in such certificates, and no further proof thereof shall be required in any court. Said certificates may have coupons attached thereto in evidence of each or any of the several installments thereof, or may have coupons for each of the first four installments, leaving the main certificate to serve for the fifth installment, which coupons may be payable to the City of Wichita Falls, or its assigns may be signed with the facsimile signatures of the Mayor and City Clerk. Said certificates shall further recite that the City of Wichita Falls, Texas, shall exercise all of its lawful powers, when requested so to do, to aid in the enforcement and collection thereof, and may contain recitals substan- tially in accordance with the above and other additional recitals pertinent or appropriate thereof, and it shall not be necessary that the recitals be in the exact form above set forth, but the substance thereof shall be sufficient. The fact that such improvements may be omitted on any portion of any of said • units adjacent to any premises exempt from the lien of such assessments shall not in anywise invalidate, effect or impair the lien of such assessments upon other premises. X. Full power to make and levy reassessments and to correct mistakes, errors, invalidities or irregularities, either in the asses=,neats or in the certificates issued in evidence thereof, is, in accordance with the law in force in this City, vested in the City. XI. All assessments levied are a personal liability and charge against the real and true owners of the premises described , notwithstanding such owners may not be named, or may be incorrectly named. XII. The assessments so levied are for the improvements in the particular unit upon which the property described abuts, and the assessments for the im- provements in any unit are in nowise affected by the improvements or assessments in any other unit, and in making assessments and in holding said hearing, the amounts assessed for improvements in any one unit have been in nowise connected with the improvements or the assessments therefor in any other unit. XIII. The assessments levied are made and levied under and by virtue of the terms, powers and provisions of an Act passed at the First Called Session of the Fortieth Legislature of the State of Texas, known as Chapter 106 of the Acts of said Session and now shown as Article 1105b of Vernon's Texas Civil Statutes, which Act has been adopted as an amendment to and made a part of the Charter of the City of Wichita Falls, Texas. XIV. The City Clerk is hereby directed to engross and enroll this ordinance by copying the caption of same in the Minute Book of the City Council of Wichita Falls Texas, and by filing the complete Ordinance in the appropriate Ordinance Records of said City. XV. The fact that the making and construction of the said improvements is being delayed pending the taking effect of this ordinance, and that the condi- tions of such portions of streets and avenues endangers public health and safety, constitutes and creates an urgent public necessity, requiring that this ordinance be passed as an emergency measure, and this ordinance is passed as an emergency measure and shall be in force and effect immediately from and after its passage. PASSED AND APPROVED this 24th day of June 1980 ATTEST: ,,� M' OR (2g e l i e,e-6v CITY CLERK • �\ . 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https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Material_flows_in_the_circular_economy
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Material flows in the circular economy - Statistics Explained
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# Material flows in the circular economy
Data extracted in December 2020.
Planned article update: May 2021.
Highlights
In 2019 in EU-27, the rate of circularity of material use was 11.9 %, 3.6 percentage points (pp) up from 2004.
Material flows, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_wassd) (env_ac_mfa) (env_ac_sd)
This article elaborates on two Eurostat statistical products related to the circular economy, namely 1) a Sankey diagram of material flows in the European Union (EU-27); and 2) the circular material use rate or circularity rate, i.e. the share of material recovered and fed back into the economy. Both the Sankey diagram and circularity rate form part of EU monitoring framework for the circular economy. The purpose of a circular economy is to maintain the value of products, materials and resources for as long as possible by returning them into the product cycle after they have reached the end of their lifecycle, while minimising the generation of waste. Materials such as biomass, metals, minerals and fossil fuels are extracted from the environment to make products or to produce energy. When their life cycle ends, products may be recycled, incinerated, or discarded as residual waste. Those material flows are an essential part, albeit not the only one, of the circular economy. The fewer products we discard and the more we recycle, the fewer materials we extract thus benefiting our environment.
### Sankey diagram of material flows
A Sankey diagram of material flows presents the flows of:
1. materials extracted to make products or be used as a source of energy;
2. products flowing in and out of our society;
3. materials and products discarded into the environment as residuals, e.g. landfilled waste or air emissions, or recovered and fed back into the economy; this latter part closes the loop in the circular economy.
Infrastructure such as buildings, roads, and machinery are used over a long period during which they mount up in our societies, until they are eventually dismantled or taken out of use.
The Eurostat Sankey diagram of material flows shows the amounts of materials extracted, imported, recycled or disposed, as well as related emissions. Figure 1 shows the flows of material in the EU-27 economy in 2018. Some basic information to help you understand the diagram:
• the flow runs left to right;
• the width of the bands is proportional to the quantity of the flow, which is measured in billions of tonnes;
• the materials shown in the diagram are: biomass — used for food and fodder, clothing (wool, cotton, etc.), timber, etc.; metals; non-metallic minerals; fossil energy carriers, such as crude oil — used to produce fossil fuels or materials such as plastics. Water is not included, nor are renewable energy sources that do not involve material flows, such as electricity from photovoltaic panels or wind power;
• fossil fuel carriers and biomass (wood) produce air emissions — shown on the right side of Figure 1 — as a result of being burned to release energy.
Figure 1 also displays imports and exports, which are flows of materials, products and waste between different economies. The closed loop represents residuals that are not discarded into the environment but are reused in the economy, either to produce secondary raw materials or for other purposes, preventing further extraction of natural resources. The incineration of waste to produce energy is not part of the loop but has its own flow and eventually produces air emissions.
Figure 1: Material flows in true scale, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_wassd) (env_ac_mfa) (env_ac_sd)
Figure 1 shows that 67 % (5.37 Gt) of raw materials processed in the EU-27 (8.07 Gt) originate from domestic extraction, 21 % from imports (1.73 Gt) and 12 % from recycling and backfilling (0.96 Gt). 56 % of raw materials processed were used to make products (4.55 Gt). The rest were mainly exported or used for producing energy. The next sections explain in more detail the different parts of Figure 1.
### Description of flows and nodes of the Sankey diagram
Eurostat's Sankey diagram is built on a series of nodes, which represent events or processes, e.g. imports and material inputs. The connections between the nodes represent material flows. Figure 2 is an excerpt of the left-hand side of Figure 1 showing the inputs into the EU-27 economy.
Figure 2: Inputs in true scale, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_ac_mfa) (env_ac_sd)
• Imports are flows of products from the rest of the world economy into the domestic economy. This flow also includes waste sent for treatment (e.g. converted into secondary raw material) in the receiving country.
• Natural resources refers to the amount of material resources extracted from the natural environment by resident production units. This concept is called domestic extraction (DE).
• Direct material input (DMI) shows the direct input of material that is directly fed into the economy. It is the sum of domestic extraction and imports. DMI includes all materials of economic value, which are available for use in production (e.g. manufacture) and consumption (e.g. purchase of manufactured goods).
The middle part of the Sankey diagram (Figure 3) shows processed materials, which are defined as the sum total of DMI and secondary material input, i.e. materials from recycling and backfilling. Processed materials can either be exported or used domestically. The part not exported is called domestic material consumption (DMC).
Figure 3: Processed materials in true scale, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_wassd) (env_ac_mfa) (env_ac_sd)
In Figure 3, the share of the green loop in the ‘processed materials’ node is a possible indicator of the economy’s circularity. The share represents materials recovered from waste from recycled and backfilled as a proportion of all materials processed. A more sophisticated indicator, called the circularity rate, is presented below. Materials and products may have a short or long lifecycle. Some are:
• single use (e.g. food);
• used for less than 1 year (e.g. paper);
• long-life products (e.g. furniture);
• assets (e.g. buildings, machinery).
In particular, a large share of construction minerals are used to extend or maintain in-use stocks of, among other things, buildings and infrastructure. These stocks often stay in use for decades and only become available for recycling when they reach the end of their lifecycles. These materials accumulate as the economy grows: each year materials add to the economy’s stock — i.e. gross additions to stock — and some old materials are removed as buildings are demolished and durable goods disposed of — i.e. removals. In 2018, the EU-27’s net material accumulation amounted to 2.76 Gt. As long as the demand for raw materials for in-use stocks with long life-times (e.g., buildings and infrastructure) exceeds the amount of materials that can be supplied from recycled materials, primary extraction will remain necessary.
The right hand-side of the Sankey diagram shows the outputs from the economy (Figure 4), namely:
• exports of products in their simple mass weight;
• emissions to air and emissions to water — flows of solid, liquid and gaseous materials that are discharged into water bodies (rivers, seas, etc.) or emitted into the atmosphere;
• dissipative flows — materials which are dispersed into the environment - with current technology - as a deliberate or unavoidable consequence of product use, for example, mineral fertilisers, and abrasion from tyres.
Several outputs come from the ‘waste treatment’ node.
• Incineration: waste is incinerated to extract energy. However, this also produces air emissions.
• Waste landfilled: disposal of waste including landfill and other operations.
• Recovery: operations involving waste materials being reprocessed into products, materials or substances to be reused either for their original purpose or other purposes. It includes recycling and backfilling operations.
Figure 4: Outputs in true scale, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_wassd) (env_ac_mfa) (env_ac_sd)
In Eurostat’s Sankey diagram, only recycling and backfilling flows are deemed to close the loop of the circular economy (some other researchers and experts also consider the recovery of energy). In 2018, recycling and backfilling flows involved around 12 % of overall material inputs to the EU-27 economy. The waste produced by the use of materials, including the material removed from the stocks at end-of-life (demolition & discards) accounted for 1.79 Gt in 2018. Part of this waste remains in the EU-27 economy through recycling (0.75 Gt) and through backfilling (0.21 Gt). The recycling stream is 42 % of all material waste flows, whereas backfilling is 12 % and landfilled waste is 40 %. Some of the waste is incinerated and part of it (0.11 Gt) is released into the environment, together with other emissions, as for example, emissions to air (2.63 Gt) and emissions to water (0.01 Gt). The outputs in Figure 4 are completed by exports (0.75 Gt) and dissipative flows (0.24 Gt). The recycling rate is the share of recycled waste out of all the waste treated. It varies significantly by material category, paper, glass, metals, plastics, etc. For this reason, recycling rates are more frequently analysed by material category than for the whole economy. Recycling rates are highest for metals and lowest for fossil fuels.
Breakdown by type of material
It is possible and relevant to consider the flows with a breakdown by material categories. An analysis by material category conveys the relative significance of various materials and their potential for reuse, recovery or recycling. The material flows data for this Sankey diagram are currently divided into four main categories: biomass (MF1), metal ores (MF2), non-metallic minerals (MF3) and fossil energy carriers/materials (MF4). Work is ongoing to improve the granularity of the categories, e.g. by isolating plastics.
Figure 5: Material flows in true scale by main type of material, EU-27, 2018
(billion tonnes = Gt)
Source: Eurostat (env_wassd) (env_ac_mfa) (env_ac_sd)
### Circularity rate
As there was no single summary indicator for the circularity of our economies at macroeconomic level, Eurostat developed a new indicator for the EU monitoring framework for the circular economy. This new indicator is called the 'circular material use rate' — referred to as the circularity rate — and it measures the contribution of recycled materials towards the overall use of materials.
The circularity rate is the share of material resources used in the EU which came from recycled products and recovered materials, thus saving primary raw materials from being extracted. A higher circularity rate means that more secondary materials replace primary raw materials, thus reducing the environmental impacts of extracting primary material.
In 2019, the EU-27's circularity rate was 11.9%, slightly up compared to the previous year and 3.6 percentage points (pp) up from 2004, the first year for which data are available.
Figure 6: Circularity rate, EU-27, 2004-2019
(%)
Source: Eurostat (env_ac_cur)
The circularity rate is lower than other indicators of circularity, such as recycling rates, which are around 56 % in the EU-27. This is because some types of materials cannot be recycled, e.g. fossil fuels burned to produce energy or biomass consumed as food or fodder. This can be seen by comparing size of the nodes at the beginning and the end of the green feedback loop in Figure 1. Examples of materials which are counted within the circularity rate are food and fodder, and fossil fuels for energy production or for material use — e.g. plastics, buildings, infrastructure, and vehicles. Only some of these materials, at the end of their life cycle, end up as waste and thus count in recycling rates. A higher circularity rate can be achieved in more ways than higher recycling rates and requires deeper transformation within our societies, e.g. replacing fossil fuel carriers by renewable energy — hydro power; tide, wave and ocean; wind power; solar photovoltaic; solar thermal and geothermal, by using more efficient production technologies or extending the lifespan of products. Similarly as the recycling rates, the circularity rate shows big differences by material category. In 2019, the circularity rate in the EU-27 was 24 % for metal ores, 15 % for non-metallic minerals (including glass), 9% for biomass (including paper, wood, tissue, etc.), and less than 3 % for fossil energy materials (including plastics and fossil fuels). Fossil fuel materials are less suitable for recycling because they are mainly used for energy purposes, implying that they are transformed into air emissions. However, a lot of progress is possible in the recycling of plastics. Biomass is also partly unsuitable for recycling — e.g. food and fodder or wood for energy — but progress is possible by means of reducing food waste, recycling natural fabrics, etc.
Figure 7: Circularity rate by material categories, EU-27, 2010-2019
Source: Eurostat (env_ac_curm)
Table 1 shows the circularity rate for the EU-27 and its Member States between 2010 and 2019.
Table 1: Circularity rate, 2010-2019
Source: Eurostat (env_ac_cur)
In 2019, the circularity rate was highest in the Netherlands (28.5%), followed by Belgium (24.0%) and France (20.1%). The lowest rate was recorded in Romania (1.5%), followed by Ireland (1.6%) and Portugal (2.2%). Differences in the circularity rate across Member States are due not only to the amount of recycling in each country, but also to structural factors in national economies. The circularity rate is high if the amount of waste recycled is high. However, the circularity rate could also be high if domestic material consumption is low, i.e. the materials that the country consumes (biomass, metals, minerals, fossil fuels, etc.). In turn, this happens if domestic extractions of materials for use in the country are low, imports of materials for use in the country are low, or exports of domestically extracted materials are high.
### How the circularity rate is related to the Sankey diagram
The circularity rate is closely related to the green loop in the Sankey diagram of material flows. This circularity of materials intuitively represents the size of the closing loop relative to the overall amount of materials fed into the economy (see Figure 1). The circularity rate is a more sophisticated version of this idea. The Sankey diagram and circularity rate ensure consistency by using the same definitions, classifications, treatment of waste, etc. However, they are not aligned on two aspects, as described below.
i) In the circularity rate, the only waste treatment operations deemed to contribute to the circular economy are those that produce secondary raw materials. These operations only include recycling and exclude backfilling. However, the Sankey diagram shows distinctively the loop for recovery and backfilling.
ii) Countries are open economies with flows of waste being imported and exported as they are collected in one country and then treated and recycled in another. Figure 1 does not explicitly show the imports and exports of waste bound for recovery from other imports and exports (NB: waste not bound for recovery is rarely exported or imported because there is no economic incentive in doing so). However, the source data for the Sankey diagram enables this breakdown to be an option (shown in Figures 2 and 4). The Sankey diagram does not take into account any import or export in the green loop. However, the circularity rate does take these into account: the waste treatment operations deemed to contribute to the circular economy also include exported waste bound for recovery (abroad). The imports in the circularity rate are net of imported waste bound for recovery (in the country). Such a correction of the waste recycled with the corresponding imports and exports better represents a country's effort to collect waste for recovery. Note that it is a design choice whether to use the circularity rate to measure the country's effort to collect waste for recovery or its capacity to produce secondary raw materials. Each of those approaches would require different adjustments in the imports and exports. The circularity rate adopts the former (i.e. measuring the country’s efforts to collect waste for recovery). This perspective credits the country's effort to collect waste bound for recovery, which indirectly contributes to the worldwide supply of secondary materials. Therefore, the extraction of primary material can be avoided. This is also the perspective taken by the Eurostat waste management indicators.
### Circularity rate – methodology
The circularity rate measures the share of material recovered and fed back into the economy in overall material use — thus reducing the extraction of primary raw materials. The indicator includes flows of materials, fossil fuels and energy products, but not flows of water. Correspondingly, the circularity rate (CMU) rate is defined as the ratio of the circular use of materials (U) to an indicator of the overall material use (M):
$CMU=U/M$
with
$U = RCV_ R – IMPw + EXPw$
with
RCVR: Recovery – recycling on the basis of the treatment operations defined in the Waste Framework Directive 75/442/EEC
IMPW: amount of imported waste bound for recovery, and
EXPW: amount of exported waste bound for recovery
and
$M = DMC + U$
M is based on Domestic Material Consumption (DMC) for practical reasons. A better indicator of overall material use would be the material footprint, also called raw material consumption (RMC). Unfortunately, RMC estimates are only available for a few European countries and the aggregated EU economy. DMC is a good proxy: data show that DMC and RMC develop in the same way over time in the EU economy. More detailed information on material footprints can be found in the Statistics Explained article Material flow accounts statistics - material footprints.
Another denominator considered for M but not selected for the circularity rate was the DMI. This is the sum of domestic extraction plus imports. Using DMI for the circularity rate in the EU would lead to double-counting because it does not balance out materials extracted in one country and then imported by another. Therefore, it was not selected.
In order to calculate the amounts of waste (IMPW) that are imported and exported waste (EXPW), Eurostat identified the CN-codes[1] which can be considered trade in waste [2]
### Data sources
The Sankey diagram and the circularity rate indicator are based on official statistics compiled by Member States and reported to Eurostat under legal obligations. The Sankey diagram and the circularity rate reuse and integrate existing data sources, imposing no additional burden on Member States. Data are available for all Member States and EU aggregates. Data exist for several years, enabling time series data sets to be produced.
The main data sources used are economy-wide material flow accounts (EW-MFA), waste statistics (WStatR) and international trade in goods statistics (ITGS).
Economy-wide material flow accounts
EW-MFA constitute a statistical framework that describes the interaction of the domestic economy with the natural environment and the worldwide economy in terms of flows of materials. The EW-MFA framework is conceptually embedded in environmental-economic accounts and compiled according to the standards of the UN System of Environmental-Economic Accounts (SEEA CF 2012). The EW-MFA data collection is based on Regulation(EU) 691/2011 on European environmental accounts.
EW-MFA provide an aggregate overview, in thousands of tonnes per year, of the material flows into and out of an economy. EW-MFA cover solid, gaseous, and liquid materials, except for bulk flows of water and air. Material flows are grouped into four main categories: biomass (MF1), metal ores (MF2), non-metallic minerals (MF3) and fossil energy carriers/materials (MF4). Most of the concepts introduced in this article are defined in the EW-MFA framework: domestic extraction, direct material input, domestic material consumption, raw material consumption, etc. The available data set is 'material flow accounts' (env_ac_mfa).
Waste statistics
Regulation (EC) 2150/2002 on waste statistics (WStatR) is a framework for harmonised European statistics in this domain. WStatR requires Member States to provide data every second year on the generation, recovery and disposal of waste. The WStatR data set used for the indicators in this article is 'treatment of waste by waste category, hazardousness and waste management operations' (env_wastrt), which is currently available for even reference years since 2004. Data are interpolated to produce annual results for the Sankey diagram and the circularity rate.
As waste data from the Regulation on waste statistics are not reported by material flow, it is necessary to ensure that correspondence EWC-Stat waste categories and four main material flow categories (MF1, MF2, MF3 and MF4) are aligned with each other.
‘Goods’ means all movable property including electricity. ‘European’ means that the statistics are compiled on the basis of the concepts and definitions set out in EU legislation.
Data are based on Regulation (EC) 638/2004 on community statistics relating to the trading of goods between Member States (Intrastat) and Regulation (CE) 471/2009 on community statistics relating to external trade with non-EU countries (Extrastat).
European international trade in goods statistics (ITGS) are the official harmonised source of information about exports, imports and the trade balances of the EU, its Member States and the euro area. Data is extracted from the COMEXT website.
The main classification for the European ITGS is the combined nomenclature (CN). This nomenclature is used by the Member States to collect detailed data on the trading of goods. CN and the EW-MFA categories of material flows are aligned with each other.
Integration of sources in the Sankey diagram
The Sankey model is based on the law of conservation of mass and combines several Eurostat statistics. To integrate the data from different sources, Eurostat created two new data sets in its online database.
Eurostat waste treatment statistics were used to create a new data set called 'management of waste by waste management operations and type of material - Sankey diagram data' (env_wassd). Where necessary, they were complemented with waste estimates for every second year. Because the waste flows are reported using classifications that are different from the EW-MFA, waste flows were reallocated to match the material flow accounts (material categories) using a mix of information, e.g. from the scientific literature and expert judgement.
Material flow accounts, international trade in goods statistics, and waste statistics have been used to create the data set 'material flows for circular economy - Sankey diagram data' (env_ac_sd). The allocation of material flows into the different material categories was based on Eurostat data.
Circularity rate
Eurostat publishes the results of the circularity rate in two data sets: 'circular material use rate' (env_ac_cur) and 'circular material use rate by material type' (env_ac_curm). The former data set reports annual estimates for all the Member States from 2010 onwards and for the EU aggregate from 2004 onwards. The latter data set includes breakdowns by categories of material flows for the EU aggregate from 2010 onwards. There is a publication Circular material use rate: calculation method presenting the reference methodology for the ‘circular material use rate’ indicator.
### Context
Action on the circular economy ties in closely with key EU policy priorities and with global initiatives on sustainable development. In 2015, the European Commission adopted an ambitious circular economy package. An EU action plan for the circular economy established a concrete programme of actions outlining measures that cover the entire product life cycle: from production and consumption to waste management and the market for secondary raw materials. As part of the action plan, in 2018, the European Commission adopted a communication on a monitoring framework for the circular economy COMM/2018/029 Final.
On 11 March 2020, the European Commission adopted a new Circular Economy Action plan. It is one of the main blocks of the European Green Deal, Europe’s new agenda for sustainable growth. The new Action Plan aims to make the economy fit for a green future, strengthening competitiveness while protecting the environment and giving new rights to consumers. Therefore, it focuses on the design, promoting circular economy processes, and fostering sustainable consumption, to ensure that the resources used are kept in the EU for as long as possible. The Circular Economy Action Plan put forward as part of the EU Industrial Strategy presents measures to make sustainable products the norm in the EU, to empower consumers, to focus on sectors that use the most resources and where the potential for circularity is high and to ensure less waste.
The European Green Deal was presented by the von der Leyen Commission on 11 December 2019. It sets an ambitious roadmap towards a climate-neutral circular economy, where economic growth is decoupled from resources use.
The circular economy also has strong synergies with the EU’s objectives on climate and energy and with the Commission’s package on clean energy for all Europeans. The circular economy is also instrumental in supporting the EU’s commitments on sustainability, as outlined in the communication Next steps for a sustainable European future and particularly in fulfilling sustainable development goal 12 - responsible consumption and production.
Other articles
Tables
Database
Dedicated section
Publications
Methodology
Legislation
Visualisations
### Main tables
Material flows for circular economy - Sankey diagram data (env_ac_sd)
Material flow accounts (env_ac_mfa)
Material flow accounts - domestic processed output (env_ac_mfadpo)
Material flow accounts - balancing items (env_ac_mfabi)
Material flow accounts - main indicators (env_ac_mfain)
Circular material use rate (env_ac_cur)
Circular material use rate by material type (env_ac_curm)
Waste generation and treatment (env_wasgt)
Management of waste by waste management operations and type of material - Sankey diagram data (env_wassd)
Treatment of waste by waste category, hazardousness and waste management operations (env_wastrt)
Secondary raw materials (cei_srm)
Circular material use rate (cei_srm030)
### Notes
1. . The updated list of codes is available online: http://ec.europa.eu/eurostat/documents/8105938/8465062/cei_srm030_esmsip_CN-codes.pdf
2. The CN codes identified are residual materials that are assumed to have been sent for treatment in recovery plants (excl. energy and backfilling), i.e. 'material to be recovered'. These CN codes are consistent with the codes used for calculating the set of Eurostat waste management indicators, which are already publicly available on Eurostat's website. More complete technical explanations about the methodology used for the circularity rate are found in the publication Circular material use rate: calculation method.
| 2021-03-07T07:10:36 |
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|
https://www.star.bnl.gov/public/estruct/ref/ESPaper.html
|
# Links to the papers in public
## From ES PWG Group members
### Publications
Autocorrelations from fluctuation scale dependence by inversion by T. A. Trainor, R. J. Porter and D. J. Prindle
J. Phys. G 31 809-824, and hep-ph/0410182
Transverse-momentum $p_t$ correlations from mean-$p_{t}$ fluctuation scale dependence in Hijing-1.37-simulated Au-Au collisions at $\sqrt{s_{NN}} =$ 200 GeV by Qingjun Liu, Duncan J. Prindle, Thomas A. Trainor
Phys. Let. B 632 197, and hep-ph/0410180
Extrapolating parton fragmentation to low $Q^2$ in $e^+$-$e^-$ collisions by T. A. Trainor and D. Kettler
Phys. Rev. D 74, 034012 (2006), and hep-ph/0606249
### Proceedings
Correlations, Fluctuations, and Flow Measurements from the STAR Experiment at Quark Matter 2002 by Lanny Ray
Long range hadron density fluctuations at soft pT in Au+Au collisions at RHIC invited talk at Xth International Wokshop on Multiparticle Production (Correlation and Flucutations in QCD) by Mikhail Kopytine
"Soft and hard components of two-particle distributions on (yt,eta,phi) from p-p collisions at sqrt(s)=200 GeV" at QM2004 by R.J. Porter, T.A. Trainor
"Event Structure at RHIC from p-p to Au-Au," at the 20th Winter Workshop on Nuclear Dynamics (2004) by Tom Trainor (hep-ph/0406116)
Correlations in STAR: interferometry and event structure plenary talk at the 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP-2005) by Mikhail Kopytine
Correlation structure of STAR events plenary talk at the International Conference on Contemporary Issues in Nuclear and Particle Physics (CINPP 2005) by Mikhail Kopytine
Correlations from p-p collisions at sqrt(s) = 200 GeV invited talk at Correlations and Fluctuations in Relativistic Nuclear Collisions Workshop (MIT, 2005) by R. J. Porter and T. A. Trainor
The equivalence of fluctuation scale dependence and autocorrelations invited talk at Correlations and Fluctuations in Relativistic Nuclear Collisions Workshop (MIT, 2005) by D. J. Prindle and T. A. Trainor
Probing the bulk medium in relativistic heavy ion collisions using two-particle correlations invited talk at Correlations and Fluctuations in Relativistic Nuclear Collisions Workshop (MIT, 2005) by R. L. Ray
Transverse momentum correlations in relativistic nuclear collisions invited talk at Correlations and Fluctuations in Relativistic Nuclear Collisions Workshop (MIT, 2005) by T. A. Trainor
Low-Q^2 partons in p-p and Au-Au collisions at XXXV International Symposium on Multiparticle Dynamics 2005 (ISMD2005) by T. A. Trainor
### Preprints
A power-law description of heavy-ion collision centrality by Thomas A. Trainor and Duncan J. Prindle (hep-ph/0411217)
Extrapolating parton fragmentation to low Q^2 in e+e- collisions by Thomas A. Trainor and David T. Kettler (hep-ph/0606249)
What Does the Balance Function Measure? by Thomas A. Trainor (hep-ph/0301122)
Jet quenching and event-wise mean-pt fluctuations in Au-Au collisions at sqrt-sNN = 200 GeV in Hijing-1.37 by Qingjun Liu, Thomas A. Trainor (hep-ph/0301214)
Event-by-Event Analysis and the Central Limit Theorem by T.A. Trainor (hep-ph/000114)
Pion Lattices in HI Transverse Phase Space and Sudden Traversal of the QCD Phase Boundary by T.A. Trainor (hep-ph/0005176)
Jet Correlations and Scale-Local Measures by T.A. Trainor and J.G. Reid
Probing small length scales in heavy-ion collisions with event-by-event correlation analysis by T.A. Trainor (hep-ph/0004258)
### Theses
J.G. Reid's dissertation
A. Ishihara's dissertation(ps)
| 2018-06-21T20:05:16 |
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|
http://wikimechanics.org/euclidean-metric-table
|
Table: Euclidean Metric
The Euclidean Metric $k_{zz} \equiv 1$ $k_{xx} = 1$ $k_{yy} = 1$ $k_{xy} = 0$ $k_{xz} = 0$ $k_{yz} = 0$
page revision: 33, last edited: 15 Mar 2014 09:47
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2018-10-15T08:26:39 |
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|
http://xxx.lanl.gov/abs/hep-ph/9712512
|
hep-ph
(what is this?)
# Title: Top Quark Physics: Overview
Authors: Stephen Parke (Fermi National Accelerator Laboratory)
Abstract: In this presentation I will primarily focus on top quark physics but I will include a discussion of the W-boson mass and the possibility of discovering a light Higgs boson via associated production at the Tevatron.
Comments: 15 pages, 12 figures, Latex, sprocl.sty presentation at the International Symposium on QCD Corrections and New Physics'' October 27-29, 1997 held at Hiroshima, Japan Subjects: High Energy Physics - Phenomenology (hep-ph) Report number: FERMILAB-Conf-97/431-T Cite as: arXiv:hep-ph/9712512 (or arXiv:hep-ph/9712512v1 for this version)
## Submission history
From: Stephen Parke [view email]
[v1] Tue, 23 Dec 1997 18:18:05 GMT (91kb)
| 2014-04-24T00:21:58 |
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|
https://par.nsf.gov/biblio/10369866-high-contrast-imaging-hd-hd-gemini-planet-imager
|
High-contrast imaging of HD 29992 and HD 196385 with the Gemini Planet Imager
ABSTRACT
Based on high-contrast images obtained with the Gemini Planet Imager (GPI), we report the discovery of two point-like sources at angular separations ρ ∼ 0.18 and 0.80 arcsec from the stars HD 29992 and HD 196385. A combined analysis of the new GPI observations and images from the literature indicates that the source close to HD 29992 could be a companion to the star. Concerning HD 196385, the small number of contaminants (∼0.5) suggests that the detected source may be gravitationally bound to the star. For both systems, we discarded the presence of other potential companions with m > 75 MJup at ρ ∼ 0.3–1.3 arcsec. From stellar model atmospheres and low-resolution GPI spectra, we derive masses of ∼0.2–0.3 M⊙ for these sources. Using a Markov-chain Monte Carlo approach, we performed a joint fit of the new astrometry measurements and published radial velocity data to characterize the possible orbits. For HD 196385B, the median dynamic mass is in agreement with that derived from model atmospheres, whilst for HD 29992B the orbital fit favours masses close to the brown dwarf regime (∼0.08 M⊙). HD 29992 and HD 196385 might be two new binary systems with M-type stellar companions. However, new high angular resolution images would help to confirm more »
Authors:
; ; ;
Publication Date:
NSF-PAR ID:
10369866
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
515
Issue:
4
Page Range or eLocation-ID:
p. 4999-5008
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. Context. HD 113337 is a main-sequence F6V field star more massive than the Sun. This star hosts one confirmed giant planet and possibly a second candidate, detected by radial velocities (RVs). The star also hosts a cold debris disc detected through the presence of an infrared excess, making it an interesting system to explore. Aims. We aim to bring new constraints on the star’s fundamental parameters, debris disc properties, and planetary companion(s) by combining complementary techniques. Methods. We used the VEGA interferometer on the CHARA array to measure the angular diameter of HD 113337. We derived its linear radius using the parallax from the Gaia Second Data Release. We computed the bolometric flux to derive its effective temperature and luminosity, and we estimated its mass and age using evolutionary tracks. Then, we used Herschel images to partially resolve the outer debris disc and estimate its extension and inclination. Next, we acquired high-contrast images of HD 113337 with the LBTI to probe the ~10–80 au separation range. Finally, we combined the deduced contrast maps with previous RVs of the star using the MESS2 software to bring upper mass limits on possible companions at all separations up to 80 au. We tookmore »
2. ABSTRACT
Improving direct detection capability close to the star through improved star subtraction and post-processing techniques is vital for discovering new low-mass companions and characterizing known ones at longer wavelengths. We present results of 17 binary star systems observed with the Magellan adaptive optics system (MagAO) and the Clio infrared camera on the Magellan Clay Telescope using binary differential imaging (BDI). BDI is an application of reference differential imaging (RDI) and angular differential imaging (ADI) applied to wide binary star systems (2 arcsec <Δρ < 10 arcsec) within the isoplanatic patch in the infrared. Each star serves as the point spread function (PSF) reference for the other, and we performed PSF estimation and subtraction using principal component analysis. We report contrast and mass limits for the 35 stars in our initial survey using BDI with MagAO/Clio in L′ and 3.95 µm bands. Our achieved contrasts varied between systems, and spanned a range of contrasts from 3.0 to 7.5 magnitudes and a range of separations from 0.2 to 2 arcsec. Stars in our survey span a range of masses, and our achieved contrasts correspond to late-type M-dwarf masses down to ∼10 MJup. We also report detection of a candidate companion signal at 0.2 arcsecmore »
3. Abstract
Stellar mass is a fundamental parameter that is key to our understanding of stellar formation and evolution, as well as the characterization of nearby exoplanet companions. Historically, stellar masses have been derived from long-term observations of visual or spectroscopic binary star systems. While advances in high-resolution imaging have enabled observations of systems with shorter orbital periods, measurements of stellar masses remain challenging, and relatively few have been precisely measured. We present a new statistical approach to measuring masses for populations of stars. Using Gaia astrometry, we analyze the relative orbital motion of >3800 wide binary systems comprising low-mass stars to establish a mass–magnitude relation in the GaiaGRPband spanning the absolute magnitude range 14.5 >$MGRP$> 4.0, corresponding to a mass range of 0.08MM≲ 1.0M. This relation is directly applicable to >30 million stars in the Gaia catalog. Based on comparison to existing mass–magnitude relations calibrated forKsmagnitudes from the Two Micron All Sky Survey, we estimate that the internal precision of our mass estimates is ∼10%. We use this relation to estimate masses for a volume-limited sample of ∼18,200 stars within 50 pc of the Sun and the present-day field mass function for stars withM≲ 1.0M, which wemore »
4. Abstract
TESS has proven to be a powerful resource for finding planets, including those that orbit the most prevalent stars in our galaxy: M dwarfs. Identification of stellar companions (both bound and unbound) has become a standard component of the transiting planet confirmation process in order to assess the level of light-curve dilution and the possibility of the target being a false positive. Studies of stellar companions have also enabled investigations into stellar multiplicity in planet-hosting systems, which has wide-ranging implications for both exoplanet detection and characterization, as well as for the formation and evolution of planetary systems. Speckle and AO imaging are some of the most efficient and effective tools for revealing close-in stellar companions; we therefore present observations of 58 M-dwarf TOIs obtained using a suite of speckle imagers at the 3.5 m WIYN telescope, the 4.3 m Lowell Discovery Telescope, and the 8.1 m Gemini North and South telescopes. These observations, as well as near-infrared adaptive optics images obtained for a subset (14) of these TOIs, revealed only two close-in stellar companions. Upon surveying the literature, and cross-matching our sample with Gaia, SUPERWIDE, and the catalog from El-Badry et al., we reveal an additional 15 widely separatedmore »
5. ABSTRACT
HD 62658 (B9p V) is a little-studied chemically peculiar star. Light curves obtained by the Kilodegree Extremely Little Telescope (KELT) and Transiting Exoplanet Survey Satellite (TESS) show clear eclipses with a period of about 4.75 d, as well as out-of-eclipse brightness modulation with the same 4.75 d period, consistent with synchronized rotational modulation of surface chemical spots. High-resolution ESPaDOnS circular spectropolarimetry shows a clear Zeeman signature in the line profile of the primary; there is no indication of a magnetic field in the secondary. PHOEBE modelling of the light curve and radial velocities indicates that the two components have almost identical masses of about 3 M⊙. The primary’s longitudinal magnetic field 〈Bz〉 varies between about +100 and −250 G, suggesting a surface magnetic dipole strength Bd = 850 G. Bayesian analysis of the Stokes V profiles indicates Bd = 650 G for the primary and Bd < 110 G for the secondary. The primary’s line profiles are highly variable, consistent with the hypothesis that the out-of-eclipse brightness modulation is a consequence of rotational modulation of that star’s chemical spots. We also detect a residual signal in the light curve after removal of the orbital and rotational modulations, which might be pulsational in origin; this could be consistent withmore »
| 2023-02-02T20:30:56 |
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|
https://par.nsf.gov/biblio/10330720-beam-spin-asymmetry-hyperon-photoproduction-off-neutron
|
This content will become publicly available on April 1, 2023
Beam-spin asymmetry Σ for Σ− hyperon photoproduction off the neutron
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10330720
Journal Name:
Physics Letters B
Volume:
827
Issue:
C
Page Range or eLocation-ID:
136985
ISSN:
0370-2693
1. Abstract We show that for some even $k\leqslant 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi$ is Euler’s totient function. We also show that for a positive proportion of all $k$, the equation $\sigma (n)=\sigma (n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath.
| 2022-09-26T14:08:28 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=S067SBT
|
# Total Flux of Active ${}^{8}\mathrm {B}$ Solar Neutrinos INSPIRE search
Total flux of active neutrinos (${{\mathit \nu}_{{e}}}$, ${{\mathit \nu}_{{\mu}}}$, and ${{\mathit \nu}_{{\tau}}}$).
VALUE ($10^{6}$ cm${}^{-2}$s${}^{-1}$) DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$5.95$ ${}^{+0.75}_{-0.71}$ ${}^{+0.28}_{-0.30}$ 1
2019
SNO+ Water phase; ${{\mathit \nu}_{{e}}}{{\mathit e}}$ scattering rate
$5.68$ ${}^{+0.39}_{-0.41}$ ${}^{+0.03}_{-0.03}$ 2
2018 B
BORX From ${{\mathit \nu}_{{e}}}{{\mathit e}}$ scattering rate
$5.25$ $\pm0.16$ ${}^{+0.11}_{-0.13}$ 3
2013
SNO All three phases combined
$5.046$ ${}^{+0.159}_{-0.152}$ ${}^{+0.107}_{-0.123}$ 4
2010
SNO From ${{\mathit \phi}_{{NC}}}$ in Phase I+II, low threshold
$5.54$ ${}^{+0.33}_{-0.31}$ ${}^{+0.36}_{-0.34}$ 5
2008
SNO $\phi _{NC}$ in Phase III
$4.94$ $\pm0.21$ ${}^{+0.38}_{-0.34}$ 6
2005 A
SNO From ${{\mathit \phi}_{{NC}}}$; ${}^{8}\mathrm {B}$ shape not const.
$4.81$ $\pm0.19$ ${}^{+0.28}_{-0.27}$ 6
2005 A
SNO From ${{\mathit \phi}_{{NC}}}$; ${}^{8}\mathrm {B}$ shape constrained
$5.09$ ${}^{+0.44}_{-0.43}$ ${}^{+0.46}_{-0.43}$ 7
2002
SNO Direct measurement from ${{\mathit \phi}}_{\mathit NC}$
$5.44$ $\pm0.99$ 8
2001
Derived from SNO+SuperKam, water Cherenkov
1 ANDERSON 2019 reports this result from the measured ${{\mathit \nu}_{{e}}}{{\mathit e}}$ elastic scattering rate using a 69.2 kton$\cdot{}$day (or 114.7 days) of exposure from May through December, 2017 during the SNO+ detector's water commissioning phase, assuming the neutrino mixing parameters given in PDG 2016 and a standard solar model given in BAHCALL 2005 .
2 AGOSTINI 2018B obtained this result from the measured ${{\mathit \nu}_{{e}}}{{\mathit e}}$ elastic scattering rate over the period between January 2008 and December 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 2017 . Assuming a high-metalicity standard solar model, the electron neutrino survival probability for the ${}^{8}\mathrm {B}$ solar neutrino is calculated to be $0.37$ $\pm0.08$.
3 AHARMIM 2013 obtained this result from a combined analysis of the data from all three phases, SNO-I, II, and III. The measurement of the ${}^{8}\mathrm {B}$ flux mostly comes from the NC signal, however, CC contribution is included in the fit.
4 AHARMIM 2010 reports this result from a joint analysis of SNO Phase I+II data with the "effective electron kinetic energy" threshold of 3.5 MeV. This result is obtained with the assumption of unitarity, which relates the NC, CC, and ES rates. The data were fit with the free parameters directly describing the total ${}^{8}\mathrm {B}$ neutrino flux and the energy-dependent ${{\mathit \nu}_{{e}}}$ survival probability.
5 AHARMIM 2008 reports the results from SNO Phase III measurement using an array of ${}^{3}\mathrm {He}$ proportional counters to measure the rate of NC interactions in heavy water, over the period between November 27, 2004 and November 28, 2006, corresponding to 385.17 live days. A simultaneous fit was made for the number of NC events detected by the proportional counters and the numbers of NC, CC, and ES events detected by the PMTs, where the spectral distributions of the ES and CC events were not constrained to the ${}^{8}\mathrm {B}$ shape.
6 AHARMIM 2005A measurements were made with dissolved NaCl (0.195$\%$ by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding to 391.4 live days, and update AHMED 2004A. The CC, ES, and NC events were statistically separated. In one method, the ${}^{8}\mathrm {B}$ energy spectrum was not constrained. In the other method, the constraint of an undistorted ${}^{8}\mathrm {B}$ energy spectrum was added for comparison with AHMAD 2002 results.
7 AHMAD 2002 determined the total flux of active ${}^{8}\mathrm {B}$ solar neutrinos by directly measuring the neutral-current reaction, ${{\mathit \nu}_{{{{\mathit \ell}}}}}$ ${{\mathit d}}$ $\rightarrow$ ${{\mathit n}}{{\mathit p}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ , which is equally sensitive to ${{\mathit \nu}_{{e}}}$, ${{\mathit \nu}_{{\mu}}}$, and ${{\mathit \nu}_{{\tau}}}$. The complete description of the SNO Phase I data set is given in AHARMIM 2007 .
8 AHMAD 2001 deduced the total flux of active ${}^{8}\mathrm {B}$ solar neutrinos by combining the SNO charged-current result (AHMAD 2001 ) and the Super-Kamiokande ${{\mathit \nu}}{{\mathit e}}$ elastic-scattering result (FUKUDA 2001 ).
References:
ANDERSON 2019
PR D99 012012 Measurement of the $^8$B solar neutrino flux in SNO+ with very low backgrounds
AGOSTINI 2018B
NAT 562 505 Comprehensive measurement of $pp$-chain solar neutrinos
AHARMIM 2013
PR C88 025501 Combined Analysis of all Three Phases of Solar Neutrino Data from the Sudbury Neutrino Observatory
AHARMIM 2010
PR C81 055504 Low-Energy-Threshold Analysis of the Phase I and Phase II Data Sets of the Sudbury Neutrino Observatory
AHARMIM 2008
PRL 101 111301 Independent Measurement of the Total Active ${}^{8}\mathrm {B}$ Solar Neutrino Flux Using an Array of ${}^{3}\mathrm {He}$ Proportional Counters at the Sudbury Neutrino Observatory
AHARMIM 2005A
PR C72 055502 Search for Periodicities in the ${}^{8}\mathrm {B}$ Solar Neutrino Flux Measured by the Sudbury Neutrino Observatory
PRL 87 071301 Measurement of Charged Current Interactions Produced by ${}^{8}\mathrm {B}$ Solar Neutrinos at the SUDBURY Neutrino Observatory
| 2020-09-21T10:35:55 |
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https://par.nsf.gov/biblio/10299603-successful-common-envelope-ejection-binary-neutron-star-formation-hydrodynamics
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Successful Common Envelope Ejection and Binary Neutron Star Formation in 3D Hydrodynamics
The coalescence of two neutron stars was recently observed in a multi-messenger detection of gravitational wave (GW) and electromagnetic (EM) radiation. Binary neutron stars that merge within a Hubble time, as well as many other compact binaries, are expected to form via common envelope evolution. Yet five decades of research on common envelope evolution have not yet resulted in a satisfactory understanding of the multi-spatial multi-timescale evolution for the systems that lead to compact binaries. In this paper, we report on the first successful simulations of common envelope ejection leading to binary neutron star formation in 3D hydrodynamics. We simulate the dynamical inspiral phase of the interaction between a 12 M⊙ red supergiant and a 1.4 M⊙ neutron star for different initial separations and initial conditions. For all of our simulations, we find complete envelope ejection and a final orbital separation of ≈1.1 - 2.8R⊙ , leading to a binary neutron star that will merge within 0.01-1 Gyr. We find an αCE -equivalent efficiency of ≈0.1 - 0.4 for the models we study, but this may be specific for these extended progenitors. We fully resolve the core of the star to ≲0.005R⊙ and our 3D hydrodynamics simulations are informed by more »
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10299603
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Astronomical Journal
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2027-5943
National Science Foundation
##### More Like this
1. ABSTRACT Tidal dissipation due to turbulent viscosity in the convective regions of giant stars plays an important role in shaping the orbits of pre-common-envelope systems. Such systems are possible sources of transients and close compact binary systems that will eventually merge and produce detectable gravitational wave signals. Most previous studies of the onset of common envelope episodes have focused on circular orbits and synchronously rotating donor stars under the assumption that tidal dissipation can quickly spin-up the primary and circularize the orbit before the binary reaches Roche lobe overflow (RLO). We test this assumption by coupling numerical models of the post-main-sequence stellar evolution of massive stars with the model for tidal dissipation in convective envelopes developed in Vick & Lai – a tidal model that is accurate even for highly eccentric orbits with small pericentre distances. We find that, in many cases, tidal dissipation does not circularize the orbit before RLO. For a $10\, {\rm M}_{\odot }$ ($15\, {\rm M}_{\odot }$) primary star interacting with a $1.4\, {\rm M}_{\odot }$ companion, systems with pericentre distances within 3 au (6 au) when the primary leaves the main sequence will retain the initial orbital eccentricity when the primary grows to the Roche radius. Even inmore »
2. Abstract
Many core-collapse supernovae (SNe) with hydrogen-poor and low-mass ejecta, such as ultra-stripped SNe and type Ibn SNe, are observed to interact with dense circumstellar material (CSM). These events likely arise from the core collapse of helium stars that have been heavily stripped by a binary companion and have ejected significant mass during the last weeks to years of their lives. In helium star models run to days before core collapse we identify a range of helium core masses ≈2.5–3Mwhose envelopes expand substantially due to the helium shell burning while the core undergoes neon and oxygen burning. When modeled in binary systems, the rapid expansion of these helium stars induces extremely high rates of late-stage mass transfer ($Ṁ≳10−2M⊙yr−1$) beginning weeks to decades before core collapse. We consider two scenarios for producing CSM in these systems: either mass transfer remains stable and mass loss is driven from the system in the vicinity of the accreting companion, or mass transfer becomes unstable and causes a common envelope event (CEE) through which the helium envelope is unbound. The ensuing CSM properties are consistent with the CSM masses (∼10−2–1M) and radii (∼1013–1016cm) inferred for ultra-stripped SNe and severalmore »
3. Common-envelope evolution is a stage in binary system evolution in which a giant star engulfs a companion. The standard energy formalism is an analytical framework to estimate the amount of energy transferred from the companion's shrinking orbit into the envelope of the star that engulfed it. We show analytically that this energy transfer is larger than predicted by the standard formalism. As the orbit of the companion shrinks, the mass it encloses becomes smaller, and the companion is less bound than if the enclosed mass had remained constant. Therefore, more energy must be transferred to the envelope for the orbit to shrink further. We derive a revised energy formalism that accounts for this effect, and discuss its consequences in two contexts: the formation of neutron star binaries, and the engulfment of planets and brown dwarfs by their host stars. The companion mass required to eject the stellar envelope is smaller by up to 50% , leading to differences in common-envelope evolution outcomes. The energy deposition in the outer envelope of the star, which is related to the transient luminosity and duration, is up to a factor of ≈7 higher. Common-envelope efficiency values above unity, as defined in the literature, aremore »
4. ABSTRACT
Tidal evolution of eccentric binary systems containing at least one massive main-sequence (MS) star plays an important role in the formation scenarios of merging compact-object binaries. The dominant dissipation mechanism in such systems involves tidal excitation of outgoing internal gravity waves at the convective-radiative boundary and dissipation of the waves at the stellar envelope/surface. We have derived analytical expressions for the tidal torque and tidal energy transfer rate in such binaries for arbitrary orbital eccentricities and stellar rotation rates. These expressions can be used to study the spin and orbital evolution of eccentric binaries containing massive MS stars, such as the progenitors of merging neutron star binaries. Applying our results to the PSR J0045-7319 system, which has a massive B-star companion and an observed, rapidly decaying orbit, we find that for the standard radius of convective core based on non-rotating stellar models, the B-star must have a significant retrograde and differential rotation in order to explain the observed orbital decay rate. Alternatively, we suggest that the convective core may be larger as a result of rapid stellar rotation and/or mass transfer to the B-star in the recent past during the post-MS evolution of the pulsar progenitor.
5. ABSTRACT
Strong dynamical interactions among stars and compact objects are expected in a variety of astrophysical settings, such as star clusters and the disks of active galactic nuclei. Via a suite of three-dimensional hydrodynamics simulations using the moving-mesh code arepo, we investigate the formation of transient phenomena and their properties in close encounters between an $2\, {\rm M}_{\odot }$ or $20\, {\rm M}_{\odot }$ equal-mass circular binary star and single $20\, {\rm M}_{\odot }$ black hole (BH). Stars can be disrupted by the BH during dynamical interactions, naturally producing electromagnetic transient phenomena. Encounters with impact parameters smaller than the semimajor axis of the initial binary frequently lead to a variety of transients whose electromagnetic signatures are qualitatively different from those of ordinary disruption events involving just two bodies. These include the simultaneous or successive disruptions of both stars and one full disruption of one star accompanied by successive partial disruptions of the other star. On the contrary, when the impact parameter is larger than the semimajor axis of the initial binary, the binary is either simply tidally perturbed or dissociated into bound and unbound single stars (‘micro-Hills’ mechanism). The dissociation of $20\, {\rm M}_{\odot }$ binaries can produce a runawaymore »
| 2023-02-08T23:01:54 |
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https://phys.libretexts.org/TextBooks_and_TextMaps/College_Physics/Book%3A_Conceptual_Physics_(Crowell)/05._Thermodynamics/5.4_Entropy_As_a_Microscopic_Quantity
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# 5.4 Entropy As a Microscopic Quantity
• Page ID
954
• ### 5.4.1 A microscopic view of entropy
To understand why the second law of thermodynamics is always true, we need to see what entropy really means at the microscopic level. An example that is easy to visualize is the free expansion of a monoatomic gas. Figure a/1 shows a box in which all the atoms of the gas are confined on one side. We very quickly remove the barrier between the two sides, a/2, and some time later, the system has reached an equilibrium, a/3. Each snapshot shows both the positions and the momenta of the atoms, which is enough information to allow us in theory to extrapolate the behavior of the system into the future, or the past. However, with a realistic number of atoms, rather than just six, this would be beyond the computational power of any computer.2
Figure a: A gas expands freely, doubling its volume.
But suppose we show figure a/2 to a friend without any further information, and ask her what she can say about the system's behavior in the future. She doesn't know how the system was prepared. Perhaps, she thinks, it was just a strange coincidence that all the atoms happened to be in the right half of the box at this particular moment. In any case, she knows that this unusual situation won't last for long. She can predict that after the passage of any significant amount of time, a surprise inspection is likely to show roughly half the atoms on each side. The same is true if you ask her to say what happened in the past. She doesn't know about the barrier, so as far as she's concerned, extrapolation into the past is exactly the same kind of problem as extrapolation into the future. We just have to imagine reversing all the momentum vectors, and then all our reasoning works equally well for backwards extrapolation. She would conclude, then, that the gas in the box underwent an unusual fluctuation, b, and she knows that the fluctuation is very unlikely to exist very far into the future, or to have existed very far into the past.
Figure b: An unusual fluctuation in the distribution of the atoms between the two sides of the box. There has been no external manipulation as in figure a/1.
What does this have to do with entropy? Well, state a/3 has a greater entropy than state a/2. It would be easy to extract mechanical work from a/2, for instance by letting the gas expand while pressing on a piston rather than simply releasing it suddenly into the void. There is no way to extract mechanical work from state a/3. Roughly speaking, our microscopic description of entropy relates to the number of possible states. There are a lot more states like a/3 than there are states like a/2. Over long enough periods of time --- long enough for equilibration to occur --- the system gets mixed up, and is about equally likely to be in any of its possible states, regardless of what state it was initially in. We define some number that describes an interesting property of the whole system, say the number of atoms in the right half of the box, $$R$$. A high-entropy value of $$R$$ is one like $$R=3$$, which allows many possible states. We are far more likely to encounter $$R=3$$ than a low-entropy value like $$R=0$$ or $$R=6$$.
Figure c: Earth orbit is becoming cluttered with space junk, and the pieces can be thought of as the “molecules” comprising an exotic kind of gas. These image shows the evolution of a cloud of debris arising from a 2007 Chinese test of an anti-satellite rocket. Panels 1-4 show the cloud five minutes, one hour, one day, and one month after the impact. The entropy seems to have maximized by panel 4.
### 5.4.2 Phase space
There is a problem with making this description of entropy into a mathematical definition. The problem is that it refers to the number of possible states, but that number is theoretically infinite. To get around the problem, we coarsen our description of the system. For the atoms in figure a, we don't really care exactly where each atom is. We only care whether it is in the right side or the left side. If a particular atom's left-right position is described by a coordinate $$x$$, then the set of all possible values of $$x$$ is a line segment along the $$x$$ axis, containing an infinite number of points. We break this line segment down into two halves, each of width $$\Delta x$$, and we consider two different values of $$x$$ to be variations on the same state if they both lie in the same half. For our present purposes, we can also ignore completely the $$y$$ and $$z$$ coordinates, and all three momentum components, $$p_x$$, $$p_y$$, and $$p_z$$.
Figure d: The phase space for two atoms in a box.
Now let's do a real calculation. Suppose there are only two atoms in the box, with coordinates $$x_1$$ and $$x_2$$. We can give all the relevant information about the state of the system by specifying one of the cells in the grid shown in figure d. This grid is known as the phase space of the system. The lower right cell, for instance, describes a state in which atom number 1 is in the right side of the box and atom number 2 in the left. Since there are two possible states with $$R=1$$ and only one state with $$R=2$$, we are twice as likely to observe $$R=1$$, and $$R=1$$ has higher entropy than $$R=2$$.
Figure e: The phase space for three atoms in a box.
Figure e shows a corresponding calculation for three atoms, which makes the phase space three-dimensional. Here, the $$R=1$$ and 2 states are three times more likely than $$R=0$$ and 3. Four atoms would require a four-dimensional phase space, which exceeds our ability to visualize. Although our present example doesn't require it, a phase space can describe momentum as well as position, as shown in figure f. In general, a phase space for a monoatomic gas has six dimensions per atom (one for each coordinate and one for each momentum component).
f / A phase space for a single atom in one dimension, taking momentum into account.
### 5.4.3 Microscopic definitions of entropy and temperature
Two more issues need to be resolved in order to make a microscopic definition of entropy.
First, if we defined entropy as the number of possible states, it would be a multiplicative quantity, not an additive one: if an ice cube in a glass of water has $$M_1$$ states available to it, and the number of states available to the water is $$M_2$$, then the number of possible states of the whole system is the product $$M_1 M_2$$. To get around this problem, we take the natural logarithm of the number of states, which makes the entropy additive because of the property of the logarithm $$\ln (M_1 M_2) = \ln M_1 + \ln M_2$$.
The second issue is a more trivial one. The concept of entropy was originally invented as a purely macroscopic quantity, and the macroscopic definition $$\Delta S = Q/T$$, which has units of J/K, has a different calibration than would result from defining $$S=\ln M$$. The calibration constant we need turns out to be simply the Boltzmann constant, $$k$$.
\mythmhdr{Microscopic definition of entropy} The entropy of a system is $$S = k \ln M$$, where $$M$$ is the number of available states.3
g / Ludwig Boltzmann's tomb, inscribed with his equation for entropy.
This also leads to a more fundamental definition of temperature. Two systems are in thermal equilibrium when they have maximized their combined entropy through the exchange of energy. Here the energy possessed by one part of the system, $$E_1$$ or $$E_2$$, plays the same role as the variable $$R$$ in the examples of free expansion above. A maximum of a function occurs when the derivative is zero, so the maximum entropy occurs when
$\begin{equation*} \frac{d\left(S_1+S_2\right)}{dE_1} = 0 . \end{equation*}$
We assume the systems are only able to exchange heat energy with each other, $$dE_1=-dE_2$$, so
$\begin{equation*} \frac{dS_1}{dE_1} = \frac{dS_2}{dE_2} , \end{equation*}$
and since the energy is being exchanged in the form of heat we can make the equations look more familiar if we write $$dQ$$ for an amount of heat to be transferred into either system:
$\begin{equation*} \frac{dS_1}{dQ_1} = \frac{dS_2}{dQ_2} . \end{equation*}$
In terms of our previous definition of entropy, this is equivalent to $$1/T_1=1/T_2$$, which makes perfect sense since the systems are in thermal equilibrium. According to our new approach, entropy has already been defined in a fundamental manner, so we can take this as a definition of temperature:
$\begin{equation*} \frac{1}{T} = \frac{dS}{dQ} , \end{equation*}$
where $$dS$$ represents the increase in the system's entropy from adding heat $$dQ$$ to it.
#### Examples with small numbers of atoms
Let's see how this applies to an ideal, monoatomic gas with a small number of atoms. To start with, consider the phase space available to one atom. Since we assume the atoms in an ideal gas are noninteracting, their positions relative to each other are really irrelevant. We can therefore enumerate the number of states available to each atom just by considering the number of momentum vectors it can have, without considering its possible locations. The relationship between momentum and kinetic energy is $$E=(p_x^2+p_y^2+p_z^2)/2m$$, so if for a fixed value of its energy, we arrange all of an atom's possible momentum vectors with their tails at the origin, their tips all lie on the surface of a sphere in phase space with radius $$|\mathbf{p}|=\sqrt{2mE}$$. The number of possible states for that atom is proportional to the sphere's surface area, which in turn is proportional to the square of the sphere's radius, $$|\mathbf{p}|^2=2mE$$.
Now consider two atoms. For any given way of sharing the energy between the atoms, $$E=E_1+E_2$$, the number of possible combinations of states is proportional to $$E_1E_2$$. The result is shown in figure h. The greatest number of combinations occurs when we divide the energy equally, so an equal division gives maximum entropy.
h / A two-atom system has the highest number of available states when the energy is equally divided. Equal energy division is therefore the most likely possibility at any given moment in time.
By increasing the number of atoms, we get a graph whose peak is narrower, i. With more than one atom in each system, the total energy is $$E=(p_{x,1}^2+p_{y,1}^2+p_{z,1}^2+p_{x,2}^2+p_{y,2}^2+p_{z,2}^2+...)/2m$$. With $$n$$ atoms, a total of $$3n$$ momentum coordinates are needed in order to specify their state, and such a set of numbers is like a single point in a $$3n$$-dimensional space (which is impossible to visualize). For a given total energy $$E$$, the possible states are like the surface of a $$3n$$-dimensional sphere, with a surface area proportional to $$p^{3n-1}$$, or $$E^{(3n-1)/2}$$. The graph in figure i, for example, was calculated according to the formula $$E_1^{29/2}E_2^{29/2}=E_1^{29/2}(E-E_1)^{29/2}$$.
i / When two systems of 10 atoms each interact, the graph of the number of possible states is narrower than with only one atom in each system.
Since graph i is narrower than graph h, the fluctuations in energy sharing are smaller. If we inspect the system at a random moment in time, the energy sharing is very unlikely to be more lopsided than a 40-60 split. Now suppose that, instead of 10 atoms interacting with 10 atoms, we had a $$10^{23}$$ atoms interacting with $$10^{23}$$ atoms. The graph would be extremely narrow, and it would be a statistical certainty that the energy sharing would be nearly perfectly equal. This is why we never observe a cold glass of water to change itself into an ice cube sitting in some warm water!
By the way, note that although we've redefined temperature, these examples show that things are coming out consistent with the old definition, since we saw that the old definition of temperature could be described in terms of the average energy per atom, and here we're finding that equilibration results in each subset of the atoms having an equal share of the energy.
#### Entropy of a monoatomic ideal gas
Let's calculate the entropy of a monoatomic ideal gas of $$n$$ atoms. This is an important example because it allows us to show that our present microscopic treatment of thermodynamics is consistent with our previous macroscopic approach, in which temperature was defined in terms of an ideal gas thermometer.
The number of possible locations for each atom is $$V/\Delta x^3$$, where $$\Delta x$$ is the size of the space cells in phase space. The number of possible combinations of locations for the atoms is therefore $$(V/\Delta x^3)^n$$.
The possible momenta cover the surface of a $$3n$$-dimensional sphere, whose radius is $$\sqrt{2mE}$$, and whose surface area is therefore proportional to $$E^{(3n-1)/2}$$. In terms of phase-space cells, this area corresponds to $$E^{(3n-1)/2} / \Delta p^{3n}$$ possible combinations of momenta, multiplied by some constant of proportionality which depends on $$m$$, the atomic mass, and $$n$$, the number of atoms. To avoid having to calculate this constant of proportionality, we limit ourselves to calculating the part of the entropy that does not depend on $$n$$, so the resulting formula will not be useful for comparing entropies of ideal gas samples with different numbers of atoms.
The final result for the number of available states is
$\begin{equation*} M = \left(\frac{V}{\Delta x^3}\right)^n\:\frac{E^{(3n-1)/2}}{\Delta p^{3n-1}} , \text{[function of n]} \end{equation*}$
so the entropy is
$\begin{equation*} S = nk \ln V + \frac{3}{2}nk\ln E + \text{(function of \Delta x, \Delta p, and n)} , \end{equation*}$
where the distinction between $$n$$ and $$n-1$$ has been ignored. Using $$PV=nkT$$ and $$E=(3/2)nkT$$, we can also rewrite this as
$\begin{equation*} S = \frac{5}{2} nk \ln T - nk \ln P + ... , \text{[entropy of a monoatomic ideal gas]} \end{equation*}$
where “$$...$$” indicates terms that may depend on $$\Delta x$$, $$\Delta p$$, $$m$$, and $$n$$, but that have no effect on comparisons of gas samples with the same number of atoms.
self-check:
Why does it make sense that the temperature term has a positive sign in the above example, while the pressure term is negative? Why does it make sense that the whole thing is proportional to $$n$$?
To show consistency with the macroscopic approach to thermodynamics, we need to show that these results are consistent with the behavior of an ideal-gas thermometer. Using the new definition $$1/T=dS/dQ$$, we have $$1/T=dS/dE$$, since transferring an amount of heat $$dQ$$ into the gas increases its energy by a corresponding amount. Evaluating the derivative, we find $$1/T=(3/2)nk/E$$, or $$E=(3/2)nkT$$, which is the correct relation for a monoatomic ideal gas.
Example 20: A mixture of molecules
$$\triangleright$$ Suppose we have a mixture of two different monoatomic gases, say helium and argon. How would we find the entropy of such a mixture (say, in terms of $$V$$ and $$E$$)? How would the energy be shared between the two types of molecules, i.e., would a more massive argon atom have more energy on the average than a less massive helium atom, the same, or less?
$$\triangleright$$ Since entropy is additive, we simply need to add the entropies of the two types of atom. However, the expression derived above for the entropy omitted the dependence on the mass $$m$$ of the atom, which is different for the two constituents of the gas, so we need to go back and figure out how to put that $$m$$-dependence back in. The only place where we threw away $$m$$'s was when we identified the radius of the sphere in momentum space with $$\sqrt{2mE}$$, but then threw away the constant factor of $$m$$. In other words, the final result can be generalized merely by replacing $$E$$ everywhere with the product $$mE$$. Since the log of a product is the sum of the logs, the dependence of the final result on $$m$$ and $$E$$ can be broken apart into two different terms, and we find
$\begin{equation*} S=nk \ln V +\frac{3}{2}nk\ln m+\frac{3}{2}nk\ln E+... \end{equation*}$
The total entropy of the mixture can then be written as
$\begin{multline*} S =n_1k\ln V +n_2k \ln V +\frac{3}{2}n_1k\ln m_1+\frac{3}{2}n_2k\ln m_2 \\ +\frac{3}{2}n_1k\ln E_1+\frac{3}{2}n_2k\ln E_2+... \end{multline*}$
Now what about the energy sharing? If the total energy is $$E=E_1+E_2$$, then the most ovewhelmingly probable sharing of energy will the the one that maximizes the entropy. Notice that the dependence of the entropy on the masses $$m_1$$ and $$m_2$$ occurs in terms that are entirely separate from the energy terms. If we want to maximize $$S$$ with respect to $$E_1$$ (with $$E_2=E-E_1$$ by conservation of energy), then we differentiate $$S$$ with respect to $$E_1$$ and set it equal to zero. The terms that contain the masses don't have any dependence on $$E_1$$, so their derivatives are zero, and we find that the molecular masses can have no effect on the energy sharing. Setting the derivative equal to zero, we have
\begin{align*} 0 &= \frac{\partial}{\partial E_1} \left(n_1k\ln V +n_2k \ln V +\frac{3}{2}n_1k\ln m_1+\frac{3}{2}n_2k\ln m_2\right. \\ & +\left.\frac{3}{2}n_1k\ln E_1+\frac{3}{2}n_2k\ln (E-E_1)+...\right) \\ &= \frac{3}{2}k \left( \frac{n_1}{E_1} - \frac{n_2}{E-E_1} \right) \\ 0 &= \frac{n_1}{E_1} - \frac{n_2}{E-E_1} \\ \frac{n_1}{E_1} &= \frac{n_2}{E_2} . \end{align*}
In other words, each gas gets a share of the energy in proportion to the number of its atoms, and therefore every atom gets, on average, the same amount of energy, regardless of its mass. The result for the average energy per atom is exactly the same as for an unmixed gas, $$\bar{K}=(3/2)kT$$.
#### Equipartition
Example 20 is a special case of a more general statement called the equipartition theorem. Suppose we have only one argon atom, named Alice, and one helium atom, named Harry. Their total kinetic energy is $$E=p_x^2/2m+p_y^2/2m+p_z^2/2m+{p'}_x^2/2m'+{p'}_y^2/2m'+{p'}_z^2/2m'$$, where the primes indicate Harry. We have six terms that all look alike. The only difference among them is that the constant factors attached to the squares of the momenta have different values, but we've just proved that those differences don't matter. In other words, if we have any system at all whose energy is of the form $$E=(...)p_1^2+(...)p_2^2+...$$, with any number of terms, then each term holds, on average, the same amount of energy, $$\frac{1}{2}kT$$. We say that the system consisting of Alice and Harry has six degrees of freedom. It doesn't even matter whether the things being squared are momenta: if you look back over the logical steps that went into the argument, you'll see that none of them depended on that. In a solid, for example, the atoms aren't free to wander around, but they can vibrate from side to side. If an atom moves away from its equilibrium position at $$x=0$$ to some other value of $$x$$, then its electrical energy is $$(1/2)\kappa x^2$$, where $$\kappa$$ is the spring constant (written as the Greek letter kappa to distinguish it from the Boltzmann constant $$k$$). We can conclude that each atom in the solid, on average, has $$\frac{1}{2}kT$$ of energy in the electrical energy due to its $$x$$ displacement along the $$x$$ axis, and equal amounts for $$y$$ and $$z$$. This is known as equipartition, meaning equal partitioning, or equal sharing. The equipartition theorem says that if the expression for the energy looks like a sum of squared variables, then each degree of freedom has an average energy of $$\frac{1}{2}kT$$. Thus, very generally, we can interpret temperature as the average energy per degree of freedom (times $$k/2$$).
#### An unexpected glimpse of the microcosm
You may have the feeling at this point that of course Boltzmann was right about the literal existence of atoms, but only very sophisticated experiments could vindicate him definitively. After all, the microscopic and macroscopic definitions of entropy are equivalent, so it might seem as though there was no real advantage to the microscopic approach. Surprisingly, very simple experiments are capable of revealing a picture of the microscopic world, and there is no possible macroscopic explanation for their results.
j / An experiment for determining the shapes of molecules.
In 1819, before Boltzmann was born, Clément and Desormes did an experiment like the one shown in figure j. The gas in the flask is pressurized using the syringe. This heats it slightly, so it is then allowed to cool back down to room temperature. Its pressure is measured using the manometer. The stopper on the flask is popped and then immediately reinserted. Its pressure is now equalized with that in the room, and the gas's expansion has cooled it a little, because it did mechanical work on its way out of the flask, causing it to lose some of its internal energy $$E$$. The expansion is carried out quickly enough so that there is not enough time for any significant amount of heat to flow in through the walls of the flask before the stopper is reinserted. The gas is now allowed to come back up to room temperature (which takes a much longer time), and as a result regains a fraction $$b$$ of its original overpressure. During this constant-volume reheating, we have $$PV=nkT$$, so the amount of pressure regained is a direct indication of how much the gas cooled down when it lost an amount of energy $$\Delta E$$.
k / The differing shapes of a helium atom (1), a nitrogen molecule (2), and a difluoroethane molecule (3) have surprising macroscopic effects.
If the gas is monoatomic, then we know what to expect for this relationship between energy and temperature: $$\Delta E=(3/2)nk\Delta T$$, where the factor of 3 came ultimately from the fact that the gas was in a three-dimensional space, k/1. Moving in this space, each molecule can have momentum in the x, y, and z directions. It has three degrees of freedom. What if the gas is not monoatomic? Air, for example, is made of diatomic molecules, k/2. There is a subtle difference between the two cases. An individual atom of a monoatomic gas is a perfect sphere, so it is exactly the same no matter how it is oriented. Because of this perfect symmetry, there is thus no way to tell whether it is spinning or not, and in fact we find that it can't rotate. The diatomic gas, on the other hand, can rotate end over end about the x or y axis, but cannot rotate about the z axis, which is its axis of symmetry. It has a total of five degrees of freedom. A polyatomic molecule with a more complicated, asymmetric shape, k/3, can rotate about all three axis, so it has a total of six degrees of freedom.
Because a polyatomic molecule has more degrees of freedom than a monoatomic one, it has more possible states for a given amount of energy. That is, its entropy is higher for the same energy. From the definition of temperature, $$1/T=dS/dE$$, we conclude that it has a lower temperature for the same energy. In other words, it is more difficult to heat $$n$$ molecules of difluoroethane than it is to heat $$n$$ atoms of helium. When the Clément-Desormes experiment is carried out, the result $$b$$ therefore depends on the shape of the molecule! Who would have dreamed that such simple observations, correctly interpreted, could give us this kind of glimpse of the microcosm?
Lets go ahead and calculate how this works. Suppose a gas is allowed to expand without being able to exchange heat with the rest of the universe. The loss of thermal energy from the gas equals the work it does as it expands, and using the result of homework problem 2 on page 335, the work done in an infinitesimal expansion equals $$PdV$$, so
$\begin{equation*} dE + P dV = 0 . \end{equation*}$
(If the gas had not been insulated, then there would have been a third term for the heat gained or lost by heat conduction.)
From section 5.2 we have $$E=(3/2)PV$$ for a monoatomic ideal gas. More generally, the equipartition theorem tells us that the 3 simply needs to be replaced with the number of degrees of freedom $$\alpha$$, so $$dE=(\alpha/2)PdV+(\alpha/2)VdP$$, and the equation above becomes
$\begin{equation*} 0 = \frac{\alpha+2}{2}PdV+\frac{\alpha}{2}VdP . \end{equation*}$
Rearranging, we have
$\begin{equation*} (\alpha+2)\frac{dV}{V} = -\alpha\frac{dP}{P} . \end{equation*}$
Integrating both sides gives
$\begin{equation*} (\alpha+2) \ln V = -\alpha \ln P + \text{constant} , \end{equation*}$
and taking exponentials on both sides yields
$\begin{equation*} V^{\alpha+2} \propto P^{-\alpha} . \end{equation*}$
We now wish to reexpress this in terms of pressure and temperature. Eliminating $$V\propto(T/P)$$ gives
$\begin{equation*} T \propto P^b , \end{equation*}$
where $$b=2/(\alpha+2)$$ is equal to 2/5, 2/7, or 1/4, respectively, for a monoatomic, diatomic, or polyatomic gas.
Example 21: Efficiency of the Carnot engine
As an application, we now prove the result claimed earlier for the efficiency of a Carnot engine. First consider the work done during the constant-temperature strokes. Integrating the equation $$dW=PdV$$, we have $$W = \int P dV$$. Since the thermal energy of an ideal gas depends only on its temperature, there is no change in the thermal energy of the gas during this constant-temperature process. Conservation of energy therefore tells us that work done by the gas must be exactly balanced by the amount of heat transferred in from the reservoir.
\begin{align*} Q &= W \\ &= \int P dV \end{align*}
For our proof of the efficiency of the Carnot engine, we need only the ratio of $$Q_H$$ to $$Q_L$$, so we neglect constants of proportionality, and simply subsitutde $$P\propto T/V$$, giving
$\begin{equation*} Q \propto \int \frac{T}{V} dV \propto T \ln \frac{V_2}{V_1} \propto T \ln \frac{P_1}{P_2} . \end{equation*}$
The efficiency of a heat engine is
$\begin{equation*} \text{efficiency} = 1 - \frac{Q_L}{Q_H} . \end{equation*}$
Making use of the result from the previous proof for a Carnot engine with a monoatomic ideal gas as its working gas, we have
$\begin{equation*} \text{efficiency} = 1-\frac{T_L\:\ln(P_4/P_3)}{T_H\:\ln(P_1/P_2)} , \end{equation*}$
where the subscripts 1, 2, 3, and 4 refer to figures d--g on page 311. We have shown above that the temperature is proportional to $$P^b$$ on the insulated strokes 2-3 and 4-1, the pressures must be related by $$P_2/P_3=P_1/P_4$$, which can be rearranged as $$P_4/P_3=P_1/P_2$$, and we therefore have
$\begin{equation*} \text{efficiency} = 1 - \frac{T_L}{T_H} . \end{equation*}$
### 5.4.4 The arrow of time, or “this way to the Big Bang”
Now that we have a microscopic understanding of entropy, what does that tell us about the second law of thermodynamics? The second law defines a forward direction to time, “time's arrow.” The microscopic treatment of entropy, however, seems to have mysteriously sidestepped that whole issue. A graph like figure b on page 316, showing a fluctuation away from equilibrium, would look just as natural if we flipped it over to reverse the direction of time. After all, the basic laws of physics are conservation laws, which don't distinguish between past and future. Our present picture of entropy suggests that we restate the second law of thermodynamics as follows: low-entropy states are short-lived. An ice cube can't exist forever in warm water. We no longer have to distinguish past from future.
But how do we reconcile this with our strong psychological sense of the direction of time, including our ability to remember the past but not the future? Why do we observe ice cubes melting in water, but not the time-reversed version of the same process?
The answer is that there is no past-future asymmetry in the laws of physics, but there is a past-future asymmetry in the universe. The universe started out with the Big Bang. (Some of the evidence for the Big Bang theory is given on page 356.) The early universe had a very low entropy, and low-entropy states are short-lived. What does “short-lived” mean here, however? Hot coffee left in a paper cup will equilibrate with the air within ten minutes or so. Hot coffee in a thermos bottle maintains its low-entropy state for much longer, because the coffee is insulated by a vacuum between the inner and outer walls of the thermos. The universe has been mostly vacuum for a long time, so it's well insulated. Also, it takes billions of years for a low-entropy normal star like our sun to evolve into the high-entropy cinder known as a white dwarf.
The universe, then, is still in the process of equilibrating, and all the ways we have of telling the past from the future are really just ways of determining which direction in time points toward the Big Bang, i.e., which direction points to lower entropy. The psychological arrow of time, for instance, is ultimately based on the thermodynamic arrow. In some general sense, your brain is like a computer, and computation has thermodynamic effects. In even the most efficient possible computer, for example, erasing one bit of memory decreases its entropy from $$k \ln 2$$ (two possible states) to $$k \ln 1$$ (one state), for a drop of about $$10^{-23}$$ J/K. One way of determining the direction of the psychological arrow of time is that forward in psychological time is the direction in which, billions of years from now, all consciousness will have ceased; if consciousness was to exist forever in the universe, then there would have to be a never-ending decrease in the universe's entropy. This can't happen, because low-entropy states are short-lived.
Relating the direction of the thermodynamic arrow of time to the existence of the Big Bang is a satisfying way to avoid the paradox of how the second law can come from basic laws of physics that don't distinguish past from future. There is a remaining mystery, however: why did our universe have a Big Bang that was low in entropy? It could just as easily have been a maximum-entropy state, and in fact the number of possible high-entropy Big Bangs is vastly greater than the number of possible low-entropy ones. The question, however, is probably not one that can be answered using the methods of science. All we can say is that if the universe had started with a maximum-entropy Big Bang, then we wouldn't be here to wonder about it. A longer, less mathematical discussion of these concepts, along with some speculative ideas, is given in “The Cosmic Origins of Time's Arrow,” Sean M. Carroll, Scientific American, June 2008, p. 48.
### 5.4.5 Quantum mechanics and zero entropy
The previous discussion would seem to imply that absolute entropies are never well defined, since any calculation of entropy will always end up having terms that depend on $$\Delta p$$ and $$\Delta x$$. For instance, we might think that cooling an ideal gas to absolute zero would give zero entropy, since there is then only one available momentum state, but there would still be many possible position states. We'll see later in this book, however, that the quantum mechanical uncertainty principle makes it impossible to know the location and position of a particle simultaneously with perfect accuracy. The best we can do is to determine them with an accuracy such that the product $$\Delta p\Delta x$$ is equal to a constant called Planck's constant. According to quantum physics, then, there is a natural minimum size for rectangles in phase space, and entropy can be defined in absolute terms. Another way of looking at it is that according to quantum physics, the gas as a whole has some well-defined ground state, which is its state of minimum energy. When the gas is cooled to absolute zero, the scene is not at all like what we would picture in classical physics, with a lot of atoms lying around motionless. It might, for instance, be a strange quantum-mechanical state called the Bose-Einstein condensate, which was achieved for the first time recently with macroscopic amounts of atoms. Classically, the gas has many possible states available to it at zero temperature, since the positions of the atoms can be chosen in a variety of ways. The classical picture is a bad approximation under these circumstances, however. Quantum mechanically there is only one ground state, in which each atom is spread out over the available volume in a cloud of probability. The entropy is therefore zero at zero temperature. This fact, which cannot be understood in terms of classical physics, is known as the third law of thermodynamics.
### 5.4.6 Summary of the laws of thermodynamics
Here is a summary of the laws of thermodynamics:
• The zeroth law of thermodynamics (page 303) If object A is at the same temperature as object B, and B is at the same temperature as C, then A is at the same temperature as C.
• The first law of thermodynamics (page 298) Energy is
[4] conserved.
• The second law of thermodynamics (page 314) The entropy of a closed system always increases, or at best stays the same: $$\Delta S\ge0$$.
• The third law of thermodynamics (page 327) The entropy of a system approaches zero as its temperature approaches absolute zero.
From a modern point of view, only the first law deserves to be called a fundamental law of physics. Once Boltmann discovered the microscopic nature of entropy, the zeroth and second laws could be understood as statements about probability: a system containing a large number of particles is overwhelmingly likely to do a certain thing, simply because the number of possible ways to do it is extremely large compared to the other possibilities. The third law is also now understood to be a consequence of more basic physical principles, but to explain the third law, it's not sufficient simply to know that matter is made of atoms: we also need to understand the quantum-mechanical nature of those atoms, discussed in chapter 13. Historically, however, the laws of thermodynamics were discovered in the eighteenth century, when the atomic theory of matter was generally considered to be a hypothesis that couldn't be tested experimentally. Ideally, with the publication of Boltzmann's work on entropy in 1877, the zeroth and second laws would have been immediately demoted from the status of physical laws, and likewise the development of quantum mechanics in the 1920's would have done the same for the third law.
l / The Otto cycle. 1. In the exhaust stroke, the piston expels the burned air-gas mixture left over from the preceding cycle. 2. In the intake stroke, the piston sucks in fresh air-gas mixture. 3. In the compression stroke, the piston compresses the mixture, and heats it. 4. At the beginning of the power stroke, the spark plug fires, causing the air-gas mixture to burn explosively and heat up much more. The heated mixture expands, and does a large amount of positive mechanical work on the piston. An animated version can be viewed in the Wikipedia article “Four-stroke engine.”
### Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
| 2018-09-20T11:25:08 |
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|
https://par.nsf.gov/biblio/10251137
|
Distribution of Si ii λ6355 velocities of Type Ia supernovae and implications for asymmetric explosions
ABSTRACT The ejecta velocity is a very important parameter in studying the structure and properties of Type Ia supernovae (SNe Ia) and is a candidate key parameter in improving the utility of SNe Ia for cosmological distance determinations. Here, we study the velocity distribution of a sample of 311 SNe Ia from the kaepora data base. The velocities are derived from the Si ii λ6355 absorption line in optical spectra measured at (or extrapolated to) the time of peak brightness. We statistically show that the observed velocity has a bimodal Gaussian distribution (population ratio 201:110 or 65 per cent:35 per cent) consisting of two groups of SNe Ia: Group I with a lower but narrower scatter ($11\, 000 \pm 700\, \mathrm{km\, s}^{-1}$), and Group II with a higher but broader scatter ($12\, 300 \pm 1800\, \mathrm{km\, s}^{-1}$). The true origin of the two components is unknown. Naturally, there could exist two intrinsic velocity distributions observed. However, we try to use asymmetric geometric models through statistical simulations to reproduce the observed distribution assuming that all SNe Ia share the same intrinsic distribution. In the two cases we consider, 35 per cent of SNe Ia are considered to be asymmetric in Case 1, and all SNe Ia are asymmetric in Case 2. Simulations for both cases can more »
Authors:
; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10251137
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
499
Issue:
4
Page Range or eLocation-ID:
5325 to 5333
ISSN:
0035-8711
National Science Foundation
##### More Like this
1. ABSTRACT After correcting for their light-curve shape and colour, Type Ia supernovae (SNe Ia) are precise cosmological distance indicators. However, there remains a non-zero intrinsic scatter in the differences between measured distance and that inferred from a cosmological model (i.e. Hubble residuals or HRs), indicating that SN Ia distances can potentially be further improved. We use the open-source relational data base kaepora to generate composite spectra with desired average properties of phase, light-curve shape, and HR. At many phases, the composite spectra from two subsamples with positive and negative average HRs are significantly different. In particular, in all spectra from 9 d before to 15 d after peak brightness, we find that SNe with negative HRs have, on average, higher ejecta velocities (as seen in nearly every optical spectral feature) than SNe with positive HRs. At +4 d relative to B-band maximum, using a sample of 62 SNe Ia, we measure a 0.091 ± 0.035 mag (2.7σ) HR step between SNe with Si ii λ6355 line velocities ($v_{Si\, rm{\small II}}$) higher/lower than −11 000 km s−1 (the median velocity). After light-curve shape and colour correction, SNe with higher velocities tend to have underestimated distance moduli relative to a cosmological model. The intrinsic scatter in our sample reduces from 0.094 to 0.082 mag after making thismore »
2. ABSTRACT Detailed spectropolarimetric studies may hold the key to probing the explosion mechanisms and the progenitor scenarios of Type Ia supernovae (SNe Ia). We present multi-epoch spectropolarimetry and imaging polarimetry of SN 2019ein, an SN Ia showing high expansion velocities at early phases. The spectropolarimetry sequence spans from ∼−11 to +10 d relative to peak brightness in the B band. We find that the level of the continuum polarization of SN 2019ein, after subtracting estimated interstellar polarization, is in the range 0.0–0.3 per cent, typical for SNe Ia. The polarization position angle remains roughly constant before and after the SN light-curve peak, implying that the inner regions share the same axisymmetry as the outer layers. We observe high polarization (∼1 per cent) across both the Si ii λ6355 and Ca ii near-infrared triplet features. These two lines also display complex polarization modulations. The spectropolarimetric properties of SN 2019ein rule out a significant departure from spherical symmetry of the ejecta for up to a month after the explosion. These observations disfavour merger-induced and double-detonation models for SN 2019ein. The imaging polarimetry shows weak evidence for a modest increase in polarization after ∼20 d since the B-band maximum. If this rise is real and is observed in other SNe Ia at similar phases, we may havemore »
3. ABSTRACT
Spectropolarimetry enables us to measure the geometry and chemical structure of the ejecta in supernova explosions, which is fundamental for the understanding of their explosion mechanism(s) and progenitor systems. We collected archival data of 35 Type Ia supernovae (SNe Ia), observed with Focal Reducer and Low-Dispersion Spectrograph (FORS) on the Very Large Telescope at 127 epochs in total. We examined the polarization of the Si ii λ6355 Å line ($p_{\rm Si\, \small {II}}$) as a function of time, which is seen to peak at a range of various polarization degrees and epochs relative to maximum brightness. We reproduced the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship identified in a previous study, and show that subluminous and transitional objects display polarization values below the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship for normal SNe Ia. We found a statistically significant linear relationship between the polarization of the Si ii λ6355 Å line before maximum brightness and the Si ii line velocity and suggest that this, along with the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship, may be explained in the context of a delayed-detonation model. In contrast, we compared our observations to numerical predictions in the $\Delta m_{15}\!-\!v_{\rm Si\, \small {II}}$ plane and found a dichotomy in the polarization propertiesmore »
4. ABSTRACT
We report a tentative detection of the circumgalactic medium (CGM) of Wolf–Lundmark–Melotte (WLM), an isolated, low-mass (logM*/M⊙ ≈ 7.6), dwarf irregular galaxy in the Local Group (LG). We analyse an HST/COS archival spectrum of a quasar sightline (PHL2525), which is 45 kpc (0.5 virial radius) from WLM and close to the Magellanic Stream (MS). Along this sightline, two ion absorbers are detected in Si ii, Si iii, Si iv, C ii, and C iv at velocities of ∼−220 km s−1 (Component v-220) and ∼−150 km s−1 (Component v-150). To identify their origins, we study the position–velocity alignment of the components with WLM and the nearby MS. Near the magellanic longitude of PHL2525, the MS-related neutral and ionized gas moves at ≲−190 km s−1, suggesting an MS origin for Component v-220, but not for Component v-150. Because PHL2525 passes near WLM and Component v-150 is close to WLM’s systemic velocity (∼−132 km s−1), it is likely that Component v-150 arises from the galaxy’s CGM. This results in a total Si mass in WLM’s CGM of $M_{\rm Si}^{\rm CGM}\sim (0.2-1.0)\times 10^5~\mathrm{M}_\odot$ using assumption from other COS dwarf studies. Comparing $M_{\rm Si}^{\rm CGM}$ to the total Si mass synthesized in WLM over its lifetime (∼1.3 × 105 M⊙), we find ∼3 per cent is locked in stars,more »
5. ABSTRACT
Optical spectropolarimetry of the normal thermonuclear supernova (SN) 2019np from −14.5 to +14.5 d relative to B-band maximum detected an intrinsic continuum polarization (pcont) of 0.21 ± 0.09 per cent at the first epoch. Between days −11.5 and +0.5, pcont remained ∼0 and by day +14.5 was again significant at 0.19 ± 0.10 per cent. Not considering the first epoch, the dominant axis of ${\rm Si\, {\small II}}$ λ6355 was roughly constant staying close the continuum until both rotated in opposite directions on day +14.5. Detailed radiation-hydrodynamical simulations produce a very steep density slope in the outermost ejecta so that the low first-epoch pcont ≈ 0.2 per cent nevertheless suggests a separate structure with an axis ratio ∼2 in the outer carbon-rich (3.5–4) × 10−3 M⊙. Large-amplitude fluctuations in the polarization profiles and a flocculent appearance of the polar diagram for the ${\rm Ca\, {\small II}}$ near-infrared triplet (NIR3) may be related by a common origin. The temporal evolution of the polarization spectra agrees with an off-centre delayed detonation. The late-time increase in polarization and the possible change in position angle are also consistent with an aspherical 56Ni core. The pcont and the absorptions due to ${\rm Si\, {\small II}}$ λ6355 and ${\rm Ca\, {\small II}}$ NIR3 formmore »
| 2023-02-09T02:54:47 |
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|
https://www.usgs.gov/centers/upper-midwest-environmental-sciences-center/science/science-topics/waterbirds
|
# Waterbirds
Filter Total Items: 6
#### Deep Learning for Automated Detection and Classification of Waterfowl, Seabirds, and other Wildlife from Digital Aerial Imagery
In collaboration with the Bureau of Ocean Energy Management, U.S. Fish and Wildlife Service, and the Vision Group at the International Computer Science Institute at the University of California - Berkeley, the U.S. Geological Survey Upper Midwest Environmental Sciences Center is developing deep learning algorithms and tools for the automatic detection, enumeration, classification, and annotation...
#### Deep Learning for Automated Detection and Classification of Waterfowl, Seabirds, and other Wildlife from Digital Aerial Imagery
In collaboration with the Bureau of Ocean Energy Management, U.S. Fish and Wildlife Service, and the Vision Group at the International Computer Science Institute at the University of California - Berkeley, the U.S. Geological Survey Upper Midwest Environmental Sciences Center is developing deep learning algorithms and tools for the automatic detection, enumeration, classification, and annotation...
#### Common Loon Migration Study
Common loons often migrate several hundred miles to reach coastal waters during fall migration. Information about this part of the loon's life history is not well known.The use of satellite telemetry allows biologists to track loon movements through distant migrations and during winter. A transmitter attached to a radiomarked loon periodically sends a signal which is detected by a satellite-based...
#### Common Loon Migration Study
Common loons often migrate several hundred miles to reach coastal waters during fall migration. Information about this part of the loon's life history is not well known.The use of satellite telemetry allows biologists to track loon movements through distant migrations and during winter. A transmitter attached to a radiomarked loon periodically sends a signal which is detected by a satellite-based...
#### River Productivity
Biological production represents the total amount of living material (biomass) that was produced during a defined period of time. This production is important because some of it is used for food and some is valued for recreation, it is a direct measure of total ecosystem processes, and it sustains biological diversity. Production is a measure of energy flow, and is therefore a natural currency for...
#### River Productivity
Biological production represents the total amount of living material (biomass) that was produced during a defined period of time. This production is important because some of it is used for food and some is valued for recreation, it is a direct measure of total ecosystem processes, and it sustains biological diversity. Production is a measure of energy flow, and is therefore a natural currency for...
#### Waterbird Distribution and Foraging Patterns on the Great Lakes with Respect to Avian Botulism
The Upper Midwest Environmental Sciences Center (UMESC) in La Crosse, Wisconsin is studying the distribution and foraging patterns of sentinel fish-eating waterbirds through aerial surveys, and by tracking migration movements coupled with foraging depth profiles of common loons equipped with archival geo-locator tags and satellite transmitters. The results of this work are expected to elucidate...
#### Waterbird Distribution and Foraging Patterns on the Great Lakes with Respect to Avian Botulism
The Upper Midwest Environmental Sciences Center (UMESC) in La Crosse, Wisconsin is studying the distribution and foraging patterns of sentinel fish-eating waterbirds through aerial surveys, and by tracking migration movements coupled with foraging depth profiles of common loons equipped with archival geo-locator tags and satellite transmitters. The results of this work are expected to elucidate...
| 2022-05-24T22:22:07 |
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https://gocompetition.energy.gov/competition/current-competition?page=evaluation
|
Detailed Information
Contact
Competing Teams
## Evaluation
Evaluation
This section describes the evaluation process used in the Beta Phase, including a description of the required output files and the evaluation platform.
The evaluation process will assess solutions against the official competition problem formulation as described in this website; however, competitors will be free to utilize any other formulation or modeling approach within their solution software. In order to ensure fairness and to enable the use of alternative problem formulations where appropriate, there will be two sections for each competition algorithm. The first section will record the computation time required by competitors’ codes to solve the PSCOPF problem and report the real power generation dispatch decisions at each bus. This information is recorded in the file, solution1.txt, described in detail below. The timer records the time for the first section to execute, from invocation to completion.
In theory, the evaluation platform could use the decision variable solution provided by competitors to calculate power flow solutions and use that solution to assess constraint violations and objective function value; however, solving for power flows and checking for the existence of feasible power flow solutions are also non-trivial problems. Existing (commercial or open-source) power flow tools that could be used by the evaluation platform may find different power flow solutions given the same inputs or may not always converge to a feasible power flow solution even when one exists. The failure of the evaluation platform to find feasible power flow solutions could unfairly penalize the scores of individual competitors; therefore, we believe the best method for evaluating solutions is to require competitors to calculate and report power flow solutions for the base case and all contingency cases (given their previously reported decision variables). Given this additional information, all PSCOPF solutions will be validated in a uniform way by forward constraint evaluation.
The second section, which is not timed, will provide the additional solution details required for solution validation via calculation of feasibilities by the evaluation platform. This information is recorded in a second file, solution2.txt, also described in detail below. Allowing solution software to calculate these quantities only after the timer has been stopped is important as some competitors will utilize insights on the problem structure or inputs to quickly screen out some contingency cases. Therefore, the software that competitors submit to the competition may not need to calculate actual power flow solutions for every contingency prior to reporting generator and equipment control set points.
Solution data generated by algorithm evaluation will include objective function values, algorithmic run-time and constraint violation magnitudes for each power system model scenario tested. This data will be logged by the competition evaluation platform and associated with a specific competitor (i.e., team). These logs and the public names of the associated competitors will be released into the public domain after the conclusion of each trial or final event.
Remember, there are two parts to the evaluation of an algorithm on a particular power system model scenario. The first part, which is timed, establishes the base case solution used to calculate the objective function value. The second part, which is not timed, establishes the contingency solutions used to determine the feasibility of the solution.
As explained in the Scoring section, if the solution does not satisfy all constraints, a power system model scenario score is determined by multiplying a nominal objective value by a constraint violation penalty factor. Similarly, if a power system model scenario runtime is greater than the specified cutoff threshold a power system model scenario score is determined by multiplying the nominal objective value by a time violation penalty factor. A power system network model score is then calculated by taking the geometric mean across all scenario scores of that network model. A final dataset score is computed by taking the geometric mean of all power system network models in a given dataset.
Evaluation Procedure
The evaluation procedure used by the competition platform is designed to evaluate solution objective function values and constraint violations. Competitors’ codes will be required to output solutions in two specific standardized formats: one (solution1.txt) to evaluate the solution objective function value (timed); and the second (solution2.txt) to evaluate constraint violations (not timed). The information that will be required in the solution output includes:
• Real and reactive power generation at each generator (timed section)
• Real power (injections or withdrawals), reactive power (injections or withdrawals), voltage magnitude and phase angle at each bus for the base case and each of the contingency cases (untimed section)
• System-wide power imbalance magnitude for each contingency case (untimed section).
The automated evaluation process will use the information in competitors’ two solution files to calculate the objective function value and to assess solution constraint violations.
Feasibility check for constraint violations
A feasibility check is performed by evaluating competitors' solutions in the constraints and limits from the standard formulations.
For an inequality constraint gi(x)≤bi and |bi|>1, a relative constraint violation (CVi) is calculated as CVi = max(gi(x)-bi, 0) / |bi|.
For an equality constraint gi(x)=band |bi|>1, a relative constraint violation (CVi) is calculated as CVi = |gi(x)-bi| / |bi|.
For an inequality constraint gi(x)≤bi and |bi|≤1, a relative constraint violation (CVi) is calculated as CVi = max(gi(x)-bi, 0).
For an equality constraint gi(x)=band |bi|≤1, a relative constraint violation (CVi) is calculated as CVi = |gi(x)-bi|.
Summary
The solution1.txt file must be generated during the timed portion of the solution.
The solution2.txt file may be generated during either the timed or untimed portion of the solution.
The detailed evaluation process can be seen in the flow chart below.
Solution1.txt
solution1.txt must contain generator dispatch information from the base case of each power system model scenario. This information is used, along with the provided cost function information, to calculate the Objective Function value that is the basis of the scenario score.
It contains the following information:
1. begin generation dispatch segment delimiter (“--generation dispatch”)
1. bus ID (“bus id”)
2. unit ID (“unit id”)
3. real power in megawatts (“pg(MW)”)
4. reactive power in megaVar (“qg(MVar)”)
3. csv data for each dispatch unit in the order given by b-i to b-iv.
4. end generation dispatch segment delimiter ("--end of generation dispatch”)
When writing out numerical values, use the full precision used to perform the calculation in order to calculate an accurate Objective Function value.
The Phase 0 IEEE 14 bus (5 generators) contents of Scenario1/solution1.txt would look like the following (competitor’s real power and reactive power values may be different):
--generation dispatch
bus id,unit id,pg(MW),qg(MVar)
1,'1 ',37.9649606792,1.8583662976
6,'1 ',110.4266998728,-13.0957522832
8,'1 ',0.3198286705,6.9978519286
2,'1 ',84.7177624287,17.5456887762
3,'1 ',5.8017882658,26.8372933492
--end of generation dispatch
Solution2.txt
solution2.txt must contain solution information from the base and contingency cases of each power system model scenario needed to compute constraint violations. The base case has contingency id of 0.
It contains the following information:
1. contingency generator dispatch (“--contingency generator”; “--end of contingency generator”) [contingency case information only]
1. contingency ID (“contingency id”)
2. generator ID (“generator id”) -- something relevant to your code; not used in the evaluation process
3. bus ID (“bus id”)
4. unit ID (“unit id”)
5. Reactive power in megaVar (“q(MW”)
2. contingency bus information (“--bus”; “--end of bus”) [base and contingency case information]
1. contingency ID (“contingency id”)
2. bus ID (“bus id”)
3. Voltage in per unit (“v(pu)”)
4. Voltage angle in degree (“theta(deg)”)
3. contingency delta (--Delta”; “--end of Delta”) [contingency case information only]
1. contingency ID (“contingency id”)
2. Delta (“Delta(MW)”)
4. contingency line flow information (“--line flow”; ”--end of line flow”) [base and contingency case information]
1. contingency ID (“contingency id”)
2. line ID (“line id”) -- something relevant to your code; not used in the evaluation process
3. origin bus ID (“origin bus id”)
4. destination bus ID (“destination bus id”)
5. circuit ID (“circuit id”)
6. real power in megawatts at origin (“p_origin(MW)”)
7. reactive power in MVar at origin (“q_origin(MVar)”)
8. real power in megawatts at destination (“p_destination(MW)”)
9. reactive power in MVar at destination (“q_destination(MVar)”)
When writing out numerical values, use the full precision used to perform the calculation.
The Phase 0 IEEE 14 bus (1 contingency) contents of Scenario1/solution2.txt would look like the following (competitor’s values may be different):
--contingency generator
contingency id,genID,bus id,unit id,q(MW)
1,l_14,1,'1 ',1.8920439657
1,l_17,6,'1 ',-13.0424143005
1,l_18,8,'1 ',7.2486797834
1,l_15,2,'1 ',17.7006839160
1,l_16,3,'1 ',26.9101533072
--end of contingency generator
--bus
contingency id,bus id,v(pu),theta(deg)
0,8,1.1000000000,5.5864770127
0,2,1.0914701645,8.1398994078
0,14,1.0628888503,6.4505375932
0,10,1.0741009382,6.1122501823
0,3,1.0654280495,3.4058096240
0,7,1.0887940120,5.5595254296
0,9,1.0791972126,5.3373738635
0,6,1.1000000000,11.3165871591
0,12,1.0865543223,10.2294798690
0,11,1.0816641774,8.5372192167
0,1,1.0956591539,8.7574065074
0,13,1.0801097385,9.7951050674
0,4,1.0697105064,5.9440132240
0,5,1.0732898620,7.2148842999
1,8,1.1000000000,-0.7532229238
1,2,1.0914701645,1.8538326988
1,14,1.0598341609,-0.0743928645
1,10,1.0733983766,-0.2261850840
1,3,1.0654280495,-2.8808294176
1,7,1.0883923500,-0.7806842204
1,9,1.0784377053,-1.0286520888
1,6,1.1000000000,5.1046567042
1,12,1.0587544948,2.7149743850
1,11,1.0812228268,2.2622242346
1,1,1.0956591539,2.4723694497
1,13,1.0738404326,3.0895688263
1,4,1.0695266224,-0.3486365532
1,5,1.0732096990,0.9333968779
--end of bus
--Delta
contingency id,Delta(MW)
1,0.0019761473
--end of Delta
--line flow
contingency id,line id,origin bus id,destination bus id,circuit id, p_origin(MW) q_origin(MVar), p_destination(MW), q_destination(MVar)
0,i_11,7,9,'BL',4.1413318422,9.5061994545,-4.1413318422,-9.4064239939
0,i_14,10,11,'BL',-22.9761326646,6.1272750623,23.3782748731,-5.1859045079
0,i_17,4,7,'BL',3.8215031717,2.6172876907,-3.8215031717,-2.5797860834
0,i_18,4,9,'BL',2.2679201960,4.9215656632,-2.2679201960,-4.7875472966
0,i_19,5,6,'BL',-35.9525204199,24.8652624433,35.9525204199,-21.2339571641
0,i_1,1,5,'BL',15.9641439290,4.3593613937,-15.8253740474,-9.5734621036
0,i_6,4,5,'BL',-57.3737425289,9.7671310853,57.7689110106,-8.5206483317
0,i_9,6,13,'BL',26.1622121170,3.8319397860,-25.7799935330,-3.0792320773
0,i_4,2,5,'BL',13.2243134554,5.1075898562,-13.1161456412,-8.8311681583
0,i_3,2,4,'BL',27.0351993991,3.0208504059,-26.6662570887,-5.8718879653
0,i_10,7,8,'BL',-0.3198286705,-6.9264133711,0.3198286705,6.9978519286
0,i_12,9,10,'BL',-14.0616138860,11.9276805523,14.1544761136,-11.6810015761
0,i_2,2,3,'BL',49.5701517682,1.9868853878,-48.5926008283,-2.9633522332
0,i_0,1,2,'BL',22.0008167502,-2.5009950960,-21.9226033984,-3.5744969015
0,i_15,12,13,'BL',3.7549512193,-0.6300386655,-3.7278244221,0.6545819582
0,i_8,6,12,'BL',9.4916104689,1.3053581664,-9.3983668501,-1.1112921822
0,i_16,13,14,'BL',17.8421446777,-2.8566525730,-17.3637689253,3.8306438523
0,i_13,9,14,'BL',-4.2129398200,8.5699707507,4.3124667999,-8.3582635299
0,i_5,3,4,'BL',-26.2675003800,7.5512088127,26.7152631642,-7.8672085362
0,i_7,6,11,'BL',27.8375735276,-2.4490101532,-27.2245772023,3.7327011314
1,i_11,7,9,'BL',4.6176371063,9.8586961607,-4.6176371063,-9.7486335316
1,i_14,10,11,'BL',-23.5600133212,6.2615917077,23.9832166878,-5.2709193053
1,i_17,4,7,'BL',4.2918799941,2.7319226632,-4.2918799941,-2.6866626481
1,i_18,4,9,'BL',2.5399988694,5.0368539304,-2.5399988694,-4.8915758208
1,i_19,5,6,'BL',-36.5584065652,24.8681177588,36.5584065652,-21.1524989951
1,i_1,1,5,'BL',15.9411089231,4.4034282171,-15.8023788808,-9.6172700944
1,i_6,4,5,'BL',-57.9146903473,9.6884187522,58.3170944534,-8.4191126168
1,i_9,6,13,'BL',34.4914896899,5.1353881864,-33.8266903513,-3.8261907587
1,i_4,2,5,'BL',13.1895860305,5.1684098512,-13.0814381054,-8.8917511979
1,i_3,2,4,'BL',27.1345130495,3.1047842675,-26.7625299406,-5.9459265667
1,i_10,7,8,'BL',-0.3257571123,-7.1720335125,0.3257571123,7.2486797834
1,i_12,9,10,'BL',-14.6398441010,12.0770070160,14.7383567702,-11.8153182215
1,i_2,2,3,'BL',49.5757963155,1.9860298956,-48.5980277346,-2.9615798140
1,i_0,1,2,'BL',22.0337324924,-2.5113842514,-21.9552873732,-3.5634001262
1,i_15,12,13,'BL',-5.6434156307,-1.7413308477,5.7121581782,1.8035264858
1,i_16,13,14,'BL',16.4488588956,-3.2586384193,-16.0320577524,4.1072614454
1,i_13,9,14,'BL',-2.8863256675,8.8357462988,2.9807556271,-8.6348811230
1,i_5,3,4,'BL',-26.1647482212,7.6222963516,26.6100283387,-7.9443808414
1,i_7,6,11,'BL',28.4705959846,-2.4752205733,-27.8295190169,3.8177159288
--end of line flow
Evaluation Platform Environment
The Evaluation Platform hardware consists of a dedicated 4-node cluster with a Mellanox 4x FDR Infiniband interconnect (54.54 Gigabits/second data bandwidth) where each node has 64 GiB of 4-channel 2133 MHz DDR4 SDRAM (68 Gigabytes/second) memory; two Intel Xeon E5-2670 v3 (Haswell) CPUs, each with 12 cores (24 cores per node) and a clock speed of 2.30 GHz (peak floating point performance per node is 883.2 GFlops/sec); and 480 GB Intel® SSD 530 Series disk drives with SATA 3.0 6 Gbit/sec interfaces (sequential read (up to)540 MB/s, sequential write (up to)490 MB/s).
One of the nodes manages the evaluations run on the other three "compute" nodes.
Results from each submission are gzipped and placed in a tar file on dtn2.pnl.gov, an externally-facing gateway for transferring large amounts of data efficiently. It has multiple 10-gigabit per second links to to the Pacific Northwest Gigapop and the Seattle Internet Exchange. It is not uncommon to see transfer rates over 1 gbps to various sites around the world.
| 2018-07-21T01:35:55 |
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|
http://pdglive.lbl.gov/Particle.action?init=0&node=M196&home=MXXX040
|
CHARMED, STRANGE MESONS($\boldsymbol C$ = $\boldsymbol S$ = $\pm1$) ${{\mathit D}_{{s}}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit D}_{{s}}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit D}_{{s}}^{*}}$'s INSPIRE search
# ${{\boldsymbol D}_{{s1}}^{*}{(2860)}^{\pm}}$ $I(J^P)$ = $0(1^{-})$
$\mathit J{}^{P}$ consitent with $1{}^{-}{}^{}$ from angular analysis of AAIJ 2014AW. Observed by AUBERT,BE 2006E and AUBERT 2009AR in inclusive production of ${{\mathit D}}{{\mathit K}}$ and ${{\mathit D}^{*}}{{\mathit K}}$ in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ annihilation.
${{\mathit D}_{{s1}}^{*}{(2860)}^{+}}$ MASS $2859 \pm27$ MeV
${{\mathit D}_{{s1}}^{*}{(2860)}^{+}}$ WIDTH $159 \pm80$ MeV
| 2019-11-12T15:42:30 |
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|
http://pdglive.lbl.gov/Particle.action?init=0&node=B119&home=BXXX040
|
CHARMED BARYONS($\boldsymbol C$ = $+1$) ${{\mathit \Lambda}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit d}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit d}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{0}}$ = ${{\mathit d}}{{\mathit d}}{{\mathit c}}$ ,${{\mathit \Xi}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit s}}{{\mathit c}}$ , ${{\mathit \Xi}_{{c}}^{0}}$ = ${{\mathit d}}{{\mathit s}}{{\mathit c}}$ , ${{\mathit \Omega}_{{c}}^{0}}$ = ${{\mathit s}}{{\mathit s}}{{\mathit c}}$ INSPIRE search
# ${{\boldsymbol \Lambda}_{{c}}{(2595)}^{+}}$ $I(J^P)$ = $0(1/2^{-})$
The ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ mode is largely, and perhaps entirely, ${{\mathit \Sigma}_{{c}}}{{\mathit \pi}}$ , which is just at threshold; since the ${{\mathit \Sigma}_{{c}}}$ has $\mathit J{}^{P} = 1/2{}^{+}$, the $\mathit J{}^{P}$ here is almost certainly ${}^{}1/2{}^{-}$. This result is in accord with the theoretical expectation that this is the charm counterpart of the strange ${{\mathit \Lambda}{(1405)}}$.
${{\mathit \Lambda}_{{c}}{(2595)}^{+}}$ MASS $2592.25 \pm0.28$ MeV
${{\mathit \Lambda}_{{c}}{(2595)}^{+}}–{{\mathit \Lambda}_{{c}}^{+}}$ MASS DIFFERENCE $305.79 \pm0.24$ MeV
${{\mathit \Lambda}_{{c}}{(2595)}^{+}}$ WIDTH $2.6 \pm0.6$ MeV
${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}}{{\mathit \pi}}$ and its submode ${{\mathit \Sigma}_{{c}}{(2455)}}{{\mathit \pi}}$ $-$ the latter just barely $-$ are the only strong decays allowed to an excited ${{\mathit \Lambda}_{{c}}^{+}}$ having this mass; and the submode seems to dominate.
| 2019-04-22T12:47:20 |
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|
https://pdglive.lbl.gov/Particle.action?node=M090&home=sumtabM
|
STRANGE MESONS($\boldsymbol S$ = $\pm1$, $\boldsymbol C$ = $\boldsymbol B$ = 0) ${{\mathit K}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit K}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit s}}}$, ${{\overline{\mathit K}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit s}}$, ${{\mathit K}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit K}^{*}}$'s INSPIRE search
# ${{\boldsymbol K}_{{3}}{(2320)}}$ $I(J^P)$ = $1/2(3^{+})$
Seen in the $\mathit J{}^{P} = 3{}^{+}$ wave of the antihyperon-nucleon system. Needs confirmation.
${{\mathit K}_{{3}}{(2320)}}$ MASS $2324 \pm24$ MeV
${{\mathit K}_{{3}}{(2320)}}$ WIDTH $150 \pm30$ MeV
| 2021-01-22T10:28:33 |
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|
http://www.scstatehouse.gov/sess118_2009-2010/sj09/20090519.htm
|
South Carolina General Assembly
118th Session, 2009-2010
Journal of the Senate
Tuesday, May 19, 2009
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
"The King will answer them, 'Truly I tell you, just as you did it to one of the least of these who are members of my family, you did it to me.' " (Matthew 25:40)
Please bow with me as we pray:
Indeed, O God, You have given each of Your servants in this place incredible responsibility to act on behalf of those who seem unable to act wisely for themselves. The poor and disadvantaged around us truly look to those in this Chamber to do what can prove to be right and fair and good. So lead these Senators, dear Lord. Guide them to act on what they know to be just and worthy. Bless them as You alone can, giving each the courage to do those things that are pleasing in Your sight. This we pray in Your loving name, O Lord.
Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Mark C. Sanford:
Statewide Appointments
Initial Appointment, South Carolina Board of Long Term Health Care Administrators, with the term to commence June 30, 2009, and to expire June 30, 2012
Nursing Home Consumer:
Martin A. Hyatt, 1775 Overbrook Dr., Rock Hill, SC 29732 VICE Brenna DeLaine
Referred to the Committee on Medical Affairs.
Initial Appointment, South Carolina Public Charter School District Board of Trustees, with the term to commence July 1, 2009, and to expire July 1, 2012
SC Association of Public Charter Schools:
Barbara S. Nielson, 11 Oketee Court, Hilton Head Island, SC 29926 VICE David Church
Referred to the Committee on Education.
Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence July 1, 2008, and to expire July 1, 2010
Research - MUSC:
Charles B. Thomas, Jr., 535 West Butler Road, Suite C, Greenville, SC 29607 VICE Louis Lynn
Referred to the Committee on Education.
Local Appointment
Initial Appointment, Oconee County Magistrate, with the term to commence April 30, 2006, and to expire April 30, 2010
Michael Todd Simmons, P. O. Box 130, Long Creek, SC 29658 VICE Becky Gerrard
MESSAGE FROM THE GOVERNOR
State of South Carolina
Office of the Governor
May 13, 2009
Mr. President and Members of the Senate:
I respectfully request withdrawal from your consideration the appointment listed below:
Respectfully,
Mark C. Sanford
Withdrawal of Statewide Appointment
Initial Appointment, South Carolina Real Estate Commission, with the term to commence June 30, 2006, and to expire June 30, 2010
Public Member:
Jonathan M. Robinson, 134 Saluda Ave., Columbia, SC 29205 VICE Daniel J. Ballou
Appointment Withdrawn
On motion of Senator L. MARTIN, the Senate acceded to the Governor's request and the Clerk was directed to return the appointment to the Governor.
Doctor of the Day
Senator SCOTT introduced Dr. Beverly Simons of Columbia, S.C., Doctor of the Day.
Leave of Absence
At 5:31 P.M., Senator RYBERG requested a leave of absence beginning at 6:00 P.M. until 9:00 P.M. this evening.
Leave of Absence
On motion of Senator ALEXANDER, at 5:45 P.M., Senator McCONNELL was granted a leave of absence from 6:00 - 8:00 P.M. this evening.
RECALLED
H. 3813 (Word version) -- Rep. Harrison: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE BRIDGE THAT CROSSES GILLS CREEK ALONG SHADY LANE IN RICHLAND COUNTY "BURWELL D. MANNING, JR. BRIDGE" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS BRIDGE THAT CONTAIN THE WORDS "BURWELL D. MANNING, JR. BRIDGE".
Senator LOURIE asked unanimous consent to make a motion to recall the Resolution from the Committee on Transportation.
The Resolution was recalled from the Committee on Transportation and ordered placed on the Calendar for consideration tomorrow.
RECALLED
H. 3749 (Word version) -- Reps. J.E. Smith and Williams: A BILL TO AMEND SECTION 25-1-380, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ASSISTANT ADJUTANT GENERAL FOR THE ARMY, SO AS TO PROVIDE UPON NATIONAL GUARD BUREAU AUTHORIZATION, AN ADDITIONAL ASSISTANT ADJUTANT GENERAL WITH THE RANK OF MAJOR GENERAL.
Senator ALEXANDER asked unanimous consent to make a motion to recall the Bill from the General Committee.
The Bill was recalled from the General Committee and ordered placed on the Calendar for consideration tomorrow.
RECALLED
H. 3944 (Word version) -- Reps. Jennings and Neilson: A BILL TO AMEND SECTION 56-3-8710, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ISSUANCE OF NASCAR SPECIAL LICENSE PLATES BY THE DEPARTMENT OF MOTOR VEHICLES, SO AS TO PROVIDE THAT A PORTION OF THE FEES COLLECTED FROM THE SALE OF THESE LICENSE PLATES MUST BE DISTRIBUTED TO THE SOUTH CAROLINA ASSOCIATION OF CHILDREN'S HOMES AND FAMILY SERVICES AND NO LONGER TO THE SOUTH CAROLINA CHILDREN'S EMERGENCY SHELTER FOUNDATION.
Senator GROOMS asked unanimous consent to make a motion to recall the Bill from the Committee on Transportation.
The Bill was recalled from the Committee on Transportation and ordered placed on the Calendar for consideration tomorrow.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 843 (Word version) -- Senator Leatherman: A CONCURRENT RESOLUTION TO CONGRATULATE MR. EMERSON F. GOWER, JR. UPON HIS RETIREMENT AND TO WISH HIM ALL THE BEST IN HIS FUTURE ENDEAVORS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 844 (Word version) -- Senator Leatherman: A CONCURRENT RESOLUTION TO CONGRATULATE MR. CHARLES LEE YOUNG OF FLORENCE, SOUTH CAROLINA, UPON HIS RETIREMENT FROM CIRCLE PARK BEHAVIORAL HEALTH SERVICES.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 845 (Word version) -- Senator Williams: A SENATE RESOLUTION TO CONGRATULATE MRS. EDNA ROGERS ON THE OCCASION OF HER RETIREMENT FROM THE MARION COUNTY COUNCIL ON AGING AND TO WISH HER MUCH HAPPINESS IN THE FUTURE.
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S. 846 (Word version) -- Senators Grooms and Thomas: A JOINT RESOLUTION TO ESTABLISH A COMMISSION TO STUDY IMPLEMENTING A FAIR TAX TO REPLACE THE STATE INDIVIDUAL AND CORPORATE INCOME TAX.
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Read the first time and referred to the Committee on Finance.
S. 847 (Word version) -- Senator Elliott: A BILL TO AMEND SECTION 48-39-40, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREATION OF THE COASTAL ZONE MANAGEMENT APPELLATE PANEL, SO AS TO CREATE THE COASTAL ZONE MANAGEMENT ADVISORY COUNCIL TO THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL'S OFFICE OF OCEAN AND COASTAL RESOURCES MANAGEMENT; TO PROVIDE CERTAIN FUNCTIONS OF THE COUNCIL, TO DELETE SPECIAL TERMS OF SERVICE FOR COUNCIL MEMBERS APPOINTED BASED ON RESIDENCE IN THE STATE'S CONGRESSIONAL DISTRICTS SO THAT THESE MEMBERS SERVE THE SAME TERMS AS ALL OTHER MEMBERS; TO PROVIDE THE COUNCIL SHALL MEET AT THE CALL OF ITS CHAIRMAN; TO PROVIDE ADVICE AND COUNSEL OF THE COUNCIL IS NOT BINDING ON THE DEPARTMENT; AND TO PROVIDE ON JULY 1, 2010, MEMBERS OF THE COASTAL ZONE APPELLATE PANEL BECOME MEMBERS OF THE COUNCIL FOR THE DURATION OF THEIR TERMS.
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Read the first time and referred to the Committee on Agriculture and Natural Resources.
S. 848 (Word version) -- Senator Reese: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 38-49-15 SO AS TO PROHIBIT MOTOR VEHICLE PHYSICAL DAMAGE APPRAISERS TO LOCATE THEIR PLACES OF BUSINESS ON THE PREMISES OF, OR ADJACENT TO, A MOTOR VEHICLE REPAIR OR BODY SHOP.
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Read the first time and referred to the Committee on Banking and Insurance.
S. 849 (Word version) -- Senator Leatherman: A BILL TO AMEND SECTION 59-67-270 OF THE 1976 CODE, RELATING TO THE INSPECTION OF SCHOOL BUSES, TO PROVIDE THAT A SCHOOL DISTRICT OWNED SCHOOL BUS SHALL BE SUBJECT TO AN ANNUAL FEDERAL DEPARTMENT OF TRANSPORTATION INSPECTION.
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Read the first time and referred to the Committee on Education.
S. 850 (Word version) -- Senator McGill: A BILL TO AMEND SECTION 12-6-5060 OF THE 1976 CODE, RELATING TO THE DESIGNATION ON AN INCOME TAX RETURN OF A VOLUNTARY CONTRIBUTION TO CERTAIN FUNDS, TO PROVIDE THAT A TAXPAYER MAY CONTRIBUTE TO THE SOUTH CAROLINA FORESTRY COMMISSION FOR USE IN THE STATE FOREST SYSTEM.
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Read the first time and referred to the Committee on Finance.
S. 851 (Word version) -- Senator Ryberg: A BILL TO AMEND SECTION 8-13-1510 OF THE 1976 CODE, RELATING TO PENALTIES FOR LATE FILING OF OR FAILURE TO FILE A REPORT OR STATEMENT REQUIRED BY CHAPTER 13, TITLE 8 AND TO PROVIDE FOR CRIMINAL PENALTIES; AND TO AMEND SECTION 2-17-50, RELATING TO PENALTIES FOR FAILING TO ABIDE BY FILING REQUIREMENTS IN CHAPTER 17, TITLE 2, TO PROVIDE FOR CRIMINAL PENALTIES.
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Read the first time and referred to the Committee on Judiciary.
S. 852 (Word version) -- Senator Bryant: A BILL TO AMEND SECTION 40-81-50 OF THE 1976 CODE, RELATING TO THE CREATION OF THE STATE ATHLETIC COMMISSION, TO PROVIDE THAT ONE AT-LARGE MEMBER OF THE COMMISSION MUST BE FROM THE MIXED MARTIAL ARTS COMMUNITY.
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Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 853 (Word version) -- Senator Anderson: A BILL TO AMEND SECTION 41-27-370, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF "UNEMPLOYED" FOR PURPOSES OF THE SOUTH CAROLINA EMPLOYMENT SECURITY LAW AND THE REDUCTION OF UNEMPLOYMENT BENEFITS TO REFLECT PENSION AND OTHER PAYMENTS ATTRIBUTABLE TO WORK, SO AS TO ELIMINATE EMPLOYER-FILED CLAIMS; TO AMEND SECTION 41-27-380, RELATING TO THE DEFINITION OF "WAGES", SO AS TO INCREASE THE TAXABLE WAGE BASE BEGINNING DECEMBER 31, 2008; TO AMEND SECTION 41-27-510, RELATING TO REGULATIONS APPLICABLE TO UNEMPLOYED INDIVIDUALS, SO AS TO CONFORM THE SECTION TO THE AMENDMENTS TO SECTION 41-27-370; TO AMEND SECTION 41-29-170, AS AMENDED, RELATING TO THE DISCLOSURE OF CERTAIN INFORMATION TO ENSURE THAT A CLAIMANT, OR HIS LEGAL REPRESENTATIVE, BE SUPPLIED WITH RECORDS IN ORDER TO MAKE A CLAIM, SO AS TO ADD A PROVISION TO PROVIDE UNEMPLOYMENT INFORMATION NECESSARY FOR WORKFORCE IMPROVEMENT AND PROGRAM EVALUATION TO THE AGENCY ADMINISTERING THE WORKFORCE INVESTMENT ACT; TO AMEND SECTION 41-31-50, AS AMENDED, RELATING TO THE COMPUTATION OF RATES OF CONTRIBUTIONS BY EMPLOYERS, SO AS TO RESTRUCTURE THE COMPUTATION FOR CERTAIN EMPLOYERS; TO AMEND SECTION 41-31-80, AS AMENDED, RELATING TO THE STATEWIDE RESERVE RATIO, SO AS TO ADJUST THE RATES OF CONTRIBUTION FOR CERTAIN EMPLOYERS; TO AMEND SECTION 41-35-50, RELATING TO THE MAXIMUM POTENTIAL BENEFITS OF AN INSURED WORKER, SO AS TO CHANGE THE FORMULA FOR CALCULATING THE BENEFIT; TO AMEND SECTION 41-35-120, AS AMENDED, RELATING TO DISQUALIFICATION OF BENEFITS, SO AS TO ADD A PROVISION PROVIDING FOR "GROSS MISCONDUCT" AND CONFORMING THE TERM "MOST RECENT BONA FIDE EMPLOYER" TO ITS DEFINITION IN SECTION 41-35-110(5), AND TO REQUIRE THE DEDUCTION OF SEVERANCE PAY FROM UNEMPLOYMENT COMPENSATION PAYMENTS.
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Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 854 (Word version) -- Senator McConnell: A BILL TO AMEND CHAPTER 23 OF TITLE 57 OF THE 1976 CODE, RELATING TO VEGETATION MANAGEMENT ALONG ROADSIDES, SO AS TO PERMIT THE DEPARTMENT OF TRANSPORTATION TO MAINTAIN AND MOW BEYOND THIRTY FEET FROM THE PAVEMENT ROADSIDE VEGETATION ADJACENT TO SAM RITTENBERG BOULEVARD IN CHARLESTON COUNTY.
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Read the first time and referred to the Committee on Transportation.
S. 855 (Word version) -- Senator Campsen: A CONCURRENT RESOLUTION TO RECOGNIZE THE CITY OF NORTH CHARLESTON'S CONTRACTUAL RIGHT TO LIMIT RAIL ACCESS TO THE CHARLESTON NAVAL COMPLEX AND TO DECLARE THAT NO ACTIONS MAY BE TAKEN TO IMPAIR THE CITY'S ABILITY TO EXERCISE ANY OF ITS CONTRACTUAL RIGHTS CONCERNING THE COMPLEX.
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The Concurrent Resolution was introduced and referred to the Committee on Transportation.
S. 856 (Word version) -- Senator Campsen: A CONCURRENT RESOLUTION TO PROVIDE THAT PURSUANT TO ARTICLE III, SECTION 9 OF THE CONSTITUTION OF THIS STATE AND SECTION 2-1-180 OF THE 1976 CODE, WHEN THE RESPECTIVE HOUSES OF THE GENERAL ASSEMBLY ADJOURN ON THURSDAY, MAY 21, 2009, NOT LATER THAN 5:00 P.M., EACH HOUSE SHALL STAND ADJOURNED TO MEET AT A TIME MUTUALLY AGREED UPON BY THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES NO LATER THAN JUNE 30, 2009, FOR A PERIOD NOT TO EXCEED THREE STATEWIDE LEGISLATIVE DAYS FOR THE CONSIDERATION OF CERTAIN MATTERS, TO PROVIDE THAT WHEN EACH HOUSE ADJOURNS AFTER THIS THREE-DAY PERIOD NOT LATER THAN 5:00 P.M. ON THE THIRD LEGISLATIVE DAY, EACH HOUSE SHALL STAND ADJOURNED TO MEET AT A TIME MUTUALLY AGREED UPON BY THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES UPON CERTAIN OCCURRENCES AND FOR THE CONSIDERATION OF SPECIFIED MATTERS, AND TO PROVIDE THAT UNLESS ADJOURNED EARLIER, THE GENERAL ASSEMBLY SHALL STAND ADJOURNED SINE DIE NO LATER THAN NOON ON TUESDAY, JANUARY 12, 2010.
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The Concurrent Resolution was introduced and referred to the Committee on Judiciary.
S. 857 (Word version) -- Senators Rose, Grooms and Matthews: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE PINEWOOD PREPARATORY SCHOOL BASEBALL TEAM FOR CAPTURING ITS FIRST BASEBALL STATE CHAMPIONSHIP AND TO HONOR THE TEAM'S EXCEPTIONAL PLAYERS, COACHES, AND STAFF.
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S. 858 (Word version) -- Senator Setzler: A SENATE RESOLUTION TO CONGRATULATE KATHARINE H. WILSON OF LEXINGTON COUNTY ON THE OCCASION OF HER ONE HUNDREDTH BIRTHDAY, AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND CONTINUED HEALTH AND HAPPINESS.
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S. 859 (Word version) -- Senator Bright: A SENATE RESOLUTION TO RECOGNIZE DR. JAMES A. LITTLEFIELD AND THANK HIM FOR HIS THIRTY-EIGHT YEARS OF SERVICE TO SPARTANBURG COUNTY SCHOOL DISTRICT ONE.
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S. 860 (Word version) -- Senator Knotts: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR SERGEANT SILLER ANDERSON, UPON THE OCCASION OF HIS RETIREMENT, AFTER TWENTY-FIVE YEARS OF FAITHFUL SERVICE TO THE COUNTY OF LEXINGTON, AND TO WISH HIM SUCCESS AND HAPPINESS IN ALL HIS FUTURE ENDEAVORS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 861 (Word version) -- Senators Nicholson and O'Dell: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE MEMBERS OF THE GREENWOOD HIGH SCHOOL TENNIS TEAM FOR ITS OUTSTANDING SEASON, AND TO CONGRATULATE THE PLAYERS AND COACH FOR CAPTURING THE 2009 CLASS AAAA STATE CHAMPIONSHIP TITLE.
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S. 862 (Word version) -- Senators Fair and Shoopman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 4 TO CHAPTER 53, TITLE 59 SO AS TO CREATE THE GREENVILLE TECHNICAL COLLEGE AREA COMMISSION AND TO PROVIDE FOR ITS MEMBERSHIP.
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Read the first time and, on motion of Senator FAIR, S. 862 was ordered placed on the Local and Uncontested Calendar.
H. 3845 (Word version) -- Reps. T. R. Young, Allen and Kelly: A BILL TO AMEND SECTION 22-3-1000, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE TIME FOR A MOTION FOR NEW TRIAL AND APPEAL IN MAGISTRATES COURT, SO AS TO INCREASE THE TIME PERIOD IN WHICH A MOTION FOR A NEW TRIAL MAY BE MADE FROM FIVE TO TEN DAYS.
Read the first time and referred to the Committee on Judiciary.
H. 4058 (Word version) -- Rep. Clemmons: A CONCURRENT RESOLUTION TO MEMORIALIZE THE SECRETARY OF THE UNITED STATES DEPARTMENT OF TRANSPORTATION, THE HONORABLE RAY H. LAHOOD, TO SET ASIDE THE FUNDS NECESSARY TO ACQUIRE THE RIGHT OF WAY AND BUILD THE APPROXIMATELY SIX-MILE PORTION OF INTERSTATE 73 FROM "THE INTERSECTION OF HOPE" AT ITS INTERSECTION WITH INTERSTATE 95 TO ITS INTERSECTION WITH UNITED STATES HIGHWAY 501 WHICH CONSTITUTES THE FIRST PHASE OF CONSTRUCTION OF INTERSTATE 73 IN SOUTH CAROLINA, AND SET ASIDE ADDITIONAL FUNDS TO COMPLETE THE REMAINING PORTION OF THIS INTERSTATE HIGHWAY AS THESE FUNDS BECOME AVAILABLE.
On motion of Senator McGILL, with unanimous consent, the Concurrent Resolution was introduced and ordered placed on the Calendar without reference.
H. 4081 (Word version) -- Reps. Allen, Dillard, Agnew, Alexander, Allison, Anderson, Anthony, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, G. A. Brown, H. B. Brown, R. L. Brown, Cato, Chalk, Clemmons, Clyburn, Cobb-Hunter, Cole, Cooper, Crawford, Daning, Delleney, Duncan, Edge, Erickson, Forrester, Frye, Funderburk, Gambrell, Gilliard, Govan, Gullick, Gunn, Haley, Hamilton, Hardwick, Harrell, Harrison, Hart, Harvin, Hayes, Hearn, Herbkersman, Hiott, Hodges, Horne, Hosey, Howard, Huggins, Hutto, Jefferson, Jennings, Kelly, Kennedy, King, Kirsh, Knight, Limehouse, Littlejohn, Loftis, Long, Lowe, Lucas, Mack, McEachern, McLeod, Merrill, Miller, Millwood, Mitchell, D. C. Moss, V. S. Moss, Nanney, J. H. Neal, J. M. Neal, Neilson, Ott, Owens, Parker, Parks, Pinson, E. H. Pitts, M. A. Pitts, Rice, Rutherford, Sandifer, Scott, Sellers, Simrill, Skelton, D. C. Smith, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Spires, Stavrinakis, Stewart, Stringer, Thompson, Toole, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis, Wylie, A. D. Young and T. R. Young: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR THE REVEREND FLORA JOHNSON WINESTOCK, OF GREENVILLE COUNTY, AND TO CONGRATULATE HER FOR HER SERVICE AS PRESIDENT OF THE BAPTIST MINISTERS FELLOWSHIP OF GREENVILLE AND VICINITY.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4084 (Word version) -- Reps. Barfield, Clemmons, Hearn, Agnew, Alexander, Allen, Allison, Anderson, Anthony, Bales, Ballentine, Bannister, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, G. A. Brown, H. B. Brown, R. L. Brown, Cato, Chalk, Clyburn, Cobb-Hunter, Cole, Cooper, Crawford, Daning, Delleney, Dillard, Duncan, Edge, Erickson, Forrester, Frye, Funderburk, Gambrell, Gilliard, Govan, Gullick, Gunn, Haley, Hamilton, Hardwick, Harrell, Harrison, Hart, Harvin, Hayes, Herbkersman, Hiott, Hodges, Horne, Hosey, Howard, Huggins, Hutto, Jefferson, Jennings, Kelly, Kennedy, King, Kirsh, Knight, Limehouse, Littlejohn, Loftis, Long, Lowe, Lucas, Mack, McEachern, McLeod, Merrill, Miller, Millwood, Mitchell, D. C. Moss, V. S. Moss, Nanney, J. H. Neal, J. M. Neal, Neilson, Ott, Owens, Parker, Parks, Pinson, E. H. Pitts, M. A. Pitts, Rice, Rutherford, Sandifer, Scott, Sellers, Simrill, Skelton, D. C. Smith, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Spires, Stavrinakis, Stewart, Stringer, Thompson, Toole, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis, Wylie, A. D. Young and T. R. Young: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR EDWARD M. "DICK" SINGLETON, COASTAL CAROLINA UNIVERSITY CHANCELLOR EMERITUS, FOR HIS MANY YEARS OF SERVICE AND DEDICATION TO HIS BELOVED UNIVERSITY.
The Concurrent Resolution was adopted, ordered returned to the House.
REPORTS OF STANDING COMMITTEES
Senator LEATHERMAN from the Committee on Finance polled out H. 3148 favorable:
H. 3148 (Word version) -- Reps. Clyburn, G.M. Smith, H.B. Brown, Branham, Ott, Agnew, R.L. Brown, Hayes, Battle, Miller, Weeks, J.R. Smith, D.C. Smith, Parks, Rice, Littlejohn, Hosey, Jefferson, Cobb-Hunter, Howard, Cooper, Gunn, McLeod, T.R. Young, Kennedy, Vick, Edge, J.E. Smith, Harrell, A.D. Young, Alexander, Neilson, Lucas, Merrill, Barfield, Bales, Allen, Hodges, Knight and Funderburk: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 50 TO TITLE 11 SO AS TO ENACT THE "SOUTH CAROLINA RURAL INFRASTRUCTURE ACT", TO ESTABLISH THE SOUTH CAROLINA RURAL INFRASTRUCTURE AUTHORITY, AND TO PROVIDE FOR ITS GOVERNANCE, POWERS, AND DUTIES; TO AUTHORIZE THE AUTHORITY TO PROVIDE LOANS AND OTHER FINANCIAL ASSISTANCE TO A MUNICIPALITY, COUNTY, SPECIAL PURPOSE OR PUBLIC SERVICE DISTRICT, AND A PUBLIC WORKS COMMISSION TO FINANCE RURAL INFRASTRUCTURE FACILITIES; TO ALLOW STATE APPROPRIATIONS, GRANTS, LOAN REPAYMENTS, AND OTHER AVAILABLE AMOUNTS TO BE CREDITED TO THE FUND OF THE AUTHORITY; TO AUTHORIZE LENDING TO AND BORROWING BY ELIGIBLE ENTITIES THROUGH THE AUTHORITY.
Poll of the Finance Committee
Polled 23; Ayes 20; Nays 1; Not Voting 2
AYES
Leatherman Land Setzler
Leventis Peeler Courson
Matthews McGill O'Dell
Reese Hayes Ryberg
Alexander Fair Grooms
Pinckney Cromer Anderson
Elliott Jackson
Total--20
NAYS
Bryant
Total--1
NOT VOTING
Thomas Verdin
Total--2
Ordered for consideration tomorrow.
Senator LEATHERMAN from the Committee on Finance polled out H. 3882 favorable:
H. 3882 (Word version) -- Labor, Commerce and Industry Committee: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 11-11-55 SO AS TO PROVIDE THE STATE BUDGET AND CONTROL BOARD SHALL DEVELOP A WEB-BASED APPLICATION FOR THE SUBMISSION OF QUESTIONS AND CONCERNS ABOUT STATE AGENCY LICENSING, PERMITTING, AND REGULATION OF ECONOMIC ACTIVITY, AND TO PROVIDE A STATE AGENCY THAT PROMULGATES REGULATIONS, ISSUES PERMITS OR LICENSES, AND HAS A WEBSITE ON THE INTERNET SHALL PLACE ON ITS WEBSITE HOMEPAGE A HYPERLINK OR UNIFORM RESOURCE LOCATOR THAT PROVIDES DIRECT ACCESS TO THIS WEB-BASED APPLICATION; BY ADDING SECTION 48-39-155 SO AS TO PROVIDE A CERTIFICATION OF CONSISTENCY WITH THE COASTAL ZONE MANAGEMENT PLAN MUST BE MADE BY THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL WITHIN THIRTY DAYS AFTER THE DATE THE REQUEST IS SUBMITTED TO THE DEPARTMENT FOR THIS CERTIFICATION, AND IF THE DEPARTMENT FAILS TO ISSUE A WRITTEN DECISION WITHIN THIS THIRTY-DAY PERIOD, THE PROPOSED ACTIVITY OR LICENSE IS CONSIDERED CONSISTENT WITH THE COASTAL ZONE MANAGEMENT PLAN AND PROGRAM; AND TO AMEND SECTION 33-41-1110, RELATING TO A RENEWAL APPLICATION FOR A REGISTERED LIMITED LIABILITY COMPANY, SO AS TO PROVIDE THIS APPLICATION ANNUALLY MUST BE RENEWED BEFORE APRIL FIRST.
Poll of the Finance Committee
Polled 21; Ayes 19; Nays 0; Not Voting 2
AYES
Leatherman Land Setzler
Peeler Courson Matthews
Thomas McGill O'Dell
Reese Hayes Alexander
Fair Grooms Pinckney
Verdin Cromer Anderson
Jackson
Total--19
NAYS
Total--0
NOT VOTING
Leventis Bryant
Total--2
Ordered for consideration tomorrow.
Message from the House
Columbia, S.C., May 19, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 116 (Word version) -- Senators Knotts and McConnell: A BILL TO AMEND SECTION 11-35-310, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS FOR PURPOSES OF THE CONSOLIDATED PROCUREMENT CODE, SO AS TO DELETE THE DEFINITION FOR "OFFICE"; TO AMEND SECTION 11-35-1524, AS AMENDED, RELATING TO VENDOR PREFERENCES, SO AS TO PROVIDE FOR PREFERENCES FOR END PRODUCTS FROM SOUTH CAROLINA AND FROM THE UNITED STATES AND FOR CONTRACTORS AND SUBCONTRACTORS WHO EMPLOY INDIVIDUALS DOMICILED IN SOUTH CAROLINA, TO DEFINE CERTAIN TERMS, PROVIDE FOR ELIGIBILITY REQUIREMENTS FOR THE PREFERENCES, PROVIDE FOR APPLICATION FOR THE PREFERENCES AND PENALTIES FOR FALSE APPLICATION, AND TO MAKE EXCEPTIONS TO THE PREFERENCES; TO AMEND SECTION 11-35-40, AS AMENDED, RELATING TO COMPLIANCE WITH FEDERAL REQUIREMENTS, SO AS TO PROVIDE FOR COMPLIANCE WITH THE CONSOLIDATED PROCUREMENT CODE; TO AMEND SECTION 11-35-3215, RELATING TO CONTRACTS FOR DESIGN SERVICES, SO AS TO PROVIDE FOR A RESIDENT PREFERENCE; AND TO REPEAL SECTION 11-35-3025 RELATING TO APPROVAL OF CHANGE ORDERS IN CONNECTION WITH CERTAIN CONTRACTS.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., May 19, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 593 (Word version) -- Senator S. Martin: A BILL TO AMEND SECTION 16-23-430 OF THE 1976 CODE, RELATING TO THE CARRYING OF WEAPONS ON SCHOOL PROPERTY, TO PROVIDE THAT THIS SECTION DOES NOT APPLY TO A PERSON WHO IS AUTHORIZED TO CARRY A CONCEALED WEAPON WHEN THE WEAPON IS INSIDE A MOTOR VEHICLE.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., May 14, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it refuses to concur in the amendments proposed by the Senate to:
H. 3572 (Word version) -- Rep. Umphlett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY REPEALING SECTION 50-5-1707 RELATING TO SHARK CATCH LIMITS.
Very respectfully,
Speaker of the House
H. 3572--SENATE INSISTS ON ITS AMENDMENTS
APPOINTS CONFERENCE COMMITTEE
H. 3572 (Word version) -- Rep. Umphlett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY REPEALING SECTION 50-5-1707 RELATING TO SHARK CATCH LIMITS.
On motion of Senator CROMER, the Senate insisted upon its amendments to H. 3572 and asked for a Committee of Conference.
Whereupon, Senators McGILL, CLEARY and KNOTTS were appointed to the Committee of Conference on the part of the Senate and a message was sent to the House accordingly.
HOUSE CONCURRENCES
S. 792 (Word version) -- Senators Scott, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Grooms, Hayes, Hutto, Jackson, Knotts, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McConnell, McGill, Mulvaney, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A CONCURRENT RESOLUTION TO DECLARE THE MONTH OF OCTOBER 2009 AS GANG AWARENESS MONTH IN SOUTH CAROLINA IN ORDER TO RAISE PUBLIC AWARENESS OF THE INCREASING PROBLEM OF CRIMINAL GANG ACTIVITY IN OUR STATE.
Returned with concurrence.
S. 839 (Word version) -- Senators Scott, Jackson, Matthews and Williams: A CONCURRENT RESOLUTION TO DECLARE THE MONTH OF SEPTEMBER 2009 YOUTH AWARENESS MONTH IN SOUTH CAROLINA AND TO ENCOURAGE ALL CITIZENS OF THIS GREAT STATE TO PROMOTE STRONG FAMILIES AND PARENTING ALONG WITH YOUTH PROGRAMS AND JOBS.
Returned with concurrence.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
ORDERED ENROLLED FOR RATIFICATION
The following Bills were read the third time and, having received three readings in both Houses, it was ordered that the titles be changed to that of Acts and enrolled for Ratification:
H. 3678 (Word version) -- Reps. D.C. Moss, Whipper, Anthony, Herbkersman, Merrill, Nanney, G.M. Smith, Thompson and Weeks: A BILL TO AMEND SECTION 56-5-4140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE MAXIMUM ALLOWABLE GROSS WEIGHTS OF VEHICLES THAT MAY BE OPERATED ALONG THE STATE'S HIGHWAYS, SO AS TO MAKE A TECHNICAL CHANGE.
H. 3678--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
H. 3118 (Word version) -- Reps. Kirsh, J.E. Smith, Funderburk, Weeks and Hutto: A BILL TO AMEND SECTION 63-11-530, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE POWERS AND DUTIES OF GUARDIANS AD LITEM IN CHILD ABUSE AND NEGLECT CASES, SO AS TO PROVIDE THAT THE SOUTH CAROLINA GUARDIAN AD LITEM PROGRAM HAS THE RIGHT TO INTERVENE IN A PROCEEDING TO PETITION TO HAVE THE GUARDIAN AD LITEM REMOVED IF THE GUARDIAN AD LITEM IS NOT IN COMPLIANCE WITH STATE LAW OR IS NOT ACTING IN THE BEST INTEREST OF THE CHILD; AND TO AMEND SECTION 63-11-550, RELATING TO CONFIDENTIALITY OF REPORTS AND INFORMATION MAINTAINED BY THE GUARDIAN AD LITEM PROGRAM, SO AS TO ALSO PROVIDE THAT REPORTS AND INFORMATION MAINTAINED BY A GUARDIAN AD LITEM IS CONFIDENTIAL.
H. 3134 (Word version) -- Reps. Bowers and Long: A BILL TO AMEND SECTION 56-3-9910, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ISSUANCE OF GOLD STAR FAMILY SPECIAL LICENSE PLATES, SO AS TO REDUCE THE FEE FOR THIS SPECIAL LICENSE PLATE.
H. 3134--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
HOUSE BILLS RETURNED
The following House Bills were read the third time and ordered returned to the House with amendments:
H. 3018 (Word version) -- Reps. E.H. Pitts, Huggins, Gunn, Bales, Limehouse, Barfield, Hardwick, Hearn, Edge, Gambrell, Thompson, Bowen, Harrison, Umphlett, Sandifer, Herbkersman, G.M. Smith, Lowe, Vick, H.B. Brown, R.L. Brown, Viers, Clemmons, Ballentine, Mitchell and M.A. Pitts: A BILL TO AMEND SECTION 12-37-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROPERTY TAX EXEMPTIONS, SO AS TO EXEMPT FROM PROPERTY TAX THE VALUE OF IMPROVEMENTS TO REAL PROPERTY CONSISTING OF A NEWLY CONSTRUCTED DETACHED SINGLE FAMILY HOME THROUGH THE EARLIER OF THE PROPERTY TAX IN WHICH THE HOME IS OCCUPIED, OR THE SECOND PROPERTY TAX YEAR ENDING DECEMBER THIRTY-FIRST AFTER THE HOME IS COMPLETED AND A CERTIFICATE FOR OCCUPANCY ISSUED THEREON IF REQUIRED.
H. 3018--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting against third reading of the Bill.
H. 3615 (Word version) -- Reps. Sandifer, Parks, King and Weeks: A BILL TO AMEND CHAPTER 7 OF TITLE 32, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACTS, SO AS TO TRANSFER THE POWERS AND DUTIES FOR THE REGULATION OF PRENEED FUNERAL CONTRACTS FROM THE STATE BOARD OF FINANCIAL INSTITUTIONS TO THE DEPARTMENT OF CONSUMER AFFAIRS AND TO CONFORM THE PROVISIONS OF THIS CHAPTER TO THIS TRANSFER OF AUTHORITY, TO INCREASE CRIMINAL FINES FOR VIOLATIONS, TO PROVIDE FOR ADMINISTRATIVE PENALTIES, TO PROVIDE FOR A CONTESTED CASE HEARING FROM AN ORDER OF THE DEPARTMENT, AND TO MAKE TECHNICAL CORRECTIONS; AND TO AMEND SECTION 40-19-290, AS AMENDED, RELATING TO LICENSED EMBALMERS AND FUNERAL DIRECTORS RECEIVING PAYMENTS FOR PRENEED FUNERAL CONTRACTS, SO AS TO CHANGE "STATE BOARD OF FINANCIAL INSTITUTIONS" TO "SOUTH CAROLINA DEPARTMENT OF CONSUMER AFFAIRS".
Senator CAMPBELL asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Senator CAMPBELL explained the Bill.
The Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
H. 3615--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
H. 3804 (Word version) -- Reps. Bedingfield, Wylie, Cato, Allen, Bannister, Hamilton and Stringer: A BILL TO AMEND SECTION 7-7-280, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN GREENVILLE COUNTY, SO AS TO REVISE AND RENAME CERTAIN VOTING PRECINCTS OF GREENVILLE COUNTY AND REDESIGNATE A MAP NUMBER FOR THE MAP ON WHICH LINES OF THESE PRECINCTS ARE DELINEATED AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD.
H. 3804--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
RETURNED TO THE HOUSE
H. 3651 (Word version) -- Reps. Duncan, Umphlett, Anthony, Knight, Forrester and Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 48-23-205 SO AS TO LIMIT THE AUTHORITY OF COUNTIES AND MUNICIPALITIES TO RESTRICT OR REGULATE CERTAIN FORESTRY ACTIVITIES, AND TO PROVIDE THE TERMS AND CONDITIONS OF CERTAIN PERMITTED REGULATIONS.
Motion Under Rule 26B
Senator FAIR asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Senator FAIR proposed the following amendment (3651R001.MLF), which was adopted:
Amend the bill, as and if amended, page 2, by striking lines 22 - 27 and inserting:
/ (1) regulate activities associated with development, provided that a county or municipality requires a deferral of consideration of an application for a building permit, a site disturbance or subdivision plan, or any other approval for development that if implemented would result in a change from forest land to nonforest or nonagricultural use, the deferral may not exceed a period of up to:
Renumber sections to conform.
Amend title to conform.
Senator FAIR explained the amendment.
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
The following Joint Resolutions were read the third time and ordered sent to the House of Representatives:
S. 813 (Word version) -- Judiciary Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE PUBLIC SERVICE COMMISSION, RELATING TO PC&N (STRETCHER VANS), DESIGNATED AS REGULATION DOCUMENT NUMBER 4020, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 813--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Resolution.
S. 817 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION, OFFICE OF OCCUPATIONAL SAFETY AND HEALTH, RELATING TO OCCUPATIONAL SAFETY AND HEALTH ACT, DESIGNATED AS REGULATION DOCUMENT NUMBER 4019, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 817--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Resolution.
S. 818 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO MILK AND MILK PRODUCTS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4017, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 818--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Resolution.
S. 819 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO STANDARDS FOR LICENSING NURSING HOMES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4013, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 819--Recorded Vote
Senators BRYANT and BRIGHT desired to be recorded as voting against the third reading of the Resolution.
S. 820 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO PUBLIC SWIMMING POOLS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4030, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 820--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Resolution.
The following Bills, having been read the second time, were ordered placed on the Third Reading Calendar:
S. 562 (Word version) -- Senator McConnell: A BILL TO AMEND SECTION 56-5-750, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATED TO THE FAILURE OF A DRIVER TO STOP A MOTOR VEHICLE WHEN SIGNALED BY A LAW ENFORCEMENT VEHICLE, SO AS TO PROVIDE THAT A DRIVER MAY PROCEED TO A REASONABLY CLOSE AND SAFE LOCATION BEFORE STOPPING.
Senator L. MARTIN explained the Bill.
H. 4023 (Word version) -- Reps. Daning, Jefferson, Merrill and Umphlett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 57-23-815 SO AS TO PROVIDE THAT THE DEPARTMENT OF TRANSPORTATION MAY MOW BEYOND THIRTY FEET FROM THE PAVEMENT ROADSIDE VEGETATION ADJACENT TO INTERSTATE HIGHWAY 26 AT EXIT 199 IN BERKELEY COUNTY.
H. 3013 (Word version) -- Reps. Limehouse, Parker and Toole: A BILL TO AMEND SECTION 16-11-650, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE OFFENSE OF REMOVING OR DESTROYING FENCES, GATES, OR OTHER BARRIERS ENCLOSING ANIMALS, CROPS, OR UNCULTIVATED LANDS, SO AS TO REVISE THE ELEMENTS OF THE OFFENSE AND INCREASE PENALTIES FOR VIOLATIONS AND TO VEST JURISDICTION TO HEAR AND DISPOSE OF THIS OFFENSE IN MAGISTRATES COURT.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD3013.001), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 16-11-650 of the 1976 Code is amended to read:
"Section 16-11-650. (A) Any A person, other than the owner or a person acting under the authority of the owner, who shall remove, destroy or leave wilfully and knowingly removes, destroys, or leaves down any portion of any a fence in this State intended to enclose animals of any kind or crops or uncultivated lands or who shall leave wilfully and knowingly leaves open any or removes a gate or leave leaves down any bars or other structure intended for a like the same purpose shall be is guilty of a misdemeanor and shall must be punished by a fine of not less than five nor more than thirty one thousand dollars or be imprisoned in the county jail not less than five and not more than imprisonment for thirty days, or both.
(B) The magistrates court is vested with jurisdiction to hear and dispose of these cases.
(C) Nothing in this section shall affect an easement holder's right and ability to maintain such easement and rights-of-way consistent with the provisions of the document granting such easement."
SECTION 2. The repeal or amendment by this act of any law, whether temporary or permanent or civil or criminal, does not affect pending actions, rights, duties, or liabilities founded thereon, or alter, discharge, release or extinguish any penalty, forfeiture, or liability incurred under the repealed or amended law, unless the repealed or amended provision shall so expressly provide. After the effective date of this act, all laws repealed or amended by this act must be taken and treated as remaining in full force and effect for the purpose of sustaining any pending or vested right, civil action, special proceeding, criminal prosecution, or appeal existing as of the effective date of this act, and for the enforcement of rights, duties, penalties, forfeitures, and liabilities as they stood under the repealed or amended laws.
SECTION 3. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3087 (Word version) -- Reps. Brady and M.A. Pitts: A BILL TO AMEND SECTION 23-3-535, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO LIMITATIONS ON PLACES OF RESIDENCE FOR SEX OFFENDERS, SO AS TO PROVIDE THAT A LOCAL GOVERNMENT MAY NOT ENACT AN ORDINANCE THAT EXPANDS OR CONTRACTS THE BOUNDARIES OF THE AREAS IN WHICH A SEX OFFENDER MAY OR MAY NOT RESIDE THAT ARE CONTAINED IN THIS SECTION.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD3087.001), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 23-3-535(E) of the 1976 Code, as added by Act 333 of 2008, is amended to read:
"(E) A local government may not enact an ordinance that:
(1) contains penalties that exceed or are less lenient than the penalties contained in this section; or
(2) expands or contracts the boundaries of areas in which a sex offender may or may not reside as contained in subsection (B)."
SECTION 2. SECTION 2 of Act 333 of 2008 shall take effect upon approval of this act by the Governor. All other sections of Act 333 of 2008 shall take effect as provided in SECTION 4 of Act 333 of 2008." SECTION 3. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3761 (Word version) -- Rep. Cooper: A BILL TO AMEND SECTION 44-53-530, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FORFEITURE PROCEDURES RELATED TO DRUG PROCEEDS, SO AS TO ALLOW THE USE OF FORFEITED MONIES AND PROCEEDS FROM THE SALE OF PROPERTY FOR TRAINING AND EDUCATION BY LAW ENFORCEMENT IN ADDITION TO OTHER USES PREVIOUSLY DELINEATED.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD3761.002), which was adopted:
Amend the bill, as and if amended, page 1, by striking lines 26-36 in their entirety and inserting:
/ SECTION 1. Section 44-53-530(g) of the 1976 Code is amended to read:
"(g) All forfeited monies and proceeds from the sale of forfeited property as defined in Section 44-53-520 must be retained by the governing body of the local law enforcement agency or prosecution agency and deposited in a separate, special account in the name of each appropriate agency. These accounts may be drawn on and used only by the law enforcement agency or prosecution agency for which the account was established. For law enforcement agencies, the accounts must be used for drug enforcement activities, or for drug or other law enforcement training or education. and for For prosecution agencies, the accounts must be used in matters relating to the prosecution of drug offenses and litigation of drug-related matters. /
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3919 (Word version) -- Reps. Mitchell, Alexander, Gunn, Dillard, Hamilton, Limehouse, J.R. Smith, King, Kirsh, Littlejohn, J.M. Neal, Herbkersman, Stavrinakis, Chalk, Cobb-Hunter, Anthony, Branham, Brantley, Parker, Allison, Gilliard, J.H. Neal, Whipper, Mack, Battle, Hosey, Allen, Weeks, Jennings, Loftis, Knight, Vick, Rutherford and Hutto: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 2-1-250 SO AS TO ESTABLISH THE SOUTH CAROLINA HOUSING COMMISSION TO PROVIDE RECOMMENDATIONS TO ENSURE AND FOSTER THE AVAILABILITY OF SAFE, SOUND, AND AFFORDABLE HOUSING AND WORKFORCE HOUSING FOR EVERY SOUTH CAROLINIAN, TO PROVIDE FOR THE MEMBERSHIP OF THE COMMISSION, AND FOR OTHER PROCEDURAL MATTERS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD3919.002), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting language and inserting therein the following:
/ SECTION 1. Chapter 1, Title 2 of the 1976 Code is amended by adding:
"Section 2-1-250. (A) The South Carolina Housing Commission (commission) is hereby established. The purpose of the commission is to provide recommendations to the Governor and the General Assembly on an annual basis to ensure and foster the availability of safe, sound, and affordable housing and workforce housing for every South Carolinian. The commission also may make recommendations relating to such other housing, real property, and community development issues as it considers desirable.
(B) The commission shall consist of fifteen members. Of these members, five must be members of the House of Representatives to be appointed by the Speaker of the House; five must be members of the Senate to be appointed by the President Pro Tempore of the Senate; and five must be nonlegislative members selected by the other legislative members. All members must be qualified electors of this State.
Legislative members shall serve terms concurrent with their terms of office. Nonlegislative members shall serve for terms of four years each. Appointments to fill vacancies, other than by expiration of a term, must be for the unexpired terms. Legislative and nonlegislative members may be reappointed for successive terms. Vacancies must be filled in the same manner as the original appointments.
The commission shall elect a chairman and vice chairman every two years from among its membership, who must be members of the General Assembly.
(C) A majority of the members shall constitute a quorum. The meetings of the commission shall be held at the call of the chairman or whenever the majority of the members request.
No recommendation of the commission shall be adopted if a majority of the Senate members or a majority of the House members appointed to the commission vote against the recommendation.
(D) The commission shall have the following powers and duties:
(1) undertake analyses, gather information and data, and pursue such other activities as may be desirable to accomplish its purposes;
(2) report annually on its activities during the preceding year and include a discussion of analyses made and recommendations for administrative or legislative action; and
(3) review newly enacted federal legislation pertaining to mortgage lending and brokering and determine if the federal legislation necessitates amendments to the laws of this State.
(E) The chairman shall submit to the General Assembly and the Governor an annual summary of the activity and work of the commission together with its recommendations no later than the first day of each regular session of the General Assembly.
(F) Staff for the commission shall be provided from the standing committees of the House of Representatives and the Senate with jurisdiction over the subject matter being studied by the commission.
(G) Members of the commission shall serve without compensation, subsistence, per diem, or mileage."
SECTION 2. This act takes effect July 1, 2009. /
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 4008 (Word version) -- Reps. Funderburk, Agnew, Alexander, Allen, Allison, Anderson, Anthony, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, G.A. Brown, H.B. Brown, R.L. Brown, Cato, Chalk, Clemmons, Clyburn, Cobb-Hunter, Cole, Cooper, Crawford, Daning, Delleney, Dillard, Duncan, Edge, Erickson, Forrester, Frye, Gambrell, Gilliard, Govan, Gullick, Gunn, Haley, Hamilton, Hardwick, Harrell, Harrison, Hart, Harvin, Hayes, Hearn, Herbkersman, Hiott, Hodges, Horne, Hosey, Howard, Huggins, Hutto, Jefferson, Jennings, Kelly, Kennedy, King, Kirsh, Knight, Limehouse, Littlejohn, Loftis, Long, Lowe, Lucas, Mack, McEachern, McLeod, Merrill, Miller, Millwood, Mitchell, D.C. Moss, Nanney, J.H. Neal, J.M. Neal, Neilson, Ott, Owens, Parker, Parks, Pinson, E.H. Pitts, M.A. Pitts, Rice, Rutherford, Sandifer, Scott, Sellers, Simrill, Skelton, D.C. Smith, G.M. Smith, G.R. Smith, J.E. Smith, J.R. Smith, Sottile, Spires, Stavrinakis, Stewart, Stringer, Thompson, Toole, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis, Wylie, A.D. Young and T.R. Young: A CONCURRENT RESOLUTION TO DESIGNATE THE MONTH OF NOVEMBER 2009 AS "EPILEPSY AWARENESS MONTH" IN SOUTH CAROLINA AND TO ENCOURAGE COMMUNITY AWARENESS AND UNDERSTANDING OF EPILEPSY.
The Concurrent Resolution was adopted, ordered returned to the House.
CARRIED OVER
H. 3342 (Word version) -- Reps. Delleney, Simrill, Nanney, Allison, Clemmons, Erickson, Hamilton, Lucas, Owens, Parker, Pinson, Scott, G.R. Smith, J.R. Smith, Loftis, Duncan, Hiott, Bedingfield, Rice and Vick: A BILL TO AMEND SECTION 2-7-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CONSTRUCTION OF THE WORDS "PERSON" AND "PARTY" AS THOSE WORDS APPEAR IN THE LAWS OF THIS STATE, SO AS TO PROVIDE FURTHER FOR THE CONSTRUCTION OF "PERSON", "HUMAN BEING", "CHILD", AND "INDIVIDUAL", SO THAT THEY INCLUDE EVERY INFANT MEMBER OF SPECIES HOMO SAPIENS WHO IS BORN ALIVE AND TO DEFINE "BORN ALIVE".
Senator L. MARTIN explained the Bill.
On motion of Senator LEVENTIS, the Bill was carried over.
H. 3377 (Word version) -- Reps. D.C. Moss, Vick, Simrill, Anthony, Bedingfield, H.B. Brown, Duncan, Gambrell, Gullick, Jennings and A.D. Young: A BILL TO AMEND SECTION 23-1-212, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ENFORCEMENT OF STATE CRIMINAL LAWS BY FEDERAL LAW ENFORCEMENT OFFICERS, SO AS TO PROVIDE THAT NATIONAL PARK SERVICE RANGERS ARE FEDERAL LAW ENFORCEMENT OFFICERS WHO ARE AUTHORIZED TO ENFORCE THE STATE'S CRIMINAL LAWS.
Senator L. MARTIN explained the Bill.
On motion of Senator MALLOY, the Bill was carried over.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
On motion of Senator McCONNELL, the Senate agreed to dispense with the Motion Period.
RECESS
At 12:52 P.M., on motion of Senator McCONNELL, the Senate receded from business until 2:00 P.M.
AFTERNOON SESSION
The Senate reassembled at 2:19 P.M. and was called to order by the PRESIDENT.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CONCURRENCE
S. 345 (Word version) -- Senator Leatherman: A BILL TO AMEND SECTION 8-11-65 OF THE 1976 CODE, RELATING TO LEAVES OF ABSENCE TO BE AN ORGAN DONOR, TO PROVIDE THAT THE NUMBER OF DAYS A PERSON MAY MISS EACH YEAR TO DONATE THEIR ORGANS SHALL BE COUNTED IN A CALENDAR YEAR INSTEAD OF A FISCAL YEAR; AND TO AMEND SECTION 8-11-120, RELATING TO THE POSTING OF JOB VACANCIES BEFORE THE VACANCY IS FILLED, TO REVISE AND SIMPLIFY THE REQUIREMENTS FOR THE NOTICE.
The House returned the Bill with amendments.
On motion of Senator LEATHERMAN, the Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification.
AMENDMENT PROPOSED, CARRIED OVER
S. 351 (Word version) -- Senators Grooms, McConnell and Ford: A BILL TO AMEND ARTICLE 1, CHAPTER 3, TITLE 54 OF THE 1976 CODE, RELATING TO THE CREATION AND ORGANIZATION OF THE SOUTH CAROLINA STATE PORTS AUTHORITY, TO CLARIFY THAT THE POWERS AND DUTIES OF THE AUTHORITY ARE EXERCISED BY A BOARD OF DIRECTORS, TO PROVIDE THAT CANDIDATES FOR APPOINTMENT MUST POSSESS CERTAIN QUALIFICATIONS, TO PROVIDE THAT CANDIDATES MUST BE SCREENED TO DETERMINE WHETHER THEY POSSESS THE REQUIRED QUALIFICATIONS BEFORE THEY MAY SERVE ON THE BOARD, TO PROVIDE THAT MEMBERS OF THE BOARD MAY BE REMOVED FROM OFFICE ONLY FOR CAUSE, TO PROVIDE THAT THE BOARD MUST PERFORM AN ANNUAL PERFORMANCE REVIEW OF THE EXECUTIVE DIRECTOR, TO ESTABLISH THAT DIRECTORS HAVE A DUTY OF GOOD FAITH AND ORDINARY CARE WHEN DISCHARGING THEIR DUTIES AS A DIRECTOR, TO PROHIBIT CONFLICT OF INTEREST TRANSACTIONS, TO ESTABLISH A SOUTH CAROLINA STATE PORTS ADVISORY BOARD, AND SET THE MEMBERSHIP, DUTIES, AND RESPONSIBILITIES OF THE ADVISORY BOARD; TO AMEND CHAPTER 3, TITLE 54, BY ADDING ARTICLE 2, RELATING TO PORTS AUTHORITY MANAGEMENT, TO PROVIDE THAT THE BOARD OF DIRECTORS MUST HIRE AN EXECUTIVE DIRECTOR OF PORT OPERATIONS AND TO ESTABLISH THE DIRECTOR'S DUTY TO OPERATE THE PORTS IN A MANNER CONSISTENT WITH THE MISSION, POLICIES, AND DIRECTION OF THE BOARD; TO AMEND SECTION 54-3-140(5), TO PROVIDE THAT THE BOARD OF DIRECTORS MUST ADOPT AN ORGANIZATIONAL STRUCTURE FOR AUTHORITY OPERATIONS; TO AMEND SECTION 54-3-140, RELATING TO THE POWERS OF THE PORTS AUTHORITY, BY ADDING TWO NEW ITEMS THAT REQUIRE A LONG-RANGE PORT DEVELOPMENT AND CAPITAL FINANCING PLAN AND TO PROVIDE THAT THE AUTHORITY MUST CONSIDER PUBLIC-PRIVATE PARTNERSHIPS FOR CURRENT AND FUTURE OPERATIONS; TO AMEND SECTION 54-3-1040, RELATING TO THE ANNUAL FINANCIAL STATEMENT, AND TO PROVIDE THAT COPIES OF THE STATEMENT MUST BE FORWARDED TO THE ADVISORY COMMITTEE AND THE GENERAL ASSEMBLY; TO AMEND ARTICLE 11, CHAPTER 3, TITLE 54, RELATING TO FINANCIAL MATTERS, BY ADDING SECTION 54-3-1060, TO PROVIDE THAT THE AUTHORITY MUST MAINTAIN A TRANSACTION REGISTER OF ALL FUNDS EXPENDED OVER ONE HUNDRED DOLLARS AND MUST MAINTAIN ON ITS INTERNET WEBSITE A COPY OF EACH MONTHLY CREDIT CARD STATEMENT FOR ALL CREDIT CARDS MAINTAINED BY THE AUTHORITY; AND TO AMEND CHAPTER 3, TITLE 54, BY ADDING ARTICLE 13, RELATING TO LEGISLATIVE OVERSIGHT, TO REQUIRE REGULAR OVERSIGHT REVIEW OF THE AUTHORITY AND THE EXECUTIVE DIRECTOR.
The Bill was returned from the House with amendments. The question then was concurrence in the House amendments.
On motion of Senator GROOMS, with unanimous consent, Amendment No. 3 was taken up for immediate consideration.
Amendment No. 3
Senators GROOMS and McCONNELL proposed the following Amendment No. 3 (351R041.LKG):
Amend the bill, as and if amended, by striking SECTION 1 in its entirety and inserting:
/ SECTION 1. Article 1, Chapter 3, Title 54 of the 1976 Code is amended to read:
"Article 1
Creation and Organization
Section 54-3-10. (A) The There is created the South Carolina State Ports Authority. is hereby created consisting of a The governing body of the authority is a board of directors consisting of nine eleven members, hereafter referred to as the Authority nine voting members appointed by the Governor as provided in Section 54-3-20 and the Secretary of Transportation, or his designee, and the Secretary of Commerce, or his designee. The voting members shall be responsible for setting policies and direction for the authority so that the authority may achieve its mission. The powers and duties of the authority shall be exercised by the board. The board may delegate to one or more officers, agents, or employees such powers and duties as it determines are necessary and proper for the effective, efficient operation of the port.
(B) The Secretary of Transportation and the Secretary of Commerce:
(1) shall serve on the board, ex officio, as non-voting members;
(2) are ineligible for election as chairman, vice chairman, secretary, treasurer, or any other office elected by the board; and
(3) may only attend meetings or portions of meetings open to the public. They are not permitted to attend executive session meetings.
Section 54-3-20. (A) The members of the board, except for the Secretary of Transportation and the Secretary of Commerce, shall be appointed by the Governor, with the advice and consent of the Senate, for terms of seven five years each and until their successors shall have been appointed, screened, and have qualified. In the event of a vacancy, however caused, a successor shall be appointed in the manner of original appointment for the unexpired term.
(B) A candidate for appointment to the board may not be confirmed by the Senate or serve on the board, even in an interim capacity, until he is found qualified by possessing the abilities, the experience, and the minimum qualifications contained in Section 54-3-60.
Section 54-3-30. They The board shall elect one of their number its members to serve as chairman and who shall serve for a term of two years in this capacity and may not serve more than three consecutive full two-year terms as chairman. The board also shall elect one member to serve as vice chairman, and shall also elect a one member to serve as secretary. The board shall meet upon the call of its chairman and a majority of its voting members shall constitute a quorum for the transaction of its business.
Section 54-3-40. The Authority board shall select one of its members to serve as its treasurer. The Authority treasurer shall require give a surety bond of such appointee in such an amount as the Authority may fix fixed by the board and the premium thereon on the bond shall be paid by the authority as a necessary expense of the Authority.
Section 54-3-50. Members of the board of directors may be removed by the Governor pursuant to Section 1-3-240(C)(1), a breach of duty required by Section 54-3-80, or entering into a conflict of interest transaction prohibited by Section 54-3-90.
Section 54-3-60. (A) Each member of the board, except for the Secretary of Transportation and the Secretary of Commerce, or their designees, must possess a four-year baccalaureate or more advanced degree from:
(1) a recognized institution of higher learning requiring face-to-face contact between its students and instructors prior to completion of the academic program;
(2) an institution of high learning that has been accredited by a regional or national accrediting body; or
(3) an institution of higher learning in this State chartered prior to 1962.
(B) In addition to the requirements in subsection (A), each board member must possess a background of at least five years in any one or any combination of the following fields of expertise:
(a) maritime shipping;
(b) labor related to maritime shipping;
(c) overland shipping by truck or rail, or both;
(d) international commerce;
(e) finance, economics, or statistics;
(f) accounting;
(g) engineering;
(h) law; or
(i) business management gained from serving as a chief executive officer, president, or managing director of a business or any upper level management position with a business that is equivalent in duties and responsibilities to the positions listed in this item.
(C) When making appointments to the board, the Governor shall ensure that that the diverse interests represented by the port are represented. To the greatest extent possible, the Governor shall ensure that the membership of the board includes a certified public accountant, a member representing port users such as manufacturers, shippers, and importers, a member representing the state's economic development interests, and a member who has served as a corporate chief executive officer. Consideration of these factors in making an appointment in no way creates a cause of action or basis for an employee grievance for a person appointed or for a person who fails to be appointed.
Section 54-3-70. The board shall conduct an annual performance review of the executive director and submit a written report of its findings to the Governor and the General Assembly. A draft of the performance review must be submitted to the executive director, and the executive director must be provided an opportunity to be heard by the board of directors before the board submits the final draft to the Governor and the General Assembly.
Section 54-3-80. (A) A member of the board of directors shall discharge his duties as a director, including his duties as a member of a committee:
(1) in good faith;
(2) with the care an ordinarily prudent person in a like position would exercise under similar circumstances; and
(3) in a manner he reasonably believes to be in the best interests of the authority. As used in this chapter, best interests means a balancing of the following:
(a) achieving the purposes of the authority as provided in Section 54-3-130;
(b) preservation of the financial integrity of the State Ports Authority and its ongoing operations;
(c) economic development and job attraction and retention;
(d) consideration given to diminish or mitigate any negative effect port operations or expansion may have upon the environment, transportation infrastructure, and quality of life of residents in communities located near existing or proposed port facilities; and
(e) exercise of the powers of the authority in accordance with good business practices and the requirements of applicable licenses, laws, and regulations.
(B) In discharging his duties, a director is entitled to rely on information, opinions, reports, or statements, including financial statements and other financial data, if prepared or presented by:
(1) one or more officers or employees of the State whom the director reasonably believes to be reliable and competent in the matters presented;
(2) legal counsel, public accountants, or other persons as to matters the director reasonably believes are within the person's professional or expert competence; or
(3) a committee of the board of directors of which he is not a member if the director reasonably believes the committee merits confidence.
(C) A director is not acting in good faith if he has knowledge concerning the matter in question that makes reliance otherwise permitted by subsection (B) unwarranted.
(D) Nothing in this article gives rise to a cause of action against a member of the board of directors or any decision of the board of directors regarding duties of the individual director or the board of directors concerning port operations or development. Willful failure of the board or any individual member of the board to discharge his duties as required by this article may be considered by the Governor in determining whether to reappoint a board member or in the confirmation proceedings of that board member.
Section 54-3-90. (A) A conflict of interest transaction is a transaction with the State Ports Authority in which a director has a direct or indirect interest. A conflict of interest transaction is not voidable by the authority solely because of the director's interest in the transaction if any one of the following is true:
(1) the material facts of the transaction and the director's interest were disclosed or known to the board or a committee of the board, and the board or a committee of the board authorized, approved, or ratified the transaction; or
(2) the transaction was fair to the authority and its customers.
If item (1) has been accomplished, the burden of proving unfairness of any transaction covered by this section is on the party claiming unfairness. If item (1) has not been accomplished, the party seeking to uphold the transaction has the burden of proving fairness.
(B) For purposes of this section, a director has an indirect interest in a transaction if:
(1) another entity in which he has a material financial interest or in which he is a general partner is a party to the transaction;
(2) another entity of which he is a director, officer, member, or trustee is a party to the transaction and the transaction is or should be considered by the board; or
(3) another entity of which an immediate family member has a material financial interest or in which an immediate family member is a general partner, director, officer, member, or trustee is a party to the transaction and the transaction is or should be considered by the board.
(C) For purposes of subsection (A)(1), a conflict of interest transaction is authorized, approved, or ratified if it receives the affirmative vote of a majority of the directors on the board of directors, or on the committee, who have no direct or indirect interest in the transaction, but a transaction may not be authorized, approved, or ratified under this section by a single director. If a majority of the directors who have no direct or indirect interest in the transaction vote to authorize, approve, or ratify the transaction, a quorum is present for the purpose of taking action under this section. The presence of, or a vote cast by, a director with a direct or indirect interest in the transaction does not affect the validity of any action taken under subsection (A)(1) if the transaction is otherwise authorized, approved, or ratified as provided in that subsection."
Amend the bill further as and if amended, page 9, by striking line 29 and inserting:
/ ( ) Shall take all necessary steps it finds reasonable to /
Amend the bill further as and if amended, by striking SECTION 5 in its entirety and inserting:
/ SECTION 5. Section 54-3-1040 of the 1976 Code is amended to read:
"Section 54-3-1040. At least once in each year the authority shall publish once in some newspaper published in Charleston County furnish the Governor, the Chairman of the Senate Transportation Committee, and the House of Representatives Ways and Means Committee, and conspicuously post on the authority's Internet website, a complete detailed statement of all moneys monies received and disbursed by the Authority authority during the preceding year. Such statement shall also show the several sources from which such funds were received and the balance on hand at the time of publishing the statement and shall show the complete financial condition of the Authority authority." /
Amend the bill further as and if amended, by striking SECTION 7 in its entirety and inserting:
/ SECTION 7. Chapter 3, Title 54 of the 1976 Code is amended by adding:
"Article 13
The Review and Oversight Commission on the South Carolina State Ports Authority
Section 54-3-1300. (A) There is hereby established a commission to be known as the Review and Oversight Commission on the South Carolina State Ports Authority, hereinafter referred to as the commission, which must exercise the powers and fulfill the duties described in this article.
(B) The commission is composed of the following ten members.
(1) From the Senate:
(a) the chairman of the Finance Committee or his designee;
(b) the chairman of the Judiciary Committee or his designee;
(c) the chairman of the Transportation Committee or his designee; and
(d) two members appointed by the President Pro Tempore, one member upon the recommendation of the Senate Majority Leader and one member upon the recommendation of the Senate Minority Leader.
(2) From the House of Representatives:
(a) the chairman of the Ways and Means Committee or his designee;
(b) the chairman of the Judiciary Committee or his designee;
(c) the chairman of the Labor, Commerce, and Industry Committee, or his designee;
(c) two members of the House of Representatives appointed by the Speaker of the House of Representatives.
(C) In making appointments to the commission, race, gender, and other demographic factors, such as residence in rural or urban areas, must be considered to assure nondiscrimination, inclusion, and representation to the greatest extent possible of all segments of the population of the State.
(D) The commission must meet as soon as practicable after appointment and organize itself by electing one of its members as chairman and such other officers as the commission may consider necessary. Thereafter, the commission must meet as necessary to screen candidates for appointment to and at the call of the chairman or by a majority of the members. A quorum consists of six members.
Section 54-3-1310. The commission has the following powers and duties:
(A) to screen each person appointed to serve on the board;
(1) in screening candidates and making its findings, the commission must give due consideration to:
(a) ability, area of expertise, dedication, compassion, common sense, and integrity of each candidate; and
(b) the impact that each candidate would have on the racial and gender composition of the commission, and each candidate's impact on other demographic factors represented on the commission, such as residence in rural or urban areas, to assure nondiscrimination to the greatest extent possible of all segments of the population of the State;
(3) to determine if each candidate is qualified and meets the requirements provided by law to serve as a member of the Board of Directors of the State Ports Authority, make findings concerning whether each candidate is qualified, and deliver its findings to the Clerk of the Senate, the Clerk of the House of Representatives, and the Senate Transportation Committee for confirmation;
(B) to conduct an oversight review of the authority and its operations at least once every two years.
(1) The oversight reviews must consider whether the authority is promoting, developing, constructing, equipping, maintaining, and operating the harbors and seaports of this State in an efficient, effective manner in accordance with all applicable laws and regulations. The oversight reviews must also include an analysis of the performance of the executive director. In performing this analysis the commission must consider the report required pursuant to 54-3-70 in addition to other information collected concerning the executive director's performance.
(a) A draft of a board member's and executive director's performance review and the evaluations of the actions of the board, must be submitted to the appropriate party, and that party must be allowed an opportunity to be heard before the commission conducting the oversight review by the performance review or evaluation, as the case may be, is final.
(b) The final performance review of a board member must be made a part of the member's record for consideration if the member seeks reappointment to the board.
(2) A written report of the findings from each oversight review must be published in the journals of both houses and made available on the General Assembly's Internet website and transmitted to the Governor and the board.
(C) to review and evaluate the complete list of the properties on Daniel and Thomas (St. Thomas) Islands transmitted to the commission pursuant to Section 54-3-119(D). The commission must recommend to the Budget and Control Board whether to approve the sale or sell, as appropriate, any or all of the all real property the authority owns on Daniel Island and Thomas (St. Thomas) Island pursuant to Section 54-3-119.
(D) undertake any additional reviews, studies, or evaluations as it considers necessary.
Section 54-3-1320. The commission by a two-thirds vote of its membership, may waive the requirements of Section 54-3-60(A) and (B) for a candidate for the board of directors for the State Ports Authority; and
Section 54-3-1330. State agencies must fully cooperate with requests from the commission for assistance in carrying out its responsibilities and duties as established in this article.
Section 54-3-1340. (A) The oversight report required by this article must at least contain:
(1) a performance review of each member of the board during the previous two years;
(2) a performance review of the State Ports Authority executive director; and
(3) an evaluation of the actions of the board, sufficient to allow the members of the General Assembly to better judge whether these actions serve the best interests of the citizens of South Carolina, both individual and corporate.
(B) To assist the commission in performing the performance reviews and evaluations required by this article, the commission may develop and distribute, as appropriate, an anonymous and confidential survey evaluating the board members and the executive director. At a minimum, the survey must include the following:
(1) knowledge and application of substantive port issues;
(2) the ability to perceive relevant issues;
(3) absence of influence by political considerations;
(4) absence of influence by identities of labor unions;
(5) courtesy to all persons appearing before the board;
(6) temperament and demeanor in general, preparation for hearings, and attentiveness during hearings; and
(7) any other issue the commission deems appropriate.
Section 54-3-1350. In order to discharge their oversight responsibilities in regard to State Ports Authority operations and management, the commission may request and shall be provided within fifteen days after the request with any documents related to the sale or disposition or contemplated sale or disposition of any real property owned by the authority. The provisions of this section supercede any conflicting provisions contained in the Freedom of Information Act and these documents may be shared only with members of the commission, staff assigned to the commission, members of the General Assembly with whom the commission chooses to consult concerning the matter, or legal counsel employed by the Senate or the House of Representatives. These documents and the information contained in them must be kept confidential, and are not subject to public disclosure, or any other disclosure not permitted by the provisions of this section.
Section 54-3-1360. (A) Commission members are entitled to such mileage, subsistence, and per diem as authorized by law for members of boards, committees, and commissions while in the performance of the duties for which appointed. These expenses shall be paid by the State Ports Authority.
(B) The State Ports Authority must pay for all reasonable expenses associated with the commission's duties to screen appointees to the authority's board and conduct oversight as required by this article.
Section 54-3-1370. The commission must use clerical and professional employees of the General Assembly for its staff, who must be made available to the commission. The commission may employ or retain other professional staff, upon the determination of the necessity for other staff by the commission and as may be funded in the legislative appropriation of the annual general appropriations act. The State Ports Authority must pay for all reasonable staff related expenses associated with the commission's activities. /
Amend the bill further, as and if amended, by striking SECTION 17 in its entirety and inserting:
/ SECTION 17. Section 54-3-700 of the 1976 Code, as added by Act 313 of 2004, is amended to read:
"Section 54-3-700. (A) Upon the effective date of this section:
(1) the State Ports Authority has no statutory responsibility to operate a marine terminal at Port Royal; and
(2) marine operations at Port Royal shall cease as soon as practicable.
(B) The State Ports Authority is hereby directed to sell all its real and personal property at Port Royal upon the effective date of this section, but in a manner that is financially responsible and advantageous to the State Ports Authority.
(C) The State Ports Authority shall, in its discretion, shall determine the manner of the sale, but in no event shall terms of the sale extend beyond December 31, 2006 2009, except for parcels which may be under long-term contract, in which case the South Carolina Ports Authority is directed to terminate such these leases as soon as possible through 'lease purchases', 'buy outs', or any other lawful means.
(D) Any real or personal property at Port Royal which is to be sold must be first appraised and then sold at fair market value. The real property appraiser must be a State Certified General Real Estate Appraiser, a member of the Appraisal Institute (MAI), and must be knowledgeable in appraisal and in appraising marine terminal facilities. The appraisal of the real property should include its future development opportunities and those of the surrounding properties. The State Ports Authority Board of Directors shall exercise its lawful discretion in the acceptance of any sales price with due regard to its fiduciary duties to the authority and for the protection of the interests of the authority's bondholders as for forth in its bond covenants, and otherwise according to law, including conversion of a nonperforming asset into revenue in the most expeditious manner. The sale of the real property shall comply with all state procedures, must be approved by the State Budget and Control Board, and must be on an open-bid basis, and no bid may be accepted which is less than the property's fair market value as shown by the appraisal. All proceeds from the sale of real and personal property at Port Royal must be retained by the State Ports Authority; provided, however, except that the Town of Port Royal shall have the right to may petition the State Budget and Control Board for a portion of the net proceeds from any a sale and may be allocated a portion of these net proceeds in an amount not to exceed five percent of the net proceeds upon showing the allocation is necessary to pay for infrastructure needs directly associated with and necessitated by the closing of the port as Port Royal. These funds must be expended at the direction of the Town Council of Port Royal with the approval of the State Budget and Control Board, solely for the infrastructure, and shall have priority over all other expenditures except usual and necessary closing costs attributable to any a sales contracts contract." /
Amend the bill further, as and if amended, by striking SECTION 15 and inserting:
/ SECTION 15. Chapter 1, Title 13 of the 1976 Code is amended by adding:
"Section 13-1-1355. All tracks, spurs, switches, terminal, terminal facilities, road beds, rights-of-way, bridges, stations, railroad cars, locomotives, or other vehicles constructed for operation over railroad tracks, crossing signs, lights, signals, storage, and all associated structures and equipment which are necessary for the operation of any railroad located on any 'applicable federal military installation' or 'applicable federal facility' as defined in Section 12-6-3450 may not be transferred without the prior approval of the Budget and Control Board. The provisions of this section are remedial and shall be deemed to be retroactive. /
Amend the bill further, as and if amended, by striking SECTION 18 and SECTION 19 in their entirety.
Amend the bill further, as and if amended, by striking SECTION 20 and SECTION 21 in its entirety and inserting:
/ SECTION 19. Chapter 3, Title 54 of the 1976 Code is amended by adding:
"Section 54-3-119. (A) Except as provided in subsection (B), the State Ports Authority Board is directed to sell under those terms and conditions it considers most advantageous to the authority and the State of South Carolina all real property it owns on Daniel Island and Thomas (St. Thomas) Island except for the dredge disposal cells that are needed in connection with the construction of the North Charleston terminal on the Charleston Naval Complex and for harbor deepening and for channel and berth maintenance. The sale shall be timed and concluded on a schedule that prudently considers all market conditions affecting the sale but in any event must be under contract for sale by December 31, 2012 and the sale completed by December 31, 2013. The property must be transferred to the Budget and Control Board for sale if authority is unable to complete the sale by December 31, 2013. To assist in the sale of the property, the board shall have the property appraised by at least two independent qualified commercial appraisers not affiliated with the authority. The real property appraisers must be a State Certified General Real Estate Appraiser, a member of the Appraisal Institute (MAI), and must be knowledgeable in appraisal and in appraising marine terminal facilities. The appraisal of the real property should include its future development opportunities and those of the surrounding properties. The sale price must be equal to or greater than at least one of the independent appraisals. The approval of the State Budget and Control Board is required to effectuate the sale if completed on or before December 31, 2013.
(B) The board shall give the right of first refusal to those former landowners on Thomas (St. Thomas) Island who sold their land located within the transportation corridor to the authority in anticipation of the authority's exercise of eminent domain. The right of first refusal must provide that the landowner may repurchase his land at the same price for which the authority purchased it from him. Each contract for the sale of a parcel located in the transportation corridor on Thomas Island must contain a covenant creating an easement over the parcel. The easement must permit the authority, and any successor in interest to the authority, reasonable ingress and egress to the real property on Daniel Island owned by the authority as of the effective date of this section. The easement must contain express language that the easement runs with the land.
(C)(1) With regards to the sale of real property pursuant to subsection (A), the Budget and Control Board is vested with all of the board's fiduciary duties to the authority and the authority's bondholders if the property is transferred to the Budget and Control Board for sale. The acceptance of any sales price by either the board or the Budget and Control Board must be exercised with due regard to the fiduciary duty owed to the authority and for the protection of the interests of the authority's bondholders as set forth in its bond covenants, and otherwise according to law, including the conversion of a nonperforming asset into revenues in the most expeditious manner.
(2) The Budget and Control Board may deduct from the proceeds of the sale an amount equal to the actual costs incurred in conjunction with the sale of the property. The balance of the proceeds must be transmitted to the authority.
(D) The authority must provide the Review and Oversight Commission on the South Carolina State Ports Authority a complete list of the properties, described in metes and bounds, on Daniel and Thomas (St. Thomas) Islands that:
(1) constitute the dredge disposal cells commonly identified as the west cell, the middle cell, and the Wando cell. These three cells may not be sold by the authority because they are necessary in connection with the construction of North Charleston terminal on the Charleston Naval Complex and harbor deepening and for channel and berth maintenance. The authority must also identify the north cell, which must be retained long enough to excavate material contained in the cell to be used for construction of the North Charleston terminal on the Charleston Naval Complex; and
(2) located within the transportation corridor."
SECTION 20. The General Assembly encourages discussions between interested parties and the Town of Port Royal concerning the building of a boat landing north of the Broad River in Beaufort County. Funds negotiated between the Town of Port Royal and the South Carolina State Ports Authority pursuant to Section 54-3-700 should be used to build the boat landing.
SECTION 21. The provisions of this act related to a time limitation for members of the Board of Directors serving in a holdover capacity do not apply to board members serving in a holdover capacity as of the effective date of this act but apply to any subsequent term.
SECTION 22. If any section, subsection, paragraph, subparagraph, sentence, clause, phrase, or word of this act is for any reason held to be unconstitutional or invalid, such holding shall not affect the constitutionality or validity of the remaining portions of this act, the General Assembly hereby declaring that it would have passed this act, and each and every section, subsection, paragraph, subparagraph, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective.
SECTION 23. The repeal or amendment by this act of any law, whether temporary or permanent or civil or criminal, does not affect pending actions, rights, duties, or liabilities founded thereon, or alter, discharge, release or extinguish any penalty, forfeiture, or liability incurred under the repealed or amended law, unless the repealed or amended provision shall so expressly provide. After the effective date of this act, all laws repealed or amended by this act must be taken and treated as remaining in full force and effect for the purpose of sustaining any pending or vested right, civil action, special proceeding, criminal prosecution, or appeal existing as of the effective date of this act, and for the enforcement of rights, duties, penalties, forfeitures, and liabilities as they stood under the repealed or amended laws.
SECTION 24. This act takes effect upon approval by the Governor. /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the amendment.
On motion of Senator SETZLER, with unanimous consent, Senators ALEXANDER, SHOOPMAN and SETZLER were granted leave to attend a meeting of a Committee of Conference on S. 12 and were granted leave to vote from the balcony.
Senator GROOMS resumed explaining the amendment.
Senator GROOMS moved to carry over the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 28; Nays 16
AYES
Alexander Bright Bryant
Campbell Campsen Cleary
Courson Cromer Davis
Elliott Fair Grooms
Hayes Knotts Leatherman
Martin, L. Martin, S. Massey
McConnell Mulvaney O'Dell
Peeler Reese Rose
Ryberg Shoopman Thomas
Verdin
Total--28
NAYS
Anderson Coleman Hutto
Jackson Land Leventis
Lourie Malloy Matthews
McGill Nicholson Pinckney
Scott Setzler Sheheen
Williams
Total--16
The Bill was carried over.
THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE.
CARRIED OVER
H. 3301 (Word version) -- Reps. Harrell, Cato, Sandifer, Sellers, Neilson, Erickson, Bannister, Bedingfield, Merrill, Mitchell, Anthony, Bingham, Huggins, Vick, Cooper, Chalk, J.R. Smith, Willis, Gilliard, Allison, Anderson, Bales, Battle, Bowers, Brady, G.A. Brown, H.B. Brown, Cole, Daning, Duncan, Edge, Forrester, Gambrell, Gullick, Hamilton, Hayes, Herbkersman, Hiott, Jefferson, Horne, Kirsh, Limehouse, Littlejohn, Long, Lowe, Lucas, Miller, Millwood, Nanney, Ott, Owens, Parker, Pinson, E.H. Pitts, M.A. Pitts, Scott, Simrill, Skelton, D.C. Smith, G.R. Smith, Sottile, Spires, Stewart, Stringer, Thompson, Toole, Umphlett, White, Whitmire and Wylie: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 34-39-175 SO AS TO REQUIRE THE CONSUMER FINANCE DIVISION OF THE BOARD OF FINANCIAL INSTITUTIONS TO IMPLEMENT A REAL-TIME INTERNET ACCESSIBLE DATABASE FOR DEFERRED PRESENTMENT PROVIDERS TO VERIFY IF DEFERRED PRESENTMENT TRANSACTIONS ARE OUTSTANDING FOR A PARTICULAR PERSON; BY ADDING SECTION 34-39-270 SO AS TO PROHIBIT A DEFERRED PRESENTMENT PROVIDER FROM ENTERING INTO A DEFERRED PRESENTMENT TRANSACTION WITH A PERSON WHO HAS AN OUTSTANDING DEFERRED PRESENTMENT TRANSACTION OR WHO HAS ENTERED INTO AN EXTENDED PAYMENT PLAN AGREEMENT AND TO REQUIRE A DEFERRED PRESENTMENT PROVIDER TO VERIFY WHETHER AN INDIVIDUAL IS ELIGIBLE TO ENTER INTO A DEFERRED PRESENTMENT TRANSACTION; BY ADDING SECTION 34-39-280 SO AS TO REQUIRE THOSE APPLYING FOR LICENSES TO ENGAGE IN THE BUSINESS OF DEFERRED PRESENTMENT TO PROVIDE CERTAIN INFORMATION REGARDING EXTENDED PAYMENT PLANS; TO AMEND SECTION 34-39-130, RELATING TO LICENSURE REQUIREMENTS FOR DEFERRED PRESENTMENT PROVIDERS, SO AS TO PROHIBIT A PERSON FROM ENGAGING IN THE BUSINESS OF DEFERRED PRESENTMENT SERVICES WITH A RESIDENT OF SOUTH CAROLINA EXCEPT IN ACCORDANCE WITH THE PROVISIONS OF CHAPTER 39, TITLE 34; TO AMEND SECTION 34-39-180, RELATING TO DEFERRED PRESENTMENT RESTRICTIONS AND REQUIREMENTS, SO AS TO PROVIDE THAT THE TOTAL AMOUNT ADVANCED TO A CUSTOMER FOR DEFERRED PRESENTMENT OR DEPOSIT, EXCLUSIVE OF PERMISSIBLE FEES, MAY NOT EXCEED SIX HUNDRED DOLLARS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Banking and Insurance.
Senator L. MARTIN, as Chairman of the Committee on Rules and under the provision of Rule 14, polled the Committee on Rules on a motion to carry over H. 3301.
Poll of the Rules Committee
Polled 17; Ayes 10; Nays 7; Not Voting 0
AYES
Martin, L. McConnell Cromer
Leatherman Elliott Massey
Davis Martin, S. Rose
Shoopman
Total-- 10
NAYS
Reese Land Hutto
Matthews Knotts Malloy
Nicholson
Total-- 7
Senator L. MARTIN moved to carry over the Bill.
A roll call vote was ordered.
Senator LEVENTIS, with unanimous consent, was recognized to make brief remarks to the Senate.
The question then was the motion to carry over the Bill.
Parliamentary Inquiry
Senators KNOTTS and LOURIE made a Parliamentary Inquiry as to whether a roll call vote on the motion to carry over the Bill was the next order of business.
The PRESIDENT stated that a roll call vote on the motion to carry over the Bill was the next order of business inasmuch as Senator LEVENTIS had completed his remarks.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 26; Nays 17
AYES
Alexander Bright Bryant
Campbell Campsen Cleary
Courson Cromer Davis
Fair Grooms Hayes
Knotts Leatherman Martin, L.
Martin, S. Massey McConnell
Mulvaney Peeler Reese
Rose Ryberg Shoopman
Thomas Verdin
Total--26
NAYS
Anderson Coleman Elliott
Hutto Jackson Land
Leventis Lourie Malloy
Matthews McGill Nicholson
Pinckney Scott Setzler
Sheheen Williams
Total--17
The Bill was carried over.
THE SENATE PROCEEDED TO THE SPECIAL ORDERS.
AMENDED, CONSIDERATION INTERRUPTED
REMAINS IN THE STATUS OF SPECIAL ORDER
S. 424 (Word version) -- Senators Bright, S. Martin, Alexander, Campbell, Fair, Knotts, Cromer, Mulvaney, Verdin, L. Martin, Shoopman, Rose, McConnell, Thomas, Cleary, Courson, Coleman, Davis, Reese, Campsen, Grooms, Ryberg, Peeler, O'Dell, Bryant and Massey: A CONCURRENT RESOLUTION TO AFFIRM SOUTH CAROLINA'S SOVEREIGNTY UNDER THE TENTH AMENDMENT TO THE UNITED STATES CONSTITUTION OVER ALL POWERS NOT ENUMERATED AND GRANTED TO THE FEDERAL GOVERNMENT BY THE UNITED STATES CONSTITUTION.
The Senate proceeded to a consideration of the Concurrent Resolution, the question being the adoption of the Concurrent Resolution.
Senator BRIGHT asked unanimous consent to take up Amendment No. 6 for immediate consideration.
There was no objection.
Amendment No. 6
Senator BRIGHT proposed the following Amendment No. 6 (424R002.LB), which was adopted:
Amend the resolution, as and if amended, by striking it in its entirety and inserting:
/ /TO AFFIRM THE RIGHTS OF ALL STATES INCLUDING SOUTH CAROLINA BASED ON THE PROVISIONS OF THE NINTH AND TENTH AMENDMENTS TO THE UNITED STATES CONSTITUTION.
Whereas, the South Carolina General Assembly declares that the people of this State have the sole and exclusive right of governing themselves as a free, sovereign, and independent State, and shall exercise and enjoy every power, jurisdiction, and right pertaining thereto, which is not expressly delegated by them to the United States of America in the congress assembled; and
Whereas, some states when ratifying the Constitution for the United States of America recommended as a change, "that it be explicitly declared that all powers not expressly and particularly delegated by the aforesaid are reserved to the several states to be by them exercised"; and
Whereas, these recommended changes were incorporated as the Ninth Amendment, where the enumeration of certain rights shall not be construed to deny or disparage others retained by the people, and as the Tenth Amendment, where the powers not delegated to the United States by the constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people; and
Whereas, the several states of the United States of America, through the Constitution and the amendments thereto, constituted a general government for special purposes and delegated to that government certain definite powers, reserving each state to itself, the residuary right to their own self government. Now, therefore,
Be it resolved by the House of Representatives, the Senate concurring:
That the General Assembly of South Carolina, based on the above principles and provisions, hereby declares by this resolution, that any act by the Congress of the United States, Executive Order of the President of the United States, or Judicial Order by the federal courts which assumes a power not delegated to the government of the United States of America by the Constitution and which serves to diminish the liberty of any of the several states or their citizens shall abridge the Constitution. The General Assembly further declares that acts which would cause such an abridgment include, but are not limited to:
(1) establishing martial law or a state of emergency within one of the states comprising the United States of America without the consent of the legislature of that state;
(2) requiring involuntary servitude, or governmental service other than a draft during a declared war, or pursuant to, or as an alternative to, incarceration after due process of law;
(3) requiring involuntary servitude or governmental service of persons under the age of eighteen other than pursuant to, or as an alternative to, incarceration after due process of law;
(4) surrendering any power delegated or not delegated to any corporation or foreign government;
(5) any act regarding religion, further limitations on freedom of political speech, or further limitations on freedom of the press; and
(6) further infringements on the right to keep and bear arms including prohibitions of type or quantity of arms or ammunition.
Be it further resolved that a copy of this resolution be forwarded to the United States Senate, the United States House of Representatives, and each member of the South Carolina Congressional Delegation./
Senator BRIGHT explained the amendment.
PRESIDENT PRO TEMPORE PRESIDES
At 3:57 P.M., the PRESIDENT assumed the Chair.
Senator BRIGHT explained the amendment.
Senator BRIGHT moved that the amendment be adopted.
Senator HUTTO argued contra to the adoption of the amendment.
Senator CAMPSEN argued contra to the adoption of the amendment.
Recorded Vote
Senator SETZLER desired to be recorded as voting in favor of the adoption of the amendment.
Amendment No. 3
Senator HUTTO proposed the following amendment (TENTHAM3), which was tabled:
Amend the concurrent resolution, as and if amended, page 1, by striking line 34 and inserting:
/ Whereas, many federal mandates, such as those which created the United States Department of Education, Medicaid, and the United States Social Security Administration, are directly in violation of the /
Renumber sections to conform.
Amend title to conform.
Senator HUTTO explained the amendment.
Senator L. MARTIN moved to lay the amendment on the table.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 6
AYES
Alexander Anderson Bryant
Campbell Campsen Cleary
Coleman Courson Cromer
Davis Elliott Fair
Hayes Hutto Jackson
Knotts Leatherman Lourie
Malloy Martin, L. Martin, S.
Massey Matthews McConnell
McGill Nicholson O'Dell
Peeler Pinckney Rose
Setzler Sheheen Shoopman
Thomas Williams
Total--35
NAYS
Bright Land Leventis
Mulvaney Ryberg Verdin
Total--6
The amendment was laid on the table.
Amendment No. 5
Senator KNOTTS proposed the following Amendment No. 5 (JUD0424.003), which was adopted:
Amend the concurrent resolution, as and if amended, by striking all after the title and inserting therein the following:
/ Whereas, the Tenth Amendment to the United States Constitution provides that "powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people"; and
Whereas, the Tenth Amendment defines the limited scope of federal power as being that specifically granted by the United States Constitution; and
Whereas, the limited scope of authority defined by the Tenth Amendment means that the federal government was created by the states specifically to be an agent of the states; and
Whereas, currently the states are treated as agents of the federal government; and
Whereas, many federal mandates are directly in violation of the Tenth Amendment to the United States Constitution; and
Whereas, the United States Supreme Court has ruled that Congress may not simply commandeer the legislative and regulatory processes of the states; and
Whereas, pursuant to the Tenth Amendment, by limiting the scope of federal power to only those specifically enumerated in the United States Constitution, the states retain plenary power to govern, and
Whereas, included among all states' plenary power to govern is the broad authority of all state legislatures to appropriate funds for the operation of state agencies and to specify and direct the conditions under which appropriated funds shall be spent; and
Whereas, the General Assembly of the State of South Carolina has exercised its broad authority to appropriate and direct the expenditure of funds by appropriating and directing the expenditure of funds in the Fiscal Year 2009-2010 budget. Now, therefore,
Be it resolved by the Senate, the House of Representatives concurring:
That the General Assembly of the State of South Carolina, by this resolution, claims for the State of South Carolina sovereignty under the Tenth Amendment to the Constitution of the United States over all powers not otherwise enumerated and granted to the federal government by the United States Constitution.
Be it further resolved that all federal governmental agencies, quasi-governmental agencies, and their agents and employees operating within the geographic boundaries of the State of South Carolina, and all federal governmental agencies and their agents and employees, whose actions have effect on the inhabitants or lands or waters of the State of South Carolina, shall operate within the confines of the original intent of the Constitution of the United States and abide by the provisions of the Constitution of South Carolina, the South Carolina statutes, or the common law as guaranteed by the Constitution of the United States.
Be it further resolved that this resolution serves as notice and demand to the federal government, as South Carolina's agent, to cease and desist immediately all mandates that are beyond the scope of the federal government's constitutionally delegated powers.
Be it further resolved that copies of this resolution be forwarded to the President of the United States, the Speaker of the United States House of Representatives, the President of the United States Senate, and each member of South Carolina's Congressional Delegation, all at Washington, D.C., and to the Speaker of the House of Representatives and the President of the Senate of the legislatures of the other forty-nine states. /
Renumber sections to conform.
Amend title to conform.
Senator KNOTTS explained the amendment.
A roll call vote was ordered.
Point of Order
Senator MULVANEY raised a Point of Order that the amendment was divisible and each section should be voted on separately.
The PRESIDENT Pro Tempore overruled the Point of Order and stated that the Point of Order came too late inasmuch as a roll call vote had been ordered.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 28; Nays 17
AYES
Alexander Anderson Campbell
Coleman Cromer Elliott
Ford Hayes Hutto
Jackson Knotts Land
Leatherman Leventis Lourie
Malloy Martin, L. Matthews
McConnell McGill Nicholson
O'Dell Peeler Pinckney
Scott Setzler Sheheen
Williams
Total--28
NAYS
Bright Bryant Campsen
Cleary Courson Davis
Fair Grooms Martin, S.
Massey Mulvaney Reese
Rose Ryberg Shoopman
Thomas Verdin
Total--17
Amendment No. 9
Senator MALLOY proposed the following Amendment No. 9 (424R005.GM), which was adopted:
Amend the concurrent resolution, as and if amended, page 1, after line 35, by adding:
/ Whereas, the State recognizes that as an independent sovereign, that the State along with the other states of the union took part in an extensive collective bargaining process through the adoption of the Constitution and the various amendments thereto, and like any other party to any other agreement, the State is bound to uphold the terms and conditions of that agreement. Through this agreement, the states have collectively created the federal government, limiting the scope of its power and authority, as well as ensuring that certain fundamental rights are guaranteed. Also, through this process the states have collectively agreed to limit their own governmental authority by providing that the rights and protections afforded to the people as citizens of the United States are also extended to each person as a citizen of an individual state. Pursuant to that agreement, this State is bound to uphold the principals and protections afforded by all of the constitutional amendments, one of the most notable being the protections afforded by the Fourteenth Amendment which guarantees the privileges and immunities of the United States, due process of law, and equal protection under the law; and /
Renumber sections to conform.
Amend title to conform.
Senator MALLOY explained the amendment.
Recorded Vote
Senator VERDIN desired to be recorded as voting against the adoption of Amendment No. 9.
Amendment No. 10
Senator LEVENTIS proposed the following Amendment No. 10 (424R007.PPL), which was not adopted:
Amend the concurrent resolution, as and if amended, page 2, by striking line 25 - 31.
Renumber sections to conform.
Amend title to conform.
Senator LEVENTIS explained the amendment.
Senator LEVENTIS moved that the amendment be adopted.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 11; Nays 31
AYES
Anderson Coleman Ford
Hutto Land Leventis
Malloy Matthews Pinckney
Scott Sheheen
Total--11
NAYS
Alexander Bright Bryant
Campbell Campsen Cleary
Courson Cromer Elliott
Fair Grooms Hayes
Knotts Leatherman Martin, L.
Martin, S. Massey McConnell
McGill Mulvaney Nicholson
O'Dell Peeler Reese
Rose Ryberg Setzler
Shoopman Thomas Verdin
Williams
Total--31
The question then was the adoption of the Concurrent Resolution.
Senator HUTTO spoke on the Concurrent Resolution.
Motion Under Rule 15A Failed
At 4:52 P.M., Senator L. MARTIN moved under the provisions of Rule 15A to vote on the entire matter of S. 424.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 22; Nays 22
AYES
Alexander Bright Bryant
Campbell Campsen Cleary
Courson Cromer Davis
Fair Grooms Hayes
Martin, L. Martin, S. Massey
Mulvaney Peeler Rose
Ryberg Shoopman Thomas
Verdin
Total--22
NAYS
Anderson Coleman Elliott
Ford Hutto Jackson
Knotts Land Leventis
Lourie Malloy Matthews
McConnell McGill Nicholson
O'Dell Pinckney Reese
Scott Setzler Sheheen
Williams
Total--22
Having failed to receive the necessary vote, the motion under Rule 15A failed.
Senator HUTTO resumed speaking on the Concurrent Resolution.
ACTING PRESIDENT PRESIDES
At 5:34 P.M., Senator L. MARTIN assumed the Chair.
Senator HUTTO resumed speaking on the Concurrent Resolution.
ACTING PRESIDENT PRESIDES
At 5:34 P.M., Senator L. MARTIN assumed the Chair.
Senator HUTTO resumed speaking on the Concurrent Resolution.
PRESIDENT PRESIDES
At 5:47 P.M., the PRESIDENT assumed the Chair.
Senator HUTTO resumed speaking on the Concurrent Resolution.
Senator HUTTO moved that the Senate stand adjourned.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 22; Nays 21
AYES
Anderson Elliott Ford
Hutto Jackson Knotts
Land Leatherman Leventis
Lourie Malloy Matthews
McGill Nicholson O'Dell
Pinckney Rankin Reese
Scott Setzler Sheheen
Williams
Total--22
NAYS
Alexander Bright Bryant
Campbell Campsen Cleary
Courson Cromer Davis
Fair Grooms Hayes
Martin, L. Martin, S. Massey
Mulvaney Peeler Rose
Shoopman Thomas Verdin
Total--21
On behalf of the President Pro Tempore, Senator L. MARTIN moved that, when the Senate adjourns today, it stand adjourned to meet tomorrow at 10:30 A.M.
Expression of Personal Interest
Senator BRIGHT rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator KNOTTS rose for an Expression of Personal Interest.
Consideration was interrupted by adjournment. The Concurrent Resolution remained in the status of Special Order.
LOCAL APPOINTMENT
Confirmation
Having received a favorable report from the Senate, the following appointment was confirmed in open session:
Initial Appointment, Oconee County Magistrate, with the term to commence April 30, 2006, and to expire April 30, 2010
Michael Todd Simmons, P.O. Box 130, Long Creek, SC 29658 VICE Becky Gerrard
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https://dlmf.nist.gov/2.6
|
# §2.6 Distributional Methods
## §2.6(i) Divergent Integrals
Consider the integral
2.6.1 $S(x)=\int_{0}^{\infty}\frac{1}{(1+t)^{1/3}(x+t)}\mathrm{d}t,$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral and $S(x)$: integral Referenced by: §2.6(i) Permalink: http://dlmf.nist.gov/2.6.E1 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
where $x>0$. For $t>1$,
2.6.2 $(1+t)^{-1/3}=\sum_{s=0}^{\infty}\genfrac{(}{)}{0.0pt}{}{-\frac{1}{3}}{s}t^{-s-% (1/3)}.$ ⓘ Symbols: $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$: binomial coefficient Referenced by: §2.6(i) Permalink: http://dlmf.nist.gov/2.6.E2 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
Motivated by Watson’s lemma (§2.3(ii)), we substitute (2.6.2) in (2.6.1), and integrate term by term. This leads to integrals of the form
2.6.3 $\int_{0}^{\infty}\frac{t^{-s-(1/3)}}{x+t}\mathrm{d}t,$ $s=1,2,3,\dots$. ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential and $\int$: integral Permalink: http://dlmf.nist.gov/2.6.E3 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
Although divergent, these integrals may be interpreted in a generalized sense. For instance, we have
2.6.4 $\int_{0}^{\infty}\frac{t^{\alpha-1}}{(x+t)^{\alpha+\beta}}\mathrm{d}t=\frac{% \Gamma\left(\alpha\right)\Gamma\left(\beta\right)}{\Gamma\left(\alpha+\beta% \right)}\frac{1}{x^{\beta}},$ $\Re\alpha>0$, $\Re\beta>0$. ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathrm{d}\NVar{x}$: differential, $\int$: integral and $\Re$: real part Referenced by: §2.6(i) Permalink: http://dlmf.nist.gov/2.6.E4 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
But the right-hand side is meaningful for all values of $\alpha$ and $\beta$, other than nonpositive integers. We may therefore define the integral on the left-hand side of (2.6.4) by the value on the right-hand side, except when $\alpha,\beta=0,-1,-2,\dots$. With this interpretation
2.6.5 $\int_{0}^{\infty}\frac{t^{-s-(1/3)}}{x+t}\mathrm{d}t=\frac{2\pi}{\sqrt{3}}% \frac{(-1)^{s}}{x^{s+(1/3)}},$ $s=0,1,2,\dots$. ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential and $\int$: integral Permalink: http://dlmf.nist.gov/2.6.E5 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
Inserting (2.6.2) into (2.6.1) and integrating formally term-by-term, we obtain
2.6.6 $S(x)\sim\frac{2\pi}{\sqrt{3}}\sum_{s=0}^{\infty}(-1)^{s}{\genfrac{(}{)}{0.0pt}% {}{-\frac{1}{3}}{s}}x^{-s-(1/3)},$ $x\to\infty$. ⓘ Symbols: $\sim$: Poincaré asymptotic expansion, $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$: binomial coefficient, $\pi$: the ratio of the circumference of a circle to its diameter and $S(x)$: integral Referenced by: §2.6(i) Permalink: http://dlmf.nist.gov/2.6.E6 Encodings: TeX, pMML, png See also: Annotations for §2.6(i), §2.6 and Ch.2
However this result is incorrect. The correct result is given by
2.6.7 $S(x)\sim\frac{2\pi}{\sqrt{3}}\sum_{s=0}^{\infty}(-1)^{s}{\genfrac{(}{)}{0.0pt}% {}{-\frac{1}{3}}{s}}x^{-s-(1/3)}-\sum_{s=1}^{\infty}\frac{3^{s}(s-1)!}{2\cdot 5% \cdots(3s-1)}x^{-s};$
see §2.6(ii).
The fact that expansion (2.6.6) misses all the terms in the second series in (2.6.7) raises the question: what went wrong with our process of reaching (2.6.6)? In the following subsections, we use some elementary facts of distribution theory (§1.16) to study the proper use of divergent integrals. An important asset of the distribution method is that it gives explicit expressions for the remainder terms associated with the resulting asymptotic expansions.
For an introduction to distribution theory, see Wong (1989, Chapter 5). For more advanced discussions, see Gel’fand and Shilov (1964) and Rudin (1973).
## §2.6(ii) Stieltjes Transform
Let $f(t)$ be locally integrable on $[0,\infty)$. The Stieltjes transform of $f(t)$ is defined by
2.6.8 $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\int_{0}^{\infty}\frac{f(% t)}{t+z}\mathrm{d}t.$ ⓘ Symbols: $\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Stieltjes transform, $\mathrm{d}\NVar{x}$: differential, $\int$: integral and $f(t)$: locally integrable function Referenced by: §2.6(ii) Permalink: http://dlmf.nist.gov/2.6.E8 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Stieltjes transform was changed to $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathcal{S}(f;z)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
To derive an asymptotic expansion of $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ for large values of $|z|$, with $|\operatorname{ph}z|<\pi$, we assume that $f(t)$ possesses an asymptotic expansion of the form
2.6.9 $f(t)\sim\sum_{s=0}^{\infty}a_{s}t^{-s-\alpha},$ $t\to+\infty$, ⓘ Symbols: $\sim$: Poincaré asymptotic expansion, $f(t)$: locally integrable function and $a_{n}$: coefficients Referenced by: §2.6(iii), §2.6(ii), §2.6(iii), §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E9 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
with $0<\alpha\leq 1$. For each $n=1,2,3,\dots$, set
2.6.10 $f(t)=\sum_{s=0}^{n-1}a_{s}t^{-s-\alpha}+f_{n}(t).$ ⓘ Defines: $f_{n}(t)$: remainder (locally) Symbols: $f(t)$: locally integrable function, $a_{n}$: coefficients and $n$: nonnegative integer Referenced by: §2.6(iii), §2.6(ii) Permalink: http://dlmf.nist.gov/2.6.E10 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
To each function in this equation, we shall assign a tempered distribution (i.e., a continuous linear functional) on the space $\mathcal{T}$ of rapidly decreasing functions on $\mathbb{R}$. Since $f(t)$ is locally integrable on $[0,\infty)$, it defines a distribution by
2.6.11 $\left\langle f,\phi\right\rangle=\int_{0}^{\infty}f(t)\phi(t)\mathrm{d}t,$ $\phi\in\mathcal{T}$.
In particular,
2.6.12 $\left\langle t^{-\alpha},\phi\right\rangle=\int_{0}^{\infty}t^{-\alpha}\phi(t)% \mathrm{d}t,$ $\phi\in\mathcal{T}$,
when $0<\alpha<1$. Since the functions $t^{-s-\alpha}$, $s=1,2,\dots$, are not locally integrable on $[0,\infty)$, we cannot assign distributions to them in a similar manner. However, they are multiples of the derivatives of $t^{-\alpha}$. Motivated by the definition of distributional derivatives, we can assign them the distributions defined by
2.6.13 $\left\langle t^{-s-\alpha},\phi\right\rangle=\frac{1}{{\left(\alpha\right)_{s}% }}\int_{0}^{\infty}t^{-\alpha}\phi^{(s)}(t)\mathrm{d}t,$ $\phi\in\mathcal{T}$,
where ${\left(\alpha\right)_{s}}=\alpha(\alpha+1)\cdots(\alpha+s-1)$. Similarly, in the case $\alpha=1$, we define
2.6.14 $\left\langle t^{-s-1},\phi\right\rangle=-\frac{1}{s!}\int_{0}^{\infty}(\ln t)% \phi^{(s+1)}(t)\mathrm{d}t,$ $\phi\in\mathcal{T}$.
To assign a distribution to the function $f_{n}(t)$, we first let $f_{n,n}(t)$ denote the $n$th repeated integral (§1.4(v)) of $f_{n}$:
2.6.15 $f_{n,n}(t)=\frac{(-1)^{n}}{(n-1)!}\int_{t}^{\infty}(\tau-t)^{n-1}f_{n}(\tau)% \mathrm{d}\tau.$ ⓘ Defines: $f_{n,n}(t)$: $n$th repeated integral (locally) Symbols: $\mathrm{d}\NVar{x}$: differential, $!$: factorial (as in $n!$), $\int$: integral, $n$: nonnegative integer and $f_{n}(t)$: remainder Referenced by: §2.6(ii), §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E15 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
For $0<\alpha<1$, it is easily seen that $f_{n,n}(t)$ is bounded on $[0,R]$ for any positive constant $R$, and is $O\left(t^{-\alpha}\right)$ as $t\to\infty$. For $\alpha=1$, we have $f_{n,n}(t)=O\left(t^{-1}\right)$ as $t\to\infty$ and $f_{n,n}(t)=O\left(\ln t\right)$ as $t\to 0+$. In either case, we define the distribution associated with $f_{n}(t)$ by
2.6.16 $\left\langle f_{n},\phi\right\rangle=(-1)^{n}\int_{0}^{\infty}f_{n,n}(t)\phi^{% (n)}(t)\mathrm{d}t,$ $\phi\in\mathcal{T}$,
since the $n$th derivative of $f_{n,n}$ is $f_{n}$.
We have now assigned a distribution to each function in (2.6.10). A natural question is: what is the exact relation between these distributions? The answer is provided by the identities (2.6.17) and (2.6.20) given below.
For $0<\alpha<1$ and $n\geq 1$, we have
2.6.17 ${\left\langle f,\phi\right\rangle}=\sum_{s=0}^{n-1}a_{s}\left\langle t^{-s-% \alpha},\phi\right\rangle-\sum_{s=1}^{n}c_{s}\left\langle{\delta}^{(s-1)},\phi% \right\rangle+\left\langle f_{n},\phi\right\rangle$
for any $\phi\in\mathcal{T}$, where
2.6.18 $c_{s}=\frac{(-1)^{s}}{(s-1)!}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s% \right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $!$: factorial (as in $n!$), $c\neq 0$: real and $f(t)$: locally integrable function Keywords: Mellin transform Referenced by: §2.6(ii) Permalink: http://dlmf.nist.gov/2.6.E18 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
$\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ being the Mellin transform of $f(t)$ or its analytic continuation (§2.5(ii)). The Dirac delta distribution in (2.6.17) is given by
2.6.19 $\left\langle{\delta}^{(s)},\phi\right\rangle=(-1)^{s}\phi^{(s)}(0),$ $s=0,1,2,\dots$; ⓘ Symbols: $\delta\left(\NVar{x-a}\right)$: Dirac delta (or Dirac delta function) and $\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle$: inner-product of distribution Permalink: http://dlmf.nist.gov/2.6.E19 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
compare §1.16(iii).
For $\alpha=1$
2.6.20 ${\left\langle f,\phi\right\rangle}=\sum_{s=0}^{n-1}a_{s}\left\langle t^{-s-1},% \phi\right\rangle-\sum_{s=1}^{n}d_{s}\left\langle{\delta}^{(s-1)},\phi\right% \rangle+\left\langle f_{n},\phi\right\rangle$
for any $\phi\in\mathcal{T}$, where
2.6.21 $(-1)^{s+1}d_{s+1}=\frac{a_{s}}{s!}\sum_{k=1}^{s}\frac{1}{k}+\frac{1}{s!}\lim_{% z\to s+1}\left(\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)+\frac{a_{s% }}{z-s-1}\right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $!$: factorial (as in $n!$), $d_{s}$: coefficients, $f(t)$: locally integrable function and $a_{n}$: coefficients Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.6.E21 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
for $s=0,1,2,\dots$.
To apply the results (2.6.17) and (2.6.20) to the Stieltjes transform (2.6.8), we take a specific function $\phi\in\mathcal{T}$. Let $\varepsilon$ be a positive number, and
2.6.22 $\phi_{\varepsilon}(t)=\frac{e^{-\varepsilon t}}{t+z},$ $t\in(0,\infty)$. ⓘ Symbols: $\in$: element of, $\mathrm{e}$: base of natural logarithm, $(\NVar{a},\NVar{b})$: open interval and $\varepsilon$: small positive number Permalink: http://dlmf.nist.gov/2.6.E22 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
From (2.6.13) and (2.6.14)
2.6.23 $\lim_{\varepsilon\to 0}\left\langle t^{-s-\alpha},\phi_{\varepsilon}\right% \rangle=\frac{\pi}{\sin\left(\pi\alpha\right)}\frac{(-1)^{s}}{z^{s+\alpha}},$
2.6.24 $\lim_{\varepsilon\to 0}\left\langle t^{-s-1},\phi_{\varepsilon}\right\rangle=% \frac{(-1)^{s+1}}{z^{s+1}}\sum_{k=1}^{s}\frac{1}{k}+\frac{(-1)^{s}}{z^{s+1}}% \ln z,$
with $s=0,1,2,\dots$. From (2.6.11) and (2.6.16), we also have
2.6.25 $\lim_{\varepsilon\to 0}\left\langle f,\phi_{\varepsilon}\right\rangle=\mathcal% {S}\mskip-3.0mu f\mskip 3.0mu \left(z\right),$ ⓘ Symbols: $\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Stieltjes transform, $\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle$: inner-product of distribution, $\varepsilon$: small positive number and $f(t)$: locally integrable function Permalink: http://dlmf.nist.gov/2.6.E25 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Stieltjes transform was changed to $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathcal{S}(f;z)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
2.6.26 $\lim_{\varepsilon\to 0}\left\langle f_{n},\phi_{\varepsilon}\right\rangle=n!% \int_{0}^{\infty}\frac{f_{n,n}(t)}{(t+z)^{n+1}}\mathrm{d}t.$
On substituting (2.6.15) into (2.6.26) and interchanging the order of integration, the right-hand side of (2.6.26) becomes
$\frac{(-1)^{n}}{z^{n}}\int_{0}^{\infty}\frac{\tau^{n}f_{n}(\tau)}{\tau+z}% \mathrm{d}\tau.$
To summarize,
2.6.27 $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\frac{\pi}{\sin\left(\pi% \alpha\right)}\sum_{s=0}^{n-1}(-1)^{s}\frac{a_{s}}{z^{s+\alpha}}-\sum_{s=1}^{n% }(s-1)!\frac{c_{s}}{z^{s}}+R_{n}(z),$ ⓘ Symbols: $\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Stieltjes transform, $\pi$: the ratio of the circumference of a circle to its diameter, $!$: factorial (as in $n!$), $\sin\NVar{z}$: sine function, $R_{n}(z)$: remainder, $c\neq 0$: real, $f(t)$: locally integrable function, $a_{n}$: coefficients and $n$: nonnegative integer Referenced by: §2.6(ii) Permalink: http://dlmf.nist.gov/2.6.E27 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Stieltjes transform was changed to $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathcal{S}(f;z)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
if $\alpha\in(0,1)$ in (2.6.9), or
2.6.28 $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\ln z\sum_{s=0}^{n-1}(-1)% ^{s}\frac{a_{s}}{z^{s+1}}+\sum_{s=0}^{n-1}(-1)^{s}\frac{\widetilde{d}_{s}}{z^{% s+1}}+R_{n}(z),$ ⓘ Symbols: $\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Stieltjes transform, $\ln\NVar{z}$: principal branch of logarithm function, $R_{n}(z)$: remainder, $f(t)$: locally integrable function, $a_{n}$: coefficients and $n$: nonnegative integer Permalink: http://dlmf.nist.gov/2.6.E28 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Stieltjes transform was changed to $\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathcal{S}(f;z)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
if $\alpha=1$ in (2.6.9). Here $c_{s}$ is given by (2.6.18),
2.6.29 $\widetilde{d}_{s}=\lim_{z\to s+1}\left(\mathscr{M}\mskip-3.0mu f\mskip 3.0mu % \left(z\right)+\frac{a_{s}}{z-s-1}\right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(t)$: locally integrable function and $a_{n}$: coefficients Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.6.E29 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.6(ii), §2.6 and Ch.2
and
2.6.30 $R_{n}(z)=\frac{(-1)^{n}}{z^{n}}\int_{0}^{\infty}\frac{\tau^{n}f_{n}(\tau)}{% \tau+z}\mathrm{d}\tau.$ ⓘ
The expansion (2.6.7) follows immediately from (2.6.27) with $z=x$ and $f(t)=(1+t)^{-(1/3)}$; its region of validity is $|\operatorname{ph}x|\leq\pi-\delta$ ($<\pi$). The distribution method outlined here can be extended readily to functions $f(t)$ having an asymptotic expansion of the form
2.6.31 $f(t)\sim e^{ict}\sum_{s=0}^{\infty}a_{s}t^{-s-\alpha},$ $t\to+\infty$,
where $c$ ($\neq 0$) is real, and $0<\alpha\leq 1$. For a more detailed discussion of the derivation of asymptotic expansions of Stieltjes transforms by the distribution method, see McClure and Wong (1978) and Wong (1989, Chapter 6). Corresponding results for the generalized Stieltjes transform
2.6.32 $\int_{0}^{\infty}\frac{f(t)}{(t+z)^{\rho}}\mathrm{d}t,$ $\rho>0$, ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral and $f(t)$: locally integrable function Permalink: http://dlmf.nist.gov/2.6.E32 Encodings: TeX, pMML, png See also: Annotations for §2.6(ii), §2.6 and Ch.2
can be found in Wong (1979). An application has been given by López (2000) to derive asymptotic expansions of standard symmetric elliptic integrals, complete with error bounds; see §19.27(vi).
## §2.6(iii) Fractional Integrals
The Riemann–Liouville fractional integral of order $\mu$ is defined by
2.6.33 $I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}\int_{0}^{x}(x-t)^{\mu-1}f(t)% \mathrm{d}t,$ $\mu>0$; ⓘ Defines: $I^{\mu}$: fractional integral (locally) Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $\mu$: order and $f(t)$: locally integrable function Referenced by: §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E33 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
see §1.15(vi). We again assume $f(t)$ is locally integrable on $[0,\infty)$ and satisfies (2.6.9). We now derive an asymptotic expansion of $I^{\mu}f(x)$ for large positive values of $x$.
In terms of the convolution product
2.6.34 $(f\ast g)(x)=\int_{0}^{x}f(x-t)g(t)\mathrm{d}t$ ⓘ Defines: $\ast$: convolution (locally) Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $g(t)$: locally integrable function and $f(t)$: locally integrable function Referenced by: §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E34 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
of two locally integrable functions on $[0,\infty)$, (2.6.33) can be written
2.6.35 $I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}(t^{\mu-1}\ast f)(x).$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mu$: order, $I^{\mu}$: fractional integral , $\ast$: convolution and $f(t)$: locally integrable function Referenced by: §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E35 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
The replacement of $f(t)$ by its asymptotic expansion (2.6.9), followed by term-by-term integration leads to convolution integrals of the form
2.6.36 $(t^{\mu-1}\ast t^{-s-\alpha})(x)=\int_{0}^{x}(x-t)^{\mu-1}t^{-s-\alpha}\mathrm% {d}t,$ $s=0,1,2,\dots$. ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $\mu$: order and $\ast$: convolution Permalink: http://dlmf.nist.gov/2.6.E36 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
Of course, except when $s=0$ and $0<\alpha<1$, none of these integrals exists in the usual sense. However, the left-hand side can be considered as the convolution of the two distributions associated with the functions $t^{\mu-1}$ and $t^{-s-\alpha}$, given by (2.6.12) and (2.6.13).
To define convolutions of distributions, we first introduce the space $K^{+}$ of all distributions of the form $D^{n}f$, where $n$ is a nonnegative integer, $f$ is a locally integrable function on $\mathbb{R}$ which vanishes on $(-\infty,0]$, and $D^{n}f$ denotes the $n$th derivative of the distribution associated with $f$. For $F=D^{n}f$ and $G=D^{m}g$ in $K^{+}$, we define
2.6.37 $F\ast G=D^{n+m}(f\ast g).$
It is easily seen that $K^{+}$ forms a commutative, associative linear algebra. Furthermore, $K^{+}$ contains the distributions $H$, $\delta$, and $t^{\lambda}$, $t>0$, for any real (or complex) number $\lambda$, where $H$ is the distribution associated with the Heaviside function $H\left(t\right)$1.16(iv)), and $t^{\lambda}$ is the distribution defined by (2.6.12)–(2.6.14), depending on the value of $\lambda$. Since $\delta=DH$, it follows that for $\mu\neq 1,2,\dots$,
2.6.38 $t^{\mu-1}\ast{\delta}^{(s-1)}=\frac{\Gamma\left(\mu\right)}{\Gamma\left(\mu+1-% s\right)}t^{\mu-s},$ $t>0$. ⓘ Symbols: $\delta\left(\NVar{x-a}\right)$: Dirac delta (or Dirac delta function), $\Gamma\left(\NVar{z}\right)$: gamma function, $\mu$: order and $\ast$: convolution Referenced by: §2.6(iii) Permalink: http://dlmf.nist.gov/2.6.E38 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
Using (5.12.1), we can also show that when $\mu\neq 1,2,\dots$ and $\mu-\alpha$ is not a nonnegative integer,
2.6.39 $t^{\mu-1}\ast t^{-s-\alpha}=\frac{\Gamma\left(\mu\right)\Gamma\left(1-s-\alpha% \right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu-s-\alpha},$ $t>0$, ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mu$: order and $\ast$: convolution Permalink: http://dlmf.nist.gov/2.6.E39 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6 and Ch.2
and
2.6.40 $t^{\mu-1}\ast t^{-s-1}=\frac{(-1)^{s}}{\mu\cdot s!}D^{s+1}\left(t^{\mu}\left(% \ln t-\gamma-\psi\left(\mu+1\right)\right)\right),$ $t>0$,
where $\gamma$ is Euler’s constant (§5.2(ii)).
To derive the asymptotic expansion of $I^{\mu}f(x)$, we recall equations (2.6.17) and (2.6.20). In the sense of distributions, they can be written
2.6.41 $f=\sum_{s=0}^{n-1}a_{s}t^{-s-\alpha}-\sum_{s=1}^{n}c_{s}{\delta}^{(s-1)}+f_{n},$
and
2.6.42 $f=\sum_{s=0}^{n-1}a_{s}t^{-s-1}-\sum_{s=1}^{n}d_{s}{\delta}^{(s-1)}+f_{n}.$
Substituting into (2.6.35) and using (2.6.38)–(2.6.40), we obtain
2.6.43 $t^{\mu-1}\ast f=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma\left(\mu\right)\Gamma\left(1% -s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu-s-\alpha}-\sum_{s=1% }^{n}c_{s}\frac{\Gamma\left(\mu\right)}{\Gamma\left(\mu-s+1\right)}t^{\mu-s}+t% ^{\mu-1}\ast f_{n}$
when $0<\alpha<1$, or
2.6.44 $t^{\mu-1}\ast f=\sum_{s=0}^{n-1}\frac{(-1)^{s}a_{s}}{\mu\cdot s!}D^{s+1}\left(% t^{\mu}\left(\ln t-\gamma-\psi\left(\mu+1\right)\right)\right)-\sum_{s=1}^{n}d% _{s}\frac{\Gamma\left(\mu\right)}{\Gamma\left(\mu-s+1\right)}t^{\mu-s}+t^{\mu-% 1}\ast f_{n}$
when $\alpha=1$. These equations again hold only in the sense of distributions. Since the function $t^{\mu}\left(\ln t-\gamma-\psi\left(\mu+1\right)\right)$ and all its derivatives are locally absolutely continuous in $(0,\infty)$, the distributional derivatives in the first sum in (2.6.44) can be replaced by the corresponding ordinary derivatives. Furthermore, since $f_{n,n}^{(n)}(t)=f_{n}(t)$, it follows from (2.6.37) that the remainder terms $t^{\mu-1}\ast f_{n}$ in the last two equations can be associated with a locally integrable function in $(0,\infty)$. On replacing the distributions by their corresponding functions, (2.6.43) and (2.6.44) give
2.6.45 $I^{\mu}f(x)=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma\left(1-s-\alpha\right)}{\Gamma% \left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-\sum_{s=1}^{n}\frac{c_{s}}{\Gamma% \left(\mu+1-s\right)}x^{\mu-s}+\frac{1}{x^{n}}\delta_{n}(x),$
when $0<\alpha<1$, or
2.6.46 $I^{\mu}f(x)=\sum_{s=0}^{n-1}\frac{(-1)^{s}a_{s}}{s!\Gamma\left(\mu+1\right)}% \frac{{\mathrm{d}}^{s+1}}{{\mathrm{d}x}^{s+1}}\left(x^{\mu}\left(\ln x-\gamma-% \psi\left(\mu+1\right)\right)\right)-\sum_{s=1}^{n}\frac{d_{s}}{\Gamma\left(% \mu-s+1\right)}x^{\mu-s}+\frac{1}{x^{n}}\delta_{n}(x),$
when $\alpha=1$, where
2.6.47 $\delta_{n}(x)=\sum_{j=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{j}\frac{\Gamma\left(\mu% +1\right)}{\Gamma\left(\mu+1-j\right)}I^{\mu}\left(t^{n-j}f_{n,j}\right)(x),$
$f_{n,j}(t)$ being the $j$th repeated integral of $f_{n}$; compare (2.6.15).
### Example
Let $f(t)=t^{1-\alpha}/(1+t)$, $0<\alpha<1$. Then
2.6.48 $I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}\int_{0}^{x}(x-t)^{\mu-1}t^{1-% \alpha}(1+t)^{-1}\mathrm{d}t,$
where $\mu>0$. For $0
2.6.49 $f(t)=\sum_{s=0}^{n-1}(-1)^{s}t^{-s-\alpha}+(-1)^{n}\frac{t^{1-n-\alpha}}{1+t}.$ ⓘ Symbols: $f(t)$: locally integrable function and $n$: nonnegative integer Permalink: http://dlmf.nist.gov/2.6.E49 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6(iii), §2.6 and Ch.2
In the notation of (2.6.10), $a_{s}=(-1)^{s}$ and
2.6.50 $f_{n}(t)=(-1)^{n}\frac{t^{1-n-\alpha}}{1+t}.$ ⓘ Symbols: $n$: nonnegative integer and $f_{n}(t)$: remainder Permalink: http://dlmf.nist.gov/2.6.E50 Encodings: TeX, pMML, png See also: Annotations for §2.6(iii), §2.6(iii), §2.6 and Ch.2
Since
2.6.51 $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)=(-1)^{s}\pi/\sin\left(\pi% \alpha\right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\sin\NVar{z}$: sine function and $f(t)$: locally integrable function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.6.E51 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(iii), §2.6(iii), §2.6 and Ch.2
from (2.6.45) it follows that
2.6.52 $I^{\mu}f(x)=\sum_{s=0}^{n-1}(-1)^{s}\frac{\Gamma\left(1-s-\alpha\right)}{% \Gamma\left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-\frac{\pi}{\sin\left(\pi% \alpha\right)}\sum_{s=1}^{n}\frac{1}{\Gamma\left(\mu+1-s\right)}\frac{x^{\mu-s% }}{(s-1)!}+\frac{1}{x^{n}}\delta_{n}(x).$
Moreover,
2.6.53 ${\left|\delta_{n}(x)\right|}\leq\frac{\Gamma\left(\mu+1\right)\Gamma\left(1-% \alpha\right)}{\Gamma\left(\mu+1-\alpha\right)\Gamma\left(n+\alpha\right)}\*% \sum_{j=0}^{n}\dbinom{n}{j}\frac{\Gamma\left(n+\alpha-j\right)}{\left|\Gamma% \left(\mu+1-j\right)\right|}x^{\mu-\alpha}$
for $x>0$.
It may be noted that the integral (2.6.48) can be expressed in terms of the hypergeometric function ${{}_{2}F_{1}}\left(1,2-\alpha;2-\alpha+\mu;-x\right)$; see §15.2(i).
For proofs and other examples, see McClure and Wong (1979) and Wong (1989, Chapter 6). If both $f$ and $g$ in (2.6.34) have asymptotic expansions of the form (2.6.9), then the distribution method can also be used to derive an asymptotic expansion of the convolution $f\ast g$; see Li and Wong (1994).
## §2.6(iv) Regularization
The method of distributions can be further extended to derive asymptotic expansions for convolution integrals:
2.6.54 $I(x)=\int_{0}^{\infty}f(t)h(xt)\mathrm{d}t.$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $f(t)$: locally integrable function, $I(x)$: convolution integral and $h(x)$: function Referenced by: §2.6(iv) Permalink: http://dlmf.nist.gov/2.6.E54 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
We assume that for each $n=1,2,3,\dots$,
2.6.55 $f(t)=\sum_{s=0}^{n-1}a_{s}t^{s+\alpha-1}+f_{n}(t),$ ⓘ Symbols: $f(t)$: locally integrable function, $n$: positive integer, $a_{n}$: coefficients and $f_{n}(t)$: remainder Referenced by: §2.6(iv) Permalink: http://dlmf.nist.gov/2.6.E55 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
where $0<\alpha\leq 1$ and $f_{n}(t)=O\left(t^{n+\alpha-1}\right)$ as $t\to 0+$. Also,
2.6.56 $h(t)=\sum_{s=0}^{n-1}b_{s}t^{-s-\beta}+h_{n}(t),$ ⓘ Symbols: $n$: positive integer, $b_{n}$: coefficients and $h(x)$: function Permalink: http://dlmf.nist.gov/2.6.E56 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
where $0<\beta\leq 1$, and $h_{n}(t)=O\left(t^{-n-\beta}\right)$ as $t\to\infty$. Multiplication of these expansions leads to
2.6.57 $f(t)h(xt)=\sum_{j=0}^{n-1}\sum_{k=0}^{n-1}a_{j}b_{k}t^{j+\alpha-1-k-\beta}x^{-% k-\beta}+\sum_{j=0}^{n-1}a_{j}t^{j+\alpha-1}h_{n}(xt)+\sum_{k=0}^{n-1}b_{k}x^{% -k-\beta}t^{-k-\beta}f_{n}(t)+f_{n}(t)h_{n}(xt).$ ⓘ Symbols: $f(t)$: locally integrable function, $n$: positive integer, $a_{n}$: coefficients, $b_{n}$: coefficients, $h(x)$: function and $f_{n}(t)$: remainder Referenced by: §2.6(iv) Permalink: http://dlmf.nist.gov/2.6.E57 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
On inserting this identity into (2.6.54), we immediately encounter divergent integrals of the form
2.6.58 $\int_{0}^{\infty}t^{\lambda}\mathrm{d}t,$ $\lambda\in\mathbb{R}$. ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\in$: element of, $\int$: integral and $\mathbb{R}$: real line Permalink: http://dlmf.nist.gov/2.6.E58 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
However, in the theory of generalized functions (distributions), there is a method, known as “regularization”, by which these integrals can be interpreted in a meaningful manner. In this sense
2.6.59 $\int_{0}^{\infty}t^{\lambda}\mathrm{d}t=0,$ $\lambda\in\mathbb{C}$. ⓘ Symbols: $\mathbb{C}$: complex plane, $\mathrm{d}\NVar{x}$: differential, $\in$: element of and $\int$: integral Referenced by: §2.6(iv) Permalink: http://dlmf.nist.gov/2.6.E59 Encodings: TeX, pMML, png See also: Annotations for §2.6(iv), §2.6 and Ch.2
From (2.6.55) and (2.6.59)
2.6.60 $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\mathscr{M}\mskip-3.0mu f% _{n}\mskip 3.0mu \left(z\right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(t)$: locally integrable function, $n$: positive integer and $f_{n}(t)$: remainder Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.6.E60 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(iv), §2.6 and Ch.2
where $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ is the Mellin transform of $f$ or its analytic continuation. Also, when $\alpha\neq\beta$,
2.6.61 $\mathscr{M}\mskip-3.0mu h_{x}\mskip 3.0mu \left(j+\alpha\right)=x^{-j-\alpha}% \mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(j+\alpha\right),$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(t)$: locally integrable function and $h(x)$: function Keywords: Mellin transform Referenced by: §2.6(iv) Permalink: http://dlmf.nist.gov/2.6.E61 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(iv), §2.6 and Ch.2
where $h_{x}(t)=h(xt)$. Inserting (2.6.57) into (2.6.54), we obtain from (2.6.59)–(2.6.61)
2.6.62 $I(x)=\sum_{j=0}^{n-1}a_{j}\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(j+\alpha% \right)x^{-j-\alpha}+\sum_{k=0}^{n-1}b_{k}\mathscr{M}\mskip-3.0mu f\mskip 3.0% mu \left(1-k-\beta\right)x^{-k-\beta}+\delta_{n}(x)$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(t)$: locally integrable function, $I(x)$: convolution integral, $n$: positive integer, $a_{n}$: coefficients, $b_{n}$: coefficients, $h(x)$: function and $\delta_{n}(x)$: integral Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.6.E62 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)$ from $\mathscr{M}(f;s)$. See also: Annotations for §2.6(iv), §2.6 and Ch.2
when $\alpha\neq\beta$, where
$\delta_{n}(x)=\int_{0}^{\infty}f_{n}(t)h_{n}(xt)\mathrm{d}t.$
There is a similar expansion, involving logarithmic terms, when $\alpha=\beta$. For rigorous derivations of these results and also order estimates for $\delta_{n}(x)$, see Wong (1979) and Wong (1989, Chapter 6).
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https://zbmath.org/authors/?q=ai%3Acaines.peter-e
|
# zbMATH — the first resource for mathematics
## Caines, Peter Edwin
Compute Distance To:
Author ID: caines.peter-e Published as: Caines, Peter E.; Caines, P. E.; Caines, Peter Homepage: https://www.gerad.ca/fr/people/peter-caines/ External Links: IdRef · MGP · Wikidata
Documents Indexed: 131 Publications since 1970, including 6 Books
all top 5
#### Co-Authors
14 single-authored 17 Malhamé, Roland P. 12 Huang, Minyi 7 Goodrich, Robert L. 6 Wei, Yuanjun 5 Meyn, Sean P. 5 Nourian, Mojtaba 4 Goodwin, Graham Clifford 4 Lemch, Ekaterina S. 4 Ramadge, Peter J. G. 4 Shaikh, Mohammad Shahid 3 Firoozi, Dena 3 Jia, Peng 3 Levanony, David 3 Pakniyat, Ali 3 Şen, Nevroz 3 Wang, Suning 3 Wynn, Henry P. 2 Bardi, Martino 2 Brillinger, David R. 2 Capuzzo Dolcetta, Italo 2 Deardon, Rob 2 Gao, Shuang 2 Gerencsér, László 2 Geweke, John F. 2 Kizilkale, Arman C. 2 Ljung, Lennart 2 Ma, Zhongjing 2 Mayne, David Q. 2 Nassiri-Toussi, Karim 2 Parzen, Emanuel 2 Rosenblatt, Murray 2 Shen, Gang 2 Taqqu, Murad S. 2 Taringoo, Farzin 2 Zhang, Jifeng 1 Adès, Michel 1 Baykal-Gursoy, Melike 1 Brotherton, T. W. 1 Buss, Martin 1 Dorer, D. 1 Dyck, Derek N. 1 Egerstedt, Magnus B. 1 Gomart, Olivier 1 Greiner, Russell 1 Gupta, Vineet 1 Helwa, Mohamed K. 1 Hermann, Robert 1 Hubbard, Paul 1 Jaimungal, Sebastian 1 Lafortune, Stéphane 1 Leibold, Marion 1 Mackling, T. 1 Martínez-Mascarúa, C. 1 Passenberg, Benjamin 1 Printis, Robert S. 1 Qu, Clare W. 1 Sabourn, Michael G. 1 Schöllig, Angela 1 Sethi, Suresh P. 1 Stursberg, Olaf 1 Tchuendom, Rinel Foguen 1 Thow, Stefan Ng Yow
all top 5
#### Serials
44 IEEE Transactions on Automatic Control 15 SIAM Journal on Control and Optimization 9 IMA Journal of Mathematical Control and Information 8 Systems & Control Letters 3 Communications in Information and Systems 3 International Journal of Control, I. Series 2 International Journal of Systems Science 2 The Annals of Statistics 2 Automatica 2 The IMA Volumes in Mathematics and its Applications 2 Dynamic Games and Applications 1 IEEE Transactions on Information Theory 1 Stochastics 1 International Journal of Adaptive Control and Signal Processing 1 Annals of Mathematics and Artificial Intelligence 1 Journal of Systems Science and Complexity 1 International Journal of Robotics and Automation 1 Classics in Applied Mathematics 1 Lecture Notes in Control and Information Sciences 1 Lie Groups: History, Frontiers and Applications. Series B. Systems Information and Control 1 Nonlinear Analysis. Hybrid Systems 1 Wiley Series in Probability and Mathematical Statistics
all top 5
#### Fields
102 Systems theory; control (93-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Probability theory and stochastic processes (60-XX) 21 Statistics (62-XX) 10 Computer science (68-XX) 10 Operations research, mathematical programming (90-XX) 6 General and overarching topics; collections (00-XX) 3 Mathematical logic and foundations (03-XX) 3 Partial differential equations (35-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH Open
92 Publications have been cited 1,370 times in 952 Documents Cited by Year
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Zbl 1136.91349
Huang, Minyi; Malhamé, Roland; Caines, Peter E.
2006
Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized $$\epsilon$$-Nash equilibria. Zbl 1366.91016
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2007
Discrete-time multivariable adaptive control. Zbl 0429.93034
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1980
Discrete time stochastic adaptive control. Zbl 0473.93075
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1981
On the hybrid optimal control problem: theory and algorithms. Zbl 1366.93061
Shaikh, M. Shahid; Caines, Peter E.
2007
Linear stochastic systems. Zbl 0658.93003
Caines, Peter E.
1988
Finite dimensional linear stochastic system identification. Zbl 0781.93093
Caines, P. E.
1991
$$\epsilon$$-Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents. Zbl 1275.93067
Nourian, Mojtaba; Caines, Peter E.
2013
Asymptotic normality of prediction error estimators for approximate system models. Zbl 0437.93044
Ljung, Lennart; Caines, Peter E.
1979
Social optima in mean field LQG control: centralized and decentralized strategies. Zbl 1369.49052
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2012
On the discrete time matrix Riccati equation of optimal control. Zbl 0205.15902
Caines, P. E.; Mayne, D. Q.
1970
Feedback between stationary stochastic processes. Zbl 0312.60018
Caines, Peter E.; Chan, C. W.
1975
An invariance principle in large population stochastic dynamic games. Zbl 1280.91020
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2007
Optimal adaptive LQG control for systems with finite state process parameters. Zbl 0571.93035
Caines, P. E.; Chen, H. F.
1985
On the adaptive control of jump parameter systems via nonlinear filtering. Zbl 0843.93076
Caines, Peter E.; Zhang, Ji-Feng
1995
On the optimal control of hybrid systems: Optimization of trajectories, switching times, and location schedules. Zbl 1038.49033
Shaikh, M. Shahid; Caines, Peter E.
2003
Nash, social and centralized solutions to consensus problems via mean field control theory. Zbl 1369.93041
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.; Huang, Minyi
2013
Prediction error identification method for stationary stochastic processes. Zbl 0334.93049
Caines, P. E.
1976
Hierarchical hybrid control systems: A lattice theoretic formulation. Zbl 0899.93001
Caines, Peter E.; Wei, Yuan-Jun
1998
Adaptive control with recursive identification for stochastic linear systems. Zbl 0538.93071
Caines, Peter E.; Lafortune, Stephane
1984
The NCE (mean field) principle with locality dependent cost interactions. Zbl 1368.49040
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2010
Nash equilibria for large-population linear stochastic systems of weakly coupled agents. Zbl 1121.91012
Huang, Minyi; Malhamé, Roland P.; Caines, Peter E.
2005
Linear system identification from nonstationary cross-sectional data. Zbl 0408.93041
Goodrich, Robert L.; Caines, Peter E.
1979
Uplink power adjustment in wireless communication systems: a stochastic control analysis. Zbl 1365.93545
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2004
Mean field LQG control in leader-follower stochastic multi-agent systems: likelihood ratio based adaptation. Zbl 1369.93732
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.; Huang, Minyi
2012
The strong consistency of the stochastic gradient algorithm of adaptive control. Zbl 0555.93057
Chen, H. F.; Caines, P. E.
1985
Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes. Zbl 0283.62085
Caines, P. E.; Rissanen, J.
1974
Mean field game theory with a partially observed major agent. Zbl 1358.35195
Şen, Nevroz; Caines, Peter E.
2016
The strong consistency of maximum likelihood estimators for ARMA processes. Zbl 0406.62018
Rissanen, J.; Caines, P. E.
1979
A hybrid Bellman equation for bimodal systems. Zbl 1221.49054
Caines, Peter; Egerstedt, Magnus; Malhame, Roland; Schöllig, Angela
2007
The zero divisor problem of multivariable stochastic adaptive control. Zbl 0579.93067
Meyn, S. P.; Caines, P. E.
1985
Preface: DGAA special issue on mean field games. Zbl 1304.00024
Bardi, Martino (ed.); Caines, Peter E. (ed.); Capuzzo Dolcetta, Italo (ed.)
2013
A mean field game synthesis of initial mean consensus problems: a continuum approach for non-Gaussian behavior. Zbl 1360.93049
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.
2014
Mean field stochastic adaptive control. Zbl 1369.93731
Kizilkale, Arman C.; Caines, Peter E.
2013
$$\epsilon$$-Nash equilibria for partially observed LQG mean field games with a major player. Zbl 1371.91012
Caines, Peter E.; Kizilkale, Arman C.
2017
Asymptotic behavior of stochastic systems possessing Markovian realizations. Zbl 0725.60070
Meyn, S. P.; Caines, P. E.
1991
On the adaptive stabilization and ergodic behaviour of stochastic systems with jump-Markov parameters via nonlinear filtering. Zbl 0793.93106
Caines, Peter E.; Nassiri-Toussi, Karim
1991
A new approach to stochastic adaptive control. Zbl 0618.93069
Meyn, Sean P.; Caines, Peter E.
1987
A globally convergent adaptive predictor. Zbl 0451.93028
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1981
On the adaptive control of a class of systems with random parameters and disturbances. Zbl 0581.93039
Chen, H. F.; Caines, P. E.
1985
Dynamical consistency in hierarchical supervisory control. Zbl 1364.93467
Hubbard, Paul; Caines, Peter E.
2002
Analysis of decentralized quantized auctions on cooperative networks. Zbl 1369.91070
Jia, Peng; Caines, Peter E.
2013
Nonlinear filtering theory for McKean-Vlasov type stochastic differential equations. Zbl 1355.60085
Şen, Nevroz; Caines, Peter E.
2016
Classical and logic-based dynamic observers for finite automata. Zbl 0734.93019
Caines, Peter E.; Greiner, Russell; Wang, Suning
1991
Stationary linear and nonlinear system identification and predictor set completeness. Zbl 0383.93039
Caines, Peter E.
1978
On persistent excitation for linear systems with stochastic coefficients. Zbl 0996.60052
Levanony, David; Caines, Peter E.
2001
The sensitivity of hybrid systems optimal cost functions with respect to switching manifold parameters. Zbl 1237.49035
Taringoo, Farzin; Caines, Peter E.
2009
Weak and strong feedback free processes. Zbl 0333.93042
Caines, P. E.
1976
Optimality zone algorithms for hybrid systems: Efficient algorithms for optimal location and control computation. Zbl 1178.93071
Caines, Peter E.; Shaikh, M. Shahid
2006
Continuous time stochastic adaptive control: Non-explosion, $$\epsilon$$- consistency and stability. Zbl 0763.93078
Caines, P. E.
1992
A note on the consistency of maximum likelihood estimates for finite families of stochastic processes. Zbl 0303.62022
Caines, P. E.
1975
On the optimal control of impulsive hybrid systems on Riemannian manifolds. Zbl 1280.49051
Taringoo, Farzin; Caines, Peter E.
2013
On the relation between the minimum principle and dynamic programming for classical and hybrid control systems. Zbl 1390.49024
Pakniyat, Ali; Caines, Peter E.
2017
Necessary and sufficient conditions for local second-order identifiability. Zbl 0393.93052
Goodrich, R. L.; Caines, P. E.
1979
Stochastic Lagrangian adaptive LQG control. Zbl 1048.93097
Levanony, David; Caines, Peter E.
2002
On the global controllability of nonlinear systems: Fountains, recurrence, and applications to Hamiltonian systems. Zbl 1175.93098
Caines, Peter E.; Lemch, Ekaterina S.
2003
Preface: DGAA 2nd special issue on mean field games. Zbl 1304.00025
Bardi, Martino (ed.); Caines, Peter E. (ed.); Capuzzo Dolcetta, Italo (ed.)
2014
On the asymptotic normality of instrumental variable and least squares estimators. Zbl 0332.93069
Caines, P. E.
1976
Nonlinear filtering in Riemannian manifolds. Zbl 0625.60051
Ng, S. K.; Caines, P. E.
1985
On the extension of robust global adaptive control results to unstructured time-varying systems. Zbl 0672.93044
Gomart, Olivier; Caines, Peter
1986
On the $$L^{\infty}$$ consistency of $$L^ 2$$ estimators. Zbl 0684.93076
Caines, P. E.; Baykal-Gürsoy, M.
1989
The execution problem in finance with major and minor traders: a mean field game formulation. Zbl 1417.91112
Firoozi, Dena; Caines, Peter E.
2017
The hierarchical control of ST-finite-state machines. Zbl 0902.93001
Caines, Peter E.; Gupta, Vineet; Shen, Gang
1997
A simple proof for a spectral factorization theorem. Zbl 0725.60030
Caines, P. E.; Gerencsér, Laszlo
1991
On the use of shift register sequences as instrumental variables for the recursive identification of multivariable linear systems. Zbl 0383.93045
Sinha, S.; Caines, P. E.
1977
Hierarchical hybrid control systems. Zbl 0880.93003
Caines, Peter E.; Wei, Yuan-Jun
1997
Correction: On the discrete time matrix Riccati equation of optimal control. Zbl 0215.21405
Caines, P. E.; Mayne, D. Q.
1971
Analysis of a class of decentralized dynamical systems: rapid convergence and efficiency of dynamical quantized auctions. Zbl 1201.91079
Jia, Peng; Caines, Peter E.
2010
Mean field (NCE) formulation of estimation based leader-follower collective dynamics. Zbl 1260.93154
Nourian, Mojtaba; Malhamé, Roland P.; Huang, Minyi; Caines, Peter E.
2011
Computationally tractable stochastic power control laws in wireless communications. Zbl 1365.93337
Huang, Minyi; Malhamé, Roland P.; Caines, Peter E.
2005
On the supervisory control of multiagent product systems. Zbl 1366.93365
Romanovski, I.; Caines, P. E.
2006
Optimal control for hybrid systems with partitioned state space. Zbl 1369.49029
Passenberg, Benjamin; Caines, Peter E.; Leibold, Marion; Stursberg, Olaf; Buss, Martin
2013
In-block controllability of affine systems on polytopes. Zbl 1369.93083
Helwa, Mohamed K.; Caines, Peter E.
2017
Mean field games with partial observation. Zbl 1428.35645
Şen, Nevroz; Caines, Peter E.
2019
Linear system identification from non-stationary cross-sectional data. Zbl 0428.93069
Goodrich, R. L.; Caines, P. E.
1979
Asymptotic normality of prediction error estimators for approximate system models. Zbl 0434.93055
Ljung, Lennart; Caines, Peter E.
1979
The logical control of an elevator. Zbl 0826.93052
Dyck, Derek N.; Caines, Peter E.
1995
COCOLOG: A conditional observer and controller logic for finite machines. Zbl 0840.93007
Caines, Peter E.; Wang, Suning
1995
Adaptive control via a simple switching algorithm. Zbl 0846.93057
Zhang, Ji Feng; Caines, Peter E.
1996
Topics in stochastic systems: modelling, estimation and adaptive control. Zbl 0778.00024
Gerencsér, L. (ed.); Caines, P. E. (ed.)
1991
Hierarchical COCOLOG for finite machines. Zbl 0823.68066
Wei, Y. J.; Caines, P. E.
1994
On the rapid convergence of a class of decentralized decision processes: quantized progressive second-price auctions. Zbl 1264.91065
Jia, Peng; Qu, Clare W.; Caines, Peter E.
2009
Modelling and maximum likelihood estimation of Gaussian ARMAX and state space systems. Zbl 0597.93054
Caines, P. E.
1983
Chen, H. F.; Caines, P. E.
1985
Parameter estimation for observed diffusions in manifolds. Zbl 0652.60049
Ng, S. K.; Caines, P. E.; Chen, H. F.
1984
Stochastic controllability and stochastic Lyapunov functions with applications to adaptive and nonlinear systems. Zbl 0684.93070
Meyn, S. P.; Caines, P. E.
1989
Ultimate objectives and prior knowledge in system identification. Zbl 0476.93065
Goodwin, G. C.; Ramadge, P. J.; Caines, P. E.
1980
Adaptive control of systems subject to a class of random parameter variations and disturbances. Zbl 0493.93045
Caines, P. E.; Dorer, D.
1981
Minimal realization of transfer function matrices. Zbl 0213.15303
Caines, P. E.
1971
Linear stochastic systems. Reprint of the 1988 original published by Wiley. Zbl 1398.93001
Caines, Peter E.
2018
Stochastic optimal control under Poisson-distributed observations. Zbl 1012.93068
Adès, Michel; Caines, Peter E.; Malhamé, Roland P.
2000
Hybrid optimal control of an electric vehicle with a dual-planetary transmission. Zbl 1376.49005
Pakniyat, Ali; Caines, Peter E.
2017
Mean field games with partial observation. Zbl 1428.35645
Şen, Nevroz; Caines, Peter E.
2019
Linear stochastic systems. Reprint of the 1988 original published by Wiley. Zbl 1398.93001
Caines, Peter E.
2018
$$\epsilon$$-Nash equilibria for partially observed LQG mean field games with a major player. Zbl 1371.91012
Caines, Peter E.; Kizilkale, Arman C.
2017
On the relation between the minimum principle and dynamic programming for classical and hybrid control systems. Zbl 1390.49024
Pakniyat, Ali; Caines, Peter E.
2017
The execution problem in finance with major and minor traders: a mean field game formulation. Zbl 1417.91112
Firoozi, Dena; Caines, Peter E.
2017
In-block controllability of affine systems on polytopes. Zbl 1369.93083
Helwa, Mohamed K.; Caines, Peter E.
2017
Hybrid optimal control of an electric vehicle with a dual-planetary transmission. Zbl 1376.49005
Pakniyat, Ali; Caines, Peter E.
2017
Mean field game theory with a partially observed major agent. Zbl 1358.35195
Şen, Nevroz; Caines, Peter E.
2016
Nonlinear filtering theory for McKean-Vlasov type stochastic differential equations. Zbl 1355.60085
Şen, Nevroz; Caines, Peter E.
2016
A mean field game synthesis of initial mean consensus problems: a continuum approach for non-Gaussian behavior. Zbl 1360.93049
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.
2014
Preface: DGAA 2nd special issue on mean field games. Zbl 1304.00025
Bardi, Martino; Caines, Peter E.; Capuzzo Dolcetta, Italo
2014
$$\epsilon$$-Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents. Zbl 1275.93067
Nourian, Mojtaba; Caines, Peter E.
2013
Nash, social and centralized solutions to consensus problems via mean field control theory. Zbl 1369.93041
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.; Huang, Minyi
2013
Preface: DGAA special issue on mean field games. Zbl 1304.00024
Bardi, Martino; Caines, Peter E.; Capuzzo Dolcetta, Italo
2013
Mean field stochastic adaptive control. Zbl 1369.93731
Kizilkale, Arman C.; Caines, Peter E.
2013
Analysis of decentralized quantized auctions on cooperative networks. Zbl 1369.91070
Jia, Peng; Caines, Peter E.
2013
On the optimal control of impulsive hybrid systems on Riemannian manifolds. Zbl 1280.49051
Taringoo, Farzin; Caines, Peter E.
2013
Optimal control for hybrid systems with partitioned state space. Zbl 1369.49029
Passenberg, Benjamin; Caines, Peter E.; Leibold, Marion; Stursberg, Olaf; Buss, Martin
2013
Social optima in mean field LQG control: centralized and decentralized strategies. Zbl 1369.49052
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2012
Mean field LQG control in leader-follower stochastic multi-agent systems: likelihood ratio based adaptation. Zbl 1369.93732
Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.; Huang, Minyi
2012
Mean field (NCE) formulation of estimation based leader-follower collective dynamics. Zbl 1260.93154
Nourian, Mojtaba; Malhamé, Roland P.; Huang, Minyi; Caines, Peter E.
2011
The NCE (mean field) principle with locality dependent cost interactions. Zbl 1368.49040
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2010
Analysis of a class of decentralized dynamical systems: rapid convergence and efficiency of dynamical quantized auctions. Zbl 1201.91079
Jia, Peng; Caines, Peter E.
2010
The sensitivity of hybrid systems optimal cost functions with respect to switching manifold parameters. Zbl 1237.49035
Taringoo, Farzin; Caines, Peter E.
2009
On the rapid convergence of a class of decentralized decision processes: quantized progressive second-price auctions. Zbl 1264.91065
Jia, Peng; Qu, Clare W.; Caines, Peter E.
2009
Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized $$\epsilon$$-Nash equilibria. Zbl 1366.91016
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2007
On the hybrid optimal control problem: theory and algorithms. Zbl 1366.93061
Shaikh, M. Shahid; Caines, Peter E.
2007
An invariance principle in large population stochastic dynamic games. Zbl 1280.91020
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2007
A hybrid Bellman equation for bimodal systems. Zbl 1221.49054
Caines, Peter; Egerstedt, Magnus; Malhame, Roland; Schöllig, Angela
2007
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Zbl 1136.91349
Huang, Minyi; Malhamé, Roland; Caines, Peter E.
2006
Optimality zone algorithms for hybrid systems: Efficient algorithms for optimal location and control computation. Zbl 1178.93071
Caines, Peter E.; Shaikh, M. Shahid
2006
On the supervisory control of multiagent product systems. Zbl 1366.93365
Romanovski, I.; Caines, P. E.
2006
Nash equilibria for large-population linear stochastic systems of weakly coupled agents. Zbl 1121.91012
Huang, Minyi; Malhamé, Roland P.; Caines, Peter E.
2005
Computationally tractable stochastic power control laws in wireless communications. Zbl 1365.93337
Huang, Minyi; Malhamé, Roland P.; Caines, Peter E.
2005
Uplink power adjustment in wireless communication systems: a stochastic control analysis. Zbl 1365.93545
Huang, Minyi; Caines, Peter E.; Malhamé, Roland P.
2004
On the optimal control of hybrid systems: Optimization of trajectories, switching times, and location schedules. Zbl 1038.49033
Shaikh, M. Shahid; Caines, Peter E.
2003
On the global controllability of nonlinear systems: Fountains, recurrence, and applications to Hamiltonian systems. Zbl 1175.93098
Caines, Peter E.; Lemch, Ekaterina S.
2003
Dynamical consistency in hierarchical supervisory control. Zbl 1364.93467
Hubbard, Paul; Caines, Peter E.
2002
Stochastic Lagrangian adaptive LQG control. Zbl 1048.93097
Levanony, David; Caines, Peter E.
2002
On persistent excitation for linear systems with stochastic coefficients. Zbl 0996.60052
Levanony, David; Caines, Peter E.
2001
Stochastic optimal control under Poisson-distributed observations. Zbl 1012.93068
Adès, Michel; Caines, Peter E.; Malhamé, Roland P.
2000
Hierarchical hybrid control systems: A lattice theoretic formulation. Zbl 0899.93001
Caines, Peter E.; Wei, Yuan-Jun
1998
The hierarchical control of ST-finite-state machines. Zbl 0902.93001
Caines, Peter E.; Gupta, Vineet; Shen, Gang
1997
Hierarchical hybrid control systems. Zbl 0880.93003
Caines, Peter E.; Wei, Yuan-Jun
1997
Adaptive control via a simple switching algorithm. Zbl 0846.93057
Zhang, Ji Feng; Caines, Peter E.
1996
On the adaptive control of jump parameter systems via nonlinear filtering. Zbl 0843.93076
Caines, Peter E.; Zhang, Ji-Feng
1995
The logical control of an elevator. Zbl 0826.93052
Dyck, Derek N.; Caines, Peter E.
1995
COCOLOG: A conditional observer and controller logic for finite machines. Zbl 0840.93007
Caines, Peter E.; Wang, Suning
1995
Hierarchical COCOLOG for finite machines. Zbl 0823.68066
Wei, Y. J.; Caines, P. E.
1994
Continuous time stochastic adaptive control: Non-explosion, $$\epsilon$$- consistency and stability. Zbl 0763.93078
Caines, P. E.
1992
Finite dimensional linear stochastic system identification. Zbl 0781.93093
Caines, P. E.
1991
Asymptotic behavior of stochastic systems possessing Markovian realizations. Zbl 0725.60070
Meyn, S. P.; Caines, P. E.
1991
On the adaptive stabilization and ergodic behaviour of stochastic systems with jump-Markov parameters via nonlinear filtering. Zbl 0793.93106
Caines, Peter E.; Nassiri-Toussi, Karim
1991
Classical and logic-based dynamic observers for finite automata. Zbl 0734.93019
Caines, Peter E.; Greiner, Russell; Wang, Suning
1991
A simple proof for a spectral factorization theorem. Zbl 0725.60030
Caines, P. E.; Gerencsér, Laszlo
1991
Topics in stochastic systems: modelling, estimation and adaptive control. Zbl 0778.00024
Gerencsér, L.; Caines, P. E.
1991
On the $$L^{\infty}$$ consistency of $$L^ 2$$ estimators. Zbl 0684.93076
Caines, P. E.; Baykal-Gürsoy, M.
1989
Stochastic controllability and stochastic Lyapunov functions with applications to adaptive and nonlinear systems. Zbl 0684.93070
Meyn, S. P.; Caines, P. E.
1989
Linear stochastic systems. Zbl 0658.93003
Caines, Peter E.
1988
A new approach to stochastic adaptive control. Zbl 0618.93069
Meyn, Sean P.; Caines, Peter E.
1987
On the extension of robust global adaptive control results to unstructured time-varying systems. Zbl 0672.93044
Gomart, Olivier; Caines, Peter
1986
Optimal adaptive LQG control for systems with finite state process parameters. Zbl 0571.93035
Caines, P. E.; Chen, H. F.
1985
The strong consistency of the stochastic gradient algorithm of adaptive control. Zbl 0555.93057
Chen, H. F.; Caines, P. E.
1985
The zero divisor problem of multivariable stochastic adaptive control. Zbl 0579.93067
Meyn, S. P.; Caines, P. E.
1985
On the adaptive control of a class of systems with random parameters and disturbances. Zbl 0581.93039
Chen, H. F.; Caines, P. E.
1985
Nonlinear filtering in Riemannian manifolds. Zbl 0625.60051
Ng, S. K.; Caines, P. E.
1985
Chen, H. F.; Caines, P. E.
1985
Adaptive control with recursive identification for stochastic linear systems. Zbl 0538.93071
Caines, Peter E.; Lafortune, Stephane
1984
Parameter estimation for observed diffusions in manifolds. Zbl 0652.60049
Ng, S. K.; Caines, P. E.; Chen, H. F.
1984
Modelling and maximum likelihood estimation of Gaussian ARMAX and state space systems. Zbl 0597.93054
Caines, P. E.
1983
Discrete time stochastic adaptive control. Zbl 0473.93075
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1981
A globally convergent adaptive predictor. Zbl 0451.93028
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1981
Adaptive control of systems subject to a class of random parameter variations and disturbances. Zbl 0493.93045
Caines, P. E.; Dorer, D.
1981
Discrete-time multivariable adaptive control. Zbl 0429.93034
Goodwin, Graham C.; Ramadge, Peter J.; Caines, Peter E.
1980
Ultimate objectives and prior knowledge in system identification. Zbl 0476.93065
Goodwin, G. C.; Ramadge, P. J.; Caines, P. E.
1980
Asymptotic normality of prediction error estimators for approximate system models. Zbl 0437.93044
Ljung, Lennart; Caines, Peter E.
1979
Linear system identification from nonstationary cross-sectional data. Zbl 0408.93041
Goodrich, Robert L.; Caines, Peter E.
1979
The strong consistency of maximum likelihood estimators for ARMA processes. Zbl 0406.62018
Rissanen, J.; Caines, P. E.
1979
Necessary and sufficient conditions for local second-order identifiability. Zbl 0393.93052
Goodrich, R. L.; Caines, P. E.
1979
Linear system identification from non-stationary cross-sectional data. Zbl 0428.93069
Goodrich, R. L.; Caines, P. E.
1979
Asymptotic normality of prediction error estimators for approximate system models. Zbl 0434.93055
Ljung, Lennart; Caines, Peter E.
1979
Stationary linear and nonlinear system identification and predictor set completeness. Zbl 0383.93039
Caines, Peter E.
1978
On the use of shift register sequences as instrumental variables for the recursive identification of multivariable linear systems. Zbl 0383.93045
Sinha, S.; Caines, P. E.
1977
Prediction error identification method for stationary stochastic processes. Zbl 0334.93049
Caines, P. E.
1976
Weak and strong feedback free processes. Zbl 0333.93042
Caines, P. E.
1976
On the asymptotic normality of instrumental variable and least squares estimators. Zbl 0332.93069
Caines, P. E.
1976
Feedback between stationary stochastic processes. Zbl 0312.60018
Caines, Peter E.; Chan, C. W.
1975
A note on the consistency of maximum likelihood estimates for finite families of stochastic processes. Zbl 0303.62022
Caines, P. E.
1975
Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes. Zbl 0283.62085
Caines, P. E.; Rissanen, J.
1974
Correction: On the discrete time matrix Riccati equation of optimal control. Zbl 0215.21405
Caines, P. E.; Mayne, D. Q.
1971
Minimal realization of transfer function matrices. Zbl 0213.15303
Caines, P. E.
1971
On the discrete time matrix Riccati equation of optimal control. Zbl 0205.15902
Caines, P. E.; Mayne, D. Q.
1970
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#### Cited by 1,202 Authors
25 Gomes, Diogo Luís Aguiar 20 Cardaliaguet, Pierre 19 Caines, Peter Edwin 15 Azhmyakov, Vadim 14 Zhang, Jifeng 12 Huang, Jianhui 11 Bauso, Dario 11 Cirant, Marco 11 de la Sen, Manuel 10 Anderson, Brian David Outram 10 Başar, Tamer 10 Bensoussan, Alain 10 Chen, Hanfu 10 Huang, Minyi 9 Carmona, René A. 9 Hjalmarsson, Håkan 9 Kolokoltsov, Vassili N. 9 Li, Xun 8 Delarue, François 8 Ferreira, Rita 8 Goodwin, Graham Clifford 8 Guo, Lei 8 Lacker, Daniel 8 Porretta, Alessio 8 Söderström, Torsten 7 Chai, Tianyou 7 Miller, Daniel E. 7 Shah, Sirish L. 7 Wang, Bingchang 7 Wu, Zhen 6 Averboukh, Yuriĭ Vladimirovich 6 Bardi, Martino 6 Bayraktar, Erhan 6 Egerstedt, Magnus B. 6 Gerencsér, László 6 Ljung, Lennart 6 Meyn, Sean P. 6 Moon, Jun-Hee 6 Radenkovic, Miloje S. 6 Silva, Francisco J. 6 Stoica, Petre Gheorghe 6 Yam, Sheung Chi Phillip 6 Ydstie, B. Erik 5 Åström, Karl Johan 5 Charalambous, Charalambos D. 5 Fisher, D. Grant 5 Fragoso, Marcelo Dutra 5 Gevers, Michel R. 5 Li, Tao 5 Nurbekyan, Levon 5 Poznyak, Aleksandr Semënovich 5 Saldi, Naci 5 Tembine, Hamidou 5 Turinici, Gabriel 5 Voskanyan, Vardan K. 5 Zhang, Huanshui 4 Bittanti, Sergio 4 Cannarsa, Piermarco 4 Cecchin, Alekos 4 Chau, Man Ho Michael 4 Cohen, Asaf 4 Feleqi, Ermal 4 Galvan-Guerra, Rosalba 4 Johnson, Charles Richard jun. 4 Lai, Tze Leung 4 Landau, Ioan Doré 4 Malhamé, Roland P. 4 Martin-Sánchez, Juan M. 4 Mayne, David Q. 4 Mélard, Guy 4 Mészáros, Alpár Richárd 4 Moore, John Barratt 4 Narendra, Kumpati S. 4 Nguyen, Son Luu 4 Ni, Yuanhua 4 Pasik-Duncan, Bozenna 4 Pimentel, Edgard A. 4 Pintelon, Rik 4 Raginsky, Maxim 4 Santambrogio, Filippo 4 Scattolini, Riccardo 4 Schoukens, Johan 4 Tonon, Daniela 4 Triacca, Umberto 4 Van den Hof, Paul M. J. 4 Wardi, Yorai 4 Wu, Xiang 4 Yin, Gang George 4 Yin, George Gang 4 Yong, Jiongmin 4 Zhang, Kanjian 4 Zhang, Qing 4 Zhang, Weihai 3 Bagagiolo, Fabio 3 Bagchi, Arunabha 3 Bahlali, Khaled 3 Basin, Michael V. 3 Bitmead, Robert R. 3 Campi, Luciano 3 Carlini, Elisabetta ...and 1,102 more Authors
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#### Cited in 183 Serials
180 Automatica 88 International Journal of Control 58 Systems & Control Letters 40 SIAM Journal on Control and Optimization 38 Dynamic Games and Applications 29 International Journal of Systems Science 28 Applied Mathematics and Optimization 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 Journal of the Franklin Institute 14 Journal of Optimization Theory and Applications 14 Nonlinear Analysis. Hybrid Systems 12 International Journal of Adaptive Control and Signal Processing 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Stochastic Processes and their Applications 10 Journal of Econometrics 10 Stochastic Analysis and Applications 9 The Annals of Applied Probability 9 NoDEA. Nonlinear Differential Equations and Applications 9 European Journal of Control 8 Journal of Time Series Analysis 8 Mathematical Problems in Engineering 8 Journal of Systems Science and Complexity 7 Journal of Differential Equations 7 MCSS. Mathematics of Control, Signals, and Systems 7 Discrete Event Dynamic Systems 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Stochastics 6 Statistics & Probability Letters 6 Communications in Statistics. Theory and Methods 6 Journal of Dynamics and Games 6 Minimax Theory and its Applications 5 Journal of Mathematical Analysis and Applications 5 Asian Journal of Control 4 Computers & Mathematics with Applications 4 Journal of Multivariate Analysis 4 Mathematics of Operations Research 4 Circuits, Systems, and Signal Processing 4 Communications in Partial Differential Equations 4 Linear Algebra and its Applications 4 Calculus of Variations and Partial Differential Equations 4 Mathematical Control and Related Fields 3 The Annals of Probability 3 Applied Mathematics and Computation 3 Proceedings of the American Mathematical Society 3 Optimal Control Applications & Methods 3 Journal of Economic Dynamics & Control 3 Economics Letters 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Computational Statistics and Data Analysis 3 International Journal of Robust and Nonlinear Control 3 Lobachevskii Journal of Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Control Theory and Applications 3 Mathematics and Financial Economics 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Acta Informatica 2 Biological Cybernetics 2 The Annals of Statistics 2 The Journal of Mathematical Sociology 2 Kybernetika 2 Mathematics and Computers in Simulation 2 Ricerche di Matematica 2 SIAM Journal on Numerical Analysis 2 Statistica Neerlandica 2 Acta Applicandae Mathematicae 2 Probability Theory and Related Fields 2 Statistical Science 2 Econometric Reviews 2 Dynamics and Control 2 Automation and Remote Control 2 European Journal of Operational Research 2 Journal of Statistical Computation and Simulation 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 Journal of Dynamics and Differential Equations 2 Bernoulli 2 Discrete and Continuous Dynamical Systems 2 Abstract and Applied Analysis 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Discrete Dynamics in Nature and Society 2 Econometric Theory 2 Entropy 2 Sādhanā 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Stochastics and Dynamics 2 Science in China. Series F 2 Stochastics 2 Games 2 Stochastic Systems 2 Research in the Mathematical Sciences 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Metrika 1 Nonlinearity 1 Physics Letters. A ...and 83 more Serials
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#### Cited in 37 Fields
605 Systems theory; control (93-XX) 276 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 224 Calculus of variations and optimal control; optimization (49-XX) 173 Probability theory and stochastic processes (60-XX) 130 Statistics (62-XX) 107 Partial differential equations (35-XX) 57 Operations research, mathematical programming (90-XX) 44 Numerical analysis (65-XX) 35 Computer science (68-XX) 27 Biology and other natural sciences (92-XX) 22 Ordinary differential equations (34-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Information and communication theory, circuits (94-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 7 Difference and functional equations (39-XX) 7 Operator theory (47-XX) 7 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 Integral equations (45-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Combinatorics (05-XX) 2 History and biography (01-XX) 2 Functional analysis (46-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Algebraic topology (55-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-09-19T03:14:40 |
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https://www.gfdl.noaa.gov/blog_held/44-heat-uptake-and-internal-variability-part-ii/
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# 44. Heat uptake and internal variability — part II
Posted on February 28th, 2014
I’m returning to an argument discussed in post #16 regarding the decomposition of the global mean warming into a part that is forced and a part that is due to internal variability. I am not looking here for the optimal way of doing this decomposition. I am just interested in getting a better feeling for whether an increasing ocean heat content over time is a “smoking gun” for the forced component being dominant, a term Jim Hansen and others have used in this context. I’ll assume that we know that the heat flux has been into, not out of, the earth system (ie the oceans) averaged over the period in question, which could be the last half century or any period longer than a decade or two to insure that we can think in terms of a transient climate sensitivity (or transient climate response TCR) for the forced component. (AR5 WG1 Ch. 3 has a synthesis of the observations of ocean heat content). We’ll think in the most traditional terms, focusing on the global mean energy balance at the top of the atmosphere (TOA). Everything is considered to be a small perturbation from a control climate, and the assumption is that we can just linearly superpose the forced component of this perturbation and the component due to internal variability.
For the forced component, there is a 3-way balance between forcing $F$, heat uptake $H$, and the radiative restoring proportional to the temperature response, $-\beta T$, with strength $\beta$ inversely proportional to the climate sensitivity $T_{EQ} \equiv F/\beta$. Here and in what follows, $F$ is the change in forcing over the interval considered, so $T_{EQ}$ is the usual sensitivity scaled by $F/F_{2XCO2}$ When I refer to TCR in the following, it is also normalized in the same way. So TCR is simply the forced response in global mean temperature $T_F$$H$ is positive into the ocean. For starters, I’ll ignore the question of the efficacy of oceanic heat uptake.
The key assumption is that the relation between global mean temperature and the energy balance of the earth is the same for both the forced and internal components. So an internally generated perturbation in the global mean temperature $T_I$ is accompanied by an increase in the net outward flux at the TOA of $\beta T_I$.
Set $T = T_F + T_I$ and similarly for the heat uptake $H = H_F + H_I = H_F - \beta T_I$. We can write the heat uptake in the forced response in terms of the equilibrium sensitivity and the $TCR$:
$T_F = TCR = (F - H_F)/\beta \implies H_F = \beta (T_{EQ} - TCR)$
So, adding the forced and internal components for the heat uptake:
$H = H_F + H_I = \beta (T_{EQ} - T)$
It is the full $T$ that enters here. The heat flux is into the ocean if the equilibrium response is larger than the observed temperature perturbation.
This expression is transparent to the relative magnitude of the forced and free parts of $T$. For this purpose, as in post #16, we can rewrite $TCR = T_F = \xi T$ so that $\xi$is the fraction of the temperature anomaly that is forced. And we get
$H = \beta (T_{EQ} - TCR/\xi)$
One can write this in different ways (the way I chose in #16 being particularly obscure). We can just leave it is this form, from which we see that if the heat flux is into the ocean we must have (given all of our assumptions);
$\xi > TCR/T_{EQ}$
This all seems reasonable, but now let’s go back and re-examine our key assumption that an internal variation in temperature $T_I$ perturbs the TOA budget by an amount $\beta T_I$, with the same value of $\beta$ that occurs in the forced response. Why should it be the same constant of proportionality, especially if the internal variability has a different spatial structure than the forced response. So how do we relate the strength of this “restoring force” for internal variability to its strength for the forced response? Before getting back to this, we need to reintroduce the notions of efficacy of heat uptake.
For the forced response, when we try to emulate the behavior of GCMs, we find that we need to replace the expression $T_F = TCR = (F - H_F)/\beta$ with
$T_F = TCR = F/\beta_F - H_F/\beta_H$
The efficacy of heat uptake is defined as $\epsilon \equiv \beta_F/\beta_H$ and is almost always larger than one when emulating GCMs – see Post #5 and Winton et al (2010). This is because the response to heat uptake is typically more polar amplified than the equilibrated response to the forcing, and perturbations at higher latitudes are restored less strongly by radiation to space than those at lower latitudes. So you get more bang for your buck by forcing at high latitudes. (Different parts of the forcing can have different efficacies as well, which is the sense in which this term was first used in this context, but I’ll ignore that here.) For a recent example of papers on this, see Rose et al 2014 which looks at the response in some aqua-planet atmospheric models to ocean heat uptake at different latitudes. Like most issues related to radiative responses, clouds feedbacks play an important role and are a major source of uncertainty in $\epsilon$.
Just as for the forced heat uptake, it is natural to expect the radiative restoring of low frequency internal variability to be weaker than that relevant for the equilibrium forced response. Both the forced heat uptake and the low frequency variability involve coupling to deeper ocean layers and this coupling is strongest in subpolar regions. So could it be the case that the restoring for low frequency variability resembles $\beta_H$? It might be interesting to see where the assumption $\beta_I = \beta_H$ leads. Setting, $T_{EQ} = F/\beta_F$, we have $H_F = \beta_H(T_{EQ} - T_F)$ and
$H = H_F + H_I = \beta_H (T_{EQ} - T_F) - \beta_H T_I = \beta_H (T_{EQ} - T)$
So we still have the result that positive heat uptake implies an equilibrium response over the time period in question (ie a temperature change over this period computed by assuming no heat uptake) that is larger than the actual temperature change. Expressing this in terms of the transient response we once again get the result that to be consistent with positive heat uptake we need $\xi > TCR/T_{EQ}$. When efficacy is not equal to one, the assumption that $\beta_I = \beta_H$ saves these intuitive and simple expressions.
Does $\beta_I = \beta_H$ hold in GCMs? How does the strength of the radiative restoring resulting from low frequency internal variability relate to that in the model’s response to heat uptake in the forced response? The smaller $\beta_I$ the weaker the constraint on $\xi$. There is no reason to expect close agreement; there are undoubtedly different parts of the internal variability — focused on Northern compared to Southern subpolar latitudes, for example — that could be damped differently. But it would be interesting if $\beta_I$ was at least correlated with $\beta_H$ across models. I am not aware of any papers that have looked at this.
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]
## 1 thought on “44. Heat uptake and internal variability — part II”
1. Paul S says:
Quite a bit to take in here. Hopefully I’ve followed your point reasonably accurately and the following is relevant:
I’ve recently started looking at correlations in CMIP5 models between SAT and TOA energy flux/Ocean heat content during periods of variability. Specifically I constructed time series of 20-year trends for every member of a particular model’s ensemble, using the RCP45 scenario data, and defined variability in terms of difference from the ensemble mean/median. Note for ocean heat content I used zostoga – global average thermosteric sea level – for ease of access. I understand this should be pretty much the same thing because the ocean mass change is small in these model runs.
The first model I’ve looked at is HadGEM2-ES, mostly because its high sensitivity provides a kind of benchmark. I found no correlation between surface-air temperature variability and TOA flux trends, but there was a small positive correlation (weak, r-squared=0.22) between surface-air temperature variability and thermosteric sea level/ocean heat content trends. That is, ocean heat content trends are slightly amplified during periods of greater warming due to internal variability (and damped during slower warming periods) in this model, yet TOA flux doesn’t reflect this. Trying to figure out how to pick that apart…
I’ve also briefly looked at CCSM4 output. Need to recheck but preliminary results indicate a negative correlation between SAT variability and TOA flux trends. Haven’t checked zostoga data yet.
| 2016-09-26T10:33:18 |
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https://alldimensions.fandom.com/wiki/Ty%C3%A0ts.vplanet
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2,885 Pages
this = new Planet(gravity = Ø, existence = Ø): \\TODO coloring and formatting for .verse scripts\\
this.delete(this); \\in order to keep from existing on start\\
this = makeCopy(Earth.vplanet); \\Use Earth as a baseline (a common move for habitable terrestrial planets)\\
mass = inherit; \\TODO fill in inherit with real values\\
existence = !Ø;
mineralAbundance(Iron) = Mars.vplanet.mineralAbundance(Iron) \\Make the planet red\\
parentStar = Mèna_Qaròsz.vstar
if(this != this): \\Fixing bug of planet corrupting\\
this.delete(this);
this.restart();
@DOCUMENTATION:
"Why would I want to create a planet that doesn't exist and then delete it immediately afterwards. Well, the way vplanet files work is that they can't run copy commands until the planet is created. However, some problems can arise if you try to make a copy of a planet onto another (existing) planet. The reason for such a bug is that the makeCopy function is meant to be run by the star, to copy planets. However, some clever planet makers wanted to make a habitable planet and copy Earth to do it but didn't have access to the star file. So, what did they do? They wrote code to copy the planet in the actual planet script, and now it is standard practice for habitable planets."
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-09-21T20:17:03 |
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http://dlmf.nist.gov/14.18
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# §14.18 Sums
## §14.18(i) Expansion Theorem
For expansions of arbitrary functions in series of Legendre polynomials see §18.18(i), and for expansions of arbitrary functions in series of associated Legendre functions see Schäfke (1961b).
In (14.18.1) and (14.18.2), $\theta_{1}$, $\theta_{2}$, and $\theta_{1}+\theta_{2}$ all lie in $[0,\pi)$, and $\phi$ is real.
14.18.1 $\mathop{\mathsf{P}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{1}% \mathop{\cos\/}\nolimits\theta_{2}+\mathop{\sin\/}\nolimits\theta_{1}\mathop{% \sin\/}\nolimits\theta_{2}\mathop{\cos\/}\nolimits\phi\right)=\mathop{\mathsf{% P}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{1}\right)\mathop{% \mathsf{P}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{2}\right)+% 2\sum_{m=1}^{\infty}(-1)^{m}\mathop{\mathsf{P}^{-m}_{\nu}\/}\nolimits\!\left(% \mathop{\cos\/}\nolimits\theta_{1}\right)\mathop{\mathsf{P}^{m}_{\nu}\/}% \nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{2}\right)\mathop{\cos\/}% \nolimits\!\left(m\phi\right),$
14.18.2 $\mathop{\mathsf{P}_{n}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{1}% \mathop{\cos\/}\nolimits\theta_{2}+\mathop{\sin\/}\nolimits\theta_{1}\mathop{% \sin\/}\nolimits\theta_{2}\mathop{\cos\/}\nolimits\phi\right)=\sum_{m=-n}^{n}(% -1)^{m}\mathop{\mathsf{P}^{-m}_{n}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits% \theta_{1}\right)\mathop{\mathsf{P}^{m}_{n}\/}\nolimits\!\left(\mathop{\cos\/}% \nolimits\theta_{2}\right)\mathop{\cos\/}\nolimits(m\phi).$
In (14.18.3), $\theta_{1}$ lies in $(0,\frac{1}{2}\pi)$, $\theta_{2}$ and $\theta_{1}+\theta_{2}$ both lie in $(0,\pi)$, $\theta_{1}<\theta_{2}$, $\phi$ is real, and $\nu\neq-1,-2,-3,\dots$.
14.18.3 $\mathop{\mathsf{Q}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{1}% \mathop{\cos\/}\nolimits\theta_{2}+\mathop{\sin\/}\nolimits\theta_{1}\mathop{% \sin\/}\nolimits\theta_{2}\mathop{\cos\/}\nolimits\phi\right)=\mathop{\mathsf{% P}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{1}\right)\mathop{% \mathsf{Q}_{\nu}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{2}\right)+% 2\sum_{m=1}^{\infty}(-1)^{m}\mathop{\mathsf{P}^{-m}_{\nu}\/}\nolimits\!\left(% \mathop{\cos\/}\nolimits\theta_{1}\right)\mathop{\mathsf{Q}^{m}_{\nu}\/}% \nolimits\!\left(\mathop{\cos\/}\nolimits\theta_{2}\right)\mathop{\cos\/}% \nolimits\!\left(m\phi\right).$
In (14.18.4) and (14.18.5), $\xi_{1}$ and $\xi_{2}$ are positive, and $\phi$ is real; also in (14.18.5) $\xi_{1}<\xi_{2}$ and $\nu\neq-1,-2,-3,\dots$.
14.18.4 $\mathop{P_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1}\mathop{% \cosh\/}\nolimits\xi_{2}-\mathop{\sinh\/}\nolimits\xi_{1}\mathop{\sinh\/}% \nolimits\xi_{2}\mathop{\cos\/}\nolimits\phi\right)=\mathop{P_{\nu}\/}% \nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1}\right)\mathop{P_{\nu}\/}% \nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{2}\right)+2\sum_{m=1}^{\infty}(% -1)^{m}\mathop{P^{-m}_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1% }\right)\mathop{P^{m}_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{2% }\right)\mathop{\cos\/}\nolimits\!\left(m\phi\right),$
14.18.5 $\mathop{Q_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1}\mathop{% \cosh\/}\nolimits\xi_{2}-\mathop{\sinh\/}\nolimits\xi_{1}\mathop{\sinh\/}% \nolimits\xi_{2}\mathop{\cos\/}\nolimits\phi\right)=\mathop{P_{\nu}\/}% \nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1}\right)\mathop{Q_{\nu}\/}% \nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{2}\right)+2\sum_{m=1}^{\infty}(% -1)^{m}\mathop{P^{-m}_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{1% }\right)\mathop{Q^{m}_{\nu}\/}\nolimits\!\left(\mathop{\cosh\/}\nolimits\xi_{2% }\right)\mathop{\cos\/}\nolimits\!\left(m\phi\right).$
## §14.18(iii) Other Sums
### Christoffel’s Formulas
14.18.6 $\displaystyle(x-y)\sum_{k=0}^{n}(2k+1)\mathop{P_{k}\/}\nolimits\!\left(x\right% )\mathop{P_{k}\/}\nolimits\!\left(y\right)$ $\displaystyle=(n+1)\left(\mathop{P_{n+1}\/}\nolimits\!\left(x\right)\mathop{P_% {n}\/}\nolimits\!\left(y\right)-\mathop{P_{n}\/}\nolimits\!\left(x\right)% \mathop{P_{n+1}\/}\nolimits\!\left(y\right)\right),$ Symbols: $\mathop{P^{\NVar{\mu}}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$: associated Legendre function of the first kind and $n$: nonnegative integer A&S Ref: 8.9.1 Referenced by: Other Changes Permalink: http://dlmf.nist.gov/14.18.E6 Encodings: TeX, pMML, png See also: info for 14.18(iii) 14.18.7 $\displaystyle(x-y)\sum_{k=0}^{n}(2k+1)\mathop{P_{k}\/}\nolimits\!\left(x\right% )\mathop{Q_{k}\/}\nolimits\!\left(y\right)$ $\displaystyle=(n+1)\left(\mathop{P_{n+1}\/}\nolimits\!\left(x\right)\mathop{Q_% {n}\/}\nolimits\!\left(y\right)-\mathop{P_{n}\/}\nolimits\!\left(x\right)% \mathop{Q_{n+1}\/}\nolimits\!\left(y\right)\right)-1.$
In these formulas the Legendre functions are as in §14.3(ii) with $\mu=0$. The formulas are also valid with the Ferrers functions as in §14.3(i) with $\mu=0$.
### Zonal Harmonic Series
14.18.8 $\mathop{\mathsf{P}_{\nu}\/}\nolimits\!\left(-x\right)=\frac{\mathop{\sin\/}% \nolimits\!\left(\nu\pi\right)}{\pi}\sum_{n=0}^{\infty}\frac{2n+1}{(\nu-n)(\nu% +n+1)}\mathop{\mathsf{P}_{n}\/}\nolimits\!\left(x\right),$ $\nu\notin\Integer$.
### Dougall’s Expansion
14.18.9 $\mathop{\mathsf{P}^{-\mu}_{\nu}\/}\nolimits\!\left(x\right)=\frac{\mathop{\sin% \/}\nolimits\!\left(\nu\pi\right)}{\pi}\sum_{n=0}^{\infty}(-1)^{n}\frac{2n+1}{% (\nu-n)(\nu+n+1)}\mathop{\mathsf{P}^{-\mu}_{n}\/}\nolimits\!\left(x\right),$ $-1, $\mu\geq 0$, $\nu\notin\Integer$.
For a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22).
## §14.18(iv) Compendia
For collections of sums involving associated Legendre functions, see Hansen (1975, pp. 367–377, 457–460, and 475), Erdélyi et al. (1953a, §3.10), Gradshteyn and Ryzhik (2000, §8.92), Magnus et al. (1966, pp. 178–184), and Prudnikov et al. (1990, §§5.2, 6.5). See also §18.18 and (34.3.19).
| 2016-09-25T05:28:05 |
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|
http://pdglive.lbl.gov/Particle.action?node=M229
|
CHARMED MESONS($\boldsymbol C$ = $\pm1$) ${{\mathit D}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit d}}}$, ${{\mathit D}^{0}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit u}}}$, ${{\overline{\mathit D}}^{0}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit u}}$, ${{\mathit D}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit d}}$, similarly for ${{\mathit D}^{*}}$'s INSPIRE search
# ${{\boldsymbol D}{(3000)}^{0}}$ $I(J^P)$ = $1/2(?^{?})$
Both natural- and unnatural-parity components observed depending on the decay mode (AAIJ 2013CC).
${{\mathit D}{(3000)}^{0}}$ MASS $3214 \pm60$ MeV
${{\mathit D}{(3000)}^{0}}$ WIDTH $186 \pm80$ MeV
${{\mathit D}{(3000)}^{0}}$ POLARIZATION AMPLITUDE A$_{{{\mathit D}_{{J}}}}$
$\Gamma_{1}$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}$ seen 971
| 2020-01-26T14:18:41 |
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|
https://arrow.fandom.com/wiki/User_talk:Zomlouis
|
6,850 Pages
# Zomlouis
## aka Louis
My favorite wikis
## Welcome
Hi, I'm an admin for the Arrowverse Wiki community. Welcome and thank you for your edit to Nora! If you need help getting started, check out our help pages or contact me or another admin here. For general help, you could also stop by Community Central to explore the forums and blogs.
Please leave me a message if I can help with anything. Enjoy your time at Arrowverse Wiki!
TimeShade (talk) 12:30, October 11, 2018 (UTC)
## Blocking
Hey, since I am only a content mod, I don't have the ability to block users. An admin will have to do that. You already messaged one. So don't go spamming others. $\int$ IHH dt 9:17, Dec 14, 2019 (UTC)
## Godspeed
Hey, just asking, what is your source for Ryan Handley playing Godspeed in his suit?Ninja72 (talk) 21:05, April 22, 2019 (UTC)
## Novels
Hey, please use our Bk template when linking to novels. It works exactly the same way as our Ep template for episodes. Thanks, $\int$ IHH dt 9:17, Dec 14, 2019 (UTC)
No problem, you can see our Manual of Style for more about how we format things. $\int$ IHH dt 9:17, Dec 14, 2019 (UTC)
## No problem
Your welcome.--Typhuss999 (talk) 14:49, September 24, 2019 (UTC)
## Images
Hey, please be sure that you include where images are from when you upload them. In order to abide by copyright laws, we must do this. You can do this by using the Image-screenshot template with the episode title in the first parameter. Thanks, $\int$ IHH dt 9:17, Dec 14, 2019 (UTC)
## Image policy
Hey there, it would be great if you could just check out our image policy, specifically regarding filetypes. We don't allow JPGs, but only PNGs, due to their lossless compression. Thanks! —MakeShift (talk page) 13:20, November 18, 2019 (UTC)
Please make sure you're fully following the image policy, just cause we want to keep the wiki nice and consistent. This includes categorising where appropriate (such as characters), as well as using a lowercase filetype. —MakeShift (talk page) 15:45, November 25, 2019 (UTC)
I'm referring to the need to categorise them properly based on what characters are in the images; see this section of our policy for what I mean. And yes, the filetype should be lowercase, it just keeps better consistency. Thanks! —MakeShift (talk page) 00:21, November 26, 2019 (UTC)
Firstly add the appropriate category to the image; in this case it would be "Images of Sabrina". The category itself would then include the following: {{OfCharacter|Sabrina|show=The Flash (CBS)}} Note the character's name, as well as the main show they appear on. —MakeShift (talk page) 14:21, November 26, 2019 (UTC)
## Move
I will later today, just need to be sure so I can update the links and all, as the auto-update JS can be faulty sometimes.TIMESHADE |Talk/Wall| - |C| 21:43, December 9, 2019 (UTC)
Thanks for the info. Didn't know about the merge.
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-12-15T22:13:39 |
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https://blog.mbedded.ninja/programming/languages/c/data-types/
|
DATA TYPES
# Data Types
Article by:
Date Published: June 14, 2013 Last Modified: June 14, 2013
## 1. The Basic Data Types
The C programming languages supports the following basic data types:
TypeDescription
char
The smallest type on an architecture. Usually 8-bits wide. Sign depends on implementation.
int
It is guaranteed to be at least 16 bits, but is defined to be the "most natural integer representation for a particular platform", so on a 32-bit machine an int is likely to be 32 bits wide. The only type that the modulus operation can be applied on.
float
Single precision floating point number. Typically 32-bits wide.
double
Double precision floating point number. Typically 64-bits wide, although can be analogous to float (i.e. 32-bits wide) on smaller systems such as 8-bit microcontrollers.
void
Special case data-type.
Some of these types can be prefixed with the modifiers short and long, which change the size of the data type, and the modifiers signed and unsigned which change whether a number can stored negative numbers or not (in this case, the size of the type does not change, but the range of numbers it can represent does). Every other data type/structure is made up from a combination of these basic data types and the modifiers.
It is strongly recommended that you don’t use the numeric data types which can vary in size such as int, and instead use fixed-width data types such as uint8_t, int32_t, e.t.c. This increases the portability of your code and increases the readability (it makes it very obvious to a reader of each integer variable’s capacity). These fixed-width types are almost always specified by architecture specific headers which essentially typedef to the correct int/long int/e.t.c for that architecture.
The fixed-width data types are usually defined in stdint.h. These include:
int8_t
uint8_t
int16_t
uint16_t
int32_t
uint32_t
int64_t
uint64_t
// Not all compilers/platforms (especially microcontroller ones) support these last two
int128_t
uint128_t
## 2. Using sizeof()
sizeof() can be used to return the number of bytes each type uses.
“There was a young man named Wight, Who invented the thirteen bit byte. You’ll get so much more, from your memory, I’m sure. But sadly your sizeof ain’t right.”[1]
— (author unknown)
## 3. Fixed-width Integral Types
The problem with using int and all of it’s derivatives (short int, long int, long long int, e.t.c) is that the width of the integer is platform specific. It is normally the same width as the platforms bus, but at least 16-bits. It is also called the natural width. For example, on an 8-bit system, an int will be 16 bits wide (remember, the C standard specifies it can’t be less than 16 bits). On a 16-bit platform, it will usually be 16 bits, 32 bits for a 32-bit platform, 64 bits for a 64-bit platform, and so on, you get the idea!
To write portable code, it is usually better to use fixed-width integral types.
Fixed-width integral types also need special symbols for printf() statements. These are specified in <cinttypes.h>. They begin with the letters PRI.
## 4. Floats And Doubles
### 4.1. Floating Point Support
Most higher-end microcontrollers and CPUs will have a hardware floating-point unit (FPU) inside them, which allows the CPU to do fast floating-point arithmetic. If you have a lower-end, cheaper microcontroller, it may not contain a FPU. In this case, you really have two options if you want to manipulate numbers with decimal precision:
### 4.2. Positive And Negative 0
Floating point numbers support both positive and negative 0 (they are represented by different raw data). To make life easy and most mathematical equations make sense, even though they are stored differently, they are made to equate to one another, that is -0.0 == +0.0 will be true.
-0.0 doesn’t usually cause any problems for an application, in fact some functions behave differently to -0.0 and +0.0 (e.g. atan2(), 1/x) such that the maths behaves "as expected"[2]. However it can be a tad unsightly to print -0.0 for a user-facing display. There are a few ways you can convert -0.0 into 0.0 before printing. The most obvious way is to:
float remove_neg_zero_obvious(float a) {
if(a == 0.0) { // This works, remembering that -0.0==0.0
return 0.0;
} else {
return a;
}
}
However, there is a simpler trick that can work:
float remove_neg_zero_simple(float a) {
return a + 0.0;
}
Both of these examples as a complete, testable program (visit https://replit.com/@gbmhunter/positive-and-negative-floats to run it online):
#include <stdio.h>
float remove_neg_zero_obvious(float a) {
if(a == 0.0) { // This works, remembering that -0.0==0.0
return 0.0;
} else {
return a;
}
}
float remove_neg_zero_simple(float a) {
return a + 0.0;
}
int main(void) {
printf("%f\n", remove_neg_zero_obvious(-0.0));
printf("%f\n", remove_neg_zero_simple(-0.0));
return 0;
}
## Authors
### Geoffrey Hunter
Dude making stuff.
This work is licensed under a Creative Commons Attribution 4.0 International License .
## Tags
comments powered by Disqus
| 2022-12-09T01:57:27 |
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|
https://wiki.cosmos.esa.int/planckpla/index.php?title=Simulation_data&diff=prev&oldid=8104
|
# Difference between revisions of "Simulation data"
The simulation data can be downloaded from the PLA Java interface (Windows -> Supplementary Data).
## Introduction
The 2013 Planck data release is supported by a set of simulated maps of the model sky, by astrophysical component, and of that sky as seen by Planck. The simulation process consists of
1. modeling each astrophysical component of the sky emission for each Planck detector, using pre-Planck data and the relevant characteristics of the Planck instruments (namely the detector plus filter transmissions curves).
2. simulating each detector's observation of each sky component following the Planck scanning strategy and using the best estimates of the detector's beam and noise properties (now obtained in flight), then combining these timelines into a single one per detector, and projecting these simulated timelines onto observed maps (the fiducial sky), as is done with the on-orbit data;
3. generating Monte Carlo realizations of the CMB and of the noise, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.
The first step is performed by the Planck Sky Model (PSM), and the last two by the Planck Simulation Tools (PST), both of which are described in the sections below.
The production of a full focal plane (FFP) simulation, and including the many MC realizations of the CMB and the noise, requires both HFI and LFI data and includes large, computationally challenging, MC realizations. They are too large to be generated on either of the DPC's own cluster. Instead the PST consists of three distinct tools, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. The simulations delivered here are part of the 6th generation FFP simulations, known as FFP6. They were primarily generated on the Hopper and Edison systems at NERSC, with some of the LFI noise MCs generated on the Louhi system at CSC.
While FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities, and is guaranteed to be internally self-consistent, there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:
• the beams do not include far side-lobes;
• the detector noise characteristics are assumed stable: a single noise spectrum per detector is used for the entire mission;
• it assumes perfect calibration, transfer function deconvolution and deglitching;
• it uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.
• it uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.
## The Planck Sky Model
### Overall description
The Planck Sky Model, PSM, consists of a set of data and of code used to simulate sky emission at millimeter-wave frequencies; it is described in detail in Delabrouille et al., (2013)[1], henceforth the PSM paper..
The Planck Sky Model is available here: http://www.apc.univ-paris7.fr/~delabrou/PSM/psm.html
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. The total sky emission is built from the CMB plus ten foreground components, namely thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).
The CMB is modeled using CAMB. It is based on adiabatic initial perturbations, with the following cosmological parameters:
• T_CMB = 2.725
• H = 0.684
• OMEGA_M = 0.292
• OMEGA_B = 0.04724
• OMEGA_NU = 0
• OMEGA_K = 0
• SIGMA_8 = 0.789
• N_S = 0.9732
• N_S_RUNNING = 0
• N_T = 0
• R = 0.0844
• TAU_REION = 0.085
• HE_FRACTION = 0.245
• N_MASSLESS_NU = 3.04
• N_MASSIVE_NU = 0
• W_DARK_ENERGY = -1
• K_PIVOT = 0.002
• SCALAR_AMPLITUDE = 2.441e-9
and all other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an fNL parameter of 20.4075.
The Galactic ISM emission comprises five components: thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (2008)[2], henceforth SFB, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the higher resolution of the Planck map).
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. Synchrotron, free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al. (2008)[3]. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular for the HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be attributed to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)[4]. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines. No CO maps has been simulated at the LFI frequnecy (30, 44 and 70 GHz).
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008)[5] mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010)[6]. Relativistic corrections following Itoh et al. (1998)[7] are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One caveat is that due to the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM paper for details about the PSM point source simulations. The PSM separates bright and faint point source; the former are initially in a catalog, and the latter in a map, though a map of the former can also be produced. In the processing below, the bright sources are simulated via the catalog, but for convenience they are delivered as a map.
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum Planck-Early-XVIII[8].
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of the ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.
### PSM Products
To build maps corresponding to the Planck channels, the models described above are convolved with the spectral response of the channel in question. The products given here are for the full frequency channels, and as such they are not used in the Planck specific simulations, which use only individual detector channels. The frequency channel spectral responses used (given in the RIMO), are averages of the responses of the detectors of each frequency channel weighted as they are in the mapmaking step. They are provided for the purpose of testing user's own software of simulations and component separation.
PSM maps of the CMB and of the ten foregrounds are given in the following map products:
HFI
LFI
Each file contains a single BINTABLE extension with either a single map (for the CMB file) or one map for each HFI/LFI frequency (for the foreground components). In the latter case the columns are named F030, F044 ,F070,F100, F143, … , F857. Units are microKCMB for the CMB, KCMB at 30, 44 and 70 GHz and MJy/sr for the others. The structure is given below for multi-column files.
Note: Original PSM foreground components has been generated at NSIDE 2048 and using a gaussian beam of 4 arcmin, LFI maps where then smoothed to LFI resolution (32.0, 27.0 and 13.0 arcmin for the 30, 44 and 70 GHz) and donwgraded at NSIDE 1024. LFI CMB maps has been smoothed at 13.0 arcmin (70 GHz resolution) and downgraded at NSIDE 1024.
HFI FITS file structure
1. EXTNAME = 'SIM-MAP' : Data columns
Column Name Data Type Units Description
F100 Real*4 MJy/sr 100GHz signal map
F143 Real*4 MJy/sr 143GHz signal map
F217 Real*4 MJy/sr 217GHz signal map
F353 Real*4 MJy/sr 353GHz signal map
F545 Real*4 MJy/sr 545GHz signal map
F857 Real*4 MJy/sr 857GHz signal map
Keyword Data Type Value Description
PIXTYPE string HEALPIX
COMP string component Astrophysical omponent
COORDSYS string GALACTIC Coordinate system
ORDERING string NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside for LFI and HFI, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI and HFI, respectively
BEAMTYPE string GAUSSIAN Type of beam
BEAMSIZE Real*4 size Beam size in arcmin
PSM-VERS string PSM Versions used
LFI FITS file structure
1. EXTNAME = 'SIM-MAP' : Data columns
Column Name Data Type Units Description
F030 Real*4 KCMB 30GHz signal map
F044 Real*4 KCMB 44GHz signal map
F070 Real*4 KCMB 70GHz signal map
Keyword Data Type Value Description
PIXTYPE string HEALPIX
COMP string component Astrophysical omponent
COORDSYS string GALACTIC Coordinate system
ORDERING string NESTED Healpix ordering
NSIDE Int 1024 Healpix Nside for LFI and HFI, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 12582911 Last pixel number, for LFI and HFI, respectively
BEAMTYPE string GAUSSIAN Type of beam
BEAMS_30 Real*4 32.0 Beam size at 30 GHz in arcmin
BEAMS_44 Real*4 27.0 Beam size at 44 GHz in arcmin
BEAMS_70 Real*4 13.0 Beam size at 70 GHz in arcmin
PSM-VERS string PSM Versions used
## The Fiducial Sky Simulations
For each detector, fiducial time-ordered data are generated separately for each of the ten PSM components using the LevelS software [9] as follows:
• the detector's beam and PSM map are converted to spherical harmonics using beam2alm and anafast respectively;
• the beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using conviqt;
• the map-based timelines are calculated sample-by-sample by interpolating over this grid using multimod;
• the catalogue-based timelines are produced sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using multimod.
For each frequency, fiducial sky maps are generated for
• the total signal (i.e. sky + instrument noise), for both the nominal mission and the halfrings thereof (see details)
• the foreground sky alone (excluding CMB but including noise),
• the point source sky, and
• the noise alone
All maps are built using the MADAM destriping map-maker [10] interfaced with the TOAST data abstraction layer . In order to construct the total timelines required by each map, for each detector TOAST reads the various component timelines separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly. HFI frequencies are mapped at HEALPix resolution Nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at Nside=1024 using 1s baselines.
### Products delivered
A single simulation is delivered, which is divided into two types of products:
1. six files of the full sky signal at each HFI and LFI frequency, and their corresponding halfring maps:
HFI_SimMap_100_2048_R1.10_nominal.fits HFI_SimMap_100_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_100_2048_R1.10_nominal_ringhalf_2.fits HFI_SimMap_143_2048_R1.10_nominal.fits HFI_SimMap_143_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_143_2048_R1.10_nominal_ringhalf_2.fits HFI_SimMap_217_2048_R1.10_nominal.fits HFI_SimMap_217_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_217_2048_R1.10_nominal_ringhalf_2.fits HFI_SimMap_353_2048_R1.10_nominal.fits HFI_SimMap_353_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_353_2048_R1.10_nominal_ringhalf_2.fits HFI_SimMap_545_2048_R1.10_nominal.fits HFI_SimMap_545_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_545_2048_R1.10_nominal_ringhalf_2.fits HFI_SimMap_857_2048_R1.10_nominal.fits HFI_SimMap_857_2048_R1.10_nominal_ringhalf_1.fits HFI_SimMap_857_2048_R1.10_nominal_ringhalf_2.fits
LFI_SimMap_030_1024_R1.10_nominal.fits LFI_SimMap_030_1024_R1.10_nominal_ringhalf_1.fits LFI_SimMap_030_1024_R1.10_nominal_ringhalf_2.fits LFI_SimMap_044_1024_R1.10_nominal.fits LFI_SimMap_044_1024_R1.10_nominal_ringhalf_1.fits LFI_SimMap_044_1024_R1.10_nominal_ringhalf_2.fits LFI_SimMap_070_1024_R1.10_nominal.fits LFI_SimMap_070_1024_R1.10_nominal_ringhalf_1.fits LFI_SimMap_070_1024_R1.10_nominal_ringhalf_2.fits
These files have the same structure as the equivalent SkyMap products described in the Frequency Maps chapter, namely one BINTABLE extension with three columns containing 1) Signal, 2) hit-count, and 3) variance. Units are KCMB for all channels.
2. Three files containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.
These files have the same structure as the PSM output maps described above, namely a single BINTABLE extension with 6 columns named F100 -- F857 each containing the given map for that HFI band and with 3 columns named F030, F044, F070 each containing the given map for that LFI band. Units are alway KCMB.
Note that the CMB alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map.
## Monte Carlo realizations of CMB and of noise
The CMB MC set is generated using FEBeCoP [11], which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.
The noise MC set is generated just as the fiducial noise maps, using MADAM/TOAST. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.
### Products delivered
100 realizations of the CMB (lensed) and of the noise are made available. They are named
• HFI_SimMap_cmb-{nnnn}_2048_R1.nn_nominal.fits
• HFI_SimMap_noise-{nnnn}_2048_R1.nn_nominal.fits
• LFI_SimMap_cmb-{nnnn}_2048_R1.nn_nominal.fits
• LFI_SimMap_noise-{nnnn}_2048_R1.nn_nominal.fits
where nnnn ranges from 0000 to 0099.
The FITS file structure is the same as for the other similar products above, with a single BINTABLE extension with six columns, one for each HFI frequency, named F100, F143, … , F857 and with three columns, one for each LFI frequency, named F030, F044, F070. Units are always microKCMB(NB: due to an error in the HFI file construction, the unit keywords in the headers indicate KCMB, the "micro" is missing there).
## Lensing Simulations
N.B. The information in this section is adapted from the package Readme.txt file.
The lensing simulations package contains 100 realisations of the Planck 2013 "MV" lensing potential estimate, as well as the input CMB and lensing potential realizations. They can be used to determine error bars for cross-correlations with other tracers of lensing. These simulations are of the PHIBAR map contained in the Lensing map release file. The production and characterisation of this lensing potential map are described in detail in [12], which describes also the procedure used to generate the realizations given here.
### Products delivered
The simulations are delivered as a single tarball of ~17 GB containing the following directories:
obs_plms/dat_plmbar.fits - contains the multipoles of the PHIBAR map in COM_CompMap_Lensing_2048_R1.10.fits
obs_plms/sim_????_plmbar.fits - simulated relizations of PHIBAR, in Alm format.
sky_plms/sim_????_plm.fits - the input multipoles of phi for each simulation
sky_cmbs/sim_????_tlm_unlensed.fits - the input unlensed CMB multipoles for each simulation
sky_cmbs/sim_????_tlm_lensed.fits - the input lensed CMB multipoles for each simulation.
inputs/cls/cltt.dat - Fiducial lensed CMB temperature power spectrum ClTT.
inputs/cls/clpp.dat - Fiducial CMB lensing potential power spectrum ClPP.
inputs/cls/cltp.dat - Fiducial correlation between lensed T and P.
inputs/cls/cltt_unlensed.dat - Fiducial unlensed CMB temperature power spectrum.
inputs/filt_mask.fits.gz - HEALpix Nside=2048 map containing the analysis mask for the lens reconstructions (equivalent to the MASK column in COM_CompMap_Lensing_2048_R1.10.fits)
All of the .fits files in this package are HEALPix Alm, to lmax=2048 unless otherwise specified.
For delivery purposes this package has been split into 2 GB chunks using the unix command
split -d -b 2048m
which produced files with names like COM_SimMap_Lensing_R1.10.tar.nn, with nn=00-07. They can be recombined and the maps extracted via
cat COM_SimMap_Lensing_R1.10.tar.* | tar xvf -
## References
1. The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths, J. Delabrouille, M. Betoule, J.-B. Melin, M.-A. Miville-Deschênes, J. Gonzalez-Nuevo, M. Le Jeune, G. Castex, G. de Zotti, S. Basak, M. Ashdown, J. Aumont, C. Baccigalupi, A. Banday, J.-P. Bernard, F. R. Bouchet, D. L. Clements, A. da Silva, C. Dickinson, F. Dodu, K. Dolag, F. Elsner, L. Fauvet, G. Faÿ, G. Giardino, S. Leach, J. Lesgourgues, M. Liguori, J. F. Macias-Perez, M. Massardi, S. Matarrese, P. Mazzotta, L. Montier, S. Mottet, R. Paladini, B. Partridge, R. Piffaretti, G. Prezeau, S. Prunet, S. Ricciardi, M. Roman, B. Schaefer, L. Toffolatti, A&A, 553, A96, (2013).
2. Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds, D. J. Schlegel, D. P. Finkbeiner, M. Davis, ApJ, 500, 525-+, (1998).
3. Separation of anomalous and synchrotron emissions using WMAP polarization data, M.-A. Deschênes, N. Ysard, A. Lavabre, N. Ponthieu, J. F. Macías-Pérez, J. Aumont, J. P. Bernard, A&A, 490, 1093-1102, (2008).
4. The Milky Way in Molecular Clouds: A New Complete CO Survey, T. M. Dame, D. Hartmann, P. Thaddeus, ApJ, 547, 792-813, (2001).
5. Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality, J. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. Warren, G. Yepes, S. Gottlöber, D. E. Holz, ApJ, 688, 709-728, (2008).
6. The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the Y$_{SZ}$ - M$_{500}$ relation, M. Arnaud, G. W. Pratt, R. Piffaretti, H. Böhringer, J. H. Croston, E. Pointecouteau, ApJ, 517, A92, (2010).
7. Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. Inclusion of Peculiar Velocities, S. Nozawa, N. Itoh, Y. Kohyama, ApJ, 508, 17-24, (1998).
8. Planck early results. XVIII. The power spectrum of cosmic infrared background anisotropies, Planck Collaboration XVIII, A&A, 536, A18, (2011).
9. A simulation pipeline for the Planck mission, M. Reinecke, K. Dolag, R. Hell, M. Bartelmann, T. A. Enßlin, A&A, 445, 373-373, (2006).
10. Fast Pixel Space Convolution for Cosmic Microwave Background Surveys with Asymmetric Beams and Complex Scan Strategies: FEBeCoP, S. Mitra, G. Rocha, K. M. Górski, K. M. Huffenberger, H. K. Eriksen, M. A. J. Ashdown, C. R. Lawrence, ApJS, 193, 5-+, (2011).
11. Planck 2013 results: Gravitational lensing by large-scale structure, Planck Collaboration XVII, A&A, in press, (2014).
Planck Legacy Archive
Cosmic Microwave background
Planck Sky Model
(Planck) High Frequency Instrument
(Planck) Low Frequency Instrument
Data Processing Center
[LFI meaning]: absolute calibration refers to the 0th order calibration for each channel, 1 single number, while the relative calibration refers to the component of the calibration that varies pointing period by pointing period.
Sunyaev-Zel'dovich
Flexible Image Transfer Specification
(Hierarchical Equal Area isoLatitude Pixelation of a sphere, <ref name="Template:Gorski2005">HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, 622, 759-771, (2005).
| 2022-05-18T03:16:24 |
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https://www.khanacademy.org/computing/computer-science/algorithms/binary-search/a/binary-search
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# Binary search
Binary search is an efficient algorithm for finding an item from an ordered list of items. It works by repeatedly dividing in half the portion of the list that could contain the item, until you've narrowed down the possible locations to just one. We used binary search in the guessing game in the introductory tutorial.
One of the most common ways to use binary search is to find an item in an array. For example, the Tycho-2 star catalog contains information about the brightest 2,539,913 stars in our galaxy. Suppose that you want to search the catalog for a particular star, based on the star's name. If the program examined every star in the star catalog in order starting with the first, an algorithm called linear search, the computer might have to examine all 2,539,913 stars to find the star you were looking for, in the worst case. If the catalog were sorted alphabetically by star names, binary search would not have to examine more than 22 stars, even in the worst case.
The next few articles discuss how to describe the algorithm carefully, how to implement the algorithm in JavaScript, and how to analyze efficiency.
### Pseudocode for binary search
When describing an algorithm to a fellow human being, an incomplete description is often good enough. Some details may be left out of a recipe for a cake; the recipe assumes that you know how to open the refrigerator to get the eggs out and that you know how to crack the eggs. People might intuitively know how to fill in the missing details, but computer programs do not. That's why we need to describe computer algorithms completely.
In order to implement an algorithm in a programming language, you will need to understand an algorithm down to the details. What are the inputs to the problem? The outputs? What variables should be created, and what initial values should they have? What intermediate steps should be taken to compute other values and to ultimately compute the output? Do these steps repeat instructions that can be written in simplified form using a loop?
Let's look at how to describe binary search carefully. The main idea of binary search is to keep track of the current range of reasonable guesses. Let's say that I'm thinking of a number between one and 100, just like the guessing game. If you've already guessed 25 and I told you my number was higher, and you've already guessed 81 and I told you my number was lower, then the numbers in the range from 26 to 80 are the only reasonable guesses. Here, the red section of the number line contains the reasonable guesses, and the black section shows the guesses that we've ruled out:
Binary search number line 26 to 80
In each turn, you choose a guess that divides the set of reasonable guesses into two ranges of roughly the same size. If your guess is not correct, then I tell you whether it's too high or too low, and you can eliminate about half of the reasonable guesses. For example, if the current range of reasonable guesses is 26 to 80, you would guess the halfway point, left parenthesis, 26, plus, 80, right parenthesis, slash, 2, or 53. If I then tell you that 53 is too high, you can eliminate all numbers from 53 to 80, leaving 26 to 52 as the new range of reasonable guesses, halving the size of the range.
Binary search number line 26 to 52
For the guessing game, we can keep track of the set of reasonable guesses using a few variables. Let the variable m, i, n be the current minimum reasonable guess for this round, and let the variable m, a, x be the current maximum reasonable guess. The input to the problem is the number n, the highest possible number that your opponent is thinking of. We assume that the lowest possible number is one, but it would be easy to modify the algorithm to take the lowest possible number as a second input.
Here's a pseudocode description of binary search:
1. Let m, i, n, equals, 1and m, a, x, equals, n.
2. Guess the average of m, a, x and $min$, rounded down so that it is an integer.
3. If you guessed the number, stop. You found it!
4. If the guess was too low, set $min$ to be one larger than the guess.
5. If the guess was too high, set $max$ to be one smaller than the guess.
6. Go back to step two.
We could make this pseudocode even more precise by clearly describing the inputs and the outputs for the algorithm and by clarifying what we mean by instructions like "guess a number" and "stop." But this will do for now.
This content is a collaboration of Dartmouth Computer Science professors Thomas Cormen and Devin Balkcom plus the Khan Academy computing curriculum team. The content is licensed CC-BY-NC-SA.
| 2017-03-28T16:12:27 |
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https://zbmath.org/authors/?q=ai%3Acurtain.ruth-f
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## Curtain, Ruth Frances
Compute Distance To:
Author ID: curtain.ruth-f Published as: Curtain, Ruth F.; Curtain, R. F.; Curtain, Ruth more...less Homepage: http://www.math.rug.nl/curtain/ External Links: MGP · Wikidata · ResearchGate · dblp · IdRef
Documents Indexed: 155 Publications since 1970, including 4 Books 5 Contributions as Editor · 1 Further Contribution Reviewing Activity: 2 Reviews Biographic References: 2 Publications Co-Authors: 38 Co-Authors with 93 Joint Publications 1,157 Co-Co-Authors
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### Co-Authors
65 single-authored 15 Zwart, Hans J. 9 Pritchard, Anthony J. 7 Bontsema, Jan 7 Sasane, Amol J. 7 Weiss, George 6 Glover, Keith 6 Opmeer, Mark R. 5 Kotelenez, Peter M. 5 Logemann, Hartmut 5 Oostveen, Job C. 4 Iftime, Orest V. 4 Weiss, Martin G. 4 Zhou, Yishao 3 Ichikawa, Akira 3 Partington, Jonathan R. 3 van Keulen, Bert A. M. 2 Falb, Peter L. 2 Hinrichsen, Diederich 2 Ito, Kazufumi 2 Kubrusly, Carlos S. 2 Rodman, Leiba X. 2 Salamon, Dietmar Arno 2 Schumacher, Johannes M. 2 Staffans, Olof Johan 2 Townley, Stuart B. 1 Amouroux, Marcel 1 Araya, Rodrigo 1 Arnold, Ludwig 1 Aubrun, J.-N. 1 Babary, Jean-Pierre 1 Bahar, Leon Y. 1 Baillieul, John B. 1 Balas, Mark J. 1 Banks, Harvey Thomas 1 Bar-Kana, Izhak 1 Bayard, David S. 1 Bensoussan, Alain 1 Bentsman, Joseph 1 Bertoni, Gianni 1 Boussalis, Dhemetrios 1 Brisbane, T. E. 1 Burke, Shawn E. 1 Burns, John A. 1 Capitani, Gloria 1 Cliff, Eugene M. 1 Costveen, Job C. 1 de Lafontaine, Jean 1 Delfour, Michel Claude 1 Demetriou, Michael A. 1 El Bagdouri, M. 1 El Jai, Abdelhaq 1 Eldred, D. 1 Fathi, Zohreh 1 Felippe de Souza, J. A. M. 1 Fiagbedzi, Yawvi A. 1 Fischl, Robert 1 Forrest-Barlach, M. G. 1 Garba, John A. 1 Gay, D. H. 1 Graham, John W. 1 Hadaegh, Fred Y. 1 Havas, T. W. 1 Helferty, John J. 1 Henninger, W. C. 1 Herczfeld, P. R. 1 Hubbard, James E. jun. 1 Ih, Che-Hang Charles 1 Jacob, Birgit 1 Jarny, Yvon 1 Jay-Chung Chen 1 Juang, Jer-Nan 1 Kaashoek, Marinus Adriaan 1 Kaufman, Howard 1 Keyhani, Ali 1 Kojima, Fumio 1 Koski, Timo J. T. 1 Kuiper, C. R. 1 Kunisch, Karl 1 Levan, Nhan 1 Levi, Mark L. 1 Lilly, John H. 1 Lions, Jacques-Louis 1 Liu, Mingyan 1 Lorell, K. R. 1 Malebranche, Helios 1 Marshall, J. E. 1 Marzwell, N. 1 Meerkov, Semyon M. 1 Meldrum, D. R. 1 Mikkola, Kalle M. 1 Milman, Mark H. 1 Minnick, D. 1 Miri, S. Mohsen 1 Modi, Vinod J. 1 Morris, Kirsten A. 1 Musalem, Andrés 1 Ohnaka, Kohzaburo 1 Omatu, Sigeru 1 Osinga, Hinke Maria 1 Ouyang, J. J. ...and 48 more Co-Authors
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### Serials
23 Systems & Control Letters 17 SIAM Journal on Control and Optimization 11 Automatica 10 IEEE Transactions on Automatic Control 9 International Journal of Control 7 Integral Equations and Operator Theory 6 Journal of Mathematical Analysis and Applications 4 Stochastics 4 MCSS. Mathematics of Control, Signals, and Systems 2 IMA Journal of Mathematical Control and Information 2 Linear Algebra and its Applications 2 International Journal of Robust and Nonlinear Control 2 Journal of Mathematical Systems, Estimation, and Control 2 International Journal of Applied Mathematics and Computer Science 2 SIAM Journal on Control 2 Lecture Notes in Control and Information Sciences 2 Texts in Applied Mathematics 1 Journal of the Franklin Institute 1 IEEE Transactions on Circuits and Systems 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Mathematical Systems Theory 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Matrix Analysis and Applications 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Review 1 Matemática Aplicada e Computacional 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Indagationes Mathematicae. New Series 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Lecture Notes in Mathematics 1 Mathematics in Science and Engineering 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Mathematical Control and Related Fields 1 IEEE Control Systems
all top 5
### Fields
151 Systems theory; control (93-XX) 48 Operator theory (47-XX) 22 Probability theory and stochastic processes (60-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 15 Ordinary differential equations (34-XX) 12 Partial differential equations (35-XX) 12 Functional analysis (46-XX) 7 Approximations and expansions (41-XX) 6 General and overarching topics; collections (00-XX) 6 Mechanics of deformable solids (74-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX)
### Citations contained in zbMATH Open
133 Publications have been cited 2,315 times in 1,620 Documents Cited by Year
An introduction to infinite-dimensional linear systems theory. Zbl 0839.93001
Curtain, Ruth F.; Zwart, Hans
1995
Infinite dimensional linear systems theory. Zbl 0389.93001
Curtain, Ruth F.; Pritchard, Anthony J.
1978
Spectral realizations for delay systems. Zbl 0646.93014
Curtain, R. F.; Zwart, H. J.
1987
Functional analysis in modern applied mathematics. Zbl 0448.46002
Curtain, Ruth F.; Pritchard, A. J.
1977
Realisation and approximation of linear infinite-dimensional systems with error bounds. Zbl 0654.93011
Glover, Keith; Curtain, Ruth F.; Partington, Jonathan R.
1988
Stochastic differential equations in Hilbert space. Zbl 0225.60028
Curtain, Ruth F.; Falb, Peter L.
1971
The infinite-dimensional Riccati equation for systems defined by evolution operators. Zbl 0352.49003
Curtain, Ruth; Pritchard, A. J.
1976
Transfer functions of distributed parameter systems: a tutorial. Zbl 1162.93300
Curtain, Ruth; Morris, Kirsten
2009
A semigroup approach to infinite dimensional system theory. Zbl 0426.93001
Curtain, Ruth F.; Pritchard, A. J.
1978
Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input. Zbl 0477.93039
Curtain, Ruth F.
1982
Dynamic stabilization of regular linear systems. Zbl 0876.93074
Weiss, George; Curtain, Ruth F.
1997
Finite dimensional compensators for parabolic distributed systems with unbounded control and observation. Zbl 0542.93056
Curtain, Ruth F.
1984
Finite dimensional compensators for infinite dimensional systems with unbounded input operators. Zbl 0598.93033
Curtain, R. F.; Salamon, D.
1986
Invariance concepts in infinite dimensions. Zbl 0602.93037
Curtain, Ruth F.
1986
The Salamon-Weiss class of well-posed infinite-dimensional linear systems: A survey. Zbl 0880.93021
Curtain, Ruth F.
1997
Ito’s lemma in infinite dimensions. Zbl 0233.60051
Curtain, Ruth F.; Falb, Peter L.
1970
Robust stabilization of infinite dimensional systems by finite dimensional controllers. Zbl 0601.93044
Curtain, Ruth F.; Glover, Keith
1986
Equivalence of input-output stability and exponential stability for infinite-dimensional systems. Zbl 0657.93050
Curtain, Ruth F.
1988
System theoretic properties of a class of spatially invariant systems. Zbl 1184.93094
Curtain, Ruth; Iftime, Orest V.; Zwart, Hans
2009
Exponential stabilization of well-posed systems by colocated feedback. Zbl 1139.93026
Curtain, Ruth F.; Weiss, George
2006
Spectral systems. Zbl 0541.93041
Curtain, Ruth F.
1984
A survey of infinite-dimensional filtering. Zbl 0308.60022
Curtain, Ruth
1975
Robust stabilizability of normalized coprime factors: The infinite- dimensional case. Zbl 0703.93050
Curtain, Ruth F.
1990
Stability of stochastic partial differential equation. Zbl 0452.60072
Curtain, Ruth F.
1981
Well posedness of triples of operators (in the sense of linear systems theory). Zbl 0686.93049
Curtain, Ruth F.; Weiss, George
1989
Stochastic evolution equations with general white noise disturbance. Zbl 0367.60067
Curtain, Ruth F.
1977
Controller design for distributed systems based on Hankel-norm approximations. Zbl 0591.93033
Curtain, R. F.; Glover, K.
1986
Well-posedness, stabilizability, and admissibility for Pritchard-Salamon systems. Zbl 0815.93046
Curtain, Ruth F.; Logemann, Hartmut; Townley, Stuart; Zwart, Hans
1994
Comparison theorems for infinite-dimensional Riccati equations. Zbl 0716.93021
Curtain, Ruth F.; Rodman, Leiba
1990
Infinite-dimensional filtering. Zbl 0296.93036
Curtain, Ruth F.
1975
Estimation theory for abstract evolution equations excited by general white noise processes. Zbl 0344.93064
Curtain, Ruth F.
1976
Linear operator inequalities for strongly stable weakly regular linear systems. Zbl 1114.93029
Curtain, Ruth F.
2001
Coprime factorization for regular linear systems. Zbl 0870.93025
Curtain, Ruth; Weiss, George; Weiss, Martin
1996
Riccati equations for strongly stabilizable bounded linear systems. Zbl 0979.93092
Oostveen, Job C.; Curtain, Ruth F.
1998
Compactness and nuclearity of the Hankel operator and internal stability of infinite-dimensional state linear systems. Zbl 1011.93024
Curtain, R. F.; Sasane, A. J.
2001
Robust control of flexible structures: A case study. Zbl 0643.93056
Bontsema, J.; Curtain, R. F.; Schumacher, J. M.
1988
Introduction to infinite-dimensional systems theory. A state-space approach. Zbl 1459.93001
Curtain, Ruth; Zwart, Hans
2020
$$L_{\infty}$$ approximation and nuclearity of delay systems. Zbl 0641.93018
Partington, J. R.; Glover, K.; Zwart, H. J.; Curtain, Ruth F.
1988
Partial fraction expansions for delay systems. Zbl 0654.93034
Zwart, H. J.; Curtain, R. F.; Partington, J. R.; Glover, K.
1988
Explicit formulas for Hankel norm approximations of infinite-dimensional systems. Zbl 0681.47008
Curtain, Ruth F.; Ran, A. C. M.
1989
Linear-quadratic control problem with fixed endpoints in infinite dimensions. Zbl 0527.93037
Curtain, R. F.
1984
Stability results of Popov-type for infinite-dimensional systems with applications to integral control. Zbl 1032.93061
Curtain, R. F.; Logemann, H.; Staffans, O.
2003
The infinite-dimensional Riccati equation. Zbl 0279.93048
Curtain, Ruth F.; Pritchard, A. J.
1974
A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version. Zbl 1204.49035
Curtain, Ruth; Iftime, Orest; Zwart, Hans
2010
The separation principle for stochastic evolution equations. Zbl 0359.60076
Curtain, Ruth F.; Ichikawa, Akira
1977
An abstract theory for unbounded control action for distributed parameter systems. Zbl 0359.93021
Curtain, Ruth F.; Pritchard, A. J.
1977
Stabilization of collocated systems by nonlinear boundary control. Zbl 1347.93216
Curtain, Ruth; Zwart, Hans
2016
Robustly stabilizing controllers for dissipative infinite-dimensional systems with collocated actuators and sensors. Zbl 0979.93101
Oostveen, Job C.; Curtain, Ruth F.
2000
(C,A,B)-pairs in infinite dimensions. Zbl 0553.93037
Curtain, Ruth F.
1984
Disturbance decoupling by measurement feedback with stability for infinite-dimensional systems. Zbl 0591.93032
Curtain, Ruth F.
1986
Compensators for infinite dimensional linear systems. Zbl 0518.93045
Curtain, Ruth F.
1983
Regular linear systems and their reciprocals: applications to Riccati equations. Zbl 1157.93345
Curtain, Ruth F.
2003
The Nehari problem for the Pritchard-Salamon class of infinite- dimensional linear systems: A direct approach. Zbl 0807.47011
Curtain, Ruth; Zwart, Hans
1994
Estimation and stochastic control for linear infinite-dimensional systems. Zbl 0444.60046
Curtain, Ruth F.
1978
Pole assignment for distributed systems by finite-dimensional control. Zbl 0558.93035
Curtain, Ruth F.
1985
Exponential stabilization of a Rayleigh beam using collocated control. Zbl 1367.74029
Weiss, George; Curtain, Ruth F.
2008
Local behaviour of Hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations. Zbl 0486.60058
Kotelenez, Peter; Curtain, Ruth F.
1982
A note on spillover and robustness for flexible systems. Zbl 0644.93043
Bontsema, J.; Curtain, Ruth F.
1988
Representations of infinite-dimensional systems. Zbl 0684.93045
Curtain, R. F.
1989
On Riccati equations in Banach algebras. Zbl 1223.46050
Curtain, Ruth; Sasane, Amol
2011
Necessary and sufficient conditions for strong stability of distributed parameter systems. Zbl 0917.93059
Curtain, Ruth F.; Oostveen, Job C.
1999
Absolute-stability results in infinite dimensions. Zbl 1074.93031
Curtain, R. F.; Logemann, H.; Staffans, O.
2004
A weighted mixed-sensitivity $$H_ \infty$$-control design for irrational transfer matrices. Zbl 0865.93021
Curtain, Ruth F.; Zhou, Yishao
1996
Old and new perspectives on the positive-real lemma in systems and control theory. Zbl 0961.93045
Curtain, R. F.
1999
Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control. Zbl 0964.93048
Logemann, Hartmut; Curtain, Ruth F.
2000
Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems. Zbl 0990.93021
Sasane, Amol J.; Curtain, Ruth F.
2001
Finite dimensional compensators for some hyperbolic systems with boundary control. Zbl 0527.93048
Curtain, R. F.
1983
Normalized doubly coprime factorizations for infinite-dimensional linear systems. Zbl 1105.93052
Curtain, Ruth F.; Opmeer, Mark R.
2006
Perturbation properties of a class of infinite-dimensional systems with unbounded control and observation. Zbl 0666.93067
Bontsema, Jan; Curtain, Ruth F.
1988
New Riccati equations for well-posed linear systems. Zbl 1157.49316
Opmeer, Mark R.; Curtain, Ruth F.
2004
Robust stabilization of infinite-dimensional systems with respect to coprime factor perturbations. Zbl 0792.93097
Curtain, Ruth F.; Pritchard, A. J.
1994
The Nehari problem for nonexponentially stable systems. Zbl 0910.93024
Curtain, Ruth F.; Costveen, Job C.
1998
The strict bounded real lemma in infinite dimensions. Zbl 0782.93043
Curtain, Ruth F.
1993
Inertia theorems for operator Lyapunov inequalities. Zbl 0974.93026
Sasane, A. J.; Curtain, R. F.
2001
Balanced realisations for infinite dimensional systems. Zbl 0619.93016
Curtain, Ruth F.; Glover, Keith
1986
The Nehari problem for infinite-dimensional linear systems of parabolic type. Zbl 0858.47017
Curtain, Ruth F.; Ichikawa, Akira
1996
Sub-optimal Hankel norm approximation for the analytic class of infinite-dimensional systems. Zbl 1007.93040
Sasane, Amol J.; Curtain, Ruth F.
2002
Riccati equations for stable well-posed linear systems: The generic case. Zbl 1048.49022
Curtain, Ruth F.
2003
A robust LQG-controller design for DPS. Zbl 1122.93325
Curtain, R. F.
2006
The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. Zbl 0877.93065
Curtain, R. F.
1996
A representation of all solutions of the control algebraic Riccati equation for infinite-dimensional systems. Zbl 1115.93041
Iftime, O. V.; Zwart, H. J.; Curtain, R. F.
2005
Robust control with respect to coprime factors of infinite-dimensional positive real systems. Zbl 0760.93061
Curtain, Ruth F.; Van Keulen, Bert
1992
$$H_{\infty}$$-control with state-feedback: The infinite-dimensional case. Zbl 0770.93031
van Keulen, Bert; Peters, Marc; Curtain, Ruth
1993
Riccati equations for second order spatially invariant partial differential systems. Zbl 1244.49061
Curtain, Ruth F.
2012
A semigroup approach to the LQG problem for infinite-dimensional systems. Zbl 0402.93045
Curtain, Ruth F.
1978
On stabilizability of linear spectral systems via state boundary feedback. Zbl 0557.93050
Curtain, Ruth F.
1985
Identification of noisy distributed parameter systems using stochastic approximation. Zbl 0351.93030
Kubrusly, C. S.; Curtain, R. F.
1977
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems. Zbl 1090.47508
Opmeer, Mark R.; Curtain, Ruth F.
2004
Stabilization of irrational transfer functions by controllers with internal loop. Zbl 1175.93186
Curtain, Ruth F.; Weiss, George; Weiss, Martin
2001
The infinite-dimensional Riccati equation with applications to affine hereditary differential systems. Zbl 0316.93054
Curtain, Ruth F.
1975
Robustly stabilizing controllers with respect to left-coprime factor perturbations for infinite-dimensional linear systems. Zbl 1129.93522
Curtain, Ruth F.
2006
Hankel norm approximation for well-posed linear systems. Zbl 1157.93419
Curtain, Ruth F.; Sasane, Amol J.
2003
An approximation theory for strongly stabilizing solutions to the operator LQ Riccati equation. Zbl 0970.49025
Oostveen, J. C.; Curtain, R. F.; Ito, K.
2000
The suboptimal Nehari problem for well-posed linear systems. Zbl 1094.47057
Curtain, Ruth F.; Opmeer, Mark R.
2005
Markov processes generated by linear stochastic evolution equations. Zbl 0461.60078
Curtain, Ruth F.
1981
Stabilility of semilinear evolution equations in Hilbert space. Zbl 0544.93056
Curtain, Ruth F.
1984
Optimal location of sensors for filtering for distributed systems. Zbl 0398.93059
Curtain, Ruth F.; Ichikawa, Akira
1978
Comments on “On optimal control of spatially distributed systems”. Zbl 1367.93277
Curtain, Ruth
2009
The Popov criterion for strongly stable distributed parameter systems. Zbl 1014.93034
Curtain, Ruth F.; Oostveen, Job C.
2001
Stabilizability and controllability of spatially invariant PDE systems. Zbl 1360.93177
Curtain, Ruth F.
2015
Introduction to infinite-dimensional systems theory. A state-space approach. Zbl 1459.93001
Curtain, Ruth; Zwart, Hans
2020
Strong stabilization of (almost) impedance passive systems by static output feedback. Zbl 1441.93219
Curtain, Ruth F.; Weiss, George
2019
A Kleinman-Newton construction of the maximal solution of the infinite-dimensional control Riccati equation. Zbl 1375.93063
Curtain, Ruth F.; Zwart, Hans; Iftime, Orest V.
2017
Stabilization of collocated systems by nonlinear boundary control. Zbl 1347.93216
Curtain, Ruth; Zwart, Hans
2016
Stabilizability and controllability of spatially invariant PDE systems. Zbl 1360.93177
Curtain, Ruth F.
2015
Riccati equations for second order spatially invariant partial differential systems. Zbl 1244.49061
Curtain, Ruth F.
2012
On Riccati equations in Banach algebras. Zbl 1223.46050
Curtain, Ruth; Sasane, Amol
2011
Riccati equations on noncommutative Banach algebras. Zbl 1262.46035
Curtain, Ruth
2011
Comments on “Distributed control of spatially invariant systems”. Zbl 1368.93267
Curtain, Ruth
2011
Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems. Zbl 1248.93148
Curtain, Ruth F.; Opmeer, Mark R.
2011
A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version. Zbl 1204.49035
Curtain, Ruth; Iftime, Orest; Zwart, Hans
2010
Analytic solutions of matrix Riccati equations with analytic coefficients. Zbl 1273.47020
Curtain, Ruth; Rodman, Leiba
2010
Transfer functions of distributed parameter systems: a tutorial. Zbl 1162.93300
Curtain, Ruth; Morris, Kirsten
2009
System theoretic properties of a class of spatially invariant systems. Zbl 1184.93094
Curtain, Ruth; Iftime, Orest V.; Zwart, Hans
2009
Comments on “On optimal control of spatially distributed systems”. Zbl 1367.93277
Curtain, Ruth
2009
Spectral properties of pseudo-resolvents under structured perturbations. Zbl 1248.93051
Curtain, Ruth F.; Jacob, Birgit
2009
State space formulas for a solution of the suboptimal Nehari problem on the unit disc. Zbl 1189.47080
Curtain, Ruth F.; Opmeer, Mark R.
2009
Exponential stabilization of a Rayleigh beam using collocated control. Zbl 1367.74029
Weiss, George; Curtain, Ruth F.
2008
The Hilbert-Schmidt property of feedback operators. Zbl 1154.93332
Curtain, Ruth; Mikkola, Kalle; Sasane, Amol
2007
Exponential stabilization of well-posed systems by colocated feedback. Zbl 1139.93026
Curtain, Ruth F.; Weiss, George
2006
Normalized doubly coprime factorizations for infinite-dimensional linear systems. Zbl 1105.93052
Curtain, Ruth F.; Opmeer, Mark R.
2006
A robust LQG-controller design for DPS. Zbl 1122.93325
Curtain, R. F.
2006
Robustly stabilizing controllers with respect to left-coprime factor perturbations for infinite-dimensional linear systems. Zbl 1129.93522
Curtain, Ruth F.
2006
Robustly stabilizing controllers with internal loop. Zbl 1118.93047
Curtain, Ruth F.
2006
A representation of all solutions of the control algebraic Riccati equation for infinite-dimensional systems. Zbl 1115.93041
Iftime, O. V.; Zwart, H. J.; Curtain, R. F.
2005
The suboptimal Nehari problem for well-posed linear systems. Zbl 1094.47057
Curtain, Ruth F.; Opmeer, Mark R.
2005
Absolute-stability results in infinite dimensions. Zbl 1074.93031
Curtain, R. F.; Logemann, H.; Staffans, O.
2004
New Riccati equations for well-posed linear systems. Zbl 1157.49316
Opmeer, Mark R.; Curtain, Ruth F.
2004
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems. Zbl 1090.47508
Opmeer, Mark R.; Curtain, Ruth F.
2004
Stability results of Popov-type for infinite-dimensional systems with applications to integral control. Zbl 1032.93061
Curtain, R. F.; Logemann, H.; Staffans, O.
2003
Regular linear systems and their reciprocals: applications to Riccati equations. Zbl 1157.93345
Curtain, Ruth F.
2003
Riccati equations for stable well-posed linear systems: The generic case. Zbl 1048.49022
Curtain, Ruth F.
2003
Hankel norm approximation for well-posed linear systems. Zbl 1157.93419
Curtain, Ruth F.; Sasane, Amol J.
2003
Adaptive compresators for perturbed positive real infinite-dimensional systems. Zbl 1051.93051
Curtain, Ruth F.; Demetriou, Michael A.; Ito, Kazufumi
2003
Sub-optimal Hankel norm approximation for the analytic class of infinite-dimensional systems. Zbl 1007.93040
Sasane, Amol J.; Curtain, Ruth F.
2002
Linear operator inequalities for strongly stable weakly regular linear systems. Zbl 1114.93029
Curtain, Ruth F.
2001
Compactness and nuclearity of the Hankel operator and internal stability of infinite-dimensional state linear systems. Zbl 1011.93024
Curtain, R. F.; Sasane, A. J.
2001
Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems. Zbl 0990.93021
Sasane, Amol J.; Curtain, Ruth F.
2001
Inertia theorems for operator Lyapunov inequalities. Zbl 0974.93026
Sasane, A. J.; Curtain, R. F.
2001
Stabilization of irrational transfer functions by controllers with internal loop. Zbl 1175.93186
Curtain, Ruth F.; Weiss, George; Weiss, Martin
2001
The Popov criterion for strongly stable distributed parameter systems. Zbl 1014.93034
Curtain, Ruth F.; Oostveen, Job C.
2001
Robustly stabilizing controllers for dissipative infinite-dimensional systems with collocated actuators and sensors. Zbl 0979.93101
Oostveen, Job C.; Curtain, Ruth F.
2000
Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control. Zbl 0964.93048
Logemann, Hartmut; Curtain, Ruth F.
2000
An approximation theory for strongly stabilizing solutions to the operator LQ Riccati equation. Zbl 0970.49025
Oostveen, J. C.; Curtain, R. F.; Ito, K.
2000
Necessary and sufficient conditions for strong stability of distributed parameter systems. Zbl 0917.93059
Curtain, Ruth F.; Oostveen, Job C.
1999
Old and new perspectives on the positive-real lemma in systems and control theory. Zbl 0961.93045
Curtain, R. F.
1999
Riccati equations for strongly stabilizable bounded linear systems. Zbl 0979.93092
Oostveen, Job C.; Curtain, Ruth F.
1998
The Nehari problem for nonexponentially stable systems. Zbl 0910.93024
Curtain, Ruth F.; Costveen, Job C.
1998
Dynamic stabilization of regular linear systems. Zbl 0876.93074
Weiss, George; Curtain, Ruth F.
1997
The Salamon-Weiss class of well-posed infinite-dimensional linear systems: A survey. Zbl 0880.93021
Curtain, Ruth F.
1997
Analytic system problems and $$J$$-lossless coprime factorization for infinite-dimensional linear systems. Zbl 0876.93028
Curtain, Ruth; Green, Michael
1997
Coprime factorization for regular linear systems. Zbl 0870.93025
Curtain, Ruth; Weiss, George; Weiss, Martin
1996
A weighted mixed-sensitivity $$H_ \infty$$-control design for irrational transfer matrices. Zbl 0865.93021
Curtain, Ruth F.; Zhou, Yishao
1996
The Nehari problem for infinite-dimensional linear systems of parabolic type. Zbl 0858.47017
Curtain, Ruth F.; Ichikawa, Akira
1996
The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. Zbl 0877.93065
Curtain, R. F.
1996
Riccati equations and normalized coprime factorizations for strongly stabilizable infinite-dimensional systems. Zbl 0875.93201
Curtain, Ruth F.; Zwart, Hans
1996
Approximate solutions to a weighted mixed-sensitivity $$H^ \infty$$-control design for irrational transfer matrices. Zbl 0863.93023
Curtain, R. F.; Weiss, M.; Zhou, Y.
1996
Closed formulae for a parametric-mixed-sensitivity problem for Pritchard-Salamon systems. Zbl 0866.93028
Curtain, R. F.; Weiss, M.; Zhou, Y.
1996
Corrections to “The Kalman-Yakubovich-Popov lemma for Pritchard-Salamon systems”. Zbl 0883.93032
Curtain, R. F.
1996
An introduction to infinite-dimensional linear systems theory. Zbl 0839.93001
Curtain, Ruth F.; Zwart, Hans
1995
Well-posedness, stabilizability, and admissibility for Pritchard-Salamon systems. Zbl 0815.93046
Curtain, Ruth F.; Logemann, Hartmut; Townley, Stuart; Zwart, Hans
1994
The Nehari problem for the Pritchard-Salamon class of infinite- dimensional linear systems: A direct approach. Zbl 0807.47011
Curtain, Ruth; Zwart, Hans
1994
Robust stabilization of infinite-dimensional systems with respect to coprime factor perturbations. Zbl 0792.93097
Curtain, Ruth F.; Pritchard, A. J.
1994
Necessary and sufficient conditions for J-spectral factorizations with a J-Lossless property for infinite-dimensional systems in continuous and discrete time. Zbl 0802.93049
Curtain, Ruth F.; Rodríguez, Alejandro
1994
The Nehari problem for the Pritchard-Salamon class of infinite-dimensional linear systems: A direct approach. Zbl 0925.93322
Zwart, Hans; Curtain, Ruth
1994
The strict bounded real lemma in infinite dimensions. Zbl 0782.93043
Curtain, Ruth F.
1993
$$H_{\infty}$$-control with state-feedback: The infinite-dimensional case. Zbl 0770.93031
van Keulen, Bert; Peters, Marc; Curtain, Ruth
1993
Analysis and optimization of systems: state and frequency domain approaches for infinite-dimensional systems. Proceedings of the 10th international conference, Sophia-Antipolis, France, June 9-12, 1992. Zbl 0771.00025
1993
Robust control with respect to coprime factors of infinite-dimensional positive real systems. Zbl 0760.93061
Curtain, Ruth F.; Van Keulen, Bert
1992
Robust stabilizability of normalized coprime factors: The infinite- dimensional case. Zbl 0703.93050
Curtain, Ruth F.
1990
Comparison theorems for infinite-dimensional Riccati equations. Zbl 0716.93021
Curtain, Ruth F.; Rodman, Leiba
1990
Well posedness of triples of operators (in the sense of linear systems theory). Zbl 0686.93049
Curtain, Ruth F.; Weiss, George
1989
Explicit formulas for Hankel norm approximations of infinite-dimensional systems. Zbl 0681.47008
Curtain, Ruth F.; Ran, A. C. M.
1989
Representations of infinite-dimensional systems. Zbl 0684.93045
Curtain, R. F.
1989
Equivalence of input-output stability and exponential stability. Zbl 0673.93041
Curtain, Ruth F.
1989
Robustness of distributed parameter systems. Zbl 0698.93061
Curtain, Ruth F.
1989
Realisation and approximation of linear infinite-dimensional systems with error bounds. Zbl 0654.93011
Glover, Keith; Curtain, Ruth F.; Partington, Jonathan R.
1988
Equivalence of input-output stability and exponential stability for infinite-dimensional systems. Zbl 0657.93050
Curtain, Ruth F.
1988
Robust control of flexible structures: A case study. Zbl 0643.93056
Bontsema, J.; Curtain, R. F.; Schumacher, J. M.
1988
$$L_{\infty}$$ approximation and nuclearity of delay systems. Zbl 0641.93018
Partington, J. R.; Glover, K.; Zwart, H. J.; Curtain, Ruth F.
1988
Partial fraction expansions for delay systems. Zbl 0654.93034
Zwart, H. J.; Curtain, R. F.; Partington, J. R.; Glover, K.
1988
A note on spillover and robustness for flexible systems. Zbl 0644.93043
Bontsema, J.; Curtain, Ruth F.
1988
Perturbation properties of a class of infinite-dimensional systems with unbounded control and observation. Zbl 0666.93067
Bontsema, Jan; Curtain, Ruth F.
1988
$$L_{\infty}$$-approximations of complex functions and robust controllers for large flexible structures. Zbl 0672.93039
Curtain, Ruth F.
1988
Spectral realizations for delay systems. Zbl 0646.93014
Curtain, R. F.; Zwart, H. J.
1987
Stochastic models for uncertain flexible systems. Zbl 0631.93069
Curtain, Ruth F.; Kotelenez, Peter
1987
Stochastic bilinear spectral systems. Zbl 0615.60055
Curtain, Ruth F.; Kotelenez, Peter
1987
Modelling, robustness and sensitivity reduction in control systems. (Proceedings of the NATO Advanced Research Workshop on Modelling, Robustness and Sensitivity Reduction in Control Systems held in Groningen, The Netherlands, December 1-5, 1986). Zbl 0624.00022
1987
Finite dimensional compensators for infinite dimensional systems with unbounded input operators. Zbl 0598.93033
Curtain, R. F.; Salamon, D.
1986
Invariance concepts in infinite dimensions. Zbl 0602.93037
Curtain, Ruth F.
1986
Robust stabilization of infinite dimensional systems by finite dimensional controllers. Zbl 0601.93044
Curtain, Ruth F.; Glover, Keith
1986
Controller design for distributed systems based on Hankel-norm approximations. Zbl 0591.93033
Curtain, R. F.; Glover, K.
1986
Disturbance decoupling by measurement feedback with stability for infinite-dimensional systems. Zbl 0591.93032
Curtain, Ruth F.
1986
Balanced realisations for infinite dimensional systems. Zbl 0619.93016
Curtain, Ruth F.; Glover, Keith
1986
Pole assignment for distributed systems by finite-dimensional control. Zbl 0558.93035
Curtain, Ruth F.
1985
On stabilizability of linear spectral systems via state boundary feedback. Zbl 0557.93050
Curtain, Ruth F.
1985
Decoupling in infinite dimensions. Zbl 0565.93038
Curtain, Ruth F.
1985
Finite dimensional compensators for parabolic distributed systems with unbounded control and observation. Zbl 0542.93056
Curtain, Ruth F.
1984
Spectral systems. Zbl 0541.93041
Curtain, Ruth F.
1984
Linear-quadratic control problem with fixed endpoints in infinite dimensions. Zbl 0527.93037
Curtain, R. F.
1984
...and 33 more Documents
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### Cited by 1,696 Authors
65 Curtain, Ruth Frances 40 Zwart, Hans J. 31 Guo, Bao-Zhu 25 Partington, Jonathan R. 24 Leiva, Hugo 19 Logemann, Hartmut 18 Sukavanam, Nagarajan 17 Weiss, George 16 Fridman, Emilia 16 Prieur, Christophe 16 Sano, Hideki 16 Sasane, Amol J. 15 Dubljevic, Stevan S. 15 Henríquez, Hernán R. 15 Wang, Junmin 15 Winkin, Joseph J. 14 Kobayashi, Toshihiro 14 Wu, Huaining 13 Iftime, Orest V. 13 Morris, Kirsten A. 13 Paunonen, Lassi 12 Jacob, Birgit 12 Wang, Junwei 11 Aksikas, Ilyasse 11 Balas, Mark J. 11 Boutoulout, Ali 11 Breiten, Tobias 11 El-Sayed, Ahmed Mohamed Ahmed 10 Caraballo Garrido, Tomás 10 Fu, Xianlong 10 Kunisch, Karl 10 Nambu, Takao 10 Opmeer, Mark R. 10 Özbay, Hitay 10 Shukla, Anurag 10 Xu, Gen-Qi 9 Callier, Frank M. 9 Demetriou, Michael A. 9 Deutscher, Joachim 9 Krstić, Miroslav 9 Mironchenko, Andrii 9 Pandey, Dwijendra Narain 9 Pritchard, Anthony J. 9 Zhou, Hua-Cheng 8 Balachandran, Krishnan 8 Bonnet, Catherine 8 Grabowski, Piotr 8 Guiver, Chris 8 Kotelenez, Peter M. 8 Tucsnak, Marius 7 Bashirov, Agamirza E. 7 Da Prato, Giuseppe 7 El Jai, Abdelhaq 7 Glover, Keith 7 Hadd, Said 7 Ibiejugba, Matthew A. 7 Ichikawa, Akira 7 Lam, James 7 Lhachemi, Hugo 7 Li, Yongxiang 7 Meurer, Thomas 7 Otsuka, Naohisa 7 Pohjolainen, Seppo A. 7 Rebarber, Richard 7 Staffans, Olof Johan 7 Zerrik, El Hassan 6 Arora, Urvashi 6 Chen, Jianhua 6 Chen, Pengyu 6 Gil’, Michael Iosif 6 Goreac, Dan 6 Katz, Rami 6 Lasiecka, Irena 6 Mahmudov, Nazim Idrisoglu 6 Makila, Pertti M. 6 Michiels, Wim 6 Rabah, Rabah 6 Rosen, I. Gary 6 Singler, John R. 6 Townley, Stuart B. 6 Wakaiki, Masashi 6 Xu, Xiaodong 6 Yang, Kunyi 6 Zhang, Xuping 5 Ahmed, Nasir Uddin 5 Bagchi, Arunabha 5 Breda, Dimitri 5 Chentouf, Boumediène 5 Cuevas, Claudio 5 Dochain, Denis 5 Emirsajlow, Zbigniew 5 Forbes, J. Fraser 5 Gao, Hang 5 Ge, Zhaoqiang 5 Guo, Faming 5 Hashem, Hind H. G. 5 Immonen, Eero 5 Inaba, Hiroshi 5 Laabissi, Mohamed 5 Le Gorrec, Yann ...and 1,596 more Authors
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### Cited in 264 Serials
181 Automatica 173 Systems & Control Letters 90 Journal of Mathematical Analysis and Applications 81 International Journal of Control 52 MCSS. Mathematics of Control, Signals, and Systems 43 SIAM Journal on Control and Optimization 37 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 34 Journal of the Franklin Institute 27 International Journal of Systems Science 27 Journal of Differential Equations 27 European Journal of Control 25 Journal of Optimization Theory and Applications 24 Applied Mathematics and Computation 24 Integral Equations and Operator Theory 20 Applied Mathematics and Optimization 20 Stochastic Analysis and Applications 20 Linear Algebra and its Applications 18 Mathematical Control and Related Fields 16 International Journal of Applied Mathematics and Computer Science 15 International Journal of Robust and Nonlinear Control 15 Abstract and Applied Analysis 15 Evolution Equations and Control Theory 14 Stochastics 14 Numerical Functional Analysis and Optimization 14 Journal of Dynamical and Control Systems 10 Journal of Systems Science and Complexity 9 Computers & Mathematics with Applications 9 Journal of Fluid Mechanics 9 Journal of Functional Analysis 9 Journal of Evolution Equations 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Discrete and Continuous Dynamical Systems. Series B 8 Nonlinear Analysis. Theory, Methods & Applications 7 Mathematical Methods in the Applied Sciences 7 Mathematics and Computers in Simulation 7 Applied Mathematics Letters 7 Mathematical and Computer Modelling 7 Discrete and Continuous Dynamical Systems 7 Advances in Difference Equations 7 Journal of Control Theory and Applications 7 Asian Journal of Control 6 Applicable Analysis 6 Kybernetika 6 Circuits, Systems, and Signal Processing 6 Acta Applicandae Mathematicae 6 Mathematical Problems in Engineering 6 Nonlinear Dynamics 6 Stochastics and Dynamics 6 Complex Analysis and Operator Theory 5 Computer Methods in Applied Mechanics and Engineering 5 Applied Numerical Mathematics 5 Stochastic Hydrology and Hydraulics 5 Applied Mathematical Modelling 5 Automation and Remote Control 5 International Journal of Computer Mathematics 5 Positivity 5 International Journal of Systems Science. Principles and Applications of Systems and Integration 4 Information Sciences 4 Mathematische Nachrichten 4 Mathematical Systems Theory 4 Numerische Mathematik 4 Quarterly of Applied Mathematics 4 Rendiconti del Seminario Matematico della Università di Padova 4 Optimal Control Applications & Methods 4 Statistics & Probability Letters 4 Stochastic Processes and their Applications 4 Cybernetics and Systems Analysis 4 Journal of Mathematical Sciences (New York) 4 Fractional Calculus & Applied Analysis 4 Communications on Pure and Applied Analysis 4 Boundary Value Problems 4 Stochastics 3 Bulletin of the Australian Mathematical Society 3 Physica A 3 Chaos, Solitons and Fractals 3 Journal of Computational and Applied Mathematics 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Zeitschrift für Analysis und ihre Anwendungen 3 SIAM Journal on Matrix Analysis and Applications 3 Japan Journal of Industrial and Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 Computational Optimization and Applications 3 Journal of Computer and Systems Sciences International 3 Computational and Applied Mathematics 3 Journal of Vibration and Control 3 Journal of Inequalities and Applications 3 Nonlinear Analysis. Modelling and Control 3 African Diaspora Journal of Mathematics 3 Networks and Heterogeneous Media 3 Numerical Algebra, Control and Optimization 3 Nonautonomous Dynamical Systems 2 Journal of Mathematical Biology 2 Journal of Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Fuzzy Sets and Systems 2 Journal of Soviet Mathematics ...and 164 more Serials
all top 5
### Cited in 46 Fields
1,249 Systems theory; control (93-XX) 362 Partial differential equations (35-XX) 303 Operator theory (47-XX) 225 Ordinary differential equations (34-XX) 179 Calculus of variations and optimal control; optimization (49-XX) 168 Probability theory and stochastic processes (60-XX) 78 Numerical analysis (65-XX) 65 Mechanics of deformable solids (74-XX) 48 Functional analysis (46-XX) 43 Dynamical systems and ergodic theory (37-XX) 40 Fluid mechanics (76-XX) 36 Biology and other natural sciences (92-XX) 32 Integral equations (45-XX) 26 Real functions (26-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 23 Mechanics of particles and systems (70-XX) 22 Operations research, mathematical programming (90-XX) 18 Approximations and expansions (41-XX) 13 Computer science (68-XX) 12 Functions of a complex variable (30-XX) 12 Statistics (62-XX) 10 Difference and functional equations (39-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Integral transforms, operational calculus (44-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Information and communication theory, circuits (94-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 Number theory (11-XX) 4 Optics, electromagnetic theory (78-XX) 4 Quantum theory (81-XX) 3 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Abstract harmonic analysis (43-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Astronomy and astrophysics (85-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 Relativity and gravitational theory (83-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-11-28T08:16:19 |
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|
https://www.usgs.gov/centers/pacific-islands-water-science-center/data
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# Data
Data of Hawaiʻi and the Pacific Islands
Filter Total Items: 33
#### Selected streamgage sites and periods of record for consideration of flood-generating mechanisms in Hawaii and Southeast Alaska, 1913-2022
This data release consists of a comma-delimited ascii file with attributes for 21 U.S. Geological Survey streamgage sites in Hawaii and Southeast Alaska selected to enable assessment of how floods might change in a future climate. Floods in Hawai`i and Southeast Alaska have led to loss of human life; damage to agricultural crops, cultural and biological resources, infrastructure, and property; th
#### SUTRA model used to evaluate long-term groundwater availability in the Waihee, Iao, and Waikapu aquifer systems, Maui, Hawaii
Groundwater levels have declined since the 1940s in the Wailuku area of central Maui, Hawaii, on the eastern flank of West Maui volcano, mainly in response to increased groundwater withdrawals. Available data since the 1980s also indicate a thinning of the freshwater lens and an increase in chloride concentrations of pumped water from production wells. These trends, combined with projected inc
#### WATRMod, a Water-budget accounting for tropical regions model--source code, executable file, and example files
This data release contains the source code, executable file, and example files for WATRMod, a Water-budget Accounting for Tropical Regions Model code that is documented in U.S. Geological Survey Open-File Report 2022-1013 available at https://doi.org/10.3133/ofr20221013. The source code is written in the Fortran computer language. The model source code was compiled using Intel(R) Visual Fortran In
#### Seepage-run discharge measurements, November 15, 2021, He'eia Stream and 'Ioleka'a Stream, O'ahu, Hawai'i
This data release contains a comma-delimited ascii file of 16 discrete discharge measurements made at sites along selected reaches of He'eia Stream and 'Ioleka'a Stream, O'ahu, Hawai'i, on November 15, 2021. These discrete discharge measurements form what is commonly referred to as a "seepage run." The intent of the seepage run is to quantify the spatial distribution of streamflow along the reach
#### Seepage-run discharge measurements, September 8, 2021, He'eia Stream and 'Ioleka'a Stream, O'ahu, Hawai'i
This data release contains a comma-delimited ascii file of nine discrete discharge measurements made at sites along selected reaches of He'eia Stream and 'Ioleka'a Stream, O'ahu, Hawai'i, on September 8, 2021. These discrete discharge measurements form what is commonly referred to as a "seepage run." The intent of the seepage run is to quantify the spatial distribution of streamflow alon
#### Basin characteristic rasters used in the update of Hawaii StreamStats, 2022
In cooperation with the State of Hawaii Department of Transportation, the U.S. Geological Survey (USGS) has computed a series of basin characteristic rasters for Hawaii to be implemented into the USGS StreamStats application (https://streamstats.usgs.gov/ss/). The basin characteristics, along with geospatial datasets for watershed delineation published as a separate USGS data release (https://doi.
#### Geospatial datasets for watershed delineation used in the update of Hawaii StreamStats, 2022
The U.S. Geological Survey (USGS), in cooperation with the State of Hawaii Department of Transportation, has compiled and processed a series of geospatial datasets for Hawaii to be implemented into the USGS StreamStats application (https://streamstats.usgs.gov/ss/). These geospatial datasets, along with basin characteristic datasets published as a separate USGS data release (https://doi.org/10.506
#### Provisional peak-streamflow information during March 8-17 at selected USGS gaging stations on the islands of Kauai, Oahu, Molokai, and Maui in the State of Hawaii
These data are preliminary or provisional and are subject to revision. They are being provided to meet the need for timely best science. The data have not received final approval by the U.S. Geological Survey (USGS) and are provided on the condition that neither the USGS nor the U.S. Government shall be held liable for any damages resulting from the authorized or unauthorized use of the data. Int
#### SUTRA model used to evaluate the effects of groundwater withdrawal and injection, Kaloko-Honokohau National Historical Park, Hawaii
A three-dimensional, variable-density solute-transport model (SUTRA) was developed to evaluate the effects of three selected withdrawal/injection scenarios on salinity of groundwater (as simulated at damselfly anchialine-pool habitat) and discharge of freshwater to the nearshore environment of Kaloko-Honokohau National Historical Park (KAHO), Hawaii. A base model was constructed using water-level,
#### MODFLOW-2005 and SWI2 models for assessing groundwater availability in the volcanic aquifers of Kauai, Oahu, and Maui, Hawaii
Steady-state numerical groundwater-flow models were constructed for the islands of Kaua'i, O'ahu, and Maui, Hawai'i. Separate models were created for each island using MODFLOW-2005 (Harbaugh, 2005) with the Seawater Intrusion (SWI2) package (Bakker and others, 2013), which allows simulation of freshwater and saltwater in ocean-island aquifers. The purpose of the models is to enable quantifica
#### Mean annual water-budget components for the Island of Maui, Hawaii, for a set of eight future climate and land-cover scenarios
These shapefiles represent the spatial distribution of mean annual water-budget components, in inches, for the Island of Maui, Hawaii for a set of eight future climate and land-cover scenarios. The future climate conditions used in the water-budget analyses were derived from two end-of-century downscaled climate projections including (1) a projected future climate condition representative of phase
#### Supporting data for Hanalei Watershed model: SWAT_Hanalei
This data release contains inputs and outputs needed to reproduce the Soil and Water Assessment Tool (SWAT) model findings for the publication: Fortini, L.B., Leopold, C.R., Perkins, K., Chadwick, O.A., Yelenik, S.G., Jacobi, J.D., Bishaw, K., II, Gregg, M. and Rosa, S., 2020, Local to landscape-level controls of water fluxes through Hawaiian forests: Effects of invasive animals and plants on soil
| 2023-01-28T12:56:44 |
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https://par.nsf.gov/biblio/10352362
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This content will become publicly available on April 25, 2023
Model-Based Offline Meta-Reinforcement Learning with Regularization
Existing offline reinforcement learning (RL) methods face a few major challenges, particularly the distributional shift between the learned policy and the behavior policy. Offline Meta-RL is emerging as a promising approach to address these challenges, aiming to learn an informative meta-policy from a collection of tasks. Nevertheless, as shown in our empirical studies, offline Meta-RL could be outperformed by offline single-task RL methods on tasks with good quality of datasets, indicating that a right balance has to be delicately calibrated between "exploring" the out-of-distribution state-actions by following the meta-policy and "exploiting" the offline dataset by staying close to the behavior policy. Motivated by such empirical analysis, we propose model-based offline ta-RL with regularized policy optimization (MerPO), which learns a meta-model for efficient task structure inference and an informative meta-policy for safe exploration of out-of-distribution state-actions. In particular, we devise a new meta-Regularized model-based Actor-Critic (RAC) method for within-task policy optimization, as a key building block of MerPO, using both conservative policy evaluation and regularized policy improvement; and the intrinsic tradeoff therein is achieved via striking the right balance between two regularizers, one based on the behavior policy and the other on the meta-policy. We theoretically show that the learnt policy more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10352362
Journal Name:
The Tenth International Conference on Learning Representations
4. We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the information-theoretical lower bounds based on different data-coverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matches $O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right).$ We also prove an information-theoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal state-action probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform data-coverage assumption, horizon-free setting, single policy concentrability, and the tight problem-dependent results. Later, we extend the result to the \emph{assumption-free} regime (where we make no assumption on $\mu$) and obtain the assumption-free intrinsicmore »
| 2023-01-30T08:52:11 |
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https://par.nsf.gov/biblio/10182753-low-density-magnetization-massive-galaxy-halo-exposed-fast-radio-burst
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The low density and magnetization of a massive galaxy halo exposed by a fast radio burst
Present-day galaxies are surrounded by cool and enriched halo gas extending for hundreds of kiloparsecs. This halo gas is thought to be the dominant reservoir of material available to fuel future star formation, but direct constraints on its mass and physical properties have been difficult to obtain. We report the detection of a fast radio burst (FRB 181112), localized with arcsecond precision, that passes through the halo of a foreground galaxy. Analysis of the burst shows that the halo gas has low net magnetization and turbulence. Our results imply predominantly diffuse gas in massive galactic halos, even those hosting active supermassive black holes, contrary to some previous results.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10182753
Journal Name:
Science
Volume:
366
Issue:
6462
Page Range or eLocation-ID:
231 to 234
ISSN:
0036-8075
3. ABSTRACT In recent years, several analytic models have demonstrated that simple assumptions about halo growth and feedback-regulated star formation can match the (limited) existing observational data on galaxies at $z \gtrsim6$. By extending such models, we demonstrate that imposing a time delay on stellar feedback (as inevitably occurs in the case of supernova explosions) induces burstiness in small galaxies. Although supernova progenitors have short lifetimes (∼5–30 Myr), the delay exceeds the dynamical time of galaxies at such high redshifts. As a result, star formation proceeds unimpeded by feedback for several cycles and ‘overshoots’ the expectations of feedback-regulated star formation models. We show that such overshoot is expected even in atomic cooling haloes, with halo masses up to ∼1010.5 M⊙ at z ≳ 6. However, these burst cycles damp out quickly in massive galaxies, because large haloes are more resistant to feedback so retain a continuous gas supply. Bursts in small galaxies – largely beyond the reach of existing observations – induce a scatter in the luminosity of these haloes (of ∼1 mag) and increase the time-averaged star formation efficiency by up to an order of magnitude. This kind of burstiness can have substantial effects on the earliest phases of star formation and reionization.
4. ABSTRACT In several models of galaxy formation feedback occurs in cycles or mainly at high redshift. At times and in regions where feedback heating is ineffective, hot gas in the galaxy halo is expected to form a cooling flow, where the gas advects inward on a cooling timescale. Cooling flow solutions can thus be used as a benchmark for observations and simulations to constrain the timing and extent of feedback heating. Using analytic calculations and idealized 3D hydrodynamic simulations, we show that for a given halo mass and cooling function, steady-state cooling flows form a single-parameter family of solutions, while initially hydrostatic gaseous haloes converge on one of these solutions within a cooling time. The solution is thus fully determined once either the mass inflow rate ${\dot{M}}$ or the total halo gas mass are known. In the Milky Way halo, a cooling flow with ${\dot{M}}$ equal to the star formation rate predicts a ratio of the cooling time to the free-fall time of ∼10, similar to some feedback-regulated models. This solution also correctly predicts observed $\rm{O\,{\small VII}}$ and $\rm{O\,{\small VIII}}$ absorption columns, and the gas density profile implied by $\rm{O\,{\small VII}}$ and $\rm{O\,{\small VIII}}$ emission. These results suggest ongoing heatingmore »
5. ABSTRACT We use a particle tracking analysis to study the origins of the circumgalactic medium (CGM), separating it into (1) accretion from the intergalactic medium (IGM), (2) wind from the central galaxy, and (3) gas ejected from other galaxies. Our sample consists of 21 FIRE-2 simulations, spanning the halo mass range Mh ∼ 1010–1012 M⊙, and we focus on z = 0.25 and z = 2. Owing to strong stellar feedback, only ∼L⋆ haloes retain a baryon mass $\gtrsim\! 50\hbox{ per cent}$ of their cosmic budget. Metals are more efficiently retained by haloes, with a retention fraction $\gtrsim\! 50\hbox{ per cent}$. Across all masses and redshifts analysed $\gtrsim \!60\hbox{ per cent}$ of the CGM mass originates as IGM accretion (some of which is associated with infalling haloes). Overall, the second most important contribution is wind from the central galaxy, though gas ejected or stripped from satellites can contribute a comparable mass in ∼L⋆ haloes. Gas can persist in the CGM for billions of years, resulting in well mixed-halo gas. Sightlines through the CGM are therefore likely to intersect gas of multiple origins. For low-redshift ∼L⋆ haloes, cool gas (T < 104.7 K) is distributed on average preferentially along the galaxy plane, howevermore »
| 2022-10-06T18:31:18 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S126STT
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# ${{\boldsymbol H}^{0}}$ SIGNAL STRENGTHS IN DIFFERENT CHANNELS
The ${{\mathit H}^{0}}$ signal strength in a particular final state ${{\mathit x}}{{\mathit x}}$ is given by the cross section times branching ratio in this channel normalized to the Standard Model (SM) value, $\sigma$ $\cdot{}$ B( ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit x}}{{\mathit x}}$ ) $/$ ($\sigma$ $\cdot{}$ B( ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit x}}{{\mathit x}}$ ))$_{{\mathrm {SM}}}$, for the specified mass value of ${{\mathit H}^{0}}$. For the SM predictions, see DITTMAIER 2011 , DITTMAIER 2012 , and HEINEMEYER 2013A. Results for fiducial and differential cross sections are also listed below.
# ${{\boldsymbol \tau}^{+}}{{\boldsymbol \tau}^{-}}$ Final State INSPIRE search
VALUE DOCUMENT ID TECN COMMENT
$\bf{ 1.12 \pm0.23}$ OUR AVERAGE
$1.11$ ${}^{+0.24}_{-0.22}$ 1, 2
2016 AN
LHC ${{\mathit p}}{{\mathit p}}$ , 7, 8 TeV
$1.68$ ${}^{+2.28}_{-1.68}$ 3
2013 M
TEVA ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 1.96 TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.3$ $\pm1.6$ 4
2016 AC
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit W}}$ / ${{\mathit Z}}{{\mathit X}}$ , 8 TeV
$1.41$ ${}^{+0.40}_{-0.36}$ 2
2016 AN
ATLS ${{\mathit p}}{{\mathit p}}$ , 7, 8 TeV
$0.88$ ${}^{+0.30}_{-0.28}$ 2
2016 AN
CMS ${{\mathit p}}{{\mathit p}}$ , 7, 8 TeV
$1.44$ ${}^{+0.30}_{-0.29}$ ${}^{+0.29}_{-0.23}$ 5
2016 K
ATLS ${{\mathit p}}{{\mathit p}}$ , 7, 8 TeV
$1.43$ ${}^{+0.27}_{-0.26}$ ${}^{+0.32}_{-0.25}$ $\pm0.09$ 6
2015 AH
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 7, 8 TeV
$0.78$ $\pm0.27$ 7
2014 K
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 7, 8 TeV
$0.00$ ${}^{+8.44}_{-0.00}$ 8
2013 L
CDF ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 1.96 TeV
$3.96$ ${}^{+4.11}_{-3.38}$ 9
2013 L
D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 1.96 TeV
$0.4$ ${}^{+1.6}_{-2.0}$ 10
2012 AI
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 7 TeV
$0.09$ ${}^{+0.76}_{-0.74}$ 11
2012 N
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit X}}$ , 7, 8 TeV
1 AAD 2016AN perform fits to the ATLAS and CMS data at $\mathit E_{{\mathrm {cm}}}$ = 7 and 8 TeV. The signal strengths for individual production processes are $1.0$ $\pm0.6$ for gluon fusion, $1.3$ $\pm0.4$ for vector boson fusion, $-1.4$ $\pm1.4$ for ${{\mathit W}}{{\mathit H}^{0}}$ production, $2.2$ ${}^{+2.2}_{-1.8}$ for ${{\mathit Z}}{{\mathit H}^{0}}$ production, and $-1.9$ ${}^{+3.7}_{-3.3}$ for ${{\mathit t}}{{\overline{\mathit t}}}{{\mathit H}^{0}}$ production.
2 AAD 2016AN: In the fit, relative production cross sections are fixed to those in the Standard Model. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125.09 GeV.
3 AALTONEN 2013M combine all Tevatron data from the CDF and D0 Collaborations with up to 10.0 fb${}^{-1}$ and 9.7 fb${}^{-1}$, respectively, of ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 1.96 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV.
4 AAD 2016AC measure the signal strength with ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit W}}$ / ${{\mathit Z}}{{\mathit X}}$ processes using 20.3 fb${}^{-1}$ of $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV.
5 AAD 2016K use up to 4.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and up to 20.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125.36 GeV.
6 AAD 2015AH use 4.5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 20.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The third uncertainty in the measurement is theory systematics. The signal strength for the gluon fusion mode is $2.0$ $\pm0.8$ ${}^{+1.2}_{-0.8}$ $\pm0.3$ and that for vector boson fusion and ${{\mathit W}}$ $/$ ${{\mathit Z}}{{\mathit H}^{0}}$ production modes is $1.24$ ${}^{+0.49}_{-0.45}{}^{+0.31}_{-0.29}$ $\pm0.08$. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125.36 GeV.
7 CHATRCHYAN 2014K use 4.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV. See also CHATRCHYAN 2014AJ.
8 AALTONEN 2013L combine all CDF results with $9.45 - 10.0$ fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 1.96 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV.
9 ABAZOV 2013L combine all D0 results with up to 9.7 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 1.96 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV.
10 AAD 2012AI obtain results based on 4.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV. The quoted signal strengths are given in their Fig. 10 for ${\mathit m}_{{{\mathit H}^{0}}}$ = 126 GeV. See also Fig. 13 of AAD 2012DA.
11 CHATRCHYAN 2012N obtain results based on 4.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$=7 TeV and 5.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$=8 TeV. The quoted signal strength is given for ${\mathit m}_{{{\mathit H}^{0}}}$=125.5 GeV. See also CHATRCHYAN 2013Y .
References:
JHEP 1608 045 Measurements of the Higgs Boson Production and Decay Rates and Constraints on its Couplings from a Combined ATLAS and CMS Analysis of the LHC ${{\mathit p}}{{\mathit p}}$ Collision Data at $\sqrt {s }$ =7 and 8 TeV
PR D93 092005 Search for the Standard Model Higgs Boson Produced in Association with a Vector Boson and Decaying into a Tau Pair in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
EPJ C76 6 Measurements of the Higgs Boson Production and Decay Rates and Coupling Strengths using ${{\mathit p}}{{\mathit p}}$ Collision Data at $\sqrt {s }$ = 7 and 8 TeV in the ATLAS Experiment
JHEP 1405 104 Evidence for the 125 GeV Higgs Boson Decaying to a Pair of ${{\mathit \tau}}$ Leptons
PR D88 052011 Combined Search for the Higgs Boson with the ${D0}$ Experiment
| 2019-04-22T12:09:46 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu4sso/sec_cu4sso_dataproperties/ssec_cu4sso_generalselection.html
|
# 4.2.1 Selection of objects for Astrometry and Photometry
Author(s): François Mignard, Laurent Galluccio
For the Gaia DR2 the SSO processing was carried out for an off-line selection of targets instead of activating the automatic recognition that will be used at a later stage. This had the advantage of limiting the volume of data entering the pipeline and offering a near certainty that only genuine SSOs were selected. This simplification was considered desirable for the first mass processing of solar-system sources over a relatively short time span. To this aim a list of transit identifiers associated to the passages of known SSOs was generated by a pre-processor and this list was added to the input data ingested by the processing chain. Several criteria were applied to select a valuable subset of objects.
• We aimed at having between 10 000 and 15 000 SSOs.
• Representatives of all the broad categories of asteroids were sought (NEAs, MBAs, Trojans, etc.).
• No transit of an object should be lost because its apparent magnitude was becoming too faint at small solar elongation, when the distance to Gaia was the largest.
• A planetary transit was not selected if a star, another SSO or a contaminant generated by a bright star was found too close to the object during its observation by Gaia.
• Each selected SSO had to have been observed at least 12 times over the 22 months covered by the Gaia DR2 data.
These conditions were applied iteratively until a satisfactory selection meeting all the requirements was achieved. The final input selection had $318\,290$ transits for $14\,125$ SSOs. The coverage in orbital semi-major axis displayed in Figure 4.6 shows that SSOs within of each of the broad categories are found in the selection.
The list has been created in three main steps:
• Prediction of all the possible transits for a set of SSOs over the Gaia DR2 time span using the Gaia orbit, the scanning law and a numerical integration of the SSO motion starting from the osculating elements and osculating epoch given in the Astorb data (see Section 4.4.1).
• Cross-matching the transits with the Gaia IDT detection to ensure that a potential candidate SSO had been actually seen by Gaia and observed during the predicted transit.
• Iterative filtering on the tentative list to ensure that the selection criteria were met and no contaminant was left.
The sky distribution of the selected observations is shown in Figure 4.7 on a density plot in equatorial coordinates. The SSOs are all found in the vicinity of the ecliptic plane, but the distribution in longitude is markedly non uniform with periodic features of higher (deep blue) and lower concentration. This is a known artefact resulting from the Gaia scanning over a relatively short duration of 22 months compared to the nominal mission of five years. The features seen every 60 ${}^{\circ}$ shift of 72 ${}^{\circ}$ every year, so that the coverage becomes nearly uniform after five years.
Besides the orbital elements, the main features of the selection procedure are shown in the set of separate plots. The scatter distribution between the computed position and the IDT solution is shown in Figure 4.8, with the data from October 2014 to May 2016 (left) and from October 2015 to May 2016 (right) being shown separately. IDT data from the transition scanning law (NSL-Smooth) in September 2014 are very poor and not included in this analysis. These are density plots and the concentration is essentially within $\pm 0.2$${}^{\prime\prime}$($>95\%$ of the data set). The distribution is more regular and compact in the right plot with data from segment 2 and this can be explained by (i) the shorter time interval covered by the numerical integration, since the osculating elements are taken in May 2017 and (ii) from a better IDT solution in the second year of the mission. There is a slight bias of 60 mas, irrelevant in this context, in right ascension. This is better seen in Figure 4.9, using a linear and log scale (left and right, respectively). The similar distributions for the declination are given in Figure 4.10, leaving a very small bias at about -10 mas. The accuracy of the observed positions in IDT is $\approx 60$ mas in each coordinate, while the computed position accuracy depends primarily on the quality of the orbital elements and to a lesser extent to the remaining uncertainty in the Gaia orbit. While the precise extent of the scatter is not very relevant, the fact that the biases are small and the scatter much below 1 ${}^{\prime\prime}$supports the claim that the selection performs well and does not miss relevant SSOs.
| 2022-08-08T03:51:30 |
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|
https://docs.dea.ga.gov.au/notebooks/Frequently_used_code/Machine_learning_with_ODC.html
|
# Machine learning with the Open Data Cube¶
• Compatability: Notebook currently compatible with both the NCI and DEA Sandbox environments
• Products used: ls8_nbart_geomedian_annual
• Special requirements: A shapefile of labelled data in shapefile format is required to use this notebook. An example dataset is provided.
• Prerequisites: A basic understanding of supervised learning techniques is required. Introduction to statistical learning is a useful resource to begin with - it can be downloaded for free here. The Scikit-learn documentation provides information on the available models and their parameters.
## Description¶
This notebook demonstrates a potential workflow using functions from the dea_classificationtools script to implement a supervised learning landcover classifier within the ODC (Open Data Cube) framework.
For larger model training and prediction implementations this notebook can be adapted into a Python file and run in a distributed fashion.
This example predicts a single class of cultivated / agricultural areas. The notebook demonstrates how to:
1. Extract the desired ODC data for each labelled area (this becomes our training dataset).
2. Train a simple decision tree model and adjust parameters.
3. Predict landcover using trained model on new data.
4. Evaluate the output of the classification using quantitative metrics and qualitative tools.
## Getting started¶
To run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.
Import Python packages that are used for the analysis.
[1]:
%matplotlib inline
import subprocess as sp
import sys
import shapely
import rasterio
import datacube
import matplotlib
import pydotplus
import numpy as np
import geopandas as gpd
import matplotlib.pyplot as plt
from io import StringIO
from sklearn import tree
from sklearn import model_selection
from sklearn.metrics import accuracy_score
from IPython.display import Image
from datacube.utils import geometry
from datacube.utils.cog import write_cog
sys.path.append('../Scripts')
from dea_classificationtools import collect_training_data
from dea_classificationtools import predict_xr
from dea_plotting import map_shapefile
import warnings
warnings.filterwarnings("ignore")
/env/lib/python3.6/site-packages/datacube/storage/masking.py:4: DeprecationWarning: datacube.storage.masking has moved to datacube.utils.masking
category=DeprecationWarning)
### Connect to the datacube¶
Connect to the datacube so we can access DEA data.
[2]:
dc = datacube.Datacube(app='Machine_learning_with_ODC')
### Analysis parameters¶
• path: The path to the input shapefile. A default shapefile is provided.
• field: This is the name of column in your shapefile attribute table that contains the class labels
• products: The name of the product to extract. In this example we use a geomedian composite from 2018, 'ls8_nbart_geomedian_annual'
• time: The time range you wish to extract data for, typically the same date the labels were created.
• reduce_func: This will determine the statistic to reduce the time dimension of the loaded datasets (if loading multiple time steps). Options include 'mean', 'median', 'std' or 'geomedian'.
• band_indices: a list of band indices to calculate for the training data see here for possible options.
• drop: If calculating band indices, we can optionally choose to drop the spectral bands loaded with the product, if 'drop=True', then only the band indices will be used for the training data.
• zonal_stats: This is an option to calculate the 'mean', 'median', or 'std' of the pixel values within each polygon feature, setting it to None will result in all pixels being extracted.
• resolution: The spatial resolution, in metres, to resample the satellite data too e.g. if working with Landsat data, then this should be (-30,30)
• ncpus: Set this value to > 1 to parallize the collection of training data. eg. npus=8
If running the notebook for the first time, keep the default settings below. This will demonstrate how the analysis works and provide meaningful results.
[3]:
path = '../Supplementary_data/Machine_learning_with_ODC/example_training_data.shp'
field = 'classnum'
products = ["ls8_nbart_geomedian_annual"]
time = ('2015')
reduce_func = None #'mean'
custom_func = None
band_indices = None # ['NDVI']
drop = False
zonal_stats = 'median'
resolution = (-25, 25)
# automatically detect number of cpus, need to
# adjust to [-4:] if working on the XXL Sandbox
ncpus= int(float(sp.getoutput('env | grep CPU')[-3:]))
print('ncpus: '+str(ncpus))
ncpus: 2
### Preview input data and study area¶
We can load and preview our input data shapefile using geopandas. The shapefile should contain a column with class labels (e.g. classnum below). These labels will be used to train our model.
[4]:
# Load input data shapefile
# Plot first five rows
[4]:
classnum geometry
0 112 POLYGON ((-1521875.000 -3801925.000, -1521900....
1 111 POLYGON ((-1557925.000 -3801125.000, -1557950....
2 111 POLYGON ((-1555325.000 -3800000.000, -1555200....
3 111 POLYGON ((-1552925.000 -3800950.000, -1552925....
4 111 POLYGON ((-1545475.000 -3800000.000, -1544325....
The data can also be explored using the interactive map below. Hover over each individual feature to see a print-out of its unique class label number above the map.
[5]:
# Plot training data in an interactive map
map_shapefile(input_data, attribute=field)
## Extract training data using a shapefile¶
To train our model, we need to obtain satellite data that corresponds with the labelled input data locations above. The function below takes our shapefile containing class labels and extracts the specified product within these areas into a single array.
The following cell can take several minutes to run. The class labels will be contained in the first column of the output array.
[6]:
#generate a datacube query object
query = {
'time': time,
'measurements': ['blue',
'green',
'red',
'nir',
'swir1',
'swir2'],
'resolution': resolution,
'group_by' :'solar_day',
}
[7]:
column_names, model_input = collect_training_data(
gdf=input_data,
products=products,
dc_query=query,
ncpus=ncpus,
custom_func=custom_func,
field=field,
calc_indices=band_indices,
reduce_func=reduce_func,
drop=drop,
zonal_stats=zonal_stats)
Taking zonal statistic: median
Collecting training data in parallel mode
100%|██████████| 217/217 [00:56<00:00, 3.83it/s]
Output training data has shape (217, 7)
Removed NaNs, cleaned input shape: (217, 7)
## Preprocessing¶
Our training data has multiple classes in it. However, we are only trying to predict one class (i.e. class label 111, Cultivated Terrestrial Vegetated) with this model. We therefore remove other classes from our training data by setting the label value for all other classes to 0.
These entries provide counter-examples to help the model distinguish the landcover classes from each other.
[8]:
# Modify the input training data for single class labels
model_input[:,0] = np.where(model_input[:,0] == 111, 1, 0)
So that we can access the accuracy of our classification, we split our data into training and testing data. 80% is used for training with 20% held back for testing. When splitting our data, we stratify the training data by the distributions of class membership. This sampling method leads to a similar distribution of class membership in the training data.
[9]:
# Split into training and testing data
model_train, model_test = model_selection.train_test_split(model_input,
stratify=model_input[:, 0],
train_size=0.8,
random_state=0)
print("Train shape:", model_train.shape)
print("Test shape:", model_test.shape)
Train shape: (173, 7)
Test shape: (44, 7)
## Model preparation¶
This section automatically creates a list of varaible names and their respective indices for each of the training data variables.
Note: To use a custom subset of the satellite bands loaded above to train our data, you can replace column_names[1:] with a list of selected band names (e.g. ['red', 'green', 'blue'])
[10]:
# Select the variables we want to use to train our model
model_variables = column_names[1:]
# Extract relevant indices from the processed shapefile
model_col_indices = [column_names.index(var_name) for var_name in model_variables]
A decision tree model is chosen as it is one of the simplest supervised machine learning models we can implement.
Its strengths are its explainability and cheap computational cost.
Parameter tuning can be conducted in the model initialisation below - details on how the different parameters will affect the model are here.
[11]:
# Initialise model
model = tree.DecisionTreeClassifier(max_depth=10)
## Train model¶
The model is fitted / trained using the prepared training data. The fitting process uses the decision tree approach to create a generalised representation of reality based on the training data. This fitted / trained model can then be used to predict which class new data belongs to.
[12]:
# Train model
model.fit(model_train[:, model_col_indices], model_train[:, 0])
[12]:
DecisionTreeClassifier(max_depth=10)
## Analyse results¶
### Feature importance¶
The decision tree classifier allows us to inspect the feature importance of each input variable. Feature importance represents the relative contribution of each variable in predicting the desired landcover class. When summed, the importance of all variables should add up to 1.0.
[13]:
# This shows the feature importance of the input features for predicting the class labels provided
plt.bar(x=model_variables, height=model.feature_importances_)
This decision tree representation visualises the trained model. Here we can see that the model decides which landcover class to assign based on the value of the important variables in the plot above.
The gini value shown in the tree represents the decrease in node impurity. This can also be understood as how heterogeneous the labels are (small values indicating better results). This metric is used by the decision tree to determine how to split the data into smaller groups.
[14]:
# Prepare a dictionary of class names
class_names = {1: 'Cultivated Terrestrial Vegetated',
0: 'Not Cultivated Terrestrial Vegetated'}
# Get list of unique classes in model
class_codes = np.unique(model_train[:, 0])
class_names_in_model = [class_names[k] for k in class_codes]
# Plot decision tree
dot_data = StringIO()
tree.export_graphviz(model,
out_file=dot_data,
feature_names=model_variables,
class_names=class_names_in_model,
filled=True,
rounded=True,
special_characters=True)
graph = pydotplus.graph_from_dot_data(dot_data.getvalue())
Image(graph.create_png())
[14]:
### Accuracy¶
We can use the 20% sample of test data we partitioned earlier to test the accuracy of the trained model on this new, “unseen” data.
An accuracy value of 1.0 indicates that the model was able to correctly predict 100% of the classes in the test data.
[15]:
predictions = model.predict(model_test[:, model_col_indices])
accuracy_score(predictions, model_test[:, 0])
[15]:
0.9545454545454546
## Prediction¶
Now that we have a trained model, we can load new data and use the predict_xr function to predict landcover classes.
The trained model can technically be used to classify any dataset or product with the same bands as the data originally used to train the data. However, it is typically highly advisable to classify data from the same product that the data was originally trained on (e.g. 'ls8_nbart_geomedian_annual' below).
[16]:
# Get extent from input shapefile
xmin, ymin, xmax, ymax = input_data.unary_union.bounds
# Set up the query parameters
query = {'time': time,
'x': (xmin, xmax),
'y': (ymin, ymax),
'crs': 'EPSG:3577',
'resolution': (-25, 25)}
**query)
Once the data has been loaded, we can classify it using predict_xr:
[17]:
# Predict landcover using the trained model
predicted = predict_xr(model, geomedian_data, progress=True)
## Plotting¶
To qualitatively evaluate how well the classification performed, we can plot the classifed/predicted data next to our input satellite imagery.
Note: The output below is unlikely to be optimal the first time the classification is run. The model training process is one of experimentation and assumption checking that occurs in an iterative cycle - you may need to revisit the steps above and make changes to model parameters or input training data until you achieve a satisfactory result.
[18]:
# Set up plot
fig, axes = plt.subplots(1, 2, figsize=(14, 6))
# Plot classified image
predicted.plot(ax=axes[0],
cmap='Greens',
# Plot true colour image
(geomedian_data[['red', 'green', 'blue']]
.squeeze('time')
.to_array()
# Remove axis on right plot
axes[1].get_yaxis().set_visible(False)
axes[0].set_title('Classified data')
axes[1].set_title('True colour image');
## Exporting classification¶
We can now export the predicted landcover out to a GeoTIFF .tif file. This file can be loaded into GIS software (e.g. QGIS, ArcMap) to be inspected more closely.
[19]:
# Write the predicted data out to a GeoTIFF
write_cog(predicted,
'predicted.tif',
overwrite=True)
[19]:
PosixPath('predicted.tif')
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github.
Compatible datacube version:
[20]:
print(datacube.__version__)
1.8.2.dev7+gdcab0e02
## Tags¶
Browse all available tags on the DEA User Guide’s Tags Index
Tags: NCI compatible, sandbox compatible, landsat 8, annual geomedian, dea_plotting, map_shapefile, dea_classificationtools, predict_xr, get_training_data_for_shp, machine learning, decision tree
| 2020-08-06T18:45:30 |
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|
https://par.nsf.gov/biblio/10347995-fast-radio-burst-population-evolves-consistent-star-formation-rate
|
This content will become publicly available on December 9, 2022
The fast radio burst population evolves, consistent with the star formation rate
ABSTRACT Fast radio bursts (FRBs) are extremely powerful sources of radio waves observed at cosmological distances. We use a sophisticated model of FRB observations – presented in detail in a companion paper – to fit FRB population parameters using large samples of FRBs detected by ASKAP and Parkes, including seven sources with confirmed host galaxies. Our fitted parameters demonstrate that the FRB population evolves with redshift in a manner consistent with, or faster than, the star formation rate (SFR), ruling out a non-evolving population at better than 98 per cent CL (depending on modelling uncertainties). Our estimated maximum FRB energy is $\log _{10} E_{\rm max} [{\rm erg}] = 41.70_{-0.06}^{+0.53}$ (68 per cent CL) assuming a 1 GHz emission bandwidth, with slope of the cumulative luminosity distribution $\gamma =-1.09_{-0.10}^{+0.14}$. We find a log-mean host DM contribution of $129_{-48}^{+66}$ pc cm−3 on top of a typical local (interstellar medium and halo) contribution of ∼80 pc cm−3, which is higher than most literature values. These results are insensitive to assumptions of the FRB spectral index, and are consistent with the model of FRBs arising as the high-energy limit of magnetar bursts, but allow for FRB progenitors that evolve faster than the SFR.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10347995
Journal Name:
Monthly Notices of the Royal Astronomical Society: Letters
Volume:
510
Issue:
1
Page Range or eLocation-ID:
L18 to L23
ISSN:
1745-3925
1. ABSTRACT We report on the discovery and localization of fast radio bursts (FRBs) from the MeerTRAP project, a commensal fast radio transient-detection programme at MeerKAT in South Africa. Our hybrid approach combines a coherent search with an average field-of-view (FoV) of 0.4 $\rm deg^{2}$ with an incoherent search utilizing a FoV of ∼1.27 $\rm deg^{2}$ (both at 1284 MHz). Here, we present results on the first three FRBs: FRB 20200413A (DM = 1990.05 pc cm−3), FRB 20200915A (DM = 740.65 pc cm−3), and FRB 20201123A (DM = 433.55 pc cm−3). FRB 20200413A was discovered only in the incoherent beam. FRB 20200915A (also discovered only in the incoherent beam) shows speckled emission in the dynamic spectrum, which cannot be explained by interstellar scintillation in our Galaxy or plasma lensing, and might be intrinsic to the source. FRB 20201123A shows a faint post-cursor burst of about 200 ms after the main burst and warrants further follow-up to confirm whether it is a repeating FRB. FRB 20201123A also exhibits significant temporal broadening, consistent with scattering, by a turbulent medium. The broadening exceeds from what is predicted for the medium along the sightline through our Galaxy. We associate this scattering with the turbulent medium in the environment of the FRB in the host galaxy. Within the approximately 1 arcmin localization region ofmore »
2. ABSTRACT We describe three different methods for exploring the hydrogen reionization epoch using fast radio bursts (FRBs) and provide arguments for the existence of FRBs at high redshift (z). The simplest way, observationally, is to determine the maximum dispersion measure (DMmax) of FRBs for an ensemble that includes bursts during the reionization. The DMmax provides information regarding reionization much like the optical depth of the cosmic microwave background to Thomson scattering does, and it has the potential to be more accurate than constraints from Planck, if DMmax can be measured to a precision better than 500 pccm−3. Another method is to measure redshifts of about 40 FRBs between z of 6 and 10 with ${\sim}10{{\ \rm per\ cent}}$ accuracy to obtain the average electron density in four different z-bins with ${\sim}4{{\ \rm per\ cent}}$ accuracy. These two methods do not require knowledge of the FRB luminosity function and its possible redshift evolution. Finally, we show that the reionization history is reflected in the number of FRBs per unit DM, given a fluence limited survey of FRBs that includes bursts during the reionization epoch; we show using FIRE simulations that the contribution to DM from the FRB host galaxy and circumgalacticmore »
| 2022-10-02T19:45:50 |
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https://leg.mt.gov/bills/mca/82/4/82-4-340.htm
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82-4-340. Successor operator. When one operator succeeds to the interest of another in any uncompleted operation by sale, assignment, lease, or otherwise, the department may release the first operator from the duties imposed upon the operator by this part as to such operation, provided that both operators have complied with the requirements of this part and the successor operator assumes the duty of the former operator to complete the reclamation of the land, in which case the department shall transfer the permit to the successor operator upon approval of the successor operator's bond as required under this part.
History: En. Sec. 10, Ch. 252, L. 1971; amd. Sec. 6, Ch. 281, L. 1974; amd. Sec. 1, Ch. 427, L. 1977; R.C.M. 1947, 50-1210(3); amd. Sec. 6, Ch. 453, L. 1985; amd. Sec. 395, Ch. 418, L. 1995.
| 2019-03-20T17:11:21 |
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https://read.dukeupress.edu/demography/article/58/3/987/172698/Gender-Segregation-in-Education-Evidence-From
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## Abstract
This paper investigates gender-based segregation across different fields of study at the senior secondary level of schooling in a large developing country. We use a nationally representative longitudinal data set from India to analyze the extent and determinants of gender gap in higher secondary stream choice. Using fixed-effects regressions that control for unobserved heterogeneity at the regional and household levels, we find that girls are about 20 percentage points less likely than boys to study in science (STEM) and commerce streams as compared with humanities. This gender disparity is unlikely to be driven by gender-specific differences in cognitive ability, given that the gap remains large and significant even after we control for individuals' past test scores. We establish the robustness of these estimates through various sensitivity analyses: including sibling fixed effects, considering intrahousehold relationships among individuals, and addressing sample selection issues. Disaggregating the effect on separate streams, we find that girls are most underrepresented in the study of science. Our findings indicate that gender inequality in economic outcomes, such as occupational segregation and gender pay gaps, is determined by gendered trajectories set much earlier in the life course, especially at the school level.
## Introduction
Various forms of gender inequality are observed in different parts of the world. In South Asia, such inequalities have manifested throughout the life course of individuals: sex imbalance at birth due to sex-selective abortions, unequal survival rates, differential human capital investments, discrimination in the labor market, and so on. The last few decades, however, have seen progress toward gender equality, most notably in education. Although the gender gap in enrollment rates at all levels of education has diminished, it has not translated into a commensurate improvement in women's labor market outcomes. For instance, female labor force participation, which is viewed as one of the important indicators of inclusive development and female economic empowerment, has remained very low and stagnant and has sometimes declined in India, despite the nation's rapid economic growth, female educational expansion, and fertility decline in the last two decades (Klasen and Pieters 2015). Underparticipation of women will restrict the country from properly utilizing its demographic gift of having a high proportion of the population at working ages. Additionally, occupational and sectoral segregation of employment by gender is remarkably persistent and is a key issue behind perpetuating female disadvantage, such as the gender pay gap in the labor market (Borrowman and Klasen 2020).
Against this backdrop, we show here that the gender gap in economic participation in adulthood in India is shaped by gendered trajectories set earlier in life, especially at the school level. Specifically, we identify the gender gap in science, technology, engineering, and mathematics (STEM) and commerce-related fields at the senior secondary level of education, which is likely to have a significant and far-reaching effect on individuals' adult-life outcomes.
The literature has analyzed the determinants and consequences of stream choice at the postsecondary and tertiary levels of education (Arcidiacono 2004; Beffy et al. 2012; Fuller et al. 1982). Some studies have also recognized the link between educational segregation and occupational segregation and have reflected on the life course processes that determine women's career trajectories relative to men's (Schneeweis and Zweimüller 2012; Xie and Shauman 2003). However, the causes of gender gap in stream choice are not fully understood, and they constitute an area of active research in the literature (Kahn and Ginther 2017; Xie et al. 2015). In addition, barring a few exceptions, most of this research has focused on developed countries.1
By investigating this issue in the context of an emerging economy, we contribute to the literature in various ways. First, India offers an important case study given the importance of STEM education in its economy. Over the last few decades after economic liberalization, the growth of the Indian economy has been led by the services sector, where the information technology–related industry has been a prime contributor (Panagariya 2004). The nature of economic growth during this period has potentially had a spillover effect on education participation (Jensen 2012; Oster and Steinberg 2013; Shastry 2012). India, along with China, has accounted for the majority of the world's recent STEM graduates, constituting a much larger share than the European Union and the United States (UNCTAD 2018). Yet, the gender composition of these STEM students and their labor market prospects have remained unexplored in the literature.
Cross-country studies have shown variation in the overall levels and patterns of sex segregation in stream choice (e.g., Charles and Bradley 2009), indicating that the processes that generate this form of gender inequality in advanced and developing nations may be distinct. This set of findings justifies an empirical analysis in a developing country setting, such as India, where the prevalence of male-favoring gender norms affects individual decisions at various life stages. In a society where economic and cultural factors drive underinvestment in girls' education (Azam and Kingdon 2013; Kingdon 2005), the magnitude and determinants of gender gap in STEM participation might be different from those in more gender-egalitarian countries. Moreover, from a demographic point of view, the Indian scenario differs from developed countries in its very low and stagnating female labor force participation. In this context, although a growing body of literature has examined the role of education in female labor force participation, it has focused on the level of education and not the type of education (Klasen and Pieters 2015; Sarkar et al. 2019). The current paper contributes to this discourse by highlighting the persistence of gender segregation of academic fields despite improvements in female education levels.
The Indian education system also has distinct structural features that imply greater importance of stream choice made at the school level. After secondary schooling, completed after 10 years of education, students entering at the higher secondary level (lasting another two years) must specialize in one of the following streams: humanities, science, commerce, engineering/vocational, and other.2 Unlike many developed countries, including the United States, stream choice at the tertiary level in India is made before admission to college, and because of eligibility requirements, this choice is largely determined by the stream studied at the higher secondary level.3 Therefore, school-level stream choice is a crucial juncture in an individual's career because it determines the subsequent course of study at the college level and the nature of jobs that the individual may obtain in the future. Thus, the life course approach proposed by Xie and Shauman (2003) is especially relevant in the context of India, where the prevailing education system implies that choices made in adolescence affect adult-life outcomes. In fact, Sahoo and Klasen (2018) showed that stream choice at the higher secondary level in India strongly influences later labor market outcomes, including participation, occupational choice, and earnings.
Another contribution of this study is its exploration of the gender gap in the commerce stream, which is equivalent to a business major. Although a vast literature has focused on the gender gap in STEM, the gender gap in business studies is less explored. Analyzing trends in college major choice in the United States, Gemici and Wiswall (2014) found that women are significantly less likely than men to choose a business major, despite the documented overall rise in women's participation in tertiary education (Goldin et al. 2006). We extend this literature by investigating gender disparity in the choice of the commerce stream at the higher secondary school level in India.
We use a nationally representative household-level panel data set that tracks the same households and individual members at two time points: 2005 and 2012. The novelty of this survey is that it asks all individuals about their performance in the secondary school leaving certificate (SSLC) examination and subsequently asks what stream they studied at the higher secondary level. Additionally, individuals aged 15–18 years (the ages corresponding to higher secondary schooling) in 2012 can be matched with information on their prior skills in mathematics, reading, and writing from an independent test conducted in the earlier round of survey in 2005. Thus, we have a unique setting to investigate individuals' higher secondary stream choice after controlling for their past academic performances, which serve as reasonable proxies of their cognitive ability.
Estimating fixed-effects regression models, we find a significant gender disparity of about 20 percentage points in the choice of nonhumanities streams (i.e., STEM and commerce) at the higher secondary level among youth aged 15–18 years. In addition to a rich set of covariates, we account for unobserved heterogeneity at the regional and household levels by including fixed effects in the regression. The gender gap remains unchanged even after we control for SSLC exam performance and lagged test scores from the previous survey. We establish the robustness of the estimates by considering the intrahousehold relationships of individuals, estimating sibling fixed-effects models, and addressing sample selection issues using an inverse probability weighting (IPW) framework.
We further investigate the determinants of gender difference in stream choice. Given the persistence of the gender gap even after we take into account the effect of cognitive ability as measured by past exam performance and test scores, we explore the roles of other relevant characteristics. We find that the gender gap does not vary with household income, suggesting that gender-based sorting into different streams is equally prevalent in richer and poorer households. Rather, the gender gap is significantly reduced when there is greater educational parity between parents, captured by the difference in education level between mother and father. We also show that better access to STEM-related education benefits girls more than boys, thus narrowing the gender gap. Additionally, investigating the choice of separate study tracks, we show that the pro-male gender bias is largest in science, followed by commerce and engineering/vocational streams.
## Background and Related Literature
The last few decades have seen considerable progress in bridging the gender gap in educational attainment around the developing world. At the same time, trends in female labor force participation have been rather uneven, with South Asia actually experiencing declining female labor force participation rates (Klasen 2019). Moreover, women have continued to be employed predominantly only in few sectors and occupations (Borrowman and Klasen 2020). This perpetuating trend in occupational and sectoral segregation is a major reason for the persistence of the male-female earnings gap (Blau and Kahn 2017). This pattern of gender stratification has also been found in the Indian labor market (Duraisamy and Duraisamy 2014).
India has experienced a major expansion in education provision, resulting in a significant rise in school enrollment of both boys and girls. The Indian education system has a common structure throughout the country: students progress through primary, middle, and secondary education in their first 10 years of schooling, followed by another two years of higher secondary schooling and subsequently three to five years of tertiary education. Data from the National Sample Survey (NSS) show that in the mid-1990s, the average enrollment rate among children in the age group corresponding to elementary (i.e. primary and middle) schooling was about 70%, with a gender gap of 10 percentage points favoring boys. Over the next 20 years, this enrollment rate increased to 93%, with the gender gap declining to only 2 percentage points. The same pattern is visible in secondary and higher secondary levels: over the last two decades, the enrollment rate increased from 50% to 77%, and the gender gap declined from 16 percentage points to 2 percentage points.
The first 10 years of education in India include a common, nonselective curriculum for all students. After that, each student enrolling in higher secondary level must specialize in a particular stream; most choose the humanities, science, or commerce stream, and a minority opt for other tracks, such as engineering or vocational education. After completing the higher secondary level, students who continue to tertiary education enroll in colleges for bachelor's and master's degrees in a chosen stream. A crucial aspect of the Indian education system is that stream choice at the higher secondary level largely determines subsequent major choice at the college level. Particularly, students who have studied in the humanities stream in higher secondary school are deemed ineligible for a STEM or commerce major in almost all colleges. Therefore, stream choice at the higher secondary level is an important decision in an individual's career because it drives the field choice at subsequent levels of education, which in turn affects labor market outcomes through occupational choice. National-level statistics from repeated cross-sectional surveys of the NSS show that the proportion of students enrolled in higher secondary level choosing humanities declined from 56% in 2007–2008 to 42% in 2014. In contrast, science enrollment increased from 31% to 39% during this period, and commerce enrollment increased from 13% to 16%. These aggregate statistics also reveal that girls have a higher propensity to study humanities than science or commerce, and boys are more likely than girls to study science (Figure 1). This gender disparity in school-level stream choice also leads to subsequent gender gaps in undergraduate studies: the share of women in STEM is only 37%, and the share in commerce is 45% (Government of India 2016).
The literature on postsecondary stream choice, mostly based on developed countries, highlights that educational choices at this level are closely linked to labor market outcomes. First, stream choice is affected by the expected future earnings from different streams (Beffy et al. 2012; Boudarbat 2008). Second, such educational choices also cause much of the variation in earnings later in life (Dustmann 2004; Joensen and Nielsen 2009). Specifically, evidence suggests that a STEM or business major yields higher returns than studying humanities (Flabbi 2011). This pattern is corroborated in the Indian context when we compare the earnings distributions of individuals who studied STEM/commerce with those of individuals who studied humanities at the higher secondary level (Figure 2).
Focusing on gender, studies have shown gender disparities in stream choice: girls are especially underrepresented in STEM at the postsecondary level of education in most countries (Hill et al. 2010; World Bank 2012). The incidence of gender segregation in education and its relation to occupational segregation has also been explored using data from the United States and Europe (Bieri et al. 2016; Daymont and Andrisani 1984; Eide 1994; Flabbi 2011; Van Puyenbroeck et al. 2012). These studies have found that men's and women's college major choice largely explains occupational choices and accounts for a significant part of the gender wage gap. For the case of India, Sahoo and Klasen (2018) found that, even with controls for exam results and household fixed effects, women who choose a STEM or commerce stream in higher secondary education have substantially higher chances of participating in the labor force, securing salaried employment, choosing a male-dominated occupation, and having higher earnings. The choice of STEM or commerce stream in turn leads to a reduction of gender gap within households in terms of all these economic outcomes. Also, among different streams, science appears to have the most significant effect.
One potential reason that girls are less likely to choose STEM subjects is that boys may have a comparative advantage in mathematics. Evidence shows that a male advantage in mathematics achievement starts manifesting in middle school and increases with age (Bharadwaj et al. 2012; Kahn and Ginther 2017), but mathematical ability does not fully account for the gender gap in STEM choice (Dickson 2010; Friedman-Sokuler and Justman 2016; Riegle-Crumb et al. 2012; Turner and Bowen 1999). Rather than inherent gender differences in cognitive ability, other societal, psychosocial, and preference-related factors play a larger role in explaining the underrepresentation of women in math-intensive STEM subjects (Antecol and Cobb-Clark 2013; Buser et al. 2014; Zafar 2013). In fact, a large part of the observed gender gap can be attributed to the stereotypical beliefs about girls' mathematical ability and gendered preferences that are often shaped by cultural norms (Charles and Bradley 2009; Kahn and Ginther 2017).
The salience of societal factors implies that contextual analysis is essential for understanding the incidence and determinants of gendered educational choices. In addition, the theoretical perspectives on the relationship between economic development and gender stratification in education do not always converge (Hannum 2005). Modernization or neoclassical theory suggests that the expansion of market forces reduces discriminatory cultural practices that are linked to economic inefficiency, thereby reducing gender disparities in education (Forsythe et al. 2000). On the other hand, Boserup (1970) hypothesized that inequality would first increase and then decrease in the process of development. Initially, men with better access to market opportunities may reap greater benefits of economic prosperity, and progress toward gender equality would be achieved as the structural transformation proceeds (Lantican et al. 1996). Traditional institutions also mediate the effect of economic development on women's educational responses (Munshi and Rosenzweig 2006). Particularly for school-age children, decisions are influenced by parents, who are likely to consider factors beyond labor market returns to education. In South Asia, these factors include dowry payment for daughters' marriage, a higher likelihood of receiving old-age support from sons than from daughters due to patrilocality, and gender norms about women's participation in activities outside the household (Alderman and King 1998; Jayachandran 2015).
Our study contributes to the literature in two ways. First, we identify the pattern of gender segregation in stream choice in an emerging economy where such evidence has been lacking.
Second, we explore the plausible determinants of the gender disparity. Specifically, we analyze the role of cognitive ability, measured by past exam performance and test scores. In addition, we examine the influence of other pertinent factors in this context. Household income is likely to be a constraining factor for poorer students while choosing a STEM education, which is more costly to study than humanities. Indeed, the NSS data reveal that the average expenditure incurred by students in the science and commerce streams is more than twice the expenditure of those studying humanities at the higher secondary level.4 Variation in household income may lead to gendered choices depending on whether resource constraints are binding and how son preference varies along with income (Alderman and King 1998; Garg and Morduch 1998). Therefore, we investigate whether household income determines the gender difference in stream choice.
Another potential determinant we consider is parental education gap. A large literature has explored the intergenerational transmission of human capital, but this research has mostly analyzed the effect of parental education on children's years of schooling or grade progression rather than stream choice (Holmlund et al. 2011). In addition, we introduce the gender dimension by focusing on the gap in educational attainment between mothers and fathers. We postulate that greater parity in parental education would induce equality in stream choice between boys and girls.
Finally, we consider access to STEM-related education, which is especially important in a developing country where students are often constrained by the availability of specific streams in the local schools. Reviewing the literature on several developing countries, Glick (2008) noted that access to education, despite being a gender-neutral factor, may disproportionately affect girls' participation. This possibility is plausible in the context of a patriarchal society like India, where strong gender norms may discourage adolescent girls from traveling long distances to attend school (Muralidharan and Prakash 2017). Safety concerns may also dissuade girls from enrolling in their preferred stream if it involves traveling longer distances (Borker 2017). Using regional variation in the availability of STEM colleges as a proxy for access, we test whether better access reduces the gender gap in stream choice.
## Data Description
We use the India Human Development Survey (IHDS), a nationally representative, two-period longitudinal data set (Desai et al. 2010, 2015).5 The first round of data was collected in 2004–2005 on 41,554 households in 1,503 villages and 971 urban neighborhoods across India. In 2011–2012, the second round of survey reinterviewed 83% of the same households; for households that could not be tracked, a replacement sample was used. Thus, the second round of survey covered 42,152 households across India. For brevity, we refer to the first round as 2005 data and the second round as 2012 data. IHDS is a multitopic survey collecting detailed information at the individual, household, and community levels. Our analysis mainly uses the sample from the 2012 survey and uses the 2005 survey to account for past characteristics of the same individuals.
We explore whether the choice of study stream exhibits a gender bias at the higher secondary level. In India, the official school entry age is 6 years, and the (lower) secondary level ends after 10 years of schooling. In the IHDS sample, the enrollment rate of children of secondary school age (14–15 years) is 87%, and the gender gap in the enrollment rate is only 2 percentage points. Because the higher secondary (or senior secondary) level consists of two years of schooling succeeding the secondary level, we concentrate on the sample of individuals who are in the corresponding age group of 15–18 years.6 Information on stream choice at the higher secondary level is available only for individuals who have passed the secondary level and enrolled in the subsequent level of education. The secondary pass rate for our sample is 39.4% for males and 40.6% for females; a t test reveals that the gender difference in the secondary pass rate is not statistically significant. After we drop observations with missing values, the final analysis sample is 5,203 children.
The first step toward specialization begins at the higher secondary level of education, when students have to choose a stream mainly from the following options: arts/humanities, commerce, science, engineering/vocational, and others (e.g., home science, craft, and design).7 Estimates from the IHDS data show patterns of stream choice that are similar to the national-level statistics around this period. Summary statistics presented in Table 1 show that 50% of students in the sample chose the humanities stream. The next most popular stream is science, followed by commerce, engineering/vocational, and others, the latter of which are chosen by very few. In the sample, 58% girls but only 41% boys chose humanities, indicating that girls are underrepresented in science, commerce, and engineering/vocational streams. Because these average differences may be confounded by various observable and unobservable factors that are correlated with both gender and stream choice, we next lay out an econometric model to identify the gender gap.
## Empirical Model
To identify if there is a gender disparity in the choice of study stream, we use the following econometric model:
$Streamihvdk=α+βFemaleihvd+γ1Xihvd+γ2Zhvd+θAbilityihvd+μd+φvd+ϕhvd+εihvd.$
(1)
We estimate a linear probability model where the dependent variable ($Streamihvdk$) is a binary indicator of whether an individual of higher secondary school age (15–18 years) has chosen to study stream $k$, where $k∈{Humanities, Commerce, Science, Engineering/$$Vocational, Other}$. The subscripts i, h, v, and d (respectively) denote individual, household, village/town, and district. The main explanatory variable is an indicator variable ($Female$) denoting whether the individual is female. In addition, we control for individual-level covariates ($Xihvd$): age, birth order, number of siblings, mother's years of education, father's years of education, and dummy variables indicating relationship to the household head. Household-level covariates ($Zhvd$) include household size, wealth, dummy variables for social group (caste and religion), and whether the household is in a rural area. To control for regional characteristics, we first include fixed effects at the district level ($μd$) and then the village/town level ($φvd$). Inclusion of village/town fixed effects also helps us to control for access to education in the locality, which is important because some schools may not offer higher secondary education or may not offer all the streams at this level. Other regional characteristics, such as local labor market conditions and societal norms toward girls' education, are also subsumed by these fixed effects.
Because household-level factors, including unobserved tastes and preferences for different types of education, potentially affect the stream choice, we control for household-level heterogeneity by including household fixed effects ($ϕhvd$) in an additional set of regressions.8 This control is especially important in the context of India, where the household's unobserved preferences are correlated with gender inequality. For example, female children in India are often more likely to be found in larger families because fertility decisions are endogenously determined; parents keep having children until they have at least one boy (Basu and de Jong 2010; Clark 2000; Yamaguchi 1989). If STEM education requires higher investments, then comparisons across households may artificially show a gender gap because girls belong to larger families, who invest less in the human capital of each child. For these and related reasons, studies investigating gender discrimination in educational investments have advocated using household fixed effects (Jensen 2002; Kingdon 2005; Sahoo 2017). Although it includes household fixed effects, our model also takes into account the potential nonindependence of observations belonging to the same household by clustering the standard errors at the household level.9
Gender differences in the choice of STEM education may be driven by girls' lower cognitive ability compared with boys, especially in mathematics. The literature on gender gaps in mathematics achievement suggests that most of the observed gap is explained by background factors (Benbow and Stanley 1980; Nollenberger et al. 2016). In India, because of systematic and continual underinvestment in girls' human capital from early childhood, girls' cognitive ability may lag behind that of boys at the higher secondary level. A novel feature of our data is that they allow us to account for an individual's cognitive ability using two distinct measures.
The first measure of cognitive ability is given by the individual's performance in the secondary level board examination, which is potentially an important predictor of stream choice at the higher secondary level. In India, a standardized examination is conducted by the education board (at the state or national level) to which each school belongs. Every student must pass this examination and obtain the SSLC to be able to continue at higher secondary levels of education. The results of this examination are typically categorized into divisions 1, 2, and 3, in the declining order of the quality of grade obtained. We use this SSLC performance indicator to control for the individual's cognitive ability.
Furthermore, in the 2005 IHDS round, children who were aged 8–11 years were given cognitive tests on mathematics, reading, and writing ability. In the 2012 survey, these children are in the age group corresponding to the higher secondary level and are considered in the regression. Therefore, we are able to control for their past cognitive ability by including their performance on these tests.10 Consequently, we control for achievement scores collected by two independent tests: one from the SSLC examination and the other conducted by IHDS enumerators in 2005. Hence, we believe that our regression adequately captures the differences in children's abilities and identifies the gender gap in stream choice.
A potential concern that remains is that stream choice is defined only for those individuals who have passed the secondary level and enrolled at the higher secondary level. In the age group considered, 40% of children passed the secondary level. These children are likely to be systematically different from those who have education below the secondary level. However, disaggregating this pass rate by boys and girls, we find that there is no gender gap in the secondary level pass rate. We also estimate a regression (see Table A2, online appendix) similar to Eq. (1) but with the dependent variable being a binary indicator of whether a child has passed the secondary level (and hence is eligible for higher secondary stream choice). The coefficient on gender in this regression is almost always insignificant, and the magnitude is almost zero, suggesting that the probability of selecting into the sample for our main regression (stream choice) does not vary by gender. Hence, this selection is unlikely to confound the effect of gender in the regression of STEM/commerce stream choice.
## Results
### Main Results
We begin by investigating the gender difference in the choice of STEM/commerce streams, combining science, engineering/vocational, and commerce into one category and comparing it with the humanities and other streams. The results, presented in Table 2, show a statistically significant female disadvantage of about 20 percentage points in the choice of STEM/commerce streams compared with the humanities. This estimate remains stable across different specifications. Although all regressions include observable control variables and SSLC results to control for cognitive ability, we sequentially add fixed effects at the level of the district, village/town, and household.11
Our final model further includes test scores from the 2005 survey.12 Among all boys and girls, 50% study STEM/commerce streams; thus, the estimated gender gap translates into a magnitude of 40% of the mean participation, which is substantial. As expected, we find that students who scored better on the SSLC examination are more likely to study STEM/commerce at the higher secondary level. Students who in 2005 scored at the highest level of difficulty in mathematics (i.e., division) also have a higher probability of choosing these quantitative streams.13 Because the estimate of the gender gap remains significant and stable even after we take into account the variation in cognitive abilities captured by two different measures, the gender gap in stream choice is unlikely to be driven by the intrinsic ability of students.
### Robustness Analysis
Our main results reveal a gender gap in stream choice after we control for explanatory factors. We further investigate the intrahousehold differences in outcomes when we include household fixed effects in the analysis. In this section, we test whether our estimates of the intrahousehold gender gap remain robust after we take household structures into account.
First, we consider the relationship of individuals in the household more explicitly. In the sample of adolescents included in the analysis, 84% are children and 12% are grandchildren of the household heads.14 To ensure that intrahousehold relationships do not confound the effect of gender, all the regressions control for dummy variables denoting an individual's relation to the household head. Moreover, we conduct a sensitivity analysis by restricting the comparison between individuals who are in a similar position within the household; in particular, we compare direct siblings by using a sibling fixed-effects model.15 The observations pertaining to the siblings sharing the same parents may not be independent because the siblings are likely to have common unobservable characteristics. To address this issue, our model estimates cluster-robust standard errors, allowing the error terms to be correlated among siblings who share the same parents. Results presented in columns 1–2 of Table 3 reveal that the estimates remain almost unchanged in this analysis. In an additional exercise, we restrict the sample to sons and daughters of the household head and estimate the model. We again find a similar estimate of the gender gap, as shown in the last two columns of Table 3. These analyses establish that the magnitude and precision of the estimated gender gap are not affected by the household structure and relationships among individuals in the household.
Next, we investigate whether the estimates from the household fixed-effects models are generalizable. Because the coefficients in these models are estimated using variation within households, observations belonging to households with multiple children contribute to this estimation. Moreover, for identification of the intrahousehold gender gap in stream choice, at least some of these households must have both multiple children and children of opposite gender. If the characteristics of these households systematically vary from those of the overall sample, then the estimates may not be generalizable.16 To address this issue, we adopt IPW, which has been widely used in the literature in similar contexts (Fitzgerald et al. 1998; Jones et al. 2006; Wooldridge 2010). This estimation technique follows two steps. In the first step, using our main sample of 5,203 adolescents, we model the probability of belonging to a household with multiple children, conditional on a set of covariates. These covariates include the observable explanatory variables used in Eq. (1) and their interaction with the gender dummy variable. In the second step, we use the inverse of these predicted probabilities as weights for the observations while estimating a household fixed-effects model restricting the sample to those households with multiple children. In another instance, we apply the IPW model for households with multiple children of opposite gender for the second step.
The findings of this robustness analysis are summarized graphically in Figure 3, which juxtaposes the estimates that do not use IPW with those using IPW. We find that the point estimates and the confidence intervals are remarkably similar even after we use IPW to correct for any potential nonrandom selection of households when fixed effects are used. This analysis bolsters our main results and indicates that the estimated gender gap is robust to the issue of sample selection.
### Heterogeneity Analysis Exploring the Determinants of the Gender Gap
To explore what drives the gender gap in stream choice, we augment our main empirical model (i.e., Eq. (1)) by including interaction terms of gender with some key explanatory factors. Estimating how the effect of gender varies along with these factors sheds light on the underlying determinants of the gender gap. We investigate variations with respect to factors that have high contextual relevance: household affluence, parental educational parity, and access to STEM education. The first two factors are related to the demand for education, and the third factor reflects the supply of education, which is also policy-relevant.
Studying STEM or related streams likely involves a higher cost, which wealthier households are better able to pay (Chandrasekhar et al. 2019). Indian households are also likely to make greater educational investments on boys (Azam and Kingdon 2013; Kingdon 2005). Therefore, the higher cost of STEM-related education may discourage households from enrolling girls in such streams, especially when households have limited resources for children's education. To check whether resource constraint leads to gender disparity, we interact the gender dummy variable in our model with household income (per capita). We mitigate the potential endogeneity in household income by using baseline income from the earlier round rather than contemporaneous income. As revealed in Table 4, household income has no significant effect on the gender gap in stream choice, although households with higher income are more likely to enroll boys in the STEM/commerce streams.17 Thus, we find that the gender gap is quite pervasive, given that it is observed both in richer and poorer households. This result implies that either resource constraint is relatively less crucial than other determinants of the gender gap, or the gendered preference concerning stream choice does not change with respect to household income.
Because the decision of stream choice is made in adolescence, parents are likely to influence it (Alderman and King 1998; Dustmann 2004). In a patriarchal society like India, parental attitudes toward gender equality in education are likely to affect the study choice of girls vis-à-vis boys. To capture this aspect, we next consider parental educational parity, as defined by the difference in years of education between the mother and father. Because mothers usually have lower levels of education than fathers, a greater parity implied by relatively higher education of the mother may reduce the gender disparity in their children's education. By interacting the female dummy variable with parental educational parity in our model, we find support for this hypothesis. On average, a mother has 1.7 fewer years of education than a father; when educational attainment between the parents is equal, it reduces the gender gap in their children's STEM/commerce stream choice by 2.2 percentage points (column 4, Table 4).
Another pertinent question from the supply side of education is whether the gender disparity declines when STEM-related education is made more accessible. Although various government policies over the last few decades have universalized access to education at the elementary levels, access to higher secondary education still varies substantially. In addition, educational institutions that offer higher secondary level grades may not offer all the streams. In many places, students have to travel long distances to study their desired stream, especially science or commerce.18 Although any such variation in access to education is captured by village/town fixed effects in our model, access may have a differential effect on girls than boys. To estimate the differential effect of access by gender, we interact with gender a variable that measures the total number of science and technical colleges in the district at the time the stream choice was made.19 The results show that districts with a higher number of colleges providing science or technical education have a smaller gender gap in stream choice (columns 5–6, Table 4). A 1 standard deviation increase in the number of science/technical colleges per 1 million population in the district is associated with a reduction of 7 percentage points in the gender gap in higher secondary stream choice.
### Gender Gap in the Choice of Individual Streams
We also estimate a linear probability model given by Eq. (1) separately for each stream. Table 5 presents results that include village/town fixed effects (panel A) and household fixed effects (panel B). Girls are 20 percentage points more likely than boys to study humanities, as estimated from both models. Underrepresentation of girls is most prominent in science (8.5–10 percentage points), followed by commerce (6–8 percentage points) and engineering/vocational education (about 3.5 percentage points). Ability sorting is also significant across streams: the humanities stream seems to attract students with worse grades in SSLC exam results, whereas science attracts the best performing students. Nonetheless, the effect of gender remains significant even after we take the effect of ability into account.
## Conclusion
Our study provides quantitative evidence on the gender segregation in higher secondary stream choice in an emerging economy. In addition to showing that girls are substantially underrepresented in STEM and commerce streams as compared with the humanities, we shed light on the plausible determinants of the gender gap. Our findings are based on data from India, which accounts for a large share of the world's STEM graduates, thus expanding on the literature, which has focused mostly on developed countries. Also, by reflecting on the underlying processes that cause the gender gap, our findings have implications beyond the Indian setting.
A recent international comparison of test scores in mathematics and science found significant heterogeneity in the relative performance of girls versus boys across different countries (UNESCO 2017). Because of the importance of math skills in STEM fields, one may presume that the extent of the gender gap in math performance would predict an underrepresentation of women in STEM fields. However, we show that variations in cognitive skills, as measured by prior exam performance and math test scores, do not subsume the effect of gender on stream choice. In addition, we show that the gender gap in STEM/commerce participation is equally prevalent among richer and poorer households, in line with the pervasiveness of women's underrepresentation in STEM fields across societies with varying levels of economic prosperity. Our results imply that individual performance or household affluence need not be the main determining factor behind gendered educational choices, and it is necessary to consider other background and societal factors in this context.
Exploring the role of other factors, we show that parental educational parity helps to reduce the gender gap in STEM education. This result underscores the influence of parents, especially in settings where streams are chosen at an early age. Unlike the United States, many European countries require students to choose a field of study in secondary school (e.g., see Dustmann [2004] for Germany; see Dahl et al. [2020] for Sweden). That gender parity in parental education encourages girls to pursue a male-dominated field indicates an intergenerational transmission of gender attitude toward education. However, intergenerational mobility may be limited if parental background determines the education choice of the next generation, as shown by Dustmann (2004) in the context of Germany. Hence, there is scope for policies to play an instrumental role in bridging the gender gap by providing equal opportunities to boys and girls. As our results highlight, one avenue through which policies can be effective is by increasing the number of local educational institutions offering STEM and commerce streams, especially in underserved areas. Such an approach is particularly relevant for developing countries, where girls may be disproportionately affected by the lack of access to STEM education.
It is important to point out that there may be other potential determinants that we have not examined here because appropriate data are not available. These factors include individual preferences or behavioral traits; for instance, gender differences in competitiveness may explain the gender gap in STEM choice (Buser et al. 2014). Teachers may also influence stream choice, but without matched teacher-student data, it is not possible to analyze this aspect. The labor market opportunities for women studying different streams can be another relevant determinant. Investigation of these additional determinants constitutes an agenda for future research.
## Acknowledgments
We are grateful to the editors and four anonymous reviewers of Demography for their constructive comments that helped us to improve the paper. We thank the participants of GrOW Workshop 2016 at Stellenbosch University, Contemporary Issues in Development Economics Conference 2016 at Jadavpur University, PEGNet Conference 2017 at ETH Zurich, GREThA International Conference on Economic Development 2018 at University of Bordeaux, Sustainability and Development Conference 2018 at University of Michigan, and CSAE Conference 2019 at University of Oxford for helpful comments. We also thank Rahul Lahoti, Abhiroop Mukhopadhyay, Nishith Prakash, Sudipa Sarkar, and Hema Swaminathan for helpful discussions. We gratefully acknowledge funding from the Growth and Economic Opportunities for Women (GrOW) initiative, a multifunder partnership between the United Kingdom's Department for International Development, the Hewlett Foundation, and the International Development Research Centre.
## Notes
1
An exception is Sookram and Strobl (2009), who analyzed this topic for Trinidad and Tobago.
2
We categorize science and engineering/vocational as STEM. Subjects like accountancy and finance that involve mathematical tools are included in the commerce stream. Hence, some of our comparisons in this paper involve humanities versus nonhumanities, including STEM and commerce. We also report analysis for each stream separately.
3
Estimates from the data we use suggest that 93% and 85% of students who are currently studying, respectively, engineering and science in college studied a STEM stream at the higher secondary level. Among students studying humanities in college, 85% studied humanities in higher secondary school as well.
4
The difference in expenditure is mainly driven by higher school fees and private tutoring costs. Compared with humanities students, students in the science and commerce streams pay, respectively, 2.7 and 2.5 times more on school fees and 2.9 and 2.2 times more on private tutoring. Science and commerce students also incur marginally higher expenses on books, school supplies, and transportation, although these expenses are relatively smaller in proportion to the total expenditure.
5
The IHDS was carried out jointly by the University of Maryland and the National Council of Applied Economic Research, New Delhi. The data set is publicly available. More details can be found online at https://ihds.umd.edu/.
6
Strictly speaking, the ages corresponding to the higher secondary level should be 16–17 years. However, we include one year below and one year above this range to allow for the possibility that some children may finish the secondary level earlier or later. The enrollment rate among children aged 16–17 is 74%; however, many of them haven’t yet completed secondary-level schooling. In an alternative specification, we remove the age restriction and estimate the regression for all individuals enrolled in the higher secondary level; the results are unchanged.
7
Students choose from physics, chemistry, mathematics, and biology/computer science/economics in the science stream; business studies, accountancy, economics, and business mathematics in the commerce stream; and fields such as history, geography, political science, sociology, and philosophy in the humanities stream. In addition, all students study languages at the higher secondary level.
8
The inclusion of household fixed effects implies that only households with at least two individuals contribute to identification in this regression. To ensure that our estimates are not biased due to the selection of such households, we also present results from analyses excluding household fixed effects. To further address this issue, we check the sensitivity of our estimates using an inverse probability weighting technique in our robustness analysis.
9
We also check the robustness of the estimates by clustering the standard errors at the level of district and village/town in the earlier specifications. We thereby take into account any potential heteroskedasticity and correlation in the error terms within the clusters (Angrist and Pischke 2009: chapter 8).
10
The sample size is reduced substantially, by about 50%, when we control for past test scores from the previous round of the survey due to many missing values in the variables capturing past test scores (see Table 1). Some individuals (about 11% of the sample) could not be found in the 2012 survey, and others may have misreported their age in the previous survey, leading to missing values for test scores among this age group. Later, we show that our estimates are not driven by variations in sample size.
11
We provide additional estimates based on an intrahousehold comparison in the subsequent section on robustness analysis. The results are also robust to the inclusion of a control variable indicating whether there was a sibling who married and left the household (results not shown).
12
Although the sample size drops after the inclusion of past test scores, which are not available for the entire sample, a comparison yields no significant difference in key variables between the entire sample and the reduced sample. Also, if we estimate regressions from columns 1–3 (Table 2) on the reduced sample, the estimates are almost unchanged. See Table A1 in the online appendix.
13
We do not find any significant effect of other measures of cognitive ability (i.e., reading and writing scores) on stream choice. This result is consistent with Arcidiacono’s (2004) finding that math ability was more important than verbal ability in explaining sorting into particular majors in the context of the United States.
14
In addition, 2% are nephews/nieces of the household head, and the sample reflects very few other relationships (each less than 1%), such as daughter-in-law, brother/sister, or other relatives.
15
These direct siblings share the same parents. In India, sometimes multiple families coreside in a household, forming an extended or joint family; hence children from multiple parents may be coresiding in a household. A sibling fixed-effects model controls for heterogeneity across different parents within a household; few such cases are found in the sample, however, given that 84% of the sample is formed by children of the household head.
16
A comparison of the key characteristics between the sample of households with multiple children and the whole sample is provided in Table A3 in the online appendix. For the samples in the stream choice analysis (i.e. 15- to 18-year-old adolescents enrolled in higher secondary schooling), there is no significant difference in the mean of the outcome variable (i.e., stream choice) across these households. However, some of the household characteristics predictably differ across these samples, although the differences are not large.
17
We find similar results if instead of household income we use household wealth measured by durable assets.
18
Data from the 2014 NSS show that in rural areas, 43% and 41% of girls in, respectively, the science and commerce streams have to travel more than 5 kilometers to reach their schools; 30% of girls who study humanities travel more than 5 kilometers for school.
19
We use data from the All India Survey of Higher Education to construct this variable. The measure is lagged with respect to the individual’s stream choice decision and is normalized by the population of the district.
The text of this article is only available as a PDF.
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This is an open access article distributed under the terms of a Creative Commons license (CC BY-NC-ND 4.0).
| 2021-09-21T06:20:49 |
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https://zbmath.org/authors/batchelor.george-k
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## Batchelor, George Keith
Compute Distance To:
Author ID: batchelor.george-k Published as: Batchelor, G. K.; Batchelor, George K.; Batchelor, George more...less External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 67 Publications since 1944, including 9 Books 5 Contributions as Editor · 2 Further Contributions Biographic References: 9 Publications Co-Authors: 19 Co-Authors with 23 Joint Publications 373 Co-Co-Authors
all top 5
### Co-Authors
50 single-authored 6 Townsend, Albert Alan 3 Nitsche, Johannes M. 2 Green, J. T. 2 Moffatt, Henry Keith 2 Proudman, Ian 2 Taylor, Geoffrey Ingram 1 Acrivos, Andreas 1 Bingham, Nicholas Hugh 1 Canuto, Vittorio M. 1 Chasnov, Jeffrey R. 1 Davidson, K. S. M. 1 Davies, Ruth M. 1 Ellison, T. H. 1 Gill, A. E. 1 Green, H. L. 1 Hayman, Walter Kurt 1 Hill, Rodney 1 Hinch, Edward John 1 Howells, I. D. 1 Hyland, J. Martin E. 1 Kendall, David George 1 Koch, Donald L. 1 Lane, W. R. 1 Lighthill, Sir Michael James 1 Lorentz, Georg Gunther 1 Love, Eric Russell 1 Mauri, Roberto 1 Mott, Nevill Francis 1 Razborov, Aleksandr Aleksandrovich 1 Robinson, Christopher Alan 1 Southwell, Richard Vynne 1 Squire, H. B. 1 Stewart, Robert W. 1 Ursell, Fritz 1 Wen, Chia-Sheng 1 Whittle, Peter 1 Worster, M. Grae
all top 5
### Serials
30 Journal of Fluid Mechanics 7 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 5 Quarterly Journal of Mechanics and Applied Mathematics 3 Quarterly of Applied Mathematics 3 Proceedings of the Cambridge Philosophical Society 1 Archives of Mechanics 1 Physics of Fluids 1 Bulletin of the London Mathematical Society 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Nature, London 1 Colloques Internationaux du Centre National de la Recherche Scientifique 1 Cambridge Mathematical Library
all top 5
### Fields
32 Fluid mechanics (76-XX) 6 History and biography (01-XX) 4 General and overarching topics; collections (00-XX) 2 Mechanics of deformable solids (74-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)
### Citations contained in zbMATH Open
62 Publications have been cited 4,980 times in 4,326 Documents Cited by Year
An introduction to fluid dynamics. Zbl 0152.44402
Batchelor, G. K.
1967
An introduction to fluid dynamics. 2nd pbk-ed. Zbl 0958.76001
Batchelor, G. K.
1999
The theory of homogeneous turbulence. Zbl 0053.14404
Batchelor, G. K.
1953
Small-scale variation of convected quantities like temperature in turbulent fluid. I: General discussion and the case of small conductivity. Zbl 0085.39701
Batchelor, G. K.
1959
The stress system in a suspension of force-free particles. Zbl 0193.25702
Batchelor, G. K.
1970
On steady laminar flow with closed streamlines at large Reynolds number. Zbl 0070.42004
Batchelor, G. K.
1956
Computation of the energy spectrum in homogeneous two-dimensional turbulence. Zbl 0217.25801
Batchelor, G. K.
1969
Slender-body theory for particles of arbitrary cross-section in Stokes flow. Zbl 0216.52401
Batchelor, G. K.
1970
Sedimentation in a dilute dispersion of spheres. Zbl 0252.76069
Batchelor, G. K.
1972
The determination of the bulk stress in a suspension of spherical particles to order c$$^2$$. Zbl 0246.76108
Batchelor, G. K.; Green, J. T.
1972
Analysis of the stability of axisymmetric jets. Zbl 0118.21102
Batchelor, G. K.; Gill, A. E.
1962
The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. Zbl 0247.76088
Batchelor, G. K.; Green, J. T.
1972
Axial flow in trailing line vortices. Zbl 0151.40401
Batchelor, G. K.
1964
Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Zbl 0042.43101
Batchelor, G. K.
1951
The nature of turbulent motion at large wave-numbers. Zbl 0036.25602
Batchelor, G. K.; Townsend, A. A.
1949
The stress generated in a on-dilute suspension of elongated particles by pure straining motion. Zbl 0225.76003
Batchelor, G. K.
1971
Brownian diffusion of particles with hydrodynamic interaction. Zbl 0346.76073
Batchelor, G. K.
1976
The effect of homogeneous turbulence on material lines and surfaces. Zbl 0046.42201
Batchelor, G. K.
1952
Decay of turbulence in the final period. Zbl 0032.22602
Batchelor, G. K.; Townsend, A. A.
1948
Small-scale variation of convected quantities like temperature in turbulent fluid. II: The case of large conductivity. Zbl 0085.39702
Batchelor, G. K.; Howells, I. D.; Townsend, A. A.
1959
On the spontaneous magnetic field in a conducting liquid in turbulent motion. Zbl 0040.14203
Batchelor, G. K.
1950
The effect of rapid distortion of a fluid in turbulent motion. Zbl 0055.19201
Batchelor, G. K.; Proudman, Ian
1954
The large-scale structure of homogeneous turbulence. Zbl 0074.42501
Batchelor, G. K.; Proudman, I.
1956
A new theory of the instability of a uniform fluidized bed. Zbl 0648.76028
Batchelor, G. K.
1988
Sedimentation in a dilute polydisperse system of interacting spheres. I. General theory. Zbl 0498.76088
Batchelor, G. K.
1982
A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. Zbl 0071.19901
Batchelor, G. K.
1956
Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Zbl 0057.41701
Batchelor, G. K.
1954
Break-up of a falling drop containing dispersed particles. Zbl 0892.76020
Nitsche, J. M.; Batchelor, G. K.
1997
The theory of homogeneous turbulence. Reissue. Zbl 0522.76051
Batchelor, G. K.
1982
Decay of isotropic turbulence in the initial period. Zbl 0030.37704
Batchelor, G. K.; Townsend, A. A.
1948
Transport properties of two-phase materials with random structure. Zbl 0297.76078
Batchelor, G. K.
1974
Pressure fluctuations in isotropic turbulence. Zbl 0042.19403
Batchelor, G. K.
1951
Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution. Zbl 0438.76082
Batchelor, G. K.
1979
Sedimentation in a dilute polydisperse system of interacting spheres. II. Numerical results. Zbl 0507.76101
Batchelor, G. K.; Wen, C.-S.
1982
The theory of axisymmetric turbulence. Zbl 0061.45503
Batchelor, G. K.
1946
Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Zbl 0046.42106
Batchelor, G. K.
1952
Homogeneous buoyancy-generated turbulence. Zbl 0743.76040
Batchelor, G. K.; Canuto, V. M.; Chasnov, J. R.
1992
Longitudinal shear-induced diffusion of spheres in a dilute suspension. Zbl 0755.76080
Acrivos, A.; Batchelor, G. K.; Hinch, E. J.; Koch, D. L.; Mauri, R.
1992
The theory of homogeneous turbulence. Zbl 0098.41001
Batchelor, G. K.
1960
Instability of stationary unbounded stratified fluid. Zbl 0850.76205
Batchelor, G. K.; Nitsche, J. M.
1991
The stability of a large gas bubble rising through liquid. Zbl 0641.76102
Batchelor, G. K.
1987
Diffusion in a dilute polydisperse system of interacting spheres. Zbl 0556.76095
Batchelor, G. K.
1983
Perspectives in fluid dynamics. A collective introduction to current research. Zbl 0952.00020
2000
Energy decay and self-preserving correlation functions in isotropic turbulence. Zbl 0035.25604
Batchelor, G. K.
1948
The effect of wire gauze on small disturbances in a uniform stream. Zbl 0036.25702
Taylor, G. I.; Batchelor, G. K.
1949
Mass transfer from small particles suspended in turbulent fluid. Zbl 0456.76068
Batchelor, G. K.
1980
The skin friction on infinite cylinders moving parallel to their length. Zbl 0055.18605
Batchelor, G. K.
1954
The role of big eddies in homogeneous turbulence. Zbl 0036.25601
Batchelor, G. K.
1949
Kolmogoroff’s theory of locally isotropic turbulence. Zbl 0029.28405
Batchelor, G. K.
1947
Diffusion in free turbulent shear flows. Zbl 0083.21002
Batchelor, G. K.
1957
Note on the Onsager symmetry of the kinetic coefficients for sedimentation and diffusion in a dilute bidispersion. Zbl 0612.76110
Batchelor, G. K.
1986
Instability of stratified fluid in a vertical cylinder. Zbl 0789.76096
Batchelor, G. K.; Nitsche, J. M.
1993
Secondary instability of a gas-fluidized bed. Zbl 0809.76035
Batchelor, G. K.
1993
Anisotropy of the spectrum of turbulence at small wave-numbers. Zbl 0040.27003
Batchelor, G. K.; Stewart, R. W.
1950
Developments in microhydrodynamics. Zbl 0364.76001
Batchelor, G. K.
1977
Obituary: Andrei Nikolaevich Kolmogorov (1903-1987). Zbl 0689.01015
1990
The life and legacy of G. I. Taylor. Zbl 0851.01016
Batchelor, George
1996
An unfinished dialogue with G. I. Taylor. Zbl 0356.76002
Batchelor, G. K.
1975
Low-Reynolds-number bubbles in fluidised beds. Zbl 0278.76041
Batchelor, G. K.
1974
A collection of surveys of the present position of research in some branches of mechanics, written in commemoration of the 70th birthday of Geoffrey Ingram Taylor. Zbl 0070.00102
1956
The singularity in the spectrum of homogeneous turbulence. Zbl 0080.19102
Batchelor, G. K.
1957
The scientific papers of Sir Geoffrey Ingram Taylor. Vol. II: Meteorology, oceanography and turbulent flow. Zbl 0089.43503
1960
Perspectives in fluid dynamics. A collective introduction to current research. Zbl 0952.00020
2000
An introduction to fluid dynamics. 2nd pbk-ed. Zbl 0958.76001
Batchelor, G. K.
1999
Break-up of a falling drop containing dispersed particles. Zbl 0892.76020
Nitsche, J. M.; Batchelor, G. K.
1997
The life and legacy of G. I. Taylor. Zbl 0851.01016
Batchelor, George
1996
Instability of stratified fluid in a vertical cylinder. Zbl 0789.76096
Batchelor, G. K.; Nitsche, J. M.
1993
Secondary instability of a gas-fluidized bed. Zbl 0809.76035
Batchelor, G. K.
1993
Homogeneous buoyancy-generated turbulence. Zbl 0743.76040
Batchelor, G. K.; Canuto, V. M.; Chasnov, J. R.
1992
Longitudinal shear-induced diffusion of spheres in a dilute suspension. Zbl 0755.76080
Acrivos, A.; Batchelor, G. K.; Hinch, E. J.; Koch, D. L.; Mauri, R.
1992
Instability of stationary unbounded stratified fluid. Zbl 0850.76205
Batchelor, G. K.; Nitsche, J. M.
1991
Obituary: Andrei Nikolaevich Kolmogorov (1903-1987). Zbl 0689.01015
1990
A new theory of the instability of a uniform fluidized bed. Zbl 0648.76028
Batchelor, G. K.
1988
The stability of a large gas bubble rising through liquid. Zbl 0641.76102
Batchelor, G. K.
1987
Note on the Onsager symmetry of the kinetic coefficients for sedimentation and diffusion in a dilute bidispersion. Zbl 0612.76110
Batchelor, G. K.
1986
Diffusion in a dilute polydisperse system of interacting spheres. Zbl 0556.76095
Batchelor, G. K.
1983
Sedimentation in a dilute polydisperse system of interacting spheres. I. General theory. Zbl 0498.76088
Batchelor, G. K.
1982
The theory of homogeneous turbulence. Reissue. Zbl 0522.76051
Batchelor, G. K.
1982
Sedimentation in a dilute polydisperse system of interacting spheres. II. Numerical results. Zbl 0507.76101
Batchelor, G. K.; Wen, C.-S.
1982
Mass transfer from small particles suspended in turbulent fluid. Zbl 0456.76068
Batchelor, G. K.
1980
Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution. Zbl 0438.76082
Batchelor, G. K.
1979
Developments in microhydrodynamics. Zbl 0364.76001
Batchelor, G. K.
1977
Brownian diffusion of particles with hydrodynamic interaction. Zbl 0346.76073
Batchelor, G. K.
1976
An unfinished dialogue with G. I. Taylor. Zbl 0356.76002
Batchelor, G. K.
1975
Transport properties of two-phase materials with random structure. Zbl 0297.76078
Batchelor, G. K.
1974
Low-Reynolds-number bubbles in fluidised beds. Zbl 0278.76041
Batchelor, G. K.
1974
Sedimentation in a dilute dispersion of spheres. Zbl 0252.76069
Batchelor, G. K.
1972
The determination of the bulk stress in a suspension of spherical particles to order c$$^2$$. Zbl 0246.76108
Batchelor, G. K.; Green, J. T.
1972
The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. Zbl 0247.76088
Batchelor, G. K.; Green, J. T.
1972
The stress generated in a on-dilute suspension of elongated particles by pure straining motion. Zbl 0225.76003
Batchelor, G. K.
1971
The stress system in a suspension of force-free particles. Zbl 0193.25702
Batchelor, G. K.
1970
Slender-body theory for particles of arbitrary cross-section in Stokes flow. Zbl 0216.52401
Batchelor, G. K.
1970
Computation of the energy spectrum in homogeneous two-dimensional turbulence. Zbl 0217.25801
Batchelor, G. K.
1969
An introduction to fluid dynamics. Zbl 0152.44402
Batchelor, G. K.
1967
Axial flow in trailing line vortices. Zbl 0151.40401
Batchelor, G. K.
1964
Analysis of the stability of axisymmetric jets. Zbl 0118.21102
Batchelor, G. K.; Gill, A. E.
1962
The theory of homogeneous turbulence. Zbl 0098.41001
Batchelor, G. K.
1960
The scientific papers of Sir Geoffrey Ingram Taylor. Vol. II: Meteorology, oceanography and turbulent flow. Zbl 0089.43503
1960
Small-scale variation of convected quantities like temperature in turbulent fluid. I: General discussion and the case of small conductivity. Zbl 0085.39701
Batchelor, G. K.
1959
Small-scale variation of convected quantities like temperature in turbulent fluid. II: The case of large conductivity. Zbl 0085.39702
Batchelor, G. K.; Howells, I. D.; Townsend, A. A.
1959
Diffusion in free turbulent shear flows. Zbl 0083.21002
Batchelor, G. K.
1957
The singularity in the spectrum of homogeneous turbulence. Zbl 0080.19102
Batchelor, G. K.
1957
On steady laminar flow with closed streamlines at large Reynolds number. Zbl 0070.42004
Batchelor, G. K.
1956
The large-scale structure of homogeneous turbulence. Zbl 0074.42501
Batchelor, G. K.; Proudman, I.
1956
A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. Zbl 0071.19901
Batchelor, G. K.
1956
A collection of surveys of the present position of research in some branches of mechanics, written in commemoration of the 70th birthday of Geoffrey Ingram Taylor. Zbl 0070.00102
1956
The effect of rapid distortion of a fluid in turbulent motion. Zbl 0055.19201
Batchelor, G. K.; Proudman, Ian
1954
Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Zbl 0057.41701
Batchelor, G. K.
1954
The skin friction on infinite cylinders moving parallel to their length. Zbl 0055.18605
Batchelor, G. K.
1954
The theory of homogeneous turbulence. Zbl 0053.14404
Batchelor, G. K.
1953
The effect of homogeneous turbulence on material lines and surfaces. Zbl 0046.42201
Batchelor, G. K.
1952
Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Zbl 0046.42106
Batchelor, G. K.
1952
Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Zbl 0042.43101
Batchelor, G. K.
1951
Pressure fluctuations in isotropic turbulence. Zbl 0042.19403
Batchelor, G. K.
1951
On the spontaneous magnetic field in a conducting liquid in turbulent motion. Zbl 0040.14203
Batchelor, G. K.
1950
Anisotropy of the spectrum of turbulence at small wave-numbers. Zbl 0040.27003
Batchelor, G. K.; Stewart, R. W.
1950
The nature of turbulent motion at large wave-numbers. Zbl 0036.25602
Batchelor, G. K.; Townsend, A. A.
1949
The effect of wire gauze on small disturbances in a uniform stream. Zbl 0036.25702
Taylor, G. I.; Batchelor, G. K.
1949
The role of big eddies in homogeneous turbulence. Zbl 0036.25601
Batchelor, G. K.
1949
Decay of turbulence in the final period. Zbl 0032.22602
Batchelor, G. K.; Townsend, A. A.
1948
Decay of isotropic turbulence in the initial period. Zbl 0030.37704
Batchelor, G. K.; Townsend, A. A.
1948
Energy decay and self-preserving correlation functions in isotropic turbulence. Zbl 0035.25604
Batchelor, G. K.
1948
Kolmogoroff’s theory of locally isotropic turbulence. Zbl 0029.28405
Batchelor, G. K.
1947
The theory of axisymmetric turbulence. Zbl 0061.45503
Batchelor, G. K.
1946
all top 5
### Cited by 6,236 Authors
34 Koch, Donald L. 23 Antonia, Robert Anthony 21 Forbes, Lawrence K. 20 Temam, Roger Meyer 18 Chakraborty, Nilanjan 18 Shaqfeh, Eric S. G. 17 Stone, Howard Alvin 17 Subramanian, Ganesh 16 Basak, Tanmay 16 Lin, Jianzhong 15 Davidson, Peter Alan 15 Guazzelli, Élisabeth 15 Roy, Satyajit 15 Vassilicos, John-Christos 14 Lauga, Eric 14 Meneveau, Charles 14 Phan-Thien, Nhan 14 Pozrikidis, Constantine 13 Foiaș, Ciprian 13 Hinch, Edward John 12 Brandt, Luca 12 Davis, Robert H. 12 Tomé, Murilo F. 12 Tran, Chuong V. 12 Yamazaki, Kazuo 12 Yariv, Ehud 11 Alben, Silas D. 11 Djenidi, Lyazid 11 Pop, Ioan 11 Schnitzer, Ory 11 Shivamoggi, Bhimsen K. 11 Yeung, P. K. 11 Zumbrun, Kevin R. 10 Jolly, Michael Summerfield 10 Meiburg, Eckart H. 10 Pullin, Dale I. 10 Rubinstein, Robert 10 Sader, John E. 10 Zhou, Ye 9 Billant, Paul 9 Blake, John Robert 9 Brady, John F. 9 Clark, Timothy T. 9 Clercx, Herman J. H. 9 Duyunova, Anna Andreevna 9 Eames, Ian 9 Leal, L. Gary 9 Lychagin, Valentin V. 9 Makinde, Oluwole Daniel 9 Matthaeus, William H. 9 McKee, Sean 9 Moffatt, Henry Keith 9 Prosperetti, Andrea 9 San, Omer 9 Tychkov, Sergey N. 9 van Heijst, Gert-Jan F. 9 Villermaux, Emmanuel 8 Acrivos, Andreas 8 Bogoyavlenskij, Oleg Igorevich 8 Buevich, Yu. A. 8 Cambon, Claude 8 Childress, Stephen 8 Colonius, Tim 8 Cuminato, José Alberto 8 Danaila, Luminita 8 Dritschel, David Gerard 8 Elcrat, Alan R. 8 Erdoğan, M. Emin 8 Foster, M. R. 8 Gus’kov, O. B. 8 Hunt, Julian C. R. 8 Jiménez, Javier 8 Kaneda, Yukio 8 Klettner, Christian A. 8 Knio, Omar M. 8 Marchioro, Carlo 8 Picano, Francesco 8 Pope, Stephen Bailey 8 Rosa, Ricardo M. S. 8 Sagaut, Pierre 8 Sarkar, Kausik 8 Sherwin, Spencer J. 8 Verzicco, Roberto 8 Vynnycky, Michael 8 Zia, Roseanna N. 7 Batchelor, George Keith 7 Bergougnoux, Laurence 7 Blackburn, Hugh M. 7 Bos, Wouter J. T. 7 Bürger, Raimund 7 Chomaz, Jean-Marc 7 de Divitiis, Nicola 7 Duck, Peter W. 7 Felderhof, B. U. 7 Fernandez-Feria, Ramon 7 Gallaire, François 7 Jacquin, Laurent 7 Jeffrey, David J. 7 Kalita, Jiten C. 7 Khair, Aditya S. ...and 6,136 more Authors
all top 5
### Cited in 335 Serials
1,105 Journal of Fluid Mechanics 485 Physics of Fluids 210 Journal of Computational Physics 132 Computers and Fluids 124 Fluid Dynamics 115 European Journal of Mechanics. B. Fluids 98 Physica D 77 Journal of Engineering Mathematics 71 Physics of Fluids, A 70 Acta Mechanica 62 International Journal for Numerical Methods in Fluids 58 International Journal of Engineering Science 58 Physics of Fluids 53 Computer Methods in Applied Mechanics and Engineering 47 Applied Mathematical Modelling 42 Journal of Applied Mathematics and Mechanics 42 ZAMP. Zeitschrift für angewandte Mathematik und Physik 42 Theoretical and Computational Fluid Dynamics 36 Geophysical and Astrophysical Fluid Dynamics 32 Journal of Statistical Physics 31 Archive for Rational Mechanics and Analysis 29 Studies in Applied Mathematics 27 International Journal of Heat and Mass Transfer 27 Physics Letters. A 26 Journal of Mathematical Physics 26 Journal of Computational and Applied Mathematics 26 Engineering Analysis with Boundary Elements 25 Journal of Turbulence 24 Computers & Mathematics with Applications 23 Applied Mathematics and Computation 22 Communications in Nonlinear Science and Numerical Simulation 21 Physica A 21 Flow, Turbulence and Combustion 19 Communications in Mathematical Physics 19 Meccanica 19 Applied Mathematics and Mechanics. (English Edition) 17 Journal of Differential Equations 17 Journal of Applied Mechanics and Technical Physics 16 Journal of Mathematical Analysis and Applications 15 Rheologica Acta 15 The ANZIAM Journal 14 Astrophysics and Space Science 14 Bulletin of Mathematical Biology 14 Mathematical and Computer Modelling 14 Acta Mechanica Sinica 13 Journal of Scientific Computing 13 Journal of Non-Newtonian Fluid Mechanics 13 International Journal of Computational Fluid Dynamics 13 Journal of Theoretical Biology 11 Computer Physics Communications 11 Journal of Geometry and Physics 11 Mathematical Problems in Engineering 10 Mathematical Methods in the Applied Sciences 10 International Journal for Numerical Methods in Engineering 10 Applied Mathematics Letters 10 Journal of Nonlinear Science 10 Chaos 10 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 10 Journal of Mathematical Fluid Mechanics 9 Wave Motion 9 European Journal of Applied Mathematics 8 International Journal of Modern Physics B 8 Journal of the Mechanics and Physics of Solids 8 Chaos, Solitons and Fractals 8 Quarterly of Applied Mathematics 8 Computational Mechanics 8 Annals of Physics 8 SIAM Journal on Applied Mathematics 8 International Journal of Numerical Methods for Heat & Fluid Flow 8 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 8 Combustion Theory and Modelling 8 Archives of Computational Methods in Engineering 8 International Journal of Applied and Computational Mathematics 8 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 7 Physics Reports 7 Transactions of the American Mathematical Society 7 Applied Numerical Mathematics 7 Computational Mathematics and Mathematical Physics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Continuum Mechanics and Thermodynamics 7 Communications in Numerical Methods in Engineering 7 Physical Review, II. Series 7 Nonlinear Analysis. Theory, Methods & Applications 6 Modern Physics Letters B 6 Reviews of Modern Physics 6 Mathematics and Computers in Simulation 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Communications in Partial Differential Equations 6 Journal of Elasticity 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Regular and Chaotic Dynamics 6 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 5 Journal of Mathematical Biology 5 Theoretical and Mathematical Physics 5 Mathematika 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Numerical Methods for Partial Differential Equations 5 Discrete and Continuous Dynamical Systems 5 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences ...and 235 more Serials
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### Cited in 49 Fields
3,912 Fluid mechanics (76-XX) 512 Partial differential equations (35-XX) 288 Numerical analysis (65-XX) 226 Classical thermodynamics, heat transfer (80-XX) 204 Mechanics of deformable solids (74-XX) 138 Biology and other natural sciences (92-XX) 135 Geophysics (86-XX) 122 Dynamical systems and ergodic theory (37-XX) 111 Statistical mechanics, structure of matter (82-XX) 67 Probability theory and stochastic processes (60-XX) 38 Mechanics of particles and systems (70-XX) 34 Astronomy and astrophysics (85-XX) 29 Optics, electromagnetic theory (78-XX) 28 Ordinary differential equations (34-XX) 23 Quantum theory (81-XX) 21 Differential geometry (53-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 17 Global analysis, analysis on manifolds (58-XX) 14 Computer science (68-XX) 13 Relativity and gravitational theory (83-XX) 12 Systems theory; control (93-XX) 10 History and biography (01-XX) 9 General and overarching topics; collections (00-XX) 9 Functions of a complex variable (30-XX) 9 Statistics (62-XX) 8 Real functions (26-XX) 7 Special functions (33-XX) 7 Integral equations (45-XX) 6 Operator theory (47-XX) 4 Topological groups, Lie groups (22-XX) 4 Potential theory (31-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Manifolds and cell complexes (57-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Sequences, series, summability (40-XX) 2 Information and communication theory, circuits (94-XX) 2 Mathematics education (97-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 General topology (54-XX)
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https://zbmath.org/authors/?q=ai%3Anirenberg.louis
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# zbMATH — the first resource for mathematics
## Nirenberg, Louis
Compute Distance To:
Author ID: nirenberg.louis Published as: Nirenberg, Louis; Nirenberg, L. Homepage: https://www.math.nyu.edu/faculty/nirenl/ External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: Chern Medal (2010) · Abel Prize (2015)
Documents Indexed: 193 Publications since 1953, including 14 Books Biographic References: 20 Publications
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#### Co-Authors
76 single-authored 21 Berestycki, Henri 18 Caffarelli, Luis Ángel 17 Brézis, Haïm 12 Li, YanYan 11 Spruck, Joel 10 Trèves, François 8 Kohn, Joseph J. 7 Kinderlehrer, David 6 Agmon, Shmuel 4 Douglis, Avron 4 Lax, Peter David 4 Varadhan, S. R. Srinivasa 3 Capuzzo Dolcetta, Italo 2 Atiyah, Michael Francis 2 Bers, Lipman 2 Bertsch, Michiel 2 Browder, Felix Earl 2 Ekeland, Ivar 2 Gidas, Basilis 2 Kohn, Robert Vita 2 Kuhn, Harold William 2 Ni, Wei-Ming 2 Peletier, Lambertus Adrianus 2 Sarnak, Peter Clive 2 Spencer, Donald Clayton 2 Stampacchia, Guido 2 Véron, Laurent 2 Weisfeld, Morris 1 Ahlfors, Lars Valerian 1 Anastasio, Sal 1 Beals, Richard W. 1 Bojarski, Bogdan 1 Bombieri, Enrico 1 Bona, Jerry Lloyd 1 Cenkl, Bohous 1 Chang, Sun-Yung Alice 1 Chanillo, Sagun 1 Chern, Shiing-Shen 1 Ching, Wai-Mee 1 Cohen, Amy 1 Córdoba Barba, Antonio Juan 1 Cordoba, Diego 1 Coron, Jean-Michel 1 Cushman, Richard H. 1 Douglas, Ronald George 1 Fisher, Joseph A. 1 Foiaş, Ciprian Ilie 1 Friedlander, Susan Jean 1 Fröhlich, Jürg Martin 1 Garabedian, Paul Roesel 1 Goldschmidt, Hubert Leopold 1 Graham, C. Robin 1 Griffiths, Phillip Augustus 1 Guillemin, Victor W. 1 Hartman, Philip 1 Heckman, Gert 1 John, Fritz 1 Karlin, Samuel 1 Klartag, Bo’az 1 Kodaira, Kunihiko 1 Kolk, Johan A. C. 1 Kra, Irwin 1 Lebowitz, Joel Louis 1 Levine, Harold I. 1 Loewner, Charles 1 Martio, Olli 1 Maskit, Bernard 1 Mastrian, Barbara 1 Mather, John N. 1 Mawhin, Jean L. 1 McKean, Henry P. jun. 1 Mironescu, Petru 1 Morrey, Charles Bradfield jun. 1 Newlander, A. 1 Nguyen Minh Chuong 1 Nussbaum, Roger David 1 Pelayo, Alvaro 1 Porta, Horacio A. 1 Protter, Murray H. 1 Rabinowitz, Paul Henry 1 Roberts, Fred S. 1 Seco, Luis Angel 1 Seregin, Gregory A. 1 Sharir, Micha 1 Sjamaar, Reyer 1 Sjöstrand, Johannes 1 Stein, Elias Menachem 1 Synge Morawetz, Cathleen 1 Tao, Terence 1 Teman, Roger 1 Tutschke, Wolfgang 1 Ural’tseva, Nina Nikolaevna 1 Van den Ban, Erik Peter 1 Vishik, Marko Iosifovich 1 Vũ Ngọc, San 1 Walker, Homer F. 1 Webster, Sidney M. 1 Weinstein, Alan David 1 Wigler, Michael 1 Willig, Paul M. ...and 1 more Co-Authors
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#### Serials
43 Communications on Pure and Applied Mathematics 7 Notices of the American Mathematical Society 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Duke Mathematical Journal 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Topological Methods in Nonlinear Analysis 2 Journal of Mathematical Analysis and Applications 2 Journal of Mathematical Sciences (New York) 2 Selecta Mathematica. New Series 2 Methods and Applications of Analysis 2 Annals of Mathematics. Second Series 2 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Russian Mathematical Surveys 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Journal of Geometry and Physics 1 Acta Mathematica 1 American Journal of Mathematics 1 Compositio Mathematica 1 Conferenze del Seminario di Matematica dell’Università di Bari 1 Journal of Differential Geometry 1 Journal of the Faculty of Science. Section I A 1 Le Matematiche 1 Mathematische Annalen 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 CWI Quarterly 1 Bulletin of the American Mathematical Society. New Series 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Mathematical Fluid Mechanics 1 Journal of the European Mathematical Society (JEMS) 1 Milan Journal of Mathematics 1 Bollettino della Unione Matematica Italiana. Series IV 1 Annals of Mathematics Studies 1 Contemporary Mathematics 1 Regional Conference Series in Mathematics 1 Courant Lecture Notes in Mathematics 1 Journal of Fixed Point Theory and Applications 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 CTM. Classical Topics in Mathematics
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#### Fields
105 Partial differential equations (35-XX) 25 Operator theory (47-XX) 19 Global analysis, analysis on manifolds (58-XX) 17 History and biography (01-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Differential geometry (53-XX) 8 General and overarching topics; collections (00-XX) 6 Functional analysis (46-XX) 5 Several complex variables and analytic spaces (32-XX) 4 Algebraic topology (55-XX) 4 Fluid mechanics (76-XX) 3 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX)
#### Citations contained in zbMATH Open
145 Publications have been cited 14,458 times in 11,863 Documents Cited by Year
Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Zbl 0541.35029
Brézis, Haïm; Nirenberg, Louis
1983
Symmetry and related properties via the maximum principle. Zbl 0425.35020
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1979
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Zbl 0093.10401
Agmon, S.; Douglis, A.; Nirenberg, Louis
1959
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Zbl 0123.28706
Agmon, S.; Douglis, A.; Nirenberg, Louis
1964
On elliptic partial differential equations. Zbl 0088.07601
Nirenberg, Louis
1959
On functions of bounded mean oscillation. Zbl 0102.04302
John, Fritz; Nirenberg, Louis
1961
Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1982
First order interpolation inequalities with weights. Zbl 0563.46024
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1984
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1985
On the method of moving planes and the sliding method. Zbl 0784.35025
Berestycki, H.; Nirenberg, L.
1991
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 0806.35129
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
1994
Topics in nonlinear functional analysis. Notes by R. A. Artino. Zbl 0286.47037
Nirenberg, Louis
1974
The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047
Caffarelli, L.; Nirenberg, Louis; Spruck, J.
1984
Complex analytic coordinates in almost complex manifolds. Zbl 0079.16102
Newlander, A.; Nirenberg, Louis
1957
Symmetry of positive solutions of nonlinear elliptic equations in $$\mathbb R^n$$. Zbl 0469.35052
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1981
Non-coercive boundary value problems. Zbl 0125.33302
Kohn, J. J.; Nirenberg, Louis
1965
Remarks on finding critical points. Zbl 0751.58006
Brézis, Haïm; Nirenberg, Louis
1991
Remarks on strongly elliptic partial differential equations. Zbl 0067.07602
Nirenberg, Louis
1955
An algebra of pseudo-differential operators. Zbl 0171.35101
Kohn, J. J.; Nirenberg, Louis
1965
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Zbl 0386.47035
Brézis, Haïm; Nirenberg, Louis
1978
Properties of solutions of ordinary differential equations in Banach space. Zbl 0117.10001
Agmon, S.; Nirenberg, Louis
1963
Interior estimates for elliptic systems of partial differential equations. Zbl 0066.08002
Douglis, Avron; Nirenberg, Louis
1955
The Weyl and Minkowski problems in differential geometry in the large. Zbl 0051.12402
Nirenberg, Louis
1953
Travelling fronts in cylinders. Zbl 0799.35073
Berestycki, Henri; Nirenberg, Louis
1992
H$$^ 1$$ versus C$$^ 1$$ local minimizers. Zbl 0803.35029
Brézis, Haïm; Nirenberg, Louis
1993
An extended interpolation inequality. Zbl 0163.29905
Nirenberg, Louis
1966
Topics in nonlinear functional analysis. Notes by Ralph A. Artino. Revised reprint of the 1974 original. Zbl 0992.47023
Nirenberg, Louis
2001
Degree theory of BMO. I: Compact manifolds without boundaries. Zbl 0852.58010
Brézis, Haïm; Nirenberg, Louis
1995
Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Zbl 0816.35030
Berestycki, H.; Capuzzo Dolcetta, I.; Nirenberg, L.
1994
A remark on Ky Fan’s minimax principle. Zbl 0264.49013
Brézis, Haïm; Nirenberg, Louis; Stampacchia, Guido
1972
Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513
Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis
1997
The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048
Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J.
1985
On spherical image maps whose Jacobians do not change sign. Zbl 0094.16303
Hartman, Philip; Nirenberg, Louis
1959
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
Variational methods for indefinite superlinear homogeneous elliptic problems. Zbl 0840.35035
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1995
Estimates for elliptic systems from composite material. Zbl 1125.35339
Li, YanYan; Nirenberg, Louis
2003
Degenerate elliptic-parabolic equations of second order. Zbl 0153.14503
Kohn, J. J.; Nirenberg, Louis
1967
Regularity in free boundary problems. Zbl 0352.35023
Kinderlehrer, D.; Nirenberg, Louis
1977
An abstract form of the nonlinear Cauchy-Kowalewski theorem. Zbl 0257.35001
Nirenberg, Louis
1972
Lectures on linear partial differential equations. Zbl 0267.35001
Nirenberg, Louis
1973
Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Zbl 0484.35057
Brézis, Haïm; Coron, Jean-Michel; Nirenberg, Louis
1980
On the analycity of the solutions of linear elliptic systems of partial differential equations. Zbl 0082.09402
Morrey, C. B. jun.; Nirenberg, Louis
1957
On nonlinear elliptic partial differential equations and Hölder continuity. Zbl 0050.09801
Nirenberg, Louis
1953
Forced vibrations for a nonlinear wave equation. Zbl 0378.35040
Brézis, Haïm; Nirenberg, Louis
1978
A strong maximum principle for parabolic equations. Zbl 0050.09601
Nirenberg, Louis
1953
The null spaces of elliptic partial differential operators in R$$^n$$. Zbl 0272.35029
Nirenberg, Louis; Walker, Homer F.
1973
Variational and topological methods in nonlinear problems. Zbl 0468.47040
Nirenberg, Louis
1981
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
Solvability of a first order linear partial differential equation. Zbl 0117.06104
Nirenberg, Louis; Trèves, François
1963
Partial differential equations invariant under conformal or projective transformations. Zbl 0298.35018
Loewner, Charles; Nirenberg, Louis
1974
Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028
Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel
1988
A pseudo-convex domain not admitting a holomorphic support function. Zbl 0248.32013
Kohn, J. J.; Nirenberg, Louis
1973
Regularity in elliptic free boundary problems. I. Zbl 0402.35045
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1978
Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations. Zbl 0698.35031
Berestycki, H.; Nirenberg, L.
1988
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
The Dirichlet problem for singularly perturbed elliptic equations. Zbl 0933.35083
Li, Yanyan; Nirenberg, Louis
1998
The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Zbl 1062.49021
Li, YanYan; Nirenberg, Louis
2005
Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space. Zbl 0147.34603
Agmon, S.; Nirenberg, Louis
1967
On local solvability of linear partial differential equations. I: Necessary conditions. Zbl 0191.39103
Nirenberg, Louis; Trèves, François
1970
Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. Zbl 0705.35004
Berestycki, H.; Nirenberg, L.
1990
On stability for difference schemes; a sharp form of Garding’s inequality. Zbl 0185.22801
Lax, Peter D.; Nirenberg, Louis
1966
Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu). Zbl 0868.58017
Brézis, Haïm; Nirenberg, Louis
1996
A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type. Zbl 0090.07401
Agmon, S.; Nirenberg, Louis; Protter, M. H.
1953
Intrinsic norms on a complex manifold. Zbl 0202.11603
Chern, S. S.; Levine, H. I.; Nirenberg, Louis
1969
On local solvability of linear partial differential equations. Part II: Sufficient conditions. Zbl 0208.35902
Nirenberg, Louis; Trèves, François
1970
On the existence of deformations of complex analytic structures. Zbl 0088.38004
Kodaira, Kunihiko; Nirenberg, Louis; Spencer, D. C.
1958
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Uniqueness in Cauchy problems for differential equations with constant leading coefficients. Zbl 0077.09402
Nirenberg, Louis
1957
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Übersetzung aus dem Englischen von L. R. Volevich. Unter Redaktion von M. I. Vishik. Zbl 0104.32305
Agmon, S.; Douglis, A.; Nirenberg, Louis
1962
Local boundary regularity of holomorphic mappings. Zbl 0436.32018
Nirenberg, Louis; Webster, S.; Yang, P.
1980
Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044
Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis
2013
On a theorem of P. Nowosad. Zbl 0165.45802
Karlin, S.; Nirenberg, Louis
1967
Estimates and existence of solutions of elliptic equations. Zbl 0070.32301
Nirenberg, Louis
1956
A minimization problem with critical exponent and nonzero data. Zbl 0763.46023
Brézis, Haïm; Nirenberg, Louis
1989
Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068
Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis
2009
The smoothness of the free boundary in the one phase Stefan problem. Zbl 0391.35060
Kinderlehrer, David; Nirenberg, Louis
1978
Topics in nonlinear functional analysis. (Lektsii po nelinejnomu funktsional’nomu analizu). Transl. from the English by N. D. Vvedenskaya. Zbl 0426.47034
Nirenberg, Louis
1977
The Dirichlet problem for the degenerate Monge-Ampère equation. Zbl 0611.35029
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Zbl 0391.35045
Kinderlehrer, David; Nirenberg, Louis
1978
On a question of Hans Lewy. Zbl 0305.35017
Nirenberg, Louis
1974
Removable singularities for nonlinear elliptic equations. Zbl 0905.35027
Brézis, Haïm; Nirenberg, Louis
1997
On a generalization of quasi-conformal mappings and its application to elliptic partial differential equations. Zbl 0057.08604
Nirenberg, Louis
1954
On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Zbl 0067.32503
Bers, Lipman; Nirenberg, Louis
1955
A correction to: On local solvability of linear partial differential equations. II: Sufficient conditions. Zbl 0221.35019
Nirenberg, Louis; Treves, J. F.
1971
Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044
Caffarelli, Luis; Li, YanYan; Nirenberg, Louis
2012
Indefinite elliptic equations and nonlinear Liouville theorems. (Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires.) Zbl 0820.35056
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1993
Variational methods in nonlinear problems. Zbl 0980.58005
Nirenberg, L.
2000
Degree and Sobolev spaces. Zbl 0956.46024
Brézis, Haïm; Li, Yanyan; Mironescu, Petru; Nirenberg, Louis
1999
A proof of the Malgrange preparation theorem. Zbl 0212.10702
Nirenberg, Louis
1971
A complex Frobenius theorem. Zbl 0099.37502
Nirenberg, Louis
1958
On linear and non-linear elliptic boundary value problems in the plane. Zbl 0067.32504
Bers, Lipman; Nirenberg, Louis
1955
Comments on nonlinear problems (with an appendix by Lin Changshou). Zbl 0544.58005
Nirenberg, Louis
1981
Pseudo-differential operators. Zbl 0218.35075
Nirenberg, Louis
1970
On a form of Bernstein’s theorem. Zbl 0668.35028
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1988
Regularity in elliptic free boundary problems. II: Equations of higher order. Zbl 0425.35097
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1979
Asymptotic behaviour via the Harnack inequality. Zbl 0840.35011
Berestycki, H.; Nirenberg, L.
1991
Uniqueness in the Cauchy problem for a degenerate elliptic second order equation. Zbl 0572.35043
Nirenberg, Louis
1985
On fully nonlinear elliptic equations of second order. Zbl 0778.35035
Nirenberg, L.
1989
Travelling front solutions of semilinear equations in $$n$$ dimensions. Zbl 0780.35054
Berestycki, H.; Nirenberg, L.
1991
Felix Browder (1927–2016). Zbl 1406.35004
Brezis, Haïim; Nussbaum, Roger D.; Cohen, Amy; Beals, Richard; Mawhin, Jean; Teman, Roger; Nirenberg, Louis; Berestycki, Henri; Mastrian, Barbara; Chanillo, Sagun; Lebowitz, Joel; Roberts, Fred; Bona, Jerry
2018
Lipman Bers and partial differential equations. Zbl 1361.35006
Nirenberg, Louis
2015
Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044
Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis
2013
Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044
Caffarelli, Luis; Li, YanYan; Nirenberg, Louis
2012
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 1316.35217
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
2012
On singular solutions of nonlinear elliptic and parabolic equations. Zbl 1226.35028
Nirenberg, Louis
2011
Remembering Johannes J. Duistermaat (1942–2010). Zbl 1225.01067
Guillemin, Victor; Pelayo, Álvaro; Vũ Ngọc, San; Weinstein, Alan; Atiyah, Michael; Cushman, Richard; Heckman, Gert; van den Ban, Erik; Kolk, Johan; Nirenberg, Louis; Sjamaar, Reyer; Sjöstrand, Johannes
2011
Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068
Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis
2009
Partial results on extending the Hopf Lemma. Zbl 1196.35062
Li, Yan Yan; Nirenberg, Louis
2009
A remark on Ky Fan’s minimax principle. Zbl 1225.49014
Brézis, H.; Nirenberg, L.; Stampacchia, G.
2008
Perspectives in nonlinear partial differential equations in honor of Haïm Brezis. Based on the conference celebration of Haïm Brezis’ 60th birthday, June 21–25, 2004. Zbl 1126.00013
Berestycki, Henri; Bertsch, Michiel; Browder, Felix E.; Nirenberg, Louis; Peletier, Lambertus A.; Véron, Laurent
2007
A geometric problem and the Hopf lemma. II. Zbl 1149.53302
Li, YanYan; Nirenberg, Louis
2006
A geometric problem and the Hopf lemma. I. Zbl 1113.53003
Li, YanYan; Nirenberg, Louis
2006
Generalization of a well-known inequality. Zbl 1284.26021
Li, YanYan; Nirenberg, Louis
2006
The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Zbl 1062.49021
Li, YanYan; Nirenberg, Louis
2005
The distance function to the boundary and singular set of viscosity solutions of Hamilton-Jacobi equation. Zbl 1387.35106
Nirenberg, L.
2005
Regularity in an unusual variational problem. Zbl 1113.49041
Ekeland, Ivar; Nirenberg, Louis
2005
Abstract and applied analysis. Proceedings of the international conference, Hanoi, Vietnam, August 13–17, 2002. Zbl 1058.00011
Nguyen Minh Chuong; Nirenberg, L.; Tutschke, W.
2004
Olga Alexandrovna Ladyzhenskaya (1922–2004). Zbl 1168.01327
Friedlander, Susan; Lax, Peter; Morawetz, Cathleen; Nirenberg, Louis; Seregin, Gregory; Ural’tseva, Nina; Vishik, Mark
2004
Estimates for elliptic systems from composite material. Zbl 1125.35339
Li, YanYan; Nirenberg, Louis
2003
A convex Darboux theorem. Zbl 1082.58501
Ekeland, Ivar; Nirenberg, Louis
2002
Topics in nonlinear functional analysis. Notes by Ralph A. Artino. Revised reprint of the 1974 original. Zbl 0992.47023
Nirenberg, Louis
2001
Variational methods in nonlinear problems. Zbl 0980.58005
Nirenberg, L.
2000
Degree and Sobolev spaces. Zbl 0956.46024
Brézis, Haïm; Li, Yanyan; Mironescu, Petru; Nirenberg, Louis
1999
The Dirichlet problem for singularly perturbed elliptic equations. Zbl 0933.35083
Li, Yanyan; Nirenberg, Louis
1998
Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513
Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis
1997
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
Removable singularities for nonlinear elliptic equations. Zbl 0905.35027
Brézis, Haïm; Nirenberg, Louis
1997
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu). Zbl 0868.58017
Brézis, Haïm; Nirenberg, Louis
1996
Degree theory of BMO. I: Compact manifolds without boundaries. Zbl 0852.58010
Brézis, Haïm; Nirenberg, Louis
1995
Variational methods for indefinite superlinear homogeneous elliptic problems. Zbl 0840.35035
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1995
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 0806.35129
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
1994
Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Zbl 0816.35030
Berestycki, H.; Capuzzo Dolcetta, I.; Nirenberg, L.
1994
Partial differential equations in the first half of the century. Zbl 0807.01017
Nirenberg, Louis
1994
H$$^ 1$$ versus C$$^ 1$$ local minimizers. Zbl 0803.35029
Brézis, Haïm; Nirenberg, Louis
1993
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Indefinite elliptic equations and nonlinear Liouville theorems. (Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires.) Zbl 0820.35056
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1993
The ground state and maximum principle for second order elliptic operators in general domains. (État fondamental et principe du maximum pour les opérateurs elliptiques du second ordre dans des domaines généraux.) Zbl 0798.35038
Berestycki, Henri; Nirenberg, Louis; Varadhan, Srinivasa
1993
Travelling fronts in cylinders. Zbl 0799.35073
Berestycki, Henri; Nirenberg, Louis
1992
On the maximum principle. Videotape. Zbl 0790.35001
Nirenberg, Louis
1992
On the method of moving planes and the sliding method. Zbl 0784.35025
Berestycki, H.; Nirenberg, L.
1991
Remarks on finding critical points. Zbl 0751.58006
Brézis, Haïm; Nirenberg, Louis
1991
Asymptotic behaviour via the Harnack inequality. Zbl 0840.35011
Berestycki, H.; Nirenberg, L.
1991
Travelling front solutions of semilinear equations in $$n$$ dimensions. Zbl 0780.35054
Berestycki, H.; Nirenberg, L.
1991
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. Zbl 0705.35004
Berestycki, H.; Nirenberg, L.
1990
A minimization problem with critical exponent and nonzero data. Zbl 0763.46023
Brézis, Haïm; Nirenberg, Louis
1989
On fully nonlinear elliptic equations of second order. Zbl 0778.35035
Nirenberg, L.
1989
Variational methods in nonlinear problems. Zbl 0679.58021
Nirenberg, L.
1989
Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028
Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel
1988
Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations. Zbl 0698.35031
Berestycki, H.; Nirenberg, L.
1988
On a form of Bernstein’s theorem. Zbl 0668.35028
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1988
Fully nonlinear elliptic equations. Zbl 0685.35045
Nirenberg, L.
1988
The Dirichlet problem for the degenerate Monge-Ampère equation. Zbl 0611.35029
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Correction to: The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Zbl 0641.35025
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1985
The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048
Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J.
1985
Uniqueness in the Cauchy problem for a degenerate elliptic second order equation. Zbl 0572.35043
Nirenberg, Louis
1985
First order interpolation inequalities with weights. Zbl 0563.46024
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1984
The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047
Caffarelli, L.; Nirenberg, Louis; Spruck, J.
1984
Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Zbl 0541.35029
Brézis, Haïm; Nirenberg, Louis
1983
Variational and topological methods in nonlinear problems. Zbl 0524.47041
Nirenberg, Louis
1983
Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1982
Symmetry of positive solutions of nonlinear elliptic equations in $$\mathbb R^n$$. Zbl 0469.35052
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1981
Variational and topological methods in nonlinear problems. Zbl 0468.47040
Nirenberg, Louis
1981
Comments on nonlinear problems (with an appendix by Lin Changshou). Zbl 0544.58005
Nirenberg, Louis
1981
Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Zbl 0484.35057
Brézis, Haïm; Coron, Jean-Michel; Nirenberg, Louis
1980
Local boundary regularity of holomorphic mappings. Zbl 0436.32018
Nirenberg, Louis; Webster, S.; Yang, P.
1980
Symmetry and related properties via the maximum principle. Zbl 0425.35020
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1979
Regularity in elliptic free boundary problems. II: Equations of higher order. Zbl 0425.35097
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1979
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Zbl 0386.47035
Brézis, Haïm; Nirenberg, Louis
1978
Forced vibrations for a nonlinear wave equation. Zbl 0378.35040
Brézis, Haïm; Nirenberg, Louis
1978
Regularity in elliptic free boundary problems. I. Zbl 0402.35045
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1978
The smoothness of the free boundary in the one phase Stefan problem. Zbl 0391.35060
Kinderlehrer, David; Nirenberg, Louis
1978
Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Zbl 0391.35045
Kinderlehrer, David; Nirenberg, Louis
1978
Régularité dans les problèmes elliptiques à frontière libre. Zbl 0386.35045
Kinderlehrer, David; Nirenberg, Louis; Spruck, Joel
1978
Hodograph methods and the smoothness of the free boundary in the one phase Stefan problem. Zbl 0456.35090
Kinderlehrer, David; Nirenberg, Louis
1978
Regularity in free boundary problems. Zbl 0352.35023
Kinderlehrer, D.; Nirenberg, Louis
1977
Topics in nonlinear functional analysis. (Lektsii po nelinejnomu funktsional’nomu analizu). Transl. from the English by N. D. Vvedenskaya. Zbl 0426.47034
Nirenberg, Louis
1977
Some first order nonlinear equations on torus. Zbl 0335.35028
Brézis, Haïm; Nirenberg, Louis
1977
Image d’une somme d’opérateurs non linéaires et applications. Zbl 0359.47035
Brézis, Haïm; Nirenberg, Louis
1977
Regularity of free boundaries. Zbl 0361.35012
Nirenberg, Louis
1977
Nonlinear differential equations invariant under certain geometric transformations. Zbl 0357.35034
Nirenberg, Louis
1976
Propagation of singularities for linear partial differential equtions and reflections at a boundary. Zbl 0335.35081
Nirenberg, Louis
1976
Monge-Ampère equations and some associated problems in geometry. Zbl 0335.35045
Nirenberg, Louis
1975
Topics in nonlinear functional analysis. Notes by R. A. Artino. Zbl 0286.47037
Nirenberg, Louis
1974
Partial differential equations invariant under conformal or projective transformations. Zbl 0298.35018
Loewner, Charles; Nirenberg, Louis
1974
On a question of Hans Lewy. Zbl 0305.35017
Nirenberg, Louis
1974
Contributions to analysis. A collection of papers dedicated to Lipman Bers. Zbl 0283.00007
Ahlfors, Lars V.; Kra, Irwin; Maskit, Bernard; Nirenberg, Louis
1974
Lectures on linear partial differential equations. Zbl 0267.35001
Nirenberg, Louis
1973
The null spaces of elliptic partial differential operators in R$$^n$$. Zbl 0272.35029
Nirenberg, Louis; Walker, Homer F.
1973
A pseudo-convex domain not admitting a holomorphic support function. Zbl 0248.32013
Kohn, J. J.; Nirenberg, Louis
1973
A remark on Ky Fan’s minimax principle. Zbl 0264.49013
Brézis, Haïm; Nirenberg, Louis; Stampacchia, Guido
1972
An abstract form of the nonlinear Cauchy-Kowalewski theorem. Zbl 0257.35001
Nirenberg, Louis
1972
A correction to: On local solvability of linear partial differential equations. II: Sufficient conditions. Zbl 0221.35019
Nirenberg, Louis; Treves, J. F.
1971
A proof of the Malgrange preparation theorem. Zbl 0212.10702
Nirenberg, Louis
1971
An application of generalized degree to a class of nonlinear problems. Zbl 0317.35036
Nirenberg, Louis
1971
Generalized degree and nonlinear problems. Zbl 0267.47034
Nirenberg, Louis
1971
...and 45 more Documents
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#### Cited by 8,596 Authors
59 Nazarov, Sergeĭ Aleksandrovich 53 Li, YanYan 52 Wei, Juncheng 49 Papageorgiou, Nikolaos S. 45 Berestycki, Henri 43 Brézis, Haïm 43 Miyagaki, Olimpio Hiroshi 41 Zou, Wenming 40 Rădulescu, Vicenţiu D. 39 Hamel, François 39 Schechter, Martin 37 Wang, Lihe 34 Yang, Dachun 33 Kang, Dongsheng 32 Dolbeault, Jean 32 Maz’ya, Vladimir Gilelevich 31 Pacella, Filomena 30 Byeon, Jaeyoung 29 Dancer, Edward Norman 29 Peral Alonso, Ireneo 28 Bao, Jiguang 28 Cao, Daomin 28 Korman, Philip L. 28 Lin, Chang-Shou 28 Nirenberg, Louis 28 Sciunzi, Berardino 28 Shivaji, Ratnasingham 27 Friedman, Avner 27 Li, Congming 27 Peng, Shuangjie 27 Wang, Zhi-Qiang 26 Guedes de Figueiredo, Djairo 26 García-Melián, Jorge 26 Li, Yi 25 Byun, Sun-Sig 25 Trudinger, Neil Sidney 25 Valdinoci, Enrico 24 Do Ó, João M. Bezerra 24 Dong, Hongjie 24 Grossi, Massimo 24 Han, Pigong 24 Ivochkina, Nina Mikhaĭlovna 24 López-Gómez, Julián 24 Ruf, Bernhard 24 Shakhmurov, Veli B. 24 Van Schaftingen, Jean 23 Caffarelli, Luis Ángel 23 Guo, Zongming 23 Niu, Pengcheng 23 Pistoia, Angela 23 Xiao, Jie 23 Yan, Shusen 22 Birindelli, Isabeau 22 Deng, Yinbin 22 Farina, Alberto 22 Mironescu, Petru 22 Ni, Wei-Ming 22 Sirakov, Boyan Slavchev 22 Trèves, François 22 Wang, Xu-Jia 21 Esteban, Maria J. 21 Lu, Guozhen 21 Quaas, Alexander 21 Seregin, Gregory A. 21 Weth, Tobias 20 Alves, Claudianor Oliveira 20 Du, Yihong 20 Li, Dongsheng 20 Musso, Monica 20 Peletier, Lambertus Adrianus 20 Tan, Zhong 19 Gazzola, Filippo 19 Li, Shujie 19 Li, Wan-Tong 19 Lions, Pierre-Louis 19 Mu, Chunlai 19 Ryazanov, Vladimir Il’ich 19 Shi, Junping 19 Wang, Yanqing 19 Willem, Michel 19 Yang, Jianfu 19 Zhong, Xin 18 Bonheure, Denis 18 Del Pino, Manuel A. 18 Kukavica, Igor 18 McKenna, Patrick Joseph 18 Montoro, Luigi 18 Nadirashvili, Nikolai S. 18 Suzuki, Takashi 18 Tang, Xianhua 18 Vitolo, Antonio 18 Wang, Mingxin 17 Capuzzo Dolcetta, Italo 17 Coville, Jerome 17 Ghoussoub, Nassif A. 17 Abreu Goncalves, Jose Valdo 17 Guan, Pengfei 17 Meziani, Abdelhamid 17 Motreanu, Dumitru 17 Ragusa, Maria Alessandra ...and 8,496 more Authors
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#### Cited in 549 Serials
769 Journal of Differential Equations 668 Journal of Mathematical Analysis and Applications 552 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 369 Archive for Rational Mechanics and Analysis 335 Journal of Functional Analysis 335 Calculus of Variations and Partial Differential Equations 276 Communications in Partial Differential Equations 267 Transactions of the American Mathematical Society 256 Nonlinear Analysis. Theory, Methods & Applications 214 Proceedings of the American Mathematical Society 188 Annali di Matematica Pura ed Applicata. Serie Quarta 188 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 169 Mathematische Zeitschrift 167 Communications in Mathematical Physics 167 Mathematische Annalen 152 Advances in Mathematics 147 Journal of Mathematical Sciences (New York) 138 Journal de Mathématiques Pures et Appliquées. Neuvième Série 138 Discrete and Continuous Dynamical Systems 124 The Journal of Geometric Analysis 115 Applicable Analysis 105 Journal of Mathematical Physics 104 Communications on Pure and Applied Analysis 101 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 101 Communications in Contemporary Mathematics 96 Journal d’Analyse Mathématique 94 Siberian Mathematical Journal 93 ZAMP. Zeitschrift für angewandte Mathematik und Physik 89 Nonlinear Analysis. Real World Applications 88 Duke Mathematical Journal 87 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 86 Manuscripta Mathematica 78 Mathematical Methods in the Applied Sciences 75 Mathematical Notes 75 Advanced Nonlinear Studies 75 Comptes Rendus. Mathématique. Académie des Sciences, Paris 71 Inventiones Mathematicae 71 NoDEA. Nonlinear Differential Equations and Applications 70 Applied Mathematics Letters 67 SIAM Journal on Mathematical Analysis 67 Complex Variables and Elliptic Equations 66 Boundary Value Problems 65 Annales de l’Institut Fourier 64 Science China. Mathematics 63 Applied Mathematics and Computation 58 Communications on Pure and Applied Mathematics 58 Bulletin of the American Mathematical Society 55 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 54 Computers & Mathematics with Applications 53 Acta Mathematica 51 Journal of Soviet Mathematics 51 Journal of Mathematical Fluid Mechanics 49 Abstract and Applied Analysis 46 Mathematische Nachrichten 45 Acta Mathematica Sinica. English Series 41 Acta Applicandae Mathematicae 41 Advances in Nonlinear Analysis 40 Ukrainian Mathematical Journal 40 Numerische Mathematik 40 Rendiconti del Seminario Matematico della Università di Padova 39 Discrete and Continuous Dynamical Systems. Series B 38 Proceedings of the Japan Academy. Series A 38 Bulletin of the American Mathematical Society. New Series 36 Tohoku Mathematical Journal. Second Series 36 Journal of Dynamics and Differential Equations 36 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 35 Israel Journal of Mathematics 35 Zeitschrift für Analysis und ihre Anwendungen 35 Journal of the European Mathematical Society (JEMS) 35 Journal of Fixed Point Theory and Applications 34 Mathematics of Computation 34 Journal of Computational and Applied Mathematics 33 Journal of Optimization Theory and Applications 33 Chinese Annals of Mathematics. Series B 32 Potential Analysis 30 Bulletin of the Australian Mathematical Society 30 Nonlinearity 30 Rocky Mountain Journal of Mathematics 30 Applied Mathematics and Optimization 30 Revista Matemática Iberoamericana 30 St. Petersburg Mathematical Journal 29 Publications of the Research Institute for Mathematical Sciences, Kyoto University 29 Annals of Global Analysis and Geometry 29 Physica D 29 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 29 Proceedings of the Japan Academy 28 Arkiv för Matematik 28 Journal für die Reine und Angewandte Mathematik 28 Results in Mathematics 28 Milan Journal of Mathematics 26 Czechoslovak Mathematical Journal 26 Differential Geometry and its Applications 26 Topological Methods in Nonlinear Analysis 25 Integral Equations and Operator Theory 25 Mediterranean Journal of Mathematics 25 Journal of Function Spaces 24 Journal of Elasticity 23 Journal of the American Mathematical Society 22 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 22 Archiv der Mathematik ...and 449 more Serials
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#### Cited in 61 Fields
8,668 Partial differential equations (35-XX) 1,236 Fluid mechanics (76-XX) 1,032 Operator theory (47-XX) 1,026 Global analysis, analysis on manifolds (58-XX) 878 Differential geometry (53-XX) 731 Functional analysis (46-XX) 639 Calculus of variations and optimal control; optimization (49-XX) 557 Ordinary differential equations (34-XX) 539 Several complex variables and analytic spaces (32-XX) 434 Numerical analysis (65-XX) 396 Harmonic analysis on Euclidean spaces (42-XX) 393 Mechanics of deformable solids (74-XX) 322 Biology and other natural sciences (92-XX) 284 Real functions (26-XX) 233 Dynamical systems and ergodic theory (37-XX) 209 Potential theory (31-XX) 189 Functions of a complex variable (30-XX) 169 Integral equations (45-XX) 152 Statistical mechanics, structure of matter (82-XX) 130 Quantum theory (81-XX) 126 Probability theory and stochastic processes (60-XX) 109 Optics, electromagnetic theory (78-XX) 102 Classical thermodynamics, heat transfer (80-XX) 88 Convex and discrete geometry (52-XX) 83 Relativity and gravitational theory (83-XX) 77 Operations research, mathematical programming (90-XX) 72 Systems theory; control (93-XX) 64 Abstract harmonic analysis (43-XX) 60 Topological groups, Lie groups (22-XX) 59 Manifolds and cell complexes (57-XX) 49 Mechanics of particles and systems (70-XX) 46 Difference and functional equations (39-XX) 45 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 43 Algebraic geometry (14-XX) 42 Measure and integration (28-XX) 42 Algebraic topology (55-XX) 38 Geophysics (86-XX) 35 Approximations and expansions (41-XX) 24 Astronomy and astrophysics (85-XX) 22 General topology (54-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 History and biography (01-XX) 18 Information and communication theory, circuits (94-XX) 17 Integral transforms, operational calculus (44-XX) 15 Geometry (51-XX) 14 Nonassociative rings and algebras (17-XX) 12 Computer science (68-XX) 11 General and overarching topics; collections (00-XX) 10 Statistics (62-XX) 8 Combinatorics (05-XX) 7 Number theory (11-XX) 7 Special functions (33-XX) 5 Associative rings and algebras (16-XX) 5 Group theory and generalizations (20-XX) 4 $$K$$-theory (19-XX) 3 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 2 Sequences, series, summability (40-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX)
#### Wikidata Timeline
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http://www.recovery.gov/Transparency/RecoveryData/pages/RecipientProjectSummary508.aspx?AwardIdSur=4886&AwardType=Grants
|
## Grants - AWARD SUMMARY
### UNIVERSITY OF NEW MEXICO
Although much progress has been made on the theoretical understanding of cryptographic protocols, security vulnerabilities are still found in protocol standards and implementations long after they have been accepted and fielded. As in the case of software verification, some kind of automated assistance is highly desirable. Indeed, we have already seen how the use of automated methods can be of help in the evaluation of security standards. The usefulness of formal methods also depends on how faithfully they can represent the system they are being used to evaluate. Traditionally, the use of formal methods for crypto protocol verification has relied upon the use of the {\em free algebra} model originally proposed by Dolev and Yao. Principals engage in protocols by performing operations on data. However, there are a number of widely used operations whose essential properties cannot be represented in the free algebra model. Examples include associativity of concatenation, associativity and commutativity in modular exponentiation-based protocols such as Diffie-Hellman, and associativity, commutativity and self-cancellation in exclusive-or. Indeed, there have been cases, such as Paulson's analysis of the Bull recursive authentication protocol in which protocols using these sorts of operations have been proven secure in the free algebra model, but have been later found to be flawed. There is thus a great need for protocol reasoning techniques that take into account the different equational properties of cryptosystems. {\em Equational unification} is a technique that shows great promise for application to these problems. Briefly, equational unification gives a compact representation of all circumstances under which two different terms are equal. Thus, it has potential as a practical means for reasoning about protocols that use cryptosystems with different equational properties. Indeed, an earlier tool, the NRL Protocol Analyzer, made very successful use of equational unification, although it could only reason about a small class of theories. The project uses the Maude-NRL Protocol Analyzer (Maude-NPA), a tool for the analysis of cryptographic protocols using functions that obey different equational theories, is being further developed by Meadows and Meseguer at UIUC NRL, in cooperation with Santiago Escobar. Other PIs, Kapur, Lynch and Narendran, as well as their students, are learning about the tool so that the new unification algorithms can be implemented.
#### Clarification of Codes
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## AWARD OVERVIEW
AWARD OVERVIEW
Award Number 0905222 Funding Agency National Science Foundation
Total Award Amount $240,000 Project Location - City Albuquerque Award Date 07/14/2009 Project Location - State NM Project Status More than 50% Completed Project Location - Zip 87131-0001 Jobs Reported 0.00 Congressional District 01 Project Location - Country US ## Recipient Information (Grants) Recipient Information (Grants) Recipient Name UNIVERSITY OF NEW MEXICO Recipient DUNS Number 868853094 Recipient Address 1700 LOMAS BLVD NE STE 2200 Recipient City ALBUQUERQUE Recipient State New Mexico Recipient Zip 87106-3807 Recipient Congressional District 01 Recipient Country USA Required to Report Top 5 Highly Compensated Officials No ## Projects and Jobs Information Projects and Jobs Information Project Title TC: Medium: Collaborative Research: Unification Laboratory: Increasing the Power of Cryptographic Protocal Analysis Tools Project Status More than 50% Completed Final Project Report Submitted No Project Activities Description Computer & Information Science Quarterly Activities/Project Description We have developed algorithms for combining asymmetric unification algorithms for theories with certain properties. This would help considerably in developing modular approaches to asymmetric unification algorithms as they are needed in cryptographic protocols based on the semantic properties of operators used in encoding/decoding. Two papers - one on asymmetric unification for the theory of exclusive and another one on hierarchical combination of unification algorithms were presented at the prestigious international conference on Automated Deduction (CADE) in Lake Placid in June 2013. The PI also met there other participants of this project and held numerous technical discussions. Jobs Created 0.00 Description of Jobs Created No jobs created/retained this quarter. ## Purchaser Information (Grants) Purchaser Information Contracting Office ID Not Reported Contracting Office Name Not Available Contracting Office Region Not Available TAS Major Program 49-0101 ## Award Information Award Information Award Date 07/14/2009 Award Number 0905222 Order Number Award Type Grants Funding Agency ID 49 Funding Agency Name National Science Foundation Funding Office Name Not Available Awarding Agency ID 49 Awarding Agency Name National Science Foundation Amount of Award$240,000
Funds Invoiced/Received $239,946 Expenditure Amount$239,946
Infrastructure Expenditure Amount $0 Infrastructure Purpose and Rationale Not Reported Infrastructure Point of Contact Name Not Reported Infrastructure Point of Contact Email Not Reported Infrastructure Point of Contact Phone Not Reported Infrastructure Point of Contact Address Not Reported Infrastructure Point of Contact City Not Reported Infrastructure Point of Contact State Not Reported Infrastructure Point of Contact Zip Not Reported ## Product or Service Information (Grants) Product or Service Information Primary Activity Code U03.02 Activity Description Computer & Information Science ## Sub-Awards Information Sub-Awards Information Sub-awards to Organizations 0 Sub-award Amounts to Organizations$0
Sub-Awards to Individuals 0
Sub-Award Amounts to Individuals $0 Number of Sub-awards less than$25,000/award 0
Amount of Sub-awards less than $25,000/award$0
Number of payments to vendors greater than $25,000 0 Total Amount of payments to vendors greater than$25,000/award $0 Number of payments to vendors less than$25,000/award 4
Total Amount of payments to vendors less than $25,000/award$3,056
## Project Location Detail
Location Information
Latitude, Longitude 35º 5' 22", -106º 37' 12"
Congressional District 01
Address 1 1 University of New Mexico
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http://home.fnal.gov/~mrenna/lu_update/lutp0613man2/node77.html
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Next: Lepton beams Up: Cross-section Calculations Previous: The simple two-body processes Contents
### Resonance production
We have now covered the simple case. In a process, the integral is absent, and the differential cross section is replaced by . The cross section may now be written as
(100)
The structure is thus exactly the same, but the -related pieces are absent, and the rôle of the dimensionless cross section is played by .
If the range of allowed decay angles of the resonance is restricted, e.g. by requiring the decay products to have a minimum transverse momentum, effectively this translates into constraints on the variable of the process. The difference is that the angular dependence of a resonance decay is trivial, and that therefore the -dependent factor can be easily evaluated. For a spin-0 resonance, which decays isotropically, the relevant weight is simply . For a transversely polarized spin-1 resonance the expression is, instead,
(101)
Since the allowed range could depend on and/or (it does for a cut), the factor has to be evaluated for each individual phase-space point and included in the expression of eq. ().
For processes where either of the final-state particles is a resonance, or both, an additional choice has to be made for each resonance mass, eq. (). Since the allowed , and ranges depend on and , the selection of masses have to precede the choice of the other phase-space variables. Just as for the other variables, masses are not selected uniformly over the allowed range, but are rather distributed according to a function , with a compensating factor in the Jacobian. The functional form picked is normally
(102)
The definition of the integrals is analogous to the one before. The coefficients are not found by optimization, but predetermined, normally to , , . Clearly, had the phase space and the cross section been independent of and , the optimal choice would have been to put and have all other vanishing -- then the factor of the Jacobian would exactly have cancelled the Breit-Wigner of eq. () in the cross section. The second and the third terms are there to cover the possibility that the cross section does not die away quite as fast as given by the naïve Breit-Wigner shape. In particular, the third term covers the possibility of a secondary peak at small , in a spirit slightly similar to the one discussed for resonance production in processes.
The fourth term is only used for processes involving production, where the propagator guarantees that the cross section does have a significant secondary peak for . Therefore here the choice is , , and .
A few special tricks have been included to improve efficiency when the allowed mass range of resonances is constrained by kinematics or by user cuts. For instance, if a pair of equal or charge-conjugate resonances are produced, such as in , use is made of the constraint that the lighter of the two has to have a mass smaller than half the c.m. energy.
Next: Lepton beams Up: Cross-section Calculations Previous: The simple two-body processes Contents
Stephen_Mrenna 2012-10-24
| 2018-01-24T01:48:07 |
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https://runescape.fandom.com/wiki/Silverlight
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## FANDOM
44,113 Pages
For other uses, see Silverlight (disambiguation).
Silverlight is a magical sword used during the Demon Slayer quest, and can be kept afterwards. This weapon cannot be made by players using the Smithing skill. If Silverlight is lost during or after the quest, it can be reclaimed from Gideon Bede in the church north of the Varrock Museum for free. It can be sold to the Wise Old Man for 80 coins.
Silverlight is dyed black during the course of the Shadow of the Storm quest to make Silverlight (dyed), and later becomes Darklight after killing the demon Agrith-Naar. Silverlight (but not dyed Silverlight) can be mounted on the wall of a Quest Hall in a player-owned house.
Requirements Class Slot Tier Weapons None Melee 6 73 - 160 - Slash 1 Fast (3.0s) 0 PvM: 0% PvP: 0% 0 0 0 0 0 [FAQ] • [doc]
## Effects
Silverlight is an extremely weak weapon when fighting non-demon monsters, with damage and accuracy equal to a Bronze longsword. However, when using the sword to fight most varieties of demon, it will gain a large accuracy increase (enough to accurately hit mid-level demons resistant to melee). It also increases ability damage by a scaling 25-124% (a 1.25×-2.24× multiplier), based on your base Attack and Strength, and the monster's base Defence; this applies to your total ability damage, including off-hand weapons, equipment, and boosts. With auto attacks, 100% is added regardless.
The increase is given by $damage\ multiplier = 1.25 + 0.01 \times \text{max} \left ( \frac{A + S}{2} - E, 0 \right )$
where:
• $A$ is your Attack level, before temporary boosts
• $S$ is your Strength level, before temporary boosts
• $E$ is your target's Defence level
Additionally, Silverlight is used to remove the fire shield from a tormented demon, the only other way being holy water. Silverlight can also be used to kill vampyres.
After Dimension of Disaster, Silverlight can be upgraded to cause more damage to demons, as well as be able to smash gargoyles if the quicker killing blows Slayer ability has been unlocked. The upgrade can be bought for five silver pennies in Gypsy Aris's Dimension of Disaster reward shop. The upgraded darklight will:
• Add 30% rather than 20% to base hit chance against demons
• Add between 50% to 149% rather than between 25% to 124% extra damage against demons if using abilities. Upgrade scaling formula is 1.5 + ((Attack+Strength)/2-EnemyDefence*2)*0.01
• Add 150% rather than 100% extra damage against demons if using auto-attacks
### Monsters affected
The following creatures will take increased damage from Silverlight:
Silverlight does not affect the following:
## History
This section is a stub. You can help by expanding it.
In 20 of the Fifth Age, a local miner named Wally Prysin used Silverlight to battle Delrith, who was about to crush Varrock, and banish him back to the Infernal Dimensions. For the next 150 years, Silverlight resided in a crypt below the church in the North-east of Varrock guarded by the spirits of those who had wielded Silverlight.
## Trivia
• Silverlight can be traded on RuneScape Classic.
• It is possible to keep Silverlight after Shadow of the Storm; one way to achieve this is to have Silverlight in your bank while you use another to kill Agrith-Naar. Another way is to obtain Silverlight normally from Gideon Bede, even after completing Shadow of the Storm. Also, if you have mounted your Silverlight in your Player-owned house before Shadow of the Storm, the monk at the start of the quest will exclaim and give you another one.
• In RuneScape Classic, Silverlight was sold in the Legends' Guild. This was the only way to re-obtain it at that time, and due to complaints about this, Silverlight was removed from the Legends' Guild and it was obtained from Sir Prysin but since Demon Slayer was updated it can now be retrieved from Gideon Bede.
• In RuneScape Classic, Silverlight will weaken a demon if it is used on the first hit.
• In While Guthix Sleeps, it is revealed that Movario, greatly fearful of the unnaturally powerful 'tormented demons', intends to seek out Silverlight in the event the sinister Lucien sets them on him, for "normal weapons will be only marginally useful, as the creature seemed to possess some sort of magical defence."
• Silverlight was graphically updated on 15 December 2009. Black Silverlight and its upgraded counterpart Darklight was updated along with the release of the 2009 Christmas event.
• The Silverlight copy in Varrock museum did not change in the graphic update, it still had the look of the old Silverlight. This has been fixed.
• Originally you could own more than 1 Silverlight at a time, by doing the drop trick from Sir Prysin in exchange for 500 coins at a time, However this was changed when the Demon Slayer quest was updated and Players could retrieve Silverlight from Gideon Bede. It is now impossible to do the drop trick since Silverlight now has a "Destroy" option instead of a "Drop" option.
• Due to the Demon Slayer rework, it is now possible for players who completed the original version to have two silverlights.
• If you have two silverlights in your inventory and use black mushroom ink on one, then both silverlights will disappear, but only a single darklight will be produced.
## References
1. ^ Official Jagex YouTube Channel. RuneScape Patch Notes #63. YouTube.com. 23 March 2015.*
2. ^ ImRubic. TL;DW 171 - Q&A + GWD2 reaction!. reddit.com. 29 March 2016.*
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-08-24T21:01:08 |
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https://ftp.aimsciences.org/article/doi/10.3934/era.2011.18.69
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Article Contents
Article Contents
# An inverse theorem for the Gowers $U^{s+1}[N]$-norm
• This is an announcement of the proof of the inverse conjecture for the Gowers $U^{s+1}[N]$-norm for all $s \geq 3$; this is new for $s \geq 4$, the cases $s = 1,2,3$ having been previously established. More precisely we outline a proof that if $f : [N] \rightarrow [-1,1]$ is a function with ||$f$|| $U^{s+1}[N] \geq \delta$ then there is a bounded-complexity $s$-step nilsequence $F(g(n)\Gamma)$ which correlates with $f$, where the bounds on the complexity and correlation depend only on $s$ and $\delta$. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. In particular, one obtains an asymptotic formula for the number of $k$-term arithmetic progressions $p_1 < p_2 < ... < p_k \leq N$ of primes, for every $k \geq 3$.
Mathematics Subject Classification: Primary: 11B99.
Citation:
• [1] N. Alon, T. Kaufman, M. Krivelevich, S. Litsyn and D. Ron, Testing low-degree polynomials over GF(2), Approximation, Randomization, and Combinatorial Optimization, 2003, 188-199. Also: Testing Reed-Muller codes, IEEE Transactions on Information Theory, 51 (2005), 4032-4039.doi: 10.1109/TIT.2005.856958. [2] A. Balog and E. Szemerédi, A statistical theorem of set addition, Combinatorica, 14 (1994), 263-268.doi: 10.1007/BF01212974. [3] V. Bergelson, B. Host and B. Kra, Multiple recurrence and nilsequences, (with an appendix by I. Ruzsa), Invent. Math., 160 (2005), 261-303.doi: 10.1007/s00222-004-0428-6. [4] V. Bergelson, T. Tao and T. Ziegler, An inverse theorem for uniformity seminorms associated with the action of $F_p^{\infty}$, Geom. Funct. Anal., 19 (2010), 1539-1596.doi: 10.1007/s00039-010-0051-1. [5] J.-P. Conze and E. Lesigne, Sur un théorème ergodique pour des mesures diagonales, (French) [On an ergodic theorem for diagonal measures], C. R. Acad. Sci. Paris Sér. I Math., 306 (1988), 491-493. [6] N. Frantzikinakis, B. Host and B. Kra, Multiple recurrence and convergence for sequences related to the prime numbers, J. Reine Angew. Math., 611 (2007), 131-144.doi: 10.1515/CRELLE.2007.076. [7] G. A. Freĭman, "Foundations of a Structural Theory of Set Addition," Translations of Mathematical Monographs, 37, AMS, Providence, RI, 1973. [8] H. Furstenberg, "Nonconventional Ergodic Averages," The legacy of John von Neumann (Hempstead, NY, 1988), 43-56, Proc. Sympos. Pure Math., 50, Amer. Math. Soc., Providence, RI, 1990. [9] H. Furstenberg and B. Weiss, "A mean ergodic theorem for $1/N\sum^N_{n=1}f (T^n x)g(T^ {n^ 2}x)$," Convergence in ergodic theory and probability (Columbus, OH, 1993), 193-227, Ohio State Univ. Math. Res. Inst. Publ., 5 de Gruyter, Berlin, 1996. [10] W. T. Gowers, A new proof of Szemerédi's theorem for progressions of length four, GAFA, 8 (1998), 529-551.doi: 10.1007/s000390050065. [11] -, A new proof of Szemerédi's theorem, GAFA, 11 (2001), 465-588. [12] B. Green, "Generalising the Hardy-Littlewood Method for Primes," International Congress of Mathematicians. Vol. II, 373-399, Eur. Math. Soc., Zürich, 2006. [13] B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. (2), 167 (2008), 481-547.doi: 10.4007/annals.2008.167.481. [14] -, An inverse theorem for the Gowers $U^3$-norm, with applications, Proc. Edinburgh Math. Soc., 51, 71-153. [15] -, Linear equations in primes, Ann. Math. (2), 171 (2010), 1753-1850. [16] -, The quantitative behaviour of polynomial orbits on nilmanifolds, to appear in Ann. Math. [17] -, The Möbius function is strongly orthogonal to nilsequences, to appear in Ann. Math. [18] -, An arithmetic regularity lemma, associated counting lemma, and applications, in "An Irregular Mind" (Szemerédi is 70), Bolyai Society Mathematical Studies, 21, 261-334. [19] B. Green, T. Tao and T. Ziegler, An inverse theorem for the Gowers $U^4[N]$-norm, Glasgow Math. J., 53 (2011), 1-50.doi: 10.1017/S0017089510000546. [20] -, An inverse theorem for the Gowers $U^{s+1}[N]$ norm, preprint, arXiv:1009.3998. [21] I. J. Håland, Uniform distribution of generalized polynomials, J. Number Theory, 45 (1993), 327-366.doi: 10.1006/jnth.1993.1082. [22] B. Host and B. Kra, Convergence of Conze-Lesigne averages, Erg. Th. Dyn. Sys., 21 (2001), 493-509. [23] -, Averaging along cubes, Modern Dynamical Systems and Applications, Cambridge University Press, Cambridge, (2004), 123-144. [24] -, Nonconventional ergodic averages and nilmanifolds, Ann. of Math. (2), 161 (2005), 397-488. [25] -, Uniformity seminorms on $l^\infty$ and applications, J. Anal. Math., 108 (2009), 219-276.doi: 10.1007/s11854-009-0024-1. [26] A. Leibman, Pointwise convergence of ergodic averages of polynomial sequences of translations on a nilmanifold, Ergodic Theory and Dynamical Systems, 25 (2005), 201-213.doi: 10.1017/S0143385704000215. [27] -, A canonical form and the distribution of values of generalized polynomials, to appear in Israel Journal of Mathematics. [28] E. Lesigne, Équations fonctionnelles, couplages de produits gauches et théorèmes ergodiques pour mesures diagonales, (French) [Functional equations, couplings of skew products, ergodic theorems for diagonal measures], Bull. Soc. Math. France, 121 (1993), 315-351. [29] I. Z. Ruzsa, Generalized arithmetical progressions and sumsets, Acta Math. Hungar., 65 (1994), 379-388.doi: 10.1007/BF01876039. [30] A. Samorodnitsky, "Low-Degree Tests at Large Distances," STOC'07, Proceedings of the 39th Annual ACM Symposium on Theory of Computing, ACM, New York, (2007), 506-515. [31] B. Szegedy, Higher order Fourier analysis as an algebraic theory I, preprint, arXiv::0903.0897. [32] -, Higher order Fourier analysis as an algebraic theory II, preprint, arXiv::0911.1157. [33] -, Higher order Fourier analysis as an algebraic theory III, preprint, arXiv::1001.4282. [34] T. Tao and T. Ziegler, The inverse conjecture for the Gowers norms over finite fields via the correspondence principle, Anal. PDE, 3 (2010), 1-20.doi: 10.2140/apde.2010.3.1. [35] T. Tao and V. Vu, "Additive Combinatorics," Cambridge Studies in Advanced Mathematics, 105, Cambridge University Press, Cambridge, 2006. [36] T. Ziegler, Universal characteristic factors and Furstenberg averages, J. Amer. Math. Soc., 20 (2007), 53-97.doi: 10.1090/S0894-0347-06-00532-7.
Open Access Under a Creative Commons license
| 2023-03-26T09:49:14 |
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https://zbmath.org/authors/?q=ai%3Ayudovich.v-i
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# zbMATH — the first resource for mathematics
## Yudovich, Viktor Iosifovich
Compute Distance To:
Author ID: yudovich.v-i Published as: Yudovich, V. I.; Yudovich, Victor; Yudovich, V.; Yudovich, Viktor Iosifovich; Judovich, V. I. External Links: MGP · Wikidata · IdRef
Documents Indexed: 119 Publications since 1959, including 3 Books 1 Contribution as Editor Biographic References: 4 Publications
all top 5
#### Co-Authors
49 single-authored 13 Kurakin, Leonid Gennadievich 7 Srubshchik, Leonid S. 5 Esipov, A. A. 4 Morgulis, Andrey Borisovich 4 Ovchinnikova, S. N. 3 Barkovskij, Yu. S. 3 Friedlander, Susan Jean 3 Kolesov, V. V. 3 Sazonov, Leonid Ivanovich 2 Izakson, V. Kh. 2 Markman, G. S. 2 Morshneva, I. V. 2 Petrovskaya, Natal’ya Vladimirovna 2 Revina, Svetlana Vasil’evna 2 Tsybulin, Vyacheslav G. 2 Zenkovskaya, Svetlana M. 2 Zhukov, Mikhail Yu. 1 Andrejchikov, I. P. 1 Antman, Stuart S. 1 Babeshko, Vladimir Andreevich 1 Batishchev, V. A. 1 Belen’kaya, L. Kh. 1 Belokon, A. V. 1 Denissenko, Petr. V. 1 Govorukhin, Vasily N. 1 Guda, S. A. 1 Kashaev, Yu. K. 1 Keller, Joseph Bishop 1 Novossiadliy, V. A. 1 Olifer, A. V. 1 Sedenko, V I. 1 Shleykel, A. L. 1 Shnirelman, Alexander I. 1 Silber, Ben 1 Slitinskaya, S. K. 1 Srubscik, L. S. 1 Trenogin, Vladilen Aleksandrovich 1 Uhovskij, M. R. 1 Ukhovskij, M. R. 1 Ustinov, Yuriĭ Anatol’evich 1 Vishik, Misha M. 1 Vladimirov, Vladimir A. 1 Vorovich, Iosif Izrailevich 1 Zakharyuta, Vyacheslav Pavlovich 1 Zaslavskiĭ, Georgiĭ Moiseevich
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#### Serials
9 Soviet Physics. Doklady 9 Chaos 6 Fluid Dynamics 6 Journal of Applied Mathematics and Mechanics 6 Prikladnaya Matematika i Mekhanika 6 Sibirskiĭ Matematicheskiĭ Zhurnal 6 PMM, Journal of Applied Mathematics and Mechanics 5 Mathematical Notes 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Soviet Mathematics. Doklady 4 U.S.S.R. Computational Mathematics and Mathematical Physics 4 Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Severo-Kavkazskiĭ Region. Estestvennye Nauki 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Siberian Mathematical Journal 3 Sbornik: Mathematics 3 Journal of Mathematical Fluid Mechanics 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Izvestiya Severo-Kavkazskogo Nauchnogo Tsentra Vyssheĭ Shkoly. Estestvennye Nauki 2 Mathematics of the USSR, Sbornik 2 Physics-Doklady 2 Doklady Physics 1 Communications on Pure and Applied Mathematics 1 Russian Mathematical Surveys 1 Soviet Mathematics 1 Communications in Partial Differential Equations 1 SIAM Journal on Applied Mathematics 1 Notices of the American Mathematical Society 1 Russian Academy of Sciences. Sbornik. Mathematics 1 Mathematical Research Letters 1 Journal of Difference Equations and Applications 1 Doklady Mathematics 1 Differential Equations 1 Matematicheskoe Modelirovanie 1 Moscow Mathematical Journal 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Translations of Mathematical Monographs 1 Translations. Series 2. American Mathematical Society
all top 5
#### Fields
53 Fluid mechanics (76-XX) 35 Partial differential equations (35-XX) 22 Ordinary differential equations (34-XX) 22 Dynamical systems and ergodic theory (37-XX) 13 Operator theory (47-XX) 7 Mechanics of particles and systems (70-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Mechanics of deformable solids (74-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX)
#### Citations contained in zbMATH Open
81 Publications have been cited 746 times in 608 Documents Cited by Year
Some estimates connected with integral operators and with solutions of elliptic equations. Zbl 0144.14501
Yudovich, V. I.
1961
Non-stationary flow of an ideal incompressible liquid. Zbl 0147.44303
Yudovich, V. I.
1967
Uniqueness theorem for the basic nonstationary problem in the dynamics on an ideal incompressible fluid. Zbl 0841.35092
Yudovich, V. I.
1995
Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid. Zbl 0148.22307
Yudovich, V. I.
1965
The linearization method in hydrodynamical stability theory. Transl. from the Russian by J.R. Schulenberger. Translation edited by Ben Silver. Zbl 0727.76039
Yudovich, V. I.
1989
Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. Zbl 1055.58500
Yudovich, V. I.
1995
Linearization method in the hydrodynamic stability theory. (Metod linearizatsii v gidrodinamicheskoj teorii ustojchivosti). Zbl 0553.76038
Yudovich, V. I.
1984
The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520
Kurakin, L. G.; Yudovich, V. I.
2002
Periodic motions of a viscous incompressible fluid. Zbl 0158.23504
Yudovich, V. I.
1960
The onset of auto-oscillations in a fluid. Zbl 0247.76044
Yudovich, V. I.
1971
Nichtstationäre Strömung einer idealen inkompressiblen Flüssigkeit. Zbl 0129.19402
Yudovich, V. I.
1963
Eleven great problems of mathematical hydrodynamics. Zbl 1061.76003
Yudovich, V. I.
2003
Axially symmetric flows of ideal and viscous fluids filling the whole space. Zbl 0172.53405
Uhovskij, M. R.; Yudovich, V. I.
1968
Instabilities in fluid motion. Zbl 0948.76003
Friedlander, Susan; Yudovich, Victor
1999
Cosymmetry, degeneration of solutions of operator equations, and origin of a filtration convection. Zbl 0747.47010
Yudovich, V. I.
1991
Free convection and bifurcation. Zbl 0173.28803
Yudovich, V. I.
1967
On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid. Zbl 0982.76014
Yudovich, V. I.
2000
The unstable spectrum of oscillating shear flows. Zbl 0949.76025
Belenkaya, L.; Friedlander, S.; Yudovich, V.
1999
Secondary flows and fluid instability between rotating cylinders. Zbl 0153.29703
Yudovich, V. I.
1966
Arnold’s method for asymptotic stability of steady inviscid incompressible flow through a fixed domain with permeable boundary. Zbl 1080.76521
Morgulis, Andrey; Yudovich, Victor
2002
Implicit function theorem for cosymmetric equations. Zbl 0897.47051
Yudovich, V. I.
1996
Bifurcations and selection of equilibria in a simple cosymmetric model of filtrational convection. Zbl 0983.76015
Govorukhin, V. N.; Yudovich, V. I.
1999
On the completeness of a system of elementary solutions of the biharmonic equation in a semi-strip. Zbl 0296.35035
Ustinov, Yu. A.; Yudovich, V. I.
1973
Stability of convection flows. Zbl 0173.28804
Yudovich, V. I.
1967
The flow of a perfect, incompressible liquid through a given region. Zbl 0139.20502
Yudovich, V. I.
1962
Bifurcation of the branching of a cycle in $$n$$-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043
Kurakin, L. G.; Yudovich, V. I.
1997
Investigation of auto-oscillations of a continuous medium, occurring at loss of stability of a stationary mode. Zbl 0257.34040
Yudovich, V. I.
1972
Some estimates for solutions of elliptic equations. (Einige Abschätzungen der Lösungen elliptischer Gleichungen.) Zbl 0161.31101
Yudovich, V. I.
1962
Initiation of self-oscillations at loss of stability of spatially-periodic, three-dimensional viscous flows with respect to long-wave perturbations. Zbl 1101.76328
Revina, S. V.; Yudovich, V. I.
2001
Compressible helical flows. Zbl 0829.76074
Morgulis, A.; Yudovich, V. I.; Zaslavsky, G. M.
1995
Asymptotic stability of a stationary flowing regime of an ideal incompressible fluid. Zbl 1032.76008
Morgulis, A. B.; Yudovich, V. I.
2002
Vibration dynamics of systems with constraints. Zbl 1050.70531
Yudovich, V. I.
1997
Unstable eigenvalues associated with inviscid fluid flows. Zbl 0972.35100
Friedlander, Susan; Vishik, Misha; Yudovich, Victor
2000
Unique solvability of the problem of impact with separation of a rigid body on a nonhomogeneous fluid. Zbl 1299.76020
Yudovich, V. I.
2005
Asymptotic treatment of the equations for large bending of a symmetrically loaded circular plate. Zbl 0111.37402
Srubshchik, L. S.; Yudovich, V. I.
1961
Die allgemeine Form eines linearen Funktionals in $$H_ p'$$. Zbl 0128.34305
Zakharyuta, V. P.; Yudovich, V. I.
1964
Stability of steady flows of viscous incompressible fluids. Zbl 0139.21901
Yudovich, V. I.
1965
Loss of smoothness and inherent instability of 2D inviscid fluid flows. Zbl 1141.76012
Morgulis, Andrey; Shnirelman, Alexander; Yudovich, Victor
2008
Instability of long-wave viscous flows. Zbl 0729.76034
Yudovich, V. I.
1990
Some bounds for the solutions of elliptic equations. Zbl 0175.11604
Yudovich, V. I.
1962
Analysis of secondary steady flow between totating cylinders. Zbl 0191.25401
Ovchinnikova, S. N.; Yudovich, V. I.
1968
Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031
Kurakin, L. G.; Yudovich, V. I.
2000
Calculation of oscillatory regimes in Couette flow in the neighborhood of the point of intersection of bifurcations initiating Taylor vortices and azimuthal waves. Zbl 0945.76022
Kolesov, V. V.; Yudovich, V. I.
1998
The cosymmetric version of the implicit function theorem. Zbl 0860.46030
Yudovich, V.
1995
Über die Entstehung von Konvektion in einer Flüssigkeitsschicht mit freier Grenze. Zbl 0193.56602
Izakson, V. H.; Yudovich, V. I.
1968
On the stability of self-oscillations of a liquid. Zbl 0227.76074
Yudovich, V. I.
1970
On the equations of steady-state convection. Zbl 0131.41807
Ukhovskij, M. R.; Yudovich, V. I.
1963
Note on the stability of membrane solutions in the nonlinear theory of plates and shells. Zbl 0163.19507
Srubshchik, L. S.; Yudovich, V. I.
1966
Resonances in the codimension-2 bifurcations in the Couette-Taylor problem. Zbl 1262.76042
Yudovich, V. I.; Ovchinnikova, S. N.
2009
Stability and bifurcation of Couette flow in the case of a narrow gap between rotating cylinders. Zbl 0323.76028
Ovchinnikova, S. N.; Yudovich, V. I.
1974
On the dynamic snap-through of nonlinear elastic system. Zbl 0631.73044
Srubshchik, L. S.; Yudovich, V. I.
1986
Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028
Kurakin, L. G.; Yudovich, V. I.
1986
The stability of the stationary solutions of parabolic equations and of the Navier-Stokes system in the whole space. Zbl 0654.47034
Sazonov, L. I.; Yudovich, V. I.
1988
Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay. Zbl 0974.34066
Judovich, V. I.
1998
Onset of chaos through intersections of bifurcations in Couette-Taylor flow. Zbl 0925.76167
Kolesov, V.; Ovchinnikova, S.; Petrovskaya, N.; Yudovich, V.
1996
Asymptotisches Verhalten der Eigenwerte des ersten Randwertproblems für eine gewöhnliche Differentialgleichung auf einem langen Segment. Zbl 0298.34019
Esipov, A. A.; Yudovich, V. I.
1974
The bifurcation of a rotating flow of liquid. Zbl 0166.46201
Yudovich, V. I.
1966
Grenzverhalten der Eigenwerte von Randwertproblemen in sich unbeschränkt erweiternden Gebieten. Zbl 0258.47036
Esipov, A. A.; Yudovich, V. I.
1973
Steady flow of a viscous fluid. Zbl 0096.41301
Vorovich, I. I.; Yudovich, V. I.
1959
The asymptotic integration of the system of equations for the large deflection of symmetrically loaded shells of revolution. Zbl 0137.20701
Srubscik, L. S.; Yudovich, V. I.
1962
On the offshoot of cycles from equilibriums of inversionly and rotationally symmetric dynamic systems. Zbl 0569.34045
Morshneva, I. V.; Yudovich, V. I.
1985
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521
Kurakin, L. G.; Yudovich, V. I.
2000
On the unbounded increase in vorticity and velocity circulation in stratified and homogeneous fluid flows. Zbl 1128.76375
Yudovich, V. I.
2000
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040
Kurakin, L. G.; Yudovich, V. I.
2004
Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067
Kurakin, L. G.; Yudovich, V. I.
2003
The method of integro-differential equations and continued fractions in the problem of parametric excitation of waves. Zbl 1095.76018
Zen’kovskaya, S. M.; Yudovich, V. I.
2004
Global solvability versus collapse in the dynamics of an incompressible fluid. Zbl 1157.76300
Yudovich, V. I.
2006
Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566
Kurakin, L. G.; Yudovich, V. I.
2001
$$L_ p$$-estimates of the resolvent of the Stokes operator in infinite tubes. Zbl 0872.76023
Revina, S. V.; Yudovich, V. I.
1996
Parametric excitation of waves on a free boundary of a horizontal fluid layer. Zbl 1386.76081
Yudovich, V. I.; Zenkovskaya, S. M.; Novossiadliy, V. A.; Shleykel, A. L.
2004
Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry. Zbl 1020.37029
Kurakin, L. G.; Yudovich, V. I.
2000
The coupled problem of a solid oscillating in a viscous fluid under the action of an elastic force. Zbl 1164.35459
Guda, S. A.; Yudovich, V. I.
2007
An example of loss of stability and generation of a secondary flow in a closed vessel. Zbl 0195.27803
Yudovich, V. I.
1969
On stability of forced oscillations of fluid. Zbl 0225.76028
Yudovich, V. I.
1970
Invariant sets and attractors of quadratic mapping of plane: computer experiment and analytical treatment. Zbl 0915.58053
Tsybulin, Vyacheslav; Yudovich, Victor
1998
Plane unsteady motion of an ideal incompressible fluid. Zbl 0098.39602
Yudovich, V. I.
1961
Spectral properties of a class of boundary value problems. Zbl 0487.34016
Barkovskij, Yu. S.; Yudovich, V. I.
1982
Spectral properties of an oscillatory differential operator on the line. Zbl 0532.47037
Yudovich, V. I.
1983
Influence of spatial modulation of the temperature field on the stability of two-dimensional steady flow in a horizontal layer of fluid. Zbl 0555.76038
Batishchev, V. A.; Kolesov, V. V.; Slitinskaya, S. K.; Yudovich, V. I.
1983
On periodic differential equations with the selfadjoint monodromy operator. Zbl 1045.34034
Yudovich, V. I.
1999
Resonances in the codimension-2 bifurcations in the Couette-Taylor problem. Zbl 1262.76042
Yudovich, V. I.; Ovchinnikova, S. N.
2009
Loss of smoothness and inherent instability of 2D inviscid fluid flows. Zbl 1141.76012
Morgulis, Andrey; Shnirelman, Alexander; Yudovich, Victor
2008
The coupled problem of a solid oscillating in a viscous fluid under the action of an elastic force. Zbl 1164.35459
Guda, S. A.; Yudovich, V. I.
2007
Global solvability versus collapse in the dynamics of an incompressible fluid. Zbl 1157.76300
Yudovich, V. I.
2006
Unique solvability of the problem of impact with separation of a rigid body on a nonhomogeneous fluid. Zbl 1299.76020
Yudovich, V. I.
2005
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040
Kurakin, L. G.; Yudovich, V. I.
2004
The method of integro-differential equations and continued fractions in the problem of parametric excitation of waves. Zbl 1095.76018
Zen’kovskaya, S. M.; Yudovich, V. I.
2004
Parametric excitation of waves on a free boundary of a horizontal fluid layer. Zbl 1386.76081
Yudovich, V. I.; Zenkovskaya, S. M.; Novossiadliy, V. A.; Shleykel, A. L.
2004
Eleven great problems of mathematical hydrodynamics. Zbl 1061.76003
Yudovich, V. I.
2003
Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067
Kurakin, L. G.; Yudovich, V. I.
2003
The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520
Kurakin, L. G.; Yudovich, V. I.
2002
Arnold’s method for asymptotic stability of steady inviscid incompressible flow through a fixed domain with permeable boundary. Zbl 1080.76521
Morgulis, Andrey; Yudovich, Victor
2002
Asymptotic stability of a stationary flowing regime of an ideal incompressible fluid. Zbl 1032.76008
Morgulis, A. B.; Yudovich, V. I.
2002
Initiation of self-oscillations at loss of stability of spatially-periodic, three-dimensional viscous flows with respect to long-wave perturbations. Zbl 1101.76328
Revina, S. V.; Yudovich, V. I.
2001
Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566
Kurakin, L. G.; Yudovich, V. I.
2001
On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid. Zbl 0982.76014
Yudovich, V. I.
2000
Unstable eigenvalues associated with inviscid fluid flows. Zbl 0972.35100
Friedlander, Susan; Vishik, Misha; Yudovich, Victor
2000
Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521
Kurakin, L. G.; Yudovich, V. I.
2000
On the unbounded increase in vorticity and velocity circulation in stratified and homogeneous fluid flows. Zbl 1128.76375
Yudovich, V. I.
2000
Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry. Zbl 1020.37029
Kurakin, L. G.; Yudovich, V. I.
2000
Instabilities in fluid motion. Zbl 0948.76003
Friedlander, Susan; Yudovich, Victor
1999
The unstable spectrum of oscillating shear flows. Zbl 0949.76025
Belenkaya, L.; Friedlander, S.; Yudovich, V.
1999
Bifurcations and selection of equilibria in a simple cosymmetric model of filtrational convection. Zbl 0983.76015
Govorukhin, V. N.; Yudovich, V. I.
1999
On periodic differential equations with the selfadjoint monodromy operator. Zbl 1045.34034
Yudovich, V. I.
1999
Calculation of oscillatory regimes in Couette flow in the neighborhood of the point of intersection of bifurcations initiating Taylor vortices and azimuthal waves. Zbl 0945.76022
Kolesov, V. V.; Yudovich, V. I.
1998
Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay. Zbl 0974.34066
Judovich, V. I.
1998
Invariant sets and attractors of quadratic mapping of plane: computer experiment and analytical treatment. Zbl 0915.58053
Tsybulin, Vyacheslav; Yudovich, Victor
1998
Bifurcation of the branching of a cycle in $$n$$-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043
Kurakin, L. G.; Yudovich, V. I.
1997
Vibration dynamics of systems with constraints. Zbl 1050.70531
Yudovich, V. I.
1997
Implicit function theorem for cosymmetric equations. Zbl 0897.47051
Yudovich, V. I.
1996
Onset of chaos through intersections of bifurcations in Couette-Taylor flow. Zbl 0925.76167
Kolesov, V.; Ovchinnikova, S.; Petrovskaya, N.; Yudovich, V.
1996
$$L_ p$$-estimates of the resolvent of the Stokes operator in infinite tubes. Zbl 0872.76023
Revina, S. V.; Yudovich, V. I.
1996
Uniqueness theorem for the basic nonstationary problem in the dynamics on an ideal incompressible fluid. Zbl 0841.35092
Yudovich, V. I.
1995
Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. Zbl 1055.58500
Yudovich, V. I.
1995
Compressible helical flows. Zbl 0829.76074
Morgulis, A.; Yudovich, V. I.; Zaslavsky, G. M.
1995
The cosymmetric version of the implicit function theorem. Zbl 0860.46030
Yudovich, V.
1995
Cosymmetry, degeneration of solutions of operator equations, and origin of a filtration convection. Zbl 0747.47010
Yudovich, V. I.
1991
Instability of long-wave viscous flows. Zbl 0729.76034
Yudovich, V. I.
1990
The linearization method in hydrodynamical stability theory. Transl. from the Russian by J.R. Schulenberger. Translation edited by Ben Silver. Zbl 0727.76039
Yudovich, V. I.
1989
The stability of the stationary solutions of parabolic equations and of the Navier-Stokes system in the whole space. Zbl 0654.47034
Sazonov, L. I.; Yudovich, V. I.
1988
On the dynamic snap-through of nonlinear elastic system. Zbl 0631.73044
Srubshchik, L. S.; Yudovich, V. I.
1986
Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028
Kurakin, L. G.; Yudovich, V. I.
1986
On the offshoot of cycles from equilibriums of inversionly and rotationally symmetric dynamic systems. Zbl 0569.34045
Morshneva, I. V.; Yudovich, V. I.
1985
Linearization method in the hydrodynamic stability theory. (Metod linearizatsii v gidrodinamicheskoj teorii ustojchivosti). Zbl 0553.76038
Yudovich, V. I.
1984
Spectral properties of an oscillatory differential operator on the line. Zbl 0532.47037
Yudovich, V. I.
1983
Influence of spatial modulation of the temperature field on the stability of two-dimensional steady flow in a horizontal layer of fluid. Zbl 0555.76038
Batishchev, V. A.; Kolesov, V. V.; Slitinskaya, S. K.; Yudovich, V. I.
1983
Spectral properties of a class of boundary value problems. Zbl 0487.34016
Barkovskij, Yu. S.; Yudovich, V. I.
1982
Stability and bifurcation of Couette flow in the case of a narrow gap between rotating cylinders. Zbl 0323.76028
Ovchinnikova, S. N.; Yudovich, V. I.
1974
Asymptotisches Verhalten der Eigenwerte des ersten Randwertproblems für eine gewöhnliche Differentialgleichung auf einem langen Segment. Zbl 0298.34019
Esipov, A. A.; Yudovich, V. I.
1974
On the completeness of a system of elementary solutions of the biharmonic equation in a semi-strip. Zbl 0296.35035
Ustinov, Yu. A.; Yudovich, V. I.
1973
Grenzverhalten der Eigenwerte von Randwertproblemen in sich unbeschränkt erweiternden Gebieten. Zbl 0258.47036
Esipov, A. A.; Yudovich, V. I.
1973
Investigation of auto-oscillations of a continuous medium, occurring at loss of stability of a stationary mode. Zbl 0257.34040
Yudovich, V. I.
1972
The onset of auto-oscillations in a fluid. Zbl 0247.76044
Yudovich, V. I.
1971
On the stability of self-oscillations of a liquid. Zbl 0227.76074
Yudovich, V. I.
1970
On stability of forced oscillations of fluid. Zbl 0225.76028
Yudovich, V. I.
1970
An example of loss of stability and generation of a secondary flow in a closed vessel. Zbl 0195.27803
Yudovich, V. I.
1969
Axially symmetric flows of ideal and viscous fluids filling the whole space. Zbl 0172.53405
Uhovskij, M. R.; Yudovich, V. I.
1968
Analysis of secondary steady flow between totating cylinders. Zbl 0191.25401
Ovchinnikova, S. N.; Yudovich, V. I.
1968
Über die Entstehung von Konvektion in einer Flüssigkeitsschicht mit freier Grenze. Zbl 0193.56602
Izakson, V. H.; Yudovich, V. I.
1968
Non-stationary flow of an ideal incompressible liquid. Zbl 0147.44303
Yudovich, V. I.
1967
Free convection and bifurcation. Zbl 0173.28803
Yudovich, V. I.
1967
Stability of convection flows. Zbl 0173.28804
Yudovich, V. I.
1967
Secondary flows and fluid instability between rotating cylinders. Zbl 0153.29703
Yudovich, V. I.
1966
Note on the stability of membrane solutions in the nonlinear theory of plates and shells. Zbl 0163.19507
Srubshchik, L. S.; Yudovich, V. I.
1966
The bifurcation of a rotating flow of liquid. Zbl 0166.46201
Yudovich, V. I.
1966
Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid. Zbl 0148.22307
Yudovich, V. I.
1965
Stability of steady flows of viscous incompressible fluids. Zbl 0139.21901
Yudovich, V. I.
1965
Die allgemeine Form eines linearen Funktionals in $$H_ p'$$. Zbl 0128.34305
Zakharyuta, V. P.; Yudovich, V. I.
1964
Nichtstationäre Strömung einer idealen inkompressiblen Flüssigkeit. Zbl 0129.19402
Yudovich, V. I.
1963
On the equations of steady-state convection. Zbl 0131.41807
Ukhovskij, M. R.; Yudovich, V. I.
1963
The flow of a perfect, incompressible liquid through a given region. Zbl 0139.20502
Yudovich, V. I.
1962
Some estimates for solutions of elliptic equations. (Einige Abschätzungen der Lösungen elliptischer Gleichungen.) Zbl 0161.31101
Yudovich, V. I.
1962
Some bounds for the solutions of elliptic equations. Zbl 0175.11604
Yudovich, V. I.
1962
The asymptotic integration of the system of equations for the large deflection of symmetrically loaded shells of revolution. Zbl 0137.20701
Srubscik, L. S.; Yudovich, V. I.
1962
Some estimates connected with integral operators and with solutions of elliptic equations. Zbl 0144.14501
Yudovich, V. I.
1961
Asymptotic treatment of the equations for large bending of a symmetrically loaded circular plate. Zbl 0111.37402
Srubshchik, L. S.; Yudovich, V. I.
1961
Plane unsteady motion of an ideal incompressible fluid. Zbl 0098.39602
Yudovich, V. I.
1961
Periodic motions of a viscous incompressible fluid. Zbl 0158.23504
Yudovich, V. I.
1960
Steady flow of a viscous fluid. Zbl 0096.41301
Vorovich, I. I.; Yudovich, V. I.
1959
all top 5
#### Cited by 623 Authors
24 Kurakin, Leonid Gennadievich 20 Yudovich, Viktor Iosifovich 13 Tsybulin, Vyacheslav G. 11 Cianchi, Andrea 11 Morgulis, Andrey Borisovich 11 Yang, Yunyan 10 Govorukhin, Vasily N. 10 Kiselev, Alexander A. 8 Levenshtam, Valeriĭ Borisovich 8 Okamoto, Hisashi 8 Ostrovskaya, Irina V. 8 Pick, Luboš 7 Hmidi, Taoufik 7 Il’in, Konstantin Ivanovich 7 Karasözen, Bülent 7 Li, Dong 7 Revina, Svetlana Vasil’evna 6 Kelliher, James P. 6 Kolesov, V. V. 6 Wang, Guodong 5 Cao, Daomin 5 Elgindi, Tarek Mohamed 5 Kim, Sun-Chul 5 Lopes Filho, Milton da Costa 5 Masmoudi, Nader 5 Nguyen Thieu Huy 5 Norkin, Mikhaĭl Viktorovich 5 Nussenzveig Lopes, Helena Judith 5 Slavíková, Lenka 5 Taniuchi, Yasushi 5 Wang, Yamin 5 Zelik, Sergey V. 5 Zlatoš, Andrej 4 Černý, Robert 4 Chen, Zhimin 4 Chepyzhov, Vladimir V. 4 Cozzi, Elaine 4 de Souza, Manassés 4 Dullin, Holger R. 4 Friedlander, Susan Jean 4 Gotoda, Takeshi 4 Hencl, Stanislav 4 Ionescu-Kruse, Delia 4 Iooss, Gérard 4 Marsden, Jerrold Eldon 4 Ovchinnikova, S. N. 4 Sinaĭ, Yakov Grigor’evich 4 Srubshchik, Leonid S. 4 Titi, Edriss Saleh 4 Vasudevan, Shibi 4 Wan, Jie 4 Watanabe, Yoshitaka 4 Worthington, Joachim 4 Zhu, Xiaobao 3 Alberico, Angela 3 Alonso-Orán, Diego 3 Berselli, Luigi Carlo 3 Bethencourt de León, Aythami 3 Brzeźniak, Zdzisław 3 Burton, Geoffrey R. 3 Do Ó, João M. Bezerra 3 Edmunds, David Eric 3 Enciso, Alberto 3 Frischmuth, Kurt 3 Henry, David 3 Ilyin, Alexei A. 3 Jeong, In-Jee 3 Kobayashi, Teppei 3 Korobkov, Mikhail V. 3 Kyed, Mads 3 Latushkin, Yuri 3 Maremonti, Paolo 3 Mateu, Joan 3 Miao, Changxing 3 Musso, Monica 3 Nemtsev, Andrew D. 3 Ogawa, Takayoshi 3 Oskolkov, Anatolii Petrovich 3 Pavlović, Nataša 3 Price, W. Geraint 3 Ruf, Bernhard 3 Sakajo, Takashi 3 Sazonov, Leonid Ivanovich 3 Severo, Uberlandio Batista 3 Shadiev, R. D. 3 Solonnikov, Vsevolod Alekseevich 3 Tintarev, Kyril 3 Troshkin, Oleg V. 3 Vu Thi Ngoc Ha 3 Wang, Xumin 3 Yao, Yao 3 Yoneda, Tsuyoshi 3 Zhang, Mengjie 3 Zheng, Xiaoxin 3 Zhu, Xiangrong 2 Abdelhafez, M. A. 2 Abidi, Hammadi 2 Afendikov, Andrei L. 2 Bardos, Claude Williams 2 Beirão da Veiga, Hugo ...and 523 more Authors
all top 5
#### Cited in 163 Serials
32 Fluid Dynamics 30 Archive for Rational Mechanics and Analysis 28 Journal of Differential Equations 24 Communications in Mathematical Physics 24 Journal of Applied Mathematics and Mechanics 22 Journal of Mathematical Analysis and Applications 22 Siberian Mathematical Journal 18 Journal of Mathematical Fluid Mechanics 13 Mathematical Notes 13 Journal of Functional Analysis 11 Physica D 11 Regular and Chaotic Dynamics 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Journal of Nonlinear Science 10 Chaos 9 Journal of Mathematical Sciences (New York) 7 Advances in Mathematics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Journal of Fluid Mechanics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Prikladnaya Matematika i Mekhanika 6 Mathematische Annalen 6 Computational Mathematics and Mathematical Physics 6 Discrete and Continuous Dynamical Systems 6 Journal of Applied Mechanics and Technical Physics 6 European Journal of Mechanics. B. Fluids 6 Acta Mathematica Sinica. English Series 6 Communications on Pure and Applied Analysis 5 Journal of Soviet Mathematics 5 Japan Journal of Industrial and Applied Mathematics 5 Discrete and Continuous Dynamical Systems. Series B 4 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 Journal of Computational and Applied Mathematics 4 Journal of Dynamics and Differential Equations 4 Physics of Fluids 4 Annals of Mathematics. Second Series 4 Differential Equations 4 Proceedings of the Steklov Institute of Mathematics 4 Nelineĭnaya Dinamika 3 Nonlinearity 3 Proceedings of the American Mathematical Society 3 Tohoku Mathematical Journal. Second Series 3 Transactions of the American Mathematical Society 3 Applied Mathematics Letters 3 Communications in Partial Differential Equations 3 SIAM Journal on Applied Mathematics 3 SIAM Journal on Mathematical Analysis 3 Bulletin of the American Mathematical Society. New Series 3 NoDEA. Nonlinear Differential Equations and Applications 3 Journal of Evolution Equations 3 Boundary Value Problems 3 Nonlinear Analysis. Theory, Methods & Applications 2 Computer Physics Communications 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Applied Mathematics and Computation 2 Czechoslovak Mathematical Journal 2 Functional Analysis and its Applications 2 Mathematische Nachrichten 2 Rendiconti del Seminario Matematico della Università di Padova 2 Tokyo Journal of Mathematics 2 Zeitschrift für Analysis und ihre Anwendungen 2 Applied Mathematics and Mechanics. (English Edition) 2 Computational Mathematics and Modeling 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Potential Analysis 2 Calculus of Variations and Partial Differential Equations 2 Russian Journal of Mathematical Physics 2 Mathematical Inequalities & Applications 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 2 Discrete and Continuous Dynamical Systems. Series S 2 Kinetic and Related Models 2 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie 2 Dal’nevostochnyĭ Matematicheskiĭ Zhurnal 2 Eurasian Mathematical Journal 2 Analysis and Mathematical Physics 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Annals of PDE 1 Computers & Mathematics with Applications 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Physics Letters. B 1 Physics Reports 1 Reviews of Modern Physics 1 Ukrainian Mathematical Journal 1 Wave Motion 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Soviet Applied Mechanics 1 Acta Mathematica Vietnamica 1 Annales de l’Institut Fourier ...and 63 more Serials
all top 5
#### Cited in 36 Fields
391 Fluid mechanics (76-XX) 360 Partial differential equations (35-XX) 60 Functional analysis (46-XX) 52 Dynamical systems and ergodic theory (37-XX) 37 Ordinary differential equations (34-XX) 27 Operator theory (47-XX) 25 Geophysics (86-XX) 20 Real functions (26-XX) 19 Numerical analysis (65-XX) 17 Mechanics of deformable solids (74-XX) 16 Mechanics of particles and systems (70-XX) 15 Classical thermodynamics, heat transfer (80-XX) 13 Global analysis, analysis on manifolds (58-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Functions of a complex variable (30-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Probability theory and stochastic processes (60-XX) 5 Potential theory (31-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral equations (45-XX) 5 Biology and other natural sciences (92-XX) 3 Differential geometry (53-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX)
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https://zbmath.org/authors/?q=ai%3Aangenent.sigurd-bernardus
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# zbMATH — the first resource for mathematics
## Angenent, Sigurd Bernardus
Compute Distance To:
Author ID: angenent.sigurd-bernardus Published as: Angenent, S.; Angenent, S. B.; Angenent, Sigurd; Angenent, Sigurd B.; Angenent, Sigurd Bernardus Homepage: http://www.math.wisc.edu/~angenent/ External Links: MGP · Wikidata
Documents Indexed: 68 Publications since 1985, including 2 Books
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#### Co-Authors
27 single-authored 9 Aronson, Donald G. 7 Tannenbaum, Allen Robert 5 Knopf, Dan 3 Gurtin, Morton Edward 3 Vandervorst, Robertus C. A. M. 2 Altschuler, Steven J. 2 Betelú, Santiago I. 2 Daskalopoulos, Panagiota 2 Haker, Steven 2 Hulshof, Joost 2 Isenberg, James A. 2 Sesum, Natasa 2 Velázquez, Juan J. L. 1 Altschuler, Dylan J. 1 Caputo, M. Cristina 1 Clément, Philippe J. E. 1 de Pagter, Bernardus 1 Dominitz, Ayelet 1 Fiedler, Bernold 1 Fila, Marek 1 Giga, Yoshikazu 1 Heijmans, Henk J. A. M. 1 Kikinis, Ron 1 Lowengrub, John Samuel 1 Mallet-Paret, John Joseph 1 Matano, Hiroshi 1 Mueller, Marshall 1 Niethammer, Marc 1 Olson, Connor 1 Peletier, Lambertus Adrianus 1 Pichon, Eric 1 Sapiro, Guillermo 1 van den Berg, Jan Bouwe 1 van Duijn, Cornelis Johannes 1 Wu, Lani F. 1 Yezzi, Anthony jun. 1 You, Qian 1 Zeitouni, Ofer
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#### Serials
5 Journal für die Reine und Angewandte Mathematik 4 Annals of Mathematics. Second Series 2 Nonlinearity 2 Rocky Mountain Journal of Mathematics 2 Journal of Differential Equations 2 Journal of Differential Geometry 2 Mathematische Annalen 2 Transactions of the American Mathematical Society 2 Ergodic Theory and Dynamical Systems 2 Physica D 2 Journal of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Duke Mathematical Journal 1 IEEE Transactions on Automatic Control 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 European Journal of Applied Mathematics 1 Differential and Integral Equations 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Communications in Analysis and Geometry 1 Physics of Fluids 1 Journal of Mathematical Sciences. University of Tokyo 1 Mathematical Research Letters 1 Acta Mathematica Sinica. English Series 1 Journal of Evolution Equations 1 Networks and Heterogeneous Media 1 Involve
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#### Fields
41 Partial differential equations (35-XX) 21 Differential geometry (53-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Fluid mechanics (76-XX) 4 Ordinary differential equations (34-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Real functions (26-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
61 Publications have been cited 1,411 times in 1,087 Documents Cited by Year
The zero set of a solution of a parabolic equation. Zbl 0644.35050
Angenent, Sigurd
1988
Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface. Zbl 0723.73017
Angenent, Sigurd; Gurtin, Morton E.
1989
One-parameter semigroups. Zbl 0636.47051
Clément, Ph.; Heijmans, H. J. A. M.; Angenent, S.; van Duijn, C. J.; de Pagter, B.
1987
On the formation of singularities in the curve shortening flow. Zbl 0731.53002
Angenent, Sigurd
1991
Nonlinear analytic semiflows. Zbl 0723.34047
Angenent, Sigurd B.
1990
The Morse-Smale property for a semilinear parabolic equation. Zbl 0581.58026
Angenent, S. B.
1986
Shrinking doughnuts. Zbl 0762.53028
Angenent, Sigurd B.
1992
Stable transition layers in a semilinear boundary value problem. Zbl 0634.35041
Angenent, S. B.; Mallet-Paret, John; Peletier, L. A.
1987
Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions. Zbl 0749.58054
Angenent, Sigurd
1991
Mean curvature flow through singularities for surfaces of rotation. Zbl 0847.58072
Altschuler, Steven; Angenent, Sigurd B.; Giga, Yoshikazu
1995
Parabolic equations for curves on surfaces. I: Curves with $$p$$-integrable curvature. Zbl 0789.58070
Angenent, Sigurd
1990
The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086
Angenent, S. B.; Fiedler, B.
1988
Uniqueness of the solution of a semilinear boundary value problem. Zbl 0576.35044
Angenent, S. B.
1985
Minimizing flows for the Monge-Kantorovich problem. Zbl 1042.49040
Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen
2003
A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology. Zbl 0939.58015
Angenent, Sigurd; van der Vorst, Robertus
1999
On the affine heat equation for non-convex curves. Zbl 0902.35048
Angenent, Sigurd; Sapiro, Guillermo; Tannenbaum, Allen
1998
Degenerate neckpinches in mean curvature flow. Zbl 0866.58055
Angenent, S. B.; Velázquez, J. J. L.
1997
An example of neckpinching for Ricci flow on $$S^{n+1}$$. Zbl 1064.58022
Angenent, Sigurd; Knopf, Dan
2004
The focusing problem for the radially symmetric porous medium equation. Zbl 0830.35062
Angenent, S. B.; Aronson, D. G.
1995
Local existence and regularity for a class of degenerate parabolic equations. Zbl 0619.35114
Angenent, Sigurd
1988
Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049
Angenent, Sigurd B.; Knopf, Dan
2007
Monotone recurrence relations, their Birkhoff orbits and topological entropy. Zbl 0667.58036
Angenent, Sigurd B.
1990
The periodic orbits of an area preserving twist map. Zbl 0665.58034
Angenent, S. B.
1988
Asymptotic shape of cusp singularities in curve shortening. Zbl 0829.35058
Angenent, S. B.; Velázquez, J. J. L.
1995
Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052
Angenent, Sigurd B.; Fila, Marek
1996
Analyticity of the interface of the porous media equation after the waiting time. Zbl 0653.35040
Angenent, Sigurd
1988
The shadowing lemma for elliptic PDE. Zbl 0653.35030
Angenent, Sigurd
1987
A priori bounds and renormalized Morse indices of solutions of an elliptic system. Zbl 0964.35037
Angenent, Sigurd B.; van der Vorst, Robertus
2000
Solutions of the one-dimensional porous medium equation are determined by their free boundary. Zbl 0679.35040
Angenent, Sigurd
1990
Unique asymptotics of ancient convex mean curvature flow solutions. Zbl 1416.53061
Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
2019
A variational interpretation of Melnikov’s function and exponentionally small separatrix splitting. Zbl 0810.34037
Angenent, Sigurd
1993
Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
2011
The radius of vanishing bubbles in equivariant harmonic map flow from $$D^2$$ to $$S^2$$. Zbl 1223.35198
Angenent, S. B.; Hulshof, J.; Matano, H.
2009
Degenerate neckpinches in Ricci flow. Zbl 1329.53102
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
2015
Focusing of an elongated hole in porous medium flow. Zbl 0989.35082
Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S.
2001
Renormalization study of two-dimensional convergent solutions of the porous medium equation. Zbl 0958.76088
Betelú, S. I.; Aronson, D. G.; Angenent, S. B.
2000
Mathematical methods in medical image processing. Zbl 1096.92027
Angenent, Sigurd; Pichon, Eric; Tannenbaum, Allen
2006
Intermediate asymptotics for convergent viscous gravity currents. Zbl 0832.76020
Angenent, S. B.; Aronson, D. G.
1995
Anisotropic motion of a phase interface. Well-posedness of the initial value problem and qualitative properties of the interface. Zbl 0784.35124
Angenent, Sigurd B.; Gurtin, Morton E.
1994
The zoo of solitons for curve shortening in $$\mathbb R^n$$. Zbl 1280.35023
Altschuler, Dylan J.; Altschuler, Steven J.; Angenent, Sigurd B.; Wu, Lani F.
2013
A remark on the topological entropy and invariant circles of an area preserving twistmap. Zbl 0769.58036
Angenent, Sigurd B.
1992
Large time asymptotics for the porous media equation. Zbl 0669.35048
Angenent, Sigurd
1988
Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow. Zbl 1267.53065
Angenent, Sigurd
2013
Curve shortening and the topology of closed geodesics on surfaces. Zbl 1137.53330
Angenent, Sigurd B.
2005
Inflection points, extatic points and curve shortening. Zbl 0960.53038
Angenent, S.
1999
Nodal properties of solutions of parabolic equations. Zbl 0727.35005
Angenent, Sigurd
1991
Non-axial self-similar hole filling for the porous medium equation. Zbl 0973.35115
Angenent, S. B.; Aronson, D. G.
2001
Singularities at $$t=\infty$$ in equivariant harmonic map flow. Zbl 1075.53057
Angenent, Sigurd; Hulshof, Joost
2005
On area preserving mappings of minimal distortion. Zbl 0976.68175
Angenent, S.; Haker, Steven; Tannenbaum, Allen; Kikinis, Ron
2000
Constructions with analytic semigroups and abstract exponential decay results for eigenfunctions. Zbl 0936.47023
Angenent, Sigurd
1999
Optimal asymptotics for solutions to the initial value problem for the porous medium equation. Zbl 0886.35112
Angenent, S. B.; Aronson, D. G.
1996
Uniqueness of two-convex closed ancient solutions to the mean curvature flow. Zbl 07264133
Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
2020
Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066
Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan
2012
Contact and non-contact type Hamiltonian systems generated by second-order Lagrangians. Zbl 1225.37064
Angenent, S. B.; van den Berg, J. B.; Vandervorst, R. C. A. M.
2007
Dynamic active contours for visual tracking. Zbl 1366.94064
Niethammer, Marc; Tannenbaum, Allen; Angenent, Sigurd
2006
Self-similarity in the post-focussing regime in porous medium flows. Zbl 0861.35049
Angenent, S. B.; Aronson, D. G.
1996
General contact-angle conditions with and without kinetics. Zbl 0867.53061
Angenent, Sigurd; Gurtin, Morton E.
1996
Some recent results on mean curvature flow. Zbl 0796.35068
Angenent, Sigurd B.
1993
Self-intersecting geodesics and entropy of the geodesic flow. Zbl 1162.53030
Angenent, Sigurd
2008
The focusing problem for the eikonal equation. Zbl 1033.35023
Angenent, S. B.; Aronson, D. G.
2003
The dynamics of a degenerate reaction diffusion equation. Zbl 0821.35013
Angenent, Sigurd B.; Aronson, Donald G.
1994
Uniqueness of two-convex closed ancient solutions to the mean curvature flow. Zbl 07264133
Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
2020
Unique asymptotics of ancient convex mean curvature flow solutions. Zbl 1416.53061
Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
2019
Degenerate neckpinches in Ricci flow. Zbl 1329.53102
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
2015
The zoo of solitons for curve shortening in $$\mathbb R^n$$. Zbl 1280.35023
Altschuler, Dylan J.; Altschuler, Steven J.; Angenent, Sigurd B.; Wu, Lani F.
2013
Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow. Zbl 1267.53065
Angenent, Sigurd
2013
Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066
Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan
2012
Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
2011
The radius of vanishing bubbles in equivariant harmonic map flow from $$D^2$$ to $$S^2$$. Zbl 1223.35198
Angenent, S. B.; Hulshof, J.; Matano, H.
2009
Self-intersecting geodesics and entropy of the geodesic flow. Zbl 1162.53030
Angenent, Sigurd
2008
Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049
Angenent, Sigurd B.; Knopf, Dan
2007
Contact and non-contact type Hamiltonian systems generated by second-order Lagrangians. Zbl 1225.37064
Angenent, S. B.; van den Berg, J. B.; Vandervorst, R. C. A. M.
2007
Mathematical methods in medical image processing. Zbl 1096.92027
Angenent, Sigurd; Pichon, Eric; Tannenbaum, Allen
2006
Dynamic active contours for visual tracking. Zbl 1366.94064
Niethammer, Marc; Tannenbaum, Allen; Angenent, Sigurd
2006
Curve shortening and the topology of closed geodesics on surfaces. Zbl 1137.53330
Angenent, Sigurd B.
2005
Singularities at $$t=\infty$$ in equivariant harmonic map flow. Zbl 1075.53057
Angenent, Sigurd; Hulshof, Joost
2005
An example of neckpinching for Ricci flow on $$S^{n+1}$$. Zbl 1064.58022
Angenent, Sigurd; Knopf, Dan
2004
Minimizing flows for the Monge-Kantorovich problem. Zbl 1042.49040
Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen
2003
The focusing problem for the eikonal equation. Zbl 1033.35023
Angenent, S. B.; Aronson, D. G.
2003
Focusing of an elongated hole in porous medium flow. Zbl 0989.35082
Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S.
2001
Non-axial self-similar hole filling for the porous medium equation. Zbl 0973.35115
Angenent, S. B.; Aronson, D. G.
2001
A priori bounds and renormalized Morse indices of solutions of an elliptic system. Zbl 0964.35037
Angenent, Sigurd B.; van der Vorst, Robertus
2000
Renormalization study of two-dimensional convergent solutions of the porous medium equation. Zbl 0958.76088
Betelú, S. I.; Aronson, D. G.; Angenent, S. B.
2000
On area preserving mappings of minimal distortion. Zbl 0976.68175
Angenent, S.; Haker, Steven; Tannenbaum, Allen; Kikinis, Ron
2000
A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology. Zbl 0939.58015
Angenent, Sigurd; van der Vorst, Robertus
1999
Inflection points, extatic points and curve shortening. Zbl 0960.53038
Angenent, S.
1999
Constructions with analytic semigroups and abstract exponential decay results for eigenfunctions. Zbl 0936.47023
Angenent, Sigurd
1999
On the affine heat equation for non-convex curves. Zbl 0902.35048
Angenent, Sigurd; Sapiro, Guillermo; Tannenbaum, Allen
1998
Degenerate neckpinches in mean curvature flow. Zbl 0866.58055
Angenent, S. B.; Velázquez, J. J. L.
1997
Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052
Angenent, Sigurd B.; Fila, Marek
1996
Optimal asymptotics for solutions to the initial value problem for the porous medium equation. Zbl 0886.35112
Angenent, S. B.; Aronson, D. G.
1996
Self-similarity in the post-focussing regime in porous medium flows. Zbl 0861.35049
Angenent, S. B.; Aronson, D. G.
1996
General contact-angle conditions with and without kinetics. Zbl 0867.53061
Angenent, Sigurd; Gurtin, Morton E.
1996
Mean curvature flow through singularities for surfaces of rotation. Zbl 0847.58072
Altschuler, Steven; Angenent, Sigurd B.; Giga, Yoshikazu
1995
The focusing problem for the radially symmetric porous medium equation. Zbl 0830.35062
Angenent, S. B.; Aronson, D. G.
1995
Asymptotic shape of cusp singularities in curve shortening. Zbl 0829.35058
Angenent, S. B.; Velázquez, J. J. L.
1995
Intermediate asymptotics for convergent viscous gravity currents. Zbl 0832.76020
Angenent, S. B.; Aronson, D. G.
1995
Anisotropic motion of a phase interface. Well-posedness of the initial value problem and qualitative properties of the interface. Zbl 0784.35124
Angenent, Sigurd B.; Gurtin, Morton E.
1994
The dynamics of a degenerate reaction diffusion equation. Zbl 0821.35013
Angenent, Sigurd B.; Aronson, Donald G.
1994
A variational interpretation of Melnikov’s function and exponentionally small separatrix splitting. Zbl 0810.34037
Angenent, Sigurd
1993
Some recent results on mean curvature flow. Zbl 0796.35068
Angenent, Sigurd B.
1993
Shrinking doughnuts. Zbl 0762.53028
Angenent, Sigurd B.
1992
A remark on the topological entropy and invariant circles of an area preserving twistmap. Zbl 0769.58036
Angenent, Sigurd B.
1992
On the formation of singularities in the curve shortening flow. Zbl 0731.53002
Angenent, Sigurd
1991
Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions. Zbl 0749.58054
Angenent, Sigurd
1991
Nodal properties of solutions of parabolic equations. Zbl 0727.35005
Angenent, Sigurd
1991
Nonlinear analytic semiflows. Zbl 0723.34047
Angenent, Sigurd B.
1990
Parabolic equations for curves on surfaces. I: Curves with $$p$$-integrable curvature. Zbl 0789.58070
Angenent, Sigurd
1990
Monotone recurrence relations, their Birkhoff orbits and topological entropy. Zbl 0667.58036
Angenent, Sigurd B.
1990
Solutions of the one-dimensional porous medium equation are determined by their free boundary. Zbl 0679.35040
Angenent, Sigurd
1990
Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface. Zbl 0723.73017
Angenent, Sigurd; Gurtin, Morton E.
1989
The zero set of a solution of a parabolic equation. Zbl 0644.35050
Angenent, Sigurd
1988
The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086
Angenent, S. B.; Fiedler, B.
1988
Local existence and regularity for a class of degenerate parabolic equations. Zbl 0619.35114
Angenent, Sigurd
1988
The periodic orbits of an area preserving twist map. Zbl 0665.58034
Angenent, S. B.
1988
Analyticity of the interface of the porous media equation after the waiting time. Zbl 0653.35040
Angenent, Sigurd
1988
Large time asymptotics for the porous media equation. Zbl 0669.35048
Angenent, Sigurd
1988
One-parameter semigroups. Zbl 0636.47051
Clément, Ph.; Heijmans, H. J. A. M.; Angenent, S.; van Duijn, C. J.; de Pagter, B.
1987
Stable transition layers in a semilinear boundary value problem. Zbl 0634.35041
Angenent, S. B.; Mallet-Paret, John; Peletier, L. A.
1987
The shadowing lemma for elliptic PDE. Zbl 0653.35030
Angenent, Sigurd
1987
The Morse-Smale property for a semilinear parabolic equation. Zbl 0581.58026
Angenent, S. B.
1986
Uniqueness of the solution of a semilinear boundary value problem. Zbl 0576.35044
Angenent, S. B.
1985
all top 5
#### Cited by 1,212 Authors
21 Fiedler, Bernold 20 Angenent, Sigurd Bernardus 20 Giga, Yoshikazu 20 Poláčik, Peter 18 Rocha, Carlos 14 Galaktionov, Victor Aleksandrovich 14 Lou, Bendong 14 Matano, Hiroshi 13 Tsai, Dong-Ho 12 Simonett, Gieri 12 Vazquez, Juan Luis 12 Wang, Xiaoliu 11 Shen, Wenxian 10 Colding, Tobias Holck 9 Du, Yihong 9 Escher, Joachim 9 Minicozzi, William Philip II 9 Souplet, Philippe 9 van den Berg, Jan Bouwe 9 Vandervorst, Robertus C. A. M. 9 Wei, Juncheng 8 Aronson, Donald G. 8 Del Pino, Manuel A. 8 Gurtin, Morton Edward 8 Ishiwata, Tetsuya 8 Knopf, Dan 8 Matioc, Bogdan-Vasile 8 Tannenbaum, Allen Robert 8 Yazaki, Shigetoshi 7 Daskalopoulos, Panagiota 7 Fusco, Giorgio 7 Guo, Jong-Shenq 7 Mizoguchi, Noriko 7 Morini, Massimiliano 7 Rybka, Piotr 6 Clément, Philippe J. E. 6 Hale, Jack Kenneth 6 Knüpfer, Hans 6 Nguyen, Xuan Hien 6 Novaga, Matteo 6 Sesum, Natasa 6 Velázquez, Juan J. L. 6 Webb, Glenn Francis 6 Yanagida, Eiji 6 Zhou, Maolin 5 Calsina, Àngel 5 Chambolle, Antonin 5 Chen, Yongxin 5 de la Llave, Rafael 5 Drugan, Gregory 5 García-Melián, Jorge 5 Giga, Mi-Ho 5 Gnann, Manuel V. 5 Guo, Zongming 5 Hulshof, Josephus 5 Isenberg, James A. 5 Maalaoui, Ali 5 Merle, Frank 5 Pan, Shengliang 5 Prüß, Jan Wilhelm 5 Qin, Wenxin 5 Sinestrari, Carlo 5 Ushijima, Takeo K. 5 Valdinoci, Enrico 5 Wo, Weifeng 5 Zhou, Dun 4 Albanese, Angela Anna 4 Amann, Herbert 4 Boulanouar, Mohamed 4 Chaves, Manuela 4 Chen, Xinfu 4 Chill, Ralph 4 Ducrot, Arnaud 4 Gang, Zhou 4 Garcke, Harald 4 Georgiou, Tryphon T. 4 Giacomelli, Lorenzo 4 Giletti, Thomas 4 Hamel, François 4 Herrero, Miguel Ángel 4 Ivaki, Mohammad N. 4 Jin, Chunhua 4 Kaneko, Yuki 4 Lavrent’ev, Mikhail Mikhaĭlovich jun. 4 LeCrone, Jeremy S. 4 Lin, Yu-Chu 4 MacKay, Robert Sinclair 4 Mangino, Elisabetta M. 4 Matsuzawa, Hiroshi 4 Miquel, Vicente 4 Monneau, Régis 4 Muniz Oliva, Waldyr 4 Ninomiya, Hirokazu 4 Otto, Felix 4 Qu, Changzheng 4 Sabina-de-Lis, José Claudio 4 Shao, Yuanzhen 4 Soner, Halil Mete 4 Wang, Yi 4 Wang, Zenggui ...and 1,112 more Authors
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#### Cited in 227 Serials
116 Journal of Differential Equations 42 Journal of Mathematical Analysis and Applications 35 Transactions of the American Mathematical Society 35 Calculus of Variations and Partial Differential Equations 34 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 Journal of Dynamics and Differential Equations 29 Archive for Rational Mechanics and Analysis 28 The Journal of Geometric Analysis 24 Communications in Partial Differential Equations 21 Proceedings of the American Mathematical Society 20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 18 Mathematische Annalen 18 Journal of Evolution Equations 17 Journal of Functional Analysis 16 Advances in Mathematics 16 Physica D 15 Duke Mathematical Journal 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 13 Discrete and Continuous Dynamical Systems 13 Nonlinear Analysis. Theory, Methods & Applications 12 Mathematische Zeitschrift 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Japan Journal of Industrial and Applied Mathematics 10 SIAM Journal on Mathematical Analysis 10 NoDEA. Nonlinear Differential Equations and Applications 9 Communications on Pure and Applied Mathematics 9 Journal of Computational Physics 9 Inventiones Mathematicae 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal für die Reine und Angewandte Mathematik 7 Communications in Mathematical Physics 7 Ergodic Theory and Dynamical Systems 7 Journal of the American Mathematical Society 7 European Journal of Applied Mathematics 7 Journal of Mathematical Sciences (New York) 6 Applicable Analysis 6 Journal of the Mechanics and Physics of Solids 6 Nonlinearity 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 Journal of Computational and Applied Mathematics 6 Siberian Mathematical Journal 6 Acta Applicandae Mathematicae 6 Annals of Mathematics. Second Series 6 Nonlinear Analysis. Real World Applications 6 Discrete and Continuous Dynamical Systems. Series B 5 Bulletin of the Australian Mathematical Society 5 Journal d’Analyse Mathématique 5 Journal of Mathematical Biology 5 Mathematical Methods in the Applied Sciences 5 Archiv der Mathematik 5 Mathematische Nachrichten 5 Applied Mathematics Letters 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 SIAM Journal on Scientific Computing 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Communications in Contemporary Mathematics 5 Advanced Nonlinear Studies 4 Journal of Statistical Physics 4 Ukrainian Mathematical Journal 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Geometriae Dedicata 4 Semigroup Forum 4 Journal of Nonlinear Science 4 Geometry & Topology 4 Journal of the European Mathematical Society (JEMS) 4 Differential Equations 3 Rocky Mountain Journal of Mathematics 3 Memoirs of the American Mathematical Society 3 Numerische Mathematik 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Rendiconti del Seminario Matematico della Università di Padova 3 Tohoku Mathematical Journal. Second Series 3 Journal of Scientific Computing 3 Bulletin of the American Mathematical Society. New Series 3 Physics of Fluids 3 Positivity 3 Interfaces and Free Boundaries 3 Acta Mathematica Sinica. English Series 3 Multiscale Modeling & Simulation 3 Mediterranean Journal of Mathematics 3 Journal of Biological Dynamics 3 Journal of Fixed Point Theory and Applications 3 Discrete and Continuous Dynamical Systems. Series S 3 Analysis & PDE 3 Science China. Mathematics 2 Computers & Mathematics with Applications 2 Chaos, Solitons and Fractals 2 Annales de l’Institut Fourier 2 Czechoslovak Mathematical Journal 2 Functional Analysis and its Applications 2 Publications Mathématiques 2 Journal of Optimization Theory and Applications 2 Kybernetika 2 Mathematica Slovaca 2 Proceedings of the Japan Academy. Series A 2 Quarterly of Applied Mathematics 2 Results in Mathematics 2 Systems & Control Letters 2 Chinese Annals of Mathematics. Series B 2 Annals of Global Analysis and Geometry ...and 127 more Serials
all top 5
#### Cited in 49 Fields
729 Partial differential equations (35-XX) 292 Differential geometry (53-XX) 134 Dynamical systems and ergodic theory (37-XX) 93 Global analysis, analysis on manifolds (58-XX) 83 Ordinary differential equations (34-XX) 80 Fluid mechanics (76-XX) 75 Operator theory (47-XX) 58 Numerical analysis (65-XX) 52 Biology and other natural sciences (92-XX) 47 Calculus of variations and optimal control; optimization (49-XX) 47 Mechanics of deformable solids (74-XX) 35 Statistical mechanics, structure of matter (82-XX) 27 Classical thermodynamics, heat transfer (80-XX) 24 Manifolds and cell complexes (57-XX) 21 Probability theory and stochastic processes (60-XX) 19 Computer science (68-XX) 17 Convex and discrete geometry (52-XX) 14 Functional analysis (46-XX) 13 Systems theory; control (93-XX) 12 Mechanics of particles and systems (70-XX) 11 Information and communication theory, circuits (94-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Combinatorics (05-XX) 8 Integral equations (45-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Difference and functional equations (39-XX) 5 Measure and integration (28-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Quantum theory (81-XX) 5 Operations research, mathematical programming (90-XX) 4 Real functions (26-XX) 4 General topology (54-XX) 4 Optics, electromagnetic theory (78-XX) 3 Potential theory (31-XX) 3 Geometry (51-XX) 3 Statistics (62-XX) 2 Number theory (11-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Algebraic topology (55-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-05-06T23:27:07 |
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|
https://www.usgs.gov/center-news/volcano-watch-isaac-hale-descendant-has-joined-staff-hvo
|
# Volcano Watch — Isaac Hale descendant has joined the staff at HVO
Release Date:
Hawaiian tradition dictates that travelers chant their genealogies upon meeting to let everyone know where they came from, both literally and figuratively. Since he has already presented his credentials to us, let us now introduce to you Lopaka Lee, who was transferred this week to the Hawaiian Volcano Observatory from the U.S. Geological Survey's offices in Denver, Colorado.
Lopaka Lee between soil cores in the Sierra Nevada foothills, California.
(Public domain.)
Lopaka grew up in Puna and attended Keaau Elementary School (the old one). He was one of the well-known Hale family of Pohoiki, and his grand uncle was Isaac Hale, for whom the popular beach park was named. Isaac was the first Hawaiian killed in the Korean War.
Lopaka's parents met at the University of Hawaii at Manoa and both worked for the Public Health Service, which offered some opportunities to travel. Their first move was to Spokane, Washington, to work with the Nez Pierce and Spokane Indian tribes. Lopaka's dad's family, from Vancouver, Washington, had a summer cabin near Harry Truman's lodge at Spirit Lake on the flank of Mount St. Helens; they saw the volcano often. Little did they realize that, after the May 18, 1980, explosion expelled tons of ash into the air, Lopaka and his classmates would be wearing dust masks to school in Spokane.
The Public Health Service moved the family to Fort Apache, Arizona, where they worked with the White Mountain Apache tribe, and to Tucson, Arizona, where Lopaka graduated from Sabino High School. Going on to college at Northern Arizona University (NAU) in Flagstaff, Lopaka majored in geology, an interest he says was spawned during his childhood in Puna on Kīlauea Volcano. His family also has volcano connections: his mother's family lost their home in the 1960 eruption of Kīlauea that destroyed the town of Kapoho, his dad's family lost their summer cabin on Mount St. Helens in 1980.
While at NAU, he participated in the first controlled flooding of the Grand Canyon. This was an experiment to simulate the seasonal flooding that ceased when the Glenn Canyon Dam was completed in 1963. Among other things, engineers were interested in whether restoring the seasonal floods could replenish beaches and habitats within the canyon.
Sticking with geology, Lopaka did graduate work at the Colorado School of Mines in Golden, Colorado. His thesis on the effect of the nation's largest natural source of lead on the local ground water in the Ozark Mountains earned him a Master of Geological Engineering degree. While at "Mines," Lopaka was hired by the USGS as a SCEP (Student Career Experience Program) student intern at the Federal Center in Denver, and a career was born.
But he really wanted to come back to Hawaii. His parents had retired from the Public Health Service and returned to Hawaii. His mother, Nani Rothfus, works for Hui Malama Ola Na Oiwi, and his father, Gary, is a realtor with Prudential Real Estate on the Big Island. But there are not many opportunities for a skilled earth scientist in Hawaii.
In addition to becoming a geoscientist, Lopaka had been developing an intimate knowledge of computers, networks, and statistics - expertise that HVO desperately needs. The several feet of snow that fell on Denver in the past few months helped seal the deal, and Lopaka and his wife, Holly, arrived last week.
The relocation has posed a few concerns, such as how to convert loads of rock-climbing gear into diving equipment. Lopaka has completed some amazing climbs, including Desert Shield and Space Shot in Zion National Park, Utah, and is hoping to add some amazing dives to his list of experiences. We hope the diving and every other pursuit goes well for this returning native son. Please join us in welcoming Lopaka to the Hawaiian Volcano Observatory.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
This past week, activity levels at the summit of Kīlauea Volcano have remained at background levels. The number of earthquakes located in the summit area is low (usually less than 10 per day are large enough to locate).
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater. Lava is fed through the PKK lava tube from its source on the southwest flank of Puu Oo to the ocean. About 1 kilometer south of Puu Oo, the Campout flow branches off from the PKK tube. The PKK and Campout tubes feed two widely separated ocean entries, at East Laeapuki and East Kailiili, respectively. Both entries are located inside Hawaii Volcanoes National Park.
A third entry, fed by an offshoot of the Campout flow, has been active since December 26. It is located at Kamokuna, about midway between the two older entries. In the last week, intermittent breakouts from the Campout tube have continued on the slope of Pulama pali and on the coastal plain near Kamokuna. A new breakout from the main PKK tube has been advancing down the pali in the past two weeks, more than a kilometer west of the Campout tube. The terminus was less than one mile from the ocean.
Access to the sea cliff near the ocean entries is closed, due to significant hazards. The surrounding area, however, is open. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
No earthquakes of Hawai`i Island were reported felt within the past week.
Mauna Loa is not erupting. During the past week, earthquake activity remained low beneath the volcano's summit (no earthquakes were located). Extension of distances between locations spanning the summit, indicating inflation, continues at slow rates.
| 2021-01-17T12:37:55 |
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|
https://zbmath.org/authors/?q=ai%3Agoss.david
|
# zbMATH — the first resource for mathematics
## Goss, David
Compute Distance To:
Author ID: goss.david Published as: Goss, D.; Goss, David Homepage: https://people.math.osu.edu/goss.3/ External Links: MGP · Wikidata · ResearchGate · GND
Documents Indexed: 50 Publications since 1978, including 4 Books Reviewing Activity: 189 Reviews Biographic References: 1 Publication
all top 5
#### Co-Authors
44 single-authored 2 Sinnott, Warren M. 1 Anglès, Bruno 1 Böckle, Gebhard 1 Hartl, Urs T. 1 Hayes, David Ryan 1 Ngo Dac, Tuan 1 Papanikolas, Matthew A. 1 Pellarin, Federico 1 Roquette, Peter 1 Rosen, Michael I. 1 Tavares Ribeiro, Floric
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#### Serials
7 Journal of Number Theory 5 Duke Mathematical Journal 3 Mathematische Annalen 2 Compositio Mathematica 2 Inventiones Mathematicae 2 Journal of Algebra 2 Proceedings of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 1 Journal für die Reine und Angewandte Mathematik 1 Pacific Journal of Mathematics 1 Transactions of the American Mathematical Society 1 $$K$$-Theory 1 Journal of the Ramanujan Mathematical Society 1 Journal de Théorie des Nombres de Bordeaux 1 Finite Fields and their Applications 1 International Journal of Applied Mathematics and Statistics 1 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
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#### Fields
48 Number theory (11-XX) 17 Algebraic geometry (14-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) 2 Functions of a complex variable (30-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX)
#### Citations contained in zbMATH
41 Publications have been cited 714 times in 425 Documents Cited by Year
Basic structures of function field arithmetic. Zbl 0874.11004
Goss, David
1996
Basic structures of function field arithmetic. 2nd correct. printing. Zbl 0892.11021
Goss, David
1998
The algebraist’s upper half-plane. Zbl 0433.14017
Goss, David
1980
Modular forms for $$\mathbb F_r[T]$$. Zbl 0422.10021
Goss, David
1980
Fourier series, measures and divided power series in the theory of function fields. Zbl 0675.12006
Goss, David
1989
$$\pi$$-adic Eisenstein series for function fields. Zbl 0422.10020
Goss, David
1980
Von Staudt for $$\mathbb F_q[T]$$. Zbl 0404.12013
Goss, David
1978
$$L$$-series of $$t$$-motives and Drinfeld modules. Zbl 0806.11028
Goss, David
1992
The arithmetic of function fields. II: The ’cyclotomic’ theory. Zbl 0516.12010
Goss, David
1983
$$p$$-adic Eisenstein series for function fields. Zbl 0388.10020
Goss, David
1980
Class-groups of function fields. Zbl 0571.12006
Goss, David; Sinnott, Warren
1985
An addendum to “$$v$$-adic zeta functions, $$L$$-series, and measures for function fields”. Zbl 0402.12007
Goss, David
1979
On a new type of $$L$$-function for algebraic curves over finite fields. Zbl 0571.14010
Goss, David
1983
Kummer and Herbrand criterion in the theory of function fields. Zbl 0473.12013
Goss, David
1982
Applications of non-Archimedean integration to the $$L$$-series of $$\tau$$-sheaves. Zbl 1080.11044
Goss, David
2005
A Riemann Hypothesis for characteristic $$p$$ $$L$$-functions. Zbl 1032.11036
Goss, David
2000
The $$\Gamma$$-function in the arithmetic of function fields. Zbl 0661.12006
Goss, David
1988
On the $$L$$-series of F. Pellarin. Zbl 1281.11045
Goss, David
2013
Drinfeld modules: Cohomology and special functions. Zbl 0827.11035
Goss, David
1994
The $$\Gamma$$-ideal and special zeta-values. Zbl 0441.12002
Goss, David
1980
$$v$$-adic zeta functions, $$L$$-series and measures for function fields. Zbl 0402.12006
Goss, David
1979
Some integrals attached to modular forms in the theory of function fields. Zbl 0805.11047
Goss, David
1992
Analogies between global fields. Zbl 0619.12009
Goss, David
1987
Zeta phenomenology. Zbl 1270.11094
Goss, David
2011
A formal Mellin transform in the arithmetic of function fields. Zbl 0746.11026
Goss, David
1991
The impact of the infinite primes on the Riemann hypothesis for characteristic $$p$$ valued $$L$$-series. Zbl 1117.11306
Goss, David
2003
The adjoint of the Carlitz module and Fermat’s Last Theorem. Zbl 0906.11030
Goss, David
1995
The theory of totally real function fields. Zbl 0602.14029
Goss, David
1986
On a Fermat equation arising in the arithmetic theory of functions fields. Zbl 0494.12008
Goss, D.
1982
A simple approach to the analytic continuation and values at negative integers for Riemann’s zeta-function. Zbl 0427.30005
Goss, David
1981
A construction of $$\mathfrak{v}$$-adic modular forms. Zbl 1326.11020
Goss, David
2014
A short introduction to rigid analytic spaces. Zbl 0794.14007
Goss, David
1992
$$L$$-series of Grössencharakters of type $$A_0$$ for function fields. Zbl 0941.11504
Goss, David
1992
The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Zbl 0771.00031
Goss, David (ed.); Hayes, David R. (ed.); Rosen, Michael I. (ed.)
1992
Harmonic analysis and the flow of a Drinfeld module. Zbl 0758.11030
Goss, David
1992
On the holomorphy on certain non-Abelian L-series. Zbl 0575.14019
Goss, David
1985
Zeroes of $$L$$-series in characteristic $$p$$. Zbl 1178.11048
Goss, David
2007
Can a Drinfeld module be modular? Zbl 1062.11034
Goss, David
2002
Special values of Artin L-series. Zbl 0669.12007
Goss, David; Sinnott, Warren
1986
Units and class-groups in the arithmetic theory of function fields. Zbl 0573.12003
Goss, David
1985
Polynomials of binomial type and Lucas’ theorem. Zbl 1347.11049
Goss, David
2016
Polynomials of binomial type and Lucas’ theorem. Zbl 1347.11049
Goss, David
2016
A construction of $$\mathfrak{v}$$-adic modular forms. Zbl 1326.11020
Goss, David
2014
On the $$L$$-series of F. Pellarin. Zbl 1281.11045
Goss, David
2013
Zeta phenomenology. Zbl 1270.11094
Goss, David
2011
Zeroes of $$L$$-series in characteristic $$p$$. Zbl 1178.11048
Goss, David
2007
Applications of non-Archimedean integration to the $$L$$-series of $$\tau$$-sheaves. Zbl 1080.11044
Goss, David
2005
The impact of the infinite primes on the Riemann hypothesis for characteristic $$p$$ valued $$L$$-series. Zbl 1117.11306
Goss, David
2003
Can a Drinfeld module be modular? Zbl 1062.11034
Goss, David
2002
A Riemann Hypothesis for characteristic $$p$$ $$L$$-functions. Zbl 1032.11036
Goss, David
2000
Basic structures of function field arithmetic. 2nd correct. printing. Zbl 0892.11021
Goss, David
1998
Basic structures of function field arithmetic. Zbl 0874.11004
Goss, David
1996
The adjoint of the Carlitz module and Fermat’s Last Theorem. Zbl 0906.11030
Goss, David
1995
Drinfeld modules: Cohomology and special functions. Zbl 0827.11035
Goss, David
1994
$$L$$-series of $$t$$-motives and Drinfeld modules. Zbl 0806.11028
Goss, David
1992
Some integrals attached to modular forms in the theory of function fields. Zbl 0805.11047
Goss, David
1992
A short introduction to rigid analytic spaces. Zbl 0794.14007
Goss, David
1992
$$L$$-series of Grössencharakters of type $$A_0$$ for function fields. Zbl 0941.11504
Goss, David
1992
The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Zbl 0771.00031
Goss, David (ed.); Hayes, David R. (ed.); Rosen, Michael I. (ed.)
1992
Harmonic analysis and the flow of a Drinfeld module. Zbl 0758.11030
Goss, David
1992
A formal Mellin transform in the arithmetic of function fields. Zbl 0746.11026
Goss, David
1991
Fourier series, measures and divided power series in the theory of function fields. Zbl 0675.12006
Goss, David
1989
The $$\Gamma$$-function in the arithmetic of function fields. Zbl 0661.12006
Goss, David
1988
Analogies between global fields. Zbl 0619.12009
Goss, David
1987
The theory of totally real function fields. Zbl 0602.14029
Goss, David
1986
Special values of Artin L-series. Zbl 0669.12007
Goss, David; Sinnott, Warren
1986
Class-groups of function fields. Zbl 0571.12006
Goss, David; Sinnott, Warren
1985
On the holomorphy on certain non-Abelian L-series. Zbl 0575.14019
Goss, David
1985
Units and class-groups in the arithmetic theory of function fields. Zbl 0573.12003
Goss, David
1985
The arithmetic of function fields. II: The ’cyclotomic’ theory. Zbl 0516.12010
Goss, David
1983
On a new type of $$L$$-function for algebraic curves over finite fields. Zbl 0571.14010
Goss, David
1983
Kummer and Herbrand criterion in the theory of function fields. Zbl 0473.12013
Goss, David
1982
On a Fermat equation arising in the arithmetic theory of functions fields. Zbl 0494.12008
Goss, D.
1982
A simple approach to the analytic continuation and values at negative integers for Riemann’s zeta-function. Zbl 0427.30005
Goss, David
1981
The algebraist’s upper half-plane. Zbl 0433.14017
Goss, David
1980
Modular forms for $$\mathbb F_r[T]$$. Zbl 0422.10021
Goss, David
1980
$$\pi$$-adic Eisenstein series for function fields. Zbl 0422.10020
Goss, David
1980
$$p$$-adic Eisenstein series for function fields. Zbl 0388.10020
Goss, David
1980
The $$\Gamma$$-ideal and special zeta-values. Zbl 0441.12002
Goss, David
1980
An addendum to “$$v$$-adic zeta functions, $$L$$-series, and measures for function fields”. Zbl 0402.12007
Goss, David
1979
$$v$$-adic zeta functions, $$L$$-series and measures for function fields. Zbl 0402.12006
Goss, David
1979
Von Staudt for $$\mathbb F_q[T]$$. Zbl 0404.12013
Goss, David
1978
all top 5
#### Cited by 269 Authors
22 Gekeler, Ernst-Ulrich 22 Goss, David 20 Thakur, Dinesh S. 18 Anglès, Bruno 13 Hamahata, Yoshinori 13 Jeong, Sangtae 12 Papanikolas, Matthew A. 12 Pellarin, Federico 11 Pink, Richard 10 Yu, Jing 9 Chang, Chieh-Yu 8 Ghioca, Dragos 7 Breuer, Florian 6 Adam, David 6 Böckle, Gebhard 6 Perkins, Rudolph Bronson 6 Tavares Ribeiro, Floric 5 Bamunoba, Alex Samuel 5 Fukasawa, Satoru 5 Kochubeĭ, Anatoliĭ Naumovych 5 Kontogeorgis, Aristides I. 5 Nguyen Ngoc Dong Quan 5 Petrov, Aleksandar 5 Taelman, Lenny 5 Yang, Zifeng 4 Demangos, Luca 4 El-Guindy, Ahmad 4 Hartl, Urs T. 4 Hsu, Chih-Nung 4 Kuo, Wentang 4 Lara Rodríguez, José Alejandro 4 Lee, Yoonjin 4 Li, Anly 4 Longhi, Ignazio 4 Ngo Dac, Tuan 4 Rosen, Michael I. 4 Wan, Daqing 4 Yin, Linsheng 3 Abhyankar, Shreeram Shankar 3 Bandini, Andrea 3 Bars, Francesc 3 Brownawell, W. Dale 3 Chen, Imin 3 Cornelissen, Gunther 3 Diaz-Vargas, Javier 3 Hayes, David Ryan 3 Logachev, Dmitry 3 López, Bartolomé 3 Poonen, Bjorn 3 Sinnott, Warren M. 3 Taguchi, Yuichiro 3 Vincent, Christelle 3 Yao, Jiayan 3 Yao, Wei-Chen 2 Anderson, Greg W. 2 Bassa, Alp 2 Basson, Dirk 2 Beelen, Pieter Hendrik Turdus 2 Bosser, Vincent 2 Conrad, Keith 2 Damamme, Gilles 2 Deolalikar, Vinay 2 Galovich, Steven 2 Gardeyn, Francis 2 Gezmiş, Oğuz 2 Grishkov, Alexander Nikolaevich 2 Hellegouarch, Yves 2 Hiranouchi, Toshiro 2 Ichimura, Humio 2 Jang, Youngho 2 Kim, Minsoo 2 Kuan, Yen-Liang 2 Li, Chunlan 2 Li, Wen-Ch’ing Winnie 2 Maurischat, Andreas 2 Mishiba, Yoshinori 2 Mohamed-Ahmed, Mohamed-Saadbouh 2 Nan, Ting-Ting 2 Nguyen, Dong Quan Ngoc 2 Okada, Shôzô 2 Reversat, Marc 2 Rück, Hans-Georg 2 Rütsche, Egon 2 Sánchez-Mirafuentes, Marco Antonio 2 Scanlon, Thomas J. 2 Shiomi, Daisuke 2 Sinha, Samarendra K. 2 Teitelbaum, Jeremy T. 2 Traulsen, Matthias 2 Tweedle, David 2 van der Heiden, Gert-Jan 2 Varela Roldán, Enrico 2 Villa-Salvador, Gabriel Daniel 2 Ward, Jacob Kenneth 2 Zhao, Jianqiang 2 Zhao, Zhengjun 2 Zywina, David 1 Akbary, Amir 1 Albert, Maximilian 1 Anbar, Nurdagül ...and 169 more Authors
all top 5
#### Cited in 75 Serials
157 Journal of Number Theory 21 Finite Fields and their Applications 19 Journal de Théorie des Nombres de Bordeaux 16 Journal of Algebra 14 Inventiones Mathematicae 14 Transactions of the American Mathematical Society 12 Proceedings of the American Mathematical Society 11 Mathematische Annalen 7 Compositio Mathematica 7 Journal of Pure and Applied Algebra 7 International Journal of Number Theory 6 Archiv der Mathematik 6 Duke Mathematical Journal 6 Manuscripta Mathematica 6 Mathematische Zeitschrift 5 Monatshefte für Mathematik 4 Israel Journal of Mathematics 4 Rocky Mountain Journal of Mathematics 4 Advances in Mathematics 4 Journal of the American Mathematical Society 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Research in the Mathematical Sciences 3 Communications in Algebra 3 Functiones et Approximatio. Commentarii Mathematici 3 Journal of Soviet Mathematics 3 Mathematische Nachrichten 3 Proceedings of the Japan Academy. Series A 3 Bulletin of the American Mathematical Society. New Series 2 Acta Arithmetica 2 Annales de l’Institut Fourier 2 Journal of Combinatorial Theory. Series A 2 Journal für die Reine und Angewandte Mathematik 2 Mathematika 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Seminario Matematico della Università di Padova 2 Experimental Mathematics 2 The Ramanujan Journal 2 Annals of Mathematics. Second Series 2 Journal of the Australian Mathematical Society 2 Journal of Algebra and its Applications 2 Journal of Noncommutative Geometry 1 Bulletin of the Australian Mathematical Society 1 Indian Journal of Pure & Applied Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Beiträge zur Algebra und Geometrie 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica Vietnamica 1 Geometriae Dedicata 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of the Korean Mathematical Society 1 Journal of the Mathematical Society of Japan 1 Nagoya Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Quaestiones Mathematicae 1 Ricerche di Matematica 1 Advances in Applied Mathematics 1 Physica D 1 Journal of Symbolic Computation 1 $$K$$-Theory 1 Forum Mathematicum 1 Elemente der Mathematik 1 L’Enseignement Mathématique. 2e Série 1 Linear Algebra and its Applications 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Turkish Journal of Mathematics 1 Documenta Mathematica 1 Annals of Combinatorics 1 Journal of the European Mathematical Society (JEMS) 1 Algebra & Number Theory 1 Advances in High Energy Physics 1 Research in Number Theory 1 Actes des Rencontres du C.I.R.M.
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#### Cited in 31 Fields
394 Number theory (11-XX) 81 Algebraic geometry (14-XX) 27 Field theory and polynomials (12-XX) 15 Commutative algebra (13-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Combinatorics (05-XX) 9 Group theory and generalizations (20-XX) 8 Functional analysis (46-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 5 Mathematical logic and foundations (03-XX) 4 Associative rings and algebras (16-XX) 4 Computer science (68-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-19T18:38:41 |
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https://bleach.fandom.com/wiki/User_talk:Arrancar109
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2,401 Pages
# Arrancar109
## Welcome
Welcome to my talk page. As an administrator, I am more than willing to answer any questions or discuss any concerns you may have. I just ask that you keep it civil. When you leave a message, please remember to sign your message with four tildes (~~~~), as it is needed to identify the poster of the message. -- Arrancar109
## SR4
Good news! A 'censored' version of Saints 4 has been approved for release in Australia. Bad news! It isn't compatible with the international release, meaning no co-op. ლ(ಠ益ಠლ
Also FateBlack is great! \o/ 01:46, August 7, 2013 (UTC)
Does one have to be an admin to edit high traffic pages, like Komamura's? I ask because I tried to edit it after the new chapter, and got rejected (basically)M149307 (talk) 09:06, November 6, 2013 (UTC)
## Block Template
I'm tempted to follow through with creating you a custom blocking template :P Kamikaze839 (Talk To Me!!) 02:42 08/9/2013
## Vote Up
The Committee Vote is up on the admin talk page.--Salubri (Chat) 12:03,8/23/2013
## Thanks
You blocked the guy who has made himself my personal enemy and been blanking pages everywhere I've been on this and a previous account...... I'm waiting for VSTF to get him again. Talk to meView my work05:46,9/21/2013 UTC
## Block Request
Yeah so for the guy whose edits you just reverted, he has had too many warnings as it is. Maybe blocking for a week or so might make him listen. Kamikaze839 (Talk To Me!!) 03:55 10/3/2013
## RE:Happy Birthday
Thank you for the wishes!! I had a great time, I had planned to go to a Science museum on Friday but then I got ill that night but the kids had heard and I woke up to them being excited!! I took them anyway and we had such a good time and they had a blast!! Only thing was Eva had a bit of a Runny issue but its fine I just felt bad for her!! They then stayed with me all night and all day Sunday and kept me happy!! Was so much more fun than last year when I got made to go out after a funeral!! I slept all night last night first time in ages so I tired myself out!! SunXia (Chat) 13:30,10/7/2013
## Talk in Chat
Yo Arrancar, next chance you get could you pop into chat with me so we can talk? Just need a favour, that's all. 05:37, October 9, 2013 (UTC)
## re: chat
Yeah me and sal saw you on the recent activity page, but not in chat, we were getting ready to perform virtual konso. Yeah, I like her voice, but I did the best I could to analyze it. I think we need more information. I thought about Colleen for a sec, but the voice does not have the same vocal qualities. Either way its not someone who has done a lot or any voice in the dub before. Also, Sal says make chat work.--LemursYou are about to enter the Twlight Zone 00:54,10/14/2013 00:54, October 14, 2013 (UTC)
## chat issues
Out of curiosity what browser are you using? Sal and I think it might be a browser issue.--LemursYou are about to enter the Twlight Zone 01:01,10/14/2013 01:01, October 14, 2013 (UTC)
This is about the Nozomi Kujo page. According to the Wikipedia page of Amanda Winn-Lee, she is the English voice actress(that could be wrong though). But some of the other here tend to disagree. I wish to get some clarification here on this issue.
SK071 (talk) 13:20, October 14, 2013 (UTC)SK071
## "Blog:Lol"
I think I might have a solution that seemingly undeletable blank blog post. Try (maybe) this, see if it takes you to the right options (dunno if you already tried this). Talk to meView my work12:13,10/18/2013 UTC
## RE Deletion Issue
I asked those I know and they all looked at it, and they are stumped too!! Is there anyway you can do a Special:Contact so that it can be in the job queue for the right people to look at?? Sorry for late reply, I've had the kids all weekend so far!! Sorry wasn't able to do more!! SunXia (Chat) 15:14,10/19/2013
It might have been how I explained it but glad it's working now!! :) SunXia (Chat) 13:31,10/20/2013
## Invitation
You've been invited to chat. To discuss a certain issue. Kamikaze839 (Talk To Me!!) 01:41 11/4/2013
## Affiliation
Hello, Arrancar. I'm an admin from Hunterpedia and I would like to ask for affiliation between our wikis. If you are interested, here is our banner. Thank you. Darkchylde (talk)
## Corrected spelling/grammar
Hi, I was having some issues changing the name of Yhwach back to Juha Bach. I was told to speak to an administrator. Would you be able to help me with that? I believe Yhwach to be the wrong name, chosen due to an error in translation. Your help would be greatly appreciated. Thank you! —This unsigned comment is by Slap2.0 (talkcontribs) . Please sign your posts with ~~~~!
## 547
Oh. Well, alright then that ends that. Sorry for causing any trouble then. xP--GodofFear (talk) 22:43, November 22, 2013 (UTC)
## Apologies
Dear Arrancar109,
## Re: Happy Birthday
Since when have you been under the impression that I've spent a single day of my life sanely? Thanks man, glad to know you're not a zombie just yet.--Xilinoc (talk) 22:55, March 13, 2017 (UTC)
## Question regarding Kenpachi page
Um, hello. Would you mind lending your opinion to the question I posed here: Talk:Kenpachi Zaraki?
FUG.L!F3 (talk) 16:29, June 15, 2017 (UTC)
Thank you for your insightful message and yes I do have a question! All the work I did today in BLEACH Wiki was recently taken down. May I ask why? If there were issues with it and thats why it was taken down, please tell what I did wrong so I can fix it!
Thanks!
Gimmekensei (talk) 06:16, August 25, 2017 (UTC)Gimmekensei
I fully understand, but I wish to make it clear that all the information is completely solid. I currently live in Japan and happened to buy all the Bleach novels and just finished reading them, which is why I have been adding everything I know to the wiki pages.
Even though I fully understand where youre coming from, it would be nice if sometime my work could be recovered! Please let me know when it is okay to add more information to the BLEACH novel wiki pages.
Thank you and sorry for the trouble!
Gimmekensei (talk)Gimmekensei
Alright, and thank you! I understand! Hopefully you dont mind...I went ahead and checked the link to the discussion you mentioned and wrote my own comment.
Gimmekensei
## Light Novel Info
It should be fine for those with the inclination to add content from the light novels to the novels respective pages as long as its referenced and written properly according to the guidelines of the site obviously. That goes with the understanding said information is not to be placed anywhere else on the site. That seems a fair way to handle that. As the information should be documented as anything else we do.--Salubri (Chat) 01:53,8/26/2017
## Forums and Discussions
Hey Arrancar109! I'm Jamie from FANDOM's Community Development team! Not sure if we never asked you if you are interested in turning on the Discussions feature for this community, and migrating the Threaded Forums across as well.
In case you are unaware of the feature, Discussions was introduced last year to help communities engage with users and fans. It lives in its own space on the wiki and allows users to interact with other members of the community. It is also mobile friendly and gives mobile users a chance to contribute and engage with the community, and possibly turn them into wiki editors as well. Discussions also links with our FANDOM Apps, which this community has and it allows app users to easily take part in Discussions as well. You can read more about Discussions here.
For more information on migrating forums to Discussions, you can check out this blog over on Community Central that explains everything in detail.
If you have some concerns, Discussions, and Forums can exist side-by-side in case you do not want to migrate just yet. However, eventually all Forums will be migrated over to Discussions and Forums will be sunsetted as a feature, so getting ahead of the curve is never a bad idea.
Feel free to have an open discussion with your community about this, and I'm available for any questions you might have. Have a good one! Jamie (profile)•(talk) 19:50, November 29, 2017 (UTC)
## AIM shutting down
Been a while since I've seen you online, and this is the only other way I know how to contact you. Is there a chat program you've adopted elsewhere? AIM only has 10 days left before they shut down the service for good. Rashkavar (talk) 05:18, December 6, 2017 (UTC)
Yeah, unless it's the really old one (Ishamael...) it should work. Rashkavar (talk) 19:22, December 6, 2017 (UTC)
## being friends
hi. i'm princess shoting star and i was wondering if you want to be friends with me? --Princess shoting star (talk) 17:12, May 1, 2018 (UTC)
Just wanted to inform you, that missing some info on Ichigo Kurosaki.
Father's Name is not Isshin Kurosaki, but Isshin Shiba (which was revealed in Chapter 529, Page 10). Which is the Uncle of Kūkaku Shiba (quote from Kūkaku Shiba page during "The Thousand-Year Blood War arc" : After Kūkaku sends them on their way, Ganju asks his sister if she is okay with this. Kūkaku tells him that she is and that if he does not go now, the next attack could be the end of Soul Society. Therefore they have to let him go even if their uncle would not be happy.)
`
That Gap in Kūkaku Shiba profile saying "Unknown Uncle" has been identified. It was kinda obvious in that scene and was confirmed in Chapter 529, Page 10. If you could update it, it would be appreciated.
--DeCoyThatGuy (talk) 14:32, May 22, 2018 (UTC) DeCoyThatGuy
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-01-20T15:08:14 |
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https://par.nsf.gov/biblio/10369572-algorithms-covering-multiple-submodular-constraints-applications
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Algorithms for covering multiple submodular constraints and applications
Abstract
We consider the problem of covering multiple submodular constraints. Given a finite ground setN, a weight function$$w: N \rightarrow \mathbb {R}_+$$$w:N\to {R}_{+}$,rmonotone submodular functions$$f_1,f_2,\ldots ,f_r$$${f}_{1},{f}_{2},\dots ,{f}_{r}$overNand requirements$$k_1,k_2,\ldots ,k_r$$${k}_{1},{k}_{2},\dots ,{k}_{r}$the goal is to find a minimum weight subset$$S \subseteq N$$$S\subseteq N$such that$$f_i(S) \ge k_i$$${f}_{i}\left(S\right)\ge {k}_{i}$for$$1 \le i \le r$$$1\le i\le r$. We refer to this problem asMulti-Submod-Coverand it was recently considered by Har-Peled and Jones (Few cuts meet many point sets. CoRR.arxiv:abs1808.03260Har-Peled and Jones 2018) who were motivated by an application in geometry. Even with$$r=1$$$r=1$Multi-Submod-Covergeneralizes the well-known Submodular Set Cover problem (Submod-SC), and it can also be easily reduced toSubmod-SC. A simple greedy algorithm gives an$$O(\log (kr))$$$O\left(log\left(kr\right)\right)$approximation where$$k = \sum _i k_i$$$k={\sum }_{i}{k}_{i}$and this ratio cannot be improved in the general case. In this paper, motivated by several concrete applications, we consider two ways to improve upon the approximation given by the greedy algorithm. First, we give a bicriteria approximation algorithm forMulti-Submod-Coverthat covers each constraint to within a factor of$$(1-1/e-\varepsilon )$$$\left(1-1/e-\epsilon \right)$while incurring an approximation of$$O(\frac{1}{\epsilon }\log r)$$$O\left(\frac{1}{ϵ}logr\right)$in the cost. Second, we consider the special case when each$$f_i$$${f}_{i}$is a obtained from a truncated coverage function and obtain an algorithm that generalizes previous work on partial set cover (Partial-SC), covering integer programs (CIPs) and multiple vertex cover constraints more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10369572
Journal Name:
Journal of Combinatorial Optimization
Volume:
44
Issue:
2
Page Range or eLocation-ID:
p. 979-1010
ISSN:
1382-6905
Publisher:
National Science Foundation
##### More Like this
1. Abstract
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_{i}{x}_{i}$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:
#SAT algorithms fornk-size$\mathcal { C}$$C$-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
#SAT algorithms for$2^{n^{{\varepsilon }}}$${2}^{{n}^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$${2}^{n-{n}^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJACC0THRcircuits of polynomialmore »
2. Abstract
It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.arXiv:2010.09793) that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scenarios such Green function estimates are equivalent to the uniform rectifiability of a set. The present paper tackles a strong analogue of these results, starting with the “flagship degenerate operators on sets with lower dimensional boundaries. We consider the elliptic operators$$L_{\beta ,\gamma } =- {\text {div}}D^{d+1+\gamma -n} \nabla$$${L}_{\beta ,\gamma }=-\text{div}{D}^{d+1+\gamma -n}\nabla$associated to a domain$$\Omega \subset {\mathbb {R}}^n$$$\Omega \subset {R}^{n}$with a uniformly rectifiable boundary$$\Gamma$$$\Gamma$of dimension$$d < n-1$$$d, the now usual distance to the boundary$$D = D_\beta$$$D={D}_{\beta }$given by$$D_\beta (X)^{-\beta } = \int _{\Gamma } |X-y|^{-d-\beta } d\sigma (y)$$${D}_{\beta }{\left(X\right)}^{-\beta }={\int }_{\Gamma }{|X-y|}^{-d-\beta }d\sigma \left(y\right)$for$$X \in \Omega$$$X\in \Omega$, where$$\beta >0$$$\beta >0$and$$\gamma \in (-1,1)$$$\gamma \in \left(-1,1\right)$. In this paper we show that the Green functionGfor$$L_{\beta ,\gamma }$$${L}_{\beta ,\gamma }$, with pole at infinity, is well approximated by multiples of$$D^{1-\gamma }$$${D}^{1-\gamma }$, in the sense that the function$$\big | D\nabla \big (\ln \big ( \frac{G}{D^{1-\gamma }} \big )\big )\big |^2$$$|D\nabla \left(ln\left(\frac{G}{{D}^{1-\gamma }}\right)\right){|}^{2}$satisfies a Carleson measure estimate on$$\Omega$$$\Omega$. We underline that the strong and the weak results are different in nature and, of course, at the levelmore »
3. Abstract
Let us fix a primepand a homogeneous system ofmlinear equations$$a_{j,1}x_1+\dots +a_{j,k}x_k=0$$${a}_{j,1}{x}_{1}+\cdots +{a}_{j,k}{x}_{k}=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$with coefficients$$a_{j,i}\in \mathbb {F}_p$$${a}_{j,i}\in {F}_{p}$. Suppose that$$k\ge 3m$$$k\ge 3m$, that$$a_{j,1}+\dots +a_{j,k}=0$$${a}_{j,1}+\cdots +{a}_{j,k}=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$and that every$$m\times m$$$m×m$minor of the$$m\times k$$$m×k$matrix$$(a_{j,i})_{j,i}$$${\left({a}_{j,i}\right)}_{j,i}$is non-singular. Then we prove that for any (large)n, any subset$$A\subseteq \mathbb {F}_p^n$$$A\subseteq {F}_{p}^{n}$of size$$|A|> C\cdot \Gamma ^n$$$|A|>C·{\Gamma }^{n}$contains a solution$$(x_1,\dots ,x_k)\in A^k$$$\left({x}_{1},\cdots ,{x}_{k}\right)\in {A}^{k}$to the given system of equations such that the vectors$$x_1,\dots ,x_k\in A$$${x}_{1},\cdots ,{x}_{k}\in A$are all distinct. Here,Cand$$\Gamma$$$\Gamma$are constants only depending onp,mandksuch that$$\Gamma $\Gamma . The crucial point here is the condition for the vectors$$x_1,\dots ,x_k$$${x}_{1},\cdots ,{x}_{k}$in the solution$$(x_1,\dots ,x_k)\in A^k$$$\left({x}_{1},\cdots ,{x}_{k}\right)\in {A}^{k}$to be distinct. If we relax this condition and only demand that$$x_1,\dots ,x_k$$${x}_{1},\cdots ,{x}_{k}$are not all equal, then the statement would follow easily from Tao’s slice rank polynomial method. However, handling the distinctness condition is much harder, and requires a new approach. While all previous combinatorial applications of the slice rank polynomial method have relied on the slice rank of diagonal tensors, we use a slice rank argument for a non-diagonal tensor in combination with combinatorial and probabilistic arguments. 4. Abstract Sequence mappability is an important task in genome resequencing. In the (km)-mappability problem, for a given sequenceTof lengthn, the goal is to compute a table whoseith entry is the number of indices$$j \ne i$$$j\ne i$such that the length-msubstrings ofTstarting at positionsiandjhave at mostkmismatches. Previous works on this problem focused on heuristics computing a rough approximation of the result or on the case of$$k=1$$$k=1$. We present several efficient algorithms for the general case of the problem. Our main result is an algorithm that, for$$k=O(1)$$$k=O\left(1\right)$, works in$$O(n)$$$O\left(n\right)$space and, with high probability, in$$O(n \cdot \min \{m^k,\log ^k n\})$$$O\left(n·min\left\{{m}^{k},{log}^{k}n\right\}\right)$time. Our algorithm requires a careful adaptation of thek-errata trees of Cole et al. [STOC 2004] to avoid multiple counting of pairs of substrings. Our technique can also be applied to solve the all-pairs Hamming distance problem introduced by Crochemore et al. [WABI 2017]. We further develop$$O(n^2)$$$O\left({n}^{2}\right)$-time algorithms to computeall(km)-mappability tables for a fixedmand all$$k\in \{0,\ldots ,m\}$$$k\in \left\{0,\dots ,m\right\}$or a fixedkand all$$m\in \{k,\ldots ,n\}$$$m\in \left\{k,\dots ,n\right\}$. Finally, we show that, for$$k,m = \Theta (\log n)$k,m=\Theta \left(logn\right)$, the (km)-mappability problem cannot be solved in strongly subquadratic time unless the Strong Exponential Time Hypothesis fails. This is an improved and extended version of a paper presented at SPIRE 2018.
5. Abstract
We present the KODIAQ-Z survey aimed to characterize the cool, photoionized gas at 2.2 ≲z≲ 3.6 in 202 Hi-selected absorbers with 14.6 ≤$logNHI$< 20 that probe the interface between galaxies and the intergalactic medium (IGM). We find that gas with$14.6≤logNHI<20$at 2.2 ≲z≲ 3.6 can be metal-rich (−1.6 ≲ [X/H] ≲ − 0.2) as seen in damped Lyαabsorbers (DLAs); it can also be very metal-poor ([X/H] < − 2.4) or even pristine ([X/H] < − 3.8), which is not observed in DLAs but is common in the IGM. For$16absorbers, the frequency of pristine absorbers is about 1%–10%, while for$14.6≤logNHI≤16$absorbers it is 10%–20%, similar to the diffuse IGM. Supersolar gas is extremely rare (<1%) at these redshifts. The factor of several thousand spread from the lowest to highest metallicities and large metallicity variations (a factor of a few to >100) between absorbers separated by less than Δv< 500 km s−1imply that the metals are poorly mixed in$14.6≤logNHI<20$gas. We show that these photoionized absorbers contribute to aboutmore »
| 2023-01-31T09:35:23 |
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|
http://math.nist.gov/opsf/misc/mr4.html
|
## OP-SF WEB
### Extract from OP-SF NET
OP-SF NET 4-4 --------- July 15, 1997
From: Tom Koornwinder [email protected]
To: Prof. Keith Dennis (Executive Editor Mathematical Reviews)
Prof. Bernd Wegner (Chefredakteur Zentralblatt fuer Mathematik)
Dear Editors,
Mathematics Subject Classification I send you here a large number of
suggestions from the community of Orthogonal Polynomials and Special
Functions. The SIAM Activity Group on Orthogonal Polynomials and Special
Functions has solicited reactions via the elctronic Newsletter OP-SF Net
(freely available for all interested people) and the printed Newsletter of
the Activity Group (only for members). On the basis of the reactions we
received I have made a comprehensive proposal for changes of those parts
of the 1991 Classification which deal with Orthogonal Plynomials and
Special Functions (in particular part 33). A preliminary version of this
final proposal I recently discussed with prof. Richard Askey, and he
agreed with it.
Experts from our Activity Group are available if you need further
feed-back in the area of Orthogonal Polynomials and Special Functions
With kind regards,
Tom Koornwinder
- 33C45, change into:
Orthogonal polynomials and functions of hypergeometric type
(Jacobi, Laguerre, Hermite, Askey scheme, etc.; see 42C05 for general
orthogonal polynomials and functions)
- add: 33C47 Other special orthogonal polynomials and functions
- 33C50: change into:
Orthogonal polynomials and functions in several variables expressible
in terms of special functions in one variable
- add: 33C52 Orthogonal polynomials and functions associated with root
systems
- 33C55, change into: Spherical harmonics
Motivation: ultraspherical polynomials unrelated to spherical harmonics
are covered by 33C45; spherical functions (on Gelfand pairs) are covered
by 33C80
- add: 33C67 Hypergeometric functions associated with root systems
- 33C80, change into: Connections with groups, algebras and related topics
- 33D10: skip this
Motivation: we know theta functions but we do not know basic theta
functions
- 33D15, change into:
Basic hypergeometric functions in one variable, ${}_r\phi_s$
- 33D20: skip this
Motivation: studying ${}_2\phi_1$ immediately gives rise to
studying more general ${}_r\phi_s$
- 33D45, change into: Basic orthogonal polynomials and functions
- add: 33D50 Orthogonal polynomials and functions in several variables
expressible in terms of basic hypergeometric functions in one variable
- add: 33D52 Basic orthogonal polynomials and functions associated with
root systems (Macdonald polynomials, etc.)
- 33D55: skip this
Motivation: Basic spherical functions in the sense of spherical
functions on quantum groups are covered by 33D80. If basic spherical
harmonics mean the elements in irreducible subspaces of the algebra of
polynomials on a quantum sphere then these are also covered by 33D80.
- add: 33D67 Basic hypergeometric functions associated with root systems
- 33D80, change into: Connections with quantum groups, Chevalley groups,
p-adic groups, Hecke algebras and related topics
- add: 33E12 Mittag-Leffler functions and generaliztions
- add: 33F10 Symbolic computation (Zeilberger algorithm, etc.)
- 34B30, change into:
Special equations (Mathieu, Hill, Bessel, Painlev\'e, etc.)
- add: 40A27 Explicit summation of series
- add: 40A29 Explicit computation of integrals
- add: 40B10 Rearrangements of explicit multiple series
- add: 40B15 Multiple integrals (should also be assigned at least one
other classification number in this section)
- 42C05, change into: Orthogonal functions and polynomials in one
- add: 42C07 Orthogonal functions and polynomials in several variables,
- add: 42C45 Biorthogonal families of functions
| 2017-01-17T23:28:39 |
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|
https://pdglive.lbl.gov/Particle.action?init=0&node=M178&home=MXXX035
|
CHARMED MESONS($\mathit C$ = $\pm1$) ${{\mathit D}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit d}}}$, ${{\mathit D}^{0}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit u}}}$, ${{\overline{\mathit D}}^{0}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit u}}$, ${{\mathit D}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit d}}$, similarly for ${{\mathit D}^{*}}$ 's
#### ${{\mathit D}_{{0}}^{*}{(2300)}^{0}}$
$I(J^P)$ = $1/2(0^{+})$
was ${{\mathit D}_{{0}}^{*}{(2400)}^{0}}$
$\mathit J{}^{P} = 0{}^{+}$ assignment favored (ABE 2004D).
FOOTNOTES
| 2022-12-09T13:34:10 |
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|
https://survivor.togaware.com/datascience/weka-decision-tree.html
|
## 20.66 Weka Decision Tree
The suite of algorithms implemented in Weka are also available to R thanks to .
library(RWeka)
model <- J48(formula=form, data=ds[tr, vars])
model
## J48 pruned tree
## ------------------
##
## humidity_3pm <= 68
## | rain_today=No
## | | wind_gust_speed <= 52
## | | | sunshine <= 7.7
## | | | | pressure_3pm <= 1014.1
## | | | | | humidity_3pm <= 27: No (327.0/33.0)
## | | | | | humidity_3pm > 27
## | | | | | | pressure_3pm <= 1008.3
## | | | | | | | wind_dir_3pm=N
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | wind_speed_3pm <= 19: No (12.0/1.0)
## | | | | | | | | | wind_speed_3pm > 19
## | | | | | | | | | | rainfall <= 0.4
## | | | | | | | | | | | pressure_3pm <= 1007.6: Yes (17.0/4.0)
## | | | | | | | | | | | pressure_3pm > 1007.6: No (3.0)
## | | | | | | | | | | rainfall > 0.4: No (2.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (16.0/4.0)
## | | | | | | | | wind_gust_dir=NE: No (1.0)
## | | | | | | | | wind_gust_dir=ENE: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=E: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSE: No (1.0)
## | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | wind_gust_dir=SSW: Yes (3.0)
## | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (2.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_gust_speed <= 43
## | | | | | | | | | | wind_speed_3pm <= 22: No (7.0)
## | | | | | | | | | | wind_speed_3pm > 22: Yes (2.0)
## | | | | | | | | | wind_gust_speed > 43: Yes (2.0)
## | | | | | | | | wind_gust_dir=WNW: No (4.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | wind_speed_9am <= 13: Yes (4.0)
## | | | | | | | | | wind_speed_9am > 13: No (2.0)
## | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | wind_speed_9am <= 17
## | | | | | | | | | | pressure_3pm <= 1005.1: Yes (8.0)
## | | | | | | | | | | pressure_3pm > 1005.1: No (8.0/3.0)
## | | | | | | | | | wind_speed_9am > 17: No (7.0)
## | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | cloud_3pm <= 6: No (12.0/1.0)
## | | | | | | | | cloud_3pm > 6
## | | | | | | | | | pressure_9am <= 1010.5
## | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | evaporation <= 3.9: No (2.0)
## | | | | | | | | | | | evaporation > 3.9: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (7.0/2.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (3.0/1.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (1.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=W: No (2.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (2.0/1.0)
## | | | | | | | | | | wind_gust_dir=NNW: Yes (4.0/1.0)
## | | | | | | | | | pressure_9am > 1010.5: Yes (10.0)
## | | | | | | | wind_dir_3pm=NE
## | | | | | | | | cloud_3pm <= 4: No (10.0/1.0)
## | | | | | | | | cloud_3pm > 4
## | | | | | | | | | wind_gust_dir=N: Yes (3.0/1.0)
## | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | sunshine <= 2: Yes (3.0)
## | | | | | | | | | | | sunshine > 2: No (3.0)
## | | | | | | | | | | rainfall > 0.1: Yes (2.0)
## | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | evaporation <= 3.7: No (3.0/1.0)
## | | | | | | | | | | evaporation > 3.7: Yes (6.0)
## | | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | | wind_gust_speed <= 37: Yes (8.0)
## | | | | | | | | | | wind_gust_speed > 37: No (4.0)
## | | | | | | | | | wind_gust_dir=E: No (1.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | | wind_gust_dir=SSE: No (1.0)
## | | | | | | | | | wind_gust_dir=S: No (2.0/1.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=WSW: No (1.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | temp_3pm <= 28.8: Yes (2.0)
## | | | | | | | | | | temp_3pm > 28.8: No (2.0)
## | | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NNW: No (2.0/1.0)
## | | | | | | | wind_dir_3pm=ENE: No (53.0/11.0)
## | | | | | | | wind_dir_3pm=E: No (39.0/7.0)
## | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | wind_dir_9am=N: No (3.0)
## | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | wind_dir_9am=NE: Yes (3.0/1.0)
## | | | | | | | | wind_dir_9am=ENE: Yes (4.0)
## | | | | | | | | wind_dir_9am=E: No (3.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (2.0)
## | | | | | | | | wind_dir_9am=SE: Yes (2.0)
## | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | wind_gust_speed <= 35: No (3.0)
## | | | | | | | | | wind_gust_speed > 35: Yes (4.0/1.0)
## | | | | | | | | wind_dir_9am=S
## | | | | | | | | | temp_3pm <= 28: No (2.0)
## | | | | | | | | | temp_3pm > 28: Yes (2.0)
## | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | wind_dir_9am=NNW: No (4.0)
## | | | | | | | wind_dir_3pm=SE
## | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (2.0)
## | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | pressure_3pm <= 1007.1: Yes (3.0)
## | | | | | | | | | pressure_3pm > 1007.1: No (2.0)
## | | | | | | | | wind_gust_dir=ENE: No (1.0)
## | | | | | | | | wind_gust_dir=E: Yes (4.0)
## | | | | | | | | wind_gust_dir=ESE: No (6.0/1.0)
## | | | | | | | | wind_gust_dir=SE: No (11.0/2.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | cloud_3pm <= 6: Yes (3.0)
## | | | | | | | | | cloud_3pm > 6: No (3.0/1.0)
## | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | temp_3pm <= 21.3: Yes (3.0)
## | | | | | | | | | | temp_3pm > 21.3: No (3.0)
## | | | | | | | | | cloud_9am > 6: Yes (5.0)
## | | | | | | | | wind_gust_dir=SW: No (2.0)
## | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | cloud_9am <= 5: Yes (3.0)
## | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | temp_9am <= 15.7: Yes (2.0)
## | | | | | | | | | | temp_9am > 15.7: No (6.0)
## | | | | | | | | wind_gust_dir=WNW: No (2.0)
## | | | | | | | | wind_gust_dir=NW: No (1.0)
## | | | | | | | | wind_gust_dir=NNW: No (2.0)
## | | | | | | | wind_dir_3pm=SSE: No (26.0/8.0)
## | | | | | | | wind_dir_3pm=S: No (35.0/11.0)
## | | | | | | | wind_dir_3pm=SSW: No (44.0/15.0)
## | | | | | | | wind_dir_3pm=SW
## | | | | | | | | rainfall <= 0.1
## | | | | | | | | | humidity_3pm <= 59: No (26.0/1.0)
## | | | | | | | | | humidity_3pm > 59
## | | | | | | | | | | wind_speed_9am <= 13: Yes (7.0/1.0)
## | | | | | | | | | | wind_speed_9am > 13: No (4.0)
## | | | | | | | | rainfall > 0.1: Yes (14.0/5.0)
## | | | | | | | wind_dir_3pm=WSW: No (54.0/21.0)
## | | | | | | | wind_dir_3pm=W: No (67.0/22.0)
## | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | wind_gust_dir=N: Yes (4.0/1.0)
## | | | | | | | | wind_gust_dir=NNE: No (2.0)
## | | | | | | | | wind_gust_dir=NE: Yes (2.0)
## | | | | | | | | wind_gust_dir=ENE: Yes (3.0/1.0)
## | | | | | | | | wind_gust_dir=E: Yes (1.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (4.0)
## | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | wind_gust_dir=SSE: No (3.0)
## | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | wind_gust_dir=SSW: No (2.0)
## | | | | | | | | wind_gust_dir=SW: Yes (2.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (5.0/1.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_dir_9am=N: No (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | wind_dir_9am=WSW: No (3.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | humidity_3pm <= 45: No (2.0)
## | | | | | | | | | | humidity_3pm > 45: Yes (2.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (6.0/1.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | rainfall <= 0.6: No (4.0)
## | | | | | | | | | | rainfall > 0.6: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NNW: No (1.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | humidity_3pm <= 65: No (20.0/6.0)
## | | | | | | | | | humidity_3pm > 65: Yes (6.0/1.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | rainfall <= 0.9: No (15.0/3.0)
## | | | | | | | | | rainfall > 0.9: Yes (2.0)
## | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | cloud_9am <= 6: Yes (5.0)
## | | | | | | | | | cloud_9am > 6: No (5.0/1.0)
## | | | | | | | wind_dir_3pm=NW
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | wind_speed_9am <= 19: No (6.0/1.0)
## | | | | | | | | | wind_speed_9am > 19: Yes (3.0)
## | | | | | | | | wind_gust_dir=NNE: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=NE: No (1.0)
## | | | | | | | | wind_gust_dir=ENE: No (1.0)
## | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | wind_gust_dir=ESE: No (2.0)
## | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | wind_gust_dir=S: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=SSW: Yes (3.0/1.0)
## | | | | | | | | wind_gust_dir=SW: Yes (2.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (8.0/1.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | pressure_3pm <= 1007.2: Yes (10.0)
## | | | | | | | | | pressure_3pm > 1007.2: No (2.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | pressure_3pm <= 1005.6: Yes (7.0)
## | | | | | | | | | pressure_3pm > 1005.6
## | | | | | | | | | | wind_gust_speed <= 35: Yes (2.0)
## | | | | | | | | | | wind_gust_speed > 35: No (4.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | humidity_3pm <= 54: No (2.0)
## | | | | | | | | | | humidity_3pm > 54: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ESE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_gust_speed <= 44: No (3.0)
## | | | | | | | | | | wind_gust_speed > 44: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NW: No (2.0)
## | | | | | | | | | wind_dir_9am=NNW: No (5.0/1.0)
## | | | | | | | | wind_gust_dir=NNW: No (19.0/7.0)
## | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | wind_dir_9am=N
## | | | | | | | | | sunshine <= 6.4: No (21.0/8.0)
## | | | | | | | | | sunshine > 6.4: Yes (6.0)
## | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | evaporation <= 2.1: Yes (5.0)
## | | | | | | | | | evaporation > 2.1: No (12.0/2.0)
## | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | wind_speed_9am <= 13: No (2.0)
## | | | | | | | | | wind_speed_9am > 13: Yes (3.0)
## | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | pressure_3pm <= 1006.5: No (2.0)
## | | | | | | | | | pressure_3pm > 1006.5: Yes (2.0)
## | | | | | | | | wind_dir_9am=E: No (4.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | wind_dir_9am=SE: Yes (3.0/1.0)
## | | | | | | | | wind_dir_9am=SSE: Yes (3.0)
## | | | | | | | | wind_dir_9am=S: No (1.0)
## | | | | | | | | wind_dir_9am=SSW: Yes (1.0)
## | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | wind_dir_9am=WSW: No (1.0)
## | | | | | | | | wind_dir_9am=W: No (3.0/1.0)
## | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | cloud_9am > 5: No (4.0/1.0)
## | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | sunshine <= 7.2: No (7.0)
## | | | | | | | | | sunshine > 7.2: Yes (2.0)
## | | | | | | | | wind_dir_9am=NNW: No (15.0/3.0)
## | | | | | | pressure_3pm > 1008.3
## | | | | | | | cloud_3pm <= 4: No (348.0/57.0)
## | | | | | | | cloud_3pm > 4
## | | | | | | | | wind_gust_speed <= 37
## | | | | | | | | | evaporation <= 3.3
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | pressure_9am <= 1013.8: No (12.0)
## | | | | | | | | | | | pressure_9am > 1013.8
## | | | | | | | | | | | | max_temp <= 19.5: Yes (17.0/5.0)
## | | | | | | | | | | | | max_temp > 19.5: No (15.0/4.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (27.0/11.0)
## | | | | | | | | | | wind_dir_9am=NE: No (15.0/7.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | temp_9am <= 11.8: No (4.0)
## | | | | | | | | | | | temp_9am > 11.8: Yes (8.0/1.0)
## | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | temp_9am <= 15.8: Yes (6.0/1.0)
## | | | | | | | | | | | temp_9am > 15.8: No (4.0)
## | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | humidity_3pm <= 64: No (8.0)
## | | | | | | | | | | | humidity_3pm > 64: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | humidity_3pm <= 50: No (2.0)
## | | | | | | | | | | | humidity_3pm > 50: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | | sunshine <= 3: Yes (3.0)
## | | | | | | | | | | | sunshine > 3: No (3.0)
## | | | | | | | | | | wind_dir_9am=S: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=SW: No (14.0/4.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | sunshine <= 4.8: Yes (2.0)
## | | | | | | | | | | | sunshine > 4.8: No (5.0)
## | | | | | | | | | | wind_dir_9am=W: No (12.0/5.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | wind_speed_3pm <= 7: Yes (3.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 7: No (7.0)
## | | | | | | | | | | wind_dir_9am=NW: No (24.0/2.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (17.0/4.0)
## | | | | | | | | | evaporation > 3.3: No (650.0/130.0)
## | | | | | | | | wind_gust_speed > 37
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | cloud_3pm <= 6: Yes (12.0/4.0)
## | | | | | | | | | | | | cloud_3pm > 6: No (16.0/5.0)
## | | | | | | | | | | | rainfall > 0.1: Yes (11.0/1.0)
## | | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | | rainfall <= 0.2
## | | | | | | | | | | | | cloud_9am <= 6: Yes (2.0)
## | | | | | | | | | | | | cloud_9am > 6
## | | | | | | | | | | | | | wind_gust_speed <= 46: No (7.0/2.0)
## | | | | | | | | | | | | | wind_gust_speed > 46: Yes (2.0)
## | | | | | | | | | | | rainfall > 0.2: No (2.0)
## | | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | | humidity_9am <= 58: No (3.0)
## | | | | | | | | | | | humidity_9am > 58: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (2.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | wind_speed_3pm <= 20
## | | | | | | | | | | | | pressure_9am <= 1016.5: Yes (6.0)
## | | | | | | | | | | | | pressure_9am > 1016.5: No (3.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 20: No (3.0)
## | | | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | evaporation <= 2.8: No (3.0/1.0)
## | | | | | | | | | | | evaporation > 2.8: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | cloud_3pm <= 7: No (15.0/1.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | cloud_9am <= 6: Yes (3.0/1.0)
## | | | | | | | | | | | cloud_9am > 6: No (10.0/2.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | max_temp <= 20
## | | | | | | | | | | | | humidity_9am <= 71: No (4.0)
## | | | | | | | | | | | | humidity_9am > 71: Yes (4.0)
## | | | | | | | | | | | max_temp > 20: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | cloud_9am <= 4: No (2.0)
## | | | | | | | | | | | cloud_9am > 4: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | wind_speed_9am <= 11: No (2.0)
## | | | | | | | | | | | wind_speed_9am > 11: Yes (6.0)
## | | | | | | | | | | wind_dir_9am=E: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (2.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (2.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (5.0/1.0)
## | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | min_temp <= 18.3: No (6.0)
## | | | | | | | | | | | min_temp > 18.3: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (9.0/4.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | humidity_3pm <= 51: No (3.0/1.0)
## | | | | | | | | | | | humidity_3pm > 51: Yes (8.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (8.0/1.0)
## | | | | | | | | | | wind_dir_9am=E: No (5.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SE: No (1.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | temp_9am <= 21.1: Yes (19.0/8.0)
## | | | | | | | | | | temp_9am > 21.1: No (43.0/11.0)
## | | | | | | | | | wind_dir_3pm=E: No (58.0/16.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (51.0/11.0)
## | | | | | | | | | wind_dir_3pm=SE: No (76.0/22.0)
## | | | | | | | | | wind_dir_3pm=SSE: No (40.0/8.0)
## | | | | | | | | | wind_dir_3pm=S: No (72.0/17.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (40.0/9.0)
## | | | | | | | | | wind_dir_3pm=SW: No (83.0/17.0)
## | | | | | | | | | wind_dir_3pm=WSW: No (68.0/19.0)
## | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | max_temp <= 19.7: No (4.0)
## | | | | | | | | | | | max_temp > 19.7: Yes (7.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=SW: No (4.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | | sunshine <= 6.1
## | | | | | | | | | | | | | | pressure_3pm <= 1010.6: No (2.0)
## | | | | | | | | | | | | | | pressure_3pm > 1010.6: Yes (3.0)
## | | | | | | | | | | | | | sunshine > 6.1: No (6.0)
## | | | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | | | rainfall > 0.1: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | humidity_3pm <= 58: No (7.0/1.0)
## | | | | | | | | | | | humidity_3pm > 58: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | cloud_3pm <= 7: No (8.0/1.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | wind_speed_9am <= 9: Yes (3.0)
## | | | | | | | | | | | wind_speed_9am > 9
## | | | | | | | | | | | | sunshine <= 4.9: No (4.0)
## | | | | | | | | | | | | sunshine > 4.9
## | | | | | | | | | | | | | max_temp <= 25: Yes (2.0)
## | | | | | | | | | | | | | max_temp > 25: No (3.0/1.0)
## | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | humidity_3pm <= 50: No (39.0/7.0)
## | | | | | | | | | | humidity_3pm > 50
## | | | | | | | | | | | pressure_3pm <= 1012.4: Yes (12.0)
## | | | | | | | | | | | pressure_3pm > 1012.4
## | | | | | | | | | | | | wind_dir_9am=N: No (4.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (2.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (2.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | max_temp <= 18.4: No (23.0/3.0)
## | | | | | | | | | | max_temp > 18.4: Yes (46.0/16.0)
## | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | pressure_9am <= 1016.1
## | | | | | | | | | | | | wind_gust_dir=N: No (9.0)
## | | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=W: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | | cloud_9am <= 6: Yes (4.0)
## | | | | | | | | | | | | | cloud_9am > 6: No (2.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: No (9.0/1.0)
## | | | | | | | | | | | pressure_9am > 1016.1: Yes (14.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | evaporation <= 4.5
## | | | | | | | | | | | | cloud_3pm <= 6: No (3.0/1.0)
## | | | | | | | | | | | | cloud_3pm > 6: Yes (10.0/1.0)
## | | | | | | | | | | | evaporation > 4.5: No (7.0/1.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | wind_speed_9am <= 13: Yes (3.0)
## | | | | | | | | | | | wind_speed_9am > 13: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | pressure_9am <= 1014.2: No (2.0)
## | | | | | | | | | | | pressure_9am > 1014.2: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | rainfall <= 0.3
## | | | | | | | | | | | | wind_speed_3pm <= 22: No (13.0/2.0)
## | | | | | | | | | | | | wind_speed_3pm > 22: Yes (2.0)
## | | | | | | | | | | | rainfall > 0.3: Yes (3.0)
## | | | | pressure_3pm > 1014.1: No (7409.0/1001.0)
## | | | sunshine > 7.7
## | | | | humidity_3pm <= 51: No (52131.0/2192.0)
## | | | | humidity_3pm > 51
## | | | | | min_temp <= 24
## | | | | | | max_temp <= 22.3
## | | | | | | | pressure_3pm <= 1013.3
## | | | | | | | | pressure_3pm <= 1005.2
## | | | | | | | | | evaporation <= 2
## | | | | | | | | | | wind_speed_9am <= 9
## | | | | | | | | | | | temp_9am <= 8.6: Yes (3.0)
## | | | | | | | | | | | temp_9am > 8.6: No (2.0)
## | | | | | | | | | | wind_speed_9am > 9: No (13.0)
## | | | | | | | | | evaporation > 2
## | | | | | | | | | | wind_gust_speed <= 31: No (15.0/6.0)
## | | | | | | | | | | wind_gust_speed > 31: Yes (94.0/30.0)
## | | | | | | | | pressure_3pm > 1005.2
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | cloud_3pm <= 3: No (22.0/1.0)
## | | | | | | | | | | cloud_3pm > 3
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | wind_gust_speed <= 39: No (8.0)
## | | | | | | | | | | | | wind_gust_speed > 39
## | | | | | | | | | | | | | cloud_9am <= 5: No (4.0/1.0)
## | | | | | | | | | | | | | cloud_9am > 5: Yes (17.0/6.0)
## | | | | | | | | | | | wind_gust_dir=NNE: No (8.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (8.0/2.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=E: No (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (2.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | | | pressure_3pm <= 1008.4: Yes (2.0)
## | | | | | | | | | | | | pressure_3pm > 1008.4: No (2.0)
## | | | | | | | | | | | wind_gust_dir=S: No (2.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SSW: No (3.0)
## | | | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | | | cloud_3pm <= 6: No (3.0)
## | | | | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | | | wind_speed_9am <= 7: No (9.0)
## | | | | | | | | | | | | wind_speed_9am > 7: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | temp_9am <= 12: No (6.0)
## | | | | | | | | | | | | temp_9am > 12
## | | | | | | | | | | | | | max_temp <= 21.8: Yes (26.0/4.0)
## | | | | | | | | | | | | | max_temp > 21.8: No (3.0)
## | | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | | evaporation <= 4.6: Yes (2.0)
## | | | | | | | | | | | | evaporation > 4.6
## | | | | | | | | | | | | | sunshine <= 8.7
## | | | | | | | | | | | | | | wind_speed_9am <= 2: Yes (4.0)
## | | | | | | | | | | | | | | wind_speed_9am > 2
## | | | | | | | | | | | | | | | temp_9am <= 13.9: No (4.0)
## | | | | | | | | | | | | | | | temp_9am > 13.9: Yes (2.0)
## | | | | | | | | | | | | | sunshine > 8.7: No (2.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | wind_dir_3pm=N: Yes (3.0)
## | | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=W: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=WNW: Yes (3.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=NW: No (10.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=NNW: No (6.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | | humidity_9am <= 67: No (4.0)
## | | | | | | | | | | | | humidity_9am > 67
## | | | | | | | | | | | | | temp_9am <= 4.5: No (3.0)
## | | | | | | | | | | | | | temp_9am > 4.5: Yes (14.0/2.0)
## | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | temp_9am <= 9.1: No (11.0)
## | | | | | | | | | | temp_9am > 9.1
## | | | | | | | | | | | wind_gust_speed <= 30: No (5.0)
## | | | | | | | | | | | wind_gust_speed > 30: Yes (43.0/13.0)
## | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | wind_speed_3pm <= 20: Yes (30.0/9.0)
## | | | | | | | | | | wind_speed_3pm > 20: No (12.0/2.0)
## | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | max_temp <= 19.3: Yes (11.0/5.0)
## | | | | | | | | | | max_temp > 19.3: No (12.0)
## | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | cloud_9am <= 6: No (24.0/5.0)
## | | | | | | | | | | cloud_9am > 6: Yes (10.0/4.0)
## | | | | | | | | | wind_dir_9am=ESE: No (38.0/14.0)
## | | | | | | | | | wind_dir_9am=SE: No (46.0/10.0)
## | | | | | | | | | wind_dir_9am=SSE: No (45.0/10.0)
## | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | wind_gust_speed <= 46: No (34.0/9.0)
## | | | | | | | | | | wind_gust_speed > 46: Yes (4.0)
## | | | | | | | | | wind_dir_9am=SSW: No (39.0/8.0)
## | | | | | | | | | wind_dir_9am=SW: No (65.0/10.0)
## | | | | | | | | | wind_dir_9am=WSW: No (63.0/20.0)
## | | | | | | | | | wind_dir_9am=W: No (86.0/24.0)
## | | | | | | | | | wind_dir_9am=WNW: No (85.0/33.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | temp_3pm <= 20.7: No (102.0/25.0)
## | | | | | | | | | | temp_3pm > 20.7
## | | | | | | | | | | | humidity_9am <= 74
## | | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | | pressure_3pm <= 1011.2: No (6.0/2.0)
## | | | | | | | | | | | | | pressure_3pm > 1011.2: Yes (4.0/1.0)
## | | | | | | | | | | | | rainfall > 0.1: No (3.0)
## | | | | | | | | | | | humidity_9am > 74: Yes (11.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | rainfall <= 0.4
## | | | | | | | | | | | | min_temp <= 4.2: Yes (3.0)
## | | | | | | | | | | | | min_temp > 4.2: No (13.0/3.0)
## | | | | | | | | | | | rainfall > 0.4: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=NNE: No (2.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (3.0)
## | | | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=E: No (2.0)
## | | | | | | | | | | wind_dir_3pm=ESE: No (3.0)
## | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | humidity_9am <= 67: No (3.0)
## | | | | | | | | | | | humidity_9am > 67: Yes (10.0/2.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SSW: No (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | wind_gust_speed <= 33: No (2.0)
## | | | | | | | | | | | wind_gust_speed > 33: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=WSW: No (2.0/1.0)
## | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | | max_temp <= 20.5: Yes (3.0)
## | | | | | | | | | | | | max_temp > 20.5: No (6.0)
## | | | | | | | | | | | cloud_3pm > 6: No (3.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | min_temp <= 5.9: No (9.0)
## | | | | | | | | | | | min_temp > 5.9
## | | | | | | | | | | | | humidity_3pm <= 62
## | | | | | | | | | | | | | min_temp <= 7.8: Yes (3.0)
## | | | | | | | | | | | | | min_temp > 7.8
## | | | | | | | | | | | | | | wind_speed_9am <= 17: No (7.0)
## | | | | | | | | | | | | | | wind_speed_9am > 17
## | | | | | | | | | | | | | | | temp_9am <= 13.2: No (2.0)
## | | | | | | | | | | | | | | | temp_9am > 13.2: Yes (2.0)
## | | | | | | | | | | | | humidity_3pm > 62: Yes (4.0)
## | | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | | evaporation <= 3.7: No (3.0)
## | | | | | | | | | | | evaporation > 3.7
## | | | | | | | | | | | | wind_gust_dir=N: No (1.0)
## | | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SW: No (1.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=W: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: No (2.0)
## | | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | | humidity_3pm <= 53: No (2.0)
## | | | | | | | | | | | | | humidity_3pm > 53
## | | | | | | | | | | | | | | wind_speed_9am <= 17: Yes (6.0)
## | | | | | | | | | | | | | | wind_speed_9am > 17: No (3.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | pressure_9am <= 1015.9: No (12.0/1.0)
## | | | | | | | | | | | | pressure_9am > 1015.9: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 6: Yes (5.0)
## | | | | | | | pressure_3pm > 1013.3: No (12026.0/1262.0)
## | | | | | | max_temp > 22.3: No (13284.0/1366.0)
## | | | | | min_temp > 24
## | | | | | | wind_gust_speed <= 44: No (898.0/183.0)
## | | | | | | wind_gust_speed > 44
## | | | | | | | sunshine <= 10.6
## | | | | | | | | wind_dir_3pm=N: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (3.0/1.0)
## | | | | | | | | wind_dir_3pm=NE: No (3.0)
## | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | sunshine <= 8.7
## | | | | | | | | | | humidity_3pm <= 62: No (15.0)
## | | | | | | | | | | humidity_3pm > 62: Yes (4.0/1.0)
## | | | | | | | | | sunshine > 8.7: Yes (3.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | cloud_9am <= 7: No (8.0/1.0)
## | | | | | | | | | cloud_9am > 7: Yes (3.0)
## | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | sunshine <= 8.3: Yes (2.0)
## | | | | | | | | | sunshine > 8.3
## | | | | | | | | | | wind_speed_9am <= 13: Yes (2.0)
## | | | | | | | | | | wind_speed_9am > 13: No (6.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | max_temp <= 31.9: Yes (5.0/1.0)
## | | | | | | | | | max_temp > 31.9: No (6.0)
## | | | | | | | | wind_dir_3pm=SSE: Yes (2.0)
## | | | | | | | | wind_dir_3pm=S: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW: No (1.0)
## | | | | | | | | wind_dir_3pm=SW: No (6.0/1.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=W: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (16.0/2.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (5.0)
## | | | | | | | sunshine > 10.6: No (13.0)
## | | wind_gust_speed > 52
## | | | sunshine <= 10.1
## | | | | sunshine <= 7.7
## | | | | | pressure_3pm <= 1014.8
## | | | | | | humidity_3pm <= 45
## | | | | | | | sunshine <= 5.6
## | | | | | | | | pressure_3pm <= 1005.2
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | cloud_3pm <= 6: No (9.0/2.0)
## | | | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | | | humidity_9am <= 47: Yes (7.0/1.0)
## | | | | | | | | | | | | humidity_9am > 47: No (9.0/3.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=NE: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SW: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=WSW: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=W: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=WNW: No (8.0/2.0)
## | | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | | rainfall <= 0.2
## | | | | | | | | | | | | wind_speed_9am <= 28
## | | | | | | | | | | | | | cloud_3pm <= 6: No (3.0/1.0)
## | | | | | | | | | | | | | cloud_3pm > 6: Yes (4.0)
## | | | | | | | | | | | | wind_speed_9am > 28: No (3.0)
## | | | | | | | | | | | rainfall > 0.2: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | cloud_3pm <= 6: No (4.0)
## | | | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | | | pressure_9am <= 1005.7: No (4.0/1.0)
## | | | | | | | | | | | | pressure_9am > 1005.7: Yes (5.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (23.0/5.0)
## | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | humidity_9am <= 53: Yes (5.0)
## | | | | | | | | | | humidity_9am > 53: No (3.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (3.0)
## | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | humidity_3pm <= 24: No (3.0)
## | | | | | | | | | | humidity_3pm > 24: Yes (3.0)
## | | | | | | | | | wind_dir_9am=ESE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (4.0/1.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (3.0)
## | | | | | | | | | wind_dir_9am=W: Yes (1.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | temp_3pm <= 23.8: Yes (9.0/2.0)
## | | | | | | | | | | temp_3pm > 23.8: No (8.0/2.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (18.0/6.0)
## | | | | | | | | pressure_3pm > 1005.2
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | evaporation <= 11.2
## | | | | | | | | | | | | | pressure_3pm <= 1007.7: No (11.0)
## | | | | | | | | | | | | | pressure_3pm > 1007.7
## | | | | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | | | | min_temp <= 9: Yes (3.0)
## | | | | | | | | | | | | | | | min_temp > 9: No (7.0/1.0)
## | | | | | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | | | | | temp_3pm <= 21: No (3.0)
## | | | | | | | | | | | | | | | temp_3pm > 21: Yes (2.0)
## | | | | | | | | | | | | | | wind_dir_9am=NE: Yes (2.0)
## | | | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | | | | wind_dir_9am=NNW: No (1.0)
## | | | | | | | | | | | | evaporation > 11.2: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | | | humidity_9am <= 65: Yes (2.0)
## | | | | | | | | | | | | humidity_9am > 65: No (2.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=WSW: No (2.0)
## | | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | | wind_gust_dir=WNW: No (1.0)
## | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NNW: Yes (4.0/1.0)
## | | | | | | | | | | cloud_3pm > 7: Yes (7.0)
## | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | wind_speed_3pm <= 17: Yes (7.0/2.0)
## | | | | | | | | | | | wind_speed_3pm > 17: No (16.0/3.0)
## | | | | | | | | | | cloud_3pm > 7: Yes (8.0/2.0)
## | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | cloud_3pm <= 6: Yes (3.0)
## | | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | | temp_3pm <= 24.8: Yes (4.0/1.0)
## | | | | | | | | | | | temp_3pm > 24.8: No (6.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | evaporation <= 8.3: No (5.0)
## | | | | | | | | | | evaporation > 8.3: Yes (5.0/1.0)
## | | | | | | | | | wind_dir_3pm=E: No (6.0/1.0)
## | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | wind_speed_3pm <= 15: Yes (3.0)
## | | | | | | | | | | wind_speed_3pm > 15: No (6.0/1.0)
## | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | pressure_3pm <= 1006.1: No (2.0)
## | | | | | | | | | | pressure_3pm > 1006.1: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | cloud_9am <= 7: No (2.0)
## | | | | | | | | | | cloud_9am > 7: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | humidity_9am <= 39: No (3.0)
## | | | | | | | | | | humidity_9am > 39: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (6.0)
## | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | pressure_3pm <= 1008.5: Yes (3.0)
## | | | | | | | | | | pressure_3pm > 1008.5: No (4.0)
## | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | temp_9am <= 25.7
## | | | | | | | | | | | pressure_9am <= 1013.7: No (10.0)
## | | | | | | | | | | | pressure_9am > 1013.7: Yes (2.0)
## | | | | | | | | | | temp_9am > 25.7: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=W: No (18.0/3.0)
## | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | rainfall <= 0.1: No (23.0/3.0)
## | | | | | | | | | | rainfall > 0.1: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | humidity_9am <= 44: No (7.0)
## | | | | | | | | | | humidity_9am > 44
## | | | | | | | | | | | wind_gust_speed <= 61
## | | | | | | | | | | | | wind_dir_9am=N: Yes (6.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (3.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_speed > 61: Yes (9.0)
## | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | wind_gust_speed <= 54
## | | | | | | | | | | | | humidity_3pm <= 40: No (4.0)
## | | | | | | | | | | | | humidity_3pm > 40: Yes (3.0)
## | | | | | | | | | | | wind_gust_speed > 54: No (24.0)
## | | | | | | | | | | cloud_9am > 7: Yes (3.0)
## | | | | | | | sunshine > 5.6: No (426.0/124.0)
## | | | | | | humidity_3pm > 45
## | | | | | | | wind_speed_9am <= 28
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | temp_3pm <= 21.2
## | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | temp_9am <= 11.6
## | | | | | | | | | | | | humidity_3pm <= 64: No (20.0/3.0)
## | | | | | | | | | | | | humidity_3pm > 64: Yes (3.0)
## | | | | | | | | | | | temp_9am > 11.6: Yes (20.0/6.0)
## | | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | | pressure_3pm <= 1013.2: No (7.0/1.0)
## | | | | | | | | | | | | pressure_3pm > 1013.2: Yes (4.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=SW: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=W: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=WNW: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NW: Yes (5.0/2.0)
## | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | wind_speed_9am <= 26: Yes (12.0/1.0)
## | | | | | | | | | | | | wind_speed_9am > 26: No (3.0/1.0)
## | | | | | | | | | | | rainfall > 0.1: No (3.0/1.0)
## | | | | | | | | | temp_3pm > 21.2: Yes (13.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (21.0/8.0)
## | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | cloud_9am <= 7: No (9.0/3.0)
## | | | | | | | | | cloud_9am > 7: Yes (3.0)
## | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | sunshine <= 4.9: Yes (4.0)
## | | | | | | | | | sunshine > 4.9: No (3.0)
## | | | | | | | | wind_gust_dir=E
## | | | | | | | | | wind_gust_speed <= 57: No (12.0/5.0)
## | | | | | | | | | wind_gust_speed > 57: Yes (7.0)
## | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | pressure_3pm <= 1006.9: Yes (6.0/1.0)
## | | | | | | | | | pressure_3pm > 1006.9: No (6.0)
## | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | evaporation <= 6.1: No (4.0)
## | | | | | | | | | evaporation > 6.1: Yes (5.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | cloud_9am <= 6: Yes (9.0)
## | | | | | | | | | cloud_9am > 6
## | | | | | | | | | | wind_gust_speed <= 65: No (5.0/1.0)
## | | | | | | | | | | wind_gust_speed > 65: Yes (2.0)
## | | | | | | | | wind_gust_dir=S: No (20.0/4.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | pressure_9am <= 1007.5: Yes (9.0/1.0)
## | | | | | | | | | pressure_9am > 1007.5: No (13.0/2.0)
## | | | | | | | | wind_gust_dir=SW: Yes (35.0/11.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (52.0/20.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_gust_speed <= 54
## | | | | | | | | | | temp_3pm <= 19.5: No (9.0)
## | | | | | | | | | | temp_3pm > 19.5: Yes (5.0/1.0)
## | | | | | | | | | wind_gust_speed > 54: Yes (75.0/13.0)
## | | | | | | | | wind_gust_dir=WNW: Yes (77.0/25.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | wind_dir_9am=N: Yes (26.0/5.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (1.0)
## | | | | | | | | | wind_dir_9am=E: No (1.0)
## | | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=W: No (2.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | wind_speed_9am <= 24: No (5.0)
## | | | | | | | | | | wind_speed_9am > 24: Yes (3.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | humidity_3pm <= 57
## | | | | | | | | | | | pressure_3pm <= 998.1: Yes (5.0/1.0)
## | | | | | | | | | | | pressure_3pm > 998.1: No (14.0)
## | | | | | | | | | | humidity_3pm > 57: Yes (7.0/1.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (61.0/20.0)
## | | | | | | | wind_speed_9am > 28
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | pressure_9am <= 1006.7: Yes (7.0/1.0)
## | | | | | | | | | | | pressure_9am > 1006.7
## | | | | | | | | | | | | cloud_3pm <= 4: No (8.0)
## | | | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | | | cloud_9am <= 4: No (5.0)
## | | | | | | | | | | | | | cloud_9am > 4
## | | | | | | | | | | | | | | pressure_9am <= 1016.6: No (21.0/4.0)
## | | | | | | | | | | | | | | pressure_9am > 1016.6
## | | | | | | | | | | | | | | | sunshine <= 2.1: No (3.0)
## | | | | | | | | | | | | | | | sunshine > 2.1: Yes (6.0)
## | | | | | | | | | | wind_gust_dir=NNE: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NNE: No (6.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | wind_speed_9am <= 33: Yes (3.0)
## | | | | | | | | | | wind_speed_9am > 33: No (5.0)
## | | | | | | | | | wind_gust_dir=NNE: No (6.0)
## | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | wind_gust_dir=WNW: No (1.0)
## | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | temp_3pm <= 22.6: Yes (3.0)
## | | | | | | | | | temp_3pm > 22.6: No (2.0)
## | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | pressure_9am <= 1013.9: Yes (3.0)
## | | | | | | | | | pressure_9am > 1013.9: No (4.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (1.0)
## | | | | | | | | wind_dir_3pm=SE: Yes (5.0)
## | | | | | | | | wind_dir_3pm=SSE: No (4.0/1.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | wind_gust_speed <= 65: No (5.0/1.0)
## | | | | | | | | | | wind_gust_speed > 65: Yes (2.0)
## | | | | | | | | | cloud_9am > 7: No (3.0)
## | | | | | | | | wind_dir_3pm=SSW: No (5.0/1.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | temp_3pm <= 12: Yes (2.0)
## | | | | | | | | | temp_3pm > 12: No (5.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | rainfall <= 0.1: No (4.0)
## | | | | | | | | | rainfall > 0.1
## | | | | | | | | | | temp_9am <= 11.5: No (2.0)
## | | | | | | | | | | temp_9am > 11.5: Yes (3.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | temp_9am <= 11.8: Yes (5.0/1.0)
## | | | | | | | | | temp_9am > 11.8: No (21.0/5.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | min_temp <= 11.9: Yes (12.0/3.0)
## | | | | | | | | | min_temp > 11.9: No (5.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | wind_gust_speed <= 70
## | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | humidity_9am <= 68: Yes (7.0)
## | | | | | | | | | | | humidity_9am > 68: No (3.0/1.0)
## | | | | | | | | | | cloud_3pm > 6: No (7.0/1.0)
## | | | | | | | | | wind_gust_speed > 70: Yes (14.0)
## | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | sunshine <= 6: Yes (11.0)
## | | | | | | | | | sunshine > 6: No (7.0/1.0)
## | | | | | pressure_3pm > 1014.8
## | | | | | | rainfall <= 0.3: No (520.0/111.0)
## | | | | | | rainfall > 0.3
## | | | | | | | wind_gust_dir=N
## | | | | | | | | evaporation <= 4.6: No (7.0)
## | | | | | | | | evaporation > 4.6: Yes (2.0)
## | | | | | | | wind_gust_dir=NNE: Yes (1.0)
## | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | wind_gust_dir=ENE: Yes (1.0)
## | | | | | | | wind_gust_dir=E
## | | | | | | | | humidity_3pm <= 60: No (3.0)
## | | | | | | | | humidity_3pm > 60: Yes (2.0)
## | | | | | | | wind_gust_dir=ESE: Yes (2.0)
## | | | | | | | wind_gust_dir=SE: No (5.0/1.0)
## | | | | | | | wind_gust_dir=SSE: No (2.0)
## | | | | | | | wind_gust_dir=S
## | | | | | | | | wind_speed_9am <= 31: No (5.0/1.0)
## | | | | | | | | wind_speed_9am > 31: Yes (2.0)
## | | | | | | | wind_gust_dir=SSW
## | | | | | | | | humidity_3pm <= 58: No (3.0)
## | | | | | | | | humidity_3pm > 58: Yes (4.0)
## | | | | | | | wind_gust_dir=SW: No (8.0/2.0)
## | | | | | | | wind_gust_dir=WSW
## | | | | | | | | humidity_9am <= 74: No (5.0)
## | | | | | | | | humidity_9am > 74: Yes (4.0)
## | | | | | | | wind_gust_dir=W: Yes (6.0/1.0)
## | | | | | | | wind_gust_dir=WNW: No (2.0/1.0)
## | | | | | | | wind_gust_dir=NW: No (2.0/1.0)
## | | | | | | | wind_gust_dir=NNW: No (2.0/1.0)
## | | | | sunshine > 7.7
## | | | | | humidity_3pm <= 48
## | | | | | | cloud_3pm <= 5
## | | | | | | | wind_dir_3pm=N
## | | | | | | | | wind_gust_speed <= 76
## | | | | | | | | | humidity_3pm <= 10: No (30.0)
## | | | | | | | | | humidity_3pm > 10
## | | | | | | | | | | pressure_3pm <= 1008.8
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | evaporation <= 6.3
## | | | | | | | | | | | | | wind_speed_3pm <= 30
## | | | | | | | | | | | | | | cloud_3pm <= 4: Yes (4.0/1.0)
## | | | | | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | | | | | pressure_9am <= 1011.2: Yes (3.0)
## | | | | | | | | | | | | | | | pressure_9am > 1011.2: No (4.0)
## | | | | | | | | | | | | | wind_speed_3pm > 30: No (22.0/5.0)
## | | | | | | | | | | | | evaporation > 6.3: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | | | wind_dir_9am=N: Yes (3.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | | | cloud_3pm <= 4: No (2.0)
## | | | | | | | | | | | | | cloud_3pm > 4: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (3.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | | humidity_9am <= 16: No (2.0)
## | | | | | | | | | | | | humidity_9am > 16: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (6.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (5.0/2.0)
## | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | pressure_3pm <= 1006.6: No (3.0)
## | | | | | | | | | | | | pressure_3pm > 1006.6: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=WNW: No (6.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | evaporation <= 5.9: Yes (13.0/5.0)
## | | | | | | | | | | | | evaporation > 5.9: No (2.0)
## | | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | | evaporation <= 8.7
## | | | | | | | | | | | | | max_temp <= 21.5: Yes (3.0)
## | | | | | | | | | | | | | max_temp > 21.5: No (10.0/1.0)
## | | | | | | | | | | | | evaporation > 8.7: Yes (2.0)
## | | | | | | | | | | pressure_3pm > 1008.8
## | | | | | | | | | | | humidity_3pm <= 45: No (177.0/25.0)
## | | | | | | | | | | | humidity_3pm > 45
## | | | | | | | | | | | | wind_speed_3pm <= 26: Yes (8.0/1.0)
## | | | | | | | | | | | | wind_speed_3pm > 26: No (3.0)
## | | | | | | | | wind_gust_speed > 76: Yes (33.0/11.0)
## | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | wind_gust_speed <= 57: No (69.0/13.0)
## | | | | | | | | wind_gust_speed > 57
## | | | | | | | | | cloud_3pm <= 1: No (9.0/1.0)
## | | | | | | | | | cloud_3pm > 1
## | | | | | | | | | | cloud_3pm <= 4: Yes (13.0)
## | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | pressure_3pm <= 1007.3: Yes (17.0/6.0)
## | | | | | | | | | | | pressure_3pm > 1007.3: No (28.0/12.0)
## | | | | | | | wind_dir_3pm=NE
## | | | | | | | | rainfall <= 0.1: No (59.0/17.0)
## | | | | | | | | rainfall > 0.1: Yes (11.0/3.0)
## | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | humidity_9am <= 54: No (66.0/10.0)
## | | | | | | | | humidity_9am > 54
## | | | | | | | | | temp_3pm <= 28.9: No (5.0)
## | | | | | | | | | temp_3pm > 28.9
## | | | | | | | | | | max_temp <= 36.5: Yes (15.0/1.0)
## | | | | | | | | | | max_temp > 36.5: No (5.0/1.0)
## | | | | | | | wind_dir_3pm=E: No (97.0/12.0)
## | | | | | | | wind_dir_3pm=ESE: No (107.0/8.0)
## | | | | | | | wind_dir_3pm=SE: No (148.0/13.0)
## | | | | | | | wind_dir_3pm=SSE: No (158.0/8.0)
## | | | | | | | wind_dir_3pm=S: No (149.0/8.0)
## | | | | | | | wind_dir_3pm=SSW: No (168.0/7.0)
## | | | | | | | wind_dir_3pm=SW: No (222.0/12.0)
## | | | | | | | wind_dir_3pm=WSW: No (381.0/15.0)
## | | | | | | | wind_dir_3pm=W: No (616.0/47.0)
## | | | | | | | wind_dir_3pm=WNW: No (719.0/80.0)
## | | | | | | | wind_dir_3pm=NW: No (551.0/103.0)
## | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | pressure_3pm <= 1015.4
## | | | | | | | | | humidity_3pm <= 21: No (162.0/30.0)
## | | | | | | | | | humidity_3pm > 21
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | cloud_3pm <= 2: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 2
## | | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | | wind_gust_speed <= 69: No (6.0)
## | | | | | | | | | | | | | | wind_gust_speed > 69: Yes (2.0)
## | | | | | | | | | | | | | cloud_9am > 6: No (2.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | cloud_3pm <= 4: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 4: No (2.0)
## | | | | | | | | | | | wind_gust_dir=WNW: No (8.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | humidity_9am <= 68: Yes (3.0)
## | | | | | | | | | | | | humidity_9am > 68: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | | temp_9am <= 9.8: No (3.0)
## | | | | | | | | | | | | temp_9am > 9.8
## | | | | | | | | | | | | | wind_speed_3pm <= 35: Yes (12.0)
## | | | | | | | | | | | | | wind_speed_3pm > 35
## | | | | | | | | | | | | | | evaporation <= 4.3: Yes (3.0)
## | | | | | | | | | | | | | | evaporation > 4.3: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (26.0/9.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | evaporation <= 3.9: No (2.0)
## | | | | | | | | | | | evaporation > 3.9
## | | | | | | | | | | | | humidity_9am <= 61: Yes (6.0/1.0)
## | | | | | | | | | | | | humidity_9am > 61: No (2.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | temp_3pm <= 31.5: No (3.0)
## | | | | | | | | | | | temp_3pm > 31.5: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=E: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (2.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (2.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=W: No (2.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (4.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | wind_gust_speed <= 74: No (14.0/2.0)
## | | | | | | | | | | | wind_gust_speed > 74: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | pressure_3pm <= 998.3: Yes (7.0)
## | | | | | | | | | | | pressure_3pm > 998.3
## | | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | | evaporation <= 5.6
## | | | | | | | | | | | | | | cloud_3pm <= 3: No (3.0)
## | | | | | | | | | | | | | | cloud_3pm > 3
## | | | | | | | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | | | | | | humidity_9am <= 51: No (5.0)
## | | | | | | | | | | | | | | | | humidity_9am > 51
## | | | | | | | | | | | | | | | | | humidity_3pm <= 33: No (2.0)
## | | | | | | | | | | | | | | | | | humidity_3pm > 33: Yes (7.0)
## | | | | | | | | | | | | | evaporation > 5.6: No (6.0)
## | | | | | | | | | | | | rainfall > 0.1: No (4.0)
## | | | | | | | | pressure_3pm > 1015.4: No (29.0)
## | | | | | | cloud_3pm > 5
## | | | | | | | humidity_3pm <= 13
## | | | | | | | | min_temp <= 8.4: Yes (3.0)
## | | | | | | | | min_temp > 8.4: No (100.0/6.0)
## | | | | | | | humidity_3pm > 13
## | | | | | | | | pressure_3pm <= 1010
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | cloud_9am <= 5
## | | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | | min_temp <= 19.5: No (8.0/1.0)
## | | | | | | | | | | | | | min_temp > 19.5: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 5: Yes (11.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | min_temp <= 10.9: No (5.0)
## | | | | | | | | | | | min_temp > 10.9
## | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | pressure_3pm <= 1006.9: No (2.0)
## | | | | | | | | | | | | | pressure_3pm > 1006.9: Yes (2.0)
## | | | | | | | | | | | | cloud_9am > 6: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | cloud_9am <= 5: Yes (3.0)
## | | | | | | | | | | | cloud_9am > 5: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | temp_3pm <= 32.7: No (2.0)
## | | | | | | | | | | | temp_3pm > 32.7: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (3.0)
## | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | humidity_9am <= 52: Yes (13.0/2.0)
## | | | | | | | | | | humidity_9am > 52: No (12.0/5.0)
## | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | cloud_3pm <= 6: No (3.0)
## | | | | | | | | | | cloud_3pm > 6: Yes (9.0/3.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | wind_gust_speed <= 65: No (7.0/1.0)
## | | | | | | | | | | wind_gust_speed > 65: Yes (4.0)
## | | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | | temp_3pm <= 32.1: Yes (4.0/1.0)
## | | | | | | | | | | temp_3pm > 32.1: No (5.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (5.0/1.0)
## | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | wind_gust_speed <= 54: Yes (3.0)
## | | | | | | | | | | wind_gust_speed > 54: No (7.0/1.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | wind_gust_speed <= 65: No (5.0)
## | | | | | | | | | | wind_gust_speed > 65: Yes (4.0)
## | | | | | | | | | wind_dir_3pm=S: No (11.0/4.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (9.0/3.0)
## | | | | | | | | | wind_dir_3pm=SW: No (21.0/4.0)
## | | | | | | | | | wind_dir_3pm=WSW: No (38.0/14.0)
## | | | | | | | | | wind_dir_3pm=W: No (63.0/10.0)
## | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | cloud_9am <= 7: No (64.0/17.0)
## | | | | | | | | | | cloud_9am > 7
## | | | | | | | | | | | pressure_3pm <= 1004: Yes (3.0)
## | | | | | | | | | | | pressure_3pm > 1004: No (8.0)
## | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | wind_gust_dir=N: No (4.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=W: Yes (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=WNW: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | temp_3pm <= 28.5: No (3.0)
## | | | | | | | | | | | | temp_3pm > 28.5: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (8.0/3.0)
## | | | | | | | | | | wind_dir_9am=NE: No (2.0/1.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=E: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | temp_9am <= 14.8: Yes (2.0)
## | | | | | | | | | | | temp_9am > 14.8: No (3.0)
## | | | | | | | | | | wind_dir_9am=NW: No (7.0/2.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=W: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=WNW: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | temp_3pm <= 17.2: No (3.0)
## | | | | | | | | | | | | temp_3pm > 17.2: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NNW: No (3.0)
## | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | wind_gust_dir=N: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (4.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (2.0/1.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (2.0/1.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (7.0/1.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | temp_3pm <= 28: No (2.0)
## | | | | | | | | | | | temp_3pm > 28: Yes (3.0)
## | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | wind_gust_speed <= 65: Yes (4.0)
## | | | | | | | | | | | wind_gust_speed > 65: No (4.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | wind_dir_9am=N: Yes (2.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (3.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (4.0/1.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (6.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | cloud_9am <= 7: Yes (11.0/3.0)
## | | | | | | | | | | | cloud_9am > 7
## | | | | | | | | | | | | temp_3pm <= 26.1: Yes (2.0)
## | | | | | | | | | | | | temp_3pm > 26.1: No (3.0)
## | | | | | | | | pressure_3pm > 1010
## | | | | | | | | | wind_speed_9am <= 6
## | | | | | | | | | | cloud_9am <= 4: Yes (7.0)
## | | | | | | | | | | cloud_9am > 4: No (15.0/6.0)
## | | | | | | | | | wind_speed_9am > 6: No (313.0/52.0)
## | | | | | humidity_3pm > 48
## | | | | | | pressure_3pm <= 1011.9
## | | | | | | | max_temp <= 22.4
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | humidity_9am <= 58: No (4.0)
## | | | | | | | | | humidity_9am > 58
## | | | | | | | | | | wind_speed_9am <= 39
## | | | | | | | | | | | wind_speed_3pm <= 20: No (3.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 20: Yes (34.0/6.0)
## | | | | | | | | | | wind_speed_9am > 39: No (3.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (20.0/8.0)
## | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | temp_3pm <= 17: Yes (2.0)
## | | | | | | | | | temp_3pm > 17: No (3.0)
## | | | | | | | | wind_dir_3pm=ENE: No (2.0)
## | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ESE: No (3.0)
## | | | | | | | | wind_dir_3pm=SE: Yes (8.0/2.0)
## | | | | | | | | wind_dir_3pm=SSE: No (10.0/1.0)
## | | | | | | | | wind_dir_3pm=S: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | sunshine <= 8.5
## | | | | | | | | | | cloud_9am <= 3: Yes (2.0)
## | | | | | | | | | | cloud_9am > 3: No (10.0/1.0)
## | | | | | | | | | sunshine > 8.5: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | sunshine <= 8.8
## | | | | | | | | | | | wind_speed_3pm <= 33: Yes (8.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 33: No (2.0)
## | | | | | | | | | | sunshine > 8.8: No (2.0)
## | | | | | | | | | cloud_9am > 6: No (12.0/1.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | rainfall <= 0.6
## | | | | | | | | | | | evaporation <= 5.1: No (24.0/5.0)
## | | | | | | | | | | | evaporation > 5.1: Yes (3.0)
## | | | | | | | | | | rainfall > 0.6: Yes (3.0)
## | | | | | | | | | cloud_9am > 7: Yes (5.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | wind_gust_dir=N: No (2.0)
## | | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (1.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (3.0/1.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | pressure_9am <= 1007.2: Yes (4.0)
## | | | | | | | | | | pressure_9am > 1007.2: No (6.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | wind_gust_speed <= 56: No (3.0)
## | | | | | | | | | | wind_gust_speed > 56: Yes (14.0/2.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | wind_speed_3pm <= 33: No (5.0)
## | | | | | | | | | | wind_speed_3pm > 33: Yes (3.0/1.0)
## | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | humidity_9am <= 55: No (2.0)
## | | | | | | | | | | humidity_9am > 55: Yes (2.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | humidity_3pm <= 49: No (8.0)
## | | | | | | | | | humidity_3pm > 49
## | | | | | | | | | | wind_gust_dir=N: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (1.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (1.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | min_temp <= 14.8: Yes (8.0/1.0)
## | | | | | | | | | | | min_temp > 14.8: No (2.0)
## | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | wind_speed_9am <= 31: Yes (24.0/6.0)
## | | | | | | | | | | | wind_speed_9am > 31: No (5.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | pressure_3pm <= 1003.7: No (2.0)
## | | | | | | | | | | | pressure_3pm > 1003.7: Yes (6.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (6.0/1.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | max_temp <= 19.9
## | | | | | | | | | | wind_dir_9am=N: Yes (16.0/5.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (2.0/1.0)
## | | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=W: No (1.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | wind_gust_speed <= 57: Yes (4.0)
## | | | | | | | | | | | wind_gust_speed > 57
## | | | | | | | | | | | | pressure_3pm <= 999.9: Yes (2.0)
## | | | | | | | | | | | | pressure_3pm > 999.9: No (9.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | wind_gust_dir=N: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=W: No (1.0)
## | | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | | pressure_3pm <= 1009.8: No (2.0)
## | | | | | | | | | | | | pressure_3pm > 1009.8: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | wind_speed_9am <= 24: Yes (5.0)
## | | | | | | | | | | | | wind_speed_9am > 24: No (5.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | | temp_9am <= 10.2: Yes (2.0)
## | | | | | | | | | | | | temp_9am > 10.2: No (2.0)
## | | | | | | | | | max_temp > 19.9: Yes (13.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (65.0/20.0)
## | | | | | | | max_temp > 22.4
## | | | | | | | | max_temp <= 22.5: No (93.0/2.0)
## | | | | | | | | max_temp > 22.5
## | | | | | | | | | wind_speed_3pm <= 31
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | wind_gust_dir=N: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: No (1.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | | pressure_3pm <= 1009.1: No (3.0/1.0)
## | | | | | | | | | | | | pressure_3pm > 1009.1: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=WSW: No (2.0/1.0)
## | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | min_temp <= 17.2: Yes (6.0)
## | | | | | | | | | | | | min_temp > 17.2: No (3.0)
## | | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | | cloud_3pm <= 6: No (2.0)
## | | | | | | | | | | | | cloud_3pm > 6: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | | cloud_3pm <= 3: No (3.0)
## | | | | | | | | | | | | cloud_3pm > 3: Yes (13.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNW: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (40.0/16.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | wind_dir_3pm=N: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: Yes (4.0)
## | | | | | | | | | | | wind_dir_3pm=NE: No (4.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=WSW: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=WNW: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=NW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: No (2.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | | cloud_3pm <= 4: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 4: No (2.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NE: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (2.0)
## | | | | | | | | | | | wind_dir_3pm=E: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSE: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=W: No (2.0)
## | | | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (14.0/6.0)
## | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | wind_speed_3pm <= 19: No (7.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 19: Yes (8.0)
## | | | | | | | | | | wind_dir_9am=SE: No (17.0/6.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (14.0/6.0)
## | | | | | | | | | | wind_dir_9am=S: No (15.0/4.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (15.0/6.0)
## | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | pressure_3pm <= 1006.9: Yes (3.0)
## | | | | | | | | | | | pressure_3pm > 1006.9: No (4.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | cloud_9am <= 4: Yes (4.0)
## | | | | | | | | | | | cloud_9am > 4: No (11.0/2.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (27.0/9.0)
## | | | | | | | | | | wind_dir_9am=NW: No (33.0/14.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (28.0/12.0)
## | | | | | | | | | wind_speed_3pm > 31: No (163.0/39.0)
## | | | | | | pressure_3pm > 1011.9
## | | | | | | | wind_speed_9am <= 20
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | sunshine <= 8.3: No (2.0)
## | | | | | | | | | | sunshine > 8.3
## | | | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | | temp_3pm <= 15.2: No (2.0)
## | | | | | | | | | | | | temp_3pm > 15.2: Yes (6.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (3.0)
## | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | sunshine <= 8.8: Yes (3.0)
## | | | | | | | | | | sunshine > 8.8: No (2.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NW: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: No (5.0)
## | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | wind_speed_3pm <= 20: Yes (7.0/1.0)
## | | | | | | | | | wind_speed_3pm > 20: No (29.0/4.0)
## | | | | | | | | wind_gust_dir=NE: No (27.0/2.0)
## | | | | | | | | wind_gust_dir=ENE: No (4.0/1.0)
## | | | | | | | | wind_gust_dir=E
## | | | | | | | | | cloud_3pm <= 6: No (16.0)
## | | | | | | | | | cloud_3pm > 6: Yes (3.0/1.0)
## | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | evaporation <= 6.9: No (14.0)
## | | | | | | | | | evaporation > 6.9: Yes (3.0/1.0)
## | | | | | | | | wind_gust_dir=SE: No (27.0/4.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | temp_9am <= 23: No (32.0/1.0)
## | | | | | | | | | temp_9am > 23: Yes (13.0/6.0)
## | | | | | | | | wind_gust_dir=S
## | | | | | | | | | evaporation <= 4.5: Yes (5.0)
## | | | | | | | | | evaporation > 4.5
## | | | | | | | | | | wind_speed_9am <= 11: Yes (10.0/2.0)
## | | | | | | | | | | wind_speed_9am > 11
## | | | | | | | | | | | humidity_3pm <= 62: No (32.0/3.0)
## | | | | | | | | | | | humidity_3pm > 62
## | | | | | | | | | | | | wind_speed_3pm <= 33: No (5.0/1.0)
## | | | | | | | | | | | | wind_speed_3pm > 33
## | | | | | | | | | | | | | pressure_3pm <= 1019.5: Yes (7.0/1.0)
## | | | | | | | | | | | | | pressure_3pm > 1019.5: No (2.0)
## | | | | | | | | wind_gust_dir=SSW: No (48.0/17.0)
## | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | cloud_9am <= 5: Yes (7.0/2.0)
## | | | | | | | | | cloud_9am > 5: No (27.0/6.0)
## | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | temp_3pm <= 19.7
## | | | | | | | | | | wind_speed_3pm <= 37: No (30.0/2.0)
## | | | | | | | | | | wind_speed_3pm > 37: Yes (2.0)
## | | | | | | | | | temp_3pm > 19.7: Yes (14.0/2.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_dir_9am=N: No (8.0/2.0)
## | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | cloud_3pm <= 6: No (3.0)
## | | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | pressure_3pm <= 1017.9: Yes (2.0)
## | | | | | | | | | | pressure_3pm > 1017.9: No (2.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | humidity_9am <= 69: No (3.0)
## | | | | | | | | | | humidity_9am > 69: Yes (3.0)
## | | | | | | | | | wind_dir_9am=WSW: No (5.0)
## | | | | | | | | | wind_dir_9am=W: No (12.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_speed_3pm <= 15: Yes (2.0)
## | | | | | | | | | | wind_speed_3pm > 15: No (10.0/1.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | evaporation <= 5.1: No (6.0/1.0)
## | | | | | | | | | | evaporation > 5.1: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | wind_speed_9am <= 17: Yes (2.0)
## | | | | | | | | | | wind_speed_9am > 17
## | | | | | | | | | | | pressure_3pm <= 1014.6: No (3.0)
## | | | | | | | | | | | pressure_3pm > 1014.6: Yes (2.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | temp_9am <= 15.9: Yes (3.0)
## | | | | | | | | | | temp_9am > 15.9: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | wind_dir_9am=WSW: No (3.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_gust_speed <= 61: No (4.0)
## | | | | | | | | | | wind_gust_speed > 61: Yes (2.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | rainfall <= 0.3: No (5.0/1.0)
## | | | | | | | | | | rainfall > 0.3: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | temp_9am <= 10.7: No (3.0)
## | | | | | | | | | | temp_9am > 10.7: Yes (5.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | rainfall <= 0.1: No (6.0/1.0)
## | | | | | | | | | | rainfall > 0.1: Yes (3.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | wind_speed_3pm <= 22: Yes (3.0)
## | | | | | | | | | | wind_speed_3pm > 22: No (5.0)
## | | | | | | | | | wind_dir_9am=NNE: No (1.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WSW: No (2.0)
## | | | | | | | | | wind_dir_9am=W: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=WNW: No (1.0)
## | | | | | | | | | wind_dir_9am=NW: Yes (8.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | wind_speed_9am <= 13: No (4.0)
## | | | | | | | | | | wind_speed_9am > 13: Yes (3.0)
## | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | evaporation <= 3.8: No (7.0)
## | | | | | | | | | evaporation > 3.8
## | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | temp_9am <= 16.9: Yes (20.0/6.0)
## | | | | | | | | | | | temp_9am > 16.9: No (7.0/2.0)
## | | | | | | | | | | cloud_9am > 6: No (8.0/1.0)
## | | | | | | | wind_speed_9am > 20: No (838.0/160.0)
## | | | sunshine > 10.1: No (2076.0/124.0)
## | rain_today=Yes
## | | humidity_3pm <= 51
## | | | sunshine <= 7
## | | | | wind_gust_speed <= 41: No (347.0/62.0)
## | | | | wind_gust_speed > 41
## | | | | | humidity_9am <= 75: No (305.0/100.0)
## | | | | | humidity_9am > 75
## | | | | | | wind_dir_9am=N
## | | | | | | | evaporation <= 2.5: No (14.0/5.0)
## | | | | | | | evaporation > 2.5: Yes (21.0/7.0)
## | | | | | | wind_dir_9am=NNE: Yes (11.0/4.0)
## | | | | | | wind_dir_9am=NE
## | | | | | | | evaporation <= 5.6: Yes (7.0)
## | | | | | | | evaporation > 5.6: No (3.0/1.0)
## | | | | | | wind_dir_9am=ENE: Yes (3.0/1.0)
## | | | | | | wind_dir_9am=E: Yes (4.0/1.0)
## | | | | | | wind_dir_9am=ESE
## | | | | | | | cloud_9am <= 6: Yes (2.0)
## | | | | | | | cloud_9am > 6: No (3.0)
## | | | | | | wind_dir_9am=SE: Yes (3.0)
## | | | | | | wind_dir_9am=SSE: No (4.0/1.0)
## | | | | | | wind_dir_9am=S
## | | | | | | | cloud_3pm <= 5: No (3.0/1.0)
## | | | | | | | cloud_3pm > 5: Yes (6.0)
## | | | | | | wind_dir_9am=SSW
## | | | | | | | humidity_3pm <= 50
## | | | | | | | | sunshine <= 1: Yes (2.0)
## | | | | | | | | sunshine > 1: No (13.0/1.0)
## | | | | | | | humidity_3pm > 50: Yes (2.0)
## | | | | | | wind_dir_9am=SW
## | | | | | | | cloud_3pm <= 6
## | | | | | | | | temp_9am <= 14.3: No (5.0/1.0)
## | | | | | | | | temp_9am > 14.3: Yes (6.0)
## | | | | | | | cloud_3pm > 6: No (6.0)
## | | | | | | wind_dir_9am=WSW
## | | | | | | | pressure_9am <= 1015.8
## | | | | | | | | rainfall <= 5.2: No (7.0/2.0)
## | | | | | | | | rainfall > 5.2: Yes (7.0)
## | | | | | | | pressure_9am > 1015.8: No (7.0)
## | | | | | | wind_dir_9am=W: Yes (30.0/8.0)
## | | | | | | wind_dir_9am=WNW
## | | | | | | | wind_speed_9am <= 19: No (6.0)
## | | | | | | | wind_speed_9am > 19
## | | | | | | | | wind_gust_speed <= 69: Yes (5.0)
## | | | | | | | | wind_gust_speed > 69: No (3.0)
## | | | | | | wind_dir_9am=NW
## | | | | | | | temp_9am <= 15.9: Yes (6.0/1.0)
## | | | | | | | temp_9am > 15.9: No (5.0)
## | | | | | | wind_dir_9am=NNW: No (20.0/8.0)
## | | | sunshine > 7: No (5252.0/669.0)
## | | humidity_3pm > 51
## | | | wind_gust_speed <= 48
## | | | | sunshine <= 8.9
## | | | | | pressure_3pm <= 1014.8
## | | | | | | wind_gust_speed <= 37
## | | | | | | | humidity_9am <= 75
## | | | | | | | | sunshine <= 7.5
## | | | | | | | | | wind_speed_3pm <= 15
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | humidity_9am <= 70: Yes (3.0)
## | | | | | | | | | | | humidity_9am > 70: No (2.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (2.0)
## | | | | | | | | | | wind_dir_9am=E: No (4.0)
## | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | cloud_9am <= 7: Yes (3.0)
## | | | | | | | | | | | cloud_9am > 7: No (3.0)
## | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | wind_speed_3pm <= 9: No (2.0)
## | | | | | | | | | | | wind_speed_3pm > 9: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | evaporation <= 5.3: No (2.0)
## | | | | | | | | | | | evaporation > 5.3: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=SW: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | cloud_3pm <= 6: No (2.0)
## | | | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | humidity_9am <= 68: Yes (3.0)
## | | | | | | | | | | | humidity_9am > 68: No (2.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (3.0)
## | | | | | | | | | wind_speed_3pm > 15: No (37.0/6.0)
## | | | | | | | | sunshine > 7.5: No (252.0/41.0)
## | | | | | | | humidity_9am > 75
## | | | | | | | | humidity_3pm <= 60: No (401.0/111.0)
## | | | | | | | | humidity_3pm > 60
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | wind_gust_speed <= 31: No (19.0/4.0)
## | | | | | | | | | | wind_gust_speed > 31: Yes (17.0/4.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (11.0/2.0)
## | | | | | | | | | wind_dir_3pm=NE: No (31.0/9.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | rainfall <= 8.8: No (28.0/12.0)
## | | | | | | | | | | rainfall > 8.8: Yes (15.0/5.0)
## | | | | | | | | | wind_dir_3pm=E: Yes (48.0/22.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (29.0/12.0)
## | | | | | | | | | wind_dir_3pm=SE: No (45.0/13.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | wind_gust_speed <= 35
## | | | | | | | | | | | cloud_9am <= 3: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 3
## | | | | | | | | | | | | humidity_3pm <= 67: No (18.0/3.0)
## | | | | | | | | | | | | humidity_3pm > 67: Yes (2.0)
## | | | | | | | | | | wind_gust_speed > 35: Yes (6.0)
## | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | sunshine <= 4.3: No (7.0)
## | | | | | | | | | | sunshine > 4.3: Yes (22.0/7.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (19.0/4.0)
## | | | | | | | | | wind_dir_3pm=SW: No (25.0/10.0)
## | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | wind_speed_3pm <= 9: Yes (10.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 9
## | | | | | | | | | | | max_temp <= 20.2: Yes (18.0/7.0)
## | | | | | | | | | | | max_temp > 20.2: No (15.0/1.0)
## | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | | cloud_9am > 5: No (27.0/9.0)
## | | | | | | | | | wind_dir_3pm=WNW: No (39.0/11.0)
## | | | | | | | | | wind_dir_3pm=NW: No (40.0/16.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (34.0/15.0)
## | | | | | | wind_gust_speed > 37
## | | | | | | | wind_speed_3pm <= 19
## | | | | | | | | wind_dir_3pm=N: Yes (36.0/15.0)
## | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | pressure_3pm <= 1006.9: No (8.0)
## | | | | | | | | | pressure_3pm > 1006.9: Yes (17.0/6.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (16.0/6.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (24.0/10.0)
## | | | | | | | | wind_dir_3pm=E: No (27.0/11.0)
## | | | | | | | | wind_dir_3pm=ESE: No (20.0/8.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | humidity_3pm <= 53
## | | | | | | | | | | max_temp <= 18.6: Yes (111.0/21.0)
## | | | | | | | | | | max_temp > 18.6
## | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | wind_speed_9am <= 4: Yes (4.0)
## | | | | | | | | | | | | wind_speed_9am > 4
## | | | | | | | | | | | | | min_temp <= 10.9: Yes (3.0)
## | | | | | | | | | | | | | min_temp > 10.9: No (8.0)
## | | | | | | | | | | | wind_dir_9am=NNE: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=NE: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_9am=ENE: No (3.0/1.0)
## | | | | | | | | | | | wind_dir_9am=E: No (3.0/1.0)
## | | | | | | | | | | | wind_dir_9am=ESE: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=SE: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=SSE: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_9am=S: No (6.0/1.0)
## | | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | | humidity_9am <= 86: Yes (3.0)
## | | | | | | | | | | | | humidity_9am > 86: No (2.0)
## | | | | | | | | | | | wind_dir_9am=SW: No (7.0/1.0)
## | | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | | humidity_9am <= 91: No (3.0)
## | | | | | | | | | | | | humidity_9am > 91: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=W: No (5.0/1.0)
## | | | | | | | | | | | wind_dir_9am=WNW: Yes (4.0/1.0)
## | | | | | | | | | | | wind_dir_9am=NW: No (12.0/1.0)
## | | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | | cloud_9am <= 5: Yes (4.0)
## | | | | | | | | | | | | cloud_9am > 5: No (4.0)
## | | | | | | | | | humidity_3pm > 53: No (25.0/4.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | cloud_3pm <= 5: No (15.0/1.0)
## | | | | | | | | | cloud_3pm > 5: Yes (15.0/6.0)
## | | | | | | | | wind_dir_3pm=S: No (29.0/10.0)
## | | | | | | | | wind_dir_3pm=SSW: No (35.0/12.0)
## | | | | | | | | wind_dir_3pm=SW: No (32.0/13.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | wind_gust_speed <= 41: No (2.0)
## | | | | | | | | | | wind_gust_speed > 41: Yes (5.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (2.0)
## | | | | | | | | | wind_dir_9am=E: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | wind_dir_9am=SSW: No (4.0/1.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | wind_speed_9am <= 15: No (3.0/1.0)
## | | | | | | | | | | wind_speed_9am > 15: Yes (5.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | wind_speed_9am <= 15: Yes (2.0)
## | | | | | | | | | | wind_speed_9am > 15: No (5.0)
## | | | | | | | | | wind_dir_9am=W: No (5.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_speed_3pm <= 17: No (4.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 17: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NW: Yes (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (5.0/1.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (1.0)
## | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SE: No (3.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (5.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | temp_9am <= 15: No (5.0)
## | | | | | | | | | | temp_9am > 15: Yes (5.0/1.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | pressure_3pm <= 1004.6: Yes (6.0)
## | | | | | | | | | | pressure_3pm > 1004.6
## | | | | | | | | | | | temp_3pm <= 19.2: No (7.0/1.0)
## | | | | | | | | | | | temp_3pm > 19.2: Yes (2.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | min_temp <= 9.2: No (3.0)
## | | | | | | | | | | min_temp > 9.2: Yes (8.0/1.0)
## | | | | | | | | | wind_gust_dir=NW: Yes (8.0/1.0)
## | | | | | | | | | wind_gust_dir=NNW: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | temp_9am <= 11: No (14.0/4.0)
## | | | | | | | | | temp_9am > 11: Yes (43.0/16.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | wind_dir_9am=N: Yes (10.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (3.0)
## | | | | | | | | | wind_dir_9am=NE: No (3.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (2.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=WSW: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=W: Yes (5.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | temp_3pm <= 15.2: No (4.0)
## | | | | | | | | | | temp_3pm > 15.2: Yes (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | | humidity_3pm <= 65: No (5.0/1.0)
## | | | | | | | | | | | humidity_3pm > 65: Yes (2.0)
## | | | | | | | | | | cloud_3pm > 5: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | pressure_9am <= 1008: Yes (6.0/1.0)
## | | | | | | | | | | pressure_9am > 1008: No (7.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (38.0/12.0)
## | | | | | | | wind_speed_3pm > 19
## | | | | | | | | sunshine <= 7.5
## | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | wind_speed_9am <= 15: Yes (9.0/1.0)
## | | | | | | | | | | wind_speed_9am > 15: No (3.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (7.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (8.0/1.0)
## | | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | | wind_gust_speed <= 44: No (9.0/3.0)
## | | | | | | | | | | wind_gust_speed > 44: Yes (5.0)
## | | | | | | | | | wind_gust_dir=E
## | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | rainfall <= 6.5: No (2.0)
## | | | | | | | | | | | rainfall > 6.5: Yes (5.0/1.0)
## | | | | | | | | | | cloud_9am > 7: No (2.0)
## | | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | | rainfall <= 6.5: No (5.0/1.0)
## | | | | | | | | | | rainfall > 6.5: Yes (4.0)
## | | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | | humidity_9am <= 83
## | | | | | | | | | | | wind_dir_9am=N: Yes (1.0)
## | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=E: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | | temp_3pm <= 25.4: No (3.0)
## | | | | | | | | | | | | temp_3pm > 25.4: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | | | humidity_3pm <= 63: No (4.0)
## | | | | | | | | | | | | humidity_3pm > 63: Yes (4.0)
## | | | | | | | | | | | wind_dir_9am=S: No (3.0)
## | | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | | humidity_9am > 83: Yes (8.0)
## | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | wind_speed_9am <= 22: No (7.0)
## | | | | | | | | | | wind_speed_9am > 22: Yes (3.0)
## | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | wind_speed_9am <= 15
## | | | | | | | | | | | wind_speed_3pm <= 24: Yes (4.0)
## | | | | | | | | | | | wind_speed_3pm > 24: No (3.0)
## | | | | | | | | | | wind_speed_9am > 15: No (13.0)
## | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | wind_gust_speed <= 44: No (11.0/3.0)
## | | | | | | | | | | wind_gust_speed > 44: Yes (4.0)
## | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | rainfall <= 9.2
## | | | | | | | | | | | | wind_speed_3pm <= 22: Yes (3.0/1.0)
## | | | | | | | | | | | | wind_speed_3pm > 22: No (11.0)
## | | | | | | | | | | | rainfall > 9.2: Yes (5.0)
## | | | | | | | | | | cloud_9am > 7: Yes (4.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | pressure_9am <= 1013.8: No (27.0/7.0)
## | | | | | | | | | | pressure_9am > 1013.8: Yes (6.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | wind_dir_3pm=N: No (4.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SE: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (3.0)
## | | | | | | | | | | wind_dir_3pm=S: No (2.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SSW: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | pressure_9am <= 1010.3: No (3.0)
## | | | | | | | | | | | pressure_9am > 1010.3: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | | humidity_9am <= 90: Yes (14.0/1.0)
## | | | | | | | | | | | humidity_9am > 90: No (4.0)
## | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | temp_3pm <= 14.9: Yes (5.0)
## | | | | | | | | | | | temp_3pm > 14.9: No (9.0/1.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | cloud_3pm <= 5: Yes (2.0)
## | | | | | | | | | | | cloud_3pm > 5: No (7.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NW: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=NNW: Yes (1.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | wind_dir_9am=N: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=NW: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | wind_speed_3pm <= 24: No (2.0)
## | | | | | | | | | | | wind_speed_3pm > 24: Yes (2.0)
## | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | temp_3pm <= 15.4: No (6.0)
## | | | | | | | | | | temp_3pm > 15.4
## | | | | | | | | | | | wind_speed_3pm <= 22: Yes (6.0)
## | | | | | | | | | | | wind_speed_3pm > 22
## | | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=WNW: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=NW: No (4.0)
## | | | | | | | | | | | | wind_dir_3pm=NNW: Yes (1.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (13.0/3.0)
## | | | | | | | | sunshine > 7.5
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | temp_9am <= 19.2
## | | | | | | | | | | | cloud_9am <= 3: No (2.0)
## | | | | | | | | | | | cloud_9am > 3: Yes (10.0/1.0)
## | | | | | | | | | | temp_9am > 19.2: No (9.0/1.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (8.0/3.0)
## | | | | | | | | | wind_dir_3pm=NE: No (11.0/1.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | pressure_3pm <= 1006.8: Yes (5.0)
## | | | | | | | | | | pressure_3pm > 1006.8
## | | | | | | | | | | | humidity_9am <= 83: No (29.0/1.0)
## | | | | | | | | | | | humidity_9am > 83: Yes (5.0/1.0)
## | | | | | | | | | wind_dir_3pm=E: No (25.0/9.0)
## | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | wind_gust_speed <= 43
## | | | | | | | | | | | cloud_9am <= 7: Yes (4.0)
## | | | | | | | | | | | cloud_9am > 7: No (4.0/1.0)
## | | | | | | | | | | wind_gust_speed > 43: No (16.0/2.0)
## | | | | | | | | | wind_dir_3pm=SE: No (64.0/23.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | max_temp <= 30.1: No (24.0/2.0)
## | | | | | | | | | | max_temp > 30.1: Yes (6.0/1.0)
## | | | | | | | | | wind_dir_3pm=S: No (25.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (20.0/7.0)
## | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | wind_dir_9am=N: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | | | wind_dir_9am=S: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=SW: No (8.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | temp_3pm <= 15.5: No (2.0)
## | | | | | | | | | | | temp_3pm > 15.5: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (1.0)
## | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | sunshine <= 8.4: Yes (5.0)
## | | | | | | | | | | sunshine > 8.4: No (32.0/9.0)
## | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | wind_dir_9am=N: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=SW: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | cloud_3pm <= 7: No (10.0/1.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | temp_3pm <= 20.7: No (11.0)
## | | | | | | | | | | | temp_3pm > 20.7: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (4.0)
## | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | pressure_9am <= 1015.5: No (34.0/5.0)
## | | | | | | | | | | pressure_9am > 1015.5: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=NW: No (44.0/20.0)
## | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | wind_gust_dir=N: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=W: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (2.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | cloud_9am <= 7: No (4.0/1.0)
## | | | | | | | | | | | cloud_9am > 7: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | min_temp <= 8.4: No (3.0)
## | | | | | | | | | | | min_temp > 8.4: Yes (5.0/1.0)
## | | | | | pressure_3pm > 1014.8
## | | | | | | rainfall <= 8
## | | | | | | | wind_gust_speed <= 37: No (2136.0/341.0)
## | | | | | | | wind_gust_speed > 37
## | | | | | | | | humidity_9am <= 82: No (1110.0/233.0)
## | | | | | | | | humidity_9am > 82
## | | | | | | | | | temp_9am <= 8.1: No (90.0/10.0)
## | | | | | | | | | temp_9am > 8.1
## | | | | | | | | | | wind_gust_dir=N: No (17.0/3.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (5.0/1.0)
## | | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | | temp_3pm <= 21.1: Yes (2.0)
## | | | | | | | | | | | temp_3pm > 21.1: No (2.0)
## | | | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | | | wind_gust_speed <= 44: Yes (2.0)
## | | | | | | | | | | | wind_gust_speed > 44: No (4.0)
## | | | | | | | | | | wind_gust_dir=E
## | | | | | | | | | | | evaporation <= 7.7: No (11.0/1.0)
## | | | | | | | | | | | evaporation > 7.7: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (16.0/3.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (18.0/7.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (21.0/5.0)
## | | | | | | | | | | wind_gust_dir=S: No (29.0/9.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (25.0/10.0)
## | | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=S: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | | pressure_3pm <= 1023.2: No (5.0)
## | | | | | | | | | | | | pressure_3pm > 1023.2: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | | sunshine <= 6.3: No (4.0)
## | | | | | | | | | | | | sunshine > 6.3: Yes (5.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | | | cloud_3pm <= 6: Yes (6.0/1.0)
## | | | | | | | | | | | | cloud_3pm > 6: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=W: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=WNW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=NW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | | wind_dir_9am=N: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_9am=NNE: No (2.0)
## | | | | | | | | | | | wind_dir_9am=NE: Yes (2.0)
## | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | wind_dir_9am=S: No (1.0)
## | | | | | | | | | | | wind_dir_9am=SSW: Yes (1.0)
## | | | | | | | | | | | wind_dir_9am=SW: No (5.0/1.0)
## | | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | | wind_speed_9am <= 19: No (9.0/1.0)
## | | | | | | | | | | | | wind_speed_9am > 19: Yes (3.0)
## | | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | | wind_speed_3pm <= 19
## | | | | | | | | | | | | | pressure_3pm <= 1016.4: No (2.0)
## | | | | | | | | | | | | | pressure_3pm > 1016.4: Yes (2.0)
## | | | | | | | | | | | | wind_speed_3pm > 19: No (6.0)
## | | | | | | | | | | | wind_dir_9am=WNW: Yes (4.0/1.0)
## | | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | | sunshine <= 6: Yes (2.0)
## | | | | | | | | | | | | sunshine > 6: No (5.0)
## | | | | | | | | | | | wind_dir_9am=NNW: Yes (4.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | min_temp <= 8.3: No (64.0/10.0)
## | | | | | | | | | | | min_temp > 8.3
## | | | | | | | | | | | | max_temp <= 18
## | | | | | | | | | | | | | pressure_3pm <= 1019.7
## | | | | | | | | | | | | | | temp_3pm <= 13.7: No (6.0/1.0)
## | | | | | | | | | | | | | | temp_3pm > 13.7
## | | | | | | | | | | | | | | | rainfall <= 1.2: No (3.0/1.0)
## | | | | | | | | | | | | | | | rainfall > 1.2: Yes (49.0/6.0)
## | | | | | | | | | | | | | pressure_3pm > 1019.7: No (50.0/17.0)
## | | | | | | | | | | | | max_temp > 18
## | | | | | | | | | | | | | cloud_3pm <= 4: No (18.0/2.0)
## | | | | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | | | | wind_speed_9am <= 6
## | | | | | | | | | | | | | | | temp_9am <= 15.8: No (26.0/5.0)
## | | | | | | | | | | | | | | | temp_9am > 15.8
## | | | | | | | | | | | | | | | | temp_9am <= 18.7: Yes (11.0/2.0)
## | | | | | | | | | | | | | | | | temp_9am > 18.7
## | | | | | | | | | | | | | | | | | cloud_9am <= 3: Yes (4.0)
## | | | | | | | | | | | | | | | | | cloud_9am > 3: No (21.0/9.0)
## | | | | | | | | | | | | | | wind_speed_9am > 6: No (96.0/30.0)
## | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NE: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=S: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=WSW: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | | pressure_3pm <= 1018: No (3.0)
## | | | | | | | | | | | | pressure_3pm > 1018: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | | temp_3pm <= 15.5: No (8.0)
## | | | | | | | | | | | | temp_3pm > 15.5: Yes (7.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=NW: Yes (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | sunshine <= 5.5: No (2.0)
## | | | | | | | | | | | sunshine > 5.5
## | | | | | | | | | | | | max_temp <= 17.6: Yes (7.0)
## | | | | | | | | | | | | max_temp > 17.6
## | | | | | | | | | | | | | wind_speed_3pm <= 15: Yes (2.0)
## | | | | | | | | | | | | | wind_speed_3pm > 15: No (4.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | humidity_9am <= 97
## | | | | | | | | | | | | wind_speed_9am <= 13: No (3.0/1.0)
## | | | | | | | | | | | | wind_speed_9am > 13: Yes (5.0)
## | | | | | | | | | | | humidity_9am > 97: No (3.0)
## | | | | | | rainfall > 8
## | | | | | | | wind_gust_speed <= 35: No (484.0/119.0)
## | | | | | | | wind_gust_speed > 35
## | | | | | | | | min_temp <= 6.5: No (98.0/20.0)
## | | | | | | | | min_temp > 6.5
## | | | | | | | | | humidity_9am <= 82
## | | | | | | | | | | humidity_3pm <= 61
## | | | | | | | | | | | max_temp <= 13.9: Yes (21.0/8.0)
## | | | | | | | | | | | max_temp > 13.9: No (271.0/71.0)
## | | | | | | | | | | humidity_3pm > 61
## | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: No (2.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=NE: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (2.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | | | cloud_3pm <= 7: No (2.0)
## | | | | | | | | | | | | cloud_3pm > 7: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | | wind_speed_9am <= 11: No (11.0/3.0)
## | | | | | | | | | | | | wind_speed_9am > 11: Yes (19.0/5.0)
## | | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | | sunshine <= 6.2: Yes (2.0)
## | | | | | | | | | | | | | sunshine > 6.2
## | | | | | | | | | | | | | | wind_gust_speed <= 44: No (5.0)
## | | | | | | | | | | | | | | wind_gust_speed > 44
## | | | | | | | | | | | | | | | wind_speed_3pm <= 17: No (2.0)
## | | | | | | | | | | | | | | | wind_speed_3pm > 17: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 7: Yes (4.0)
## | | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (2.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: Yes (3.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (9.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (2.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | | pressure_3pm <= 1018.6: No (6.0)
## | | | | | | | | | | | | pressure_3pm > 1018.6: Yes (8.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=S: No (2.0)
## | | | | | | | | | | | | wind_gust_dir=SSW: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: No (3.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | | cloud_9am <= 4: No (2.0)
## | | | | | | | | | | | | | cloud_9am > 4: Yes (3.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | | | min_temp <= 9.9: No (7.0)
## | | | | | | | | | | | | min_temp > 9.9: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=W: Yes (6.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=WNW: Yes (6.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=NW: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: No (1.0)
## | | | | | | | | | humidity_9am > 82
## | | | | | | | | | | wind_speed_3pm <= 7
## | | | | | | | | | | | sunshine <= 5.3: Yes (2.0)
## | | | | | | | | | | | sunshine > 5.3: No (17.0)
## | | | | | | | | | | wind_speed_3pm > 7
## | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | | wind_gust_speed <= 41
## | | | | | | | | | | | | | | sunshine <= 5: Yes (3.0/1.0)
## | | | | | | | | | | | | | | sunshine > 5
## | | | | | | | | | | | | | | | temp_9am <= 19.7
## | | | | | | | | | | | | | | | | cloud_9am <= 5: Yes (3.0/1.0)
## | | | | | | | | | | | | | | | | cloud_9am > 5: No (26.0/4.0)
## | | | | | | | | | | | | | | | temp_9am > 19.7: Yes (9.0/2.0)
## | | | | | | | | | | | | | wind_gust_speed > 41: Yes (7.0/2.0)
## | | | | | | | | | | | | cloud_9am > 7
## | | | | | | | | | | | | | cloud_3pm <= 3: No (2.0)
## | | | | | | | | | | | | | cloud_3pm > 3: Yes (31.0/3.0)
## | | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | | humidity_3pm <= 58: No (6.0/1.0)
## | | | | | | | | | | | | humidity_3pm > 58: Yes (3.0)
## | | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | | wind_speed_9am <= 11
## | | | | | | | | | | | | | wind_speed_9am <= 7
## | | | | | | | | | | | | | | rainfall <= 18.6: No (2.0)
## | | | | | | | | | | | | | | rainfall > 18.6: Yes (2.0)
## | | | | | | | | | | | | | wind_speed_9am > 7: No (4.0)
## | | | | | | | | | | | | wind_speed_9am > 11: Yes (4.0)
## | | | | | | | | | | | wind_dir_9am=ENE: Yes (4.0)
## | | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | | cloud_9am <= 7: No (2.0)
## | | | | | | | | | | | | cloud_9am > 7: Yes (5.0/1.0)
## | | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | | humidity_9am <= 92: Yes (2.0)
## | | | | | | | | | | | | humidity_9am > 92: No (3.0)
## | | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | | temp_9am <= 24.4: Yes (25.0/4.0)
## | | | | | | | | | | | | temp_9am > 24.4: No (3.0)
## | | | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | | | max_temp <= 22.1
## | | | | | | | | | | | | | temp_3pm <= 13.2: No (2.0)
## | | | | | | | | | | | | | temp_3pm > 13.2: Yes (5.0)
## | | | | | | | | | | | | max_temp > 22.1: No (7.0)
## | | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | | evaporation <= 3.7: No (3.0)
## | | | | | | | | | | | | evaporation > 3.7
## | | | | | | | | | | | | | wind_speed_9am <= 9: No (3.0)
## | | | | | | | | | | | | | wind_speed_9am > 9: Yes (15.0/3.0)
## | | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | | humidity_3pm <= 60: No (11.0/1.0)
## | | | | | | | | | | | | humidity_3pm > 60
## | | | | | | | | | | | | | pressure_9am <= 1016.1: No (2.0)
## | | | | | | | | | | | | | pressure_9am > 1016.1: Yes (6.0)
## | | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NE: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ESE: Yes (3.0)
## | | | | | | | | | | | | wind_dir_3pm=SE: Yes (8.0)
## | | | | | | | | | | | | wind_dir_3pm=SSE: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | | | wind_speed_3pm <= 28
## | | | | | | | | | | | | | | wind_speed_9am <= 19: Yes (5.0)
## | | | | | | | | | | | | | | wind_speed_9am > 19: No (3.0/1.0)
## | | | | | | | | | | | | | wind_speed_3pm > 28: No (2.0)
## | | | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | | | wind_speed_9am <= 20: No (5.0)
## | | | | | | | | | | | | | wind_speed_9am > 20: Yes (2.0)
## | | | | | | | | | | | | wind_dir_3pm=SW: No (2.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=WSW: No (2.0)
## | | | | | | | | | | | | wind_dir_3pm=W: No (1.0)
## | | | | | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=WSW: Yes (28.0/10.0)
## | | | | | | | | | | | wind_dir_9am=W: No (22.0/9.0)
## | | | | | | | | | | | wind_dir_9am=WNW: No (18.0/7.0)
## | | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | | min_temp <= 7.5: No (3.0)
## | | | | | | | | | | | | min_temp > 7.5: Yes (25.0/4.0)
## | | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | | temp_9am <= 10.7: No (7.0/2.0)
## | | | | | | | | | | | | temp_9am > 10.7: Yes (8.0/2.0)
## | | | | sunshine > 8.9: No (772.0/107.0)
## | | | wind_gust_speed > 48
## | | | | pressure_3pm <= 1012.5
## | | | | | humidity_9am <= 84
## | | | | | | wind_gust_speed <= 69
## | | | | | | | wind_speed_9am <= 30
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | humidity_9am <= 63: No (4.0)
## | | | | | | | | | humidity_9am > 63
## | | | | | | | | | | rainfall <= 8: Yes (13.0)
## | | | | | | | | | | rainfall > 8
## | | | | | | | | | | | wind_speed_9am <= 13: No (5.0)
## | | | | | | | | | | | wind_speed_9am > 13: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (17.0/6.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (15.0/5.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (20.0/9.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | wind_speed_9am <= 15: Yes (7.0/1.0)
## | | | | | | | | | wind_speed_9am > 15
## | | | | | | | | | | humidity_3pm <= 63: No (13.0)
## | | | | | | | | | | humidity_3pm > 63: Yes (4.0/1.0)
## | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | wind_speed_3pm <= 33: Yes (11.0/2.0)
## | | | | | | | | | wind_speed_3pm > 33: No (3.0)
## | | | | | | | | wind_dir_3pm=SE: Yes (32.0/13.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | pressure_3pm <= 1003.9: Yes (3.0)
## | | | | | | | | | pressure_3pm > 1003.9: No (18.0/3.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | pressure_9am <= 1005.3: Yes (4.0)
## | | | | | | | | | pressure_9am > 1005.3: No (18.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | cloud_3pm <= 7: No (24.0/5.0)
## | | | | | | | | | cloud_3pm > 7: Yes (4.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | rainfall <= 2.7: Yes (9.0/1.0)
## | | | | | | | | | rainfall > 2.7
## | | | | | | | | | | cloud_3pm <= 6: Yes (18.0/5.0)
## | | | | | | | | | | cloud_3pm > 6: No (13.0/4.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | wind_dir_9am=N: Yes (5.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (2.0)
## | | | | | | | | | wind_dir_9am=ENE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | wind_speed_3pm <= 24: No (3.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 24: Yes (4.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | cloud_9am <= 5: Yes (4.0)
## | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | rainfall <= 6.5: No (6.0)
## | | | | | | | | | | | rainfall > 6.5
## | | | | | | | | | | | | humidity_3pm <= 58: Yes (4.0)
## | | | | | | | | | | | | humidity_3pm > 58: No (2.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | sunshine <= 6.1: Yes (10.0)
## | | | | | | | | | | sunshine > 6.1
## | | | | | | | | | | | evaporation <= 6.1
## | | | | | | | | | | | | pressure_9am <= 1005.6: Yes (7.0)
## | | | | | | | | | | | | pressure_9am > 1005.6
## | | | | | | | | | | | | | max_temp <= 16.9: No (5.0)
## | | | | | | | | | | | | | max_temp > 16.9: Yes (4.0/1.0)
## | | | | | | | | | | | evaporation > 6.1: No (4.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | evaporation <= 1.2: No (3.0)
## | | | | | | | | | | evaporation > 1.2
## | | | | | | | | | | | sunshine <= 7.4: Yes (7.0)
## | | | | | | | | | | | sunshine > 7.4: No (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NW: Yes (6.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | wind_gust_dir=N: Yes (1.0)
## | | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | | wind_gust_dir=SE: No (2.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | cloud_3pm <= 6: Yes (3.0/1.0)
## | | | | | | | | | | cloud_3pm > 6: No (3.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | cloud_3pm <= 4: No (2.0)
## | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | cloud_9am <= 7: Yes (19.0/2.0)
## | | | | | | | | | | | cloud_9am > 7: No (2.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | wind_dir_9am=N: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (7.0/1.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | pressure_3pm <= 1005.5: No (3.0)
## | | | | | | | | | | | pressure_3pm > 1005.5
## | | | | | | | | | | | | min_temp <= 14.3: Yes (13.0)
## | | | | | | | | | | | | min_temp > 14.3: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | wind_gust_speed <= 61: No (2.0)
## | | | | | | | | | | | wind_gust_speed > 61: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (2.0)
## | | | | | | | | | wind_gust_dir=WNW: Yes (21.0/5.0)
## | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | wind_speed_9am <= 20
## | | | | | | | | | | | cloud_9am <= 5: Yes (3.0/1.0)
## | | | | | | | | | | | cloud_9am > 5: No (3.0)
## | | | | | | | | | | wind_speed_9am > 20: Yes (4.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (3.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | temp_9am <= 10.4
## | | | | | | | | | | wind_gust_speed <= 56: No (11.0)
## | | | | | | | | | | wind_gust_speed > 56
## | | | | | | | | | | | evaporation <= 3.3: No (3.0)
## | | | | | | | | | | | evaporation > 3.3
## | | | | | | | | | | | | pressure_3pm <= 1005.6: Yes (5.0)
## | | | | | | | | | | | | pressure_3pm > 1005.6: No (5.0/1.0)
## | | | | | | | | | temp_9am > 10.4: Yes (83.0/24.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | cloud_9am <= 5: No (2.0)
## | | | | | | | | | | cloud_9am > 5: Yes (2.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NE: No (2.0)
## | | | | | | | | | wind_gust_dir=ENE: No (1.0)
## | | | | | | | | | wind_gust_dir=E: Yes (1.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (2.0)
## | | | | | | | | | wind_gust_dir=SE: No (3.0/1.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=WSW: Yes (4.0/1.0)
## | | | | | | | | | wind_gust_dir=W: Yes (4.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | humidity_9am <= 80
## | | | | | | | | | | | wind_gust_speed <= 50: Yes (2.0)
## | | | | | | | | | | | wind_gust_speed > 50: No (12.0/2.0)
## | | | | | | | | | | humidity_9am > 80: Yes (6.0)
## | | | | | | | | | wind_gust_dir=NW: Yes (25.0/11.0)
## | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | min_temp <= 7.7: No (5.0)
## | | | | | | | | | | min_temp > 7.7: Yes (7.0)
## | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | evaporation <= 1.2: No (5.0)
## | | | | | | | | | evaporation > 1.2
## | | | | | | | | | | cloud_3pm <= 3: No (3.0)
## | | | | | | | | | | cloud_3pm > 3: Yes (38.0/7.0)
## | | | | | | | wind_speed_9am > 30
## | | | | | | | | humidity_9am <= 64: No (27.0/1.0)
## | | | | | | | | humidity_9am > 64
## | | | | | | | | | wind_dir_9am=N: No (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: No (1.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | wind_speed_9am <= 31: Yes (2.0)
## | | | | | | | | | | wind_speed_9am > 31: No (4.0)
## | | | | | | | | | wind_dir_9am=SSE: No (3.0)
## | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | cloud_9am <= 6: Yes (2.0)
## | | | | | | | | | | cloud_9am > 6: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (4.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | sunshine <= 8.4: Yes (3.0)
## | | | | | | | | | | sunshine > 8.4: No (6.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | humidity_3pm <= 64
## | | | | | | | | | | | humidity_9am <= 65: Yes (2.0)
## | | | | | | | | | | | humidity_9am > 65: No (6.0)
## | | | | | | | | | | humidity_3pm > 64: Yes (3.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | cloud_3pm <= 6: No (5.0/2.0)
## | | | | | | | | | | cloud_3pm > 6: Yes (3.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_speed_3pm <= 31: No (3.0)
## | | | | | | | | | | wind_speed_3pm > 31: Yes (8.0/1.0)
## | | | | | | | | | wind_dir_9am=NW: No (5.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | pressure_3pm <= 997.8: Yes (2.0)
## | | | | | | | | | | pressure_3pm > 997.8: No (2.0)
## | | | | | | wind_gust_speed > 69: Yes (231.0/65.0)
## | | | | | humidity_9am > 84
## | | | | | | wind_gust_speed <= 61
## | | | | | | | wind_dir_9am=N: Yes (42.0/6.0)
## | | | | | | | wind_dir_9am=NNE: Yes (22.0/4.0)
## | | | | | | | wind_dir_9am=NE
## | | | | | | | | wind_gust_dir=N: Yes (5.0)
## | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | wind_gust_dir=NE: No (1.0)
## | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | wind_gust_dir=SW: No (2.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | wind_gust_dir=W: No (1.0)
## | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | wind_dir_9am=ENE
## | | | | | | | | wind_gust_speed <= 52
## | | | | | | | | | cloud_3pm <= 4: Yes (2.0)
## | | | | | | | | | cloud_3pm > 4: No (2.0)
## | | | | | | | | wind_gust_speed > 52: Yes (2.0)
## | | | | | | | wind_dir_9am=E
## | | | | | | | | wind_speed_9am <= 6: No (2.0)
## | | | | | | | | wind_speed_9am > 6: Yes (4.0)
## | | | | | | | wind_dir_9am=ESE
## | | | | | | | | wind_speed_3pm <= 31: No (6.0)
## | | | | | | | | wind_speed_3pm > 31: Yes (2.0)
## | | | | | | | wind_dir_9am=SE
## | | | | | | | | pressure_3pm <= 1009.7: Yes (4.0)
## | | | | | | | | pressure_3pm > 1009.7: No (2.0)
## | | | | | | | wind_dir_9am=SSE
## | | | | | | | | humidity_3pm <= 61: No (3.0)
## | | | | | | | | humidity_3pm > 61
## | | | | | | | | | sunshine <= 4.1: No (2.0)
## | | | | | | | | | sunshine > 4.1: Yes (3.0)
## | | | | | | | wind_dir_9am=S
## | | | | | | | | temp_9am <= 16.6: No (6.0/1.0)
## | | | | | | | | temp_9am > 16.6: Yes (5.0)
## | | | | | | | wind_dir_9am=SSW
## | | | | | | | | wind_gust_speed <= 56: No (7.0)
## | | | | | | | | wind_gust_speed > 56: Yes (5.0/1.0)
## | | | | | | | wind_dir_9am=SW: Yes (22.0/7.0)
## | | | | | | | wind_dir_9am=WSW
## | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | min_temp <= 8.7: No (3.0/1.0)
## | | | | | | | | | min_temp > 8.7: Yes (11.0)
## | | | | | | | | cloud_3pm > 6: No (10.0/1.0)
## | | | | | | | wind_dir_9am=W: Yes (35.0/12.0)
## | | | | | | | wind_dir_9am=WNW
## | | | | | | | | cloud_9am <= 4: No (3.0)
## | | | | | | | | cloud_9am > 4: Yes (33.0/8.0)
## | | | | | | | wind_dir_9am=NW: Yes (43.0/12.0)
## | | | | | | | wind_dir_9am=NNW: Yes (46.0/10.0)
## | | | | | | wind_gust_speed > 61: Yes (217.0/27.0)
## | | | | pressure_3pm > 1012.5
## | | | | | humidity_9am <= 67
## | | | | | | wind_dir_9am=N: No (16.0/3.0)
## | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | wind_dir_9am=ENE: No (2.0/1.0)
## | | | | | | wind_dir_9am=E
## | | | | | | | wind_gust_speed <= 57: No (8.0)
## | | | | | | | wind_gust_speed > 57: Yes (3.0/1.0)
## | | | | | | wind_dir_9am=ESE
## | | | | | | | pressure_3pm <= 1022.4
## | | | | | | | | humidity_3pm <= 62: No (11.0)
## | | | | | | | | humidity_3pm > 62
## | | | | | | | | | temp_3pm <= 20.1: No (2.0)
## | | | | | | | | | temp_3pm > 20.1: Yes (2.0)
## | | | | | | | pressure_3pm > 1022.4: Yes (7.0/1.0)
## | | | | | | wind_dir_9am=SE
## | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | wind_gust_dir=E: No (2.0)
## | | | | | | | wind_gust_dir=ESE
## | | | | | | | | cloud_3pm <= 5: Yes (4.0/1.0)
## | | | | | | | | cloud_3pm > 5: No (3.0)
## | | | | | | | wind_gust_dir=SE
## | | | | | | | | rainfall <= 12.2: No (16.0/4.0)
## | | | | | | | | rainfall > 12.2: Yes (5.0)
## | | | | | | | wind_gust_dir=SSE: Yes (8.0/1.0)
## | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | wind_gust_dir=SSW: Yes (2.0)
## | | | | | | | wind_gust_dir=SW: No (1.0)
## | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | wind_gust_dir=W: Yes (0.0)
## | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | wind_dir_9am=SSE: No (56.0/10.0)
## | | | | | | wind_dir_9am=S: No (53.0/8.0)
## | | | | | | wind_dir_9am=SSW
## | | | | | | | wind_speed_3pm <= 39
## | | | | | | | | rainfall <= 22.5: No (34.0/2.0)
## | | | | | | | | rainfall > 22.5: Yes (3.0/1.0)
## | | | | | | | wind_speed_3pm > 39
## | | | | | | | | temp_9am <= 12.6: No (2.0)
## | | | | | | | | temp_9am > 12.6: Yes (6.0)
## | | | | | | wind_dir_9am=SW: No (85.0/16.0)
## | | | | | | wind_dir_9am=WSW
## | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | wind_dir_3pm=SSE: No (2.0)
## | | | | | | | wind_dir_3pm=S: No (5.0/1.0)
## | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | cloud_3pm <= 5: Yes (5.0)
## | | | | | | | | cloud_3pm > 5: No (3.0/1.0)
## | | | | | | | wind_dir_3pm=SW
## | | | | | | | | wind_gust_speed <= 63: No (14.0)
## | | | | | | | | wind_gust_speed > 63
## | | | | | | | | | wind_speed_9am <= 28: Yes (3.0)
## | | | | | | | | | wind_speed_9am > 28: No (2.0)
## | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | pressure_3pm <= 1019.4
## | | | | | | | | | humidity_9am <= 60: Yes (11.0/1.0)
## | | | | | | | | | humidity_9am > 60
## | | | | | | | | | | wind_speed_3pm <= 24: Yes (4.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 24: No (6.0)
## | | | | | | | | pressure_3pm > 1019.4: No (9.0)
## | | | | | | | wind_dir_3pm=W
## | | | | | | | | cloud_9am <= 5: Yes (3.0)
## | | | | | | | | cloud_9am > 5: No (11.0/2.0)
## | | | | | | | wind_dir_3pm=WNW: No (2.0)
## | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | wind_dir_3pm=NNW: No (1.0)
## | | | | | | wind_dir_9am=W
## | | | | | | | cloud_9am <= 7
## | | | | | | | | evaporation <= 2.9: No (10.0)
## | | | | | | | | evaporation > 2.9
## | | | | | | | | | sunshine <= 6.4: Yes (5.0)
## | | | | | | | | | sunshine > 6.4
## | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | cloud_3pm <= 4: No (2.0)
## | | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | | pressure_9am <= 1017.3: Yes (11.0/2.0)
## | | | | | | | | | | | | pressure_9am > 1017.3: No (6.0/1.0)
## | | | | | | | | | | cloud_3pm > 6: No (6.0)
## | | | | | | | cloud_9am > 7: Yes (4.0)
## | | | | | | wind_dir_9am=WNW: No (20.0/4.0)
## | | | | | | wind_dir_9am=NW
## | | | | | | | rainfall <= 11.1: No (5.0/1.0)
## | | | | | | | rainfall > 11.1: Yes (2.0)
## | | | | | | wind_dir_9am=NNW: No (5.0/1.0)
## | | | | | humidity_9am > 67
## | | | | | | wind_speed_9am <= 20
## | | | | | | | wind_gust_dir=N
## | | | | | | | | wind_speed_3pm <= 26: No (11.0/2.0)
## | | | | | | | | wind_speed_3pm > 26: Yes (5.0)
## | | | | | | | wind_gust_dir=NNE
## | | | | | | | | wind_gust_speed <= 56: No (6.0)
## | | | | | | | | wind_gust_speed > 56: Yes (2.0)
## | | | | | | | wind_gust_dir=NE: No (4.0)
## | | | | | | | wind_gust_dir=ENE: Yes (8.0/1.0)
## | | | | | | | wind_gust_dir=E
## | | | | | | | | cloud_3pm <= 4: No (2.0)
## | | | | | | | | cloud_3pm > 4
## | | | | | | | | | wind_speed_9am <= 13: Yes (2.0)
## | | | | | | | | | wind_speed_9am > 13: No (3.0/1.0)
## | | | | | | | wind_gust_dir=ESE: Yes (18.0/7.0)
## | | | | | | | wind_gust_dir=SE: Yes (29.0/7.0)
## | | | | | | | wind_gust_dir=SSE
## | | | | | | | | humidity_9am <= 84
## | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SE: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | humidity_3pm <= 58: Yes (5.0/1.0)
## | | | | | | | | | | humidity_3pm > 58: No (8.0)
## | | | | | | | | | wind_dir_3pm=S: No (4.0)
## | | | | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | humidity_9am > 84: Yes (9.0)
## | | | | | | | wind_gust_dir=S
## | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=E: Yes (1.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SE: No (1.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | sunshine <= 8.3: Yes (3.0)
## | | | | | | | | | sunshine > 8.3: No (7.0/1.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | pressure_9am <= 1022.8
## | | | | | | | | | | wind_speed_3pm <= 28: No (7.0)
## | | | | | | | | | | wind_speed_3pm > 28
## | | | | | | | | | | | temp_3pm <= 12.7: Yes (2.0)
## | | | | | | | | | | | temp_3pm > 12.7: No (4.0)
## | | | | | | | | | pressure_9am > 1022.8: Yes (6.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | cloud_9am <= 4: No (3.0)
## | | | | | | | | | cloud_9am > 4: Yes (10.0/1.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=W: Yes (0.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | wind_gust_dir=SSW
## | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=E: No (1.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SE: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | cloud_3pm <= 6: Yes (2.0)
## | | | | | | | | | cloud_3pm > 6: No (2.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | pressure_3pm <= 1018.8: No (5.0/1.0)
## | | | | | | | | | pressure_3pm > 1018.8: Yes (9.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | cloud_9am <= 4: No (4.0)
## | | | | | | | | | cloud_9am > 4
## | | | | | | | | | | temp_9am <= 13.8
## | | | | | | | | | | | wind_speed_3pm <= 19: No (3.0)
## | | | | | | | | | | | wind_speed_3pm > 19: Yes (18.0/3.0)
## | | | | | | | | | | temp_9am > 13.8: No (4.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | rainfall <= 8.2: No (8.0)
## | | | | | | | | | rainfall > 8.2
## | | | | | | | | | | cloud_3pm <= 6: Yes (4.0)
## | | | | | | | | | | cloud_3pm > 6: No (3.0/1.0)
## | | | | | | | | wind_dir_3pm=WSW: No (4.0/1.0)
## | | | | | | | | wind_dir_3pm=W: Yes (1.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | wind_gust_dir=SW
## | | | | | | | | wind_dir_3pm=N: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | wind_dir_3pm=ESE: No (1.0)
## | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | wind_dir_3pm=S: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | temp_9am <= 9.6: Yes (7.0/1.0)
## | | | | | | | | | temp_9am > 9.6: No (10.0/1.0)
## | | | | | | | | wind_dir_3pm=SW: No (27.0/12.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | pressure_3pm <= 1015.3: No (9.0/1.0)
## | | | | | | | | | pressure_3pm > 1015.3: Yes (6.0/1.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | humidity_9am <= 88: Yes (7.0/1.0)
## | | | | | | | | | humidity_9am > 88: No (2.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | wind_gust_dir=WSW
## | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | wind_dir_3pm=SE: No (1.0)
## | | | | | | | | wind_dir_3pm=SSE: No (1.0)
## | | | | | | | | wind_dir_3pm=S: No (4.0)
## | | | | | | | | wind_dir_3pm=SSW: No (9.0/2.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (19.0/5.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | wind_dir_9am=N: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | temp_3pm <= 13.5: No (2.0)
## | | | | | | | | | | temp_3pm > 13.5: Yes (2.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_gust_speed <= 56: No (9.0/1.0)
## | | | | | | | | | | wind_gust_speed > 56: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | temp_3pm <= 10.9: Yes (2.0)
## | | | | | | | | | | temp_3pm > 10.9: No (3.0)
## | | | | | | | | | wind_dir_9am=NW: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | sunshine <= 6.9: Yes (6.0)
## | | | | | | | | | sunshine > 6.9
## | | | | | | | | | | pressure_9am <= 1019.7: No (11.0/2.0)
## | | | | | | | | | | pressure_9am > 1019.7: Yes (2.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | max_temp <= 13.3: No (3.0)
## | | | | | | | | | max_temp > 13.3: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | wind_gust_dir=W
## | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SE: Yes (6.0)
## | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=S: No (1.0)
## | | | | | | | | wind_dir_3pm=SSW: No (6.0/1.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | evaporation <= 3.2: Yes (5.0)
## | | | | | | | | | evaporation > 3.2: No (4.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (18.0/5.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | sunshine <= 6.1: Yes (9.0)
## | | | | | | | | | sunshine > 6.1
## | | | | | | | | | | rainfall <= 4.6: No (13.0/1.0)
## | | | | | | | | | | rainfall > 4.6: Yes (6.0/1.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (18.0/5.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (5.0/1.0)
## | | | | | | | | wind_dir_3pm=NNW: No (1.0)
## | | | | | | | wind_gust_dir=WNW
## | | | | | | | | wind_dir_9am=N: Yes (3.0/1.0)
## | | | | | | | | wind_dir_9am=NNE: Yes (3.0)
## | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | wind_dir_9am=E: No (3.0/1.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | wind_dir_9am=SSW: No (2.0/1.0)
## | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | pressure_9am <= 1014.9: Yes (4.0)
## | | | | | | | | | pressure_9am > 1014.9: No (2.0)
## | | | | | | | | wind_dir_9am=W: No (7.0/1.0)
## | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | wind_dir_3pm=WSW: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | wind_dir_3pm=WNW: No (3.0/1.0)
## | | | | | | | | | wind_dir_3pm=NW: No (1.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | humidity_3pm <= 57: No (2.0)
## | | | | | | | | | humidity_3pm > 57: Yes (6.0/1.0)
## | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | humidity_9am <= 92: No (3.0)
## | | | | | | | | | humidity_9am > 92: Yes (3.0)
## | | | | | | | wind_gust_dir=NW: Yes (33.0/11.0)
## | | | | | | | wind_gust_dir=NNW
## | | | | | | | | pressure_3pm <= 1016.3: Yes (15.0/5.0)
## | | | | | | | | pressure_3pm > 1016.3: No (5.0)
## | | | | | | wind_speed_9am > 20
## | | | | | | | wind_gust_speed <= 65
## | | | | | | | | cloud_9am <= 3: No (34.0/4.0)
## | | | | | | | | cloud_9am > 3
## | | | | | | | | | wind_gust_dir=N: No (9.0/1.0)
## | | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | cloud_3pm <= 7: No (5.0)
## | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | | wind_gust_speed <= 54
## | | | | | | | | | | | humidity_3pm <= 63: Yes (2.0)
## | | | | | | | | | | | humidity_3pm > 63: No (2.0)
## | | | | | | | | | | wind_gust_speed > 54: Yes (3.0)
## | | | | | | | | | wind_gust_dir=E
## | | | | | | | | | | sunshine <= 6: Yes (4.0)
## | | | | | | | | | | sunshine > 6
## | | | | | | | | | | | wind_speed_9am <= 22: Yes (4.0/1.0)
## | | | | | | | | | | | wind_speed_9am > 22: No (16.0/2.0)
## | | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | | wind_gust_speed <= 59: No (14.0/4.0)
## | | | | | | | | | | wind_gust_speed > 59: Yes (4.0)
## | | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | | rainfall <= 21
## | | | | | | | | | | | temp_9am <= 22.1
## | | | | | | | | | | | | temp_3pm <= 14.3: Yes (2.0)
## | | | | | | | | | | | | temp_3pm > 14.3: No (19.0)
## | | | | | | | | | | | temp_9am > 22.1
## | | | | | | | | | | | | max_temp <= 26.6: Yes (7.0)
## | | | | | | | | | | | | max_temp > 26.6
## | | | | | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | | | | | pressure_3pm <= 1016.1: Yes (2.0)
## | | | | | | | | | | | | | | pressure_3pm > 1016.1: No (2.0)
## | | | | | | | | | | | | | cloud_3pm > 5: No (2.0)
## | | | | | | | | | | rainfall > 21: Yes (5.0)
## | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | cloud_9am <= 5: Yes (4.0)
## | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | wind_speed_3pm <= 24: No (7.0)
## | | | | | | | | | | | wind_speed_3pm > 24
## | | | | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | | | wind_speed_9am <= 31: No (3.0/1.0)
## | | | | | | | | | | | | | wind_speed_9am > 31: Yes (3.0)
## | | | | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | | humidity_3pm <= 60: No (5.0)
## | | | | | | | | | | | | | | humidity_3pm > 60
## | | | | | | | | | | | | | | | humidity_3pm <= 62: Yes (3.0)
## | | | | | | | | | | | | | | | humidity_3pm > 62: No (3.0)
## | | | | | | | | | | | | | cloud_9am > 6
## | | | | | | | | | | | | | | cloud_3pm <= 7: Yes (4.0)
## | | | | | | | | | | | | | | cloud_3pm > 7: No (3.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | | | wind_speed_9am <= 31
## | | | | | | | | | | | | | | wind_gust_speed <= 52: Yes (2.0)
## | | | | | | | | | | | | | | wind_gust_speed > 52: No (8.0/1.0)
## | | | | | | | | | | | | | wind_speed_9am > 31: Yes (3.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | wind_speed_9am <= 22: No (11.0)
## | | | | | | | | | | wind_speed_9am > 22
## | | | | | | | | | | | wind_speed_9am <= 35
## | | | | | | | | | | | | sunshine <= 6.1: Yes (13.0/1.0)
## | | | | | | | | | | | | sunshine > 6.1
## | | | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | | | wind_speed_3pm <= 41: No (26.0/6.0)
## | | | | | | | | | | | | | | wind_speed_3pm > 41: Yes (3.0)
## | | | | | | | | | | | | | cloud_3pm > 7: Yes (7.0/1.0)
## | | | | | | | | | | | wind_speed_9am > 35: No (8.0)
## | | | | | | | | | wind_gust_dir=SSW: No (63.0/11.0)
## | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (1.0)
## | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | cloud_3pm <= 6: Yes (4.0)
## | | | | | | | | | | | cloud_3pm > 6: No (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | wind_speed_3pm <= 28: No (11.0/3.0)
## | | | | | | | | | | | wind_speed_3pm > 28: Yes (9.0/2.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | | | | cloud_9am > 5: No (10.0)
## | | | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (5.0)
## | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=SW: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=WSW: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=W: No (1.0)
## | | | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | wind_speed_9am <= 22: Yes (3.0)
## | | | | | | | | | | | wind_speed_9am > 22: No (12.0/4.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | pressure_9am <= 1014: Yes (9.0/3.0)
## | | | | | | | | | | | pressure_9am > 1014: No (10.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | temp_9am <= 9.4: No (2.0)
## | | | | | | | | | | | temp_9am > 9.4: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (0.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | evaporation <= 3.8: No (17.0/2.0)
## | | | | | | | | | | evaporation > 3.8
## | | | | | | | | | | | sunshine <= 7.9: Yes (3.0)
## | | | | | | | | | | | sunshine > 7.9: No (37.0/15.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | wind_dir_9am=N: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=WSW: No (3.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | humidity_3pm <= 61: Yes (3.0)
## | | | | | | | | | | | humidity_3pm > 61: No (2.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | temp_3pm <= 16.1: Yes (2.0)
## | | | | | | | | | | | temp_3pm > 16.1: No (2.0)
## | | | | | | | | | | wind_dir_9am=NW: No (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (1.0)
## | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | temp_9am <= 13.2: No (10.0/2.0)
## | | | | | | | | | | temp_9am > 13.2: Yes (10.0/3.0)
## | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | temp_3pm <= 14.6: No (2.0)
## | | | | | | | | | | temp_3pm > 14.6: Yes (3.0)
## | | | | | | | wind_gust_speed > 65
## | | | | | | | | wind_dir_3pm=N: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | wind_dir_3pm=E: No (3.0/1.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | cloud_3pm <= 6: Yes (7.0/1.0)
## | | | | | | | | | cloud_3pm > 6: No (3.0/1.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | evaporation <= 5.6
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | | min_temp <= 17.4: No (5.0)
## | | | | | | | | | | | min_temp > 17.4
## | | | | | | | | | | | | wind_speed_3pm <= 46: Yes (3.0)
## | | | | | | | | | | | | wind_speed_3pm > 46: No (3.0/1.0)
## | | | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | evaporation > 5.6: Yes (2.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (3.0)
## | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | wind_dir_9am=N: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | evaporation <= 4.1: Yes (2.0)
## | | | | | | | | | | | evaporation > 4.1: No (6.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSW: No (2.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (2.0)
## | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=W: Yes (0.0)
## | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | temp_3pm <= 12.4: No (4.0)
## | | | | | | | | | temp_3pm > 12.4: Yes (12.0/2.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (7.0/1.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (4.0/1.0)
## | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | rainfall <= 3: No (3.0)
## | | | | | | | | | | rainfall > 3: Yes (8.0)
## | | | | | | | | | wind_dir_9am=W: No (2.0)
## | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | wind_dir_9am=NNW: No (1.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | evaporation <= 6.1
## | | | | | | | | | | min_temp <= 2.8: No (2.0)
## | | | | | | | | | | min_temp > 2.8
## | | | | | | | | | | | evaporation <= 4.2: No (3.0/1.0)
## | | | | | | | | | | | evaporation > 4.2: Yes (11.0)
## | | | | | | | | | evaporation > 6.1: No (2.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | rainfall <= 22.6: No (12.0/2.0)
## | | | | | | | | | rainfall > 22.6: Yes (3.0)
## | | | | | | | | wind_dir_3pm=WNW: No (10.0/4.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (8.0/1.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (2.0)
## humidity_3pm > 68
## | humidity_3pm <= 82
## | | rainfall <= 1.2
## | | | wind_gust_speed <= 41
## | | | | cloud_3pm <= 6
## | | | | | sunshine <= 8.6
## | | | | | | min_temp <= 1.9: No (411.0/41.0)
## | | | | | | min_temp > 1.9
## | | | | | | | pressure_3pm <= 1022.8
## | | | | | | | | humidity_3pm <= 76: No (2474.0/581.0)
## | | | | | | | | humidity_3pm > 76
## | | | | | | | | | rainfall <= 0.5
## | | | | | | | | | | wind_speed_3pm <= 17
## | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | | humidity_3pm <= 78: No (5.0/1.0)
## | | | | | | | | | | | | | | humidity_3pm > 78: Yes (8.0)
## | | | | | | | | | | | | | cloud_9am > 6: No (2.0)
## | | | | | | | | | | | | wind_dir_3pm=NNE: No (12.0/3.0)
## | | | | | | | | | | | | wind_dir_3pm=NE: Yes (3.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | | | | humidity_9am <= 93
## | | | | | | | | | | | | | | temp_9am <= 19.3: Yes (2.0)
## | | | | | | | | | | | | | | temp_9am > 19.3: No (2.0)
## | | | | | | | | | | | | | humidity_9am > 93: No (3.0)
## | | | | | | | | | | | | wind_dir_3pm=E: No (1.0)
## | | | | | | | | | | | | wind_dir_3pm=ESE: No (2.0)
## | | | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | | | humidity_3pm <= 78: No (19.0/2.0)
## | | | | | | | | | | | | | humidity_3pm > 78
## | | | | | | | | | | | | | | wind_speed_9am <= 11: Yes (2.0)
## | | | | | | | | | | | | | | wind_speed_9am > 11
## | | | | | | | | | | | | | | | humidity_3pm <= 80: Yes (6.0/1.0)
## | | | | | | | | | | | | | | | humidity_3pm > 80
## | | | | | | | | | | | | | | | | humidity_9am <= 61: Yes (2.0)
## | | | | | | | | | | | | | | | | humidity_9am > 61
## | | | | | | | | | | | | | | | | | temp_3pm <= 12.1: Yes (3.0/1.0)
## | | | | | | | | | | | | | | | | | temp_3pm > 12.1: No (6.0)
## | | | | | | | | | | | | wind_dir_3pm=SSE: No (6.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | | | wind_speed_9am <= 2: No (4.0/1.0)
## | | | | | | | | | | | | | wind_speed_9am > 2: Yes (2.0)
## | | | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SSE: Yes (1.0)
## | | | | | | | | | | | | | wind_gust_dir=S: Yes (3.0/1.0)
## | | | | | | | | | | | | | wind_gust_dir=SSW: No (2.0)
## | | | | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | | | humidity_3pm <= 78: Yes (2.0)
## | | | | | | | | | | | | | humidity_3pm > 78: No (3.0)
## | | | | | | | | | | | | wind_dir_3pm=WSW: Yes (4.0)
## | | | | | | | | | | | | wind_dir_3pm=W: Yes (2.0)
## | | | | | | | | | | | | wind_dir_3pm=WNW: No (7.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | | | | humidity_9am <= 98: Yes (5.0)
## | | | | | | | | | | | | | humidity_9am > 98: No (2.0)
## | | | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | | | temp_9am <= 12.3: No (8.0)
## | | | | | | | | | | | | | temp_9am > 12.3: Yes (3.0)
## | | | | | | | | | | | wind_dir_9am=NNE: Yes (33.0/13.0)
## | | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | | sunshine <= 1.7: Yes (4.0)
## | | | | | | | | | | | | sunshine > 1.7: No (32.0/4.0)
## | | | | | | | | | | | wind_dir_9am=ENE: No (22.0/5.0)
## | | | | | | | | | | | wind_dir_9am=E: No (21.0/8.0)
## | | | | | | | | | | | wind_dir_9am=ESE: No (21.0/8.0)
## | | | | | | | | | | | wind_dir_9am=SE: No (22.0/6.0)
## | | | | | | | | | | | wind_dir_9am=SSE: No (26.0/5.0)
## | | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | | humidity_3pm <= 78: No (10.0/1.0)
## | | | | | | | | | | | | humidity_3pm > 78: Yes (9.0/2.0)
## | | | | | | | | | | | wind_dir_9am=SSW: No (35.0/11.0)
## | | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | | temp_9am <= 18.2: Yes (14.0/6.0)
## | | | | | | | | | | | | temp_9am > 18.2: No (14.0/3.0)
## | | | | | | | | | | | wind_dir_9am=WSW: Yes (15.0/7.0)
## | | | | | | | | | | | wind_dir_9am=W: No (18.0/7.0)
## | | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | | | | humidity_3pm <= 81: No (26.0/1.0)
## | | | | | | | | | | | | | humidity_3pm > 81: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 5: Yes (3.0)
## | | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | | temp_9am <= 17.9: No (17.0/4.0)
## | | | | | | | | | | | | temp_9am > 17.9: Yes (7.0)
## | | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | | temp_9am <= 14.2: Yes (10.0/2.0)
## | | | | | | | | | | | | temp_9am > 14.2: No (16.0/7.0)
## | | | | | | | | | | wind_speed_3pm > 17: No (250.0/51.0)
## | | | | | | | | | rainfall > 0.5
## | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | humidity_3pm <= 80: Yes (7.0/1.0)
## | | | | | | | | | | | humidity_3pm > 80: No (2.0)
## | | | | | | | | | | wind_gust_dir=NNE: Yes (3.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (6.0/2.0)
## | | | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | | | temp_3pm <= 20.6: No (5.0)
## | | | | | | | | | | | temp_3pm > 20.6: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=E: Yes (7.0/2.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (2.0/1.0)
## | | | | | | | | | | wind_gust_dir=SE: No (7.0/2.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (9.0/2.0)
## | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | temp_3pm <= 16.4: No (2.0)
## | | | | | | | | | | | temp_3pm > 16.4: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (5.0/1.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (5.0/1.0)
## | | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | | humidity_9am <= 97: Yes (5.0/1.0)
## | | | | | | | | | | | humidity_9am > 97: No (3.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | humidity_3pm <= 79: No (12.0/3.0)
## | | | | | | | | | | | humidity_3pm > 79: Yes (10.0/2.0)
## | | | | | | | | | | wind_gust_dir=WNW: Yes (4.0/1.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | wind_speed_9am <= 7: No (2.0)
## | | | | | | | | | | | wind_speed_9am > 7: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | rainfall <= 0.9: Yes (4.0/1.0)
## | | | | | | | | | | | rainfall > 0.9: No (5.0)
## | | | | | | | pressure_3pm > 1022.8: No (814.0/117.0)
## | | | | | sunshine > 8.6
## | | | | | | rainfall <= 0.3: No (405.0/30.0)
## | | | | | | rainfall > 0.3
## | | | | | | | evaporation <= 6.3: No (39.0/6.0)
## | | | | | | | evaporation > 6.3: Yes (7.0/1.0)
## | | | | cloud_3pm > 6
## | | | | | pressure_3pm <= 1019.3
## | | | | | | humidity_3pm <= 78
## | | | | | | | pressure_3pm <= 1009.3
## | | | | | | | | wind_dir_9am=N: Yes (41.0/12.0)
## | | | | | | | | wind_dir_9am=NNE: Yes (15.0/5.0)
## | | | | | | | | wind_dir_9am=NE: No (17.0/7.0)
## | | | | | | | | wind_dir_9am=ENE: Yes (18.0/3.0)
## | | | | | | | | wind_dir_9am=E
## | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | temp_9am <= 27: No (3.0)
## | | | | | | | | | | temp_9am > 27: Yes (2.0)
## | | | | | | | | | cloud_3pm > 7: Yes (5.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (21.0/8.0)
## | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | evaporation <= 4.2: Yes (4.0)
## | | | | | | | | | evaporation > 4.2: No (8.0)
## | | | | | | | | wind_dir_9am=SSE: Yes (14.0/6.0)
## | | | | | | | | wind_dir_9am=S: No (12.0/6.0)
## | | | | | | | | wind_dir_9am=SSW: No (13.0/5.0)
## | | | | | | | | wind_dir_9am=SW: No (10.0/4.0)
## | | | | | | | | wind_dir_9am=WSW: No (9.0/3.0)
## | | | | | | | | wind_dir_9am=W: Yes (21.0/9.0)
## | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | humidity_3pm <= 75
## | | | | | | | | | | | rainfall <= 0.3: No (7.0/1.0)
## | | | | | | | | | | | rainfall > 0.3: Yes (2.0)
## | | | | | | | | | | humidity_3pm > 75: Yes (4.0)
## | | | | | | | | | cloud_3pm > 7: No (9.0/1.0)
## | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | cloud_9am <= 5: No (3.0)
## | | | | | | | | | cloud_9am > 5: Yes (15.0/6.0)
## | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | wind_speed_3pm <= 15: Yes (9.0/3.0)
## | | | | | | | | | wind_speed_3pm > 15: No (10.0/3.0)
## | | | | | | | pressure_3pm > 1009.3: No (1095.0/401.0)
## | | | | | | humidity_3pm > 78
## | | | | | | | min_temp <= 22.8
## | | | | | | | | humidity_9am <= 75: Yes (107.0/26.0)
## | | | | | | | | humidity_9am > 75
## | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | wind_dir_3pm=N: Yes (11.0/4.0)
## | | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | | min_temp <= 15.4: No (6.0)
## | | | | | | | | | | | min_temp > 15.4: Yes (4.0)
## | | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | | temp_3pm <= 24: No (4.0)
## | | | | | | | | | | | temp_3pm > 24: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=ENE: No (4.0/1.0)
## | | | | | | | | | | wind_dir_3pm=E: No (7.0/1.0)
## | | | | | | | | | | wind_dir_3pm=ESE: No (5.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | humidity_3pm <= 79: No (5.0)
## | | | | | | | | | | | humidity_3pm > 79
## | | | | | | | | | | | | pressure_9am <= 1017: Yes (6.0)
## | | | | | | | | | | | | pressure_9am > 1017
## | | | | | | | | | | | | | temp_3pm <= 15.3: Yes (4.0)
## | | | | | | | | | | | | | temp_3pm > 15.3: No (9.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (9.0/3.0)
## | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | wind_gust_speed <= 37: No (13.0/3.0)
## | | | | | | | | | | | wind_gust_speed > 37: Yes (6.0)
## | | | | | | | | | | wind_dir_3pm=SSW: No (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SW: No (6.0/1.0)
## | | | | | | | | | | wind_dir_3pm=WSW: No (9.0/1.0)
## | | | | | | | | | | wind_dir_3pm=W: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | humidity_9am <= 85: No (3.0)
## | | | | | | | | | | | humidity_9am > 85: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=NW: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | humidity_3pm <= 80: No (6.0/1.0)
## | | | | | | | | | | | humidity_3pm > 80: Yes (3.0)
## | | | | | | | | | rainfall > 0.1
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | wind_speed_3pm <= 6: Yes (7.0)
## | | | | | | | | | | | wind_speed_3pm > 6: No (19.0/4.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | rainfall <= 0.7: Yes (5.0)
## | | | | | | | | | | | rainfall > 0.7: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | humidity_3pm <= 80: Yes (5.0/1.0)
## | | | | | | | | | | | humidity_3pm > 80: No (2.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | temp_3pm <= 15.7: Yes (3.0)
## | | | | | | | | | | | temp_3pm > 15.7: No (4.0)
## | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | pressure_3pm <= 1012.2: Yes (2.0)
## | | | | | | | | | | | pressure_3pm > 1012.2: No (2.0)
## | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | wind_gust_speed <= 33: No (3.0)
## | | | | | | | | | | | wind_gust_speed > 33: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | rainfall <= 0.9: Yes (4.0)
## | | | | | | | | | | | rainfall > 0.9: No (2.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (8.0/1.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (5.0/1.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | evaporation <= 3.6: No (3.0)
## | | | | | | | | | | | evaporation > 3.6: Yes (9.0/1.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | humidity_3pm <= 79: No (2.0)
## | | | | | | | | | | | humidity_3pm > 79: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (9.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (1.0)
## | | | | | | | min_temp > 22.8: Yes (21.0)
## | | | | | pressure_3pm > 1019.3
## | | | | | | evaporation <= 6.3: No (1009.0/215.0)
## | | | | | | evaporation > 6.3: Yes (32.0/13.0)
## | | | wind_gust_speed > 41
## | | | | sunshine <= 6.2
## | | | | | pressure_3pm <= 1015.1: Yes (564.0/152.0)
## | | | | | pressure_3pm > 1015.1
## | | | | | | humidity_3pm <= 77
## | | | | | | | wind_dir_3pm=N
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | humidity_3pm <= 76
## | | | | | | | | | | wind_gust_speed <= 63: No (6.0)
## | | | | | | | | | | wind_gust_speed > 63
## | | | | | | | | | | | cloud_9am <= 6: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 6: No (3.0/1.0)
## | | | | | | | | | humidity_3pm > 76: Yes (2.0)
## | | | | | | | | wind_gust_dir=NNE: No (5.0/1.0)
## | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | rainfall <= 0.1
## | | | | | | | | | humidity_3pm <= 75: No (13.0/4.0)
## | | | | | | | | | humidity_3pm > 75: Yes (2.0)
## | | | | | | | | rainfall > 0.1: Yes (3.0)
## | | | | | | | wind_dir_3pm=NE: Yes (7.0/1.0)
## | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | temp_9am <= 21.4: Yes (3.0)
## | | | | | | | | temp_9am > 21.4: No (3.0)
## | | | | | | | wind_dir_3pm=E
## | | | | | | | | pressure_9am <= 1017.8: Yes (3.0/1.0)
## | | | | | | | | pressure_9am > 1017.8: No (9.0)
## | | | | | | | wind_dir_3pm=ESE: No (13.0/5.0)
## | | | | | | | wind_dir_3pm=SE: Yes (16.0/5.0)
## | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | cloud_3pm <= 6: Yes (2.0)
## | | | | | | | | cloud_3pm > 6
## | | | | | | | | | min_temp <= 15.4: Yes (12.0/5.0)
## | | | | | | | | | min_temp > 15.4: No (8.0)
## | | | | | | | wind_dir_3pm=S
## | | | | | | | | rainfall <= 0.3: No (34.0/4.0)
## | | | | | | | | rainfall > 0.3: Yes (11.0/3.0)
## | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | wind_gust_dir=N: No (1.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | wind_gust_dir=S: Yes (10.0/1.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | min_temp <= 9.9: Yes (3.0)
## | | | | | | | | | min_temp > 9.9: No (8.0/2.0)
## | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | wind_gust_dir=WSW: No (4.0/1.0)
## | | | | | | | | wind_gust_dir=W: No (1.0)
## | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | wind_dir_3pm=SW
## | | | | | | | | rainfall <= 0.3: Yes (8.0/2.0)
## | | | | | | | | rainfall > 0.3: No (2.0)
## | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | pressure_9am <= 1020
## | | | | | | | | | wind_speed_3pm <= 22: Yes (5.0)
## | | | | | | | | | wind_speed_3pm > 22
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (2.0)
## | | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | | wind_gust_speed <= 52: No (6.0/1.0)
## | | | | | | | | | | | wind_gust_speed > 52: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=W: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | pressure_9am > 1020: No (7.0)
## | | | | | | | wind_dir_3pm=W
## | | | | | | | | cloud_3pm <= 7: No (14.0/5.0)
## | | | | | | | | cloud_3pm > 7: Yes (6.0/2.0)
## | | | | | | | wind_dir_3pm=WNW: Yes (15.0/4.0)
## | | | | | | | wind_dir_3pm=NW: Yes (2.0)
## | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | wind_speed_9am <= 7: Yes (2.0)
## | | | | | | | | wind_speed_9am > 7: No (4.0/1.0)
## | | | | | | humidity_3pm > 77: Yes (102.0/30.0)
## | | | | sunshine > 6.2
## | | | | | pressure_9am <= 1009
## | | | | | | temp_3pm <= 13.8: Yes (86.0/15.0)
## | | | | | | temp_3pm > 13.8
## | | | | | | | wind_dir_3pm=N: Yes (23.0/8.0)
## | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | humidity_3pm <= 78: No (19.0/5.0)
## | | | | | | | | humidity_3pm > 78: Yes (5.0)
## | | | | | | | wind_dir_3pm=NE: Yes (29.0/10.0)
## | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | temp_3pm <= 28.7: No (11.0/1.0)
## | | | | | | | | temp_3pm > 28.7: Yes (3.0)
## | | | | | | | wind_dir_3pm=E
## | | | | | | | | pressure_3pm <= 1004.5: No (4.0)
## | | | | | | | | pressure_3pm > 1004.5: Yes (3.0/1.0)
## | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | wind_speed_3pm <= 11: Yes (2.0)
## | | | | | | | | wind_speed_3pm > 11: No (6.0)
## | | | | | | | wind_dir_3pm=SE
## | | | | | | | | sunshine <= 8.7: Yes (12.0/5.0)
## | | | | | | | | sunshine > 8.7: No (2.0)
## | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | wind_gust_dir=E: Yes (1.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | wind_speed_9am <= 26: No (6.0)
## | | | | | | | | | wind_speed_9am > 26: Yes (2.0)
## | | | | | | | | wind_gust_dir=S: No (4.0/1.0)
## | | | | | | | | wind_gust_dir=SSW: Yes (3.0)
## | | | | | | | | wind_gust_dir=SW: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | wind_gust_dir=WNW: No (1.0)
## | | | | | | | | wind_gust_dir=NW: No (1.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | wind_dir_3pm=S
## | | | | | | | | pressure_9am <= 1005.4: No (11.0)
## | | | | | | | | pressure_9am > 1005.4: Yes (34.0/8.0)
## | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | min_temp <= 9.1: No (2.0)
## | | | | | | | | min_temp > 9.1: Yes (5.0)
## | | | | | | | wind_dir_3pm=SW
## | | | | | | | | wind_gust_dir=N: No (1.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | wind_gust_dir=S: No (2.0)
## | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | wind_gust_dir=SW: Yes (3.0)
## | | | | | | | | wind_gust_dir=WSW: Yes (4.0/1.0)
## | | | | | | | | wind_gust_dir=W: No (2.0/1.0)
## | | | | | | | | wind_gust_dir=WNW: No (2.0)
## | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | wind_dir_3pm=WSW: Yes (8.0/1.0)
## | | | | | | | wind_dir_3pm=W
## | | | | | | | | pressure_9am <= 1005.5: Yes (11.0)
## | | | | | | | | pressure_9am > 1005.5
## | | | | | | | | | rainfall <= 0.3: No (16.0/6.0)
## | | | | | | | | | rainfall > 0.3: Yes (4.0/1.0)
## | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | rainfall <= 0.1
## | | | | | | | | | cloud_9am <= 7: No (20.0/7.0)
## | | | | | | | | | cloud_9am > 7: Yes (4.0/1.0)
## | | | | | | | | rainfall > 0.1: Yes (6.0)
## | | | | | | | wind_dir_3pm=NW
## | | | | | | | | pressure_9am <= 1001.3: No (4.0)
## | | | | | | | | pressure_9am > 1001.3: Yes (17.0/1.0)
## | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | cloud_3pm <= 4: Yes (2.0)
## | | | | | | | | cloud_3pm > 4
## | | | | | | | | | wind_speed_3pm <= 20: Yes (3.0)
## | | | | | | | | | wind_speed_3pm > 20: No (8.0/2.0)
## | | | | | pressure_9am > 1009
## | | | | | | temp_3pm <= 20.6
## | | | | | | | max_temp <= 8.6: No (74.0/8.0)
## | | | | | | | max_temp > 8.6
## | | | | | | | | pressure_3pm <= 1014.1
## | | | | | | | | | wind_gust_dir=N: Yes (50.0/14.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (30.0/8.0)
## | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | | pressure_3pm <= 1010.6: Yes (3.0)
## | | | | | | | | | | | pressure_3pm > 1010.6: No (13.0/3.0)
## | | | | | | | | | | cloud_3pm > 5: Yes (3.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (2.0)
## | | | | | | | | | wind_gust_dir=E: Yes (3.0/1.0)
## | | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | | temp_9am <= 15.8: Yes (3.0)
## | | | | | | | | | | temp_9am > 15.8: No (4.0)
## | | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | | humidity_9am <= 84: Yes (6.0)
## | | | | | | | | | | humidity_9am > 84: No (5.0)
## | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | wind_gust_speed <= 48: No (7.0)
## | | | | | | | | | | wind_gust_speed > 48: Yes (8.0/3.0)
## | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | cloud_9am <= 5: No (3.0/1.0)
## | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | temp_9am <= 19.2: Yes (11.0/3.0)
## | | | | | | | | | | | temp_9am > 19.2: No (6.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (30.0/12.0)
## | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | humidity_3pm <= 79: No (18.0/8.0)
## | | | | | | | | | | humidity_3pm > 79: Yes (6.0/1.0)
## | | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | | humidity_3pm <= 71: No (6.0/1.0)
## | | | | | | | | | | humidity_3pm > 71
## | | | | | | | | | | | pressure_9am <= 1010.5: No (3.0/1.0)
## | | | | | | | | | | | pressure_9am > 1010.5: Yes (20.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | humidity_3pm <= 75: No (31.0/10.0)
## | | | | | | | | | | humidity_3pm > 75: Yes (19.0/7.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | humidity_3pm <= 77
## | | | | | | | | | | | wind_gust_speed <= 54: No (14.0/3.0)
## | | | | | | | | | | | wind_gust_speed > 54: Yes (12.0/4.0)
## | | | | | | | | | | humidity_3pm > 77: Yes (19.0/2.0)
## | | | | | | | | | wind_gust_dir=NW: Yes (72.0/23.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (41.0/11.0)
## | | | | | | | | pressure_3pm > 1014.1
## | | | | | | | | | wind_gust_speed <= 50
## | | | | | | | | | | humidity_3pm <= 73
## | | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | | max_temp <= 18.9
## | | | | | | | | | | | | | wind_speed_3pm <= 17: Yes (2.0)
## | | | | | | | | | | | | | wind_speed_3pm > 17: No (12.0/1.0)
## | | | | | | | | | | | | max_temp > 18.9: Yes (6.0)
## | | | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | | | rainfall <= 0.1: No (7.0/1.0)
## | | | | | | | | | | | | | rainfall > 0.1: Yes (2.0)
## | | | | | | | | | | | | cloud_3pm > 6: Yes (3.0)
## | | | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | | | pressure_9am <= 1017.9: Yes (2.0)
## | | | | | | | | | | | | pressure_9am > 1017.9: No (27.0)
## | | | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | | | rainfall <= 0.5: No (5.0)
## | | | | | | | | | | | | rainfall > 0.5: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=E: No (3.0)
## | | | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | | | cloud_3pm <= 6: No (7.0/1.0)
## | | | | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | | humidity_9am <= 58: Yes (2.0)
## | | | | | | | | | | | | humidity_9am > 58: No (21.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | | temp_9am <= 19.2: No (22.0)
## | | | | | | | | | | | | temp_9am > 19.2: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=S: No (29.0/9.0)
## | | | | | | | | | | | wind_dir_3pm=SSW: No (16.0/3.0)
## | | | | | | | | | | | wind_dir_3pm=SW: No (17.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | | humidity_9am <= 87: Yes (5.0/1.0)
## | | | | | | | | | | | | | humidity_9am > 87: No (5.0)
## | | | | | | | | | | | | cloud_9am > 7: No (5.0)
## | | | | | | | | | | | wind_dir_3pm=W: No (27.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | | wind_gust_speed <= 43: No (3.0)
## | | | | | | | | | | | | wind_gust_speed > 43
## | | | | | | | | | | | | | cloud_9am <= 4: No (2.0)
## | | | | | | | | | | | | | cloud_9am > 4: Yes (5.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | | | wind_dir_9am=N: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: Yes (1.0)
## | | | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | | | min_temp <= 10: Yes (4.0/1.0)
## | | | | | | | | | | | | | min_temp > 10: No (4.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (4.0)
## | | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | | humidity_9am <= 89: No (8.0/1.0)
## | | | | | | | | | | | | humidity_9am > 89: Yes (5.0)
## | | | | | | | | | | humidity_3pm > 73
## | | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | | max_temp <= 10.8
## | | | | | | | | | | | | | | wind_gust_speed <= 44: No (2.0)
## | | | | | | | | | | | | | | wind_gust_speed > 44: Yes (3.0)
## | | | | | | | | | | | | | max_temp > 10.8: No (8.0)
## | | | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | | | humidity_9am <= 83: No (2.0)
## | | | | | | | | | | | | | humidity_9am > 83: Yes (4.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (2.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: No (2.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | | wind_gust_speed <= 43: Yes (4.0)
## | | | | | | | | | | | | | wind_gust_speed > 43: No (7.0/1.0)
## | | | | | | | | | | | | rainfall > 0.1: Yes (4.0)
## | | | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | | cloud_3pm <= 7: No (12.0/1.0)
## | | | | | | | | | | | | | cloud_3pm > 7: Yes (2.0)
## | | | | | | | | | | | | rainfall > 0.1: Yes (3.0)
## | | | | | | | | | | | wind_dir_3pm=ENE: No (13.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | | | | temp_3pm <= 14.6: Yes (2.0)
## | | | | | | | | | | | | temp_3pm > 14.6: No (5.0)
## | | | | | | | | | | | wind_dir_3pm=ESE: No (9.0/2.0)
## | | | | | | | | | | | wind_dir_3pm=SE: No (15.0/6.0)
## | | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | | wind_gust_speed <= 44: No (11.0/1.0)
## | | | | | | | | | | | | wind_gust_speed > 44
## | | | | | | | | | | | | | cloud_9am <= 6: Yes (10.0)
## | | | | | | | | | | | | | cloud_9am > 6
## | | | | | | | | | | | | | | temp_3pm <= 15.6: No (2.0)
## | | | | | | | | | | | | | | temp_3pm > 15.6: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | | pressure_3pm <= 1019.3: No (12.0/3.0)
## | | | | | | | | | | | | pressure_3pm > 1019.3: Yes (14.0/4.0)
## | | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | | max_temp <= 18.2: No (8.0/1.0)
## | | | | | | | | | | | | max_temp > 18.2: Yes (4.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | | wind_speed_3pm <= 17: Yes (6.0)
## | | | | | | | | | | | | wind_speed_3pm > 17
## | | | | | | | | | | | | | cloud_3pm <= 7: No (5.0)
## | | | | | | | | | | | | | cloud_3pm > 7: Yes (3.0/1.0)
## | | | | | | | | | | | wind_dir_3pm=WSW: No (20.0/6.0)
## | | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | | rain_today=No
## | | | | | | | | | | | | | temp_3pm <= 18: No (20.0/5.0)
## | | | | | | | | | | | | | temp_3pm > 18: Yes (2.0)
## | | | | | | | | | | | | rain_today=Yes: Yes (3.0)
## | | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | | wind_dir_9am=N: Yes (2.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=WSW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=W: Yes (1.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: No (4.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (4.0/1.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: Yes (2.0)
## | | | | | | | | | | | wind_dir_3pm=NW: Yes (19.0/6.0)
## | | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | | wind_gust_speed <= 48
## | | | | | | | | | | | | | wind_speed_9am <= 4: Yes (3.0)
## | | | | | | | | | | | | | wind_speed_9am > 4
## | | | | | | | | | | | | | | humidity_3pm <= 79: No (13.0)
## | | | | | | | | | | | | | | humidity_3pm > 79
## | | | | | | | | | | | | | | | wind_gust_speed <= 46: Yes (3.0)
## | | | | | | | | | | | | | | | wind_gust_speed > 46: No (2.0)
## | | | | | | | | | | | | wind_gust_speed > 48: Yes (4.0)
## | | | | | | | | | wind_gust_speed > 50
## | | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | | wind_speed_9am <= 9: Yes (6.0)
## | | | | | | | | | | | wind_speed_9am > 9
## | | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | | wind_gust_speed <= 57: Yes (4.0)
## | | | | | | | | | | | | | wind_gust_speed > 57: No (7.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | | | | cloud_9am <= 5: Yes (3.0/1.0)
## | | | | | | | | | | | | | cloud_9am > 5: No (8.0)
## | | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (13.0/4.0)
## | | | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | | | temp_3pm <= 17.7: Yes (3.0/1.0)
## | | | | | | | | | | | temp_3pm > 17.7: No (12.0)
## | | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | | sunshine <= 8.3: No (3.0)
## | | | | | | | | | | | sunshine > 8.3
## | | | | | | | | | | | | temp_3pm <= 13.9: No (3.0)
## | | | | | | | | | | | | temp_3pm > 13.9
## | | | | | | | | | | | | | wind_speed_9am <= 33: Yes (8.0)
## | | | | | | | | | | | | | wind_speed_9am > 33: No (2.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (12.0/3.0)
## | | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | | sunshine <= 8.1: Yes (3.0)
## | | | | | | | | | | | sunshine > 8.1: No (15.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | evaporation <= 4.2: Yes (2.0)
## | | | | | | | | | | | evaporation > 4.2
## | | | | | | | | | | | | temp_9am <= 19.1: No (17.0/2.0)
## | | | | | | | | | | | | temp_9am > 19.1: Yes (4.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (48.0/18.0)
## | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (2.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (12.0/4.0)
## | | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | | max_temp <= 19.7: Yes (8.0/1.0)
## | | | | | | | | | | | | max_temp > 19.7
## | | | | | | | | | | | | | min_temp <= 16.8: No (13.0)
## | | | | | | | | | | | | | min_temp > 16.8: Yes (5.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | | wind_speed_3pm <= 44: No (10.0/2.0)
## | | | | | | | | | | | | wind_speed_3pm > 44: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=SW: No (1.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=W: No (1.0)
## | | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | humidity_3pm <= 78
## | | | | | | | | | | | | wind_dir_9am=N: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=S: No (3.0)
## | | | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=S: Yes (2.0)
## | | | | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | | | | cloud_3pm <= 6: Yes (3.0/1.0)
## | | | | | | | | | | | | | | cloud_3pm > 6: No (4.0)
## | | | | | | | | | | | | | wind_gust_dir=SW: No (1.0)
## | | | | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | | | wind_speed_3pm <= 31: No (8.0/1.0)
## | | | | | | | | | | | | | wind_speed_3pm > 31: Yes (3.0)
## | | | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | | | humidity_3pm <= 71: Yes (3.0)
## | | | | | | | | | | | | | humidity_3pm > 71: No (3.0)
## | | | | | | | | | | | | wind_dir_9am=W: No (2.0)
## | | | | | | | | | | | | wind_dir_9am=WNW: Yes (2.0)
## | | | | | | | | | | | | wind_dir_9am=NW: No (1.0)
## | | | | | | | | | | | | wind_dir_9am=NNW: Yes (1.0)
## | | | | | | | | | | | humidity_3pm > 78: Yes (10.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | | wind_gust_speed <= 65
## | | | | | | | | | | | | rain_today=No
## | | | | | | | | | | | | | temp_9am <= 15.6: Yes (15.0/5.0)
## | | | | | | | | | | | | | temp_9am > 15.6: No (8.0/1.0)
## | | | | | | | | | | | | rain_today=Yes: No (3.0)
## | | | | | | | | | | | wind_gust_speed > 65: Yes (6.0)
## | | | | | | | | | | wind_dir_3pm=WSW: Yes (24.0/10.0)
## | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | sunshine <= 8.4: No (6.0)
## | | | | | | | | | | | sunshine > 8.4
## | | | | | | | | | | | | min_temp <= 6.5: No (6.0)
## | | | | | | | | | | | | min_temp > 6.5: Yes (20.0/7.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | humidity_3pm <= 70: No (3.0)
## | | | | | | | | | | | humidity_3pm > 70
## | | | | | | | | | | | | temp_3pm <= 12.1: No (2.0)
## | | | | | | | | | | | | temp_3pm > 12.1: Yes (10.0)
## | | | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | | | temp_9am <= 15.4: Yes (4.0)
## | | | | | | | | | | | | | temp_9am > 15.4: No (2.0)
## | | | | | | | | | | | | cloud_3pm > 6: No (3.0)
## | | | | | | | | | | | rainfall > 0.1: Yes (8.0)
## | | | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | | | pressure_3pm <= 1015.7
## | | | | | | | | | | | | humidity_3pm <= 73: No (7.0/1.0)
## | | | | | | | | | | | | humidity_3pm > 73: Yes (8.0/1.0)
## | | | | | | | | | | | pressure_3pm > 1015.7: Yes (2.0)
## | | | | | | temp_3pm > 20.6
## | | | | | | | cloud_3pm <= 5
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | wind_gust_speed <= 56: No (41.0/7.0)
## | | | | | | | | | wind_gust_speed > 56: Yes (5.0)
## | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | humidity_3pm <= 74: No (73.0/4.0)
## | | | | | | | | | humidity_3pm > 74
## | | | | | | | | | | rainfall <= 0.3
## | | | | | | | | | | | humidity_9am <= 81: No (19.0/6.0)
## | | | | | | | | | | | humidity_9am > 81: Yes (9.0/3.0)
## | | | | | | | | | | rainfall > 0.3: Yes (4.0)
## | | | | | | | | wind_gust_dir=NE: No (193.0/22.0)
## | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | wind_speed_9am <= 28
## | | | | | | | | | | humidity_3pm <= 75
## | | | | | | | | | | | temp_9am <= 20.5: Yes (2.0)
## | | | | | | | | | | | temp_9am > 20.5: No (12.0/2.0)
## | | | | | | | | | | humidity_3pm > 75: Yes (5.0)
## | | | | | | | | | wind_speed_9am > 28: No (13.0)
## | | | | | | | | wind_gust_dir=E: No (42.0/8.0)
## | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | evaporation <= 4.6: Yes (3.0)
## | | | | | | | | | evaporation > 4.6: No (19.0/3.0)
## | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | wind_gust_speed <= 59: No (62.0/16.0)
## | | | | | | | | | wind_gust_speed > 59: Yes (8.0)
## | | | | | | | | wind_gust_dir=SSE: No (71.0/23.0)
## | | | | | | | | wind_gust_dir=S
## | | | | | | | | | rainfall <= 0.1: No (70.0/12.0)
## | | | | | | | | | rainfall > 0.1
## | | | | | | | | | | temp_3pm <= 22.6
## | | | | | | | | | | | humidity_9am <= 70: No (3.0)
## | | | | | | | | | | | humidity_9am > 70: Yes (6.0/1.0)
## | | | | | | | | | | temp_3pm > 22.6: No (9.0/3.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | wind_gust_speed <= 43
## | | | | | | | | | | | cloud_3pm <= 3: Yes (2.0)
## | | | | | | | | | | | cloud_3pm > 3
## | | | | | | | | | | | | temp_3pm <= 23.7: Yes (2.0)
## | | | | | | | | | | | | temp_3pm > 23.7: No (2.0)
## | | | | | | | | | | wind_gust_speed > 43: No (44.0/4.0)
## | | | | | | | | | cloud_9am > 7: Yes (5.0/1.0)
## | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | humidity_3pm <= 71: No (3.0)
## | | | | | | | | | humidity_3pm > 71: Yes (7.0/1.0)
## | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | max_temp <= 22.8: No (2.0)
## | | | | | | | | | max_temp > 22.8: Yes (8.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_gust_speed <= 50: Yes (3.0)
## | | | | | | | | | wind_gust_speed > 50
## | | | | | | | | | | temp_3pm <= 24.7: No (4.0)
## | | | | | | | | | | temp_3pm > 24.7: Yes (2.0)
## | | | | | | | | wind_gust_dir=WNW: No (17.0/6.0)
## | | | | | | | | wind_gust_dir=NW: No (11.0/2.0)
## | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | humidity_3pm <= 75: No (11.0)
## | | | | | | | | | humidity_3pm > 75: Yes (7.0/1.0)
## | | | | | | | cloud_3pm > 5
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | pressure_3pm <= 1007.9: No (3.0/1.0)
## | | | | | | | | | pressure_3pm > 1007.9: Yes (7.0)
## | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | cloud_9am <= 3: Yes (3.0)
## | | | | | | | | | cloud_9am > 3
## | | | | | | | | | | wind_speed_3pm <= 17: Yes (4.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 17: No (8.0)
## | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | max_temp <= 27.4: No (21.0/6.0)
## | | | | | | | | | max_temp > 27.4
## | | | | | | | | | | pressure_3pm <= 1013.6: Yes (14.0/4.0)
## | | | | | | | | | | pressure_3pm > 1013.6: No (3.0)
## | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | wind_gust_speed <= 50: No (12.0/1.0)
## | | | | | | | | | wind_gust_speed > 50: Yes (5.0/1.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | temp_9am <= 21.2: Yes (4.0)
## | | | | | | | | | temp_9am > 21.2
## | | | | | | | | | | temp_3pm <= 27.7
## | | | | | | | | | | | humidity_3pm <= 75: No (17.0)
## | | | | | | | | | | | humidity_3pm > 75
## | | | | | | | | | | | | temp_3pm <= 21.8: Yes (4.0/1.0)
## | | | | | | | | | | | | temp_3pm > 21.8: No (3.0)
## | | | | | | | | | | temp_3pm > 27.7: Yes (4.0)
## | | | | | | | | wind_dir_3pm=ESE: No (18.0/7.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | cloud_3pm <= 6: Yes (6.0/1.0)
## | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | temp_3pm <= 26
## | | | | | | | | | | | pressure_3pm <= 1017.4: No (22.0)
## | | | | | | | | | | | pressure_3pm > 1017.4: Yes (4.0/1.0)
## | | | | | | | | | | temp_3pm > 26: Yes (8.0/2.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | pressure_3pm <= 1014.4
## | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | humidity_3pm <= 74: Yes (2.0)
## | | | | | | | | | | | humidity_3pm > 74: No (2.0)
## | | | | | | | | | | rainfall > 0.1: No (2.0)
## | | | | | | | | | pressure_3pm > 1014.4: Yes (9.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | wind_gust_speed <= 57: Yes (24.0/10.0)
## | | | | | | | | | wind_gust_speed > 57: No (10.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | cloud_3pm <= 7: No (2.0)
## | | | | | | | | | cloud_3pm > 7: Yes (8.0/1.0)
## | | | | | | | | wind_dir_3pm=SW: No (1.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | temp_3pm <= 23.6: No (2.0)
## | | | | | | | | | temp_3pm > 23.6: Yes (3.0)
## | | | | | | | | wind_dir_3pm=W: No (2.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | pressure_3pm <= 1008: No (2.0)
## | | | | | | | | | pressure_3pm > 1008: Yes (5.0)
## | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | wind_speed_3pm <= 22: Yes (2.0)
## | | | | | | | | | wind_speed_3pm > 22: No (2.0)
## | | rainfall > 1.2
## | | | wind_gust_speed <= 41
## | | | | pressure_3pm <= 1014.4
## | | | | | sunshine <= 4.2
## | | | | | | min_temp <= 21
## | | | | | | | wind_gust_dir=N
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | temp_3pm <= 15: No (2.0)
## | | | | | | | | | temp_3pm > 15: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (2.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SSW: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=W: Yes (0.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNW: No (3.0)
## | | | | | | | wind_gust_dir=NNE
## | | | | | | | | evaporation <= 2.3: No (3.0)
## | | | | | | | | evaporation > 2.3: Yes (4.0)
## | | | | | | | wind_gust_dir=NE: Yes (14.0/1.0)
## | | | | | | | wind_gust_dir=ENE: Yes (12.0/3.0)
## | | | | | | | wind_gust_dir=E
## | | | | | | | | pressure_9am <= 1011.8: No (4.0/1.0)
## | | | | | | | | pressure_9am > 1011.8: Yes (7.0)
## | | | | | | | wind_gust_dir=ESE
## | | | | | | | | cloud_9am <= 7
## | | | | | | | | | wind_speed_9am <= 9: No (3.0)
## | | | | | | | | | wind_speed_9am > 9: Yes (2.0)
## | | | | | | | | cloud_9am > 7: Yes (5.0)
## | | | | | | | wind_gust_dir=SE
## | | | | | | | | pressure_9am <= 1006.1: No (2.0)
## | | | | | | | | pressure_9am > 1006.1: Yes (11.0/1.0)
## | | | | | | | wind_gust_dir=SSE: Yes (15.0/7.0)
## | | | | | | | wind_gust_dir=S: No (21.0/8.0)
## | | | | | | | wind_gust_dir=SSW: No (20.0/10.0)
## | | | | | | | wind_gust_dir=SW: No (19.0/8.0)
## | | | | | | | wind_gust_dir=WSW: Yes (23.0/10.0)
## | | | | | | | wind_gust_dir=W
## | | | | | | | | wind_gust_speed <= 31: No (11.0/1.0)
## | | | | | | | | wind_gust_speed > 31: Yes (52.0/11.0)
## | | | | | | | wind_gust_dir=WNW
## | | | | | | | | temp_9am <= 15.3: Yes (7.0)
## | | | | | | | | temp_9am > 15.3: No (2.0)
## | | | | | | | wind_gust_dir=NW
## | | | | | | | | cloud_9am <= 7
## | | | | | | | | | rainfall <= 7.9: No (2.0)
## | | | | | | | | | rainfall > 7.9: Yes (6.0)
## | | | | | | | | cloud_9am > 7: No (4.0)
## | | | | | | | wind_gust_dir=NNW: No (11.0/5.0)
## | | | | | | min_temp > 21: Yes (170.0/31.0)
## | | | | | sunshine > 4.2
## | | | | | | sunshine <= 9.7
## | | | | | | | wind_gust_dir=N
## | | | | | | | | wind_dir_9am=N
## | | | | | | | | | humidity_9am <= 80: No (5.0)
## | | | | | | | | | humidity_9am > 80
## | | | | | | | | | | sunshine <= 6.7: Yes (3.0)
## | | | | | | | | | | sunshine > 6.7
## | | | | | | | | | | | rainfall <= 4
## | | | | | | | | | | | | temp_3pm <= 22.5: No (6.0)
## | | | | | | | | | | | | temp_3pm > 22.5: Yes (2.0)
## | | | | | | | | | | | rainfall > 4: Yes (11.0/1.0)
## | | | | | | | | wind_dir_9am=NNE: No (8.0/2.0)
## | | | | | | | | wind_dir_9am=NE: Yes (3.0)
## | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | temp_3pm <= 21.2: No (2.0)
## | | | | | | | | | temp_3pm > 21.2: Yes (2.0)
## | | | | | | | | wind_dir_9am=E: No (3.0/1.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (1.0)
## | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | wind_dir_9am=SSE: No (4.0/1.0)
## | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | wind_dir_9am=SSW: No (1.0)
## | | | | | | | | wind_dir_9am=SW: No (2.0/1.0)
## | | | | | | | | wind_dir_9am=WSW: No (3.0)
## | | | | | | | | wind_dir_9am=W
## | | | | | | | | | cloud_3pm <= 1: No (2.0)
## | | | | | | | | | cloud_3pm > 1: Yes (2.0)
## | | | | | | | | wind_dir_9am=WNW: Yes (4.0/1.0)
## | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | cloud_3pm <= 3: No (2.0)
## | | | | | | | | | cloud_3pm > 3: Yes (5.0/1.0)
## | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | wind_gust_speed <= 35: Yes (5.0/1.0)
## | | | | | | | | | wind_gust_speed > 35: No (2.0)
## | | | | | | | wind_gust_dir=NNE: No (60.0/22.0)
## | | | | | | | wind_gust_dir=NE: No (63.0/25.0)
## | | | | | | | wind_gust_dir=ENE: Yes (69.0/27.0)
## | | | | | | | wind_gust_dir=E
## | | | | | | | | humidity_3pm <= 70: No (5.0)
## | | | | | | | | humidity_3pm > 70
## | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=NE: No (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | | wind_speed_9am <= 2: No (2.0)
## | | | | | | | | | | wind_speed_9am > 2: Yes (9.0/1.0)
## | | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | | pressure_3pm <= 1011.3: No (2.0)
## | | | | | | | | | | pressure_3pm > 1011.3: Yes (7.0)
## | | | | | | | | | wind_dir_3pm=ESE: Yes (5.0)
## | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | evaporation <= 3.9: No (3.0)
## | | | | | | | | | | evaporation > 3.9: Yes (4.0)
## | | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=S: Yes (1.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (1.0)
## | | | | | | | | | wind_dir_3pm=SW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=W: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | wind_gust_dir=ESE: Yes (42.0/19.0)
## | | | | | | | wind_gust_dir=SE
## | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NE: Yes (4.0)
## | | | | | | | | wind_dir_3pm=ENE: No (2.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | wind_speed_9am <= 13: No (2.0)
## | | | | | | | | | wind_speed_9am > 13: Yes (3.0)
## | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | pressure_9am <= 1014.5: Yes (6.0)
## | | | | | | | | | pressure_9am > 1014.5: No (3.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | pressure_3pm <= 1006.2: Yes (6.0)
## | | | | | | | | | | pressure_3pm > 1006.2
## | | | | | | | | | | | wind_speed_3pm <= 28: No (11.0/2.0)
## | | | | | | | | | | | wind_speed_3pm > 28: Yes (2.0)
## | | | | | | | | | cloud_9am > 7: Yes (8.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | cloud_9am <= 7: Yes (5.0)
## | | | | | | | | | cloud_9am > 7: No (3.0/1.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | cloud_3pm <= 6: Yes (2.0)
## | | | | | | | | | cloud_3pm > 6: No (5.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=W: Yes (0.0)
## | | | | | | | | wind_dir_3pm=WNW: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (1.0)
## | | | | | | | wind_gust_dir=SSE
## | | | | | | | | wind_dir_9am=N: Yes (3.0)
## | | | | | | | | wind_dir_9am=NNE: No (1.0)
## | | | | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | wind_dir_9am=E: Yes (2.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (4.0)
## | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | cloud_9am <= 6: Yes (3.0)
## | | | | | | | | | cloud_9am > 6: No (3.0)
## | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | pressure_9am <= 1008.8: Yes (2.0)
## | | | | | | | | | | pressure_9am > 1008.8: No (7.0)
## | | | | | | | | | cloud_3pm > 7: Yes (6.0)
## | | | | | | | | wind_dir_9am=S
## | | | | | | | | | cloud_3pm <= 6: Yes (7.0/1.0)
## | | | | | | | | | cloud_3pm > 6: No (3.0)
## | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | max_temp <= 22.6: No (3.0)
## | | | | | | | | | max_temp > 22.6: Yes (6.0)
## | | | | | | | | wind_dir_9am=SW: No (1.0)
## | | | | | | | | wind_dir_9am=WSW: Yes (2.0)
## | | | | | | | | wind_dir_9am=W: No (4.0)
## | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | wind_dir_9am=NW: Yes (1.0)
## | | | | | | | | wind_dir_9am=NNW: Yes (0.0)
## | | | | | | | wind_gust_dir=S
## | | | | | | | | wind_dir_9am=N
## | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | humidity_3pm <= 76: No (2.0)
## | | | | | | | | | | humidity_3pm > 76: Yes (2.0)
## | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | | | | wind_dir_9am=ENE: Yes (2.0)
## | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | wind_dir_9am=ESE: No (1.0)
## | | | | | | | | wind_dir_9am=SE: No (3.0)
## | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | humidity_3pm <= 74: No (6.0)
## | | | | | | | | | humidity_3pm > 74: Yes (11.0/1.0)
## | | | | | | | | wind_dir_9am=S
## | | | | | | | | | temp_3pm <= 19.2: Yes (3.0)
## | | | | | | | | | temp_3pm > 19.2: No (20.0/7.0)
## | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | humidity_3pm <= 72: Yes (6.0)
## | | | | | | | | | humidity_3pm > 72: No (6.0/1.0)
## | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | cloud_9am <= 5: Yes (2.0)
## | | | | | | | | | cloud_9am > 5: No (13.0/3.0)
## | | | | | | | | wind_dir_9am=WSW: No (3.0/1.0)
## | | | | | | | | wind_dir_9am=W: Yes (3.0)
## | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | wind_dir_9am=NW: Yes (1.0)
## | | | | | | | | wind_dir_9am=NNW: Yes (2.0)
## | | | | | | | wind_gust_dir=SSW
## | | | | | | | | wind_dir_9am=N: No (4.0/2.0)
## | | | | | | | | wind_dir_9am=NNE: No (1.0)
## | | | | | | | | wind_dir_9am=NE: No (3.0/1.0)
## | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | wind_dir_9am=E: No (1.0)
## | | | | | | | | wind_dir_9am=ESE: Yes (3.0/1.0)
## | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | wind_dir_9am=SSE: Yes (4.0/1.0)
## | | | | | | | | wind_dir_9am=S: Yes (7.0/1.0)
## | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | evaporation <= 6: No (13.0/1.0)
## | | | | | | | | | evaporation > 6: Yes (2.0)
## | | | | | | | | wind_dir_9am=SW: No (12.0/4.0)
## | | | | | | | | wind_dir_9am=WSW: No (4.0/1.0)
## | | | | | | | | wind_dir_9am=W: Yes (4.0)
## | | | | | | | | wind_dir_9am=WNW: No (1.0)
## | | | | | | | | wind_dir_9am=NW: Yes (3.0/1.0)
## | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | humidity_9am <= 92: No (3.0)
## | | | | | | | | | humidity_9am > 92: Yes (3.0)
## | | | | | | | wind_gust_dir=SW: Yes (48.0/18.0)
## | | | | | | | wind_gust_dir=WSW
## | | | | | | | | wind_dir_9am=N
## | | | | | | | | | humidity_3pm <= 74: No (2.0)
## | | | | | | | | | humidity_3pm > 74: Yes (3.0)
## | | | | | | | | wind_dir_9am=NNE: No (0.0)
## | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | wind_dir_9am=ENE: No (1.0)
## | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | wind_dir_9am=SE: Yes (1.0)
## | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | wind_dir_9am=S: No (2.0)
## | | | | | | | | wind_dir_9am=SSW: No (2.0)
## | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | humidity_3pm <= 72: Yes (3.0)
## | | | | | | | | | humidity_3pm > 72: No (2.0)
## | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | wind_speed_3pm <= 20
## | | | | | | | | | | wind_gust_speed <= 31: No (2.0)
## | | | | | | | | | | wind_gust_speed > 31: Yes (5.0)
## | | | | | | | | | wind_speed_3pm > 20: No (4.0)
## | | | | | | | | wind_dir_9am=W
## | | | | | | | | | temp_3pm <= 17.2: Yes (2.0)
## | | | | | | | | | temp_3pm > 17.2: No (3.0)
## | | | | | | | | wind_dir_9am=WNW: Yes (4.0/1.0)
## | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | pressure_3pm <= 1010.4: No (2.0)
## | | | | | | | | | pressure_3pm > 1010.4: Yes (2.0)
## | | | | | | | | wind_dir_9am=NNW: Yes (6.0/1.0)
## | | | | | | | wind_gust_dir=W
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | pressure_9am <= 1009.1: Yes (4.0)
## | | | | | | | | | pressure_9am > 1009.1: No (2.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (11.0/5.0)
## | | | | | | | | wind_dir_3pm=NE: No (4.0)
## | | | | | | | | wind_dir_3pm=ENE: Yes (3.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | pressure_3pm <= 1011.1: Yes (3.0)
## | | | | | | | | | pressure_3pm > 1011.1: No (3.0)
## | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | cloud_3pm <= 6: No (2.0)
## | | | | | | | | | cloud_3pm > 6: Yes (2.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | pressure_3pm <= 1010.4
## | | | | | | | | | | humidity_9am <= 84: No (4.0/1.0)
## | | | | | | | | | | humidity_9am > 84: Yes (5.0)
## | | | | | | | | | pressure_3pm > 1010.4: No (7.0)
## | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | pressure_3pm <= 1001.9: Yes (2.0)
## | | | | | | | | | pressure_3pm > 1001.9: No (3.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | cloud_3pm <= 6: No (5.0)
## | | | | | | | | | cloud_3pm > 6: Yes (4.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | temp_3pm <= 16.9: Yes (3.0)
## | | | | | | | | | temp_3pm > 16.9: No (2.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | humidity_3pm <= 75
## | | | | | | | | | | wind_speed_9am <= 26: No (9.0/1.0)
## | | | | | | | | | | wind_speed_9am > 26: Yes (2.0)
## | | | | | | | | | humidity_3pm > 75: Yes (4.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | wind_dir_9am=N: No (2.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (3.0)
## | | | | | | | | | wind_dir_9am=WSW: No (1.0)
## | | | | | | | | | wind_dir_9am=W: Yes (2.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | humidity_9am <= 90: No (2.0)
## | | | | | | | | | | humidity_9am > 90: Yes (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NW: No (6.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (3.0)
## | | | | | | | | wind_dir_3pm=W: No (28.0/13.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | min_temp <= 14
## | | | | | | | | | | cloud_3pm <= 7: No (7.0)
## | | | | | | | | | | cloud_3pm > 7: Yes (3.0/1.0)
## | | | | | | | | | min_temp > 14: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | sunshine <= 8.7: Yes (9.0/1.0)
## | | | | | | | | | sunshine > 8.7: No (2.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (5.0)
## | | | | | | | wind_gust_dir=WNW: Yes (61.0/26.0)
## | | | | | | | wind_gust_dir=NW: Yes (60.0/22.0)
## | | | | | | | wind_gust_dir=NNW
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | rainfall <= 5.1: Yes (3.0)
## | | | | | | | | | rainfall > 5.1: No (4.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (4.0)
## | | | | | | | | wind_dir_3pm=NE: No (4.0/1.0)
## | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SE: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SSW: No (1.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=WSW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=W: Yes (1.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | rainfall <= 7.2: No (3.0)
## | | | | | | | | | rainfall > 7.2: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NW: Yes (10.0/2.0)
## | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | humidity_9am <= 92: No (8.0)
## | | | | | | | | | humidity_9am > 92
## | | | | | | | | | | temp_3pm <= 11.3: No (3.0)
## | | | | | | | | | | temp_3pm > 11.3: Yes (7.0/1.0)
## | | | | | | sunshine > 9.7: No (40.0/7.0)
## | | | | pressure_3pm > 1014.4
## | | | | | min_temp <= 12.1
## | | | | | | wind_speed_3pm <= 26
## | | | | | | | wind_gust_speed <= 33: No (809.0/211.0)
## | | | | | | | wind_gust_speed > 33
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | wind_speed_3pm <= 15: Yes (3.0)
## | | | | | | | | | wind_speed_3pm > 15
## | | | | | | | | | | cloud_9am <= 6: Yes (3.0/1.0)
## | | | | | | | | | | cloud_9am > 6: No (4.0)
## | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | humidity_3pm <= 72: No (2.0)
## | | | | | | | | | humidity_3pm > 72: Yes (6.0)
## | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | wind_speed_3pm <= 15: No (3.0)
## | | | | | | | | | wind_speed_3pm > 15: Yes (3.0)
## | | | | | | | | wind_gust_dir=ENE: Yes (3.0)
## | | | | | | | | wind_gust_dir=E
## | | | | | | | | | pressure_3pm <= 1016.9: No (2.0)
## | | | | | | | | | pressure_3pm > 1016.9: Yes (2.0)
## | | | | | | | | wind_gust_dir=ESE: No (11.0/3.0)
## | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | evaporation <= 3.8: Yes (4.0)
## | | | | | | | | | evaporation > 3.8
## | | | | | | | | | | humidity_3pm <= 72: Yes (3.0)
## | | | | | | | | | | humidity_3pm > 72: No (6.0/1.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | rainfall <= 2.2: No (7.0)
## | | | | | | | | | rainfall > 2.2: Yes (11.0/4.0)
## | | | | | | | | wind_gust_dir=S: No (49.0/15.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | cloud_9am <= 7: Yes (33.0/12.0)
## | | | | | | | | | cloud_9am > 7: No (6.0)
## | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | temp_9am <= 7.1: No (2.0)
## | | | | | | | | | | | temp_9am > 7.1: Yes (2.0)
## | | | | | | | | | | cloud_3pm > 6: No (2.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (1.0)
## | | | | | | | | | wind_dir_9am=S: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (8.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | sunshine <= 5.8: Yes (5.0)
## | | | | | | | | | | sunshine > 5.8
## | | | | | | | | | | | wind_gust_speed <= 39
## | | | | | | | | | | | | humidity_3pm <= 71: Yes (3.0/1.0)
## | | | | | | | | | | | | humidity_3pm > 71: No (7.0)
## | | | | | | | | | | | wind_gust_speed > 39: Yes (3.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | wind_gust_speed <= 37: No (6.0)
## | | | | | | | | | | wind_gust_speed > 37
## | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | cloud_3pm <= 5: No (3.0)
## | | | | | | | | | | | | cloud_3pm > 5: Yes (4.0/1.0)
## | | | | | | | | | | | cloud_9am > 7: Yes (2.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_speed_9am <= 15: Yes (6.0/1.0)
## | | | | | | | | | | wind_speed_9am > 15: No (4.0)
## | | | | | | | | | wind_dir_9am=WNW: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NW: No (2.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (2.0)
## | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | wind_dir_9am=N: No (1.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=NE: No (0.0)
## | | | | | | | | | wind_dir_9am=ENE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=E: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (0.0)
## | | | | | | | | | wind_dir_9am=SE: No (0.0)
## | | | | | | | | | wind_dir_9am=SSE: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=SSW: No (6.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | cloud_9am <= 7: Yes (7.0/1.0)
## | | | | | | | | | | cloud_9am > 7: No (2.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | sunshine <= 3.8: Yes (4.0)
## | | | | | | | | | | sunshine > 3.8
## | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | sunshine <= 7.8: No (3.0)
## | | | | | | | | | | | | sunshine > 7.8: Yes (5.0/1.0)
## | | | | | | | | | | | cloud_9am > 6: No (9.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_speed_9am <= 9: Yes (3.0/1.0)
## | | | | | | | | | | wind_speed_9am > 9: No (7.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_speed_3pm <= 17: Yes (2.0)
## | | | | | | | | | | wind_speed_3pm > 17: No (2.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | rainfall <= 3.8: No (3.0/1.0)
## | | | | | | | | | | rainfall > 3.8: Yes (5.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (5.0/1.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | rainfall <= 2.9: No (15.0)
## | | | | | | | | | | rainfall > 2.9
## | | | | | | | | | | | cloud_3pm <= 4: Yes (4.0)
## | | | | | | | | | | | cloud_3pm > 4
## | | | | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | | | | humidity_3pm <= 75: No (24.0/4.0)
## | | | | | | | | | | | | | humidity_3pm > 75
## | | | | | | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | | | | | | rainfall <= 11.2: Yes (13.0/4.0)
## | | | | | | | | | | | | | | | rainfall > 11.2: No (2.0)
## | | | | | | | | | | | | | | cloud_3pm > 5: No (6.0/2.0)
## | | | | | | | | | | | | cloud_3pm > 7: Yes (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | wind_dir_9am=ENE: No (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (1.0)
## | | | | | | | | | wind_dir_9am=ESE: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=SSE: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=S: No (2.0)
## | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | pressure_3pm <= 1027.8: No (5.0)
## | | | | | | | | | | pressure_3pm > 1027.8: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | evaporation <= 3.5: Yes (5.0)
## | | | | | | | | | | evaporation > 3.5
## | | | | | | | | | | | wind_speed_3pm <= 17
## | | | | | | | | | | | | temp_3pm <= 16.2: Yes (3.0)
## | | | | | | | | | | | | temp_3pm > 16.2: No (2.0)
## | | | | | | | | | | | wind_speed_3pm > 17: No (3.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | wind_gust_speed <= 39: Yes (8.0/2.0)
## | | | | | | | | | | wind_gust_speed > 39: No (3.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_speed_9am <= 15: Yes (7.0)
## | | | | | | | | | | wind_speed_9am > 15
## | | | | | | | | | | | sunshine <= 2.8: Yes (3.0)
## | | | | | | | | | | | sunshine > 2.8
## | | | | | | | | | | | | rainfall <= 2.9: Yes (2.0)
## | | | | | | | | | | | | rainfall > 2.9: No (7.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | cloud_9am <= 7: No (15.0/3.0)
## | | | | | | | | | | cloud_9am > 7: Yes (8.0/3.0)
## | | | | | | | | | wind_dir_9am=NW: No (16.0/6.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | rainfall <= 8.2
## | | | | | | | | | | | pressure_3pm <= 1023.6: No (6.0)
## | | | | | | | | | | | pressure_3pm > 1023.6: Yes (4.0/1.0)
## | | | | | | | | | | rainfall > 8.2: Yes (4.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | humidity_9am <= 73: No (2.0)
## | | | | | | | | | | humidity_9am > 73: Yes (13.0/1.0)
## | | | | | | | | | cloud_3pm > 6: No (10.0/3.0)
## | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | temp_3pm <= 12.9: No (10.0)
## | | | | | | | | | temp_3pm > 12.9
## | | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SSW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SW: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=W: No (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | humidity_9am <= 90: Yes (3.0/1.0)
## | | | | | | | | | | | humidity_9am > 90: No (6.0)
## | | | | | | | | | | wind_dir_3pm=NW: Yes (5.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NNW: Yes (2.0)
## | | | | | | | | wind_gust_dir=NNW: No (22.0/8.0)
## | | | | | | wind_speed_3pm > 26: Yes (31.0/10.0)
## | | | | | min_temp > 12.1
## | | | | | | cloud_9am <= 2: No (35.0/7.0)
## | | | | | | cloud_9am > 2
## | | | | | | | max_temp <= 27.1
## | | | | | | | | humidity_3pm <= 71
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | pressure_3pm <= 1015.2
## | | | | | | | | | | | temp_9am <= 18.1
## | | | | | | | | | | | | humidity_9am <= 89: No (3.0/1.0)
## | | | | | | | | | | | | humidity_9am > 89: Yes (4.0)
## | | | | | | | | | | | temp_9am > 18.1: No (7.0)
## | | | | | | | | | | pressure_3pm > 1015.2: No (16.0/5.0)
## | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | sunshine <= 7.2: Yes (3.0)
## | | | | | | | | | | sunshine > 7.2: No (2.0)
## | | | | | | | | | wind_dir_9am=NE: No (3.0)
## | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | temp_3pm <= 20.3: Yes (2.0)
## | | | | | | | | | | temp_3pm > 20.3: No (4.0)
## | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | humidity_3pm <= 70: No (4.0/1.0)
## | | | | | | | | | | humidity_3pm > 70: Yes (3.0)
## | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | pressure_3pm <= 1032.1: No (9.0)
## | | | | | | | | | | pressure_3pm > 1032.1: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | rainfall <= 4: Yes (3.0)
## | | | | | | | | | | rainfall > 4: No (6.0/1.0)
## | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | wind_dir_3pm=N: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=ENE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | pressure_9am <= 1016.9: No (3.0)
## | | | | | | | | | | | pressure_9am > 1016.9: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | cloud_3pm <= 6: No (3.0)
## | | | | | | | | | | | cloud_3pm > 6: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=S: No (3.0)
## | | | | | | | | | | wind_dir_3pm=SSW: No (3.0)
## | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | wind_dir_9am=S: No (22.0/6.0)
## | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | temp_3pm <= 18.7: No (8.0/1.0)
## | | | | | | | | | | temp_3pm > 18.7: Yes (23.0/9.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | cloud_9am <= 5: No (4.0)
## | | | | | | | | | | cloud_9am > 5: Yes (38.0/9.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (1.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (2.0/1.0)
## | | | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | | | pressure_3pm <= 1020: No (2.0)
## | | | | | | | | | | | pressure_3pm > 1020: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (2.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (1.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (6.0/1.0)
## | | | | | | | | | | wind_gust_dir=W: No (5.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | wind_dir_9am=W: No (13.0/3.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_gust_speed <= 33: No (4.0)
## | | | | | | | | | | wind_gust_speed > 33: Yes (2.0)
## | | | | | | | | | wind_dir_9am=NW: No (8.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | temp_3pm <= 21.5: No (3.0)
## | | | | | | | | | | temp_3pm > 21.5: Yes (2.0)
## | | | | | | | | humidity_3pm > 71
## | | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | temp_9am <= 21
## | | | | | | | | | | | | humidity_9am <= 91: Yes (20.0/8.0)
## | | | | | | | | | | | | humidity_9am > 91: No (25.0/6.0)
## | | | | | | | | | | | temp_9am > 21: Yes (8.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | cloud_9am <= 7: Yes (5.0/1.0)
## | | | | | | | | | | | cloud_9am > 7: No (2.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | cloud_3pm <= 3: No (2.0)
## | | | | | | | | | | | cloud_3pm > 3: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (9.0/2.0)
## | | | | | | | | | | wind_dir_9am=E: No (7.0/1.0)
## | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | wind_gust_speed <= 37: Yes (10.0/4.0)
## | | | | | | | | | | | wind_gust_speed > 37: No (3.0)
## | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | min_temp <= 15.4: Yes (5.0)
## | | | | | | | | | | | min_temp > 15.4
## | | | | | | | | | | | | wind_speed_3pm <= 13
## | | | | | | | | | | | | | humidity_9am <= 86: No (2.0)
## | | | | | | | | | | | | | humidity_9am > 86: Yes (4.0)
## | | | | | | | | | | | | wind_speed_3pm > 13: No (8.0)
## | | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | | sunshine <= 4.2: Yes (2.0)
## | | | | | | | | | | | sunshine > 4.2
## | | | | | | | | | | | | rainfall <= 16.2: No (14.0/1.0)
## | | | | | | | | | | | | rainfall > 16.2: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=S: No (40.0/19.0)
## | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | rainfall <= 9.1: No (34.0/15.0)
## | | | | | | | | | | | rainfall > 9.1: Yes (21.0/7.0)
## | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | | | wind_speed_9am <= 9: No (3.0)
## | | | | | | | | | | | | wind_speed_9am > 9: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=ESE
## | | | | | | | | | | | | max_temp <= 22.9: No (3.0)
## | | | | | | | | | | | | max_temp > 22.9: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=SE: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | | min_temp <= 16.6
## | | | | | | | | | | | | | min_temp <= 13.6: Yes (5.0/1.0)
## | | | | | | | | | | | | | min_temp > 13.6: No (7.0)
## | | | | | | | | | | | | min_temp > 16.6: Yes (5.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (7.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SW: No (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=W: No (2.0)
## | | | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NW: No (1.0)
## | | | | | | | | | | | wind_gust_dir=NNW: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | humidity_3pm <= 73: No (5.0)
## | | | | | | | | | | | humidity_3pm > 73
## | | | | | | | | | | | | humidity_9am <= 90: Yes (9.0)
## | | | | | | | | | | | | humidity_9am > 90
## | | | | | | | | | | | | | wind_gust_speed <= 31: No (6.0)
## | | | | | | | | | | | | | wind_gust_speed > 31: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=W: Yes (11.0/4.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | sunshine <= 6: Yes (2.0)
## | | | | | | | | | | | sunshine > 6: No (9.0/4.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | wind_speed_9am <= 9: No (4.0)
## | | | | | | | | | | | | wind_speed_9am > 9: Yes (4.0)
## | | | | | | | | | | | cloud_9am > 7: No (4.0)
## | | | | | | | | | | wind_dir_9am=NNW: No (11.0/4.0)
## | | | | | | | | | cloud_3pm > 5: Yes (349.0/125.0)
## | | | | | | | max_temp > 27.1
## | | | | | | | | min_temp <= 19
## | | | | | | | | | pressure_9am <= 1018.7: Yes (10.0/1.0)
## | | | | | | | | | pressure_9am > 1018.7: No (3.0)
## | | | | | | | | min_temp > 19: No (57.0/10.0)
## | | | wind_gust_speed > 41
## | | | | pressure_3pm <= 1006.8: Yes (790.0/133.0)
## | | | | pressure_3pm > 1006.8
## | | | | | min_temp <= 0.9: No (30.0/6.0)
## | | | | | min_temp > 0.9
## | | | | | | wind_gust_speed <= 54
## | | | | | | | wind_speed_3pm <= 22: Yes (855.0/286.0)
## | | | | | | | wind_speed_3pm > 22
## | | | | | | | | sunshine <= 5.1
## | | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | | humidity_3pm <= 73: No (2.0)
## | | | | | | | | | | humidity_3pm > 73: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | | humidity_9am <= 85: No (2.0)
## | | | | | | | | | | humidity_9am > 85: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=NE: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=ENE: Yes (7.0)
## | | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | | rainfall <= 3.5: No (4.0/1.0)
## | | | | | | | | | | rainfall > 3.5: Yes (8.0)
## | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | pressure_9am <= 1020.6
## | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | cloud_3pm <= 6: No (2.0)
## | | | | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | | | | wind_gust_speed <= 48: Yes (3.0)
## | | | | | | | | | | | | | wind_gust_speed > 48: No (3.0/1.0)
## | | | | | | | | | | | cloud_9am > 7: No (2.0)
## | | | | | | | | | | pressure_9am > 1020.6: Yes (8.0)
## | | | | | | | | | wind_dir_3pm=SE: Yes (17.0/3.0)
## | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | temp_3pm <= 20.4
## | | | | | | | | | | | evaporation <= 5.3: No (8.0)
## | | | | | | | | | | | evaporation > 5.3: Yes (3.0)
## | | | | | | | | | | temp_3pm > 20.4: Yes (10.0)
## | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | cloud_3pm <= 5: Yes (5.0)
## | | | | | | | | | | cloud_3pm > 5
## | | | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=SE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SSE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | | wind_speed_3pm <= 35: No (9.0/2.0)
## | | | | | | | | | | | | wind_speed_3pm > 35: Yes (3.0)
## | | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | | wind_speed_3pm <= 28: No (5.0/1.0)
## | | | | | | | | | | | | | wind_speed_3pm > 28: Yes (3.0)
## | | | | | | | | | | | | cloud_9am > 7: Yes (4.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=W: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | humidity_3pm <= 78: No (6.0)
## | | | | | | | | | | | humidity_3pm > 78: Yes (2.0)
## | | | | | | | | | | cloud_3pm > 6
## | | | | | | | | | | | humidity_9am <= 74: No (2.0)
## | | | | | | | | | | | humidity_9am > 74: Yes (14.0/1.0)
## | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | pressure_9am <= 1019.5: Yes (14.0/1.0)
## | | | | | | | | | | pressure_9am > 1019.5: No (3.0)
## | | | | | | | | | wind_dir_3pm=WSW: Yes (17.0/6.0)
## | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (4.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | temp_3pm <= 17.7: Yes (4.0)
## | | | | | | | | | | | temp_3pm > 17.7: No (2.0)
## | | | | | | | | | | wind_gust_dir=WNW: Yes (3.0)
## | | | | | | | | | | wind_gust_dir=NW: No (1.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | pressure_3pm <= 1020.4: Yes (2.0)
## | | | | | | | | | | | | pressure_3pm > 1020.4: No (2.0)
## | | | | | | | | | | | cloud_9am > 6: No (4.0)
## | | | | | | | | | | cloud_9am > 7: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=NW: Yes (5.0)
## | | | | | | | | | wind_dir_3pm=NNW: Yes (2.0)
## | | | | | | | | sunshine > 5.1
## | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | cloud_9am <= 2: No (6.0)
## | | | | | | | | | | cloud_9am > 2
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | temp_9am <= 13.8: No (3.0)
## | | | | | | | | | | | | temp_9am > 13.8: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=NE: No (5.0/1.0)
## | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=S: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SSW: Yes (1.0)
## | | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | | | wind_gust_dir=W: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=WNW: No (4.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NW: Yes (5.0)
## | | | | | | | | | | | wind_gust_dir=NNW: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | wind_gust_dir=N: No (1.0)
## | | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | | wind_gust_speed <= 46: Yes (2.0)
## | | | | | | | | | | | wind_gust_speed > 46: No (2.0)
## | | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | | humidity_3pm <= 77: No (6.0/1.0)
## | | | | | | | | | | | humidity_3pm > 77: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=S: No (0.0)
## | | | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: No (0.0)
## | | | | | | | | | | wind_gust_dir=W: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=WNW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (2.0/1.0)
## | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | humidity_3pm <= 73: Yes (4.0)
## | | | | | | | | | | humidity_3pm > 73
## | | | | | | | | | | | rainfall <= 21.4: No (10.0/1.0)
## | | | | | | | | | | | rainfall > 21.4: Yes (2.0)
## | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | rainfall <= 16.5: No (18.0/5.0)
## | | | | | | | | | | rainfall > 16.5: Yes (5.0)
## | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=ENE: Yes (3.0/1.0)
## | | | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | | | wind_speed_3pm <= 26: Yes (4.0/1.0)
## | | | | | | | | | | | wind_speed_3pm > 26: No (10.0/1.0)
## | | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | | wind_speed_9am <= 26: No (6.0)
## | | | | | | | | | | | wind_speed_9am > 26: Yes (2.0)
## | | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | | wind_dir_3pm=SSE: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=S: No (1.0)
## | | | | | | | | | | wind_dir_3pm=SSW: No (1.0)
## | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | pressure_9am <= 1020.5: No (12.0/1.0)
## | | | | | | | | | | pressure_9am > 1020.5: Yes (13.0/3.0)
## | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | humidity_3pm <= 69: Yes (4.0)
## | | | | | | | | | | humidity_3pm > 69: No (24.0/7.0)
## | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | cloud_9am <= 5: Yes (9.0)
## | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | evaporation <= 4.6: Yes (4.0)
## | | | | | | | | | | | evaporation > 4.6
## | | | | | | | | | | | | evaporation <= 6.8
## | | | | | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=E: No (2.0)
## | | | | | | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | | | | | | cloud_9am <= 7: Yes (2.0)
## | | | | | | | | | | | | | | cloud_9am > 7: No (3.0)
## | | | | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | | | | cloud_9am <= 7: No (12.0/2.0)
## | | | | | | | | | | | | | | cloud_9am > 7: Yes (7.0/1.0)
## | | | | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | | | | humidity_3pm <= 74: No (5.0/1.0)
## | | | | | | | | | | | | | | humidity_3pm > 74: Yes (5.0)
## | | | | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | | | | wind_speed_9am <= 30: No (2.0)
## | | | | | | | | | | | | | | wind_speed_9am > 30: Yes (2.0)
## | | | | | | | | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=WSW: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=W: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | | | | | evaporation > 6.8: Yes (3.0)
## | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | wind_dir_3pm=N: No (1.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: Yes (1.0)
## | | | | | | | | | | wind_dir_3pm=ENE: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | | | humidity_3pm <= 75
## | | | | | | | | | | | | wind_speed_3pm <= 31: No (4.0)
## | | | | | | | | | | | | wind_speed_3pm > 31
## | | | | | | | | | | | | | temp_9am <= 24.6: Yes (2.0)
## | | | | | | | | | | | | | temp_9am > 24.6: No (2.0)
## | | | | | | | | | | | humidity_3pm > 75: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=SSE
## | | | | | | | | | | | cloud_9am <= 5: No (3.0)
## | | | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | | | cloud_9am <= 7
## | | | | | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SE: Yes (3.0)
## | | | | | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | | | | | humidity_3pm <= 74: No (4.0)
## | | | | | | | | | | | | | | humidity_3pm > 74: Yes (3.0/1.0)
## | | | | | | | | | | | | | wind_gust_dir=S: Yes (4.0/1.0)
## | | | | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=W: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | | | | | cloud_9am > 7: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | | | wind_speed_3pm <= 33
## | | | | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: Yes (2.0)
## | | | | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | | | | temp_3pm <= 19.6: No (3.0)
## | | | | | | | | | | | | | temp_3pm > 19.6: Yes (2.0)
## | | | | | | | | | | | | wind_gust_dir=S: Yes (6.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | | | humidity_9am <= 81: Yes (2.0)
## | | | | | | | | | | | | | humidity_9am > 81: No (3.0)
## | | | | | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=W: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | | | | wind_speed_3pm > 33: No (5.0)
## | | | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | | | pressure_3pm <= 1014.3: Yes (3.0)
## | | | | | | | | | | | pressure_3pm > 1014.3: No (2.0)
## | | | | | | | | | | wind_dir_3pm=SW: No (1.0)
## | | | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=W: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=WNW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (4.0/1.0)
## | | | | | | | | | | wind_gust_dir=SSE: No (4.0)
## | | | | | | | | | | wind_gust_dir=S
## | | | | | | | | | | | humidity_3pm <= 72: No (10.0)
## | | | | | | | | | | | humidity_3pm > 72
## | | | | | | | | | | | | rainfall <= 16
## | | | | | | | | | | | | | wind_speed_3pm <= 33: No (6.0)
## | | | | | | | | | | | | | wind_speed_3pm > 33
## | | | | | | | | | | | | | | temp_9am <= 19.6: Yes (2.0)
## | | | | | | | | | | | | | | temp_9am > 19.6: No (2.0)
## | | | | | | | | | | | | rainfall > 16: Yes (3.0)
## | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | | temp_3pm <= 13.5: Yes (3.0)
## | | | | | | | | | | | | temp_3pm > 13.5: No (18.0/1.0)
## | | | | | | | | | | | cloud_3pm > 6: Yes (6.0/1.0)
## | | | | | | | | | | wind_gust_dir=SW: No (7.0/1.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=W: No (0.0)
## | | | | | | | | | | wind_gust_dir=WNW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=NW: No (0.0)
## | | | | | | | | | | wind_gust_dir=NNW: No (0.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | pressure_9am <= 1011.6: No (5.0)
## | | | | | | | | | | pressure_9am > 1011.6: Yes (46.0/13.0)
## | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | temp_3pm <= 10.8: No (5.0)
## | | | | | | | | | | temp_3pm > 10.8
## | | | | | | | | | | | humidity_9am <= 74: No (5.0/1.0)
## | | | | | | | | | | | humidity_9am > 74: Yes (28.0/5.0)
## | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=NNE: No (1.0)
## | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | | temp_9am <= 13: Yes (3.0)
## | | | | | | | | | | | temp_9am > 13: No (3.0/1.0)
## | | | | | | | | | | wind_gust_dir=SW: No (5.0/1.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (3.0)
## | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | cloud_9am <= 7: Yes (2.0)
## | | | | | | | | | | | cloud_9am > 7: No (7.0/1.0)
## | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | pressure_9am <= 1012.9: Yes (4.0)
## | | | | | | | | | | | pressure_9am > 1012.9: No (5.0)
## | | | | | | | | | | wind_gust_dir=NW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=NE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=SE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=SSE: No (1.0)
## | | | | | | | | | | wind_dir_3pm=S: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_3pm=SSW: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=SW: Yes (0.0)
## | | | | | | | | | | wind_dir_3pm=WSW: No (5.0)
## | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | evaporation <= 2.6: No (2.0)
## | | | | | | | | | | | evaporation > 2.6: Yes (8.0)
## | | | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | | | humidity_9am <= 87: No (4.0)
## | | | | | | | | | | | humidity_9am > 87: Yes (3.0)
## | | | | | | | | | | wind_dir_3pm=NW: No (2.0/1.0)
## | | | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | humidity_9am <= 96: No (33.0/8.0)
## | | | | | | | | | | humidity_9am > 96: Yes (6.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | wind_gust_dir=N: No (3.0)
## | | | | | | | | | | wind_gust_dir=NNE: Yes (2.0)
## | | | | | | | | | | wind_gust_dir=NE: No (3.0)
## | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | | wind_gust_dir=WSW: Yes (1.0)
## | | | | | | | | | | wind_gust_dir=W: Yes (4.0)
## | | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | | humidity_9am <= 89: No (3.0)
## | | | | | | | | | | | humidity_9am > 89: Yes (5.0)
## | | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | | rainfall <= 2.2: No (3.0)
## | | | | | | | | | | | rainfall > 2.2: Yes (5.0/1.0)
## | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | temp_3pm <= 16.2: Yes (5.0/1.0)
## | | | | | | | | | | | temp_3pm > 16.2: No (5.0)
## | | | | | | wind_gust_speed > 54
## | | | | | | | humidity_3pm <= 73
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | rainfall <= 4.6: Yes (5.0)
## | | | | | | | | | rainfall > 4.6: No (3.0/1.0)
## | | | | | | | | wind_dir_3pm=NNE: Yes (5.0/1.0)
## | | | | | | | | wind_dir_3pm=NE
## | | | | | | | | | pressure_9am <= 1011.4: No (2.0)
## | | | | | | | | | pressure_9am > 1011.4: Yes (4.0)
## | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | wind_speed_3pm <= 24: No (2.0)
## | | | | | | | | | wind_speed_3pm > 24: Yes (4.0)
## | | | | | | | | wind_dir_3pm=E
## | | | | | | | | | pressure_3pm <= 1014.8: Yes (3.0)
## | | | | | | | | | pressure_3pm > 1014.8: No (5.0)
## | | | | | | | | wind_dir_3pm=ESE
## | | | | | | | | | wind_dir_9am=N: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | temp_3pm <= 23: Yes (2.0)
## | | | | | | | | | | temp_3pm > 23: No (2.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SSE: No (2.0)
## | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | wind_dir_9am=N: No (1.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | pressure_9am <= 1017.8: No (4.0)
## | | | | | | | | | | pressure_9am > 1017.8: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (8.0/1.0)
## | | | | | | | | | wind_dir_9am=S: Yes (4.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (1.0)
## | | | | | | | | wind_dir_3pm=SSE: Yes (45.0/13.0)
## | | | | | | | | wind_dir_3pm=S
## | | | | | | | | | humidity_3pm <= 69
## | | | | | | | | | | wind_gust_speed <= 65
## | | | | | | | | | | | wind_dir_9am=N: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=SSE: Yes (1.0)
## | | | | | | | | | | | wind_dir_9am=S: No (2.0)
## | | | | | | | | | | | wind_dir_9am=SSW: Yes (3.0)
## | | | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=WSW: No (1.0)
## | | | | | | | | | | | wind_dir_9am=W: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=WNW: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=NW: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=NNW: Yes (0.0)
## | | | | | | | | | | wind_gust_speed > 65: No (9.0)
## | | | | | | | | | humidity_3pm > 69
## | | | | | | | | | | wind_dir_9am=N: Yes (1.0)
## | | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NE: No (1.0)
## | | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (7.0/1.0)
## | | | | | | | | | | wind_dir_9am=S: Yes (16.0/3.0)
## | | | | | | | | | | wind_dir_9am=SSW: Yes (18.0/6.0)
## | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | rainfall <= 5.2: Yes (3.0)
## | | | | | | | | | | | rainfall > 5.2: No (3.0)
## | | | | | | | | | | wind_dir_9am=WSW: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=W: No (2.0/1.0)
## | | | | | | | | | | wind_dir_9am=WNW: No (1.0)
## | | | | | | | | | | wind_dir_9am=NW: Yes (0.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=SSW
## | | | | | | | | | cloud_3pm <= 7
## | | | | | | | | | | wind_speed_3pm <= 35: Yes (19.0/3.0)
## | | | | | | | | | | wind_speed_3pm > 35: No (4.0)
## | | | | | | | | | cloud_3pm > 7: No (16.0/6.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | temp_3pm <= 9.3: No (4.0)
## | | | | | | | | | temp_3pm > 9.3
## | | | | | | | | | | evaporation <= 1.4: No (3.0)
## | | | | | | | | | | evaporation > 1.4
## | | | | | | | | | | | cloud_9am <= 3: No (2.0)
## | | | | | | | | | | | cloud_9am > 3: Yes (33.0/3.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | min_temp <= 15.5: Yes (49.0/8.0)
## | | | | | | | | | min_temp > 15.5: No (3.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | cloud_9am <= 5
## | | | | | | | | | | sunshine <= 8.6: No (7.0/1.0)
## | | | | | | | | | | sunshine > 8.6: Yes (2.0)
## | | | | | | | | | cloud_9am > 5
## | | | | | | | | | | rainfall <= 3.7
## | | | | | | | | | | | temp_3pm <= 12.7: Yes (4.0/1.0)
## | | | | | | | | | | | temp_3pm > 12.7: No (5.0)
## | | | | | | | | | | rainfall > 3.7: Yes (33.0/3.0)
## | | | | | | | | wind_dir_3pm=WNW
## | | | | | | | | | wind_gust_dir=N: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | wind_gust_dir=S: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=SW: Yes (0.0)
## | | | | | | | | | wind_gust_dir=WSW: Yes (4.0)
## | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | wind_speed_9am <= 26
## | | | | | | | | | | | rainfall <= 2.5: No (3.0/1.0)
## | | | | | | | | | | | rainfall > 2.5: Yes (10.0)
## | | | | | | | | | | wind_speed_9am > 26: No (5.0/1.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | temp_3pm <= 14.7: Yes (8.0)
## | | | | | | | | | | temp_3pm > 14.7: No (4.0/1.0)
## | | | | | | | | | wind_gust_dir=NW: No (1.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (0.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | temp_9am <= 8: No (5.0)
## | | | | | | | | | temp_9am > 8
## | | | | | | | | | | wind_gust_speed <= 57: No (2.0)
## | | | | | | | | | | wind_gust_speed > 57: Yes (16.0/1.0)
## | | | | | | | | wind_dir_3pm=NNW: Yes (15.0/1.0)
## | | | | | | | humidity_3pm > 73: Yes (609.0/119.0)
## | humidity_3pm > 82
## | | temp_3pm <= 6.2
## | | | pressure_3pm <= 1015: Yes (53.0/3.0)
## | | | pressure_3pm > 1015
## | | | | rainfall <= 3.7
## | | | | | wind_gust_speed <= 41: No (129.0/20.0)
## | | | | | wind_gust_speed > 41
## | | | | | | wind_dir_9am=N
## | | | | | | | rain_today=No: Yes (18.0/7.0)
## | | | | | | | rain_today=Yes: No (6.0)
## | | | | | | wind_dir_9am=NNE: Yes (2.0)
## | | | | | | wind_dir_9am=NE: Yes (3.0/1.0)
## | | | | | | wind_dir_9am=ENE
## | | | | | | | rain_today=No
## | | | | | | | | temp_3pm <= 4.6: Yes (7.0)
## | | | | | | | | temp_3pm > 4.6: No (2.0)
## | | | | | | | rain_today=Yes: No (2.0)
## | | | | | | wind_dir_9am=E: No (15.0/5.0)
## | | | | | | wind_dir_9am=ESE
## | | | | | | | rainfall <= 0.2: No (10.0)
## | | | | | | | rainfall > 0.2
## | | | | | | | | temp_3pm <= 1.4: Yes (2.0)
## | | | | | | | | temp_3pm > 1.4: No (3.0/1.0)
## | | | | | | wind_dir_9am=SE: No (10.0)
## | | | | | | wind_dir_9am=SSE: No (7.0/1.0)
## | | | | | | wind_dir_9am=S: No (6.0)
## | | | | | | wind_dir_9am=SSW: No (12.0)
## | | | | | | wind_dir_9am=SW: No (26.0/6.0)
## | | | | | | wind_dir_9am=WSW
## | | | | | | | humidity_3pm <= 94: No (13.0)
## | | | | | | | humidity_3pm > 94
## | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | wind_dir_3pm=SW: Yes (3.0/1.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | wind_gust_speed <= 76: No (11.0)
## | | | | | | | | | wind_gust_speed > 76: Yes (3.0/1.0)
## | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | humidity_9am <= 96: No (2.0)
## | | | | | | | | | humidity_9am > 96: Yes (6.0)
## | | | | | | | | wind_dir_3pm=WNW: No (1.0)
## | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | wind_dir_9am=W
## | | | | | | | rain_today=No
## | | | | | | | | wind_gust_dir=N: No (0.0)
## | | | | | | | | wind_gust_dir=NNE: No (0.0)
## | | | | | | | | wind_gust_dir=NE: No (0.0)
## | | | | | | | | wind_gust_dir=ENE: No (0.0)
## | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | wind_gust_dir=ESE: No (0.0)
## | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | wind_gust_dir=SSE: No (0.0)
## | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | wind_gust_dir=SSW: No (0.0)
## | | | | | | | | wind_gust_dir=SW: No (0.0)
## | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | wind_speed_9am <= 28
## | | | | | | | | | | humidity_3pm <= 99: Yes (6.0/1.0)
## | | | | | | | | | | humidity_3pm > 99: No (2.0)
## | | | | | | | | | wind_speed_9am > 28: No (4.0)
## | | | | | | | | wind_gust_dir=W: No (23.0/7.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | wind_speed_3pm <= 22: No (3.0)
## | | | | | | | | | wind_speed_3pm > 22: Yes (3.0)
## | | | | | | | | wind_gust_dir=NW: No (4.0)
## | | | | | | | | wind_gust_dir=NNW: No (1.0)
## | | | | | | | rain_today=Yes
## | | | | | | | | wind_gust_speed <= 70: Yes (11.0)
## | | | | | | | | wind_gust_speed > 70
## | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSE: No (0.0)
## | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (0.0)
## | | | | | | | | | wind_dir_3pm=SW: No (0.0)
## | | | | | | | | | wind_dir_3pm=WSW: Yes (3.0/1.0)
## | | | | | | | | | wind_dir_3pm=W: No (2.0)
## | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | wind_dir_9am=WNW
## | | | | | | | humidity_9am <= 99
## | | | | | | | | wind_speed_9am <= 17: Yes (7.0)
## | | | | | | | | wind_speed_9am > 17
## | | | | | | | | | humidity_9am <= 70: No (4.0)
## | | | | | | | | | humidity_9am > 70
## | | | | | | | | | | wind_gust_speed <= 50: No (3.0)
## | | | | | | | | | | wind_gust_speed > 50: Yes (15.0/3.0)
## | | | | | | | humidity_9am > 99: No (7.0)
## | | | | | | wind_dir_9am=NW
## | | | | | | | rainfall <= 0.1
## | | | | | | | | humidity_3pm <= 99
## | | | | | | | | | humidity_3pm <= 95: No (3.0)
## | | | | | | | | | humidity_3pm > 95: Yes (9.0/1.0)
## | | | | | | | | humidity_3pm > 99: No (7.0)
## | | | | | | | rainfall > 0.1: Yes (9.0)
## | | | | | | wind_dir_9am=NNW
## | | | | | | | min_temp <= -0.4: No (4.0/1.0)
## | | | | | | | min_temp > -0.4: Yes (7.0)
## | | | | rainfall > 3.7
## | | | | | wind_dir_9am=N
## | | | | | | rainfall <= 10.2: No (7.0/2.0)
## | | | | | | rainfall > 10.2: Yes (16.0/3.0)
## | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | wind_dir_9am=NE: Yes (1.0)
## | | | | | wind_dir_9am=ENE: Yes (1.0)
## | | | | | wind_dir_9am=E
## | | | | | | rainfall <= 14.4: No (4.0/1.0)
## | | | | | | rainfall > 14.4: Yes (7.0)
## | | | | | wind_dir_9am=ESE: Yes (15.0/2.0)
## | | | | | wind_dir_9am=SE
## | | | | | | humidity_9am <= 83: Yes (2.0)
## | | | | | | humidity_9am > 83: No (4.0/1.0)
## | | | | | wind_dir_9am=SSE: No (2.0)
## | | | | | wind_dir_9am=S
## | | | | | | temp_3pm <= 2.2: Yes (2.0)
## | | | | | | temp_3pm > 2.2: No (2.0)
## | | | | | wind_dir_9am=SSW: No (11.0/3.0)
## | | | | | wind_dir_9am=SW
## | | | | | | humidity_9am <= 96: Yes (2.0)
## | | | | | | humidity_9am > 96
## | | | | | | | max_temp <= -0.2: Yes (3.0/1.0)
## | | | | | | | max_temp > -0.2: No (8.0)
## | | | | | wind_dir_9am=WSW
## | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | wind_dir_3pm=ESE: Yes (1.0)
## | | | | | | wind_dir_3pm=SE: Yes (0.0)
## | | | | | | wind_dir_3pm=SSE: Yes (2.0)
## | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | wind_dir_3pm=SW
## | | | | | | | min_temp <= -3.5: No (4.0)
## | | | | | | | min_temp > -3.5
## | | | | | | | | wind_speed_3pm <= 15: No (2.0)
## | | | | | | | | wind_speed_3pm > 15: Yes (2.0)
## | | | | | | wind_dir_3pm=WSW: Yes (15.0/1.0)
## | | | | | | wind_dir_3pm=W
## | | | | | | | temp_3pm <= -2.2: Yes (2.0)
## | | | | | | | temp_3pm > -2.2: No (7.0/1.0)
## | | | | | | wind_dir_3pm=WNW: No (1.0)
## | | | | | | wind_dir_3pm=NW: Yes (0.0)
## | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | wind_dir_9am=W
## | | | | | | wind_speed_9am <= 28: Yes (42.0/4.0)
## | | | | | | wind_speed_9am > 28
## | | | | | | | wind_speed_9am <= 30: No (5.0)
## | | | | | | | wind_speed_9am > 30
## | | | | | | | | max_temp <= 6.8: Yes (5.0)
## | | | | | | | | max_temp > 6.8: No (3.0)
## | | | | | wind_dir_9am=WNW
## | | | | | | humidity_9am <= 84: No (5.0/1.0)
## | | | | | | humidity_9am > 84: Yes (17.0/1.0)
## | | | | | wind_dir_9am=NW: Yes (9.0)
## | | | | | wind_dir_9am=NNW: Yes (2.0)
## | | temp_3pm > 6.2
## | | | rainfall <= 2.3
## | | | | humidity_9am <= 96
## | | | | | humidity_3pm <= 86
## | | | | | | pressure_3pm <= 1013.5
## | | | | | | | max_temp <= 20.4: Yes (257.0/34.0)
## | | | | | | | max_temp > 20.4
## | | | | | | | | cloud_3pm <= 5
## | | | | | | | | | wind_gust_dir=N: No (16.0/7.0)
## | | | | | | | | | wind_gust_dir=NNE
## | | | | | | | | | | wind_speed_3pm <= 30: No (12.0/5.0)
## | | | | | | | | | | wind_speed_3pm > 30: Yes (3.0)
## | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | humidity_3pm <= 84
## | | | | | | | | | | | pressure_3pm <= 1007.9: Yes (4.0)
## | | | | | | | | | | | pressure_3pm > 1007.9: No (10.0)
## | | | | | | | | | | humidity_3pm > 84: Yes (3.0)
## | | | | | | | | | wind_gust_dir=ENE: No (4.0)
## | | | | | | | | | wind_gust_dir=E: No (2.0/1.0)
## | | | | | | | | | wind_gust_dir=ESE: Yes (7.0)
## | | | | | | | | | wind_gust_dir=SE: Yes (5.0/1.0)
## | | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | | humidity_3pm <= 84: No (4.0)
## | | | | | | | | | | humidity_3pm > 84: Yes (6.0)
## | | | | | | | | | wind_gust_dir=S: Yes (24.0/11.0)
## | | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | | rainfall <= 0.1
## | | | | | | | | | | | pressure_3pm <= 1007.9: Yes (2.0)
## | | | | | | | | | | | pressure_3pm > 1007.9: No (8.0)
## | | | | | | | | | | rainfall > 0.1: Yes (4.0)
## | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | temp_9am <= 19.4: No (2.0)
## | | | | | | | | | | temp_9am > 19.4: Yes (2.0)
## | | | | | | | | | wind_gust_dir=WSW: Yes (4.0)
## | | | | | | | | | wind_gust_dir=W: No (13.0/6.0)
## | | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | | temp_3pm <= 18.1: Yes (2.0)
## | | | | | | | | | | temp_3pm > 18.1: No (4.0)
## | | | | | | | | | wind_gust_dir=NW
## | | | | | | | | | | wind_gust_speed <= 35: No (3.0/1.0)
## | | | | | | | | | | wind_gust_speed > 35: Yes (6.0)
## | | | | | | | | | wind_gust_dir=NNW: Yes (4.0/1.0)
## | | | | | | | | cloud_3pm > 5: Yes (224.0/63.0)
## | | | | | | pressure_3pm > 1013.5
## | | | | | | | humidity_9am <= 79: Yes (318.0/108.0)
## | | | | | | | humidity_9am > 79
## | | | | | | | | wind_gust_speed <= 50
## | | | | | | | | | temp_3pm <= 22.6
## | | | | | | | | | | humidity_3pm <= 83: No (109.0/38.0)
## | | | | | | | | | | humidity_3pm > 83
## | | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | | humidity_3pm <= 84: No (12.0/3.0)
## | | | | | | | | | | | | humidity_3pm > 84: Yes (22.0/10.0)
## | | | | | | | | | | | wind_dir_9am=NNE: Yes (15.0/6.0)
## | | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | | wind_speed_9am <= 17: Yes (4.0/1.0)
## | | | | | | | | | | | | wind_speed_9am > 17: No (6.0)
## | | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | | wind_gust_speed <= 35
## | | | | | | | | | | | | | pressure_9am <= 1020.4: Yes (5.0)
## | | | | | | | | | | | | | pressure_9am > 1020.4: No (4.0/1.0)
## | | | | | | | | | | | | wind_gust_speed > 35: No (6.0)
## | | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | | evaporation <= 3.5: No (4.0)
## | | | | | | | | | | | | evaporation > 3.5
## | | | | | | | | | | | | | humidity_9am <= 89: No (2.0)
## | | | | | | | | | | | | | humidity_9am > 89: Yes (6.0)
## | | | | | | | | | | | wind_dir_9am=ESE
## | | | | | | | | | | | | wind_speed_9am <= 13: Yes (3.0)
## | | | | | | | | | | | | wind_speed_9am > 13: No (3.0)
## | | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | | sunshine <= 6: No (2.0)
## | | | | | | | | | | | | sunshine > 6: Yes (5.0)
## | | | | | | | | | | | wind_dir_9am=SSE: Yes (11.0/5.0)
## | | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | humidity_3pm <= 84
## | | | | | | | | | | | | | | wind_speed_9am <= 13: Yes (2.0)
## | | | | | | | | | | | | | | wind_speed_9am > 13: No (2.0)
## | | | | | | | | | | | | | humidity_3pm > 84: No (3.0)
## | | | | | | | | | | | | cloud_9am > 6
## | | | | | | | | | | | | | sunshine <= 5.8: Yes (9.0)
## | | | | | | | | | | | | | sunshine > 5.8
## | | | | | | | | | | | | | | wind_speed_3pm <= 9: Yes (2.0)
## | | | | | | | | | | | | | | wind_speed_3pm > 9: No (2.0)
## | | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | | wind_gust_speed <= 44: Yes (15.0/4.0)
## | | | | | | | | | | | | wind_gust_speed > 44: No (4.0/1.0)
## | | | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | | | wind_speed_3pm <= 15: Yes (12.0/1.0)
## | | | | | | | | | | | | wind_speed_3pm > 15
## | | | | | | | | | | | | | evaporation <= 3: Yes (2.0)
## | | | | | | | | | | | | | evaporation > 3: No (16.0/5.0)
## | | | | | | | | | | | wind_dir_9am=WSW: Yes (16.0/4.0)
## | | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=ENE: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=E: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | | | | wind_dir_3pm=SE: No (4.0)
## | | | | | | | | | | | | wind_dir_3pm=SSE: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=S: No (1.0)
## | | | | | | | | | | | | wind_dir_3pm=SSW: Yes (2.0)
## | | | | | | | | | | | | wind_dir_3pm=SW: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=WSW: No (4.0/1.0)
## | | | | | | | | | | | | wind_dir_3pm=W
## | | | | | | | | | | | | | temp_3pm <= 14.4: No (2.0)
## | | | | | | | | | | | | | temp_3pm > 14.4: Yes (3.0)
## | | | | | | | | | | | | wind_dir_3pm=WNW: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=NW: Yes (1.0)
## | | | | | | | | | | | | wind_dir_3pm=NNW: Yes (0.0)
## | | | | | | | | | | | wind_dir_9am=WNW: No (16.0/5.0)
## | | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | | temp_3pm <= 13.3: Yes (9.0/2.0)
## | | | | | | | | | | | | temp_3pm > 13.3: No (10.0/4.0)
## | | | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | | | wind_gust_dir=N: Yes (5.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=NNE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ENE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=E: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=ESE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SSE: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=S: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=SSW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=SW: Yes (1.0)
## | | | | | | | | | | | | wind_gust_dir=WSW: No (1.0)
## | | | | | | | | | | | | wind_gust_dir=W: Yes (3.0)
## | | | | | | | | | | | | wind_gust_dir=WNW: Yes (0.0)
## | | | | | | | | | | | | wind_gust_dir=NW: No (2.0/1.0)
## | | | | | | | | | | | | wind_gust_dir=NNW: No (7.0/1.0)
## | | | | | | | | | temp_3pm > 22.6
## | | | | | | | | | | sunshine <= 0.8: Yes (2.0)
## | | | | | | | | | | sunshine > 0.8: No (35.0/3.0)
## | | | | | | | | wind_gust_speed > 50: Yes (63.0/17.0)
## | | | | | humidity_3pm > 86
## | | | | | | temp_3pm <= 28.5
## | | | | | | | sunshine <= 8.5: Yes (2823.0/488.0)
## | | | | | | | sunshine > 8.5: No (28.0/8.0)
## | | | | | | temp_3pm > 28.5
## | | | | | | | min_temp <= 25.8: No (21.0)
## | | | | | | | min_temp > 25.8: Yes (5.0/1.0)
## | | | | humidity_9am > 96
## | | | | | pressure_3pm <= 1021.8
## | | | | | | pressure_3pm <= 1014.4
## | | | | | | | rainfall <= 0.5
## | | | | | | | | humidity_9am <= 98: Yes (68.0/13.0)
## | | | | | | | | humidity_9am > 98
## | | | | | | | | | wind_dir_9am=N: Yes (40.0/11.0)
## | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | pressure_3pm <= 1012.3: No (4.0/1.0)
## | | | | | | | | | | pressure_3pm > 1012.3: Yes (3.0)
## | | | | | | | | | wind_dir_9am=NE: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | temp_3pm <= 21: Yes (5.0)
## | | | | | | | | | | temp_3pm > 21: No (2.0)
## | | | | | | | | | wind_dir_9am=E: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (4.0)
## | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | wind_gust_speed <= 37: No (4.0/1.0)
## | | | | | | | | | | wind_gust_speed > 37: Yes (3.0)
## | | | | | | | | | wind_dir_9am=SSE
## | | | | | | | | | | pressure_9am <= 1012: No (5.0)
## | | | | | | | | | | pressure_9am > 1012: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_9am=S: No (2.0)
## | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | temp_9am <= 20.6: No (6.0)
## | | | | | | | | | | temp_9am > 20.6: Yes (4.0)
## | | | | | | | | | wind_dir_9am=SW
## | | | | | | | | | | humidity_3pm <= 88: Yes (2.0)
## | | | | | | | | | | humidity_3pm > 88: No (5.0)
## | | | | | | | | | wind_dir_9am=WSW: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=W: Yes (6.0/1.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | wind_speed_9am <= 17: Yes (6.0)
## | | | | | | | | | | wind_speed_9am > 17: No (2.0)
## | | | | | | | | | wind_dir_9am=NW: No (3.0)
## | | | | | | | | | wind_dir_9am=NNW
## | | | | | | | | | | wind_speed_3pm <= 22: Yes (5.0/1.0)
## | | | | | | | | | | wind_speed_3pm > 22: No (2.0)
## | | | | | | | rainfall > 0.5: Yes (142.0/22.0)
## | | | | | | pressure_3pm > 1014.4
## | | | | | | | temp_9am <= 7.6
## | | | | | | | | wind_dir_3pm=N
## | | | | | | | | | temp_3pm <= 8.6: Yes (6.0/2.0)
## | | | | | | | | | temp_3pm > 8.6: No (16.0/3.0)
## | | | | | | | | wind_dir_3pm=NNE
## | | | | | | | | | temp_9am <= 5.1: No (4.0/1.0)
## | | | | | | | | | temp_9am > 5.1: Yes (3.0)
## | | | | | | | | wind_dir_3pm=NE: No (7.0/2.0)
## | | | | | | | | wind_dir_3pm=ENE
## | | | | | | | | | rain_today=No: No (8.0/1.0)
## | | | | | | | | | rain_today=Yes: Yes (2.0)
## | | | | | | | | wind_dir_3pm=E: No (12.0)
## | | | | | | | | wind_dir_3pm=ESE: No (5.0/1.0)
## | | | | | | | | wind_dir_3pm=SE
## | | | | | | | | | temp_3pm <= 12.7
## | | | | | | | | | | cloud_3pm <= 6
## | | | | | | | | | | | min_temp <= 2.6: No (9.0/1.0)
## | | | | | | | | | | | min_temp > 2.6: Yes (2.0)
## | | | | | | | | | | cloud_3pm > 6: No (2.0)
## | | | | | | | | | temp_3pm > 12.7: Yes (7.0)
## | | | | | | | | wind_dir_3pm=SSE: No (6.0/1.0)
## | | | | | | | | wind_dir_3pm=S: No (2.0/1.0)
## | | | | | | | | wind_dir_3pm=SSW: No (11.0/5.0)
## | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | cloud_3pm <= 7: No (4.0)
## | | | | | | | | | cloud_3pm > 7: Yes (6.0/2.0)
## | | | | | | | | wind_dir_3pm=WSW
## | | | | | | | | | temp_3pm <= 12.2: No (7.0)
## | | | | | | | | | temp_3pm > 12.2: Yes (2.0)
## | | | | | | | | wind_dir_3pm=W: No (18.0/6.0)
## | | | | | | | | wind_dir_3pm=WNW: Yes (16.0/5.0)
## | | | | | | | | wind_dir_3pm=NW
## | | | | | | | | | wind_speed_9am <= 4: Yes (8.0/3.0)
## | | | | | | | | | wind_speed_9am > 4: No (13.0/5.0)
## | | | | | | | | wind_dir_3pm=NNW
## | | | | | | | | | max_temp <= 9.4: Yes (4.0/1.0)
## | | | | | | | | | max_temp > 9.4: No (13.0/4.0)
## | | | | | | | temp_9am > 7.6
## | | | | | | | | humidity_3pm <= 94
## | | | | | | | | | wind_gust_speed <= 48
## | | | | | | | | | | wind_dir_9am=N
## | | | | | | | | | | | wind_gust_dir=N
## | | | | | | | | | | | | rain_today=No
## | | | | | | | | | | | | | cloud_3pm <= 6: Yes (4.0)
## | | | | | | | | | | | | | cloud_3pm > 6: No (2.0)
## | | | | | | | | | | | | rain_today=Yes: No (2.0)
## | | | | | | | | | | | wind_gust_dir=NNE: No (4.0)
## | | | | | | | | | | | wind_gust_dir=NE
## | | | | | | | | | | | | pressure_3pm <= 1017: No (2.0)
## | | | | | | | | | | | | pressure_3pm > 1017: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=ENE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=E: No (0.0)
## | | | | | | | | | | | wind_gust_dir=ESE: No (1.0)
## | | | | | | | | | | | wind_gust_dir=SE: No (0.0)
## | | | | | | | | | | | wind_gust_dir=SSE: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=S: No (2.0/1.0)
## | | | | | | | | | | | wind_gust_dir=SSW: No (2.0)
## | | | | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | | | | sunshine <= 4.4: No (2.0)
## | | | | | | | | | | | | sunshine > 4.4: Yes (3.0/1.0)
## | | | | | | | | | | | wind_gust_dir=WSW: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=W
## | | | | | | | | | | | | evaporation <= 3.3: No (2.0)
## | | | | | | | | | | | | evaporation > 3.3
## | | | | | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | | | | | humidity_9am <= 99: No (4.0)
## | | | | | | | | | | | | | | humidity_9am > 99
## | | | | | | | | | | | | | | | max_temp <= 14.8: Yes (3.0)
## | | | | | | | | | | | | | | | max_temp > 14.8
## | | | | | | | | | | | | | | | | temp_3pm <= 16.7: No (7.0)
## | | | | | | | | | | | | | | | | temp_3pm > 16.7: Yes (2.0)
## | | | | | | | | | | | | | cloud_9am > 6: Yes (2.0)
## | | | | | | | | | | | wind_gust_dir=WNW: Yes (5.0)
## | | | | | | | | | | | wind_gust_dir=NW: No (2.0/1.0)
## | | | | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | | | | max_temp <= 13.8: No (2.0)
## | | | | | | | | | | | | max_temp > 13.8: Yes (8.0/1.0)
## | | | | | | | | | | wind_dir_9am=NNE
## | | | | | | | | | | | rain_today=No: No (7.0/1.0)
## | | | | | | | | | | | rain_today=Yes: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=NE
## | | | | | | | | | | | wind_speed_9am <= 13: Yes (3.0)
## | | | | | | | | | | | wind_speed_9am > 13: No (2.0)
## | | | | | | | | | | wind_dir_9am=ENE
## | | | | | | | | | | | temp_3pm <= 14.1: No (3.0)
## | | | | | | | | | | | temp_3pm > 14.1: Yes (2.0)
## | | | | | | | | | | wind_dir_9am=E
## | | | | | | | | | | | wind_speed_3pm <= 4: Yes (3.0)
## | | | | | | | | | | | wind_speed_3pm > 4: No (7.0)
## | | | | | | | | | | wind_dir_9am=ESE: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=SE
## | | | | | | | | | | | humidity_9am <= 98: No (2.0)
## | | | | | | | | | | | humidity_9am > 98: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=SSE: No (4.0)
## | | | | | | | | | | wind_dir_9am=S
## | | | | | | | | | | | cloud_3pm <= 6: Yes (8.0/2.0)
## | | | | | | | | | | | cloud_3pm > 6: No (2.0)
## | | | | | | | | | | wind_dir_9am=SSW
## | | | | | | | | | | | rain_today=No: No (10.0/4.0)
## | | | | | | | | | | | rain_today=Yes: Yes (3.0)
## | | | | | | | | | | wind_dir_9am=SW: Yes (10.0/3.0)
## | | | | | | | | | | wind_dir_9am=WSW
## | | | | | | | | | | | cloud_3pm <= 7: No (5.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (4.0/1.0)
## | | | | | | | | | | wind_dir_9am=W
## | | | | | | | | | | | cloud_3pm <= 7: No (6.0/1.0)
## | | | | | | | | | | | cloud_3pm > 7: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | | pressure_3pm <= 1018.7: No (7.0/1.0)
## | | | | | | | | | | | pressure_3pm > 1018.7: Yes (5.0)
## | | | | | | | | | | wind_dir_9am=NW
## | | | | | | | | | | | humidity_3pm <= 92
## | | | | | | | | | | | | pressure_3pm <= 1020.5: No (12.0)
## | | | | | | | | | | | | pressure_3pm > 1020.5: Yes (2.0)
## | | | | | | | | | | | humidity_3pm > 92: Yes (4.0)
## | | | | | | | | | | wind_dir_9am=NNW: Yes (15.0/4.0)
## | | | | | | | | | wind_gust_speed > 48: Yes (18.0/1.0)
## | | | | | | | | humidity_3pm > 94: Yes (207.0/59.0)
## | | | | | pressure_3pm > 1021.8
## | | | | | | wind_gust_speed <= 17: No (67.0/8.0)
## | | | | | | wind_gust_speed > 17
## | | | | | | | temp_9am <= 7.9: No (104.0/24.0)
## | | | | | | | temp_9am > 7.9
## | | | | | | | | wind_gust_dir=N
## | | | | | | | | | temp_9am <= 10.9: No (2.0)
## | | | | | | | | | temp_9am > 10.9: Yes (2.0)
## | | | | | | | | wind_gust_dir=NNE: Yes (5.0/1.0)
## | | | | | | | | wind_gust_dir=NE: Yes (4.0)
## | | | | | | | | wind_gust_dir=ENE
## | | | | | | | | | wind_speed_3pm <= 11: Yes (4.0/1.0)
## | | | | | | | | | wind_speed_3pm > 11: No (2.0)
## | | | | | | | | wind_gust_dir=E: No (2.0)
## | | | | | | | | wind_gust_dir=ESE: No (4.0)
## | | | | | | | | wind_gust_dir=SE
## | | | | | | | | | cloud_9am <= 6
## | | | | | | | | | | humidity_3pm <= 87: Yes (2.0)
## | | | | | | | | | | humidity_3pm > 87: No (3.0)
## | | | | | | | | | cloud_9am > 6: No (2.0)
## | | | | | | | | wind_gust_dir=SSE
## | | | | | | | | | wind_speed_9am <= 7: Yes (2.0)
## | | | | | | | | | wind_speed_9am > 7: No (3.0)
## | | | | | | | | wind_gust_dir=S
## | | | | | | | | | sunshine <= 4.3: No (6.0)
## | | | | | | | | | sunshine > 4.3
## | | | | | | | | | | wind_speed_9am <= 20: Yes (8.0/1.0)
## | | | | | | | | | | wind_speed_9am > 20: No (3.0)
## | | | | | | | | wind_gust_dir=SSW
## | | | | | | | | | temp_9am <= 10.2: No (7.0)
## | | | | | | | | | temp_9am > 10.2: Yes (17.0/2.0)
## | | | | | | | | wind_gust_dir=SW
## | | | | | | | | | wind_dir_3pm=N: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: No (0.0)
## | | | | | | | | | wind_dir_3pm=NE: No (0.0)
## | | | | | | | | | wind_dir_3pm=ENE: No (0.0)
## | | | | | | | | | wind_dir_3pm=E: No (0.0)
## | | | | | | | | | wind_dir_3pm=ESE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SE: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSE: Yes (1.0)
## | | | | | | | | | wind_dir_3pm=S: No (0.0)
## | | | | | | | | | wind_dir_3pm=SSW: No (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=SW
## | | | | | | | | | | temp_3pm <= 13.5: No (6.0)
## | | | | | | | | | | temp_3pm > 13.5: Yes (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=WSW: No (4.0/1.0)
## | | | | | | | | | wind_dir_3pm=W: Yes (3.0)
## | | | | | | | | | wind_dir_3pm=WNW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NW: No (0.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (0.0)
## | | | | | | | | wind_gust_dir=WSW
## | | | | | | | | | temp_9am <= 10.7
## | | | | | | | | | | temp_3pm <= 10.6: No (2.0)
## | | | | | | | | | | temp_3pm > 10.6: Yes (6.0)
## | | | | | | | | | temp_9am > 10.7: No (4.0)
## | | | | | | | | wind_gust_dir=W
## | | | | | | | | | wind_dir_9am=N: No (4.0)
## | | | | | | | | | wind_dir_9am=NNE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=NE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=E: Yes (0.0)
## | | | | | | | | | wind_dir_9am=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_9am=S: Yes (0.0)
## | | | | | | | | | wind_dir_9am=SSW: Yes (2.0)
## | | | | | | | | | wind_dir_9am=SW: Yes (0.0)
## | | | | | | | | | wind_dir_9am=WSW: Yes (1.0)
## | | | | | | | | | wind_dir_9am=W: Yes (2.0)
## | | | | | | | | | wind_dir_9am=WNW
## | | | | | | | | | | pressure_3pm <= 1024.5: Yes (2.0)
## | | | | | | | | | | pressure_3pm > 1024.5: No (2.0)
## | | | | | | | | | wind_dir_9am=NW: No (3.0/1.0)
## | | | | | | | | | wind_dir_9am=NNW: Yes (4.0/1.0)
## | | | | | | | | wind_gust_dir=WNW
## | | | | | | | | | wind_dir_3pm=N: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=NNE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=NE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=ENE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=E: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=ESE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=SE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=SSE: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=S: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=SSW: Yes (1.0)
## | | | | | | | | | wind_dir_3pm=SW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=WSW: Yes (0.0)
## | | | | | | | | | wind_dir_3pm=W: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=WNW: Yes (2.0)
## | | | | | | | | | wind_dir_3pm=NW: No (3.0)
## | | | | | | | | | wind_dir_3pm=NNW: No (1.0)
## | | | | | | | | wind_gust_dir=NW: Yes (6.0)
## | | | | | | | | wind_gust_dir=NNW
## | | | | | | | | | cloud_3pm <= 7: No (6.0)
## | | | | | | | | | cloud_3pm > 7: Yes (3.0/1.0)
## | | | rainfall > 2.3: Yes (5202.0/645.0)
##
## Number of Leaves : 4586
##
## Size of the tree : 6175
### References
Hornik, Kurt. 2021. RWeka: R/Weka Interface. https://CRAN.R-project.org/package=RWeka.
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/567/4766
|
Effect of Nitrate Ester on the Combustion Characteristics of PET/HMX-based Propellants
The effect of nitrate ester NG/TEGDN on the combustion characteristics of PET/HMX-based propellants has been experimentally investigated using of high-speed photography technique and scanning electron microscopy. It is indicated that the increase of NG/TEGDN content has little impact on the propellant burning rates at the same pressure. Furthermore, propellant can not be self-sustaining combustion at low pressure (≤1 MPa). The increase of NG/TEGDN content does not affect the flame structure of propellant, but it plays an important role in condensed phase reaction zone. The flame structure of propellant is estimated. The thermal decomposition products in different combustion zones are also discussed. Scanning electron microscopy examination of quenched sample indicates that a liquified layer forms during combustion of these propellants. Numerous gas bubbles are present. Especially, the burning surface of propellant with low NG/TEGDN content shows signs of crystallization. The thickness of condensed phase reaction zone, by cross-section examination of propellant burning surface, has also been investigated. The results show that the thickness of condensed phase reaction zone increases with NG/TEGDN content increasing. These observations suggest that the condensed phase zone plays significant role in propellant combustion.
Ethylene oxide-tetrahydrofuran copolyether (PET), as a polymer binder and cyclotetramethylenetetranitramine (HMX) as an oxidiser are the major components of nitrate ester plasticised polyether (NEPE) propellants. Over the past several years, advances in energetic materials have been made in many types of propellant ingredients, including binders, oxidisers, and metal additives. Numerous literatures studies describe how to decrease the burning rate pressure exponent of NEPE propellants or how to enhance its combustion performance1-3. However, few data are available regarding the effect of nitrate ester nitroglycerine/triethylene glycol dinitrate (NG/TEGDN) on combustion characteristics of propellants, so the present paper is efforts to increase our knowledge in interpreting the combustion characteristics of PET/HMX-based propellants with different NG/TEGDN contents.
Plasticiser is a key ingredient of high-energetic solid propellant and plays a vital role in controlling the solid propellant property. Extensive studies for plasticiser concentrate on thermodynamic, structural, mechanical, ballistic implication and sensitivity in high energy propellant4-8. Literature survey reveals that few studies have been conducted on the effect of nitrate ester NG/TEGDN on the combustion characteristics of PET/HMX-based propellants.
The primary objective of this study is to characterise and compare the combustion behaviour of PET/HMX based solid propellants with different NG/TEGDN contents. It is hoped that this work would be useful in providing a clearer understanding of high performance energetic solid propellant studies.
2.1 Propellant Formulations
The propellant samples (E-1 and E-2) investigated in this study consist of HMX particles with PET as a binder and NG/TEGDN as plasticisers. The particle size of HMX is 5-80 ì m. Their main compositions are shown in Table 1.
2.2 Burning Rate Measurement
A high-pressure optical strand burner (Fig. 1) was used to measure the burning rates of the samples between 1-3 MPa. The propellant strands were burned under constant-pressure condition and the burning rates were deduced from video images recorded using a CCD camera, and the pressure exponent was calculated according to Vieile r=aPn. In this investigation, nitrogen was used as the purge gas.
2.3 Flame Images of Propellants
The experimental set-up used for flame image consists of a combustion chamber, fitted with two quartz side windows (Fig.1). Propellant sample size was 2×4×15 mm. The sample was ignited by a hot nickel-chrome wire. The flame picture was obtained by CCD.
2.4 SEM Measurement
To study the effect of NG/TEGDN on the quenched surface, the experiment was carried out for E-1 and E-2 propellants. The quenched surfaces of propellants were acquired by slack water. The quenched surface images were observed by scanning electron microscopy.
3.1 Effect of Nitrate Ester NG/TEGDN on the Burning Characteristics of PET/HMX-based Propellants
The burning rates and burning rate pressure index of propellants E-1 and E-2 are shown in Table 2. As shown in Table 2, E-1 and E-2 propellants can not be self-sustaining combustion at 1MPa. Increasing the pressure to 2 MPa, the burning rates of both propellants were nearly the same. While at 3MPa, the burning rate of E-2 propellant was slightly higher than that of E-1 propellant, but the difference was not obvious. It is clear that the content of NG/TEGDN has little impact on the burning rates of PET/HMX-based propellants at the same pressure. The burning rates of both propellants were increased with the pressure increasing. The burning rate pressure index of E-1and E-2 propellants was 0.8417 and 0.8917, respectively. This result is similar to Y. Wang9, et.al. They reported that the burning rate pressure index of only binder/HMX was 0.96. The high HMX or nitrate ester content is the root cause of high burning rate pressure index of propellant10.
It is well known that the burning rate is determined by the heat generated at the burning surface and the heat transferred back from the gas phase to the burning surface. In other words, the heat feedback from the exothermic reactions occurring in the gas phase along with the condensed- phase heat release sustains the combustion process. The specific processes in the condensed and gas phases depend on the particular ingredient under consideration.
At 1MPa, the flame stands-off relatively farther from the burning surface. This causes a reduction in the heat flux to the propellant surface, and the net heat flux at the burning surface is insufficient to sustain the decomposition of HMX in the condensed phase. Also, PET binder forms a melt layer on the burning surface. The heat, which is transfered back from the gas phase to the burning surface is absorbed by the melt layer. Thus, HMX oxidiser can not get enough heat to sustain the combustion process. So the propellants can not be self-sustaining combustion and take place self-extinguished phenomena. When the pressure increases, the flame may be close to the burning surface and the heat feedback from the gas phase to the condensed phase may increase. This increase accelerates the decomposition of melt PET binder, and causes the thickness of melt layer to become thin. The net heat flux at the burning surface is sufficient to sustain the decomposition of HMX in the condensed phase, so the propellants can be self-sustaining combustion. However, NG/TEGDN content increase can not modify the burning rate as expected. As shown in Table 2, the changes of burning rate are not obvious at the same pressure. This may have relations to the decomposition of HMX and nitrate ester in the following.
Oxidiser HMX is characterised by-N-NO2 chemical bonds that are attached to hydrocarbon structures. The bond breakage of N–N produces NO2, which acts as an oxidiser. The remaining hydrocarbon fragments act as fuel components.
The total initial decomposition reaction of HMX is as follows11-13:
$3{\left(C{H}_{2}NN{O}_{2}\right)}_{4}\text{\hspace{0.17em}}\to \text{\hspace{0.17em}}4N{O}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4{N}_{2}O\text{\hspace{0.17em}}+6{N}_{2}+\text{\hspace{0.17em}}12C{H}_{2}O$ (1)
Since formaldehyde reacts quite rapidly with nitrogen dioxide14, the gas phase reaction is as follows:
$7N{O}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}5C{H}_{2}O\text{\hspace{0.17em}}\to \text{\hspace{0.17em}}7NO+3CO+2C{O}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}5{H}_{2}O$ (2)
It is probably the dominating reaction15. This reaction determines the burning rate of the propellant. The reaction between NO2 and CH2O releases a large amount of heat, and the reaction rate is much faster than other reactions. Plasticiser NG/TEGDN is characterised by-O-NO2 chemical bonds. The bond breakage of O-N produces NO2, which acts as an oxidiser. The remaining hydrocarbon fragments act as fuel components.
The decomposition of nitrate ester is as follows:
(3)
Then,
(4)
It can be seen from that HMX oxidiser and NG/TEGDN plasticisers all contain elements C, H, O, N, and the decomposition products are nearly the same. The contents of NO2 and aldehyde increase as the nitrate ester content increases, while the ratio of NO2/aldehyde shows a little change. Thus, the decomposition of NG/TEGDN does not obviously accelerate the HMX reaction, and the change of NG/TEGDN content does not apparently increase the burning rate of PET/HMX-based propellants. This leads to small difference of both propellant burning rates at the same pressure.
3.2 Characteristics of Combustion Flame
Typical flame images of PET/HMX-based propellants containing NG/TEGDN are shown in Figs 2 and 3 as a function of pressure. It is evident that the flame presents dark zone. Furthermore, the combustion process presents a lot of smoke. When the pressure is 1MPa, the flame of E-1 propellant is very weak, and the luminous flame will be blown away from the burning surface, as shown in Fig. 2. The flame zone approaches the burning surface as pressure increases16. Moreover, the flame intensity increases and dark zone becomes thin due to increasing pressure.
For E-2 propellant, a thin luminous flame sheet stands-off some distance from the burning surface and a reddish flame was produced above this luminous flame zone, as shown in Fig.3. The flame also presents dark zone. The thickness of dark zone changes as the pressure increases, especially for the pressure between 1MPa and 2MPa. The flame intensity of E-2 propellant increases compared to that of E-1 propellant. Furthermore, the quantity of smoke involved in the combustion process was greatly reduced, so it can be concluded that the combustion of E-2 propellant is more complete than that of E-1 propellant as NG/TEGDN content increases.
From the comparisons between the flame photographs of E-1 and E-2 propellants, it can be found that the increase of NG/TEGDN content does not affect the flame image but only enhances the flame intensity. The flame structures of E-1 and E-2 propellants are similar to HMX-CMDB combustion model. It is reported that the flame structures of both propellants belong to premix flame structure17, so the diffusion flame between HMX and PET/NG/TEGDN was not found. Since HMX is a stoichiometrically balanced crystalline material, no diffusion flamelets were formed above the burning surface. The gaseous decomposition of the HMX particles diffuse and mix with the gaseous decomposition products of the base matrix and form a reactive homogeneous gas, which reacts to produce a pre-mixed flame above the burning surface. As in the case of double-base propellants, the luminous flame is distended from the burning surface for both HMX-CMDB propellants. Furthermore, the flame stand-off distances decrease as the pressure increases because of the increase in the reactant concentrations and gas densities, which in turn increase the reaction rate and reduce the transport velocity.
Photographic observations of the flame are useful to understand the overall combustion characteristics of propellants. The flame characterisation must be controlled by inherent factors in both condensed phase and gas phase. To make it clearer as to how the inherent factors affect the flame characterisation of PET/HMX-based propellants which contain different NG/TEGDN contents, the combustion process was simulated by the flame schematic (Fig. 4).
The condensed phase zone, as shown in Fig. 4, is the thermal-chemical reaction layer, where many changes take place such as crystal transformation, melting, thermal decomposition, sublimation, and vapourisation. The burning surface that contacts the condensed phase and gas phase is gas/liquid interface at low pressure, where most of the thermolysis products are released and parts of HMX, NG and TEGDN are evaporated. The dark zone is a nonluminous region which separates the primary reaction zone near the propellant surface from the luminous secondary flame zone. As discussed above, the decomposed species are expelled and transported away from the burning surface via both diffusion and convection. Subsequent reactions occur among the decomposed products, and produce intermediate species such as HCN, NO, CO, and N2O in the dark zone.
The -NO2 contents in the binder system directly influence the exothermic reaction between NO2 and aldehydes, thus affecting the heat balance of burning surface and the average temperature of burning surface. According to the results in Section 3.1, in the condensed phase zone, NG/ TEGDN decomposition produces NO2 and organic molecules (mainly aldehydes). The concentration of NO2 and aldehydes increases as the content of NG/TEGDN increases, thus the reaction rate of reaction 2 [(Eqn. 2)] increases. This increase can result in higher exothermal heat rate of the reaction 2 [(Eqn. 2)]. Then released thermal energy continuously accelerates the next reaction, so it can be found that the flame intensity of E-2 propellant is stronger than that of E-1 propellant at the same pressure.
3.3 Analysis of Quenched Surface
Information on the nature and importance of condensed phase reactions in propellant combustion is needed as input for modelling studies. This information is also expected to be very important in understanding combustion behaviour of propellants. To understand the nature and importance of condensed phase reactions in the combustion of PET/ HMX-based propellant containing NG/TEGDN, the burning surface and cross-section of extinguished propellants were studied.
Figure 5 shows the SEM photographs of unburned surface of E-1 propellant. It could be seen found that the oxidiser HMX was homogeneously distributed among the propellant.
Typical SEM photograph of the extinguished surface of E-1 propellant is shown in Fig. 6 (a). The extinguished surface appears as a hole or crater. SEM examination reveals that the extinguished surface of E-1 sample contain numerous bubbles, which appear as holes on the surface. The phenomeon seems in agreement with the reports18,19. The diameters of these holes are 9~20μm. The very top layer of the surface usually appears relatively smoother with only occasional signs of crystallisation.
It can be shown that the cross-section of burned surface of E-1 propellant presents a melt layer that covers the surface (Fig.6 (b)). The thickness of condensed phase reaction zone is ~120 to 190μm. Evidence of the melt layer includes numerous bubbles and the formations which appear to be columns crystalline material, especially in the area immediately close to the holes of the unburned propellant. This suggests that crystallisation may have been seeded by the HMX crystals in the unburned propellant, due to the preponderance of HMX in the melt layer.
The extinguished surface of E-2 propellant appears relatively smoother, but cracked [(Fig. 7(a)]. It contains numerous holes on the extinguished surface, whose diameters are 11~34 μm. Compared with E-1 propellant, the extinguished surface near the hole is relatively smoother; with few signs of crystallisation, but there are globosity grains.
A comparison between the extinguished surfaces of E-1 and E-2 propellants reveals that the burning surface of E-1 propellant is rather rough, and with crystallisation near the holes. The burning surface of E-2 propellant near the hole is relatively smoother; with few signs of crystallisation, but there are some globosity grains. The difference of burning surface can be attributed to the content of NG/ TEGDN.
With regard to the content of nitrate ester, it may play an important role in the quenched surface characteristics. E-1 propellant combustion generates lower heat release due to relatively lower NG/TEGDN content. According to E. W. Price’s theory of surface disproportionation20, under this condition, the PET binder with the lower activation energy will decompose more rapidly than oxidiser HMX (Table 3), leading to rising concentration of HMX and the ratio of O/F at the surface. Moreover, the melting and vapourisation being almost simultaneous (Table 3), the small HMX particle will melt, and then liquid HMX will be recrystallised on cooling after quenching. This results in evident sign of crystallisation for E-1 propellant. By the same reasoning for E-2 propellant, E-2 propellant combustion generates higher heat release than that of E-1 propellant due to higher NG/TEGDN content. The concentration profile of burning surface has to change with surface temperature, (and hence, burning rate), to satisfy the mass flux ratio (O/F)p. The binder would tend to melt. The melt binder and its decomposition products tend to accumulate in the region just under the burning surface. The surface layers during combustion contain enhanced amount of the binder and/or its condensed-phase decomposition products19, so the melt layer of the burning surface of E-2 propellant shows few signs of crystallisation.
Figure 7 (b) shows the cross-sections of the burned E-2 propellant. The burning surface is uneven. The thickness of condensed phase reaction zone is ~170 μm to 253 μm, which increases compared to that of E-1 propellant.
The increase of NG/TEGDN content has little impact on the burning rates of PET/HMX-based propellants at the same pressure. Furthermore, these propellants can not self-sustain combustion at lower pressure (≤1MPa). NG/ TEGDN content does not affect the flame structure of PET/HMX-based propellants, but it plays an important role in condensed phase reaction zone. The flame structure is similar to HMX-CMDB combustion model, and belongs to premix flame structure.
The quenched surfaces of PET/HMX-based propellant are relatively even, and there are signs of bubbles. Moreover, the burning surface of propellant with lower NG/TEGDN content is relatively rough, and crystallisation is near the holes. The burning surface of propellant with higher NG/ TEGDN content is relatively smooth; with few signs of crystallisation, but there are some globosity grains.
The cross-section of burned PET/HMX-based propellant indicates that the thickness of the condensed phase reaction zone increases as the NG/TEGDN content increases.
The authors acknowledge for the financial support provided by the National Natural Science Foundation of China (No. 50806001.) and Education Department Foundation of Anhui Province (KJ2008B184).
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16. Moskaleva, L.V. & Lin, M.C. The spin-conserved reaction CH+N!H+NCN: a major pathway to prompt NO studied by quantum/statistical theory calculations and kinetic modeling of rate constant. Proc. Combust. Inst., 2000, 28(2), 393-401.
17. Kubota, N. Propellants and explosives: Thermochemical aspects of combustion. Wiley-VCH, Germany, 2001. 236 p.
18. Schroender, M.A.; Fifer, R.A.; Miller, M.S.; Pescerodriguez, R.A.; Mcnesby, C.J.S. & Singh, G. Condensed-phase processes during combustion of solid gun propellants. I. nitrate ester propellants. Combustion Flame, 2001, 126(1-2), 1569-576.
19. Schroender, M.A.; Fifer, R.A.; Miller, M.S.; Pescerodriguez, R.A.; Mcnesby, C.J.S.; Singh, G. & Widder, J.M. Condensed-phase processes during combustion of solid gun propellants-II. nitramine composite propellants, Combustion Flame, 2001, 126(1-2), 1577-598.
20. Price, E.W.; Chakravarthy, S.R. & Sigman, R.K. Pressure dependence of burning rate of Ammonium Perchlorate- hydrocarbon binder solid propellants. In the 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Seattle, WA, 6-9 July, 1997.
21. Jiang, Z.; Li, S.F.; Zhao, F.Q.; Chen, P.; Yin, C.M. & Li, S.W. Effect of nano metal powder on the thermal decomposition characteristics of HMX. J. Propul. Technol., 2002, 23(3), 258-261 (Chinese).
22. Sun, Y.L.; Dang, H.C.; Zhu, B.Z. & Li, S.F. Thermal decomposition characteristics of the Ethylene Oxide-Tetrahydrofuran copolyether binder. In the 2nd International Conference on Energy and Environment Technology, ChangSha, China, December 2010.
Dr Yunlan Sun received her PhD from University of Science and Technology of China, Hefei, Anhui, in 2007. Presently, she is an Assistant Professor of Anhui University of Technology. Her research is focused on combustion characteristics and mechanisms of propellants. Mr Baozhong Zhu received his MSc from Guizhou University, Guiyang, Guizhou, China, in 2008. Presently, he is a Lecturer of Anhui University of Technology. His research is focused on combustion chemistry. Prof Shufen Li is a Professor in Department of Chemical Physics at University of Science and Technology of China (USTC). Her research area is combustion chemistry. She has served as the Director of Laboratory of Combustion Chemistry of USTC. She is an Adjunct Professor of the Natioal Key Laboratory and is on its academia committee. She is the editor of Chinese Journal of Explosives & Propellant, Journal of Solid Rocket Technology and Energetic Materials. She has published more than 150 research papers in national/international journals.
| 2019-10-14T03:29:07 |
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|
https://par.nsf.gov/biblio/10367378-investigating-diskjet-structure-m87-through-flux-separation-linear-circular-polarization-images
|
Investigating the Disk–Jet Structure in M87 through Flux Separation in the Linear and Circular Polarization Images
Abstract
For testing different electron temperature (Te) prescriptions in general relativistic magnetohydrodynamics (GRMHD) simulations through observations, we propose to utilize linear polarization (LP) and circular polarization (CP) images. We calculate the polarization images based on a semi-magnetically arrested disk GRMHD model for variousTeparameters, bearing M87 in mind. We find an LP–CP separation in the images of the low-Tedisk cases at 230GHz; namely, the LP flux mainly originates from downstream of the jet, and the CP flux comes from the counter-side jet, while the total intensity is maximum at the jet base. This can be understood as follows: although the LP flux is generated through synchrotron emission widely around the black hole, most of the LP flux from the jet base does not reach the observer, since it undergoes Faraday rotation ($∝Te−2$) when passing through the outer cold disk and is thus depolarized. Hence, only the LP flux from the downstream (not passing the cold dense plasmas) can survive. Meanwhile, the CP flux is generated from the LP flux by Faraday conversion ( ∝Te) in the inner hot region. Stronger CP flux is thus observed from the counter-side jet. Moreover, the LP–CP separation is more enhanced at more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10367378
Journal Name:
The Astrophysical Journal
Volume:
931
Issue:
1
Page Range or eLocation-ID:
Article No. 25
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
We present the discovery of the first millimeter afterglow of a short-durationγ-ray burst (SGRB) and the first confirmed afterglow of an SGRB localized by the GUANO system on Swift. Our Atacama Large Millimeter/Sub-millimeter Array (ALMA) detection of SGRB 211106A establishes an origin in a faint host galaxy detected in Hubble Space Telescope imaging at 0.7 ≲z≲ 1.4. From the lack of a detectable optical afterglow, coupled with the bright millimeter counterpart, we infer a high extinction,AV≳ 2.6 mag along the line of sight, making this one of the most highly dust-extincted SGRBs known to date. The millimeter-band light curve captures the passage of the synchrotron peak from the afterglow forward shock and reveals a jet break at$tjet=29.2−4.0+4.5$days. For a presumed redshift ofz= 1, we infer an opening angle,θjet= (15.°5 ± 1.°4), and beaming-corrected kinetic energy of$log(EK/erg)=51.8±0.3$, making this one of the widest and most energetic SGRB jets known to date. Combining all published millimeter-band upper limits in conjunction with the energetics for a large sample of SGRBs, we find that energetic outflows in high-density environments are more likely to have detectable millimeter counterparts. Concerted afterglow searches with ALMA shouldmore »
2. Abstract
We compare 500 pc scale, resolved observations of ionized and molecular gas for thez∼ 0.02 starbursting disk galaxy IRAS08339+6517, using measurements from KCWI and NOEMA. We explore the relationship of the star-formation-driven ionized gas outflows with colocated galaxy properties. We find a roughly linear relationship between the outflow mass flux ($Σ̇out$) and star formation rate surface density (ΣSFR),$Σ̇out∝ΣSFR1.06±0.10$, and a strong correlation between$Σ̇out$and the gas depletion time, such that$Σ̇out∝tdep−1.1±0.06$. Moreover, we find these outflows are so-calledbreakoutoutflows, according to the relationship between the gas fraction and disk kinematics. Assuming that ionized outflow mass scales with total outflow mass, our observations suggest that the regions of highest ΣSFRin IRAS08 are removing more gas via the outflow than through the conversion of gas into stars. Our results are consistent with a picture in which the outflow limits the ability of a region of a disk to maintain short depletion times. Our results underline the need for resolved observations of outflows in more galaxies.
3. A theoretical analysis on crack formation and propagation was performed based on the coupling between the electrochemical process, classical elasticity, and fracture mechanics. The chemical potential of oxygen, thus oxygen partial pressure, at the oxygen electrode-electrolyte interface ($μO2OE∣El$) was investigated as a function of transport properties, electrolyte thickness and operating conditions (e.g., steam concentration, constant current, and constant voltage). Our analysis shows that: a lower ionic area specific resistance (ASR),$riOE,$and a higher electronic ASR ($reOE$) of the oxygen electrode/electrolyte interface are in favor of suppressing crack formation. The$μO2OE∣El,$thus local pO2, are sensitive towards the operating parameters under galvanostatic or potentiostatic electrolysis. Constant current density electrolysis provides better robustness, especially at a high current density with a high steam content. While constant voltage electrolysis leads to greater variations of$μO2OE∣El.$Constant current electrolysis, however, is not suitable for an unstable oxygen electrode because$μO2OE∣El$can reach a very high value with a gradually increased$riOE.$A crack may only occur under certain conditions when$pO2TPB>pcr.$
4. Abstract
We measure the molecular-to-atomic gas ratio,Rmol, and the star formation rate (SFR) per unit molecular gas mass, SFEmol, in 38 nearby galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We stack ALMA12CO (J= 2−1) spectra coherently using Hivelocities from the VIVA survey to detect faint CO emission out to galactocentric radiirgal∼ 1.2r25. We determine the scale lengths for the molecular and stellar components, finding a ∼3:5 relation compared to ∼1:1 in field galaxies, indicating that the CO emission is more centrally concentrated than the stars. We computeRmolas a function of different physical quantities. While the spatially resolvedRmolon average decreases with increasing radius, we find that the mean molecular-to-atomic gas ratio within the stellar effective radiusRe,Rmol(r<Re), shows a systematic increase with the level of Hi, truncation and/or asymmetry (HIperturbation). Analysis of the molecular- and the atomic-to-stellar mass ratios withinRe,$R⋆mol(rand$R⋆atom(r, shows that VERTICO galaxies have increasingly lower$R⋆atom(rfor larger levels of HIperturbation (compared to field galaxies matched in stellar mass), but no significant change in$R⋆mol(r. We also measure a clear systematic decrease of the SFEmolwithinRe, SFEmol(r<Re),more »
5. Abstract
We present the latest and most precise characterization of the architecture for the ancient (≈11 Gyr) Kepler-444 system, which is composed of a K0 primary star (Kepler-444 A) hosting five transiting planets and a tight M-type spectroscopic binary (Kepler-444 BC) with an A–BC projected separation of 66 au. We have measured the system’s relative astrometry using the adaptive optics imaging from Keck/NIRC2 and Kepler-444 A’s radial velocities from the Hobby-Eberly Telescope and reanalyzed relative radial velocities between BC and A from Keck/HIRES. We also include the Hipparcos-Gaia astrometric acceleration and all published astrometry and radial velocities in an updated orbit analysis of BC’s barycenter. These data greatly extend the time baseline of the monitoring and lead to significant updates to BC’s barycentric orbit compared to previous work, including a larger semimajor axis ($a=52.2−2.7+3.3$au), a smaller eccentricity (e= 0.55 ± 0.05), and a more precise inclination ($i=85.°4−0.°4+0.°3$). We have also derived the first dynamical masses of B and C components. Our results suggest that Kepler-444 A’s protoplanetary disk was likely truncated by BC to a radius of ≈8 au, which resolves the previously noticed tension between Kepler-444 A’s disk mass and planet masses. Kepler-444more »
| 2023-01-30T15:03:27 |
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|
https://par.nsf.gov/biblio/10363124-interferometric-detections-sdo-companions-orbiting-three-classical-stars
|
Interferometric Detections of sdO Companions Orbiting Three Classical Be Stars
Abstract
Classical Be stars are possible products of close binary evolution, in which the mass donor becomes a hot, stripped O- or B-type subdwarf (sdO/sdB), and the mass gainer spins up and grows a disk to become a Be star. While several Be+sdO binaries have been identified, dynamical masses and other fundamental parameters are available only for a single Be+sdO system, limiting the confrontation with binary evolution models. In this work, we present direct interferometric detections of the sdO companions of three Be stars—28 Cyg, V2119 Cyg, and 60 Cyg—all of which were previously found in UV spectra. For two of the three Be+sdO systems, we present first orbits and preliminary dynamical masses of the components, revealing that one of them could be the first identified progenitor of a Be/X-ray binary with a neutron star companion. These results provide new sets of fundamental parameters that are crucially needed to establish the evolutionary status and origin of Be stars.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
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Publication Date:
NSF-PAR ID:
10363124
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
2
Page Range or eLocation-ID:
Article No. 213
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
Because many classical Be stars may owe their nature to mass and angular-momentum transfer in a close binary, the present masses, temperatures, and radii of their components are of high interest for comparison to stellar evolution models. ObjectκDra is a 61.5 day single-lined binary with a B6 IIIe primary. With the CHARA Array instruments MIRC/MIRC-X and MYSTIC, we detected the secondary at (approximately photospheric) flux ratios of 1.49% ± 0.10% and 1.63% ± 0.09% in theHandKband, respectively. From a large and diverse optical spectroscopic database, only the radial velocity curve of the Be star could be extracted. However, employing the parallaxes from Hipparcos and Gaia, which agree within their nominal 1σerrors, we could derive the total mass and found component masses of 3.65 ± 0.48 and 0.426 ± 0.043Mfor the Be star and the companion, respectively. Previous cross-correlation of the observed FUV spectrum with O-type subdwarf (sdO) spectral model templates had not detected a companion belonging to the hot sdO population known from ∼20 earlier-type Be stars. Guided by our full 3D orbital solution, we found a strong cross-correlation signal for a stripped subdwarf B-type companion (FUV flux ratio of 2.3% ± 0.5%), enabling the first firm characterization ofmore »
2. Abstract
We describe the public release of the Cluster Monte Carlo (CMC) code, a parallel, star-by-starN-body code for modeling dense star clusters.CMCtreats collisional stellar dynamics using Hénon’s method, where the cumulative effect of many two-body encounters is statistically reproduced as a single effective encounter between nearest-neighbor particles on a relaxation timescale. The star-by-star approach allows for the inclusion of additional physics, including strong gravitational three- and four-body encounters, two-body tidal and gravitational-wave captures, mass loss in arbitrary galactic tidal fields, and stellar evolution for both single and binary stars. The public release ofCMCis pinned directly to theCOSMICpopulation synthesis code, allowing dynamical star cluster simulations and population synthesis studies to be performed using identical assumptions about the stellar physics and initial conditions. As a demonstration, we present two examples of star cluster modeling: first, we perform the largest (N= 108) star-by-starN-body simulation of a Plummer sphere evolving to core collapse, reproducing the expected self-similar density profile over more than 15 orders of magnitude; second, we generate realistic models for typical globular clusters, and we show that their dynamical evolution can produce significant numbers of black hole mergers with masses greater than those produced from isolated binary evolution (such as GW190521, amore »
3. Abstract
Stellar mass is a fundamental parameter that is key to our understanding of stellar formation and evolution, as well as the characterization of nearby exoplanet companions. Historically, stellar masses have been derived from long-term observations of visual or spectroscopic binary star systems. While advances in high-resolution imaging have enabled observations of systems with shorter orbital periods, measurements of stellar masses remain challenging, and relatively few have been precisely measured. We present a new statistical approach to measuring masses for populations of stars. Using Gaia astrometry, we analyze the relative orbital motion of >3800 wide binary systems comprising low-mass stars to establish a mass–magnitude relation in the GaiaGRPband spanning the absolute magnitude range 14.5 >$MGRP$> 4.0, corresponding to a mass range of 0.08MM≲ 1.0M. This relation is directly applicable to >30 million stars in the Gaia catalog. Based on comparison to existing mass–magnitude relations calibrated forKsmagnitudes from the Two Micron All Sky Survey, we estimate that the internal precision of our mass estimates is ∼10%. We use this relation to estimate masses for a volume-limited sample of ∼18,200 stars within 50 pc of the Sun and the present-day field mass function for stars withM≲ 1.0M, which wemore »
4. Abstract
Helium-rich subdwarf O stars (sdOs) are hot compact stars in a pre-white dwarf evolutionary state. Most of them have effective temperatures and surface gravities in the range Teff = 40 000–50 000 K and log g = 5.5–6.0. Their atmospheres are helium dominated. If present at all, C, N, and O are trace elements. The abundance patterns are explained in terms of nucleosynthesis during single star evolution (late helium core flash) or a binary He-core white dwarf merger. Here we announce the discovery of two hot hydrogen-deficient sdOs (PG1654+322 and PG1528+025) that exhibit unusually strong carbon and oxygen lines. A non-LTE model atmosphere analysis of spectra obtained with the Large Binocular Telescope and by the LAMOST survey reveals astonishingly high abundances of C ($\approx 20{{\ \rm per\ cent}}$) and O ($\approx 20{{\ \rm per\ cent}}$) and that the two stars are located close to the helium main sequence. Both establish a new spectroscopic class of hot H-deficient subdwarfs (CO-sdO) and can be identified as the remnants of a He-core white dwarf that accreted matter of a merging low-mass CO-core white dwarf. We conclude that the CO-sdOs represent an alternative evolutionary channel creating PG1159 stars besides the evolution of single stars that experience a late helium-shell flash.
5. ABSTRACT
We present a detailed study of the stellar and orbital parameters of the post-common envelope binary central star of the planetary nebula Ou 5. Low-resolution spectra obtained during the primary eclipse – to our knowledge the first isolated spectra of the companion to a post-common-envelope planetary nebula central star – were compared to catalogue spectra, indicating that the companion star is a late K- or early M-type dwarf. Simultaneous modelling of multiband photometry and time-resolved radial velocity measurements was then used to independently determine the parameters of both stars as well as the orbital period and inclination. The modelling indicates that the companion star is low mass (∼0.25 M⊙) and has a radius significantly larger than would be expected for its mass. Furthermore, the effective temperature and surface gravity of nebular progenitor, as derived by the modelling, do not lie on single-star post-AGB evolutionary tracks, instead being more consistent with a post-RGB evolution. However, an accurate determination of the component masses is challenging. This is principally due to the uncertainty on the locus of the spectral lines generated by the irradiation of the companion’s atmosphere by the hot primary (used to derive companion star’s radial velocities), as well as the lackmore »
| 2023-02-02T21:27:23 |
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|
https://read.dukeupress.edu/demography/article/58/6/2243/257657/Environmental-Inequality-and-Residential-Sorting
|
## Abstract
Previous research has shown that low-income households bear a higher exposure to environmental pollution than high-income households. Some scholars have argued that selective siting of industrial facilities accounts for such environmental inequality, while others have argued that those citizens who can afford to move out of polluted regions do so, and the socioeconomically disadvantaged are sorted into polluted areas. Yet empirical evidence regarding the processes of environmental inequality is not conclusive. We build on an original data set that includes annual georeferenced data of 6,570 highly polluting industrial facilities in Germany from 2008 to 2017 and validate the fluctuation in facilities with geographical land-use data. We then connect the facilities to income and demographic data for 4,455 municipalities and investigate sociodemographic changes before and after the appearance of new facilities. Spatial models are employed to measure local relative changes, and fixed-effects individual slopes estimators are used to account for selection on economic trajectories. Results provide only limited support for the selective siting thesis but show that an area's average income decreases after the appearance of new industrial facilities, thereby resonating with the selective migration hypothesis. In contrast, facility closure does not attract, or reattract, more affluent households.
## Introduction
The exposure level to environmental pollution is not equally distributed across households. Research has shown that ethnic and racial minorities in the United States as well as in Europe are disproportionately exposed to environmental harms (e.g., Ard 2015; Glatter-Götz et al. 2019; Jünger 2021; Mohai and Saha 2015a; Pasetto et al. 2019; Pastor et al. 2005; Rüttenauer 2018, 2019a). Similarly, economically disadvantaged households tend to live in areas with higher levels of environmental pollution (e.g., Ash and Fetter 2004; Downey and Hawkins 2008; Raddatz and Mennis 2013; Wolverton 2009). Meanwhile, recent studies have documented the severe impacts of environmental pollution on health (European Environment Agency 2019) and long-term educational trajectories (e.g., Colmer and Voorheis 2020). Environmental inequality thus constitutes a severe dimension of social inequality, and it is important to understand the processes associated with the unequal distribution of environmental harms. With a comprehensive understanding of the underlying dynamics, policies can successfully target environmental inequalities and injustices.
Existing research points to two potential mechanisms involved: (1) firms selectively build new sites in socioeconomically disadvantaged areas or close old sites in affluent regions, and (2) households residentially sort into areas of different environmental quality on the basis of income. While the first explanation assumes that socioeconomic differences already existed prior to the siting of hazardous facilities, the second explanation hypothesizes that post-siting sorting processes induce socioeconomic changes regarding already existing sites. Longitudinal studies have provided mixed results (for a review, see Banzhaf et al. 2019a; Mohai and Saha 2015a), and it remains a puzzle whether environmental inequality stems from selective siting of facilities, selective migration of households, or a combination of both. Here, we address the question of “which came first?” (Pastor et al. 2001)—hazardous facilities or socioeconomically disadvantaged residents—and analyze the population dynamics related to the siting and closure of industrial sites.
In this longitudinal study, we provide new insights on the dynamics of environmental inequality in Germany by testing for evidence of selective siting and selective migration. We use georeferenced pollution data from the European Pollutant Release and Transfer Register (E-PRTR)—which documents the location of high-emission facilities in Germany—for the period from 2008 to 2017. We validate this information against longitudinal land-use data to measure the appearance and disappearance of industrial facilities. These facility data are then combined with annual socioeconomic and demographic data for 4,455 German municipalities. This allows us to test whether the socioeconomic composition of a municipality influences the likelihood of receiving new industrial disamenities (such as factories, power plants, or waste-processing sites) and whether these subsequently induce residential sorting processes.
We contribute to existing research in three ways. First, we use annual panel data of German municipalities to provide a detailed account of how demographic changes relate to changes in the presence of industrial disamenities, and distinguish between the demographic consequences of the siting of new facilities and the closing of old ones. Second, we disentangle the effect of changes in industrial sites from general economic trends and path dependencies. These trends may result in different income trajectories over time, which are correlated to—but not driven by—changes in environmental disamenities. We accomplish this by using fixed-effects individual slopes (FEIS) estimators that account for community-specific economic trends over time. Third, we consider an earlier critique that demographic changes depend on changes in environmental quality in the focal municipality, but also on changes in residential alternatives (Banzhaf and Walsh 2013). We use spatial modeling techniques to include changes in adjacent municipalities and also investigate changes in income after a reordering of environmental quality among neighboring municipalities. Hence, we provide a comprehensive test of selective siting and selective migration while considering potential reasons for the heterogeneity of previous findings.
## Theoretical Background
Two opposing processes are often employed to explain the disproportionate exposure of socioeconomically disadvantaged households to environmental hazards: selective siting and selective migration. In the first process, pollution or industrial sites might be placed selectively close to specific groups of inhabitants. In the second, certain groups might selectively escape polluted areas and others might selectively move toward polluted areas.1
### Selective Siting
The selective siting argument claims that hazardous facilities are disproportionately sited in neighborhoods characterized by low income (Been and Gupta 1997; Mohai and Saha 2015a; Pastor et al. 2001; Saha and Mohai 2005; Wolverton 2009). The reason for this selective siting behavior can be twofold. First, the market explanation assumes that companies seek to minimize their land and housing costs when identifying locations for new facilities. Because of lower land prices and housing costs, socioeconomically disadvantaged regions are an attractive siting location for new facilities (Downey 2005; Farber 1998; Saha and Mohai 2005; Wolverton 2009, 2012). Furthermore, low-income households have been found to express a lower “willingness to pay”—also in the sense of ability to afford—for environmental goods (Franzen and Vogl 2013; Liebe et al. 2010). Following the Coase theorem, companies would thus need to pay lower compensation costs for emissions in areas with a higher share of low-income residents (Banzhaf et al. 2019a, 2019b), and hence it would be a rational strategy for a profit-maximizing company to locate facilities in low-income areas.
Second, the social and political capital explanation assumes that the level of both social and political capital is lower in socioeconomically disadvantaged regions and that their inhabitants are therefore less likely to organize collective protests against hazardous facilities (Hamilton 1995; Pastor et al. 2001), to influence political decisions by engaging in collective action (e.g., efforts to ban hazardous facilities), or to take legal actions (Wolverton 2009). Affluent residents, in contrast, are more likely to influence political actors via social ties or political engagement and more likely to engage in legal actions. If the respective executive decision makers anticipate potential problems in affluent regions, they may choose the “path of least political resistance” (Saha and Mohai 2005) and selectively place industrial sites in socioeconomically disadvantaged regions.
Following the theory of selective siting, empirical research usually investigates whether aggregated demographic characteristics influence the likelihood of receiving industrial sites. Studies by Pastor et al. (2001), Richardson et al. (2010), Saha and Mohai (2005), Shaikh and Loomis (1999), and Wolverton (2009) support the theory of selective siting and found a negative correlation between income and the likelihood of becoming a facility-hosting area. However, other studies that looked at poverty rates or income did not find any effect on the likelihood of facility siting (Been and Gupta 1997; Downey 2005; Oakes et al. 1996) or found rather inconsistent results (Mitchell et al. 1999; Wolverton 2012). Other studies that focused on the influence of racial composition on the siting of facilities (Funderburg and Laurian 2015; Mohai and Saha 2015b) found that differences in the minority share of an area's population already existed prior to the siting. Still, Elliott and Frickel (2013, 2015) showed that for a number of cities, the reuse of former industrial sites was a much stronger predictor for the location of currently operating industrial facilities than the demographic characteristics of nearby inhabitants. Overall, the empirical support for selective siting as an explanation for environmental inequality is mixed.
### Selective Sorting
The selective migration or sorting argument, in contrast, assumes that socioeconomic changes in polluted areas sequentially follow the siting process. Here it is hypothesized that specific households sort into residential areas with different environmental qualities according to their income (Banzhaf and McCormick 2012; Banzhaf and Walsh 2008; Best and Rüttenauer 2018; Crowder and Downey 2010; Mohai and Saha 2015a; Pais et al. 2014; Sieg et al. 2004).
In general, the argument follows Tiebout's (1956) model of the “consumer-voter”: that households can adjust the level of public goods provision to their preferences by moving between municipalities—they are “voting with their feet.” Because households prefer a higher environmental quality over a lower one (Bayer et al. 2009; Currie et al. 2015), the demand for high-quality neighborhoods exceeds that for low-quality ones, thereby increasing the housing and land prices in high-quality areas (Banzhaf and McCormick 2012). Neighborhoods with low environmental quality are thus more likely to offer low-cost housing opportunities (Bayer et al. 2009; Currie et al. 2015; Farber 1998). At the same time, households are willing to pay more for environmental goods as their income increases (Franzen and Vogl, 2013; Liebe et al. 2010). It follows that high-income households have an increased likelihood of moving out of low-quality neighborhoods (selective out-migration) because they are willing and able to pay for higher housing prices. Simultaneously, low-income households are steered into low-quality neighborhoods because of the need for affordable housing. The selective out-migration of high-income households and the resulting decrease in housing demand further reinforce the process of selective in-migration of low-income households.
So far, few studies have assessed this argument by using household-level panel data. In line with the selective migration theory, Crowder and Downey (2010) showed that household income helps in reducing the proximity to industrial hazards in the neighborhood of destination when households move. Similarly, Pais et al. (2014) found that income reduces the likelihood of being in a persistently high pollution trajectory compared with a persistently low trajectory when analyzing the moving paths of households. For Germany, Best and Rüttenauer (2018) reported slightly higher reductions in households' perceived local pollution after residential moves for households with a higher income. Hence, longitudinal studies on the household level support the theory of selective migration or sorting.
Still, studies on the spatially aggregated level provide less conclusive results than those using individual-level survey data (for a detailed literature review, see Banzhaf et al. 2019a). Usually, such studies investigate if an area's socioeconomic composition changes after shifts in environmental quality, and hence whether selective migration on the micro level influences the aggregated income. If increasing pollution leads to selective sorting processes, this could be observed by a decreasing average income (and vice versa). This line of reasoning is supported by studies identifying post-siting demographic changes (Baden and Coursey 2002; Banzhaf and Walsh 2008; Depro et al. 2015; Gamper-Rabindran and Timmins 2011; Richardson et al. 2010). For instance, Banzhaf and Walsh (2008) reported lower income growth rates after an area received a new TRI (toxics release inventory) facility in California. Similarly, Gamper-Rabindran and Timmins (2011) reported an increase in local average income after the cleanup of Superfund sites in the United States. However, other studies did not find increasing poverty rates (Been and Gupta 1997) or a decreasing average income (Downey 2005), nor did they find increasing minority shares in area populations (Funderburg and Laurian 2015; Mohai and Saha 2015b; Oakes et al. 1996; Pastor et al. 2001; Shaikh and Loomis 1999) following the siting of new facilities. Empirical support for the selective migration or sorting argument on the macro level thus remains mixed, while individual-level results underpin the theory.
### Identifying Selective Sorting
Banzhaf and McCormick (2012), Banzhaf and Walsh (2008, 2013), and Depro et al. (2015) have argued that relying solely on aggregated data and changes in the focal unit may fail to identify selective sorting processes. For instance, if a municipality experiences a marginal increase in pollution and some households with a relatively high income in the “treated” municipality sort into a cleaner municipality, the moving population might still have a lower income than the average of the receiving municipality (even though they are richer than the average of the municipality of origin). In this case, we would observe decreases in average income in the “treated” and the “control” municipality, thereby estimating a null effect of pollution changes on income changes when using within-estimators. Banzhaf and McCormick (2012) and Banzhaf and Walsh (2008) showed formally that we can only expect unambiguous shifts in average income if pollution changes in a way such that the hierarchy or rank in environmental quality among local alternatives is reordered. In this case, every household prefers to move to the municipality that has become better in terms of environmental quality than its local alternatives. We would then expect perfect residential sorting based on income, thereby increasing income in the improved municipality and decreasing income in the deteriorated municipality.
This argument holds two important implications for the modeling of selective migration processes on the macro level. First, it is important that only relative changes in quality matter for changes in demographics, and more importantly changes that are relative in local terms. To assess the impact of a change in pollution, we also need to control for what is happening in adjacent areas. Second, and directly following the argument by Banzhaf and McCormick (2012) and Banzhaf and Walsh (2008), only a reordering in the quality rank system of local alternatives leads to unambiguous changes in the relative socioeconomic composition of neighborhoods. Thus, we employ two spatial modeling strategies in our study that are intended to capture these two arguments. First, we incorporate the characteristics of adjacent municipalities in spatial lag models and, second, we create a measure of the environmental quality rank among these adjacent municipalities to test if a reordering of environmental quality leads to demographic changes other than a mere marginal change compared to local alternatives.
A second issue for the identification of any effect of changes in environmental disamenities on the changes in income is the visibility or perception of environmental quality (Banzhaf et al. 2019b). For instance, Messer et al. (2006) showed that initial efforts of site cleanup (e.g., accompanied by construction works) might actually increase the risk perception of local residents and thus impose adverse effects on the desirability of a neighborhood. Former hosting areas may remain stigmatized and thus not experience an inflow of more affluent residents. Similarly, Currie et al. (2015) found a decrease in housing prices after the opening of new industrial plants, but no significant increase in prices after the closing of existing plants. This contrasts with the positive consequences due to site cleanup identified elsewhere (Gamper-Rabindran and Timmins 2011). However, the simple closing of a facility does not mean that the respective site has been repurposed or properly cleaned up, and a closed facility might still constitute a signal of low environmental quality. This implies that the impacts due to a reduction in objective environmental hazards are less clear than impacts due to an increase in environmental disamenities.
We tackle these two issues in the following way. First, in the main analysis we focus on the number of (high-polluting) industrial facilities rather than pollution itself. We assume this is a more important indicator for the subjective perception of environmental quality than objective health risks due to toxic pollution. Especially on the geographic level of municipalities, it seems unlikely that residents have an accurate estimate of actual health risks, as toxic pollutants are often very localized, colorless, and odorless. For instance, Currie et al. (2015) found that the negative effect of plant openings on the housing market was independent of the level of toxicity and the amount of emissions from the respective plants. Moreover, it seems more likely that residents would oppose the construction of a new industrial facility rather than marginal increases in emissions from already existing facilities. As shown in the online supplement, we repeated our analyses with the amount of toxicity-weighted emissions from the facilities (see Supplement S6). Second, we separate the effect of newly emerging and disappearing facilities: after performing an overall analysis, we use event time functions to estimate temporal changes in income after increases and decreases in the number of facilities separately. We cannot determine if a site was properly cleaned up or mainly remained as an abandoned brownfield site. We thus expect the effect of a site closing to be less clear than the effect of newly operating sites (Currie et al. 2015; Messer et al. 2006).
## Data and Methods
To test selective siting and selective migration, we build on an original data set combining socioeconomic information from all German municipalities obtained from the INKAR database (BBSR 2019) with facility-specific pollution data of the E-PRTR. The socioeconomic information is available for 4,455 municipalities annually between 2007 and 2017. On average, a municipality comprises 18,584 inhabitants (median = 8,976) and covers an area of 79 km2. We use stable municipality borders as of December 31, 2017, for all years. The E-PRTR contains annual information about industrial facilities within Germany; it includes all facilities falling under the 65 E-PRTR economic activities (European Commission 2006:79ff.) and exceeding a pollutant-specific threshold of emissions (European Commission 2006:83ff.). Facilities are required to report their emissions and geographic location. We restrict the register to facilities reporting industrial or waste management activities, thereby excluding all agricultural facilities. We do so because agricultural establishments in Germany often consist of multiple smaller farms or facilities in rural settings, and thus are a weaker signal of environmental disamenities. From 2007 to 2017, the data contain a total of 6,570 unique industrial facilities with an average annual number of 4,472. To validate the appearance and closing of facilities, we use georeferenced land-use data from the Leibniz Institute of Ecological Urban and Regional Development (IOER) monitor (Meinel 2011). This data set provides annual information on the share of land used for industry and trade, using a 1-km × 1-km grid. By validating the facility register against land-use data, we ensure that the fluctuation of facilities over time is not driven by changing emissions around the reporting threshold.
### Demographic Variables
To approximate the socioeconomic composition, we use the average income tax revenue per capita of each municipality. Additional analyses using a higher aggregation level (county) confirm that the income tax revenue is highly correlated with actual household income. From the INKAR database, we also derived a few time-varying control variables that we include in the main analyses. These are the proportion of inhabitants aged 18 or younger, the proportion of inhabitants aged 65 or older, population density, population density squared, and a proxy for the share of foreigners (approximated by the share of foreigners in the unemployment statistics, as this is the best annual data available in INKAR). Furthermore, we use the trade tax revenue per capita as linear and squared terms to account for the economic development of municipalities. If we find an effect of industrial facilities net of economic development, this indicates that something else (such as residential sorting between place of work and place of residence) contributes to the dissolution between the economic development and inhabitants' income.
### Industrial Facilities
We measure environmental quality by the number of industrial facilities. Because our empirical models rely on changes over time, it is crucial to have a reliable measure for the appearance and disappearance of industrial facilities. Thus, we need to take into account that facilities may either newly appear in the E-PRTR register because they started to exceed the reporting threshold or disappear because they dropped below the threshold. This would artificially indicate the siting of new or closing of old facilities, even though the facility was present throughout the entire period. Thus, we validate the E-PRTR register against the IOER land-use data by (1) constructing the first and last operating year for each facility based on the first and last E-PRTR report and (2) assigning the industrial land-use share from 2006 to 2018 to each facility location. Subsequently, we counted a facility as a new industrial site only if the industrial land-use share increased (a) in the year before, (b) in the recent year, or (c) in the year after the first E-PRTR operation period. Similarly, we validated the closing of facilities by a decrease in industrial land use around the last period. If land-use development is either constant or contradicting the increase or decrease of E-PRTR facilities, we assume that the facility was there from the beginning (to the end, respectively) of the observation period (for more details, see online Supplement S4). This ensures that we capture only changes in the number of facilities if such changes coincide with physical changes in buildings or land use within the area. This validation is critical, because only 1,334 out of 2,617 (51%) new facilities coincide with an increase in industrial land use, and only 632 out of 1,829 (35%) disappearing facilities coincide with a reduction. Although the validation has little influence on the first set of results, it matters for the temporal impact functions, because with the raw data we start counting in years without any actual or recognizable change in many instances (see online Supplement S5 for results with raw data).
From this validated database, we then calculate the number of industrial facilities for each municipality and year using the geolocation of E-PRTR reports and municipality borders. To account for the possibility of facilities located at administrative borders, we use a method proposed by Banzhaf and Walsh (2008) to combine E-PRTR and municipality data: we create a 1-km buffer around each facility location and allocate the number of facilities to the municipalities weighted by the proportional overlap between the buffer and each municipality's area (see also Mohai and Saha 2006, 2007).
This matching strategy results in a data set of 4,455 municipalities per year containing demographics and the proportional number of industrial sites. Note that we exclude the first year (2007) from the analyses because the data show a relatively large increase in the number of facilities from 2007 to 2008, which is likely to occur because of an underreporting throughout the first year of data collection. Additionally, our validation strategy induces missing values for 2007: we cannot measure increases in the year before 2007, as IOER data are only available from 2006 on, thereby not allowing us to measure differences around 2007. In sum, this leaves us with a final data set of 44,550 observations nested within 4,455 municipalities. Summary statistics are presented in Table S1.1 (see the online supplement), and Figure 1 illustrates the spatial distribution of our main indicators for the year 2015. The map shows that the number of industrial facilities tends to be highest in the mid-west of Germany, while high-income communities are clustered in the south. Furthermore, income levels (and trends) differ strongly between former East Germany and West Germany, so we later stratify our analysis into these historical regions.
### Modeling Relativity of Changes
We employ two spatial methods to measure relative changes in pollution and income. First, we apply spatial SLX models to incorporate the pollution changes in adjacent municipalities (e.g., Halleck Vega and Elhorst 2015; Rüttenauer 2019b). We define a spatial weights matrix W, specifying all units as neighbors that share at least a common border or edge (row-normalized “Queens” neighbors). All elements within the N × N weights matrix are wij > 0 for all neighboring i and j, wij = 0 otherwise (for all ij), and wii = 0. Subsequently, the SLX model allows us to account for the number of facilities in the focal and neighboring areas:
$y=Xβ+WXθ+ε,$
where y is an NT vector of the dependent variable for i = (1, . . . , N) observations and t = (1, . . . , T) time periods per observation, X is an NT × K matrix of covariates k = (1, . . . , K), β and θ are K × 1 vectors of coefficients, and ɛ is an NT × 1 vector of residuals.
In this model, WX represents the average values of the covariates in neighboring units. This means that we can estimate the effect of a change in X in the focal unit, while controlling for or keeping constant the X value of the neighboring units. Thus, changes in X constitute changes in X relative to neighboring units. It follows that we can estimate whether a change in the number of facilities (average income, respectively)—while keeping the average number of facilities (average income, respectively) in the local surrounding constant—affects the average income of a community (the number of facilities, respectively).
Still, this strategy does not capture if a municipality becomes “better” or “worse” than the neighboring alternatives. As outlined earlier, marginal relative changes might not unambiguously induce relative changes in the demographic composition (Banzhaf and McCormick 2012; Banzhaf and Walsh 2008). Thus, we apply a second strategy, shown in Figure 2, to account for the ordering of communities in a local “environmental quality rank system.” For each municipality i and its neighbors as defined in W, we use the number of facilities per km2 to compute the rank in the system of local communities. For instance, in panel a of Figure 2, the focal unit (outlined in red) has 11 neighbors, and it holds the highest number of facilities per km2 compared to its neighbors. Thus, the focal unit receives the rank of 11. This procedure is done for each unit i with its own local neighbors. For instance, the focal unit in panel b of Figure 2 does not receive the rank of 8, as measured in panel a, but rather the rank of 5, because this is its rank when comparing the community with all its adjacent units. The resulting measure has no substantial meaning in cross-sectional terms, as the absolute rank depends on the number of neighbors for each unit. Still, when measuring changes over time (see the following), this rank variable indicates if a reordering in the ranks of environmental quality occurred among local adjacent communities, which should induce unambiguous sorting processes.
### Fixed-Effects Individual Slopes
To test selective siting and selective sorting, we employ panel data methods based on within-municipality variance only. More precisely, we want to estimate if changes in income in period t − 1 influence the number of facilities in period t (selective siting), and if changes in the number of industrial facilities in period t − 1 influence the average income in period t (selective migration).
Conventional two-way fixed-effects (FE) estimators rely on the assumption of parallel trends between municipalities receiving new facilities (or experiencing a decline) and those not experiencing a change, as observations without variance in facilities remain in the effective estimation sample as a “control group” for temporal shocks (Rüttenauer and Ludwig 2020). Still, different regimes of economic development likely lead to diverging trends in income and the number of facilities over time. For instance, more industrialized areas likely experience a steeper increase in facilities, and at the same time a slower increase in income, which is causally unrelated to the occurrence of new facilities. An Artificial Regression Test (ART) (Rüttenauer and Ludwig 2020) confirms that the data exhibit substantial heterogeneity in the effect of trade tax revenue on income and that this heterogeneity is correlated with the municipality-specific variance in the number of facilities. The ART is an extension of the conventional Hausman test (of FE vs. random effects), indicating that the coefficient of interest changes significantly when relaxing the parallel trends assumption, thereby giving reason to believe that conventional FE estimates are biased.
To overcome the problem of nonparallel trends in “treated” and “untreated” municipalities, we use fixed-effects individual slopes estimators (Brüderl and Ludwig 2015; Rüttenauer and Ludwig 2020). FEIS accounts for municipality-specific time-constant differences and municipality-specific economic trends, which we measure using the trade tax revenue. The FEIS is given by
$y˜=X˜β+α˜t+ε˜,$
where $y˜$, $X˜$, and $ε˜$ are individually “de-trended” data $y˜=y – y^$, $X˜=X – X^$, and $ε˜=ε – ε^$, with $y^$ and $X^$ being stacked vectors of municipality-specific predicted values, and $α˜t$ are residualized time fixed effects. For each municipality i, we estimate a municipality-specific trend in income, the number of industrial sites, and further controls ($y^i$ and $X^i$) on the basis of trade tax revenue and trade tax revenue squared. Subsequently, we subtract the predicted individual trend for each municipality from the original data and run a regression on the residualized data. We would obtain similar coefficients when interacting the municipality dummy variables in a least-squares dummy variable approach with trade tax revenue.
In terms of selective migration, β then indicates if an increase in facilities above the general trend influences income beyond the average income we would have expected based on each municipality's economic development. Relying on this residualized variance is then less likely to be driven by selection into “treatment” based on diverging trends and increases the confidence in a causal interpretation of the results. To identify an unbiased effect, we now rely on the assumption that deviations from a municipality-specific trend (which are likely influenced by unmeasured characteristics) rather than deviations from the municipality-specific mean are independent of the error term. Supplementary results based on conventional FE models (see online Figures S3.3 and S3.5) underpin this argument: conventional FE estimators return a significant “treatment effect” already in the year before “treatment,” as the correlated trends are added to the effect of interest, thus producing larger effect sizes than the FEIS models in the main analysis. As in the conventional FE models, the FEIS estimator is based on municipalities exhibiting relevant within-variance, while we keep those without within-variance as a “control group” for exogenous time shocks by including time dummy variables (as in two-way FE). Obviously, we still rely on the strict exogeneity assumption of no time-varying unobserved confounders being correlated with our covariates net of included controls and municipality-specific economic trends (for more details, see Brüderl and Ludwig 2015; Rüttenauer and Ludwig 2020).
## Results
Before analyzing the processes of environmental inequality, we first present results from a between model (comparing between cross-sectional units) to illustrate that there is indeed a high correlation between the number of industrial facilities and the socioeconomic composition. All variables are scaled by the overall standard deviation. Full tables with results of control variables can be found in the online Supplement S7.
Table 1 shows a relatively strong and highly significant negative correlation between average income and the number of industrial sites in Germany. Controlling for additional demographic variables dramatically reduces the magnitude of this correlation, indicating that there are large-scale spatial differences (e.g., relating to economic and demographic characteristics). Furthermore, the overall correlation is mainly driven by former West Germany. In the region of former East Germany, correlations are weak and nonsignificant in the full model. This indicates that the issue of environmental inequality and income is less severe in East Germany, but is relatively strong in West Germany. To account for this regional difference, we conduct separate analyses in the following sections.
### Selective Siting
Turning to the temporal processes, Table 2 tests the argument of selective siting. The dependent variable is the number of industrial facilities at t regressed on the socioeconomic composition at t − 1. Following the argument of selective siting, we would expect a negative effect of income on the number of facilities.
When looking at the overall model, the estimates point in the expected direction: increases in income in the focal unit—while neighboring units remain unchanged—are associated with a decrease in the number of industrial facilities below the level we would expect based on the economic development of the respective municipality. Similarly, an increase in income within neighboring municipalities (as indicated by W) has a positive effect on the focal municipality. This resonates with the theoretical expectation that affluent surrounding communities tend to steer away industrial facilities, thereby increasing the pressure for the focal unit. Still, the effects are not statistically significant at the 5% level and are very weak in magnitude. Because of a one-standard-deviation increase in average income tax revenue (156 EUR per capita), the number of facilities is estimated to be 0.013 standard deviations (or 0.045 facilities) lower than expected in the following year.
Furthermore, when distinguishing between West and East Germany, it appears that a large part of the effect size stems from East Germany. Nevertheless, the precision of the point estimate is much lower in East Germany. The effect in West Germany is even smaller than the effect observed in the overall model and is not statistically significant. Altogether, the results provide very limited support for the idea that facilities are selectively sited in areas with a decreasing average income. At least during our observation period, selective siting does not contribute substantially to environmental inequality.
### Selective Migration
An alternative explanation for environmental inequality is that households selectively move into and escape from polluted areas. In Table 3, we test the selective migration thesis by regressing the income tax revenue at time t on the number of industrial facilities at time t − 1 in models 1–3, and on the relative facility rank compared to surrounding municipalities at t − 1 in models 4–6.
When first looking at the SLX specification in models 1–3, the number of industrial facilities exhibits a negative and significant effect on the average income in the following period. If the number of facilities increases by one standard deviation (or 3.46 facilities)—while keeping neighboring municipalities at a constant level—income tax revenue per capita is found to be 0.053 standard deviations (or 8.3 EUR) lower in the following year than we would have expected based on the municipality's economic trajectory. At the level of counties (for which income tax revenue and income data are available), this decrease in income tax revenue would translate to an approximately 20 EUR lower monthly gross income per person. This seems to be a small to moderate effect of the number of industrial facilities on the socioeconomic composition of the municipality. Still, this effect is significant and much stronger than the siting effect discussed earlier. Again, in the overall model, the spatial lag indicates a countervailing but nonsignificant effect due to industrial facilities in neighboring municipalities.
When separating by West and East, it appears that the effect of industrial facilities on subsequent income tax revenues is stronger in West Germany than in the overall model. In East Germany, in contrast, changes in industrial facilities exhibit a null effect on the income distribution within a municipality. Surprisingly, we observe a relatively strong effect of the spatial lag indicator. This might, however, result from different municipality sizes in East Germany. In total, the results support the selective migration thesis in West Germany: an increase in industrial disamenities above the expected trend leads to a decrease in income below what we would have expected based on the pure economic development of a municipality. The effect size is moderate but stronger than for the siting process. Results for East Germany, in contrast, are less conclusive and point toward a null finding. This is consistent with the absence of a cross-sectional correlation between income tax revenue and industrial facilities in East Germany.
To gain further confidence in our results, models 4–6 repeat the same task, but use the measure of relative rank in the number of industrial facilities per area. If a municipality changes from a lower rank (fewer facilities per area than neighbors) to a higher rank (more facilities), this leads to a decrease in average income below the predicted level in the following period. The effect size is smaller than in the previous models and remains relatively stable in West Germany. Again, for East Germany, we observe only nonsignificant results. The negative impact in East Germany, as opposed to a slightly positive one in model 3, provides some support for the idea that only reordering processes lead to unambiguous demographic migration processes. Overall, this second measure of relative environmental quality fosters the previous conclusion: in West Germany, changes in the number of industrial facilities induce demographic sorting processes according to income, while this is not the case in East Germany.
### Selective Migration Over Time
Although we see selective migration processes in West Germany, the magnitude of demographic changes is moderate. Still, we might underestimate the total effect, as residential sorting processes may get more severe after a temporal delay. Moreover, decreases in the number of facilities might have a lower impact than increases as we cannot identify if sites have been cleaned up or just closed. Therefore, we also estimated models using flexible event time functions, which start to count after an increase or decrease in the number of facilities. Results are shown in Figure 3 for West Germany and in Figure 4 for East Germany. The figures present averaged effects in FEIS SLX models of receiving a new industrial facility (panel a) or experiencing a reduction in facilities (panel b) between t − 1 and t, as indicated by the vertical line. The event time clock starts counting from the first instance of any increase or decrease observed in the data, thereby summing potentially accumulating new facilities into the later years. However, the results are robust to different specifications because the number of municipalities with multiple increases and decreases is relatively small (15% and 5% of municipalities showing any within-change for increases and decreases, respectively). We use a threshold of ±0.9 facilities, as this comes close to an entire facility but allows for small overlaps of the 1-km buffer with neighboring communities.
In West Germany (see Figure 3), communities exhibit a continuously declining income during the years after receiving an industrial facility, in addition to the general trend (while controlling for increases and decreases in neighboring units). Five years after this increase in industrial sites relative to local neighbors, on average, hosting communities exhibit an income that is more than 0.1 standard deviations lower than we would have expected based on the respective economic development. The effect size due to an increase by at least 0.9 facilities is substantial: a new industrial facility is predicted to lower income tax revenue per capita by 15.6 EUR in year 5 after siting, which translates to an approximately 38 EUR lower monthly gross income per person. This temporal pattern is completely in line with the expectations based on selective migration or sorting theory, and documents an accumulating negative effect over a relatively short period of time.
Interestingly, we basically observe a null effect after a reduction in the number of facilities (panel b of Figure 3). If an industrial facility is closed, there is no reversal of the negative effect due to new facilities, that is, a significant increase in average income. This conforms to results from the United States indicating no positive effects on the housing market due to the closure of industrial plants (Currie et al. 2015). A reduction in the number of operating facilities does not necessarily mean that industrial sites are sufficiently cleaned up or repurposed, and it is not clear whether this decrease goes along with visible and recognizable changes in environmental quality, though obviously it goes along with a reduction in emissions. As has been argued earlier (Messer et al. 2006), areas around former industrial sites may remain stigmatized and thus not experience an inflow of wealthy households even following improvements in environmental quality.
Turning to East Germany (see Figure 4), we again observe a different picture. We do not find any influence due to an increase in facilities relative to local alternatives over time. Although the trend goes downward from year 2 on, the effect is weak and not significant. For decreases, we observe no influence on the average income either. Though the last period shows a steep upward shock, this should be considered with caution, as the indicator for period 8 after the event is based on a very low number of cases. In general, these time patterns strengthen our previous conclusions: a continuously increasing sorting effect due to new sites in West Germany, but no sorting pattern in East Germany. Indeed, migration patterns may be different in East Germany, and thereby not exhibit the sorting of high-income households into cleaner areas and of the socioeconomically disadvantaged into more polluted areas. It is difficult to speculate about the reasons. Differences in infrastructure or the housing market might contribute to these diverging patterns in similar ways as general differences in economic conditions.
Supplement S2 in the online material presents results of the same modeling approach for the relative rank measure. In general, Figures S2.1 and S2.2 conform to the patterns presented here. The only difference is that at least within the first three years after a decline in the rank—which means an increase in relative environmental quality—we observe an increase in average income by trend (though not significant). This can be interpreted in favor of the argument by Banzhaf and McCormick (2012) and Banzhaf and Walsh (2008, 2013): only rank reordering processes unambiguously trigger selective migration processes. Still, in this case, the changes due to site closing are not statistically different from zero, which adds further confidence in the conclusions drawn earlier. Even “getting better” than neighbors does not significantly reattract affluent households beyond expectations based on the economic trends.
## Discussion and Conclusions
The unequal distribution of environmental harms across society is a major dimension of social inequality given its severe impact on other domains of life (Colmer and Voorheis 2020; European Environment Agency 2019). In this study, we add new insights on the processes generating this unequal distribution by using spatially aggregated longitudinal data at the level of German municipalities. We account for potential explanations of diverging results between micro- and macro-level studies and model environmental changes in relation to changes in neighboring regions—the likely alternatives for residential choices. Moreover, we control for time-constant heterogeneity and selection on diverging economic trajectories using fixed-effects individual slopes estimators.
Our results found no support for the argument of selective siting. In former West and East Germany, we do not find significant effects of a community's socioeconomic composition on the number of industrial facilities. Although we observe a negative cross-sectional correlation between average income and the number of facilities in West Germany, within-estimators challenge the hypothesis of a causal link between income and the likelihood of receiving new industrial facilities. At least during our observation period (2008–2017), changes in income did not affect the placement or closing of industrial sites net of municipality-specific trends. This result conforms to previous results in the United States showing that other (infrastructural) characteristics are more important for the placement of new sites than demographic characteristics (Elliott and Frickel 2013, 2015). Of course, facilities might have been placed selectively in the past or may be placed selectively within municipalities. Future research should thus aim to conduct similar analyses with larger time frames and on a more fine-grained level within municipalities. However, in the recent decade and on the spatial scale employed here, selective siting does not substantially contribute to environmental inequality.
In West Germany, we find evidence for selective sorting or migration patterns. If a community experiences an increase in the number of sites while surrounding communities are kept at a constant level, the hosting municipality's average income drops in the following years. The magnitude is moderate in the first year after a change in environmental quality, but the disadvantage continuously accumulates over time. Within a period of five years, this disadvantage reaches a substantial size. In contrast, the closing of existing sites does not reattract affluent households. In the online supplement, we replicated our main analyses using the toxicity-weighted pollution instead of the number of facilities (see Supplement S6). Although low-income communities are exposed to higher levels of toxic emissions in between models, we do not find any evidence for selective sorting processes based on changes in toxic pollution. One reason for this finding might be that—at least on this spatial scale—industrial sites are a stronger and more visible sign of environmental quality than toxic pollution itself, which may be difficult to assess by residents (see also Currie et al. 2015). Still, sorting based on industrial sites likely contributes to the higher exposure of low-income municipalities to toxic pollution (see Table S6.7).
These results provide some practical implications for tackling environmental inequality. First, municipalities should be aware of the negative consequences on their economic returns attributable to population dynamics following an increase in industrial activities. Second, at least during our observation period, population dynamics play a more important role in environmental inequality than siting decisions. Successful policies should thus focus on reducing income inequalities and residential sorting mechanisms rather than on pure environmental zoning, which is directed toward industrial siting and likely to be counteracted by migration dynamics. Third, the simple closing of industrial facilities does not counterbalance the negative effect of new industrial sites. Shutting down facilities might be a less visible signal of environmental change, or former industrial areas may remain stigmatized, thereby not reattracting affluent households.
Our results also generate new questions for further research. First, studies could investigate in more detail which environmental cues influence individual perceptions of environmental quality and thus trigger residential sorting. The finding of sorting based on industrial sites but not on toxic emissions raises some doubt about the accuracy of individual perception of environmental risks. Second, the role of site cleanup should be investigated in more detail. It is important to know in which instances closing or cleanup of industrial sites triggers positive population changes, but also when these actions lead to environmental gentrification (Banzhaf et al. 2019b; Banzhaf and McCormick 2012), thereby potentially exerting greater pressure on low-income households. Indeed, our results indicate that the mere closing of potentially hazardous facilities does not significantly change the composition of the local population, and so may reduce inequalities in exposure to industrial emissions. Nevertheless, future research should compare different levels of cleanup to assess whether they may lead to more robust conclusions. Third, we find stark differences in the level of environmental inequality between West and East Germany, with industrial sites being more equally distributed in the latter. Indeed, we do not find evidence for selective migration processes in East Germany. The region of former East Germany experienced a different level of industrial development, and the average income is still below that of West Germany. However, the presence of a less pressured housing market and different infrastructural characteristics might also contribute to lower environmental inequality in the region.
Overall, we demonstrate the importance of selective sorting processes for the unequal distribution of environmental disamenities. The placement of industrial facilities leads to selective sorting processes and significantly changes the socioeconomic composition of an area, thereby steering less affluent households into areas closer to environmental hazards. Taking these negative demographic consequences and impacts on individual households into account can help to reduce social inequality and protect socioeconomically disadvantaged populations.
## Acknowledgments
We are grateful to seminar and workshop participants at universities in Bern, Kaiserslautern, Konstanz, Oxford, and Zurich and the WZB Berlin for helpful comments on this project. We also profited considerably from feedback at several conferences. We thank Stefan Jünger for providing helpful insights on the IOER monitor, and Charlotte Haußmann, Leonore Röseler, and Elo Schneider for research assistance. We received very constructive feedback from Mark D. Hayward and three anonymous reviewers.
## Note
1
Research in the United States often focuses on the severe disadvantage of ethnic or racial minorities (Banzhaf et al. 2019a; Mohai and Saha 2015a). Because we have only limited longitudinal data on ethnic minorities in Germany, we focus on environmental inequality according to income. We hope that better longitudinal data will allow us to investigate ethnic disadvantages in the future.
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# A
Source edition 1965. Please read the Introduction to find out about this dictionary and our plans for it. Caution, many entries have not been updated since the 1965 edition.
Greek symbols may not appear correctly in some browsers. For example a gamma may appear as γ.
aberration
1. In astronomy, the apparent angular displacement of the position of a celestial body in the direction of motion of the observer, caused by the combination of the velocity of the observer and the velocity of light. See constant of aberration, planetary aberration. Compare parallax.
2. In optics, a specific deviation from perfect imagery, as, for example: spherical aberration, coma, astigmatism, curvature of field, and distortion.
aberration constant = constant of aberration
ablate
To carry away; specifically, to carry away heat generated by aerodynamic heating, from a vital part, by arranging for its absorption in a nonvital part, which may melt or vaporize, then fall away taking the heat with it. See heat shield, ablation.
ablating material
A material, especially a coating material, designed to provide thermal protection to a body in a fluid stream through loss of mass.
Ablating materials are used on the surfaces of some reentry vehicles to absorb heat by removal of mass, thus blocking the transfer of heat to the rest of the vehicle and maintaining temperatures within design limits. Ablating materials absorb heat by increasing in temperature and changing in chemical or physical state. The heat is carried away from the surface by a loss of mass (liquid or vapor). The departing mass also blocks part of the convective heat transfer to the remaining material in the same manner as transpiration cooling.
ablating nose cone
A nose cone designed to reduce heat transfer to the internal structure by the use of an ablating material.
ablation
The removal of surface material from a body by vaporization, melting, chipping, or other erosive process; specifically, the intentional removal of material from a nose cone or spacecraft during high-speed movement through a planetary atmosphere to provide thermal protection to the underlying structure. See ablating material.
ablatively
By a process of ablation, as in ablatively cooled .
ablative material = ablating material.
ablator
A material designed to provide thermal protection through ablation.
abort
1. To cut short or break off an action, operation, or procedure with an aircraft, space vehicle, or the like, especially because of equipment failure, as to abort a mission, the launching was aborted.
2. An aircraft, space vehicle, or the like that aborts.
3. An act or instance of aborting.
Abridged Nautical Almanac
See Nautical Almanac.
absolute
1. Pertaining to a measurement relative to a universal constant or natural datum, as absolute coordinate system, absolute altitude, absolute temperature.
2. Complete, as in absolute vacuum.
absolute altimeter
An instrument intended to give acceptably accurate, direct indications of absolute altitude.
absolute altitude
Altitude above the actual surface, either land or water, of a planet or natural satellite. Compare true altitude.
absolute coordinate system
An inertial coordinate system which is fixed with respect to the stars.
In theory, no absolute coordinate system can be established because the reference stars are themselves in motion. In practice, such a system can be established to meet the demands of the problem concerned by the selection of appropriate reference stars.
absolute delay
1. The time interval between the transmission of sequential signals. Also called delay .
2. Specifically, in loran, the time interval between transmission of a signal from the A-station and transmission of the next signal from the B-station.
absolute humidity
The amount of water vapor actually present in unit quantity of a gas, generally expressed as mass of water vapor per unit volume of gas + water vapor, e.g., as grains per cubic foot.
absolute index of refraction = index of refraction (sense 1).
absolute instrument
An instrument whose calibration can be determined by means of physical measurements on the instrument. Compare secondary instrument.
absolute magnitude (symbol M)
1. A measure of the brightness of a star equal to the magnitude the star would have at a distance of 10 parsecs from the observer.
where m is apparent magnitude, and p is the parallax of the star (in seconds of arc). Absolute magnitudes may be visual, photographic, etc., according to the way in which the apparent magnitude was measured.
2. The stellar magnitude any meteor would have if placed in the observer's zenith at a height of 100 kilometers.
absolute manometer
1. A gas manometer whose calibration, which is the same for all ideal gases, can be calculated from the measurable physical constants of the instrument.
2. A manometer that measures absolute pressure.
absolute motion
Motion relative to a fixed point. See absolute coordinate system, note.
absolute pressure
In engineering literature, a term used to indicate pressure above the absolute zero value of pressure that theoretically obtains in empty space or at the absolute zero of temperature as distinguished from gage pressure.
In high-vacuum technology, pressure is understood to correspond to absolute pressure, not gage pressure, and therefore the term absolute pressure is rarely used.
absolute refractive index = index of refractory (sense 1)
absolute system of units
1. A system of units in which a small number of units are chosen as fundamental, and all other units are derived from them.
2. Specifically, a system of electrical units put into effect by international agreement on 1 January 1948.
Prior to 1 January 1948 the international system was in effect; the two systems can be converted by the following relationships:
1 mean international ohm = 1.00049 absolute ohm
1 mean international volt = 1.00034 absolute volt.
"Electric units, called "international," for current and resistance had been introduced by the International Electrical Congress held in Chicago in 1893, and the definitions of the "international" ampere and the "international" ohm were confirmed by the International Conference of London in 1908.
Although it was already obvious on the occasion of the 8th CGPM (1933) that there was a unanimous desire to replace those "international" units by so-called "absolute" units, the official decision to abolish them was only taken by the 9th CGPM (1948), which adopted for the unit of electric current, the ampere," which see.
The previous is an excerpt from WWW version of the National Institute of Standards and Technology: Physics Laboratory's International System of Units (SI).
absolute temperature
Temperature value relative to absolute zero.
absolute temperature scale
A temperature scale based upon the value zero as the lowest possible value. Thus, all obtainable temperatures are positive. The Kelvin and Rankine scales are absolute scales.
absolute vacuum
A void completely empty of matter. Also called perfect vacuum.
An absolute vacuum is not obtainable.
absolute vorticity
1. The vorticity of a fluid particle expressed with respect to an absolute coordinate system. 2. The vertical component of the absolute vorticity (as defined above).
absolute zero
The theoretical temperature at which molecular motion vanishes and a body would have no heat energy; the zero point of the Kelvin and Rankine temperature scales.
Absolute zero may be interpreted as the temperature at which the volume of a perfect gas vanishes or, more generally, as the temperature of the cold source which would render a Carnot cycle 100 percent efficient. The value of absolute zero is now estimated to be - 273.15° Celsius, -459.67° Fahrenheit, 0° Kelvin, and 0° Rankine.
absorptance, absorbtance(symbol A, a, or )
The ratio of the radiant flux absorbed by a body to that incident upon it. Also called absorption factor. Compare absorptivity.
Total absorptance refers to absorptance measured over all wavelengths.
Spectral absorptance refers to absorptance measured at a specified wavelength.
absorption
1. The process by which radiant energy is absorbed and converted into other forms of energy. See attenuation.
Absorption takes place only after the radiant flux enters a medium and thus acts only on the entering flux not on the incident flux, some of which may be reflected at the surface of the medium. A substance which absorbs energy may also be a medium of refraction, diffraction, or scattering; these processes, however, involve no energy retention or transformation and are to be clearly differentiated from absorption.
2. In general, the taking up or assimilation of one substance by another. See sorption, adsorption.
3. In vacuum technology, gas entering into the interior of a solid.
absorption band
A range of wavelengths (or frequencies) in the electromagnetic spectrum within which radiant energy is absorbed by a substance. See absorption spectrum.
When the absorbing substance is a polyatomic gas, an absorption band actually is composed of a group of discrete absorption lines which appear to overlap. Each line is associated with a particular mode of vibration or rotation induced in a gas molecule by the incident radiation.
The absorption bands of oxygen and ozone are often referred to in the literature of atmospheric physics.
The important bands for oxygen are: (a) the Hopfield bands, very strong, between about 670 and 1000 angstroms in the ultraviolet; (b) a diffuse system between 1019 and 1300 angstroms; (c) the Schumann-Runge continuum, very strong, between 1350 and 1760 angstroms; (d) the Schumann-Runge bands between 1760 and 1926 angstroms; (e) the Herzberg bands between 2400 and 2600 angstroms; (f) the atmospheric bands between 5380 and 7710 angstroms in the visible spectrum; and (g) a system in the infrared at about 1 micron.
The important bands for ozone are: (a) the Hartley bands between 2000 and 3000 angstroms in the ultraviolet, with a very intense maximum absorption at 2550 angstroms; (b) the Huggins bands, weak absorption between 3200 and 3600 angstroms; (c) the Chappius bands, a weak diffuse system between 4500 and 6500 angstroms in the visible spectrum; and (d) the infrared bands centered at 4.7, 9.6 and 14.1 microns, the latter being the most intense.
absorption coefficient (symbol )
1. A measure of the amount of normally incident radiant energy absorbed through a unit distance or by a unit mass of absorbing medium. Compare transmission coefficient.
The absorption coefficient is frequently identified as follows: where ILx is the flux density of radiation of wavelength L, initially of flux density IL0, after traversing a distance x in some absorbing medium. (Substitute L for lambda.)
2. In acoustics, the ratio of the sound energy absorbed by a surface of a medium (or material) exposed to a sound field or sound radiation to the sound energy incident on the surface. The stated values of this ratio are to hold for an infinite area of the surface. The conditions under which measurements of absorption coefficients are made are to be stated explicitly.
Three types of absorption coefficients associated with three methods of measurement are: chamber absorption coefficient, obtained in a certain reverberation chamber; free-wave absorption coefficient, obtained when a plane, progressive, sound wave is incident on the surface of the medium; sabine absorption coefficient, obtained when the sound is incident from all directions on the sample.
absorption cross section
In radar, the ratio of the amount of power removed from a beam by absorption of radio energy by a target to the power in the beam incident upon the target. Compare scattering cross section. See cross section.
absorption-emission pyrometer
A thermometer for determining gas temperature from measurement of the radiation emitted by a calibrated reference source before and after this radiation has passed through and been partially absorbed by the gas. Both measurements are made over the same wavelength interval.
absorption factor = absorptance.
absorption line
A minute range of wavelength (or frequency) in the electromagnetic spectrum within which radiant energy is absorbed by the medium through which it is passing. Each line is associated with a particular mode of electronic excitation induced in the absorbing atoms by the incident radiation. See absorption spectrum, spectral line, telluric lines, Fraunhofer lines, absorption band.
absorption spectrum
The array of absorption lines and absorption bands which results from the passage of radiant energy from a continuous source through a selectively absorbing medium cooler than the source. See electromagnetic spectrum.
The absorption spectrum is a characteristic of the absorbing medium, just as an emission spectrum is a characteristic of a radiator.
An absorption spectrum formed by a monatomic gas exhibits discrete dark lines, whereas that formed by a polyatomic gas exhibits ordered arrays (bands) of dark lines, which appear to overlap. This type of absorption is often referred to as line absorption. The spectrum formed by a selectively absorbing liquid or solid is typically continuous in nature (continuous absorption).
absorptive index
The imaginary part of the complex index of refraction of a medium. It represents the energy loss by absorption and has a nonzero value for all media which are not dielectrics. Also called index of absorption . Compare absorption coefficient.
absorptive power
The total flux of radiant energy absorbed in a unit area of absorbing substance; expressed, for example, in ergs per square centimeter per second or in watts per square centimeter.
absorptivity (symbol )
The capacity of a material to absorb incident radiant energy, measured as the absorptance of a specimen of the material thick enough to be completely opaque, and having an optically smooth surface.
absorptivity-emissivity ratio
In space applications, the ratio of absorptivity for solar radiation of a material to its infrared emissivity. Also called A/E ratio.
acceleration
1. The rate of change of velocity.
2. The act or process of accelerating, or the state of being accelerated. Negative acceleration is called deceleration .
acceleration of gravity (symbol g)
By the International Gravity Formula, $g = 978.0495 \left[1 + 0.0052892 sin2\left(p\right) - 0.0000073 sin2\left(2p\right)\right]$ centimeters per second squared at sea level at latitude p. See gravity.
The standard value of gravity, or normal gravity, g, is defined as go=980.665 centimeters per second squared, or 32.1741 feet per second squared. This value corresponds closely to the International Gravity Formula value of g at 45° latitude at sea level.
accelerator
Short for particle accelerator .
accelerometer
A transducer which measures acceleration or gravitational forces capable of imparting acceleration.
An accelerometer usually uses a concentrated mass (seismic mass) which resists movement because of its inertia. The displacement of the seismic mass relative to its supporting frame or container is used as a measure of acceleration.
acceptor
In transistors, the P-type semiconductor, the electrode containing trivalent impurities (boron, gallium, or indium) to increase the number of holes which can accept electrons. Contrast with donor.
accidental error
In experimental observations, an error which does not always recur when an observation is repeated under the same conditions. Contrast systematic error.
acclimatization
The adjustments of a human body or other organism to a new environment; the bodily changes which tend to increase efficiency and reduce energy loss. Compare adaptation, accustomization.
accommodation coefficient (symbol )
The ratio of the average energy actually transferred between a surface and impinging gas molecules which are scattered by the surface to the average energy which would theoretically by transferred if the impinging molecules reached complete thermal equilibrium with the surface before leaving the surface or $a = \left(E$r-E i)/Es-Ei) where a is the accommodation coefficient, Er is the energy carried away from unit surface area per second by the scattered or re-evaporated molecules, Ei is the energy per unit surface area per second carried toward the surface by the impinging molecules, and Es is the energy per unit surface area per second which would be carried away by the molecules if the molecules reached complete thermal equilibrium with the surface before leaving.
accumulator
1. A device or apparatus that accumulates or stores up, as: (a) a contrivance in a hydraulic system that stores fluid under pressure; (b) a device sometimes incorporated in the fuel system of a gas-turbine engine to store up and release fuel under pressure as an aid in starting; (c) an electrical storage battery (British usage).
2. In computer technology, a device which stores a number and upon receipt of another number adds it to the number already stored and stores the sum. See counter.
accustomization
The process of learning the techniques of living with a minimum of discomfort in an extreme or new environment. Compare acclimatization, adaptation.
aclinic line
The line through those points on the earth's surface at which magnetic dip is zero. The aclinic line is a particular case of an isoclinic line. Also call dip equator, magnetic equator. Compare agonic line, geomagnetic equator.
acoustic, acoustical
Containing, producing, arising from, actuated by, related to, or associated with sound.
Acoustic is used to modify terms that designate an object, or physical characteristics, associated with sound waves; acoustical is used when the term being qualified does not designate explicitly something that has such properties, dimensions, or physical characteristics.
The following terms are examples of those modified by acoustic; impedance, intertance, load (radiation field), output (sound power), energy, wave, medium, signal, conduit, absorptivity, transducer.
The following examples do not have the requisite physical characteristics and therefore take acoustical; society, method, engineer, school, glossary, symbol, problem, measurement, point of view, device.
As illustrated, the generic term is usually modified by acoustical, whereas the specific technical term calls for acoustic.
acoustic delay line
A device used in a communications link or a computer memory in which the signal is delayed by the propagation of a sound wave. Also call sonic delay line .
acoustic description
The change of speed of sound with frequency.
acoustic excitation
The process of inducing vibration in a structure by exposure to sound waves.
acoustic generator
A transducer which converts electric, mechanical, or other forms of energy into sound.
acoustic Mach meter
A device which obtains data on sound propagation for the calculation of Mach number.
Some acoustics Mach meters measure transit time or velocity of a sound pulse; others measure an angle, as the angle of the Mach cone.
A unidirectional, steady-state pressure exerted upon a surface exposed to a sound wave.
acoustic refraction
The process by which the direction of sound propagation is changed due to spatial variation in the speed of sound in the medium.
acoustics
1. The study of sound, including its production, transmission, and effects.
2. Those qualities of an enclosure that together determine its character with respect to distinct hearing.
acoustic streaming
Unidirectional flow currents in a fluid that are due to the presence of sound waves.
acoustic velocity (symbol ) =speed of sound
acoustic vibration
With respect to operational environments, vibrations transmitted through a gas. These vibrations may be subsonic, sonic, and ultrasonic.
acoustic wave = sound wave.
acquisition
1. The process of locating the orbit of a satellite or trajectory of a space probe so that tracking or telemetry data can be gathered.
2. The process of pointing an antenna or telescope so that it is properly oriented to allow gathering of tracking or telemetry data from a satellite or space probe.
A radar set that locks onto a strong signal and track the object reflecting the signal.
actinic
Pertaining to electromagnetic radiation capable of initiating photochemical reactions, as in photography or the fading of pigments.
Because of the particularly strong action of ultra violet radiation on photochemical processes, the term has come to be almost synonymous with ultraviolet, as in actinic rays.
actinic balance =bolometer.
actinogram
The record of a recording actinometer.
actinograph
A recording actinometer.
actinometer
The general name for any instrument used to measure the intensity of radiant energy, particularly that of the sun. See actinometry. See also bolometer, dosimeter, photometer, radiometer.
Actinometers may be classified, according to the quantities which they measure, in the following manner: (a) pyrheliometer, which measures the intensity of direct solar radiation; (b) pyranometer, which measure global radiation (the combined intensity of direct solar radiation and diffuse sky radiation); and (c) pyrgeometer, which measures the effective terrestrial radiation.
actinometry
The science of measurement of radiant energy, particularly that of the sun, in its thermal, chemical, and luminous aspects. Compare photometry. See actinometer.
active
1. Transmitting a signal, as active satellite . Antonym of passive.
2. = radioactive, as active sample .
3. = fissionable, as active material .
4. Receiving energy from some source other than a signal, as active element .
active element
In a computer, a circuit or device which receives energy from some source other than the signal input.
active homing
The homing of an aerodynamic or space vehicle in which energy waves (as radar) are transmitted from the vehicle to the target and reflected back to the vehicle to direct the vehicle toward the target. Compare passive homing.
active homing guidance
See homing guidance.
active leg
An electrical element within a transducer which changes its electrical characteristics as a function of the application of a stimulus.
active satellite
A satellite which transmits a signal, in contrast to passive satellite .
active tracking system
A system which requires addition of a transponder, or transmitter on board the vehicle to repeat, transmit, or retransmit information to the tracking equipment, e.g. Dovap, Secor, Azusa, Miran, Minitrack.
active transducer
A transducer whose output is dependent upon sources of power, apart from that supplied by any of the actuating signals, which power is controlled by one or more of these signals.
actuating system
A mechanical system that supplies and transmits energy for the operation of other mechanisms or systems.
The adjustment, alteration, or modification of an organism to fit it more perfectly for existence in its environment. Compare acclimatization, accustomization.
Adaptation is applied particularly to evolutionary change.
The average luminance (or brightness) of those objects and surfaces in the immediate vicinity of an observer. Also called adaptation brightness, adaptation level, adaptation illuminance.
The adaptation luminance has a marked influence on an observer's estimate of the visual range because, along with the visual angle of the object under observation, it determines the observer's threshold contrast. High adaptation luminance tends to produce a high threshold contrast, thus reducing the estimated visual range. This effect of the adaptation luminance is to be distinguished from the influence of background luminance.
1. Any device or contrivance used or designed primarily to fit or adjust one thing to another, as: (a) a buckle or clip on a parachute harness, used in adjusting the harness to the wearer; (b) a joint attaching an afterburner to a turbine casing on a jet engine; (c) a fitting for connecting pipes, valves, etc., that have different types of threads.
2. Any device, appliance or the like used to alter something so as to make it suitable for a use for which it was not originally designed.
A flange or extension of a space vehicle stage or section that provides a ready means for fitting some object to the stage or section.
A control system which continuously monitors the dynamic response of the controlled system and automatically adjusts critical system parameters to satisfy preassigned response criteria, thus producing the same response over a wide range of environmental conditions.
ADC (abbr) = analog to digital converter.
A pair of vertical antennas separated by a distance of one-half wavelength or less, and connected in phase opposition to produce a radiation pattern having the shape of a figure eight.
In a computer, a device which can form the sum of two or more numbers or quantities.
Any material or substance added to something else. Specifically, a substance added to a propellant to achieve some purpose, such as a more even rate of combustion, or a substance added to fuels or lubricants to improve them or give them some desired quality, such as tetraethyl lead added to a fuel as an antidetonation agent, or graphite, talc, or other substances added to certain oils and greases to improve lubrication qualities.
1. Of a computer, a location where information is stored.
2. An expression, usually numerical, identifying an address (sense 1).
ADF (abbr) = automatic direction finder.
A line on a thermodynamic diagram representing a constant potential temperature. See adiabatic process.
Without gain or loss of heat.
A model atmosphere in which the pressure decreases with height according to: $p = p$0[1 - (-gz/cp,dT0)] Cp,dRd where $p$0 and $T$0 are the pressure and temperature (° K) at sea level or other datum; z is the geometric height; $R$d is the gas constant for dry gas; $c$p,d is the specific heat for dry gas at constant pressure; and g is the acceleration of gravity. Also called dry-adiabatic atmosphere, convective atmosphere, homogeneous atmosphere . See homogeneous atmosphere, barotropy.
The efficiency with which work is done with respect to heat gains or losses. See adiabatic process.
See equivalent temperature, sense 2.
A thermodynamic change of state of a system in which there is no transfer of heat or mass across the boundaries of the system. In an adiabatic process, compression always results in warming, expansion in cooling. See diabatic process.
1. The temperature reached by a moving fluid when brought to rest through an adiabatic process. Also called recovery temperature, stagnation temperature .
3. The final and initial temperature in an adiabatic, Carnot cycle.
The temperature assumed by a wall in a moving fluid stream when there is no heat transfer between the wall and the stream.
A-display
In radar, a display in which targets appear as vertical deflections from a line representing a time base. Also called A-scan or A-scope .
Target distance is indicated by the horizontal position of the deflection from one end of the time base. The amplitude of the vertical deflection is a function of the signal intensity.
ADP (abbr) = automatic data processing.
A material which takes up gas by adsorption.
The adhesion of a thin film of liquid or gas to the surface of a solid substance. The solid does not combine chemically with the adsorbed substance. See sorption, absorption, chemisorption.
The process of transport of an atmospheric property solely by the mass motion of the atmosphere; also, the rate of change of the value of the advected property at a given point.
Regarding the general distinction (in meteorology) between advection and convection, the former describes the predominantly horizontal, large-scale motions of the atmosphere whereas convection describes the predominantly vertical, locally induced motions.
aeon
$109$ years. This term was suggested by Harold Urey in 1957.
A/E ratio= absorptivity-emissivity ratio.
aerial
1. = antenna.
2. Of or pertaining to the air, atmosphere, or aviation.
aeroastromedicine= aerospace medicine.
aeroballistics
The study of the interaction of projectiles or high speed vehicles with the atmosphere. See ballistics.
The problem of the effect of reentry on the trajectory of a vehicle is a problem in aeroballistics.
aerobiology
The study of the distribution of living organisms freely suspended in the atmosphere.
aerodontalgia
A toothache brought on by a change in ambient pressure.
aeroduct
A ramjet type of engine designed to scoop up ions and electrons freely available in the outer reaches of the atmosphere or in the atmospheres of other spatial bodies, and by a metachemical process within the duct of this engine, expel particles derived from the ions and electrons as a propulsive jetstream.
aerodynamic
Of or pertaining to aerodynamics.
aerodynamic coefficient
Any nondimensional coefficient relating to aerodynamic forces or moments, such as a coefficient of drag, a coefficient of lift, etc.
aerodynamic force
The force exerted by a moving gaseous fluid upon a body completely immersed in it.
The aerodynamic force is proportional to the expression
p u 2 L 2 R n
where p is the fluid density; u is the velocity of the undisturbed stream relative to the body; L is a characteristic linear dimension of the body; and Rn is the Reynolds number raised to the power of n, a constant usually determined experimentally. This form for the aerodynamic force is sometimes called
Rayleigh formula. The component of the aerodynamic force parallel to the direction of flow is called the drag.
aerodynamic heating
The heating of a body produced by passage of air or other gases over the body; caused by friction and by compression processes and significant chiefly at high speeds. See radiative heating.
aerodynamics
1. The science that deals with the motion of air and other gaseous fluids, and of the forces acting on bodies when the bodies move through such fluids, or when such fluids move against or around the bodies, as, his research in aerodynamics .
2. (a) The actions and forces resulting from the movement or flow of gaseous fluids against or around bodies, as, the aerodynamics of a wing in supersonic flight . (b) The properties of a body or bodies with respect to these actions or forces, as, the aerodynamics of a turret or of a configuration .
3. The application of the principles of gaseous fluid flows and of their actions against and around bodies to the design and construction of bodies intended to move through such fluids, as a design used in aerodynamics.
aerodynamic trail
A condensation trail formed by adiabatic cooling to saturation (or slightly supersaturation) of air passing over the surfaces of high-speed aircraft.
Aerodynamic trails form off the tips of wings and propellers and other points of maximum pressure decrease. They are relatively rare and of short duration compared to exhaust trails.
aerodynamic vehicle
A device, such as an airplane, glider, etc., capable of flight only within a sensible atmosphere and relying on aerodynamic forces to maintain flight.
The term is used when the context calls for discrimination from space vehicle.
aeroelasticity
Any phenomenon which includes the mutual interaction between aerodynamic loads and structural deformation.
aeroembolism
1. The formation or liberation of gases in the blood vessels of the body, as brought on by a too-rapid change from a high, or relatively high, atmospheric pressure to a lower one.
2. The disease or condition caused by the formation of gas bubbles (mostly nitrogen) in the body fluids. The disease is characterized principally by neuralgic pains, cramps, and swelling, and sometimes results in death. Also call decompression sickness .
aeroemphysema
A swelling condition caused by the formation of gas in the tissues of the body.
aerolite
A meteorite composed principally of stony material.
aerology
1. As officially used in the U.S. Navy until early 1957, same as meteorology; this usage was more administrative than scientific.
2. As a subdivision of meteorology, the study of the free atmosphere through its vertical extend, as distinguished from studies confined to the layer of the atmosphere adjacent to the earth's surface.
aeronomy
The study of the upper regions of the atmosphere where ionization, dissociation, and chemical reactions take place.
aero-otitis media
An inflammatory reaction of the middle ear resulting from a difference in pressure between the gas in the middle ear and the surrounding atmosphere. Also called otitic barotrauma . c
aeropause
A region of indeterminate limits in the upper atmosphere, considered as a boundary or transition region between the denser portion of the atmosphere and space.
From a functional point of view, it is considered to be that region in which the atmosphere is so tenuous as to have a negligible, or almost negligible, effect on men and aircraft, and in which the physiological requirements of man become increasingly important in the design of aircraft and auxiliary equipment.
aeropulse engine = pulsejet engine.
aerosinusitis
An inflammatory reaction of one or more of the accessory nasal sinuses resulting from a difference in pressure between the gas in the sinus and the surrounding atmosphere. Also called sinus barotrauma .
aerosonator = resojet engine.
aerospace
(From aeronautics and space).
1. Of or pertaining to both the earth's atmosphere and space, as in aerospace industries.
2. Earth's envelope of air and space above it; the two considered as a single realm for activity in the flight of air vehicles and in the launching, guidance, and control of ballistic missiles, earth satellites, dirigible space vehicles, and the like.
Aerospace in sense 2 is used primarily by the U.S. Air Force. The term aerospace first appeared in print in the Interim Glossary; Aero-Space Terms (edited by Woodford Agee Heflin) published in February 1958 at the Air University, Maxwell Air Force Base, Alabama.
aerospace medicine
That branch of medicine dealing with the effects of flight through the atmosphere or in space upon the human body and with the prevention or cure of physiological or psychological malfunctions arising from these effects.
aerospace vehicle
A vehicle capable of flight within and outside the sensible atmosphere.
aerothermodynamic border
An altitude at about 100 miles, above which the atmosphere is so rarefied that the skin of an object moving through it at high speeds generates no significant heat.
aerothermodynamic duct
The full term for athodyd .
aerothermodynamics
The study of aerodynamic phenomena at sufficiently high gas velocities that thermodynamic properties of the gas are important.
aerothermoelasticity
The study of the response of elastic structures to the combined effect of aerodynamic heating and loading.
AFC (abbr) = automatic frequency control.
afterbody
1. A companion body that trails a satellite.
2. A section or piece of a rocket or spacecraft that enters the atmosphere unprotected behind the nose cone or other body that is protected for entry.
3. The afterpart of a vehicle.
afterburner
A device for augmenting the thrust of a jet engine by burning additional fuel in the uncombined oxygen in the gases from the turbine.
afterburning
1. Irregular burning of fuel left in the firing chamber or a rocket after fuel cutoff.
2. The function of an afterburner, a device for augmenting the thrust of a jet engine by burning additional fuel in the uncombined oxygen in the gases from the turbine.
aftercooling
1. The cooling of a gas after compression.
2. The necessary cooling of a reactor core after its shutdown by pumping a liquid or gas through it to carry off the excess heat generated by continuing radioactive decay of fission products within the core.
afterglow
1. A broad, high arch of radiance or glow seen occasionally in the western sky above the highest clouds in deepening twilight, caused by the scattering effect of very fine particles of dust suspended in the upper atmosphere.
2. The transient decay of a plasma after the power has been turned off.
The decay time involved is a direct consequence of the charged particle loss mechanisms, such as diffusion and recombination. The magnitude of these quantities is determined by measuring the decay time under controlled conditions.
afterheat
The heat generated in a reactor core after shutdown by continuing radioactive decay of fission products.
AGE (abbr) = aerospace ground equipment. See GSE.
age of the moon
The elapsed time, usually expressed in days, since the last new moon. See phase of the moon.
aging
In a metal or alloy, a change in properties that generally occurs slowly at room temperature and more rapidly at higher temperatures.
Agiwarn
Code name for the Western Hemisphere Regional Center for the IGY World Warning Agency.
agonic line
A line joining points at which the magnetic variation is zero. The agonic line is a particular case of an isogonic line.
agravic
Or pertaining to a condition of no gravitation. See weightlessness.
agravic illusion
An apparent movement of a target in the visual field due to otolith response in zerogravity. Also called oculoagravic illusion .
air
1. The mixture of gases comprising the earth's atmosphere.
The percent by volume of those gases found in relatively constant amount in dry air near sea level in very nearly as follows:
ELEMENT % nitrogen (N2) 78.084 oxygen (O2) 20.9476 argon (A) 0.934 carbon dioxide (CO2) 0.0314 (variable) neon (Ne) 0.001818 helium (He) 0.000524 methane (CH4) 0.0002 (variable) krypton (Kr) 0.000114 hydrogen (H2) 0.00005 nitruous oxide (N2O) 0.00005 xenon (Xe) 0.0000087
This table is from the 1965 edition of the Aerospace Dictionary.
In addition to the above constituents there are many variable constituents. Chief of these is water vapor, which may vary from zero to volume percentages close to 4 percent. Ozone, sulfur dioxide, ammonia, carbon monoxide, iodine, and other trace gases occur in small and varying amounts.
The above composition of dry air is true to about 90 kilometers. See upper atmosphere.
2. The realm or medium in which aircraft operate.
air breakup
The breakup of a test reentry body after reentry into the atmosphere.
Air breakup is sometimes provided for, as by the firing of a cartridge inside the reentry body, so as to retard the fall of certain pieces and increase the chances of their recovery. See blowoff.
airbreather
An aerodynamic vehicle propelled by fuel oxidized by intake from the atmosphere; an air breathing vehicle.
airbreathing
Of an engine or aerodynamic vehicle, required to take in air for the purpose of combustion.
aircraft
Any structure, machine, or contrivance, especially a vehicle, designed to be supported by the air, being borne up either by the dynamic action of the air upon the surfaces of the structure or object, or by its own buoyancy; such structures, machines, or vehicles collectively, as, fifty aircraft.
Aircraft, in its broadest meaning, includes fixed-wing airplanes, helicopters, gliders, airships, free and captive balloons, ornithopters, flying model aircraft, kites, etc., but since the term carries a strong vehicular suggestion, it is more often applied, or recognized to apply, only to such of these craft as are designed to support or convey a burden in or through the air.
aircraft rocket
A rocket missile designed to be carried by, and launched from, an aircraft.
airflow
A flow or stream of air. An airflow may take place in a wind tunnel, in the induction system of an engine, etc., or a relative airflow can occur, as past the wing or other parts of a moving craft; a rate of flow, measured by mass or volume per unit of time. See flow.
airfoil
A structure, piece, or body, originally likened to a foil or leaf in being wide and thin, designed to obtain a useful reaction on itself in its motion through the air.
airframe
The assembled structural and aerodynamic components of an aircraft or rocket vehicle that support the different systems and subsystems integral to the video.
The word airframe, a carryover from aviation usage, remains appropriate for rocket vehicles since a major function of the airframe is performed during flight within the atmosphere. There is disagreement as to whether the nose cone and combustion chambers are included in the term airframe while they are attached to the vehicle.
airglow
The quasi-steady radiant emission from the upper atmosphere as distinguished from the sporadic emission of the auroras.
Airglow is a chemiluminescence due primarily to the emission of the molecules O2 and N2, the radical OH, and the atoms O and Na. Emissions observed in airglow could arise from three-body atom collisions forming molecules, from two-body reactions between atoms and molecules, or from recombination of ions.
Historically, airglow has referred to visual radiation. Some recent studies use airglow to refer to radiation outside the visual range.
air launch
To launch from an aircraft in the air, as to air launch a guided missile .
air light
Light from sun and sky which is scattered into the eyes of an observer by atmospheric suspensoids (and, to slight extent, by air molecules) lying in the observer's cone of vision. That is, air light reaches the eye in the same manner that diffuse sky radiation reaches the earth's surface.
Air light is not be confused with airglow .
air lock
1. A stoppage or diminution of flow in a fuel system, hydraulic system, or the like, caused by a pocket of air or vapor. 2. A chamber capable of being hermetically sealed that provides for passage between two places of different pressure, as between an altitude chamber and the outside atmosphere.
air position indicator (abbr API)
An airborne computing system which presents a continuous indication of the aircraft position on the basis of aircraft heading, airspeed, and elapsed time.
airscoop
A hood or open end of an air duct or a similar structure, projecting into the airstream about a vehicle in such a way as to utilize the motion of the vehicle in capturing air to be conducted to an engine, a ventilator, etc.
air shower
A grouping of cosmic-ray particles observed in the atmosphere; a cascade shower in the atmosphere. Also called shower .
Primary cosmic rays slowed down in the atmosphere emit bremsstrahlung photons of high energy. Each of these photons produces secondary electrons which generate more photons and the process continues until the available energy is absorbed.
airsickness
Motion sickness occurring in flight.
air sounding
The act of measuring atmospheric phenomena or determining atmospheric conditions at altitude, especially by means of apparatus carried by balloons or rockets. See sounding.
airspace
Specifically, the atmosphere above a particular portion of the earth, usually defined by the boundaries of an area on the surface projected upward.
Airspace is sometimes particularized by altitude, as the airspace above 20,000 feet.
air-space
Of or pertaining to both the atmosphere and space.
Because this adjective is pronounced as the noun airspace is, it is subject to misunderstanding. Aerospace is commonly used instead.
air start
An act or instance of starting an aircraft's engine while in flight, especially a jet engine after flameout. Compare in-flight start, ground start.
airstream = airflow
air vane
A vane that acts in the air, as contrasted to a jet vane which acts within a jetstream. See control vane.
air vehicle = aircraft
Aitken dust counter
An instrument developed by John Aitken for determining the dust content of the atmosphere. In operation, a sample of air is mixed, in an expandable chamber, with a larger volume of dust-free air containing water vapor. Upon a sudden expansion, the chamber cools adiabatically below its dewpoint, and the droplets form with the dust particles as nuclei (Aitken nuclei). A portion of these droplets settle on a ruled plate in the instrument and are counted with the aid of a microscope. Also called Aitken nucleus counter .
Aitken nuclei
The microscopic particles in the atmosphere which serve as condensation nuclei for droplet growth during the rapid adiabatic expansion produced by an Aitken dust counter. These nuclei are both solid and liquid particles whose diameters are of the order of tenths of microns or even smaller.
The Aitken nuclei play an important role in atmospheric electrical processes, for they are the particles which capture (by adsorption or other surface electrical processes) small ions and thereby form large ions. In air containing large numbers of Aitken nuclei, the small ion population is small, the large ion population is large, and the air conductivity is low.
Aitken nucleus counter =Aitken dust counter.
albedo
The ratio of the amount of electromagnetic radiation reflected by a body to the amount incident upon it, often expressed as a percentage, as, the albedo of the earth is 34% . Compare Bond albedo.
The concept defined above is identical with reflectance. However, albedo is more commonly used in astronomy and meteorology and reflectance in physics.
Albedo is sometimes used to mean the flux of the reflected radiation as, the earth albedo is 0.64 calorie per square centimeter. This usage should be discouraged.
The albedo is to be distinguished from the spectral reflectance which refers to one specific wavelength (monochromatic radiation).
Usage varies somewhat with regard to the exact wavelength interval implied in albedo figures; sometimes just the visible portion of the spectrum is considered, sometimes the totality of wavelengths in the solar spectrum.
albedometer
An instrument used for the measurement of the reflecting power, the albedo, of a surface. A pyranometer adapted for the measurement of radiation reflected from the earth's surface is sometimes employed as an albedometer.
Alford loop
A multielement antenna, having approximately equal and in-phase currents uniformly distributed along each of its peripheral elements, producing a substantially circular radiation pattern in the plane of polarization.
Alfvén Mach number
The ratio of the local flow velocity to the local Alfvén speed. See Alfvén wave.
Alfvén speed
The speed at which Alfvén waves are propagated along the magnetic field.
For a perfectly conducting fluid with a mass density of 1 kilogram per cubic meter in a magnetic field of 10,000 gauss, the Alfvén speed is about 1,000 meters per second while the speed of sound in air is about 300 meters per second.
Alfvén wave
A transverse wave in a magnetohydrodynamic field in which the driving force is the tension introduced by the magnetic field along the lines of force. Also called magnetohydrodynamic wave .
The dynamics of such waves are analogous to those in a vibrating string, the phase speed C being given by
where u is the permeability; H is the magnitude of the magnetic field; and p is the fluid density. Dissipative effects due to fluid viscosity and electrical resistance may be also present.
alga (plural, algae)
Any plants of a group of unicellular and multicellular primitive organisms that include the Chlorella, Scenedesmus, and other genera.
The green algae and blue-green algae, for example, provide a possible means of photosynthesis in a closed ecological system, also a source of food.
algorism
The art or system of calculating with any species of notation, as in arithmetic with nine figures and a zero. Also called algorithm.
Different algorisms have been used in the design of computing machines.
algorithm
1. A special mathematical procedure for solving a particular type of problem.
2. = algorism.
That part of an optical measuring instrument comprising the optical system, indicator, vernier, etc.
In modern practice the term is used principally to refer to a telescope mounted over a compass or compass repeater to facilitate observation of bearings, and to a surveying instrument consisting of a telescope mounted over a compass rose, for measuring directions.
alkali metal
A metal in group IA of the periodic system; namely, lithium, sodium, potassium, rubidium, cesium, and francium. Alkali metals have been considered as coolants (in liquid state) for nuclear reactors for spacecraft. See liquid-metal corrosion.
all burnt
The time at which a rocket consumes its propellants. See burnout, note.
all-inertial guidance
The guidance of a rocket vehicle entirely by use of inertial devices; the equipment used for this.
alloy
A substance having metallic properties and being composed of two or more chemical elements of which at least one is an elemental metal.
alloying element
An element added to a metal to effect changes in properties and which remains within the metal.
almucantar = parallel of altitude.
alpha decay
The radioactive transformation of a nuclide by alpha-particle emission. Also called alpha disintegration.
The decay product is the nuclide having a mass number four units smaller and an atomic number two units smaller than the original nuclide.
alpha disintegration = alpha decay
alphanumeric (alphabet plus numeric)
Including letters and digits.
alpha particle
A positively charged particle emitted from the nuclei of certain atoms during radioactive disintegration. The alpha particle has an atomic weight of 4 and a positive charge equal in magnitude to 2 electronic charges; hence it is essentially a helium nucleus (helium atom stripped of its two planetary electrons). Compare beta particle, gamma ray.
alpha ray
A stream of alpha particles.
altimeter
An instrument for measuring height above a reference datum; specifically, an instrument similar to an aneroid barometer that utilizes the change of atmospheric pressure with altitude to indicate the approximate elevation above a given point or plane used as a reference. See absolute altimeter, pressure altimeter, radio altimeter.
altitude (symbol h)
1. In astronomy, angular displacement above the horizon; the arc of a vertical circle between the horizon and a point on the celestial sphere, measured upward from the horizon.
Angular displacement below the horizon is called negative altitude or dip. See horizon system.
2. Height, especially radial distance as measured above a given datum, as average sea level. See absolute altitude, true altitude.
In space navigation altitude designates distance from the mean surface of the reference body as contrasted to distance, which designates distance from the center of the reference body.
altitude acclimatization
A physiological adaptation to reduced atmospheric and oxygen pressure.
altitude chamber
A chamber within which the air pressure, temperature, etc., can be adjusted to simulate conditions at different altitudes; used for experimentation and testing.
altitude circle = parallel of altitude
altitude difference
In navigation, the difference between computed and observed altitudes, or between precomputed and sextant altitudes. It is labeled T (toward) or A (away) as the observed (or sextant) altitude is greater or smaller than the computed (or precomputed) altitude. Also called altitude intercept, intercept .
altitude intercept = altitude difference
Often shortened to intercept.
altitude sickness
In general, any sickness brought on by exposure to reduced oxygen tension and barometric pressure.
Many writers have proposed specific definitions for this term but the definitions are highly variable.
altitude wind tunnel
A wind tunnel in which the air pressure, temperature, and humidity can be varied to simulate conditions at different altitudes.
In an altitude wind tunnel for testing engines, provision is made for exchanging fresh air for exhaust-laden air during operation.
alveolar air
The respiratory air in the alveoli (air sacs) deep within the lungs.
alveolar oxygen pressure
The oxygen pressure in the alveoli. The value is about 105 millimeters of mercury.
alveoli
The terminal air sacs deep within the lungs. The inhaled oxygen diffuses across the thin alveolar membranes (the walls of the air sacs) into the blood stream, and at the same time carbon dioxide diffuses from the blood into the alveoli and is exhaled through the lungs.
AM (abbr) = amplitude modulation.
ambient (symbol , used as a subscript)
Surrounding; especially, of or pertaining to the environment about a flying aircraft or other body but undisturbed or unaffected by it, as in ambient air, or ambient temperature.
ambient noise
The pervasive noise associated with a given environment, being usually a composite of sounds from sources both near and distant.
ambiguity
In navigation, the condition arising when a given set of observations defines more than one point, direction, line of position, or surface of position.
American Ephemeris and Nautical Almanac
An annual publication of the U.S. Naval Observatory, containing elaborate tables of the predicted positions of various celestial bodies and other data of use to astronomers and navigators.
Beginning with the editions for 1960, The American Ephemeris and Nautical Almanac issued by the Nautical Almanac Office, United States Naval Observatory, and the Astronomical Ephemeris issued by H.M. Nautical Almanac Office, Royal Greenwich Observatory, were unified. With the exception of a few introductory pages, the two publications are identical; they are printed separately in the two countries, from reproducible material prepared partly in the United States of America and partly in the United Kingdom.
American Nautical Almanac
See Nautical Almanac.
ampere (abbr A)
The unit of electric current; the constant current which, if maintained in two straight, parallel conductors of infinite length, of negligible circular cross sections, and placed 1 meter apart in a vacuum will produce between these conductors a force equal to 2*10-7 newtons per meter of length.
amplidyne
A special type of direct current generator used as a power amplifier in which the output voltage responds to changes in field excitation; used extensively in servo systems.
amplifier
A device which enables an input signal to control a source of power, and thus is capable of delivering at its output an enlarged reproduction of the essential characteristics of the signal.
Typical amplifying elements are electron tubes, transistors, and magnetic circuits.
amplitude
1. The maximum value of the displacement of a wave or other periodic phenomenon from a reference position.
2. Angular distance north or south of the prime vertical; the arc of the horizon, or the angle at the zenith between the prime vertical and a vertical circle, measured north or south from the prime vertical to the vertical circle.
The term is customarily used only with reference to bodies whose centers are on the celestial horizon, and is prefixed E or W, as the body is rising or setting, respectively; and suffixed N or S to agree with the declination. The prefix indicates the origin, and the suffix indicates the direction of measurement. Amplitude is designated as true, magnetic, compass, or grid as the reference direction is true, magnetic, compass, or grid east or west, respectively.
amplitude-modulated indicator
One of two general classes of radar indicators, in which the sweep of the electron beam is deflected vertically or horizontally from a base line to indicate the existence of an echo from a target. The amount of deflection is usually a function of the echo signal strength. Also called deflection-modulated indicator . Compare intensity modulated indicator.
amplitude modulation
1. In general, modulation in which the amplitude of a wave is the characteristic subject to variation.
2. Specifically, in telemetry those systems of modulation in which each component frequency, f, of the transmitted intelligence produces a pair of sideband frequencies at carrier frequency plus f and carrier minus f.
In special cases: (a) the carrier may be suppressed, (b) either the lower or upper sets of sideband frequencies may be suppressed; (c) the lower set of sideband frequencies may be produced by one or more channels of information and the upper set of sideband frequencies may be produced by one or more other channels of information; (d) the carrier may be transmitted without intelligence carrying sideband frequencies.
AMR = Atlantic Missile Range (definition 4)
anacoustic zone
The region above an altitude of about 100 miles where the distance between the air molecules is greater than the wavelength of sound, and sound waves can no longer be propagated.
analog
In computers, pertaining to the use of physical variables such as voltage, distance, rotation, etc. To represent numerical variable as in analog computer, analog output . Compare digital.
analog computer
A computing machine working on the principle of measuring, as distinguished from counting, in which the input data is analogous to a measurement continuum, such as linear lengths, voltages, resistances, etc., which can be manipulated by the computer.
Analog computers range in complexity from a slide rule to electrical computers used for solving mathematical problems.0
analog output
Transducer output in which the amplitude is continuously proportional to a function of the stimulus. Distinguished from digital output .
analog to digital conversion
A process by which a sample of analog information is transformed into a digital code.
analog to digital converter
A device which will convert an analog voltage sample to an equivalent digital code of some finite resolution. Also called digitizer, encoder .
analytical photography
Photography, either motion picture or still, accomplished to determine (by qualitative, quantitative, or any other means) whether a particular phenomenon does or does not occur. See technical photography.
Differs from metric photography in that measurements are not a prime requisite.
AND
In Boolean algebra, the operation of intersection.
And, Andr.
International Astronomical Union abbreviations for Andromeda . See constellation.
AND circuit = AND gate.
AND gate, and gate
A circuit or device used in computers whose output is energized only when every input is in its prescribed state. It performs the logical function of the AND, the Boolean operation of intersection. Also called intersector , AND circuit .
AND-NOT gate = exclusive OR circuit.
Andromeda (abbr And, Andr).
See constellation.
aneroid
A thin, disk-shaped box or capsule, usually metallic, partially evacuated of air and sealed, which expands and contracts with changes in atmospheric or gaseous pressure.
The aneroid is the sensing and actuating element in various meters or gages, such as barometers, altimeters, manifold-pressure gages, etc; it is also the triggering or operating element in various automatic mechanisms. A device similar to an aneroid, but open to outside pressures, such as the capsule in an airspeed indicator, is not commonly called an aneroid .
angel
A radar echo caused by a physical phenomenon not discernible to the eye.
Angels are usually coherent echoes and sometimes of great signal strength (up to 40 decibels above the noise level). They have been ascribed to insects flying through the radar beam, but have also been observed under atmospheric conditions which indicate there must be other causes. Studies indicate that a fair portion of them are caused by strong temperature or moisture gradients, or both, such as might be found near the boundaries of bubbles of especially warm or moist air (see blob). They frequently occur in shallow layers at or near temperature inversions within the lowest few thousand feet of the atmosphere.
angle
The inclination to each other of two intersecting lines, measured by the arc of a circle intercepted between the two lines forming the angle, the center of the circle being the point of intersection.
An acute angle is less than 90°; a right angle 90 °; an obtuse angle, more than 90° but less than 180 °; a straight angle, 180°; a reflex angle, more than 180° but less than 360°; a perigon, 360°. Any angle not a multiple of 90° is an oblique angle. If the sum of two angles is 90°, they are complementary angles; if 180°, supplementary angles; if 360°, explementary angles. Two adjacent angles have a common vertex and lie on opposite sides of a common side. A dihedral angle is the angle between two intersecting planes. A spherical angle is the angle between two intersecting great circles.
angle modulation
Modulation in which the angle of a sine-wave carrier is the characteristic varied from its normal value.
Phase and frequency modulation are particular forms of angle modulation.
angle of arrival
A measure of the direction of propagation of electromagnetic radiation upon arrival at a receiver (most commonly used in radio). It is the angle between the plane of the phase front and some plane of reference, usually the horizontal, at the receiving antenna. This angle is a function of the index of refraction gradient of the medium through which the energy is traveling, and the relative positions of the transmitter and receiver. Compare angle of incidence.
Angles of arrival can be measured for both the direct and reflected components of a wave using a multiple-antenna receiving system called an interferometer .
angle of attack
The angle between a reference line fixed with respect to an airframe and a line in the direction of movement of the body.
angle of climb
The angle between the flight path of a climbing vehicle and the local horizontal.
angle of depression
The angle in a vertical plan between the local horizontal and a descending line. Also called depression angle . See angle of elevation.
angle of descent
The angle between the flightpath of a descending vehicle and the local horizontal.
angle of deviation
The angle through which a ray is bent by refraction.
angle of elevation
The angle in a vertical plane between the local horizontal and an ascending line, as from an observer to an object. Also called elevation angle.
A negative angle of elevation is usually called an angle of depression.
angle of incidence
1. The angle at which a ray of energy impinges upon a surface, usually measured between the direction of propagation of the energy and a perpendicular to the surface at the point of impingement, or incidence. Compare angle of arrival. See also angle of reflection, angle of refraction.
In some cases involving radio waves, the angle of incidence is measured relative to the surface.
2. = angle of attack. (British usage).
angle of minimum deviation
See minimum deviation.
angle of pitch
1. The angle, as seen from the side, between the longitudinal body axis of an aircraft or similar body and a chosen reference line or plane, usually the horizontal plane. This angle is positive when the forward part of the longitudinal axis is directed above the reference line.
2. Same as blade angle (in all senses).
angle of reflection
The angle at which a reflected ray of energy leaves a reflecting surface, measured between the direction of the outgoing ray and a perpendicular to the surface at the point of reflection. Compare angle of incidence.
In some cases involving radio waves, the angle of reflection is measured relative to the surface.
angle of refraction
The angle at which a refracted ray of energy leaves the interface at which the refraction occurred, measured between the direction of the refracted ray and perpendicular to the interface at the point of refraction.
angle of roll
The angle that the lateral body axis of an aircraft or similar body makes with a chosen reference plane in rolling; usually the angle between the lateral axis and a horizontal plane. The angle of roll is considered positive if the roll is to starboard.
angle of yaw
The angle, as seen from above, between the longitudinal body axis of an aircraft, rocket, or the like and a chosen reference direction. This angle is positive when the forward part of the longitudinal axis is directed to starboard. Also called yaw angle .
angstrom(abbr A, Å)
A unit of length, used chiefly in expressing short wavelengths. It equals $10-10meter or 10-8$ centimeters.
Ångström compensation pyrheliometer
An instrument developed by K. Ångström for the measurement of direct solar radiation. The radiation receiver station consists of two identical manganin strips whose temperatures are measured by attached thermocouples. One of the strips is shaded, whereas the other is exposed to sunlight. An electrical heating current is passed through the shaded strip so as to raise its temperature to that of the exposed strip. The electric power required to accomplish this is a measure of the solar radiation. See actinometer, pyrheliometer. Compare Ångström pyrgeometer.
Ångström pyrgeometer
An instrument developed by K. Ångström for measuring the effective terrestrial radiation. It consists of four manganin strips, of which two are blackened and two are polished. The blackened strips are allowed to radiate to the atmosphere while the polished strips are shielded. The electrical power required to equalize the temperature of the four strips is taken as a measure of the outgoing radiation. See actinometer, pyrgeometer. Compare Ångström compensation pyrheliometer.
angular acceleration (symbol )
The rate of change of angular velocity.
angular distance
1. The angular difference between two directions, numerically equal to the angle between two lines extending in the given directions.
2. The arc of the great circle joining two points, expressed in angular units.
3. Distance between two points, expressed in wave lengths at a specified frequency.
It is equal to the number of waves between the points multiplied by if expressed in radians, or multiplied by 360° if measured in degrees.
angular frequency (symbol )
The frequency of a periodic quantity expressed in radians per second. It is equal to the frequency in cycles per second multiplied by . Also called circular frequency .
angular momentum
Quantity of rotational motion.
Linear momentum is the quantity obtained by multiplying the mass of a body by its linear speed. Angular momentum is the quantity obtained by multiplying the moment of inertia of a body by its angular speed. The momentum of a system of particles is given by the sum of the momentums of the individual particles which make up the system or by the product of the total mass of the system and the velocity of the center of gravity of the system. The momentum of a continuous medium is given by the integral of the velocity over the mass of the medium or by the product of the total mass of the medium and the velocity of the center of gravity of the medium.
See momentum
angular rate = angular speed, sense 1
angular resolution
Specifically, the ability of a radar to distinguish between two targets solely by the measurement of angles.
It is generally expressed in terms of the minimum angle by which targets must be spaced to be separately distinguishable. See resolution.
angular speed
1. Change of direction per unit time, as of a target on a radar screen. Also called angular rate .
2. = angular velocity.
angular velocity (symbol )
The change of angle per unit time; specifically, in celestial mechanics, the change in angle of the radius vector per unit time.
anisotropic
Exhibiting different properties when tested along axes in different directions.
annealing
Application of heat energy to a material cooling at a suitable rate to: relieve stresses, change certain properties, improve machinability, etc., or for realignment of atoms in a distorted crystal lattice as caused, for example, by radiation damage.
annual parallax.
See parallax.
annular
Pertaining to an annulus or ring; ring shaped.
annular eclipse
An eclipse in which a thin ring of the source of light appears around the obscuring body.
anode
The positive pole or electrode of any electron emitter, such as an electron tube or an electric cell.
The negative pole or electrode is called a cathode.
anomalistic month
The average period of revolution of the moon from perigee to perigee, a period of 27 days 13 hours 18 minutes 33.2 seconds.
anomalistic period
The interval between two successive perigee passages of a satellite in orbit about a primary. Also called perigee-to-perigee period .
anomalistic year
The period of one revolution of the earth about the sun from perihelion to perihelion; 365 days 6 hours 13 minutes 53.0 seconds in 1900 and increasing at the rate of 0.26 second per century.
anomalous dispersion
Dispersion of electromagnetic radiation characterized by a decrease in refractive index with increase in frequency.
anomalous propagation
The propagation of energy when it arrives at a destination via a path significantly different from the normally expected path.
The term is usually applied to the transmission of various forms of energy through the atmosphere when, in addition to the line-of-sight path, the energy is refracted by density discontinuities at one or more levels in atmosphere. Therefore, it propagates to a point that could not be reached via a line-of-sight path. In radio and radar studies, it refers to the abnormal refraction of a beam of radio energy, usually applied to superstandard propagation rather than to substandard propagation. In either case, anomalous propagation results from an unusual vertical distribution of temperature and moisture in the atmosphere.
The anomalous propagation of sound refers to the downward refraction of an oblique sound wave from an explosion, the refraction occurring in the region of increasing temperature with height in the lower mesosphere. The anomalous propagation of sound has been used as a method for determining upper air temperatures and winds.
anomaly
1. In general, a deviation from the norm.
2. In geodesy, a deviation of an observed value from a theoretical value, due to an abnormality in the observed quantity.
3. In celestial mechanics, the angle between the radius vector to an orbiting body from its primary (the focus of the orbital ellipse) and the line of apsides of the orbit, measured in the direction of travel, from the point of closest approach to the primary (perifocus).
The term defined above is usually called true anomaly v to distinguished it from the eccentric anomaly E which is measured at the center of the orbital ellipse to the projection of the body onto the auxiliary circle of the ellipse, or from the mean anomaly M which is what the true anomaly would become if the orbiting body had a uniform annular motion. The mean anomaly M can be computed by
M = n (t - T)
where n is mean motion; t is time of the computation; and T is time of perifocus. The eccentric anomaly E and the mean anomaly M are related by the Kepler equation
M = E - e sin E
where e is eccentricity of the ellipse. From E, the true anomaly v can be obtained by
$tan v/2=\left[\left(1+e\right)/\left(1-e\right)\right]1/2 tan E/2.$
anoxaemia = hypoxaemia.
anoxia
A complete lack of oxygen available for physiological use within the body. Compare hypoxia.
Anoxia is popularly used as a synonym for hypoxia . This usage should be avoided.
Ant, Antl.
International Astronomical Union abbreviations for Antlia . See constellation.
antapex
See solar apex.
antenna
A conductor or system of conductors for radiating or receiving radio waves.
antenna array
A system of antennas coupled together to obtain directional effects, or to increase sensitivity.
antenna effect
A weakening of the effectiveness of the directional properties of a loop antenna by the capacitance of the loop to the ground. Also called height effect .
In usual direction-finding practice on ground waves, antenna effect would be manifested: (a) if in phase, by an angular displacement of the nulls from 180° displacement and (b), if in quandrature, by a residual signal obscuring the nulls. The in-phase effect is often used to eliminate the 180° ambiguity (i.e., to permit sense finding).
antenna field
A group of antennas placed in a geometric configuration.
antenna gain
See gain, sense 2(a).
antenna null
See null.
antenna pair
Two antennas located on a base line of accurately surveyed length.
antenna temperature
In radio astronomy, a measure of the power absorbed by the antenna. In an ideal, loss-free radio telescope, the antenna temperature is equal to the brightness temperature if the intensity of the received radiation is constant within the main lobe. If the angular dimension of the source is small compared to the main lobe, the antenna temperature is equal to the brightness temperature multiplied by the ratio of the solid angle subtended by the source to the effective solid angle of the antenna.
anticyclonic
Having a sense of rotation about the local vertical opposite to the rotation of the earth; that is, clockwise in the northern hemisphere, counterclockwise in the southern hemisphere, undefined at the equator; the opposite of cyclonic.
antigravity
A hypothetical effect that would arise from cancellation by some energy field of the effect of the central force field of the earth or other body.
Antigravity is common in science fiction but has not yet been reported in scientific literature.
anti-g suit = g-suit.
anti-matter
Matter consisting of anti-particles.
antinode
1. Either of the two points on an orbit where a line in the orbit plane, perpendicular to the line of nodes, and passing through the focus, intersects the orbit.
2. A point, line, or surface in a standing wave where some characteristic of the wave field has maximum amplitude. Also called loop .
In sense 2, the appropriate modifier should be used before the word antinode to signify the type that is intended; e.g., displacement antinode, velocity antinode, pressure antinode.
anti-particle
Any particle with a charge of opposite sign to the same particle in normal matters.
Thus, the proton has a positive charge; the antiproton, a negative charge. When a particle and its anti-particle collide, both may disappear with the creation of lighter particles; this process is called annihilation .
antipode
Anything exactly opposite to something else. Particularly, that point on the earth 180° from a given place.
antiresonance
For a system in forced oscillation, the condition existing at a point when any change, however small, in the frequency of excitation causes an increase in the response at this point.
antisolar point
The point on the celestial sphere 180° from the sun.
Antlia (abbr Ant, Antl.)
See constellation.
apareon
The point on a Mars-centered orbit where a satellite is at its greatest distance from Mars. Apareon is analogous to apogee . See geo.
apastron
That point of the orbit of one member of a binary star system at which the stars are farthest apart. That point at which they are closes together is called periastron .
aperiodic
Without a period; not cyclic; completely damped.
aperture
1. An opening; particularly, that opening in the front of a camera through which light rays pass when a picture is taken.
2. The diameter of the objective of a telescope or other optical instrument, usually expressed in inches, but sometimes as the angle between lines from the principal focus to opposite ends of diameter of the objective.
3. Of a unidirectional antenna, that portion of a plane surface near the antenna, perpendicular to the direction of maximum radiation, through which the major part of the radiation passes. See effective area.
aperture ratio
The ratio of the useful diameter of a lens to its focal length. It is the reciprocal of the f-number.
In application to an optical instrument, rather than to a lens, numerical aperture is more commonly used. The aperture ratio is then twice the tangent of the angle whose sine is the numerical aperture.
apex of the sun's motion = solar apex
apex of the sun's way = solar apex
aphelion
That point in a solar orbit which is most distant from the sun. The point nearest the sun is called perihelion.
apoapsis
That point in an orbit farthest from the center of attraction.
apocenter = apofocus
apocynthion
That point in the orbit of a moon satellite which is farthest from the moon.
apofocus
The point on an elliptic orbit at the greatest distance from the principal focus.
apogee
1. That point in a geocentric orbit which is most distant from the earth. That orbital point nearest the earth is called perigee . See geo.
By extension, apogee and perigee are also used in reference to orbits about other planets and natural satellites.
2. Of a satellite or rocket: To reach its apogee (sense 1), as in the Vanguard apogees at 2,560 miles .
apostilb
A unit of luminance equal to international candles per square centimeter. Compare stilb.
apparent
In astronomy, observed.
True values are reduced from apparent (observed) values by eliminating those factors such as refraction, light time, etc., which affected the observation.
A fictitious mass of fluid added to the mass of the body to represent the force required to accelerate the body through the fluid.
The apparent additional mass has inertia and momentum equal to the apparent increase of the inertia and momentum of the body.
apparent force
A force introduced in a relative coordinate system in order that Newton laws of motion be satisfied in this system. This force must be equal and opposite to an acceleration in an inertial coordinate system, in which Newton laws are (by definition) satisfied. Examples are the coriolis force, and the centrifugal force incorporated in gravity.
apparent gravity = acceleration of gravity.
apparent horizon
See horizon.
apparent motion
Motion relative to a specified or implied reference point which may itself be in motion. Also called relative motion . See relative movement.
In astronomy apparent motion usually refers to movement of celestial bodies as observed from the earth.
apparent position
The position on the celestial sphere at which a heavenly body (or a space vehicle) would be seen from the center of the earth at a particular time. Compare astrometric position.
The apparent position of a body is displaced from the true position at the time of observation by the motion of the body during the time it takes light to travel from the body to the earth (see planetary aberration) and by aberration.
Most ephemerides tabulate apparent position of the sun, moon, and planets.
apparent solar day
The duration of one rotation of the earth on its axis, with respect to the apparent sun. It is measured by successive transits of the apparent sun over the lower branch of a meridian. The length of the apparent solar day is 24 hours of apparent time and averages the length of the mean solar day, but varies somewhat from day to day.
apparent solar time
See solar time.
apparent stresses = Reynolds stresses.
apparent sun
The actual sun as it appears in the sky. Also called true sun . See mean sun, dynamical mean sun.
apparent time
Time based upon the rotation of the earth relative to the apparent or true sun. This is the time shown by a sundial. See equation of time.
Apparent time may be designated as either local or Greenwich, as the local or Greenwich meridian is used as the reference.
apparent wander
Apparent change in the direction of the axis of rotation of a spinning body, as a gyro, due to rotation of the earth. Often shortened to wander . See precession.
The horizontal component of apparent wander is called drift, and the vertical component is called topple .
Appleton layer = F2-layer
See ionosphere.
approximate absolute temperature scale(abbr AA)
A temperature scale with the ice point at 273° and boiling point of water at 373°. It is intended to approximate the Kelvin temperature scale with sufficient accuracy for many sciences, notably meteorology, and is widely used in the meteorological literature. Also called tercentesimal thermometric scale .
appulse
1. The near approach of one celestial body to another on the celestial sphere, as in occultation, conjunction, etc.
2. A penumbral eclipse of the moon.
apron
Specifically, a protective device specially designed to cover an area surrounding the fuel inlet on a rocket or spacecraft.
Aps, Apus
International Astronomical Union abbreviations for Apus . See constellation.
apse = apsis
apsides
Plural of apsis.
apsis (plural apsides)
In celestial mechanics, either of the two orbital points nearest or farthest from the center of attraction. Also called apse . The apsides are the perihelion and aphelion in the case of an orbit about the sun, and the perigee and apogee in the case of an orbit about the earth. The line connecting these two points is called line of apsides . The nearest point is the lower apsis while the farthest point if the higher apsis.
APU (abbr) = auxiliary power unit.
Aql, Aqil.
International Astronomical Union abbreviations for Aquila . See constellation.
Aquarius (abbr Aqr, Aqar).
See constellation.
aqueous vapor = water vapor.
Aquila (abbr Aqr, Aqar)
See constellation.
Ara (abbr Ara, Arae)
See constellation.
Arago point
One of the three commonly detectable points along the vertical circle through the sun at which the degree of polarization of diffuse sky radiation goes to zero; a neutral point.
The Arago point, so named for its discoverer, is customarily located at about 20° above the antisolar point; but it lies at higher altitudes in turbid air. The latter property makes the Arago distance a useful measure of atmospheric turbidity.
arc
1. A part of a curved line, as a circle.
2. A luminous glow which appears when an electric current passes through ionized air or gas.
3. An auroral arc. See aurora. See arc discharge.
arc discharge
A luminous, gaseous, electrical discharge in which the charge transfer occurs continuously along a narrow channel of high ion density. An arc discharge requires a continuous source of electric potential difference across the terminals of the arc.
Arc discharge is to be distinguished from corona discharge, point discharge, and spark discharge.
arc spectrum
The spectrum of a neutral atom, designated by the Roman numeral I following the symbol for the element, and He I. See spark spectrum.
arcs with ray structure
See aurora.
arctic blackout = blackout.
ARDC model atmosphere
See standard atmosphere.
areal velocity
In celestial mechanics, the area swept out by the radius vector per unit time.
The areal velocity is constant for a central force. See Kepler laws.
area rule
A prescribed method of design for obtaining minimum zero-lift drag for a given aerodynamic configuration, such as a wing-body configuration, at a given speed.
For a transonic body, the area rule is applied by subtracting from, or adding to, its cross-sectional area distribution normal to the air stream at various stations so as to make its cross-sectional area distribution approach that of an ideal body of minimum drag; for a supersonic body, the sectional areas are frontal projections of areas intercepted by planes inclined at the Mach angle.
areo
Combining form of Mars (Ares), as in areography.
Words formed with aero are considered pedantic by some. See geo.
areographic
Referring to positions on Mars measured in latitude from Mars' equator and in longitude from a reference meridian.
areography
The study of the surface features of Mars; the geography of Mars.
Ares
Mars.
Ares is seldom used except in combining forms as areocentric, apareon.
Arg
International Astronomical Union abbreviation for Argo . See constellation.
Argo (abbr Arg).
See constellation.
argument
In astronomy, an angle or arc, as in argument of perigee .
argument of latitude
In celestial mechanics, the angular distance measured in the orbit plane from the ascending node to the orbiting object; the sum of the argument of perigee and the true anomaly.
argument of perigee
In celestial mechanics, the angle or arc, as seen from a focus of an elliptical orbit, from the ascending node to the closest approach of the orbiting body to the focus. The angle is measured in the orbital plane in the direction of motion of the orbiting body.
Ari, Arie
International Astronomical Union abbreviations for Aries. See constellation.
Ariel
A satellite of Uranus orbiting at a mean distance of 192,000 kilometers.
Aries (abbr Ari, Arie)
See constellation.
arithmetic element = arithmetic unit.
arithmetic mean
One of several accepted measures of central tendency, physically analogous to center of gravity. Pertaining to a set of numbers $x$1, x2,...xn, the arithmetic mean, usually denoted by the symbol , is the sum x1+x2+...+xn divided by n. Also called mean, average, simple average .
Since the word mean is also applied to other measures of central tendency, such as weighted means, geometric means, harmonic means, the adjective arithmetic is used for clarity. However, when used without further qualification, the term mean is understood as arithmetic mean.
arithmetic unit
That part of a computer which performs arithmetic operations. Also called arithmetic element .
array = antenna array.
arrhythmia
Absence of rhythm, as, for example, in heart beat.
arrow wing
An aircraft wing of V-shaped planform, either tapering or of constant chord, suggesting a stylized arrowhead.
artificial antenna
A device which has the equivalent impedance characteristics of an antenna and the necessary power-handling capabilities, but which does not radiate nor intercept radiofrequency energy. Also called dummy antenna .
artificial asteroid
artificial earth satellite
A manmade earth satellite, as distinguished from the moon.
artificial feel
A control feel simulated by mechanisms incorporated in the control system of an aircraft or spacecraft where the forces acting on the control surfaces are not transmitted to the cockpit controls, as in the case of an irreversible control system or a power boosted system.
artificial gravity
A simulated gravity established within a space vehicle by rotation or acceleration.
artificial horizon
1. A gyro-operated flight instrument that shows the pitching and banking attitudes of an aircraft or spacecraft with respect to a reference line horizon, within limited degrees of movement, by means of the relative position of lines or marks on the face of the instrument representing the aircraft and the horizon. See attitude gyro.
2. A device, such as a spirit level, pendulum, etc., that establishes a horizontal reference in a navigation instrument.
artificial satellite
A-scan = A-display.
ascendent
The negative of the gradient. The ascendent of a function is a vector with magnitude equal to the maximum spatial rate of change of that function at a given point at a given time. It is directed toward increasing values of the function along the line of maximum change, and is represented by , where F is the function and the del-operator.
ascending node
That point at which a planet, planetoid, or comet crosses to the north side of the ecliptic; that point at which a satellite crosses to the north side of the equatorial plane of its primary. Also called northbound node . The opposite is descending node or southbound node .
A-scope = A-display.
asdic
British term for sonar .
aspect ratio
The ratio of the square of the span of an airfoil to the total airfoil area, or the ratio of its span to its mean chord.
An airfoil of high aspect ratio is of relatively long span and short chord; one of low aspect ratio is of relatively short span and long chord.
aspects
The apparent positions of celestrial bodies relative to one another; particularly, the apparent positions of the moon or a planet relative to the sun.
aspiration condenser
An ion counter collecting element consisting of a cylindrical condenser which when charged produces a radial field which collects ions from the aspirated air.
assemble
In computer terminology, to organize the subroutines into a complete program.
assisted take-off
A take-off of an aircraft using a supplementary source of power, usually rockets. See RATO.
associated corpuscular emission
The full complement of secondary charged particles (usually limited to electrons) associated with an X-ray or gamma ray beam in its passage through matter.
The full complement of electrons is obtained after the radiation has traversed sufficient matter to bring about equilibrium between the primary photons and secondary electrons. Electronic equilibrium with the secondary photons is intentionally excluded.
assumed latitude
See latitude.
assumed longitude
See longitude.
A-station
In loran, the designation applied to the transmitting station of a pair, the signal of which always occurs less than half a repetition period after the next preceding signal and more than half a repetition period before the next succeeding signal of the other station of the pair, designated a B-station.
asteroid
One of the many small celestial bodies revolving around the sun, most of the orbits being between those of Mars and Jupiter. Also called planetoid, minor planet . See planet.
The term minor planet is preferred by many astronomers but asteroid continues to be used in astronomical literature, especially attributively, as in asteroid belt.
All asteroids with determined orbits (except for a few discovered during World War II) are numbered for identification in the order of their discovery. The Ephemerides of the Minor Planets published by the U.S.S.R. Academy of Sciences lists all numbered asteroids, data concerning them, and their predicted positions. The daily positions of the first four minor planets are tabulated in the American Ephemeris and Nautical Almanac. Orbits have been determined for approximately 1700 asteroids. Asteroids have names as well as numbers, see Table I. The names are usually feminine but masculine names have been used for asteroids closer to or farther away from the Sun than the majority. The first asteroid to be given a masculine name, Eros (number 443) was the first to be discovered inside the orbit of Mars. The Trojan asteroids, named for heroes of the Trojan war, are in the orbit of Jupiter.
astral dome = astrodome.
astre fictif
A point on the celestial sphere used as a reference in measuring time intervals. See day.
astro
A prefix meaning star or stars and, by extension, sometimes used as the equivalent of celestial , as in astro nautics.
astroballistics
The study of the phenomena arising out of the motion of a solid through a gas at speeds high enough to cause ablation; for example, the interaction of a meteoroid with the atmosphere.
Astroballistics uses the data and methods of astronomy, aerodynamics, ballistics, and physical chemistry.
astrobiology
The study of living organisms on celestial bodies other than the earth.
astrocompass
An instrument used to determine direction by sighting heavenly bodies of known position.
astrodome
A transparent dome in the fuselage or body of an aircraft or spacecraft intended primarily to permit taking celestial observations in navigating. Also called a navigation dome, astral dome .
astrodynamics
The practical application of celestial mechanics, astroballistics, propulsion theory, and allied fields to the problem of planning and directing the trajectories of space vehicles.
Astrodynamics is sometimes used as a synonym for celestial mechanics. This usage should be discouraged.
astrogation
astrographic position = astrometric position.
astrolabe
1. In general, any instrument designed to measure the altitudes of celestial bodies.
2. Specifically, an instrument designed for very accurate celestial altitude measurements, as in survey work.
astrometric position
The position of a heavenly body (or space vehicle) on the celestial sphere corrected for aberration but not for planetary aberration. Compare apparent position.
Astrometric positions are used in photographic observations where the position of the observed body can be measured in reference to the positions of comparison stars in the field of the photograph.
astrometry
The branch of astronomy dealing with geometrical relations of the celestial bodies and their real and apparent motions. The techniques of astrometry, especially the determination of accurate position by photographic means, are used in tracking satellite and space probes.
astronaut
1. A person who rides in a space vehicle.
2. Specifically, one of the test pilots selected to participate in Project Mercury, Project Gemini, Project Apollo, or any other United States program for manned space flight.
astronautic centrifuge
See centrifuge.
astronautics
1. The art, skill, or activity of operating spacecraft.
2. In a broader sense the science of space flight.
The plotting and directing of the movement of a spacecraft from within the craft by means of observations on celestial bodies. Sometimes contracted to astrogation or called celestial navigation .
astron machine
An experimental thermonuclear device where a magnetic filed is generated by a relativistic ring of electrons and shaped into a magnetic mirror configuration. The hot electrons serve as a heat source to heat the ions.
astronomic = astronomical.
In any combination, such as astronomic coordinates, astronomic is equivalent to astronomical.
astronomical
Of or pertaining to astronomy or to observations of the celestial bodies. Also called astronomic .
Astronomers have long preferred astronomical. Geodesists usually use astronomic as an intended parallel to geodetic. The Coast and Geodetic Survey uses astronomic in their publications insofar as is compatible with established practice.
astronomical constants
1. The elements of the orbits of the bodies of the solar system, their masses relative to the sun, their size, shape, orientation, rotation, and inner constitution, and the velocity of light.
2. = system of astronomical constants.
The astronomical constants used in the calculations of The American Ephemeris and Nautical Almanac, as well as other national ephemerides, were adopted at various times between 1896 and 1930. Although the system was known to contain many inconsistencies, the International Astronomical Union recommended their continued use in 1952. Space-related research has provided data for the computation of a more accurate system, and in January 1964 The Working Group on the System of Astronomical Constants recommended a new system of constants to be introduced into the national and international ephemerides at the earliest practicable date. Both the conventional and revised systems are given in Table II. The constants in Table III were recommended for use in trajectory calculations for NASA programs by the Ad Hoc NASA Standards Constants Committee May 16, 1963.
astronomical coordinates
Coordinates defining a point on the surface of the earth, or of the geoid, in which the local direction of gravity is used as a reference. Sometimes called geographic coordinates. See astronomical equator, astronomical latitude, astronomical longitude.
astronomical day
A mean solar day beginning at mean noon, 12 hours later than the beginning of the civil day of the same date. Astronomers now generally use the civil day. See Julian day, astronomical time.
astronomical equator
A line on the surface of the earth connecting points having 0° astronomical latitude. Sometimes called terrestrial equator.
When the astronomical equator is corrected for station error, it becomes the geodetic equator.
astronomical latitude
Angular distance between the direction of gravity and the plane of the celestial equator. Sometimes called geographic latitude .
Astronomical latitude corrected for the meridional component of station error becomes geodetic latitude .
astronomical longitude
The angle between the plane of the reference meridian and the plane of the celestial meridian. Sometimes called geographic longitude .
Astronomical longitude corrected for the prime-vertical component of station error divided by the cosine of the latitude becomes geodetic longitude .
astronomical meridian
A line connecting points having the same astronomical longitude. Also called terrestrial meridian .
Because the deflection of the vertical varies from point to point, the astronomical meridian is an irregular line. When the astronomical meridian is corrected for station error, it becomes the geodetic meridian.
astronomical parallel
A line connecting points having the same astronomical latitude.
Because the deflection of the vertical caries from point to point, the astronomical parallel is an irregular line. When the astronomical parallel is corrected for station error, it becomes the geodetic parallel.
astronomical position
1. A point on the earth whose coordinates have been determined as a result of observation of celestial bodies.
The expression is usually used in connection with position on land determined with great accuracy for survey purposes.
2. A point on the earth, defined in terms of astronomical latitude and longitude.
astronomical refraction
1. The angular difference between the apparent zenith distance of a celestial body and its true zenith distance, produced by refraction effects as the light from the body penetrates the atmosphere. Also called atmospheric refraction, astronomical refraction error. See Bemporad formula.
For bodies near zenith the astronomical refraction is only about 0.1 minute, but for bodies near the horizon it becomes about 30 minutes or more and contributes measurably to the length of the apparent day.
2. Any refraction phenomenon observed in the light originating from a source outside of the earth's atmosphere; as contrasted with terrestrial refraction. This is applied only to refraction caused by inhomogeneities of the atmosphere itself, and not to that caused by ice crystals suspended in the atmosphere.
astronomical refraction error = astronomical refraction, sense 1.
astronomical scintillation
Any scintillation phenomena, such as irregular oscillatory motion, variation of intensity, and color fluctuation observed in the light emanating from am extraterrestrial source; to be distinguished from terrestrial scintillation primarily in that the light source for the latter lies somewhere within the earth's atmosphere. Also called stellar scintillation . See seeing.
Astronomical scintillation is typically strongest for celestial objects lying at large zenith distances and is not easily observed by eye for objects whose zenith distances are under 30°. Nonperiodic vibratory motions of stellar images with frequencies of the order of 1 to 10 cycles per second create a troublesome problem of seeing in astronomical work. The size of the schlieren producing vibratory scintillations has been estimated to be of the order of centimeters, and chromatic scintillations of celestial objects appear to be produced by parcels whose dimensions are of the order of decimeters or, perhaps, meters. Hence, astronomical scintillation is primarily a consequence of the high-frequency, short-wavelength type of atmospheric turbulence.
astronomical seeing
See seeing.
astronomical solar time
See solar time.
astronomical time
Mean time reckoned from the upper branch of the meridian. See astronomical day.
astronomical triangle
The navigational triangle, either terrestrial or celestial, used in the solution of celestial observations.
astronomical twilight
See twilight.
astronomical unit (abbr AU)
1. A unit of length, usually defined as the distance from the earth to the sun, 149,599,000 kilometers.
This value for the AU was derived from radar observations of the distance of Venus. The value given in astronomical ephemerides, 149,500,000 kilometers, was derived from observations of the minor planet Eros.
2. The unit of distance in terms of which, in the Kepler Third Law,$n2a3= k2\left(1+m\right)$, the semimajor axis a of an elliptical orbit must be expressed in order that the numerical value of the Gaussian constant k may be exactly 0.01720209895 when the unit of time is the ephemeris day.
In astronomical units, the mean distance of the earth from the sun, calculated by the Kepler law from the observed mean motion n and adopted mass m, is 1.00000003.
astronomical year= tropical year.
astronomy
The science concerning the location, magnitudes, motions, and constitution of celestial bodies and structures.
astrophysics
A branch of astronomy concerning the physical properties of celestial bodies, such as luminosity, size, mass, density, temperature, and chemical composition.
astrotracker = star tracker.
asynchronous computer
An automatic computer in which succeeding operations are started by signals indicating the completion of the previous operation, rather than by signals from a master synchronizer. Contrast to synchronous computer. See variable cycle.
atelectasis
Collapsed or airless state of all or part of a lung. Also called apneumatosis .
athodyd
A type of jet engine consisting essentially of a duct or tube of varying diameter and open at both ends, which admits air at one end, compresses it by the forward motion of the engine, adds heat to it by the combustion of fuel, and discharges the resulting gases at the other end to produce thrust.
The ramjet is an athodyd; the pulsejet, especially the earlier type, is usually not considered an athodyd.
atmosphere
1. The envelope of air surrounding the earth; also the body of gases surrounding or comprising any planet or other celestial body. Compare biosphere, geosphere, hydrosphere, lithosphere. See atmospheric shell.
2. = standard atmosphere.
3. (abbr atm) A unit of pressure equal to 14.7 pounds per square inch.
atmospheric boil = terrestrial scintillation.
atmospheric boundary layer = planetary boundary layer.
atmospheric braking
The action of slowing down an object entering the atmosphere of the earth or other planet from space, by using the drag exerted by air or other gas particles in the atmosphere; the action of the drag so exerted.
atmospheric duct
An almost horizontal layer in the troposphere, extending from the level of a local minimum of the modified refractive index as a function of height, down to the level where the minimum value is again encountered, or down to earth's surface if the minimum value is not encountered again.
atmospheric electric field
1. The electric field strength of the atmosphere at any specified point in space and time.
2. The distribution of electrical potential in the atmosphere regarded merely from a geometric point of view as a typical scalar field (rarely used).
atmospheric electricity
1. Electrical phenomena, regarded collectively, which occur in the earth's atmosphere.
2. The study of electrical processes occurring within the atmosphere.
atmospheric entry
The penetration of any planetary atmosphere by any object from outer space; specifically, the penetration of the earth's atmosphere by a manned or unmanned capsule or spacecraft.
atmospheric interference = atmospherics.
atmospheric ion
See ion.
atmospheric layer = atmospheric shell.
atmospheric noise = atmospherics.
atmospheric optics
The study of the optical characteristics of the atmosphere and of the optical phenomena produced by the atmosphere's suspensoids and hydrometeors. It embraces the study of refraction, reflection, diffraction, scattering, and polarization of light, but is not commonly regarded as including the study of any other kinds of radiation. Also called meteorological optics.
atmospheric oscillation = atmospheric tide.
atmospheric physics = physical meteorology.
atmospheric pressure
The pressure at any point in an atmosphere due solely to the weight of the atmospheric gases above the point concerned. See station pressure, sea-level pressure.
Infrared radiation emitted by or being propagated through the atmosphere. See insolation.
Atmospheric radiation, lying almost entirely within the wavelength interval of from 3 to 80 microns, provides one of the most important mechanisms by which the heat balance of the earth-atmosphere system is maintained. Infrared radiation emitted by the earth's surface (terrestrial radiation) is partially absorbed by the water vapor of the atmosphere which in turn remits it, partly upward, partly downward. This secondarily emitted radiation is then, in general, repeatedly absorbed and reemitted, as the radiant energy progresses through the atmosphere. The downward flux, or counterradiation, is of basic importance in the greenhouse effect; the upward flux is essential to the radiative balance of the planet.
atmospheric region = atmospheric shell.
atmospheric refraction
Refraction resulting when a ray of radiant energy passes obliquely through an atmosphere.
It may be called "astronomical refraction" if the ray enters the atmosphere from outer space, or "terrestrial refraction" if it emanates from a point on or near the surface of the earth.
atmospherics
The radiofrequency electromagnetic radiation originating, principally, in the irregular surges of charge in thunderstorm lightning discharges. Atmospherics are heard as a quasi-steady background or crackling noise (static) in ordinary amplitude-modulated radio receivers. Also called atmospheric interference, strays, sferics . See sferics.
Since any acceleration of electric charge leads to emission of electromagnetic radiation, and since the several processes involved in propagation of lightning lead to very large charge accelerations, the lightning channel acts like a huge transmitter, sending out broad band radiation; the 10-kilocycle range propagates best and is used in detecting atmospherics. Atmospherics may occasionally be detected at distances in excess of 2000 miles from their source. Advantage has been taken of this in using radio direction-finding equipment to locate active thunderstorm areas in remote regions and in between weather reporting stations.
atmospheric scintillation = terrestrial scintillation.
atmospheric shell
Any one of a number of strata or layers of the earth's atmosphere. Also called atmospheric layer, atmospheric region .
Temperature distribution is the most common criterion used for denoting the various shells. The troposphere (the region of change) is the lowest 10 or 20 kilometers of the atmosphere, characterized by decreasing temperature with height. The top of the troposphere is called the tropopause. Above the tropopause, the stratosphere, a region in which the temperature generally increases with altitude, extends to the stratopause, the top of the inversion layer, at about 50 to 55 kilometers. Above the stratosphere, the mesosphere, a region of generally decreasing temperatures with height extends to the mesopause, the base of an inversion layer at about 80 to 85 kilometers. The region above the mesopause, in which temperature generally increases with height, is the thermosphere.
The distribution of various physicochemical processes is another criterion. The ozonosphere, lying roughly between 10 and 50 kilometers, is the general region of the upper atmosphere in which there is an appreciable ozone concentration and in which ozone plays an important part in the radiative balance of the atmosphere; the ionosphere, starting at about 70 or 80 kilometers, is the region in which ionization of one or more of the atmospheric constituents is significant; the neutrosphere is the shell below this which is, by contrast, relatively unionized; and the chemosphere, with no very definite height limits, is the region in which photochemical reactions take place.
Dynamic and kinetic processes are a third criterion. The exosphere is the region at the top of the atmosphere, above the critical level of escape, in which atmospheric particles can move in free orbits, subject only to the earth's gravitation.
Composition is a fourth criterion. The homosphere is the shell in which there is so little photodissociation or gravitational separation that the mean molecular weight of the atmosphere is sensibly constant; the heterosphere is the region above this, where the atmospheric composition and mean molecular weight are not constant. The boundary between the two is probably at the level at which molecular oxygen begins to be dissociated, and this occurs in the vicinity of 80 or 90 kilometers.
The term mesosphere has been given another definition which does not fit into any logical set of criteria, i.e., the shell between the exosphere and the ionosphere. This use of mesosphere has not been widely accepted.
For further subdivisions, see ionosphere, troposphere, geocorona.
atmospheric shimmer = terrestrial scintillation.
atmospheric tide
Defined in analogy to the oceanic tide as an atmospheric motion on a worldwide scale, in which vertical accelerations are neglected (but compressibility is taken into account). Also called atmospheric oscillation .
Both the sun and moon produce atmospheric tides; and there exist both gravitational tides and thermal tides. The harmonic component of greatest amplitude, the 12-hour or semidiurnal solar atmospheric tide, is both gravitational and thermal in origin, the fact that it is greater than the corresponding lunar atmospheric tide being ascribed usually to a resonance in the atmosphere with a free period very close to the tidal period. Other tides of 6, 8, and 24 hours have been observed.
atmospheric transmissivity
See transmission coefficient.
atomic clock
A timekeeping device controlled by the frequency of the natural vibrations of certain atoms.
atomic mass
The mass of a neutral atom of a nuclide usually expressed in atomic mass units. See atomic weight, mass number.
The atomic mass unit, amu, is exactly one-twelfth of the mass of a neutral atom of the most abundant isotope of carbon, C12=12.0000.
atomic mass unit (abbr amu)
See atomic mass, note.
atomic number (symbol Z)
An integer that expresses the positive charge of the nucleus in multiples of the electronic charge e. It is the number of electrons outside the nucleus of a neutral (un-ionized) atom and, according to widely accepted theory, the number of protons in the nucleus. See atomic weight, Table IV.
An element of atomic number Z occupies the Zth place in the periodic table of the elements. Its atom has a nucleus with a charge +Ze, which is normally surrounded by Z electrons, each of charge -e.
For example, the carbon isotope 6C14 has an atomic number of 6 and an atomic mass of 14.
atomic particle
One of the particles of which an atom is constituted, as an electron, neutron, or a positively charged nuclear particle.
atomic rocket
A projected rocket engine in which the energy for the jetstream is to be generated by atomic fission or fusion.
atomic weight (abbr at. wt.)
The weight of an atom according to a scale of atomic weight units, awu, valued as one-twelfth the mass of the carbon atom ($C12$ = 12.00000). See Table IV.
Thus expressed, the atomic weight to the nearest integer is identical with the mass number.
atomic weight unit (abbr awu)
See atomic weight, note.
A-trace
The first trace of an oscilloscope, as the upper trace of a loran indicator.
attached shock = attached shock wave.
attached shock wave
An oblique or conical shock wave that appears to be in contact with the leading edge of an airfoil or the nose of a body in a supersonic flow field. Also called attached shock.
attachment
The process in which two particles collide and stick together forming a single complex particle. The most common attachment process is the formation of a negative ion from electron attachment to an atom or molecule. Some negative ions are unstable, however, and cannot survive.
The usual measure for this process is the attachment coefficient, which on the average is the fraction of a large number of collisions that result in attachment. Typical values of this fraction run from 1 in 10,000 to 1 in 1,000.
attachment coefficient
See attachment, note.
attenuation
Reduction in intensity.
attenuation coefficient (symbol )
A measure of the space rate of attenuation of any transmitted electromagnetic radiation. The attenuation coefficient is defined by
$dI = -aI$0dx
or
I = I0e-ax
where I is the flux density at the selected point in space; $I$0 is the flux density at the source; x is the distance from the source; and a is the attenuation coefficient.
In general, the attenuation coefficient is specified only when the attenuation is known to be due to both absorption and scattering, or when it is impossible to determine which is the cause. See absorption coefficient, scattering coefficient.
attenuation constant
1. A measure of the rate of attenuation per unit length; the rate of flux-density (or power) reduction as energy (visual, electromagnetic, acoustic) propagates from its source. Also called attenuation factor, decay constant . Compare attenuation coefficient.
For free-space transmission of radar frequency energy, the attenuation constant is usually expressed in decibels per mile or kilometer (db/mi or db/km).
2. Specifically, of a traveling plane wave at a given frequency, the relative rate of decrease of amplitude of a field component (or of voltage or current) in direction of propagation in nepers per unit length.
attenuation factor = attenuation constant.
attenuation length
The reciprocal of the attenuation coefficient.
attenuation ratio
The magnitude of the propagation ratio.
attitude
The position or orientation of an aircraft, spacecraft, etc., either in motion or at rest, as determined by the relationship between its axes and some reference line or plane or some fixed system of reference axes.
attitude control
1. The regulation of the attitude of an aircraft, spacecraft, etc.
2. A device or system that automatically regulates and corrects attitude, especially of a pilotless vehicle.
attitude gyro
1. A gyro-operated flight instrument that indicates the attitude of an aircraft or spacecraft with respect to a reference coordinate system throughout 360° of rotation about each axis of the craft.
This instrument is similar to the artificial horizon, but has greater angular indication.
2. Broadly, any gyro-operated instrument that indicates attitude.
attitude jet
A jetstream used to correct or alter the attitude of a flying body either in the atmosphere or in space; the nozzle that directs this jetstream.
The jet may be continuous or intermittent. A vernier engine is sometimes used to produce it.
attribute
A characteristic of a thing which can be appraised only in terms of whether it does or does not exist. See method of attributes.
attributes testing
A reliability test procedure where the items under test are classified according to qualitative rather than quantitative characteristics.
AU (abbr) = astronomical unit.
audible sound
Sound containing frequency components lying between about 15 and 20,000 cycles per second.
audio
Pertaining to the audiofrequency range.
The word audio may be used as a modifier to indicate a device or system intended to operate at audiofrequencies, e.g., audioamplifier.
audio frequency
Any frequency corresponding to a normally audible sound wave. See audiofrequency range.
audio frequency range
The range of frequencies to which the human ear is sensitive, approximately 15 cycles per second to 20,000 cycles per second. Also called audiorange.
audiorange = audio frequency range.
auditory sensation area
In acoustics, the frequency region enclosed by the curves defining the threshold of pain and the threshold of audibility.
Auger shower
A very large cosmic-ray shower. Also called extensive air shower .
augmentation
The apparent increase in the semidiameter of a celestial body, as observed from the earth, as its altitude increases, due to reduced distance from the observer.
The term is used principally in reference to the moon.
augmentation correction
A correction due to augmentation, particularly that sextant altitude correction due to the apparent increase in the semidiameter of a celestial body as its altitude increases.
augmenter tube
A tube or pipe, usually one of several, through which the exhaust gases from an aircraft reciprocating engine are directed especially to provide additional thrust.
Aur, Auri
International Astronomical Union abbreviations for Auriga . See constellation.
aural null
See null.
Auriga (abbr Aur, Auri)
See constellation.
aurora
The sporadic radiant emission from the upper atmosphere over middle and high latitudes. It is believed to be due primarily to the emission from nitrogen - atomic N I and N II, molecular, N2, and ionic N2+; atomic oxygen (O I and O II); atomic sodium (Na I); the hydroxyl radical (OH); and hydrogen. Compare airglow.
According to various theories, auroras seem definitely to be related to magnetic storms and the influx of charged particles from the sun. The exact details of the nature of the mechanisms involved are still being investigated, but release of trapped particles from Van Allen belt apparently plays an important part. The aurora is most intense at times of magnetic storms (when it is also observed farthest equatorward), and shows a periodicity which is related to the sun's 27-day rotation period and the 11-year sunspot cycle. The distribution with height shows a pronounced maximum near 100 kilometers. The lower limit is probably near 80 kilometers.
The aurora can often be clearly seen, and it assumes a variety of shapes and colors which are characteristic patterns of auroral emission.
The following is the general classification and abbreviations of the forms of the auroras adopted by the International Union of Geodesy and Geophysics in 1930 for reporting of visual observations. The classification was modified slightly and expanded in 1963. The new classification is described in the
International Auroral Atlas , Aldine Pub. Co., Chicago, 1963.
I. Forms without ray structure:
HA (abbr for homogeneous quiet area). These can appear near the horizon, and between the arc and the horizon a dark segment is often seen. These arcs can be narrow or broad, and are very often diffuse along the upper border but sharp along the lower one.
HB (abbr for homogeneous bands). These forms do not have the regular shape of the arcs; they are more rapidly moving phenomena. The lower border is often irregular and sharp. The breadth can vary from a very narrow band to a band which is so large that it resembles a curtain hanging down. These bands very often turn into bands with ray structure.
PA (abbr for pulsating arcs). Parts of an arc flash up and disappear regularly within a period of about 20 seconds. This form quite often stands isolated in the sky without other auroras.
DS (abbr for diffuse luminous surfaces). These either appear like a diffuse veil or glow over great parts of the heavens without distinct boundaries, often appearing after intense displays of rays and curtains, or as more isolated feeble luminous streaks which sometimes bear a striking resemblance to clouds. Sometimes large areas of the heavens can be discolored by a green, violet, or red diffuse light.
PS (abbr for pulsating surfaces). Diffuse patches appear and disappear rhythmically at the same place, retaining the same irregular shape, When the patches are lying near the magnetic zenith the contours can be more sharp, and form a sort of corona. These forms appear often in connection with flaming auroras.
G (abbr for feeble glow near the horizon resembling the dawn). Of white or redlike color, this form is often the upper part of an arc whose lower border is below the horizon.
II. Forms with ray structure: These forms consist of short or long rays which can be arranged in different ways.
RA (abbr for arcs with ray structure). A homogeneous arc which has remained quiet and unaltered for a rather long time may become sharp and luminous along the lower border and they very rapidly change into an arc of rays. The rays can be short or long.
RBI (abbr for bands with ray structure). These resemble the bands mentioned under HB but are constituted of a series of rays which are arranged close to each other along the band, or they can appear more scattered. Often a series of parallel bands appear. When a band is near the magnetic zenith is may have the form of a corona.
D (abbr for draperies). If the ray become very long the band appears like a curtain or drapery whose lower border is often more luminous. Several parallel curtains frequently appear at the same time. Near the zenith the curtain may have a fanlike form on account of the perspective.
R (abbr for rays). The rays can be isolated, narrow or broad, short or long. They may appear in great segments or like masses or rays, very often resembling curtains.
C (abbr for corona). When the rays approach the magnetic zenith they seem, on account of the perspective, to converge to this point and form a corona. This may be formed by long rays or by short ones, it may be completed or incomplete. A corona can also be formed by bands, draperies, or more diffuse forms near the magnetic zenith.
III. Flaming auroras (abbr F). A characteristic, rapidly moving form, consisting of strong waves of light which move upwards, one after the other, in the direction of the magnetic zenith. The waves have the form of detached arcs which move upwards normally to the direction of the arc; they can be compared to invisible waves illuminating broad rays and patches which appear and disappear rhythmically when the waves pass them. The flaming aurora frequently appears after strong displays of rays and curtains and is often followed by the formation of a corona.
aurora australis
The aurora of the Southern Hemisphere.
aurora borealis
The aurora of northern latitudes. Also called aurora polaris, northern lights .
auroral zone
A roughly circular band around either geomagnetic pole above which there is a maximum of auroral activity. It lies about 10 to 15° of geomagnetic latitude from the geomagentic poles.
The auroral zone broadens and extends equatorward during intense auroral displays. The northern auroral zone is centered along a line passing near Point Barrow, Alaska, through the lower half of Hudson Bay, slightly off the southern tip of Greenland, through Iceland, northern Norway and northern Siberia. Along this line auroras are seen on an average of 240 nights a year. The frequency of auroras falls off both to the north and to the south of this line but more rapidly to the south. The most severe blackouts occur in the auroral zone.
aurora polaris = aurora borealis.
austausch coefficient = exchange coefficient.
australite
See tektite.
authorized carrier frequency
A specific carrier frequency authorized for use, from which the actual carrier frequency is permitted to deviate, solely because of frequency instability, by an amount not to exceed the frequency tolerance.
autoconvection gradient = autoconvective lapse rate.
autoconvective lapse rate
The environmental lapse rate of temperature in an atmosphere in which the density is constant with height (homogenous atmosphere), equal to g/R, where g is the acceleration of gravity and R the gas constant. For dry air the autoconvective lapse rate is approximately $+3.4 x 10-4$°C per centimeter. Also called autoconvection gradient.
autocorrelation
In statistics the simple linear internal correlation of members of a time series (ordered in time or other domains).
autocorrelation function
Autocorrelation for variable lag.
autoigniting propellant
Any propellant that ignites by itself without external stimulation.
autoignition temperature
The temperature at which combustible materials ignite spontaneously in air.
autokinetic illusion
The illusion of a fixed object or light moving when gazed at steadily.
automatic celestial navigation = celestial guidance.
automatic computer
A computer which can automatically perform a comprehensive sequence of operations.
automatic control
Control of devices and equipment, including aerospace vehicles, by automatic means.
automatic data processing system
An electronic system that includes an electronic data processing system plus auxiliary and connecting communications equipment.
A radio direction finder which automatically and continuously provides a measure of the direction of arrival of the received signal. Data are usually displayed visually.
automatic frequency control (abbr AFC)
An arrangement whereby the frequency of an oscillator is automatically maintained within specified limits.
automatic gain control (abbr AGC)
A process by which gain is automatically adjusted as a function of input or other specified parameter.
automatic pilot
Equipment which automatically stabilizes the attitude of a vehicle about its pitch, roll, and yaw axes. Also called autopilot .
automatic stability
Stability achieved with the controls operated by automatic devices, as by an automatic pilot.
automatic tracking
Tracking in which a servomechanism automatically follows some characteristic of the signal; specifically, a process by which tracking or data acquisition systems are enabled to keep their antennas continually directed at a moving target without manual operation.
autopilot= automatic pilot.
autosyn
(A trade name, from autosynchronous, often capitalized). A remote-indicating instrument or system based upon the synchronous-motor principle, in which the angular position of the rotor of one motor at the measuring source is duplicated by the rotor of the indicator motor, used, e.g., in fuel-quantity or fuel-flow measuring systems, position-indicating systems, etc.
autosynchronous
Full term of autosyn .
autumnal equinox
1. That point of intersection on the celestial sphere of the ecliptic and the celestial equator occupied by the sun as it changes from north to south declination, on or about September 23. Also called September equinox, first point of Libra .
2. That instant the sun reaches the point of zero declination when crossing the celestial equator from north to south.
auxiliary circle
In celestial mechanics, a circumscribing circle to an orbital ellipse with a radius a, the semimajor axis. The auxiliary circle is related to the ellipse by
$QN = Q\text{'}N\left(1 - e2\right)1/2$
where e is the eccentricity; Q is any point on the ellipse; N is the foot of the perpendicular through Q to the line of apsides; and Q' is the intersection of the perpendicular and the auxiliary circle.
auxiliary fluid ignition
A method of ignition of a liquid-propellant rocket engine in which a liquid which is hypergolic with either the fuel or the oxidizer is injected into the combustion chamber to initiate combustion.
Aniline is used as an auxiliary fluid with nitric acid and some organic fuels to initiate combustion.
auxiliary landing gear
That part or parts of a landing gear, as an outboard wheel, which is intended to stabilize the craft on the surface but which bears no significant part of the weight.
auxiliary power unit (abbr APU)
A power unit carried on an aircraft or spacecraft which can be used in addition to the main sources of power of the craft.
avalanche
The cumulative process in which charged particles accelerated by an electric field produce additional charged particles through collision with natural gas molecules or atoms. See Townsend ionization coefficient.
average = arithmetic mean.
average deviation
In statistics, the average or arithmetic mean of the deviations, taken without regard to sign, from some fixed value, usually the arithmetic mean of the data. Also called mean deviation . See standard deviation.
average information content
The average of the information content per symbol emitted from a source. Also called entropy and negentropy .
aviation medicine
See aerospace medicine.
Avogadro number, Avogadro constant (symbol $N$A)
The number of molecules in 1 mole of gas ($6.02252 X 1023$ per mole).
That this number is a constant for permanent gases is the Avogadro law: under normal conditions, i.e., pressure of 1 standard atmosphere and temperature of 0° C, the volume occupied by 1 mole of gas is the same for all permanent gases (22,414 cubic centimeters). See Loschmidt number.
axial flow compressor
A rotary compressor having interdigitated rows or stages of rotary and of stationary blades through which the flow of fluid is substantially parallel to the rotor's axis of rotation. Compare centrifugal compressor.
axis (plural axes)
1. A straight line about which a body rotates, or along which its center of gravity moves (axis of translation).
2. A straight line around which a plane figure may rotate to produce a solid; a line of symmetry.
3. One of a set of reference lines for a coordinate system.
axis of freedom
Of a gyro, an axis about which a gimbal provides a degree of freedom.
axis of thrust = thrust axis.
azimuth
1. Horizontal direction or bearing. Compare azimuth angle.
2. In navigation, the horizontal direction of a celestial point from a terrestrial point, expressed as the angular distance from a reference direction, usually measured from 0° at the reference direction clockwise through 360°.
An azimuth is often designated as true, magnetic, compass, grid, or relative as the reference direction is true, magnetic, compass, grid north, or heading, respectively. Unless otherwise specified, the term is generally understood to apply to true azimuth, which may be further defined as the arc of the horizon, or the angle at the zenith, between the north part of the celestial meridian or principal vertical circle and a vertical circle, measured from 0° at the north part of the principal vertical circle clockwise through 360°.
3. In astronomy, the direction of a celestial point from a terrestrial point measured clockwise from the north or the south point of the meridian plane. See horizon system.
4. In surveying, the horizontal direction of an object measured clockwise from the south point of the meridian plane.
In surveying, an azimuth of a celestial body is called an astronomic azimuth.
azimuth angle
1. Azimuth measured from 0° at the north or south reference direction clockwise or counterclockwise through 90° or 180°.
Azimuth angle is labeled with the reference direction as a prefix and the direction of measurement from the reference direction as a suffix. Thus, azimuth angle S 144° W is 144° west of south, or azimuth 324°. When azimuth angle is measured through 180°, it is labeled N or S to agree with the latitude and E or W to agree with the meridian angle.
2. In surveying, an angle in triangulation or in traverse through which the computation of azimuth is carried.
azimuth error
An error in the indicated azimuth of a target detected by radar, resulting from horizontal refraction. Compare range error.
Inasmush as significant gradients of index of refraction are very uncommon in the atmosphere, these errors almost invariably are negligible. Seacoast areas may give rise on occasion to appreciable horizontal bending of radio waves because of the contrast of refractive index values between the air over land and the air over water.
azimuth marker
1. A scale encircling the plan position indicator (PPI) scope of a radar on which the azimuth of a target from the radar may be measured.
2. Reference limits inserted electronically at 10° or 15° intervals which extend radially from the relative position of the radar on an off center PPI scope. These are employed for target azimuth determination when the radar position is not at the center of the PPI scope and hence the fixed azimuth scale on the edge of the scope cannot be employed.
On such markers north is usually 0°, east 90°, etc. Occasionally, on ship or airborne radars, 0° is used to indicate the direction in which the craft is heading, in which cases the relative bearing, not azimuth, of the target is indicated.
azran
Azimuth and range.
This term was coined in the field of radar, and has since been extended in application to the locating of any object (or target) by means of polar coordinates.
Azusa
A short-baseline, continuous wave, phase comparison, single-station, tracking system operating at C-band and giving two direction cosines and slant range which can be used to determine space position and velocity.
| 2017-04-26T13:38:37 |
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|
http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc552.htm
|
2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.5. Propagation of error considerations
## Formulas for functions of two variables
Case: Y=f(X,Z) Standard deviations of reported values that are functions of measurements on two variables are reproduced from a paper by H. Ku (Ku).
The reported value, Y is a function of averages of N measurements on two variables.
Function $$Y$$ of $$\bar{X}$$ , $$\bar{Z}$$ $$\bar{X}$$ and $$\bar{Z}$$ are averages of $$N$$ measurements Standard deviation of $$Y$$ $$s_x$$ = standard deviation of $$X$$ $$s_z$$ = standard deviation of $$Z$$ $$s_{xz}^2$$ = covariance of $$X,Z$$ Note: Covariance term is to be included only if there is a reliable estimate $$\large{ Y = A \bar{X} + B \bar{Z} }$$ $$\large{ \frac{1}{\sqrt{N}} \sqrt{A^2 s_x^2 + B^2 s_z^2 + 2AB s_{xz}^2} }$$ $$\large{ Y = \frac{\bar{X}}{\bar{Z}} }$$ $$\large{ \frac{1}{\sqrt{N}} \frac{\bar{X}}{\bar{Z}} \sqrt{\frac{s_x^2}{(\bar{X})^2} + \frac{s_z^2}{(\bar{Z})^2} - 2\frac{s_{xz}^2}{\bar{X} \bar{Z}}} }$$ $$\large{ Y = \frac{\bar{X}}{\bar{X} + \bar{Z}} }$$ $$\large{ \left( \frac{Y}{\bar{X}}\right)^2 \frac{1}{\sqrt{N}} \sqrt{(\bar{X})^2 s_z^2 + (\bar{Z})^2 s_x^2 - 2 \bar{X} \bar{Z} s_{xz}^2}}$$ $$\large{ Y = \bar{X} \bar{Z} }$$ $$\large{ \frac{\bar{X} \bar{Z}}{\sqrt{N}} \sqrt{\frac{s_x^2}{\bar{X}^2} + \frac{s_z^2}{\bar{Z}^2} + 2 \frac{s_{xz}^2}{\bar{X} \bar{Z}} } }$$ $$\large{ Y = c(\bar{X})^a (\bar{Z})^b }$$ $$\large{ \frac{Y}{\sqrt{N}} \sqrt{ a^2 \frac{s_x^2}{\bar{X}^2} + b^2 \frac{s_z^2}{\bar{Z}^2} + 2ab \frac{s_{xz}^2}{\bar{X} \bar{Z}} } }$$ Note: this is an approximation. The exact result could be obtained starting from the exact formula for the standard deviation of a product derived by Goodman (1960).
| 2015-07-30T06:05:01 |
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|
https://par.nsf.gov/biblio/10008417-topological-phase-transitions-driven-magnetic-phase-transitions-fexbi2te3-single-crystals
|
Topological Phase Transitions Driven by Magnetic Phase Transitions in $FexBi2Te3$ ( $0≤x≤0.1$ ) Single Crystals
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10008417
Journal Name:
Physical Review Letters
Volume:
110
Issue:
13
ISSN:
0031-9007
Publisher:
American Physical Society
| 2022-11-26T15:40:11 |
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|
https://indico.fnal.gov/event/19348/contributions/186602/
|
Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
# Neutrino 2020
June 22, 2020 to July 2, 2020
US/Central timezone
## Forecast on lepton asymmetry from future CMB experiments
Not scheduled
10m
Poster
### Speaker
Mr Alexander Bonilla Rivera (UFJF)
### Description
We consider a cosmological lepton asymmetry in the form of neutrinos and impose new expected sensitivities on such asymmetry through the degeneracy parameter ($\xi_{\nu}$) by using some future CMB experiment configurations, such as CORE and CMB-S4. Taking the default scenario with three neutrino states, we find $\xi _{\mu } = 0.05 \pm 0.10 \, (\pm \, 0.04)$, from CORE (CMB-S4) at 95 per cent CL, respectively. Also, within this scenario, we evaluate the neutrino mass scale, obtaining that the normal hierarchy mass scheme is privileged. Our results are an update concerning on the cosmological lepton asymmetry and the neutrino mass scale within this context, from which can bring a perspective on the null hypothesis for $\xi_{\nu}$ (and its effects on $\Delta N_{eff}$), where perhaps, $\xi_{\nu}$ may take a non-null value up to 95 per cent CL from future experiments such as CMB-S4.
### Mini-abstract
Our results are an update concerning on the cosmological lepton asymmetry and the neutrino mass.
### Presentation Materials
poster de models.pdf Video_Nv_2020.mov
| 2021-11-27T18:09:33 |
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|
http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc32.htm
|
2. Measurement Process Characterization
2.3. Calibration
## What is artifact (single-point) calibration?
Purpose Artifact calibration is a measurement process that assigns values to the property of an artifact relative to a reference standard(s). The purpose of calibration is to eliminate or reduce bias in the user's measurement system relative to the reference base.
The calibration procedure compares an "unknown" or test item(s) with a reference standard(s) of the same nominal value (hence, the term single-point calibration) according to a specific algorithm called a calibration design.
Assumptions The calibration procedure is based on the assumption that individual readings on test items and reference standards are subject to:
• Bias that is a function of the measuring system or instrument
• Random error that may be uncontrollable
What is bias? The operational definition of bias is that it is the difference between values that would be assigned to an artifact by the client laboratory and the laboratory maintaining the reference standards. Values, in this sense, are understood to be the long-term averages that would be achieved in both laboratories.
Calibration model for eliminating bias requires a reference standard that is very close in value to the test item One approach to eliminating bias is to select a reference standard that is almost identical to the test item; measure the two artifacts with a comparator type of instrument; and take the difference of the two measurements to cancel the bias. The only requirement on the instrument is that it be linear over the small range needed for the two artifacts.
The test item has value X*, as yet to be assigned, and the reference standard has an assigned value R*. Given a measurement, X, on the test item and a measurement, R, on the reference standard, \begin{eqnarray} X = Bias + X^* + error_1 \\ R = Bias + R^* + error_2 \end{eqnarray} the difference between the test item and the reference is estimated by $$D = X - R \, ,$$ and the value of the test item is reported as $$\widehat{Test} = X^* = D + R^* \, .$$
Need for redundancy leads to calibration designs A deficiency in relying on a single difference to estimate D is that there is no way of assessing the effect of random errors. The obvious solution is to:
• Repeat the calibration measurements J times
• Average the results
• Compute a standard deviation from the J results
Schedules of redundant intercomparisons involving measurements on several reference standards and test items in a connected sequence are called calibration designs and are discussed in later sections.
| 2017-10-22T17:04:22 |
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|
https://huggingface.co/cl-tohoku/bert-base-japanese-v2/blob/main/README.md
|
# cl-tohoku /bert-base-japanese-v2
1 --- 2 language: ja 3 license: cc-by-sa-4.0 4 datasets: 5 - wikipedia 6 widget: 7 - text: 東北大学で[MASK]の研究をしています。 8 --- 9 10 # BERT base Japanese (unidic-lite with whole word masking, jawiki-20200831) 11 12 This is a [BERT](https://github.com/google-research/bert) model pretrained on texts in the Japanese language. 13 14 This version of the model processes input texts with word-level tokenization based on the Unidic 2.1.2 dictionary (available in [unidic-lite](https://pypi.org/project/unidic-lite/) package), followed by the WordPiece subword tokenization. 15 Additionally, the model is trained with the whole word masking enabled for the masked language modeling (MLM) objective. 16 17 The codes for the pretraining are available at [cl-tohoku/bert-japanese](https://github.com/cl-tohoku/bert-japanese/tree/v2.0). 18 19 ## Model architecture 20 21 The model architecture is the same as the original BERT base model; 12 layers, 768 dimensions of hidden states, and 12 attention heads. 22 23 ## Training Data 24 25 The models are trained on the Japanese version of Wikipedia. 26 The training corpus is generated from the Wikipedia Cirrussearch dump file as of August 31, 2020. 27 28 The generated corpus files are 4.0GB in total, containing approximately 30M sentences. 29 We used the [MeCab](https://taku910.github.io/mecab/) morphological parser with [mecab-ipadic-NEologd](https://github.com/neologd/mecab-ipadic-neologd) dictionary to split texts into sentences. 30 31 ## Tokenization 32 33 The texts are first tokenized by MeCab with the Unidic 2.1.2 dictionary and then split into subwords by the WordPiece algorithm. 34 The vocabulary size is 32768. 35 36 We used [fugashi](https://github.com/polm/fugashi) and [unidic-lite](https://github.com/polm/unidic-lite) packages for the tokenization. 37 38 ## Training 39 40 The models are trained with the same configuration as the original BERT; 512 tokens per instance, 256 instances per batch, and 1M training steps. 41 For training of the MLM (masked language modeling) objective, we introduced whole word masking in which all of the subword tokens corresponding to a single word (tokenized by MeCab) are masked at once. 42 43 For training of each model, we used a v3-8 instance of Cloud TPUs provided by [TensorFlow Research Cloud program](https://www.tensorflow.org/tfrc/). 44 The training took about 5 days to finish. 45 46 ## Licenses 47 48 The pretrained models are distributed under the terms of the [Creative Commons Attribution-ShareAlike 3.0](https://creativecommons.org/licenses/by-sa/3.0/). 49 50 ## Acknowledgments 51 52 This model is trained with Cloud TPUs provided by [TensorFlow Research Cloud](https://www.tensorflow.org/tfrc/) program. 53
| 2022-01-17T19:37:54 |
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|
https://tjyj.stats.gov.cn/CN/Y2016/V33/I8/21
|
• 论文 •
### 基于PMI分解的制造业损失评估
• 出版日期:2016-08-15 发布日期:2016-08-11
### China's Manufacturing Loss Assessment Based on PMI Decompostion
Gui Wenlin & Tang Cuiwei
• Online:2016-08-15 Published:2016-08-11
2008年金融危机对我国制造业造成巨大冲击，对危机的影响进行评估对建立科学的危机预防机制具有重要的意义。文章运用X-13A-S模型将我国制造业PMI进行分解，研究各成分在危机期间的波动情况，分析金融危机的动态演变过程并构建本底趋势线进行损失评估，最后划分金融危机的生命周期。结论表明：①X-13A-S模型对指数调整效果较好，长期波动趋势分为三个时期；季节成分波动表现为“三波峰、三波谷”；异常值与危机事件相对应。②全面爆发前期PMI指数损失5.11%，平均损失1.28%，爆发后期指数损失49.31%，平均损失4.11%，本轮危机共损失54.42个百分点。③2008年1月至4月为生成期，2008年5月至12月为全面爆发期，2009年1月至5月为衰退期，2009年6月至8月为消亡期，整个危机持续16个月。④全面爆发时期以8月份为分界点，表现出“前期趋势-循环成分，后期不规则变动”的动态机制。
Abstract:
A significant damage to China's manufacturing industry has been made by the 2008 international financial crisis. It is of great importance to evaluate the crisis' impact for the establishment of scientific prevention mechanism. In this article we use X-13A-S model to decompose China's manufacturing PMI, study the volatility of sub-composition in crisis and crisis' dynamic evolution process. In addition, we build the natural trend line, divide life cycle and make assessment. The main conclusions are as follows: 1)X-13A-S model has a good effect on the adjustment of the index, the long-term trend is divided into three periods and seasonality's fluctuation is significantly characterized by ‘three peaks and three tough’. Outliers correspond to the crisis events. 2)The PMI lost 5.11% and 49.31% informer and later period of full-blown, the average is 1.28% and 4.11%. the sum loss is 54.42%. 3)The whole crisis lasted 16 months: from January to April 2008 was generation period, from May to December 2008 was full-blown period, from January to May 2009 was recession period, from June to August 2009 was dying-out period. 4)The full-blown period is divided into two parts by August, the dynamic mechanism shows ‘former is trend-cycle, later is irregular’.
| 2022-08-18T13:09:23 |
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https://wiki.cosmos.esa.int/planckpla/index.php?title=CMB_and_astrophysical_component_maps&diff=cur&oldid=7282
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# Difference between revisions of "CMB and astrophysical component maps"
## Overview
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the product and how it is obtained, followed by a description of the FITSFlexible Image Transfer Specification file containing the data and associated information. All the details can be found in Planck-2013-XII[1].
## CMBCosmic Microwave background maps
CMBCosmic Microwave background maps have been produced by the SMICA, NILC, SEVEM and COMMANDER-Ruler pipelines. Of these, the SMICA product is considered the preferred one overall and is labelled Main product in the Planck Legacy Archive, while the other two are labeled as Additional product.
SMICA and NILC also produce inpainted maps, in which the Galactic Plane, some bright regions and masked point sources are replaced with a constrained CMBCosmic Microwave background realization such that the whole map has the same statistical distribution as the observed CMBCosmic Microwave background.
The results of SMICA, NILC and SEVEM pipeline are distributed as a FITSFlexible Image Transfer Specification file containing 4 extensions:
1. CMBCosmic Microwave background maps and ancillary products (3 or 6 maps)
2. CMBCosmic Microwave background-cleaned foreground maps from LFI(Planck) Low Frequency Instrument (3 maps)
3. CMBCosmic Microwave background-cleaned foreground maps from HFI(Planck) High Frequency Instrument (6 maps)
4. Effective beam of the CMBCosmic Microwave background maps (1 vector)
The results of COMMANDER-Ruler are distributed as two FITSFlexible Image Transfer Specification files (the high and low resolution) containing the following extensions: High resolution N$_\rm{side}$=2048 (note that we don't provide the CMBCosmic Microwave background-cleaned foregrounds maps for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument because the Ruler resolution (~7.4') is lower than the HFI(Planck) High Frequency Instrument highest channel and and downgrading it will introduce noise correlation).
1. CMBCosmic Microwave background maps and ancillary products (4 maps)
2. Effective beam of the CMBCosmic Microwave background maps (1 vector)
Low resolution N$_\rm{side}$=256
1. CMBCosmic Microwave background maps and ancillary products (3 maps)
2. 10 example CMBCosmic Microwave background maps used in the montecarlo realization (10 maps)
3. Effective beam of the CMBCosmic Microwave background maps (1 vector)
For a complete description of the data structure, see the below; the content of the first extensions is illustrated and commented in the table below.
The maps (CMBCosmic Microwave background, noise, masks) contained in the first extension
Col name SMICA NILC SEVEM COMMANDER-Ruler H COMMANDER-Ruler L Description / notes
1: I Raw CMBCosmic Microwave background anisotropy map. These are the maps used in the component separation paper Planck-2013-XII[1].
2: NOISE not applicable Noise map. Obtained by propagating the half-ring noise through the CMBCosmic Microwave background cleaning pipelines.
3: VALMASK Confidence map. Pixels with an expected low level of foreground contamination. These maps are only indicative and obtained by different ad hoc methods. They cannot be used to rank the CMBCosmic Microwave background maps.
4: I_MASK not applicable not applicable not applicable Some areas are masked for the production of the raw CMBCosmic Microwave background maps (for NILC: point sources from 44 GHz to 857 GHz; for SMICA: point sources from 30 GHz to 857 GHz, Galatic region and additional bright regions).
5: INP_CMBCosmic Microwave background not applicable not applicable not applicable Inpainted CMBCosmic Microwave background map. The raw CMBCosmic Microwave background maps with some regions (as indicated by INP_MASK) replaced by a constrained Gaussian realization. The inpainted SMICA map was used for PR.
6: INP_MASK not applicable not applicable not applicable Mask of the inpainted regions. For SMICA, this is identical to I_MASK. For NILC, it is not.
The component separation pipelines are described in the CMB and foreground separation section and also in Section 3 and Appendices A-D of Planck-2013-XII[1] and references therein.
The union (or common) mask is defined as the union of the confidence masks from the four component separation pipelines, the three listed above and Commander-Ruler. It leaves 73% of the sky available, and so it is denoted as U73.
### Product description
#### SMICA
Principle
SMICA produces a CMBCosmic Microwave background map by linearly combining all Planck input channels (from 30 to 857 GHz) with weights which vary with the multipole. It includes multipoles up to .
Resolution (effective beam)
The SMICA map has an effective beam window function of 5 arc-minutes truncated at and deconvolved from the pixel window. It means that, ideally, one would have , where is the angular spectrum of the map, where is the angular spectrum of the CMBCosmic Microwave background and is a 5-arcminute Gaussian beam function. Note however that, by convention, the effective beam window function provided in the FITSFlexible Image Transfer Specification file does include a pixel window function. Therefore, it is equal to where denotes the pixel window function for an Nside=2048 pixelization.
A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and the masked point sources. This mask provides a qualitative (and subjective) indication of the cleanliness of a pixel.
The raw SMICA CMBCosmic Microwave background map has valid pixels except at the location of masked areas: point sources, Galactic plane, some other bright regions. Those invalid pixels are indicated with the mask named 'I_MASK'. The raw SMICA map has been inpainted, producing the map named "INP_CMBCosmic Microwave background". Inpainting consists in replacing some pixels (as indicated by the mask named INP_MASK) by the values of a constrained Gaussian realization which is computed to ensure good statistical properties of the whole map (technically, the inpainted pixels are a sample realisation drawn under the posterior distribution given the un-masked pixels.
#### NILC
Principle
The Needlet-ILC (hereafter NILC) CMBCosmic Microwave background map is constructed from all Planck channels from 44 to 857 GHz and includes multipoles up to . It is obtained by applying the Internal Linear Combination (ILC) technique in needlet space, that is, with combination weights which are allowed to vary over the sky and over the whole multipole range.
Resolution (effective beam)
As in the SMICA product except that there is no abrupt truncation at but a smooth transition to over the range .
A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and the masked point sources. This mask provides a qualitative indication of the cleanliness of a pixel. The threshold is somewhat arbitrary.
The raw NILC map has valid pixels except at the location of masked point sources. This is indicated with the mask named 'I_MASK'. The raw NILC map has been inpainted, producing the map named "INP_CMBCosmic Microwave background". The inpainting consists in replacing some pixels (as indicated by the mask named INP_MASK) by the values of a constrained Gaussian realization which is computed to ensure good statistical properties of the whole map (technically, the inpainted pixels are a sample realisation drawn under the posterior distribution given the un-masked pixels.
#### SEVEM
The aim of SEVEM is to produce clean CMBCosmic Microwave background maps at one or several frequencies by using a procedure based on template fitting. The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. The method has been successfully applied to Planck simulations[2] and to WMAP polarisation data[3]. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. Note that unlike the other products, SEVEM does not provide the mask of regions not used in the productions of the CMBCosmic Microwave background ma (I_MASK) nor an inpainted version of the map and its associated mask. On the other hand, it provides channel maps and 100, 143, and 217 GHz which are used as the building blocks of the final map.
#### COMMANDER-Ruler
COMMANDER-Ruler is the Planck software implementing a pixel based parametric component separation. Amplitude of CMBCosmic Microwave background and the main diffuse foregrounds along with the relevant spectral parameters for those (see below in the Astrophysical Foreground Section for the latter) are parametrized and fitted in single MCMC chains conducted at $N_\rm{side}$=256 using COMMANDER, implementing a Gibbs Sampling. The CMBCosmic Microwave background amplitude which is obtained in these runs corresponds to the delivered low resolution CMBCosmic Microwave background component from COMMANDER-Ruler which has a FWHMFull-Width-at-Half-Maximum of 40 arcminutes. The sampling of the foreground parameters is applied to the data at full resolution for obtaining the high resolution CMBCosmic Microwave background component from Ruler which is available on the PLAPlanck Legacy Archive. In the Planck Component Separation paper[1] additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps. The products mainly consist of:
• Maps of the Amplitudes of the CMBCosmic Microwave background at low resolution, $N_\rm{side}$=256, along with the standard deviations of the outputs, beam profiles derived from the production process.
• Maps of the CMBCosmic Microwave background amplitude, along with the standard deviations, at high resolution, $N_\rm{side}$=2048, beam profiles derived from the production process.
• Mask obtained on the basis of the precision in the fitting procedure; the thresholding is evaluated through the COMMANDER-Ruler likelihood analysis and excludes 13% of the sky, see Planck-2013-XII[1].
### Production process
#### SMICA
1) Pre-processing
All input maps undergo a pre-processing step to deal with point sources. The point sources with SNR > 5 in the PCCS catalogue are fitted in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole is filled in by a simple diffusive process to ensure a smooth transition and mitigate spectral leakage. This is done at all frequencies but 545 and 857 GHz, here all point sources with SNR > 7.5 are masked and filled-in similarly.
2) Linear combination
The nine pre-processed Planck frequency channels from 30 to 857 GHzare harmonically transformed up to and co-added with multipole-dependent weights as shown in the figure.
3) Post-processing
The areas masked in the pre-processing step are replaced by a constrained Gaussian realization.
Note: The visible power deficit in the raw CMBCosmic Microwave background map around the galactic plane is due to the smooth fill-in of the masked areas in the input maps (the result of the pre-processing). It is not to be confused with the post-processing step of inpainting of the CMBCosmic Microwave background map with a constrained Gaussian realization.
Weights given by SMICA to the input maps (after they are re-beamed to 5 arcmin and expressed in K), as a function of multipole.
#### NILC
1) Pre-processing
Same pre-processing as SMICA (except the 30 GHz channel is not used).
2) Linear combination
The pre-processed Planck frequency channels from 44 to 857 GHz are linearly combined with weights which depend on location on the sky and on the multipole range up to . This is achieved using a needlet (redundant spherical wavelet) decomposition. For more details, see Planck-2013-XII[1].
3) Post-processing
The areas masked in the pre-processing plus other bright regions step are replaced by a constrained Gaussian realization as in the SMICA post-processing step.
#### SEVEM
The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. The fitting can be done in real or wavelet space (using a fast wavelet adapted to the HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], <ref name="[[:Template:Gorski2005]]">[http://iopscience.iop.org/0004-637X/622/2/759/pdf/0004-637X_622_2_759.pdf '''HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere'''], K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, '''622''', 759-771, (2005). pixelization[4]) to properly deal with incomplete sky coverage. By expediency, however, we fill in the small number of unobserved pixels at each channel with the mean value of its neighbouring pixels before applying SEVEM.
We construct our templates by subtracting two close Planck frequency channel maps, after first smoothing them to a common resolution to ensure that the CMBCosmic Microwave background signal is properly removed. A linear combination of the templates is then subtracted from (hitherto unused) map d to produce a clean CMBCosmic Microwave background map at that frequency. This is done either in real or in wavelet space (i.e., scale by scale) at each position on the sky: where is the number of templates. If the cleaning is performed in real space, the coefficients are obtained by minimising the variance of the clean map outside a given mask. When working in wavelet space, the cleaning is done in the same way at each wavelet scale independently (i.e., the linear coefficients depend on the scale). Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas).
An additional level of flexibility can also be considered: the linear coefficients can be the same for all the sky, or several regions with different sets of coefficients can be considered. The regions are then combined in a smooth way, by weighting the pixels at the boundaries, to avoid discontinuities in the clean maps. Since the method is linear, we may easily propagate the noise properties to the final CMBCosmic Microwave background map. Moreover, it is very fast and permits the generation of thousands of simulations to character- ize the statistical properties of the outputs, a critical need for many cosmological applications. The final CMBCosmic Microwave background map retains the angular resolution of the original frequency map.
There are several possible configurations of SEVEM with regard to the number of frequency maps which are cleaned or the number of templates that are used in the fitting. Note that the production of clean maps at different frequencies is of great interest in order to test the robustness of the results. Therefore, to define the best strategy, one needs to find a compromise between the number of maps that can be cleaned independently and the number of templates that can be constructed.
In particular, we have cleaned the 143 GHz and 217 GHz maps using four templates constructed as the difference of the following Planck channels (smoothed to a common resolution): (30-44), (44-70), (545-353) and (857-545). For simplicity, the three maps have been cleaned in real space, since there was not a significant improvement when using wavelets (especially at high latitude). In order to take into account the different spectral behaviour of the foregrounds at low and high galactic latitudes, we have considered two independent regions of the sky, for which we have used a different set of coefficients. The first region corresponds to the 3 per cent brightest Galactic emission, whereas the second region is defined by the remaining 97 per cent of the sky. For the first region, the coefficients are actually estimated over the whole sky (we find that this is more optimal than perform the minimisation only on the 3 per cent brightest region, where the CMBCosmic Microwave background emission is very sub-dominant) while for the second region, we exclude the 3 per cent brightest region of the sky, point sources detected at any frequency and those pixels which have not been observed at all channels. Our final CMBCosmic Microwave background map has then been constructed by combining the 143 and 217 GHz maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of fwhm=5 arcminutes.
Moreover, additional CMBCosmic Microwave background clean maps (at frequencies between 44 and 353 GHz) have also been produced using different combinations of templates for some of the analyses carried out in Planck-2013-XXIII[5] and Planck-2013-XIX[6]. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in Planck-2013-XIX[6], while frequencies from 70 to 217 GHz were used for consistency tests in Planck-2013-XXIII[5].
#### COMMANDER-Ruler
The production process consist in low and high resolution runs according to the description above.
Low Resolution Runs
Same as the Astrophysics Foregrounds Section below; The CMBCosmic Microwave background amplitude is fitted along with the other foreground parameters and constitutes the CMBCosmic Microwave background Low Resolution Rendering which is in the PLAPlanck Legacy Archive.
Ruler Runs
the sampling at high resolution is used to infer the probability distribution of spectral parameters which is exploited at full resolution in order to obtain the High Resolution CMBCosmic Microwave background Rendering which is in the PLAPlanck Legacy Archive.
Summary table with the different masks that have been used by the component separation methods to pre-process and to process the frequency maps and the CMBCosmic Microwave background maps.
Commander 2013 (PR1) Used for diffuse inpainting of input frequency maps Used for constrained Gaussian realization inpaiting of CMBCosmic Microwave background map Description
VALMASK NO NO VALMASK is the confidence mask that defines the region where the reconstructed CMBCosmic Microwave background is trusted. It can be found inside
COM_CompMap_CMB-commrul_2048_R1.00.fits and COM_CompMap_CMB-commrul_0256_R1.00.fits for low resolution analyses.
SEVEM 2013 (PR1) Used diffuse inpainting of input frequency maps Used for Constrained Gaussian realization inpaiting of CMBCosmic Microwave background map Description
VALMASK NO NO VALMASK is the confidence mask that defines the region where the reconstructed CMBCosmic Microwave background is trusted. It can be found inside
NILC 2013 (PR1) Used for diffuse inpainting of input frequency maps Used for constrained Gaussian realization inpaiting of CMBCosmic Microwave background map Description
VALMASK NO NO VALMASK is the confidence mask that defines the region where the reconstructed CMBCosmic Microwave background is trusted. It can be found inside COM_CompMap_CMB-nilc_2048_R1.20.fits.
I_MASK NO NO I_MASK defines the regions over which CMBCosmic Microwave background is not built. It is a combination of point source masks, Galactic plane mask and other bright regions like LMC, SMC, etc. It can be found inside COM_CompMap_CMB-nilc_2048_R1.20.fits.
INP_MASK NO YES It can be found inside COM_CompMap_CMB-nilc_2048_R1.20.fits.
SMICA 2013 (PR1) Used for diffuse inpainting of input frequency maps Used for constrained Gaussian realization inpaiting of CMBCosmic Microwave background map Description
VALMASK NO NO VALMASK is the confidence mask that defines the region where the reconstructed CMBCosmic Microwave background is trusted. It can be found inside
I_MASK YES YES I_MASK defines the regions over which CMBCosmic Microwave background is not built. It is a combination of point source masks, Galactic plane mask and other bright regions like LMC, SMC, etc. It can be found inside COM_CompMap_CMB-smica_2048_R1.20.fits.
### Inputs
The input maps are the sky temperature maps described in the Sky temperature maps section. SMICA and SEVEM use all the maps between 30 and 857 GHz; NILC uses the ones between 44 and 857 GHz. Commander-Ruler uses frequency channel maps from 30 to 353 GHz.
### File names and structure
The FITSFlexible Image Transfer Specification files corresponding to the three CMBCosmic Microwave background products are the following:
The files contain a minimal primary extension with no data and four BINTABLE data extensions. Each column of the BINTABLE is a (Healpix) map; the column names and the most important keywords of each extension are described in the table below; for the remaining keywords, please see the FITSFlexible Image Transfer Specification files directly.
CMBCosmic Microwave background map file data structure
Ext. 1. EXTNAME = COMP-MAP (BINTABLE)
Column Name Data Type Units Description
I Real*4 uK_cmb CMBCosmic Microwave background temperature map
NOISE Real*4 uK_cmb Estimated noise map (note 1)
I_STDEV Real*4 uK_cmb Standard deviation, ONLY on COMMANDER-Ruler products
I_MASK Byte none Mask of regions over which CMBCosmic Microwave background map is not built (Optional - see note 3)
INP_CMBCosmic Microwave background Real*4 uK_cmb Inpainted CMBCosmic Microwave background temperature map (Optional - see note 3)
INP_MASK Byte none mask of inpainted pixels (Optional - see note 3)
Keyword Data Type Value Description
AST-COMP String CMBCosmic Microwave background Astrophysical compoment name
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
Ext. 2. EXTNAME = FGDS-LFI(Planck) Low Frequency Instrument (BINTABLE) - Note 4
Column Name Data Type Units Description
LFI(Planck) Low Frequency Instrument_030 Real*4 K_cmb 30 GHz foregrounds
LFI(Planck) Low Frequency Instrument_044 Real*4 K_cmb 44 GHz foregrounds
LFI(Planck) Low Frequency Instrument_070 Real*4 K_cmb 70 GHz foregrounds
Keyword Data Type Value Description
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 1024 Healpix Nside
METHOD String name Cleaning method (SMICA/NILC/SEVEM)
Ext. 3. EXTNAME = FGDS-HFI(Planck) High Frequency Instrument (BINTABLE) - Note 4
Column Name Data Type Units Description
HFI(Planck) High Frequency Instrument_100 Real*4 K_cmb 100 GHz foregrounds
HFI(Planck) High Frequency Instrument_143 Real*4 K_cmb 143 GHz foregrounds
HFI(Planck) High Frequency Instrument_217 Real*4 K_cmb 217 GHz foregrounds
HFI(Planck) High Frequency Instrument_353 Real*4 K_cmb 353 GHz foregrounds
HFI(Planck) High Frequency Instrument_545 Real*4 MJy/sr 545 GHz foregrounds
HFI(Planck) High Frequency Instrument_857 Real*4 MJy/sr 857 GHz foregrounds
Keyword Data Type Value Description
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
Ext. 4. EXTNAME = BEAM_WF (BINTABLE)
Column Name Data Type Units Description
BEAM_WF Real*4 none The effective beam window function, including the pixel window function. See Note 5.
Keyword Data Type Value Description
LMIN Int value First multipole of beam WF
LMAX Int value Lsst multipole of beam WF
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
Notes:
1. The half-ring half-difference (HRHD) map is made by passing the half-ring frequency maps independently through the component separation pipeline, then computing half their difference. It approximates a noise realisation, and gives an indication of the uncertainties due to instrumental noise in the corresponding CMBCosmic Microwave background map.
2. The confidence mask indicates where the CMBCosmic Microwave background map is considered valid.
3. This column is not present in the SEVEM and COMMANDER-Ruler product file. For SEVEM these three columns give the CMBCosmic Microwave background channel maps at 100, 143, and 217 GHz (columns C100, C143, and C217, in units of K_cmb.
4. The subtraction of the CMBCosmic Microwave background from the sky maps in order to produce the foregrounds map is done after convolving the CMBCosmic Microwave background map to the resolution of the given frequency. Those columns are not present in the COMMANDER-Ruler product file.
5. The beam window function given here includes the pixel window function for the Nside=2048 pixelization. It means that, ideally, .
The low resolution COMMANDER-Ruler CMBCosmic Microwave background product is organized in the following way:
CMBCosmic Microwave background low resolution COMMANDER-Ruler map file data structure
Ext. 1. EXTNAME = COMP-MAP (BINTABLE)
Column Name Data Type Units Description
I Real*4 uK_cmb CMBCosmic Microwave background temperature map obtained as average over 1000 samples
I_stdev Real*4 uK_cmb Corresponding Standard deviation amongst the 1000 samples
Keyword Data Type Value Description
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
Ext. 2. EXTNAME = CMBCosmic Microwave background-Sample (BINTABLE)
Column Name Data Type Units Description
I_SIM01 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM02 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM03 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM04 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM05 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM06 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM07 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM08 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM09 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
I_SIM10 Real*4 K_cmb CMBCosmic Microwave background Sample, smoothed to 40 arcmin
Keyword Data Type Value Description
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 1024 Healpix Nside
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
Ext. 4. EXTNAME = BEAM_WF (BINTABLE)
Column Name Data Type Units Description
BEAM_WF Real*4 none The effective beam window function, including the pixel window function.
Keyword Data Type Value Description
LMIN Int value First multipole of beam WF
LMAX Int value Lsst multipole of beam WF
METHOD String name Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)
The FITSFlexible Image Transfer Specification files containing the union (or common) maks is:
which contains a single BINTABLE extension with a single column (named U73) for the mask, which is boolean (FITSFlexible Image Transfer Specification TFORM = B), in GALACTIC coordinates, NESTED ordering, and Nside=2048.
For the benefit of users who are only looking for a small file containing the SMICA cmb map with no additional information (noise or masks) we provide such a file here
This file contains a single extension with a single column containing the SMICA cmb temperature map.
### Cautionary notes
1. The half-ring CMBCosmic Microwave background maps are produced by the pipelines with parameters/weights fixed to the values obtained from the full maps. Therefore the CMBCosmic Microwave background HRHD maps do not capture all of the uncertainties due to foreground modelling on large angular scales.
2. The HRHD maps for the HFI(Planck) High Frequency Instrument frequency channels underestimate the noise power spectrum at high l by typically a few percent. This is caused by correlations induced in the pre-processing to remove cosmic ray hits. The CMBCosmic Microwave background is mostly constrained by the HFI(Planck) High Frequency Instrument channels at high l, and so the CMBCosmic Microwave background HRHD maps will inherit this deficiency in power.
3. The beam transfer functions do not account for uncertainties in the beams of the frequency channel maps.
## Astrophysical foregrounds from parametric component separation
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper Planck-2013-XII[1] for a detailed description and astrophysical discussion of those.
### Product description
Low frequency foreground component
The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.
Thermal dust
The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided.
The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.
### Production process
CODE: COMMANDER-RULER. The code exploits a parametrization of CMBCosmic Microwave background and main diffuse foreground observables. The naive resolution of input frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper Planck-2013-XII[1] additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.
### Inputs
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz (LFI 30 GHz frequency maps, LFI 44 GHz frequency maps and LFI 70 GHz frequency maps, HFI 100 GHz frequency maps, HFI 143 GHz frequency maps,HFI 217 GHz frequency maps and HFI 353 GHz frequency maps) and their II column corresponding to the noise covariance matrix. Halfrings at the same frequencies. Beam window functions as reported in the LFI and HFI RIMO.
None.
### Meta Data
#### Low frequency foreground component
##### Low frequency component at N$_\rm{side}$ = 256
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits
Name HDU -- COMP-MAP
The Fits extension is composed by the columns described below:
Column Name Data Type Units Description
I Real*4 uK Intensity
I_stdev Real*4 uK standard deviation of intensity
Beta Real*4 effective spectral index
B_stdev Real*4 standard deviation on the effective spectral index
Notes
Comment: The Intensity is normalized at 30 GHz
Comment: The intensity was estimated during mixing matrix estimation
##### Low frequency component at N$_\rm{side}$ = 2048
File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits
Name HDU -- COMP-MAP
The Fits extension is composed by the columns described below:
Column Name Data Type Units Description
I Real*8 uK Intensity
I_stdev Real*8 uK standard deviation of intensity
I_hr1 Real*8 uK Intensity on half ring 1
I_hr2 Real*8 uK Intensity on half ring 2
Notes
Comment: The intensity was computed after mixing matrix application
Name HDU -- BeamWF
The Fits second extension is composed by the columns described below:
Column Name Data Type Units Description
BeamWF Real*4 beam profile
Notes
Comment: Beam window function used in the Component separation process
#### Thermal dust
##### Thermal dust component at N$_\rm{side}$=256
File name: COM_CompMap_dust-commrul_0256_R1.00.fits
Name HDU -- COMP-MAP
The Fits extension is composed by the columns described below:
Column Name Data Type Units Description
I Real*4 MJy/sr Intensity
I_stdev Real*4 MJy/sr standard deviation of intensity
Em Real*4 emissivity
Em_stdev Real*4 standard deviation on emissivity
T Real*4 uK temperature
T_stdev Real*4 uK standard deviation on temerature
Notes
Comment: The intensity is normalized at 353 GHz
##### Thermal dust component at N$_\rm{side}$=2048
File name: COM_CompMap_dust-commrul_2048_R1.00.fits
Name HDU -- COMP-MAP
The Fits extension is composed by the columns described below:
Column Name Data Type Units Description
I Real*8 MJy/sr Intensity
I_stdev Real*8 MJy/sr standard deviation of intensity
I_hr1 Real*8 MJy/sr Intensity on half ring 1
I_hr2 Real*8 MJy/sr Intensity on half ring 2
Name HDU -- BeamWF
The Fits second extension is composed by the columns described below:
Column Name Data Type Units Description
BeamWF Real*4 beam profile
Notes
Comment: Beam window function used in the Component separation process
The Fits extension is composed by the columns described below:
Column Name Data Type Units Description
## Thermal dust emission
Thermal emission from interstellar dust is captured by Planck-HFI(Planck) High Frequency Instrument over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. The details of the model can be found here Planck-2013-XI[7].
### Model of all-sky thermal dust emission
The model of the thermal dust emission is based on a modified black body (MBB) fit to the data
where is the Planck function for dust equilibirum temperature , is the amplitude of the MBB and the dust spectral index. The dust optical depth at frequency is
The dust parameters provided are , and . They were obtained by fitting the Planck data at 353, 545 and 857 GHz (from which the Planck zodiacal light model was removed) together with the IRAS 100 micron data. The latter is a combination of the 100 micron maps from IRIS (Miville-Deschenes & Lagache, 2005) and from Schlegel et al. (1998), SFD1998. The IRIS (SFD1998) map is used at scales smaller (larger) than 30 arcmin; this combination allows to take advantage of the higher angular resolution and better control of gain variations of the IRIS map and of the better removal of the zodiacal light emission of the SFD1998 map.
All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMBCosmic Microwave background anisotropies, clearly visible at 353 GHz, were removed from all the HFI(Planck) High Frequency Instrument maps using the SMICA map. An offset was removed from each map to set a Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.
The MBB fit was performed using a minimization method, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMBCosmic Microwave background anisotropies) and uncertainties on the zero levels. Because of the known degeneracy between and in the presence of noise, we performed tge fit in two steps. First we produced a model of dust emission using data smoothed to 30 arcmin; at such resolution no systematic bias of the parameters is observed. In a second step the map of the spectral index at 30 arcmin was used to fit the data for and at 5 arcmin.
### The map for extra-galactic studies
For the production of the map, we used a MBB fit to Planck and IRAS data from which point sources were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map is proportional to dust column density and therefore often used to estimate E(B-V). The analysis of Planck data revealed that the ratio and are not constant, even in the diffuse ISM, but that they depend on revealing possible spatial variations of the dust emission cross-section. It appears that the dust radiance, , i.e. the dust emission integrated in frequency, is a better tracer of column density in the diffuse ISM, implying small spatial variations of the radiation field strength at high Galactic latitude. Given those results, we also deliver the map of as a dust product and we propose to use it as an estimator of Galactic dust reddening for extra-galactic studies: .
To estimate the calibration factor q, we followed a method similar to[8] based on SDSS reddening measurements of quasars in the u, g, r, i and z bands[9]. We used a sample of 53 399 quasars, selecting objects at redshifts for which Ly does not enter the SDSS filters. The interstellar HI column densities covered on the lines of sight of this sample ranges from to . Therefore this sample allows us to estimate q in the diffuse ISM where this map of E(B-V) is intended to be used.
### Dust optical depth products
The dust model maps are found in the file HFI_CompMap_ThermalDustModel_2048_R1.20.fits (see the note below for an important clarification regarding the thermal dust model); its characteristics are:
• Dust optical depth at 353 GHz: Nside=2048, fwhm=5', no units
• Dust temperature: Nside 2048, fwhm=5', units=Kelvin
• Dust spectral index: Nside=2048, fwhm=30', no units
• Dust radiance: Nside=2048, fwhm=5', units=Wm-2sr-1
• E(B-V) for extragalactic studies: Nside=2048, fwhm=5', units=magnitude, obtained with data from which point sources were removed.
Dust opacity file data structure
1. EXTNAME = 'COMP-MAP'
Column Name Data Type Units Description
TAU353 Real*4 none The optical depth at 353GHz
ERR_TAU Real*4 none Error on the optical depth
EBV Real*4 mag E(B-V) for extra-galactic studies
TEMP Real*4 K Dust temperature
ERR_TEMP Real*4 K Error on the temperature
BETA Real*4 none Dust spectral index
ERR_BETA Real*4 none Error on Beta
Keyword Data Type Value Description
AST-COMP String DUST Astrophysical compoment name
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
IMPORTANT NOTE: The dust model has recently (4 December 2013) been updated and the new model is the one being distributed by default. A detailed description of the model can be found here Planck-2013-XI[7]. Users interested in the old dust model map should contact the PLA help desk.
## CO emission maps
CO rotational transition line emission is present in all HFI(Planck) High Frequency Instrument bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI(Planck) High Frequency Instrument maps and to make three types of CO products. A full description of how these products were produced is given in Planck-2013-XIII[10].
• Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI(Planck) High Frequency Instrument channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.
• Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.
• Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see above).
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI(Planck) High Frequency Instrument maps (K_CMBCosmic Microwave background) is provided in the header of the data files and in the RIMOreduced IMO. Four maps are given per transition and per type:
• The signal map
• The standard deviation map (same unit as the signal),
• A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.
• A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.
All products of a given type belong to a single file. Type 1 products have the native HFI(Planck) High Frequency Instrument resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively. Type 2 products have a 15 arcminute resolution The Type 3 product has a 5.5 arcminute resolution.
Type-1 CO map file data structure
1. EXTNAME = 'COMP-MAP'
Column Name Data Type Units Description
I10 Real*4 K_RJ km/sec The CO(1-0) intensity map
E10 Real*4 K_RJ km/sec Uncertainty in the CO(1-0) intensity
N10 Real*4 K_RJ km/sec Map built from the half-ring difference maps
M10 Byte none Region over which the CO(1-0) intensity is considered reliable
I21 Real*4 K_RJ km/sec The CO(2-1) intensity map
E21 Real*4 K_RJ km/sec Uncertainty in the CO(2-1) intensity
N21 Real*4 K_RJ km/sec Map built from the half-ring difference maps
M21 Byte none Region over which the CO(2-1) intensity is considered reliable
I32 Real*4 K_RJ km/sec The CO(3-2) intensity map
E32 Real*4 K_RJ km/sec Uncertainty in the CO(3-2) intensity
N32 Real*4 K_RJ km/sec Map built from the half-ring difference maps
M32 Byte none Region over which the CO(3-2) intensity is considered reliable
Keyword Data Type Value Description
AST-COMP string CO-TYPE2 Astrophysical compoment name
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
CNV 1-0 Real*4 value Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s))
CNV 2-1 Real*4 value Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s))
CNV 3-2 Real*4 value Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s))
Type-2 CO map file data structure
1. EXTNAME = 'COMP-MAP'
Column Name Data Type Units Description
I10 Real*4 K_RJ km/sec The CO(1-0) intensity map
E10 Real*4 K_RJ km/sec Uncertainty in the CO(1-0) intensity
N10 Real*4 K_RJ km/sec Map built from the half-ring difference maps
M10 Byte none Region over which the CO(1-0) intensity is considered reliable
I21 Real*4 K_RJ km/sec The CO(2-1) intensity map
E21 Real*4 K_RJ km/sec Uncertainty in the CO(2-1) intensity
N21 Real*4 K_RJ km/sec Map built from the half-ring difference maps
M21 Byte none Region over which the CO(2-1) intensity is considered reliable
Keyword Data Type Value Description
AST-COMP String CO-TYPE2 Astrophysical compoment name
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
CNV 1-0 Real*4 value Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s))
CNV 2-1 Real*4 value Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s))
Type-3 CO map file data structure
1. EXTNAME = 'COMP-MAP'
Column Name Data Type Units Description
INTEN Real*4 K_RJ km/sec The CO intensity map
ERR Real*4 K_RJ km/sec Uncertainty in the intensity
NUL Real*4 K_RJ km/sec Map built from the half-ring difference maps
MASK Byte none Region over which the intensity is considered reliable
Keyword Data Type Value Description
AST-COMP String CO-TYPE1 Astrophysical compoment name
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI(Planck) Low Frequency Instrument and HFI(Planck) High Frequency Instrument, respectively
CNV Real*4 value Factor to convert to Kcmb (units Kcmb/(Krj*km/s))
## References
1. Planck 2013 results: Component separation, Planck Collaboration XII, A&A, in press, (2014).
2. Component separation methods for the PLANCK mission, S. M. Leach, J.-F. Cardoso, C. Baccigalupi, R. B. Barreiro, M. Betoule, J. Bobin, A. Bonaldi, J. Delabrouille, G. de Zotti, C. Dickinson, H. K. Eriksen, J. González-Nuevo, F. K. Hansen, D. Herranz, M. Le Jeune, M. López-Caniego, E. Martínez-González, M. Massardi, J.-B. Melin, M.-A. Miville-Deschênes, G. Patanchon, S. Prunet, S. Ricciardi, E. Salerno, J. L. Sanz, J.-L. Starck, F. Stivoli, V. Stolyarov, R. Stompor, P. Vielva, A&A, 491, 597-615, (2008).
3. Multiresolution internal template cleaning: an application to the Wilkinson Microwave Anisotropy Probe 7-yr polarization data, R. Fernández-Cobos, P. Vielva, R. B. Barreiro, E. Martínez-González, MNRAS, 420, 2162-2169, (2012).
4. Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator, B. Casaponsa, R. B. Barreiro, A. Curto, E. Martínez-González, P. Vielva, MNRAS, 411, 2019-2025, (2011).
5. Planck 2013 results: Isotropy and statistics of the CMB, Planck Collaboration XXIII, A&A, in press, (2014).
6. Planck 2013 results: The integrated Sachs-Wolfe effect, Planck Collaboration XIX, A&A, in press, (2014).
7. Planck 2013 results: All-sky model of thermal dust emission, Planck Collaboration XI, A&A, in press, (2014).
8. Calibrating Milky Way dust extinction using cosmological sources, E. Mörtsell, A&A, 550, A80, (2013).
9. The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release, D. P. Schneider, P. B. Hall, G. T. Richards, M. A. Strauss, D. E. Vanden Berk, S. F. Anderson, W. N. Brandt, X. Fan, S. Jester, J. Gray, J. E. Gunn, M. U. SubbaRao, A. R. Thakar, C. Stoughton, A. S. Szalay, B. Yanny, D. G. York, N. A. Bahcall, J. Barentine, M. R. Blanton, H. Brewington, J. Brinkmann, R. J. Brunner, F. J. Castander, I. Csabai, J. A. Frieman, M. Fukugita, M. Harvanek, D. W. Hogg, Z. Ivezic, S. M. Kent, S. J. Kleinman, G. R. Knapp, R. G. Kron, J. Krzesinski, D. C. Long, R. H. Lupton, A. Nitta, J. R. Pier, D. H. Saxe, Y. Shen, S. A. Snedden, D. H. Weinberg, J. Wu, ApJ, 134, 102-117, (2007).
10. Planck 2013 results: Galactic CO emission as seen by Planck, Planck Collaboration XIII, A&A, in press, (2014).
| 2019-03-19T23:08:03 |
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|
https://pos.sissa.it/396/129/
|
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Generalized parton distributions of the proton from lattice QCD
A. Scapellato*, C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen and F. Steffens
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
Generalized parton distributions (GPDs) are among the most fundamental quantities for describing the internal structure of hadrons. In this work, we present results on isovector GPDs of the proton obtained within lattice Quantum Chromodynamics. We use the quasi-distribution formalism and perform the calculations on an ensemble of $N_f = 2 + 1 + 1$ twisted mass fermions, with pion mass $M_\pi=260$ MeV and lattice spacing $a\simeq 0.093$ fm. Results are presented for unpolarized, helicity, and transversity GPDs at zero and nonzero skewness with controlled statistical uncertainties. Comparisons with their forward limit show qualitative features anticipated from
model calculations.
DOI: https://doi.org/10.22323/1.396.0129
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2022-06-27T08:13:44 |
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http://dlmf.nist.gov/10.8
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# §10.8 Power Series
For $\mathop{J_{\nu}\/}\nolimits\!\left(z\right)$ see (10.2.2) and (10.4.1). When $\nu$ is not an integer the corresponding expansions for $\mathop{Y_{\nu}\/}\nolimits\!\left(z\right)$, $\mathop{{H^{(1)}_{\nu}}\/}\nolimits\!\left(z\right)$, and $\mathop{{H^{(2)}_{\nu}}\/}\nolimits\!\left(z\right)$ are obtained by combining (10.2.2) with (10.2.3), (10.4.7), and (10.4.8).
When $n=0,1,2,\ldots$,
10.8.1 $\mathop{Y_{n}\/}\nolimits\!\left(z\right)=-\frac{(\tfrac{1}{2}z)^{-n}}{\pi}% \sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}% {\pi}\mathop{\ln\/}\nolimits\!\left(\tfrac{1}{2}z\right)\mathop{J_{n}\/}% \nolimits\!\left(z\right)-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(% \mathop{\psi\/}\nolimits\!\left(k+1\right)+\mathop{\psi\/}\nolimits\!\left(n+k% +1\right))\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!},$
where $\mathop{\psi\/}\nolimits\!\left(x\right)=\mathop{\Gamma\/}\nolimits'\!\left(x% \right)/\mathop{\Gamma\/}\nolimits\!\left(x\right)$5.2(i)). In particular,
10.8.2 $\mathop{Y_{0}\/}\nolimits\!\left(z\right)=\frac{2}{\pi}\left(\mathop{\ln\/}% \nolimits\!\left(\tfrac{1}{2}z\right)+\EulerConstant\right)\mathop{J_{0}\/}% \nolimits\!\left(z\right)+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}% }-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+% \tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\cdots\right),$
where $\EulerConstant$ is Euler’s constant (§5.2(ii)).
For negative values of $n$ use (10.4.1).
The corresponding results for $\mathop{{H^{(1)}_{n}}\/}\nolimits\!\left(z\right)$ and $\mathop{{H^{(2)}_{n}}\/}\nolimits\!\left(z\right)$ are obtained via (10.4.3) with $\nu=n$.
10.8.3 $\mathop{J_{\nu}\/}\nolimits\!\left(z\right)\mathop{J_{\mu}\/}\nolimits\!\left(% z\right)=(\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-% \tfrac{1}{4}z^{2})^{k}}{k!\mathop{\Gamma\/}\nolimits\!\left(\nu+k+1\right)% \mathop{\Gamma\/}\nolimits\!\left(\mu+k+1\right)}.$
| 2016-08-29T19:53:55 |
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|
https://oscars.bnl.gov/examples/GettingStarted_ImportingFieldData.html
|
# Importing Field Data¶
OSCARS supports several basic data formats for importing. We are interested in supporting more.
One basic format ('OSCARS1D') is where you have the magnetic field (1, 2, or 3D) given as a function of position and your file format lists rows of (for instance) 'Z Bx By Bz'. In this case, specify X, Y, or Z, and whichever of the B's you have in the format field: iformat='Z Bx By Bz'.
OSCARS format: Has 10 lines of header information, followed by lines consisting of 'Bx By Bz'. You must specify iformat='OSCARS'. The header is as follows:
• Comment line
• Initial X position
• Step size in X
• Number of points in X
• Initial Y position
• Step size in Y
• Number of points in Y
• Initial Z position
• Step size in Z
• Number of points in Z
OSCARS also supports iformat='SPECTRA' and iformat='SRW'. See the All About Magnetic Fields tutorial for mroe information.
In [1]:
# matplotlib plots inline
%matplotlib inline
# Import the OSCARS SR module
import oscars.sr
# Import OSCARS plots (matplotlib)
from oscars.plots_mpl import *
OSCARS v2.1.8 - Open Source Code for Advanced Radiation Simulation
Brookhaven National Laboratory, Upton NY, USA
http://oscars.bnl.gov
[email protected]
In [2]:
# Create a new OSCARS object. Default to 8 threads and always use the GPU if available
## OSCARS1D Format¶
In [3]:
# To illustrate the basic 1D format let's create a data file, then import it.
# It will be plotted before and after the import
# Create an undulator field
osr.clear_bfields()
osr.add_bfield_undulator(bfield=[0, 1, 0], period=[0, 0, 0.05], nperiods=31)
plot_bfield(osr)
# Now write the field to a file
osr.write_bfield(
ofile='GettingStarted_OSCARS1D.dat',
oformat='OSCARS1D Z By Bx Bz',
zlim=[-1, 1],
nz=5000
)
# Clear fields and import the field from the file created above
osr.clear_bfields()
osr.add_bfield_file(ifile='GettingStarted_OSCARS1D.dat', iformat='OSCARS1D Z By Bx Bz')
plot_bfield(osr)
## OSCARS Format¶
In [4]:
# To illustrate the basic 3D format let's create a data file, then import it.
# It will be plotted before and after the import
# Create an undulator field
osr.clear_bfields()
osr.add_bfield_undulator(bfield=[1, 0, 0], period=[0, 0, 0.050], nperiods=11)
plot_bfield(osr)
# Now write the field to a file
osr.write_bfield(
ofile='GettingStarted_OSCARS.dat',
oformat='OSCARS',
xlim=[-1, 1],
nx=2,
ylim=[-1, 1],
ny=2,
zlim=[-1, 1],
nz=5000
)
# Clear fields and import the field from the file created above
# You can also scale position, in case your input is not in [m]
osr.clear_bfields()
| 2023-03-29T06:40:30 |
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|
https://terraria.fandom.com/wiki/Use_Time
|
## FANDOM
5,026 Pages
Value Speed
≤8 Insanely Fast
9-20 Very Fast
21-25 Fast
26-30 Average
31-35 Slow
36-45 Very Slow
46-55 Extremely Slow
≥56 Snail
Use time is a game mechanic that determines the rate of fire for ranged and magic weapons in game. Use time is a solid number (for example, the use time for the Minishark is 8). The Use time is the number of frames it takes for one shot to be fired, (Which means the Minishark would fire one round every 8 frames). To calculate the DPS (Damage Per Second) use the following equation:
$\mathit{DPS}=\frac{\text{Your FPS}}{\text{Use time}} \times \text{Damage per Shot}$
The equation above does not include multipliers and modifiers.
## Tips
• Remember that the faster your weapon is (or the lower your Use Time value is), the more ammunition you will use in a quicker amount of time.
• As a result of this, Slower, more Damage Per Shot weapons should be chosen over more Faster but less Damage per Shot weapons if the player does not resources or Money for ammunition. This being said, if you have enough resources to make lots of ammunition, then chose the faster weapon, as missing your target with a slower weapon is a lot less unforgiving then missing a shot with a faster weapon.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-02-21T11:26:07 |
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|
https://par.nsf.gov/biblio/10283284-search-double-beta-decay-mathrm-te-states-mathrm-xe-cuore
|
Search for double-beta decay of $$\mathrm {^{130}Te}$$ to the $$0^+$$ states of $$\mathrm {^{130}Xe}$$ with CUORE
Abstract The CUORE experiment is a large bolometric array searching for the lepton number violating neutrino-less double beta decay ( $$0\nu \beta \beta$$ 0 ν β β ) in the isotope $$\mathrm {^{130}Te}$$ 130 Te . In this work we present the latest results on two searches for the double beta decay (DBD) of $$\mathrm {^{130}Te}$$ 130 Te to the first $$0^{+}_2$$ 0 2 + excited state of $$\mathrm {^{130}Xe}$$ 130 Xe : the $$0\nu \beta \beta$$ 0 ν β β decay and the Standard Model-allowed two-neutrinos double beta decay ( $$2\nu \beta \beta$$ 2 ν β β ). Both searches are based on a 372.5 kg $$\times$$ × yr TeO $$_2$$ 2 exposure. The de-excitation gamma rays emitted by the excited Xe nucleus in the final state yield a unique signature, which can be searched for with low background by studying coincident events in two or more bolometers. The closely packed arrangement of the CUORE crystals constitutes a significant advantage in this regard. The median limit setting sensitivities at 90% Credible Interval (C.I.) of the given searches were estimated as $$\mathrm {S^{0\nu }_{1/2} = 5.6 \times 10^{24} \, \mathrm {yr}}$$ S 1 / 2 0 more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10283284
Journal Name:
The European Physical Journal C
Volume:
81
Issue:
7
ISSN:
1434-6044
2. A bstract We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe − e − amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $$p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k)$$ p p 1 ′ p p 2 ′ W − k , in analogy to the Cottingham formula for the electromagneticmore »
3. A bstract The NA62 experiment reports the branching ratio measurement $$\mathrm{BR}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right)=\left({10.6}_{-3.4}^{+4.0}\left|{}_{\mathrm{stat}}\right.\pm {0.9}_{\mathrm{syst}}\right)\times {10}^{-11}$$ BR K + → π + ν ν ¯ = 10.6 − 3.4 + 4.0 stat ± 0.9 syst × 10 − 11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016–2018. This provides evidence for the very rare K + → $${\pi}^{+}\nu \overline{\nu}$$ π + ν ν ¯ decay, observed with a significance of 3.4 σ . The experimentmore »
5. Abstract A metallic state with a vanishing activation gap, at a filling factor $$\nu = 8/5$$ ν = 8 / 5 in the untilted specimen with $$n= 2 \times 10^{11} cm^{-2}$$ n = 2 × 10 11 c m - 2 , and at $$\nu = 4/3$$ ν = 4 / 3 at $$n=1.2 \times 10^{11} cm^{-2}$$ n = 1.2 × 10 11 c m - 2 under a $$\theta = 66^{0}$$ θ = 66 0 tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest,more »
| 2022-08-09T08:13:40 |
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|
https://b2b.partcommunity.com/community/knowledge/en/detail/123/Hydraulic+cylinder
|
Hydraulic cylinder (15348 views - Mechanical Engineering)
A hydraulic cylinder (also called a linear hydraulic motor) is a mechanical actuator that is used to give a unidirectional force through a unidirectional stroke. It has many applications, notably in construction equipment (engineering vehicles), manufacturing machinery, and civil engineering.
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Hydraulic cylinder
Hydraulic cylinder
A hydraulic cylinder (also called a linear hydraulic motor) is a mechanical actuator that is used to give a unidirectional force through a unidirectional stroke. It has many applications, notably in construction equipment (engineering vehicles), manufacturing machinery, and civil engineering.[1]
Operation
Hydraulic cylinders get their power from pressurized hydraulic fluid, which is typically oil. The hydraulic cylinder consists of a cylinder barrel, in which a piston connected to a piston rod moves back and forth. The barrel is closed on one end by the cylinder bottom (also called the cap) and the other end by the cylinder head (also called the gland) where the piston rod comes out of the cylinder. The piston has sliding rings and seals. The piston divides the inside of the cylinder into two chambers, the bottom chamber (cap end) and the piston rod side chamber (rod end / head end).
Flanges, trunnions, clevises, and lugs are common cylinder mounting options. The piston rod also has mounting attachments to connect the cylinder to the object or machine component that it is pushing or pulling.
A hydraulic cylinder is the actuator or "motor" side of this system. The "generator" side of the hydraulic system is the hydraulic pump which delivers a fixed or regulated flow of oil to the hydraulic cylinder, to move the piston. The piston pushes the oil in the other chamber back to the reservoir. If we assume that the oil enters from cap end, during extension stroke, and the oil pressure in the rod end / head end is approximately zero, the force F on the piston rod equals the pressure P in the cylinder times the piston area A:
${\displaystyle F=P\cdot A}$
Retraction force difference
For double-acting single-rod cylinders, when the input and output pressures are reversed, there is a force difference between the two sides of the piston due to one side of the piston being covered by the rod attached to it. The cylinder rod reduces the surface area of the piston and reduces the force that can be applied for the retraction stroke.[2]
During the retraction stroke, if oil is pumped into the head (or gland) at the rod end and the oil from the cap end flows back to the reservoir without pressure, the fluid pressure in the rod end is (Pull Force) / (piston area - piston rod area):
${\displaystyle P={\frac {F_{p}}{A_{p}-A_{r}}}}$
where P is the fluid pressure, Fp is the pulling force, Ap is the piston face area and Ar is the rod cross-section area.
For double-acting, double-rod cylinders, when the piston surface area is equally covered by a rod of equal size on both sides of the head, there is no force difference. Such cylinders typically have their cylinder body affixed to a stationary mount.
Parts
A hydraulic cylinder has the following parts:
Cylinder barrel
The main function of the cylinder body is to hold cylinder pressure. The cylinder barrel is mostly made from a seamless tube. The cylinder barrel is ground and/or honed internally with a typical surface finish of 4 to 16 microinch. The piston reciprocates in the cylinder.
Cylinder base or cap
The main function of the cap is to enclose the pressure chamber at one end. The cap is connected to the body by means of welding, threading, bolts, or tie rod. Caps also perform as cylinder mounting components [cap flange, cap trunnion, cap clevis]. Cap size is determined based on the bending stress. A static seal / o-ring is used in between cap and barrel (except welded construction).
The main function of the head is to enclose the pressure chamber from the other end. The head contains an integrated rod sealing arrangement or the option to accept a seal gland. The head is connected to the body by means of threading, bolts, or tie rod. A static seal / o-ring is used in between head and barrel.
Piston
The main function of the piston is to separate the pressure zones inside the barrel. The piston is machined with grooves to fit elastomeric or metal seals and bearing elements. These seals can be single acting or double acting. The difference in pressure between the two sides of the piston causes the cylinder to extend and retract. The piston is attached with the piston rod by means of threads, bolts, or nuts to transfer the linear motion.
Piston rod
The piston rod is typically a hard chrome-plated piece of cold-rolled steel which attaches to the piston and extends from the cylinder through the rod-end head. In double rod-end cylinders, the actuator has a rod extending from both sides of the piston and out both ends of the barrel. The piston rod connects the hydraulic actuator to the machine component doing the work. This connection can be in the form of a machine thread or a mounting attachment. The piston rod is highly ground and polished so as to provide a reliable seal and prevent leakage.
Seal gland
The cylinder head is fitted with seals to prevent the pressurized oil from leaking past the interface between the rod and the head. This area is called the seal gland. The advantage of a seal gland is easy removal and seal replacement. The seal gland contains a primary seal, a secondary seal / buffer seal, bearing elements, wiper / scraper and static seal. In some cases, especially in small hydraulic cylinders, the rod gland and the bearing elements are made from a single integral machined part.
Seals
The seals are considered / designed as per the cylinder working pressure, cylinder speed, operating temperature, working medium and application. Piston seals are dynamic seals, and they can be single acting or double acting. Generally speaking, Elastomer seals made from nitrile rubber, Polyurethane or other materials are best in lower temperature environments, while seals made of Fluorocarbon Viton are better for higher temperatures. Metallic seals are also available and commonly use cast iron for the seal material. Rod seals are dynamic seals and generally are single acting. The compounds of rod seals are nitrile rubber, Polyurethane, or Fluorocarbon Viton. Wipers / scrapers are used to eliminate contaminants such as moisture, dirt, and dust, which can cause extensive damage to cylinder walls, rods, seals and other components. The common compound for wipers is polyurethane. Metallic scrapers are used for sub zero temperature applications, and applications where foreign materials can deposit on the rod. The bearing elements / wear bands are used to eliminate metal to metal contact. The wear bands are designed as per the side load requirements. The primary compounds used for wear bands are filled PTFE, woven fabric reinforced polyester resin and bronze
Other parts
There are many component parts that make up the internal portion of a hydraulic cylinder. All of these pieces combine to create a fully functioning component.[3]
• Cylinder base connection
• Cushions
• Polypak Pistons
• Butt Plates
• Eye Brackets/Clevis Brackets
• MP Detachable Mounts
• Rod Eyes/Rod Clevis
• Pivot Pins
• Spherical Ball Bushings
• Spherical Rod Eye
• Alignment Coupler
• Ports and Fittings
Single acting vs. double acting
• Single acting cylinders are economical and the simplest design. Hydraulic fluid enters through a port at one end of the cylinder, which extends the rod by means of area difference. An external force, internal retraction spring or gravity returns the piston rod.
• Double acting cylinders have a port at each end or side of the piston, supplied with hydraulic fluid for both the retraction and extension.[4]
Designs
There are primarily two main styles of hydraulic cylinder construction used in industry: tie rod style cylinders and welded body style cylinders.
Tie rod cylinder
Tie rod style hydraulic cylinders use high strength threaded steel rods to hold the two end caps to the cylinder barrel. They are most often seen in industrial factory applications. Small bore cylinders usually have 4 tie rods, and large bore cylinders may require as many as 16 or 20 tie rods in order to retain the end caps under the tremendous forces produced. Tie rod style cylinders can be completely disassembled for service and repair, and they are not always customizable.[5]
The National Fluid Power Association (NFPA) has standardized the dimensions of hydraulic tie rod cylinders. This enables cylinders from different manufacturers to interchange within the same mountings.
Welded body cylinder
Welded body cylinders have no tie rods. The barrel is welded directly to the end caps. The ports are welded to the barrel. The front rod gland is usually threaded into or bolted to the cylinder barrel. That allows the piston rod assembly and the rod seals to be removed for service.
A Cut Away of a Welded Body Hydraulic Cylinder showing the internal components
Welded body cylinders have a number of advantages over tie rod style cylinders. Welded cylinders have a narrower body and often a shorter overall length enabling them to fit better into the tight confines of machinery. Welded cylinders do not suffer from failure due to tie rod stretch at high pressures and long strokes. The welded design also lends itself to customization. Special features are easily added to the cylinder body, including special ports, custom mounts, valve manifolds, and so on.[5]
The smooth outer body of welded cylinders also enables the design of multi-stage telescopic cylinders.
Welded body hydraulic cylinders dominate the mobile hydraulic equipment market such as construction equipment (excavators, bulldozers, and road graders) and material handling equipment (forklift trucks, telehandlers, and lift-gates). They are also used by heavy industry in cranes, oil rigs, and large off-road vehicles for above-ground mining operations.
Piston rod construction
The piston rod of a hydraulic cylinder operates both inside and outside the barrel, and consequently both in and out of the hydraulic fluid and surrounding atmosphere.
Coatings
Wear and corrosion resistant surfaces are desirable on the outer diameter of the piston rod. The surfaces are often applied using coating techniques such as Chrome (Nickel) Plating, Lunac 2+ duplex, Laser Cladding, PTA welding and Thermal Spraying. These coatings can be finished to the desirable surface roughness (Ra, Rz) where the seals give optimum performance. All these coating methods have their specific advantages and disadvantages. It is for this reason that coating experts play a crucial role in selecting the optimum surface treatment procedure for protecting Hydraulic Cylinders.
Cylinders are used in different operational conditions and that makes it a challenge to find the right coating solution. In dredging there might be impact from stones or other parts, in salt water environments there are extreme corrosion attacks, in off-shore cylinders facing bending and impact in combination with salt water, and in the steel industry there are high temperatures involved, etc. It is important to understand that currently there is no single coating solution which successfully combats all the specific operational wear conditions. Every single technique has its own benefits and disadvantages.
Length
Piston rods are generally available in lengths which are cut to suit the application. As the common rods have a soft or mild steel core, their ends can be welded or machined for a screw thread.
Distribution of forces on components
The forces on the piston face and the Piston Head Retainer vary depending on what Piston Head retention system is used.
If a circlip (or any non preloaded system) is used, the force acting to separate the Piston Head and the Cylinder Shaft shoulder is the applied pressure multiplied by the area of the Piston Head. The Piston Head and Shaft shoulder will separate and the load is fully reacted by the Piston Head Retainer.
If a preloaded system is used the force between the Cylinder Shaft and Piston Head is initially the Piston Head Retainer preload value. Once pressure is applied this force will reduce. The Piston Head and Cylinder Shaft shoulder will remain in contact unless the applied pressure multiplied by Piston Head area exceeds the preload.
The maximum force the Piston Head Retainer will see is the larger of the preload and the applied pressure multiplied by the full Piston Head area. It is interesting to note that the load on the Piston Head Retainer is greater than the external load, which is due to the reduced shaft size passing through the Piston Head. Increasing this portion of shaft reduces the load on the Retainer. [6]
Side loading is unequal pressure that is not centered on the cylinder rod. This off-center strain can lead to bending of the rod in extreme cases, but more commonly causes leaking due to warping the circular seals into an oval shape. It can also damage and enlarge the bore hole around the rod and the inner cylinder wall around the piston head, if the rod is pressed hard enough sideways to fully compress and deform the seals to make metal-on-metal scraping contact.[7]
The strain of side loading can be directly reduced with the use of internal stop tubes which reduce the maximum extension length, leaving some distance between the piston and bore seal, and increasing leverage to resist warping of the seals. Double pistons also spread out the forces of side loading while also reducing stroke length. Alternately, external sliding guides and hinges can support the load and reduce side loading forces applied directly on the cylinder.[8]
Repair
Hydraulic cylinders form the heart of many hydraulic systems. It is a common practice to dissemble and rebuild an entire device in the case of hydraulic cylinder repair. Inspection of the leakage issue and scrutinizing cylinder parts (especially the seals) is helpful in recognizing the exact problem and choosing the repair options accordingly. Steps involved in the repair of hydraulic cylinders:[9]
Disassembly
First of all, you should place the cylinder in a suitable location, which has sufficient space to work. If you are working in a cluttered space, it will be difficult for you to keep track of opened up parts. After bringing the cylinder to an appropriate spot, open the cylinder ports and drain out all the hydraulic fluid. The cover of cylinder can be removed by unscrewing the bolts. Once you take off the cover, remove the piston by loosening the input valves.
Diagnosis
Once the piston is completely removed, you will be able to see multiple seals on different parts that are connected to the piston rod . First of all, you need to examine the piston rod to see if there is any damage. If the shaft of the rod is bent or if the cylinder bore has scratches, then get them repaired at a professional repair shop. If the damage is permanent, then you can order or manufacture a new piston rod for your hydraulic cylinder. Piston seals can get damaged, be distorted, or worn. Such damaged seals can cause leakage of hydraulic fluid from the cylinder leading to lower overall pressure or inability to hold pressure. When such events occur, you know that these seals need to be replaced.
Repairing or replacing damaged parts
The parts of the hydraulic cylinder that are distorted ( piston rod, rod seal, piston seal and/ or head of rod), need to be either repaired or completely replaced with new parts. The seals can be repacked with the help of a hydraulic cylinder seal kit. These kits will have seals and suitable o-rings. Remember the size and type of old seal while removing them and fix the new ones accordingly. Make sure that you handle the new seals with utmost care so that they do not get damaged in any way.
Rebuilding
Before reassembling all the parts of your cylinder, you should clean and dry the cylinder barrel completely. Also clean the piston rod, shaft, and other parts of the cylinder. Get the broken and damaged seals repacked. Then assemble the parts back on the piston rod. The assembly needs to be done in a reverse order. Once you have assembled all the parts back, put the rod into the soft-jaw vise and screw back the bolts onto the piston rod.
Important tip
If the parts of the hydraulic cylinder are severely damaged, then it is advisable to replace them with new parts with the help of a professional repair expert. Trying to replace/ repair too many parts on your own can lead to faulty reassembly. By following the above steps, you can accomplish the task of hydraulic cylinder repair. Make sure that you prevent ingress of moisture or dirt after assembly of the parts is done.
Cylinder mounting methods
Mounting methods also play an important role in cylinder performance. Generally, fixed mounts on the centerline of the cylinder are best for straight line force transfer and avoiding wear. Common types of mounting include:
Flange mounts—Very strong and rigid, but have little tolerance for misalignment. Experts recommend cap end mounts for thrust loads and rod end mounts where major loading puts the piston rod in tension. Three types are head rectangular flange, head square flange or rectangular head. Flange mounts function optimally when the mounting face attaches to a machine support member.[10]
Side-mounted cylinders—Easy to install and service, but the mounts produce a turning moment as the cylinder applies force to a load, increasing wear and tear. To avoid this, specify a stroke at least as long as the bore size for side mount cylinders (heavy loading tends to make short stroke, large bore cylinders unstable). Side mounts need to be well aligned and the load supported and guided.
Centerline lug mounts —Absorb forces on the centerline, and require dowel pins to secure the lugs to prevent movement at higher pressures or under shock conditions. Dowel pins hold it to the machine when operating at high pressure or under shock loading.[10]
Pivot mounts —Absorb force on the cylinder centerline and let the cylinder change alignment in one plane. Common types include clevises, trunnion mounts and spherical bearings. Because these mounts allow a cylinder to pivot, they should be used with rod-end attachments that also pivot. Clevis mounts can be used in any orientation and are generally recommended for short strokes and small- to medium-bore cylinders. [11]
Special hydraulic cylinders
Telescopic cylinder
The length of a hydraulic cylinder is the total of the stroke, the thickness of the piston, the thickness of bottom and head and the length of the connections. Often this length does not fit in the machine. In that case the piston rod is also used as a piston barrel and a second piston rod is used. These kinds of cylinders are called telescopic cylinders. If we call a normal rod cylinder single stage, telescopic cylinders are multi-stage units of two, three, four, five or more stages. In general telescopic cylinders are much more expensive than normal cylinders. Most telescopic cylinders are single acting (push). Double acting telescopic cylinders must be specially designed and manufactured.[12]
Plunger cylinder
A hydraulic cylinder without a piston or with a piston without seals is called a plunger cylinder. A plunger cylinder can only be used as a pushing cylinder; the maximum force is piston rod area multiplied by pressure. This means that a plunger cylinder in general has a relatively thick piston rod.
Differential cylinder
A differential cylinder acts like a normal cylinder when pulling. If the cylinder however has to push, the oil from the piston rod side of the cylinder is not returned to the reservoir, but goes to the bottom side of the cylinder. In such a way, the cylinder goes much faster, but the maximum force the cylinder can give is like a plunger cylinder. A differential cylinder can be manufactured like a normal cylinder, and only a special control is added.
The above differential cylinder is also called a regenerative cylinder control circuit. This term means that the cylinder is a single rod, double acting hydraulic cylinder. The control circuit includes a valve and piping which during the extension of the piston, conducts the oil from the rod side of the piston to the other side of the piston instead of to the pump’s reservoir. The oil which is conducted to the other side of the piston is referred to as the regenerative oil.
Position sensing "smart" hydraulic cylinder
Position sensing hydraulic cylinders eliminate the need for a hollow cylinder rod. Instead, an external sensing "bar" using Hall Effect technology senses the position of the cylinder’s piston. This is accomplished by the placement of a permanent magnet within the piston. The magnet propagates a magnetic field through the steel wall of the cylinder, providing a locating signal to the sensor.
Terminology
In the United States, popular usage refers to the whole assembly of cylinder, piston, and piston rod (or more) collectively as a "piston", which is incorrect. Instead, the piston is the short, cylindrical metal component that separates the two parts of the cylinder barrel internally.
1. ^ http://www.edgeroamer.com/sweethaven/mechanics/hydraulics01/default.asp?iNum=0401
2. ^ Management of Hazardous Energy: Deactivation, De-Energization, Isolation, and Lockout, Thomas Neil McManus, page 678, August 8, 2012 by CRC Press, Reference - 942 Pages - 273 B/W Illustrations, ISBN 9781439878361
3. ^ Component Parts of a Hydraulic Cylinder | http://www.crconline.com/component-parts.html
4. ^ "Hydraulic Cylinders", Metro Hydraulic, Retrieved June 6, 2016.
5. ^ a b "Welded Cylinders vs. Tie Rod Cylinders", Best Metal Products, Retrieved June 6, 2016.
6. ^ http://www.cylinder.co.uk/technical/cylindercomponentforces.html
7. ^ Maximizing Cylinder Performance: A checklist of design guidelines ensures the best pneumatic cylinder for an application, Aug 20, 1998, Kenneth Korane, Machine Design magazine
8. ^ Fluid Power Design Handbook, Third Edition, page 112, By Frank Yeaple, CRC Press, 1995, 854 pages, ISBN 9780824795627
9. ^ The Process of Cylinder Repair and Servicing
10. ^ a b "Mounting Style Can Dramatically Improve Hydraulic and Pneumatic Cylinder Performance", Hydraulics & Pneumatics, Retrieved June 6, 2016
11. ^ http://www.mobilehydraulictips.com/what-are-hydraulic-cylinders/
12. ^ "What are Telescopic Cylinders, and How Do They Work?", Pneu-Hyd, Retrieved June 6, 2016.
This article uses material from the Wikipedia article "Hydraulic cylinder", which is released under the Creative Commons Attribution-Share-Alike License 3.0. There is a list of all authors in Wikipedia
| 2018-12-16T08:35:14 |
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https://www.pnnl.gov/projects?projects%5B0%5D=research-topic%3AEnvironmental%20Remediation&projects%5B1%5D=research-topic%3AHydropower%20and%20the%20Electric%20Grid&projects%5B2%5D=research-topic%3ARadiation%20Measurement&projects%5B3%5D=research-topic%3AVehicle%20Technologies&projects%5B4%5D=research-topic%3AWater%20Power
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# Projects
161 results found
Filtered by Environmental Remediation, Hydropower and the Electric Grid, Radiation Measurement, Vehicle Technologies, and Water Power
# Future Hydropower Generation and Consequences for Global Electricity Supply Investment Needs
Changes in future precipitation and temperature present both opportunities and risks for hydropower generation around the globe.
Changes in precipitation and temperature could affect electricity investments across the globe
February 9, 2018
February 9, 2018
The Science
Hydropower dams produce almost one-fifth of global electricity supplies. However, changes in precipitation and temperature patterns could influence water availability for hydropower around the world.
Researchers at the U.S. Department of Energy's Pacific Northwest National Laboratory explored how sustained losses and gains in hydropower generation could affect the investments needed to meet global electricity demands in the 21st century. Under the most extreme scenario, they projected changes in cumulative electricity investment costs of more than $100 billion by 2100 for many countries and regions of the world. The Impact Whereas previous studies quantified possible effects of changes in future precipitation and temperature on hydropower, this study explored the possible implications for the mix of electricity supplies. The study combined detailed, global-scale hydrological and dam modeling with integrated human-Earth system modeling, providing a new means for assessing the effects of Earth system changes on global energy systems. Summary Precipitation and temperature patterns could be very different in the future. Some river basins may receive more water on average, while others may receive less. These changes could increase or reduce power generation at hydroelectric dams. In this study, scientists aimed to quantify these effects and then explore some potential implications for investments in electricity generation technologies resulting from increases or decreases in hydropower. Applying global projections of rainfall and temperature, researchers generated flows for all global rivers. They used the flows to simulate power generation at approximately 1,600 of the world's major hydropower dams. Researchers ran the Global Change Assessment Model (GCAM) to understand how losses or gains in hydropower might affect the deployment of alternative generating technologies. The study showed that, in certain drying regions such as the Balkans, significant financial outlays could be required to deploy new generating capacity to address shortfalls in hydropower. For instance, under one scenario applied in the model, the additional cumulative investment requirement for the Balkans region totaled$68 billion by 2100.
Researchers estimated a global, cumulative investment need—summed across all drying regions—of approximately $1 trillion (±$500 billion) in this century. For regions projected to experience increased precipitation, total investments avoided were of a similar magnitude.
Acknowledgments
Sponsors: The U.S. Department of Energy Office of ScienceBiological and Environmental Research supported this research as part of the Integrated Assessment Research program.
Reference: S.W.D. Turner, M. Hejazi, S.H. Kim, L. Clarke, J. Edmonds, "Climate Impacts on Hydropower and Consequences for Global Electricity Supply Investment Needs." Energy 141, 2081-2090 (2017). [DOI: 10.1016/j.energy.2017.11.089]
## Key Capabilities
Web Feature
### Research Team
Sean W.D. Turner, Mohamad Hejazi, Son H. Kim, Leon Clarke, and Jae Edmonds, PNNL (Joint Global Change Research Institute)
# Research Hints at Double the Driving Range for Electric Vehicles
Researchers at PNNL developed a novel electrolyte for vehicle batteries that successfully creates a protective layer around electrodes — so they won't corrode — achieving significantly increased charge/discharge cycles.
PNNL scientists spice up electrolyte solution to increase charge cycles
March 28, 2018
March 28, 2018
When it comes to the special sauce of batteries, researchers at the Department of Energy's Pacific Northwest National Laboratory have discovered it's all about the salt concentration. By getting the right amount of salt, right where they want it, they've demonstrated a small lithium-metal battery can re-charge about seven times more than batteries with conventional electrolytes.
A battery's electrolyte solution shuttles charged atoms between electrodes to generate electricity. Finding an electrolyte solution that doesn't corrode the electrodes in a lithium-metal battery is a challenge but the PNNL approach, published online in Advanced Materials, successfully creates a protective layer around the electrodes and achieves significantly increased charge/discharge cycles.
Conventional electrolytes used in lithium-ion batteries, which power household electronics like computers and cell phones, are not suitable for lithium-metal batteries. Lithium-metal batteries that replace a graphite electrode with a lithium electrode are the 'holy grail' of energy storage systems because lithium has a greater storage capacity and, therefore, a lithium-metal battery has double or triple the storage capacity. That extra power enables electric vehicles to drive more than two times longer between charges.
Adding more lithium-based salt to the liquid electrolyte mix creates a more stable interface between the electrolyte and the electrodes which, in turn, affects the life of the battery. But that high concentration of salt comes with distinct downsides - including the high cost of lithium salt. The high concentration also increases viscosity and lowers conductivity of the ions through the electrolyte.
"We were trying to preserve the advantage of the high concentration of salt, but offset the disadvantages," said Ji-Guang "Jason" Zhang, a senior battery researcher at PNNL. "By combining a fluorine-based solvent to dilute the high concentration electrolyte, our team was able to significantly lower the total lithium salt concentration yet keep its benefits."
In this process, they were able to localize the high concentrations of lithium-based salt into "clusters" which are able to still form protective barriers on the electrode and prevent the growth of dendrites - microscopic, pin-like fibers - that cause rechargeable batteries to short circuit and limit their life span.
PNNL's patent-pending electrolyte was tested in PNNL's Advanced Battery Facility on an experimental battery cell similar in size to a watch battery. It was able to retain 80 percent of its initial charge after 700 cycles of discharging and recharging. A battery using a standard electrolyte can only maintain its charge for about 100 cycles.
Researchers will test this localized high concentration electrolyte on 'pouch' batteries developed at the lab, which are the size and power of a cell phone battery, to see how it performs at that scale. They say the concept of using this novel fluorine-based diluent to manipulate salt concentration also works well for sodium-metal batteries and other metal batteries.
This research is part of the Battery500 Consortium led by PNNL which aims to develop smaller, lighter, and less expensive batteries that nearly triple the specific energy found in batteries that power today's electric cars. Specific energy measures the amount of energy packed into a battery based on its weight.
Acknowledgments
Sponsor: Department of Energy's Office of Energy Efficiency and Renewable Energy's Vehicle Technologies Office
Reference: Chen S, J Zheng, D Mei, KS Han, MH Engelhard, W Zhao, W Xu, J Liu, and JG Zhang. 2018. "High-Voltage Lithium-Metal Batteries Enabled by Localized High Concentration Electrolytes." Advanced Materials. Early online. DOI: 10.1002/adma.201706102
Read the original media release by Susan Bauer here.
## Facilities
Web Feature
### PNNL Research Team
Shuru Chen, Jianming Zheng, Donghai Mei, Kee Sung Han, Mark H. Engelhard, Wengao Zhao, Wu Xu, Jun Liu and Ji-Guang Zhang
# Marine and Coastal Research Laboratory
Facility
The Marine and Coastal Research Laboratory is uniquely positioned for marine-based research that focuses on helping the nation achieve sustainable energy, a sustaining environment, and coastal security.
Andrea Starr | Pacific Northwest National Laboratory
The Marine and Coastal Research Laboratory (MCRL), which was previously known as the Marine Sciences Laboratory, is the U.S. Department of Energy’s only marine research facility. MCRL, located at PNNL-Sequim, is uniquely positioned for marine-based research that is focused on helping the nation achieve sustainable energy, a sustaining environment, and coastal security.
Sequim Bay links a small, but relatively undisturbed, watershed to the Strait of Juan de Fuca in the Puget Sound. This allows for:
• direct studies of environmental impacts on marine species
• a potential study area for energy deployment
• use of seawater in adjacent lab facilities
• testing of innovative marine sensors
Nearly 15,000 square feet of research laboratories are connected to the bay via a supply system that delivers 200 gallons of seawater per minute and returns it to the bay after treatment. MCRL's unique location is also within one of the cleanest airsheds in the world, providing an ultratrace background for work in measurement and signature sciences.
To defend coastal regions, MCRL researchers engineer new approaches to address the greatest challenges in detecting and responding to national and global threats. Programs focus on developing efficient and effective ways to translate data acquired from environmental media—air, water, sediment, and biota—into information that can be acted upon.
MCRL research is supported by more than 80 staff members with expertise in biotechnology, biogeochemistry, ecosystems science, toxicology, and Earth systems modeling. A dive team is also on staff to support in-water research and testing. Projects at MCRL span algal biofuels, biofouling and biocorrosion, climate change and ocean acidification, environmental monitoring, quantification of transport and effects of chemicals in marine environments, and coastal risk and hazard prediction and analysis.
# Aquatic Research Laboratory
Facility
At the Aquatic Research Laboratory, PNNL scientists explore solutions for our nation’s growing need for clean, renewable energy. Projects are focused on monitoring and predicting the impacts of hydropower development and operation on water resources. The research supports the nation’s ability to optimize power production while minimizing environmental effects.
Scientists are using the Aquatic Research Laboratory to:
• expand sustainable hydropower through research and assessment of operational impacts
• advance understanding of how climate change impacts energy production, especially related to hydropower and other renewable energy
• integrate environmental protection into hydropower operations, especially related to fish passage and survival
• understand the effects of Hanford Site operations on the Columbia River ecosystem.
The availability of Columbia River water in a facility with specialized research equipment makes the Aquatic Research Laboratory a unique and valuable asset within the national laboratory system and among stakeholders in the region and beyond. The 7,400-square-foot laboratory has the following distinctive features and capabilities:
• advanced aquaculture and water reuse system for accurate and precise control of experimental conditions while conserving water and energy resources
• research equipment that simulates conditions at water development projects to study fish passage, including hyperbaric and hypobaric chambers, shear and turbulence tanks, and fish respirometers
• training and project implementation in facilities dedicated to surgery, necropsy, and analytics.
# This Historic PNNL Lab Runs 'Hot' and 'Quiet'
Jeff Katalenich, a recent PNNL Linus Pauling Postdoctoral Fellow, prepares equipment in a glove box for research on new, cleaner methods for processing plutonium-238 � a radioisotope used to heat and power space exploration probes and extraterrestrial rovers when solar power is insufficient. Rather than the very fine, easily dispersed powder used in conventional methods, he developed a wet method that reduces the risk of contamination.
Photo courtesy of Pacific Northwest National Laboratory
July 22, 2018
July 22, 2018
Peering through the thick, green glass of a decades-old "hot cell," an expert technician manipulates robotic arms to study highly radioactive waste from Hanford, in support of ongoing cleanup.
Nearby, in a recently refurbished "quiet suite," an exquisitely sensitive electron microscope reveals the atomic structure of plutonium, advancing scientific understanding of the metal that plays a central role in our community's history.
This juxtaposition of old and new is found in the Radiochemical Processing Laboratory, a 65-year-old facility that is essential to nuclear science and engineering research at the Department of Energy's Pacific Northwest National Laboratory.
For 65 years, RPL has been advancing solutions for environmental cleanup, nuclear security, energy and medicine.
Beyond hot cells, glove boxes and radiological fume hoods, this facility — known as RPL — houses specialized research equipment and scientific expertise in nuclear materials characterization, chemistry, physics and engineering to address the nation's most significant nuclear challenges.
The RPL was built to support uranium recovery and plutonium processing associated with Hanford operations in the 1950s and '60s. Its contributions to numerous programs over the decades have earned it a special place in history. Last November, the American Nuclear Society honored RPL as a Nuclear Historic Landmark.
The award recognized RPL's unique capabilities and how they underpinned scientific discoveries and technological solutions for environmental cleanup, nuclear nonproliferation, reactor safety and medical isotopes.
Harkening back to its roots, including studies in the late 1970s to investigate vitrification (where waste is solidified in a stable glass waste form), RPL still delivers solutions for Hanford cleanup. This spring, about three gallons of low-activity Hanford tank waste were vitrified at RPL, using a continuous process similar to that planned for the Vit Plant.
By demonstrating the process with actual waste instead of a simulant, researchers in RPL helped confirm the science and engineering as the plant moves toward full-scale operations.
RPL also serves a unique function related to global nuclear security and nonproliferation. It is the only radionuclide laboratory in the United States — and one of only 13 in the world — that is certified by the Comprehensive Nuclear-Test-Ban Treaty Organization to process air particulate samples collected at monitoring stations around the globe. Each year, RPL researchers analyze about 60 samples for the CTBTO, looking for signs of possible nuclear explosions.
In support of the Department of Homeland Security's efforts in counter nuclear terrorism, PNNL researchers recently established a test bed that replicates different ways plutonium can be processed. By identifying and capturing information about the resulting variations in color or density, for example, it may be possible to correlate plutonium with where it may have originated.
Addressing the need for safe and secure nuclear energy generation, PNNL developed dosimetry monitoring capsules that are custom-designed and constructed at RPL for specific reactor environments. After being installed in reactors at labs, universities and commercial facilities around the world, the capsules are returned to RPL for analysis that helps reveal radiation damage and the status of the reactor.
RPL is also contributing to the fight against cancer. Leveraging its capabilities, PNNL researchers have developed processes for making highly pure medical isotopes for research and treatment. Nearly 20 years ago, a patented process for producing yttrium-90 was licensed to a pharmaceutical company that now makes the isotope widely available.
Today, a new treatment developed by PNNL and the University of Washington is in clinical trials. This treatment is based on work at RPL to automate the radiochemical process for faster, purer production with more consistent quality.
For 65 years, RPL has been advancing solutions for environmental cleanup, nuclear security, energy and medicine. With DOE's recent approval to operate through at least 2045, it will remain an enduring asset for the nation and the world, bridging its historic past to the many contributions it will make in the decades to come.
Steven Ashby, director of Pacific Northwest National Laboratory, writes this column monthly. His other columns and opinion pieces are available here.
## Our Facilities
Director's Column
# PNNL Tech Serves as Fish Body Double
PNNL's Sensor Fish has been licensed to ATS, which will manufacture the acoustic sensors for use in studies of fish traveling through dams worldwide, along with injectable tracking devices.
PNNL's autonomous 'Sensor fish' and acoustic transmitter licensed by wildlife tracking company ATS
January 8, 2019
January 8, 2019
Hundreds of surrogate "fish" will be put to work at dams around the world through an agreement between ATS - Advanced Telemetry Systems - and the Department of Energy's Pacific Northwest National Laboratory to improve operations and increase sustainability.
PNNL developed the Sensor Fish to understand what happens to fish as they pass through turbulent waters and turbines at hydroelectric facilities. The Sensor Fish is a small autonomous device filled with sensors that analyze the physical stressors that fish, such as juvenile salmon, experience when passing through or around dams.
The technology was recently licensed to ATS through a process known as technology transfer, which enables federally-funded research to be made commercially available.
"There is a big need for the type of data provided by the Sensor Fish."
-Peter Kuechle
The sensors provide dam operators and fisheries researchers with accurate, physical measurements such as acceleration, pressure, rotational velocity and orientation, which convey what real fish experience during downstream passage. Each sensor provides roughly 2,000 measurements per second and typically takes less than two minutes to pass through the dam due to the water's velocity.
"The vast majority of juvenile salmon and steelhead passing through the turbines survive without injury in the Columbia River Basin," said Daniel Deng, a Laboratory Fellow at PNNL. "Still, we want to understand more about the injuries and mortality that do occur from abrupt pressure changes in dam turbine chambers. The Sensor Fish provides information to help engineers design more fish-friendly turbines going forward."
Once the Sensor Fish comes out on the other side of the dam, an automatic retrieval system brings it to the surface. Radio signals and flashing LED lights from the Sensor Fish will then allow them to be collected quickly from boats stationed nearby.
The Sensor Fish has demonstrated its value in many field studies, for which Deng's team has built individual Sensor Fish in their lab at PNNL. Now, with the technology licensed to ATS, the manufacturing process can be streamlined, and more hydropower operators and researchers will be able to put it to use.
"There is a big need for the type of data provided by the Sensor Fish," says ATS president Peter Kuechle. "Mature hydropower industries in the U.S. and Europe hope to modify operations in order to help fish survive. In Europe, regulations insist on testing for this information, and certainly there's a need for the data in emerging hydropower projects globally."
ATS has also licensed two other fish technologies developed at PNNL. The Juvenile Salmon Acoustic Telemetry System (JSATS) and its advanced decoder software that can track fish passage through dams and beyond, and also monitor fish behavior. PNNL developed the JSATS transmitters and battery to be so small it can be injected into young fish — eliminating the need to surgically implant a tag, which puts extra stress on a fish. The JSATS includes the smallest acoustic transmitters in the world. PNNL has also recently developed an even smaller tag technology that allows for research on the tiniest fish including juvenile eel and lamprey.
"This new acoustic fish tag meets the Army Corps of Engineers' JSATS specifications and weighs less than one one-hundredth of an ounce," said Kuechle. "The JSATS technology is complementary to our long history offering innovative and cost-effective wildlife tracking products and we're proud to have supplied the devices to the Army Corps this year for an important study on the lower Snake River."
PNNL also has developed bigger, rugged tags with larger batteries to enable research on large and long-lived species such as sturgeon. PNNL is working to develop a self-powered tag that would enable long-term monitoring.
PNNL's tracking and sensing technologies are applicable to a wide range of species, research goals, commercial applications and locations. The laboratory has validated its tracking and sensing technologies with more than 100,000 fish in the U.S., Australia, Brazil, Germany and East Asian countries since 2007. They are also applicable to a wide range of species, research, locations and commercial applications. They are available for testing with small mammals and amphibians.
The development of these technologies was funded over many years by the Army Corps of Engineers, DOE's Office of Energy Efficiency and Renewable Energy and the Electric Power Research Institute.
Pacific Northwest National Laboratory draws on signature capabilities in chemistry, earth sciences, and data analytics to advance scientific discovery and create solutions to the nation's toughest challenges in energy resiliency and national security. Founded in 1965, PNNL is operated by Battelle for the U.S. Department of Energy's Office of Science. DOE's Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit PNNL's News Center. Follow us on FacebookInstagramLinkedIn and Twitter.
News Release
# Sue Clark Re-Elected to Washington State Academy of Sciences Board of Directors
September 11, 2017
September 11, 2017
Congratulations to Dr. Sue Clark on being elected to a second term on the Washington State Academy of Sciences Board of Directors. As a board member, she works to provide objective scientific and technological information on important issues to inform public policy making and increase the role and visibility of research in the Evergreen State. Clark is a Battelle Fellow who holds a joint appointment at Pacific Northwest National Laboratory (PNNL) and Washington State University (WSU). She is also the Chief Scientist and Technology Officer for the Energy and Environment Directorate at PNNL.
Currently, Clark leads research into the processing of high-level radioactive wastes and the environmental chemistry of plutonium and other actinides. She is the director of the Interfacial Dynamics in Radiation Environments and Materials (IDREAM) Energy Frontier Research Center, funded by the U.S. Department of Energy's Office of Science and Office of Environmental Management. At WSU, she is a Regents Professor in the Chemistry Department, having served on the faculty for more than 20 years.
Clark's expertise is sought after in the United States and abroad. For example, she served for 3 years on the U.S. Nuclear Waste Technical Review Board, appointed by the U.S. President. She has also completed consultancies with the International Atomic Energy Agency, supporting the development of educational programs and policies related to nuclear security and nuclear forensics.
Clark's expertise, drive, and mentoring have earned her awards and honors, including the American Chemical Society Garvan-Olin Medal for her research activities and advocacy for advancing women chemists, Fink Distinguished Lecturer at Georgia Institute of Technology, and the Edward R. Meyer Distinguished Professor of Chemistry at WSU. She is a member of the American Chemical Society, the American Association for the Advancement of Science, and Sigma Xi.
## Researchers
### Sue Clark
Chief Science and Technology Officer, Battelle Fellow, IDREAM Director
## Key Capabilities
Staff Accomplishment
### Research topics
Facility
Researchers at PNNL use the Advanced Battery Facility to prepare, fabricate, and validate pouch cells. The laboratory includes a semi-automatic system for film casting and pouch-cell assembly, and an ambient lab for powder handling and mixing.
Andrea Starr | Pacific Northwest National Laboratory
Bridging the gap between fundamental battery research and development
Focused on accelerating the development of the next generation of energy storage technologies, PNNL features a host of facilities that make up a holistic development program. The Advanced Battery Facility (ABF) houses much of the critical work done in this process.
The ABF was built to bridge the gap between fundamental battery research and commercial-scale battery development. The facility provides an ideal system for exploring a broad range of chemistries and materials at a commercially relevant scale. It also contains a complete process line capable of preparing, fabricating, and validating pouch cells from powder materials to battery testing.
The ABF is a user facility that compliments the Department of Energy’s other facilities in the development of high-density energy storage systems for electric vehicles. Scientists there collaborate with their counterparts in industry, academia, and national security. The lab features:
• a 600-square-foot dry room
• a 600-square-foot ambient lab dedicated to developing anode materials, slurry, and electrolytes, and performing pouch-cell lifetime testing
• standard pouch cell capacity of 1 ampere hour (Ah), which can be adjusted from 100 milliampere hours to 2 Ah
This makes the ABF ideal for the development of new battery chemistries, including lithium-sulfur, sodium-ion, and magnesium batteries, as well as the next generation of lithium-ion batteries.
With its capabilities spanning development and validation of new chemistries, to validating consumer-developed and commercial materials, the ABF is at the heart of energy storage research efforts at PNNL.
The ABF is part of the integrated facility for battery research at PNNL that include state-of-the-art imaging and spectroscopic characterization tools, and a variety of standard testing and diagnostic equipment, and unique capabilities for grid applications to test and validate the performance of the batteries for both grid and transportation.
# Detailed Look at Hanford Site Waste Offers Insights, Ideas
January 10, 2018
January 10, 2018
Congratulations to Reid Peterson, Jaehun Chun, and Sue Clark of the IDREAM Energy Frontier Research Center on their role in a groundbreaking paper. They were part of a team of authors representing Pacific Northwest National Laboratory, Washington River Protection Solutions and Washington State University and funded by PNNL's Nuclear Processing Science Initiative. The paper provides a view into the radioactive waste stored in the Hanford Site's underground tanks and offers some new perspectives on understanding of tank waste properties.
The paper, "Review of the Scientific Understanding of Radioactive Waste at the U.S. DOE Hanford Site," was published in December 2017 in the online version of Environmental Science and Technology.
At the Hanford Site in southeastern Washington State, approximately 56 million gallons of mixed radioactive and chemical waste were produced from the processing of irradiated fuel to recover plutonium for nuclear weapons. The waste was generated over a 40-year period, is stored in 177 underground tanks, and is expected to cost many billions of dollars to remediate.
The paper examines the history and general character of the tank waste, including complexity and physical and chemical behaviors that impact treatment and disposal. The document asserts that prediction and control of waste behavior will require quantitative information on the physics and chemistry of particle-fluid interfaces, as well as higher spatial and chemical resolution of the solid phase. The authors point out that new microscopy advances are enabling physics/chemistry-based predictive models of waste behavior, which could lead to more effective processing methods.
The research team members are Reid Peterson, Edgar Buck, Jaehun Chun, Richard Daniel, Eugene Ilton and Gregg Lumetta of PNNL; Daniel Herting of WRPS; and Sue Clark, who serves in a joint PNNL-WSU appointment.
## Researchers
### Sue Clark
Chief Science and Technology Officer, Battelle Fellow, IDREAM Director
Web Feature
# Environmental Health Risks and the Human Microbiome
January 19, 2018
January 19, 2018
Brian Thrall, who directs PNNL's Biological Systems Science group, was among 18 authors of a report just released online assessing the role of the human microbiome in exposure to environmental chemicals.
"Environmental Chemicals, the Human Microbiome, and Health Risk: A Research Strategy" was sponsored by the National Academies of Sciences, Engineering and Medicine on behalf of the U.S. Environmental Protection Agency and the National Institute of Environmental Health Science.
A lot is known about how the human microbiome interacts with chemicals, said Thrall. But that has more to do with therapeutic drugs than environmental chemicals.
Although the United States has a robust framework for assessing the risks of chemical exposure, that framework does not account for how the human microbiome responds to environmental chemicals or how it modifies, mitigates, or aggravates such exposures.
So far, he said, "the microbiome has not been considered, by itself, a potential component of variation and response to chemical exposures."
The research agenda set out by the report could change that, said Thrall, with PNNL well poised to play an important role. He cited the Lab's strengths in chemical biology, microbiome function, chemical exposure, and multiomics and health.
Web Feature
# Ambitious IDREAM Meeting Nets Insights and Ideas
Kevin Rosso, Pacific Northwest National Laboratory, talks with Patricia Huestis, University of Notre Dame, about her research on surface and bulk effects of heat and radiation on boehmite.
February 13, 2018
February 13, 2018
Congratulations to the IDREAM Energy Frontier Research Centeron their latest all-hands meeting. At this 3-day event, researchers and advisors discussed how the center is answering tough questions about complex radioactive environments. Throughout the gathering, scientists from Pacific Northwest National Laboratory, Georgia Institute of Technology, Oak Ridge National Laboratory, University of Notre Dame, University of Washington, and Washington State University presented their research and shared ideas.
Their efforts were rewarded with thoughtful insights from the center's advisory committee. The advisors gave detailed advice about the current research and future directions.
At the meeting, two popular collaboration events were the poster session and the early career dinner. At the poster session, scientists spent nearly 2 hours talking about their work, whether that was reactivity in highly alkaline electrolytes or the influence of radiation on such systems. At the dinner, graduate students and postdoctoral fellows, many of whom had never met in person before, became fast friends over the task of building the tallest freestanding tower that could support a marshmallow. The bragging rights went to a trio from Washington State University: David Semrouni, Trent Graham, and Tyler Biggs.
In addition, the scientists had in-depth conversations about the best practices and upcoming plans for sharing their results. They also discussed data management, including the need for access and context, and planned for upcoming scientific publications in high-profile journals.
"Within IDREAM, we benefit tremendously from the energy and enthusiasm of all team members, especially our early career scientists," said Dr. Sue Clark, IDREAM Director. "We also benefit from the constructive comments we receive from our advisory committee."
The team is already acting on the advisory committee's suggestions and taking steps to further elevate the research as they go into their mid-year review with the U.S. Department of Energy, Office of Science, Basic Energy Sciences, which funds the center.
The all-hands meeting was held in Richland, Washington, from January 14 through 16, 2018.
## Key Capabilities
Staff Accomplishment
# Bio-Acoustics and Flow Laboratory
Facility
Pacific Northwest National Laboratory (PNNL) is supporting the design of new hydropower systems that minimize or avoid environmental impacts by understanding fish injury and mortality through hydropower systems.
Researchers Huidong Li and Aljon Salalila are assembling next-generation acoustic transmitters for remotely tracking sensitive species in one, two, or three dimensions with sub-meter accuracy. PNNL’s tracking and sensing technologies are applicable to a wide range of species, research goals, commercial applications, and locations.
Andrea Starr | Pacific Northwest National Laboratory
At PNNL’s Bio-Acoustics and Flow Laboratory, scientists explore ways to integrate environmental protection for fish passage and survival in hydropower operations. The Bio-Acoustics and Flow Laboratory addresses a range of engineering and ecological issues, with an emphasis on environmental monitoring and risk assessment for conventional hydropower, wind, marine, and hydrokinetic renewable energy systems.
The laboratory includes an applied acoustics team consisting of chemists, battery engineers, electrical engineers, mechanical engineers, materials scientists, mathematicians, and fish biologists. This multi-disciplinary team allows PNNL to address acoustic technology problems across the range from basic material properties of acoustic system elements, instrumentation, and applications, to propagation modeling.
The American Association for Laboratory Accreditation has accredited the Bio-Acoustics and Flow Laboratory. This certification permits PNNL to perform primary certified testing on instruments made by others and also perform certified testing on instruments that PNNL builds. The laboratory supports thorough system calibration checks and troubleshooting for the many active and passive acoustic instruments used for projects conducted by PNNL.
Laboratory staffers have extensive experience in flow measurements both in the laboratory and field environments. Projects include the development of acoustic microtransmitters and receivers for aquatic animals, , radio-frequency transmitter for small bats and birds, sensor fish to support advanced hydropower development, and the development of the Marine Animal Alert System.
# Sawdust Reinvented into Super Sponge for Oil Spills
PNNL microbiologist George Bonheyo displays the original sawdust material (left) and how it appears after being chemically modified (right) to be exceptionally oil-attracting and buoyant, qualities that are ideal for cleaning up oil spills in the Arctic.
Environmentally friendly material tweaked to soak up to 5 times its weight in oil, float 4 months in icy, rough waters
December 12, 2016
December 12, 2016
Lowly sawdust, the sawmill waste that's sometimes tossed onto home garage floors to soak up oil spilled by amateur mechanics, could receive some new-found respect thanks to science.
Researchers at the Department of Energy's Pacific Northwest National Laboratory have chemically modified sawdust to make it exceptionally oil-attracting and buoyant, characteristics that are ideal for cleaning oil spills in the icy, turbulent waters of the Arctic. The nontoxic material absorbs up to five times its weight in oil and stays afloat for at least four months.
"The chance of an oil spill in the Arctic is real. We hope materials like our modified sawdust can help if an accident happens."
-Robert Jeters
"Most of today's oil remediation materials are designed for warm water use," said PNNL microbiologist George Bonheyo, who leads the modified sawdust's development from PNNL's Marine Sciences Laboratory.
"But as ice retreats in the Arctic Sea, fossil fuel developers are looking north, and we need new oil spill response methods that perform well in extreme conditions," added Bonheyo, who also holds a joint appointment in bioengineering with Washington State University.
"The chance of an oil spill in the Arctic is real," said fellow PNNL microbiologist Robert Jeters, who is also part of the project. "We hope materials like our modified sawdust can help if an accident happens."
## Fire & ice
Containing oil spills in cold waters is especially tricky, as bobbing ice chunks push oil below the water's surface, making it difficult to collect. The same goes for rough waters, whose tall, clashing waves disperse oil.
The modified saw dust pulls double duty. Beyond absorbing oil, it also enhances another approach to combatting oil spills — controlled burns. If changing weather or tides move spilled oil toward a sensitive area fast, oil can be burned before it can cause further harm. Called in-situ burning, the practice can significantly reduce the amount of oil in water and minimize its adverse environmental effects.
Bonheyo and his team looked to develop an environmentally friendly and inexpensive material that floats despite rough or freezing waters and can support in-situ burning. Not wanting to create more pollution if emergency responders can't retrieve oil cleanup material, Bonheyo's team considered other natural ingredients like rice hulls and silica. But they ultimately found their winner in a fine dust called wood flour. A woodworking byproduct, wood flour is often used to make wood composites.
To turn the dust into a thirsty oil mop, researchers chemically attach components of vegetable oil onto the material's surface. These attachments make the modified material oil-grabbing and water-shunning. The final product is a light, fluffy, bleached powder. The team is also trying out adding tiny, oil-eating microbes — fungi and bacteria — to the powder's surface so any left-behind material could naturally break down oil over time.
## Just a sprinkle
Applying the modified sawdust is simple: sprinkle a thin layer over oil on the water's surface. The material immediately starts soaking up oil, creating a concentrated and solid slick that stays afloat thanks to the material's buoyant nature. The oil-soaked material can either be burned or retrieved.
The team is using PNNL's unique Arctic simulation lab in Sequim, Washington to evaluate the material in icy waters. The facility is a customized shipping container that cools down to as low as 5 degrees Fahrenheit, which prompts researchers to don snowmobile suits and ski masks while they work. Ice slush forms on the surface of water that circulates inside a 290-gallon raceway pond placed inside the bitterly cold lab space. Oil is spilled on the slushy surface, followed by a sprinkle of modified sawdust. Tests have shown the material's water-repellent nature prevents ice from forming on it, allowing it to soak up oil and remain at the surface.
Researchers are also testing how well the material performs in controlled burns. They conducted initial burns this fall at the U.S. Coast Guard and Naval Research Laboratory's Joint Maritime Test Facility near Mobile, Alabama. Burn tests continue today at PNNL's Marine Science Laboratory. Early results indicate a small amount of material enables burning of both thin and thick layers of spilled oil.
In the coming months, PNNL will further evaluate the modified sawdust. The material will need additional testing and approval by multiple agencies before it can be used at actual oil spills.
PNNL is developing the material for the Department of Interior's Bureau of Safety of Environmental Enforcement. BSEE is the lead federal agency charged with improving safety and ensuring environmental protection related to the offshore energy industry, primarily oil and natural gas on the U.S. Outer Continental Shelf.
The material's development team includes Bonheyo, Jeters, Yongsoon Shin, Jiyeon Park, Andrew Avila and Maren Symes.
News Release
# PNNL Moves Cybersecurity Software and a Novel Disinfecting System Beyond the Lab
Cybersecurity software developed at Pacific Northwest National Laboratory learns about a company to better protect it. Called CHAMPION, the software can reason like an analyst to determine if network activity is suspicious. It then issues an alert in near-real-time. PNNL Shawn Hampton (left), Champion Technology Company's Ryan Hohimer (right) and their teams received an R&D 100 and FLC Award for developing this technology.
PNNL Wins Federal Laboratory Consortium Award for Bringing Government Technologies to the Marketplace
January 28, 2016
January 28, 2016
Software that helps cybersecurity analysts prevent hacks and a microbial disinfecting system that kills with an activated salt spray are two of the latest innovations Pacific Northwest National Laboratory has successfully commercialized with the help of business partners.
Due to the unique paths the development teams took to get the technology from Department of Energy lab to the private sector, the Federal Laboratory Consortium has honored the two teams made up of lab and commercial business staff with 2016 Excellence in Technology Transfer awards. The consortium is a nationwide network that encourages federal laboratories to transfer laboratory-developed, taxpayer-funded technologies to commercial markets.
PNNL has earned a total of 83 such awards since the program began in 1984 — far more than any other national laboratory. The 2016 awards will be presented April 27 in Chicago, Illinois, at the consortium's annual meeting.
## Software "CHAMPIONs" cybersecurity experts
If you're a hacker aimed at stealing credit card information from a retail company and you want to evade detection, you hide in massive amounts of network data. Analysts have the know-how to sort through this digital mess to find hackers, but they often identify attacks too late. Analytical software developed at PNNL and licensed to Champion Technology Company Inc. can help find these and other threats in near-real-time. That's because the software, called Columnar Hierarchical Auto-associative Memory Processing in Ontological Networks — or CHAMPION, has the knowledge to sort through data like an analyst, but on a much greater scale.
Scientists designed CHAMPION to use human analysts and historical data to learn about the company it's protecting. Starting with advanced Semantic Web technologies, which translate human knowledge into something that's machine readable, CHAMPION then uses descriptive logic to reason whether activity is suspicious. For example, if a retail company's HVAC data back-up account tries to access the point-of-sale system, CHAMPION could use historical data to conclude that this is unusual. Once identified, the software alerts an analyst of the suspicious activity — in time to potentially thwart an attack.
Sorting through data can consume up to 40 percent of an analyst's day. By streamlining these tasks, CHAMPION can save money and free analysts to focus on higher-priority tasks. And cybersecurity isn't CHAMPION's only trick. Change its diet of knowledge and the software can learn to analyze financial services or health care data.
This technology transfer involved a unique collaboration between PNNL and Early X, a non-profit education foundation spun out from Pepperdine University's Graziadio School of Business and Management. In this effort, a group of MBA students and diverse business executives identified 70 market opportunities for CHAMPION. This groundwork led to the start of Champion Technology Company Inc.
The team receiving an FLC Award for CHAMPION includes: PNNL's Shawn Hampton and Kannan Krishnaswami; Champion Technology Company's Ryan Hohimer; and former PNNL staff John McEntire, Frank Greitzer and Matthew Love.
## Killing pathogens with a fine, salty mist
Microbes — tiny bits of life such as bacteria, viruses and mold — can wreak havoc on our bodies by causing sickness and even death. Ranging from staph infections to Ebola, many microbe-caused ailments can now be prevented with the Micro Aerosol Disinfecting System.
The system turns a simple table salt solution into a fine mist containing natural molecules that disinfect an entire room. Tests have shown the system can kill at least 99.9999 percent of health-harming microbes. It could be used to disinfect hospitals, gymnasiums, schools and other enclosed spaces. It's far more effective, easier to apply and less expensive than other disinfection methods.
It works by running an electrical current through a diluted salt solution, which creates super-reactive molecules, ions, and free radicals that have exceptionally strong disinfecting properties. A device then turns the activated solution into a micro aerosol mist, which is released into a room. The aerosol's microscopic droplets disinfect the air and every surface. Its activated molecules destroy microbes inside a treated room within minutes to a few hours, depending on a room's size and the amount of pathogens present.
Watertech Equipment and Sales LLC of Mount Pleasant, South Carolina, licensed the Micro Aerosol Disinfecting System from PNNL. PNNL initially developed a prototype of the technology through a now-concluded DOE program that supported former weapons scientists in non-weapons research and development across the former Soviet Union. The technology was further developed with internal PNNL funding and support from the Defense Threat Reduction Agency, which attracted Watertech's attention.
The award recognizes PNNL's extensive development and testing of the technology using internal funding to advance the technology to the point that Watertech licensed the technology just eight months after initially visiting with PNNL.
Watertech has adapted the system into an easy-to-deploy product to be sold for various uses, including hospital and clinical disinfection, mold remediation, and supporting the agricultural and food processing industries. The team recognized for transferring this process includes: PNNL's Evguenia Rainina, Ron Thomas and Derek Maughan, as well as Watertech's Glenn Barrett, Keith Johnson and Eric Frische.
For more information on technology transfer programs at PNNL, visit their website.
News Release
# Adventures of Women in Science
Molly O'Hagan, a catalysis scientist at PNNL, creates more efficient catalysts that convert renewable energy into fuels such as hydrogen. Much of her inspiration comes from studying enzymes found in nature.
Videos feature women who lead and inspire at PNNL
March 30, 2017
March 30, 2017
When salmon journey down the Columbia River or molecules rearrange to become renewable fuel, you can count on research teams at Department of Energy's Pacific Northwest National Laboratory to follow. At the center of many of these teams are women-scientists and engineers who chase mystery and replace it with discoveries. In honor of Women's History Month, four scientists at PNNL share their stories in a video series called Women in Research:
• Alison Colotelo, an ecology scientist, studies how hydropower dams affect salmon and other migratory fish.
• Nicole Nichols, a data scientist, studies how to find answers hidden in complex data-like identifying cancer cells in images or locating whales by the sound they make. Nicole has a doctorate in electrical engineering.
• Molly O'Hagan, a catalysis scientist, studies natural enzymes to learn how to make better synthetic catalysts that convert renewable energy into fuels such as hydrogen.
• Kathe Todd-Brown, a soil scientist, studies how soil produces carbon dioxide-and how to model that cycle on a global scale. Kathe has a doctorate in Earth systems science and is a Linus Pauling Postdoctoral Fellow.
The researchers talk about their journey becoming who they are today. They give advice on finding allies and mentors; overcoming failure and adversity; and balancing career and family. You can find the Women in Research video series on PNNL's YouTube channel.
News Release
# Steel Structure Shelters Sarcophagus at Chernobyl
Battelle researcher Andrei Glukhov, "on loan" to Bechtel at Slavutych, stands in front of the New Safe Confinement steel structure then still under construction at the Chernobyl Nuclear Power Plant.
Engineering wonder slid into place more than three decades later
April 26, 2017
April 26, 2017
Today marks the 31st anniversary of the catastrophic explosion at the Chernobyl Nuclear Power Plant's Unit 4 reactor. The blast discharged 400 times the radioactivity released by the Hiroshima bomb and drove nearly 200,000 people from their homes near the plant in Ukraine.
Now, the hastily built sarcophagus used to temporarily contain what remained of the reactor's hull after the meltdown has been permanently entombed. A massive steel arch was built, and in 2016, slid over the sarcophagus where it is expected to safely and securely contain the radioactive debris for 100 years.
In the early 1990s, Battelle, operator of the Department of Energy's Pacific Northwest National Laboratory, was part of an international consortium looking at the long-term safety and containment of Unit 4 at Chernobyl. Through 2014, Battelle researchers at PNNL applied their expertise in nuclear science, safety, remediation and engineering to help Ukrainians.
## The World's Largest Moveable Structure
Among their many contributions, researchers led the early designs for the arch steel structure called the New Safe Confinement. The effort was billed as the world's largest moveable structure — 843 feet across, 355 feet high and 492 feet in length. That's roughly the size of two Manhattan blocks and tall enough to enclose the Statue of Liberty.
Though Battelle withdrew from the project in 2014, a few Battelle researchers remained "on loan" to Bechtel at Slavutych to oversee construction and movement of the NSC to its final destination. Construction of the nearly 40,000-ton structure began in 2010, and it was delicately moved in November 2016 over the sarcophagus.
Battelle's Andrei Glukhov, who was a reactor operator at the Chernobyl Nuclear Power Plant when the catastrophe occurred, was among those who remained. Glukhov and other researchers recently returned to PNNL. But from 1994 through 2014, more than 200 employees contributed to help improve safety at the Chernobyl site. Several researchers uprooted entire families, relocating them from the Tri-Cities to Slavutych to be closer to where the solutions were needed. In addition to contributing scientific research and engineering, they introduced to Slavutych one of the U.S.'s favorite games — baseball.
Read more about our work at Chernobyl and view photos of the NSC here.
News Release
# Video Captures Bubble-blowing Battery in Action
PNNL researcher Chongmin Wang and colleagues have developed the first step-by-step explanation of how a lithium-air battery forms bubbles, which expand the battery and create wear and tear that can cause it to fail. The research was aided by an environmental transmission electron microscope (shown here), which enabled the creation of a first-of-a-kind video that shows bubbles inflating and later deflating inside a nanobattery.
Researchers propose how bubbles form, could lead to smaller, more stable lithium-air batteries
April 26, 2017
April 26, 2017
With about three times the energy capacity by weight of today's lithium-ion batteries, lithium-air batteries could one day enable electric cars to drive farther on a single charge.
But the technology has several holdups, including losing energy as it stores and releases its charge. If researchers could better understand the basic reactions that occur as the battery charges and discharges electricity, the battery's performance could be improved. One reaction that hasn't been fully explained is how oxygen blows bubbles inside a lithium-air battery when it discharges. The bubbles expand the battery and create wear and tear that can cause it to fail.
A paper in Nature Nanotechnology provides the first step-by-step explanation of how lithium-air batteries form bubbles. The research was aided by a first-of-a-kind video that shows bubbles inflating and later deflating inside a nanobattery. Researchers had previously only seen the bubbles, but not how they were created.
"If we fully understand the bubble formation process, we could build better lithium-air batteries that create fewer bubbles," noted the paper's corresponding author, Chongmin Wang, of the Department of Energy's Pacific Northwest National Laboratory. "The result could be more compact and stable batteries that hold onto their charge longer."
PNNL researchers used an environmental transmission electron microscope to record a first-of-a-kind video that shows bubbles inflating and later deflating inside a tiny lithium-air battery. The video helped researchers develop the first step-by-step explanation of how lithium-air batteries form bubbles. The knowledge could help make lithium-air batteries that are more compact, stable and can hold onto a charge longer.
Wang works out of EMSL, the Environmental Molecular Sciences Laboratory, a DOE Office of Science user facility located at PNNL. His co-authors include other PNNL staff and a researcher from Tianjin Polytechnic University in China.
The team's unique video may be a silent black-and-white film, but it provides plenty of action. Popping out from the battery's flat surface is a grey bubble that grows bigger and bigger. Later, the bubble deflates, the top turning inside of itself until only a scrunched-up shell is left behind.
The popcorn-worthy flick was captured with an in-situ environmental transmission electron microscope at EMSL. Wang and his colleagues built their tiny battery inside the microscope's column. This enabled them to watch as the battery charged and discharged inside.
Video evidence led the team to propose that as the battery discharges, a sphere of lithium superoxide jets out from the battery's positive electrode and becomes coated with lithium oxide. The sphere's superoxide interior then goes through a chemical reaction that forms lithium peroxide and oxygen. Oxygen gas is released and inflates the bubble. When the battery charges, lithium peroxide decomposes, and leaves the former bubble to look like a deflated balloon.
This finding was the focus of a Nature News & Views column written by researchers at Korea's Hanyang University, who describe the research as "a solid foundation for future Li-O2 battery designs and optimization."
This research was supported by DOE's Office of Energy Efficiency and Renewable Energy.
Reference: Langli Luo, Bin Liu, Shidong Song, Wu Xu, Ji-Guang Zhang, Chongmin Wang, Revealing the reaction mechanisms of Li-O2 batteries using environmental transmission electron microscopy, Nature Nanotechnology, March 27, 2017, DOI: 10.1038/nnano.2017.27.
Read more in this News & Views article: Yang-Kook Sun and Chong S. Yoon, Lithium-oxygen batteries: The reaction mechanism revealed, Nature Nanotechnology, March 27, 2017, DOI: 10.1038/nnano.2017.40.
News Release
# DOE's Environmental Management Leader Visits PNNL Glass Lab
The acting head of DOE's Environmental Management Office, Sue Cange (second from right) learns about immobilizing nuclear waste in glass at PNNL.
April 28, 2017
April 28, 2017
Glass scientists at Pacific Northwest National Laboratory hosted the Department of Energy's Acting Assistant Secretary for Environmental Management, Sue Cange earlier this month. DOE's Office of Environmental Management's mission is to complete the safe cleanup of the environmental legacy brought about from five decades of nuclear weapons development and government-sponsored nuclear energy research.
Cange was visiting the Hanford nuclear site along with her chief of staff Betsy Connell and associate principle deputy assistant secretary for field operations Stacy Charboneau. They took time out to tour the laboratory where PNNL researchers study the science underpinning vitrification — the process of turning nuclear waste into glass. PNNL scientists support DOE's Waste Treatment and Immobilization Plant, under construction now, where the waste will be mixed with glass-forming materials and melted into a durable glass form for safe, long-term storage.
Cange learned how the challenges of Hanford's chemically diverse waste are met using scientific glass formulation methods to increase waste loading in the glass and minimize the volume of glass and hence reduce the cost of the clean-up effort. Cange also saw the Laboratory Scale Melter system which is being used to understand the dynamic process of converting the liquid waste into solid glass.
PNNL is world-renowned for its expertise in glass formulation and processing — knowledge that is instrumental to the work done in partnership with the DOE Office of River Protection to develop the vitrification process.
The PNNL Director's Column has more information on how the laboratory supports Hanford cleanup efforts.
News Release
# ShAPEing the Future of Magnesium Car Parts
A 50 mm diameter tube with a 1.5 mm wall thickness created from a solid chunk of magnesium alloy using PNNL's ShAPE™ extrusion process.
New approach makes lightest automotive metal more economic, useful
August 22, 2017
August 22, 2017
Magnesium — the lightest of all structural metals — has a lot going for it in the quest to make ever lighter cars and trucks that go farther on a tank of fuel or battery charge.
Magnesium is 75 percent lighter than steel, 33 percent lighter than aluminum and is the fourth most common element on earth behind iron, silicon and oxygen. But despite its light weight and natural abundance, auto makers have been stymied in their attempts to incorporate magnesium alloys into structural car parts. To provide the necessary strength has required the addition of costly, tongue-twisting rare elements such as dysprosium, praseodymium and ytterbium — until now.
"Using our process, we have enhanced the mechanical properties of magnesium to the point where it can now be considered instead of aluminum for these applications — without the added cost of rare-earth elements."
-Scott Whalen
A new process developed at the Department of Energy's Pacific Northwest National Laboratory, should make it more feasible for the auto industry to incorporate magnesium alloys into structural components. The method has the potential to reduce cost by eliminating the need for rare-earth elements, while simultaneously improving the material's structural properties. It's a new twist on extrusion, in which the metal is forced through a tool to create a certain shape, kind of like dough pushed through a pasta maker results in different shapes.
Initial research, described recently in Materials Science and Engineering A, and Magnesium Technology, found the PNNL-developed process greatly improves the energy absorption of magnesium by creating novel microstructures which are not possible with traditional extrusion methods. It also improves a property called ductility — which is how far the metal can be stretched before it breaks. These enhancements make magnesium easier to work with and more likely to be used in structural car parts. Currently, magnesium components account for only about 1 percent, or 33 pounds, of a typical car's weight according to a DOE report.
"Today, many vehicle manufacturers do not use magnesium in structural locations because of the two Ps; price and properties," said principal investigator and mechanical engineer Scott Whalen. "Right now, manufacturers opt for low-cost aluminum in components such as bumper beams and crush tips. Using our process, we have enhanced the mechanical properties of magnesium to the point where it can now be considered instead of aluminum for these applications — without the added cost of rare-earth elements."
## A new spin on things
Researchers theorized that spinning the magnesium alloy during the extrusion process would create just enough heat to soften the material so it could be easily pressed through a die to create tubes, rods and channels. Heat generated from mechanical friction deforming the metal, provides all of the heat necessary for the process, eliminating the need for power hungry resistance heaters used in traditional extrusion presses.
## The shape of things to come
The PNNL team designed and commissioned an industrial version of their idea and received a one-of-a-kind, custom built Shear Assisted Processing and Extrusion machine — coining the acronym for ShAPE™.
With it, they've successfully extruded very thin-walled round tubing, up to two inches in diameter, from magnesium-aluminum-zinc alloys AZ91 and ZK60A, improving their mechanical properties in the process. For example, room temperature ductility above 25 percent has been independently measured, which is a large improvement compared to typical extrusions.
"In the ShAPE™ process, we get highly refined microstructures within the metal and, in some cases, are even able to form nanostructured features," said Whalen. "The higher the rotations per minute, the smaller the grains become which makes the tubing stronger and more ductile or pliable. Additionally, we can control the orientation of the crystalline structures in the metal to improve the energy absorption of magnesium so it's equal to that of aluminum."
## The push to save energy
The billets or chunks of bulk magnesium alloys flow through the die in a very soft state, thanks to the simultaneous linear and rotational forces of the ShAPE™ machine. This means only one tenth of the force is needed to push the material through a die compared to conventional extrusion.
This significant reduction in force would enable substantially smaller production machinery, thus lowering capital expenditures and operations costs for industry adopting this patent pending process. The force is so low, that the amount of electricity used to make a one-foot length of two-inch diameter tubing is about the same as it takes to run a residential kitchen oven for just 60 seconds.
Energy is saved since the heat generated at the billet/die interface is the only process heat required to soften the magnesium. "We don't need giant heaters surrounding the billets of magnesium like industrial extrusion machines, said Whalen. "We are heating — with friction only — right at the place that matters."
Magna-Cosma, a global auto industry parts supplier, is teaming with PNNL on this DOE funded research project to advance low cost magnesium parts and, as larger tubes are developed, will be testing them at one of their production facilities near Detroit.
PNNL's ShAPE™ technology is available for licensing and could help to make a dent in the auto industry's magnesium target, and slim down cars which currently weigh an average of 3,360 pounds.
Reference:
N. Overman, S. Whalen, M. Olszta, K. Kruska, J. Darsell, V. Joshi, X. Jiang, K. Mattlin, E. Stephens, T. Clark, S. Mathaudhu, "Homogenization and Texture Development in Rapidly Solidified AZ91E Consolidated by Shear Assisted Processing and Extrusion (ShAPE)," Materials Science and Engineering A, 701, 56-68, 2017, June 12, 2017, DOI: 10.1016/j.msea.2017.06.062.
S. Whalen, V. Joshi, N. Overman, D. Caldwell, C. Lavender, T. Skszek, "Scaled-Up Fabrication of Thin-Walled Magnesium ZK60 Tubing using Shear Assisted Processing and Extrusion (ShAPE)," Magnesium Technology, 315-321, Feb 16, 2017, DOI: 10.1007/978-3-319-52392-7_45.
News Release
# How Low Can You Go?
More than 100 experts in detecting extremely low levels of radiation met in the United States for the first time in 2016. Proceedings of the meeting, held in Seattle, have recently been published in the Journal of Applied Radiation and Isotopes.
Scientists worldwide are measuring ever smaller amounts of radiation
October 19, 2017
October 19, 2017
Very low levels of radiation can tell scientists a lot about our world. New approaches and techniques for measuring very low or trace levels of radiation have recently been featured in a special issue of the Journal Applied Radiation and Isotopes which published the proceedings of the 7th Low-Level Radioactivity Measurement Techniques conference.
The international conference was held for the first time in the U.S. and focused on low-level radiation measurement techniques from around the world. The ability to measure trace levels of radiation activity is challenging but crucial for:
• Water Security — understanding environmental processes via radioisotope transport in oceans and groundwater resources
• Food Security — meeting standards for radioactivity in everything from drinking water, to food products, to building materials
• Nuclear Security — monitoring nuclear treaties with sensitive measurements of radioactivity released by nuclear tests
• Energy Security — supporting a new generation of fundamental physics experiments with measurements of ultra-pure materials important to dark matter detection
The Department of Energy's Pacific Northwest National Laboratory hosted the U.S. conference and served as guest editors for the special issue. PNNL was recently extended an invitation to join the International Committee for Radionuclide Metrology which sponsored the Low-Level Radiation Measurement Techniques conference where 123 scientists from over 20 countries presented a total of 121 papers.
News Release
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https://par.nsf.gov/biblio/10321637-doppler-narrowing-zeeman-laser-beam-shape-effects-type-electromagnetically-induced-transparency-rb-d2-line-vapor-cell
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Doppler narrowing, Zeeman and laser beam-shape effects in Λ-type electromagnetically induced transparency on the 85 Rb D2 line in a vapor cell
Abstract We study Λ-type Electromagnetically Induced Transparency (EIT) on the Rb D2 transition in a buffer-gas-free thermal vapor cell without anti-relaxation coating. Experimental data show well-resolved features due to velocity-selective optical pumping and one EIT resonance. The Zeeman splitting of the EIT line in magnetic fields up to 12 Gauss is investigated. One Zeeman component is free of the first-order shift and its second-order shift agrees well with theory. The full width at half maximum (FWHM) of this magnetic-field-insensitive EIT resonance is reduced due to Doppler narrowing, scales linearly in Rabi frequency over the range studied, and reaches about 100 kHz at the lowest powers. These observations agree with an analytic model for a Doppler-broadened medium developed in (Javan et al 2002 Phys. Rev. A 66 013805; Lee et al 2003 Appl. Phys. B, Lasers Opt. (Germany) B 76 , 33–9; Taichenachev et al 2000 JETP Lett. 72 , 119). Numerical simulation using the Lindblad equation reveals that the transverse laser intensity distribution and two Λ-EIT systems must be included to fully account for the measured line width and line shape of the signals. Ground-state decoherence, caused by effects that include residual optical frequency fluctuations, atom-wall and trace-gas collisions, is more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10321637
Journal Name:
Journal of Physics Communications
Volume:
4
Issue:
9
ISSN:
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Physical systems with non-trivial topological order find direct applications in metrology (Klitzinget al1980Phys.Rev. Lett.45494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math.1183–204; Kitaev 2003Ann. Phys.3032–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev.B235632–33). At magnetic fields beyond the reach of current condensed matter experiment, around$104$T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al1982Phys. Rev. Lett.49405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2Dmore »
| 2022-09-27T08:47:43 |
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http://hitchhikersgui.de/Summation
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Summation
Calculation results
Addition (+)
${\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{summand}}\,+\,{\text{summand}}\\\scriptstyle {\text{addend (broad sense)}}\,+\,{\text{addend (broad sense)}}\\\scriptstyle {\text{augend}}\,+\,{\text{addend (strict sense)}}\end{matrix}}\right\}\,=\,}$ ${\displaystyle \scriptstyle {\text{sum}}}$
Subtraction (−)
${\displaystyle \scriptstyle {\text{minuend}}\,-\,{\text{subtrahend}}\,=\,}$ ${\displaystyle \scriptstyle {\text{difference}}}$
Multiplication (×)
${\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplicand}}\,\times \,{\text{multiplier}}\end{matrix}}\right\}\,=\,}$ ${\displaystyle \scriptstyle {\text{product}}}$
Division (÷)
${\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,}$ ${\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}}$
Exponentiation
${\displaystyle \scriptstyle {\text{base}}^{\text{exponent}}\,=\,}$ ${\displaystyle \scriptstyle {\text{power}}}$
nth root (√)
${\displaystyle \scriptstyle {\sqrt[{\text{degree}}]{\scriptstyle {\text{radicand}}}}\,=\,}$ ${\displaystyle \scriptstyle {\text{root}}}$
Logarithm (log)
${\displaystyle \scriptstyle \log _{\text{base}}({\text{antilogarithm}})\,=\,}$ ${\displaystyle \scriptstyle {\text{logarithm}}}$
In mathematics, summation (capital Greek sigma symbol: ) is the addition of a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.
The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid).
For finite sequences of such elements, summation always produces a well-defined sum. The summation of an infinite sequence of values is called a series. A value of such a series may often be defined by means of a limit (although sometimes the value may be infinite, and often no value results at all). Another notion involving limits of finite sums is integration.
The summation of the sequence [1, 2, 4, 2] is an expression whose value is the sum of each of the members of the sequence. In the example, 1 + 2 + 4 + 2 = 9. Because addition is associative, the sum does not depend on how the additions are grouped, for instance (1 + 2) + (4 + 2) and 1 + ((2 + 4) + 2) both have the value 9; therefore, parentheses are usually omitted in repeated additions. Addition is also commutative, so permuting the terms of a finite sequence does not change its sum. For infinite summations this property may fail. See Absolute convergence for conditions under which it still holds.
There is no special notation for the summation of such explicit sequences, as the corresponding repeated addition expression will do. There is only a slight difficulty if the sequence has fewer than two elements: the summation of a sequence of one term involves no plus sign (it is indistinguishable from the term itself) and the summation of the empty sequence cannot even be written down (but one can write its value "0" in its place). If, however, the terms of the sequence are given by a regular pattern, possibly of variable length, then a summation operator may be useful or even essential.
For the summation of the sequence of consecutive integers from 1 to 100, one could use an addition expression involving an ellipsis to indicate the missing terms: 1 + 2 + 3 + 4 + ... + 99 + 100. In this case, the reader can easily guess the pattern. However, for more complicated patterns, one needs to be precise about the rule used to find successive terms, which can be achieved by using the summation operator "Σ". Using this sigma notation the above summation is written as:
${\displaystyle \sum _{i\mathop {=} 1}^{100}i.}$
The value of this summation is 5050. It can be found without performing 99 additions, since it can be shown (for instance by mathematical induction) that
${\displaystyle \sum _{i\mathop {=} 1}^{n}i={\frac {n(n+1)}{2}}}$
for all natural numbers n.[1] More generally, formulae exist for many summations of terms following a regular pattern.
The term "indefinite summation" refers to the search for an inverse image of a given infinite sequence s of values for the forward difference operator, in other words for a sequence, called antidifference of s, whose finite differences are given by s. By contrast, summation as discussed in this article is called "definite summation".
When it is necessary to clarify that numbers are added with their signs, the term algebraic sum[2] is used. For example, in electric circuit theory Kirchhoff's circuit laws consider the algebraic sum of currents in a network of conductors meeting at a point, assigning opposite signs to currents flowing in and out of the node.
Notation
Capital-sigma notation
The capital sigma
Mathematical notation uses a symbol that compactly represents summation of many similar terms: the summation symbol, , an enlarged form of the upright capital Greek letter Sigma. This is defined as:
${\displaystyle \sum _{i\mathop {=} m}^{n}a_{i}=a_{m}+a_{m+1}+a_{m+2}+\cdots +a_{n-1}+a_{n}}$
where i represents the index of summation; ai is an indexed variable representing each successive term in the series; m is the lower bound of summation, and n is the upper bound of summation. The "i = m" under the summation symbol means that the index i starts out equal to m. The index, i, is incremented by 1 for each successive term, stopping when i = n.[3]
Here is an example showing the summation of squares:
${\displaystyle \sum _{i=3}^{6}i^{2}=3^{2}+4^{2}+5^{2}+6^{2}=86.}$
Informal writing sometimes omits the definition of the index and bounds of summation when these are clear from context, as in:
${\displaystyle \sum a_{i}^{2}=\sum _{i\mathop {=} 1}^{n}a_{i}^{2}.}$
One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition. Here are some common examples:
${\displaystyle \sum _{0\leq k<100}f(k)}$
is the sum of ${\displaystyle f(k)}$ over all (integers) ${\displaystyle k}$ in the specified range,
${\displaystyle \sum _{x\mathop {\in } S}f(x)}$
is the sum of ${\displaystyle f(x)}$ over all elements ${\displaystyle x}$ in the set ${\displaystyle S}$, and
${\displaystyle \sum _{d|n}\;\mu (d)}$
is the sum of ${\displaystyle \mu (d)}$ over all positive integers ${\displaystyle d}$ dividing ${\displaystyle n}$.[4]
There are also ways to generalize the use of many sigma signs. For example,
${\displaystyle \sum _{\ell ,\ell '}}$
is the same as
${\displaystyle \sum _{\ell }\sum _{\ell '}.}$
A similar notation is applied when it comes to denoting the product of a sequence, which is similar to its summation, but which uses the multiplication operation instead of addition (and gives 1 for an empty sequence instead of 0). The same basic structure is used, with ${\displaystyle \prod }$, an enlarged form of the Greek capital letter Pi, replacing the ${\displaystyle \sum }$.
Special cases
It is possible to sum fewer than 2 numbers:
• If the summation has one summand ${\displaystyle x}$, then the evaluated sum is ${\displaystyle x}$.
• If the summation has no summands, then the evaluated sum is zero, because zero is the identity for addition. This is known as the empty sum.
These degenerate cases are usually only used when the summation notation gives a degenerate result in a special case. For example, if ${\displaystyle n=m}$ in the definition above, then there is only one term in the sum; if ${\displaystyle n=m-1}$, then there is none.
Formal definition
Summation may be defined recursively as follows
${\displaystyle \sum _{i=a}^{b}g(i)=0}$ , for b < a.
${\displaystyle \sum _{i=a}^{b}g(i)=g(b)+\sum _{i=a}^{b-1}g(i)}$, for ba.
Measure theory notation
In the notation of measure and integration theory, a sum can be expressed as a definite integral,
${\displaystyle \sum _{k\mathop {=} a}^{b}f(k)=\int _{[a,b]}f\,d\mu }$
where ${\displaystyle [a,b]}$ is the subset of the integers from ${\displaystyle a}$ to ${\displaystyle b}$, and where ${\displaystyle \mu }$ is the counting measure.
Fundamental theorem of discrete calculus
Indefinite sums can be used to calculate definite sums with the formula:[5]
${\displaystyle \sum _{k=a}^{b}f(k)=\Delta ^{-1}f(b+1)-\Delta ^{-1}f(a)}$
where ${\displaystyle \Delta ^{-1}}$ is the antidifference operator, the inverse of the forward difference operator ${\displaystyle \Delta }$.
Approximation by definite integrals
Many such approximations can be obtained by the following connection between sums and integrals, which holds for any:
increasing function f:
${\displaystyle \int _{s=a-1}^{b}f(s)\ ds\leq \sum _{i=a}^{b}f(i)\leq \int _{s=a}^{b+1}f(s)\ ds.}$
decreasing function f:
${\displaystyle \int _{s=a}^{b+1}f(s)\ ds\leq \sum _{i=a}^{b}f(i)\leq \int _{s=a-1}^{b}f(s)\ ds.}$
For more general approximations, see the Euler–Maclaurin formula.
For summations in which the summand is given (or can be interpolated) by an integrable function of the index, the summation can be interpreted as a Riemann sum occurring in the definition of the corresponding definite integral. One can therefore expect that for instance
${\displaystyle {\frac {b-a}{n}}\sum _{i=0}^{n-1}f\left(a+i{\frac {b-a}{n}}\right)\approx \int _{a}^{b}f(x)\ dx,}$
since the right hand side is by definition the limit for ${\displaystyle n\to \infty }$ of the left hand side. However, for a given summation n is fixed, and little can be said about the error in the above approximation without additional assumptions about f: it is clear that for wildly oscillating functions the Riemann sum can be arbitrarily far from the Riemann integral.
Identities
The formulae below involve finite sums; for infinite summations or finite summations of expressions involving trigonometric functions or other transcendental functions, see list of mathematical series.
General manipulations
${\displaystyle \sum _{n=s}^{t}C\cdot f(n)=C\cdot \sum _{n=s}^{t}f(n)}$, where C is a constant
${\displaystyle \sum _{n=s}^{t}f(n)\pm \sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)\pm g(n)\right]}$
${\displaystyle \sum _{n=s}^{t}f(n)=\sum _{n=s+p}^{t+p}f(n-p)}$
${\displaystyle \sum _{n\in B}f(n)=\sum _{m\in A}f(\sigma (m))}$, for a bijection σ from a finite set A onto a finite set B; this generalizes the preceding formula.
${\displaystyle \sum _{n=s}^{j}f(n)+\sum _{n=j+1}^{t}f(n)=\sum _{n=s}^{t}f(n)}$
${\displaystyle \sum _{i=k_{0}}^{k_{1}}\sum _{j=l_{0}}^{l_{1}}a_{i,j}=\sum _{j=l_{0}}^{l_{1}}\sum _{i=k_{0}}^{k_{1}}a_{i,j}}$
${\displaystyle \sum _{k\leq j\leq i\leq n}a_{i,j}=\sum _{i=k}^{n}\sum _{j=k}^{i}a_{i,j}=\sum _{j=k}^{n}\sum _{i=j}^{n}a_{i,j}=\sum _{j=0}^{n-k}\sum _{i=k}^{n-j}a_{i+j,i}}$
${\displaystyle \sum _{n=0}^{t}f(2n)+\sum _{n=0}^{t}f(2n+1)=\sum _{n=0}^{2t+1}f(n)}$
${\displaystyle \sum _{n=0}^{t}\sum _{i=0}^{z-1}f(z\cdot n+i)=\sum _{n=0}^{z\cdot t+z-1}f(n)}$
${\displaystyle \sum _{i=s}^{m}\sum _{j=t}^{n}{a_{i}}{c_{j}}=\left(\sum _{i=s}^{m}a_{i}\right)\cdot \sum _{j=t}^{n}c_{j}}$
${\displaystyle \sum _{n=s}^{t}\ln f(n)=\ln \prod _{n=s}^{t}f(n)}$
${\displaystyle c^{\left[\sum _{n=s}^{t}f(n)\right]}=\prod _{n=s}^{t}c^{f(n)}}$
${\displaystyle \left(\sum _{k=0}^{n}a_{k}\right)\cdot \left(\sum _{k=0}^{n}b_{k}\right)=\sum _{k=0}^{2n}\sum _{i=0}^{k}a_{i}b_{k-i}-\sum _{k=0}^{n-1}\left(a_{k}\sum _{i=n+1}^{2n-k}b_{i}+b_{k}\sum _{i=n+1}^{2n-k}a_{i}\right)}$
${\displaystyle \sum _{n=a}^{b}f(n)=\sum _{n=0}^{b}f(n)-\sum _{n=0}^{a-1}f(n)}$
Known summation expressions
${\displaystyle \sum _{i=1}^{n}1=n}$
${\displaystyle \sum _{i=1}^{n}2i-1=n^{2}}$ (Defines the sum of odd integers)
${\displaystyle \sum _{i=1}^{n}3i^{2}-3i+1=n^{3}}$ (This closed form results in the cubic)
${\displaystyle \sum _{i=1}^{n}4i^{3}-6i^{2}+4i-1=n^{4}}$ (This closed form results in the quartic)
${\displaystyle \sum _{i=1}^{n}5i^{4}-10i^{3}+10i^{2}-5i+1=n^{5}}$ (This closed form results in the quintic)
${\displaystyle \sum _{i=1}^{n}6i^{5}-15i^{4}+20i^{3}-15i^{2}+6i-1=n^{6}}$
${\displaystyle \sum _{i=1}^{n}7i^{6}-21i^{5}+35i^{4}-35i^{3}+21i^{2}-7i+1=n^{7}}$
${\displaystyle \sum _{i=1}^{n}8i^{7}-28i^{6}+56i^{5}-70i^{4}+56i^{3}-28i^{2}+8i-1=n^{8}}$
${\displaystyle \sum _{i=1}^{n}9i^{8}-36i^{7}+84i^{6}-126i^{5}+126i^{4}-84i^{3}+36i^{2}-9i+1=n^{9}}$
${\displaystyle \sum _{i=1}^{n}10i^{9}-45i^{8}+120i^{7}-210i^{6}+252i^{5}-210i^{4}+120i^{3}-45i^{2}+10i-1=n^{10}}$
${\displaystyle \sum _{i=0}^{n}i=\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}}$ (This equation defines the sum of consecutive integers. See arithmetic series. Reference [CRC, p 52])
${\displaystyle \sum _{i=0}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}={\frac {n^{3}}{3}}+{\frac {n^{2}}{2}}+{\frac {n}{6}}}$ (See square pyramidal number. Reference [CRC, p 52])
${\displaystyle \sum _{i=0}^{n}i^{3}=\left[\ \!\sum _{i=0}^{n}i\,\right]^{2}=\left[\,\!{\frac {n\!\,(n+1)}{2}}\,\!\right]^{2}={\frac {n^{4}}{4}}+{\frac {n^{3}}{2}}+{\frac {n^{2}}{4}}}$ (See Nicomachus's theorem. Reference [CRC, p 52])
${\displaystyle \sum _{i=0}^{n}i^{4}={\frac {n(n+1)(2n+1)(3n^{2}+3n-1)}{30}}={\frac {n^{5}}{5}}+{\frac {n^{4}}{2}}+{\frac {n^{3}}{3}}-{\frac {n}{30}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{5}={\frac {n^{2}(n+1)^{2}(2n^{2}+2n-1)}{12}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{6}={\frac {n(n+1)(2n+1)(3n^{4}+6n^{3}-3n+1)}{42}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{7}={\frac {n^{2}(n+1)^{2}(3n^{4}+6n^{3}-n^{2}-4n+2)}{24}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{8}={\frac {n(n+1)(2n+1)(5n^{6}+15n^{5}+5n^{4}-15n^{3}-n^{2}-9n-3)}{90}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{9}={\frac {n^{2}(n+1)^{2}(2n^{6}+6n^{5}+n^{4}-8n^{3}+n^{2}+6n-3)}{20}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=1}^{n}i^{10}={\frac {n(n+1)(2n+1)(3n^{8}+12n^{7}+8n^{6}-18n^{5}-10n^{4}+24n^{3}+2n^{2}-15n+5)}{66}}}$ Reference [CRC, p 52]
${\displaystyle \sum _{i=0}^{n}i^{p}={\frac {(n+1)^{p+1}}{p+1}}+\sum _{k=1}^{p}{\frac {B_{k}}{p-k+1}}{p \choose k}(n+1)^{p-k+1},}$
where ${\displaystyle B_{k}}$ denotes a Bernoulli number (see Faulhaber's formula) and ${\displaystyle c}$ denotes a constant.
${\displaystyle \sum _{i=0}^{n}c=c(n+1)}$
${\displaystyle \sum _{i=0}^{n}2i=n(n+1)}$ (Defines the sum of even integers)
${\displaystyle \sum _{i=0}^{n}2i+1=(n+1)^{2}}$ (Defines the sum of odd integers)
${\displaystyle \sum _{i=0}^{n}2i+1=(n+1)^{2}}$
${\displaystyle \sum _{i=0}^{n}3i^{2}+i=n(n+1)^{2}}$
${\displaystyle \sum _{i=0}^{n}i(i-1)(4i-5)=n(n+1)(n-1)^{2}}$
${\displaystyle \sum _{i=1}^{n}2i^{3}-3i^{2}+3i-1={\frac {n^{2}(n^{2}+1)}{2}}}$ (This closed form sums the intermediate terms of a quartic)
${\displaystyle \sum _{i=1}^{n}\log i=\log n!}$ (The property of logarithms)
${\displaystyle \sum _{i=2}^{n}2\ln \left({\frac {i}{i-1}}\right)=2\ln(n)}$
${\displaystyle \sum _{i=2}^{n}i\ln \left({\frac {i}{i-1}}\right)+\ln(i-1)=n\ln(n)}$
${\displaystyle \sum _{i=1}^{n}2\log \left({\frac {1}{i}}\right)=2\log \left({\frac {1}{n!}}\right)}$
The following formulae are manipulations of
${\displaystyle \sum _{i=0}^{n}i^{3}=\left(\sum _{i=0}^{n}i\right)^{2}}$
generalized to begin a series at any natural number value (i.e., ${\displaystyle m\in \mathbb {N} }$):
${\displaystyle \left(\sum _{i=m}^{n}i\right)^{2}=\sum _{i=m}^{n}(i^{3}-im(m-1))}$
${\displaystyle \sum _{i=m}^{n}i^{3}=\left(\sum _{i=m}^{n}i\right)^{2}+m(m-1)\sum _{i=m}^{n}i}$
The Technique
At the bottom of [CRC, p. 52], the editor gives one way to find summation formulas of a particular form. More generally, and if intuition does not work, then how were some of the summation formulas above deduced? Without an extensive definition on the function ${\displaystyle f(),}$ only to say that:
1) ${\displaystyle f()}$ exists ${\displaystyle \forall i,}$ ${\displaystyle b\leq i\leq n,}$ where ${\displaystyle b,i,n\in {\mbox{the set of natural numbers and zero.}}}$
2) ${\displaystyle b}$ is some lower bound and is dependent on ${\displaystyle f(i)-f(i-1),}$
3) ${\displaystyle n}$ is some upper bound and ${\displaystyle n\geq i.}$
Use the following equation to find the left-hand side of the closed form.
${\displaystyle \sum _{i=b}^{n}f(i)-f(i-1)=f(n).}$
Example: Given ${\displaystyle f(n)=n^{3}+n^{2},}$ find the corresponding sum. Solution:
${\displaystyle \sum 3i^{2}-i=n^{3}+n^{2}}$
because
${\displaystyle f(i)-f(i-1)=i^{3}+i^{2}-[(i-1)^{3}+(i-1)^{2}]=}$
${\displaystyle i^{3}+i^{2}-[(i^{2}-2i+1)(i-1)+(i^{2}-2i+1)]=}$
${\displaystyle i^{3}+i^{2}-[i^{3}-i^{2}-2i^{2}+2i+i-1+i^{2}-2i+1]=}$
${\displaystyle i^{3}+i^{2}-[i^{3}-2i^{2}+i]=}$
${\displaystyle i^{3}+i^{2}-i^{3}+2i^{2}-i=3i^{2}-i.}$
Thus, with the proper lower bound, we conclude that
${\displaystyle \sum _{i=0}^{n}3i^{2}-i=n^{3}+n^{2}.}$
This technique works well when ${\displaystyle f()}$ is a polynomial-like function. It seems to work for exponential-like functions and logarithmic-like functions, too.
Exponential terms
In the summations below, ${\displaystyle a\neq 1}$.
${\displaystyle \sum _{i=0}^{n-1}a^{i}={\frac {1-a^{n}}{1-a}}}$ (see geometric series)
${\displaystyle \sum _{i=0}^{n}{\frac {1}{2^{i}}}=2-{\frac {1}{2^{n}}}}$ (special case when a = 1/2)
${\displaystyle \sum _{i=0}^{n-1}ia^{i}={\frac {a-na^{n}+(n-1)a^{n+1}}{(1-a)^{2}}}}$
${\displaystyle \sum _{i=0}^{n-1}i2^{i}=2+(n-2)2^{n}}$ (special case when a = 2)
${\displaystyle \sum _{i=0}^{n-1}{\frac {i}{2^{i}}}=2-{\frac {n+1}{2^{n-1}}}}$ (special case when a = 1/2)
{\displaystyle {\begin{aligned}\sum _{i=0}^{n-1}\left(b+id\right)a^{i}&=\sum _{i=1}^{n}\left[b+(i-1)d\right]a^{i-1}\\&=b+[b+d]a+[b+2d]a^{2}+\cdots +[b+(n-1)d]a^{n-1}\\&={\frac {b-[b+(n-1)d]a^{n}}{1-a}}+{\frac {da(1-a^{n-1})}{(1-a)^{2}}}\end{aligned}}}
(arithmetico-geometric series)
Binomial coefficients and factorials
There exist very many summation identities involving binomial coefficients (a whole chapter of Concrete Mathematics is devoted to just the basic techniques). Some of the most basic ones are the following.
${\displaystyle \sum _{i=0}^{n}{n \choose i}=2^{n}}$ (Gives the number of combinations in the binomial distribution)
${\displaystyle \sum _{k=0}^{m}\left({\begin{array}{c}n+k\\n\\\end{array}}\right)=\left({\begin{array}{c}n+m+1\\n+1\\\end{array}}\right)}$
${\displaystyle \sum _{i=1}^{n}i{n \choose i}=n(2^{n-1})}$
${\displaystyle \sum _{i=0}^{n}{}_{i}P_{k}{n \choose i}={}_{n}P_{k}(2^{n-k})}$
${\displaystyle \sum _{i=0}^{n}{\frac {n \choose i}{i+1}}={\frac {2^{n+1}-1}{n+1}}}$
${\displaystyle \sum _{i=0}^{n}i!\cdot {n \choose i}=\sum _{i=0}^{n}{}_{n}P_{i}=\lfloor n!\cdot e\rfloor ,\quad n\in \mathbb {Z} ^{+}}$, where ${\displaystyle {}_{n}P_{i}}$ is the number of k-permutations of n and ${\displaystyle \lfloor x\rfloor }$ denotes the floor function.
${\displaystyle \sum _{i=k}^{n}{i \choose k}={n+1 \choose k+1}}$
${\displaystyle \sum _{i=0}^{n}{n \choose i}a^{n-i}b^{i}=(a+b)^{n}}$, the binomial theorem
${\displaystyle \sum _{i=0}^{n}i\cdot i!=(n+1)!-1}$
${\displaystyle \sum _{i=1}^{n}{}_{i+k}P_{k+1}=\sum _{i=1}^{n}\prod _{j=0}^{k}(i+j)={\frac {(n+k+1)!}{(n-1)!(k+2)}}}$
${\displaystyle \sum _{i=0}^{n}{m+i-1 \choose i}={m+n \choose n}}$
${\displaystyle \sum _{i=0}^{n}{n \choose i}^{2}={2n \choose n}}$
Growth rates
The following are useful approximations (using theta notation):
${\displaystyle \sum _{i=1}^{n}i^{c}\in \Theta (n^{c+1})}$ for real c greater than −1
${\displaystyle \sum _{i=1}^{n}{\frac {1}{i}}\in \Theta (\log _{e}n)}$ (See Harmonic number)
${\displaystyle \sum _{i=1}^{n}c^{i}\in \Theta (c^{n})}$ for real c greater than 1
${\displaystyle \sum _{i=1}^{n}\log(i)^{c}\in \Theta (n\cdot \log(n)^{c})}$ for non-negative real c
${\displaystyle \sum _{i=1}^{n}\log(i)^{c}\cdot i^{d}\in \Theta (n^{d+1}\cdot \log(n)^{c})}$ for non-negative real c, d
${\displaystyle \sum _{i=1}^{n}\log(i)^{c}\cdot i^{d}\cdot b^{i}\in \Theta (n^{d}\cdot \log(n)^{c}\cdot b^{n})}$ for non-negative real b > 1, c, d
Miscellaneous
${\displaystyle \sum _{i=1}^{n}{\frac {1}{i}}=H_{n}}$ (See Harmonic number)
${\displaystyle \sum _{i=1}^{n}{\frac {1}{i^{k}}}=H_{n}^{k}}$ (See Generalized harmonic number)
Notes
1. ^ For details, see Triangular number.
2. ^ Oxford English Dictionary, 2nd ed. - algebraic (esp. of a sum): taken with consideration of the sign (plus or minus) of each term.
3. ^ For a detailed exposition on summation notation, and arithmetic with sums, see Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 2: Sums". Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (PDF). Addison-Wesley Professional. ISBN 978-0201558029.
4. ^ Although the name of the dummy variable does not matter (by definition), one usually uses letters from the middle of the alphabet (${\displaystyle i}$ through ${\displaystyle q}$) to denote integers, if there is a risk of confusion. For example, even if there should be no doubt about the interpretation, it could look slightly confusing to many mathematicians to see ${\displaystyle x}$ instead of ${\displaystyle k}$ in the above formulae involving ${\displaystyle k}$. See also typographical conventions in mathematical formulae.
5. ^ "Handbook of discrete and combinatorial mathematics", Kenneth H. Rosen, John G. Michaels, CRC Press, 1999, ISBN 0-8493-0149-1
Further reading
1) W. H. Boyer (Editor), CRC Standard Mathematical Tables, 27-th Edition, CRC Press, Boca Raton, FL, 1984, p. 52.
2) R. L. Goodwin, Book 3, Norfolk, VA, 1990.
3) Nicholas J. Higham, "The accuracy of floating point summation", SIAM J. Scientific Computing 14 (4), 783–799 (1993).
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| 2018-03-24T02:22:05 |
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https://par.nsf.gov/biblio/10353482
|
The SABRE experiment for dark matter search
The SABRE (Sodium-iodide with Active Background REjection) experiment is a new detector based on NaI(Tl) scintillating crystals for the dark matter detection through the annual modulation. With ultra-pure crystals and an active veto system, based on liquid scintillator surrounding the crystal array, SABRE will reach unprecedented low background and the highest sensitivity among the present NaI(Tl) experiments. Moreover SABRE will be the first dark matter search with twin detectors located in the North and South hemispheres, in Gran Sasso National Laboratories (LNGS), Italy, and Stawell Underground Laboratories (SUPL), Australia, respectively. The double location will help to quantify possible seasonal effects, and is a unique feature to identify a modulation of dark matter origins. SABRE is presently in the Proof-of-Principle (PoP) phase, with the goal to measure the crystal intrinsic and cosmogenic backgrounds of one 5 kg crystal and the active veto efficiency. We have performed a full geometry Monte Carlo simulation in order to evaluate the background contributions in the two distinct operation modes foreseen for the PoP: the potassium Measurement Mode (KMM) and the Dark Matter Measurement Mode (DMM), where the liquid scintillator detector is used in coincidence or anti-coincidence with the crystal, respectively. This paper presents the results more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10353482
Journal Name:
The SABRE experiment for dark matter search
Page Range or eLocation-ID:
653
We present here a characterization of the low background NaI(Tl) crystal NaI-33 based on a period of almost one year of data taking (891 kg$$\times$$$×$days exposure) in a detector configuration with no use of organic scintillator veto. This remarkably radio-pure crystal already showed a low background in the SABRE Proof-of-Principle (PoP) detector, in the low energy region of interest (1–6 keV) for the search of dark matter interaction via the annual modulation signature. As the vetoable background components, such as$$^{40}$$${}^{40}$K, are here sub-dominant, we reassembled the PoP setup with a fully passive shielding. We upgraded the selection of events based on a Boosted Decision Tree algorithm that rejects most of the PMT-induced noise while retaining scintillation signals with > 90% efficiency in 1–6 keV. We find an average background of 1.39 ± 0.02 counts/day/kg/keV in the region of interest and a spectrum consistent with data previously acquired in the PoP setup, where the external veto background suppression was in place. Our background model indicates that the dominant background component is due to decays of$$^{210}$$${}^{210}$Pb, only partly residing in the crystal itself. The other location of$$^{210}$$${}^{210}$Pb is the reflector foil that wraps the crystal. We now proceed to designmore »
| 2023-02-03T10:29:29 |
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https://www.aimsciences.org/article/doi/10.3934/proc.2011.2011.457
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Article Contents
Article Contents
# Phase-field study of solute trapping effect in rapid solidification
• The phase-field model of Echebarria, Folch, Karma, and Plapp [Phys. Rev. E 70 (2004) 061604] is extended to the case of rapid solidification in which local non-equilibrium phenomena occur in the bulk phases and within the diffuse solid-liquid interface. Such an extension leads to the fully hyperbolic system of equations given by the atomic diffusion equation and the phase-field equation of motion. This model is applied to the problem of solute trapping, which is accompanied by the entrapment of solute atoms beyond chemical equilibrium by a rapidly moving interface. The model predicts the beginning of complete solute trapping and diffusionless solidification at a finite solidification velocity.
Mathematics Subject Classification: Primary: 80A22, 74D10; Secondary: 35L20.
Citation:
Open Access Under a Creative Commons license
| 2023-03-23T16:40:33 |
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https://zbmath.org/authors/?q=ai%3Ajames.richard-d
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# zbMATH — the first resource for mathematics
## James, Richard D.
Compute Distance To:
Author ID: james.richard-d Published as: James, R.; James, R. D.; James, Richard; James, Richard D. External Links: MGP · Wikidata · ORCID
Documents Indexed: 64 Publications since 1979, including 2 Books
all top 5
#### Co-Authors
18 single-authored 9 Ball, John M. 8 Friesecke, Gero 8 Müller, Stefan 4 Kinderlehrer, David 3 Dabade, Vivekanand 3 Nota, Alessia 3 Velázquez, Juan J. L. 2 Bhattacharya, Kaushik 2 Dayal, Kaushik 2 Dumitrică, Traian 2 Jüstel, Dominik 2 Rizzoni, Raffaella 2 Spector, Scott J. 2 Venkatraman, Raghavendra 1 Banerjee, Amartya S. 1 Chen, Xian 1 DeSimone, Antonio 1 Elliott, Ryan S. 1 Ericksen, Jerald Laverne 1 Feng, Fan 1 Firoozye, Nikan B. 1 Fosdick, Roger L. 1 Ganor, Yaniv 1 Golden, Kenneth M. 1 Grimmett, Geoffrey R. 1 Holmes, Philip J. 1 Kohn, Robert Vita 1 Leo, Perry H. 1 Lipton, Robert P. 1 Liu, Ling Pu 1 Luskin, Mitchell 1 Lutoborski, Adam 1 Milton, Graeme Walter 1 Mora, Maria Giovanna 1 Pego, Robert L. 1 Sen, Pabitra N. 1 Srivastava, Vijay Kumar 1 Swart, Pieter J.
all top 5
#### Serials
10 Journal of the Mechanics and Physics of Solids 9 Archive for Rational Mechanics and Analysis 5 Journal of Elasticity 5 Journal of Nonlinear Science 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 SIAM Journal on Applied Mathematics 2 Continuum Mechanics and Thermodynamics 2 Oberwolfach Reports 2 The IMA Volumes in Mathematics and its Applications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 International Journal of Solids and Structures 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 Nonlinearity 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Bulletin of the American Mathematical Society. New Series 1 Philosophical Transactions of the Royal Society of London. Series A 1 Acta Crystallographica. Section A 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
all top 5
#### Fields
52 Mechanics of deformable solids (74-XX) 24 Statistical mechanics, structure of matter (82-XX) 13 Partial differential equations (35-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 4 General and overarching topics; collections (00-XX) 3 Mechanics of particles and systems (70-XX) 3 Fluid mechanics (76-XX) 3 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX)
#### Citations contained in zbMATH Open
53 Publications have been cited 1,815 times in 1,127 Documents Cited by Year
Fine phase mixtures as minimizers of energy. Zbl 0629.49020
Ball, J. M.; James, R. D.
1987
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Zbl 1021.74024
Friesecke, Gero; James, Richard D.; Müller, Stefan
2002
Proposed experimental tests of a theory of fine microstructure and the two-well problem. Zbl 0758.73009
Ball, J. M.; James, R. D.
1992
A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Zbl 1100.74039
Friesecke, Gero; James, Richard D.; Müller, Stefan
2006
Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. Zbl 1140.74481
Friesecke, Gero; James, Richard D.; Mora, Maria Giovanna; Müller, Stefan
2003
A theory of thin films of martensitic materials with applications to microactuators. Zbl 0960.74046
Bhattacharya, K.; James, R. D.
1999
The propagation of phase boundaries in elastic bars. Zbl 0443.73010
James, Richard D.
1980
Finite deformation by mechanical twinning. Zbl 0537.73031
James, Richard D.
1981
A constrained theory of magnetoelasticity. Zbl 1008.74030
DeSimone, Antonio; James, Richard D.
2002
On the dynamics of fine structure. Zbl 0791.35030
Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J.
1991
Co-existent phases in the one-dimensional static theory of elastic bars. Zbl 0429.73001
James, Richard D.
1979
Displacive phase transformations in solids. Zbl 0585.73198
James, R. D.
1986
Restrictions on microstructure. Zbl 0808.73063
Bhattacharya, Kaushik; Firoozye, Nikan B.; James, Richard D.; Kohn, Robert V.
1994
A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. Zbl 0984.74009
Friesecke, Gero; James, Richard D.
2000
Rigorous derivation of nonlinear plate theory and geometric rigidity. Zbl 1012.74043
Friesecke, Gero; Müller, Stefan; James, Richard D.
2002
Theory of diffusionless phase transitions. Zbl 0991.74504
James, Richard; Kinderlehrer, David
1989
Objective structures. Zbl 1120.74312
James, R. D.
2006
The Föppl-von Kármán plate theory as a low energy $$\Gamma$$-limit of nonlinear elasticity. Zbl 1041.74043
Friesecke, Gero; James, Richard D.; Müller, Stefan
2002
Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape memory cantilever. Zbl 1100.74549
James, R. D.
2002
Internal variables and fine-scale oscillations in micromagnetics. Zbl 0814.73054
James, R. D.; Müller, Stefan
1994
The formation of filamentary voids in solids. Zbl 0761.73020
James, Richard D.; Spector, Scott J.
1991
The elastica and the problem of the pure bending for a non-convex stored energy function. Zbl 0481.73018
Fosdick, R. L.; James, R. D.
1981
The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy. Zbl 0514.73029
James, Richard D.
1981
Incompatible sets of gradients and metastability. Zbl 1343.49041
Ball, J. M.; James, R. D.
2015
Nonequilibrium molecular dynamics for bulk materials and nanostructures. Zbl 1193.82038
Dayal, Kaushik; James, Richard D.
2010
Objective molecular dynamics. Zbl 1170.74005
Dumitrică, Traian; James, Richard D.
2007
Study of the cofactor conditions: conditions of supercompatibility between phases. Zbl 1294.74050
Chen, Xian; Srivastava, Vijay; Dabade, Vivekanand; James, Richard D.
2013
Magnetostrictive composites in the dilute limit. Zbl 1120.74465
Liu, L. P.; James, R. D.; Leo, P. H.
2006
Piecewise rigid body mechanics. Zbl 1057.74006
James, R. D.; Rizzoni, R.
2003
Pressurized shape memory thin films. Zbl 0990.74038
James, Richard D.; Rizzoni, Raffaella
2000
Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy. Zbl 1430.82012
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2019
The scientific life and influence of Clifford Ambrose Truesdell III. Zbl 0988.01007
Ball, J. M.; James, R. D.
2002
Remarks on $$W^{1,p}$$-quasiconvexity, interpenetration of matter, and function spaces for elasticity. Zbl 0773.73022
James, R. D.; Spector, S. J.
1992
On the stability of phases. Zbl 0588.73024
James, R. D.
1984
Stress-free joints and polycrystals. Zbl 0558.73007
James, R. D.
1984
A spectral scheme for Kohn-Sham density functional theory of clusters. Zbl 1351.81014
Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.
2015
Design of viscometers corresponding to a universal molecular simulation method. Zbl 1241.76328
Dayal, Kaushik; James, Richard D.
2012
Hysteresis in phase transformations. Zbl 0848.73002
James, R. D.
1996
A characterization of plane strain. Zbl 0721.73004
Ball, J. M.; James, R. D.
1991
Local minimizers and phase transformations. Zbl 0918.49019
Ball, J. M.; James, R. D.
1996
A relation between the jump in temperature across a propagating phase boundary and the stability of solid phases. Zbl 0523.73098
James, Richard D.
1983
Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: collision-dominated case. Zbl 1453.35133
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2019
Materials from mathematics. Zbl 1409.74035
James, Richard D.
2019
Bragg-von Laue diffraction generalized to twisted X-rays. Zbl 1370.82086
Jüstel, Dominik; Friesecke, Gero; James, Richard D.
2016
New materials from theory: Trends in the development of active materials. Zbl 1075.74032
James, Richard D.
2000
Frustration and microstructure: An example in magnetostriction. Zbl 0797.49037
James, R. D.; Kinderlehrer, D.
1993
Laminar elastic composites with crystallographic symmetry. Zbl 0726.73042
James, Richard; Lipton, Robert; Lutoborski, Adam
1990
The arrangement of coherent phases in a loaded body. Zbl 0594.73114
James, R. D.
1984
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case. Zbl 1440.35229
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2020
Micromagnetics of Galfenol. Zbl 1415.74025
Dabade, Vivekanand; Venkatraman, Raghavendra; James, Richard D.
2019
Twisted X-rays: incoming waveforms yielding discrete diffraction patterns for helical structures. Zbl 1342.78028
Friesecke, Gero; James, Richard D.; Jüstel, Dominik
2016
Magnetoelastic interactions. Zbl 0894.73131
James, R.; Kinderlehrer, David
1996
Microstructure and weak convergence. Zbl 0645.73005
James, R. D.
1988
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case. Zbl 1440.35229
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2020
Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy. Zbl 1430.82012
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2019
Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: collision-dominated case. Zbl 1453.35133
James, Richard D.; Nota, Alessia; Velázquez, Juan J. L.
2019
Materials from mathematics. Zbl 1409.74035
James, Richard D.
2019
Micromagnetics of Galfenol. Zbl 1415.74025
Dabade, Vivekanand; Venkatraman, Raghavendra; James, Richard D.
2019
Bragg-von Laue diffraction generalized to twisted X-rays. Zbl 1370.82086
Jüstel, Dominik; Friesecke, Gero; James, Richard D.
2016
Twisted X-rays: incoming waveforms yielding discrete diffraction patterns for helical structures. Zbl 1342.78028
Friesecke, Gero; James, Richard D.; Jüstel, Dominik
2016
Incompatible sets of gradients and metastability. Zbl 1343.49041
Ball, J. M.; James, R. D.
2015
A spectral scheme for Kohn-Sham density functional theory of clusters. Zbl 1351.81014
Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.
2015
Study of the cofactor conditions: conditions of supercompatibility between phases. Zbl 1294.74050
Chen, Xian; Srivastava, Vijay; Dabade, Vivekanand; James, Richard D.
2013
Design of viscometers corresponding to a universal molecular simulation method. Zbl 1241.76328
Dayal, Kaushik; James, Richard D.
2012
Nonequilibrium molecular dynamics for bulk materials and nanostructures. Zbl 1193.82038
Dayal, Kaushik; James, Richard D.
2010
Objective molecular dynamics. Zbl 1170.74005
Dumitrică, Traian; James, Richard D.
2007
A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Zbl 1100.74039
Friesecke, Gero; James, Richard D.; Müller, Stefan
2006
Objective structures. Zbl 1120.74312
James, R. D.
2006
Magnetostrictive composites in the dilute limit. Zbl 1120.74465
Liu, L. P.; James, R. D.; Leo, P. H.
2006
Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. Zbl 1140.74481
Friesecke, Gero; James, Richard D.; Mora, Maria Giovanna; Müller, Stefan
2003
Piecewise rigid body mechanics. Zbl 1057.74006
James, R. D.; Rizzoni, R.
2003
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Zbl 1021.74024
Friesecke, Gero; James, Richard D.; Müller, Stefan
2002
A constrained theory of magnetoelasticity. Zbl 1008.74030
DeSimone, Antonio; James, Richard D.
2002
Rigorous derivation of nonlinear plate theory and geometric rigidity. Zbl 1012.74043
Friesecke, Gero; Müller, Stefan; James, Richard D.
2002
The Föppl-von Kármán plate theory as a low energy $$\Gamma$$-limit of nonlinear elasticity. Zbl 1041.74043
Friesecke, Gero; James, Richard D.; Müller, Stefan
2002
Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape memory cantilever. Zbl 1100.74549
James, R. D.
2002
The scientific life and influence of Clifford Ambrose Truesdell III. Zbl 0988.01007
Ball, J. M.; James, R. D.
2002
A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. Zbl 0984.74009
Friesecke, Gero; James, Richard D.
2000
Pressurized shape memory thin films. Zbl 0990.74038
James, Richard D.; Rizzoni, Raffaella
2000
New materials from theory: Trends in the development of active materials. Zbl 1075.74032
James, Richard D.
2000
A theory of thin films of martensitic materials with applications to microactuators. Zbl 0960.74046
Bhattacharya, K.; James, R. D.
1999
Hysteresis in phase transformations. Zbl 0848.73002
James, R. D.
1996
Local minimizers and phase transformations. Zbl 0918.49019
Ball, J. M.; James, R. D.
1996
Magnetoelastic interactions. Zbl 0894.73131
James, R.; Kinderlehrer, David
1996
Restrictions on microstructure. Zbl 0808.73063
Bhattacharya, Kaushik; Firoozye, Nikan B.; James, Richard D.; Kohn, Robert V.
1994
Internal variables and fine-scale oscillations in micromagnetics. Zbl 0814.73054
James, R. D.; Müller, Stefan
1994
Frustration and microstructure: An example in magnetostriction. Zbl 0797.49037
James, R. D.; Kinderlehrer, D.
1993
Proposed experimental tests of a theory of fine microstructure and the two-well problem. Zbl 0758.73009
Ball, J. M.; James, R. D.
1992
Remarks on $$W^{1,p}$$-quasiconvexity, interpenetration of matter, and function spaces for elasticity. Zbl 0773.73022
James, R. D.; Spector, S. J.
1992
On the dynamics of fine structure. Zbl 0791.35030
Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J.
1991
The formation of filamentary voids in solids. Zbl 0761.73020
James, Richard D.; Spector, Scott J.
1991
A characterization of plane strain. Zbl 0721.73004
Ball, J. M.; James, R. D.
1991
Laminar elastic composites with crystallographic symmetry. Zbl 0726.73042
James, Richard; Lipton, Robert; Lutoborski, Adam
1990
Theory of diffusionless phase transitions. Zbl 0991.74504
James, Richard; Kinderlehrer, David
1989
Microstructure and weak convergence. Zbl 0645.73005
James, R. D.
1988
Fine phase mixtures as minimizers of energy. Zbl 0629.49020
Ball, J. M.; James, R. D.
1987
Displacive phase transformations in solids. Zbl 0585.73198
James, R. D.
1986
On the stability of phases. Zbl 0588.73024
James, R. D.
1984
Stress-free joints and polycrystals. Zbl 0558.73007
James, R. D.
1984
The arrangement of coherent phases in a loaded body. Zbl 0594.73114
James, R. D.
1984
A relation between the jump in temperature across a propagating phase boundary and the stability of solid phases. Zbl 0523.73098
James, Richard D.
1983
Finite deformation by mechanical twinning. Zbl 0537.73031
James, Richard D.
1981
The elastica and the problem of the pure bending for a non-convex stored energy function. Zbl 0481.73018
Fosdick, R. L.; James, R. D.
1981
The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy. Zbl 0514.73029
James, Richard D.
1981
The propagation of phase boundaries in elastic bars. Zbl 0443.73010
James, Richard D.
1980
Co-existent phases in the one-dimensional static theory of elastic bars. Zbl 0429.73001
James, Richard D.
1979
all top 5
#### Cited by 996 Authors
39 Conti, Sergio 34 Müller, Stefan 33 James, Richard D. 27 Ciarlet, Philippe Gaston 23 Mardare, Cristinel 21 Dolzmann, Georg 20 Hornung, Peter 19 Kružík, Martin 16 Mora, Maria Giovanna 16 Stefanelli, Ulisse 16 Zhang, Kewei 15 Bhattacharya, Kaushik 15 Ortiz, Michael 15 Roubíček, Tomáš 14 DeSimone, Antonio 14 Lewicka, Marta , Wang, Dehua 14 Steigmann, David J. 14 Velčić, Igor 13 Ericksen, Jerald Laverne 13 Fonseca, Irene 13 Friedrich, Manuel 13 Kohn, Robert Vita 13 Mielke, Alexander 13 Truskinovsky, Lev 12 Hackl, Klaus 12 Luskin, Mitchell 12 Spector, Scott J. 11 Carstensen, Carsten 11 Li, Zhiping 11 Schlömerkemper, Anja 10 Ball, John M. 10 Grabovsky, Yury 10 Griso, Georges 10 Paroni, Roberto 10 Pruchnicki, Erick 10 Tomassetti, Giuseppe 9 Friesecke, Gero 9 Harutyunyan, Davit 9 Miehe, Christian 9 Neff, Patrizio 9 Pedregal, Pablo 8 Bartels, Sören 8 Benešová, Barbora 8 Blanchard, Dominique 8 Neukamm, Stefan 8 Pence, Thomas J. 8 Schmidt, Bernd 8 Sivaloganathan, Jeyabal 8 Yan, Baisheng 7 Abeyaratne, Rohan C. 7 Agostiniani, Virginia 7 Bělík, Pavel 7 Dacorogna, Bernard 7 Dai, Hui-Hui 7 Della Porta, Francesco 7 Kupferman, Raz 7 Levitas, Valery I. 7 Lorent, Andrew 7 Olbermann, Heiner 7 Pakzad, Mohammad Reza 7 Palombaro, Mariapia 7 Rosakis, Phoebus 7 Rumpf, Martin 7 Wang, Jiong 7 Zwicknagl, Barbara Maria 6 Dayal, Kaushik 6 Dondl, Patrick Werner 6 Fosdick, Roger L. 6 Gurtin, Morton Edward 6 Kim, Seonghak 6 Kochmann, Dennis M. 6 Mainini, Edoardo 6 Marcellini, Paolo 6 Petryk, Henryk 6 Rindler, Filip 6 Šilhavý, Miroslav 5 Goriely, Alain 5 Govindjee, Sanjay 5 Grandi, Diego 5 Gratie, Liliana 5 Heinen, Rainer 5 Kinderlehrer, David 5 Kirchheim, Bernd 5 Kreisbeck, Carolin 5 Kumar, Ajeet 5 Le Khanh Chau 5 Maor, Cy 5 Mardare, Sorin 5 Marohnić, Maroje 5 Mihai, L. Angela 5 Monneau, Régis 5 Nota, Alessia 5 Piovano, Paolo 5 Plecháč, Petr 5 Rüland, Angkana 5 Stupkiewicz, Stanisław 5 Székelyhidi, László jun. 5 Tambača, Josip 5 Triantafyllidis, Nicolas 5 Velázquez, Juan J. L. ...and 896 more Authors
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#### Cited in 152 Serials
140 Archive for Rational Mechanics and Analysis 104 Journal of the Mechanics and Physics of Solids 93 Journal of Elasticity 47 Continuum Mechanics and Thermodynamics 46 Mathematics and Mechanics of Solids 35 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 35 Calculus of Variations and Partial Differential Equations 35 Comptes Rendus. Mathématique. Académie des Sciences, Paris 30 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 30 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 25 Computer Methods in Applied Mechanics and Engineering 21 SIAM Journal on Mathematical Analysis 20 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 20 Journal of Nonlinear Science 17 Journal of Differential Equations 15 International Journal of Engineering Science 13 Journal de Mathématiques Pures et Appliquées. Neuvième Série 12 Journal of Mathematical Analysis and Applications 11 Meccanica 10 Communications on Pure and Applied Mathematics 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Physica D 9 Acta Mechanica 9 Journal of Functional Analysis 9 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 8 International Journal of Plasticity 8 Journal of Computational Physics 8 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 8 GAMM-Mitteilungen 7 European Journal of Mechanics. A. Solids 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 7 Discrete and Continuous Dynamical Systems. Series S 6 Mathematics of Computation 6 International Journal for Numerical Methods in Engineering 6 Computational Mechanics 6 Analysis and Applications (Singapore) 5 Mathematical Methods in the Applied Sciences 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Applied Numerical Mathematics 5 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Communications in Mathematical Physics 4 International Journal of Solids and Structures 4 Nonlinearity 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Journal of Optimization Theory and Applications 4 Transactions of the American Mathematical Society 4 Journal of Dynamics and Differential Equations 4 NoDEA. Nonlinear Differential Equations and Applications 4 Advances in Calculus of Variations 3 Journal of Engineering Mathematics 3 Journal of Statistical Physics 3 Rocky Mountain Journal of Mathematics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Mathematische Zeitschrift 3 Numerical Functional Analysis and Optimization 3 Quarterly of Applied Mathematics 3 Chinese Annals of Mathematics. Series B 3 Mathematical and Computer Modelling 3 European Journal of Applied Mathematics 3 Applied Mathematical Modelling 3 Communications in Partial Differential Equations 3 Bulletin of the American Mathematical Society. New Series 3 Journal of the European Mathematical Society (JEMS) 3 Communications in Contemporary Mathematics 3 Nonlinear Analysis. Real World Applications 3 Communications on Pure and Applied Analysis 2 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Acta Mathematica 2 Applied Mathematics and Optimization 2 Journal of Computational and Applied Mathematics 2 Mathematische Annalen 2 Mathematics and Computers in Simulation 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Integral Equations and Applications 2 The Journal of Geometric Analysis 2 Journal of Non-Equilibrium Thermodynamics 2 SIAM Journal on Applied Mathematics 2 Journal of Mathematical Sciences (New York) 2 Discrete and Continuous Dynamical Systems 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Acta Mechanica Sinica 2 Networks and Heterogeneous Media 2 PAMM. Proceedings in Applied Mathematics and Mechanics 2 Analysis & PDE 2 Nonlinear Analysis. Theory, Methods & Applications 1 Applicable Analysis 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Applied Mathematics and Mechanics 1 Journal of Fluid Mechanics 1 Reports on Mathematical Physics 1 Prikladnaya Matematika i Mekhanika 1 Applied Mathematics and Computation 1 BIT ...and 52 more Serials
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#### Cited in 38 Fields
890 Mechanics of deformable solids (74-XX) 291 Calculus of variations and optimal control; optimization (49-XX) 272 Partial differential equations (35-XX) 130 Statistical mechanics, structure of matter (82-XX) 59 Numerical analysis (65-XX) 57 Differential geometry (53-XX) 48 Classical thermodynamics, heat transfer (80-XX) 36 Fluid mechanics (76-XX) 24 Real functions (26-XX) 22 Functional analysis (46-XX) 20 Optics, electromagnetic theory (78-XX) 17 Global analysis, analysis on manifolds (58-XX) 13 Functions of a complex variable (30-XX) 13 Mechanics of particles and systems (70-XX) 11 Ordinary differential equations (34-XX) 9 Quantum theory (81-XX) 9 Biology and other natural sciences (92-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Operations research, mathematical programming (90-XX) 7 Measure and integration (28-XX) 7 Operator theory (47-XX) 6 Integral equations (45-XX) 5 Convex and discrete geometry (52-XX) 5 Computer science (68-XX) 4 Geophysics (86-XX) 3 History and biography (01-XX) 3 Approximations and expansions (41-XX) 3 Abstract harmonic analysis (43-XX) 3 Probability theory and stochastic processes (60-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-05-10T05:33:24 |
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|
https://ftp.aimsciences.org/article/doi/10.3934/proc.2011.2011.1061
|
Article Contents
Article Contents
A necessary and sufficient condition for oscillation of second order sublinear delay dynamic equations
• Time scale calculus approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this article we use this tool to establish a necessary and sucient condition for the oscillation of a class of second order sublinear delay dynamic equations on time scales. Some well known results in the literature are improved and extended.
Mathematics Subject Classification: 34K11, 34C10, 39A11, 39A13.
Citation:
Open Access Under a Creative Commons license
| 2023-03-26T09:28:12 |
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https://par.nsf.gov/biblio/10183410-choosing-preemption-points-minimize-typical-running-times
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Choosing preemption points to minimize typical running times
The problem of selecting "effective preemption points" in a program --- points in the code at which to permit preemption --- in order to minimize overall running time is considered. Prior solutions that have been proposed for this problem are based on workload models in which worst-case known upper bounds are assumed for the duration needed to perform preemptions at particular points in the code, and of the time needed to non-preemptively execute the code between preemption points. Since these solutions are based on worst-case assumptions, they tend to select effective preemption points in a conservative manner; consequently the overall execution time of the program may be needlessly large under most typical run-time circumstances. We consider a more general workload model in which "typical" values, as well as upper bounds, are assumed to be known for the preemption durations and the non-preemptive code-execution durations; given such information, we derive algorithms for the optimal placement of preemption points in a manner that minimizes the typical overall running time (while continuing to guarantee, if needed, upper bounds on the worst-case over-all running time). Both off-line solutions (in which all preemption points are selected prior to run-time) and on-line solutions (where the selection more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10183410
Journal Name:
Proceedings of the International Conference on Real-Time Networks and Systems (RTNS)
Page Range or eLocation-ID:
198 to 208
National Science Foundation
##### More Like this
1. Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures themore »
2. A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in the design of competitive online algorithms. However, the question of improving algorithm running times with predictions has largely been unexplored. We take a first step in this direction by combining the idea of machine-learned predictions with the idea of "warm-starting" primal-dual algorithms. We consider one of the most important primitives in combinatorial optimization: weighted bipartite matching and its generalization to b-matching. We identify three key challenges when using learned dual variables in a primal-dual algorithm. First, predicted duals may be infeasible, so we give an algorithm that efficiently maps predicted infeasible duals to nearby feasible solutions. Second, once the duals are feasible, they may not be optimal, so we show that they can be used to quickly find an optimal solution. Finally, such predictions are useful only if they can be learned, so we show that the problem of learning duals for matching has low sample complexity. We validate our theoretical findings through experiments on both real and synthetic data. As a result we give a rigorous,more »
3. We study the communication cost (or message complexity) of fundamental distributed symmetry breaking problems, namely, coloring and MIS. While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems. In fact, all known algorithms need at least Ω(m) communication for these problems, where m is the number of edges in the graph. We addressthe following question in this paper: can we solve problems such as coloring and MIS using sublinear, i.e., o(m) communication, and if sounder what conditions? In a classical result, Awerbuch, Goldreich, Peleg, and Vainish [JACM 1990] showed that fundamental global problems such asbroadcast and spanning tree construction require at least o(m) messages in the KT-1 Congest model (i.e., Congest model in which nodes have initial knowledge of the neighbors' ID's) when algorithms are restricted to be comparison-based (i.e., algorithms inwhich node ID's can only be compared). Thirty five years after this result, King, Kutten, and Thorup [PODC 2015] showed that onecan solve the above problems using Õ(n) messages (n is the number of nodes in the graph) in Õ(n) rounds in the KT-1 Congest model if non-comparison-based algorithms are permitted. Anmore »
4. Neuromorphic computing systems execute machine learning tasks designed with spiking neural networks. These systems are embracing non-volatile memory to implement high-density and low-energy synaptic storage. Elevated voltages and currents needed to operate non-volatile memories cause aging of CMOS-based transistors in each neuron and synapse circuit in the hardware, drifting the transistor’s parameters from their nominal values. If these circuits are used continuously for too long, the parameter drifts cannot be reversed, resulting in permanent degradation of circuit performance over time, eventually leading to hardware faults. Aggressive device scaling increases power density and temperature, which further accelerates the aging, challenging the reliable operation of neuromorphic systems. Existing reliability-oriented techniques periodically de-stress all neuron and synapse circuits in the hardware at fixed intervals, assuming worst-case operating conditions, without actually tracking their aging at run-time. To de-stress these circuits, normal operation must be interrupted, which introduces latency in spike generation and propagation, impacting the inter-spike interval and hence, performance (e.g., accuracy). We observe that in contrast to long-term aging, which permanently damages the hardware, short-term aging in scaled CMOS transistors is mostly due to bias temperature instability. The latter is heavily workload-dependent and, more importantly, partially reversible. We propose a new architectural techniquemore »
5. Abstract
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_{i}{x}_{i}$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:
#SAT algorithms fornk-size$\mathcal { C}$$C$-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
#SAT algorithms for$2^{n^{{\varepsilon }}}$${2}^{{n}^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$${2}^{n-{n}^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJACC0THRcircuits of polynomialmore »
| 2023-01-27T08:18:03 |
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https://par.nsf.gov/biblio/10366409-brightest-cluster-galaxies-trace-weak-lensing-mass-bias-halo-triaxiality-three-hundred-project
|
Brightest cluster galaxies trace weak lensing mass bias and halo triaxiality in the three hundred project
ABSTRACT
Galaxy clusters have a triaxial matter distribution. The weak-lensing signal, an important part in cosmological studies, measures the projected mass of all matter along the line of sight, and therefore changes with the orientation of the cluster. Studies suggest that the shape of the brightest cluster galaxy (BCG) in the centre of the cluster traces the underlying halo shape, enabling a method to account for projection effects. We use 324 simulated clusters at four redshifts between 0.1 and 0.6 from ‘The Three Hundred Project’ to quantify correlations between the orientation and shape of the BCG and the halo. We find that haloes and their embedded BCGs are aligned, with an average ∼20 degree angle between their major axes. The bias in weak lensing cluster mass estimates correlates with the orientation of both the halo and the BCG. Mimicking observations, we compute the projected shape of the BCG, as a measure of the BCG orientation, and find that it is most strongly correlated to the weak-lensing mass for relaxed clusters. We also test a 2D cluster relaxation proxy measured from BCG mass isocontours. The concentration of stellar mass in the projected BCG core compared to the total stellar mass provides more »
Authors:
; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10366409
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
513
Issue:
2
Page Range or eLocation-ID:
p. 2178-2193
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. Abstract
We present our determination of the baryon budget for an X-ray-selected XXL sample of 136 galaxy groups and clusters spanning nearly two orders of magnitude in mass (M500 ∼ 1013–1015 M⊙) and the redshift range 0 ≲ z ≲ 1. Our joint analysis is based on the combination of Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) weak-lensing mass measurements, XXL X-ray gas mass measurements, and HSC and Sloan Digital Sky Survey multiband photometry. We carry out a Bayesian analysis of multivariate mass-scaling relations of gas mass, galaxy stellar mass, stellar mass of brightest cluster galaxies (BCGs), and soft-band X-ray luminosity, by taking into account the intrinsic covariance between cluster properties, selection effect, weak-lensing mass calibration, and observational error covariance matrix. The mass-dependent slope of the gas mass–total mass (M500) relation is found to be $1.29_{-0.10}^{+0.16}$, which is steeper than the self-similar prediction of unity, whereas the slope of the stellar mass–total mass relation is shallower than unity; $0.85_{-0.09}^{+0.12}$. The BCG stellar mass weakly depends on cluster mass with a slope of $0.49_{-0.10}^{+0.11}$. The baryon, gas mass, and stellar mass fractions as a function of M500 agree with the results from numerical simulations and previous observations. We successfully constrain the full intrinsicmore »
2. ABSTRACT
Galaxy cluster masses, rich with cosmological information, can be estimated from internal dark matter (DM) velocity dispersions, which in turn can be observationally inferred from satellite galaxy velocities. However, galaxies are biased tracers of the DM, and the bias can vary over host halo and galaxy properties as well as time. We precisely calibrate the velocity bias, bv – defined as the ratio of galaxy and DM velocity dispersions – as a function of redshift, host halo mass, and galaxy stellar mass threshold ($M_{\rm \star , sat}$), for massive haloes ($M_{\rm 200c}\gt 10^{13.5} \, {\rm M}_\odot$) from five cosmological simulations: IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and MultiDark Planck-2. We first compare scaling relations for galaxy and DM velocity dispersion across simulations; the former is estimated using a new ensemble velocity likelihood method that is unbiased for low galaxy counts per halo, while the latter uses a local linear regression. The simulations show consistent trends of bv increasing with M200c and decreasing with redshift and $M_{\rm \star , sat}$. The ensemble-estimated theoretical uncertainty in bv is 2–3 per cent, but becomes percent-level when considering only the three highest resolution simulations. We update the mass–richness normalization for an SDSSmore »
3. ABSTRACT
Galaxy sizes correlate closely with the sizes of their parent dark matter haloes, suggesting a link between halo formation and galaxy growth. However, the precise nature of this relation and its scatter remains to be understood fully, especially for low-mass galaxies. We analyse the galaxy–halo size relation (GHSR) for low-mass ($M_\star \sim 10^{7-9}\, {\rm M}_\odot$) central galaxies over the past 12.5 billion years with the help of cosmological volume simulations (FIREbox) from the Feedback in Realistic Environments (FIRE) project. We find a nearly linear relationship between the half-stellar mass galaxy size R1/2 and the parent dark matter halo virial radius Rvir. This relation evolves only weakly since redshift z = 5: $R_{1/2}\, [{\rm kpc}] = (0.053\pm 0.002)(R_{\rm vir}/35\, {\rm kpc})^{0.934\pm 0.054}$, with a nearly constant scatter $\langle \sigma \rangle = 0.084\, [{\rm dex}]$. While this ratio is similar to what is expected from models where galaxy disc sizes are set by halo angular momentum, the low-mass galaxies in our sample are not angular momentum supported, with stellar rotational to circular velocity ratios vrot/vcirc ∼ 0.15. Introducing redshift as another parameter to the GHSR does not decrease the scatter. Furthermore, this scatter does not correlate with any of the halo propertiesmore »
4. ABSTRACT
Secondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter haloes. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, ΔΣ. We build an emulator trained on N-body simulations to model ΔΣ and quantify the impact of different secondary parameters on the ΔΣ profile. We focus on the impact of MAR on ΔΣ. We show that a 3σ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey assuming no baryonic effects and a proxy for MAR with scatter <1.5. We show that the full radial profile of ΔΣ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than two times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentring and MAR impact the radial profile of ΔΣ in a similar fashion, implying that miscentring and MAR need to be modelled jointly for unbiased estimates of both effects. We show that present-day lensing datamore »
5. ABSTRACT
We present the study of the internal dynamics of the intriguing galaxy cluster Abell 1703, a system hosting a probable giant radio halo whose dynamical status is still controversial. Our analysis is based on unpublished spectroscopic data acquired at the Italian Telescopio Nazionale Galileo and data publicly available in the literature. We also use photometric data from the Sloan Digital Sky Survey. We select 147 cluster members and compute the cluster redshift 〈z〉 ∼ 0.277 and the global line-of-sight velocity dispersion σv ∼ 1300 km s−1. We infer that Abell 1703 is a massive cluster: M200 ∼ 1–2 × 1015 M⊙. The results of our study disagree with the picture of an unimodal, relaxed cluster as suggested by previous studies based on the gravitational lensing analysis and support the view of a perturbed dynamics proposed by recent works based on Chandra X-ray data. The first strong evidence of a dynamically disturbed cluster comes from the peculiarity of the BCG velocity with respect to the first moment of the velocity distribution of member galaxies. Moreover, several statistical tests employed to study the cluster galaxies kinematics find significant evidence of substructure, being Abell 1703 composed by at least two or three subclumps probably caught after the core–core passage. In this observational scenario,more »
| 2023-03-31T12:00:17 |
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https://par.nsf.gov/biblio/10227267-measurements-higgs-boson-inclusive-differential-fiducial-cross-sections-ell-decay-channel-sqrt-tev
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Measurements of the Higgs boson inclusive and differential fiducial cross sections in the 4$$\ell$$ decay channel at $$\sqrt{s}$$ = 13 TeV
Abstract Inclusive and differential fiducial cross sections of the Higgs boson are measured in the $$H \rightarrow ZZ^{*} \rightarrow 4\ell$$ H → Z Z ∗ → 4 ℓ ( $$\ell = e,\mu$$ ℓ = e , μ ) decay channel. The results are based on proton-proton collision data produced at the Large Hadron Collider at a centre-of-mass energy of 13 TeV and recorded by the ATLAS detector from 2015 to 2018, equivalent to an integrated luminosity of 139 $$\hbox {fb}^{-1}$$ fb - 1 . The inclusive fiducial cross section for the $$H \rightarrow ZZ^{*} \rightarrow 4\ell$$ H → Z Z ∗ → 4 ℓ process is measured to be $$\sigma _\mathrm {fid} = 3.28 \,{\pm }\, 0.32$$ σ fid = 3.28 ± 0.32 fb, in agreement with the Standard Model prediction of $$\sigma _\mathrm {fid, SM} = 3.41 \pm 0.18$$ σ fid , SM = 3.41 ± 0.18 fb. Differential fiducial cross sections are measured for a variety of observables which are sensitive to the production and decay of the Higgs boson. All measurements are in agreement with the Standard Model predictions. The results are used to constrain anomalous Higgs boson interactions with Standard Model particles.
Authors:
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| 2022-08-12T19:23:31 |
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https://www.futurelearn.com/info/courses/python-in-hpc/0/steps/65107
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# Random numbers
In this article we show how to generate NumPy arrays with random numbers.
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd.
NumPy provides a wide range of functions to generate random numbers in arrays. These functions are available in the numpy.random module.
The random numbers are generated using the same, excellent pseudo-random number generator called Mersenne Twister that is also used in the normal random module. Mersenne Twister has a period of 2^19937-1 and is generally regarded as a very good pseudo-random number generator (for non-cryptographic purposes).
Several functions for constructing random arrays are provided, including:
• random: uniform random numbers
• normal: normal distribution
• choice: random sample from given array
a = numpy.random.random((2,2))print(a)# output:# [[ 0.02909142 0.90848 ]# [ 0.9471314 0.31424393]]b = numpy.random.choice(numpy.arange(4), 10)print(b)# output: [0 1 1 2 1 1 2 0 2 3]
What kind of random numbers do you need in your won work? Can you find them in NumPy?
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd.
| 2022-12-06T03:12:17 |
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https://pdglive.lbl.gov/DataBlock.action?node=M185W&home=sumtabM
|
# ${{\boldsymbol \pi}_{{2}}{(1880)}}$ WIDTH INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT
$\bf{ 237 {}^{+33}_{-30}}$ OUR AVERAGE Error includes scale factor of 1.2.
$246$ ${}^{+33}_{-28}$ 46M 1
2018 B
COMP 190 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit p}}$
$323$ $\pm87$ $\pm43$ 4k
2008
B852 - 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit p}}$
$146$ $\pm17$ $\pm62$ 145k
2005
B852 - 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit p}}$
$306$ $\pm132$ $\pm121$ 69k
2004
B852 - 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit p}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$255$ $\pm45$
2001 B
SPEC 0 $0.6 - 1.94$ ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
1 Statistical error negligible.
References:
AGHASYAN 2018B
PR D98 092003 Light isovector resonances in $\pi^- p \to \pi^-\pi^-\pi^+ p$ at 190 GeV/${\it c}$
EUGENIO 2008
PL B660 466 Observation of the ${{\mathit \pi}{(1800)}}$ and ${{\mathit \pi}_{{2}}{(1880)}}$ Mesons in ${{\mathit \eta}}{{\mathit \eta}}{{\mathit \pi}^{-}}$ Decay
LU 2005
PRL 94 032002 Exotic Meson Decay to ${{\mathit \omega}}{{\mathit \pi}^{0}}{{\mathit \pi}^{-}}$
KUHN 2004
PL B595 109 Exotic Meson Production in the ${{\mathit f}_{{1}}{(1285)}}{{\mathit \pi}^{-}}$ System Observed in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit p}}$ at 18 GeV/$\mathit c$
ANISOVICH 2001B
PL B500 222 Study of ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ in Flight
| 2021-03-03T11:59:12 |
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https://www.zbmath.org/authors/?q=ai%3Ashu.chi-wang
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# zbMATH — the first resource for mathematics
## Shu, Chi-Wang
Compute Distance To:
Author ID: shu.chi-wang Published as: Shu, C.; Shu, C.-W.; Shu, Chi-Wang; Shu, Chi-wang; Shu, Chiwang Homepage: http://www.dam.brown.edu/people/shu/ External Links: MGP · Wikidata · ResearchGate · dblp · GND
Documents Indexed: 415 Publications since 1987, including 10 Books Biographic References: 1 Publication
all top 5
#### Co-Authors
25 single-authored 38 Zhang, Mengping 18 Xu, Yan 18 Zhang, Qiang 16 Cockburn, Bernardo 16 Qiu, Jianxian 15 Cheng, Juan 13 Gottlieb, David I. 13 Zhang, Yongtao 12 Xing, Yulong 11 Carrillo de la Plata, José Antonio 11 Cheng, Yingda 11 Martínez Gamba, Irene 11 Zhang, Shuhai 11 Zhang, Xiangxiong 10 Wang, Wei 9 Wang, Haijin 9 Zhu, Jun 8 Liu, Yingjie 8 Xia, Yinhua 7 E, Weinan 6 Gottlieb, Sigal 6 Jerome, Joseph W. 6 Li, Fengyan 6 Majorana, Armando 6 Osher, Stanley Joel 6 Tadmor, Eitan 5 Hu, Changqing 5 Huang, Juntao 5 Liu, Yunxian 5 Qiu, Jingmei 5 Sun, Zheng 5 Tan, Sirui 5 Xu, Zhiliang 5 Yee, Helen C. 4 Amat, Sergio P. 4 Chou, Ching-Shan 4 Du, Jie 4 Fu, Guosheng 4 Meng, Xiong 4 Ruiz, Juan P. 4 Sjogreen, Bjorn 4 Xiong, Tao 4 Xu, Zhengfu 3 Abgrall, Rémi 3 Bokanowski, Olivier 3 Cai, Wei 3 Cao, Waixiang 3 Chen, Shanqin 3 Chen, Tianheng 3 Dong, Bo 3 Filbet, Francis 3 Guo, Yan 3 Guzmán, Johnny 3 Hesthaven, Jan S. 3 Jiang, Shufen 3 Jiang, Yan 3 Karniadakis, George Em 3 Ling, Dan 3 Noelle, Sebastian 3 Ryan, Jennifer K. 3 Shi, Cengke 3 Vilar, François 3 Wu, Boying 3 Wu, Kailiang 3 Yan, Jue 3 Yang, Yang 3 Zhang, Hanxin 3 Zhang, Zhimin 3 Zhong, Xinghui 3 Zhou, Tie 2 Atkins, Harold L. 2 Balsara, Dinshaw S. 2 Carpenter, Mark H. 2 Cercignani, Carlo 2 Chen, Yanlai 2 Chen, Zheng 2 Cheng, Shiu-Yuen 2 Dumbser, Michael 2 Erlebacher, Gordon 2 Fang, Jinwei 2 Jiang, Guangshan 2 Ketcheson, David I. 2 Kotov, Dmitry V. 2 Lam, William H. K. 2 Lepsky, Olga 2 Levy, Doron 2 Li, Jichun 2 Li, Tingting 2 Li, Yunzhang 2 Liu, Jianguo 2 Liu, Wei 2 Liu, Xuliang 2 Liu, Yuan 2 Liu, Yuanyuan 2 Lu, Jianfang 2 Luskin, Mitchell 2 Maire, Pierre-Henri 2 Ning, Jianguo 2 Qin, Tong 2 Sapiro, Guillermo ...and 155 more Co-Authors
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#### Serials
96 Journal of Computational Physics 42 Journal of Scientific Computing 28 SIAM Journal on Numerical Analysis 23 SIAM Journal on Scientific Computing 16 Communications in Computational Physics 14 Mathematics of Computation 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Computer Methods in Applied Mechanics and Engineering 8 Computers and Fluids 8 Journal of Computational and Applied Mathematics 7 Numerische Mathematik 7 Journal of Computational Mathematics 7 Applied Numerical Mathematics 6 Science China. Mathematics 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Methods and Applications of Analysis 4 Physica D 4 Physics of Fluids 4 International Journal of Numerical Analysis and Modeling 3 SIAM Review 3 Multiscale Modeling & Simulation 3 Communications on Applied Mathematics and Computation 2 Computers & Mathematics with Applications 2 IMA Journal of Numerical Analysis 2 Journal of Fluid Mechanics 2 Transport Theory and Statistical Physics 2 International Journal for Numerical Methods in Engineering 2 Quarterly of Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Applied Mathematics Letters 2 Handbook of Numerical Analysis 2 Kinetic and Related Models 1 AIAA Journal 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Physics of Fluids, A 1 Applied Mathematics and Computation 1 Mathematica Numerica Sinica 1 SIAM Journal on Scientific and Statistical Computing 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematical Modelling 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Chinese Science Bulletin 1 Engineering Analysis with Boundary Elements 1 International Journal of Computational Fluid Dynamics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Mathematical Study 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Acta Mechanica Sinica 1 Inverse Problems and Imaging 1 S$$\vec{\text{e}}$$MA Journal 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Annals of Mathematical Sciences and Applications 1 Advanced Courses in Mathematics – CRM Barcelona
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#### Fields
324 Numerical analysis (65-XX) 208 Partial differential equations (35-XX) 140 Fluid mechanics (76-XX) 27 Statistical mechanics, structure of matter (82-XX) 10 General and overarching topics; collections (00-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Biology and other natural sciences (92-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Mechanics of deformable solids (74-XX) 7 Operations research, mathematical programming (90-XX) 6 Optics, electromagnetic theory (78-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 History and biography (01-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 4 Astronomy and astrophysics (85-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Differential geometry (53-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH
352 Publications have been cited 18,812 times in 6,146 Documents Cited by Year
Efficient implementation of weighted ENO schemes. Zbl 0877.65065
Jiang, Guang-Shan; Shu, Chi-Wang
1996
Efficient implementation of essentially nonoscillatory shock-capturing schemes. Zbl 0653.65072
Shu, Chi-Wang; Osher, Stanley
1988
Efficient implementation of essentially nonoscillatory shock-capturing schemes. II. Zbl 0674.65061
Shu, Chi-Wang; Osher, Stanley
1989
The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118
Cockburn, Bernardo; Shu, Chi-Wang
1998
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: General framework. Zbl 0662.65083
Cockburn, Bernardo; Shu, Chi-Wang
1989
The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059
Cockburn, Bernardo; Shu, Chi-Wang
1998
Strong stability-preserving high-order time discretization methods. Zbl 0967.65098
Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan
2001
Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135
Cockburn, Bernardo; Shu, Chi-Wang
2001
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems. Zbl 0677.65093
Cockburn, Bernardo; Lin, San-Yih; Shu, Chi-Wang
1989
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case. Zbl 0695.65066
Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang
1990
Total variation diminishing Runge-Kutta schemes. Zbl 0897.65058
Gottlieb, Sigal; Shu, Chi-Wang
1998
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Zbl 0927.65111
Shu, Chi-Wang
1998
Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Zbl 0961.65078
Balsara, Dinshaw S.; Shu, Chi-Wang
2000
Total-variation-diminishing time discretizations. Zbl 0662.65081
Shu, Chiwang
1988
The development of discontinuous Galerkin methods. Zbl 0989.76045
Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
2000
Weighted essentially non-oscillatory schemes on triangular meshes. Zbl 0926.65090
Hu, Changqing; Shu, Chi-Wang
1999
High order weighted essentially nonoscillatory schemes for convection dominated problems. Zbl 1160.65330
Shu, Chi-Wang
2009
High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066
Osher, Stanley; Shu, Chi-Wang
1991
The Runge-Kutta local projection $$P^ 1$$-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0732.65094
Cockburn, Bernardo; Shu, Chi-Wang
1991
On the Gibbs phenomenon and its resolution. Zbl 0885.42003
Gottlieb, David; Shu, Chi-Wang
1997
On maximum-principle-satisfying high order schemes for scalar conservation laws. Zbl 1187.65096
Zhang, Xiangxiong; Shu, Chi-Wang
2010
On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. Zbl 1282.76128
Zhang, Xiangxiong; Shu, Chi-Wang
2010
A technique of treating negative weights in WENO schemes. Zbl 0992.65094
Shi, Jing; Hu, Changqing; Shu, Chi-Wang
2002
A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050
Yan, Jue; Shu, Chi-Wang
2002
Runge-Kutta discontinuous Galerkin method using WENO limiters. Zbl 1077.65109
Qiu, Jianxian; Shu, Chi-Wang
2005
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case. Zbl 1039.65068
Qiu, Jianxian; Shu, Chi-Wang
2004
TVB uniformly high-order schemes for conservation laws. Zbl 0628.65075
Shu, Chiwang
1987
High order finite difference WENO schemes with the exact conservation property for the shallow water equations. Zbl 1114.76340
Xing, Yulong; Shu, Chi-Wang
2005
Strong stability preserving Runge-Kutta and multistep time discretizations. Zbl 1241.65064
Gottlieb, Sigal; Ketcheson, David; Shu, Chi-Wang
2011
Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Zbl 1222.65107
Zhang, Xiangxiong; Shu, Chi-Wang
2011
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case. Zbl 1134.65358
Qiu, Jianxian; Shu, Chi-Wang
2005
High order strong stability preserving time discretizations. Zbl 1203.65135
Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang
2009
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019
Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang
2004
Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Zbl 1364.65205
Xu, Yan; Shu, Chi-Wang
2010
On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. Zbl 1018.65106
Qiu, Jianxian; Shu, Chi-Wang
2002
High-order well-balanced finite volume WENO schemes for shallow water equation with moving water. Zbl 1120.76046
Noelle, Sebastian; Xing, Yulong; Shu, Chi-Wang
2007
Local discontinuous Galerkin methods for nonlinear Schrödinger equations. Zbl 1072.65130
Xu, Yan; Shu, Chi-Wang
2005
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Zbl 1089.65091
Xing, Yulong; Shu, Chi-Wang
2006
Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. Zbl 1078.65080
Zhang, Qiang; Shu, Chi-Wang
2004
High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Zbl 1034.76044
Shu, Chi-Wang
2003
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes. Zbl 1157.65453
Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang; Dumbser, Michael
2008
Resolution of high order WENO schemes for complicated flow structures. Zbl 1047.76081
Shi, Jing; Zhang, Yong-Tao; Shu, Chi-Wang
2003
A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. Zbl 0946.65090
Hu, Changqing; Shu, Chi-Wang
1999
Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes. Zbl 1247.65131
Zhang, Xiangxiong; Xia, Yinhua; Shu, Chi-Wang
2012
Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043
Cockburn, Bernardo (ed.); Karniadakis, George E. (ed.); Shu, Chi-Wang (ed.)
2000
High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. Zbl 1034.65051
Zhang, Yong-Tao; Shu, Chi-Wang
2003
A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. Zbl 1092.65084
Qiu, Jianxian; Shu, Chi-Wang
2005
Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. Zbl 1003.65115
Yan, Jue; Shu, Chi-Wang
2002
On a cell entropy inequality for discontinuous Galerkin methods. Zbl 0801.65098
Jiang, Guangshan; Shu, Chi-Wang
1994
On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022
Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé
1992
Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension. Zbl 1208.65137
Cheng, Yingda; Shu, Chi-Wang
2010
Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. Zbl 1391.76375
Zhang, Xiangxiong; Shu, Chi-Wang
2011
A high-order ENO conservative Lagrangian type scheme for the compressible Euler equations. Zbl 1126.76035
Cheng, Juan; Shu, Chi-Wang
2007
Third order WENO scheme on three dimensional tetrahedral meshes. Zbl 1364.65177
Zhang, Yong-Tao; Shu, Chi-Wang
2009
A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives. Zbl 1141.65075
Cheng, Yingda; Shu, Chi-Wang
2008
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. Zbl 1131.65088
Xia, Yinhua; Xu, Yan; Shu, Chi-Wang
2007
Local discontinuous Galerkin methods for nonlinear dispersive equations. Zbl 1055.65109
Levy, Doron; Shu, Chi-Wang; Yan, Jue
2004
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049
Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre
2003
On positivity preserving finite volume schemes for Euler equations. Zbl 0857.76062
Perthame, Benoit; Shu, Chi-Wang
1996
Small-scale structures in Boussinesq convection. Zbl 0822.76087
E, Weinan; Shu, Chi-Wang
1994
Numerical experiments on the accuracy of ENO and modified ENO schemes. Zbl 0732.65085
Shu, Chi-Wang
1990
A local discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1173.65063
Xu, Yan; Shu, Chi-Wang
2008
High order ENO and WENO schemes for computational fluid dynamics. Zbl 0937.76044
Shu, Chi-Wang
1999
Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. Zbl 1157.65450
Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping
2007
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes. Zbl 1349.65501
Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian
2013
Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws. Zbl 1217.65178
Zhang, Qiang; Shu, Chi-Wang
2010
A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Zbl 1115.65096
Xing, Yulong; Shu, Chi-Wang
2006
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. Zbl 1426.76493
Zhang, Xiangxiong; Shu, Chi-Wang
2012
Locally divergence-free discontinuous Galerkin methods for MHD equations. Zbl 1123.76341
Li, Fengyan; Shu, Chi-Wang
2005
The discontinuous Galerkin method with Lax–Wendroff type time discretizations. Zbl 1093.76038
Qiu, Jianxian; Dumbser, Michael; Shu, Chi-Wang
2005
Finite difference WENO schemes with Lax-Wendroff-type time discretizations. Zbl 1034.65073
Qiu, Jianxian; Shu, Chi-Wang
2003
Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085
Cockburn, Bernardo; Shu, Chi-Wang
1994
An efficient class of WENO schemes with adaptive order. Zbl 1422.65146
Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang
2016
Anti-diffusive flux corrections for high order finite difference WENO schemes. Zbl 1087.76080
Xu, Zhengfu; Shu, Chi-Wang
2005
Analysis of optimal superconvergence of discontinuous Galerkin method for linear hyperbolic equations. Zbl 1276.65055
Yang, Yang; Shu, Chi-Wang
2012
Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system. Zbl 1273.65147
Qiu, Jing-Mei; Shu, Chi-Wang
2011
Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations. Zbl 1173.65338
Xu, Yan; Shu, Chi-Wang
2007
Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. Zbl 1311.76088
Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang
2013
Development of nonlinear weighted compact schemes with increasingly higher order accuracy. Zbl 1152.65094
Zhang, Shuhai; Jiang, Shufen; Shu, Chi-Wang
2008
A high-order discontinuous Galerkin method for 2D incompressible flows. Zbl 0963.76069
Liu, Jian-Guo; Shu, Chi-Wang
2000
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws. Zbl 1198.65174
Tan, Sirui; Shu, Chi-Wang
2010
Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations. Zbl 1124.76035
Xu, Yan; Shu, Chi-Wang
2006
Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for advection-diffusion problems. Zbl 1327.65179
Wang, Haijin; Shu, Chi-Wang; Zhang, Qiang
2015
High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations. Zbl 1287.76181
Liu, Wei; Cheng, Juan; Shu, Chi-Wang
2009
A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. Zbl 1034.82063
Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang
2003
Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. Zbl 1247.65121
Xu, Yan; Shu, Chi-Wang
2012
An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Zbl 1138.76391
Zhang, Mengping; Shu, Chi-Wang
2005
An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations. Zbl 1050.65094
Zhang, Mengping; Shu, Chi-Wang
2003
$$L^{2}$$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. Zbl 1152.65095
Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping
2008
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations. Zbl 1124.65090
Cheng, Yingda; Shu, Chi-Wang
2007
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. Zbl 1243.80011
Wang, Cheng; Zhang, Xiangxiong; Shu, Chi-Wang; Ning, Jianguo
2012
Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow. Zbl 1391.76489
Qiu, Jing-Mei; Shu, Chi-Wang
2011
Analysis of a local discontinuous Galerkin method for linear time-dependent fourth-order problems. Zbl 1204.65123
Dong, Bo; Shu, Chi-Wang
2009
A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes. Zbl 1083.65093
Qiu, Jianxian; Khoo, Boo Cheong; Shu, Chi-Wang
2006
Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations. Zbl 1078.35111
Xu, Yan; Shu, Chi-Wang
2005
Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes. Zbl 1284.65140
Zhang, Yifan; Zhang, Xiangxiong; Shu, Chi-Wang
2013
A survey of high order schemes for the shallow water equations. Zbl 1324.76035
Xing, Yulong; Shu, Chi-Wang
2014
Superconvergence of discontinuous Galerkin methods for scalar nonlinear conservation laws in one space dimension. Zbl 1267.65115
Meng, Xiong; Shu, Chi-Wang; Zhang, Qiang; Wu, Boying
2012
On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. Zbl 1409.76086
Xing, Yulong; Shu, Chi-Wang; Noelle, Sebastian
2011
Efficient time discretization for local discontinuous Galerkin methods. Zbl 1141.65076
Xia, Yinhua; Xu, Yan; Shu, Chi-Wang
2007
An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives. Zbl 1446.65118
Tao, Qi; Xu, Yan; Shu, Chi-Wang
2020
On a new WENO algorithm of order $$2 r$$ with improved accuracy close to discontinuities. Zbl 07187420
Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang
2020
A discontinuous Galerkin method for stochastic conservation laws. Zbl 07149719
Li, Yunzhang; Shu, Chi-Wang; Tang, Shanjian
2020
Strong stability of explicit Runge-Kutta time discretizations. Zbl 1422.65224
Sun, Zheng; Shu, Chi-Wang
2019
Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems. Zbl 1434.65195
Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang
2019
The $$\mathrm{L}^2$$-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1422.65272
Xu, Yuan; Zhang, Qiang; Shu, Chi-Wang; Wang, Haijin
2019
Stability analysis and error estimates of arbitrary Lagrangian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws. Zbl 1418.65141
Zhou, Lingling; Xia, Yinhua; Shu, Chi-Wang
2019
Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Zbl 1419.76446
Wu, Kailiang; Shu, Chi-Wang
2019
Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. Zbl 1420.35190
Huang, Juntao; Shu, Chi-Wang
2019
An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1407.65187
Fu, Guosheng; Shu, Chi-Wang
2019
On new strategies to control the accuracy of WENO algorithms close to discontinuities. Zbl 1436.65095
Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang
2019
A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows. Zbl 1444.35125
Huang, Juntao; Zhao, Weifeng; Shu, Chi-Wang
2019
Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1449.65250
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2019
Numerical solutions of stochastic PDEs driven by arbitrary type of noise. Zbl 07114866
Chen, Tianheng; Rozovskii, Boris; Shu, Chi-Wang
2019
An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. Zbl 1420.65095
Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang
2019
High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. Zbl 1411.76111
Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian
2019
Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow. Zbl 1405.65129
Wang, Haijin; Liu, Yunxian; Zhang, Qiang; Shu, Chi-Wang
2019
A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. Zbl 1380.65287
Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang
2018
Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations. Zbl 1450.65116
Cao, Waixiang; Shu, Chi-Wang; Yang, Yang; Zhang, Zhimin
2018
A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Zbl 1416.65286
Zhu, Jun; Shu, Chi-Wang
2018
Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes. Zbl 1380.76162
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018
Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms. Zbl 1422.65259
Huang, Juntao; Shu, Chi-Wang
2018
A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. Zbl 1404.65184
Wu, Kailiang; Shu, Chi-Wang
2018
On local conservation of numerical methods for conservation laws. Zbl 1410.65327
Shi, Cengke; Shu, Chi-Wang
2018
Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions. Zbl 1448.65178
Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang
2018
Discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials on unstructured meshes. Zbl 06887280
Shi, Cengke; Li, Jichun; Shu, Chi-Wang
2018
Implicit positivity-preserving high-order discontinuous Galerkin methods for conservation laws. Zbl 1380.65285
Qin, Tong; Shu, Chi-Wang
2018
Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1383.65108
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018
Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations. Zbl 1407.65196
Ling, Dan; Cheng, Juan; Shu, Chi-Wang
2018
Positivity-preserving high-order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter. Zbl 1414.65012
Du, Jie; Shu, Chi-Wang
2018
Discontinuous Galerkin methods for a kinetic model of self-organized dynamics. Zbl 1404.65168
Filbet, Francis; Shu, Chi-Wang
2018
Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. Zbl 1380.65253
Chen, Tianheng; Shu, Chi-Wang
2017
Local discontinuous Galerkin method for the Keller-Segel chemotaxis model. Zbl 1384.92015
Li, Xingjie Helen; Shu, Chi-Wang; Yang, Yang
2017
Optimal non-dissipative discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials. Zbl 1370.74143
Li, Jichun; Shi, Cengke; Shu, Chi-Wang
2017
H(div) conforming and DG methods for incompressible Euler’s equations. Zbl 1433.76085
Guzmán, Johnny; Shu, Chi-Wang; Sequeira, Filánder A.
2017
Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations. Zbl 1381.65079
Sun, Zheng; Shu, Chi-Wang
2017
A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. Zbl 1380.65262
Fu, Guosheng; Shu, Chi-Wang
2017
Superconvergence of discontinuous Galerkin methods for 1-D linear hyperbolic equations with degenerate variable coefficients. Zbl 1382.65274
Cao, Waixiang; Shu, Chi-Wang; Zhang, Zhimin
2017
Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation. Zbl 1383.65105
Song, Huailing; Shu, Chi-Wang
2017
Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids. Zbl 1378.76086
Shen, Hua; Wen, Chih-Yung; Parsani, Matteo; Shu, Chi-Wang
2017
A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model. Zbl 1360.65235
Huang, Juntao; Shu, Chi-Wang
2017
Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws. Zbl 1361.65067
Huang, Juntao; Shu, Chi-Wang
2017
Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes. Zbl 1380.76074
Zhu, Jun; Shu, Chi-Wang
2017
Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates. Zbl 1390.76473
Ling, Dan; Cheng, Juan; Shu, Chi-Wang
2017
Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs. Zbl 1407.65204
Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang
2017
Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations. Zbl 1415.65204
Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian
2017
Analysis of an embedded discontinuous Galerkin method with implicit-explicit time-marching for convection-diffusion problems. Zbl 1380.65261
Fu, Guosheng; Shu, Chi-Wang
2017
A simple bound-preserving sweeping technique for conservative numerical approximations. Zbl 1381.65087
Liu, Yuan; Cheng, Yingda; Shu, Chi-Wang
2017
Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. Zbl 1372.65251
Shu, Chi-Wang
2017
Stability analysis and error estimates of Lax-Wendroff discontinuous Galerkin methods for linear conservation laws. Zbl 1373.65063
Sun, Zheng; Shu, Chi-Wang
2017
Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations. Zbl 1361.65062
Li, Tingting; Shu, Chi-Wang; Zhang, Mengping
2017
Handbook on numerical methods for hyperbolic problems. Applied and modern issues. Zbl 1364.65001
Abgrall, Rémi (ed.); Shu, Chi-Wang (ed.)
2017
A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber. Zbl 1439.65183
Lam, Chi Yeung; Shu, Chi-Wang
2017
An efficient class of WENO schemes with adaptive order. Zbl 1422.65146
Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang
2016
High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments. Zbl 1349.65486
Shu, Chi-Wang
2016
Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations. Zbl 1332.65148
Meng, Xiong; Shu, Chi-Wang; Wu, Boying
2016
Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics. Zbl 1349.83037
Qin, Tong; Shu, Chi-Wang; Yang, Yang
2016
Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems. Zbl 1351.65078
Wang, Haijin; Wang, Shiping; Zhang, Qiang; Shu, Chi-Wang
2016
Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems. Zbl 1410.65383
Wang, Haijin; Shu, Chi-Wang; Zhang, Qiang
2016
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. II: The two-dimensional case. Zbl 1351.76128
Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri
2016
Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter. Zbl 1373.76113
Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian
2016
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. I: The one-dimensional case. Zbl 1351.76127
Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri
2016
A boundary condition-enforced immersed boundary method for compressible viscous flows. Zbl 1390.76504
Qiu, Y. L.; Shu, C.; Wu, J.; Sun, Y.; Yang, L. M.; Guo, T. Q.
2016
Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations. Zbl 1349.65319
Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping
2016
Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices. Zbl 1342.65183
Liu, YunXian; Shu, Chi-Wang
2016
Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes. Zbl 1333.65101
Li, Tingting; Shu, Chi-Wang; Zhang, Mengping
2016
Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues. Zbl 1352.65001
Abgrall, Remi (ed.); Shu, Chi-Wang (ed.)
2016
A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schrödinger equation. Zbl 1342.65169
Dong, Bo; Shu, Chi-Wang; Wang, Wei
2016
High order fixed-point sweeping WENO methods for steady state of hyperbolic conservation laws and its convergence study. Zbl 1388.65068
Wu, Liang; Zhang, Yong-Tao; Zhang, Shuhai; Shu, Chi-Wang
2016
Convergence of discontinuous Galerkin schemes for front propagation with obstacles. Zbl 1353.65104
Bokanowski, Olivier; Cheng, Yingda; Shu, Chi-Wang
2016
Three-dimensional ghost-fluid large-scale numerical investigation on air explosion. Zbl 1390.76635
Wang, Cheng; Ding, JianXu; Shu, Chi-Wang; Li, Tao
2016
Discontinuous Galerkin methods for time-dependent convection dominated problems: basics, recent developments and comparison with other methods. Zbl 1357.65179
Shu, Chi-Wang
2016
High order positivity-preserving discontinuous Galerkin methods for radiative transfer equations. Zbl 1351.65105
Yuan, Daming; Cheng, Juan; Shu, Chi-Wang
2016
Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for advection-diffusion problems. Zbl 1327.65179
Wang, Haijin; Shu, Chi-Wang; Zhang, Qiang
2015
An SPH model for multiphase flows with complex interfaces and large density differences. Zbl 1351.76231
Chen, Z.; Zong, Z.; Liu, M. B.; Zou, L.; Li, H. T.; Shu, C.
2015
Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations. Zbl 1328.65195
Cao, Waixiang; Shu, Chi-Wang; Yang, Yang; Zhang, Zhimin
2015
A new class of central compact schemes with spectral-like resolution. II: Hybrid weighted nonlinear schemes. Zbl 1351.76170
Liu, Xuliang; Zhang, Shuhai; Zhang, Hanxin; Shu, Chi-Wang
2015
Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes. Zbl 1311.65116
Vilar, François; Shu, Chi-Wang
2015
A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. Zbl 1327.65193
Luo, Juan; Shu, Chi-Wang; Zhang, Qiang
2015
Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation. Zbl 1349.76159
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang
2015
A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework. Zbl 1320.65114
Du, Jie; Shu, Chi-Wang; Zhang, Mengping
2015
High order finite difference methods with subcell resolution for stiff multispecies discontinuity capturing. Zbl 1373.76197
Wang, Wei; Shu, Chi-Wang; Yee, H. C.; Kotov, Dmitry V.; Sjögreen, Björn
2015
A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows. Zbl 1349.76751
Yang, L. M.; Shu, C.; Wu, J.
2015
A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework on unstructured meshes. Zbl 1326.65130
Du, Jie; Shu, Chi-Wang; Zhang, Mengping
2015
Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities. Zbl 1331.65145
Chen, Zheng; Shu, Chi-Wang
2015
Numerical solution of the viscous surface wave with discontinuous Galerkin method. Zbl 1321.35143
Wu, Lei; Shu, Chi-Wang
2015
High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates. Zbl 1318.65051
Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping
2015
A survey of high order schemes for the shallow water equations. Zbl 1324.76035
Xing, Yulong; Shu, Chi-Wang
2014
Positivity-preserving Lagrangian scheme for multi-material compressible flow. Zbl 1349.76439
Cheng, Juan; Shu, Chi-Wang
2014
Discontinuous Galerkin method for time-dependent problems: survey and recent developments. Zbl 1282.65122
Shu, Chi-Wang
2014
Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media. Zbl 1349.65446
Chou, Ching-Shan; Shu, Chi-Wang; Xing, Yulong
2014
Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data. Zbl 1293.65122
Zhang, Qiang; Shu, Chi-Wang
2014
Free-stream preserving finite difference schemes on curvilinear meshes. Zbl 1292.65091
Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping
2014
A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows. Zbl 1351.76257
Yang, L. M.; Shu, C.; Wu, J.
2014
Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates. Zbl 1349.65367
Cheng, Juan; Shu, Chi-Wang
2014
A discontinuous Galerkin scheme for front propagation with obstacles. Zbl 1291.65182
Bokanowski, Olivier; Cheng, Yingda; Shu, Chi-Wang
2014
Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients. Zbl 1307.65171
Zhang, Yifan; Wang, Wei; Guzmán, Johnny; Shu, Chi-Wang
2014
Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities. Zbl 1311.65013
Chen, Zheng; Shu, Chi-Wang
2014
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes. Zbl 1349.65501
Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian
2013
Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. Zbl 1311.76088
Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang
2013
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#### Cited by 7,722 Authors
226 Shu, Chi-Wang 82 Dumbser, Michael 63 Qiu, Jianxian 46 Cockburn, Bernardo 46 Osher, Stanley Joel 43 Kurganov, Alexander 40 Adams, Nikolaus A. 39 Baccouch, Mahboub 38 Dawson, Clint N. 38 Xu, Yan 37 Li, Jichun 36 Toro, Eleuterio F. 35 Balsara, Dinshaw S. 35 Qiu, Jingmei 33 Don, Wai Sun 33 Liu, Hailiang 32 Cheng, Yingda 32 Mulet, Pep 32 Zhang, Mengping 31 Abgrall, Rémi 31 Dehghan Takht Fooladi, Mehdi 31 Hesthaven, Jan S. 30 Li, Fengyan 30 Xiao, Feng 29 Qian, Jianliang 29 Xing, Yulong 29 Xu, Kun 28 Bürger, Raimund 28 Fedkiw, Ronald P. 28 Zhu, Jun 27 Christlieb, Andrew J. 26 Gassner, Gregor J. 26 Munz, Claus-Dieter 26 Yu, Xijun 24 Jameson, Antony 24 Loubère, Raphaël 23 Chertock, Alina E. 23 Drikakis, Dimitris 23 Guermond, Jean-Luc 23 Karniadakis, George Em 23 Ren, Yuxin 23 van der Vegt, Jaap J. W. 22 Amat, Sergio P. 22 Gelb, Anne 22 Luo, Hong 22 Popov, Boyan 22 Ryan, Jennifer K. 22 Tang, Huazhong 22 Zhang, Yongtao 22 Zhang, Zhimin 21 Carpenter, Mark H. 21 Castro, Manuel J. 21 Gao, Zhen 21 Huang, Yunqing 21 Kuzmin, Dmitri 20 Adjerid, Slimane 20 Liu, Tiegang 20 Xia, Yinhua 20 Zhang, Qiang 19 Boscheri, Walter 19 Martínez Gamba, Irene 19 Gottlieb, Sigal 19 Seaïd, Mohammed 19 Xiong, Tao 18 Mishra, Siddhartha 18 Yee, Helen C. 17 Bassi, Francesco 17 Carrillo de la Plata, José Antonio 17 Deng, Xiaogang 17 Filbet, Francis 17 Gibou, Frédéric 17 Guo, Wei 17 Ketcheson, David I. 17 Kubatko, Ethan J. 17 Li, Gang 17 Pullin, Dale I. 17 Ricchiuto, Mario 17 Russo, Giovanni 17 Schötzau, Dominik 17 Sjogreen, Bjorn 17 Wei, LeiLei 17 Zhang, Xiangxiong 16 Donat, Rosa 16 Jung, Jae-Hun 16 Kang, Myungjoo 16 Parés Madroñal, Carlos 16 Tadmor, Eitan 16 Westerink, Joannes J. 15 Capdeville, Guy 15 Chandrashekar, Praveen 15 Ha, Youngsoo 15 Hu, Xiangyu Y. 15 Kesserwani, Georges 15 Kirby, Robert M. II 15 Leung, Shingyu 15 Nogueira, Xesús 15 Nordström, Jan 15 Pareschi, Lorenzo 15 Pirozzoli, Sergio 15 Shen, Yiqing ...and 7,622 more Authors
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#### Cited in 286 Serials
1,722 Journal of Computational Physics 680 Journal of Scientific Computing 496 Computers and Fluids 216 Computer Methods in Applied Mechanics and Engineering 199 Applied Numerical Mathematics 198 Journal of Computational and Applied Mathematics 166 Computers & Mathematics with Applications 165 Applied Mathematics and Computation 133 Mathematics of Computation 124 Journal of Fluid Mechanics 120 SIAM Journal on Scientific Computing 96 International Journal for Numerical Methods in Fluids 85 SIAM Journal on Numerical Analysis 68 Applied Mathematical Modelling 55 Numerical Methods for Partial Differential Equations 54 Numerische Mathematik 43 International Journal for Numerical Methods in Engineering 40 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 38 Numerical Algorithms 38 Physics of Fluids 31 Engineering Analysis with Boundary Elements 29 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 29 International Journal of Computer Mathematics 29 Advances in Computational Mathematics 27 International Journal of Computational Methods 26 Computational Geosciences 25 Applied Mathematics and Mechanics. (English Edition) 24 Mathematics and Computers in Simulation 21 Computer Physics Communications 21 BIT 19 Computational Mechanics 19 Acta Mechanica Sinica 18 Journal of Mathematical Analysis and Applications 18 Physica D 18 Applied Mathematics Letters 18 Computational Mathematics and Mathematical Physics 18 Mathematical Problems in Engineering 18 International Journal of Computational Fluid Dynamics 16 Journal of Differential Equations 16 Mathematical and Computer Modelling 16 Communications in Nonlinear Science and Numerical Simulation 16 Multiscale Modeling & Simulation 14 Shock Waves 14 Communications in Numerical Methods in Engineering 14 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 14 Science China. Mathematics 13 Mathematical Methods in the Applied Sciences 13 European Journal of Mechanics. B. Fluids 13 Matematicheskoe Modelirovanie 13 AMM. Applied Mathematics and Mechanics. (English Edition) 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 12 Applied and Computational Harmonic Analysis 11 Computational and Applied Mathematics 11 Combustion Theory and Modelling 11 Archives of Computational Methods in Engineering 10 Wave Motion 10 Kinetic and Related Models 10 S$$\vec{\text{e}}$$MA Journal 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 COMPEL 9 International Journal of Numerical Methods for Heat & Fluid Flow 9 Flow, Turbulence and Combustion 9 International Journal of Modern Physics C 9 Discrete and Continuous Dynamical Systems. Series B 9 Journal of Numerical Mathematics 9 Journal of Hyperbolic Differential Equations 9 International Journal for Numerical Methods in Biomedical Engineering 8 Archive for Rational Mechanics and Analysis 8 Journal of Engineering Mathematics 8 Journal of Mathematical Physics 8 Acta Mathematicae Applicatae Sinica. English Series 8 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 8 Abstract and Applied Analysis 8 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 8 Communications on Applied Mathematics and Computation 7 Communications in Mathematical Physics 7 Journal of Mathematical Biology 7 Transport Theory and Statistical Physics 7 Bulletin of Mathematical Biology 7 Calcolo 7 Numerical Functional Analysis and Optimization 7 SIAM Journal on Applied Mathematics 7 Computing and Visualization in Science 7 Foundations of Computational Mathematics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Advances in Difference Equations 7 Communications in Applied and Industrial Mathematics 7 Journal of Theoretical Biology 7 SMAI Journal of Computational Mathematics 6 Applicable Analysis 6 Meccanica 6 Discrete and Continuous Dynamical Systems 6 Doklady Mathematics 6 Nonlinear Analysis. Real World Applications 6 Communications in Applied Mathematics and Computational Science 6 Networks and Heterogeneous Media 5 Theoretical and Computational Fluid Dynamics 5 Studies in Applied Mathematics 5 RAIRO. Modélisation Mathématique et Analyse Numérique ...and 186 more Serials
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#### Cited in 46 Fields
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#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-03-03T22:08:26 |
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|
http://ucsdquals.wikidot.com/fall-2005-1-mech
|
Fall 2005 1 Mech
A meteorite of mass M1 is incident with the relative velocity v0 and impact parameter s on a planet of radius R and mass M2. Determine the largest s for the collision to occur assuming that the two bodies attract each other according to Newton’s law of gravitation.
Hint: Use polar coordinates.
***
Answer
***
(1)
\begin{align} \mbox{const} = H =\frac{p_r^2}{2m}+\frac{p_{\theta}^2}{2mr^2}-\frac{G M_1 M_2}{r} \end{align}
where $m = \frac{M_1 M_2}{M_1+M_2}$ and $p_{\theta}=mv_0 s$
set $p_r = 0$ at r=R.
(2)
\begin{align} \frac{mv_0^2}{2}+\frac{GM_1M_2}{R}=\frac{m^2v_0^2s^2}{2mR^2} \end{align}
(3)
\begin{align} s^2 = R^2 \left[1+\frac{G M_1 M_2}{R}\frac{1}{\frac{1}{2}\left( \frac{M_1M_2}{M_1+M_2}\right) v_0^2 } \right] \end{align}
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| 2017-12-16T16:44:32 |
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|
https://par.nsf.gov/biblio/10369941
|
A Tendency Toward Alignment in Single-star Warm-Jupiter Systems
Abstract
The distribution of spin–orbit angles for systems with wide-separation, tidally detached exoplanets offers a unique constraint on the prevalence of dynamically violent planetary evolution histories. Tidally detached planets provide a relatively unbiased view of the primordial stellar obliquity distribution, as they cannot tidally realign within the system lifetime. We present the third result from our Stellar Obliquities in Long-period Exoplanet Systems (SOLES) survey: a measurement of the Rossiter–McLaughlin effect across two transits of the tidally detached warm Jupiter TOI-1478 b with the WIYN/NEID and Keck/HIRES spectrographs, revealing a sky-projected spin–orbit angle$λ=6.2−5.5+5.9°$. Combining this new measurement with the full set of archival obliquity measurements, including two previous constraints from the SOLES survey, we demonstrate that, in single-star systems, tidally detached warm Jupiters are preferentially more aligned than closer-orbiting hot Jupiters. This finding has two key implications: (1) planets in single-star systems tend to form within aligned protoplanetary disks, and (2) warm Jupiters form more quiescently than hot Jupiters, which, in single-star systems, are likely perturbed into a misaligned state through planet–planet interactions in the post-disk-dispersal phase. We also find that lower-mass Saturns span a wide range of spin–orbit angles, suggesting a prevalence of planet–planet scattering and/or secular more »
Authors:
; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10369941
Journal Name:
The Astronomical Journal
Volume:
164
Issue:
3
Page Range or eLocation-ID:
Article No. 104
ISSN:
0004-6256
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
TOI-2076 b is a sub-Neptune-sized planet (R= 2.39 ± 0.10R) that transits a young (204 ± 50 MYr) bright (V= 9.2) K-dwarf hosting a system of three transiting planets. Using spectroscopic observations obtained with the NEID spectrograph on the WIYN 3.5 m Telescope, we model the Rossiter–McLaughlin effect of TOI-2076 b, and derive a sky-projected obliquity of$λ=−3−15+16°$. Using the size of the star (R= 0.775 ± 0.015R), and the stellar rotation period (Prot= 7.27 ± 0.23 days), we estimate an obliquity of$ψ=18−9+10°$(ψ< 34° at 95% confidence), demonstrating that TOI-2076 b is in a well-aligned orbit. Simultaneous diffuser-assisted photometry from the 3.5 m telescope at Apache Point Observatory rules out flares during the transit. TOI-2076 b joins a small but growing sample of young planets in compact multi-planet systems with well-aligned orbits, and is the fourth planet with an age ≲300 Myr in a multi-transiting system with an obliquity measurement. The low obliquity of TOI-2076 b and the presence of transit timing variations in the system suggest the TOI-2076 system likely formed via convergent disk migration in an initially well-aligned disk.
2. Abstract
The orientation between a star’s spin axis and a planet’s orbital plane provides valuable information about the system’s formation and dynamical history. For non-transiting planets at wide separations, true stellar obliquities are challenging to measure, but lower limits on spin–orbit orientations can be determined from the difference between the inclination of the star’s rotational axis and the companion’s orbital plane (Δi). We present results of a uniform analysis of rotation periods, stellar inclinations, and obliquities of cool stars (SpT ≳ F5) hosting directly imaged planets and brown dwarf companions. As part of this effort, we have acquired new$vsini*$values for 22 host stars with the high-resolution Tull spectrograph at the Harlan J. Smith telescope. Altogether our sample contains 62 host stars with rotation periods, most of which are newly measured using light curves from the Transiting Exoplanet Survey Satellite. Among these, 53 stars have inclinations determined from projected rotational and equatorial velocities, and 21 stars predominantly hosting brown dwarfs have constraints on Δi. Eleven of these (52$−11+10$% of the sample) are likely misaligned, while the remaining 10 host stars are consistent with spin–orbit alignment. As an ensemble, the minimum obliquity distribution between 10 andmore »
3. Abstract
The warm Neptune GJ 3470b transits a nearby (d= 29 pc) bright slowly rotating M1.5-dwarf star. Using spectroscopic observations during two transits with the newly commissioned NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak Observatory, we model the classical Rossiter–McLaughlin effect, yielding a sky-projected obliquity of$λ=98−12+15◦$and a$vsini=0.85−0.33+0.27kms−1$. Leveraging information about the rotation period and size of the host star, our analysis yields a true obliquity of$ψ=95−8+9◦$, revealing that GJ 3470b is on a polar orbit. Using radial velocities from HIRES, HARPS, and the Habitable-zone Planet Finder, we show that the data are compatible with a long-term radial velocity (RV) slope of$γ̇=−0.0022±0.0011ms−1day−1$over a baseline of 12.9 yr. If the RV slope is due to acceleration from another companion in the system, we show that such a companion is capable of explaining the polar and mildly eccentric orbit of GJ 3470b using two different secular excitation models. The existence of an outer companion can be further constrained with additional RV observations, Gaia astrometry, and future high-contrast imaging observations. Lastly, we show that tidal heating frommore »
4. Abstract
We present the latest and most precise characterization of the architecture for the ancient (≈11 Gyr) Kepler-444 system, which is composed of a K0 primary star (Kepler-444 A) hosting five transiting planets and a tight M-type spectroscopic binary (Kepler-444 BC) with an A–BC projected separation of 66 au. We have measured the system’s relative astrometry using the adaptive optics imaging from Keck/NIRC2 and Kepler-444 A’s radial velocities from the Hobby-Eberly Telescope and reanalyzed relative radial velocities between BC and A from Keck/HIRES. We also include the Hipparcos-Gaia astrometric acceleration and all published astrometry and radial velocities in an updated orbit analysis of BC’s barycenter. These data greatly extend the time baseline of the monitoring and lead to significant updates to BC’s barycentric orbit compared to previous work, including a larger semimajor axis ($a=52.2−2.7+3.3$au), a smaller eccentricity (e= 0.55 ± 0.05), and a more precise inclination ($i=85.°4−0.°4+0.°3$). We have also derived the first dynamical masses of B and C components. Our results suggest that Kepler-444 A’s protoplanetary disk was likely truncated by BC to a radius of ≈8 au, which resolves the previously noticed tension between Kepler-444 A’s disk mass and planet masses. Kepler-444more »
5. Abstract
HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations (∼16–78 au), which are undergoing orbital motion and have been continuously monitored with adaptive optics imaging since their discovery over a decade ago. We present a dynamical mass of HR 8799 using 130 epochs of relative astrometry of its planets, which include both published measurements and new medium-band 3.1μm observations that we acquired with NIRC2 at Keck Observatory. For the purpose of measuring the host-star mass, each orbiting planet is treated as a massless particle and is fit with a Keplerian orbit using Markov chain Monte Carlo. We then use a Bayesian framework to combine each independent total mass measurement into a cumulative dynamical mass using all four planets. The dynamical mass of HR 8799 is$1.47−0.17+0.12$Massuming a uniform stellar mass prior, or$1.46−0.15+0.11$Mwith a weakly informative prior based on spectroscopy. There is a strong covariance between the planets’ eccentricities and the total system mass; when the constraint is limited to low-eccentricity solutions ofe< 0.1, which are motivated by dynamical stability, our mass measurement improves to$1.43−0.07+0.06$M. Our dynamical mass and other fundamental measured parameters of HRmore »
| 2023-03-31T13:59:24 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=S017BNC&home=sumtabB
|
# ${{\boldsymbol n}}$ $\rightarrow$ ${{\boldsymbol p}}{{\boldsymbol e}^{-}}{{\overline{\boldsymbol \nu}}_{{e}}}$ DECAY PARAMETERS
See the above Note on Baryon Decay Parameters.'' For discussions of recent results, see the references cited at the beginning of the section on the neutron mean life. For discussions of the values of the weak coupling constants ${\mathit g}_{{{\mathit A}}}$ and ${\mathit g}_{{{\mathit V}}}$ obtained using the neutron lifetime and asymmetry parameter$~\mathit A$, comparisons with other methods of obtaining these constants, and implications for particle physics and for astrophysics, see DUBBERS 1991 and WOOLCOCK 1991 . For tests of the $\mathit V−\mathit A$ theory of neutron decay, see EROZOLIMSKII 1991B, MOSTOVOI 1996 , NICO 2005 , SEVERIJNS 2006 , and ABELE 2008 .
# ${{\boldsymbol e}}-{{\overline{\boldsymbol \nu}}_{{e}}}$ ANGULAR CORRELATION COEFFICIENT $\boldsymbol a$ INSPIRE search
For a review of past experiments and plans for future measurements of the $\mathit a$ parameter, see WIETFELDT 2005 . In the Standard Model, $\mathit a$ is related to $\lambda {}\equiv\mathit g_{A}/\mathit g_{V}$ by $\mathit a$ = (1 $−$ $\lambda {}^{2}$) $/$ (1 + 3$\lambda {}^{2}$); this assumes that $\mathit g_{A}$ and $\mathit g_{V}$ are real.
VALUE DOCUMENT ID TECN COMMENT
$\bf{ -0.1059 \pm0.0028}$ OUR AVERAGE
$-0.1090$ $\pm0.0030$ $\pm0.0028$ 1
2017
SPEC Cold ${{\mathit n}}$, unpolarized
$-0.1054$ $\pm0.0055$
2002
SPEC Proton recoil spectrum
$-0.1017$ $\pm0.0051$
1978
CNTR Proton recoil spectrum
$-0.091$ $\pm0.039$
1968
SPEC Proton recoil spectrum
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-0.1045$ $\pm0.0014$ 2
2001
CNTR Inferred
1 DARIUS 2017 exploits a "wishbone" correlation, where the ${{\mathit p}}$ time of flight is correlated with the momentum of the electron in delayed coincidence.
2 MOSTOVOI 2001 calculates this from its measurement of $\lambda =\mathit g_{\mathit A}/\mathit g_{\mathit V}$ above.
References:
DARIUS 2017
PRL 119 042502 Measurement of the Electron-Antineutrino Angular Correlation in Neutron $\beta$ Decay
BYRNE 2002
JP G28 1325 Determination of the ${{\overline{\mathit \nu}}_{{e}}}$ Angular Correlation Coefficient a$_{0}$ and the Parameter $\vert \Lambda \vert$ = $\vert \mathit G_{A}/G_{V}\vert$ in Free Neutron $\beta$-Decay from Measurements of the Integrated Energy Spectrum of Recoil Protons Stored in an Ion Trap
MOSTOVOI 2001
PAN 64 1955 Experimental Value of $\mathit G_{a}/G_{v}$ from a Measurement of Both $\mathit P$-odd Correlations in Free-neutron Decay
STRATOWA 1978
PR D18 3970 Ratio $\vert \mathit g_{A}$/g$_{V}\vert$ Derived from the Proton Spectrum in Free Neutron Decay
GRIGOREV 1968
SJNP 6 239 Measurement of Angular (${{\mathit e}}$, ${{\overline{\mathit \nu}}_{{e}}}$) Correlation at Free Neutron Decay
| 2021-03-02T21:29:59 |
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|
http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lecture10_4.htm
|
##### Personal tools
•
You are here: Home Markov Processes
# Markov Processes
##### Document Actions
Concepts :: Discrete :: Continuous :: States
## Classes of States
Let . Then state is recurrent if .
If , then state is said to be transient .
• If started in a transient state, then the state does not recur an infinite number of times.
• If in a recurrent state, then the state recurs an infinite number of times.
Let denote the Markov chain with . Let
Then
We see that recurrent means that .
Transient means that .
Observation: The states of an irreducible, finite-state Markov chain are all recurrent.
## Limiting probabilities
If all states are transient, then all the state probabilities approach 0 as . If a M.C. has some transient classes and some recurrent classes, then eventually the process enters and remains in one of the recurrent classes. For limiting purposes, we can focus on individual recurrent classes.
Suppose a M.C. starts in a recurrent state at time 0. Let denote the times when the process returns to state , where is the time that elapses between the
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 08). Markov Processes. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lecture10_4.htm. This work is licensed under a Creative Commons License
| 2017-12-17T23:16:40 |
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|
https://pages.nist.gov/feasst/tutorial/tutorial.html
|
# Tutorial¶
## Installation and Interface¶
Installation is described in the README of the base directory of FEASST. Or visit the website at https://pages.nist.gov/feasst
### Python or C++?¶
Although this tutorial will focus upon the python interface, FEASST may also be utilized as a C++ library. For a C++ example, see the file tutorial/tutorial.cpp which is virtually identical to the Python tutorial. Thus Python tutorials are sufficient for learning the C++ library. While the majority of FEASST users prefer the Python interface, FEASST is written almost entirely in C++ for speed. Thus, both interfaces will be supported in the long term.
Some HPC clusters may not have the required Python libraries. If that is the case, do not hesitate to give the C++ interface a try, even if you have never written C++ before. For example, the only minor differences between tutorial/tutorial.cpp and tutorial/tutorial.py are the argument parsing syntax, semi-colons at the end of every line, and compiling any binary with int main().
## Canonical ensemble Lennard-Jones Monte Carlo¶
The following simulation based on tutorial/tutorial.py demonstrates the basics of FEASST.
To begin, FEASST is imported, and it is recommended to log the exact version used for the simulation.
[1]:
import feasst
print("version:", feasst.version())
version: v0.7.0-90-g6cb364c4ae hwh/branch
Then a MonteCarlo object is created and the random number generator is initialized using the C++ implementation of the Mersenne Twister seeded by the time and date.
[2]:
monte_carlo = feasst.MonteCarlo()
monte_carlo.set(feasst.MakeRandomMT19937(feasst.args({"seed" : "time"})))
Care must be taken not to run two identical simulations at the same second on an HPC node using the time and date, or they will have the same seed and may be equivalent. Instead, consider using a thread safe random number generator to seed the simulations.
FEASST standard output and error goes to the Jupyter notebook terminal. Thus, you should see output like “# Info 0 [plugin/math/src/random.cpp:30] time(seed): 1572362164” but with a different seed. This seed is provided in case you wanted to reproduce your simulation exactly, which we will do now. Note that your simulation may still be different than presented here, possibly because of different compiler implementations.
[3]:
monte_carlo.set(feasst.MakeRandomMT19937(feasst.args({"seed" : "1572362164"})))
The second step is to add a Configuration. In this example, a simple cubic periodic box of length 8 is defined with a single type of particle as described in forcefield/data.lj. See Forcefield for more information about the format of the data file, which is a LAMMPS-inspired file with some major differences.
[4]:
monte_carlo.add(feasst.Configuration(feasst.MakeDomain(feasst.args({"cubic_box_length": "8"})),
feasst.args({"particle_type": feasst.install_dir() + "/forcefield/data.lj"})))
FEASST arguments are input as a dictionary of strings with limited type checking. Thus, care must be taken to input strings which follow the documentation.
Next, initializing the Potential proceeds as follows:
[5]:
monte_carlo.add(feasst.Potential(feasst.MakeLennardJones()))
In this example, we introduce both the pair-wise Lennard-Jones (LJ) model, and also long-range corrections, which approximately account for the cut off of the LJ potential by assuming a pair-wise radial distance distribution function of unity. A FEASST convention is to use a helper function which appends the word Make onto the class name when creating pointers to FEASST derived class objects. This serves two purposes involving C++11 smart pointers and brace enclosed initializer lists.
Initialize ThermoParams, such as temperature, and the acceptance Criteria.
[6]:
monte_carlo.set(feasst.MakeThermoParams(feasst.args({"beta": "1.5"})))
monte_carlo.set(feasst.MakeMetropolis())
A TrialTranslate is then introduced which attempts to translate a random particle by a random distance which is bound in each dimension by a tunable_param. This parameter may be adjusted to obtain a desired acceptance ratio, tunable_target_acceptance, with the help of Tuner.
[7]:
monte_carlo.add(feasst.MakeTrialTranslate(feasst.args(
{"tunable_param": "2.", "tunable_target_acceptance": "0.2"})))
steps_per = int(1e3)
With the help of TrialTranslate, we can now initialize the number of particles.
[8]:
feasst.SeekNumParticles(50)\
.with_thermo_params(feasst.args({"beta": "0.1", "chemical_potential": "10"}))\
.with_metropolis()\
A grand canonical simulation is performed here by utilizing a temporary TrialAdd, which is why chemical potential was input to Criteria.
Additional Analyze or Modify may be added at any time to perform some task contingent upon the number of attempted trials.
[9]:
monte_carlo.add(feasst.MakeLog(feasst.args({"steps_per" : str(steps_per),
"file_name" : "log.txt",
"clear_file" : "true"})))
{"steps_per" : str(steps_per), "file_name" : "movie.xyz"})))
{"steps_per" : str(steps_per), "tolerance" : "1e-8"})))
In this example, Log outputs the current status of the trials, Movie outputs the configuration, and CheckEnergy asserts that the optimized energy calculations match the unoptimized ones.
The simulation is finally run for a number of trial attempts.
[10]:
%%time
monte_carlo.attempt(int(1e5))
CPU times: user 797 ms, sys: 3.79 ms, total: 801 ms
Wall time: 798 ms
Now we can analyze the simulation by, for example, plotting the instantaneous energy as a function of the number of attempts.
[11]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
import pandas as pd
[11]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fd1f117e7d0>
You should also find the movie.xyz trajectory file with an automatically-generated movie.xyz.vmd file for use with VMD (e.g., vmd -e movie.xyz.vmd).
| 2021-08-04T06:28:01 |
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https://www.zbmath.org/authors/?q=ai%3Aplonka.gerlind
|
# zbMATH — the first resource for mathematics
## Plonka, Gerlind
Compute Distance To:
Author ID: plonka.gerlind Published as: Plonka, Gerlind; Plonka, G. External Links: MGP · Wikidata · GND
Documents Indexed: 79 Publications since 1992, including 3 Books Reviewing Activity: 184 Reviews
all top 5
#### Co-Authors
17 single-authored 12 Tasche, Manfred 5 Roşca, Daniela 5 Steidl, Gabriele 4 Berg, Lothar 3 Iske, Armin 3 Ma, Jianwei 3 Tenorth, Stefanie 3 Wannenwetsch, Katrin 2 Beinert, Robert 2 Bittens, Sina Vanessa 2 Hasannasab, Marzieh 2 Heinen, Dennis 2 Hertrich, Johannes 2 Keller, Ingeborg 2 Neumayer, Sebastian 2 Peter, Thomas 2 Setzer, Simon 2 Stampfer, Kilian 2 Strela, Vasily 2 Wischerhoff, Marius 1 Budinich, Renato 1 Chen, Dirong 1 Cohen, Albert 1 Cuyt, Annie A. M. 1 Daubechies, Ingrid Chantal 1 Gonska, Heinz Herbert 1 Guillemard, Mijail 1 Hoffmann, Sebastian 1 Jetter, Kurt 1 Knirsch, Hanna 1 Krause-Solberg, Sara 1 Krommweh, Jens 1 Kutyniok, Gitta 1 Lee, Wen-shin 1 Liu, Lina 1 Loock, Stefan 1 Petz, Markus 1 Pototskaia, Vlada 1 Potts, Daniel 1 Ron, Amos 1 Schumacher, Hagen 1 Selig, Kathi K. 1 von Wulffen, Therese 1 Weickert, Joachim 1 Zheng, Yi 1 Zhou, Dingxuan
all top 5
#### Serials
6 Results in Mathematics 5 Numerical Algorithms 5 Linear Algebra and its Applications 5 Applied and Computational Harmonic Analysis 5 Advances in Computational Mathematics 5 The Journal of Fourier Analysis and Applications 5 International Journal of Wavelets, Multiresolution and Information Processing 4 Journal of Approximation Theory 3 Inverse Problems 3 Journal of Computational and Applied Mathematics 3 Rostocker Mathematisches Kolloquium 3 Constructive Approximation 2 Mathematics of Computation 2 GAMM-Mitteilungen 1 Numerische Mathematik 1 Journal of Symbolic Computation 1 SIAM Journal on Mathematical Analysis 1 IEEE Transactions on Image Processing 1 Journal of Applied Mathematics and Computing 1 Multiscale Modeling & Simulation 1 Analysis and Applications (Singapore) 1 Mathematical Geosciences 1 Applied and Numerical Harmonic Analysis
all top 5
#### Fields
45 Numerical analysis (65-XX) 40 Harmonic analysis on Euclidean spaces (42-XX) 26 Information and communication theory, circuits (94-XX) 25 Approximations and expansions (41-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Computer science (68-XX) 5 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Special functions (33-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
62 Publications have been cited 464 times in 306 Documents Cited by Year
Approximation order provided by refinable function vectors. Zbl 0870.41015
Plonka, G.
1997
Regularity of refinable function vectors. Zbl 0914.42025
Cohen, Albert; Daubechies, Ingrid; Plonka, Gerlind
1997
Construction of multiscaling functions with approximation and symmetry. Zbl 0928.42017
Plonka, G.; Strela, V.
1998
Prony methods for recovery of structured functions. Zbl 1311.65012
Plonka, Gerlind; Tasche, Manfred
2014
A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators. Zbl 1276.47093
Peter, Thomas; Plonka, Gerlind
2013
A survey on $$L_2$$-approximation orders from shift-invariant spaces. Zbl 1039.42033
Jetter, K.; Plonka, G.
2001
From wavelets to multiwavelets. Zbl 0905.65138
Plonka, Gerlind; Strela, Vasily
1998
A unified approach to periodic wavelets. Zbl 0874.42026
Plonka, Gerlind; Tasche, Manfred
1994
On the computation of periodic spline wavelets. Zbl 0810.42018
Plonka, Gerlind; Tasche, Manfred
1995
Fast and numerically stable algorithms for discrete cosine transforms. Zbl 1072.65171
Plonka, Gerlind; Tasche, Manfred
2005
How many Fourier samples are needed for real function reconstruction? Zbl 1296.42001
Plonka, Gerlind; Wischerhoff, Marius
2013
Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes. Zbl 1388.42004
Beinert, Robert; Plonka, Gerlind
2015
Some notes on two-scale difference equations. Zbl 0978.39004
Berg, Lothar; Plonka, Gerlind
2000
On the construction of wavelets on a bounded interval. Zbl 0838.65140
Plonka, Gerlind; Selig, Kathi; Tasche, Manfred
1995
A deterministic sparse FFT algorithm for vectors with small support. Zbl 1341.65056
Plonka, Gerlind; Wannenwetsch, Katrin
2016
Spectral properties of two-slanted matrices. Zbl 0931.15004
Berg, Lothar; Plonka, Gerlind
1999
Numerical Fourier analysis. Zbl 1412.65001
Plonka, Gerlind; Potts, Daniel; Steidl, Gabriele; Tasche, Manfred
2018
Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks. Zbl 1017.42029
Chen, Di-Rong; Plonka, Gerlind
2002
A multiscale wavelet-inspired scheme for nonlinear diffusion. Zbl 1111.65075
Plonka, Gerlind; Steidl, Gabriele
2006
The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data. Zbl 1175.65158
Plonka, Gerlind
2009
Curvelet-wavelet regularized split Bregman iteration for compressed sensing. Zbl 1208.94017
Plonka, Gerlind; Ma, Jianwei
2011
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain. Zbl 1394.42001
Beinert, Robert; Plonka, Gerlind
2018
Deterministic sparse FFT for $$M$$-sparse vectors. Zbl 06871983
Plonka, Gerlind; Wannenwetsch, Katrin; Cuyt, Annie; Lee, Wen-Shin
2018
Compactly supported solutions of two-scale difference equations. Zbl 0935.39003
Berg, Lothar; Plonka, Gerlind
1998
Two-scale symbol and autocorrelation symbol for B-splines with multiple knots. Zbl 0828.41007
Plonka, Gerlind
1995
Periodic spline interpolation with shifted nodes. Zbl 0803.41003
Plonka, Gerlind
1994
Uniform spherical grids via equal area projection from the cube to the sphere. Zbl 1231.65044
Roşca, Daniela; Plonka, Gerlind
2011
A sparse fast Fourier algorithm for real non-negative vectors. Zbl 1366.65118
Plonka, Gerlind; Wannenwetsch, Katrin
2017
Representation of sparse Legendre expansions. Zbl 1261.65016
Peter, Thomas; Plonka, Gerlind; Roşca, Daniela
2013
Factorization of refinement masks of function vectors. Zbl 0927.42028
Plonka, Gerlind
1995
A new factorization technique of the matrix mask of univariate refinable functions. Zbl 0982.65150
Plonka, Gerlind; Ron, Amos
2001
Reconstruction of polygonal shapes from sparse Fourier samples. Zbl 1362.94012
Wischerhoff, Marius; Plonka, Gerlind
2016
Directional Haar wavelet frames on triangles. Zbl 1177.42031
Krommweh, Jens; Plonka, Gerlind
2009
Sparse fast DCT for vectors with one-block support. Zbl 07107362
Bittens, Sina; Plonka, Gerlind
2019
Computation of adaptive Fourier series by sparse approximation of exponential sums. Zbl 1420.42002
2019
Efficient algorithms for periodic Hermite spline interpolation. Zbl 0769.65005
Plonka, G.; Tasche, M.
1992
Spline wavelets with higher defect. Zbl 0815.65012
Plonka, G.
1994
A new hybrid method for image approximation using the easy path wavelet transform. Zbl 1372.94210
Plonka, Gerlind; Tenorth, Stefanie; Roşca, Daniela
2011
Phase retrieval for Fresnel measurements using a shearlet sparsity constraint. Zbl 1293.42034
Loock, Stefan; Plonka, Gerlind
2014
Optimal approximation with exponential sums by a maximum likelihood modification of Prony’s method. Zbl 1415.65095
Zhang, Ran; Plonka, Gerlind
2019
Optimally sparse image representation by the easy path wavelet transform. Zbl 1251.42012
Plonka, Gerlind; Tenorth, Stefanie; Iske, Armin
2012
Easy path wavelet transform on triangulations of the sphere. Zbl 1198.42052
Plonka, Gerlind; Roşca, Daniela
2010
Real sparse fast DCT for vectors with short support. Zbl 1464.65296
Bittens, Sina; Plonka, Gerlind
2019
Generalized spline wavelets. Zbl 0848.41009
Plonka, G.
1996
Approximation properties of multi-scaling functions: A Fourier approach. Zbl 0852.42021
Plonka, Gerlind
1995
Necessary and sufficient conditions for orthonormality of scaling vectors. Zbl 0903.42017
Plonka, Gerlind
1997
Invertible integer DCT algorithms. Zbl 1030.65144
Plonka, Gerlind; Tasche, Manfred
2003
Integer DCT-II by lifting steps. Zbl 1036.65118
Plonka, Gerlind; Tasche, Manfred
2003
Parseval proximal neural networks. Zbl 07233296
Hasannasab, Marzieh; Hertrich, Johannes; Neumayer, Sebastian; Plonka, Gerlind; Setzer, Simon; Steidl, Gabriele
2020
Wavelet shrinkage on paths for denoising of scattered data. Zbl 1253.42034
Heinen, Dennis; Plonka, Gerlind
2012
An area preserving projection from the regular octahedron to the sphere. Zbl 1260.86015
Roşca, Daniela; Plonka, Gerlind
2012
Optimal representation of piecewise Hölder smooth bivariate functions by the easy path wavelet transform. Zbl 1281.42040
Plonka, Gerlind; Iske, Armin; Tenorth, Stefanie
2013
A tree-based dictionary learning framework. Zbl 1458.94077
Budinich, Renato; Plonka, Gerlind
2020
Reconstruction of stationary and non-stationary signals by the generalized Prony method. Zbl 1422.94015
Plonka, Gerlind; Stampfer, Kilian; Keller, Ingeborg
2019
On stability of scaling vectors. Zbl 0939.65148
Plonka, Gerlind
1997
An efficient algorithm for periodic Hermite spline interpolation with shifted nodes. Zbl 0803.65009
Plonka, Gerlind
1993
Cardinal Hermite spline interpolation with shifted nodes. Zbl 0819.65008
Plonka, Gerlind; Tasche, Manfred
1994
Properties of locally linearly independent refinable function vectors. Zbl 1031.41020
Plonka, G.; Zhou, D.-X.
2003
A global method for invertible integer DCT and integer wavelet algorithms. Zbl 1053.65103
Plonka, Gerlind
2004
Numerical stability of fast trigonometric and orthogonal wavelet transforms. Zbl 1060.65139
Plonka, Gerlind; Tasche, Manfred
2004
Pseudo-inverses of difference matrices and their application to sparse signal approximation. Zbl 1338.15013
Plonka, Gerlind; Hoffmann, Sebastian; Weickert, Joachim
2016
Seismic data interpolation and denoising by learning a tensor tight frame. Zbl 1411.86004
Liu, Lina; Plonka, Gerlind; Ma, Jianwei
2017
Parseval proximal neural networks. Zbl 07233296
Hasannasab, Marzieh; Hertrich, Johannes; Neumayer, Sebastian; Plonka, Gerlind; Setzer, Simon; Steidl, Gabriele
2020
A tree-based dictionary learning framework. Zbl 1458.94077
Budinich, Renato; Plonka, Gerlind
2020
Sparse fast DCT for vectors with one-block support. Zbl 07107362
Bittens, Sina; Plonka, Gerlind
2019
Computation of adaptive Fourier series by sparse approximation of exponential sums. Zbl 1420.42002
2019
Optimal approximation with exponential sums by a maximum likelihood modification of Prony’s method. Zbl 1415.65095
Zhang, Ran; Plonka, Gerlind
2019
Real sparse fast DCT for vectors with short support. Zbl 1464.65296
Bittens, Sina; Plonka, Gerlind
2019
Reconstruction of stationary and non-stationary signals by the generalized Prony method. Zbl 1422.94015
Plonka, Gerlind; Stampfer, Kilian; Keller, Ingeborg
2019
Numerical Fourier analysis. Zbl 1412.65001
Plonka, Gerlind; Potts, Daniel; Steidl, Gabriele; Tasche, Manfred
2018
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain. Zbl 1394.42001
Beinert, Robert; Plonka, Gerlind
2018
Deterministic sparse FFT for $$M$$-sparse vectors. Zbl 06871983
Plonka, Gerlind; Wannenwetsch, Katrin; Cuyt, Annie; Lee, Wen-Shin
2018
A sparse fast Fourier algorithm for real non-negative vectors. Zbl 1366.65118
Plonka, Gerlind; Wannenwetsch, Katrin
2017
Seismic data interpolation and denoising by learning a tensor tight frame. Zbl 1411.86004
Liu, Lina; Plonka, Gerlind; Ma, Jianwei
2017
A deterministic sparse FFT algorithm for vectors with small support. Zbl 1341.65056
Plonka, Gerlind; Wannenwetsch, Katrin
2016
Reconstruction of polygonal shapes from sparse Fourier samples. Zbl 1362.94012
Wischerhoff, Marius; Plonka, Gerlind
2016
Pseudo-inverses of difference matrices and their application to sparse signal approximation. Zbl 1338.15013
Plonka, Gerlind; Hoffmann, Sebastian; Weickert, Joachim
2016
Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes. Zbl 1388.42004
Beinert, Robert; Plonka, Gerlind
2015
Prony methods for recovery of structured functions. Zbl 1311.65012
Plonka, Gerlind; Tasche, Manfred
2014
Phase retrieval for Fresnel measurements using a shearlet sparsity constraint. Zbl 1293.42034
Loock, Stefan; Plonka, Gerlind
2014
A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators. Zbl 1276.47093
Peter, Thomas; Plonka, Gerlind
2013
How many Fourier samples are needed for real function reconstruction? Zbl 1296.42001
Plonka, Gerlind; Wischerhoff, Marius
2013
Representation of sparse Legendre expansions. Zbl 1261.65016
Peter, Thomas; Plonka, Gerlind; Roşca, Daniela
2013
Optimal representation of piecewise Hölder smooth bivariate functions by the easy path wavelet transform. Zbl 1281.42040
Plonka, Gerlind; Iske, Armin; Tenorth, Stefanie
2013
Optimally sparse image representation by the easy path wavelet transform. Zbl 1251.42012
Plonka, Gerlind; Tenorth, Stefanie; Iske, Armin
2012
Wavelet shrinkage on paths for denoising of scattered data. Zbl 1253.42034
Heinen, Dennis; Plonka, Gerlind
2012
An area preserving projection from the regular octahedron to the sphere. Zbl 1260.86015
Roşca, Daniela; Plonka, Gerlind
2012
Curvelet-wavelet regularized split Bregman iteration for compressed sensing. Zbl 1208.94017
Plonka, Gerlind; Ma, Jianwei
2011
Uniform spherical grids via equal area projection from the cube to the sphere. Zbl 1231.65044
Roşca, Daniela; Plonka, Gerlind
2011
A new hybrid method for image approximation using the easy path wavelet transform. Zbl 1372.94210
Plonka, Gerlind; Tenorth, Stefanie; Roşca, Daniela
2011
Easy path wavelet transform on triangulations of the sphere. Zbl 1198.42052
Plonka, Gerlind; Roşca, Daniela
2010
The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data. Zbl 1175.65158
Plonka, Gerlind
2009
Directional Haar wavelet frames on triangles. Zbl 1177.42031
Krommweh, Jens; Plonka, Gerlind
2009
A multiscale wavelet-inspired scheme for nonlinear diffusion. Zbl 1111.65075
Plonka, Gerlind; Steidl, Gabriele
2006
Fast and numerically stable algorithms for discrete cosine transforms. Zbl 1072.65171
Plonka, Gerlind; Tasche, Manfred
2005
A global method for invertible integer DCT and integer wavelet algorithms. Zbl 1053.65103
Plonka, Gerlind
2004
Numerical stability of fast trigonometric and orthogonal wavelet transforms. Zbl 1060.65139
Plonka, Gerlind; Tasche, Manfred
2004
Invertible integer DCT algorithms. Zbl 1030.65144
Plonka, Gerlind; Tasche, Manfred
2003
Integer DCT-II by lifting steps. Zbl 1036.65118
Plonka, Gerlind; Tasche, Manfred
2003
Properties of locally linearly independent refinable function vectors. Zbl 1031.41020
Plonka, G.; Zhou, D.-X.
2003
Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks. Zbl 1017.42029
Chen, Di-Rong; Plonka, Gerlind
2002
A survey on $$L_2$$-approximation orders from shift-invariant spaces. Zbl 1039.42033
Jetter, K.; Plonka, G.
2001
A new factorization technique of the matrix mask of univariate refinable functions. Zbl 0982.65150
Plonka, Gerlind; Ron, Amos
2001
Some notes on two-scale difference equations. Zbl 0978.39004
Berg, Lothar; Plonka, Gerlind
2000
Spectral properties of two-slanted matrices. Zbl 0931.15004
Berg, Lothar; Plonka, Gerlind
1999
Construction of multiscaling functions with approximation and symmetry. Zbl 0928.42017
Plonka, G.; Strela, V.
1998
From wavelets to multiwavelets. Zbl 0905.65138
Plonka, Gerlind; Strela, Vasily
1998
Compactly supported solutions of two-scale difference equations. Zbl 0935.39003
Berg, Lothar; Plonka, Gerlind
1998
Approximation order provided by refinable function vectors. Zbl 0870.41015
Plonka, G.
1997
Regularity of refinable function vectors. Zbl 0914.42025
Cohen, Albert; Daubechies, Ingrid; Plonka, Gerlind
1997
Necessary and sufficient conditions for orthonormality of scaling vectors. Zbl 0903.42017
Plonka, Gerlind
1997
On stability of scaling vectors. Zbl 0939.65148
Plonka, Gerlind
1997
Generalized spline wavelets. Zbl 0848.41009
Plonka, G.
1996
On the computation of periodic spline wavelets. Zbl 0810.42018
Plonka, Gerlind; Tasche, Manfred
1995
On the construction of wavelets on a bounded interval. Zbl 0838.65140
Plonka, Gerlind; Selig, Kathi; Tasche, Manfred
1995
Two-scale symbol and autocorrelation symbol for B-splines with multiple knots. Zbl 0828.41007
Plonka, Gerlind
1995
Factorization of refinement masks of function vectors. Zbl 0927.42028
Plonka, Gerlind
1995
Approximation properties of multi-scaling functions: A Fourier approach. Zbl 0852.42021
Plonka, Gerlind
1995
A unified approach to periodic wavelets. Zbl 0874.42026
Plonka, Gerlind; Tasche, Manfred
1994
Periodic spline interpolation with shifted nodes. Zbl 0803.41003
Plonka, Gerlind
1994
Spline wavelets with higher defect. Zbl 0815.65012
Plonka, G.
1994
Cardinal Hermite spline interpolation with shifted nodes. Zbl 0819.65008
Plonka, Gerlind; Tasche, Manfred
1994
An efficient algorithm for periodic Hermite spline interpolation with shifted nodes. Zbl 0803.65009
Plonka, Gerlind
1993
Efficient algorithms for periodic Hermite spline interpolation. Zbl 0769.65005
Plonka, G.; Tasche, M.
1992
all top 5
#### Cited by 396 Authors
34 Plonka, Gerlind 10 Charina, Maria 10 Conti, Costanza 9 Tasche, Manfred 8 Chen, Dirong 8 Prestin, Jurgen 8 Yang, Shouzhi 7 Han, Bin 7 Jiang, Qingtang 7 Protasov, Vladimir Yu. 6 Potts, Daniel 6 Roşca, Daniela 5 Berg, Lothar 5 Krüppel, Manfred 5 Li, Song 5 Romani, Lucia 5 Sun, Qiyu 5 Yomdin, Yosef 4 Aldroubi, Akram 4 Bendory, Tamir 4 Cui, Lihong 4 Goldman, Gil 4 Iwen, Mark A. 4 Jia, Rong-Qing 4 Kunis, Stefan 4 Li, Baobin 4 Peng, Lizhong 4 Perera, Sirani M. 4 Shen, Zuowei 4 Steidl, Gabriele 4 Yang, Jianbin 3 Ashino, Ryuichi 3 Beinert, Robert 3 Bittens, Sina Vanessa 3 Cabrelli, Carlos A. 3 Chen, Hanlin 3 Cuyt, Annie A. M. 3 Huang, Yongdong 3 Iske, Armin 3 Jetter, Kurt 3 Krishtal, Ilya Arkadievich 3 Lee, Wen-shin 3 Peter, Thomas 3 Putinar, Mihai 3 Ron, Amos 3 Sauer, Tomas 3 Sheng, Qiuhui 3 Unser, Michael A. 3 von der Ohe, Ulrich 3 Wannenwetsch, Katrin 3 Xie, Changzhen 3 Zhang, Qingyue 3 Zhou, Dingxuan 2 Akinshin, Andrey 2 Andersson, Fredrik K. 2 Bergmann, Ronny 2 Britaňák, Vladimír 2 Budinich, Renato 2 Bultheel, Adhemar François 2 Carlsson, Marcus 2 Choi, Bosu 2 Christlieb, Andrew J. 2 Chui, Charles Kam-tai 2 Cotronei, Mariantonia 2 Daubechies, Ingrid Chantal 2 Edidin, Dan 2 Forster-Heinlein, Brigitte 2 Gao, Xieping 2 Goh, Say Song 2 Guglielmi, Nicola 2 Heil, Christopher E. 2 Holhoş, Adrian 2 Kutyniok, Gitta 2 Lebedeva, Elena A. 2 Li, Youfa 2 Lian, Jian’ao 2 Liu, Jianhua 2 Lou, Yifei 2 Marchesini, Stefano 2 März, Maximilian 2 Michelle, Michelle 2 Möller, Hans Michael 2 Molter, Ursula Maria 2 Neumayer, Sebastian 2 Peng, Silong 2 Ruch, David K. 2 Sauer, Thomas 2 Sprengel, Frauke 2 Stampfer, Kilian 2 Tang, Sui 2 Tenorth, Stefanie 2 Vaillancourt, Rémi 2 Van Fleet, Patrick J. 2 Volkmer, Toni 2 Zeng, Tie Yong 2 Zhang, Ruochuan 1 Abascal, Juan-Felipe P. J. 1 Akhtar, Md. Nasim 1 Alkhidhr, Hanan 1 Aràndiga, Francesc ...and 296 more Authors
all top 5
#### Cited in 86 Serials
31 Applied and Computational Harmonic Analysis 21 Advances in Computational Mathematics 19 International Journal of Wavelets, Multiresolution and Information Processing 17 Journal of Approximation Theory 15 The Journal of Fourier Analysis and Applications 13 Journal of Computational and Applied Mathematics 12 Results in Mathematics 10 Numerical Algorithms 9 Computers & Mathematics with Applications 9 Journal of Mathematical Analysis and Applications 9 Acta Mathematica Sinica. English Series 8 Inverse Problems 8 Mathematics of Computation 8 Linear Algebra and its Applications 6 Applied Mathematics and Computation 4 Numerische Mathematik 4 Proceedings of the American Mathematical Society 4 Constructive Approximation 3 Numerical Functional Analysis and Optimization 3 Computer Aided Geometric Design 3 Applied Numerical Mathematics 3 SIAM Journal on Imaging Sciences 2 Applicable Analysis 2 Journal of Functional Analysis 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Transactions of the American Mathematical Society 2 Zeitschrift für Analysis und ihre Anwendungen 2 Journal of Symbolic Computation 2 Journal of Complexity 2 SIAM Journal on Matrix Analysis and Applications 2 Science in China. Series A 2 Signal Processing 2 St. Petersburg Mathematical Journal 2 ETNA. Electronic Transactions on Numerical Analysis 2 Abstract and Applied Analysis 2 Journal of Applied Mathematics and Computing 2 Analysis in Theory and Applications 2 Analysis and Applications (Singapore) 2 Science in China. Series F 2 Complex Analysis and Operator Theory 2 Science China. Mathematics 2 SIAM Journal on Applied Algebra and Geometry 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of the Franklin Institute 1 Lithuanian Mathematical Journal 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 BIT 1 Czechoslovak Mathematical Journal 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Monatshefte für Mathematik 1 SIAM Journal on Numerical Analysis 1 Theoretical Computer Science 1 Circuits, Systems, and Signal Processing 1 Discrete & Computational Geometry 1 Computational Mechanics 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Multidimensional Systems and Signal Processing 1 International Journal of Computer Mathematics 1 SIAM Journal on Mathematical Analysis 1 Acta Mathematica Sinica. New Series 1 The Journal of Analysis 1 Turkish Journal of Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 Mathematical Problems in Engineering 1 The ANZIAM Journal 1 Foundations of Computational Mathematics 1 Sampling Theory in Signal and Image Processing 1 GAMM-Mitteilungen 1 Frontiers of Mathematics in China 1 Inverse Problems and Imaging 1 EURASIP Journal on Advances in Signal Processing 1 Mathematical Geosciences 1 Proceedings of the Estonian Academy of Sciences 1 Journal of Singularities 1 Acta Crystallographica. Section A 1 Information and Inference 1 Axioms 1 Mathematical Sciences 1 Journal of Classical Analysis 1 International Journal of Applied and Computational Mathematics 1 SMAI Journal of Computational Mathematics 1 SIAM Journal on Mathematics of Data Science
all top 5
#### Cited in 37 Fields
174 Harmonic analysis on Euclidean spaces (42-XX) 155 Numerical analysis (65-XX) 77 Information and communication theory, circuits (94-XX) 74 Approximations and expansions (41-XX) 23 Computer science (68-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 18 Difference and functional equations (39-XX) 16 Functional analysis (46-XX) 14 Operator theory (47-XX) 8 Operations research, mathematical programming (90-XX) 7 Statistics (62-XX) 6 Functions of a complex variable (30-XX) 5 Number theory (11-XX) 5 Commutative algebra (13-XX) 5 Special functions (33-XX) 5 Partial differential equations (35-XX) 4 Algebraic geometry (14-XX) 4 Geophysics (86-XX) 4 Systems theory; control (93-XX) 3 Real functions (26-XX) 3 Integral transforms, operational calculus (44-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 2 Biology and other natural sciences (92-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-09-24T02:55:16 |
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|
https://par.nsf.gov/biblio/10356273-pruning-search-efficient-neural-architecture-search-via-channel-pruning-structural-reparameterization
|
This content will become publicly available on July 1, 2023
Pruning-as-Search: Efficient Neural Architecture Search via Channel Pruning and Structural Reparameterization
Neural architecture search (NAS) and network pruning are widely studied efficient AI techniques, but not yet perfect.NAS performs exhaustive candidate architecture search, incurring tremendous search cost.Though (structured) pruning can simply shrink model dimension, it remains unclear how to decide the per-layer sparsity automatically and optimally.In this work, we revisit the problem of layer-width optimization and propose Pruning-as-Search (PaS), an end-to-end channel pruning method to search out desired sub-network automatically and efficiently.Specifically, we add a depth-wise binary convolution to learn pruning policies directly through gradient descent.By combining the structural reparameterization and PaS, we successfully searched out a new family of VGG-like and lightweight networks, which enable the flexibility of arbitrary width with respect to each layer instead of each stage.Experimental results show that our proposed architecture outperforms prior arts by around 1.0% top-1 accuracy under similar inference speed on ImageNet-1000 classification task.Furthermore, we demonstrate the effectiveness of our width search on complex tasks including instance segmentation and image translation.Code and models are released.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10356273
Journal Name:
Thirty-First International Joint Conference on Artificial Intelligence
Page Range or eLocation-ID:
3236 to 3242
National Science Foundation
##### More Like this
1. Weight pruning is an effective model compression technique to tackle the challenges of achieving real-time deep neural network (DNN) inference on mobile devices. However, prior pruning schemes have limited application scenarios due to accuracy degradation, difficulty in leveraging hardware acceleration, and/or restriction on certain types of DNN layers. In this article, we propose a general, fine-grained structured pruning scheme and corresponding compiler optimizations that are applicable to any type of DNN layer while achieving high accuracy and hardware inference performance. With the flexibility of applying different pruning schemes to different layers enabled by our compiler optimizations, we further probe into the new problem of determining the best-suited pruning scheme considering the different acceleration and accuracy performance of various pruning schemes. Two pruning scheme mapping methods—one -search based and the other is rule based—are proposed to automatically derive the best-suited pruning regularity and block size for each layer of any given DNN. Experimental results demonstrate that our pruning scheme mapping methods, together with the general fine-grained structured pruning scheme, outperform the state-of-the-art DNN optimization framework with up to 2.48 $\times$ and 1.73 $\times$ DNN inference acceleration on CIFAR-10 and ImageNet datasets without accuracy loss.
2. Deep convolutional neural network (DNN) has demonstrated phenomenal success and been widely used in many computer vision tasks. However, its enormous model size and high computing complexity prohibits its wide deployment into resource limited embedded system, such as FPGA and mGPU. As the two most widely adopted model compression techniques, weight pruning and quantization compress DNN model through introducing weight sparsity (i.e., forcing partial weights as zeros) and quantizing weights into limited bit-width values, respectively. Although there are works attempting to combine the weight pruning and quantization, we still observe disharmony between weight pruning and quantization, especially when more aggressive compression schemes (e.g., Structured pruning and low bit-width quantization) are used. In this work, taking FPGA as the test computing platform and Processing Elements (PE) as the basic parallel computing unit, we first propose a PE-wise structured pruning scheme, which introduces weight sparsification with considering of the architecture of PE. In addition, we integrate it with an optimized weight ternarization approach which quantizes weights into ternary values ({-1,0,+1}), thus converting the dominant convolution operations in DNN from multiplication-and-accumulation (MAC) to addition-only, as well as compressing the original model (from 32-bit floating point to 2-bit ternary representation) by at least 16more »
3. Though recent years have witnessed remarkable progress in single image super-resolution (SISR) tasks with the prosperous development of deep neural networks (DNNs), the deep learning methods are confronted with the computation and memory consumption issues in practice, especially for resource-limited platforms such as mobile devices. To overcome the challenge and facilitate the real-time deployment of SISR tasks on mobile, we combine neural architecture search with pruning search and propose an automatic search framework that derives sparse super-resolution (SR) models with high image quality while satisfying the real-time inference requirement. To decrease the search cost, we leverage the weight sharing strategy by introducing a supernet and decouple the search problem into three stages, including supernet construction, compiler-aware architecture and pruning search, and compiler-aware pruning ratio search. With the proposed framework, we are the first to achieve real-time SR inference (with only tens of milliseconds per frame) for implementing 720p resolution with competitive image quality (in terms of PSNR and SSIM) on mobile platforms (Samsung Galaxy S20).
4. Efficient machine learning implementations optimized for inference in hardware have wide-ranging benefits, depending on the application, from lower inference latency to higher data throughput and reduced energy consumption. Two popular techniques for reducing computation in neural networks are pruning, removing insignificant synapses, and quantization, reducing the precision of the calculations. In this work, we explore the interplay between pruning and quantization during the training of neural networks for ultra low latency applications targeting high energy physics use cases. Techniques developed for this study have potential applications across many other domains. We study various configurations of pruning during quantization-aware training, which we term quantization-aware pruning , and the effect of techniques like regularization, batch normalization, and different pruning schemes on performance, computational complexity, and information content metrics. We find that quantization-aware pruning yields more computationally efficient models than either pruning or quantization alone for our task. Further, quantization-aware pruning typically performs similar to or better in terms of computational efficiency compared to other neural architecture search techniques like Bayesian optimization. Surprisingly, while networks with different training configurations can have similar performance for the benchmark application, the information content in the network can vary significantly, affecting its generalizability.
5. The key challenge in photorealistic style transfer is that an algorithm should faithfully transfer the style of a reference photo to a content photo while the generated image should look like one captured by a camera. Although several photorealistic style transfer algorithms have been proposed, they need to rely on post- and/or pre-processing to make the generated images look photorealistic. If we disable the additional processing, these algorithms would fail to produce plausible photorealistic stylization in terms of detail preservation and photorealism. In this work, we propose an effective solution to these issues. Our method consists of a construction step (C-step) to build a photorealistic stylization network and a pruning step (P-step) for acceleration. In the C-step, we propose a dense auto-encoder named PhotoNet based on a carefully designed pre-analysis. PhotoNet integrates a feature aggregation module (BFA) and instance normalized skip links (INSL). To generate faithful stylization, we introduce multiple style transfer modules in the decoder and INSLs. PhotoNet significantly outperforms existing algorithms in terms of both efficiency and effectiveness. In the P-step, we adopt a neural architecture search method to accelerate PhotoNet. We propose an automatic network pruning framework in the manner of teacher-student learning for photorealistic stylization. Themore »
| 2023-02-09T06:23:55 |
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|
https://www.usgs.gov/center-news/volcano-watch-ten-year-long-eruption-resumes-after-short-lull
|
# Volcano Watch — Ten-year-long eruption resumes after short lull
Release Date:
The 10-year-long eruption at Kīlauea Volcano started up again during the morning of February 16, after a period of inactivity lasting about 10 days. The eruption began at the episode 51 vents on the west flank of Puu Oo, with only small volumes of pasty lava flowing through the pre-existing tubes.
The 10-year-long eruption at Kīlauea Volcano started up again during the morning of February 16, after a period of inactivity lasting about 10 days. The eruption began at the episode 51 vents on the west flank of Puu Oo, with only small volumes of pasty lava flowing through the pre-existing tubes.
By the afternoon of February 18, lava had advanced to the 1,900-foot level, where sluggish pahoehoe flows broke out of the tube system. By the morning of February 20, these flows had advanced to between the 300- and 500-foot elevation on the pali; their volume was still very small.
However, in the early afternoon of February 20, a new eruptive fissure opened up on the south side of Puu Oo adjacent to the episode 52 vents. We have called this new vent the episode 53 vent. On Saturday, this new vent had small lava fountains, about 2-3 meters high. A small flow from this new vent headed south. The lava flows within the tube system below the episode 51 vents continued at small volume, so at this time, two vents were erupting side-by-side: the crusted-over episode 51 vent and the new episode 53 vent.
About 1:00 a.m. on Sunday morning, February 21, the tremor recorded at our seismic station nearest Puu Oo increased dramatically in amplitude. This increase suggested that the eruption had quickly become more vigorous and its volume, greater. Observations made the next morning revealed that the fountains at the new episode 53 vent had increased in vigor and were now about 15 meters high. The lava was ponding to the south of the vent. The flows along the pali that were erupted from the adjacent episode 51 vent were also still active. The glow for the next few nights was very strong because of the eruption and active lava pond at the episode 53 vent.
By Monday, the lava pond from the episode 53 vent had overtopped a skylight in the tube system below the episode 51 vent, and the lava from the episode 53 vent was draining into the pre-existing tube and moving underground to the top of the pali. It was no longer possible to visually determine whether the episode 51 vents were still active, as lava from the two vents was now commingled in the tube. At the top of the pali, the flow broke out of the tube and quickly advanced, as aa flows, over the pali. By the next day, the flows were two-thirds of the way to the base of the pali.
By last Friday, the largest of these new flows had advanced to Paliuli above Kamoamoa and had begun to cascade over the pali just east of the flows that buried Kamoamoa between November and early February. Another, larger flow is also advancing down the main pali on the east side - and a smaller flow is advancing on the west side - of the earlier Kamoamoa flows. These flows should reach the ocean within a matter of days. They will probably flow over the earlier flows at Kamoamoa, or just to the east of those flows. The active surface lava flows are visible from the end of Chain of Craters Road in Hawaii Volcanoes National Park.
A small lava lake once again occupies Puu Oo Crater. The lava lake is about 215 feet below the rim, and overflows from the pond have coated the floor of the crater with new lava.
| 2021-09-27T00:20:01 |
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|
https://pos.sissa.it/332/037/
|
Volume 332 - XIV International Conference on Heavy Quarks and Leptons (HQL2018) - Spectroscopy
Spectroscopy and exotica of heavy flavor states in ATLAS
R. Novotny* on behalf of the ATLAS collaboration
*corresponding author
Full text: pdf
Pre-published on: 2018 December 05
Published on: 2018 December 11
Abstract
Several studies were performed using $4.9~\mathrm{fb}^{-1}$ of $\sqrt{s} = 7~\mathrm{TeV}$ and $19.2~\mathrm{fb}^{-1}$ of $\sqrt{s} = 8~\mathrm{TeV}$ $pp$ collision data collected with the ATLAS detector at the LHC and the results of the latest studies are presented here. The first study is devoted to the search for a structure in the $B_s^0\pi^\pm$ invariant mass spectrum in the ATLAS detector particularly the search for the resonance X(5568) which is a tetra-quark candidate. The second study is devoted to the search for excited states of the $B^\pm_c$ through its hadronic transition to the ground state, detected in the decay $B^\pm_c\rightarrow J/\psi\pi^\pm$. The state appears in the $m(B_c^\pm\pi^+\pi^-) - m(B_c^\pm)-2m(\pi^\pm)$ mass difference distribution with a significance of 5.2 standard deviations.
DOI: https://doi.org/10.22323/1.332.0037
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2019-03-23T03:05:40 |
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|
https://lammps.sandia.gov/doc/compute_temp_region.html
|
# compute temp/region command
## Syntax
compute ID group-ID temp/region region-ID
• ID, group-ID are documented in compute command
• temp/region = style name of this compute command
• region-ID = ID of region to use for choosing atoms
## Examples
compute mine flow temp/region boundary
## Description
Define a computation that calculates the temperature of a group of atoms in a geometric region. This can be useful for thermostatting one portion of the simulation box. E.g. a McDLT simulation where one side is cooled, and the other side is heated. A compute of this style can be used by any command that computes a temperature, e.g. thermo_modify, fix temp/rescale, etc.
Note that a region-style temperature can be used to thermostat with fix temp/rescale or fix langevin, but should probably not be used with Nose/Hoover style fixes (fix nvt, fix npt, or fix nph), if the degrees-of-freedom included in the computed T varies with time.
The temperature is calculated by the formula KE = dim/2 N k T, where KE = total kinetic energy of the group of atoms (sum of 1/2 m v^2), dim = 2 or 3 = dimensionality of the simulation, N = number of atoms in both the group and region, k = Boltzmann constant, and T = temperature.
A kinetic energy tensor, stored as a 6-element vector, is also calculated by this compute for use in the computation of a pressure tensor. The formula for the components of the tensor is the same as the above formula, except that v^2 is replaced by vx*vy for the xy component, etc. The 6 components of the vector are ordered xx, yy, zz, xy, xz, yz.
The number of atoms contributing to the temperature is calculated each time the temperature is evaluated since it is assumed atoms can enter/leave the region. Thus there is no need to use the dynamic option of the compute_modify command for this compute style.
The removal of atoms outside the region by this fix is essentially computing the temperature after a “bias” has been removed, which in this case is the velocity of any atoms outside the region. If this compute is used with a fix command that performs thermostatting then this bias will be subtracted from each atom, thermostatting of the remaining thermal velocity will be performed, and the bias will be added back in. Thermostatting fixes that work in this way include fix nvt, fix temp/rescale, fix temp/berendsen, and fix langevin. This means that when this compute is used to calculate the temperature for any of the thermostatting fixes via the fix modify temp command, the thermostat will operate only on atoms that are currently in the geometric region.
Unlike other compute styles that calculate temperature, this compute does not subtract out degrees-of-freedom due to fixes that constrain motion, such as fix shake and fix rigid. This is because those degrees of freedom (e.g. a constrained bond) could apply to sets of atoms that straddle the region boundary, and hence the concept is somewhat ill-defined. If needed the number of subtracted degrees-of-freedom can be set explicitly using the extra option of the compute_modify command.
See the Howto thermostat doc page for a discussion of different ways to compute temperature and perform thermostatting.
Output info:
This compute calculates a global scalar (the temperature) and a global vector of length 6 (KE tensor), which can be accessed by indices 1-6. These values can be used by any command that uses global scalar or vector values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.
The scalar value calculated by this compute is “intensive”. The vector values are “extensive”.
The scalar value will be in temperature units. The vector values will be in energy units.
none
| 2020-01-21T00:58:43 |
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|
https://dlmf.nist.gov/35.6#E8
|
# §35.6 Confluent Hypergeometric Functions of Matrix Argument
## §35.6(i) Definitions
35.6.1 ${{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\sum_{k=0}^{\infty}\frac{1}{k!% }\sum_{|\kappa|=k}\frac{{\left[a\right]_{\kappa}}}{{\left[b\right]_{\kappa}}}Z% _{\kappa}\left(\mathbf{T}\right).$
35.6.2 $\Psi\left(a;b;\mathbf{T}\right)=\frac{1}{\Gamma_{m}\left(a\right)}\int_{% \boldsymbol{\Omega}}\mathrm{etr}\left(-\mathbf{T}\mathbf{X}\right)\left|% \mathbf{X}\right|^{a-\frac{1}{2}(m+1)}\*{\left|\mathbf{I}+\mathbf{X}\right|}^{% b-a-\frac{1}{2}(m+1)}\mathrm{d}{\mathbf{X}},$ $\Re\left(a\right)>\frac{1}{2}(m-1)$, $\mathbf{T}\in{\boldsymbol{\Omega}}$.
### Laguerre Form
35.6.3 $L^{(\gamma)}_{\nu}\left(\mathbf{T}\right)=\frac{\Gamma_{m}\left(\gamma+\nu+% \frac{1}{2}(m+1)\right)}{\Gamma_{m}\left(\gamma+\frac{1}{2}(m+1)\right)}\*{{}_% {1}F_{1}}\left({-\nu\atop\gamma+\frac{1}{2}(m+1)};\mathbf{T}\right),$ $\Re\left(\gamma\right),\Re\left(\gamma+\nu\right)>-1$. ⓘ Defines: $L^{(\NVar{\gamma})}_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$: Laguerre function of matrix argument Symbols: ${{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_% {q}};\NVar{\mathbf{T}}\right)$ or ${{}_{\NVar{p}}F_{\NVar{q}}}\left({\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},% \dots,b_{q}}};\NVar{\mathbf{T}}\right)$: generalized hypergeometric function of matrix argument, $\Gamma_{\NVar{m}}\left(\NVar{a}\right)$: multivariate gamma function, $\Re$: real part, $\mathbf{T}$: real symmetric $m\times m$ matrix and $m$: positive integer Permalink: http://dlmf.nist.gov/35.6.E3 Encodings: TeX, pMML, png See also: Annotations for §35.6(i), §35.6(i), §35.6 and Ch.35
## §35.6(ii) Properties
35.6.4 ${{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\frac{1}{\mathrm{B}_{m}\left(a% ,b-a\right)}\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I}}\mathrm{etr}% \left(\mathbf{T}\mathbf{X}\right)\left|\mathbf{X}\right|^{a-\frac{1}{2}(m+1)}% \left|\mathbf{I}-\mathbf{X}\right|^{b-a-\frac{1}{2}(m+1)}\mathrm{d}{\mathbf{X}},$ $\Re\left(a\right),\Re\left(b-a\right)>\frac{1}{2}(m-1)$.
35.6.5 $\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-\mathbf{T}\mathbf{X}\right)\left|% \mathbf{X}\right|^{b-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a\atop b};\mathbf{S}% \mathbf{X}\right)\mathrm{d}{\mathbf{X}}=\Gamma_{m}\left(b\right)\left|\mathbf{% I}-\mathbf{S}\mathbf{T}^{-1}\right|^{-a}\left|\mathbf{T}\right|^{-b},$ $\mathbf{T}>\mathbf{S}$, $\Re\left(b\right)>\frac{1}{2}(m-1)$.
35.6.6 $\mathrm{B}_{m}\left(b_{1},b_{2}\right)\left|\mathbf{T}\right|^{b_{1}+b_{2}-% \frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a_{1}+a_{2}\atop b_{1}+b_{2}};\mathbf{T}% \right)=\int_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{T}}\left|\mathbf{X}\right|^{% b_{1}-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a_{1}\atop b_{1}};\mathbf{X}\right)% {\left|\mathbf{T}-\mathbf{X}\right|}^{b_{2}-\frac{1}{2}(m+1)}{{}_{1}F_{1}}% \left({a_{2}\atop b_{2}};\mathbf{T}-\mathbf{X}\right)\mathrm{d}{\mathbf{X}},$ $\Re\left(b_{1}\right),\Re\left(b_{2}\right)>\frac{1}{2}(m-1)$.
35.6.7 ${{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\mathrm{etr}\left(\mathbf{T}% \right){{}_{1}F_{1}}\left({b-a\atop b};-\mathbf{T}\right).$
35.6.8 $\int_{\boldsymbol{\Omega}}\left|\mathbf{T}\right|^{c-\frac{1}{2}(m+1)}\Psi% \left(a;b;\mathbf{T}\right)\mathrm{d}{\mathbf{T}}=\frac{\Gamma_{m}\left(c% \right)\Gamma_{m}\left(a-c\right)\Gamma_{m}\left(c-b+\frac{1}{2}(m+1)\right)}{% \Gamma_{m}\left(a\right)\Gamma_{m}\left(a-b+\frac{1}{2}(m+1)\right)},$ $\Re\left(a\right)>\Re\left(c\right)+\frac{1}{2}(m-1)>m-1$, $\Re\left(c-b\right)>-1$.
## §35.6(iii) Relations to Bessel Functions of Matrix Argument
35.6.9 $\lim_{a\to\infty}{{}_{1}F_{1}}\left({a\atop\nu+\frac{1}{2}(m+1)};-a^{-1}% \mathbf{T}\right)=\frac{A_{\nu}\left(\mathbf{T}\right)}{A_{\nu}\left(% \boldsymbol{{0}}\right)}.$
35.6.10 $\lim_{a\to\infty}\Gamma_{m}\left(a\right)\Psi\left(a+\nu;\nu+\tfrac{1}{2}(m+1)% ;a^{-1}\mathbf{T}\right)=B_{\nu}\left(\mathbf{T}\right).$
## §35.6(iv) Asymptotic Approximations
For asymptotic approximations for confluent hypergeometric functions of matrix argument, see Herz (1955) and Butler and Wood (2002).
| 2021-10-26T17:21:52 |
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|
https://hacklog.mu/post/bash-source-file/
|
#### Bash source file
##### March 22, 2015
While I had no particular reason why to code it in Perl or Python, I ended writing my scripts in Bash on this Sunday afternoon. No huge tasks were meant to be executed, just some database reading. However, all of the short scripts would be using common variables, namely regarding the DB credentials. Sourcing variables from an external file could be achieved using . filename or source filename.
A little heck comes when passwords containing special characters such as $< > [] {} ‘ “ \ | & ; * ? are used. In your source file you need to escape each of those characters using a backslash </code> symbol. For example we could have a configuration file db.conf as follows: HOST=localhost DBNAME=testdb DBUSER=user001 DBPASS=\[email protected]\$ Now, let’s get the variables as follows: #!/bin/bash . db.conf echo \$DBPASS Copy the above in a file named getSQLPass.sh and we run it. The backslash symbols do not get printed.
This work is licensed under a Creative Commons Attribution 4.0 International License. `
| 2019-03-20T19:58:34 |
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https://lessonplanet.com/teachers/calculus-derivatives-3-11th-higher-ed
|
# Calculus: Derivatives 3
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, "Calculus Derivatives 2Ó and "Calculus Derivatives 2.5 (HD).Ó Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Concepts
Resource Details
11th - Higher Ed
Subjects
Math
2 more...
Resource Types
Videos
1 more...
Audiences
For Teacher Use
1 more...
Instructional Strategy
Flipped Classroom
Accessibility
Closed Captions
Usage Permissions
Creative Commons
BY-NC-SA: 3.0
| 2019-04-25T18:13:26 |
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|
https://tjyj.stats.gov.cn/CN/abstract/abstract4794.shtml
|
• 论文 •
### 产能约束下国内需求对工业制成品出口的非线性影响
• 出版日期:2016-04-15 发布日期:2016-04-05
### The Nonlinear Impact of Domestic Demand on Export of Industrial Manufactured Goods under Production Capacity Constraints
Han Guogao
• Online:2016-04-15 Published:2016-04-05
Abstract:
Based on the sample data from the first quarter of 2000 to the third quarter of 2014, this paper examines the effect of domestic demand fluctuation on the export of industrial manufactured goods under production capacity constraints in China with nonlinear smoothing transition model. The study finds that the domestic demand fluctuation has a nonlinear effect on the export of industrial manufactures goods, that is, the effect of domestic demand fluctuation on the export of industrial manufactured goods is asymmetric. When China’s economic growth slows and the industrial production capacity utilization level is lower than the threshold value, the domestic demand fluctuation has a negative impact on the export of manufactured goods and these two variables show alternative relations. And when the economic situation is good and the industrial production capacity utilization level is higher than the threshold value, the domestic demand fluctuation has a positive impact on the export of manufactured goods and these two variables show complementary relations. When the industrial production capacity utilization level is near threshold value, the effect of domestic demand fluctuation on the export of industrial manufactured goods will switch smoothly between the two mechanisms.
| 2022-09-30T21:49:59 |
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|
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