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https://www.usgs.gov/center-news/volcano-watch-25-years-later-what-have-we-learned-mount-st-helens
|
# Volcano Watch - 25 years later, what have we learned from Mount St. Helens?
Release Date:
This week marks the 25th anniversary of the May 18, 1980, eruption of Mount St. Helens. At 8:32 a.m. that Sunday morning, a magnitude-5.1 earthquake occurred, and the north flank of the volcano collapsed in the largest landslide ever witnessed.
The plume from Mount St. Helens rose nearly 3,000 feet (1,000 meters) above the volcano's rim.
(Credit: Lyn Topinka, USGS. Public domain.)
As the mountainside slid away, magma that had been accumulating within the volcano for the previous 2 months exploded outward in a lateral blast unlike anything observed before. The landslide and blast destroyed 230 square miles of forest and killed 57 people, including USGS geologist David Johnston, who was observing the volcano from a ridge 5 miles away.
Mount St. Helens erupted for the rest of that day, blasting hot ash and gas 15 miles into the atmosphere and sending numerous pyroclastic flows down the flanks of the mountain. The landslide also generated a destructive mudflow that traveled all the way to the Columbia River. This slurry reduced the depth of the shipping channel in the river from 40 feet to 14 feet overnight and stranded numerous ocean-going vessels in upstream ports.
In the 25 years since that fateful Sunday morning, the science of volcanology has dramatically changed, thanks, in part, to lessons learned from that eruption. Prior to 1980, the landslide and lateral blast had never previously been witnessed and were completely unknown to volcanologists.
A similar landslide and blast occurred at Bezymianny volcano in Kamchatka, Russia, in 1956, but no people or cameras were there to document the activity. Only after the 1980 eruption of Mount St. Helens was the style of the Bezymianny eruption fully recognized.
In fact, similar volcano landslides, called sector collapses, have now been identified at over 200 volcanoes around the world. Detailed studies of the sector collapse, lateral blast, and large mudflow at Mount St. Helens led to a reassessment of volcano hazards at other sites in the United States and around the world, better preparing communities situated near such volcanoes for possible future eruptions.
In addition, studies of eruptions at Mount St. Helens following the May 18, 1980, explosion demonstrated that volcanic eruptions could indeed be accurately predicted. The growth of a lava dome in the newly formed crater between 1980 and 1986 provided an ideal natural laboratory with a series of repetitive "experiments" (eruptions) for scientists to observe.
Through continuous monitoring and bold research by a team of interdisciplinary earth scientists using gas emissions, earthquake activity, surface deformation, and other techniques (many of which had been developed at HVO before their application at Mount St. Helens), 14 eruptions of lava between 1980 and 1986 were successfully predicted within days to weeks of their occurrence.
This well-organized effort was made possible by the creation of the Cascades Volcano Observatory (CVO), based on the model of the Hawaiʻian Volcano Observatory, in existence since 1912.
The experience gained from Mount St. Helens by CVO, along with the years of pioneering research at HVO, demonstrated the value of the observatory concept, where a group of scientists with different backgrounds could focus their efforts on understanding volcanic processes.
Within a few years of the Mount St. Helens blast, a mobile volcano observatory, the Volcano Disaster Assistance Program, had been established by the U.S. Geological Survey to respond to volcanic crises around the world. In addition, new volcano observatories were established to study Alaskan volcanoes, Long Valley caldera in California, and Yellowstone caldera in Wyoming.
Still, there is much progress to be made in understanding how volcanoes work, and why and when they will erupt. As the sudden, unanticipated reawakening of Mount St. Helens in September 2004 demonstrated, constant vigilance is essential for identifying and heeding signs of impending volcanic activity.
Although we have learned much from the May 18, 1980, blast at Mount St. Helens and other eruptions, including the now 22-year-long eruption of Kīlauea, volcanoes continue to challenge us, teaching new lessons with every eruption.
### Volcano Activity Update
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater and on the southwest side of the cone.
The PKK lava tube continues to produce intermittent surface flows from above the top of Pulama pali to the ocean. Three ocean entries were active as of May 19. The two largest are at East Laeapuki and East Kamoamoa, with a much smaller entry halfway in between. The East Laeapuki and East Kamoamoa entries both have benches about 350 m (385 yards) long and up to 75 m (80 yards) wide. Surface flows are active intermittently inland of the entries. The East Laeapuki entry is the closest activity to the end of Chain of Craters Road, in Hawaii Volcanoes National Park, and is located about 4.5 km (3 miles) from the ranger shed. Expect a 2-hour walk each way and bring lots of water.
Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Remember-the beaches that sometimes form next to an active bench are just as dangerous as the bench itself. Stay off both, and heed the National Park warning signs.
During the week ending May 18, 3 earthquakes were reported felt on Hawaii Island. A magnitude 5.1 earthquake on May 13 at 0:06 a.m. was felt widely across the island. The event was located 5 km (3 miles) east-southeast of submarine Loihi Volcano at a depth of 40 km (25 miles). A magnitude-3.2 quake occurred 14 km (9 miles) northwest of Naalehu at a depth of 16 km (10 miles) at 5:14 a.m. on May 16; this earthquake was felt at Na`alehu. Another magnitude-3.2 quake occurred 1 km (0.6 miles) east-northeast of Pahala with a depth of 11 km (7 miles) at 6:28 a.m. on May 17; the quake was felt in the Volcano Golf Course area.
Mauna Loa is not erupting. During the week ending May 18, 7 earthquakes were recorded beneath the summit area. Inflation has slowed beneath the summit and flanks over the last few weeks.
| 2020-01-26T14:03:29 |
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|
https://pdglive.lbl.gov/Particle.action?node=M188&init=0&home=sumtabM
|
LIGHT UNFLAVORED MESONS($\boldsymbol S$ = $\boldsymbol C$ = $\boldsymbol B$ = 0) For $\mathit I = 1$ (${{\mathit \pi}}$, ${{\mathit b}}$, ${{\mathit \rho}}$, ${{\mathit a}}$): ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit d}}}$, ( ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit u}}}−$ ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit d}}})/\sqrt {2 }$, ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit u}}}$;for $\mathit I = 0$ (${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit h}}$, ${{\mathit h}^{\,'}}$, ${{\mathit \omega}}$, ${{\mathit \phi}}$, ${{\mathit f}}$, ${{\mathit f}^{\,'}}$): ${\mathit {\mathit c}}_{{\mathrm {1}}}$( ${{\mathit u}}{{\overline{\mathit u}}}$ $+$ ${{\mathit d}}{{\overline{\mathit d}}}$ ) $+$ ${\mathit {\mathit c}}_{{\mathrm {2}}}$( ${{\mathit s}}{{\overline{\mathit s}}}$ ) INSPIRE search
# ${{\boldsymbol \rho}{(1570)}}$ $I^G(J^{PC})$ = $1^+(1^{- -})$
May be an OZI-violating decay mode of ${{\mathit \rho}{(1700)}}$. See our mini-review under the ${{\mathit \rho}{(1700)}}$.
${{\mathit \rho}{(1570)}}$ MASS $1570 \pm70$ MeV
${{\mathit \rho}{(1570)}}$ WIDTH $144 \pm90$ MeV
| 2021-03-06T10:14:20 |
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|
https://open-music-kontrollers.ch/chimaera/build/
|
# Chimaera
### Reflow-solder the SU-16 Unit
The building of a sensor unit is straight-forward and should be doable even for a skilled beginner in SMD soldering. We deliberately choose the big chips (SOIC) for the multi-legged chips and a 0603 footprint for the smallest passive components.
• get yourself a PCB (e.g. from our shop)
• export the BOM from the KiCAD project at the hardware repository
• get yourself the parts, e.g. from Digi-Key
• get yourself a solder paste stencil (e.g. from OSH Stencils)
• apply the solder paste
• pick and place the SMD parts
• multiplexer, OpAmp and diode must not be misaligned
• 200k (1x) and 50k (1x) trim pots must not be mistaken
• all other parts are unproblematic
• bake the assembled PCB
• check the circuitry thoroughly with a multimeter
• solder the TH socket and header
### Reflow-solder the DSP-F3 Unit
The building of a DSP unit is a bit more tricky (because of the two 48-pin, 0.5mm pitch LQFP packages). If this will be your first project with 0.5mm pitch components, you may want to do some preliminary exercises first. We deliberately choose the 0603 footprint for the remaining components.
• get yourself a PCB (e.g. from our shop)
• export the BOM from the KiCAD project at the hardware repository
• get yourself the parts, e.g. from Digi-Key
• get yourself a solder paste stencil (e.g. from OSH Stencils)
• apply the solder paste
• pick and place the SMD parts
• The LQFP (2x) and the SOIC (3x) packages must not be misaligned
• The diodes (2x) and LED (1x) must not be misaligned
• The tantalum capacitors (4x) must not be misaligned
• all other parts are unproblematic
• bake the assembled PCB
• check the legs of the two LQFP packages for solder bridges!!
• check the circuitry thoroughly with a multimeter
• solder the MagJack and USB connectors, tactile switch, TH socket and headers
### Prepare the case
Get yourself a case (e.g. from our shop) or create your own at the next FabLab.
The case can be cut and engraved from a plain sheet of 2-3mm material. It consists of an inner rib construction, embedding and holding in-place the printed circuit boards, wrapped in an enclosure and held together with just a couple of nuts and bolts on the back side. It was designed for wooden materials (laser-grad plywood, e.g. birch or beech), other materials and thicknesses may need adaptations.
The wrapping sheet has been designed as a kerf-bent enclosure. Depending on the material thickness, the wrapping sheet may need pre-heating (e.g. with an iron) to not stress the wood too much while bending.
### Wiring up the units
The Chimaera is modular in design and can be equipped with varying amounts of sensor units. As the DSP unit has three analog-to-digital converters running in parallel, the analog inputs from the sensor units are distributed evenly for best performance. The analog-to-digital channels are adjacent on the socket header: 4 channels (pins 1-4) for ADC1 followed by 4 channels (pins 5-8) for ADC2 and 2 channels (pins 9-A) for ADC3.
ADC: ADC1 ADC2 ADC3 PIN: .... .... ..
Each sensor unit is connected to the DSP unit by 7 lines (6 towards the sensor unit): Out of those, there are four digital lines for the channel select on the sensor units 16:1 multiplexer. Those lines can simply be daisy-chained between the sensor units. The remaining 3 lines have to be connected by wires individually to the DSP unit. This is strictly needed for a robust grounding and powering scheme. Apart from ground and power to drive the sensor unit, the third of the three lines carries the multiplexed and amplified analog signal back to the DSP unit.
Note: The sensor units are protected against negative current (e.g. if ground and power are switched) with a diode, but they are NOT protected against a switch of power and analog return lines. So, check the wiring twice before powering up!
For the configurations for 1 sensor unit (S16) up to 10 sensor units (S160), the sensor units row assignment is defined as follows:
1
.... .... .1
2
1... 2... ..
3
1... 2... .3
4
12.. 34.. ..
5
12.. 34.. .5
6
123. 456. ..
7
123. 456. .7
8
1234 5678 ..
9
1234 5678 .9
A
1234 5678 A9
### Hardware calibration
Apart from the four lines S0-S3 which switch channels on the multiplexer, the sensor units are purely analog circuitry and can be and/or need to be tweaked at different points for optimal performance. Please read up the corresponding section in the hardware documentation in order to understand what the exact function of each of the three trim potentiometers is.
Due to the modular design of the Chimaera, each sensor unit can be tweaked individually. One purpose of the hardware calibration therefore is that all connected sensor units roughly are set to the same quiescent values and amplification factor. This will make event detection and interpolation along the sensor array much more accurate.
The other purpose of the hardware calibration is to optimize sensor output range to match a given maximal range of magnetic field strength. Let us make an example to clarify this: A given sensor can output voltages between 0V and 5V. With no magnetic field present, its quiescent output voltage is around 2.5V. Let us assume, that the sensor has a sensitivity of 2.5mV/G. If we now bring a given permanent magnet as near as we can to the sensor, e.g. directly down to the case surface, the sensor will sense the maximal magnetic field strength of the permanent magnet. If the magnet is e.g. magnetized to 500G, the maximal voltage difference relative to quiescent output for the sensor will be 500G*2.5mV/G=1.25V. The output voltage therefore will be in the range of 1.25-3.75V. This configuration would only span half of the possible output voltage range. By increasing the amplification factor from 1 to 2 in this case, the whole range of 0-5V will be spanned over and the subsequent digital-to-analog conversion on the DSP unit will have twice the resolution.
Hardware calibration ideally has to be done once only before closing the case at the end of the build process. If you will change the strength of used permanent magnets considerably in the future, you may have to recalibrate for best performance, though.
For a good hardware calibration, you will need a visual feedback. There is a ready-to-use program in our Supercollider repository which will show a sensor dump of the whole sensor array and guide you through the below described hardware calibration procedure step by step.
The first step in hardware calibration is to reset all sensor units to an amplification factor of 1 (no amplification). We do this by turning counter-clock-wise all the way trim potentiometer RV1 (amplification factor) on all sensor units.
Next we calibrate for a correct reference voltage. Keep any magnetic source away from the sensor array. Increase the amplification factor to e.g. half-max (with RV1). Quiescent output for that given sensor unit will now be offset to the zero line. Adjust the trim potentiometer RV3 until the quiescent voltage of a given sensor unit comes to lie around the zero line again. Set the amplification factor again to 1 (with RV1).
Now all the sensor units will be calibrated to a common quiescent output voltage and will have set the reference voltage correctly. The last step is a tricky one, that's were we need to set the amplification factors for each sensor unit based on the permanent magnets the device will be used with. This is the only step in hardware calibration were we will need the permanent magnets. The goal is to bring the magnet as close as possible to the sensor array (vicinity = 1) and adjust the amplification factor (by turning RV1) so that the most sensitive sensor of a given sensor unit just reaches slightly below the highest possible voltage output still resolvable by the microcontrollers analog-to-digital converter.
This is an iterative procedure: continuously run the magnet along all sensors of a given sensor unit. Increase the amplification factor until one sensor value at least starts to show up in yellow (value just starts to fall outside the resolvable range by the analog-to-digital converter). Now decrease the amplification factor in small steps until all yellow sensor values only show up in their correct color again (sensor value now lies just in the resolvable range by the analog-to-digital converter). Do this for all the sensor units and hardware calibration is done and the sensor output range will optimally match the resolvable range of the analog-to-digital converters for your chosen magnets.
Chimaera graphical sensor dump implemented in SuperCollider showing 2 present magnetic sources, the left one with an ideal hardware calibration, the right one with a sensor value overshoot and therefore less than ideal hardware calibration.
### WANTED:Beta Testers
After a high interest at Maker Faire Rome, we are now running a beta-testing campaign to collect more comprehensive feedback of first-hand experiences of our final Chimaera prototype design from interested individuals. Get in contact with us. Now.
Please support free/libre software and hardware designs.
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request bank credentials via encrypted mail for SEPA transfers.
Last update - 16 Sep 2017
Copyright © 2014-2017, Hanspeter Portner, Open Music Kontrollers, cc-by-sa 4.0. Uses libre javascript.
| 2017-11-23T13:12:02 |
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|
https://da.khanacademy.org/computing/computer-science/algorithms/towers-of-hanoi/a/towers-of-hanoi
|
# Towers of Hanoi
If you've gone through the tutorial on recursion, then you're ready to see another problem where recursing multiple times really helps. It's called the Towers of Hanoi. You are given a set of three pegs and n disks, with each disk a different size. Let's name the pegs A, B, and C, and let's number the disks from 1, the smallest disk, to n, the largest disk. At the outset, all n disks are on peg A, in order of decreasing size from bottom to top, so that disk n is on the bottom and disk 1 is on the top. Here's what the Towers of Hanoi looks like for n, equals, 5 disks:
Towers of Hanoi initial configuration 5 disks
The goal is to move all n disks from peg A to peg B:
Towers of Hanoi final configuration 5 disks
Sounds easy, right? It's not quite so simple, because you have to obey two rules:
1. You may move only one disk at a time.
2. No disk may ever rest atop a smaller disk. For example, if disk 3 is on a peg, then all disks below disk 3 must have numbers greater than 3.
You might think that this problem is not terribly important. Au contraire! Legend has it that somewhere in Asia (Tibet, Vietnam, India—pick which legend on the Internet you like), monks are solving this problem with a set of 64 disks, and—so the story goes—the monks believe that once they finish moving all 64 disks from peg A to peg B according to the two rules, the world will end. If the monks are correct, should we be panicking in the streets?
First, let's see how to solve the problem recursively. We'll start with a really easy case: one disk, that is, n, equals, 1. The case of n, equals, 1 will be our base case. You can always move disk 1 from peg A to peg B, because you know that any disks below it must be larger. And there's nothing special about pegs A and B. You can move disk 1 from peg B to peg C if you like, or from peg C to peg A, or from any peg to any peg. Solving the Towers of Hanoi problem with one disk is trivial, and it requires moving only the one disk one time.
How about two disks? How do you solve the problem when n, equals, 2? You can do it in three steps. Here's what it looks like at the start:
Towers of Hanoi initial configuration 2 disks
First, move disk 1 from peg A to peg C:
Towers of Hanoi move 1, 2 disks
Notice that we're using peg C as a spare peg, a place to put disk 1 so that we can get at disk 2. Now that disk 2—the bottommost disk—is exposed, move it to peg B:
Towers of Hanoi move 2, 2 disks
Finally, move disk 1 from peg C to peg B:
Towers of Hanoi move 3, 2 disks
This solution takes three steps, and once again there's nothing special about moving the two disks from peg A to peg B. You can move them from peg B to peg C by using peg A as the spare peg: move disk 1 from peg B to peg A, then move disk 2 from peg B to peg C, and finish by moving disk 1 from peg A to peg C. Do you agree that you can move disks 1 and 2 from any peg to any peg in three steps? (Say "yes.")
Dette indhold er et samarbejde mellem Dartmouth Computer Science professorerne Thomas Cormen og Devin Balkcom plus Khan Academys computing curriculum team. Indholdet er licenseret under CC-BY-NC-SA.
| 2017-09-22T02:49:31 |
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|
https://www.nist.gov/publications/optical-microwave-frequency-comparison-fractional-uncertainty-10-15
|
An official website of the United States government
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# Optical-to-microwave frequency comparison with fractional uncertainty of 10-15
Published
### Author(s)
Jason Stalnaker, Scott A. Diddams, Tara M. Fortier, K Kim, Leo W. Hollberg, James C. Bergquist, Wayne M. Itano, Marie Delaney, Luca Lorini, Windell Oskay, Thomas P. Heavner, Steven R. Jefferts, Filippo Levi, Thomas E. Parker, Jon H. Shirley
### Abstract
We report the technical aspects of the optical-to-microwave comparison for our recent measurements of the optical frequency of the mercury single-ion frequency standard in terms of the SI second as realized by the NIST-F1 cesium fountain clock. Over the course of six years, these measurements have resulted in a determination of the mercury single-ion frequency with a fractional uncertainty less than $7 \times 10^{-16}$ making it the most accurately measured optical frequency to date. In this paper, we focus on the details of the comparison techniques used in the experiment and discuss the uncertainties associated with the optical-to-microwave synthesis based on a femtosecond laser frequency comb. We also present our most recent results in the context of the previous measurements of the mercury single-ion frequency and arrive at a final determination of the mercury single ion optical frequency: $f({\rm Hg}^+) = 1 \, 064 \, 721 \, 609 \, 899 \, 145.30(69) \: {\rm Hz}$.
Citation
Applied Physics B
### Keywords
cesium frequency standard, femtosecond frequency comb, mercury ion clock, optical clock, optical frequency measurement, optical-to-microwave conversion
Created October 1, 2007, Updated November 29, 2016
| 2020-09-21T10:34:30 |
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|
https://www.nist.gov/node/587086?pub_id=909694
|
# Airflow and Indoor Air Quality Models of DOE Reference Commercial Buildings
Created February 24, 2012, Updated August 15, 2012
| 2016-09-24T22:47:47 |
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https://www.zbmath.org/authors/?q=ai%3Atodd.john
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## Todd, John
Compute Distance To:
Author ID: todd.john Published as: Todd, John; Todd, J. External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 82 Publications since 1935, including 5 Books 3 Contributions as Editor · 2 Further Contributions Biographic References: 2 Publications Co-Authors: 23 Co-Authors with 40 Joint Publications 309 Co-Co-Authors
all top 5
### Co-Authors
47 single-authored 19 Taussky-Todd, Olga 5 Kreyszig, Erwin 3 Fan, Ky 2 Carlson, Bille Chandler 2 Cooper, Ralph 2 Och, Christian 2 Osborne, Richard M. 1 Beckenbach, Edwin Ford 1 Chowla, S. D. S. 1 de Bruijn, Nicolaas Govert 1 Diaz, Joaquin Basilio 1 Ellis, Clarence A. 1 Friedman, Avner 1 Gaier, Dieter 1 Getrich, Nathan 1 Gosselin, Richard P. 1 Hwang, William G. 1 Karlin, Samuel 1 Keddara, Karim 1 Liang, J. J. Y. 1 Littlewood, John Edensor 1 Marcus, Marvin D. 1 Marshall, Albert W. 1 McIver, William J. jun. 1 Metcalf, Frederic T. 1 Metropolis, Nicholas Constantine 1 Motzkin, Theodore Samuel 1 Newman, Morris 1 Olkin, Ingram 1 Payne, Lawrence Edward 1 Pólya, George 1 Proschan, Frank 1 Schoenberg, Isaac Jacob 1 Shisha, D. 1 Shisha, Oved 1 Stembridge, John R. 1 Szasz, Otto 1 Taub, Abraham Haskel 1 Temple, Brian 1 Tompkins, Charles B. 1 Varga, Richard Steven 1 Weinstein, Alexander 1 Ziegler, Zvi
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### Serials
5 Numerische Mathematik 5 Journal of the London Mathematical Society 4 ISNM. International Series of Numerical Mathematics 3 Journal of Research of the National Bureau of Standards 3 Linear Algebra and its Applications 2 Communications on Pure and Applied Mathematics 2 The Mathematical Intelligencer 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences 2 SIAM Review 2 The Philosophical Magazine, VII. Series 2 Proceedings of the London Mathematical Society. Second Series 2 Journal of Research of the National Bureau of Standards 2 The Quarterly Journal of Mathematics. Oxford Series 1 American Mathematical Monthly 1 Annals of the History of Computing 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical and Physical Sciences 1 The Mathematical Gazette 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Mathematics Magazine 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Illinois Journal of Mathematics 1 Journal of Approximation Theory 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 SIAM Journal on Numerical Analysis 1 Numerical Algorithms 1 Aequationes Mathematicae 1 Communications of the ACM 1 Elemente der Mathematik 1 Concurrency and Computation: Practice & Experience 1 Proceedings of the Cambridge Philosophical Society 1 Bollettino della Unione Matematica Italiana. Series III 1 Bulletin of the American Mathematical Society 1 Journal of the Society for Industrial & Applied Mathematics 1 Annales de la Société Polonaise de Mathématique 1 Proceedings of Symposia in Applied Mathematics
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### Fields
15 Numerical analysis (65-XX) 10 History and biography (01-XX) 10 Special functions (33-XX) 5 Real functions (26-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Approximations and expansions (41-XX) 3 Sequences, series, summability (40-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Integral equations (45-XX)
### Citations contained in zbMATH Open
51 Publications have been cited 345 times in 302 Documents Cited by Year
Discrete analogs of inequalities of Wirtinger. Zbl 0064.29803
Fan, Ky; Taussky, Olga; Todd, John
1955
Survey of numerical analysis. Zbl 0101.33601
1962
Another look at a matrix of Mark Kac. Zbl 0727.15010
Taussky, Olga; Todd, John
1991
Covering theorems for groups. Zbl 0035.29505
Taussky, Olga; Todd, John
1949
The radius of univalence of Bessel functions. Zbl 0091.06203
Kreyszig, Erwin; Todd, John
1960
Introduction to the constructive theory of functions. Zbl 0114.26903
Todd, John
1963
The Stieltjes constants. Zbl 0257.10017
Liang, J. J. Y.; Todd, John
1973
The degenerating behavior of elliptic functions. Zbl 0531.33004
Carlson, B. C.; Todd, John
1983
The evaluation of matrix inversion programs. Zbl 0085.34305
Newman, Morris; Todd, John
1958
Zolotarev’s first problem - the best approximation by polynomials of degree $$\leq n-2$$ to $$x^ n-n\sigma x^{n-1}$$ in [-1,1]. Zbl 0535.41029
Carlson, B. C.; Todd, John
1983
On smallest isolated Gerschgorin disks for eigenvalues. Zbl 0148.01703
Todd, John
1965
Basic numerical mathematics. Vol. 2: Numerical algebra. Zbl 0354.65018
Todd, John
1977
The condition of the finite segments of the Hilbert matrix. Zbl 0058.01003
Todd, John
1954
A direct approach to the problem of stability in the numerical solution of partial differential equations. Zbl 0070.35107
Todd, John
1956
Inequalities. Proceedings of a symposium held at Wright-Patterson Air Force Base, Ohio, August 19–27, 1965. Zbl 0178.00102
1967
The condition of a certain matrix. Zbl 0034.37601
Todd, John
1950
A problem on arc tangent relations. Zbl 0036.16101
Todd, John
1949
Applications of transformation theory: a legacy from Zolotarev (1847–1878). Zbl 0579.41001
Todd, John
1984
The lemniscate constants. Zbl 0298.33001
Todd, John
1975
The radius of univalence of the error function. Zbl 0086.06203
Kreyszig, Erwin; Todd, John
1959
The condition of certain matrices. I. Zbl 0034.37602
Todd, John
1949
Matrices with finite period. Zbl 0061.01304
Taussky, Olga; Todd, John
1940
Computational problems concerning the Hilbert matrix. Zbl 0096.32304
Todd, John
1961
Nonsingular cubic curves as determinantal loci. Historical remarks by John Todd. Zbl 0652.14022
Taussky, Olga
1987
Evaluation of the exponential integral for large complex arguments. Zbl 0055.36002
Todd, John
1954
Matrices of finite period. Zbl 0061.01305
Taussky, Olga; Todd, John
1941
Motivation for working in numerical analysis. Zbl 0064.37402
Todd, John
1955
The condition of certain matrices. III. Zbl 0093.13301
Todd, John
1958
On the rate of convergence of optimal ADI processes. Zbl 0154.41101
Gaier, Dieter; Todd, John
1967
The problem of error in digital computation. Zbl 0171.12802
Todd, John
1965
Hardy’s inequality and ultrametric matrices. Zbl 0952.15011
Todd, John; Varga, Richard S.
1999
The density of reducible integers. Zbl 0039.03603
Chowla, S. D.; Todd, John
1949
Systems of equations, matrices and determinants. I, II. Zbl 0048.24906
Taussky, Olga; Todd, John
1952
On a trigonometrical sum. Zbl 0453.33001
Stembridge, John R.; Todd, John
1981
Numerical analysis at the National Bureau of Standards. Zbl 0301.65001
Todd, John
1975
Cholesky, Toeplitz and the triangular factorization of symmetric matrices. Zbl 1093.65030
Taussky, Olga; Todd, John
2006
A determinantal inequality. Zbl 0064.01401
Fan, Ky; Todd, John
1955
Commuting bilinear transformations and matrices. Zbl 0073.00804
Taussky, O.; Todd, John
1956
Todd, J.
1967
Infinite powers of matrices. Zbl 0028.20103
Taussky, Olga; Todd, John
1942
On the relative extrema of the Laguerre orthogonal functions. Zbl 0039.07601
Todd, John
1950
Experiments on the inversion of a $$16\times 16$$ matrix. Zbl 0052.35001
Todd, John
1953
Oberwolfach - 1945. Zbl 0517.01042
Todd, John
1983
Inversion in groups. JFM 67.0977.01
Taussky, O.; Todd, J.
1941
A characterisation of algebraic numbers. JFM 66.1210.03
Taussky, O.; Todd, J.
1940
A legacy from E. I. Zolotarev (1847-1878). Zbl 0642.01007
Todd, John
1988
G. H. Hardy as an editor. Zbl 0821.01045
Todd, John
1994
The best polynomial approximation to $$(1+x)^{-1}$$ in [0,1]. Zbl 0604.41032
Todd, John
1986
The condition of certain matrices. II. Zbl 0055.35502
Todd, John
1954
Experiments in the computation of conformal maps. Zbl 0067.35901
1955
On the radius of univalence of the function $$\exp z^2 \int\limits_0^z \exp (-t^2)dt$$. Zbl 0085.06601
Kreyszig, Erwin; Todd, John
1959
Cholesky, Toeplitz and the triangular factorization of symmetric matrices. Zbl 1093.65030
Taussky, Olga; Todd, John
2006
Hardy’s inequality and ultrametric matrices. Zbl 0952.15011
Todd, John; Varga, Richard S.
1999
G. H. Hardy as an editor. Zbl 0821.01045
Todd, John
1994
Another look at a matrix of Mark Kac. Zbl 0727.15010
Taussky, Olga; Todd, John
1991
A legacy from E. I. Zolotarev (1847-1878). Zbl 0642.01007
Todd, John
1988
Nonsingular cubic curves as determinantal loci. Historical remarks by John Todd. Zbl 0652.14022
Taussky, Olga
1987
The best polynomial approximation to $$(1+x)^{-1}$$ in [0,1]. Zbl 0604.41032
Todd, John
1986
Applications of transformation theory: a legacy from Zolotarev (1847–1878). Zbl 0579.41001
Todd, John
1984
The degenerating behavior of elliptic functions. Zbl 0531.33004
Carlson, B. C.; Todd, John
1983
Zolotarev’s first problem - the best approximation by polynomials of degree $$\leq n-2$$ to $$x^ n-n\sigma x^{n-1}$$ in [-1,1]. Zbl 0535.41029
Carlson, B. C.; Todd, John
1983
Oberwolfach - 1945. Zbl 0517.01042
Todd, John
1983
On a trigonometrical sum. Zbl 0453.33001
Stembridge, John R.; Todd, John
1981
Basic numerical mathematics. Vol. 2: Numerical algebra. Zbl 0354.65018
Todd, John
1977
The lemniscate constants. Zbl 0298.33001
Todd, John
1975
Numerical analysis at the National Bureau of Standards. Zbl 0301.65001
Todd, John
1975
The Stieltjes constants. Zbl 0257.10017
Liang, J. J. Y.; Todd, John
1973
Inequalities. Proceedings of a symposium held at Wright-Patterson Air Force Base, Ohio, August 19–27, 1965. Zbl 0178.00102
1967
On the rate of convergence of optimal ADI processes. Zbl 0154.41101
Gaier, Dieter; Todd, John
1967
Todd, J.
1967
On smallest isolated Gerschgorin disks for eigenvalues. Zbl 0148.01703
Todd, John
1965
The problem of error in digital computation. Zbl 0171.12802
Todd, John
1965
Introduction to the constructive theory of functions. Zbl 0114.26903
Todd, John
1963
Survey of numerical analysis. Zbl 0101.33601
1962
Computational problems concerning the Hilbert matrix. Zbl 0096.32304
Todd, John
1961
The radius of univalence of Bessel functions. Zbl 0091.06203
Kreyszig, Erwin; Todd, John
1960
The radius of univalence of the error function. Zbl 0086.06203
Kreyszig, Erwin; Todd, John
1959
On the radius of univalence of the function $$\exp z^2 \int\limits_0^z \exp (-t^2)dt$$. Zbl 0085.06601
Kreyszig, Erwin; Todd, John
1959
The evaluation of matrix inversion programs. Zbl 0085.34305
Newman, Morris; Todd, John
1958
The condition of certain matrices. III. Zbl 0093.13301
Todd, John
1958
A direct approach to the problem of stability in the numerical solution of partial differential equations. Zbl 0070.35107
Todd, John
1956
Commuting bilinear transformations and matrices. Zbl 0073.00804
Taussky, O.; Todd, John
1956
Discrete analogs of inequalities of Wirtinger. Zbl 0064.29803
Fan, Ky; Taussky, Olga; Todd, John
1955
Motivation for working in numerical analysis. Zbl 0064.37402
Todd, John
1955
A determinantal inequality. Zbl 0064.01401
Fan, Ky; Todd, John
1955
Experiments in the computation of conformal maps. Zbl 0067.35901
1955
The condition of the finite segments of the Hilbert matrix. Zbl 0058.01003
Todd, John
1954
Evaluation of the exponential integral for large complex arguments. Zbl 0055.36002
Todd, John
1954
The condition of certain matrices. II. Zbl 0055.35502
Todd, John
1954
Experiments on the inversion of a $$16\times 16$$ matrix. Zbl 0052.35001
Todd, John
1953
Systems of equations, matrices and determinants. I, II. Zbl 0048.24906
Taussky, Olga; Todd, John
1952
The condition of a certain matrix. Zbl 0034.37601
Todd, John
1950
On the relative extrema of the Laguerre orthogonal functions. Zbl 0039.07601
Todd, John
1950
Covering theorems for groups. Zbl 0035.29505
Taussky, Olga; Todd, John
1949
A problem on arc tangent relations. Zbl 0036.16101
Todd, John
1949
The condition of certain matrices. I. Zbl 0034.37602
Todd, John
1949
The density of reducible integers. Zbl 0039.03603
Chowla, S. D.; Todd, John
1949
Infinite powers of matrices. Zbl 0028.20103
Taussky, Olga; Todd, John
1942
Matrices of finite period. Zbl 0061.01305
Taussky, Olga; Todd, John
1941
Inversion in groups. JFM 67.0977.01
Taussky, O.; Todd, J.
1941
Matrices with finite period. Zbl 0061.01304
Taussky, Olga; Todd, John
1940
A characterisation of algebraic numbers. JFM 66.1210.03
Taussky, O.; Todd, J.
1940
all top 5
### Cited by 354 Authors
9 Baricz, Árpád 8 Monte Carmelo, Emerson L. 7 Schiefermayr, Klaus 6 Todd, John 5 Agarwal, Ravi P. 5 Aktaş, İbrahim 5 Blagouchine, Iaroslav V. 5 da Fonseca, Carlos Martins 5 Orhan, Halit 5 Szasz, Robert Zoltan 5 Varga, Richard Steven 4 Peherstorfer, Franz 4 Toklu, Evrim 3 Bresquar, Anna Maria 3 Deniz, Erhan 3 Gustafson, Sven-Åke 3 Kilic, Emrah 3 Martelli, Mario 3 Medley, H. I. 3 Nakaoka, Irene N. 3 Pang, Peter Y. H. 3 Pesenson, Isaac Zalmanovich 3 Rashidinia, Jalil 3 Schultz, Martin H. 3 Taussky-Todd, Olga 3 Uhlig, Frank 3 Zielke, Gerhard 2 Aziz, Tariq 2 Brezinski, Claude 2 Busenberg, Stavros N. 2 Campbell, John Maxwell 2 Carlson, Bille Chandler 2 Castoldi, André Guerino 2 Chu, Wenchang 2 Coffey, Mark William 2 Crouzet, Jean-François 2 Gautschi, Walter 2 Hadeler, Karl-Peter 2 Herbold, R. J. 2 Kovačec, Alexander 2 Leng, Tuo 2 Mancino, Otello Giacomo 2 Mohammadi, Reza 2 Oste, Roy 2 Pachpatte, Baburao Govindrao 2 Rack, Heinz-Joachim 2 Rakotch, E. 2 Senechal, Marjorie Wikler 2 Starke, Gerhard 2 Van der Jeugt, Joris 2 van Diejen, Jan Felipe 2 Wilf, Herbert S. 2 Yagmur, Nihat 2 Yamamoto, Tetsuro 1 Agarwal, Hans 1 Aharoni, Ron 1 Ahlbrandt, Calvin D. 1 Alaylioglu, Ayse 1 Allgower, Eugene L. 1 Alzer, Horst 1 Amdeberhan, Tewodros 1 Angel, Edward S. 1 Arıkan, Talha 1 Avgustinovich, Sergeĭ Vladimirovich 1 Axelsson, Axel Owe Holger 1 Bailey, David Harold 1 Barnhill, Robert E. 1 Bedratyuk, Leonid 1 Belforte, Gustavo 1 Benson, Donald Charles 1 Berndt, Bruce Carl 1 Bevilacqua, Roberto 1 Block, Henry David 1 Bogatyrev, Andrei Borisovich 1 Bohra, Nisha 1 Boros, Tibor 1 Borwein, Peter Benjamin 1 Bozzo, Enrico 1 Braess, Dietrich 1 Brazier, P. H. 1 Bridges, Douglas Suth 1 Brown, Richard Clark 1 Bullynck, Maarten 1 Bulut, Fatih 1 Bürgisser, Balz 1 Capovani, Milvio 1 Carlson, David Hilding 1 Carmelo, Emerson L. do Monte 1 Carta, David G. 1 Chang, Jeongwook 1 Chang, Xiangke 1 Charmonman, S. 1 Chatterjee, Tapas 1 Chen, Weiyu 1 Cheng, Sui Sun 1 Choi, Junesang 1 Chung, Jaeyoung 1 Constantin, Julien 1 Cooke, Charlie C. 1 Cooper, Charles J. ...and 254 more Authors
all top 5
### Cited in 117 Serials
22 Numerische Mathematik 17 Linear Algebra and its Applications 16 Mathematics of Computation 14 Journal of Mathematical Analysis and Applications 11 Proceedings of the American Mathematical Society 10 Journal of Computational and Applied Mathematics 7 Calcolo 7 Aequationes Mathematicae 6 Linear and Multilinear Algebra 6 Journal of Number Theory 6 Bulletin of the American Mathematical Society 5 Applied Mathematics and Computation 5 Computing 5 Journal of Approximation Theory 5 Journal of Combinatorial Theory. Series A 5 Monatshefte für Mathematik 5 Numerical Algorithms 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Optimization Theory and Applications 4 Rendiconti del Seminario Matematico della Università di Padova 4 Constructive Approximation 4 The Ramanujan Journal 4 Computational Methods and Function Theory 3 The Mathematical Intelligencer 3 Archiv der Mathematik 3 Acta Mathematica Hungarica 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Turkish Journal of Mathematics 3 Integral Transforms and Special Functions 3 BIT. Nordisk Tidskrift for Informationsbehandling 2 Applicable Analysis 2 Computers & Mathematics with Applications 2 Israel Journal of Mathematics 2 Journal of Computational Physics 2 Mathematical Biosciences 2 Rocky Mountain Journal of Mathematics 2 Fuzzy Sets and Systems 2 Journal of Soviet Mathematics 2 Numerical Functional Analysis and Optimization 2 Results in Mathematics 2 Transactions of the American Mathematical Society 2 Applied Mathematics Letters 2 International Journal of Computer Mathematics 2 Hacettepe Journal of Mathematics and Statistics 2 Complex Variables and Elliptic Equations 2 Special Matrices 1 American Mathematical Monthly 1 Archive for History of Exact Sciences 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Mathematical Notes 1 Periodica Mathematica Hungarica 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 1 Compositio Mathematica 1 Integral Equations and Operator Theory 1 Journal of Differential Equations 1 Journal of Econometrics 1 Journal of Geometry 1 Journal of the Korean Mathematical Society 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Mathematika 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 SIAM Journal on Numerical Analysis 1 Theoretical Computer Science 1 European Journal of Combinatorics 1 Advances in Applied Mathematics 1 Bulletin of the Korean Mathematical Society 1 Operations Research Letters 1 Applied Numerical Mathematics 1 Discrete & Computational Geometry 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 Dynamics and Stability of Systems 1 SIAM Journal on Matrix Analysis and Applications 1 Historia Mathematica 1 Bulletin of the American Mathematical Society. New Series 1 Computational Statistics and Data Analysis 1 Computers and Mathematics with Applications. Part B 1 Journal of Mathematical Imaging and Vision 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 The Electronic Journal of Combinatorics 1 Journal of Difference Equations and Applications 1 Sbornik: Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 Journal of Mathematical Chemistry 1 Mathematical Communications 1 Journal of Inequalities and Applications 1 Annales Henri Poincaré ...and 17 more Serials
all top 5
### Cited in 45 Fields
73 Numerical analysis (65-XX) 44 Special functions (33-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 31 Functions of a complex variable (30-XX) 26 Number theory (11-XX) 26 Real functions (26-XX) 26 Approximations and expansions (41-XX) 19 Information and communication theory, circuits (94-XX) 15 History and biography (01-XX) 14 Combinatorics (05-XX) 13 Operator theory (47-XX) 12 Partial differential equations (35-XX) 12 Difference and functional equations (39-XX) 11 Ordinary differential equations (34-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 7 Mechanics of deformable solids (74-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 5 Operations research, mathematical programming (90-XX) 4 Commutative algebra (13-XX) 4 Functional analysis (46-XX) 4 Computer science (68-XX) 4 Quantum theory (81-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 3 Group theory and generalizations (20-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Geometry (51-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Biology and other natural sciences (92-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-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.
| 2022-05-22T04:06:03 |
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|
https://indico.fnal.gov/event/15949/contributions/34682/
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Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
36th Annual International Symposium on Lattice Field Theory
22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone
Complex Langevin for Lattice QCD
Jul 23, 2018, 2:00 PM
20m
Centennial (Kellogg Hotel and Conference Center)
Centennial
Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Nonzero Temperature and Density
Speaker
Donald Sinclair (Argonne National Laboratory)
Description
We are applying complex-Langevin simulations to lattice QCD at finite quark-number chemical potential $\mu$ and zero temperature. While we observe some improvement as we move to weaker coupling we only find agreement with the expected physics at very small and at large $\mu$. It has been observed by others that at least part of the problem is that at small and even zero $\mu$ the gauge fields show large departures from the $SU(3)$ manifold. We are therefore quantifying how these departures depend on the size of the gauge coupling and the quark mass. It appears that these departures decrease as we move to weaker couplings and to smaller quark masses. One might ask whether this means that the complex Langevin will produce correct results in the continuum limit. We are also extending our simulations to finite $\mu$ and temperature where it is believed that the complex Langevin should be better behaved.
Primary authors
Donald Sinclair (Argonne National Laboratory) Dr J. B. Kogut (DOE/University of Maryland)
Slides
| 2021-10-24T02:14:17 |
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|
https://zbmath.org/authors/?q=ai%3Awaki.katsushi
|
# zbMATH — the first resource for mathematics
## Waki, Katsushi
Compute Distance To:
Author ID: waki.katsushi Published as: Waki, K.; Waki, Katsushi External Links: MGP · Wikidata
Documents Indexed: 25 Publications since 1993
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#### Co-Authors
9 single-authored 5 Koshitani, Shigeo 4 Kunugi, Naoko 3 Sakiyama, Hiroshi 2 Michler, Gerhard O. 2 Okuyama, Tetsuro 1 Ahara, Kazushi 1 Harada, Masaaki 1 Kratzer, Mathias 1 Lempken, Wolfgang 1 Ozeki, Michio 1 Tsuchihashi, Takuma 1 Weller, Michael
all top 5
#### Serials
7 Journal of Algebra 4 Communications in Algebra 2 Journal of Pure and Applied Algebra 2 Journal of Mathematical Chemistry 1 The Science Reports of the Hirosaki University 1 Bulletin of Yamagata University. Natural Science 1 Analele Ştiinţifice ale Universităţii “Ovidius” Constanţa. Seria: Matematică 1 Journal of Group Theory 1 RIMS Kokyuroku 1 Journal of Algebra and its Applications 1 Advances in Mathematics of Communications 1 RIMS Kôkyûroku Bessatsu 1 Journal of Math-for-Industry 1 Iranian Journal of Mathematical Chemistry
all top 5
#### Fields
21 Group theory and generalizations (20-XX) 3 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Computer science (68-XX)
#### Citations contained in zbMATH Open
14 Publications have been cited 94 times in 61 Documents Cited by Year
Decomposition numbers of $$\text{Sp}(4,q)$$. Zbl 0891.20009
Okuyama, Tetsuro; Waki, Katsushi
1998
Decomposition numbers of $$\text{SU}(3,q^2)$$. Zbl 1023.20005
Okuyama, Tetsuro; Waki, Katsushi
2002
Broué’s Abelian defect group conjecture for the Held group and the sporadic Suzuki group. Zbl 1065.20021
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2004
Broué’s conjecture for non-principal 3-blocks of finite groups. Zbl 1013.20009
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2002
The Loewy structure of the projective indecomposable modules for the Mathieu groups in characteristic 3. Zbl 0797.20014
Waki, Katsushi
1993
A note on decomposition numbers of $$G_2(2^n)$$. Zbl 1057.20009
Waki, Katsushi
2004
Broué’s Abelian defect group conjecture holds for the Janko simple group $$J_4$$. Zbl 1148.20008
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2008
The projective indecomposable modules for the Higman-Sims group in characteristic 3. Zbl 0791.20011
Waki, Katsushi
1993
The Green correspondents of the Mathieu group $$M_{12}$$ in characteristic $$3$$. Zbl 0924.20002
Koshitani, Shigeo; Waki, Katsushi
1999
On Loewy structure of the projective modules of the Mathieu group $$M_{12}$$ and its automorphism group in characteristic $$3$$. Zbl 0924.20001
Koshitani, Shigeo; Waki, Katsushi
1999
Enumeration of conformers for octahedral $$[\mathrm{MX(AB)}_{5}]$$ and $$[\mathrm{MX(ABC)}_{5}]$$ complexes on the basis of computational group theory. Zbl 1370.92181
Sakiyama, Hiroshi; Waki, Katsushi
2017
Decomposition numbers of non-principal blocks of $$J_4$$ for characteristic 3. Zbl 1172.20013
Waki, Katsushi
2009
GAP program for uniform constructions of some finite simple groups. Zbl 1173.20306
Waki, Katsushi
2007
A note on the decomposition numbers of $$\text{Sp}(4,q)$$. Zbl 0867.20015
Waki, Katsushi
1996
Enumeration of conformers for octahedral $$[\mathrm{MX(AB)}_{5}]$$ and $$[\mathrm{MX(ABC)}_{5}]$$ complexes on the basis of computational group theory. Zbl 1370.92181
Sakiyama, Hiroshi; Waki, Katsushi
2017
Decomposition numbers of non-principal blocks of $$J_4$$ for characteristic 3. Zbl 1172.20013
Waki, Katsushi
2009
Broué’s Abelian defect group conjecture holds for the Janko simple group $$J_4$$. Zbl 1148.20008
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2008
GAP program for uniform constructions of some finite simple groups. Zbl 1173.20306
Waki, Katsushi
2007
Broué’s Abelian defect group conjecture for the Held group and the sporadic Suzuki group. Zbl 1065.20021
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2004
A note on decomposition numbers of $$G_2(2^n)$$. Zbl 1057.20009
Waki, Katsushi
2004
Decomposition numbers of $$\text{SU}(3,q^2)$$. Zbl 1023.20005
Okuyama, Tetsuro; Waki, Katsushi
2002
Broué’s conjecture for non-principal 3-blocks of finite groups. Zbl 1013.20009
Koshitani, Shigeo; Kunugi, Naoko; Waki, Katsushi
2002
The Green correspondents of the Mathieu group $$M_{12}$$ in characteristic $$3$$. Zbl 0924.20002
Koshitani, Shigeo; Waki, Katsushi
1999
On Loewy structure of the projective modules of the Mathieu group $$M_{12}$$ and its automorphism group in characteristic $$3$$. Zbl 0924.20001
Koshitani, Shigeo; Waki, Katsushi
1999
Decomposition numbers of $$\text{Sp}(4,q)$$. Zbl 0891.20009
Okuyama, Tetsuro; Waki, Katsushi
1998
A note on the decomposition numbers of $$\text{Sp}(4,q)$$. Zbl 0867.20015
Waki, Katsushi
1996
The Loewy structure of the projective indecomposable modules for the Mathieu groups in characteristic 3. Zbl 0797.20014
Waki, Katsushi
1993
The projective indecomposable modules for the Higman-Sims group in characteristic 3. Zbl 0791.20011
Waki, Katsushi
1993
all top 5
#### Cited by 49 Authors
17 Koshitani, Shigeo 12 Waki, Katsushi 8 Himstedt, Frank 7 Kunugi, Naoko 5 Hiss, Gerhard 4 Dudas, Olivier 4 Müller, Jürgen 4 Noeske, Felix 3 Lassueur, Caroline 2 Craven, David A. 2 Huang, Shih-Chang 2 Kessar, Radha 2 Malle, Gunter 2 Miyachi, Hyohe 2 Okuyama, Tetsuro 2 Schaeffer Fry, Amanda A. 2 Tiep Pham Huu 1 An, Jianbei 1 Ben Souf, M. A. 1 Bleher, Frauke M. 1 Bouchoucha, Faker 1 Brough, Julian M. A. 1 Brunat, Olivier 1 Danz, Susanne 1 Dessombz, Olivier 1 Di Martino, Lino 1 Geck, Meinolf 1 Guralnick, Robert Michael 1 Haddar, Mohamed Amine 1 Ichchou, Mohamed Najib 1 Kimmerle, Wolfgang 1 Külshammer, Burkhard 1 Le, Tung 1 Linckelmann, Markus 1 Magaard, Kay 1 Mazza, Nadia Paola 1 Mitsuhashi, Naofumi 1 Paolini, Alessandro 1 Rouquier, Raphaël 1 Sakiyama, Hiroshi 1 Sakurai, Taro 1 Sambale, Benjamin 1 Sin, Peter K. W. 1 Szczepański, Andrzej 1 Taylor, Jay 1 Wada, Tomoyuki 1 White, Donald L. 1 Yoshii, Yutaka 1 Zalesski, Alexandre Efimovich
all top 5
#### Cited in 19 Serials
29 Journal of Algebra 6 Communications in Algebra 5 Journal of Pure and Applied Algebra 4 LMS Journal of Computation and Mathematics 2 Advances in Mathematics 2 Annals of Mathematics. Second Series 1 Computer Methods in Applied Mechanics and Engineering 1 Rocky Mountain Journal of Mathematics 1 Archiv der Mathematik 1 Mathematische Zeitschrift 1 Nagoya Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 International Journal of Algebra and Computation 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Indagationes Mathematicae. New Series 1 Journal of Mathematical Chemistry 1 Journal of Group Theory 1 Algebras and Representation Theory 1 Journal of Algebra and its Applications
all top 5
#### Cited in 12 Fields
59 Group theory and generalizations (20-XX) 4 Associative rings and algebras (16-XX) 2 $$K$$-theory (19-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-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.
| 2021-05-06T19:02:33 |
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https://www.anl.gov/article/argonne-achates-power-and-delphi-automotive-to-investigate-new-approach-to-engines
|
# Argonne National Laboratory
Press Release | Argonne National Laboratory
# Argonne, Achates Power and Delphi Automotive to investigate new approach to engines
The U.S. Department of Energy’s (DOE’s) Argonne National Laboratory is working with Achates Power, Inc., and Delphi Automotive to develop an innovative new engine that could yield efficiency gains of up to 50 percent over a comparable conventional engine.
The research is being conducted under a three-year project funded by a $9 million award from DOE’s Advanced Research Projects Agency-Energy (ARPA-E) and an additional$4 million of cost share from the team members.
The new engine combines two promising technologies — gasoline compression ignition and opposed pistons — to create a super engine” that could fundamentally change the way internal combustion engines work in the light-duty transportation market.
Conventional spark-ignited engines have improved so dramatically over the past few decades that there is little room to make big efficiency gains,” said Steve Ciatti, who will be the experimental lead for Argonne. You need a game-changer to get into large double-digit efficiency gains, and we believe this engine is capable of doing that.”
The new engine will meld the best characteristics of gasoline and compression ignition engines with an innovative piston architecture refined by Achates Power that sets two pistons moving in opposition in one cylinder. As the crowns of the pistons slide toward each other, they compress a mixture of air and gasoline to such extreme pressures that the mixture auto-ignites without the need for spark plugs in a process known as compression ignition.
As the pistons reverse course and slide to opposite ends of the cylinder, ports machined into the cylinder allow exhaust gases to escape while fresh air is taken in, then the pistons move together again to compress and ignite in a two-stroke cycle. The design eliminates cylinder heads — which are a major cause of heat loss and inefficiency in conventional engines — and allows the engine to run with diesel-like efficiency and power, while maintaining gasoline’s emissions benefits.
An analysis by Achates Power indicates the new engine will yield fuel efficiency gains of more than 50 percent compared with a downsized, turbo-charged, direct-injection gasoline engine, while reducing the overall cost of the powertrain system.
The new engine combines two promising technologies to create a super engine” that could fundamentally change the way internal combustion engines work.
Creating such a novel engine will require the expertise of all the team members, who bring together decades of experience in various aspects of engine design and production.
The dynamics of this team are really perfect to make this project work,” said Doug Longman, who will be the project manager for Argonne. Combining Argonne’s scientific and engineering experience with Achates Power’s engine architecture and Delphi’s expertise in fuel injection and gasoline direct-injection compression ignition will give us the tools to develop an engine we think is going to show very large efficiency gains.”
Another key to the success of the project will be the modeling and simulation of the complex fluid dynamics and combustion inside the engine, which will be conducted through Argonne’s Virtual Engine Research Institute and Fuels Initiative (VERIFI). By using high-performance computing to model and predict the movement of fuel and air in the cylinders, the VERIFI team will be able to optimize the design of the engine and fuel injectors using computing rather than prototyping, which will enable accelerated development.
Modeling and simulation have become ever more important to engine designers in recent years,” said Sibendu Som, Argonne’s computational lead for the project. Using VERIFI to optimize combustion technologies for industry has significantly shortened development times and helped lead to more efficient engines.”
Shorter development time through computational modeling and efficiency gains developed through experimental research will be critical to the creation of an engine that can be widely adopted commercially. Many engines have been proposed over the years that show benefits over conventional spark-ignited gasoline engines, but the efficiency gains have not been dramatic enough to convince auto manufacturers to retool production lines and car designs to incorporate the new approaches. This novel research team is poised to break that barrier and create an engine that could transform the automotive market.
Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’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 the Office of Science website.
| 2023-02-08T10:58:27 |
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|
http://dlmf.nist.gov/30.6
|
§30.6 Functions of Complex Argument
The solutions
30.6.1 $\mathop{\mathit{Ps}^{m}_{n}\/}\nolimits\!\left(z,\gamma^{2}\right),$ $\mathop{\mathit{Qs}^{m}_{n}\/}\nolimits\!\left(z,\gamma^{2}\right),$
of (30.2.1) with $\mu=m$ and $\lambda=\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)$ are real when $z\in(1,\infty)$, and their principal values (§4.2(i)) are obtained by analytic continuation to $\Complex\setminus(-\infty,1]$.
¶ Relations to Associated Legendre Functions
30.6.2 $\displaystyle\mathop{\mathit{Ps}^{m}_{n}\/}\nolimits\!\left(z,0\right)$ $\displaystyle=\mathop{P^{m}_{n}\/}\nolimits\!\left(z\right),$ $\displaystyle\mathop{\mathit{Qs}^{m}_{n}\/}\nolimits\!\left(z,0\right)$ $\displaystyle=\mathop{Q^{m}_{n}\/}\nolimits\!\left(z\right);$
compare §14.3(ii).
¶ Wronskian
30.6.3 $\mathop{\mathscr{W}\/}\nolimits\left\{\mathop{\mathit{Ps}^{m}_{n}\/}\nolimits% \!\left(z,\gamma^{2}\right),\mathop{\mathit{Qs}^{m}_{n}\/}\nolimits\!\left(z,% \gamma^{2}\right)\right\}=\frac{(-1)^{m}(n+m)!}{(1-z^{2})(n-m)!}A_{n}^{m}(% \gamma^{2})A_{n}^{-m}(\gamma^{2}),$
with $A_{n}^{\pm m}(\gamma^{2})$ as in (30.11.4).
¶ Values on $(-1,1)$
30.6.4 $\displaystyle\mathop{\mathit{Ps}^{m}_{n}\/}\nolimits\!\left(x\pm i0,\gamma^{2}\right)$ $\displaystyle=(\mp i)^{m}\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits\!\left(x,% \gamma^{2}\right),$ 30.6.5 $\displaystyle\mathop{\mathit{Qs}^{m}_{n}\/}\nolimits\!\left(x\pm i0,\gamma^{2}\right)$ $\displaystyle={(\mp i)^{m}\left(\mathop{\mathsf{Qs}^{m}_{n}\/}\nolimits\!\left% (x,\gamma^{2}\right)\mp\tfrac{1}{2}i\pi\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits% \!\left(x,\gamma^{2}\right)\right)}.$
For further properties see Arscott (1964b).
For results for Equation (30.2.1) with complex parameters see Meixner and Schäfke (1954).
| 2014-07-22T18:52:49 |
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https://par.nsf.gov/biblio/10294252-radio-afterglows-from-compact-binary-coalescences-prospects-next-generation-telescopes
|
Radio afterglows from compact binary coalescences: prospects for next-generation telescopes
ABSTRACT The detection of gravitational waves from a neutron star merger, GW170817, marked the dawn of a new era in time-domain astronomy. Monitoring of the radio emission produced by the merger, including high-resolution radio imaging, enabled measurements of merger properties including the energetics and inclination angle. In this work, we compare the capabilities of current and future gravitational wave facilities to the sensitivity of radio facilities to quantify the prospects for detecting the radio afterglows of gravitational wave events. We consider three observing strategies to identify future mergers – wide field follow-up, targeting galaxies within the merger localization and deep monitoring of known counterparts. We find that while planned radio facilities like the Square Kilometre Array will be capable of detecting mergers at gigaparsec distances, no facilities are sufficiently sensitive to detect mergers at the range of proposed third-generation gravitational wave detectors that would operate starting in the 2030s.
Authors:
; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10294252
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
505
Issue:
2
Page Range or eLocation-ID:
2647 to 2661
ISSN:
0035-8711
2. Abstract We discuss observational strategies to detect prompt bursts associated with gravitational wave (GW) events using the Australian Square Kilometre Array Pathfinder (ASKAP). Many theoretical models of binary neutron stars mergers predict that bright, prompt radio emission would accompany the merger. The detection of such prompt emission would greatly improve our knowledge of the physical conditions, environment, and location of the merger. However, searches for prompt emission are complicated by the relatively poor localisation for GW events, with the 90% credible region reaching hundreds or even thousands of square degrees. Operating in fly’s eye mode, the ASKAP field of view can reach $\sim1\,000$ deg $^2$ at $\sim$ $888\,{\rm MHz}$ . This potentially allows observers to cover most of the 90% credible region quickly enough to detect prompt emission. We use skymaps for GW170817 and GW190814 from LIGO/Virgo’s third observing run to simulate the probability of detecting prompt emission for GW events in the upcoming fourth observing run. With only alerts released after merger, we find it difficult to slew the telescope sufficiently quickly as to capture any prompt emission. However, with the addition of alerts released before merger by negative-latency pipelines, we find that it should be possible to searchmore »
| 2022-10-06T14:48:50 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S029MT
|
# Majoron Searches in Neutrinoless Double $\beta$ Decay INSPIRE search
Limits are for the half-life of neutrinoless ${{\mathit \beta}}{{\mathit \beta}}$ decay with a Majoron emission. No experiment currently claims any such evidence. Only the best or comparable limits for each isotope are reported. Also see the reviews ZUBER 1998 and FAESSLER 1998B.
${\mathrm {\mathit t_{1/2}}}$ ($10^{21}$ yr) CL$\%$ ISOTOPE METHOD DOCUMENT ID
$\bf{>7200}$ $\bf{90}$ $\bf{{}^{128}\mathrm {Te}}$ $\bf{\text{CNTR}}$ 1
1992
• • • We do not use the following data for averages, fits, limits, etc. • • •
$>420$ $90$ ${}^{76}\mathrm {Ge}$ $0$ $\text{GERDA}$ 2
2015 A
$>400$ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 3
2015
$>1200$ $90$ ${}^{136}\mathrm {Xe}$ $0$ $\text{EXO-200}$ 4
2014 A
$>2600$ $90$ ${}^{136}\mathrm {Xe}$ $0$ $\text{KamLAND-Zen}$ 5
2012
$>16$ $90$ ${}^{130}\mathrm {Te}$ $0$ $\text{NEMO-3}$ 6
2011
$>1.9$ $90$ ${}^{96}\mathrm {Zr}$ $2$ $\text{NEMO-3}$ 7
2010
$>1.52$ $90$ ${}^{150}\mathrm {Nd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 8
2009
$>27$ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 9
2006
$>15$ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 10
2006
$>14$ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 11
2004
$>12$ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{NEMO-3}$ 12
2004
$>2.2$ $90$ ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $\text{Cryog. det.}$ 13
2003
$>0.9$ $90$ ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ $\text{Cryog. det.}$ 14
2003
$>8$ $90$ ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ $CdWO_{4} \text{ scint.}$ 15
2003
$>0.8$ $90$ ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ $CdWO_{4} \text{ scint.}$ 16
2003
$>500$ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Liquid Xe Scint. 17
2002 D
$>5.8$ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ELEGANT V 18
2002
$>0.32$ $90$ ${}^{100}\mathrm {Mo}$ $0$ $\text{Liq. Ar ioniz.}$ 19
2001
$>0.0035$ $90$ ${}^{160}\mathrm {Gd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}\text{ SiO_}{5}:Ce$ 20
2001
$>0.013$ $90$ ${}^{160}\mathrm {Gd}$ 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}\text{ SiO_}{5}:Ce$ 21
2001
$>2.3$ $90$ ${}^{82}\mathrm {Se}$ $0$ $\text{NEMO 2}$ 22
2000
$>0.31$ $90$ ${}^{96}\mathrm {Zr}$ $0$ $\text{NEMO 2}$ 23
2000
$>0.63$ $90$ ${}^{82}\mathrm {Se}$ $0$ $\text{NEMO 2}$ 24
2000
$>0.063$ $90$ ${}^{96}\mathrm {Zr}$ $0$ $\text{NEMO 2}$ 24
2000
$>0.16$ $90$ ${}^{100}\mathrm {Mo}$ $0$ $\text{NEMO 2}$ 24
2000
$>2.4$ $90$ ${}^{82}\mathrm {Se}$ $0$ $\text{NEMO 2}$ 25
1998
$>7.2$ $90$ ${}^{136}\mathrm {Xe}$ 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ $\text{TPC}$ 26
1998
$>7.91$ $90$ ${}^{76}\mathrm {Ge}$ $\text{SPEC}$ 27
1996
$>17$ $90$ ${}^{76}\mathrm {Ge}$ $\text{CNTR}$
1993
1 BERNATOWICZ 1992 studied double-$\beta$ decays of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$, and found the ratio $\tau ({}^{130}\mathrm {Te})/\tau ({}^{128}\mathrm {Te}$) = ($3.52$ $\pm0.11$) $\times 10^{-4}$ in agreement with relatively stable theoretical predictions. The bound is based on the requirement that Majoron-emitting decay cannot be larger than the observed double-beta rate of ${}^{128}\mathrm {Te}$ of ($77$ $\pm4$) $\times 10^{23}$ year. We calculated 90$\%$ CL limit as ($7.7 - 1.28{\times }0.4=7.2){\times }10^{24}$.
2 AGOSTINI 2015A analyze a 20.3 kg yr of data set of the GERDA calorimeter to determine $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $3.4 - 8.7$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
3 ARNOLD 2015 use the NEMO-3 tracking calorimeter with 3.43 kg yr exposure to determine the limit on Majoron emission. The limit corresponds to $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $1.6 - 3.0$. The spread reflects different nuclear matrix elements. Supersedes ARNOLD 2006 .
4 ALBERT 2014A utilize 100 kg yr of exposure of the EXO-200 tracking calorimeter to place a limit on the $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $0.8 - 1.7$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
5 GANDO 2012 use the KamLAND-Zen detector to obtain the limit on the 0${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission. It implies that the coupling constant $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $0.8 - 1.6$ depending on the nuclear matrix elements used.
6 ARNOLD 2011 use the NEMO-3 detector to obtain the reported limit on Majoron emission. It implies that the coupling constant ${{\mathit g}}_{ {{\mathit \nu}} {{\mathit \chi}} }$ $<$ $0.6 - 1.6$ depending on the nuclear matrix element used. Supercedes ARNABOLDI 2003 .
7 ARGYRIADES 2010 use the NEMO-3 tracking detector and ${}^{96}\mathrm {Zr}$ to derive the reported limit. No limit for the Majoron electron coupling is given.
8 ARGYRIADES 2009 use ${}^{150}\mathrm {Nd}$ data taken with the NEMO-3 tracking detector. The reported limit corresponds to $\langle$ $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <$ $1.7 - 3.0$ using a range of nuclear matrix elements that include the effect of nuclear deformation.
9 ARNOLD 2006 use ${}^{100}\mathrm {Mo}$ data taken with the NEMO-3 tracking detector. The reported limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.4 - 1.8){\times }10^{-4}$ using a range of matrix element calculations. Superseded by ARNOLD 2015 .
10 NEMO-3 tracking calorimeter is used in ARNOLD 2006 . Reported half-life limit for ${}^{82}\mathrm {Se}$ corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.66 - 1.9){\times }10^{-4}$ using a range of matrix element calculations. Supersedes ARNOLD 2004 .
11 ARNOLD 2004 use the NEMO-3 tracking detector. The limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.5 - 0.9)10^{-4}$ using the matrix elements of SIMKOVIC 1999 , STOICA 2001 and CIVITARESE 2003 . Superseded by ARNOLD 2006 .
12 ARNOLD 2004 use the NEMO-3 tracking detector. The limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.7 - 1.6)10^{-4}$ using the matrix elements of SIMKOVIC 1999 , STOICA 2001 and CIVITARESE 2003 .
13 Supersedes ALESSANDRELLO 2000 . Array of TeO$_{2}$ crystals in high resolution cryogenic calorimeter. Some enriched in ${}^{130}\mathrm {Te}$. Derive $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ $17 - 33 \times 10^{-5}$ depending on matrix element.
14 Supersedes ALESSANDRELLO 2000 . Cryogenic calorimeter search.
15 Limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{116}\mathrm {Cd}$ using enriched CdWO$_{4}$ scintillators. $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <4.6 - 8.1 \times 10^{-5}$ depending on the matrix element. Supersedes DANEVICH 2000 .
16 Limit for the 0${{\mathit \nu}}2{{\mathit \chi}}$ decay of ${}^{116}\mathrm {Cd}$. Supersedes DANEVICH 2000 .
17 BERNABEI 2002D obtain limit for 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{136}\mathrm {Xe}$ using liquid Xe scintillation detector. They derive $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <2.0 - 3.0 \times 10^{-5}$ with several nuclear matrix elements.
18 Replaces TANAKA 1993 . FUSHIMI 2002 derive half-life limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ $~$decay by means of tracking calorimeter ELEGANT$~$V. Considering various matrix element calculations, a range of limits for the Majoron-neutrino coupling is given: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <(6.3 - 360){\times }10^{-5}$.
19 ASHITKOV 2001 result for 0 ${{\mathit \nu}}{{\mathit \chi}}$ of ${}^{100}\mathrm {Mo}$ is less stringent than ARNOLD 2000 .
20 DANEVICH 2001 obtain limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{160}\mathrm {Gd}$ using Gd$_{2}$SiO$_{5}$:Ce crystal scintillators.
21 DANEVICH 2001 obtain limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with 2 Majoron emission of ${}^{160}\mathrm {Gd}$.
22 ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission derived from tracking calorimeter NEMO$~$2. Using ${}^{82}\mathrm {Se}$ source: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <1.6 \times 10^{-4}$. Matrix element from GUENTHER 1996 .
23 Using ${}^{96}\mathrm {Zr}$ source: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <2.6 \times 10^{-4}$. Matrix element from ARNOLD 1999 .
24 ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with two Majoron emission derived from tracking calorimeter NEMO$~$2.
25 ARNOLD 1998 determine the limit for 0${{\mathit \nu}_{{\chi}}}$ decay with Majoron emission of ${}^{82}\mathrm {Se}$ using the NEMO-2 tracking detector. They derive $\langle \mathit g_{{{\mathit \nu}_{{\chi}}}}\rangle$ $<2.3 - 4.3 \times 10^{-4}$ with several nuclear matrix elements.
26 LUESCHER 1998 report a limit for the 0${{\mathit \nu}}$ decay with Majoron emission of ${}^{136}\mathrm {Xe}$ using ${}^{}\mathrm {Xe}$ TPC. This result is more stringent than BARABASH 1989 . Using the matrix elements of ENGEL 1988 , they obtain a limit on $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ of $2.0 \times 10^{-4}$.
27 See Table$~$1 in GUENTHER 1996 for limits on the Majoron coupling in different models.
References:
AGOSTINI 2015A
EPJ C75 416 Results on ${{\mathit \beta}}{{\mathit \beta}}$ Decay with Emission of Two Neutrinos or Majorons in ${}^{76}\mathrm {Ge}$ from GERDA Phase I
ARNOLD 2015
PR D92 072011 Results of the Search for Neutrinoless Double-${{\mathit \beta}}$ Decay in ${}^{100}\mathrm {Mo}$ with the NEMO-3 Experiment
ALBERT 2014A
PR D90 092004 Search for Majoron-Emitting Modes of Double-Beta Decay of ${}^{136}\mathrm {Xe}$ with EXO-200
GANDO 2012
PR C86 021601 Limits on Majoron-Emitting Double-${{\mathit \beta}}$ Decays of ${}^{136}\mathrm {Xe}$ in the KamLAND-Zen Experiment
ARNOLD 2011
PRL 107 062504 Measurement of the ${{\mathit \beta}}{{\mathit \beta}}$ Decay Half-Life of ${}^{130}\mathrm {Te}$ with the NEMO-3 Detector
NP A847 168 Measurement of the Two Neutrino Double $\beta$ Decay Half-Life of ${}^{96}\mathrm {Zr}$ with the NEMO-3 Detector
PR C80 032501 Measurement of the Double-${{\mathit \beta}}$ Decay Half-Life of ${}^{150}\mathrm {Nd}$ and Search for Neutrinoless Decay Modes with the NEMO-3 Detector
ARNOLD 2006
NP A765 483 Limits on Different Majoron Decay Modes of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ for Neutrinoless Double Beta Decays in the NEMO-3 Experiment
ARNOLD 2004
JETPL 80 377 Study of 2${{\mathit \beta}}$ Decay of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ using the NEMO3 Detector
ARNABOLDI 2003
PL B557 167 A Calorimetric Search on Double beta Decay of ${}^{130}\mathrm {Te}$
DANEVICH 2003
PR C68 035501 Search for 2$\beta$ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment
BERNABEI 2002D
PL B546 23 Investigation of $\beta \beta$ Decay Modes in ${}^{134}\mathrm {Xe}$ and ${}^{135}\mathrm {Xe}$
FUSHIMI 2002
PL B531 190 Limits on Majoron Emitting Neutrinoless Double-beta Decay of ${}^{100}\mathrm {Mo}$
ASHITKOV 2001
JETPL 74 529 Double beta Decay in ${}^{100}\mathrm {Mo}$
DANEVICH 2001
NP A694 375 Quest for Double $\beta$ Decay of ${}^{160}\mathrm {Gd}$ and ${}^{}\mathrm {Ce}$ Isotopes
ARNOLD 2000
NP A678 341 Limits on Different Majoron Decay Modes of ${}^{100}\mathrm {Mo}$, ${}^{116}\mathrm {Cd}$, ${}^{82}\mathrm {Se}$ and ${}^{96}\mathrm {Zr}$ for Neutrinoless Double $\beta$ Decay in the NEMO-2 Experiment
ARNOLD 1998
NP A636 209 Double beta Decay of ${}^{82}\mathrm {Se}$
LUESCHER 1998
PL B434 407 Search for $\beta$ $\beta$ Decay in ${}^{136}\mathrm {Xe}$: New Results from the Gotthard Experiment
GUENTHER 1996
PR D54 3641 Bounds on New Majoron Models from the Heidelberg-Moscow Experiment
BECK 1993
PRL 70 2853 Investigation of the Majoron Accompanied Double $\beta$ Decay Mode of ${}^{76}\mathrm {Ge}$
BERNATOWICZ 1992
PRL 69 2341 Neutrino Mass Limits from a Precise Determination of $\beta$ $\beta$ Decay Rates of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$
ZUBER 1998
PRPL 305 295 On the Physics of Massive Neutrinos
FAESSLER 1998B
JP G24 2139 Double $\beta$ Decay
| 2019-03-25T09:49:58 |
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|
https://par.nsf.gov/biblio/10200738-locally-decodable-codes-resource-bounded-channels
|
On Locally Decodable Codes in Resource Bounded Channels
Constructions of locally decodable codes (LDCs) have one of two undesirable properties: low rate or high locality (polynomial in the length of the message). In settings where the encoder/decoder have already exchanged cryptographic keys and the channel is a probabilistic polynomial time (PPT) algorithm, it is possible to circumvent these barriers and design LDCs with constant rate and small locality. However, the assumption that the encoder/decoder have exchanged cryptographic keys is often prohibitive. We thus consider the problem of designing explicit and efficient LDCs in settings where the channel is slightly more constrained than the encoder/decoder with respect to some resource e.g., space or (sequential) time. Given an explicit function f that the channel cannot compute, we show how the encoder can transmit a random secret key to the local decoder using f(⋅) and a random oracle 𝖧(⋅). We then bootstrap the private key LDC construction of Ostrovsky, Pandey and Sahai (ICALP, 2007), thereby answering an open question posed by Guruswami and Smith (FOCS 2010) of whether such bootstrapping techniques are applicable to LDCs in channel models weaker than just PPT algorithms. Specifically, in the random oracle model we show how to construct explicit constant rate LDCs with locality of more »
Authors:
; ;
Editors:
Award ID(s):
Publication Date:
NSF-PAR ID:
10200738
Journal Name:
Leibniz international proceedings in informatics
Volume:
163
Page Range or eLocation-ID:
16:1--16:23
ISSN:
1868-8969
2. We formally introduce, define, and construct {\em memory-hard puzzles}. Intuitively, for a difficulty parameter $t$, a cryptographic puzzle is memory-hard if any parallel random access machine (PRAM) algorithm with small'' cumulative memory complexity ($\ll t^2$) cannot solve the puzzle; moreover, such puzzles should be both easy'' to generate and be solvable by a sequential RAM algorithm running in time $t$. Our definitions and constructions of memory-hard puzzles are in the standard model, assuming the existence of indistinguishability obfuscation (\iO) and one-way functions (OWFs), and additionally assuming the existence of a {\em memory-hard language}. Intuitively, a language is memory-hard if it is undecidable by any PRAM algorithm with small'' cumulative memory complexity, while a sequential RAM algorithm running in time $t$ can decide the language. Our definitions and constructions of memory-hard objects are the first such definitions and constructions in the standard model without relying on idealized assumptions (such as random oracles). We give two applications which highlight the utility of memory-hard puzzles. For our first application, we give a construction of a (one-time) {\em memory-hard function} (MHF) in the standard model, using memory-hard puzzles and additionally assuming \iO and OWFs. For our second application, we show any cryptographic puzzle (\eg,more »
3. We construct locally decodable codes (LDCs) to correct insertion-deletion errors in the setting where the sender and receiver share a secret key or where the channel is resource-bounded. Our constructions rely on a so-called Hamming-to-InsDel'' compiler (Ostrovsky and Paskin-Cherniavsky, ITS '15 \& Block et al., FSTTCS '20), which compiles any locally decodable Hamming code into a locally decodable code resilient to insertion-deletion (InsDel) errors. While the compilers were designed for the classical coding setting, we show that the compilers still work in a secret key or resource-bounded setting. Applying our results to the private key Hamming LDC of Ostrovsky, Pandey, and Sahai (ICALP '07), we obtain a private key InsDel LDC with constant rate and polylogarithmic locality. Applying our results to the construction of Blocki, Kulkarni, and Zhou (ITC '20), we obtain similar results for resource-bounded channels; i.e., a channel where computation is constrained by resources such as space or time.
| 2022-12-06T04:43:57 |
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https://articles.jsime.org/1/5/Simulation-Framework-for-Asynchronous-Iterative-Methods
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Journal of Simulation Engineering, Volume 1 (2018). Article URL: https://articles.jsime.org/1/5
5
# Simulation Framework for Asynchronous Iterative Methods
Simulation Framework for Asynchronous Iterative Methods
Evan C. Coleman1,2
Erik Jensen2
Masha Sosonkina2
1 Naval Surface Warfare Center, Dahlgren Division, Dahlgren, VA, United States
2 Old Dominion University, Norfolk, VA, United States
# ACM Subject Categories
• Hardware~Fault tolerance
• Computing methodologies~Linear algebra algorithms
• Applied computing~Mathematics and statistics
# Keywords
• Asynchronous Iterative Methods
• Fault Tolerance
• Asynchronous Simulation
• Shared Memory
• Intel® Xeon Phi
# Abstract
As high-performance computing (HPC) platforms progress towards exascale, computational methods must be revamped to successfully leverage them. In particular, (1) asynchronous methods become of great importance because synchronization becomes prohibitively expensive and (2) resilience of computations must be achieved, e.g., using checkpointing selectively which may otherwise become prohibitively expensive due to the sheer scale of the computing environment. In this work, a simulation framework for asynchronous iterative methods is proposed and tested on HPC accelerator (shared-memory) architecture. The design proposed here offers a lightweight alternative to existing computational frameworks to allow for easy experimentation with various relaxation iterative techniques, solution updating schemes, and predicted performance. The simulation framework is implemented in MATLAB® using function handles, which offers a modular and easily extensible design. An example of a case study using the simulation framework is presented to examine the efficacy of different checkpointing schemes for asynchronous relaxation methods.
# Introduction
Asynchronous iterative methods are increasing in popularity recently due to their ability to be parallelized naturally on modern co-processors such as GPUs and Intel® Xeon Phi. Many examples of recent work using fine-grained parallel methods are available (see Anzt, Dongarra, & Quintana-Ortí, 2016, Anzt, 2012, Chow, Anzt, & Dongarra, 2015, Chow & Patel, 2015, Anzt, Chow, & Dongarra, 2015 and many others in Section 2). A specific area of interest is on techniques that utilize fixed point iteration, i.e., those techniques that solve equations of the form
$\begin{array}{c}x=G\left(x\right)\end{array}$
for some vector 𝑥 ∈ 𝐷 and some map 𝐺 : 𝐷 → 𝐷. These techniques are well suited for fine-grained computation and they can be executed either synchronously or asynchronously, which helps tolerate latency in high-performance computing (HPC) environments. Looking forward to the future of HPC, it is important to prioritize the develop of algorithms that are resilient to faults since on future platforms, the rate at which faults occur is expected to increase dramatically (Cappello et al., 2009; Cappello et al., 2014; Asanović et al., 2006; Geist & Lucas, 2009).
While many asynchronous methods are designed for shared memory architectures and asynchronous iterative methods have gained popularity for their efficient use of resources on shared memory accelerators in modern HPC environments (Venkatasubramanian & Vuduc, 2009), lately there has been some work done at improving the performance of asynchronous iterative methods in distributed memory environments. Such works include attempts to implement asynchronous iterative methods in MPI-3 using one sided remote memory access (Gerstenberger, Besta, & Hoefler, 2014) as well as efforts to reduce the cost of communication in these environments (Wolfson-Pou & Chow, 2016).
Developing algorithms that are resilient to faults is of paramount importance, and fine-grained parallel fixed point methods are no exception. In this paper, we propose a simulation framework that can help developing algorithms resilient to faults. These types of frameworks allow for experimentation that is not specific to any singular platform or hardware architectures and allows experiments to simulate performance on both current computing environments and look at how those results may continue to evolve along with the computer hardware. Hence, they enable the possibility to: (1) test and validate different fault-models (which are still emerging), (2) experiment with different checkpointing libraries/mechanisms, and (3) help in efficiently implementing asynchronous iterative methods. Additionally, it can be difficult to implement asynchronous iterative methods on a variety of architectures to observe performance behavior in different computing environments, and having a working simulation framework allows users to conduct extensive experiments without any major programming investment.
This study aims to develop a simulation framework that is focused on the performance of asynchronous iterative methods. The goal is to produce a lightweight computational framework capable of being used for various asynchronous iterative methods, with an emphasis on methods for solving linear systems, and simulating the performance of these methods on shared memory devices. The contributions of this work are
1. the development, testing, and validation of a modular simulation framework for asynchronous iterative methods that can be used in the creation of new and improved algorithms,
2. a process for the generation of time models from HPC implementation code, which may be used to initialize the framework,
3. a case study on how to use the framework in the development of fault tolerant algorithms, and
4. a comparison of several implementations of an asynchronous iterative relaxation method, used in the proposed framework.
The simulation framework developed here is capable of predicting performance on various HPC system configurations and to show the performance of an algorithm subject to resiliency or reproducibility requirements.
The rest of this paper is organized as follows. Section 2 provides a brief summary of related studies. Section 3 gives an overview of asynchronous iterative methods, while Section 4 describes the design and utilization of the simulation framework in modeling the behavior of these methods. Section 5 describes a process for collecting time data from HPC implementations and developing time models from the data for use in the simulation framework. A comparison of different implementations is given in Section 5.3, while framework validation is considered in Section 5.4. Section 6 gives background information related to the creation of efficient checkpointing routines and provides a series of numerical results. Section 7 provides conclusions.
# Related Work
Development of computational frameworks for the purposes of simulating performance has a long history in the literature. Examples of such frameworks include SimGrid (Casanova, 2001; Casanova, Legrand, & Quinson, 2008) that focuses on distributed experiments, GangSim (Dumitrescu & Foster, 2005) and GridSim (Buyya & Murshed, 2002) that focus on grid scheduling, and CloudSim (Calheiros, Ranjan, De Rose, & Buyya, 2009; Calheiros, Ranjan, Beloglazov, De Rose, & Buyya, 2011) that models performance of cloud computing environments. These environments focus on specific HPC implementation features, such as job scheduling and data movement, and on providing a view of how the systems themselves behave in HPC-like scenarios. On the other hand, the framework developed here is intended to simulate not only the HPC performance but also the algorithmic performance of a particular class of problems (e.g., iterative convergence to a linear system solution) under various system configurations (e.g., asynchronous thread behavior in shared-memory systems) and with various additional requirements (e.g., resiliency or reproducibility).
The class of problems that the framework proposed in this study addresses are stationary solvers, also referred to as relaxation methods. The focus is on the behavior of these methods in asynchronous computing environments. However, the framework also easily admits synchronous updates; the key is the fine-grained nature of the algorithm. Fine-grained parallel methods, specifically parallel fixed point methods, are an area of increased research activity due to their practical use on HPC environments. An initial exploration of fault tolerance for stationary iterative linear solvers (i.e., Jacobi) is given in (Anzt, Dongarra, & Quintana-Ortí, 2015) and expanded on (Anzt, Dongarra, & Quintana-Ortí, 2016). The general convergence of parallel fixed point methods has been explored extensively (Addou & Benahmed, 2005; Frommer & Szyld, 2000; Bertsekas & Tsitsiklis, 1989; Ortega & Rheinboldt, 2000; Baudet, 1978; Benahmed, 2007).
Examples of work examining the performance of asynchronous iterative methods include an in-depth analysis from the perspective of utilizing a system with a co-processor (Anzt, 2012; Avron, Druinsky, & Gupta, 2015), as well as performance analysis of asynchronous methods (Bethune, Bull, Dingle, & Higham, 2011; Bethune, Bull, Dingle, & Higham, 2014; Hook, & Dingle, 2018). In particular, both (Bethune, Bull, Dingle, & Higham, 2011) and (Bethune, Bull, Dingle, & Higham, 2014) focus on low level analysis of the asynchronous Jacobi method, similar to the example problem that is featured here. While many recent research results for asynchronous iterative methods are focused on implementations that utilize a shared memory architecture, one area of asynchronous iterative methods that has seen significant development using a distributed memory architecture is optimization (Cheung & Cole, 2016; Iutzeler, Bianchi, Ciblat, & Hachem, 2013; Hong, 2017; Zhong & Cassandras, 2010; Srivastava & Cassandras, 2011; Tsitsiklis, Bertsekas, & Athans, 1986; Boyd, Parikh, Chu, Peleato, & Eckstein, 2011).
The use case of the simulation framework that is featured in Section 6 shows the ability of the framework to be used in the development of fault tolerance techniques. The development of these techniques is important as HPC platforms continue to become both larger and more susceptible to faults. The expected increase in faults for future HPC systems is detailed in a variety of different sources. A high level article detailing the expected increase in failure rate from a reasonably non-technical point of view is available in the various versions of the "Monster in the Closet" talk and paper (Geist, 2011; Geist, 2012; Geist, 2016). More technical and detailed reports are given in a variety of sources composed of groups of different researchers from both academia and industry (Asanović et al., 2006; Cappello et al., 2009; Cappello et al., 2014; Snir et al., 2014; Geist & Lucas, 2009). Additionally, the Department of Energy has commissioned two very detailed reports about the progression towards exascale level computing; one from a general computing standpoint (Ashby et al., 2010), and a report aimed specifically at applied mathematics for exascale computing (Dongarra et al., 2014). Fault tolerance for fine-grained asynchronous iterative methods has been studied at a fundamental level (Gärtner, 1999; Coleman & Sosonkina, 2017), as well as made specific to certain algorithms (Coleman, Sosonkina, & Chow, 2017; Coleman, & Sosonkina, 2018; Anzt, Dongarra, & Quintana-Ortí, 2015; Anzt, Dongarra, & Quintana-Ortí, 2016). Fault tolerance for synchronous fixed point algorithms from a numerical analysis has been investigated in (Stoyanov & Webster, 2015). Error correction for GPU based oriented asynchronous methods were investigated in (Anzt, Luszczek, Dongarra, & Heuveline, 2012).
Several numerically based fault models similar to the one that is used in this study have been developed recently, and are used as a basis for the generalized fault simulation that is developed here. These include a "numerical" fault model that is predicated on shuffling the components of an important data structure (Elliott, Hoemmen, & Mueller, 2015), and a perturbation based model put forth in (Stoyanov & Webster, 2015) and (Coleman & Sosonkina, 2016b). Other models that are not based upon directly injecting a bit flip, such as inducing a small shift to a single component of a vector have been considered as well (Hoemmen & Heroux, 2011; Bridges, Ferreira, Heroux, & Hoemmen, 2012). Comparisons between various numerical soft fault models have been made in (Coleman & Sosonkina, 2016a; Coleman, Jamal, Baboulin, Khabou, & Sosonkina, 2018).
# Asynchronous Iterative Methods
In fine-grained parallel computation, each component of the problem (i.e., a matrix or vector entry) is updated in a manner that does not require information from the computations involving other components while the update is being made. This allows for each computing element (e.g., for a single processor, CUDA core, or Xeon Phi core) to act independently from all other computing elements. Depending on the size of both the problem and the computing environment, each computing element may be responsible for updating a single entry to update, or may be assigned a block that contains multiple components. The generalized mathematical model that is used throughout this paper comes from (Frommer & Szyld, 2000), which in turn comes from (Chazan & Miranker, 1969; Baudet, 1978; Szyld, 1998) among many others.
To keep the mathematical model as general as possible, consider a function, 𝐺 : 𝐷 → 𝐷, where 𝐷 is a domain that represents a product space 𝐷 = 𝐷1 × 𝐷2 × … × 𝐷2. The goal is to find a fixed point of the function 𝐺 inside of the domain 𝐷. To this end, a fixed point iteration is performed, such that
$\begin{array}{c}{x}^{k+1}=G\left({x}^{k}\right)\mathrm{\text{,}}\end{array}$
and a fixed point is declared if 𝑥𝑘+1 ≈ 𝑥𝑘. Note that the function 𝐺 has internal component functions 𝐺𝑖 for each sub-domain, 𝐷𝑖, in the product space, 𝐷. In particular, 𝐺𝑖 : 𝐷 → 𝐷𝑖, which gives that
$\begin{array}{rl}x& =\left({x}_{1},{x}_{2},\dots ,{x}_{m}\right)\in D\to \\ G\left(x\right)& =G\left({x}_{1},{x}_{2},\dots ,{x}_{m}\right)\\ & =\left({G}_{1}\left(x\right),{G}_{2}\left(x\right),\dots ,{G}_{m}\left(x\right)\right)\in D.\end{array}$
As a concrete example, let each 𝐷𝑖 = ℝ . Forming the product space of each of these 𝐷𝑖's gives that 𝐷 = ℝ𝑚 . This leads to the more formal functional mapping, 𝑓 : ℝ𝑚 → ℝ𝑚 . Additionally, let $f\left(\stackrel{\to }{x}\right)=2\stackrel{\to }{x}$ . In this case, each of the individual 𝑓𝑖 component functions is defined by $f\left(\stackrel{\to }{x}\right)=2{x}_{i}$ . Note that each component functions operates on all of the vector $\stackrel{\to }{x}$ even if the individual function definition does not require all of the components of $\stackrel{\to }{x}$ to perform its specific update.
The assumption is also made that there is some finite number of processing elements 𝑃1, 𝑃2, …, 𝑃𝑝 each of which is assigned to a block 𝐵 of components 𝐵1, 𝐵2, …, 𝐵𝑚 to update. Note that the number 𝑝 of processing elements will typically be significantly smaller than the number 𝑚 of blocks to update. With these assumptions, the computational model can be stated in Algorithm 1.
Algorithm 1 General computational model
1:for each processing element ${P}_{l}$ do
2:for $i=1,2,\dots$ until convergence do
3:Read $x$ from common memory
4:Compute ${x}_{j}^{i+1}={G}_{j}\left(x\right)$ for all $j\in {𝐵}_{l}$
5:Update ${x}_{j}$ in common memory with ${x}_{j}^{i+1}$ for all $j\in {𝐵}_{l}$
6:end for
7:end for
This computational model has each processing element read all pertinent data from global memory that is accessible by each of the processors, update the pieces of data specific to the component functions that it has been assigned, and update those components in the global memory. Note that the computational model presented in Algorithm 1 allows for either synchronous or asynchronous computation; it only prescribes that an update has to be made as an "atomic" operation (in line 5), i.e., without interleaving of its result. If each processing element 𝑃𝑙 is to wait for the other processors to finish each update, then the model describes a parallel synchronous form of computation. On the other hand, if no order is established for 𝑃𝑙s, then an asynchronous form of computation arises.
To continue formalizing this computational model a few more definitions are necessary. First, set a global iteration counter 𝑘 that increases every time any processor reads $\stackrel{\to }{x}$ from common memory. At the end of the work done by any individual processor, 𝑝, the components associated with the block 𝐵𝑝 will be updated. This results in a vector, $\stackrel{\to }{x}=\left({x}_{1}^{{s}_{1}\left(x\right)},{x}_{2}^{{s}_{2}\left(x\right)},\dots ,{x}_{m}^{{s}_{m}\left(x\right)}\right)$ where the function 𝑠𝑙(𝑘) indicates how many times an specific component has been updated. Finally, a set of individual components can be grouped into a set, 𝐼𝑘 , that contains all of the components that were updated on the 𝑘th iteration. Given these basic definitions, the three following conditions (along with the model presented in Algorithm 1) provide a working mathematical framework for fine-grained asynchronous computation.
Definition 1. If the following three conditions hold
1. ${s}_{i}\left(k\right)\le k-1$, i.e., only components that have finished computing are used in the current approximation.
2. ${\text{lim}}_{k\to \infty }{s}_{i}\left(k\right)=\infty$, i.e., the newest updates for each component are used.
3. $\left|k\in ℕ:i\in {I}^{k}\right|=\infty$, i.e., all components will continue to be updated.
Then given an initial ${\stackrel{\to }{x}}^{0}\in D$ , the iterative update process defined by
${x}_{i}^{k}=\left\{\begin{array}{cc}{x}_{i}^{k-1}& i\notin {I}_{k}\\ {G}_{i}\left(\stackrel{\to }{x}\right)& i\in {I}_{k}\end{array}$
where the function ${G}_{i}\left(\stackrel{\to }{x}\right)$ uses the latest updates available is called an asynchronous iteration.
This basic computational model (i.e., the combination of Algorithm 1 and Definition 1 together) allows for many different results on fine-grained iterative methods that are both synchronous and asynchronous, though the three conditions given in Definition 1 are unnecessary in the synchronous case.
# Asynchronous Relaxation Methods
Relaxation methods have been the focus of many of the works mentioned in Section 2 such as (Chazan & Miranker, 1969) and (Baudet, 1978); a much more detailed description can be found in (Bertsekas & Tsitsiklis, 1989) among many other sources. This section provides an introduction that will serve as a reference for the later work in this study.
Relaxation methods can be expressed as general fixed point iterations of the form
$\begin{array}{}\text{(1)}& {x}^{k+1}=C{x}^{k}+d,\end{array}$
where 𝐶 is the 𝑛 × 𝑛 iteration matrix, 𝑥 is an 𝑥-dimensional vector that represents the solution, and 𝑑 is another 𝑥-dimensional vector that can be used to help define the particular problem at hand.
The Jacobi method is an asynchronous relaxation method built for solving linear systems of the form
$\begin{array}{c}Ax=b\end{array}$
and following the methodology put forth in (Bertsekas & Tsitsiklis, 1989), this can be broken down to view a specific row — say the 𝑖th — of the matrix 𝐴,
$\begin{array}{c}\sum _{j=1}^{n}{a}_{ij}{x}_{j}={b}_{i}\end{array}$
and this equation can be solved for the 𝑖th component of the solution, 𝑥𝑖, to give,
$\begin{array}{}\text{(2)}& \hfill {x}_{i}=\frac{-1}{{a}_{ii}}\left[{\sum }_{j\ne i}{a}_{ij}{x}_{j}-{b}_{i}\right]\mathrm{\text{.}}\hfill \end{array}$
This equation can then be computed in an iterative manner in order to give successive updates to the solution vector. In synchronous computing environments, each update to an element of the solution vector, 𝑥𝑖 is computed sequentially using the same data for the other components of the solution vector (i.e., the 𝑥𝑗, in Equation (2). Conversely, in an asynchronous computing environment, each update to an element of the solution vector occurs when the computing element responsible for updating that component is ready to write the update to memory and the other components used are simply the latest ones available to the computing element.
Expressing Equation (2) in a block matrix form more similar to the original form of the iteration expressed in Equation (1),
$\begin{array}{rl}x& =-{D}^{-1}\left(\left(L+U\right)x-b\right)\\ x& =-{D}^{-1}\left(L+U\right)x+{D}^{-1}b.\end{array}$
where 𝐷 is the diagonal portion of 𝐴, and 𝐿 and 𝑈 are the strictly lower and upper triangular portions of 𝐴 respectively. This gives an iteration matrix of 𝐶 = -𝐷−1(𝐿 + 𝑈) .
Convergence of asynchronous fixed point methods of the form presented in Equation (1) is determined by the spectral radius of the iteration matrix, 𝐶, and dates back to the pioneering work done by both (Chazan & Miranker, 1969) and (Baudet, 1978):
Theorem 1. For a fixed point iteration of the form given in Equation (1) that adheres to the asynchronous computational model provided by Algorithm 1 and Definition 1, if the spectral radius of 𝐶, ρ(|𝐶|), is less than one, then the iterative method will converge to the fixed point solution.
As noted in (Wolfson-Pou & Chow, 2016), the iteration matrix 𝐶 that is used in the Jacobi relaxation method serves as a worst case for relaxation methods of the form discussed here. However, because of the ubiquitous use of the Jacobi method in parallel solutions of large problems in many different domains in science and engineering we use the Asynchronous (Block) Jacobi method predominantly throughout the remainder of this study. Note that many of the concepts and ideas expressed in this paper can be easily adapted to more complex algorithms.
# Design of Simulation Framework
The simulation framework proposed here is designed to simulate the performance of an asynchronous iterative method operating on multiple computing elements using a single processing element. In this simulation framework, the emphasis is on fixed-point iterations1
$\begin{array}{c}\stackrel{\to }{x}=G\left(\stackrel{\to }{x}\right)\end{array}$
for some $\stackrel{\to }{x}\in {ℝ}^{n}$ . In the framework, certain components are assigned (possibly distinct) times for performing an update to their components, and the effects of various delay structures can be examined.
The development of the present computational framework is shown by the flow diagram in Figure 1, which is typical for computation frameworks, except for the third Timing Distributions stage. A mathematical formulation of a problem (e.g., as a set of equations) is presented first (Mathematical Model stage). The mathematical model is then implemented in an HPC environment (Parallel Implementation stage). Timing and algorithm-performance data (e.g., iterations to convergence) are collected from parallel executions on a subset of configurations and problem sizes, such that, in the proposed framework, timing distributions may be constructed (Timing Distributions stage) and used to simulate the performance of the mathematical model for target configurations and requirements. Since such simulations are faster and less-cumbersome to set-up, they allow for easy experimenting with variations of the underlying mathematical model, parallel implementation type and environment, or, eventually, in the expected performance.
The simulation framework developed here works to simulate the performance of generic asynchronous relaxation methods in shared memory environments. The simulation framework can then be modified to reflect changes in the environment, or else can be utilized to demonstrate the effectiveness of algorithmic modifications.
As a simple example, take 𝑛 = 2. Then $\stackrel{\to }{x}=\left({x}_{1},{x}_{2}\right)\in {ℝ}^{2}$ and, using the terminology of Section 3,
$\begin{array}{rl}{x}_{1}& ={G}_{1}\left(\stackrel{\to }{x}\right)={G}_{1}\left({x}_{1},{x}_{2}\right),\\ {x}_{2}& ={G}_{2}\left(\stackrel{\to }{x}\right)={G}_{2}\left({x}_{1},{x}_{2}\right)\mathrm{\text{.}}\end{array}$
In a traditional fully synchronous environment, both functions, 𝐺1 and 𝐺2, would be called simultaneously and no subsequent calls would be executed until both functions had returned and synchronized all results. In a fully asynchronous environment, both functions would be allowed to execute again immediately upon their own return, leading to a case where one of 𝑥1 or 𝑥2 may be updated more frequently than the other. Per Definition 1, both functions use the latest values of $\stackrel{\to }{x}$ that are available to them when the function call is initiated. For instance, if the processing element that was assigned to update the component 𝑥1 was ten times as fast as the processing element assigned to update 𝑥2, then in the amount of time needed to update 𝑥2 once, the component 𝑥1 will have been updated ten times, and when 𝐺2 is called for the second time it will be called using the latest component of 𝑥1 (which has been updated 10 times), and the latest component of 𝑥2 (which has only been updated once).
A block diagram showing the flow of the simulation framework is provided in Figure 2. The framework models the performance of methods that solve the linear system
$\begin{array}{c}Ax=b\end{array}$
using relaxation methods in either a synchronous or asynchronous manner.
The simulation requires as input the matrix 𝐴, the right hand side 𝑏 and an initial guess at the solution, 𝑥0. The important pieces of the simulation are all passed as functions to the tool. There are three functions required:
1. An update function that specifies how to perform the relaxation. A common technique for this is given by Equation (2). It is certainly possible to modify this equation to obtain different updates, as described, e.g., in (Saad, 2003).
2. An update pattern function that determines which elements of the matrix 𝐴 are assigned to each simulated processor. A common technique for this assignment, is to evenly divide the work among all of the available processors, however other patterns are also possible. For example, the use of randomization in the solution of linear systems via relaxation methods has gained some popularity in the fields of optimization and machine learning (see, e.g., (Avron, Druinsky, & Gupta, 2015) and references therein) and update patterns such as this are easy to implement inside of this framework.
3. An update time function that captures the empirical information that was captured from parallel performance runs on the HPC hardware. This function will typically be used to sample from the timing distribution that was generated beforehand. Note that, since each simulated processor makes calls to this function independently, the simulated performance will be asynchronous so long as the function returns different values upon different calls. Defining an update time function that has constant return (or constant return for every processor) provides a means to show synchronous performance.
By varying the three functions that are passed to the framework, not only can the HPC performance be predicted by making changes to the update time function, but various modifications to the basic algorithm can be quickly and easily compared in a manner that reflects real world asynchronous performance. With the renewed research interest in asynchronous iterative methods that perform relaxation updates, oftentimes performance between new variants and existing algorithms is only compared in simple synchronous experiments; the simulation framework proposed here allows for a more meaningful comparison between methods that does not require development of parallel implementations of all the methods or algorithm variations that are involved.
The simulation framework requires some data that specifies parameters concerning the particular run of the simulation such as the desired tolerance, the number of processors to simulate, and a computational scale factor. The framework itself is developed in MATLAB® and the three required functions are passed as function handles.
The simulation itself (see Simulation block in Figure 2) progresses by reading in the user provided input data, assigning an initial update pattern and time to each processor, and then beginning the main loop. Inside of the main loop, the time increments and a check is performed to see if the current time matches with the scheduled update time for any of the processors, if so, the update function is called and then a time for the next update is assigned to the processor that just updated and (if desired) the update pattern for the current processor is changed. After this, a check is performed on the size of the residual to determine if the exit criteria is met before the time is incremented again and the loop starts over. A pseudocode representation of the simulation framework for simulated asynchronous Jacobi is given in Algorithm 2.
Algorithm 2 Asynchronous Jacobi simulation
1:Input: ${a}_{ij}\in A$ , initial guess for ${x}_{0}$ , a number of processing elements $p$ , an input random number distribution
2:Output: Solution vector $x$
3:Assign processor update times. ${\tau }_{1},{\tau }_{2},\dots ,{\tau }_{p}$ by sampling from an appropriate random number distribution
4:Assign elements ${x}_{i}\in x$ to each simulated processing element
5:for $t=1,2,\dots$ until convergence do
6:for each processing element ${P}_{l}$ do
7:if ${\tau }_{l}=t$ then
8:for each element ${x}_{i}\in x$ assigned to ${P}_{l}$ do
9: ${x}_{i}=\frac{-1}{{a}_{ii}}\left[{\sum }_{j\ne i}{a}_{ij}{x}_{j}-{b}_{i}\right]$
10:end for
11:Retrieve a new update time ${\tau }_{l}$ by sampling from the input distribution
12:end if
13:end for
14:Calculate the residual as in Equation (3) and check termination conditions
15:end for
Algorithm 2, a given update time τ𝑙 will often not be sampled as an integer. The simulation adjusts for this by scaling the number that is sampled by the appropriate order of magnitude, adjusting the maximum value allowed for 𝑡 accordingly, and then scaling back the final time calculated by the simulation. For example, if the desired time precision is hundredths of a second, and the time resulting for the first sampling of τ𝑙 was 1.234𝑠, then the simulation would perform the following steps:
1. ${\tau }_{l}^{\text{new}}=s×{\tau }_{l}^{\text{old}}$
2. ${\tau }_{\text{max}}^{\text{new}}=s×{\tau }_{\text{max}}^{\text{old}}$
3. ${\tau }_{\text{final}}^{\text{new}}=\left(\frac{1}{s}\right)×{\tau }_{\text{final}}^{\text{old}}\mathrm{\text{,}}$
where 𝑠 referenced is the scale_factor defined in the block diagram given by Figure 2. For example, if the desired precision is hundredths of a second, 𝑠 = 102, and the sampled value τ𝑙 becomes
$\begin{array}{l}{\tau }_{l}=1.234\mathrm{\text{– initial sample}}\\ {\tau }_{l}=123.4\mathrm{\text{– apply scale factor}}\\ {\tau }_{l}=123\mathrm{\text{– round to the nearest integer.}}\end{array}$
Inside of the simulation framework, time is abstracted away to units of time, and then the final time is scaled back into the appropriate units. This allows the framework to be adapted to future HPC environments, as well as examining the impact of the standard variance of single core performance on multi-core hardware elements if the method that is used is tuned to be completely asynchronous. It should be possible — by adding or removing appropriate communication penalties — to simulate the performance of different memory architectures (e.g., distributed or cloud computing environments). This is left as future work although the method for doing this inside of the proposed framework is straightforward.
# Sample Use-Cases for the Framework
Let the matrix 𝐴 result from a simple two dimensional finite-difference discretization of the Laplacian over a 10 × 10 grid, resulting in a 100 × 100 matrix with an average of 4.6 non-zero entries per row. The Laplacian
$\begin{array}{rl}\Delta u& =g\mathrm{\text{,}}\\ {u}_{xx}+{u}_{yy}& =g\end{array}$
is a partial differential equation (PDE) commonly found in both science and engineering. The example problems taken in this study can be thought of as simulating the diffusion of heat across a two dimensional surface given some heat source along the boundary of the problem.
Once the PDE is discretized over the desired grid using finite differences, typically central finite differences, the linear system
$\begin{array}{c}Ax=b\end{array}$
is set up to be solved for a random right-hand side b that represents the desired boundary conditions. All problems considered in this study use Dirichlet boundary conditions. For the examples in this particular subsection, the righthand side is generated by taking each component sampled as a uniform random number between −0:5 and 0:5, and then normalizing the resultant vector. The iterative Jacobi method proceeds until the residual
$\begin{array}{}\text{(3)}& \hfill r=b-Ax\hfill \end{array}$
is reduced past some desired threshold.
To begin with, an example of nominal performance of the solution of the two dimensional Laplacian in a synchronous environment is provided by Figure 3.
Next, consider the same problem from above, but in two slightly more complicated scenarios. In Figure 4 one of the ten processors involved in updating blocks of components of 𝑥 is provided updates more slowly than the other processors. This could reflect the scenario where updates are either performed synchronously or asynchronously where the effect of variance in performance is negligible, and a single processor has degraded performance. This can also be viewed as a look at the impact of asynchronous behavior on the Jacobi algorithm. Each curve shows the progression of the (global) residual subject to having a single slower processor with different degrees of slowdown (from zero to 11x).
In Figure 5 the processor updates are not restricted to occur synchronously. Instead, the processors are assumed to have similar performance and perform their updates in time 𝑡𝑖 ∼ 𝑁(u, σ2) where the mean is set to 10 units of time and the variance is different for each curve depicted in the plot. An increase in the variance of processor performance, regardless of the timing distribution, could come about for a variety of reasons; an example of a scenario in the future could be having chips with more cores and lower voltage that are designed to address the challenges in creating very large scale HPC environments.
# Asynchronous Jacobi Implementations for the Framework
Figure 4 and Figure 5 show relative differences in compute times among sharedmemory computing elements for a specific problem and a specific asynchronous iterative method. A more general simulation framework, which can be used for modeling and testing any synchronous or asynchronous iterative relaxation method, is presented here. Baseline, non-resilient method behavior may be reproduced in the framework; further, the user may also investigate fault injection and checkpointing.
The user decomposes the method according to the input parameters required by the simulation framework. The update function that performs the relaxation has an associated operational time, both of which are defined by the user. Functionality within the relaxation may be isolated into discrete operations with corresponding time information; the level of granularity is decided by the user. For example, time to complete an operation in the simulation framework may be modeled with a probability density function derived from empirical data. To model time to perform specific operations or calculations during method execution, data is collected from the application during execution. In the implementation code, operations are enclosed within calls to time functions, which measure time to perform the operations. In this work the OpenMP® library function omp_get_wtime() is used to measure wall time. For HPC implementations that use MPI, MPI_Wtime() may be used to measure wall time. Fine-grained operations in the code should not overlap such that measurements overlap, i.e., for one operation, do not measure time function calls of another operation. After taking sufficient measurements, an operation is modeled by fitting a probability density function to a normalized histogram of the time data. This function may be included as part of the input to the framework. Note that when comparing simulated run times with HPC run times, it may be preferable to use an unmodified version of the HPC implementation code that does not have time function calls and mechanisms for storing or printing times. These functions and activities may increase run time and provide an inaccurate metric for comparison.
This section describes two asynchronous relaxation method implementations and two corresponding use cases of the simulation framework. For both implementations, the test problem is a two dimensional discretization of the Laplacian
$\begin{array}{c}\Delta u=b\mathrm{\text{,}}\end{array}$
where the right-hand side is initialized with Dirichlet boundary conditions. Both implementations use OpenMP® for shared-memory parallelism and are executed on the shared-memory computing platform nicknamed Rulfo, which is an Intel® Xeon Phi Knight's Landing2 having 7210 model processor with 64 cores. Each core may optimally execute 4 threads for 256 threads total, and runs at 1.30 GHz. The simulation framework and experiments were implemented in MATLAB® R2018a, while the Jacobi implementations were written in C/C++ using the Intel C compiler version 17.04 and OpenMP® version 4.5.
# Implementation 1: General Jacobi Solver
In this case, the heat problem is represented mathematically by a sparse matrix, which is solved by an asynchronous general Jacobi method. The Laplacian is generated over a 100 × 100 grid resulting in a matrix of size 10,000 × 10,000 with 49,600 non-zeros with an average of 4.96 non-zeros per row. The vector b from the resulting linear system,
$\begin{array}{c}Ax=b\end{array}$
is initialized such that the final solution vector has 𝑥𝑖 = 1 for all 𝑖. The initial guess 𝑥0 is all zeros.
In this implementation, all threads but one perform relaxations on assigned components, and a dedicated thread computes the global residual norm value 𝑏−𝐴𝑥(𝑡) that determines satisfactory convergence. Each thread retrieves the data it needs from shared memory, performs the necessary computations, and, in the case of the relaxation threads, writes the result back to shared memory. Synchronous shared-memory implementations of all classes of algorithms commonly use mutex locks to avoid race conditions with read and write operations. However, this type of asynchronous relaxation method may be less dependent on these safeguards for two reasons: (1) iterative methods can correct some errors with more iterations, if necessary, and (2) threads executing operations in asynchronous iterative methods are more likely to be at different stages of the iterative cycle, meaning fewer threads may be writing to and reading from the same memory location concurrently. This general Jacobi solver has two varieties: (a) Safe which uses mutex locks to avoid race conditions, and (b) Race which permits race conditions. Safe uses OpenMP® locks to copy 𝑥(𝑡) safely from shared memory and to update 𝑥(𝑡+1). Pseudocode for this process is given in Algorithm 3, where bold upper-case text indicates that OpenMP® locks are employed. The algorithm for Race is identical to Algorithm 3, with the exception that locks are omitted.
Algorithm 3 OpenMP Implementation 1 (a) Safe
1:Input: ${a}_{ij}\in A$ , $b$ , initial guess for ${X}_{0}$ , $n$ , processing elements $p$
2:Output: Solution vector $X$
3:Assign elements ${X}_{i}\in X$ to $n-1$ processing elements, $i=\left[\alpha ,\omega \right]$
4:for parallel each processing element in ${p}_{1}\dots {p}_{n}$ do
5:while residual norm $>$ tolerance do
6:COPY global ${X}^{\left(t\right)}$ from shared memory to local ${x}^{\left(t\right)}$
7:if ${p}_{1}$ then
8:Compute residual norm $||b-Ax||2$
9:else if ${p}_{2}\dots {p}_{n}$ then
10:for $x$ index $i=\alpha \dots \omega$ do
11:Compute ${x}_{i}^{\left(t+1\right)}=\frac{-1}{{a}_{ii}}\left[{\sum }_{j\ne i}{a}_{ij}{x}_{j}^{\left(t\right)}-{b}_{i}\right]$
12:end for
13:UPDATE ${X}_{i}^{\left(t+1\right)}$ in shared memory with ${x}_{i}^{\left(t+1\right)}$ for all $i$ belonging to processing element
14:end if
15:end while
16:end for
Figure 6 compares Safe and Race calculation times and number of iterations. Calculation times and average iteration counts are similar for thread counts up to 81, but behavior diverges beyond that. For thread counts 101 through 501, Race requires more iterations, perhaps to compensate for threads reading and computing with inaccurate 𝑥 vectors. Despite this, Figure 6(a) shows that Race is still quicker for the largest thread counts, perhaps because threads do not use locks to access data and eliminate that overhead cost. Figure 6(a) also shows that perhaps locks are not too costly for intermediate thread counts 101, 201, and 251, where Safe outperforms Race in terms of calculation time.
(a) Calculation time. (b) Number of iterations, average per thread.
Both Safe and Race were executed over several trials and varying thread counts on the experimental HPC platform. For each trial, the times for a thread to access the solution in shared memory (Line 6 of Algorithm 3), compute the relaxation for the rows assigned to it (Line 11), and to update the solution in shared memory (Line 13) were captured. This data was used to generate MATLAB® kernel probability density functions for modeling the amount of time a thread takes to complete a copy, compute, or update operation. These distributions may be used in the simulation framework as an input parameter, for the generation of random variables corresponding to key operational times in the HPC architecture. Algorithm 2 demonstrates the use of a time distribution in the framework. Thread counts of 11, 21, 41, 81, 101, 201, 251, and 401 were used to collect data for the generation of distributions, some of which are in Figure 7 and Figure 8. For 201 threads, Safe in Figure 7(d) and Figure 7(f) shows the tendency of locks to stratify copy and update times, compared with Race in Figure 8(d) and Figure 8(f), which are less uniform. These findings are mirrored in Table 1, which provides mean times for each of the three operations that were benchmarked in this implementation, for Safe and Race. Race copy and update times are slightly or significantly quicker than comparable Safe times. Compute times typically dominate total iteration time, except for Safe copy and update times for threads 201, 251, and 401. Table 1 shows that increasing the number of threads decreases Race copy, compute, and update times until cores are sufficiently over-subscribed: at 201 threads, these operations have become significantly more costly, as compared with 101 threads. This cost may be attributed to thread context switching. Compute times for Safe do not increase with higher thread counts because thread behavior is controlled explicitly using locks. These statistics can be used to validate the performance of the time distributions, so that the framework provides results comparable to the HPC hardware.
Table 1. Mean times for copy, compute, and update operations.
Threads Safe Race
Copy
(10−5s)
Compute
(10−4s)
Update
(10−6s)
Copy
(10−5s)
Compute
(10−4s)
Update
(10−6s)
11 1.28 167.00 7.76 1.15 167.00 2.79
21 1.31 84.30 6.98 1.17 83.60 1.96
41 1.38 43.00 7.09 1.23 43.10 1.63
81 2.98 27.30 20.60 1.43 27.20 1.79
101 36.70 23.40 357.00 1.64 25.20 1.79
201 251.00 15.30 2500.00 11.80 74.30 4.33
251 345.00 13.30 3440.00 16.60 90.90 4.55
401 1880.00 8.23 18,700.00 20.20 91.60 4.52
(a) 𝑥 copy, 11 threads. (b) 𝑥 compute, 11 threads. (c) 𝑥 update, 11 threads. (d) 𝑥 copy, 81 threads. (e) 𝑥 compute, 81 threads. (f) 𝑥 update, 81 threads. (g) 𝑥 copy, 201 threads. (h) 𝑥 compute, 201 threads. (i) 𝑥 update, 201 threads.
(a) 𝑥 copy, 11 threads. (b) 𝑥 compute, 11 threads. (c) 𝑥 update, 11 threads. (d) 𝑥 copy, 81 threads. (e) 𝑥 compute, 81 threads. (f) 𝑥 update, 81 threads. (g) 𝑥 copy, 201 threads. (h) 𝑥 compute, 201 threads. (i) 𝑥 update, 201 threads.
# Implementation 2: Finite Difference Jacobi Solver
This second implementation performs the Jacobi relaxation on the grid directly using the neighboring points required by the 5-point stencil as opposed to explicitly forming the matrix 𝐴, and in a sense implements a matrix-free solution. For this implementation, the Laplacian was discretized over a 600 × 600 grid with boundary conditions set according to Table 2.
0 100 … … 100 0 75 XXX … … XXX 50 ⋮ XXX … … XXX ⋮ ⋮ XXX … … XXX ⋮ 75 XXX … … XXX 50 0 0 … … 0 0
The implementation used here stems from code provided by (Hager & Wellein, 2010); similar code solves a three dimensional discretization of the Laplacian in the study featured in (Bethune, Bull, Dingle, & Higham, 2011) and (Bethune, Bull, Dingle, & Higham, 2014). The routine solves a heat diffusion problem, in which a two-dimensional heated plate has Dirichlet boundary-condition temperatures. Two matrices, 𝑢0 and 𝑢1, store grid point values that each thread reads, e.g., from 𝑢1, to compute newer values to write, e.g., to 𝑢0. As the method is asynchronous, each thread independently determines which matrix stores its newer 𝑢(𝑡+1)(𝑖, 𝑗) values and older 𝑢(𝑡)(𝑖, 𝑗) values. For an 𝑁 + 2 by 𝑁 + 2 grid, each thread solves for 𝑁2 grid points divided by 𝑛 processing elements, such that the grid is evenly divided along the y-axis. When a thread copies grid point values above or below its domain for the computation, OpenMP® locks are employed to ensure that data is safely captured from a single iteration. Further, locks are used when updating values on domain boundaries. Each thread 𝑝𝑛 computes its local residual value every 𝑘th iteration, which it contributes to the global residual value using an OpenMP® atomic operation, such that it adds the local residual from the current iteration and subtracts the local residual from the previous iteration. A single thread checks for convergence with an atomic capture operation, and updates a shared flag variable if the criterion is satisfied. Pseudocode for this implementation is provided in Algorithm 4, where bold upper-case text indicates that OpenMP® locks are employed. Locks are used only with interior boundary rows, meaning they are unnecessary for the first and last rows in the domain.
In this implementation, data was collected only for the time to complete an iteration. Thread counts of 10, 25, 50, 75, 100, and 150 were used in these series of experiments. The average total iteration time for the varying.
Algorithm 4 OpenMP Implementation 2
1:Input: Initial guess for ${u}^{\left(0\right)}\left(i,j\right)$ , $n$ processing elements $p$
2:Output: Solution vector $u\left(i,j\right)$
3:Assign rows $u\left(i\right)\in u$ to each processing element, $i=\left[\alpha ,\omega \right]$
4:for parallel each processing element in ${p}_{1}\dots {p}_{n}$ do
5:while residual norm $>$ tolerance do
6:for row index $i=\alpha \dots \omega$ do
7:if $i\ne 1$ AND $i\ne N$ $i=\alpha$ OR $i=\omega$ then
8:COPY neighbor ${p}_{n-1}$ or ${p}_{n+1}$ boundary row values ${u}^{\left(t\right)}\left(i,j\right)$ for ${u}^{\left(t+1\right)}\left(i,j\right)$
9:end if
10:Compute ${u}^{\left(t+1\right)}\left(i,j\right)=\frac{1}{4}\ast \left({u}^{\left(t\right)}\left(i+1,j\right)+{u}^{\left(t\right)}\left(i-1,j\right)+{u}^{\left(t\right)}\left(i,j+1\right)+{u}^{\left(t\right)}\left(i,j-1\right)\right)$
11:if $i\ne 1$ AND $i\ne N$ $i=\alpha$ OR $i=\omega$ then
12:UPDATE own ${p}_{n}$ boundary row values ${u}_{j}^{\left(t\right)}\left(i,j\right)$ in shared memory with ${u}_{j}^{\left(t+1\right)}\left(i,j\right)$
13:end if
14:end for
15:end while
16:end for
Figure 9 provides histograms and kernel fits for each of the thread counts. Table 3 and Figure 9 show that with increasing thread count, mean iteration time decreases, but iteration times variance increases. This increase in iteration time variation may result from increased opportunities for lock collisions with greater thread counts.
(a) 10 threads. (b) 25 threads. (c) 50 threads. (d) 75 threads. (e) 100 threads. (f) 150 threads.
Since this implementation is even more compute bound than the first one, Table 3 shows a general decrease in the time for each iteration as the thread count is increased. While there is no inflection point evident in the data presented in Table 3, compared to Race in Table 1, Table 3 still suggests that once the number of threads outnumbers physical cores, performance gains diminish. For denser matrices, or for different applications on different systems, these trends could change as the memory-based activities become relatively more expensive. The finite difference discretization of the Laplacian is a very sparse matrix that does not require much data movement.
Table 3. Mean iteration time and standard deviation by thread count.
Threads Mean
(10−5s)
Std.
(10−6s)
10 8.86 3.87
25 3.92 2.08
50 2.55 2.34
75 2.53 5.80
100 2.61 5.95
150 2.64 5.76
# Implementation Comparison
The Safe variant of the first implementation incurs significant overhead costs for 𝑥 copy and update operations, as thread count increases, because each thread must copy the entire 𝑥 vector. In the second implementation, data shared between threads is differentiated and specific to domain location; therefore, specific locks may be used when copying and updating segments of the subdomain. Assuming an appropriate number of processing elements for a given grid, i.e., a thread has significantly more middle rows than boundary rows, copy operations, and the associated variability and costs, are minimal compared with compute operations. The Race implementation of the general solver eliminates much of the overhead cost from mutex locks, and convergence time is satisfactory for the given system. Implementation 2 is more constrained than Implementation 1, generalizing only to finite difference discretizations of partial differential equations over rectangular grids. Implementation 1 generalizes further to any sparse matrix, 𝐴 with which the Jacobi method can be used. According to Theorem 1, convergence will occur if the spectral radius of the iteration matrix, 𝐶, is less than 1. In the case of the Jacobi method, the iteration matrix is given by
$\begin{array}{c}C={-D}^{-1}\left(L+U\right)\mathrm{\text{.}}\end{array}$
Note that in the two dimensional discretization of the Laplacian, the spectral radius of the Jacobian is less than l, which says that both the synchronous and asynchronous variants of the Jacobi algorithm will converge. Note Race behavior is unknown for different problems and HPC systems.
The purpose of the two distinct implementations is to emphasize that the simulation framework proposed here can adapt to the behavior of different problems and platforms. The framework may be apdapted to any asynchronous iterative method through the process of collecting data representative of individual update times and using the resultant data to model the system in the framework.
# Framework Validation
To validate the performance of the simulation framework when initialized with appropriate distributions, a case study utilizing output from Implementation 1 (see Section 5.1 for details) was considered. Data was collected for a smaller problem size only in order to facilitate the collection of data over a large number of runs. Specifically, the Laplacian was discretized over a 20 × 20 grid resulting in a matrix of size 400 × 400. Similarly to the process in Section 5.1, distributions were fit to the output of the OpenMP® implementation, and these distributions were used in the simulation framework to provide update times to the simulated processors that are reflective of the HPC hardware that the data was collected on. Output from the average of these runs is provided in Table 4. The leftmost column provides the number of threads that were used (or simulated), the middle column shows the average over multiple runs of the parallel implementation, and the rightmost column shows the average over multiple runs of the simulation generated by the simulation framework. In the case of this small problem, the similarity of actual and simulated run times helps to validate the model. Running multiple trials of larger problems in the framework is currently time-prohibitive, which is an issue that may be improved with framework implementation changes. Future work includes model validation for other problems and larger problems.
Table 4. Comparisons of run times between parallel executions and simulation.
Thread
Count
Run
Average (s)
Simulation
Average (s)
11 0.01 0.01
21 0.02 0.02
41 0.04 0.04
51 0.04 0.05
81 0.09 0.09
101 0.12 0.12
201 0.34 0.35
# Framework Extension for Fault-Tolerance Requirements
The modular nature of this framework allows for extra functionality to be easily added to the framework itself that can be used to adapt the base algorithm to suit a specific set of requirements. With the projected increase of faults (see the references in Section 2), development of fault tolerant algorithms is an important endeavor. A block diagram showing the additional functionality dealing with fault-tolerance is shown in Figure 10. The new functionality is achieved by passing in another function handle that performs the fault tolerance check and recovery work.
The contents of the newly added Fault tolerance check module may be organized as follows: Each processor makes a call to find the global residual and rolls the state back to the previous known good state if the behavior of the residual is not as expected. See Section 6.2 for more details. Note that this strategy is not being advocated for due to its optimality, but is being shown as an example of how to extend the framework for algorithm development. Techniques such as monitoring the progression of the component-wise residuals (e.g., (Anzt, Dongarra, & Quintana-Ortí, 2015; Anzt, Dongarra, & Quintana-Ortí, 2016)) or only rolling back portions of the state vector (e.g., (Coleman & Sosonkina, 2017; Coleman & Sosonkina, 2018)) would probably be more computationally efficient.
# Fault Model
For this part of the study, faults are modeled as perturbations similar to several recent studies (Coleman & Sosonkina, 2016b; Coleman, Sosonkina, & Chow, 2017; Stoyanov & Webster, 2015); the goal being producing fault tolerant algorithms for future computing platforms that are not too dependent on the precise mechanism of a fault (e.g., bit flip). Modifying the perturbation-based fault model described in (Coleman, Sosonkina, & Chow, 2017), a single data structure is targeted and a small random perturbation is injected into each component transiently. For example, if the targeted data structure is a vector 𝑥 and the maximum size of the perturbation-based fault is ε then proceed as follows: sample a random number 𝑟𝑖 ∈ (-ε, ε) , using a uniform distribution, and then set
$\begin{array}{c}{\stackrel{^}{x}}_{i}={x}_{i}+{r}_{i}\end{array}$
for all values of 𝑖. The resultant vector $\stackrel{\to }{x}$ is then perturbed away from the original vector 𝑥. Other similar perturbation-based fault models have sampled the components 𝑟𝑖 from different ranges. This can allow the creation of scenarios where some components are perturbed by large amounts, and some are only changed incrementally.
In this study, faults are injected into the asynchronous Jacobi algorithm following the perturbation based methodology described above. Due to the relatively short execution time of the asynchronous Jacobi algorithm on the given test problems, a fault is induced only once during each run, and the fault is designated to occur at a random iteration number before convergence. To be precise — since "iteration" loses some meaning in an asynchronous iterative algorithm — the fault is injected on a single simulated time before the algorithm terminates. It is not necessary for the program to have an update scheduled on the same simulated time for the fault to be injected.
# Experiments with the Fault-Tolerance Module
Similar to the earlier results in the paper, this study covers the solution of the linear system resulting from a two-dimensional finite difference discretization of the Laplacian. Before presenting simulation results, it is important to note that faults, as modeled here, will not prevent the eventual solution of the linear system using the (asynchronous) Jacobi method. Since the spectral radius of the associated iteration matrix is strictly less than 1, it will converge for any initial guess 𝑥(0).
Since faults are assumed to only affect the memory storing the vector 𝑥 and are assumed to occur in a transient manner, if a fault occurs on iteration 𝐹 then the subsequent iterate, 𝑥(𝐹+1) can be taken to be the new starting iterate and eventual convergence is guaranteed due to the iteration matrix which has remained the same throughout the occurrence of the fault. This model can reflect the scenario where certain parts of the routine are designated to run on hardware with a higher reliability threshold, and other parts of the algorithm are allowed to run on hardware that may be more susceptible to the occurrence of a fault. This sandbox type design has been suggested as a possible means for providing energy efficient fault tolerance on future HPC environments (Bridges, Ferreira, Heroux, & Hoemmen, 2012; Hoemmen & Heroux, 2011; Sao & Vuduc, 2013).
While eventual convergence may be guaranteed, greatly accelerated convergence is possible through a simple checkpointing scheme. An example of such a scheme (as an extension of the asynchronous Jacobi simulation provided by Algorithm 2) is provided in Algorithm 5.
Algorithm 5 Asynchronous Jacobi simulation with checkpointing
1:Input: ${a}_{ij}\in A$ ; initial guess ${x}_{0}$ ; number of processing elements $p$ ; input random number distribution; checkpointing tolerance $\alpha$ ; checkpointing frequency $\omega$
2:Output: Solution vector $x$
3:Assign processor update times ${\tau }_{1},{\tau }_{2},\dots ,{\tau }_{p}$ by sampling from an appropriate random number distribution
4:Assign a part of $x$ to each processing element
5:Initialize ${r}_{\text{old}}$ to a large value
6:for $t=1,2,\dots$ , until convergence do
7:for each processing element, ${P}_{l}$ do
8:if ${\tau }_{k}=t$ then
9:for each element ${x}_{i}\in x$ assigned to ${P}_{l}$ do
10: ${x}_{i}=\frac{-1}{{a}_{ii}}\left[{\sum }_{j\ne i}{a}_{ij}{x}_{j}-{b}_{i}\right]$
11:end for
12:Retrieve a new update time ${\tau }_{k}$ by sampling from the input distribution
13:end if
14:end for
15:Inject a fault if appropriate
16:Calculate the residual ${r}_{\text{new}}$ as in Equation (3)
17:if ${r}_{\text{new}}>\alpha x{r}_{\text{old}}$ then
18: $x←{x}_{\text{cp}}$
19:end if
20:if $\text{mod}\left(t,\omega \right)==0$ then
21: ${x}_{\text{cp}}←x$
22:end if
23:Check termination conditions
24:end for
Note that the asynchronous nature of the iterative method means that a strict check on the decrease of the residual (i.e., expecting monotonic decrease) is not possible. In particular, the checkpointing tolerance α needs to be taken such that α > 1. However, the expected manifestation of faults as rare, transient events allows α to be taken fairly large. Taking α too large results in a fault having a substantial impact on the convergence rate of algorithm since large faults will be allowed to impact the algorithm with no correction. Conversely, taking α too small causes the algorithm to checkpoint more frequently than needed. Examples of the effects of a fault with different values selected for α are given by Figure 11.
(a) Effect of fault — no checkpointing. (b) Effect of fault — α = 1. (c) Effect of fault — α = 2. (d) Effect of fault — α = 10.
Note in Figure 11 that no checkpointing results in a delay to convergence relative to the use of checkpointing with either α = 1 or α = 10. The size of the fault selected in this study, 𝑟𝑖 ∈ (-100, 100) , which may be reflective of an exponent or sign bit flip (Coleman & Sosonkina, 2018), results in the values α = 1 and α = 10 having the same performance since the error induced by the fault is sufficiently large that the new residual is more than α = 10 times the prior residual. Faults that induce a smaller error may be detected by certain values of α and not by others which would lead to differing performance.
The residual progress in the plot showing the effects of using α = 1 can be explained by the updates provided by certain simulated processing elements being rejected despite being necessary for the convergence of the algorithm. This can be seen in the small, momentary jumps in the progression of the residual visible in the other graphs. These rejections lead to stagnation in the progression of the algorithm and show why the value of α = 1 should not be selected for a checkpointing scheme for an asynchronous iterative method.
# Conclusions and Future Work
This work has developed a framework that can be used to efficiently simulate the outcomes of asynchronous methods for future High Performance Computing environments. Given that asynchronous methods are notoriously difficult to study theoretically, their simulation is an invaluable tool for observing behavior and making quantitative and qualitative assertions. The modular and extensible nature of the framework proposed here allows for easy experimentation with modifications to a popular class of algorithms that finds uses in many areas of science and engineering.
The work presented was designed to show the ability of the framework to adapt to new algorithm variants, such as those capable of handling algorithm recovery in the presence of transient soft faults as was shown by example in Section 6.2.
The simulation framework presented here is extensible and flexible and is able to:
1. admit a variety of asynchronous methods (i.e., beyond the simple Jacobi algorithm)
2. incorporate different fault models and recovery techniques for the development of fault tolerant algorithms, and
3. vary hardware parameters such as thread and processor counts and the performance of those parameters as governed by the timing distributions that are supplied.
In the future, the most obvious extension of the simulation framework is to add modules that allow it to be accurately used for experiments on either distributed or cloud-based computing environments. Additionally, it is planned to add features for optimization that could allow for the automation of the selection of the checkpointing tolerance as well as checkpointing frequency in the course of simulation. Adding the capability for the framework to take a range of parameters and find optimal values without direct input from the user could aid in the development of algorithms. Furthermore, the simulation framework is intended to be augmented with runtime simulation measurements, such those provided by Intel® Running Average Power Limit (RAPL) interface (Intel, 2016), to obtain simulated application execution traces in order to model application performance and energy consumption.
# Acknowledgements
This work was supported in part by the Air Force Office of Scientific Research under the AFOSR award FA9550-12-1-0476, by the U.S. Department of Energy (DOE) Office of Advanced Scientific Computing Research under the grant DE-SC-0016564 and the Exascale Computing Project (ECP) through the Ames Laboratory, operated by Iowa State University under contract No. DE-AC00-07CH11358, by the U.S. Department of Defense High Performance Computing Modernization Program, through a HASI grant, the High Performance Computing facilities at Old Dominion University, and through the ILIR/IAR program at the Naval Surface Warfare Center — Dahlgren Division. Edmond Chow provided the MATLAB® script that evolved into part of the proposed simulation framework.
# Footnotes
1. Throughout the text, vector notation is occasionally adopted to emphasize when functions take all components of 𝑥 as opposed to a single component, such as 𝑥1.[back]
2. Rulfo is a part of computing resources of the Department of Modeling, Simulation and Visualization Engineering at Old Dominion University.[back]
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# Copyright Information
Copyright © 2018 Evan C. Coleman, Erik Jensen, Masha Sosonkina. This article is licensed under a Creative Commons Attribution 4.0 International License.
| 2019-05-24T23:12:11 |
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|
http://legisquebec.gouv.qc.ca/en/showversion/cs/R-10%20?code=se:36_1_6&pointInTime=20210107
|
### R-10 - Act respecting the Government and Public Employees Retirement Plan
36.1.6. For the purposes of section 34.3, the annualization of salaries for the years of service subsequent to 2009 is obtained,
(1) when computing the average pensionable salary referred to in subparagraph 1 of the first paragraph of section 34.2, by dividing the aggregate of the adjusted pensionable salary for such a year and the lump sum attributed to that year under section 36.1.20 by the harmonized service for the year; and
(2) when computing the average pensionable salary referred to in subparagraph 2 of the first paragraph of section 34.2, by dividing the aggregate of the adjusted pensionable salary for such a year and the lump sum attributed to that year under section 36.1.20 by the harmonized service for the year. The limit imposed by the first paragraph of section 18.1 applies to the result obtained for each year.
2008, c. 25, s. 10.
| 2021-02-28T04:48:41 |
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|
https://par.nsf.gov/biblio/10282587-liquid-metal-swirling-flow-affected-transverse-magnetic-field
|
Liquid metal swirling flow affected by transverse magnetic field
In this work we study numerically liquid metal flow in a square duct under the influence of a transverse magnetic field applied in a spanwise direction (coplanar). The key interest of the present study is an attempt of passive control of flow regimes developed under magnetic field and thermal loads by applying specially shaped conditions, such as swirling, at the duct inlet. In this paper, we report results of numerical simulations of the interaction of swirling flow and transverse magnetic field in a square duct flow. Analysis of the obtained regimes might be important for the development of an experimental setup, in order to design corresponding inlet sections.
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10282587
Journal Name:
Magnetohydrodynamics
Volume:
56
Issue:
2-3
Page Range or eLocation-ID:
121 to 130
ISSN:
0024-998X
5. We study the emergence of precessing vortex core (PVC) oscillations in a swirling jet experiment. We vary the swirl intensity while keeping the net mass flow rate fixed using a radial-entry swirler with movable blades upstream of the jet exit. The swirl intensity is quantified in terms of a swirl number $S$ . Time-resolved velocity measurements in a radial–axial plane anchored at the jet exit for various $S$ values are obtained using stereoscopic particle image velocimetry. Spectral proper orthogonal decomposition and spatial cross-spectral analysis reveal the simultaneous emergence of a bubble-type vortex breakdown and a strong helical limit-cycle oscillation inmore »
| 2022-09-29T13:47:05 |
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https://www.pnnl.gov/news-media/dispatch-delivers-good-energy-news
|
August 29, 2019
Feature
## This Dispatch Delivers Good Energy News
PNNL demonstrates a new approach with benefits all around
Field testing of PNNL’s Economic Dispatch technology has demonstrated that the approach can effectively and economically coordinate CHP units, building operations, energy costs, and other factors to deliver benefits in energy efficiency, grid resiliency, and clean energy.
A promising Pacific Northwest National Laboratory-developed technology optimizes the operation of large heating and cooling units that also generate electricity. This advance could be key in bringing more clean, renewable energy onto the power grid.
The automated technology, which also could save energy and enhance grid reliability, successfully enabled “Economic Dispatch” during a recent multi-month field test at a New York energy provider’s plant. “This result represents a step forward in establishing next-generation integrated energy systems,” says PNNL’s Srinivas Katipamula, a mechanical engineer who led technology development efforts.
## Economic Dispatch: A Novel Energy Approach
Economic Dispatch is a concept that links a combined heating, cooling, and power system (CHP) with a building’s operational systems and the power grid, while concurrently monitoring a range of factors that impact electricity supply and demand. These factors include weather conditions, local energy consumption, and current electricity costs.
The goal of Economic Dispatch is to coordinate all of these various elements in a manner that optimizes CHP generation, keeps the building completely functional (occupants warm or cool, etc.), and contributes to reliable and resilient grid operations. A more resilient grid then has increased flexibility to incorporate intermittent renewables, such as wind power, which can disrupt grid operations due to sudden starts or stops in generation based on weather.
“Ideally, the CHP is operating so effectively under Economic Dispatch that it can meet all needs and earn more income than usual from selling its excess electricity to the grid,” Katipamula says. “With CHP prevalence expected to grow significantly over time, Economic Dispatch capabilities can render these units as key assets in meeting multiple energy, environmental, and economic needs.”
The technology designed and developed by PNNL for Economic Dispatch represents a cost and performance breakthrough that’s highly appealing to CHP owners/operators. The technology’s supervisory controller—the open source VOLTTRON™ distributed control and sensing software platform—can be deployed from a low-cost (less than $200) computing resource or from the Cloud. PNNL-crafted Economic Dispatch algorithms are launched from the platform to the CHP and associated building systems. This fully-automated approach, which includes data collection and analysis capabilities, then optimally weighs multiple factors and makes decisions related to CHP production and building energy needs, while communicating and coordinating with power grid operations. ## Putting It to the Test The VOLTTRON™-based Economic Dispatch system deployment and testing were initiated in late fall 2018 in Utica, New York, at Burrstone Energy Corporation’s CHP plant, which contains four natural-gas-fueled units serving a college, hospital, and nursing home. PNNL’s system proved relatively easy to configure and deploy. Once operational, the system established and evaluated operation strategies, sending commands to the CHPs regarding whether the units should run and the modes they should operate in. Testing was conducted and concluded in spring 2019, with several key outcomes: • The automated system successfully dispatched control signals to the CHP. • A benchmarking analysis, which examined a few days of operation in March and compared the Economic Dispatch system to the previous CHP control method, demonstrated savings on the order of$50 per day. This equates to \$20,000 per year in additional profit from a CHP.
• Preliminary results strongly suggest the system can be deployed in the field and customized at lower cost than existing options.
• A New York-based energy services provider that supported the project, Frontier Energy, was impressed with the technology and adopted the Economic Dispatch tool for its customers.
The testing also yielded lessons learned that will inform future advancements in automated Economic Dispatch. Extended testing will continue through summer 2019.
The technology development was funded through the U.S. Department of Energy (DOE) Building Technologies office as part of DOE’s Grid Modernization Laboratory Consortium.
###
| 2022-11-26T12:05:19 |
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|
https://earthquake.usgs.gov/data/ground-failure/background.php
|
Earthquake-triggered landslides and liquefaction, collectively referred to as ground failure, can be a significant contributor to earthquake losses. The USGS Ground Failure (GF) earthquake product provides near-real-time spatial estimates of earthquake-triggered landslide and liquefaction hazard following significant earthquakes worldwide.
We developed this product to provide initial awareness of the overall extent and importance of potential landslides and liquefaction, and to indicate areas in which they are most likely to have occurred. It takes time for first responders and experts to survey the actual damage in the area, so our product provides early estimates of where to focus attention and response planning. Though our models provide regional estimates of landslide and liquefaction hazard triggered by this earthquake, they do not predict specific occurrences.
The GF product is based on a suite of geospatial models that relate ground motion estimates provided by the USGS ShakeMap and proxies for ground failure susceptibility to rapidly provide regional estimates of earthquake-triggered ground failure hazard over a grid of evenly-spaced points. See Models section for details.
## Product Overview
### Triggering
The GF product is generally triggered when a USGS ShakeMap is created for earthquakes greater than M5 within the United States and greater than M6 worldwide. It can also be triggered manually. Results are always shown if it is run, even for events for which little to no ground failure is estimated. However, a pending status may sometimes be reported for significant events undergoing manual ShakeMap review. This means no GF alert levels will be reported until that review is done. Although the maps will still be available, the preliminary nature of the shaking inputs should be considered when interpreting the ground failure results.
### Product Card
Ground Failure is considered a new earthquake information product, one of the suite of USGS Earthquake Program information systems that provide situational awareness and scientific content pertaining to each significant earthquake around the globe. The user will typically navigate to the Ground Failure page for a specific earthquake by starting at the overview of the earthquake-specific webpage (Figure 1) and selecting the card titled “Ground Failure.” This card will only appear if GF was triggered (see above). The card summarizes the landslide and liquefaction hazard for this event qualitatively (e.g., significant area affected, extensive population exposed). The color of the icon next to each ground failure type corresponds to the maximum of the two alert levels.
### Summary Page
Selecting the Ground Failure card takes the user to the Summary page for Ground Failure. This page gives the user an overview of the hazard and population exposure for the two different types of ground failure and allows the user to navigate to interactive maps and other features, as described in the following sections and labeled in Figure 2.
#### A) Earthquake Summary
The top of all earthquake event webpages consists of a summary of the most up-to-date earthquake information (magnitude, geographic location, event time, and epicentral location). Below this is the title of the product and time of last update.
This tab provides basic information for the general public that describes why we developed this product, how to use it, what earthquake-triggered landslides and liquefaction are, and what hazards they pose to human populations. The simplified information provided in this tab is intended for non-expert users who may not be interested in the level of detail provided on this detailed webpage.
#### C, D) Landslide and Liquefaction Models
The left column of the summary webpage summarizes the landslide hazard and exposure alert levels for this earthquake based on our preferred landslide model, and the right column corresponds to the same for liquefaction. On mobile devices, these columns will be stacked on top of each other.
The focal points of our summary webpage are the four alert level bars that give a quick overview of the expected hazard and population exposure for each ground failure type (Figure 3).
The alert levels are determined using two statistical parameters for each model type: Estimated Area Exposed to Hazard ($\text{H}_\text{tot}$) and Estimated Population Exposure ($\text{pop}_\text{exp}$). $\text{H}_\text{tot}$ is equivalent to the model’s estimate of the total area exposed to hazard in km2, and $\text{pop}_\text{exp}$ is the approximate number of people who live in the areas exposed to hazard. See the Statistics section for details about how these are computed.
The alert level bins are each defined by a qualitative order-of-magnitude range for each statistic, which were chosen based on historic earthquakes with known consequences. See the Alert Level Definitions section for details.
#### F, G) Interactive Map
Selecting the “View Landslide Map” button takes the user to the interactive map with the preferred landslide model shown by default. The same applies to the “View Liquefaction Map” button. The interactive map includes numerous alternative basemap layers and earthquake layers that can be superimposed on the landslide or liquefaction hazard maps (Figure 4). The colorbars for both landslides and liquefaction (Figure 5) show the areal coverage probability type (see Interpretation of Maps) using logarithmic bins to better visualize the range of typical values. The colorbar saturates at 0.2, which for areal coverage, equates to severe ground failure. Neither model reaches values much higher than 0.2 for areal coverage. Probabilities are never exactly zero for logistic models, but we mask areas with insignificant probabilities on the interactive maps, as indicated by the lower bound of the color bars (Figure 5).
#### H) Ground Failure Background Page
A footer appears at the bottom of all Ground Failure product pages with basic disclaimers about the product and a link to a static webpage that provides detailed technical information for advanced users (this webpage).
The Downloads expansion panel allows advanced users to download GIS files of all ground failure model results, including the alternative model results, which are not currently shown on the interactive map.
## Models
The GF models are designed to be rapidly and consistently applicable in any region of the world, requiring that they be relatively simple and depend on globally-available input datasets. There are many factors that contribute to a given occurrence of ground failure that are unknowable at the global scale; thus the models are not able to account for local characteristics of topography or geology nor to predict specific occurrences.
Although the models differ in detail, in general, they indicate that landsliding is more likely where shaking is strong and slopes are steep, and that liquefaction is more likely where shaking is strong and the land is flat and wet. The quality of the model outputs also depend, in part, on the quality of the ShakeMap estimates of ground motion. Model calibration was done using final ShakeMaps for about two dozen earthquakes. Thus, our estimates generally improve with time as observed shaking data and estimates of rupture extent are incorporated (Figure 6).
We currently use one preferred landslide model and one preferred liquefaction model for the product summary and interactive maps, but we also run several alternative models that are available for users to download. All implemented models are summarized below; details can be found in the original publications. For more detailed information on our implementation of these models, see the ground failure manual and github page.
### Preferred Landslide Model
Nowicki Jessee and others (2018) is the preferred model for earthquake-triggered landslide hazard. Our primary landslide model is the empirical model of Nowicki Jessee and others (2018). The model was developed by relating 23 inventories of landslides triggered by past earthquakes with different combinations of predictor variables (summarized below) using logistic regression. The output resolution is ~250 m. The model inputs are described below. More details about the model can be found in the original publication. We modify the published model by excluding areas with slopes <5° and changing the coefficient for the lithology layer "unconsolidated sediments" from -3.22 to -1.36, the coefficient for "mixed sedimentary rocks" to better reflect that this unit is expected to be weak (more negative coefficient indicates stronger rock).To exclude areas of insignificantly small probabilities in the computation of aggregate statistics for this model, we use a probability threshold of 0.002.
#### Table 1: Summary of Nowicki Jessee and others (2018) model inputs
Input Source
Slope Derived from Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010) (Danielson and Gesch, 2011)
Peak Ground Velocity (PGV) U.S. Geological Survey ShakeMap (Worden and Wald, 2016)
Lithology Global Lithological Map Database (GLiM) (Hartmann and Moosdorf, 2012)
Land cover Moderate resolution (300 m) Envisat MERIS (MEdium Resolution Imaging Spectrometer) GlobCover land cover dataset for 2009 (Arino and others, 2012)
Compound topographic index (CTI) (wetness index) U.S. Geological Survey HYDRO1k geographic database (Moore and others, 1991)
### Preferred Liquefaction Model
Zhu and others (2017) is the preferred model for liquefaction hazard. The model was developed by relating 27 inventories of liquefaction triggered by past earthquakes to globally-available geospatial proxies (summarized below) using logistic regression. We have implemented the global version of the model and have added additional modifications proposed by Baise and Rashidian (2017), including a peak ground acceleration (PGA) threshold of 0.1 g and linear interpolation of the input layers. We also exclude areas with slopes >5°. We linearly interpolate the original input layers of ~1 km resolution to 500 m resolution. The model inputs are described below. More details about the model can be found in the original publication.
#### Table 2: Summary of Zhu and others (2017) model inputs
Input Source
Peak Ground Velocity (PGV) U.S. Geological Survey ShakeMap (Worden and Wald, 2016)
Shear wave velocity averaged over top 30 m (Vs30) Computed from GMTED2010 using methods of Wald and Allen (2007) based on topographic slope
Mean Annual Precipitation WorldClim database, last accessed March 2014 (Hijmans and others, 2005)
Distance from coast Global distance to coast dataset by NASA's Ocean Color Group
Distance from rivers Computed from U.S. Geological Survey HydroSHEDS database
Water table depth Global model by Fan and others (2013)
Our initial testing of the Zhu and others (2017) model indicated that some moderate magnitude events were over predicting liquefaction probabilities. Thus, we applied the following ad-hoc equation to mitigate this problem:
$$\text{SF} = \frac{1}{1 + \exp(-2[M - 6])}$$
where M is the earthquake magnitude. We multiply PGV by SF before it is evaluated in the Zhu and others (2017) model. This is analogous to how the Youd and others (2001) magnitude scaling factor works for PGA, except that it is applied to PGV, and we compare the two in Figure 7. Note that we are showing
### Alternative Models
We currently run two alternative landslide models and one alternative liquefaction model, described in Table 3. These models are not currently rendered on the interactive map or used to determine alert levels, but are available for download.
#### Table 3: Summary of Alternative Models
Type Model Name Input Layers Resolution
Landslide Nowicki and others (2014) Maximum slope (~90 m resolution), Peak Ground Acceleration, Friction angle, Compound topographic index (wetness proxy) ~1 km
Landslide Godt and others (2008) Slope quantiles (~1 km resolution derived from ~90 m resolution), Peak Ground Acceleration, Cohesion, Friction angle ~1 km
Liquefaction Zhu and others (2015) Peak Ground Acceleration, Shear wave velocity averaged over top 30 m (Vs30), Compound topographic index ~1 km
## Interpretation of Maps
Both of our preferred models are logistic models. Logistic models estimate probability, but the meaning of that probability depends on how the model was developed. The methods of our preferred models (Nowicki Jessee and others 2018 and Zhu and others 2017) result in a native output of relative hazard. This does not have a physical meaning. Therefore, both authors calibrated their models against completely mapped inventories to develop a relation to convert relative hazard to a different type of probability that does have a physical meaning: areal coverage (Ac). The meaning of Ac is illustrated in Figure 8.
The Godt and others (2008) and Zhu and others (2015) models both estimate areal coverage natively without requiring a conversion. The Nowicki and others (2014) model is distinct from the others in that it estimates the probability of any landslide occurring within a given grid cell.
## Statistics
Statistical parameters used to summarize the model results and to assign hazard and population exposure alert levels are Estimated Area Exposed to Hazard (Htot), and population exposure (popexp). We use a ground motion threshold of 0.1g to compute these statistics in order to control for differences in the ShakeMap areas between events. The spatial extent of the ShakeMap can vary substantially from event to event and even for subsequent versions of the same event, and this can have an artificial impact on the statistics if not controlled for. Using a ground motion threshold also helps mitigate the inflation of these statistics due to small probabilities over large areas by only considering areas of relatively strong shaking. Additionally, due to the statistical nature of the models, probabilities can be very small but are never actually equal to zero. This can be problematic because very small insignificant probabilities over very large areas or over very large population centers can add up to large statistical values that can be misleading. Therefore, we exclude areas of insignificantly small probabilities from the statistics.
### Estimated Area Exposed to Hazard
The estimated area exposed to hazard, (Htot) represents the sum of the area of each cell multiplied by the probability (areal coverage) estimated for that cell. This gives the model’s estimate of the total area affected by ground failure. However, the models are conservative so these areas are often overestimated, thus Htot serves more as a proxy for total area affected.
Htot is calculated by:
$$\text{H}_{tot} = \sum_{i=1}^m \sum_{j=1}^n \text{P}_{i,j} \text{A}_{i,j} \; \text {for} \; gm_{i,j} \ge gm_{thresh} \; \text {and} \; \text{P}_{i,j} \ge \text{P}_{thresh}$$
where Pi,j is the ground failure probability (areal coverage) at grid cell i, j, Ai,j is the area of cell i, j (in km2), m is the number of rows, n is the number of columns, gmi,j is the ground motion parameter (peak ground acceleration or peak ground velocity) at grid cell i, j, gmthresh is the ground motion threshold, and Pthresh is the probability threshold.
### Estimated Population Exposure
The estimated population exposure, popexp, represents the population of each grid cell multiplied by the areal coverage:
$$\text{pop}_{exp} = \sum_{i=1}^m \sum_{j=1}^n \text{L}_{i,j} \text{P}_{i,j} \; \text {for} \; gm_{i,j} \ge gm_{thresh} \; \text {and} \; \text{P}_{i,j} \ge \text{P}_{thresh}$$
where Li,j is the population of grid cell i, j, m is the number of rows, n is the number of columns, Pi,j is the ground failure probability (areal coverage) at cell i,j, gmi,j is the ground motion parameter (peak ground acceleration or peak ground velocity) at grid cell i, j, gmthresh is the ground motion threshold, and Pthresh is the probability threshold. The population grid we use is LandScan 2016™ (Bright and others, 2017). Since population is reported in whole numbers, resampling is problematic. Therefore, to compute this statistic we resample the probability grid to the Landscan grid using a block mean before multiplying. Popexp is not an estimate of fatalities, but instead represents the number of people estimated to be living near areas prone to ground failure hazard triggered by the earthquake. This serves as a proxy for potential human impacts.
The alert level bins are each defined by an order-of-magnitude range of the relevant statistic (Htot or popexp), a qualitative descriptor (little to no, limited, significant, extensive), and a corresponding color (green to red). The alert bin edges were determined by computing these statistics for historic earthquakes and using knowledge about what actually occurred to select bin edges that grouped them most appropriately for each qualitative descriptor (see Figure 9 for examples). We do not have quantified measures of fatalities or economic losses specific to each type of ground failure for many historic events, so we use the model statistics and expert opinion to select the bin edges that best qualitatively captured the character of the historic events. Table 4 describes the alert levels currently implemented. Note that the liquefaction alert levels are an order of magnitude higher than the landslide bin levels. This is because liquefaction hazard tends to be elevated over low-lying flat areas, which can have much larger total areas than the more isolated steep areas where landslide hazard is elevated and damage from liquefaction is different in nature from that of landslides. This results in much larger values of the statistics for the same expert-defined alert level for liquefaction than for landslides.
#### Table 4: Summary of Alert Level Definitions
Estimated Area Exposed to Hazard Estimated Population Exposure
Bin edges Description Bin edges Description
Landslides Green < 1 km2 Little or no landsliding is expected, but some landslides could have occurred in highly susceptible areas. < 100 The number of people living near areas prone to landslides triggered by this earthquake is low, but landslide damage or fatalities are still possible in highly susceptible areas.
Yellow 1 - 10 km2 Landslides triggered by this earthquake are estimated to be limited in number and (or) spatial extent. 100 - 1,000 The number of people living near areas that could have produced landslides in this earthquake is limited. This is not a direct estimate of landslide fatalities or losses.
Orange 10 - 100 km2 Landslides triggered by this earthquake are estimated to be significant in number and (or) spatial extent. 1,000 - 10,000 The number of people living near areas that could have produced landslides in this earthquake is significant. This is not a direct estimate of landslide fatalities or losses.
Red > 100 km2 Landslides triggered by this earthquake are estimated to be extremely large in number and (or) spatially extensive. > 10,000 The number of people living near areas that could have produced landslides in this earthquake is extensive. This is not a direct estimate of landslide fatalities or losses.
Liquefaction Green < 10 km2 Little or no liquefaction is expected, but some liquefaction could have occurred in highly susceptible areas. < 100o The number of people living near areas that could have produced liquefaction in this earthquake is low, but liquefaction damage or fatalities are still possible in highly susceptible areas. This is not a direct estimate of liquefaction fatalities or losses.
Yellow 10 - 100 km2 Liquefaction triggered by this earthquake is estimated to be limited in severity and (or) spatial extent. 1,000 - 10,000 The number of people living near areas that could have produced liquefaction in this earthquake is limited. This is not a direct estimate of liquefaction fatalities or losses.
Orange 100 - 1,000 km2 Liquefaction triggered by this earthquake is estimated to be significant in severity and (or) spatial extent. 10,000 - 100,000 The number of people living near areas that could have produced liquefaction in this earthquake is significant. This is not a direct estimate of liquefaction fatalities or losses.
Red > 1,000 km2 Liquefaction triggered by this earthquake is estimated to be extensive in severity and (or) spatial extent. > 100,000 The number of people living near areas that could have produced liquefaction in this earthquake is extensive. This is not a direct estimate of liquefaction fatalities or losses.
In general, alerts qualitatively capture the hazard and population exposure, with some exceptions. Low probabilities in a highly populated area (e.g., Hirakata, Japan) can inflate the population alert. For some events, most of the losses were due to exceptional site-specific circumstances that these simple ground failure models cannot capture (e.g., large deep-seated slide impacting a remote village). In addition, the model results for historic events can be inconsistent because ShakeMap quality varies between historic events so some model results are more accurate than others. Furthermore, population exposure is currently our only proxy for potential impacts, but it does not account well for indirect remote effects (e.g., landslide dam hazards, blocked or damaged roads).
## References
• Allstadt, K.E., Jibson, R. W., Thompson, E.M., Massey, C.I., Wald, D.J., Godt, J.W., Rengers, F.K., 2018, Improving Near-Real-Time Coseismic Landslide Models: Lessons Learned from the 2016 Kaikoura, New Zealand, Earthquake: Bulletin of the Seismological Society of America, (in press).
• Arino, O., Ramos Perez, J.J., Kalogirou, V., Bontemps, S., Defourny, P., Van Bogaert, E., 2012, Global Land Cover Map for 2009 (GlobCover 2009): European Space Agency (ESA) and Université catholique de Louvain (UCL), PANGAEA.
• Baise, L.G., and Rashidian, V., 2017, Validation of a Geospatial Liquefaction Model for Noncoastal Regions Including Nepal: Final Technical Report for USGS Award G16AP00014.
• Bright, E.A., Rose, A.N., Urban, M.L., and McKee, J.J., 2017, LandScan 2016 High-Resolution Global Population Data Set: U.S. Dept. of Energy, Oak Ridge National Laboratory.
• Danielson, J., and Gesch, D., 2011, Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010): U.S. Department of the Interior, U.S. Geological Survey, Open-File Report 2011-1073.
• Fan, Y., Li, H., and Miguez-Macho, G., 2013, Global Patterns of Groundwater Table Depth: Science, 339, 940-943.
• Godt, J.W., Sener, B., Verdin, K.L., Wald, D.J., Earle, P.S., Harp, E.L. and Jibson, R.W., 2008, Rapid Assessment of Earthquake-induced Landsliding: Proceedings of the First World Landslide Forum, United Nations University, Tokyo, Japan, p. 392-395.
• Harp, E.L., and Jibson, R.W., 1995, Inventory of landslides triggered by the 1994 Northridge, California earthquake: U.S. Geological Survey Open-File Report 95-213, 17 p., 2 plates.
• Hartmann, J. and Moosdorf, N., 2012, The new global lithological map database GLiM: A representation of rock properties at the Earth surface: G3, vol 13, no. 12., 37 p.
• Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G., and Jarvis, A., 2005, Very high resolution interpolated climate surfaces for global land areas: International Journal of Climatology, 25(15), 1965–1978.
• Massey, C., Townsend D., Rathje, E., Allstadt, K., Kaneko, Y., Lukovic, B., Bradley, B., Wartman, J., Horspool, N., Hamling, I., Carey, J., Cox, S., Davidson, J., Dellow, S., Godt, J.W., Holden, C., Jones, K., Kaiser, A., Little, M., Lyndsell, B., McColl, S., Morgenstern, R., Rengers, F.K., Rhoades, D., Rosser, B., Strong, D., Singeisen, C., Villeneuve, M., 2018, Landslides triggered by the 14 November 2016, Mw 7.8 earthquake, Kaikōura, New Zealand, Bulletin of the Seismological Society of America.
• Moore, I.D., Grayson, R.B., and Ladson, A.R., 1991, Digital terrain modelling: a review of hydrological, geomorphological, and biological applications: Hydrological Processes, 5(1), 3–30.
• Nowicki, M.A., Wald, D.J., Hamburger, M.W., Hearne, M., and Thompson, E.M., 2014, Development of a globally applicable model for near real-time prediction of seismically induced landslides: Engineering Geology, v. 173, p. 54–65.
• Nowicki Jessee, M.A., Hamburger, H.W., Allstadt, K.E., Wald, D.J., Robeson, S.M., Tanyas, H., Hearne, M., Thompson, E.M., 2018, A Global Empirical Model for Near Real-time Assessment of Seismically Induced Landslides, J. Geophys. Res. (in press).
• Wald, D.J., and Allen, T.I., 2007, Topographic Slope as a Proxy for Seismic Site Conditions and Amplification: Bulletin of the Seismological Society of America, 97 (5), 1379–1395.
• Worden, C.B. and D.J. Wald, 2016, ShakeMap Manual Online: technical manual, user’s guide, and software guide: U. S. Geological Survey.
• Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G., Christian, J.T., Dobry, R., Finn, W.D.L., Harder, L F., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson, W.F., Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., and Stokoe, K.H., 2001, Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on the evaluation of liquefaction resistance of soils: Journal of Geotechnical and Geoenvironmental Engineering, v. 127, pp. 817–833.
• Zhu, J., Daley, D., Baise, L.G., Thompson, E.M., Wald, D.J., and Knudsen, K.L., 2015, A geospatial liquefaction model for rapid response and loss estimation: Earthquake Spectra, v. 31, no. 3, p. 1813–1837.
• Zhu, J., Baise, L. G., Thompson, E. M., 2017, An Updated Geospatial Liquefaction Model for Global Application, Bulletin of the Seismological Society of America, 107, p 1365-1385, doi: 0.1785/0120160198
| 2018-11-21T11:04:23 |
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http://dlmf.nist.gov/25.21
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# §25.21(i) Introduction
In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. Citations in bulleted lists refer to papers for which research software has been made available and can be downloaded via the Web. References to research software that is available in other ways is listed separately.
A more complete list of available software for computing these functions is found in the Software Index.
# §25.21(ii) Zeta Functions for Real Arguments
• Brent (1978b). Fortran.
# §25.21(iii) Zeta Functions for Complex Arguments
• Bañuelos and Depine (1980). Fortran.
# §25.21(iv) Hurwitz Zeta Function
No research software has been found for these functions. For other software see the Software Index.
# §25.21(v) Dilogarithms, Polylogarithms
• Brent (1978b). Fortran.
• Ginsberg and Zaborowski (1975). Fortran.
# §25.21(vi) Clausen’s Integral
See §25.12(i).
• MacLeod (1996a). Fortran.
# §25.21(vii) Fermi–Dirac and Bose–Einstein Integrals
• Antia (1993). Fortran.
• Bañuelos et al. (1981). Fortran.
• Cloutman (1989). Fortran.
• Fullerton and Rinker (1986). Fortran.
• Gautschi (1993). Fortran.
• Goano (1995). Fortran.
• Gong et al. (2001). Fortran.
• MacLeod (1998). Fortran.
| 2015-05-22T19:08:17 |
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https://par.nsf.gov/biblio/10184512-infrared-interferometry-spatially-spectrally-resolve-jets-ray-binaries
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Infrared interferometry to spatially and spectrally resolve jets in X-ray binaries
ABSTRACT Infrared interferometry is a new frontier for precision ground-based observing, with new instrumentation achieving milliarcsecond (mas) spatial resolutions for faint sources, along with astrometry on the order of 10 microarcseconds (μas). This technique has already led to breakthroughs in the observations of the supermassive black hole at the Galactic centre and its orbiting stars, active galactic nucleus, and exo-planets, and can be employed for studying X-ray binaries (XRBs), microquasars in particular. Beyond constraining the orbital parameters of the system using the centroid wobble and spatially resolving jet discrete ejections on mas scales, we also propose a novel method to discern between the various components contributing to the infrared bands: accretion disc, jets, and companion star. We demonstrate that the GRAVITY instrument on the Very Large Telescope Interferometer should be able to detect a centroid shift in a number of sources, opening a new avenue of exploration for the myriad of transients expected to be discovered in the coming decade of radio all-sky surveys. We also present the first proof-of-concept GRAVITY observation of a low-mass XRB transient, MAXI J1820+070, to search for extended jets on mas scales. We place the tightest constraints yet via direct imaging on the size of more »
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10184512
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
495
Issue:
1
Page Range or eLocation-ID:
525 to 535
ISSN:
0035-8711
3. ABSTRACT Without additional heating, radiative cooling of the halo gas of massive galaxies (Milky Way-mass and above) produces cold gas or stars exceeding that observed. Heating from active galactic nucleus (AGN) jets is likely required, but the jet properties remain unclear. This is particularly challenging for galaxy simulations, where the resolution is orders-of-magnitude insufficient to resolve jet formation and evolution. On such scales, the uncertain parameters include the jet energy form [kinetic, thermal, cosmic ray (CR)]; energy, momentum, and mass flux; magnetic fields; opening angle; precession; and duty cycle. We investigate these parameters in a $10^{14}\, {\rm M}_{\odot }$ halo using high-resolution non-cosmological magnetohydrodynamic simulations with the FIRE-2 (Feedback In Realistic Environments) stellar feedback model, conduction, and viscosity. We explore which scenarios qualitatively meet observational constraints on the halo gas and show that CR-dominated jets most efficiently quench the galaxy by providing CR pressure support and modifying the thermal instability. Mildly relativistic (∼MeV or ∼1010K) thermal plasma jets work but require ∼10 times larger energy input. For fixed energy flux, jets with higher specific energy (longer cooling times) quench more effectively. For this halo mass, kinetic jets are inefficient at quenching unless they have wide opening or precession angles. Magnetic fieldsmore »
| 2022-12-07T01:13:57 |
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https://www.aimsciences.org/article/doi/10.3934/dcdss.2019055
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Article Contents
Article Contents
# Uyghur morphological analysis using joint conditional random fields: Based on small scaled corpus
• * Corresponding author: Ghalip Abdukerim
• As a fundamental research in the field of natural language processing, the Uyghur morphological analysis is used mainly to determine the part of speech (POS) and segmental morphemes (stem and affix) of a word in a given sentence, as well as to automatically annotate the grammatical function of the morphemes based on the context. It is necessary to provide various information for other tasks of natural language processing including syntactic analysis, machine translation, automatic summarization, and semantic analysis, etc. In order to increase the morphological analysis efficiency, this paper puts forward a hybrid approach to create a statistical model for Uyghur morphological tagging through a small-scale corpus. Experimental results show that this plan can obtain an overall accuracy of 92.58 % with a limited training corpus.
Mathematics Subject Classification: Primary: 68T50, 68U15; Secondary: 60G60.
Citation:
• Figure 1. The morphological analysis result and hierarchical relationship of a Uyghur sentence
Figure 2. The Architecture of a semi-supervised morphological analysis based on the hybrid approach
Figure 3. Morphological Tag Decoding Process of Words in the Sentence
Figure 4. The Relationship between Parameter $\beta$ and Accuracy
Table 1. Feature Template of POS Tagging Model
Features Description ${{w}_{i-2}}{{pos}_{i}}$, ${{w}_{i-1}}{{pos}_{i}}$, ${{w}_{i}}{{pos}_{i}}$, ${{w}_{i+1}}{{pos}_{i}}$, ${{w}_{i+2}}{{pos}_{i}}$ Unary context features of the word ${{w}_{i-2}}{{w}_{i-1}}{{pos}_{i}}$, ${{w}_{i-1}}{{w}_{i}}{{pos}_{i}}$, ${{w}_{i}}{{w}_{i+1}}{{pos}_{i}}$, ${{w}_{i+1}}{{w}_{i+2}}{{pos}_{i}}$, ${{w}_{i-1}}{{w}_{i+1}}{{pos}_{i}}$ Binary context features of the word $h_1(w_i){{pos}_{i}}$, $h_2(w_i){{pos}_{i}}$, $h_3(w_i){{pos}_{i}}$, $h_4(w_i){{pos}_{i}}$, $h_5(w_i){{pos}_{i}}$ n characters selected from the beginning of the word $t_1(w_i){{pos}_{i}}$, $t_2(w_i){{pos}_{i}}$, $t_3(w_i){{pos}_{i}}$, $t_4(w_i){{pos}_{i}}$, $t_5(w_i){{pos}_{i}}$ n characters selected from the end of the word ${{pos}_{i-1}}{{pos}_{i}}$ POS tag transition feature
Table 2. Feature Template of the Morphological Tagging Model
Features Description ${{m}_{i-2}}{{t}_{i}}$, ${{m}_{i-1}}{{t}_{i}}$, ${{m}_{i}}{{t}_{i}}$, ${{m}_{i+1}}{{t}_{i}}$, ${{m}_{i+2}}{{t}_{i}}$ Unary context features of the morpheme ${{m}_{i-2}}{{m}_{i-1}}{{t}_{i}}$, ${{m}_{i-1}}{{m}_{i}}{{t}_{i}}$, ${{m}_{i}}{{m}_{i+1}}{{t}_{i}}$, ${{m}_{i+1}}{{m}_{i+2}}{{t}_{i}}$, ${{m}_{i-1}}{{m}_{i+1}}{{t}_{i}}$ Binary context features of the morpheme ${{t}_{i-1}}{{t}_{i}}$ Morphological tag transition feature
Table 3. List of Morphological Tag Candidates of Words in the Sentence
Table 4. Manually Tagged Corpus Format and Content Example
Table 5. Details of Experimental Data
Number of sentences Number of words (including punctuation marks) Number of Uyghur words Training set 1000 12433 10391 Development set 200 2564 2151 Test set 200 2492 2075
Table 6. Experimental Results
Method Accuracy (%) Stemming Morpheme segmentation POS Overall Tag sequence Markov model 90.18 83.25 86.17 75.13 Joint CRF model 91.98 85.79 92.7 77.95 Tag sequence Markov model, $\alpha$=0.95 92.65 88.47 88.12 79.65 Joint CRF model, $\alpha$=0.9 92.85 89.76 92.6 80.73
Table 7. Analysis for the Influence of Filtering Rules on Morphological Tagging
Method(Joint CRF model, $\alpha$=0.9, $\beta$=0.1) Accuracy (%) Stemming Morpheme segmentation POS Overall Joint CRF model, $\alpha$=0.9, $\beta$=0.1, When filtering rules are not used 92.85 89.76 92.6 80.73 Joint CRF model, $\alpha$=0.9, $\beta$=0.1, When filtering rules are used 97.4 94.58 96.35 92.58 Tag sequence transition model, $\alpha$=0.95, When filtering rules are used 94.35 93.22 94.78 91.81
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Open Access Under a Creative Commons license
Figures(4)
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| 2023-03-20T16:46:56 |
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https://ftp.aimsciences.org/article/doi/10.3934/proc.2013.2013.837
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Article Contents
Article Contents
# Anosov diffeomorphisms
• We use Adler, Tresser and Worfolk decomposition of Anosov automorphisms to give an explicit construction of the stable and unstable $C^{1+}$ self-renormalizable sequences.
Mathematics Subject Classification: Primary: 37D20; Secondary: 37E10.
Citation:
• [1] R. Adler, C. Tresser and P. A. Worfolk, Topological conjugacy of linear endomorphisms of the 2-torus, Trans. Amer. Math. Soc., 349 (1997), 1633-1652. [2] J. P. Almeida, A. M. Fisher, A. A. Pinto and D. A. Rand, Anosov and circle diffeomorphisms, in "Dynamics Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer Verlag, 2011, 11-23. [3] J. P. Almeida, A. A. Pinto and D. A. Rand, Renormalization of circle diffeomorphism sequences and Markov sequences, to appear in "Proceedings of the Conference NOMA11," Évora, Portugal, Springer Proceedings in Mathematics, Springer Verlag, 2012. [4] V. I. Arnol'd, Small denominators I: On the mapping of a circle into itself, Investijia Akad. Nauk. Math., 25 (1961), 21-96; Transl. A.M.S., 2nd series, 46, 213-284. [5] E. Cawley, The Teichmüller space of an Anosov diffeomorphism of $T^2$, Inventiones Mathematicae, 112 (1993), 351-376. [6] P. Coullet and C. Tresser, Itération d'endomorphismes et groupe de renormalisation, Journal de Physique Colloques, 39 (1978), C5-25-C5-28. [7] J. Franks, Anosov diffeomorphisms, in "Global Analysis" (ed. S. Smale), Proc. Sympos. Pure Math., 14, Amer. Math. Soc., Providence, R.I., 1970, 61-93. [8] E. Ghys, Rigidité différentiable des groupes Fuchsiens, Publ. IHES, 78 (1993), 163-185. [9] M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. IHES, 49 (1979), 5-233. [10] Y. Jiang, Teichmüller structures and dual geometric Gibbs type measure theory for continuous potentials, preprint, (2008), 1-67. [11] Y. Jiang, Metric invariants in dynamical systems, Journal of Dynamics and Differentiable Equations, 17 (2005), 51-71. [12] O. Lanford, Renormalization group methods for critical circle mappings with general rotation number, in "VIIIth International Congress on Mathematical Physics," World Sci. Publishing, Singapore, 1987, 532-536. [13] R. de la Llave, Invariants for smooth conjugacy of hyperbolic dynamical systems II, Commun. Math. Phys., 109 (1987), 369-378. [14] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429. [15] R. Manẽ, "Ergodic Theory and Differentiable Dynamics," Springer-Verlag, Berlin, 1987. [16] J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems I, Commun. Math. Phys., 109 (1987), 681-689. [17] J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems III, Commun. Math. Phys., 112 (1989), 317-333. [18] H. Masur, Interval exchange transformations and measured foliations, The Annals of Mathematics. 2nd Ser., 115 (1982), 169-200. [19] W. de Melo and S. van Strien, "One-dimensional Dynamics," A series of Modern Surveys in Mathematics, Springer-Verlag, New York, 1993. [20] R. C. Penner and J. L. Harer, "Combinatorics of Train-Tracks," Princeton University Press, Princeton, New Jersey, 1992. [21] A. A. Pinto, J. P. Almeida and A. Portela, Golden tilings, Transactions of the American Mathematical Society, 364 (2012), 2261-2280. [22] A. A. Pinto, J. P. Almeida and D. A. Rand, Anosov and renormalized circle diffeomorphisms, submitted, (2012), 1-33. [23] A. A. Pinto and D. A. Rand, Train-tracks with $C^{1+}$ self-renormalisable structures, Journal of Difference Equations and Applications, 16 (2010), 945-962. [24] A. A. Pinto and D. A. Rand, Solenoid functions for hyperbolic sets on surfaces, in "Dynamics, Ergodic Theory and Geometry" (ed. Boris Hasselblatt), 54, MSRI Publications, 2007, 145-178. [25] A. A. Pinto and D. A. Rand, Rigidity of hyperbolic sets on surfaces, J. London Math. Soc., 71 (2004), 481-502. [26] A. A. Pinto and D. A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics, Bull. London Math. Soc., 34 (2002), 341-352. [27] A. A. Pinto and D. A. Rand, Teichmüller spaces and HR structures for hyperbolic surface dynamics, Ergodic Theory & Dynamical Systems, 22 (2002), 1905-1931. [28] A. A. Pinto and D. A. Rand, Existence, uniqueness and ratio decomposition for Gibbs states via duality, Ergodic Theory & Dynamical Systems, 21 (2001), 533-543. [29] A. A. Pinto and D. A. Rand, Characterising rigidity and flexibility of pseudo-Anosov and other transversally laminated dynamical systems on surfaces, Warwick preprint, 1995. [30] A. A. Pinto, D. A. Rand and F. Ferreira, Arc exchange systems and renormalization, Journal of Difference Equations and Applications, 16 (2010), 347-371. [31] A. A. Pinto, D. A. Rand and F. Ferreira, Cantor exchange systems and renormalization, Journal of Differential Equations, 243 (2007), 593-616. [32] A. A. Pinto, D. A. Rand and F. Ferreira, "Fine structures of hyperbolic diffeomorphisms," Springer Monographs in Mathematics, Springer, 2009. [33] A. A. Pinto and D. Sullivan, The circle and the solenoid, Dedicated to Anatole Katok On the Occasion of his 60th Birthday, DCDS A, 16 (2006), 463-504. [34] M. Shub, "Global Stability of Dynamical Systems," Springer-Verlag, 1987. [35] Ya. Sinai, Markov Partitions and C-diffeomorphisms, Anal. and Appl., 2 (1968), 70-80. [36] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc., 19 (1988), 417-431. [37] W. Veech, Gauss measures for transformations on the space of interval exchange maps, The Annals of Mathematics, 2nd Ser., 115 (1982), 201-242. [38] R. F. Williams, Expanding attractors, Publ. I.H.E.S., 43 (1974), 169-203. [39] R. F. Williams, The "DA" maps of Smale and structural stability, in "Global Analysis" (ed. S. Smale), Proc. Symp. in Pure Math., 14, Amer. Math. Soc., Providence, RI, 1970, 329-334. [40] J. C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne, Ann. Scient. Éc. Norm. Sup., 4 série, t., 17 (1984), 333-359.
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http://hitchhikersgui.de/Small-bias_sample_space
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# Small-bias sample space
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In theoretical computer science, a small-bias sample space (also known as ${\displaystyle \epsilon }$-biased sample space, ${\displaystyle \epsilon }$-biased generator, or small-bias probability space) is a probability distribution that fools parity functions. In other words, no parity function can distinguish between a small-bias sample space and the uniform distribution with high probability, and hence, small-bias sample spaces naturally give rise to pseudorandom generators for parity functions.
The main useful property of small-bias sample spaces is that they need far fewer truly random bits than the uniform distribution to fool parities. Efficient constructions of small-bias sample spaces have found many applications in computer science, some of which are derandomization, error-correcting codes, and probabilistically checkable proofs. The connection with error-correcting codes is in fact very strong since ${\displaystyle \epsilon }$-biased sample spaces are equivalent to ${\displaystyle \epsilon }$-balanced error-correcting codes.
## Definition
### Bias
Let ${\displaystyle X}$ be a probability distribution over ${\displaystyle \{0,1\}^{n}}$. The bias of ${\displaystyle X}$ with respect to a set of indices ${\displaystyle I\subseteq \{1,\dots ,n\}}$ is defined as[1]
${\displaystyle {\text{bias}}_{I}(X)=\left|\Pr _{x\sim X}\left(\sum _{i\in I}x_{i}=0\right)-\Pr _{x\sim X}\left(\sum _{i\in I}x_{i}=1\right)\right|=\left|2\cdot \Pr _{x\sim X}\left(\sum _{i\in I}x_{i}=0\right)-1\right|\,,}$
where the sum is taken over ${\displaystyle \mathbb {F} _{2}}$, the finite field with two elements. In other words, the sum ${\displaystyle \sum _{i\in I}x_{i}}$ equals ${\displaystyle 0}$ if the number of ones in the sample ${\displaystyle x\in \{0,1\}^{n}}$ at the positions defined by ${\displaystyle I}$ is even, and otherwise, the sum equals ${\displaystyle 1}$. For ${\displaystyle I=\emptyset }$, the empty sum is defined to be zero, and hence ${\displaystyle {\text{bias}}_{\emptyset }(X)=1}$.
### ϵ-biased sample space
A probability distribution ${\displaystyle X}$ over ${\displaystyle \{0,1\}^{n}}$ is called an ${\displaystyle \epsilon }$-biased sample space if ${\displaystyle {\text{bias}}_{I}(X)\leq \epsilon }$ holds for all non-empty subsets ${\displaystyle I\subseteq \{1,2,\ldots ,n\}}$.
### ϵ-biased set
An ${\displaystyle \epsilon }$-biased sample space ${\displaystyle X}$ that is generated by picking a uniform element from a multiset ${\displaystyle X\subseteq \{0,1\}^{n}}$ is called ${\displaystyle \epsilon }$-biased set. The size ${\displaystyle s}$ of an ${\displaystyle \epsilon }$-biased set ${\displaystyle X}$ is the size of the multiset that generates the sample space.
### ϵ-biased generator
An ${\displaystyle \epsilon }$-biased generator ${\displaystyle G:\{0,1\}^{\ell }\to \{0,1\}^{n}}$ is a function that maps strings of length ${\displaystyle \ell }$ to strings of length ${\displaystyle n}$ such that the multiset ${\displaystyle X_{G}=\{G(y)\;\vert \;y\in \{0,1\}^{\ell }\}}$ is an ${\displaystyle \epsilon }$-biased set. The seed length of the generator is the number ${\displaystyle \ell }$ and is related to the size of the ${\displaystyle \epsilon }$-biased set ${\displaystyle X_{G}}$ via the equation ${\displaystyle s=2^{\ell }}$.
## Connection with epsilon-balanced error-correcting codes
There is a close connection between ${\displaystyle \epsilon }$-biased sets and ${\displaystyle \epsilon }$-balanced linear error-correcting codes. A linear code ${\displaystyle C:\{0,1\}^{n}\to \{0,1\}^{s}}$ of message length ${\displaystyle n}$ and block length ${\displaystyle s}$ is ${\displaystyle \epsilon }$-balanced if the Hamming weight of every nonzero codeword ${\displaystyle C(x)}$ is between ${\displaystyle ({\frac {1}{2}}-\epsilon )s}$ and ${\displaystyle ({\frac {1}{2}}+\epsilon )s}$. Since ${\displaystyle C}$ is a linear code, its generator matrix is an ${\displaystyle (n\times s)}$-matrix ${\displaystyle A}$ over ${\displaystyle \mathbb {F} _{2}}$ with ${\displaystyle C(x)=x\cdot A}$.
Then it holds that a multiset ${\displaystyle X\subset \{0,1\}^{n}}$ is ${\displaystyle \epsilon }$-biased if and only if the linear code ${\displaystyle C_{X}}$, whose columns are exactly elements of ${\displaystyle X}$, is ${\displaystyle \epsilon }$-balanced.[2]
## Constructions of small epsilon-biased sets
Usually the goal is to find ${\displaystyle \epsilon }$-biased sets that have a small size ${\displaystyle s}$ relative to the parameters ${\displaystyle n}$ and ${\displaystyle \epsilon }$. This is because a smaller size ${\displaystyle s}$ means that the amount of randomness needed to pick a random element from the set is smaller, and so the set can be used to fool parities using few random bits.
### Theoretical bounds
The probabilistic method gives a non-explicit construction that achieves size ${\displaystyle s=O(n/\epsilon ^{2})}$.[2] The construction is non-explicit in the sense that finding the ${\displaystyle \epsilon }$-biased set requires a lot of true randomness, which does not help towards the goal of reducing the overall randomness. However, this non-explicit construction is useful because it shows that these efficient codes exist. On the other hand, the best known lower bound for the size of ${\displaystyle \epsilon }$-biased sets is ${\displaystyle s=\Omega (n/(\epsilon ^{2}\log(1/\epsilon ))}$, that is, in order for a set to be ${\displaystyle \epsilon }$-biased, it must be at least that big.[2]
### Explicit constructions
There are many explicit, i.e., deterministic constructions of ${\displaystyle \epsilon }$-biased sets with various parameter settings:
• Naor & Naor (1990) achieve ${\displaystyle \displaystyle s={\frac {n}{{\text{poly}}(\epsilon )}}}$. The construction makes use of Justesen codes (which is a concatenation of Reed–Solomon codes with the Wozencraft ensemble) as well as expander walk sampling.
• Alon et al. (1992) achieve ${\displaystyle \displaystyle s=O\left({\frac {n}{\epsilon \log(n/\epsilon )}}\right)^{2}}$. One of their constructions is the concatenation of Reed–Solomon codes with the Hadamard code; this concatenation turns out to be an ${\displaystyle \epsilon }$-balanced code, which gives rise to an ${\displaystyle \epsilon }$-biased sample space via the connection mentioned above.
• Concatenating Algebraic geometric codes with the Hadamard code gives an ${\displaystyle \epsilon }$-balanced code with ${\displaystyle \displaystyle s=O\left({\frac {n}{\epsilon ^{3}\log(1/\epsilon )}}\right)}$.[2]
• Ben-Aroya & Ta-Shma (2009) achieves ${\displaystyle \displaystyle s=O\left({\frac {n}{\epsilon ^{2}\log(1/\epsilon )}}\right)^{5/4}}$.
• Ta-Shma (2017) achieves ${\displaystyle \displaystyle s=O\left({\frac {n}{\epsilon ^{2+o(1)}}}\right)}$ which is almost optimal because of the lower bound.
These bounds are mutually incomparable. In particular, none of these constructions yields the smallest ${\displaystyle \epsilon }$-biased sets for all settings of ${\displaystyle \epsilon }$ and ${\displaystyle n}$.
## Application: almost k-wise independence
An important application of small-bias sets lies in the construction of almost k-wise independent sample spaces.
### k-wise independent spaces
A random variable ${\displaystyle Y}$ over ${\displaystyle \{0,1\}^{n}}$ is a k-wise independent space if, for all index sets ${\displaystyle I\subseteq \{1,\dots ,n\}}$ of size ${\displaystyle k}$, the marginal distribution ${\displaystyle Y|_{I}}$ is exactly equal to the uniform distribution over ${\displaystyle \{0,1\}^{k}}$. That is, for all such ${\displaystyle I}$ and all strings ${\displaystyle z\in \{0,1\}^{k}}$, the distribution ${\displaystyle Y}$ satisfies ${\displaystyle \Pr _{Y}(Y|_{I}=z)=2^{-k}}$.
#### Constructions and bounds
k-wise independent spaces are fairly well understood.
• A simple construction by Joffe (1974) achieves size ${\displaystyle n^{k}}$.
• Alon, Babai & Itai (1986) construct a k-wise independent space whose size is ${\displaystyle n^{k/2}}$.
• Chor et al. (1985) prove that no k-wise independent space can be significantly smaller than ${\displaystyle n^{k/2}}$.
#### Joffe's construction
Joffe (1974) constructs a ${\displaystyle k}$-wise independent space ${\displaystyle Y}$ over the finite field with some prime number ${\displaystyle n>k}$ of elements, i.e., ${\displaystyle Y}$ is a distribution over ${\displaystyle \mathbb {F} _{n}^{n}}$. The initial ${\displaystyle k}$ marginals of the distribution are drawn independently and uniformly at random:
${\displaystyle (Y_{0},\dots ,Y_{k-1})\sim \mathbb {F} _{n}^{k}}$.
For each ${\displaystyle i}$ with ${\displaystyle k\leq i, the marginal distribution of ${\displaystyle Y_{i}}$ is then defined as
${\displaystyle Y_{i}=Y_{0}+Y_{1}\cdot i+Y_{2}\cdot i^{2}+\dots +Y_{k-1}\cdot i^{k-1}\,,}$
where the calculation is done in ${\displaystyle \mathbb {F} _{n}}$. Joffe (1974) proves that the distribution ${\displaystyle Y}$ constructed in this way is ${\displaystyle k}$-wise independent as a distribution over ${\displaystyle \mathbb {F} _{n}^{n}}$. The distribution ${\displaystyle Y}$ is uniform on its support, and hence, the support of ${\displaystyle Y}$ forms a ${\displaystyle k}$-wise independent set. It contains all ${\displaystyle n^{k}}$ strings in ${\displaystyle \mathbb {F} _{n}^{k}}$ that have been extended to strings of length ${\displaystyle n}$ using the deterministic rule above.
### Almost k-wise independent spaces
A random variable ${\displaystyle Y}$ over ${\displaystyle \{0,1\}^{n}}$ is a ${\displaystyle \delta }$-almost k-wise independent space if, for all index sets ${\displaystyle I\subseteq \{1,\dots ,n\}}$ of size ${\displaystyle k}$, the restricted distribution ${\displaystyle Y|_{I}}$ and the uniform distribution ${\displaystyle U_{k}}$ on ${\displaystyle \{0,1\}^{k}}$ are ${\displaystyle \delta }$-close in 1-norm, i.e., ${\displaystyle {\Big \|}Y|_{I}-U_{k}{\Big \|}_{1}\leq \delta }$.
#### Constructions
Naor & Naor (1990) give a general framework for combining small k-wise independent spaces with small ${\displaystyle \epsilon }$-biased spaces to obtain ${\displaystyle \delta }$-almost k-wise independent spaces of even smaller size. In particular, let ${\displaystyle G_{1}:\{0,1\}^{h}\to \{0,1\}^{n}}$ be a linear mapping that generates a k-wise independent space and let ${\displaystyle G_{2}:\{0,1\}^{\ell }\to \{0,1\}^{h}}$ be a generator of an ${\displaystyle \epsilon }$-biased set over ${\displaystyle \{0,1\}^{h}}$. That is, when given a uniformly random input, the output of ${\displaystyle G_{1}}$ is a k-wise independent space, and the output of ${\displaystyle G_{2}}$ is ${\displaystyle \epsilon }$-biased. Then ${\displaystyle G:\{0,1\}^{\ell }\to \{0,1\}^{n}}$ with ${\displaystyle G(x)=G_{1}(G_{2}(x))}$ is a generator of an ${\displaystyle \delta }$-almost ${\displaystyle k}$-wise independent space, where ${\displaystyle \delta =2^{k/2}\epsilon }$.[3]
As mentioned above, Alon, Babai & Itai (1986) construct a generator ${\displaystyle G_{1}}$ with ${\displaystyle h={\tfrac {k}{2}}\log n}$, and Naor & Naor (1990) construct a generator ${\displaystyle G_{2}}$ with ${\displaystyle \ell =\log s=\log h+O(\log(\epsilon ^{-1}))}$. Hence, the concatenation ${\displaystyle G}$ of ${\displaystyle G_{1}}$ and ${\displaystyle G_{2}}$ has seed length ${\displaystyle \ell =\log k+\log \log n+O(\log(\epsilon ^{-1}))}$. In order for ${\displaystyle G}$ to yield a ${\displaystyle \delta }$-almost k-wise independent space, we need to set ${\displaystyle \epsilon =\delta 2^{-k/2}}$, which leads to a seed length of ${\displaystyle \ell =\log \log n+O(k+\log(\delta ^{-1}))}$ and a sample space of total size ${\displaystyle 2^{\ell }\leq \log n\cdot {\text{poly}}(2^{k}\cdot \delta ^{-1})}$.
## Notes
1. ^ cf., e.g., Goldreich (2001)
2. ^ a b c d cf., e.g., p. 2 of Ben-Aroya & Ta-Shma (2009)
3. ^ Section 4 in Naor & Naor (1990)
## References
• Alon, Noga; Babai, László; Itai, Alon (1986), "A fast and simple randomized parallel algorithm for the maximal independent set problem" (PDF), Journal of Algorithms, 7 (4): 567–583, doi:10.1016/0196-6774(86)90019-2
• Alon, Noga; Goldreich, Oded; Håstad, Johan; Peralta, René (1992), "Simple Constructions of Almost k-wise Independent Random Variables" (PDF), Random Structures & Algorithms, 3 (3): 289–304, doi:10.1002/rsa.3240030308
• Ben-Aroya, Avraham; Ta-Shma, Amnon (2009), "Constructing Small-Bias Sets from Algebraic-Geometric Codes" (PDF), Proceedings of the 50th Annual Symposium on Foundations of Computer Science, FOCS 2009: 191–197, doi:10.1109/FOCS.2009.44, ISBN 978-1-4244-5116-6
• Chor, Benny; Goldreich, Oded; Håstad, Johan; Freidmann, Joel; Rudich, Steven; Smolensky, Roman (1985), "The bit extraction problem or t-resilient functions", Proceedings of the 26th Annual Symposium on Foundations of Computer Science, FOCS 1985: 396–407, doi:10.1109/SFCS.1985.55, ISBN 0-8186-0644-4
• Goldreich, Oded (2001), Lecture 7: Small bias sample spaces
• Joffe, Anatole (1974), "On a Set of Almost Deterministic k-Independent Random Variables", Annals of Probability, 2 (1): 161–162, doi:10.1214/aop/1176996762
• Naor, Joseph; Naor, Moni (1990), "Small-bias Probability Spaces: efficient constructions and Applications", Proceedings of the 22nd annual ACM symposium on Theory of computing, STOC 1990: 213–223, doi:10.1145/100216.100244, ISBN 0897913612
• Amnon, Ta-Shma (2017), "Explicit, Almost Optimal, Epsilon-balanced Codes", Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing: 238––251, doi:10.1145/3055399.3055408, ISBN 9781450345286
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| 2018-08-22T08:04:02 |
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https://par.nsf.gov/biblio/10093430-exploring-redshift-space-distortions-large-scale-structure
|
Exploring redshift-space distortions in large-scale structure
We explore and compare different ways large-scale structure observables in redshift-space and real space can be connected. These include direct computation in La- grangian space, moment expansions and two formulations of the streaming model. We derive for the first time a Fourier space version of the streaming model, which yields an algebraic relation between the real- and redshift-space power spectra which can be compared to ear- lier, phenomenological models. By considering the redshift-space 2-point function in both configuration and Fourier space, we show how to generalize the Gaussian streaming model to higher orders in a systematic and computationally tractable way. We present a closed- form solution to the Zeldovich power spectrum in redshift space and use this as a framework for exploring convergence properties of different expansion approaches. While we use the Zeldovich approximation to illustrate these results, much of the formalism and many of the relations we derive hold beyond perturbation theory, and could be used with ingredients measured from N-body simulations or in other areas requiring decomposition of Cartesian tensors times plane waves. We finish with a discussion of the redshift-space bispectrum, bias and stochasticity and terms in Lagrangian perturbation theory up to 1-loop order.
Authors:
;
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Publication Date:
NSF-PAR ID:
10093430
Journal Name:
Journal of cosmology and astroparticle physics
Volume:
03
Page Range or eLocation-ID:
007
ISSN:
1475-7516
National Science Foundation
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4. (Ed.)
Weak lensing measurements suffer from well-known shear estimation biases, which can be partially corrected for with the use of image simulations. In this work we present an analysis of simulated images that mimic Hubble Space Telescope/Advance Camera for Surveys observations of high-redshift galaxy clusters, including cluster specific issues such as non-weak shear and increased blending. Our synthetic galaxies have been generated to have similar observed properties as the background-selected source samples studied in the real images. First, we used simulations with galaxies placed on a grid to determine a revised signal-to-noise-dependent ( S / N KSB ) correction for multiplicative shear measurement bias, and to quantify the sensitivity of our KSB+ bias calibration to mismatches of galaxy or PSF properties between the real data and the simulations. Next, we studied the impact of increased blending and light contamination from cluster and foreground galaxies, finding it to be negligible for high-redshift ( z > 0.7) clusters, whereas shear measurements can be affected at the ∼1% level for lower redshift clusters given their brighter member galaxies. Finally, we studied the impact of fainter neighbours and selection bias using a set of simulated images that mimic the positions and magnitudes of galaxies inmore »
5. Context. Galaxy clusters are an important tool for cosmology, and their detection and characterization are key goals for current and future surveys. Using data from the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant Clusters of WISE Survey (MaDCoWS) located 2839 significant galaxy overdensities at redshifts 0.7 ≲ z ≲ 1.5, which included extensive follow-up imaging from the Spitzer Space Telescope to determine cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has produced large area millimeter-wave maps in three frequency bands along with a large catalog of Sunyaev-Zeldovich (SZ)-selected clusters as part of its Data Release 5 (DR5). Aims. We aim to verify and characterize MaDCoWS clusters using measurements of, or limits on, their thermal SZ effect signatures. We also use these detections to establish the scaling relation between SZ mass and the MaDCoWS-defined richness. Methods. Using the maps and cluster catalog from DR5, we explore the scaling between SZ mass and cluster richness. We do this by comparing cataloged detections and extracting individual and stacked SZ signals from the MaDCoWS cluster locations. We use complementary radio survey data from the Very Large Array, submillimeter data from Herschel , and ACT 224 GHz data to assess the impact of contaminating sourcesmore »
| 2023-01-27T10:48:13 |
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|
https://par.nsf.gov/biblio/10291371-tidal-disruption-event-at2018hyz-double-peaked-emission-lines-flat-balmer-decrement
|
The tidal disruption event AT 2018hyz – I. Double-peaked emission lines and a flat Balmer decrement
ABSTRACT We present results from spectroscopic observations of AT 2018hyz, a transient discovered by the All-Sky Automated Survey for Supernova survey at an absolute magnitude of MV ∼ −20.2 mag, in the nucleus of a quiescent galaxy with strong Balmer absorption lines. AT 2018hyz shows a blue spectral continuum and broad emission lines, consistent with previous TDE candidates. High cadence follow-up spectra show broad Balmer lines and He i in early spectra, with He ii making an appearance after ∼70–100 d. The Balmer lines evolve from a smooth broad profile, through a boxy, asymmetric double-peaked phase consistent with accretion disc emission, and back to smooth at late times. The Balmer lines are unlike typical active galactic nucleus in that they show a flat Balmer decrement (Hα/Hβ ∼ 1.5), suggesting the lines are collisionally excited rather than being produced via photoionization. The flat Balmer decrement together with the complex profiles suggests that the emission lines originate in a disc chromosphere, analogous to those seen in cataclysmic variables. The low optical depth of material due to a possible partial disruption may be what allows us to observe these double-peaked, collisionally excited lines. The late appearance of He ii may be due to an expanding photosphere or outflow, or more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10291371
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
498
Issue:
3
Page Range or eLocation-ID:
4119 to 4133
ISSN:
0035-8711
4. ABSTRACT We present the results of a multiwavelength follow-up campaign for the luminous nuclear transient Gaia16aax, which was first identified in 2016 January. The transient is spatially consistent with the nucleus of an active galaxy at z = 0.25, hosting a black hole of mass ${\sim }6\times 10^8\, \mathrm{M}_\odot$. The nucleus brightened by more than 1 mag in the Gaia G band over a time-scale of less than 1 yr, before fading back to its pre-outburst state over the following 3 yr. The optical spectra of the source show broad Balmer lines similar to the ones present in a pre-outburst spectrum. During the outburst, the H α and H β emission lines develop a secondary peak. We also report on the discovery of two transients with similar light-curve evolution and spectra: Gaia16aka and Gaia16ajq. We consider possible scenarios to explain the observed outbursts. We exclude that the transient event could be caused by a microlensing event, variable dust absorption or a tidal encounter between a neutron star and a stellar mass black hole in the accretion disc. We consider variability in the accretion flow in the inner part of the disc, or a tidal disruption event of a star ${\ge } 1 \, \mathrm{M}_{\odot }$ bymore »
| 2023-02-05T02:32:01 |
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https://www.aimsciences.org/article/doi/10.3934/nhm.2021015
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Article Contents
Article Contents
# Qualitative properties of mathematical model for data flow
• * Corresponding author: Giuseppe Visconti
The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan)
• In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.
Mathematics Subject Classification: 35L65, 35L40.
Citation:
• Figure 1. Shape of the throttling functions used in the definition of the flux $\Phi$ in (13)
Figure 2. Left: Contour plot of the density $\rho(t,x,z)$ for a fixed time $t.$ Processed data with constant density $r>0$ is depicted in blue up to a stage of completion $z = \zeta(t,x).$ Zero data (grey) is prescribed for completion stages $z> \zeta(t,x)$, c.f. equation (28). Right: Similar plot of a density with constant values $r_1$ and $r_2$ and regions separated by functions $\zeta_1(t,x)$ and $\zeta_2(t,x)$
Figure 3. Domain of hyperbolicity of system (42). In both cases, the non-hyperbolic region (gray) is bounded by the $\xi_1$-axis and by $\xi_2 = \pm C \xi_1$ with slope $C = \frac{4 \epsilon \alpha \rho_* \eta}{\left(\epsilon \alpha -\rho_*\right)^2} \to 0$ as $\epsilon \to 0^+$
Figure 4. Density profiles for Example 1
Figure 5. Density profiles based on the a simulation of the constant front solution (69) with the scheme in (58). The simulations in panels (a)-(c) use $N^x = N^z = 800$ computational cells, while in panel (d), numerical solutions are computed at different refinement levels. In the top row, the analytical front is marked by circles
Figure 6. Density profiles based on the simulation of the $\textsf{V}$-shaped initial front (70) with the scheme in (58) using $N^x = N^z = 800$. The analytic solution is computed using (72). In the top row, the analytical front is marked by circles
Figure 7. Density profiles based on the simulation of the $\textsf{V}$-shaped initial front in (70), using the scheme in (58) with $N^x = N^z = 800$. The analytic solution is computed using (72). In the top row, the analytical front is marked by circles
Figure 8. Density profiles based on the simulation of the $\textsf{V}$-shaped initial front (70) with the scheme in (58) using $N^x = N^z = 800$. The analytical solution is computed using (74). In the top row, the analytical front is marked by circles
Figure 9. Density profiles for two different policies choices of $\alpha$ with the scheme in (58) using $N^x = N^z = 800$
Figure 10. Comparison of the quantities of interest $w_i, i = 1,2,3$ given in (78)
• [1] C. Appert-Rolland, P. Degond and S. Motsch, Two-way multi-lane traffic model for pedestrians in corridors, Netw. Heterog. Media, 6 (2011), 351-381. doi: 10.3934/nhm.2011.6.351. [2] D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains, SIAM J. Appl. Math., 66 (2006), 896-920. doi: 10.1137/040604625. [3] D. Armbruster, S. Göttlich and M. Herty, A scalar conservation law with discontinuous flux for supply chains with finite buffers, SIAM J. Appl. Math., 71 (2011), 1070-1087. doi: 10.1137/100809374. [4] A. Aw, A. Klar, T. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), 259-278. doi: 10.1137/S0036139900380955. [5] R. C. Barnard, K. Huang and C. Hauck, A mathematical model of asynchronous data flow in parallel computers, IMA Journal of Applied Mathematics, 85 (2020), 865-891. doi: 10.1093/imamat/hxaa031. [6] N. Bellomo and C. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models, Mathematical Models and Methods in Applied Sciences, 18 (2008), 1317-1345. doi: 10.1142/S0218202508003054. [7] H. Chan, M. J. Cherukara, B. Narayanan, T. D. Loeffler, C. Benmore, S. K. Gray and S. K. R. S. Sankaranarayanan, Machine learning coarse grained models for water, Nature Communications, 10 (2019), 379. doi: 10.1038/s41467-018-08222-6. [8] A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev, Pedestrian flow models with slowdown interactions, Mathematical Models and Methods in Applied Sciences, 24 (2014), 249-275. doi: 10.1142/S0218202513400083. [9] C. M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), 33-41. doi: 10.1016/0022-247X(72)90114-X. [10] C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edition doi: 10.1007/3-540-29089-3. [11] M. Di Francesco and M. D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit, Archive for Rational Mechanics and Analysis, 217 (2015), 831-871. doi: 10.1007/s00205-015-0843-4. [12] J. Dongarra, J. Hittinger, J. Bell, L. Chacón, R. Falgout, M. Heroux, P. Hovland, E. Ng, C. Webster and S. Wild, Applied Mathematics Research for Exascale Computing, Technical report, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research Program, 2014. doi: 10.2172/1149042. [13] L. C. Evans, Partial Differential Equations, American Mathematical Society, 2010. doi: 10.1090/gsm/019. [14] A. Galante and D. Levy, Modeling selective local interactions with memory, Physica D: Nonlinear Phenomena, 260 (2013), 176-190. doi: 10.1016/j.physd.2012.10.010. [15] D. Helbing, A fluid dynamic model for the movement of pedestrians, Complex Systems, 6 (1992), 391-415. [16] H. Holden and N. H. Risebro, Models for dense multilane vehicular traffic, SIAM J. Math. Anal., 51 (2019), 3694-3713. doi: 10.1137/19M124318X. [17] C. Murray et al., Basic Research Needs for Microelectronics: Report of the Office of Science Workshop on Basic Research Needs for Microelectronics, Technical report, USDOE Office of Science (SC)(United States), 2018. [18] J. S. Vetter et al., Extreme Heterogeneity 2018-Productive Computational Science in the Era of Extreme Heterogeneity: Report for DOE ASCR Workshop on Extreme Heterogeneity, Technical report, USDOE Office of Science (SC), Washington, DC (United States), 2018. doi: 10.2172/1473756. [19] S. Williams, A. Waterman and D. Patterson, Roofline: An insightful visual performance model for multicore architectures, Communications of the ACM, 52 (2009), 65-76. doi: 10.1145/1498765.1498785.
Open Access Under a Creative Commons license
Figures(10)
| 2023-03-25T16:55:05 |
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https://pos.sissa.it/157/079/
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Volume 157 - Sixth International Conference on Quarks and Nuclear Physics (QNP2012) - SESSION B
A first prediction of the electromagnetic rare decays \eta ^{\prime} \rightarrow \pi °\gamma \gamma and \eta ^{\prime} \rightarrow \eta \gamma \gamma
R. Escribano
Full text: pdf
Published on: October 01, 2012
DOI: https://doi.org/10.22323/1.157.0079
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-ShareAlike.
| 2022-05-19T11:12:21 |
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https://phys.libretexts.org/TextBooks_and_TextMaps/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/4%3A_The_Second_Law_of_Thermodynamics/4.1%3A_Reversible_and_Irreversible_Processes
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$$\require{cancel}$$
# 4.1: Reversible and Irreversible Processes
Consider an ideal gas that is held in half of a thermally insulated container by a wall in the middle of the container. The other half of the container is under vacuum with no molecules inside. Now, if we remove the wall in the middle quickly, the gas expands and fills up the entire container immediately, as shown in Figure $$\PageIndex{1}$$.
Figure $$\PageIndex{1}$$: A gas expanding from half of a container to the entire container (a) before and (b) after the wall in the middle is removed.
Because half of the container is under vacuum before the gas expands there, we do not expect any work to be done by the system—that is, $$W = 0$$ - because no force from the vacuum is exerted on the gas during the expansion. If the container is thermally insulated from the rest of the environment, we do not expect any heat transfer to the system either, so $$Q = 0$$. Then the first law of thermodynamics leads to the change of the internal energy of the system,
$\Delta E_{int} = Q - W = 0.$
For an ideal gas, if the internal energy doesn’t change, then the temperature stays the same. Thus, the equation of state of the ideal gas gives us the final pressure of the gas, $$p = nRT/V = p_0/2$$, where $$p_0$$ is the pressure of the gas before the expansion. The volume is doubled and the pressure is halved, but nothing else seems to have changed during the expansion.
All of this discussion is based on what we have learned so far and makes sense. Here is what puzzles us: Can all the molecules go backward to the original half of the container in some future time? Our intuition tells us that this is going to be very unlikely, even though nothing we have learned so far prevents such an event from happening, regardless of how small the probability is. What we are really asking is whether the expansion into the vacuum half of the container is reversible.
A reversible process is a process in which the system and environment can be restored to exactly the same initial states that they were in before the process occurred, if we go backward along the path of the process. The necessary condition for a reversible process is therefore the quasi-static requirement. Note that it is quite easy to restore a system to its original state; the hard part is to have its environment restored to its original state at the same time. For example, in the example of an ideal gas expanding into vacuum to twice its original volume, we can easily push it back with a piston and restore its temperature and pressure by removing some heat from the gas. The problem is that we cannot do it without changing something in its surroundings, such as dumping some heat there.
A reversible process is truly an ideal process that rarely happens. We can make certain processes close to reversible and therefore use the consequences of the corresponding reversible processes as a starting point or reference. In reality, almost all processes are irreversible, and some properties of the environment are altered when the properties of the system are restored. The expansion of an ideal gas, as we have just outlined, is irreversible because the process is not even quasi-static, that is, not in an equilibrium state at any moment of the expansion.
From the microscopic point of view, a particle described by Newton’s second law can go backward if we flip the direction of time. But this is not the case, in practical terms, in a macroscopic system with more than $$10^{23}$$ particles or molecules, where numerous collisions between these molecules tend to erase any trace of memory of the initial trajectory of each of the particles. For example, we can actually estimate the chance for all the particles in the expanded gas to go back to the original half of the container, but the current age of the universe is still not long enough for it to happen even once.
An irreversible process is what we encounter in reality almost all the time. The system and its environment cannot be restored to their original states at the same time. Because this is what happens in nature, it is also called a natural process. The sign of an irreversible process comes from the finite gradient between the states occurring in the actual process. For example, when heat flows from one object to another, there is a finite temperature difference (gradient) between the two objects. More importantly, at any given moment of the process, the system most likely is not at equilibrium or in a well-defined state. This phenomenon is called irreversibility.
Let us see another example of irreversibility in thermal processes. Consider two objects in thermal contact: one at temperature $$T_1$$ and the other at temperature $$T_2 > T_1$$, as shown in Figure $$\PageIndex{2}$$.
Figure $$\PageIndex{2}$$: Spontaneous heat flow from an object at higher temperature $$T_2$$ to another at lower temperature $$T_1$$.
We know from common personal experience that heat flows from a hotter object to a colder one. For example, when we hold a few pieces of ice in our hands, we feel cold because heat has left our hands into the ice. The opposite is true when we hold one end of a metal rod while keeping the other end over a fire. Based on all of the experiments that have been done on spontaneous heat transfer, the following statement summarizes the governing principle:
Second Law of Thermodynamics (Clausius statement)
Heat never flows spontaneously from a colder object to a hotter object.
This statement turns out to be one of several different ways of stating the second law of thermodynamics. The form of this statement is credited to German physicist Rudolf Clausius (1822−1888) and is referred to as the Clausius statement of the second law of thermodynamics. The word “spontaneously” here means no other effort has been made by a third party, or one that is neither the hotter nor colder object. We will introduce some other major statements of the second law and show that they imply each other. In fact, all the different statements of the second law of thermodynamics can be shown to be equivalent, and all lead to the irreversibility of spontaneous heat flow between macroscopic objects of a very large number of molecules or particles.
Both isothermal and adiabatic processes sketched on a pV graph (discussed in The First Law of Thermodynamics) are reversible in principle because the system is always at an equilibrium state at any point of the processes and can go forward or backward along the given curves. Other idealized processes can be represented by pV curves; Table $$\PageIndex{1}$$ summarizes the most common reversible processes.
Table $$\PageIndex{1}$$: Summary of Simple Thermodynamic Processes
Process Constant Quantity and Resulting Fact
Isobaric Constant pressure $$W = p\Delta V$$
Isochoric Constant volume $$W = 0$$
Isothermal Constant temperature $$\Delta T = 0$$
Adiabatic No heat transfer $$Q = 0$$
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2018-07-17T17:34:51 |
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https://pdglive.lbl.gov/DataBlock.action?node=S030DP2
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# For ${\boldsymbol m}_{{{\boldsymbol X}^{0}}}$ = 100 GeV INSPIRE search
For limits from ${{\mathit X}^{0}}$ annihilation in the Sun, the assumed annihilation final state is shown in parenthesis in the comment.
VALUE (pb) CL% DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<4 \times 10^{-5}$ 90 1
2019
PICO ${}^{}\mathrm {C}_{3}{}^{}\mathrm {F}_{8}$
$<4 \times 10^{-4}$ 90 2
2019 A
XE1T ${}^{}\mathrm {Xe}$, SD
$<8 \times 10^{-4}$ 90 3
2019 A
PNDX SD WIMP on ${}^{}\mathrm {Xe}$
$<8 \times 10^{-4}$ 90 4
2017 A
LUX ${}^{}\mathrm {Xe}$
$<5 \times 10^{-5}$ 90 5
2017
PICO ${}^{}\mathrm {C}_{3}{}^{}\mathrm {F}_{8}$
$<0.033$ 90 6
2017 A
X100 ${}^{}\mathrm {Xe}$ inelastic
$<0.28$ 90 7
2017
DRFT ${}^{}\mathrm {C}{}^{}\mathrm {S}_{2}$
$<1.5 \times 10^{-3}$ 90 8
2017
PNDX ${}^{}\mathrm {Xe}$
$\text{< 0.553 - 0.019}$ 95 9
2016 D
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}$ + $\not E_T$
$<1 \times 10^{-5}$ 90 10
2016 F
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}$ + $\not E_T$
$<1 \times 10^{-4}$ 90 11
2016 C
ICCB solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<2 \times 10^{-4}$ 90 12
2016
ANTR solar ${{\mathit \nu}}$ ( ${{\mathit W}}{{\mathit W}}$ , ${{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit \tau}}{{\overline{\mathit \tau}}}$ )
$<3 \times 10^{-3}$ 90 13
2016 A
LUX ${}^{}\mathrm {Xe}$
$<5 \times 10^{-4}$ 90 14
2016
PICO CF$_{3}$I
$<1.5 \times 10^{-3}$ 90
2015
PICO ${}^{}\mathrm {C}_{3}{}^{}\mathrm {F}_{8}$
$<3.19 \times 10^{-3}$ 90
2015
SKAM ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<2.80 \times 10^{-4}$ 90
2015
SKAM ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<1.24 \times 10^{-4}$ 90
2015
SKAM ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ )
$<800$ 90 15
2015
NAGE ${}^{}\mathrm {C}{}^{}\mathrm {F}_{4}$
$<1.7 \times 10^{-3}$ 90 16
2014
BAIK ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<0.045$ 90 16
2014
BAIK ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<7.1 \times 10^{-4}$ 90 16
2014
BAIK ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ )
$<6 \times 10^{-3}$ 90
2014
SMPL C$_{2}$ClF$_{5}$
$<2.68 \times 10^{-4}$ 90 17
2013
ICCB ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<0.0147$ 90 17
2013
ICCB ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<8.5 \times 10^{-4}$ 90 18
2013
ANTR ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<0.055$ 90 18
2013
ANTR ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<3.4 \times 10^{-4}$ 90 18
2013
ANTR ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ )
$<0.01$ 90 19
2013
X100 ${}^{}\mathrm {Xe}$
$<7.1 \times 10^{-4}$ 90 20
2013
BAKS ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<8.4 \times 10^{-3}$ 90 20
2013
BAKS ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<3.1 \times 10^{-4}$ 90 20
2013
BAKS ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ )
$<7.07 \times 10^{-4}$ 90 21
2012
ICCB ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<0.0453$ 90 21
2012
ICCB ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
$<0.07$ 90 22
2012
PICA ${}^{}\mathrm {F}$ (C$_{4}F_{10}$)
$<0.01$ 90
2012
COUP CF$_{3}$I
$<1.8$ 90
2012
DRFT F (CF$_{4}$)
$<9 \times 10^{-3}$
2012
SMPL C$_{2}$ClF$_{5}$
$<0.02$ 90
2012
KIMS CsI
$<2 \times 10^{3}$ 90 15
2011
DMTP F (CF$_{4}$)
$<0.07$ 90
2011
COUP CF$_{3}$I
$<2.7 \times 10^{-4}$ 90 23
2011
SKAM ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit W}^{+}}{{\mathit W}^{-}}$ )
$<4.5 \times 10^{-3}$ 90 23
2011
SKAM ${}^{}\mathrm {H}$, solar ${{\mathit \nu}}$ ( ${{\mathit b}}{{\overline{\mathit b}}}$ )
24
2010
SMPL C$_{2}$ClF$_{3}$
$<6 \times 10^{3}$ 90 15
2010
NAGE CF$_{4}$
$<0.4$ 90
2009
PICA ${}^{}\mathrm {F}$
$<0.8$ 90
2009 A
ZEP3 ${}^{}\mathrm {Xe}$
$<1.0$ 90
2008 A
XE10 ${}^{}\mathrm {Xe}$
$<15$ 90
2007
ZEP2 ${}^{}\mathrm {Xe}$
$<0.2$ 90
2007 A
KIMS CsI
$<1 \times 10^{4}$ 90 15
2007
NAGE F (CF$_{4}$)
$<5$ 90 25
2006
CDMS ${}^{73}\mathrm {Ge}$, ${}^{29}\mathrm {Si}$
$<2$ 90
2006 A
CNTR F (CaF$_{2}$)
$<0.3$ 90
2005
NAIA NaI
$<2$ 90
2005
PICA F (C$_{4}F_{10}$)
$<100$ 90
2005
EDEL ${}^{73}\mathrm {Ge}$
$<1.5$ 90
2005
SMPL F (C$_{2}$ClF$_{5}$)
$<0.7$ 26
2005 A
RVUE
27
2004
RVUE
28
2004 A
RVUE
$<35$ 90
2003
BOLO LiF
$<40$ 90
2003
BOLO NaF
1 AMOLE 2019 search for SD WIMP scatter on ${}^{}\mathrm {C}_{3}{}^{}\mathrm {F}_{8}$ in PICO-60 bubble chamber; no signal: set limit for spin dependent coupling ${{\mathit \sigma}^{SD}}$( ${{\mathit \chi}}{{\mathit p}}$ ) $<$ $4 \times 10^{-5}$ pb for m(${{\mathit \chi}}$) = 100 GeV.
2 APRILE 2019A search for SD WIMP scatter on 1 t yr ${}^{}\mathrm {Xe}$; no signal, limits placed in ${{\mathit \sigma}^{SD}}$ ( ${{\mathit \chi}}{{\mathit p}}$ ) vs. m(${{\mathit \chi}}$) plane for m $\sim{}$ $6 - 1000$ GeV.
3 XIA 2019A search for WIMP scatter on ${}^{}\mathrm {Xe}$ in PandaX-II; limits placed in ${{\mathit \sigma}^{SD}}$( ${{\mathit \chi}}{{\mathit p}}$ ) vs. m(${{\mathit \chi}}$) plane for m(${{\mathit \chi}}$) $\sim{}$ $5 - 1 \times 10^{5}$ GeV.
4 AKERIB 2017A search for SD WIMP scatter on ${}^{}\mathrm {Xe}$ using 129.5 kg yr exposure; limits placed in ${{\mathit \sigma}^{SD}}$( ${{\mathit \chi}}{{\mathit p}}$ ) vs. m(${{\mathit \chi}}$) plane for m(${{\mathit \chi}}$) $\sim{}$ $6 - 1 \times 10^{5}$ GeV.
5 AMOLE 2017 require ${\mathit \sigma (}WIMP-{{\mathit p}}{)}{}^{SD}$ $<$ $5 \times 10^{-5}$ pb for m(WIMP) = 100 GeV using PICO-60 1167 kg-days exposure at SNOLab.
6 APRILE 2017A require require ${\mathit \sigma (}WIMP-{{\mathit p}}{)}$(inelastic)${}^{SD}$ $<$ $0.033$ pb for m(WIMP) = 100 GeV, based on 7640 kg day exposure at LNGS.
7 BATTAT 2017 use directional detection of ${}^{}\mathrm {C}{}^{}\mathrm {S}_{2}$ ions to require ${\mathit \sigma (}SD{)}$ $<$ $0.28$ pb for 100 GeV WIMP with a 55 days exposure at the Boulby Underground Science Facility.
8 FU 2017 from a 33000 kg d exposure at CJPL, PANDAX II derive for m(DM) = 100 GeV, ${{\mathit \sigma}^{SD}}(WIMP-{{\mathit p}}$) $<2 \times 10^{-3}$ pb.
9 AABOUD 2016D use ATLAS 13 TeV 3.2 ${\mathrm {fb}}{}^{-1}$ of data to search for monojet plus missing $\mathit E_{T}$; agree with SM rates; present limits on large extra dimensions, compressed SUSY spectra and wimp pair production.
10 AABOUD 2016F search for monophoton plus missing $\mathit E_{T}$ events at ATLAS with 13 Tev and 3.2 fb${}^{-1}$; signal agrees with SM background; place limits on SD WIMP-proton scattering vs. mediator mass and large extra dimension models.
11 AARTSEN 2016C search for high energy ${{\mathit \nu}}$s from WIMP annihilation in solar core; limits set on SD WIMP-${{\mathit p}}$ scattering (Fig. 8).
12 ADRIAN-MARTINEZ 2016 search for WIMP annihilation into ${{\mathit \nu}}$s from solar core; exclude SD cross section $<$ few $10^{-4}$ depending on $\mathit m$(WIMP).
13 AKERIB 2016A using 2013 data exclude SD WIMP-proton scattering $>$ $3 \times 10^{-3}$ pb for $\mathit m$(WIMP) = 100 GeV.
14 AMOLE 2016 use bubble technique on CF$_{3}$I target to exclude SD WIMP-${{\mathit p}}$ scattering $>$ $5 \times 10^{-4}$ pb for $\mathit m$(WIMP) = 100 GeV.
15 Use a direction-sensitive detector.
16 AVRORIN 2014 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the Sun in data taken between 1998 and 2003. See their Table 1 for limits assuming annihilation into neutrino pairs.
17 AARTSEN 2013 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the sun in data taken between June 2010 and May 2011.
18 ADRIAN-MARTINEZ 2013 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the sun in data taken between Jan. 2007 and Dec. 2008.
19 The value has been provided by the authors. APRILE 2013 note that the proton limits on ${}^{}\mathrm {Xe}$ are highly sensitive to the theoretical model used. See also APRILE 2014A.
20 BOLIEV 2013 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the sun in data taken from 1978 to 2009. See also SUVOROVA 2013 for an older analysis of the same data.
21 ABBASI 2012 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the Sun. The amount of ${{\mathit X}^{0}}$ depends on the ${{\mathit X}^{0}}$-proton cross section.
22 ARCHAMBAULT 2012 search for WIMP scatter on ${}^{}\mathrm {C}_{4}{}^{}\mathrm {F}_{10}$; limits set in ${{\mathit \sigma}^{SD}}$( ${{\mathit \chi}}{{\mathit p}}$ ) vs. m(${{\mathit \chi}}$) plane for m $\sim{}$ $4 - 500$ GeV.
23 TANAKA 2011 search for neutrinos from the Sun arising from the pair annihilation of ${{\mathit X}^{0}}$ trapped by the Sun. The amount of ${{\mathit X}^{0}}$ depends on the ${{\mathit X}^{0}}$-proton cross section.
24 See their Fig. 3 for limits on spin-dependent proton couplings for ${{\mathit X}^{0}}$ mass of 50 GeV.
26 GIULIANI 2005A analyze available data and give combined limits.
27 GIULIANI 2004 reanalyze COLLAR 2000 data and give limits for spin-dependent ${{\mathit X}^{0}}$-proton coupling.
28 GIULIANI 2004A give limits for spin-dependent ${{\mathit X}^{0}}$-proton couplings from existing data.
References:
AMOLE 2019
PR D100 022001 Dark Matter Search Results from the Complete Exposure of the PICO-60 C$_3$F$_8$ Bubble Chamber
APRILE 2019A
PRL 122 141301 Constraining the spin-dependent WIMP-nucleon cross sections with XENON1T
XIA 2019A
PL B792 193 PandaX-II Constraints on Spin-Dependent WIMP-Nucleon Effective Interactions
AKERIB 2017A
PRL 118 251302 Limits on Spin-Dependent WIMP-Nucleon Cross Section Obtained from the Complete LUX Exposure
AMOLE 2017
PRL 118 251301 Dark Matter Search Results from the PICO-60 C$_{3}F_{8}$ Bubble Chamber
APRILE 2017A
PR D96 022008 Search for WIMP Inelastic Scattering off Xenon Nuclei with XENON100
BATTAT 2017
ASP 91 65 Low Threshold Results and Limits from the DRIFT Directional Dark Matter Detector
FU 2017
PRL 118 071301 Spin-Dependent Weakly-Interacting-Massive-Particle-Nucleon Cross Section Limits from First Data of PandaX-II Experiment
AABOUD 2016F
JHEP 1606 059 Search for New Phenomena in Events with a Photon and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
AABOUD 2016D
PR D94 032005 Search for New Phenomena in Final States with an Energetic Jet and Large Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV using the ATLAS Detector
AARTSEN 2016C
JCAP 1604 022 Improved Limits on Dark Matter Annihilation in the Sun with the 79-string IceCube Detector and Implications for Supersymmetry
PL B759 69 Limits on Dark Matter Annihilation in the Sun using the ANTARES Neutrino Telescope
AKERIB 2016A
PRL 116 161302 Results on the Spin-Dependent Scattering of Weakly Interacting Massive Particles on Nucleons from the Run 3 Data of the LUX Experiment
AMOLE 2016
PR D93 052014 Dark Matter Search Results from the PICO-60 CF$_{3}$I Bubble Chamber
AMOLE 2015
PRL 114 231302 Dark Matter Search Results from the PICO-2L C$_{3}F_{8}$ Bubble Chamber
CHOI 2015
PRL 114 141301 Search for Neutrinos from Annihilation of Captured Low-Mass Dark Matter Particles in the Sun by Super-Kamiokande
NAKAMURA 2015
PTEP 2015 4 043F01 Direction-Sensitive Dark Matter Search with Gaseous Tracking Detector NEWAGE-0.3b'
AVRORIN 2014
ASP 62 12 Search for Neutrino Emission from Relic Dark Matter in the Sun with the Baikal NT200 Detector
FELIZARDO 2014
PR D89 072013 The SIMPLE Phase II Dark Matter Search
AARTSEN 2013
PRL 110 131302 Search for Dark Matter Annihilations in the Sun with the 79-String IceCube Detector
JCAP 1311 032 First Results on Dark Matter Annihilation in the Sun using the ANTARES Neutrino Telescope
APRILE 2013
PRL 111 021301 Limits on Spin-Dependent WIMP-Nucleon Cross Sections from 225 Live Days of XEENON100 Data
BOLIEV 2013
JCAP 1309 019 Search for Muon Signal from Dark Matter Annihilations in the Sun with the Baksan Underground Scintillator Telescope for 24.12 Years
ABBASI 2012
PR D85 042002 Multiyear Search for Dark Matter Annihilations in the Sun with the AMANDA-II and IceCube Detectors
ARCHAMBAULT 2012
PL B711 153 Constraints on Low-Mass WIMP Interactions on ${}^{19}\mathrm {F}$ from PICASSO
BEHNKE 2012
PR D86 052001 First Dark Matter Search Results from a 4-kg CF$_{3}$I Bubble Chamber Operated in a Deep Underground Site
DAW 2012
ASP 35 397 Spin-Dependent Limits from the DRIFT-IId Directional Dark Matter Detector
FELIZARDO 2012
PRL 108 201302 Final Analysis and Results of the Phase II SIMPLE Dark Matter Search
KIM 2012
PRL 108 181301 New Limits on Interactions between Weakly Interacting Massive Particles and Nucleons Obtained with CsI(Tl) Crystal Detectors
AHLEN 2011
PL B695 124 First Dark Matter Search Results from a Surface Run of the 10-L DMTPC (Dark Matter Time Projection Chamber) Directional Dark Matter Detector
BEHNKE 2011
PRL 106 021303 Improved Limits on Spin-Dependent WIMP-Proton Interactions from a Two Liter CF$_{3}$I Bubble Chamber
TANAKA 2011
APJ 742 78 An Indirect Search for WIMPs in the Sun using 3109.6 Days of Upward-Going Muons in Super-Kamiokande
FELIZARDO 2010
PRL 105 211301 First Results of the Phase II SIMPLE Dark Matter Search
MIUCHI 2010
PL B686 11 First Underground Results with NEWAGE-0.3a Direction-Sensitive Dark Matter Detector
ARCHAMBAULT 2009
PL B682 185 Dark Matter Spin-Dependent Limits for WIMP Interactions on ${}^{19}\mathrm {F}$ by PICASSO
LEBEDENKO 2009A
PRL 103 151302 Limits on the Spin-Dependent WIMP-Nucleon Cross Sections from the First Science Run of the ZEPLIN-III Experiment
ANGLE 2008A
PRL 101 091301 Limits on Spin-Dependent WIMP-Nucleon Cross Sections from the XENON10 Experiment
ALNER 2007
PL B653 161 Limits on Spin-Dependent WIMP-Nucleon Cross-Sections from the First ZEPLIN-II Data
LEE 2007A
PRL 99 091301 Limits on Interactions between Weakly Interacting Massive Particles and Nucleons Obtained with CsI(Tl) Crystal Detectors
MIUCHI 2007
PL B654 58 Direction-Sensitive Dark Matter Search Results in a Surface Laboratory
AKERIB 2006
PR D73 011102 Limits on Spin-dependent WIMP $−$ Nucleon Interactions from the Cryogenic Dark Matter Search
SHIMIZU 2006A
PL B633 195 Dark Matter Search Experiment with CaF$_{2}$(Eu) scintillator at Kamioka Observatory
ALNER 2005
PL B616 17 Limits on WIMP Cross-Sections from the NAIAD Experiment at the Boulby Underground Laboratory
BARNABE-HEIDER 2005
PL B624 186 Improved Spin-Dependent Limits from the PICASSO Dark Matter Search Experiment
BENOIT 2005
PL B616 25 Sensitivity of the EDELWEISS WIMP Search to Spin-Dependent Interactions
GIRARD 2005
PL B621 233 Simple Dark Matter Search Results
GIULIANI 2005A
PR D71 123503 Model-Independent Limits from Spin-Dependent WIMP Dark Matter Experiments
GIULIANI 2004
PL B588 151 Exclusion Limits on Spin Dependent WIMP-Nucleon Couplings from the SIMPLE Experiment
GIULIANI 2004A
PRL 93 161301 Model-Independent Assessment of Current Direct Searches for Spin-Dependent Dark Matter
MIUCHI 2003
ASP 19 135 First Results from Dark Matter Search Experiment with LiF Bolometer at Kamioka Underground Laboratory
TAKEDA 2003
PL B572 145 Limits on the WIMP$−$Nucleon Coupling Coefficients from Dark Matter Search Experiment with NaF Bolometer
| 2020-09-18T18:11:19 |
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|
https://dlmf.nist.gov/13.26
|
# §13.26 Addition and Multiplication Theorems
## §13.26(i) Addition Theorems for $M_{\kappa,\mu}\left(z\right)$
The function $M_{\kappa,\mu}\left(x+y\right)$ has the following expansions:
13.26.1 $e^{-\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-\frac{1}{2}}\sum_{n=0}^{% \infty}\frac{{\left(-2\mu\right)_{n}}}{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n}% \*M_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.2 $e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\mu+\frac{1}{2}}\sum_{n=0}^{% \infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}}{{\left(1+2\mu\right)_{% n}}n!}\left(\frac{y}{\sqrt{x}}\right)^{n}\*M_{\kappa-\frac{1}{2}n,\mu+\frac{1}% {2}n}\left(x\right),$ 13.26.3 $e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\kappa}\sum_{n=0}^{\infty}\frac{{% \left(\frac{1}{2}+\mu-\kappa\right)_{n}}y^{n}}{n!(x+y)^{n}}M_{\kappa-n,\mu}% \left(x\right),$ $\Re(y/x)>-\frac{1}{2}$, 13.26.4 $e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-\frac{1}{2}}\sum_{n=0}^{\infty% }\frac{{\left(-2\mu\right)_{n}}}{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n}\*M_{% \kappa+\frac{1}{2}n,\mu-\frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.5 $e^{\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\mu+\frac{1}{2}}\sum_{n=0}^{\infty% }\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}n!}% \left(\frac{-y}{\sqrt{x}}\right)^{n}\*M_{\kappa+\frac{1}{2}n,\mu+\frac{1}{2}n}% \left(x\right),$ 13.26.6 $e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\kappa}\sum_{n=0}^{\infty}\frac{{% \left(\frac{1}{2}+\mu+\kappa\right)_{n}}y^{n}}{n!(x+y)^{n}}M_{\kappa+n,\mu}% \left(x\right),$ $\Re((y+x)/x)>\frac{1}{2}$.
## §13.26(ii) Addition Theorems for $W_{\kappa,\mu}\left(z\right)$
The function $W_{\kappa,\mu}\left(x+y\right)$ has the following expansions:
13.26.7 $e^{-\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-\frac{1}{2}}\sum_{n=0}^{% \infty}\frac{{\left(\frac{1}{2}-\mu-\kappa\right)_{n}}}{n!}\left(\frac{-y}{% \sqrt{x}}\right)^{n}\*W_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.8 $e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\mu+\frac{1}{2}}\sum_{n=0}^{% \infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}}{n!}\left(\frac{-y}{% \sqrt{x}}\right)^{n}\*W_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.9 $e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\kappa}\sum_{n=0}^{\infty}\frac{{% \left(\frac{1}{2}+\mu-\kappa\right)_{n}}{\left(\frac{1}{2}-\mu-\kappa\right)_{% n}}}{n!}\*\left(\frac{y}{x+y}\right)^{n}W_{\kappa-n,\mu}\left(x\right),$ $\Re(y/x)>-\frac{1}{2}$, 13.26.10 $e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-\frac{1}{2}}\sum_{n=0}^{\infty% }\frac{1}{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n}\*W_{\kappa+\frac{1}{2}n,\mu-% \frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.11 $e^{\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\mu+\frac{1}{2}}\sum_{n=0}^{\infty% }\frac{1}{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n}\*W_{\kappa+\frac{1}{2}n,\mu+% \frac{1}{2}n}\left(x\right),$ $|y|<|x|$, 13.26.12 $e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\kappa}\sum_{n=0}^{\infty}\frac{1}% {n!}\left(\frac{-y}{x+y}\right)^{n}W_{\kappa+n,\mu}\left(x\right),$ $\Re(y/x)>-\frac{1}{2}$.
## §13.26(iii) Multiplication Theorems for $M_{\kappa,\mu}\left(z\right)$ and $W_{\kappa,\mu}\left(z\right)$
To obtain similar expansions for $M_{\kappa,\mu}\left(xy\right)$ and $W_{\kappa,\mu}\left(xy\right)$, replace $y$ in the previous two subsections by $(y-1)x$.
| 2020-07-12T03:36:59 |
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|
https://indico.fnal.gov/event/13106/contributions/17482/
|
# 2017 JINA-CEE Frontiers in Nuclear Astrophysics
Feb 7 – 9, 2017
US/Eastern timezone
## Properties of Core-Collapse Supernova Progenitors From Monte Carlo Stellar Models
Feb 7, 2017, 4:45 PM
1h 15m
111 N Grand Ave, Lansing, MI 48933
Poster [Main Conference]
### Speaker
Mr Carl Fields (Michigan State University)
### Description
We investigate properties of core-collapse supernova (CCSN) progenitors with respect to the composite uncertainties in the reaction rates using the stellar evolution toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the probability density functions in the reaction rate library, STARLIB. In total, 1000 15 solar mass stellar models are evolved from the pre main-sequence to core O-depletion at solar and subsolar metallicities for a total of 2000 Monte Carlo stellar models. In each stellar model, we independently and simultaneously sample 665 forward thermonuclear reaction rates using a robust, in-situ network that follows 127 isotopes from Hydrogen to Zinc. Within this Monte Carlo framework, we survey the remnant O-core mass, composition, and structural properties using a Principal Component Analysis and Spearman Rank- Order Correlation. Relative to the arithmetic mean value, we find the width of the 95% confidence interval to be approximately 1.0 solar mass for the core mass at oxygen depletion, ≈ 0.211 Myr for the age, ≈ 0.047 for the compactness parameter with M = 2.5 solar mass, ∆X(28Si) ≈ 0.464, and ∆X(32S) ≈ 0.73 for models with solar metallicity. Uncertainties in the experimental 12C + 12C → 1H + 23Na, 16O + 16O → n + 31S, triple - α, and 12C(α,γ)16O reaction rates dominate these variations.
### Primary author
Mr Carl Fields (Michigan State University)
### Co-authors
Prof. Frank Timmes (Arizona State University) Dr Ilka Petermann (Arizona State University) Dr Rob Farmer (Arizona State University) Prof. Sean Couch (Michigan State University)
### Presentation materials
There are no materials yet.
| 2022-12-03T20:10:59 |
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|
https://www.peertechzpublications.com/articles/AEST-7-164.php
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ISSN: 2641-2969
##### Annals of Environmental Science and Toxicology
Research Article Open Access Peer-Reviewed
# Characteristics of environmental degradation in mining areas (A case study of the Southern Trans-Urals)
### Aufar Gareev1* and Emil Gareev2
1Department of Geology, Hydrometeorology and Geoecology, Ufa, University of Science and Technology, 450076, Ufa, Russia
2LLC Uralnefteprodukt, PhD in Geography, Head of Environmental Protection Unit, Russia
*Corresponding author: Aufar Gareev, Professor, Doctor of Geographical Sciences, Department of Geology, Hydrometeorology and Geoecology, Ufa, University of Science and Technology, 450076, Ufa, Russia, Tel: +79177493680; Fax: +73472521193; E-mail: [email protected]
Received: 19 December, 2022 | Accepted: 13 January, 2023 | Published: 14 January, 2023
Keywords: Mining industry; Ecology; Components; Natural environment; Pollution; Morbidity
Cite this as
Gareev A, Gareev E (2023) Characteristics of environmental degradation in mining areas (A case study of the Southern Trans-Urals). Ann Environ Sci Toxicol 7(1): 004-012. DOI: 10.17352/aest.000064
Copyright
© 2023 Gareev A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The areas affected by mining operations are characterized by extremely complex environmental changes that affect all components of the natural complexes. In several cases, radical negative changes (transformations) take place, which cause the formation of the habitat, characterized by changes in characteristics of all components of the natural environment, including geological structure, soil cover, surface and groundwater and atmospheric air, respectively, flora and fauna. This generally leads to a sharp deterioration of ecological conditions, including living conditions of living organisms and human habitation, causing stressful situations, inconveniences, as well as characteristic diseases due to the influence of factors of excessive pollution of components of the natural environment. As one of the objects of the study, the impact zone of mining enterprises within the town of Sibai and its surroundings in the Republic of Bashkortostan was chosen. It is typical for the assessment of occurring changes and other industrial centers and districts located within the vast strip of the Southern Urals. It has been revealed that the greatest damage is inflicted on ecosystems of small rivers, which is caused by both direct and indirect entry of pollutants into them as a result of dissolution, leaching and entry from rock dumps, emissions into the atmosphere, and settling on the surface of soil and snow cover; direct discharge of wastewater into them, etc. It is shown that with the lingering impact of the regional response to global climate change, environmental problems are exacerbated. This calls for urgent measures to restore favorable environmental conditions and address a wide range of economic and social problems.
### Introduction
The regularities reflecting the changes that have occurred in the state of the environment have been identified based on a synthesis of materials obtained by us during a series of research works carried out in the late twentieth century and also in 2010 -2020. They covered the areas of location and activity of mining and processing plants, non-ferrous metal ore mining sites within a vast space stretching over the Southern Trans-Urals, including the impact zones of industrial enterprises in the cities of Karabash in the Chelyabinsk Region, Uchaly, Sibay, Buribay - in the Republic of Bashkortostan and Mednogorsk - in the Orenburg Region (Figure 1). A characteristic feature is that for each of the settlements shown in Figure 1 and their surroundings, approximately the same structural changes are observed. It is indicative that during the long-term exploitation of non-ferrous metal ore deposits and mining and processing plants, technogenic-disturbed and degraded territories have formed, including quarries, mines, rock dumps, wastewater accumulators, etc., which have similar specific physical, chemical and other impacts on the environment. Given the limited number of observations and analysis of changes in most of them, those sites for which full-scale studies are available are of great interest, making it possible to identify characteristic patterns reflecting changes in the quantitative and qualitative characteristics of the natural environment components. The characteristics of their impact on the general environmental conditions of the territories, as well as the morbidity of the population, are also indicative.
The structure and characteristics of the changes that have occurred are reflected in more detail in this article on the example of the zone of influence of enterprises located within the urban district of Sibai city. That, materials of comprehensive studies conducted in 2020 have been taken into account as the basis [1]. The materials obtained make it possible to assess the changes taking place in other areas of influence of the mining industry facilities and to substantiate the necessary environmental protection measures.
### Materials and Methods
The validity and representativeness of the materials used are based on the analysis of extensive baseline information obtained in the course of a large number of studies conducted under the scientific leadership of Prof. A.M. Gareev over many decades. They included studies of the hydrological regime, water-resource indicators of water bodies, spatial and temporal variability of hydrometeorological conditions and climate, as well as characteristics and scales of formation of negative processes in the natural environment depending on the predominant impact of mining facilities.
Comprehensive geochemical studies to assess the state of the environment at several polymetallic, copper-pyrite, rare-metal and other deposits show that the most intensive pollution of the environment is associated with the following migration chains:
− Dust emissions from open-pit mining, pollute atmospheric air, forming contrasting and significant geochemical anomalies in soils;
− Deflation and scouring of tailings ponds forming intense dispersion fluxes in aquatic systems and relatively localized dispersion halos in soils;
− Run-off from underground mine workings and quarries, which form intense and extensive dispersion fluxes in aquatic systems;
− Effluents from enrichment plants after treatment plants which contaminate water systems;
− Dispersion of ore material during transportation, polluting soils;
− Organised and unorganized emissions to air from beneficiation processes;
− Natural geochemical anomalies - secondary dispersion halos in soils, dispersion fluxes in surface water courses, hydrogeochemical anomalies in groundwater, etc. [2-5].
In the course of the study of the main regularities reflecting the changes that have occurred within the base site - the zone of influence of industrial enterprises of Sibai city - field surveys and observations were carried out. They were accompanied by water and bottom sediment sampling from surface water bodies (Karagaily and Khudolaz rivers), soil samples in the watershed, as well as assessment of the degree of variability of species composition of hydrobionts (including ichthyofauna), indicators of degradation of plant communities, etc. The types and concentrations of pollutants directly affecting the environmental conditions in the watercourses in question, as well as natural and anthropogenic systems and their components, were determined under laboratory conditions for the components of the natural environment. At present, one of the additional tools widely used in assessing the state of the environment and predicting further changes is geoinformation analysis. The following geoinformation data were used to study the territory of Sibai Urban District: Landsat satellite images (date of survey 26.04.2020), Shuttle Radar Topography Mission (SRTM) 1 Arc-Second Global (date of survey 11.02.2000, resolution 30 m). Based on the application of information, reflecting locations of negatively influenced objects, indicators and level of pollution of environmental components, as well as generalization of statistical materials, characteristic features of changes in environmental conditions within particular territories were subsequently identified and population morbidity indicators were assessed. A schematic map of the study area is shown in Figure 2.
As can be seen from the mentioned figure, the territory adjacent to Sibai is characterized by an extreme density of polluted, littered and other disturbed areas, which is the consequence of prolonged extensive mining, without paying appropriate attention to solving environmental and social problems. The Sibai quarry and waste dumps are located in the southwestern part of the city, bordering residential settlements (Gorny and Zoloto settlements) to the north and west. The dumps are composed of spilites, rhyolites, quartz rhyolites, tuffs and tufobreccias of spilites and quartz-rich rhyolites, chlorite-sericite-quartz, sericite-quartz and chlorite-quartz metasomatites, clays. The rocks contain impurities of sulfide minerals: pyrite, sphalerite, chalcopyrite, etc. Waste dumps are complex geochemical filters, including successively acting evaporative, cryogenic, redox, acid-alkaline and temperature geochemical barriers [3,4]. They are practically not isolated from water systems, which determines the entry of chemical elements into watercourses.
Underground water from the northern waste dumps at the Sibaysky mine until 2020 was pumped to the surface and discharged to the Karagaily River via a collector. To this day, the effluent from the southern dumps is also discharged untreated into the Karagaily River. Underground waters are highly mineralized - up to 515 g/l, pH 2.1-2.6, sulfate ion concentration reaches 29500 mg/l, copper content - from 330 to 645 mg/l, zinc - 718-890 mg/l, iron - 188-731 mg/l, magnesium - 190 mg/l, increased concentration of manganese, nickel, cobalt, cadmium, mercury, etc. [2,4]. Thus, rock dumps are a source of the formation of aggressive acidic waters containing high concentrations of chalcophile elements with high toxicity. Low volatility and low freezing temperatures cause their high mobility during all seasons. As a result of their influence, intensive, complex in composition and extended along the channel technogenic geochemical anomalies are formed. In the bottom sediments of the Khudolaz Karagaily and Kamysh-Uzyak rivers, flowing in a direct zone of influence of economic objects, the maintenance of heavy metals in tens and hundreds of times exceeds background concentration - Cu 20 - 125 MPC (75 - 500 backgrounds), Zn 30 - 59 MPC (100 - 200 backgrounds), As 50 - 90 MPC (18 - 60 backgrounds), Cd 4 - 30 MPC (40 - 300 backgrounds), Sb 4 MPC (20 backgrounds), Hq 2 - 3 MPC (25 backgrounds). Pb 1 - 3 MAC (3 - 10 background), Co 2 – 7 - background, Mo 2 - 4 background.
The highest pollution was found in the Karagaily river and Khudolaz river downstream the Karagaily river [1-4]. It was found that high values of concentrations of pollutants in drinking water were supplied to households in the village Kalinino, located in the southeastern part of the study area - a short distance from the old and new wastewater treatment plant and the city landfill.
In general, the scale of the negative impact of industrial enterprises and disturbed areas on the components of the natural environment and human health can be expressed in the form of accumulated environmental and economic damage over a multi-year period. Their parameters for many territories covered by mining activities in the Southern Trans-Urals have not been studied. Given the above, in the course of the study conducted in 2020, we paid much attention to the performance of calculations and estimations of accumulated damage from the destruction of soil invertebrates; damage caused to soils, natural vegetation, ichthyofauna, as well as damage caused by environmentally caused morbidity of Sibai population.
It is necessary to pay attention to the fact that at present there is no unified methodology for the evaluation of economic damage, caused by ecologically conditioned morbidity of the population. At the same time, it can be emphasized that the methodology of determining economic damage from environmental pollution can be represented by the following logical chain: emission (discharge) of a pollutant into the environment - change in the environment (increase in the concentration of pollutants) - natural damage - economic damage [6-17].
There are three instrumental methods for the assessment of natural damage:
− empirical relationships - it is based on analysis and statistical processing of empirical data about the influence of different factors on the recipient’s condition;
− factor elimination - based on the selection of a control area and comparison of the recipient’s condition in it with the contaminated area;
− combined - allows detailing the results of the factor elimination method using statistical processing of empirical data on the impact of individual factors on recipients.
Some authors combine the listed methods into direct counting methods and additionally distinguish the indirect method, which is based on the principle of transferring general regularities to a specific object and assumes the use of a system of normative indicators (for example, MACs). Exactly this type of method belongs to the Temporary Typical Methodology...[9] and the Methodology of Determination of the Prevented Environmental Damage [12].
In today’s environmentally tense situation, to form an effective environmental policy it is necessary to have a comprehensive multilateral methodology for assessing the economic damage from the population morbidity, caused by environmental pollution, which will reflect both personal and public losses. Only then can a realistic understanding of the necessary costs for restoring health and planning measures of a socio-environmental nature be obtained. From this point of view, the approaches to damage assessment proposed by T. Anopchenko [18] and G. Denisov [19] are closest to the proposed ideal. A similar estimation of economic damage from the population morbidity caused by environmental pollution was developed and carried out for the subjects of the Russian Federation in the Privolzhsky federal district. As well the mentioned works, it takes into account both personal and public losses.
The empirical material in the course of this study was formed based on data on the general morbidity of the population, which allowed it to cover all its age groups. The difference of the proposed approach is that the personal expenses of the population were taken into account based on the share of health care expenses per capita and specifically, on the treatment of environmentally dependent diseases [20-22]. On the whole, the proposed approach to damage assessment is less detailed, but it does not require the collection of a large amount of data while maintaining the order of the damage value, which allows it to be used as an indicative indicator of the region’s environmental policy.
Stooping to the methodology of calculation of the economic damage, caused by the ecologically conditioned morbidity of the population, we should note that it can consist of two components (groups): 1) damage to society as a whole; 2) personal damage to citizens.
The damage to society as a whole covers:
1. The state’s expenditures in the system of compulsory health insurance for the treatment of the population.
2. The payment of sick pay.
3. The loss of a share of tax revenues to the budget due to reduced profits due to temporary and permanent disability of workers.
4. Loss of a share in the gross regional product (GRP).
Personal losses to citizens include:
1. The cost of preventive medicine.
2. The cost of medicines for the treatment of chronic and acute diseases.
3. Costs of emergency treatment (ambulance, intensive care).
4. Costs of inpatient treatment (nursing and outpatient services).
5. Cost of treatment at home.
6. Cost of rehabilitation.
7. Cost of sanatorium treatment.
8. Loss of well-being (e.g. suffering due to death or illness).
9. Property loss in earnings due to temporary incapacity for work.
10. Decrease in occupational level and loss of qualifications due to temporary incapacity for work.
11. The psychological discomfort caused by the loss of qualifications and professional qualifications.
12. Deterioration of psychological well-being caused by an unaesthetic visual environment.
Both these and other losses are equally important, so a full economic evaluation of the damage caused by public illness must include both public and personal losses to citizens. However, not all of the forms of damage represented can be objectively assessed. For example, there are no methodologies capable of providing an economic assessment of the damage caused by psychological discomfort. The personal damage in the majority of cases is estimated on expenses on out-patient and sanatorium treatment. Therefore, to obtain the closest to real data on the economic damage from environmentally caused morbidity promptly, the following variants of its estimation are proposed.
Assessment of societal damage. Detailed data on the number of sick leave days taken or reductions in tax payments are difficult to find when making economic damage assessments. A more accessible and convenient indicator for damage assessment is the Gross Regional Product (GRP) per capita. Losses related to GRP will constitute the largest percentage of the real value of the damage, i.e. the data obtained allows us to determine the order of the damage.
We assessed the damage based on GRP per capita since the main damage to the economy of the RF subject is caused by the increase in person-days of disability (in this case we mean the underproduced GRP during the above-mentioned period). Knowing GRP per capita, as well as population morbidity, the average duration of illness and the share of cases of diseases caused by environmental factors, we can calculate the corresponding damage for the study area as a whole [14,23].
The calculation is carried out according to the formula (1):
Where Yo - social damage from the morbidity of the population from the i-th group of diseases, caused by environmental pollution, rub./year; ni - number of people affected by an i-th group of diseases, caused by environmental pollution, people; t - average duration of disability, day/year; GRP - gross regional product per capita, rub./person/year.
An important point in assessing the damage from the morbidity of the population caused by the negative impact of environmental factors is the determination of the percentage of those who fall ill from the specified cause. But it is difficult to determine the exact number of sick people, therefore, in this work, we used the method of control areas to determine the number of sick people.
Personal damage estimation. It is difficult to determine the cost to the population of treating individual diseases. An optimal statistical indicator that combines the cost of preventive medicine, the cost of medicines for chronic and acute diseases, the cost of emergency treatment (emergency care, intensive care), the cost of inpatient treatment (nursing care and outpatient services), the cost of home care, the cost of rehabilitation, the cost of sanatorium treatment are indicators of health care costs per capita, in our opinion. With this in mind, we used per capita expenditure and the percentage of health care expenditure.
However, not all types of healthcare expenditure are associated with environmentally-dependent morbidity. For example, there is currently no reliable evidence that dental prosthetics are an environmentally relevant disease. To exclude dental prosthetics costs in the calculations, we have calculated their share in the total expenditure on health services. The percentage for Ufa is 18.32%. We assumed that the same percentage of costs for dental prosthetics makes up the health care costs, so we excluded 18.32% going to this type of service in the calculations. The calculation was done using the following formula:
Where: Y1 - personal damage from the incidence of the population of the i-th group of diseases caused by environmental pollution, $/year; ni - the number of people affected by the i-th group of diseases caused by environmental pollution, people; LRd - the number of personal expenses per capita,$/year;
Based on the data from the statistical handbook Russian Health Care [24], the following items of citizens’ expenditures on treatment have been highlighted:
1. Paid medical services;
2. Health resort services;
3. Expenses for purchase of medicines
Briefly dwelling on the review of methodological regulations for calculating cumulative damage by each of the studied components, it should be noted that calculation of the environmental damage caused to soil invertebrates as a result of the formation and functioning of open pits for copper ore mining, formation of waste rock dumps, is based on the Order of RF Ministry of Natural Resources from 28 April 2008 (№ 107). The said order approved the Methodology...[25], which contains provisions on the calculation of the amount of damage caused to wildlife listed in the Red Book of the Russian Federation, as well as other wildlife objects not related to the objects of hunting and fishing and their habitat. The damage is formed due to the destruction of soil invertebrates’ habitats (soil cover of the territory) by establishing quarries, rock dumps, wastewater reservoirs, etc. on the originally sparsely disturbed territories. Their total area within the boundaries of the investigated territory was determined by GIS analysis of the map - scheme and classification of the raster image - Landsat - 8 space image, which is 11,782,520.8 m2 or 11.783 km2. Taking this into account, the value of ecological damage to soil invertebrates living within the boundaries of disturbed lands (Up) was determined according to the formula
Up = F*Y, (3)
Where F is - the total area of disturbed territories and Y is - the value of damage per unit of investigated territory (rub./m2). The inflation rate in 2020 about 2008 (the year of the methodology approval) according to Rosstat’s inflation calculator is 241,168%. Accordingly, the total damage figures have been recalculated taking into account this inflation rate.
Calculation of damage, caused to soils of the study area, was made based on the “Methodology for calculating the amount of damage, caused to soils as an object of environmental protection” [26]. According to it the calculation of damage caused to soils as a result of pollution with toxic ingredients was made by the formula 4:
Where: UShzagr - the amount of damage (rub.); СХВ - degree of chemical pollution, which is calculated following paragraph 6 of the mentioned methodology; S - an area of contaminated soil (m2); Kr - index, reflecting the depth of chemical pollution (deterioration) of soil, which is calculated following paragraph 7 of the mentioned methodology; Kish - index determined depending on the category of land and designated purpose where the contaminated plot is located (calculated following paragraph 8 of the mentioned methodology); Tx - tax for calculation of the amount of damage caused to soils as an object of environment. In the case of chemical pollution of soils, it is determined according to appendix 1 to the methodology (rub./m2) [27].
ARS - the degree of chemical pollution is the ratio (C) of the actual content of the i-th chemical substance in the soil to the standard of environmental quality for soils is calculated by the following formula (5):
Where: Xi is the actual content of the i-th chemical in the soil (mg/kg); Xn is the environmental quality standard for soils (mg/kg).
Standardized protocols for sampling plant diversity were used in assessing damage to plant communities. It was taken into account that the study area is characterized by the lasting impact of various economic activities on them. This should include, first of all, mainly unorganized pasturing, development of settlements, livestock complexes, road networks, etc. Further increase in the scale of anthropogenic load, formed as a result of the impact of mining facilities, occurred in already developed areas. This did not allow for assessing the damage caused by mining facilities directly. Following the above, the total amount of damage was assumed to be RUR 0.
Assessment of damage, caused to hydrobionts of the rivers Karagaily and Khudolaz, was carried out based on own research, observations, as well as analysis of published sources [28-31]. At the same time both indicators of complex pollution of water and bottom sediments in water bodies (rivers Khudolaz, Karagaily) and transformation of the hydrographic network as a result of the influence of man-made formations (quarries, rock dumps, etc.) were taken into account. Analysis of water and bottom sediment samples was carried out in certified laboratories. Accordingly, it was revealed that by now there has been a general degradation of the hydrographic network, hydrological regime and environmental conditions in the specified watercourses have drastically changed. This is due in part to the complete isolation of the upper Karagaily River from the Khudolaz River, which has resulted in a drastic reduction in the species composition of the ichthyofauna. Previously inhabited species have been accepted as having been destroyed during economic activity by the mining industry, reflecting the direct damage to hydrobionts (ichthyofauna). In assessing the characteristics of the destruction of fish species in degraded and polluted areas, consideration has been given to similar indicators for rivers that are currently in a more favorable condition. The Khudolaz River within the upper and middle parts of its basin was taken as such a water body (analog). Here, the river is characterized by minimal anthropogenic pressures and favorable hydrological and ecological conditions.
The damage caused to ichthyofauna in the above water bodies takes the form of extinction of fish species. Calculations were made by determining the value of fecundity of each fish species, including pike, roach, sprat, ide, chub, minnow, gudgeon, redeye, silver carp, carp, tench and burbot [30]. Calculation of material damage - the value of dead and lost bioresources was carried out according to the “Methodology...” [31]. The value of aquatic bioresources (fish), was determined following the rates, approved by the resolution of the Government of the Russian Federation [32].
### Results and Discussion
It is known that the extraction of mineral resources is accompanied by a large number of types and scales of negative impacts on the natural environment. Production activities are associated with the alienation of vast territories for mining in the form of open pits, rock dumps, storage (settling) tanks of liquid fractions formed at the stage of enrichment of extracted elements, as well as the direct discharge of wastewater into water bodies and wind dispersion of substances from the surface of technogenic-disturbed territories. Thus, under conditions of prolonged operation of industrial facilities, as well as direct and indirect impact of disturbed areas, natural complexes and their components undergo quantitative and qualitative changes. As it is known, from the point of view of the assessment of changes in the condition of plant communities and fauna, as well as public health, the indicators of excess pollutant concentrations over their maximum permissible values in sanitary-hygienic and fishery indicators can be accepted with the highest correlation. At the same time, for example, in contrast to hydrobionts, in the course of human life, pollutants can enter the human body in different ways: as part of drinking water, food, as a result of breathing, etc. Accordingly, under conditions of significant contamination of components of the natural environment, including surface and ground waters, soil cover, atmospheric air, plant communities and fauna and consumption of food obtained from the contaminated environment, processes may occur that reflect the cumulative impact of negative factors, increasing as substances pass through the food chain. Typically, in these contexts, foci or ranges of characteristic diseases occur, due to the nature of the influence of external and internal factors.
To study the formation of characteristic diseases in the population and assess the ecological and economic damage within the study area, we chose the method of experimental and control areas. As shown in papers [4,5,33,34], this method usually selects pilot areas, where the negative impact of environmental factors is high, as well as control areas, conventionally assumed to be environmentally friendly. Then a comparison is made of the parameter under study, in this case, the morbidity of the population. The resulting difference indicates the number of people who fell ill as a result of the negative impact of environmental factors. In the case of the Sibai City District, the morbidity rate of the population of the Republic of Bashkortostan was taken as a reference. The latter is explained by the fact that districts close in socio-economic characteristics (Kumertau, Beloretsk, Tuimazy) differ in natural conditions and vice versa, districts close in natural conditions (Abzelilovsky district) differ in socio-economic terms.
Data on groups and levels of morbidity were obtained from data presented in the state reports of the Federal Service for Surveillance on Consumer Rights Protection and Human Welfare in the Republic of Bashkortostan (Rospotrebnadzor) for 2015 - 2019. The year 2020 was not included in the calculations for two reasons: 1) statistical data for this year have not yet been generated and 2) the spread of the coronavirus infection epidemic (COVID-19) has changed the morbidity pattern very significantly, which is typical not only for the territory under study but also for the whole world.
The period analyzed in the calculations is chosen to be 5 years (2015-2019). The latter is due to the established socio-economic situation in the Russian Federation after the 2014 crisis. The analysis was conducted for the following age groups: adults (18 years and older), adolescents (15-17 years), children (up to and including 14 years) and children in the first year of life.
Drawing attention to the prevalence of diseases such as high blood pressure, gastritis and duodenitis, anemia, chronic bronchitis, blood and circulatory diseases and digestive diseases, it should be pointed out that due to the lack of reliable information, indicators of hormonal defects are not accounted for.
Based on the data on the population of Sibai, the number of cases of environmentally caused morbidity in different age groups was subsequently determined.
To assess the economic damage from environmentally caused morbidity indicators of the gross regional product (GRP, Table 1) and the average duration of disability (Table 2) were used [24].
Based on the data presented above, as well as on formula 1, the societal damage from environmentally-caused morbidity of the population has been calculated. Thus, it was determined that the total amount of public economic damage is more than 454, 453 million rubles. In addition, the total amount of personal damage to citizens from environmentally conditioned diseases in Sibai city for the period of 2015-2019 was 73, 366 million rubles. In total, the total damage from environmentally caused diseases in the population is estimated the amount 527, 819 million rubles.
Calculations made to assess the damage caused to hydrobionts (ichthyofauna) by the Khudolaz and Karagaily rivers showed that it is estimated at 113, 862 million rubles. Methodological provisions for making calculations have been shown earlier.
It has been also defined that the total amount of damage caused to the soil invertebrates is 6 251, 447 million RUR; the damage to the soils is 22, 320 million RUR/ha.
In general, the data obtained by calculation allowed for estimating the total amount of accumulated economic damage, caused by the adverse effects of altered environmental conditions within the zone of influence of industrial facilities of Sibay city. It was more than 113 billion rubles at the level of 2020. This amount does not include the indicators of those damages that reflect the characteristics of degradation of the Khudolaz and Karagaily rivers channels, changes in their hydrological regime, and deterioration of water use conditions. They, as shown in [35] and according to our observations in recent years under the influence of global climate change are becoming critical. Namely, in the summer of 2020, the mentioned rivers in the zone of influence of the objects of the mining industry dried up. Consequently, all species of higher hydrobionts have died in the dried riverbeds. It was also found that large areas of the vegetation communities on the slopes of the river valleys had dried up. This causes additional ecological and social damage to both natural complexes in general and public health.
Similar changes are observed in other areas affected by the long-term impact of mining facilities. For example, in the zone of influence of the Karabash mine the waters of the Sak-Elga River have remained extremely polluted for many years, the Uchalinsky mine - of the Buida and Kidysh Rivers, Buribaysky mine - of the Tanalyk River, Mednogorsky mine - of the Blyava River, etc. The specificity and scale of influence of technogenic disturbed territories (quarries, rock dumps, waste accumulators, etc.) are approximately similar. This is reflected in the formation of the corresponding environmental and economic damage (in terms of specific indicators) to the environment and public health. It should be noted that a characteristic feature in all areas of influence of disturbed territories is the lack of necessary treatment systems for mine and tailing wastewater, which, as was shown earlier, is the main source of pollutants in the river systems. The existing experience of treating small volumes of such wastewater using electrodialysis in the impact area of the Uchaly facilities has not been further developed, although, it is the most promising for solving environmental problems both at present and in the future.
Municipalities do not have the necessary funds to eliminate the violations. In general, the solution to the accumulated environmental problems, including the restoration of the morphometric characteristics of river channels and their water protection zones, as well as the landscape-ecological improvement of the disturbed areas and the improvement of living conditions of people requires the attraction of huge financial and material resources. This can be allowed only based on the targeted involvement of federal, republican and municipal funds
### Conclusion
It should be emphasized that the previously listed industrial centers and hubs located within the Southern Trans-Urals (Figure 1) have much in common in terms of their impact on the state of the natural environment and public health. However, for most of them, no serious calculations on the assessment of the accumulated environmental and economic damage have been carried out so far. There is also a lack of information about the targeted clinical research on the level of morbidity of the population. At the same time, the complex research, conducted by us to study changes in ecological conditions in natural-territorial and natural-aquatic complexes, experiencing an excessive and prolonged impact by mining facilities, located in Sibai city, allowed us to estimate indicators of economic damage, caused to the natural environment and public health. Methodological provisions on their calculation with high reliability can be adopted for other, previously listed industrial centers, characterized by similar features of their impact on the state of the environment and public health. The main provisions aimed at the restoration of favorable environmental conditions in the river basins exposed to the negative impact of mining facilities are as follows.
1. Within a zone of influence of economic objects of Sibay city the natural complexes located in the lower part of basins of the rivers Karagaily and Khudolaz are characterized by an extremely high degree of degradation, and also high indexes of accumulation of polluting substances. Here large areas of formerly fertile land and water bodies are allocated for quarries, rock dumps, accumulation of industrial effluents, urban landfills, etc. Radical changes have also taken place in the beds of small rivers themselves, manifested in their deformations, as well as a sharp deterioration in their hydrological and ecological conditions. This requires full-scale implementation of reclamation and environmental protection measures.
2. As a result of the long-term operation of mining facilities, huge environmental and economic damage has been caused to the natural environment and the local population. In the zone of influence of objects confined to Sibai town, the total amount of the caused economic damage is estimated at 113 billion rubles. However, there are no such calculations in the context of other territories covered by the impact of mining facilities. This requires adequate fundraising for the elimination (minimization) of committed violations in the context of all degraded and contaminated territories. The methodological provisions and results of the calculations and assessments made on the example of the zone of influence of Sibai city district reflect the necessity of urgently carrying out similar complex investigations on the zones of influence in other mining districts of the Eastern Trans-Ural Region. Their locations have been shown in Figure 1. Accordingly, necessary nature protection actions should be substantiated and carried out.
3. With the formation of a low-water phase of rivers and increasing aridity of the climate since the early 2000s, environmental and economic problems have become more acute. Municipalities of the cities do not have the necessary funds for the elimination of the violations. In general, the solution to the accumulated problems, including the restoration of the morphometric characteristics of river channels and their water protection zones, as well as the landscape-ecological improvement of disturbed areas requires the need to attract huge financial and material resources. This can only be resolved through the targeted involvement of federal, republican and municipal funds.
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| 2023-03-20T12:16:30 |
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|
https://www.lessonplanet.com/teachers/iit-jee-trigonometry-constraints
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IIT JEE Trigonometry Constraints
Sal solves a challenging trigonometric problem for finding the number of values of _ that satisfy a number of constraints over a given interval. He shows a clear step-by-step solution and uses some trigonometric identities that he derives.
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| 2019-04-22T17:59:45 |
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|
https://par.nsf.gov/biblio/10190450-large-magellanic-cloud-stellar-content-smash-assessing-stability-magellanic-spiral-arms
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The Large Magellanic Cloud stellar content with SMASH: I. Assessing the stability of the Magellanic spiral arms
The Large Magellanic Cloud (LMC) is the closest and most studied example of an irregular galaxy. Among its principal defining morphological features, its off-centred bar and single spiral arm stand out, defining a whole family of galaxies known as the Magellanic spirals (Sm). These structures are thought to be triggered by tidal interactions and possibly maintained via gas accretion. However, it is still unknown whether they are long-lived stable structures. In this work, by combining photometry that reaches down to the oldest main sequence turn-off in the colour-magnitude diagrams (CMD, up to a distance of ∼4.4 kpc from the LMC centre) from the SMASH survey and CMD fitting techniques, we find compelling evidence supporting the long-term stability of the LMC spiral arm, dating the origin of this structure to more than 2 Gyr ago. The evidence suggests that the close encounter between the LMC and the Small Magellanic Cloud (SMC) that produced the gaseous Magellanic Stream and its Leading Arm also triggered the formation of the LMC’s spiral arm. Given the mass difference between the Clouds and the notable consequences of this interaction, we can speculate that this should have been one of their closest encounters. These results set important more »
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0004-6361
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1. ABSTRACT We use the SMASH survey to obtain unprecedented deep photometry reaching down to the oldest main-sequence turn-offs in the colour–magnitude diagrams (CMDs) of the Small Magellanic Cloud (SMC) and quantitatively derive its star formation history (SFH) using CMD fitting techniques. We identify five distinctive peaks of star formation in the last 3.5 Gyr, at ∼3, ∼2, ∼1.1, ∼0.45 Gyr ago, and one presently. We compare these to the SFH of the Large Magellanic Cloud (LMC), finding unequivocal synchronicity, with both galaxies displaying similar periods of enhanced star formation over the past ∼3.5 Gyr. The parallelism between their SFHs indicates that tidal interactions between the MCs have recurrently played an important role in their evolution for at least the last ∼3.5 Gyr, tidally truncating the SMC and shaping the LMC’s spiral arm. We show, for the first time, an SMC–LMC correlated SFH at recent times in which enhancements of star formation are localized in the northern spiral arm of the LMC, and globally across the SMC. These novel findings should be used to constrain not only the orbital history of the MCs but also how star formation should be treated in simulations.
2. Abstract The Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are the closest massive satellite galaxies of the Milky Way. They are probably on their first passage on an infalling orbit towards our Galaxy 1 and trace the continuing dynamics of the Local Group 2 . Recent measurements of a high mass for the LMC ( M halo ≈ 10 11.1–11.4 M ⊙ ) 3–6 imply that the LMC should host a Magellanic Corona: a collisionally ionized, warm-hot gaseous halo at the virial temperature (10 5.3–5.5 K) initially extending out to the virial radius (100–130 kiloparsecs (kpc)). Such a corona would have shaped the formation of the Magellanic Stream 7 , a tidal gas structure extending over 200° across the sky 2,8,9 that is bringing in metal-poor gas to the Milky Way 10 . Here we show evidence for this Magellanic Corona with a potential direct detection in highly ionized oxygen (O +5 ) and indirectly by means of triply ionized carbon and silicon, seen in ultraviolet (UV) absorption towards background quasars. We find that the Magellanic Corona is part of a pervasive multiphase Magellanic circumgalactic medium (CGM) seen in many ionization states with a declining projected radial profilemore »
3. ABSTRACT
The highly-substructured outskirts of the Magellanic Clouds provide ideal locations for studying the complex interaction history between both Clouds and the Milky Way (MW). In this paper, we investigate the origin of a >20° long arm-like feature in the northern outskirts of the Large Magellanic Cloud (LMC) using data from the Magellanic Edges Survey (MagES) and Gaia EDR3. We find that the arm has a similar geometry and metallicity to the nearby outer LMC disc, indicating that it is comprised of perturbed disc material. Whilst the azimuthal velocity and velocity dispersions along the arm are consistent with those in the outer LMC, the in-plane radial velocity and out-of-plane vertical velocity are significantly perturbed from equilibrium disc kinematics. We compare these observations to a new suite of dynamical models of the Magellanic/MW system, which describe the LMC as a collection of tracer particles within a rigid potential, and the SMC as a rigid Hernquist potential. Our models indicate the tidal force of the MW during the LMC’s infall is likely responsible for the observed increasing out-of-plane velocity along the arm. Our models also suggest close LMC/SMC interactions within the past Gyr, particularly the SMC’s pericentric passage ∼150 Myr ago and amore »
4. ABSTRACT
The structure of the Small Magellanic Cloud (SMC) is very complex, in particular in the periphery that suffers more from the interactions with the Large Magellanic Cloud (LMC). A wealth of observational evidence has been accumulated revealing tidal tails and bridges made up of gas, stars, and star clusters. Nevertheless, a full picture of the SMC outskirts is only recently starting to emerge with a 6D phase-space map plus age and metallicity using star clusters as tracers. In this work, we continue our analysis of another outer region of the SMC, the so-called West Halo, and combined it with the previously analysed Northern Bridge. We use both structures to define the Bridge and Counter-bridge trailing and leading tidal tails. These two structures are moving away from each other, roughly in the SMC–LMC direction. The West Halo form a ring around the SMC inner regions that goes up to the background of the Northern Bridge shaping an extended layer of the Counter-bridge. Four old Bridge clusters were identified at distances larger than 8 kpc from the SMC centre moving towards the LMC, which is consistent with the SMC–LMC closest distance of 7.5 kpc when the Magellanic Bridge was formed about 150Myr ago;more »
5. Abstract
The Magellanic Stream is sculpted by its infall through the Milky Way’s circumgalactic medium, but the rates and directions of mass, momentum, and energy exchange through the stream-halo interface are relative unknowns critical for determining the origin and fate of the Stream. Complementary to large-scale simulations of LMC-SMC interactions, we apply new insights derived from idealized, high-resolutioncloud-crushingand radiative turbulent mixing layer simulations to the Leading Arm and Trailing Stream. Contrary to classical expectations of fast cloud breakup, we predict that the Leading Arm and much of the Trailing Stream should be surviving infall and even gaining mass due to strong radiative cooling. Provided a sufficiently supersonic tidal swing-out from the Clouds, the present-day Leading Arm could be a series of high-density clumps in the cooling tail behind the progenitor cloud. We back up our analytic framework with a suite of converged wind-tunnel simulations, finding that previous results on cloud survival and mass growth can be extended to high Mach number ($$) flows with a modified drag time$tdrag∝1+$and longer growth time. We also simulate the Trailing Stream; we find that the growth time is long (approximately gigayears) compared to the infall time,more »
| 2023-03-22T14:07:55 |
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|
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/30%3A_Atomic_Physics/30.09%3A_Quantum_Numbers_and_Rules
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$$\require{cancel}$$
# 30.8: Quantum Numbers and Rules
Physical characteristics that are quantized -- such as energy, charge, and angular momentum -- are of such importance that names and symbols are given to them. The values of quantized entities are expressed in terms of quantum numbers , and the rules governing them are of the utmost importance in determining what nature is and does. This section covers some of the more important quantum numbers and rules—all of which apply in chemistry, material science, and far beyond the realm of atomic physics, where they were first discovered. Once again, we see how physics makes discoveries which enable other fields to grow.
The energy states of bound systems are quantized, because the particle wavelength can fit into the bounds of the system in only certain ways. This was elaborated for the hydrogen atom, for which the allowed energies are expressed as
$E_{n} \propto \frac{1}{n^{2}},\label{30.9.1}$
where $$n = 1,2,3, \cdot \cdot \cdot$$. We define $$n$$ to be the principal quantum number that labels the basic states of a system. The lowest-energy state has $$n = 1$$, the first excited state has $$n=2$$, and so on. Thus the allowed values for the principal quantum number are
$n = 1, 2, 3, ...\label{30.9.2}$
This is more than just a numbering scheme, since the energy of the system, such as the hydrogen atom, can be expressed as some function of $$n$$, as can other characteristics (such as the orbital radii of the hydrogen atom).
The fact that the magnitude of angular momentum is quantized was first recognized by Bohr in relation to the hydrogen atom; it is now known to be true in general. With the development of quantum mechanics, it was found that the magnitude of angular momentum $$L$$ can only have the values
$L = \sqrt{l \left( l+1 \right) } \frac{h}{2\pi} \left(l = 0, 1, 2, ..., n-1\right), \label{30.9.3}$
where $$l$$ is defined to be the angular momentum quantum number. The rule for $$l$$ in atoms is given in the parentheses. Given $$n$$, the value $$l$$ can be any integer from zero up to $$n-1$$. For example, if $$n = 4$$, then $$l$$ can be 0, 1, 2, or 3.
Note that for $$n = 1$$, $$l$$ can only be zero. This means that the ground-state angular momentum for hydrogen is actually zero, not $$h/2\pi$$ as Bohr proposed. The picture of circular orbits is not valid, because there would be angular momentum for any circular orbit. A more valid picture is the cloud of probability shown for the ground state of hydrogen in this link. The electron actually spends time in and near the nucleus. The reason the electron does not remain in the nucleus is related to Heisenberg’s uncertainty principle -- the electron’s energy would have to be much too large to be confined to the small space of the nucleus. Now the first excited state of hydrogen has $$n=2$$, so that $$l$$ can be either 0 or 1, according to the rule in Equation $$\ref{30.9.3}$$. Similarly, for $$n =3$$, $$l$$ can be 0, 1, or 2. It is often most convenient to state the value of $$l$$, a simple integer, rather than calculating the value of $$L$$ from Equation $$\ref{30.9.3}$$. For example, for $$l = 2$$, we see that
$L = \sqrt{l \left( l+1 \right) } \frac{h}{2\pi} = \sqrt{6} \frac{h}{2 \pi} = 0.390 h = 2.58 \times 10^{-34} J \cdot s.$
It is much simpler to state $$l = 2$$. As recognized in the Zeeman effect, the direction of angular momentum is quantized. We now know this is true in all circumstances. It is found that the component of angular momentum along one direction in space, usually called the z-axis, can have only certain values of $$L_{z}$$. The direction in space must be related to something physical, such as the direction of the magnetic field at that location. This is an aspect of relativity. Direction has no meaning if there is nothing that varies with direction, as does magnetic force. The allowed values of $$L_{z}$$ are $L_{z} = m_{l} \frac{h}{2\pi} \left( m_{l} = -l, -l + 1, ..., -1, 0, 1, ... l-1, l\right),\label{30.9.4}$ where $$L_{z}$$ is the z-component of the angular momentum and $$m_{l}$$ is the angular momentum projection quantum number. The rule in parentheses for the values of $$m_{l}$$ is that it can range from $$-l$$ to $$l$$ in steps of one. For example, if $$l = 2$$, then $$m_{l}$$ can have the five values –2, –1, 0, 1, and 2. Each $$m_{l}$$ corresponds to a different energy in the presence of a magnetic field, so that they are related to the splitting of spectral lines into discrete parts, as discussed in the preceding section. If the $$z$$- component of angular momentum can have only certain values, then the angular momentum can have only certain directions, as illustrated in Figure 30.9.1.
Figure $$\PageIndex{1}$$. The component of a given angular momentum along the z-axis (defined by the direction of a magnetic field) can have only certain values; these are shown here for $$l =1$$, for which $$m_{l} = -1, 0, and +1$$. The direction of $$L$$ is quantized in the sense that it can have only certain angles relative to the z-axis.
Example $$\PageIndex{1}$$: What are the Allowed Directions?
Calculate the angles that the angular momentum vector $$L$$ can make with the z-axis for $$l = 1$$, as illustrated in Figure 30.9.1.
Strategy:
Figure 30.9.1. represents the vectors $$L$$ and $$L_{z}$$ as usual, with arrows proportional to their magnitudes and pointing in the correct directions. $$L$$ and $$L_{z}$$ form a right triangle, with $$L$$ being the hypotenuse and $$L_{z}$$ the adjacent side. This means that the ratio of $$L_{z}$$ to $$L$$ is the cosine of the angle of interest. We can find $$L$$ and $$L_{z}$$ using $$L = \sqrt{l\left(l + 1\right)}\frac{h}{2\pi}$$ and $$L_{z} = m \frac{h}{2\pi}$$.
Solution:
We are give $$l = 1$$, so that $$m_{l}$$ can be =1, 0, or -1. Thus $$L$$ has the value given by $$L = \sqrt{l\left(l + 1\right)}\frac{h}{2\pi}$$.
$L = \frac{\sqrt{l\left(l + 1\right)}h}{2\pi} = \frac{\sqrt{2}h}{2\pi} \label{30.9.5}$
$$L_{z}$$ can have three values, given by $$L_{z} = m_{l} \frac{h}{2\pi}$$. $L_{z} = m_{l} \frac{h}{2\pi} = \begin{cases} \frac{h}{2\pi}, ~ m_{l} = +1 \\[2ex] 0, ~ m_{l} = 0 \\[2ex] \frac{h}{2\pi}, ~ m_{l} = -1 \end{cases} \label{30.9.6}$
As can be seen in Figure $$\cos{\theta} = L_{z}/L$$, and so for $$m_{l} \pm 1$$, we have $\cos{\theta_{1}} = \frac{L_{z}}{L} = \frac{\frac{h}{2\pi}}{\frac{\sqrt{2}h}{2\pi}} = \frac{1}{\sqrt{2}} = -.707.\label{30.9.7}$
Thus, $\theta_{1} = \cos{0.707}^{-1} = 45.0 ^{\circ}.\label{30.9.8}$
Similarly, for $$m_{l} = 0$$, we find $$\cos_{2} = 0$$; thus, $\theta_{2} = \cos{0}^{-1} = 90.0. ^{\circ} \label{30.9.9}$
And for $$m_{l} = -1$$, $\cos{\theta_{3}} = \frac{L_{z}}{L} = \frac{-\frac{h}{2\pi}}{\frac{\sqrt{2}h}{2\pi}} = -\frac{1}{\sqrt{2}} = -0.707, \label{30.9.10}$
so that $\theta_{3} = \cos{\left(-0.707\right)}^{-1} = 135.0^{\circ}.\label{30.9.11}$
Discussion:
The angles are consistent with the figure. Only the angle relative to the z-axis is quantized. $$L$$ can point in any direction as long as it makes the proper angle with the z-axis. Thus the angular momentum vectors lie on cones as illustrated. This behavior is not observed on the large scale. To see how the correspondence principle holds here, consider that the smallest angle ($$\theta_{1}$$ in the example) is for the maximum value of $$m_{l} = 0$$, namely $$m_{l} = l$$. For that smallest angle, $\cos{\theta} = \frac{L_{z}}{L} = \frac{l}{\sqrt{l\left(l + 1 \right) }},\label{30.9.12}$ which approaches 1 as $$l$$ becomes very large. If $$\cos{\theta} = 1$$, then $$\theta = 0^{\circ}$$. Furthermore, for large $$l$$, there are many values of $$m_{l}$$, so that all angles become possible as $$l$$ gets very large.
# Intrinsic Spin Angular Momentum Is Quantized in Magnitude and Direction
There are two more quantum numbers of immediate concern. Both were first discovered for electrons in conjunction with fine structure in atomic spectra. It is now well established that electrons and other fundamental particles have intrinsic spin, roughly analogous to a planet spinning on its axis. This spin is a fundamental characteristic of particles, and only one magnitude of intrinsic spin is allowed for a given type of particle. Intrinsic angular momentum is quantized independently of orbital angular momentum. Additionally, the direction of the spin is also quantized. It has been found that the magnitude of the intrinsic (internal) spin angular momentum, $$S$$, of an electron is given by
$S = \sqrt{s\left(s+1\right)}\frac{h}{2\pi} \left( s = 1/2 ~ for ~ electrons\right), \label{30.9.13}$
where $$s$$ is defined to be the spin quantum number. This is very similar to the quantization of $$L$$ given in $$L = \sqrt{l\left(l+1\right)}\frac{h}{2\pi}$$, except that the only value allowed for $$s$$ for electrons is 1/2.
The direction of intrinsic spin is quantized, just as is the direction of orbital angular momentum. The direction of spin angular momentum along one direction in space, again called the z-axis, can have only the values
$s_{z} = m_{s} \frac{h}{2\pi} \left( m_{s} = -\frac{1}{2}, +\frac{1}{2} \right) \label{30.9.14}$
for electrons. $$s_{z}\0 is the z-component of spin angular momentum and \(m_{s}$$ is the spin projection quantum number. For electrons, $$s$$ can only be 1/2, and $$m_{s}$$ can be either +1/2 or –1/2. Spin projection $$m_{s} = + 1/2$$ is referred to as spin up, whereas $$m_{s} = -1/2$$ is called $$m_{s} = - 1/2$$ is called spin down. These are illustrated in this link.
INTRINSIC SPIN
In later chapters, we will see that intrinsic spin is a characteristic of all subatomic particles. For some particles $$s$$ is half-integral, whereas for others $$s$$ is integral -- there are crucial differences between half-integral spin particles and integral spin particles. Protons and neutrons, like electrons, have $$s = 1/2$$, whereas photons have $$s = 1$$, and other particles called pions have $$s = 0$$, and so on.
To summarize, the state of a system, such as the precise nature of an electron in an atom, is determined by its particular quantum numbers. These are expressed in the form $$n, l, m_{l}, m_{s}$$ -- see Table For electrons in atoms, the principal quantum number can have the values $$n = 1, 2, 3, ...$$. Once $$n$$ is known, the values of the angular momentum quantum number are limited to $$l = 1, 2, 3, ..., n-1$$. For a given value of $$l$$, the angular momentum projection quantum number can have only the values $$m_{l} = -l, -l + 1, ..., -1, 0, 1, ..., l-1, l$$. Electron spin is independent of $$n$$, $$l$$, and $$m_{l}$$, always having $$s = 1/2$$. The spin projection quantum number can have two values. $$m_{s} = 1/2 ~ or ~ -1/2$$.
Name Symbol Allowed Values
Principal quantum number $$n$$ $$1,2,3,...$$
Angular momentum $$l$$ $$0, 1, 2, ... n-1$$
Angular momentum projection $$m_{l}$$ $$-l, -l+1, ..., -1, 0, 1, ..., l-1, l \left(or ~ 0, \pm 1, \pm 2, ..., \pm l \right)$$
Spin $$s$$ $$1/2 \left(electrons\right)$$
Spin projection $$m_{s}$$ $$\pm 1/2$$
Figure 30.9.2. shows several hydrogen states corresponding to different sets of quantum numbers. Note that these clouds of probability are the locations of electrons as determined by making repeated measurements -- each measurement finds the electron in a definite location, with a greater chance of finding the electron in some places rather than others. With repeated measurements, the pattern of probability shown in the figure emerges. The clouds of probability do not look like nor do they correspond to classical orbits. The uncertainty principle actually prevents us and nature from knowing how the electron gets from one place to another, and so an orbit really does not exist as such. Nature on a small scale is again much different from that on the large scale.
Figure $$\PageIndex{2}$$. Probability clouds for the electron in the ground state and several excited states of hydrogen. The nature of these states is determined by their sets of quantum numbers, here given as $$n, l, m_{l}$$. The ground state is (0, 0, 0); one of the possibilities for the second excited state is (3, 2, 1). The probability of finding the electron is indicated by the shade of color; the darker the coloring the greater the chance of finding the electron.
We will see that the quantum numbers discussed in this section are valid for a broad range of particles and other systems, such as nuclei. Some quantum numbers, such as intrinsic spin, are related to fundamental classifications of subatomic particles, and they obey laws that will give us further insight into the substructure of matter and its interactions.
PHET EXPLORATIONS: STERN-GERLACH EXPERIMENT
The classic Stern-Gerlach Experiment shows that atoms have a property called spin. Spin is a kind of intrinsic angular momentum, which has no classical counterpart. When the z-component of the spin is measured, one always gets one of two values: spin up or spin down.
Figure $$\PageIndex{3}$$: Stern-Gerlach Experiment
# Summary
• Quantum numbers are used to express the allowed values of quantized entities. The principal quantum number $$n$$ labels the basic states of a system and is given by $$n = 1, 2, 3, ...$$
• The magnitude of angular momentum is given by $$L = \sqrt{l \left( l+1 \right) } \frac{h}{2\pi} \left(l = 0, 1, 2, ..., n-1\right),$$ where $$l$$ is the angular momentum quantum number. The direction of angular momentum is quantized, in that its component along an axis defined by a magnetic field, called the z-axis is given by $$L_{z} = m_{l} \frac{h}{2\pi} ~ \left(m_{l} = -l, -l+1, ..., -1, 0, 1, ... l-1, l\right),$$ where $$L_{z}$$ is the z-component of the angular momentum and $$m_{l}$$ is the angular momentum projection quantum number. Similarly, the electron’s intrinsic spin angular momentum $$S$$ is given by $$S = \sqrt{s\left(s+1\right)}\frac{h}{2\pi} ~ \left(s = 1/2 ~ for ~ electrons \right),$$ where $$S_{z}$$ is the z-component of spin angular momentum and $$m_{s}$$ is the spin projection quantum number. Spin projection $$m_{s} = +1/2$$ is referred to as spin up, whereas $$m_{s} = -1/2$$ is called spin down. The table summarizes the atomic quantum numbers and their allowed values.
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
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https://zbmath.org/authors/?q=ai%3Acoleman.bernard-d
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# zbMATH — the first resource for mathematics
## Coleman, Bernard David
Compute Distance To:
Author ID: coleman.bernard-d Published as: Coleman, Bernard D.; Coleman, B. D.; Coleman, Bernard External Links: MGP · Wikidata · GND
Documents Indexed: 133 Publications since 1958, including 4 Books Biographic References: 2 Publications
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#### Co-Authors
31 single-authored 19 Owen, David R. 10 Gurtin, Morton Edward 10 Noll, Walter 9 Mizel, Victor J. 8 Dill, Ellis Harold 6 Renninger, George H. 6 Swigon, David 4 Fabrizio, Mauro 4 Falk, Richard S. 4 Hodgdon, Marion L. 4 Hsieh, Ying-Hen 4 Markovitz, Hershel 4 Moakher, Maher 3 Duffin, Richard James 3 Knowles, Gregory P. 2 Alouges, François 2 Asvadurov, Sergey 2 Bragg, L. E. 2 Brézis, Haïm 2 Coffman, Charles V. 2 Greenberg, James M. 2 Lembo, Marzio 2 Newman, Daniel C. 2 Tobias, Irwin 2 Truesdell, Clifford Ambrose III 1 Antman, Stuart S. 1 Bethuel, Fabrice 1 Biton, Yoav Y. 1 Gurlin, M. E. 1 Hélein, Frédéric 1 Herrera R., I. 1 Herrera, Ismael 1 Hrusa, William J. 1 Jenkins, James T. 1 Lai, Po-Hsien 1 Lu, Zheng 1 Marcus, Moshe M. 1 Nohel, John A. 1 Olson, Wilma K. 1 Serrin, James 1 Toupin, Richard A. 1 Zapas, Louis J. 1 Ziemer, William Paul
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#### Serials
48 Archive for Rational Mechanics and Analysis 5 Journal of Mathematical Biology 5 Mathematical Biosciences 3 Physics of Fluids 3 Physica D 3 Journal of Elasticity 3 Istituto Lombardo, Accademia di Scienze e Lettere, Rendiconti, Sezione A 2 Acta Mechanica 2 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Journal of the Mechanics and Physics of Solids 2 Soochow Journal of Mathematics 2 Proceedings of the National Academy of Sciences of the United States of America 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of Applied Physics 1 Biological Cybernetics 1 International Journal of Engineering Science 1 Journal of Fluid Mechanics 1 Journal of Rheology 1 Reviews of Modern Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Meccanica 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rendiconti del Seminario Matematico della Università di Padova 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Scientific Computing 1 Advances in Applied Mechanics 1 Annals of the New York Academy of Sciences 1 Transactions of the Society of Rheology
all top 5
#### Fields
53 Mechanics of deformable solids (74-XX) 22 Biology and other natural sciences (92-XX) 14 Fluid mechanics (76-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Numerical analysis (65-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 2 Real functions (26-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
108 Publications have been cited 2,690 times in 1,735 Documents Cited by Year
The thermodynamics of elastic materials with heat conduction and viscosity. Zbl 0113.17802
Coleman, Bernard D.; Noll, Walter
1963
An approximation theorem for functionals, with applications in continuum mechanics. Zbl 0097.16403
Coleman, Bernard D.; Noll, Walter
1960
Foundations of linear viscoelasticity. Zbl 0103.40804
Coleman, Bernard D.; Noll, Walter
1961
A mathematical foundation for thermodynamics. Zbl 0306.73004
Coleman, Bernard D.; Owen, David R.
1974
Norms and semi-groups in the theory of fading memory. Zbl 0146.46104
Coleman, B. D.; Mizel, V. J.
1966
On thermodynamics, strain impulses, and viscoelasticity. Zbl 0125.13603
Coleman, B. D.
1964
Instability, uniqueness, and nonexistence theorems for the equation $$u_t=u_{xx}-u_{xtx}$$ on a strip. Zbl 0292.35016
Coleman, Bernard D.; Duffin, Richard J.; Mizel, Victor J.
1965
On the thermostatics of continuous media. Zbl 0231.73003
Coleman, Bernard D.; Noll, Walter
1959
Waves in materials with memory. II: On the growth and decay of one- dimensional acceleration waves. Zbl 0244.73017
Coleman, Bernard D.; Gurtin, Morton E.
1965
On the general theory of fading memory. Zbl 0167.24704
Coleman, B. D.; Mizel, V. J.
1968
On the thermodynamics of second sound in dielectric crystals. Zbl 0501.73008
Coleman, Bernard D.; Fabrizio, Mauro; Owen, David R.
1982
Thermodynamics and departures from Fourier’s law of heat conduction. Zbl 0114.44905
Coleman, B. D.; Mizel, V. J.
1963
Material symmetry and thermostatic inequalities in finite elastic deformations. Zbl 0123.40703
Coleman, Bernard D.; Noll, Walter
1964
On the dynamics of rods in the theory of Kirchhoff and Clebsch. Zbl 0784.73044
Coleman, Bernard D.; Dill, Ellis H.; Lembo, Marzio; Lu, Zheng; Tobias, Irwin
1992
Normal stress effects in second-order fluids. Zbl 0133.19205
Coleman, Bernard D.; Markovitz, Hershel
1964
Viscometrie flows of non-newtonian fluids. Theory and experiment. Zbl 0137.21903
Coleman, Bernard D.; Markovitz, H.; Noll, Walter
1966
Nonautonomous logistic equations as models of the adjustment of populations to environmental change. Zbl 0425.92013
Coleman, Bernard D.
1979
Thermodynamic restrictions on the constitutive equations of electromagnetic theory. Zbl 0218.35072
Coleman, B. D.; Dill, E. H.
1971
Waves in materials with memory. III: Thermodynamic influences on the growth and decay of acceleration waves. Zbl 0244.73018
Coleman, Bernard D.; Gurtin, Morton E.
1968
On the stability of solutions of functional-differential equations. Zbl 0184.36801
Coleman, B. D.; Mizel, V. J.
1968
On the thermodynamics of periodic phases. Zbl 0788.73015
Coleman, Bernard D.; Marcus, Moshe; Mizel, Victor J.
1992
On shear bands in ductile materials. Zbl 0625.73041
Coleman, Bernard D.; Hodgdon, Marion L.
1985
Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids. Zbl 1014.74038
Coleman, Bernard D.; Swigon, David
2000
On certain steady flows of general fluids. Zbl 0087.19402
Coleman, Bernard D.; Noll, Walter
1959
Recent results in the continuum theory of viscoelastic fluids. Zbl 0122.43506
Coleman, Bernard D.; Noll, Walter
1961
On thermodynamics and elastic-plastic materials. Zbl 0332.73003
Coleman, Bernard D.; Owen, David R.
1975
Stability of equilibrium for a nonlinear hyperbolic system describing heat propagation by second sound in solids. Zbl 0621.73132
Coleman, Bernard D.; Hrusa, William J.; Owen, David R.
1986
Necking and drawing in polymeric fibers under tension. Zbl 0535.73016
Coleman, Bernard D.
1983
Incompressible second-order fluids. Zbl 0136.45104
Markovitz, Hershel; Coleman, Bernard D.
1964
On thermodynamics and the stability of motions of material with memory. Zbl 0275.73003
Coleman, Bernard D.; Dill, Ellis H.
1973
Waves in materials with memory. V: On the amplitude of acceleration waves and mild discontinuities. Zbl 0247.73022
Coleman, Bernard D.; Greenberg, James M.; Gurtin, Morton E.
1966
Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders. Zbl 0825.76062
Bethuel, F.; Brézis, Haïm; Coleman, B. D.; Hélein, F.
1992
On the optimal choice of r for a population in a periodic environment. Zbl 0429.92022
Coleman, Bernard D.; Hsieh, Ying-Hen; Knowles, Gregory P.
1979
Waves in materials with memory. I: The velocity of one-dimensional shock and acceleration waves. Zbl 0138.22006
Coleman, B. D.; Gurtin, M. E.; Herrera, I.
1965
Growth and decay of discontinuities in fluids with internal state variables. Zbl 0173.27701
Coleman, B. D.; Gurlin, M. E.
1967
On the stability of certain motions of incompressible materials with memory. Zbl 0167.54203
Coleman, B. D.; Dill, E. H.
1968
On the stability against shear waves of steady flows of non-linear viscoelastic fluids. Zbl 0207.25302
Coleman, B. D.; Gurtin, M. E.
1968
On the stability of equilibrium states of general fluids. Zbl 0211.28802
Coleman, B. D.
1970
On the growth of populations with narrow spread in reproductive age. I. General theory and examples. Zbl 0385.92015
Coleman, Bernard D.
1978
Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids. Zbl 0109.18001
Coleman, B. D.
1962
Thermodynamics and the stability of fluid motion. Zbl 0156.23901
Coleman, B. D.; Greenberg, J. M.
1967
Steady extension of incompressible simple fluids. Zbl 0131.40801
Coleman, Bernard D.; Noll, Walter
1962
A constitutive relation for rate-independent hysteresis in ferromagnetically soft materials. Zbl 0582.73002
Coleman, Bernard D.; Hodgdon, Marion L.
1986
Nonsteady helical flows of second-order fluids. Zbl 0151.40101
Markovitz, Hershel; Coleman, Bernard D.
1964
On the thermodynamics of semi-systems with restrictions on the accessibility of states. Zbl 0412.93001
Coleman, Bernard D.; Owen, David R.
1977
On the dynamics of flexure and stretch in the theory of elastic rods. Zbl 0872.73020
Coleman, Bernard D.; Dill, Ellis H.; Swigon, David
1995
On the thermodynamics of materials with memory. Zbl 0197.23402
Coleman, B. D.; Owen, D. R.
1970
On the initial value problem for a class of functional-differential equations. Zbl 0293.34094
Coleman, Bernard D.; Owen, David R.
1974
Space-time finite element methods for surface diffusion with applications to the theory of the stability of cylinders. Zbl 0868.65069
Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1996
On thermodynamics and intrinsically equilibrated materials. Zbl 0351.73006
Coleman, Bernard D.; Owen, David R.
1976
Wave propagation in dissipative materials. A reprint of five memoirs. Zbl 0151.39401
Coleman, B. D.; Gurtin, M. E.; Herrera R., I.; Truesdell, C.
1965
On waves in slender elastic rods. Zbl 0716.73013
Coleman, Bernard D.; Newman, Daniel C.
1990
Homogeneous motions of incompressible materials. Zbl 0139.20203
Coleman, B. D.; Truesdell, C.
1965
Simple liquid crystals. Zbl 0145.22104
Coleman, B. D.
1965
On thermodynamic conditions for the stability of evolving systems. Zbl 0159.56106
Coleman, B. D.; Mizel, V. J.
1968
Statistics and time dependence of mechanical break-down in fibers. Zbl 0082.38103
Coleman, Bernard D.
1958
Waves in materials with memory. IV: Thermodynamics and the velocity of general acceleration waves. Zbl 0244.73019
Coleman, Bernard D.; Gurtin, Morton E.
1965
The second law of thermodynamics for systems with approximate cycles. Zbl 0474.73002
Coleman, Bernard D.; Owen, David R.; Serrin, James
1981
Periodic solutions of certain nonlinear integral equations with a time lag. Zbl 0328.45008
Coleman, Bernard D.; Renninger, George H.
1976
Theory of the response of the Limulus retina to periodic excitation. Zbl 0328.92001
Coleman, B. D.; Renninger, G. H.
1976
On the thermodynamics of elastic-plastic materials with temperature- dependent moduli and yield stresses. Zbl 0441.73007
Coleman, Bernard D.; Owen, David R.
1979
Stability of cylindrical bodies in the theory of surface diffusion. Zbl 0885.35048
Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1995
On a class of constitutive relations for ferromagnetic hysteresis. Zbl 0631.73093
Coleman, Bernard D.; Hodgdon, Marion L.
1987
On the interaction of solitary waves of flexure in elastic rods. Zbl 0849.73029
Coleman, B. D.; Xu, J.-M.
1995
On the growth of populations with narrow spread in reproductive age. II. Conditions of convexity. Zbl 0414.92023
Coffman, Charles; Coleman, Bernard D.
1978
On random placement and species-area relations. Zbl 0465.92020
Coleman, Bernard D.
1981
On the use of symmetry to simplify the constitutive equations of isotropic materials with memory. Zbl 0167.24701
Coleman, B. D.
1968
On the growth of populations with narrow spread in reproductive age: III. Periodic variations in the environment. Zbl 0414.92024
Coffman, Charles V.; Coleman, Bernard D.
1979
Periodic solutions of a nonlinear functional equation describing neural interactions. Zbl 0323.92002
Coleman, Bernard D.; Renniger, George H.
1975
On the cold drawing of polymers. Zbl 0634.73030
Coleman, Bernard D.
1985
A mathematical theory of lateral sensory inhibition. Zbl 0284.92003
Coleman, Bernard D.
1971
On the nonequilibrium behavior of solids that transport heat by second sound. Zbl 0569.35047
Coleman, Bernard D.; Owen, David R.
1983
A phenomenological theory of streaming birefringence. Zbl 0212.58704
Coleman, B. D.; Dill, E. H.; Toupin, R. A.
1970
Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids. Zbl 1091.92002
Coleman, Bernard D.; Swigon, David
2004
Theory of delayed lateral inhibition in the compound eye of Limulus. Zbl 0293.92003
Coleman, Bernard D.; Renninger, George H.
1974
The energy criterion for stability in continuum thermodynamics. Zbl 0336.73002
Coleman, Bernard D.
1974
Mechanical and thermodynamical admissibility of stressstrain functions. Zbl 0124.40304
Coleman, B. D.
1962
A new class of flexure-free torsional vibrations of annular rods. Zbl 0888.73029
Coleman, Bernard D.; Lembo, Marzio; Tobias, Irwin
1996
On optimal intrinsic growth rates for populations in periodically changing environments. Zbl 0485.92017
Coleman, Bernard D.
1981
On retardation theorems. Zbl 0325.46042
Coleman, Bernard D.
1971
Similarity solutions in the theory of curvature driven diffusion along planar curves. I: Symmetric curves expanding in time. Zbl 0934.65111
Asvadurov, Sergey; Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1998
On strain energy functions for isotropic elastic materials. Zbl 0111.20405
Bragg, L. E.; Coleman, B. D.
1963
A thermodynamical limitation on compressibility. Zbl 0124.41902
Bragg, L. E.; Coleman, B. D.
1963
Existence of entropy as a consequence of asymptotic stability. Zbl 0156.23902
Coleman, B. D.; Mizel, V. J.
1967
Implications of the dependence of the elastic properties of DNA on nucleotide sequence. Zbl 1091.92034
Olson, Wilma K.; Swigon, David; Coleman, Bernard D.
2004
On bifurcations of equilibria of intrinsically curved, electrically charged, rod-like structures that model DNA molecules in solution. Zbl 1151.74381
Biton, Yoav Y.; Coleman, Bernard D.; Swigon, David
2007
Theory of the dependence of population levels on environmental history for semelparous species with short reproductive seasons. Zbl 0408.92007
Coleman, Bernard D.; Hsieh, Ying-Hen
1979
Theory of induced birefringence in materials with memory. Zbl 0258.73002
Coleman, Bernard D.; Dill, Ellis H.
1971
On the integral equations of the linear theory of recurrent lateral interaction in vision. Zbl 0283.92007
Coleman, Bernard D.; Renninger, George H.
1974
Theory of spatially synchronized oscillatory responses in the retina of limulus. Zbl 0373.92008
Coleman, Bernard D.; Renninger, George H.
1978
On adiabatic shear bands in rigid-plastic materials. Zbl 0687.73052
Coleman, B. D.; Newman, D. C.
1989
Simple fluids with fading memory. Zbl 0131.23401
Coleman, Bernard D.; Noll, Walter
1964
Thermodynamics and wave propagation in elastic and viscoelastic media. Zbl 0219.73016
Coleman, B. D.; Gurtin, M. E.
1966
Thermodynamics of elastic-plastic materials. Zbl 0414.73007
Coleman, Bernard D.; Owen, David R.
1977
Thermodynamics of materials with memory. Course held at the Department of Mechanics of Solids, July 1971, Udine. Zbl 0286.73006
Coleman, Bernard D.
1972
Finitely convergent learning programs for the separation of sets of shaded figures. Zbl 0366.92002
Coleman, B. D.
1977
Waves of discontinuity and sinusoidal waves in the theory of second sound in solids. Zbl 0808.73016
Coleman, Bernard D.; Lai, Po-Hsien
1994
On the dynamical stability of fluid phases. Zbl 0261.76033
Coleman, B. D.
1971
Methods of constructing non-linear functionals which separate sets in Hilbert spaces. Zbl 0384.46012
Coleman, Bernard D.; Mizel, Victor J.
1977
On the energy criterion for stability. Zbl 0386.73053
Coleman, Bernard D.
1973
On bifurcations of equilibria of intrinsically curved, electrically charged, rod-like structures that model DNA molecules in solution. Zbl 1151.74381
Biton, Yoav Y.; Coleman, Bernard D.; Swigon, David
2007
Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids. Zbl 1091.92002
Coleman, Bernard D.; Swigon, David
2004
Implications of the dependence of the elastic properties of DNA on nucleotide sequence. Zbl 1091.92034
Olson, Wilma K.; Swigon, David; Coleman, Bernard D.
2004
Numerical bifurcation of equilibria of nematic crystals between non-coaxial cylinders. Zbl 1035.76004
Alouges, François; Coleman, Bernard D.
2001
Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids. Zbl 1014.74038
Coleman, Bernard D.; Swigon, David
2000
Similarity solutions in the theory of curvature driven diffusion along planar curves. II: Curves that travel at constant speed. Zbl 1066.74575
Asvadurov, Sergey; Coleman, Bernard
1999
Similarity solutions in the theory of curvature driven diffusion along planar curves. I: Symmetric curves expanding in time. Zbl 0934.65111
Asvadurov, Sergey; Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1998
Space-time finite element methods for surface diffusion with applications to the theory of the stability of cylinders. Zbl 0868.65069
Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1996
A new class of flexure-free torsional vibrations of annular rods. Zbl 0888.73029
Coleman, Bernard D.; Lembo, Marzio; Tobias, Irwin
1996
On the dynamics of flexure and stretch in the theory of elastic rods. Zbl 0872.73020
Coleman, Bernard D.; Dill, Ellis H.; Swigon, David
1995
Stability of cylindrical bodies in the theory of surface diffusion. Zbl 0885.35048
Coleman, Bernard D.; Falk, Richard S.; Moakher, Maher
1995
On the interaction of solitary waves of flexure in elastic rods. Zbl 0849.73029
Coleman, B. D.; Xu, J.-M.
1995
Waves of discontinuity and sinusoidal waves in the theory of second sound in solids. Zbl 0808.73016
Coleman, Bernard D.; Lai, Po-Hsien
1994
On the dynamics of rods in the theory of Kirchhoff and Clebsch. Zbl 0784.73044
Coleman, Bernard D.; Dill, Ellis H.; Lembo, Marzio; Lu, Zheng; Tobias, Irwin
1992
On the thermodynamics of periodic phases. Zbl 0788.73015
Coleman, Bernard D.; Marcus, Moshe; Mizel, Victor J.
1992
Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders. Zbl 0825.76062
Bethuel, F.; Brézis, Haïm; Coleman, B. D.; Hélein, F.
1992
On waves in slender elastic rods. Zbl 0716.73013
Coleman, Bernard D.; Newman, Daniel C.
1990
On adiabatic shear bands in rigid-plastic materials. Zbl 0687.73052
Coleman, B. D.; Newman, D. C.
1989
A phenomenological theory of the influence of strain history on the rate of isothermal stress relaxation. Zbl 0709.76613
Coleman, Bernard D.; Zapas, Louis J.
1989
On a class of constitutive relations for ferromagnetic hysteresis. Zbl 0631.73093
Coleman, Bernard D.; Hodgdon, Marion L.
1987
Stability of equilibrium for a nonlinear hyperbolic system describing heat propagation by second sound in solids. Zbl 0621.73132
Coleman, Bernard D.; Hrusa, William J.; Owen, David R.
1986
A constitutive relation for rate-independent hysteresis in ferromagnetically soft materials. Zbl 0582.73002
Coleman, Bernard D.; Hodgdon, Marion L.
1986
Thermodynamics and the constitutive relations for second sound in crystals. Zbl 0623.73010
Coleman, B. D.; Fabrizio, M.; Owen, D. R.
1986
On shear bands in ductile materials. Zbl 0625.73041
Coleman, Bernard D.; Hodgdon, Marion L.
1985
On the cold drawing of polymers. Zbl 0634.73030
Coleman, Bernard D.
1985
Thermodynamics and the constitutive relations for second sound in crystals. Zbl 0605.73006
Coleman, Bernard D.; Fabrizio, Mauro; Owen, David R.
1985
Necking and drawing in polymeric fibers under tension. Zbl 0535.73016
Coleman, Bernard D.
1983
On the nonequilibrium behavior of solids that transport heat by second sound. Zbl 0569.35047
Coleman, Bernard D.; Owen, David R.
1983
On the thermodynamics of second sound in dielectric crystals. Zbl 0501.73008
Coleman, Bernard D.; Fabrizio, Mauro; Owen, David R.
1982
The second law of thermodynamics for systems with approximate cycles. Zbl 0474.73002
Coleman, Bernard D.; Owen, David R.; Serrin, James
1981
On random placement and species-area relations. Zbl 0465.92020
Coleman, Bernard D.
1981
On optimal intrinsic growth rates for populations in periodically changing environments. Zbl 0485.92017
Coleman, Bernard D.
1981
Nonautonomous logistic equations as models of the adjustment of populations to environmental change. Zbl 0425.92013
Coleman, Bernard D.
1979
On the optimal choice of r for a population in a periodic environment. Zbl 0429.92022
Coleman, Bernard D.; Hsieh, Ying-Hen; Knowles, Gregory P.
1979
On the thermodynamics of elastic-plastic materials with temperature- dependent moduli and yield stresses. Zbl 0441.73007
Coleman, Bernard D.; Owen, David R.
1979
On the growth of populations with narrow spread in reproductive age: III. Periodic variations in the environment. Zbl 0414.92024
Coffman, Charles V.; Coleman, Bernard D.
1979
Theory of the dependence of population levels on environmental history for semelparous species with short reproductive seasons. Zbl 0408.92007
Coleman, Bernard D.; Hsieh, Ying-Hen
1979
On the growth of populations with narrow spread in reproductive age. I. General theory and examples. Zbl 0385.92015
Coleman, Bernard D.
1978
On the growth of populations with narrow spread in reproductive age. II. Conditions of convexity. Zbl 0414.92023
Coffman, Charles; Coleman, Bernard D.
1978
Theory of spatially synchronized oscillatory responses in the retina of limulus. Zbl 0373.92008
Coleman, Bernard D.; Renninger, George H.
1978
On the thermodynamics of semi-systems with restrictions on the accessibility of states. Zbl 0412.93001
Coleman, Bernard D.; Owen, David R.
1977
Thermodynamics of elastic-plastic materials. Zbl 0414.73007
Coleman, Bernard D.; Owen, David R.
1977
Finitely convergent learning programs for the separation of sets of shaded figures. Zbl 0366.92002
Coleman, B. D.
1977
Methods of constructing non-linear functionals which separate sets in Hilbert spaces. Zbl 0384.46012
Coleman, Bernard D.; Mizel, Victor J.
1977
On thermodynamics and intrinsically equilibrated materials. Zbl 0351.73006
Coleman, Bernard D.; Owen, David R.
1976
Periodic solutions of certain nonlinear integral equations with a time lag. Zbl 0328.45008
Coleman, Bernard D.; Renninger, George H.
1976
Theory of the response of the Limulus retina to periodic excitation. Zbl 0328.92001
Coleman, B. D.; Renninger, G. H.
1976
On thermodynamics and elastic-plastic materials. Zbl 0332.73003
Coleman, Bernard D.; Owen, David R.
1975
Periodic solutions of a nonlinear functional equation describing neural interactions. Zbl 0323.92002
Coleman, Bernard D.; Renniger, George H.
1975
A mathematical foundation for thermodynamics. Zbl 0306.73004
Coleman, Bernard D.; Owen, David R.
1974
On the initial value problem for a class of functional-differential equations. Zbl 0293.34094
Coleman, Bernard D.; Owen, David R.
1974
Theory of delayed lateral inhibition in the compound eye of Limulus. Zbl 0293.92003
Coleman, Bernard D.; Renninger, George H.
1974
The energy criterion for stability in continuum thermodynamics. Zbl 0336.73002
Coleman, Bernard D.
1974
On the integral equations of the linear theory of recurrent lateral interaction in vision. Zbl 0283.92007
Coleman, Bernard D.; Renninger, George H.
1974
On thermodynamics and the stability of motions of material with memory. Zbl 0275.73003
Coleman, Bernard D.; Dill, Ellis H.
1973
On the energy criterion for stability. Zbl 0386.73053
Coleman, Bernard D.
1973
Thermodynamics of materials with memory. Course held at the Department of Mechanics of Solids, July 1971, Udine. Zbl 0286.73006
Coleman, Bernard D.
1972
Thermodynamic restrictions on the constitutive equations of electromagnetic theory. Zbl 0218.35072
Coleman, B. D.; Dill, E. H.
1971
A mathematical theory of lateral sensory inhibition. Zbl 0284.92003
Coleman, Bernard D.
1971
On retardation theorems. Zbl 0325.46042
Coleman, Bernard D.
1971
Theory of induced birefringence in materials with memory. Zbl 0258.73002
Coleman, Bernard D.; Dill, Ellis H.
1971
On the dynamical stability of fluid phases. Zbl 0261.76033
Coleman, B. D.
1971
On the stability of equilibrium states of general fluids. Zbl 0211.28802
Coleman, B. D.
1970
On the thermodynamics of materials with memory. Zbl 0197.23402
Coleman, B. D.; Owen, D. R.
1970
A phenomenological theory of streaming birefringence. Zbl 0212.58704
Coleman, B. D.; Dill, E. H.; Toupin, R. A.
1970
On the general theory of fading memory. Zbl 0167.24704
Coleman, B. D.; Mizel, V. J.
1968
Waves in materials with memory. III: Thermodynamic influences on the growth and decay of acceleration waves. Zbl 0244.73018
Coleman, Bernard D.; Gurtin, Morton E.
1968
On the stability of solutions of functional-differential equations. Zbl 0184.36801
Coleman, B. D.; Mizel, V. J.
1968
On the stability of certain motions of incompressible materials with memory. Zbl 0167.54203
Coleman, B. D.; Dill, E. H.
1968
On the stability against shear waves of steady flows of non-linear viscoelastic fluids. Zbl 0207.25302
Coleman, B. D.; Gurtin, M. E.
1968
On thermodynamic conditions for the stability of evolving systems. Zbl 0159.56106
Coleman, B. D.; Mizel, V. J.
1968
On the use of symmetry to simplify the constitutive equations of isotropic materials with memory. Zbl 0167.24701
Coleman, B. D.
1968
Thermodynamics and wave propagation in non-linear materials with memory. Zbl 0207.24903
Coleman, B. D.; Gurtin, M. E.
1968
Growth and decay of discontinuities in fluids with internal state variables. Zbl 0173.27701
Coleman, B. D.; Gurlin, M. E.
1967
Thermodynamics and the stability of fluid motion. Zbl 0156.23901
Coleman, B. D.; Greenberg, J. M.
1967
Existence of entropy as a consequence of asymptotic stability. Zbl 0156.23902
Coleman, B. D.; Mizel, V. J.
1967
Norms and semi-groups in the theory of fading memory. Zbl 0146.46104
Coleman, B. D.; Mizel, V. J.
1966
Viscometrie flows of non-newtonian fluids. Theory and experiment. Zbl 0137.21903
Coleman, Bernard D.; Markovitz, H.; Noll, Walter
1966
Waves in materials with memory. V: On the amplitude of acceleration waves and mild discontinuities. Zbl 0247.73022
Coleman, Bernard D.; Greenberg, James M.; Gurtin, Morton E.
1966
Thermodynamics and wave propagation in elastic and viscoelastic media. Zbl 0219.73016
Coleman, B. D.; Gurtin, M. E.
1966
Instability, uniqueness, and nonexistence theorems for the equation $$u_t=u_{xx}-u_{xtx}$$ on a strip. Zbl 0292.35016
Coleman, Bernard D.; Duffin, Richard J.; Mizel, Victor J.
1965
Waves in materials with memory. II: On the growth and decay of one- dimensional acceleration waves. Zbl 0244.73017
Coleman, Bernard D.; Gurtin, Morton E.
1965
Waves in materials with memory. I: The velocity of one-dimensional shock and acceleration waves. Zbl 0138.22006
Coleman, B. D.; Gurtin, M. E.; Herrera, I.
1965
Wave propagation in dissipative materials. A reprint of five memoirs. Zbl 0151.39401
Coleman, B. D.; Gurtin, M. E.; Herrera R., I.; Truesdell, C.
1965
Homogeneous motions of incompressible materials. Zbl 0139.20203
Coleman, B. D.; Truesdell, C.
1965
Simple liquid crystals. Zbl 0145.22104
Coleman, B. D.
1965
Waves in materials with memory. IV: Thermodynamics and the velocity of general acceleration waves. Zbl 0244.73019
Coleman, Bernard D.; Gurtin, Morton E.
1965
On thermodynamics, strain impulses, and viscoelasticity. Zbl 0125.13603
Coleman, B. D.
1964
Material symmetry and thermostatic inequalities in finite elastic deformations. Zbl 0123.40703
Coleman, Bernard D.; Noll, Walter
1964
Normal stress effects in second-order fluids. Zbl 0133.19205
Coleman, Bernard D.; Markovitz, Hershel
1964
Incompressible second-order fluids. Zbl 0136.45104
Markovitz, Hershel; Coleman, Bernard D.
1964
Nonsteady helical flows of second-order fluids. Zbl 0151.40101
Markovitz, Hershel; Coleman, Bernard D.
1964
Simple fluids with fading memory. Zbl 0131.23401
Coleman, Bernard D.; Noll, Walter
1964
The thermodynamics of elastic materials with heat conduction and viscosity. Zbl 0113.17802
Coleman, Bernard D.; Noll, Walter
1963
Thermodynamics and departures from Fourier’s law of heat conduction. Zbl 0114.44905
Coleman, B. D.; Mizel, V. J.
1963
On strain energy functions for isotropic elastic materials. Zbl 0111.20405
Bragg, L. E.; Coleman, B. D.
1963
A thermodynamical limitation on compressibility. Zbl 0124.41902
Bragg, L. E.; Coleman, B. D.
1963
Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids. Zbl 0109.18001
Coleman, B. D.
1962
Steady extension of incompressible simple fluids. Zbl 0131.40801
Coleman, Bernard D.; Noll, Walter
1962
Mechanical and thermodynamical admissibility of stressstrain functions. Zbl 0124.40304
Coleman, B. D.
1962
...and 8 more Documents
all top 5
#### Cited by 1,816 Authors
69 Coleman, Bernard David 42 Gurtin, Morton Edward 35 Fabrizio, Mauro 27 Cimmelli, Vito Antonio 24 Morro, Angelo 20 Joseph, Daniel D. 18 Chen, Peter J. 18 Mizel, Victor J. 18 Owen, David R. 18 Rajagopal, Kumbakonam Ramamani 17 Zaslavski, Alexander Yakovlevich 14 Amendola, Giovambattista 14 Giorgi, Claudio 14 Goriely, Alain 13 Bowen, Ray M. 13 Guidugli, Paolo Podio 11 Messaoudi, Salim A. 11 Nunziato, Jace W. 11 Šilhavý, Miroslav 10 Day, William Alan 10 Fosdick, Roger L. 10 Golden, John Murrough 10 Hayat, Tasawar 10 Mosler, Jörn 10 Noll, Walter 10 Tokuoka, Tatsuo 9 Huilgol, Raja R. 9 Tatar, Nasser-eddine 8 Bloom, Frederick 8 Dunwoody, J. 8 Holzapfel, Gerhard A. 8 Lazzari, Barbara 8 Marcus, Moshe M. 8 Sellitto, Antonio 8 Slemrod, Marshall 8 Tomassetti, Giuseppe 8 Williams, William O. 8 Wineman, Alan S. 7 Man, Chi-Sing 7 Miehe, Christian 7 Seguin, Brian 7 Siddiqui, Abdul Majeed 7 Straughan, Brian 6 Dill, Ellis Harold 6 Hoger, Anne 6 Hutter, Kolumban 6 Lion, Alexander 6 Mariano, Paolo Maria 6 Naghdi, Paul Mansour 6 Oliveri, Francesco 6 Regueiro, Richard A. 6 Rivlin, Ronald Samuel 6 Rogolino, Patrizia 6 Senchenkov, Igor’ Konstantinovich 6 Svendsen, Bob 6 Triani, Vita 5 Aifantis, Elias C. 5 an der Heiden, Uwe 5 Antman, Stuart S. 5 Asghar, Saleem 5 Bargmann, Swantje 5 Bellout, Hamid 5 Carillo, Sandra 5 Ciarletta, Michele 5 Colli, Pierluigi 5 Del Piero, Gianpietro 5 Garikipati, Krishna 5 Goddard, Joe D. 5 Gopalsamy, Kondalsamy 5 Jou, David 5 Khemmoudj, Ammar 5 Lembo, Marzio 5 Massoudi, Mehrdad 5 Narain, Amitabh 5 Ortiz, Michael 5 Renardy, Michael 5 Renninger, George H. 5 Steigmann, David J. 5 Tabor, Michael 5 Triantafyllidis, Nicolas 5 Tsakmakis, Ch. 5 Vajravelu, Kuppalapalle 5 Ván, Peter 5 Wang, Yongqi 4 Beavers, Gordon S. 4 Berkani, Amirouche 4 Ciarletta, Pasquale 4 Clayton, John D. 4 Crochet, Marcel J. 4 Cushing, Jim M. 4 Dafermos, Constantine M. 4 Dai, Hui-Hui 4 Dunwoody, N. T. 4 Favata, Antonino 4 Francaviglia, Mauro 4 Franke, John E. 4 Fried, Eliot 4 Gil, Antonio J. 4 Green, Albert E. 4 Haldar, Krishnendu ...and 1,716 more Authors
all top 5
#### Cited in 253 Serials
271 Archive for Rational Mechanics and Analysis 115 Acta Mechanica 73 Journal of Elasticity 62 Computer Methods in Applied Mechanics and Engineering 60 Rheologica Acta 55 International Journal of Engineering Science 52 Journal of Mathematical Analysis and Applications 52 ZAMP. Zeitschrift für angewandte Mathematik und Physik 49 Journal of the Mechanics and Physics of Solids 42 Continuum Mechanics and Thermodynamics 33 Journal of Differential Equations 32 Meccanica 28 Journal of Non-Equilibrium Thermodynamics 27 Mathematics and Mechanics of Solids 21 Journal of Mathematical Physics 21 Physica D 20 Journal of Fluid Mechanics 19 Journal of Mathematical Biology 19 European Journal of Mechanics. A. Solids 16 Wave Motion 15 Applicable Analysis 14 Computational Mechanics 13 Computers & Mathematics with Applications 13 International Journal of Solids and Structures 13 Annali di Matematica Pura ed Applicata. Serie Quarta 13 Applied Mathematics and Computation 13 Mathematical and Computer Modelling 13 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Rendiconti del Seminario Matematico della Università di Padova 11 Mathematical Methods in the Applied Sciences 11 Quarterly of Applied Mathematics 10 Soviet Applied Mechanics 10 Nonlinear Analysis. Real World Applications 9 Journal of Computational Physics 9 Journal of Engineering Mathematics 9 International Journal for Numerical Methods in Engineering 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Archive of Applied Mechanics 9 Communications in Nonlinear Science and Numerical Simulation 9 Nonlinear Analysis. Theory, Methods & Applications 8 Ingenieur-Archiv 8 Mathematical Biosciences 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 International Journal of Plasticity 6 Applied Mathematics Letters 6 Applied Mathematical Modelling 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 Biological Cybernetics 5 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 5 Automatica 5 Journal of Computational and Applied Mathematics 5 Mathematics and Computers in Simulation 5 Tohoku Mathematical Journal. Second Series 5 Transactions of the American Mathematical Society 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Journal of Nonlinear Science 5 Archives of Computational Methods in Engineering 5 Evolution Equations and Control Theory 4 International Journal of Heat and Mass Transfer 4 Journal of the Franklin Institute 4 Reviews of Modern Physics 4 Proceedings of the American Mathematical Society 4 Studies in Applied Mathematics 4 Theoretical Population Biology 4 Applied Mathematics and Mechanics. (English Edition) 4 Acta Applicandae Mathematicae 4 Calculus of Variations and Partial Differential Equations 4 Mathematical Problems in Engineering 4 Nonlinear Dynamics 4 Abstract and Applied Analysis 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Theoretical Biology 3 Computers and Fluids 3 Journal of Applied Mathematics and Mechanics 3 Bulletin of Mathematical Biology 3 Theoretical and Computational Fluid Dynamics 3 Prikladnaya Matematika i Mekhanika 3 Applied Mathematics and Optimization 3 Mechanics Research Communications 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Rendiconti del Seminario Matemàtico e Fisico di Milano 3 Journal of Integral Equations and Applications 3 European Journal of Applied Mathematics 3 Applications of Mathematics 3 Computational Mathematics and Mathematical Physics 3 SIAM Journal on Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Computational and Applied Mathematics 3 Acta Mechanica Sinica 3 Mathematical Modelling of Natural Phenomena 3 International Journal of Biomathematics 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 International Journal of Modern Physics B 2 Astrophysics and Space Science 2 Bulletin of the Australian Mathematical Society 2 Geophysical and Astrophysical Fluid Dynamics 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 Mathematical Proceedings of the Cambridge Philosophical Society ...and 153 more Serials
all top 5
#### Cited in 45 Fields
883 Mechanics of deformable solids (74-XX) 388 Fluid mechanics (76-XX) 314 Partial differential equations (35-XX) 204 Classical thermodynamics, heat transfer (80-XX) 120 Biology and other natural sciences (92-XX) 105 Ordinary differential equations (34-XX) 83 Statistical mechanics, structure of matter (82-XX) 70 Numerical analysis (65-XX) 55 Calculus of variations and optimal control; optimization (49-XX) 50 Systems theory; control (93-XX) 46 Integral equations (45-XX) 35 Optics, electromagnetic theory (78-XX) 31 Dynamical systems and ergodic theory (37-XX) 25 Operator theory (47-XX) 20 Global analysis, analysis on manifolds (58-XX) 18 Mechanics of particles and systems (70-XX) 17 Differential geometry (53-XX) 15 Difference and functional equations (39-XX) 11 Probability theory and stochastic processes (60-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Statistics (62-XX) 7 Integral transforms, operational calculus (44-XX) 7 Functional analysis (46-XX) 6 History and biography (01-XX) 6 Special functions (33-XX) 6 Computer science (68-XX) 6 Geophysics (86-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Real functions (26-XX) 5 Operations research, mathematical programming (90-XX) 4 Topological groups, Lie groups (22-XX) 4 Quantum theory (81-XX) 4 Relativity and gravitational theory (83-XX) 3 Information and communication theory, circuits (94-XX) 2 Measure and integration (28-XX) 2 Astronomy and astrophysics (85-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-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.
| 2021-10-17T09:48:12 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Data_analysis/chap_cu7var/ssec_cu7var_sos_ceprrl/ssec_cu7var_sos_ceprrl_props.html
|
# 7.4.2 Properties of the input data
Selection criteria:
• sources classified as candidate Cepheid and RR Lyrae variables from the Classifiers;
• a minimum number of 12 $G$-FoV transits, before applying an outlier removal procedure specifically tailored to Cepheids and RR Lyrae stars to discard obvious wrong epoch data;
• a peak-to-peak amplitude $>$ 0.1 mag in the $G$-band;
• periods in the range of 0.2-1.0 days for the RR Lyrae variables.
| 2019-03-19T19:14:51 |
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http://dergipark.gov.tr/atnaa/issue/39947/401104
|
Yıl 2018, Cilt 2, Sayı 4, Sayfalar 184 - 194 2018-12-24
| | | |
## Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays
#### Hocine Gabsi [1] , Abdelouaheb Ardjouni [2] , Ahcene Djoudi [3]
##### 42 74
We consider two types of second-order neutral functional differential equations with infinite distributed delays and offer existence criteria for periodic solutions. During the process we invert the integro-differential equations into equivalent integral equations and derive suitable fixed point mappings. We show that these mappings fit into the framework of Schauder's fixed point theorem so that periodic solutions are readily obtained.
Second order, Nonlinear neutral differential equations, Periodic solutions, Fixed point theorem, Distributed delays.
• 1) A. Ardjouni, A. Rezaiguia and A. Djoudi, Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with infinite distributed delay, J. Appl. Math. Comput. (2015) 47:291--314.
• A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two types of second order nonlinear neutral differential equations with variable delay, Proyecciones J. Math. 32 (4) (2013) 377--391.
• A. Ardjouni, A. Djoudi, Existence of periodic solutions in totally nonlinear neutral dynamic equations with variable delay on a time scale, Math. Eng. Sci. Aerosp. MESA 4 (3) (2013) 305--318.
• A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two kinds of nonlinear neutral differential equations with variable delay, Dyn. Continuous Discrete Impulsive Syst. Ser. A Math. Anal. 20 (2013) 357--366.
Birincil Dil en Matematik Articles Yazar: Hocine Gabsi (Sorumlu Yazar) Yazar: Abdelouaheb ArdjouniÜlke: Algeria Yazar: Ahcene Djoudi
Bibtex @araştırma makalesi { atnaa401104, journal = {Advances in the Theory of Nonlinear Analysis and its Application}, issn = {}, eissn = {2587-2648}, address = {Erdal KARAPINAR}, year = {2018}, volume = {2}, pages = {184 - 194}, doi = {10.31197/atnaa.401104}, title = {Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays}, key = {cite}, author = {Gabsi, Hocine and Ardjouni, Abdelouaheb and Djoudi, Ahcene} } APA Gabsi, H , Ardjouni, A , Djoudi, A . (2018). Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays. Advances in the Theory of Nonlinear Analysis and its Application, 2 (4), 184-194. DOI: 10.31197/atnaa.401104 MLA Gabsi, H , Ardjouni, A , Djoudi, A . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 184-194 Chicago Gabsi, H , Ardjouni, A , Djoudi, A . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 184-194 RIS TY - JOUR T1 - Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays AU - Hocine Gabsi , Abdelouaheb Ardjouni , Ahcene Djoudi Y1 - 2018 PY - 2018 N1 - doi: 10.31197/atnaa.401104 DO - 10.31197/atnaa.401104 T2 - Advances in the Theory of Nonlinear Analysis and its Application JF - Journal JO - JOR SP - 184 EP - 194 VL - 2 IS - 4 SN - -2587-2648 M3 - doi: 10.31197/atnaa.401104 UR - http://dx.doi.org/10.31197/atnaa.401104 Y2 - 2018 ER - EndNote %0 Advances in the Theory of Nonlinear Analysis and its Application Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays %A Hocine Gabsi , Abdelouaheb Ardjouni , Ahcene Djoudi %T Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays %D 2018 %J Advances in the Theory of Nonlinear Analysis and its Application %P -2587-2648 %V 2 %N 4 %R doi: 10.31197/atnaa.401104 %U 10.31197/atnaa.401104 ISNAD Gabsi, Hocine , Ardjouni, Abdelouaheb , Djoudi, Ahcene . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 / 4 (Aralık 2018): 184-194. http://dx.doi.org/10.31197/atnaa.401104
| 2019-03-25T09:37:18 |
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|
https://lammps.sandia.gov/doc/fix_nve_asphere_noforce.html
|
# fix nve/asphere/noforce command
## Syntax
fix ID group-ID nve/asphere/noforce
• ID, group-ID are documented in fix command
• nve/asphere/noforce = style name of this fix command
## Examples
fix 1 all nve/asphere/noforce
## Description
Perform updates of position and orientation, but not velocity or angular momentum for atoms in the group each timestep. In other words, the force and torque on the atoms is ignored and their velocity and angular momentum are not updated. The atom velocities and angular momenta are used to update their positions and orientation.
This is useful as an implicit time integrator for Fast Lubrication Dynamics, since the velocity and angular momentum are updated by the pair_style lubricuteU command.
Restart, fix_modify, output, run start/stop, minimize info:
No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
## Restrictions
This fix is part of the ASPHERE package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
This fix requires that atoms store torque and angular momentum and a quaternion as defined by the atom_style ellipsoid command.
All particles in the group must be finite-size. They cannot be point particles, but they can be aspherical or spherical as defined by their shape attribute.
| 2018-10-21T23:07:12 |
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https://zbmath.org/authors/?q=ai%3Astanley.richard-p
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## Stanley, Richard Peter
Compute Distance To:
Author ID: stanley.richard-p Published as: Stanley, Richard P.; Stanley, Richard; Stanley, R. P.; Stanley, R. Homepage: http://www-math.mit.edu/~rstan/ External Links: MGP · Wikidata · ResearchGate · MathOverflow · dblp · GND · IdRef
Documents Indexed: 193 Publications since 1969, including 17 Books 20 Contributions as Editor · 3 Further Contributions Biographic References: 3 Publications Co-Authors: 89 Co-Authors with 86 Joint Publications 3,123 Co-Co-Authors
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### Co-Authors
125 single-authored 17 Jerison, David S. 17 Yau, Shing-Tung 11 Mrowka, Tomasz S. 9 Mazur, Barry 9 Schmid, Wilfried 8 Kisin, Mark 8 Yau, Horng-Tzer 7 Zanello, Fabrizio 6 Seidel, Paul 4 Björner, Anders 4 Friedmann, Tamar 4 Greene, Curtis 4 Hanlon, Phil 4 Rota, Gian-Carlo 4 Simion, Rodica E. 3 Ardila Mantilla, Federico 3 Chen, William Yong-Chuan 3 Du, Rosena R. X. 3 Wang, Yinghui 2 Bessenrodt, Christine 2 Billera, Louis J. 2 Bóna, Miklós 2 Doubilet, Peter 2 Gessel, Ira Martin 2 Liu, Fu 2 Odlyzko, Andrew M. 2 Postnikov, Alexander 2 Sagan, Bruce Eli 2 Stembridge, John R. 2 Wachs, Michelle Lynn 1 Arias-Castro, Ery 1 Beck, Matthias 1 Bernardi, Olivier 1 Beschler, Edwin F. 1 Billey, Sara C. 1 Boros, George 1 Buchsbaum, David A. 1 Cai, Tommy Wuxing 1 Calkin, Neil J. 1 Canfield, Rodney E. 1 Carlitz, Leonard 1 Chen, Beifang 1 Chen, Xiaomei 1 Chung Graham, Fan-Rong King 1 Clifford, Peter 1 Corteel, Sylvie 1 Crapo, Henry H. 1 Cristofaro-Gardiner, Dan 1 De Loera, Jesús A. 1 Deng, Eva Y. P. 1 Develin, Mike 1 Diaconis, Persi Warren 1 Edelman, Paul H. 1 Elkies, Noam David 1 Fomin, Sergey Vladimirovich 1 Fraenkel, Aviezri Siegmund 1 Frankl, Péter 1 Furedi, Zoltan 1 Garsia, Adriano M. 1 Hersh, Patricia 1 Hibi, Takayuki 1 Hutchinson, Joan P. 1 Jockusch, William 1 Kahaner, David K. 1 Kim, Hana 1 Knuth, Donald Ervin 1 Lam, Thomas F. 1 Lazebnik, Felix 1 Li, Teresa Xueshan 1 Little, John Brittain 1 Lusztig, George 1 Massey, David Bradley 1 Moll, Victor Hugo 1 Morales, Alejandro Henry 1 Mosteig, Edward 1 Mu, Lili 1 Nijenhuis, Albert 1 Olsson, Jorn Borling 1 Pak, Igor 1 Pang, Sabrina X. M. 1 Park, Sung Gi 1 Petkovšek, Marko 1 Pfeifle, Julian 1 Pitman, Jim William 1 Propp, James Gary 1 Pylyavskyy, Pavlo 1 Qu, Ellen X. Y. 1 Reiner, Victor 1 Roulet, Geoffrey 1 Savage, Carla D. 1 Savitt, David 1 Schwartz, Jacob Theodore 1 Stanton, Dennis W. 1 Taylor, Brian D. 1 Vershik, Anatoliĭ Moiseevich 1 Vertigan, Dirk 1 Welsh, Dominic J. A. 1 Williams, Lauren K. 1 Yan, Catherine Huafei 1 Zeilberger, Doron ...and 1 more Co-Authors
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### Serials
18 Journal of Combinatorial Theory. Series A 10 Discrete Mathematics 9 European Journal of Combinatorics 7 Advances in Mathematics 7 The Electronic Journal of Combinatorics 6 Annals of Combinatorics 5 Studies in Applied Mathematics 5 Discrete & Computational Geometry 5 Journal of Algebraic Combinatorics 5 Cambridge Studies in Advanced Mathematics 4 Transactions of the American Mathematical Society 4 Advances in Applied Mathematics 4 Progress in Mathematics 3 Algebra Universalis 3 Journal of Algebra 3 Proceedings of the American Mathematical Society 3 Graphs and Combinatorics 2 American Mathematical Monthly 2 Discrete Applied Mathematics 2 The Mathematical Intelligencer 2 Duke Mathematical Journal 2 Journal of Combinatorial Theory. Series B 2 Journal of Pure and Applied Algebra 2 Order 2 Journal of the American Mathematical Society 2 SIAM Journal on Discrete Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Séminaire Lotharingien de Combinatoire 2 The Ramanujan Journal 2 Bulletin of the American Mathematical Society 2 Journal of Combinatorics 2 Undergraduate Texts in Mathematics 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Linear and Multilinear Algebra 1 Mathematische Semesterberichte 1 Nuclear Physics. B 1 Rocky Mountain Journal of Mathematics 1 The Fibonacci Quarterly 1 Inventiones Mathematicae 1 Journal of Number Theory 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 SIAM Journal on Algebraic and Discrete Methods 1 Combinatorica 1 Linear Algebra and its Applications 1 Proceedings of the National Academy of Sciences of the United States of America 1 Combinatorics, Probability and Computing 1 Journal of Integer Sequences 1 La Gaceta de la Real Sociedad Matemática Española 1 DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 1 Mathematical Sciences Research Institute Publications 1 Monographies de l’Enseignement Mathématique
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### Fields
170 Combinatorics (05-XX) 48 Order, lattices, ordered algebraic structures (06-XX) 40 Convex and discrete geometry (52-XX) 29 Number theory (11-XX) 29 Group theory and generalizations (20-XX) 23 General and overarching topics; collections (00-XX) 21 Algebraic geometry (14-XX) 17 Commutative algebra (13-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Algebraic topology (55-XX) 11 Probability theory and stochastic processes (60-XX) 6 History and biography (01-XX) 6 Nonassociative rings and algebras (17-XX) 5 Topological groups, Lie groups (22-XX) 5 Geometry (51-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Differential geometry (53-XX) 3 Special functions (33-XX) 3 Manifolds and cell complexes (57-XX) 3 Quantum theory (81-XX) 2 Associative rings and algebras (16-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 General algebraic systems (08-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX)
### Citations contained in zbMATH Open
179 Publications have been cited 9,998 times in 7,141 Documents Cited by Year
Enumerative combinatorics. Volume 2. Zbl 0928.05001
Stanley, Richard P.
1999
Enumerative combinatorics. Vol. 1. Zbl 0889.05001
Stanley, Richard P.
1997
Enumerative combinatorics. Vol. I. Zbl 0608.05001
Stanley, Richard P.
1986
Combinatorics and commutative algebra. 2nd ed. Zbl 0838.13008
Stanley, Richard P.
1996
Enumerative combinatorics. Vol. 1. 2nd ed. Zbl 1247.05003
Stanley, Richard P.
2012
Hilbert functions of graded algebras. Zbl 0384.13012
Stanley, Richard P.
1978
Log-concave and unimodal sequences in algebra, combinatorics, and geometry. Zbl 0792.05008
Stanley, Richard P.
1989
Weyl groups, the hard Lefschetz theorem, and the Sperner property. Zbl 0502.05004
Stanley, Richard P.
1980
The number of faces of a simplicial convex polytope. Zbl 0427.52006
Stanley, Richard P.
1980
Some combinatorial properties of Jack symmetric functions. Zbl 0743.05072
Stanley, Richard P.
1989
Two poset polytopes. Zbl 0595.52008
Stanley, Richard P.
1986
Ordered structures and partitions. Zbl 0246.05007
Stanley, Richard P.
1972
Acyclic orientations of graphs. Zbl 0258.05113
Stanley, Richard P.
1973
Invariants of finite groups and their applications to combinatorics. Zbl 0497.20002
Stanley, Richard P.
1979
Some combinatorial properties of Schubert polynomials. Zbl 0790.05093
Billey, Sara C.; Jockusch, William; Stanley, Richard P.
1993
Combinatorics and commutative algebra. Zbl 0537.13009
Stanley, Richard P.
1983
Decompositions of rational convex polytopes. Zbl 0812.52012
Stanley, Richard P.
1980
Supersolvable lattices. Zbl 0256.06002
Stanley, R. P.
1972
On the number of reduced decompositions of elements of Coxeter groups. Zbl 0587.20002
Stanley, Richard P.
1984
A symmetric function generalization of the chromatic polynomial of a graph. Zbl 0831.05027
Stanley, Richard P.
1995
Differentiably finite power series. Zbl 0445.05012
Stanley, R. P.
1980
Linear Diophantine equations and local cohomology. Zbl 0516.10009
Stanley, Richard P.
1982
Catalan numbers. Zbl 1317.05010
Stanley, Richard P.
2015
Enumerative combinatorics. Volume 2. Paperback ed. Zbl 0978.05002
Stanley, Richard P.
2001
The upper bound conjecture and Cohen-Macaulay rings. Zbl 0308.52009
Stanley, Richard P.
1975
Some aspects of groups acting on finite posets. Zbl 0496.06001
Stanley, Richard P.
1982
An introduction to hyperplane arrangements. Zbl 1136.52009
Stanley, Richard P.
2007
Theory and application of plane partitions. II. Zbl 0225.05012
Stanley, Richard P.
1971
Crossings and nestings of matchings and partitions. Zbl 1108.05012
Chen, William Y. C.; Deng, Eva Y. P.; Du, Rosena R. X.; Stanley, Richard P.; Yan, Catherine H.
2007
Balanced Cohen-Macaulay complexes. Zbl 0411.05012
Stanley, Richard P.
1979
Differential posets. Zbl 0658.05006
Stanley, Richard P.
1988
Schubert polynomials and the nilCoxeter algebra. Zbl 0809.05091
Fomin, Sergey; Stanley, Richard P.
1994
Theory and application of plane partitions. I. Zbl 0225.05011
Stanley, Richard P.
1971
Binomial posets, Möbius inversion, and permutation enumeration. Zbl 0331.05004
Stanley, Richard P.
1976
Stirling polynomials. Zbl 0378.05006
Gessel, Ira; Stanley, Richard P.
1978
Subdivisions and local $$h$$-vectors. Zbl 0768.05100
Stanley, Richard P.
1992
Symmetries of plane partitions. Zbl 0602.05007
Stanley, Richard P.
1986
A polytope related to empirical distributions, plane trees, parking functions, and the associahedron. Zbl 1012.52019
Stanley, Richard P.; Pitman, Jim
2002
A survey of alternating permutations. Zbl 1231.05288
Stanley, Richard P.
2010
On immanants of Jacobi-Trudi matrices and permutations with restricted position. Zbl 0772.05097
Stanley, Richard P.; Stembridge, John R.
1993
A bound on the spectral radius of graphs with $$e$$ edges. Zbl 0617.05045
Stanley, Richard P.
1987
Positivity problems and conjectures in algebraic combinatorics. Zbl 0955.05111
Stanley, Richard P.
2000
Linear homogeneous Diophantine equations and magic labelings of graphs. Zbl 0269.05109
Stanley, Richard P.
1973
Modular elements of geometric lattices. Zbl 0229.05032
Stanley, Richard P.
1971
Hyperplane arrangements, interval orders, and trees. Zbl 0848.05005
Stanley, Richard P.
1996
Flag $$f$$-vectors and the $$cd$$-index. Zbl 0805.06003
Stanley, Richard P.
1994
Deformations of Coxeter hyperplane arrangements. Zbl 0962.05004
Postnikov, Alexander; Stanley, Richard P.
2000
Structure of incidence algebras and their automorphism groups. Zbl 0205.31702
Stanley, R. P.
1970
Combinatorial reciprocity theorems. Zbl 0294.05006
Stanley, Richard P.
1974
Graph colorings and related symmetric functions: ideas and applications: A description of results, interesting applications, and notable open problems. Zbl 1061.05508
Stanley, Richard P.
1998
Parking functions and noncrossing partitions. Zbl 0883.06001
Stanley, Richard P.
1997
Relative invariants of finite groups generated by pseudoreflections. Zbl 0383.20029
Stanley, Richard P.
1977
A monotonicity property of $$h$$-vectors and $$h^*$$-vectors. Zbl 0799.52008
Stanley, Richard P.
1993
f-vectors and h-vectors of simplicial posets. Zbl 0727.06009
Stanley, Richard P.
1991
On the Hilbert function of a graded Cohen-Macaulay domain. Zbl 0735.13010
Stanley, Richard P.
1991
A super-class walk on upper-triangular matrices. Zbl 1056.60006
Arias-Castro, Ery; Diaconis, Persi; Stanley, Richard
2004
Some combinatorial aspects of the spectra of normally distributed random matrices. Zbl 0789.05092
Hanlon, Philip J.; Stanley, Richard P.; Stembridge, John R.
1992
On the foundations of combinatorial theory. VI: The idea of generating function. Zbl 0267.05002
Doubilet, Peter; Rota, Gian-Carlo; Stanley, Richard
1972
Cohen-Macaulay complexes. Zbl 0376.55007
Stanley, Richard P.
1977
Robinson-Schensted algorithms for skew tableaux. Zbl 0732.05061
Sagan, Bruce E.; Stanley, Richard P.
1990
Two combinatorial applications of the Aleksandrov-Fenchel inequalities. Zbl 0484.05012
Stanley, Richard P.
1981
Hyperplane arrangements, parking functions and tree inversions. Zbl 0917.52013
Stanley, Richard P.
1998
Promotion and evacuation. Zbl 1169.06002
Stanley, Richard P.
2009
A zonotope associated with graphical degree sequences. Zbl 0737.05057
Stanley, Richard P.
1991
Generalized h-vectors, intersection cohomology of toric varieties, and related results. Zbl 0652.52007
Stanley, Richard
1987
Exponential structures. Zbl 0381.05004
Stanley, Richard P.
1978
Coefficients and roots of Ehrhart polynomials. Zbl 1153.52300
Beck, M.; De Loera, Jesús A.; Develin, M.; Pfeifle, J.; Stanley, R. P.
2005
Smith normal form in combinatorics. Zbl 1343.05026
Stanley, Richard P.
2016
Longest alternating subsequences of permutations. Zbl 1247.05016
Stanley, Richard P.
2008
The Catalan case of Armstrong’s conjecture on simultaneous core partitions. Zbl 1311.05017
Stanley, Richard P.; Zanello, Fabrizio
2015
Finite lattices and Jordan-Hölder sets. Zbl 0303.06006
Stanley, Richard P.
1974
Cohen-Macaulay rings and constructible polytopes. Zbl 0304.52005
Stanley, Richard P.
1975
The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem. Zbl 0651.05010
Björner, A.; Frankl, P.; Stanley, R.
1987
Factorization of permutations into n-cycles. Zbl 0467.20005
Stanley, Richard P.
1981
Hipparchus, Plutarch, Schröder, and Hough. Zbl 0873.01002
Stanley, Richard P.
1997
The stable behavior of some characters of SL(n,$${\mathbb{C}})$$. Zbl 0573.20042
Stanley, Richard P.
1984
The Fibonacci lattice. Zbl 0328.06007
Stanley, Richard P.
1975
Some remarks on sign-balanced and maj-balanced posets. Zbl 1097.06004
Stanley, Richard P.
2005
Algebraic combinatorics. Walks, trees, tableaux, and more. Zbl 1278.05002
Stanley, Richard P.
2013
Quotients of Peck posets. Zbl 0564.06002
Stanley, Richard P.
1984
The conjugate trace and trace of a plane partition. Zbl 0251.05006
Stanley, Richard P.
1973
Formulae for Askey-Wilson moments and enumeration of staircase tableaux. Zbl 1269.05116
Corteel, S.; Stanley, R.; Stanton, D.; Williams, L.
2012
Generalized riffle shuffles and quasisymmetric functions. Zbl 1010.05078
Stanley, Richard P.
2001
On the number of open sets of finite topologies. Zbl 0214.21001
Stanley, R. P.
1971
Increasing and decreasing subsequences and their variants. Zbl 1133.05002
Stanley, Richard P.
2007
Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings. Zbl 0335.05010
Stanley, Richard P.
1976
Eulerian partitions of a unit hypercube. Zbl 0359.05001
Stanley, Richard P.
1977
Algebraic enumeration. Zbl 0853.05002
Gessel, Ira M.; Stanley, Richard P.
1995
Polygon dissections and standard Young tableaux. Zbl 0859.05075
Stanley, Richard P.
1996
Enumeration of posets generated by disjoint unions and ordinal sums. Zbl 0297.05009
Stanley, Richard P.
1974
Chains in the Bruhat order. Zbl 1238.14036
Postnikov, Alexander; Stanley, Richard P.
2009
On the number of faces of centrally-symmetric simplicial polytopes. Zbl 0611.52002
Stanley, Richard P.
1987
Introduction to enumerative combinatorics. With a foreword by Richard Stanley. Zbl 1208.05001
Bóna, Miklós
2007
Reconstruction from vertex-switching. Zbl 0572.05046
Stanley, Richard P.
1985
Irreducible symmetric group characters of rectangular shape. Zbl 1068.20017
Stanley, Richard P.
2003
A survey of Eulerian posets. Zbl 0816.52004
Stanley, Richard P.
1994
Two enumerative results on cycles of permutations. Zbl 1238.05015
Stanley, Richard P.
2011
Finite operator calculus. With the collaboration of P. Doubilet, C. Greene, D. Kahaner, A: Odlyzko and R. Stanley. Zbl 0328.05007
Rota, Gian-Carlo
1975
Unimodal sequences arising from Lie algebras. Zbl 0451.05004
Stanley, Richard P.
1980
Spanning trees and a conjecture of Kontsevich. Zbl 0927.05087
Stanley, Richard P.
1998
On a generalization of Lie$$(k)$$: a CataLAnKe theorem. Zbl 1477.17043
Friedmann, Tamar; Hanlon, Phil; Stanley, Richard P.; Wachs, Michelle L.
2021
A generalization of a 1998 unimodality conjecture of Reiner and Stanton. Zbl 1427.05011
Stanley, Richard P.; Zanello, Fabrizio
2020
Irrational triangles with polynomial Ehrhart functions. Zbl 1407.52015
Cristofaro-Gardiner, Dan; Li, Teresa Xueshan; Stanley, Richard P.
2019
Algebraic combinatorics. Walks, trees, tableaux, and more. 2nd edition. Zbl 1397.05003
Stanley, Richard P.
2018
Action of the symmetric group on the free LAnKe: a CataLAnKe theorem. Zbl 1411.05282
Friedmann, Tamar; Hanlon, Philip; Stanley, Richard P.; Wachs, Michelle L.
2018
The Smith normal form distribution of a random integer matrix. Zbl 1372.05006
Wang, Yinghui; Stanley, Richard P.
2017
A walk through combinatorics. An introduction to enumeration and graph theory. With a foreword by Richard Stanley. 4th edition. Zbl 1361.05001
Bóna, Miklós
2017
The Smith normal form of a specialized Jacobi-Trudi matrix. Zbl 1358.05025
Stanley, Richard P.
2017
Smith normal form in combinatorics. Zbl 1343.05026
Stanley, Richard P.
2016
Some asymptotic results on $$q$$-binomial coefficients. Zbl 1347.05011
Stanley, Richard P.; Zanello, Fabrizio
2016
A formula for the specialization of skew Schur functions. Zbl 1347.05248
Chen, Xiaomei; Stanley, Richard P.
2016
A refined enumeration of hex trees and related polynomials. Zbl 1331.05109
Kim, Hana; Stanley, Richard P.
2016
Catalan numbers. Zbl 1317.05010
Stanley, Richard P.
2015
The Catalan case of Armstrong’s conjecture on simultaneous core partitions. Zbl 1311.05017
Stanley, Richard P.; Zanello, Fabrizio
2015
Unimodality of partitions with distinct parts inside Ferrers shapes. Zbl 1315.05016
Stanley, Richard P.; Zanello, Fabrizio
2015
Supersolvability and freeness for $$\psi$$-graphical arrangements. Zbl 1314.05076
Mu, Lili; Stanley, Richard P.
2015
Smith normal form of a multivariate matrix associated with partitions. Zbl 1307.05009
Bessenrodt, Christine; Stanley, Richard P.
2015
Valid orderings of real hyperplane arrangements. Zbl 1322.52018
Stanley, Richard P.
2015
The Smith normal form of a matrix associated with Young’s lattice. Zbl 1320.05138
Cai, Tommy Wuxing; Stanley, Richard P.
2015
The lecture hall parallelepiped. Zbl 1304.52018
Liu, Fu; Stanley, Richard P.
2014
Separation probabilities for products of permutations. Zbl 1290.05003
Bernardi, Olivier; Du, Rosena R. X.; Morales, Alejandro H.; Stanley, Richard P.
2014
How the upper bound conjecture was proved. Zbl 1408.05144
Stanley, Richard P.
2014
Counting conjugacy classes of elements of finite order in Lie groups. Zbl 1284.05335
Friedmann, Tamar; Stanley, Richard P.
2014
Algebraic combinatorics. Walks, trees, tableaux, and more. Zbl 1278.05002
Stanley, Richard P.
2013
The string landscape: on formulas for counting vacua. Zbl 1262.81135
Friedmann, Tamar; Stanley, Richard P.
2013
Enumerative combinatorics. Vol. 1. 2nd ed. Zbl 1247.05003
Stanley, Richard P.
2012
Formulae for Askey-Wilson moments and enumeration of staircase tableaux. Zbl 1269.05116
Corteel, S.; Stanley, R.; Stanton, D.; Williams, L.
2012
Orientations, lattice polytopes, and group arrangements. II: Modular and integral flow polynomials of graphs. Zbl 1256.05111
Chen, Beifang; Stanley, Richard P.
2012
An equivalence relation on the symmetric group and multiplicity-free flag $$h$$-vectors. Zbl 1291.05012
Stanley, Richard P.
2012
On the rank function of a differential poset. Zbl 1253.06003
Stanley, Richard P.; Zanello, Fabrizio
2012
Two enumerative results on cycles of permutations. Zbl 1238.05015
Stanley, Richard P.
2011
Two remarks on skew tableaux. Zbl 1238.05277
Stanley, Richard P.
2011
A survey of alternating permutations. Zbl 1231.05288
Stanley, Richard P.
2010
Some combinatorial properties of hook lengths, contents, and parts of partitions. Zbl 1234.05234
Stanley, Richard P.
2010
Tilings. Zbl 1242.52022
Ardila, Federico; Stanley, Richard P.
2010
Promotion and evacuation. Zbl 1169.06002
Stanley, Richard P.
2009
Chains in the Bruhat order. Zbl 1238.14036
Postnikov, Alexander; Stanley, Richard P.
2009
Pairs of noncrossing free Dyck paths and noncrossing partitions. Zbl 1189.05023
Chen, William Y. C.; Pang, Sabrina X. M.; Qu, Ellen X. Y.; Stanley, Richard P.
2009
Longest alternating subsequences of permutations. Zbl 1247.05016
Stanley, Richard P.
2008
Current developments in mathematics, 2006. Zbl 1149.00018
2008
An introduction to hyperplane arrangements. Zbl 1136.52009
Stanley, Richard P.
2007
Crossings and nestings of matchings and partitions. Zbl 1108.05012
Chen, William Y. C.; Deng, Eva Y. P.; Du, Rosena R. X.; Stanley, Richard P.; Yan, Catherine H.
2007
Increasing and decreasing subsequences and their variants. Zbl 1133.05002
Stanley, Richard P.
2007
Introduction to enumerative combinatorics. With a foreword by Richard Stanley. Zbl 1208.05001
Bóna, Miklós
2007
Alternating permutations and symmetric functions. Zbl 1118.05002
Stanley, Richard P.
2007
Acyclic orientations of graphs. (Reprint). Zbl 1094.05031
Stanley, Richard P.
2006
Ordering events in Minkowski space. Zbl 1109.05020
Stanley, Richard P.
2006
Coefficients and roots of Ehrhart polynomials. Zbl 1153.52300
Beck, M.; De Loera, Jesús A.; Develin, M.; Pfeifle, J.; Stanley, R. P.
2005
Some remarks on sign-balanced and maj-balanced posets. Zbl 1097.06004
Stanley, Richard P.
2005
The descent set and connectivity set of a permutation. Zbl 1101.05002
Stanley, Richard P.
2005
Combinatorics and commutative algebra. 2nd ed. Zbl 1157.13302
Stanley, Richard P.
2005
Properties of some character tables related to the symmetric groups. Zbl 1062.05144
Bessenrodt, Christine; Olsson, Jørn B.; Stanley, Richard P.
2005
A map on the space of rational functions. Zbl 1096.33003
Boros, G.; Little, J.; Moll, V.; Mosteig, E.; Stanley, R.
2005
A super-class walk on upper-triangular matrices. Zbl 1056.60006
Arias-Castro, Ery; Diaconis, Persi; Stanley, Richard
2004
Recent developments in algebraic combinatorics. Zbl 1061.05100
Stanley, Richard P.
2004
Irreducible symmetric group characters of rectangular shape. Zbl 1068.20017
Stanley, Richard P.
2003
Recent progress in algebraic combinatorics. Zbl 1119.14002
Stanley, Richard P.
2003
On the enumeration of skew Young tableaux. Zbl 1027.05109
Stanley, R. P.
2003
A polytope related to empirical distributions, plane trees, parking functions, and the associahedron. Zbl 1012.52019
Stanley, Richard P.; Pitman, Jim
2002
The rank and minimal border strip decompositions of a skew partition. Zbl 1018.05105
Stanley, Richard P.
2002
Enumerative combinatorics. Volume 2. Paperback ed. Zbl 0978.05002
Stanley, Richard P.
2001
Generalized riffle shuffles and quasisymmetric functions. Zbl 1010.05078
Stanley, Richard P.
2001
Positivity problems and conjectures in algebraic combinatorics. Zbl 0955.05111
Stanley, Richard P.
2000
Deformations of Coxeter hyperplane arrangements. Zbl 0962.05004
Postnikov, Alexander; Stanley, Richard P.
2000
A note on symmetric powers of the standard representation of $$S_n$$. Zbl 0959.05119
Savitt, David; Stanley, Richard P.
2000
Enumerative combinatorics. Volume 2. Zbl 0928.05001
Stanley, Richard P.
1999
Flag-symmetry of the poset of shuffles and a local action of the symmetric group. Zbl 0931.06004
Simion, Rodica; Stanley, Richard P.
1999
Enumerative combinatorics. Vol. 1. With a foreword by Gian-Carlo Rota. Corrected reprint of the 1986 hardback edition. Zbl 0945.05006
Stanley, Richard P.
1999
Domino tilings with barriers. Zbl 0948.05020
Propp, James; Stanley, Richard
1999
New perspectives in algebraic combinatorics. Zbl 0927.00011
1999
Graph colorings and related symmetric functions: ideas and applications: A description of results, interesting applications, and notable open problems. Zbl 1061.05508
Stanley, Richard P.
1998
Hyperplane arrangements, parking functions and tree inversions. Zbl 0917.52013
Stanley, Richard P.
1998
Spanning trees and a conjecture of Kontsevich. Zbl 0927.05087
Stanley, Richard P.
1998
A $$q$$-deformation of a trivial symmetric group action. Zbl 0921.20009
Hanlon, Phil; Stanley, Richard P.
1998
Mathematical essays in honor of Gian-Carlo Rota’s 65th birthday. Zbl 0890.00032
1998
Enumerative combinatorics. Vol. 1. Zbl 0889.05001
Stanley, Richard P.
1997
Parking functions and noncrossing partitions. Zbl 0883.06001
Stanley, Richard P.
1997
Hipparchus, Plutarch, Schröder, and Hough. Zbl 0873.01002
Stanley, Richard P.
1997
Lê numbers of arrangements and matroid identities. Zbl 0884.05029
Massey, David B.; Simion, Rodica; Stanley, Richard P.; Vertigan, Dirk; Welsh, Dominic J. A.; Ziegler, Günter M.
1997
Combinatorics and commutative algebra. 2nd ed. Zbl 0838.13008
Stanley, Richard P.
1996
Hyperplane arrangements, interval orders, and trees. Zbl 0848.05005
Stanley, Richard P.
1996
Polygon dissections and standard Young tableaux. Zbl 0859.05075
Stanley, Richard P.
1996
Flag-symmetric and locally rank-symmetric partially ordered sets. Zbl 0857.05091
Stanley, Richard P.
1996
A matrix for counting paths in acyclic digraphs. Zbl 0860.05054
Stanley, Richard P.
1996
A symmetric function generalization of the chromatic polynomial of a graph. Zbl 0831.05027
Stanley, Richard P.
1995
Algebraic enumeration. Zbl 0853.05002
Gessel, Ira M.; Stanley, Richard P.
1995
Schubert polynomials and the nilCoxeter algebra. Zbl 0809.05091
Fomin, Sergey; Stanley, Richard P.
1994
Flag $$f$$-vectors and the $$cd$$-index. Zbl 0805.06003
Stanley, Richard P.
1994
A survey of Eulerian posets. Zbl 0816.52004
Stanley, Richard P.
1994
Some combinatorial properties of Schubert polynomials. Zbl 0790.05093
Billey, Sara C.; Jockusch, William; Stanley, Richard P.
1993
On immanants of Jacobi-Trudi matrices and permutations with restricted position. Zbl 0772.05097
Stanley, Richard P.; Stembridge, John R.
1993
A monotonicity property of $$h$$-vectors and $$h^*$$-vectors. Zbl 0799.52008
Stanley, Richard P.
1993
A combinatorial decomposition of acyclic simplicial complexes. Zbl 0782.55004
Stanley, Richard P.
1993
Derangements on the $$n$$-cube. Zbl 0774.05002
Chen, William Y. C.; Stanley, Richard P.
1993
Subdivisions and local $$h$$-vectors. Zbl 0768.05100
Stanley, Richard P.
1992
Some combinatorial aspects of the spectra of normally distributed random matrices. Zbl 0789.05092
Hanlon, Philip J.; Stanley, Richard P.; Stembridge, John R.
1992
Sets of vectors with many orthogonal pairs. Zbl 0768.05005
Füredi, Zoltán; Stanley, Richard
1992
f-vectors and h-vectors of simplicial posets. Zbl 0727.06009
Stanley, Richard P.
1991
On the Hilbert function of a graded Cohen-Macaulay domain. Zbl 0735.13010
Stanley, Richard P.
1991
A zonotope associated with graphical degree sequences. Zbl 0737.05057
Stanley, Richard P.
1991
...and 79 more Documents
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### Cited by 5,971 Authors
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### Cited in 496 Serials
600 Journal of Combinatorial Theory. Series A 473 Discrete Mathematics 364 Journal of Algebra 333 Advances in Applied Mathematics 313 European Journal of Combinatorics 294 Advances in Mathematics 262 The Electronic Journal of Combinatorics 252 Journal of Algebraic Combinatorics 201 Transactions of the American Mathematical Society 155 Proceedings of the American Mathematical Society 150 Journal of Pure and Applied Algebra 146 Annals of Combinatorics 139 Communications in Algebra 133 Linear Algebra and its Applications 112 Discrete & Computational Geometry 108 Séminaire Lotharingien de Combinatoire 91 Discrete Applied Mathematics 78 Theoretical Computer Science 69 Algebraic Combinatorics 64 Order 57 Graphs and Combinatorics 50 Mathematische Zeitschrift 49 Journal of Symbolic Computation 49 The Ramanujan Journal 47 Journal of Number Theory 47 SIAM Journal on Discrete Mathematics 46 Journal of Combinatorial Theory. Series B 43 Israel Journal of Mathematics 41 Journal of Mathematical Sciences (New York) 39 Journal of Mathematical Physics 38 Communications in Mathematical Physics 37 Duke Mathematical Journal 34 Journal of Integer Sequences 30 Inventiones Mathematicae 30 Journal of Commutative Algebra 29 Manuscripta Mathematica 27 Linear and Multilinear Algebra 27 Bulletin of the American Mathematical Society. New Series 26 Journal of Mathematical Analysis and Applications 26 Selecta Mathematica. New Series 25 Rocky Mountain Journal of Mathematics 25 Journal of High Energy Physics 24 Annales de l’Institut Fourier 24 The Annals of Probability 24 Journal of Statistical Planning and Inference 24 The Australasian Journal of Combinatorics 23 Mathematische Annalen 23 Studies in Applied Mathematics 23 Combinatorica 23 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 21 Archiv der Mathematik 21 Nagoya Mathematical Journal 20 Journal of Statistical Physics 20 Comptes Rendus. Mathématique. Académie des Sciences, Paris 19 Letters in Mathematical Physics 19 Applied Mathematics and Computation 19 Algebras and Representation Theory 19 Journal of Algebra and its Applications 18 Collectanea Mathematica 17 Journal of the American Mathematical Society 17 Experimental Mathematics 16 Mathematics of Computation 16 Tohoku Mathematical Journal. Second Series 15 Algebra Universalis 15 Combinatorics, Probability and Computing 15 Transformation Groups 14 Mathematical Proceedings of the Cambridge Philosophical Society 14 International Journal of Algebra and Computation 13 Compositio Mathematica 13 Probability Theory and Related Fields 13 Designs, Codes and Cryptography 13 Finite Fields and their Applications 12 Mathematical Notes 12 Nuclear Physics. B 12 Functional Analysis and its Applications 12 Mathematika 11 American Mathematical Monthly 11 The Annals of Statistics 11 Journal of Functional Analysis 11 Journal für die Reine und Angewandte Mathematik 11 Random Structures & Algorithms 11 The Annals of Applied Probability 11 Journal of Algebraic Geometry 11 Integers 10 Information Processing Letters 10 Journal of Mathematical Psychology 10 Monatshefte für Mathematik 10 SIAM Journal on Algebraic and Discrete Methods 10 Journal of Theoretical Probability 10 Aequationes Mathematicae 10 Applicable Algebra in Engineering, Communication and Computing 10 Algebraic & Geometric Topology 9 Bulletin of the Australian Mathematical Society 9 Journal of Geometry and Physics 9 The Mathematical Intelligencer 9 Fuzzy Sets and Systems 9 Journal of Computational and Applied Mathematics 9 Journal of Multivariate Analysis 9 Memoirs of the American Mathematical Society 9 Journal of the European Mathematical Society (JEMS) ...and 396 more Serials
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### Cited in 61 Fields
4,431 Combinatorics (05-XX) 1,116 Commutative algebra (13-XX) 1,005 Group theory and generalizations (20-XX) 884 Convex and discrete geometry (52-XX) 820 Order, lattices, ordered algebraic structures (06-XX) 816 Algebraic geometry (14-XX) 771 Number theory (11-XX) 405 Probability theory and stochastic processes (60-XX) 393 Associative rings and algebras (16-XX) 370 Computer science (68-XX) 354 Linear and multilinear algebra; matrix theory (15-XX) 262 Special functions (33-XX) 227 Nonassociative rings and algebras (17-XX) 191 Manifolds and cell complexes (57-XX) 174 Algebraic topology (55-XX) 163 Quantum theory (81-XX) 125 Statistical mechanics, structure of matter (82-XX) 99 Operations research, mathematical programming (90-XX) 97 Several complex variables and analytic spaces (32-XX) 92 Category theory; homological algebra (18-XX) 92 Statistics (62-XX) 84 Geometry (51-XX) 81 Information and communication theory, circuits (94-XX) 78 Numerical analysis (65-XX) 77 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 76 Topological groups, Lie groups (22-XX) 66 Dynamical systems and ergodic theory (37-XX) 65 Biology and other natural sciences (92-XX) 53 Functions of a complex variable (30-XX) 51 Mathematical logic and foundations (03-XX) 50 Real functions (26-XX) 47 Field theory and polynomials (12-XX) 47 Differential geometry (53-XX) 45 Operator theory (47-XX) 44 Functional analysis (46-XX) 40 Ordinary differential equations (34-XX) 36 Approximations and expansions (41-XX) 31 Abstract harmonic analysis (43-XX) 29 Difference and functional equations (39-XX) 29 Global analysis, analysis on manifolds (58-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 25 $$K$$-theory (19-XX) 24 Integral transforms, operational calculus (44-XX) 24 General topology (54-XX) 18 Partial differential equations (35-XX) 15 Measure and integration (28-XX) 14 History and biography (01-XX) 14 Relativity and gravitational theory (83-XX) 13 General and overarching topics; collections (00-XX) 9 General algebraic systems (08-XX) 8 Systems theory; control (93-XX) 6 Sequences, series, summability (40-XX) 3 Mechanics of deformable solids (74-XX) 3 Mathematics education (97-XX) 2 Potential theory (31-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-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.
| 2022-05-16T08:31:07 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M033M4&home=MXXX005
|
# ${{\boldsymbol \pi}^{-}}$ ${{\boldsymbol p}}$ $\rightarrow$ ${{\boldsymbol K}^{+}}{{\boldsymbol K}^{-}}{{\boldsymbol n}}$ INSPIRE search
VALUE (MeV) DOCUMENT ID TECN CHG COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2307$ $\pm6$
1980
CNTR 0 62 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$
References:
ALPER 1980
PL 94B 422 Evidence for a Spin-5 Boson Resonance at 2300 MeV
| 2021-03-03T10:59:13 |
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|
https://par.nsf.gov/biblio/10339269-infrared-active-phonon-modes-static-dielectric-constants-al-ga-alloys
|
This content will become publicly available on March 14, 2023
Infrared-active phonon modes and static dielectric constants in α -(Al x Ga 1− x ) 2 O 3 (0.18 ≤ x ≤ 0.54) alloys
We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(Al x Ga 1− x ) 2 O 3 alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al 2 O 3 substrates with x = 0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga 2 O 3 and α-Al 2 O 3 . The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.
Authors:
; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10339269
Journal Name:
Applied Physics Letters
Volume:
120
Issue:
11
Page Range or eLocation-ID:
112202
ISSN:
0003-6951
4. SiC and Ga 2 O 3 are promising wide band gap semiconductors for applications in power electronics because of their high breakdown electric field and normally off operation. However, lack of a suitable dielectric material that can provide high interfacial quality remains a problem. This can potentially lead to high leakage current and conducting loss. In this work, we present a novel atomic layer deposition process to grow epitaxially Mg x Ca 1− x O dielectric layers on 4H-SiC(0001) and β-Ga 2 O 3 $\left( {\bar 201} \right)$ substrates. By tuning the composition of Mg x Ca 1− x O toward the substrate lattice constant, better interfacial epitaxy can be achieved. The interfacial and epitaxy qualities were investigated and confirmed by cross-sectional transmission electron microscopy and X-ray diffraction studies. Mg 0.72 Ca 0.28 O film showed the highest epitaxy quality on 4H-SiC(0001) because of its closest lattice match with the substrate. Meanwhile, highly textured Mg 0.25 Ca 0.75 O films can be grown on β-Ga 2 O 3 $\left( {\bar 201} \right)$ with a preferred orientation of (111).
| 2022-10-02T22:53:08 |
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https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/plane-of-array-poa-irradiance/calculating-poa-irradiance/poa-sky-diffuse/perez-sky-diffuse-model/
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While the sky diffuse model presented up to this point separated the isotropic, circumsolar, and horizon components explicitly, Perez developed a more complex model that relies on a set of empirical coefficients for each term.
The basic form of the model is:
$E_{d}=DHI\times&space;\left&space;[&space;\left&space;(&space;1-F_{1}&space;\right&space;)\left&space;(&space;\frac{1+\cos&space;\left&space;(&space;\theta_{T}&space;\right&space;)}{2}&space;\right&space;)+F_{1}\left&space;(&space;\frac{a}{b}&space;\right&space;)+F_{2}&space;\sin&space;\left&space;(&space;\theta_{T}&space;\right&space;)&space;\right&space;]$,
where $F_{1}$ and $F_{2}$ are complex empirically fitted functions that describe circumsolar and horizon brightness, respectively.
$a&space;=&space;\max&space;\left&space;(&space;0,\cos&space;\left&space;(&space;AOI&space;\right&space;)&space;\right&space;)$, and $b=\max&space;\left&space;(&space;\cos&space;\left&space;(&space;85^{\circ}&space;\right&space;),\cos&space;\left&space;(&space;\theta_{Z}&space;\right&space;)&space;\right&space;)$.
• $DHI$ is diffuse horizontal irradiance,
• $AOI$ is the angle of incidence between the sun and the plane of the array.
• $\theta_{Z}$ is the solar zenith angle.
• $\theta_{T}$ is the array tilt angle from horizontal.
$F_{1}=\max&space;\left&space;[&space;0,\left&space;(&space;f_{11}+f_{12}\Delta&space;+\frac{\pi&space;\theta_{Z}}{180^{\circ}}f_{13}&space;\right)&space;\right&space;]$,
$F_{2}=&space;f_{21}+f_{22}\Delta&space;+\frac{\pi&space;\theta_{Z}}{180^{\circ}}f_{23}$
The $f$ coefficients are defined for specific bins of clearness ($\varepsilon$), which is defined as:
$\varepsilon&space;=\frac{(DHI+DNI)/DHI+\kappa&space;\theta_{Z}^{3}&space;}{1+\kappa&space;\theta_{Z}^{3}&space;}$,
where $DNI$ is direct normal irradiance and $\kappa$ is a constant equal to $1.041$ for angles are in radians, or $5.535\times&space;10^{-6}$ for angles in degrees.
$\Delta&space;=\frac{DHI\times&space;AM_{a}}{E_{a}}$
where $AM_{a}$ is the absolute air mass, and $E_{a}$ is extraterrestrial radiation.
Perez has published a number of different versions of the $f$ coefficients fitted to various data sets [2, 3 , 4]. Table 1 shows the $f$ coefficient values published in [3] for irradiance. The $\varepsilon$ bin refers to bins of clearness, $\varepsilon$, defined in Table 2.
Table 1. Perez model coefficients for irradiance (from Table 6 in [3])
$\varepsilon$ bin f11 f12 f13 f21 f22 f23 1 -0.008 0.588 -0.062 -0.06 0.072 -0.022 2 0.13 0.683 -0.151 -0.019 0.066 -0.029 3 0.33 0.487 -0.221 0.055 -0.064 -0.026 4 0.568 0.187 -0.295 0.109 -0.152 -0.014 5 0.873 -0.392 -0.362 0.226 -0.462 0.001 6 1.132 -1.237 -0.412 0.288 -0.823 0.056 7 1.06 -1.6 -0.359 0.264 -1.127 0.131 8 0.678 -0.327 -0.25 0.156 -1.377 0.251
Table 2. Sky clearness bins (from Table 1 in [3])
$\varepsilon$ bin Lower Bound Upper Bound 1 Overcast 1 1.065 2 1.065 1.230 3 1.230 1.500 4 1.500 1.950 5 1.950 2.800 6 2.800 4.500 7 4.500 6.200 8 Clear 6.200 —
References
• [1] Loutzenhiser P.G. et. al. “Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation” 2007, Solar Energy vol. 81. pp. 254-267
• [2] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987. A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy 39 (3), 221–232.
• [3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990. Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44 (5), 271–289.
• [4] Perez, R. et. al 1988. “The Development and Verification of the Perez Diffuse Radiation Model”. SAND88-7030
Content contributed by Sandia National Laboratories
| 2022-09-29T18:50:04 |
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https://wwwn.cdc.gov/nchs/nhanes/tutorials/module4.aspx
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# Module 4: Variance Estimation
This module introduces the basic concepts of variance (sampling error) estimation for NHANES data. You will learn how the complex survey design of NHANES and clustering of the data affect variance estimation, which methods are appropriate to use when calculating variance for NHANES data, how to properly calculate the variance for subgroups of interest, and how to specify the sampling design parameters in common statistical software packages.
In general, using statistical weights that reflect the probability of selection and propensity of response for sampled individuals will affect parameter estimates, while incorporating the attributes of the complex sample design (i.e. differential weighting, clustering and stratification) will affect variance estimates (estimated standard errors and thereby test statistics and confidence intervals).
## IMPORTANT NOTE
For NHANES datasets, the use of sampling weights and sample design variables is necessary to obtain unbiased estimates and accurate standard errors and confidence intervals.
NHANES survey design affects variance estimates
As stated in the module on sampling in NHANES, the NHANES has a complex, multistage, probability cluster design. Typically, individuals within a cluster (i.e., county, school, city, census block) are more similar to one another than those in other clusters and this homogeneity of individuals within a given cluster is measured by the intracluster correlation. When designing a survey with a complex sample, you ideally want to decrease the amount of correlation between sample persons within clusters. To achieve this, you want to sample fewer people within each cluster but sample more clusters. However, NHANES can only sample 30 Primary Sampling Units (PSUs) within a 2-year survey cycle because of operational limitations such as the cost of moving the survey MECs and geographic distances between PSUs. The sample size in each PSU is roughly equal and it is intended to yield about 5,000 examined persons per year.
For a complex sample survey such as NHANES, variance estimates computed using standard statistical software packages that assume simple random sampling are generally too low (i.e., significance levels are overstated) and biased because they do not account for the differential weighting and the correlation among sample persons within a cluster. There is a loss of precision and a reduction in the effective sample size because individuals are chosen within clusters instead of being sampled randomly throughout the population.
## WARNING
Standard statistical software packages that assume simple random sampling calculate variance estimates that are generally too low and biased because they do not account for differential weighting and the correlation among sample persons within a cluster.
The impact of the complex sample design upon variance estimates is measured by the design effect (DEFF). It is defined as the ratio of the variance of a statistic which accounts for the complex sample design to the variance of the same statistic based on a hypothetical simple random sample of the same size.
If the DEFF is 1, the variance for the estimate under the cluster sampling is the same as the variance under simple random sampling. The DEFFs for NHANES are typically greater than 1.
When the DEFF is greater than 1, the effective sample size is less than the number of sample persons but greater than the number of clusters. The effective sample size is calculated by dividing the sample size in a subgroup by the DEFF. The design effect is an attribute of a statistic calculated on a particular variable, rather than for the overall NHANES survey cycle. DEFF can be very different for different variables due to differences in variation by geography, by household intra class correlation, and by demographic heterogeneity. Design effects for a variable can also be different for different demographic subgroups (i.e. race and Hispanic origin or age groups.)
## IMPORTANT NOTE
Statistical software that accounts for the sampling design effect must be used to calculate an asymptotically unbiased estimate of the variance and should be used for all statistical tests and the construction of confidence limits. These procedures require information on the first stage of the sample design (identification of the PSU and stratum) for each sample person.
Reference
Park, I and Lee, H (2004) "Design Effects for the weighted mean and total estimators under complex survey sampling." Survey methodology 30:183-193.
Brief description of variance estimation procedures used with NHANES data
Variance of estimates (sampling errors) should be calculated for all survey estimates to aid in determining statistical reliability. For complex sample surveys, exact mathematical formulas for variance estimates are usually not available. Variance approximation procedures are required to provide reasonable, approximately unbiased, and design-consistent estimates of sampling error. Two variance approximation procedures which account for the complex sample design and compute design effects are replication methods and Taylor Series Linearization.
Currently NCHS recommends the use of the Taylor Series Linearization methods for variance estimation in all NHANES surveys, and this tutorial and the example code provide assistance on the linearization method only. SUDAAN, Stata, SAS Survey procedures, SPSS, and R can be used to obtain variance estimated by this method. Survey design variables identifying strata and PSU are required in order to utilize these software packages.
Initially, for the NHANES 1999-2000 survey, the delete-one jackknife (replication) method was used to estimate variances, and these weights are available on the public-use file for that cycle. Balance repeated replication was used for NHANES III. If replication methods are used for other survey cycles, you must compute your own replicate weights.
Taylor Linearization Procedures
To use the linearization method, information about the first stage of the sample design (strata and PSU variables) must be available on the survey data file. The "true" design variables are not released on the public-use data files in order to protect the confidentiality of information provided by survey participants and to reduce disclosure risks associated with a two-year data release. Instead, Masked Variance Units (MVUs) were created and provided on the demographic data files for each survey cycle. These MVUs produce variance estimates that closely approximate the variances that would have been estimated using the true design variables, and should be used for all analyses on public release data. The variable name for the masked variance unit pseudo-stratum is sdmvstra and the variable name for the masked variance unit pseudo-PSU is sdmvpsu.
As described in Module 2: Sample Design, the first stage of the NHANES sampling selects PSUs from strata. This can be treated as sampling "with replacement" because the sampling fraction (the number of PSUs selected compared to the total number of PSUs within each stratum) is small. Therefore, the finite population correction factor = (1 - the sampling fraction) is close to 1 and has a negligible effect on the formula for the design based estimate of variance.
Frequently, analysts wish to produce estimates for certain demographic subgroups of interest, such as a particular age range or gender. (Such subgroups may also be referenced in the survey literature and software documentation as "subpopulations," "domains," or "subdomains.") The calculations to generate point estimates for statistics such as means, percentages, and totals require only the observations that are within your subgroup of interest. However, to properly estimate the variance of these statistics with Taylor series linearization, your statistical software requires all observations with a non-zero value for your weight variable, as well as an indicator for which records are in your subpopulation of interest. For example, to estimate mean body mass index (BMI) and its standard error for men aged 20 and over, the entire dataset of examined individuals who have an exam weight, including females and those younger than 20 years, must be read into the statistical software procedure.
You may be wondering why the variance estimation requires information on records that are not in your subpopulation of interest. The subpopulation sample size within each PSU is actually a random variable. Conceptually, if samples were drawn repeatedly using the original complex survey design, the number of sampled persons in your subpopulation of interest within each PSU would vary somewhat from sample to sample. The variance estimation takes into account this sample-to-sample variability in the subpopulation sample size in calculating the variability of the estimated statistic (e.g. the standard error of the mean BMI for men aged 20 and over). If you were to subset your dataset and only keep the records that are in your subpopulation, then the variance estimation formula would effectively treat the subpopulation sample size as if it were fixed. This would underestimate the variability of the estimated mean BMI. For more information, refer to the suggested sources or a textbook on survey statistics.
## WARNING
As a general rule when working with complex survey data such as NHANES, you should never drop records from your analysis dataset before executing your analysis procedures. Instead, use the special statements provided in your software's analysis procedure to perform subgroup analyses.
It is important that you do not create a smaller subset of your data based on any non weight-related groups of interest (e.g. demographic, laboratory or examination variables) before executing your analysis procedures. For example, you should not create a subset of your data in the SAS data step before executing a SUDAAN procedure. Instead, it is highly recommended that you specify your subgroup of interest using the subpopx statement in the SUDAAN procedure itself. It may be helpful to create a binary indicator variable to define your population of interest in your SAS data step, which you can then use in the subpopx statement.
Each software package that can analyze complex survey data has commands to produce subgroup estimates while properly accounting for the survey design. The following table presents a summary of proper and improper approaches to subgroup analysis in several software packages. See the section below, "Degrees of Freedom for Subgroup Analysis in NHANES," for additional considerations in subgroup analysis.
Summary of proper and improper approaches to subgroup analysis in selected statistical software:
Software Improper approaches Proper approaches
SUDAAN
• Subsetting your dataset in SAS before executing SUDAAN procedures
• SUBPOPN or SUBPOPX statement
• TABLES statement to produce cross-tabulations in PROC DESCRIPT
SAS Survey
• Subsetting your dataset before executing SAS Survey procedures
• Using a where or if data set option on your input dataset in a SAS Survey procedure
• Using a BY statement to produce a separate estimate for each level of the "by" variable
• DOMAIN statement (Procedures other than SURVEYFREQ)
• TABLES statement (Proc SURVEYFREQ)
Stata
• Dropping observations from your dataset
• Using IF or IN options to subset your data during an estimation command
• subpop option in the svy prefix command
• over() option in the svy:mean, svy:proportion, svy:ratio, and svy:total commands (to request estimates at multiple levels of a categorical variable)
R ("survey" package)
• SVYBY function
References
West BT, Berglund P, Heeringa SG. "A closer examination of subpopulation analysis of complex-sample survey data." Stata Journal. 2008;8(4):520-531.
Graubard BI, Korn EL. "Survey inference for subpopulations." Am J Epidemiol. 1996;144(1):102-106.
Degrees of Freedom for a Complex Survey
Continuous NHANES uses a complex, multistage probability sampling design. The number of independent pieces of information, or degrees of freedom, depends upon the number of PSUs rather than on the number of sample persons. Sample persons within a given PSU are not independent.
For a complex survey, the design degrees of freedom are properly calculated by subtracting the number of clusters (strata) in the first stage of sampling from the number of primary sampling units (PSUs) selected in the first stage of sampling, as shown the in equation below. Most two-year public data releases of Continuous NHANES have 15 degrees of freedom (30 PSUs – 15 strata.)
Degrees of freedom are needed to perform hypothesis tests and to compute confidence intervals. To calculate the correct value for the t-statistic from a t-distribution and a selected level of significance, you must calculate the proper degrees of freedom for the estimate.
Degrees of Freedom when Analyzing Subgroups in NHANES
Estimates are often calculated for various subgroups of interest within the total NHANES population. For an analysis on a subgroup, the degrees of freedom should be based on the number of strata and PSUs containing the observations of interest. When you analyze data on a subgroup of sample persons who may not be represented in all strata and PSUs (e.g., some racial and ethnic groups), those estimates would have fewer degrees of freedom, compared to estimates for the overall sample.
Software packages differ in how they define the degrees of freedom for subgroups, and many packages do not correct for the reduction in the degrees of freedom for subgroups where not all PSUs and strata are represented. Analysts should be aware of how the software package they are using determines the degrees of freedom. It may be necessary to output the number of PSUs and strata from the survey procedure to calculate the correct degrees of freedom. In SUDAAN, the DESCRIPT procedure allows users to output the number of strata and PSUs represented in the subpopulation. In other packages, the user may need to calculate the number of PSUs and strata separately. See the Sample Code page for examples of calculating the correct degrees of freedom for subgroups and using that information to calculate a confidence interval.
## WARNING
Many software packages do not correct for the reduction in the degrees of freedom for subgroups where not all PSUs and strata are represented. Analysts should be aware of how the software package they are using determines the degrees of freedom.
To understand more about variance estimation methods you may wish to review the Analytic Guidelines on the NHANES web site; read the text by Korn and Graubard (Korn EL and Graubard BI. Analysis of Health Surveys. Wiley Series in Probability and Statistics. 1999. New York, New York.); or take a course in SUDAAN or complex survey sampling.
This section provides a brief overview of how to request the Taylor series linearization method, specify the survey design variables, and correctly calculate the variance for subpopulations of interest using SUDAAN. These code portions include only the statements required to account for the complex sample design of NHANES, and do not include all code required to request statistical estimates. See the sample code page for complete, specific examples. The software tips page contains additional helpful hints about each software package.
In SUDAAN, the user must specify the survey design variables within each procedure step. This example shows the SUDAAN procedure PROC DESCRIPT, but the same statements would be used in other procedures (e.g. PROC CROSSTAB, PROC REGRESS, etc.)
PROC DESCRIPT data=one design=wr;
NEST sdmvstra sdmvpsu;
WEIGHT WTMEC4YR;
SUBPOPX ridageyr>=20;
* more statements...;
run;
Statements Explanation
PROC SORT data=one;
By sdmvstra sdmvpsu;
run;
Use the SAS procedure, proc sort, to sort the data by the design parameters, strata (sdmvstra) and primary sampling units (sdmvpsu), before running the procedure in SUDAAN.
PROC DESCRIPT data=one design=wr;
The design=wr option specifies that the sample design option is Taylor series linearization and that the first-stage sampling can be treated as "with replacement." (WR is the default design option in SUDAAN. If you omit the DESIGN= option from your PROC statement, SUDAAN assumes a WR design and Taylor series linearization.)
NEST sdmvstra sdmvpsu;
The NEST statement specifies that the first-stage sampling is described by the strata (variable sdmvstra) and PSU (variable sdmvpsu) variables.
WEIGHT WTMEC4YR;
The WEIGHT statement specifies the sampling weight to be used for the analysis.
See Module 3: Weighting for more discussion of how to select the correct weight for your analysis.
SUBPOPX ridageyr>=20;
The SUBPOPX statement specifies the subpopulation of interest. In this example, the subpopulation of interest is adults aged 20 and over.
Alternatively, the SUBPOPN statement does the same thing as SUBPOPX, but it has less flexibility in coding; SUBPOPX was added in SUDAAN 11.
* more statements...;
run;
This example only shows the statements required to specify the sample design parameters using SUDAAN procedures. Your code will include additional statements to request estimates for your analytic project.
SUDAAN syntax is described as of release 11.0.0, but the syntax may change in future releases. Review the documentation for the software version you are using for any changes.
This section provides a brief overview of how to request the Taylor series linearization method, specify the survey design variables, and correctly calculate the variance for subpopulations of interest using SAS Survey Procedures. These code portions include only the statements required to account for the complex sample design of NHANES, and do not include all code required to request statistical estimates. See the sample code page for complete, specific examples. The software tips page contains additional helpful hints about each software package.
SAS provides a number of survey analysis procedures that properly account for the sample design. The procedure names all start with SURVEY – such as SURVEYMEANS, SURVEYFREQ, SURVEYREG, and others. (Note that the Base SAS procedures – PROC MEANS, PROC FREQ, etc. – do not account for the complex sample design of NHANES.)
In SAS Survey procedures, the user must specify the survey design variables within each procedure step. This example shows PROC SURVEYMEANS, but the same statements would be used in most other survey procedures (e.g. PROC SURVEYREG, PROC SURVEYLOGISTIC, etc.)
PROC SURVEYMEANS data=one varmethod=taylor nomcar;
STRATA sdmvstra;
CLUSTER sdmvpsu;
WEIGHT WTMEC4YR;
DOMAIN Select;
* more statements...;
run;
Statements Explanation
PROC SURVEYMEANS data=one varmethod=taylor nomcar;
The varmethod=taylor option on the procedure statement specifies that the procedure should use Taylor series linearization for variance estimates. This is the default method if you do not specify the varmethod= option.
The nomcar option treats missing values in the variance computation as "not missing completely at random." Use of the nomcar option is recommended in SAS Survey procedures to obtain the correct standard error estimates.
STRATA sdmvstra;
The STRATA statement identifies the variables that form the strata.
CLUSTER sdmvpsu;
The CLUSTER statement identifies the variables that form the clusters (PSUs) in a clustered sample design such as NHANES. If both STRATA and CLUSTER statements are specified, then the SAS Survey procedure assumes the clusters are nested within strata (as is the case for NHANES.)
WEIGHT WTMEC4YR;
The WEIGHT statement specifies the sampling weight to be used for the analysis. See Module 3: Weighting for more discussion of how to select the correct weight for your analysis.
DOMAIN Select;
The DOMAIN statement specifies the subpopulation of interest. In this generic example, the variable Select would have been created in an earlier SAS data step as a binary indicator for whether the observation was in the subpopulation of interest, e.g. adults aged 20 and over.
Note that the DOMAIN statement is not valid syntax in the SURVEYFREQ procedure, and instead the TABLES statement may be used to specify subpopulations of interest. See the Software Tips page and the SAS documentation for more information.
* more statements...;
run;
This example only shows the statements required to specify the sample design parameters using SAS Survey procedures. Your code will include additional statements to request estimates for your analytic project.
SAS syntax is described as of version 9.4, maintenance release 3 (SAS/STAT version 14.1), but the syntax may change in future releases. Review the documentation for the software version you are using for any changes.
This section provides a brief overview of how to request the Taylor series linearization method, specify the survey design variables, and correctly calculate the variance for subpopulations of interest using Stata. These code portions include only the statements required to account for the complex sample design of NHANES, and do not include all code required to request statistical estimates. See the sample code page for complete, specific examples. The software tips page contains additional helpful hints about each software package.
Stata's SVY commands are a series of commands specifically designed to analyze complex survey designs like NHANES. In Stata, the user must first declare the survey design for a dataset using the svyset command. Stata then remembers these survey design characteristics and applies them to every subsequent SVY command. (You can issue a new svyset command if you want to update the survey design specification within your session.) Generally, the survey analysis commands in Stata use similar syntax as the standard data analysis commands but require the prefix svy: be used, which adjusts the results for the survey design as specified in the svyset command.
svyset [w=wtmec4yr], psu(sdmvpsu) strata(sdmvstra) vce(linearized)
svy, subpop(inAnalysis): mean Depression_Indicator
Statements Explanation
svyset [w=wtmec4yr], psu(sdmvpsu) strata(sdmvstra) vce(linearized)
The svyset command defines the weight, PSU, and strata variables.
The vce(linearized) option specifies that Taylor series linearization should be used for variance estimation. This is also the default method, if you do not specify the vce option.
svy, subpop(inAnalysis): mean Depression_Indicator
The second command requests the mean of the variable Depression_Indicator for the subpopulation of interest, accounting for the survey design previously specified by the svyset command.
The svy: prefix requests that the survey design be applied, and the subpop option restricts the analysis to the subpopulation of interest. In this generic example, the variable inAnalysis would have been created by an earlier Stata command as a binary indicator for whether the observation was in the subpopulation of interest, e.g. adults aged 20 and over.
Stata syntax is described as of version 15, but the syntax may change in future releases. Review the documentation for the software version you are using for any changes.
This section provides a brief overview of how to request the Taylor series linearization method, specify the survey design variables, and correctly calculate the variance for subpopulations of interest using R. These code portions include only the statements required to account for the complex sample design of NHANES, and do not include all code required to request statistical estimates. See the sample code page for complete, specific examples. The software tips page contains additional helpful hints about each software package.
The R "survey" package provides functions for analyzing data from complex surveys. In R, the user must use the svydesign function to create a "survey design object" that contains the data frame along with all the survey design information required to analyze it. This survey design object is then passed as an argument to the survey analysis functions.
NHANES_all <- svydesign(data=One, id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTMEC4YR, nest=TRUE)
NHANES <- subset(NHANES_all, inAnalysis==1)
svymean(~Depression, NHANES)
Statements Explanation
NHANES_all <- svydesign(data=One, id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTMEC4YR, nest=TRUE)
The svydesign command defines a survey design object called NHANES_all, which contains the data frame One (specified by the data=One argument) and information about the survey design information specified in the other arguments.
Note that the id (i.e. the PSU), strata, and weights arguments are specified as R formulas, which is why the tilde operator (~) is used.
The nest=TRUE option must be used for continuous NHANES data because the unique PSUs are identified by the combination of the strata and the PSU variables (i.e. the PSU identifiers reuse the same values for the PSUs within each stratum.)
NHANES <- subset(NHANES_all, inAnalysis==1)
The subset statement restricts your survey design object NHANES_all to a subpopulation (where inAnalysis is equal to 1) while keeping the original design information about the number of PSU and strata, and creates a new survey design object named NHANES.
In this generic example, the variable inAnalysis would have been created by an earlier R command as a binary indicator for whether the observation was in the subpopulation of interest, e.g. adults aged 20 and over.
Note that this command calls the subset function for objects of class "survey.design" (subset.survey.design from the survey package) and is the recommended way to specify your analysis population. If you instead subset your data frame before defining your survey design object, you may produce incorrect variance estimates.
svymean(~Depression, NHANES)
The svymean command requests the mean and standard error of variable Depression for our subpopulation of interest, as defined in the survey design object NHANES.
R syntax is described as of version 3.5.2 and survey package version 3.35.1, but the syntax may change in future releases. Review the documentation for the software version you are using for any changes.
Page last reviewed: 8/4/2020
| 2020-10-29T01:52:19 |
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|
http://dlmf.nist.gov/6.4
|
# §6.4 Analytic Continuation
Analytic continuation of the principal value of $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ yields a multi-valued function with branch points at $z=0$ and $z=\infty$. The general value of $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ is given by
6.4.1 $\mathop{E_{1}\/}\nolimits\!\left(z\right)=\mathop{\mathrm{Ein}\/}\nolimits\!% \left(z\right)-\mathop{\mathrm{Ln}\/}\nolimits z-\EulerConstant;$
compare (6.2.4) and (4.2.6). Thus
6.4.2 $\mathop{E_{1}\/}\nolimits\!\left(ze^{2m\pi i}\right)=\mathop{E_{1}\/}\nolimits% \!\left(z\right)-2m\pi i,$ $m\in\Integer$,
and
6.4.3 $\mathop{E_{1}\/}\nolimits\!\left(ze^{\pm\pi i}\right)=\mathop{\mathrm{Ein}\/}% \nolimits\!\left(-z\right)-\mathop{\ln\/}\nolimits z-\EulerConstant\mp\pi i,$ $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\pi$.
The general values of the other functions are defined in a similar manner, and
6.4.4 $\displaystyle\mathop{\mathrm{Ci}\/}\nolimits\!\left(ze^{\pm\pi i}\right)$ $\displaystyle=\pm\pi i+\mathop{\mathrm{Ci}\/}\nolimits\!\left(z\right),$ 6.4.5 $\displaystyle\mathop{\mathrm{Chi}\/}\nolimits\!\left(ze^{\pm\pi i}\right)$ $\displaystyle=\pm\pi i+\mathop{\mathrm{Chi}\/}\nolimits\!\left(z\right),$ 6.4.6 $\displaystyle\mathop{\mathrm{f}\/}\nolimits\!\left(ze^{\pm\pi i}\right)$ $\displaystyle=\pi e^{\mp iz}-\mathop{\mathrm{f}\/}\nolimits\!\left(z\right),$ 6.4.7 $\displaystyle\mathop{\mathrm{g}\/}\nolimits\!\left(ze^{\pm\pi i}\right)$ $\displaystyle=\mp\pi ie^{\mp iz}+\mathop{\mathrm{g}\/}\nolimits\!\left(z\right).$
Unless indicated otherwise, in the rest of this chapter and elsewhere in the DLMF the functions $\mathop{E_{1}\/}\nolimits\!\left(z\right)$, $\mathop{\mathrm{Ci}\/}\nolimits\!\left(z\right)$, $\mathop{\mathrm{Chi}\/}\nolimits\!\left(z\right)$, $\mathop{\mathrm{f}\/}\nolimits\!\left(z\right)$, and $\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$ assume their principal values, that is, the branches that are real on the positive real axis and two-valued on the negative real axis.
| 2016-05-30T10:43:36 |
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|
https://par.nsf.gov/biblio/10365012-multiphase-ism-hyperluminous-starburst-spt
|
Multiphase ISM in the z = 5.7 Hyperluminous Starburst SPT 0346–52
Abstract
With ΣSFR∼ 4200Myr−1kpc−2, SPT 0346–52 (z= 5.7) is the most intensely star-forming galaxy discovered by the South Pole Telescope. In this paper, we expand on previous spatially resolved studies, using ALMA observations of dust continuum, [Nii] 205μm, [Cii] 158μm, [Oi] 146μm, and undetected [Nii] 122μm and [Oi] 63μm emission to study the multiphase interstellar medium (ISM) in SPT 0346–52. We use pixelated, visibility-based lens modeling to reconstruct the source-plane emission. We also model the source-plane emission using the photoionization codecloudyand find a supersolar metallicity system. We calculateTdust= 48.3 K andλpeak= 80μm and see line deficits in all five lines. The ionized gas is less dense than comparable galaxies, withne< 32 cm−3, while ∼20% of the [Cii] 158μm emission originates from the ionized phase of the ISM. We also calculate the masses of several phases of the ISM. We find that molecular gas dominates the mass of the ISM in SPT 0346–52, with the molecular gas mass ∼4× higher than the neutral atomic gas mass and ∼100× higher than the ionized gas mass.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10365012
Journal Name:
The Astrophysical Journal
Volume:
928
Issue:
2
Page Range or eLocation-ID:
Article No. 179
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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One of the most fundamental baryonic matter components of galaxies is the neutral atomic hydrogen (Hi). At low redshifts, this component can be traced directly through the 21 cm transition, but to infer the Higas content of the most distant galaxies, a viable tracer is needed. We here investigate the fidelity of the fine-structure transition of the (2P3/22P1/3) transition of singly ionized carbon Ciiat 158μm as a proxy for Hiin a set simulated galaxies atz≈ 6, following the work by Heintz et al. We select 11,125 star-forming galaxies from thesimbasimulations, with far-infrared line emissions postprocessed and modeled within the Sigameframework. We find a strong connection between Ciiand Hi, with the relation between this Cii-to-Hirelation (β[CII]) being anticorrelated with the gas-phase metallicity of the simulated galaxies. We further use these simulations to make predictions for the total baryonic matter content of galaxies atz≈ 6, and specifically the Higas mass fraction. We find mean values ofMH I/M= 1.4 andMH I/Mbar,tot= 0.45. These results provide strong evidence for Hibeing the dominant baryonic matter component by mass in galaxies atz≈ 6.
5. Abstract
The nearby, luminous infrared galaxy NGC 7469 hosts a Seyfert nucleus with a circumnuclear star-forming ring and is thus the ideal local laboratory for investigating the starburst–AGN (active galactic nucleus) connection in detail. We present integral-field observations of the central 1.3 kpc region in NGC 7469 obtained with the JWST Mid-InfraRed Instrument. Molecular and ionized gas distributions and kinematics at a resolution of ∼100 pc over the 4.9–7.6μm region are examined to study the gas dynamics influenced by the central AGN. The low-ionization [Feii]λ5.34μm and [Arii]λ6.99μm lines are bright on the nucleus and in the starburst ring, as opposed to H2S(5)λ6.91μm, which is strongly peaked at the center and surrounding ISM. The high-ionization [Mgv] line is resolved and shows a broad, blueshifted component associated with the outflow. It has a nearly face-on geometry that is strongly peaked on the nucleus, where it reaches a maximum velocity of −650 km s−1, and extends about 400 pc to the east. Regions of enhanced velocity dispersion in H2and [Feii] ∼ 180 pc from the AGN that also show highL(H2)/L(PAH) andL([Feii])/L(Pfα) ratios to the W and N of the nucleus pinpoint regions where the ionized outflow is depositing energy, via shocks, into themore »
| 2023-02-04T18:46:47 |
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https://cosmos.esa.int/web/gaia-users/archive/extract-data
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### Help support
Should you have any question, please check the Gaia FAQ section or contact the Gaia Helpdesk
# Graphical User Interface
The Graphical User Interface (GUI) of the Gaia ESA Archive offers the possibility to carry out basic and advanced queries using ADQL (Astronomical Data Query Language). The outputs of these queries can be easily downloaded in a variety of formats, including VOTable, FITS, CSV, and eCSV. Below you can find a brief description of the main features offered by the Archive, as well as two video tutorials explaining how to use it.
### Landing page
This is the landing page to the Gaia ESA Archive. From here, you can:
• explore the catalogues hosted by the Archive,
• access the documentation and help pages,
• learn about the Gaia mission.
### Basic query form
This form allows to easily search for data in all the catalogues hosted by the Archive. Restrictions can be added to the query using the 'Extra conditions' wizard. The output fields can be selected by means of the 'Display columns' option panel.
This form allows to execute ADQL queries. Each query generates a job at the server side. The jobs executed by the user can be inspected in the list provided in this page. All the public tables and the user-uploaded tables are visible on the left side of the browser.
### Query results
The output of queries are displayed in this window. The ADQL query that generated these results can be inspected by clicking on the 'Show query in ADQL form' link.
### Video: How to use the Archive
Author: Deborah Baines
### Video: How to use the Archive basic form
Author: Deborah Baines
# Tutorial: Basic queries
Authors: Héctor Cánovas, Jos de Bruijne and Alcione Mora.
The main function of the Gaia Archive is to provide data to the astronomers. The Search tab in the GUI landing page provides two different ways of accesing the Archive for Basic (default option) and Advanced (ADQL) queries. The main objectives for the Basic tab are:
• To ease the exploration of the Archive catalogues for simple use cases, and
• To help users into the transition towards the Advanced (ADQL) tab for complex use cases.
To that end, the Basic tab allows to perform two of the most common operations executed when exploring an astronomy archive in a very simple and intuitive manner. These operations are the ADQL cone search, which allows to search by coordinates for one or more sources in a given catalogue, and an ADQL query to retrieve all the sources encompassed by a circular or box-like region in the projected sky.
All Basic queries are synchronous, which means that they will time out after 60 and 90 seconds for non-registered and registered users, respectively (see this FAQ). Furthermore, the output of these queries is limited to 2000 sources. Therefore, we recommend to use the Advanced (ADQL) tab to execute complex and/or long queries. Through this tutorial you will learn to use the Basic tab to:
### 1. single source data retrieval
The most basic use case could be formulated as "I want the most relevant Gaia results for a single object". It can be accomplished using the Basic > Position subtab. The first step is to fill in the "Name" box with either the object identifier (e.g. "UX Ori") or its ICRS coordinates. The accepted input formats are described in the pop-up window that appears when clicking on top of the "Name" tooltip (see Fig. 1). The single object search launches an ADQL cone search around the celestial coordinates of the input object, which are provided by the Sesame name resolver. The drop-down menu highlighted by the thin solid circle in Fig. 1 allows to choose the service that will be queried to obtain the object coordinates (by default the system tries Simbad, then NED, and then Vizier, but if the input name is a Gaia designation the system queries the Gaia Archive). Once the name or coordinates are successfully resolved the object box turns green and a confirmation message is shown. Note that epoch propagation (see this tutorial) is applied if the proper motions of the resolved source are included in the databases searched for by the name resolver. The cone search radius can be tuned using the "Radius" box, and its units can be adjusted using its associated drop-down menu (highlighted by the dashed circle in Fig. 1).
Figure 1: Content of the Basic > Position subtab (single source resolver). The vertical arrows highlight the tooltips with explanatory text, while the circles and the horizontal arrow highlight the drop-down menus and extra options available to customize the query, respectively.
The cone search is centred around the coordinates provided by the name resolver. These coordinates are propagated to the target catalogue epoch if the proper motions of the object are known.
The next step is to choose the catalogue that is going to be explored. The latest Gaia data release is the default one, but all the catalogues hosted by the Archive (e.g., previous Gaia data releases, external catalogues) containing geometric information in the form of celestial coordinates can be explored by clicking on the drop-down menu highlighted by the thick circle in Fig. 1. Registered users can also access to their user-uploaded tables provided that their tables contain indexed celestial coordinates (see this tutorial). By default, only a few pre-selected columns of the choosen catalogue are shown in the query outputs. Therefore, you may want to verify that the output of your search will contain the columns that you are interested in. To do so, simply click on the "Display columns" menu (indicated by the dashed horizontal arrow in Fig. 1) and mark the columns that you want to retrieve.
Now you are ready to hit the "Submit Query" button. If you are interested in learning how your query is expressed in the ADQL language, you can hit the "Show Query" button. The query results are shown in the Query Results tab, whose contents are explained in the Understanding the query results section below.
### 2. Multiple source data retrieval
Three common use cases are:
An informative message is displayed once the content of the uploaded file is validated. Please wail until the validation finishes before pressing the “submit query” button.
#### 2.1 Search for the Gaia counterparts of my source list
This popular use case can be accomplished using the Basic > File subtab of the GUI. First of all, you must prepare a single column ascii file (without header) with the names or ICRS oordinates of the objects you are interested in. The input file must be formatted as described in the pop-up window that appears when clicking on top of the "Select a file with Target names" tooltip (see Fig. 2). Second, select the file that you want to upload using the wizard that appears when clicking on top of the "Choose file" button. Be aware that the query output is limitted to 2000 sources. If you aim to retrieve a larger dataset you should upload your target list to your user space as explained in this tutorial, and then use the Advanced (ADQL) tab to perform a cross-match as explained in this other tutorial.
Figure 2: Content of the Basic > File subtab (multi source resolver). The arrow highlight the tooltip with explanatory text.
#### 2.2 Search for the neighbours of my favourite source
Imagine that we want to retrieve all the sources from the Gaia EDR3 catalogue that, on-sky, are separated by less than 5 arc minutes from UX Ori. This can easily be achieved by simply updating the cone search radius units (using the drop-down menu highlighted by the red dashed circle in Fig. 1). This query outputs 195 sources, including several sources without parallax data. The Basic > Position subtab allows to apply additional selection criteria to e.g., filter out the targets with parallax signal-to-noise below a given threshold. To do so simply click on the "Extra conditions" drop-down menu as highlighted by the horizontal solid arrow in Fig. 1. A menu that allows to apply and combine different filters will show up as illustrated by Fig. 3. Applying the condition exemplified in Fig. 3 reduces the output of the previous query to 30 sources.
Figure 3: Content of the "Extra conditions" menu of the Basic > Position subtab. The arrow indicate how to select the operators that will be included in the query. The solid and dashed circles highlight the drop-down menus allowing to select the column over which the operator is going to be applied and the filter combination, respectively.
#### 2.3 Search for the neighbours of my source list
This use case is a combination of the previous two cases. If you are interested in retrieving the neighbours of a pre-computed source list you should 1) upload the target list as explained in Sect 2.1 and 2) then adjust the cone search radius as described in Sect 2.2. As before, you should keep in mind that the output catalogue of the query is limitted to 2000 sources so you may want to apply a selection criteria using the "Extra conditions" menu as described in Sect 2.2.
### 3. Retrieve sources in a region of the sky
A cone search with an arbitrary radius can be generated around any point on the celestial sphere by entering the target coordinates in the "Name" box and adjusting the cone search radius as explained in the Single source data retrieval section. Alternatively, it is also possible to use the "Equatorial" button under the Basic > Position subtab (see Fig. 1) and choosing the "Circle" option (see Fig. 4). The Basic > Position subtab also allows to retrieve the sources encompassed by a box region in the projected sky. To do so, simply select the "Box" option, as illustrated by Fig. 4. The accepted formats of the input coordinates are described in the RA and Dec tooltips of the coordinate boxes. As with the previous options, it is also possible to add different selection criteria to filter out the query output by means of the "Extra conditions" menu.
Figure 4: Content of the "Box" menu of the Basic > Position (Equatorial) subtab. The arrows indicate the tooltips with explanatory text.
A box is defined as a spherical quadrilateral delimited by great circle segments. This can provide counter-intuitive results, and require extra care, when the area analysed is large or close to the celestial poles. The reason is parallels (constant declination loci) are not great circles, and thus unsupported by ADQL.
### 4. Query Results
The query results are presented in tabular format in the Query Results subtab that is automatically opened once the query is finished, as shown by Fig. 5. The columns provide units when available. Further details on the meaning of each field can be found in the "<Target Catalogue> Data Model" accessible in the bottom part. Figure 5 shows the results of searching for the Gaia EDR3 counterparts of a list of sources (Sect. 2.1) and therefore the link points to the authoritative reference on the Gaia EDR3 contents. For this example only five columns ("source_id", "ra", "dec", "parallax", and "phot_g_mean_mag") were selected for displaying (using the "Displayed columns" menu as explained in Sect. 1). When the query consist in finding counterparts of an input source list in a given catalogue (as in this example), the output table contains additional columns that are automatically added by the Archive to aid the user in finding the correspondence between the input targets and the query results. These columns are:
• "target_id": contains the input target name as provided by the user in the input target list.
• "target_id, target_ra, target_dec, target_parallax, target_pm_ra, target_pm_dec, target_radial_velocity": contain data provided by the Name resolver (see Sect. 1).
• "target_distance": contains the on-sky angular separation (in units of degrees) between the target coordinates provided by the Name resolver and the target coordinates of the selected catalogue (Gaia EDR3 in this example).
Figure 5: Query Results subtab (see text for detailed explanation). The arrows indicate the tooltips with explanatory text.
Clicking over the "Show query in ADQL form" button will open the Advanced (ADQL) tab to show the ADQL query that has been launched. This utility can be helpful for non-expert users aiming to learn the ADQL query language. Finally,the query output can be downloaded using the "Download results" menu (indicated by a vertical arrow in Fig. 5). The format of the output file can be set by means of the drop-down menu highlighted by the red circle in Fig. 5.
Authors: Héctor Cánovas & Alcione Mora
The Advanced (ADQL) form of the GUI allows to execute complex ADQL queries, inspect the Archive catalogues, upload tables to the user space, and take advantage of a number of utilities developed by our team to facilitate the exploration and scientific exploitation of the Gaia Archive. All Advanced (ADQL) queries are asynchronous, which means that they will time out after 90 and 120 minutes for non-registered and registered users, respectively (see the "Why does my query time out after 90 minutes? Why is my query limited to 3 million rows?" FAQ). The output of these queries is limited to 3,000,000 sources for non-authenticated users, whereas it is unlimited for authenticated ones. The Advanced (ADQL) tab is divided in three main areas that are highlighted in Fig. 1.:
Figure 1: Content of the Advanced (ADQL) tab. The large red-wrinkled and blue-solid rectangles encompass the ADQL query editor and Jobs list areas, respectively. The large black rectangle contains the tables tree.
### 1. The ADQL query editor
This box allows to introduce ADQL queries to explore the catalogues hosted by the Archive. Many of the most common types of queries that are executed in the Archive (like cone searches, cross-matches, or computing the proper motion propagation of a given sample of objects) can be loaded by clicking on top of the "Query Examples" text (see Fig. 1). All these examples, along with a basic explanation and a reference (when appropriate) can also be found under the "Writting Queries/Query Examples" section of the left-side menu of this page. For more information and references about the ADQL language please take a look at the "Writting queries/ADQL syntax" section of that menu. Pressing the "Submit Query" button launches the query, which in turn generates a "job" in the Archive. A job has several attributes, including the results that contain the output of the launched ADQL query. The job ID can be specified before launching the query using the "Job name" box. This utility helps reminding the goal of a given query when visiting the Archive in the future. The job results are presented in a tabular form and - once a job succesfully finishes - they can be examined by clicking on top of the table-like icon located in the Jobs list (highlighted by the red circle in Fig. 1). This action will show up a table in the Query Results tab (see the "Understanding the Query Results" section of this tutorial to learn more details about the content of this tab).
### 2. The jobs LIST
Each row of the Jobs list contains relevant information about the jobs previously launched, like:
• The status (a job can be succesfully finished, failed, or it can be under execution),
• The job ID (either an alpha-numeric code assigned by the Archive or a user-defined name),
• The creation date,
• The number of rows of the job result, and
• The size of the job result.
The jobs launched by registered users are stored in their accounts, which have a job quota limit of 2 GB. The number of jobs stored in an account is shown at the bottom left of the page (in the example shown in Fig. 1 there are 183 jobs stored). This number appears surrounded by two pair of arrows that allow to navigate through the job list. The expandable menu "Apply jobs filter" allows to select jobs executed within a given range of time, as well as to filter out jobs by their status (e.g., completed, aborted, executing, etc.) Jobs can be deleted by means of the "Delete selected jobs" option. Additionaly, the Jobs list contains 7 buttons (encompassed by the small blue rectangle in Fig. 1) that, from left to right, allow to:
• Obtain detailed job information,
• Export the job result to a table and upload it to the user account (see this tutorial for details),
• Upload the job result to the user VOspace,
• Examine the job result in the Query Results tab,
• Show the ADQL query that generated the job in the ADQL parser, and
• Explore the datalink products (if any) associated to the job results.
### 3. The tables tree
The tables tree allows to directly access to all the catalogues hosted by the Archive. These catalogues are organised under different branches that can be expanded by clicking on the "+" sign next to each schema name (see Fig. 2). A first look at this box shows that the tables have three different types of associated icons. Tables having indexed celestial coordinates are marked with an spherical-like icon, and they can be explored within the Basic query tab (see Fig. 1 in this tutorial). The tables lacking indexed coordinates column are marked with a table-like icon, while the cross-matches between two tables are marked with a double-star like icon. Clicking on top of a table name will open a pop-up window with basic information about the table. From that window it is also possible to directly show the first 20 rows of the table, which will open in the Query Results tab. Clicking on the "+" sign next to each table name will expand the table content to show its column names. Indexed columns appear with bold fonts, and the (indexed) primary key of the table appears in bold red fonts.
Figure 2. Left: Selected content of the Catalogue box. The yellow pop-up window appears after clicking on top of the table name. Right: Content of the "gaiaedr3.gaia_source" catalogue, that is revealed by clicking on top of the "+" sign next to the table name.
From left to right, the five buttons placed on top of the catalogue schemas (encompassed by the small black rectangle in Fig. 1) allow to:
• Remove a table from the user space,
• Run a positional cross-match between two tables,
• Edit the table properties, and
• Share a table with the members of a given group (see this tutorial for more information about the sharing capabilities of the Archive).
Furthermore, it is possible to easily combine the catalogues and tables hosted by the Gaia Archive with other catalogues hosted by external TAP services. To access to this advanced utility click on top of the arrow encompassed by the black circle as indicated in Fig. 1. This dedicated tutorial explains how to make use of this this powerful functionality.
Authors: Héctor Cánovas, Jos de Bruijne, and Alcione Mora
The Gaia ESA Archive is based on the Virtual Observatory Table Access Protocol (TAP), which allows to retrieve data from astronomical databases using ADQL queries. The Archive offers a number of powerful functionalities for advanced users, as presented in this tutorial.
Tutorial content:
This mechanism allows to run a query against a job that already exists in the Archive, using the unique alpha-numeric code assigned to each job (the job ID, as explained in Sect. 2 of this tutorial). For example, let us assume that we have retrieved a sample of Gaia DR2 sources encompassed by a 1 degree radius circle centred in HL Tauri, located in the Taurus star forming region, as follows:
SELECT source_id, ra, dec, pmra, pmdec, parallax, phot_g_mean_mag
WHERE 1 = CONTAINS(POINT(67.91046, 18.23274), CIRCLE(ra, dec, 1.))
AND parallax_over_error > 10.
The job associated to this query will appear in the job list area of the Advanced (ADQL) tab of the Archive. In our case, it is job ID "1641568769115O". Having this information at hand, it is easy to identify the Gaia EDR3 sources matched to the output of the previous query using the pre-computed Gaia EDR3 - Gaia DR2 cross-match table ("gaiaedr3.dr2_neighbourhood" - see Chapter 10 of the Gaia EDR3 online documentation) as follows:
SELECT intermediate.*, dr3Xdr2.*
JOIN gaiaedr3.dr2_neighbourhood AS dr3Xdr2
ON dr3xdr2.dr2_source_id = source_id
There are many TAP services around the globe (an extensive list of TAP servers can be found here). This section explains how to discover, explore, and combine data from external TAPs within the Gaia Archive, which implements the Global TAP Schema (GloTS) maintained by GAVO. Advanced users may also use the excellent TAP client TOPCAT to retrieve data from different TAP servers.
Imagine we want to combine HST/ACS photometry from the NGC 346 open cluster analysed by Gouliermis+ (2006) with Gaia data. The first step is to look for this resource. First, once in the Advanced (ADQL) tab of the Archive, we need to click on the scrollable menu showing "gaia" on top of the tables tree, and then in "External TAP search" as indicated in Fig. 1 below:
Figure 1: Screenshot of the Advanced (ADQL) tab showing how to use the external TAP search functionality. First, click on the downwards arrow encompassed by the red circle. After selecting "External TAP search", a pop-up window appears on the screen. In this example, introducing "gouliermis ngc 346" in the "Search keywords" box shows 3 TAP tables, all of them hosted by the VizieR TAP service at CDS. The content of these tables can be visually inspected by selecting them and clicking on top of of the "Add selected" button encompassed by the red ellipsoid.
After clicking on "Add selected", the Archive is instructed to send future requests to the external TAP of our choice (in this example that would be the TAP VizieR service at CDS). At this stage, standard ADQL commands can be entered in the Gaia Archive user interface while these commands will be run at CDS. For example, the following query retrieves the entire Gouliermis+ (2006) catalogue:
SELECT * FROM "J/ApJS/166/549/table2"
*Note: VizieR table names include special characters and must be enclosed within quotes inside the ADQL query.
When selecting an external TAP, the Advanced (ADQL) tab interface changes as illustrated by Fig. 2 to highlight that only the external TAP tables are accessible at this time. This means that, in addition to the selected table, all catalogues hosted by the TAP service of the external data centre can be queried using the ADQL query editor on the Gaia Archive, provided we know the table name (and associated field names) of the external catalogue. For example, the following query will retrieve the first 10 entries from the Spitzer C2D legacy catalogue (Evans et al. 2009):
SELECT TOP 10 * FROM "J/ApJ/672/914/table2"
Figure 2: Screenshot of the Advanced (ADQL) tab showing the interface changes that appear when the Gaia Archive is connected to an external TAP server: 1) the tables tree only displays the selected table in the previous step (see Fig. 1), 2) the ADQL query editor background adopts a "blueish" colour and the external TAP url is shown on top of the editor, and 3) the executed jobs are displayed in the job list using blue fonts.
In order to stop the connection to the external TAP server, simply click on the drop-down menu on top of the table tree (see red circle in Fig. 1) and select "gaia".
The typical workflow for using external catalogues requires the combination (join) of the externally retrieved data with those hosted in the Gaia Archive. One possibility is uploading the table to the user space, as explained in the "Upload a user table" tutorial. For small catalogues, or those to be used only once, it is also possible to use JOB_UPLOAD functionality as explained in Sect. 1.
## 3. TAP_UPLOAD: Run queries in an external TAP
Sometimes the combination goes in the opposite direction. Imagine that we want to complement the dataset created in Sect. 1 above with the CATWISE 2020 photometry that available in the VizieR TAP server. As a first step, we can find the catalogue following the steps listed in Sect. 2 above and searching for keyword "catwise". Once the external TAP connection is established, our dataset can be uploaded and included in the query using the TAP_UPLOAD ADQL feature as follows:
SELECT upload.*, catwise.*
JOIN "II/365/catwise" AS catwise ON 1 = CONTAINS(
POINT('ICRS', catwise.RA_ICRS, catwise.DE_ICRS),
*Note: The VizieR TAP server requires that the first element of the POINT & CIRCLE functions is an string. Additionaly, these functions are optimised differently than in the Gaia Archive, as the coordinates of the larger (smaller) catalogue should be placed in the POINT (CIRCLE) function to obtain optimal performance.
Authors: Héctor Cánovas, Jos de Bruijne, Enrique Utrilla, and Alcione Mora
## Directory structure
### Gaia (E)DR3
The content of the entire gaia_source table is partitioned in multiple files based on 3386 ranges of HEALPix level-8 indexes. In this way, each file (except for the last one) contains around 500,000 sources. There is one file for each of those ranges, identified by a suffix containing the first and the last HEALPix level-8 indexes included in it (except if the range contains no source at all, in which case no file is generated). For example, the file "GaiaSource_000000-003111.csv.gz" contains all Gaia DR3 sources encompassed between HEALPix level-8 indices 0 and 3111. The same partitioning has been applied to all the tables in the (E)DR3 release, with the following exceptions:
• the tables that do not have a source_id field, i.e., total_galactic_extinction_map, total_galactic_extinction_map_opt, oa_neuron_information, and oa_neuron_xp_spectra, are very small and are each stored in a single file;
• the tables that do have a source_id field but have few entries (such as gaia_crf3_xm, science_alerts, and alerts_mixedin_sourceids) are each stored in a single file;
• the solar-system object (SSO) tables are split into 20 files.
Several tables that have been published in the Gaia EDR3 release are also applicable to Gaia DR3. These include pre-computed cross-match tables, simulated data, and the commanded scan law. These tables have not been duplicated in the DR3 repository but can be downloaded from the EDR3 repository.
For detailed information about the generation of these files, please read the Data Consolidation chapter in the Gaia DR3 documentation. For maximum compatibility, all files are plain text files in Enhanced Character Separated Value format (ECSV) format, compressed with the standard GZIP algorithm. ECSV files are regular CSV files, with an extra header with metadata about the table itself and its columns in YAML format, preceded with the "#" comment character.
### Gaia DR2
The content of the tables is partitioned in the same way as in the Gaia (E)DR3 case described above. However, in Gaia DR2 the file names contain the minimum and maximum source_id included in each file (instead of HEALPix index). For example, the file "GaiaSource_1000172165251650944_1000424567594791808.csv.gz" contains all Gaia DR2 sources encompassed between source_ids 1000172165251650944 and 1000424567594791808. For Gaia DR2, all files are plain text files in CSV format, compressed with the standard GZIP algorithm.
### entire catalogue
As explained in this FAQ, the "wget" command is a useful tool to download catalogues from the Gaia Archive bulk download directory. The following example shows how to retrieve the entire EDR3 gaia_source table:
wget --recursive --no-parent 'http://cdn.gea.esac.esa.int/Gaia/gedr3/gaia_source/'
As explained above, the Gaia (E)DR3 files have their associated minimum and maximum HEALPix level-8 indexes included in their names. By construction, a HEALPix index represents a selected area in the projected sky and it is possible to recover the central coordinates of this region using diffent tools available in the literature (like the Astropy-healpix package). The notebook below takes advantage of this information and utilities to identify all the files that contain sources in a circular region of the sky. In practice, it does something similar to an ADQL cone-search operation, but targeting the user-selected files stored in the bulk download directory. This notebook is convenient for users aiming to download large fractions of the Archive catalogues. This code has been tested in Python >= 3.8. The Jupyter notebook is included in this .zip file that also contains complementary notebooks, supplementary files, and a "tutorials.yml" environment file that can be used to create a conda environment with all dependencies needed to execute it (as explained in the official conda documentation). The file also includes a similar notebook but adapted to download Gaia DR1 and DR2 data.
Release number: v1.1 (2022-08-06)
Applicable Gaia Data Releases: Gaia EDR3, Gaia DR3
Author: Héctor Cánovas Cabrera; [email protected]
Summary:
This code computes the list of Gaia (E)DR3 files associated to a circular region in the sky defined by the user. The granularity of this region is set by the HEALPix level selected.
Input parameters:
• target catalogue (e.g., gaia_source, auxiliary/agn_cross_id, or auxiliary/frame_rotator_source),
• the cone-search parameters (centre and radius), and
• the desired healpix level.
Once the variables above are set the notebook creates a reference file that contains the min/max HEALPix index (levels: 6,7,8, and 9) encompassed by each gaia_source file available in the (E)DR3 bulk download directory.. The convertion between the different HEALPix levels is done by means of bit-shifting operations.
Useful URLs:
In [1]:
import os
from datetime import datetime
import numpy as np
import pandas as pd
from astropy import units as u
from astropy_healpix import HEALPix
## Set input variables¶
Default input paramers:
• DR3 = True ; Default Value. Set it to False to retrieve EDR3 files
• target_table = 'gaia_source' ; Alternative values: 'Astrophysical_parameters/astrophysical_parameters', 'Variability/vari_cepheid', etc - see all the content in: http://cdn.gea.esac.esa.int/Gaia/gdr3/ & http://cdn.gea.esac.esa.int/Gaia/gedr3/
• Cone-search parameters: radius = 0.5 degrees, centred in the Large Magallanic Cloud (in ICRS coordinates).
• Healpix-level = 6 (choose a larger one to increase granularity, and viceversa).
In [2]:
# Set input parameters below ===========
DR3 = True # Set it to False to select EDR3
target_table = 'gaia_source' # Alternative values: 'Astrophysical_parameters/astrophysical_parameters/', etc
hpx_level = 6
lon = 80.894 * u.deg # Right Ascencion (ICRS)
lat = -69.756 * u.deg # Declination (ICRS)
print(f'Input Variables: ')
print(f'* HEALPix level = {hpx_level} ')
print(f'* ICRS longitude (~ Right Ascension) = {lon} ')
print(f'* ICRS latitude (~ Declination) = {lat} ')
print()
Input Variables:
* HEALPix level = 6
* ICRS longitude (~ Right Ascension) = 80.894 deg
* ICRS latitude (~ Declination) = -69.756 deg
In [5]:
# Download basic parameters ============
if os.path.isdir(f'{output_dir}'):
now = datetime.now()
output_dir_2 = output_dir + now.strftime("_%Y-%m-%d")
print(f'>> Warning: {output_dir} directory exist. Creating alternative directory: {output_dir_2}')
print()
output_dir = output_dir_2
else:
os.system(f'mkdir {output_dir}')
Files will be downloaded to: downloads
## Create reference file¶
In [9]:
if DR3:
gaia_dr_flag = 'DR3'
else:
gaia_dr_flag = 'EDR3'
print('='*120)
print(f'Preparing selection of Gaia {gaia_dr_flag}: ""{target_table}" files')
print('='*120)
url_prefix = f'http://cdn.gea.esac.esa.int/Gaia/g{gaia_dr_flag.lower()}/{target_table}/'
md5sum_file_url = url_prefix + '_MD5SUM.txt'
if DR3:
md5sum_file.drop(md5sum_file.tail(1).index,inplace=True) # The last row in the "_MD5SUM.txt" file in the DR3 directories includes the md5Sum value of the _MD5SUM.txt file
md5sum_file
========================================================================================================================
Preparing selection of Gaia DR3: ""gaia_source" files
========================================================================================================================
Out[9]:
md5Sum file
2 0ee8a887c3db8cb5110354c42289b0a2 GaiaSource_005264-006601.csv.gz
4 b178d83fbe020b1f131c0aedcdc0cd29 GaiaSource_007953-010234.csv.gz
... ... ...
3381 20c69195b88742d586b0227d1831893a GaiaSource_783518-784479.csv.gz
3382 bf8bf6562d676df85787a23e62a05b79 GaiaSource_784480-784992.csv.gz
3383 158b295db422e9d024b8f6c8429aaa9d GaiaSource_784993-785417.csv.gz
3384 57c5737e81e2548ff0f1d57d7b667096 GaiaSource_785418-786096.csv.gz
3385 c084a93c691e81e616cb020d1bba2c60 GaiaSource_786097-786431.csv.gz
3386 rows × 2 columns
In [10]:
# Extract HEALPix level-8 from file name ======================================
healpix_8_min = [int(file[file.find('_')+1:file.rfind('-')]) for file in md5sum_file['file']]
healpix_8_max = [int(file[file.rfind('-')+1:file.rfind('.csv')]) for file in md5sum_file['file']]
reference_file = pd.DataFrame({'file':md5sum_file['file'], 'healpix8_min':healpix_8_min, 'healpix8_max':healpix_8_max}).reset_index(drop=True)
# Compute HEALPix levels 6,7, and 9 ===========================================
reference_file['healpix7_min'] = [inp >> 2 for inp in reference_file['healpix8_min']]
reference_file['healpix7_max'] = [inp >> 2 for inp in reference_file['healpix8_max']]
reference_file['healpix6_min'] = [inp >> 2 for inp in reference_file['healpix7_min']]
reference_file['healpix6_max'] = [inp >> 2 for inp in reference_file['healpix7_max']]
reference_file['healpix9_min'] = [inp << 2 for inp in reference_file['healpix8_min']]
reference_file['healpix9_max'] = [(inp << 2) + 3 for inp in reference_file['healpix8_max']]
# Generate reference file =====================================================
ncols = ['file', 'healpix6_min', 'healpix6_max', 'healpix7_min', 'healpix7_max', 'healpix8_min', 'healpix8_max', 'healpix9_min', 'healpix9_max']
reference_file = reference_file[ncols]
reference_file
Out[10]:
file healpix6_min healpix6_max healpix7_min healpix7_max healpix8_min healpix8_max healpix9_min healpix9_max
0 GaiaSource_000000-003111.csv.gz 0 194 0 777 0 3111 0 12447
1 GaiaSource_003112-005263.csv.gz 194 328 778 1315 3112 5263 12448 21055
2 GaiaSource_005264-006601.csv.gz 329 412 1316 1650 5264 6601 21056 26407
3 GaiaSource_006602-007952.csv.gz 412 497 1650 1988 6602 7952 26408 31811
4 GaiaSource_007953-010234.csv.gz 497 639 1988 2558 7953 10234 31812 40939
... ... ... ... ... ... ... ... ... ...
3381 GaiaSource_783518-784479.csv.gz 48969 49029 195879 196119 783518 784479 3134072 3137919
3382 GaiaSource_784480-784992.csv.gz 49030 49062 196120 196248 784480 784992 3137920 3139971
3383 GaiaSource_784993-785417.csv.gz 49062 49088 196248 196354 784993 785417 3139972 3141671
3384 GaiaSource_785418-786096.csv.gz 49088 49131 196354 196524 785418 786096 3141672 3144387
3385 GaiaSource_786097-786431.csv.gz 49131 49151 196524 196607 786097 786431 3144388 3145727
3386 rows × 9 columns
## Compute Healpix indexes associated to the selected circular region¶
In [11]:
print('='*120)
print(f'Computing HEALPix Level {hpx_level} encompasing a Cone Search (Radius, longitude, latitude): {radius.value} {radius.unit}, {lon.value} {lon.unit}, {lat.value} {lat.unit}')
print('='*120)
hp = HEALPix(nside=2**hpx_level, order='nested')
========================================================================================================================
Computing HEALPix Level 6 encompasing a Cone Search (Radius, longitude, latitude): 0.5 deg, 80.894 deg, -69.756 deg
========================================================================================================================
A .txt file with the list of files to be downloaded will be firts created. This file will be read and a secuencial download of all the files listed will start. A progress message will be in the terminal from where this Notebook was launched.
In [12]:
f = open(output_file, "w")
subset = []
for index in reference_file.index:
row = reference_file.iloc[index]
hp_min, hp_max = row[f'healpix{hpx_level}_min'], row[f'healpix{hpx_level}_max']
if np.any(np.logical_and(hp_min <= hp_cone_search, hp_cone_search <= hp_max)):
bulk_file = url_prefix + row['file'] + '\n'
f.write(bulk_file)
subset.append(bulk_file)
f.close()
print('='*120)
print('='*120)
========================================================================================================================
========================================================================================================================
In [13]:
print('='*120)
print('='*120)
os.system(f'wget -i {output_file} -P {output_dir}/ -q --show-progress --progress=bar:force 2>&1')
========================================================================================================================
0
| 2022-12-03T04:57:17 |
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|
https://control.com/textbook/continuous-level-measurement/echo/
|
Ultrasonic (Sound) Echo Level Measurement
Chapter 20 - Introduction to Continuous Level Measurement
A completely different way of measuring liquid level in vessels is to bounce a traveling wave off the surface of the liquid – typically from a location at the top of the vessel – using the time-of-flight for the waves as an indicator of distance, and therefore an indicator of liquid height inside the vessel. Echo-based level instruments enjoy the distinct advantage of immunity to changes in liquid density, a factor crucial to the accurate calibration of hydrostatic and displacement level instruments. In this regard, they are quite comparable with float-based level measurement systems.
From a historical perspective, hydrostatic and displacement level instruments have a richer pedigree. These instruments are simpler in nature than echo-based instruments, and were practical long before the advent of modern electronic technology. Echo-based instruments require precision timing and wave-shaping circuitry, plus sensitive (and rugged!) transceiver elements, demanding a much higher level of technology. However, modern electronic design and instrument manufacturing practices are making echo-based level instruments more and more practical for industrial applications. At the time of this writing (2008), it is common practice in some industries to replace old displacer level instruments with guided-wave radar instruments, even in demanding applications operating at high pressures.
Liquid-liquid interfaces may also be measured with some types of echo-based level instruments, most commonly guided-wave radar.
The single most important factor to the accuracy of any echo-based level instrument is the speed at which the wave travels en route to the liquid surface and back. This wave propagation speed is as fundamental to the accuracy of an echo instrument as liquid density is to the accuracy of a hydrostatic or displacer instrument. So long as this velocity is known and stable, good level measurement accuracy is possible. Although it is true that the calibration of an echo-based level instrument does not depend on process fluid density for the reason it does in hydrostatic- or displacement-based level instruments, this does not necessarily mean the calibration of an echo-based level instrument remains fixed as process fluid density changes. The propagation velocity of the wave used in an echo-based level instrument may indeed be subject to change as the process fluids change temperature or composition. For ultrasonic (sound) echo instruments, the speed of sound is a function of medium density. Thus, an ultrasonic level transmitter measuring time-of-flight through a vapor above the liquid may drift out of calibration if the speed of sound through that vapor changes substantially, which may happen if the vapor’s temperature or pressure happens to change. If the sound wave time-of-flight is measured while the waves pass through liquid, the calibration may drift if the speed of sound in that liquid changes substantially, which may happen if the liquid’s temperature changes. For radar (radio wave) echo instruments, the speed of radio wave propagation varies according to the dielectric permittivity of the medium. Permittivity is also affected by changes in density for the fluid medium, and so even radar level instruments may suffer calibration drift with process fluid density changes.
To summarize these effects, the speed of sound through any medium is a function of density and bulk modulus (the “compressibility” of the medium), with density generally being the more variable of the two. For gases and vapors, this means the speed of sound is strongly affected by changes in gas pressure and/or gas temperature. For liquids, this means the speed of sound is strongly affected by temperature. For solids, this means the speed of sound is weakly affected by temperature. The degree to which the speed of sound will be affected by temperature changes is directly related to the degree the medium’s density changes with temperature: solid materials generally expand and contract less than liquids over the same temperature range, thus the strong temperature effect for liquids and the weak temperature effect for solids.
Radio wave velocity is a function of dielectric permittivity, which is also a function of density. However, the degree of change in dielectric permittivity resulting from changes in pressure and/or temperature are generally much less than the degree of change in speed of sound for the same media and the same changes in pressure and/or temperature. This means that – all other factors being equal – an echo-based level instrument using radio waves will suffer far less calibration error than an echo-based level instrument using sound waves when process fluid pressure and/or temperature change. However, it should be noted that process fluid composition (i.e. its chemical make-up) may have a strong effect on radio wave propagation, not just on its time-of-flight but also on its ability to produce an adequate echo at the interface between two fluids.
Echo-based level instruments may also be “fooled” by layers of foam resting on top of the liquid, and the liquid-to-liquid interface detection models may have difficulty detecting non-distinct interfaces (such as emulsions). Irregular structures residing within the vapor space of a vessel (such as access portals, mixer paddles and shafts, ladders, etc.) may wreak havoc with echo-based level instruments by casting false echoes back to the instrument, although this problem may be mitigated by installing guide tubes for the waves to travel in, or using wave probes as in the cases of guided-wave radar instruments. Liquid streams pouring in to the vessel through the vapor space may similarly cause problems for an echo instrument. Additionally, all echo-based instruments have dead zones where liquid level is too close to the transceiver to be accurately measured or even detected (the echo time-of-flight being too short for the receiving electronics to distinguish from the incident pulse).
As you can see, echo-based level instruments have strengths and weaknesses just like any other type of level instrument. There is no “perfect” level instrument, but rather a wide array of choices from which the end-user must judiciously select for the particular application in mind. Beware of sales pitches urging you to buy the “perfect” level meter! The wise approach is to first research the underlying physics of the instrument, then determine how strongly its accuracy will be affected by realistic changes in process conditions (e.g. pressure, temperature, composition).
Ultrasonic level measurement
Ultrasonic level instruments measure the distance from the transmitter (located at some high point) to the surface of a process material located farther below using reflected sound waves. The frequency of these waves extend beyond the range of human hearing, which is why they are called ultrasonic. The time-of-flight for a sound pulse indicates this distance, and is interpreted by the transmitter electronics as process level. These transmitters may output a signal corresponding either to the fullness of the vessel (fillage) or the amount of empty space remaining at the top of a vessel (ullage).
Ullage is the “natural” mode of measurement for this sort of level instrument, because the sound wave’s time-of-flight is a direct function of how much empty space exists between the liquid surface and the top of the vessel. Total tank height will always be the sum of fillage and ullage, though. If the ultrasonic level transmitter is programmed with the vessel’s total height, it may calculate fillage via simple subtraction:
$\hbox{Fillage} = \hbox{Total height} - \hbox{Ullage}$
If a sound wave encounters a sudden change in the material’s speed of sound, some of that wave’s energy will be reflected in the form of another wave in the opposite direction. In other words, the sound wave will “echo” when it encounters a material having a different sonic velocity. This is the basis of all ultrasonic ranging devices. Thus, in order for an ultrasonic level transmitter to function reliably, the difference in sonic velocities at the interface between liquid and gas must be large. Distinct interfaces of liquid and gas almost always exhibit huge differences in their speeds of sound, and so are relatively easy to detect using ultrasonic waves. Liquids with a heavy layer of foam floating on top are more difficult, since the foam is less dense than the liquid, but considerably denser than the gas above. A weak echo will be generated at the interface of foam and gas, and another generated at the interface of liquid and foam, with the foam acting to scatter and dissipate much of the second echo’s energy.
The instrument itself consists of an electronics module containing all the power, computation, and signal processing circuits; plus an ultrasonic transducer to send and receive the sound waves. This transducer is typically piezoelectric in nature, being the equivalent of a very high-frequency audio speaker. The following photographs show a typical electronics module (left) and sonic transducer (right):
The ISA-standard designations for each component would be “LT” (level transmitter) for the electronics module and “LE” (level element) for the transducer, respectively. Even though we call the device responsible for transmitting and receiving the sound waves a transducer (in the scientific sense of the word), its function as a process instrument is to be the primary sensing element for the level measurement system, and therefore it is more properly designated a “level element” (LE).
This photograph shows a typical installation for an ultrasonic level-sensing element (LE), here sensing the level of wastewater in an open channel:
Electrical conduit serves to protect the signal cable from exposure to the elements as it routes back to an indoor location where the level transmitter (LT) is located.
If the ultrasonic transducer is rugged enough, and the process vessel sufficiently free of sludge and other sound-damping materials accumulating at the vessel bottom, the transducer may be mounted at the bottom of the vessel, bouncing sound waves off the liquid surface through the liquid itself rather than through the vapor space. As stated previously, any significant difference in sonic velocity between the two materials is sufficient to reflect a sound wave. This being the case, it shouldn’t matter which material the incident sound wave propagates through first:
This arrangement makes fillage the natural measurement, and ullage a derived measurement (calculated by subtraction from total vessel height).
$\hbox{Ullage} = \hbox{Total height} - \hbox{Fillage}$
As mentioned previously, the calibration of an ultrasonic level transmitter depends on the speed of sound through the medium between the transducer and the interface. For top-mounted transducers, this is the speed of sound through the air (or vapor) over the liquid, since this is the medium through which the incident and reflected wave travel time is measured. For bottom-mounted transducers, this is the speed of sound through the liquid. In either case, to ensure good accuracy, one must make sure the speed of sound through the “timed” travel path remains reasonably constant (or else compensate for changes in the speed of sound through that medium by use of temperature or pressure measurements and a compensating algorithm).
Ultrasonic level instruments enjoy the advantage of being able to measure the height of solid materials such as powders and grains stored in vessels, not just liquids. Again, the fundamental criterion for detecting a level of material is that the speeds of sound through the upper and lower materials must differ (the greater the difference, the stronger the echo). A unique challenge to solids measurement is the distinct possibility of uneven material profiles. A classic problem encountered when measuring the level of a powdered or granular material in a vessel is the angle of repose formed by the material as a result of being fed into the vessel at one point:
[Repose angle]
This angled surface is difficult for an ultrasonic device to detect because it tends to scatter the sound waves laterally instead of reflecting them strongly back toward the instrument. However, even if the scattering problem is not significant, there still remains the problem of interpretation: what is the instrument actually measuring? The detected level near the vessel wall will certainly register less than at the center, but the level detected mid-way between the vessel wall and vessel center may not be an accurate average of those two heights. Moreover, this angle may decrease over time if mechanical vibrations cause the material to “flow” and tumble from center to edge.
For this reason, solids storage measurement applications demanding high accuracy generally use other techniques, such as weight-based measurement (see section 20.6 for more information) or three-dimensional scanning (see section 26.3 for more information).
Radar level instruments measure the distance from the transmitter (located at some high point) to the surface of a process material located farther below in much the same way as ultrasonic transmitters – by measuring the time-of-flight of a traveling wave. The fundamental difference between a radar instrument and an ultrasonic instrument is the type of wave used: radio waves instead of sound waves. Radio waves are electromagnetic in nature (comprised of alternating electric and magnetic fields), and very high frequency (in the microwave frequency range – GHz). Sound waves are mechanical vibrations (transmitted from molecule to molecule in a fluid or solid substance) and of much lower frequency (tens or hundreds of kilohertz – still too high for a human being to detect as a tone) than radio waves. In any case, a wave will refect off of an interface of two different substances if those two substances possess different wave-propagation velocities.
Some radar level instruments use waveguide “probes” to guide the electromagnetic waves to and from the process liquid while others send electromagnetic waves out through open space to reflect off the process material. The instruments using waveguides are called guided-wave radar instruments, whereas the radar instruments relying on open space for signal propagation are called non-contact radar. The differences between these two varieties of radar instruments is shown in the following illustration:
Photographs of non-contact (left) and guided-wave (right) radar level transmitters are shown below. The non-contact transmitter is placed on a table for inspection while the guided-wave transmitter is installed in a “cage” similar to that of a displacement-style level transmitter attached to the vessel by two pipes:
Non-contact radar devices suffer much more signal loss than guided-wave radar devices, due to the natural tendency of electromagnetic radiation to disperse over space. Waveguides combat this signal loss by channeling the radio energy along a straight-line path. Probes used in guided-wave radar instruments may be single metal rods, parallel pairs of metal rods, or a coaxial metal rod-and-tube structure. Single-rod probes suffer the greatest energy losses, while coaxial probes excel at guiding the microwave energy to the liquid interface and back. However, single-rod probes are much more tolerant of process fouling than two-rod or (especially) coaxial probes, where sticky masses of viscous liquid and/or solid matter cling to the probe. Such fouling deposits, if severe enough, will cause electromagnetic wave reflections that “look” to the transmitter like the reflection from an actual liquid level or interface.
Non-contact radar instruments rely on antennas to direct microwave energy into the vessel, and to receive the echo (return) energy. These antennas must be kept clean and dry, which may be a problem if the liquid being measured emits condensible vapors. For this reason, non-contact radar instruments are often separated from the vessel interior by means of a dielectric window (made of some substance such as plastic that is relatively “transparent” to electromagnetic waves yet acts as an effective vapor barrier):
Electromagnetic waves travel at the speed of light, $$2.9979 \times 10^8$$ meters per second in a perfect vacuum. The velocity of an electromagnetic wave through space depends on the dielectric permittivity (symbolized by the Greek letter “epsilon,” $$\epsilon$$) of that space. A formula relating wave velocity ($$v$$) to relative permittivity (the ratio of a substance’s permittivity to that of a perfect vacuum, symbolized as $$\epsilon_r$$ and sometimes called the dielectric constant of the substance) and the speed of light in a perfect vacuum ($$c$$) is shown here:
$v = {c \over \sqrt{\epsilon_r}}$
As mentioned previously, the calibration of any echo-based level transmitter depends on knowing the speed of wave propagation through the medium separating the instrument from the process fluid interface. For radar transmitters sensing a single liquid below a gas or vapor, this speed is the speed of light through that gas or vapor space, which we know to be a function of electrical permittivity.
The relative permittivity of air at standard pressure and temperature is very nearly unity (1). This means the speed of light in air under atmospheric pressure and ambient temperature will very nearly be the same as it is for a perfect vacuum ($$2.9979 \times 10^8$$ meters per second). If, however, the vapor space above the liquid is not ambient air, and is subject to large changes in temperature and/or pressure which cause the vapor’s density to change, the permittivity of that vapor may substantially change and consequently skew the speed of light, and therefore the calibration of the level instrument. This calibration shift is sometimes referred to as the gas phase effect.
A formula useful for calculating the permittivity of any gas or vapor based on both pressure and temperature is shown here:
$\epsilon_r = 1 + (\epsilon_{ref} - 1) {P T_{ref} \over P_{ref} T}$
Where,
$$\epsilon_r$$ = Relative permittivity of a gas at a given pressure ($$P$$) and temperature ($$T$$)
$$\epsilon_{ref}$$ = Relative permittivity of the same gas at standard pressure ($$P_{ref}$$) and temperature ($$T_{ref}$$)
$$P$$ = Absolute pressure of gas (bars)
$$P_{ref}$$ = Absolute pressure of gas under standard conditions ($$\approx$$ 1 bar)
$$T$$ = Absolute temperature of gas (Kelvin)
$$T_{ref}$$ = Absolute temperature of gas under standard conditions ($$\approx$$ 273 K)
This formula is based on the principle that bulk permittivity is a function of density. We may see why this is by running a “thought experiment” in which a sample of gas becomes denser. As gas density increases, more gas molecules will become packed into the same volume of space. If each gas molecule’s permittivity is greater than the permittivity of empty space, then having more of those gas molecules present will mean the permittivity of that volume increases. Greater permittivity, of course, decreases the velocity of light through the gas, and thereby affects the calibration of the radar instrument.
Relating this concept to pressure and temperature variations in the gas, we can see that the permittivity of a gas increases with increasing pressure (by increasing gas density), and decreases with increasing temperature (by decreasing gas density). This means the speed of light through a gas decreases with increasing pressure, and increases with increasing temperature. For radar level instruments operating in gas environments subject to significant pressure and temperature (i.e. density) variations, the consequent variations in the speed of light through that gas will compromise the instrument’s accuracy.
For any echo-based level instruments, the necessary condition for an echo to occur is that the wave encounters a sudden change in propagation velocity. With ultrasonic level instruments, the velocity of propagation for the sound wave depends on both the densities and the bulk moduli (incompressibilities) of the substances, so that a sudden change in either parameter from one substance to another will cause the sound wave to reflect. With radar level instruments, the necessary condition for wave reflection is a sudden change in dielectric permittivity ($$\epsilon$$). When an electromagnetic wave encounters a sudden change in dielectric permittivity, some of that wave’s energy will be reflected in the form of another wave traveling the opposite direction, while the balance of the wave’s energy continues forward to propagate into the new material. The strength of the reflected signal depends on how greatly the two materials’ permittivities differ:
This same principle explains reflected signals in copper transmission lines as well. Any discontinuities (sudden changes in characteristic impedance) along the length of a transmission line will reflect a portion of the electrical signal’s power back to the source. In a transmission line, continuities may be formed by pinches, breaks, or short-circuits. In a radar level measurement system, any sudden change in electrical permittivity is a discontinuity that reflects some of the incident wave energy back to the source. Thus, radar level instruments function best when there is a large difference in permittivity between the two substances at the interface. As shown in the previous illustration, air and water meet this criterion, having an 80:1 permittivity ratio.
The ratio of reflected power to incident (transmitted) power at any interface of materials is called the power reflection factor ($$R$$). This may be expressed as a unitless ratio, or more often as a decibel figure. The relationship between dielectric permittivity and reflection factor is as follows:
$R = {\left({\sqrt{\epsilon_{r2}} - \sqrt{\epsilon_{r1}}}\right)^2 \over \left(\sqrt{\epsilon_{r2}} + \sqrt{\epsilon_{r1}}\right)^2}$
Where,
$$R$$ = Power reflection factor at interface, as a unitless ratio
$$\epsilon_{r1}$$ = Relative permittivity (dielectric constant) of the first medium
$$\epsilon_{r2}$$ = Relative permittivity (dielectric constant) of the second medium
The fraction of incident power transmitted through the interface ($$P_{forward} \over P_{incident}$$) is, of course, the mathematical complement of the power reflection factor: $$1 - R$$.
For situations where the first medium is air or some other low-permittivity gas, the formula simplifies to the following form (with $$\epsilon_r$$ being the relative permittivity of the reflecting substance):
$R = {\left({\sqrt{\epsilon_{r}} - 1}\right)^2 \over \left(\sqrt{\epsilon_{r}} + 1 \right)^2}$
In the previous illustration, the two media were air ($$\epsilon_r \approx 1$$) and water ($$\epsilon_r \approx 80$$) – a nearly ideal scenario for strong signal reflection. Given these relative permittivity values, the power reflection factor has a value of 0.638 (63.8%), or $$-1.95$$ dB. This means well over half the incident power reflects off the air/water interface to form a strong echo signal, with the remaining 0.362 (36.2%) of the wave’s power traveling through the air-water interface and propagating into water. If the liquid in question is gasoline rather than water (having a rather low relative permittivity value of approximately 2), the power reflection ratio will only be 0.0294 (2.94%) or $$-15.3$$ dB, with the vast majority of the wave’s power successfully penetrating the air-gasoline interface.
The longer version of the power reflection factor formula suggests liquid-liquid interfaces should be detectable using radar, and indeed they are. All that is needed is a sufficiently large difference in permittivity between the two liquids to create a strong enough echo to reliably detect. Liquid-liquid interface level measurement with radar works best when the upper liquid has a substantially lesser permittivity value than the lower liquid. A layer of hydrocarbon oil on top of water (or any aqueous solution such as an acid or a caustic) is a good candidate for guided-wave radar level measurement. An example of a liquid-liquid interface that would be very difficult for a radar instrument to detect is water ($$\epsilon_r \approx 80$$) above glycerin ($$\epsilon_r \approx 42$$).
If the radar instrument uses a digital network protocol to communicate information with a host system (such as HART or any number of “fieldbus” standards), it may perform as a multi-variable transmitter, transmitting both the interface level measurement and the total liquid level measurement simultaneously. This capability is rather unique to guided-wave radar transmitters, and is very useful in some processes because it eliminates the need for multiple instruments measuring multiple levels.
One reason why a lesser-$$\epsilon$$ fluid above a greater-$$\epsilon$$ fluid is easier to detect than the inverse is due to the necessity of the signal having to travel through a gas-liquid interface above the liquid-liquid interface. With gases and vapors having such small $$\epsilon$$ values, the signal would have to pass through the gas-liquid interface first in order to reach the liquid-liquid interface. This gas-liquid interface, having the greatest difference in $$\epsilon$$ values of any interface within the vessel, will be most reflective to electromagnetic energy in both directions. Thus, only a small portion of the incident wave will ever reach the liquid-liquid interface, and a similarly small portion of the wave reflected off the liquid-liquid interface (which itself is a fraction of the forward wave power that made it through the gas-liquid interface on its way down) will ever make it through the gas-liquid interface on its way back up to the instrument. The situation is much improved if the $$\epsilon$$ values of the two liquid layers are inverted, as shown in this hypothetical comparison (all calculations assume no power dissipation along the way, only reflection at the interfaces):
As you can see in the illustration, the difference in power received back at the instrument is nearly two to one, just from the upper liquid having the lesser of two identical $$\epsilon$$ values. Of course, in real life you do not have the luxury of choosing which liquid will go on top of the other (this being determined by fluid density), but you do have the luxury of choosing the appropriate liquid-liquid interface level measurement technology, and as you can see here certain orientations of $$\epsilon$$ values are less detectable with radar than others.
Another factor working against radar as a liquid-liquid interface measurement technology for interfaces where the upper liquid has a greater dielectric constant is that fact that many high-$$\epsilon$$ liquids are aqueous in nature, and water readily dissipates microwave energy. This fact is exploited in microwave ovens, where microwave radiation excites water molecules in the food, dissipating energy in the form of heat. For a radar-based level measurement system consisting of gas/vapor over water over some other (heavier) liquid, the echo signal will be extremely weak because the signal must pass through the “lossy” water layer twice before it returns to the radar instrument.
Electromagnetic energy losses are important to consider in radar level instrumentation, even when the detected interface is simply gas (or vapor) over liquid. The power reflection factor formula only predicts the ratio of reflected power to incident power at an interface of substances. Just because an air-water interface reflects 63.8% of the incident power does not mean 63.8% of the incident power will actually return to the transceiver antenna! Any dissipative losses between the transceiver and the interface(s) of concern will weaken the signal, to the point where it may become difficult to distinguish from noise.
Another important factor in maximizing reflected power is the degree to which the microwaves disperse on their way to the liquid interface(s) and back to the transceiver. Guided-wave radar instruments receive a far greater percentage of their transmitted power than non-contact radar instruments because the metal probe used to guide the microwave signal pulses help prevent the waves from spreading (and therefore weakening) throughout the liquids as they propagate. In other words, the probe functions as a transmission line to direct and focus the microwave energy, ensuring a straight path from the instrument into the liquid, and a straight echo return path from the liquid back to the instrument. This is why guided-wave radar is the only practical radar technology for measuring liquid-liquid interfaces.
A critically important factor in accurate level measurement using radar instruments is that the dielectric permittivity of every substance lying between the radar instrument and the interface of interest be accurately known. The reason for this is rooted in the dependence of electromagnetic wave propagation velocity to relative permittivity. Recalling the wave velocity formula shown earlier:
$v = {c \over \sqrt{\epsilon_r}}$
Where,
$$v$$ = Velocity of electromagnetic wave through a particular substance
$$c$$ = Speed of light in a perfect vacuum ($$\approx 3 \times 10^8$$ meters per second)
$$\epsilon_r$$ = Relative permittivity (dielectric constant) of the substance
In the case of a single-liquid application where nothing but gas or vapor exists above the liquid, the permittivity of that gas or vapor must be precisely known. In the case of a two-liquid interface with gas or vapor above, the relative permittivities of both gas and upper liquids must be accurately known in order to accurately measure the liquid-liquid interface. Changes in dielectric constant value of the medium or media through which the microwaves must travel and echo will cause the microwave radiation to propagate at different velocities. Since all radar measurement is based on time-of-flight through the media separating the radar transceiver from the echo interface, changes in wave velocity through this media will affect the amount of time required for the wave to travel from the transceiver to the echo interface, and reflect back to the transceiver. Therefore, changes in dielectric constant are relevant to the accuracy of any radar level measurement.
Factors influencing the dielectric constant of gases include pressure and temperature, which means the accuracy of a radar level instrument will vary as gas pressure and/or gas temperature vary! This is often referred to as the gas phase effect. Whether or not this variation is substantial enough to consider for any application depends on the desired measurement accuracy and the degree of permittivity change from one pressure/temperature extreme to another. In no case should a radar instrument be considered for any level measurement application unless the dielectric constant value(s) of the upper media are precisely known. This is analogous to the dependence on liquid density that hydrostatic level instruments face. It is futile to attempt level measurement based on hydrostatic pressure if liquid density is unknown or widely varying, and it is just as futile to attempt level measurement based on radar if the dielectric constants are unknown or varies widely.
One way to compensate for the gas phase effect in radar level instruments is to equip the instrument with a reference probe of fixed length oriented in such a way that its entire length is always above the liquid level (i.e. it only senses gas). If the permittivity of the gas is constant, the echo time along this reference probe will remain the same. If, however, the gas permittivity changes, the reference probe’s echo time will correspondingly change, allowing the instrument’s microprocessor to measure gas permittivity and consequently adjust calculations for liquid level based on this known change. This concept is analogous to the compensating probe sometimes used in capacitive level sensors, designed to measure fluid permittivity so as to compensate for any changes in this critical parameter.
As with ultrasonic level instruments, radar level instruments can sense the level of solid substances in vessels (e.g. powders and granules) and not just liquids. The same caveat of repose angle applicable to ultrasonic level measurement (see section [Repose angle] beginning on page ), however, is a factor for radar measurement as well. Also, low particulate solid density (i.e. significant amounts of air between the solid particles) tends to reduce the material’s dielectric constant and thereby weaken the radar echo.
Modern radar level instruments provide a wealth of diagnostic information to aid in troubleshooting. One of the most informative is the echo curve, showing each reflected signal received by the instrument along the incident signal’s path of travel. The following image is a screen capture of a computer display, from software used to configure a Rosemount model 3301 guided-wave radar level transmitter with a coaxial probe:
To view a flip-book animation showing how a guided-wave radar (GWR) instrument detects both liquid surface level and liquid-liquid interface level, turn to Appendix [animation_GWR_level] beginning on page .
Pulse P1 is the reference or fiducial pulse, resulting from the change in dielectric permittivity between the extended “neck” of the probe (connecting the transmitter to the probe tube) and the coaxial probe itself. This pulse marks the top of the probe, thereby establishing a point of reference for ullage measurement.
This next screen capture shows the same level transmitter measuring a water level that is 8 inches higher than before. Note how pulse P2 is further to the left (indicating an echo received sooner in time), indicating a lesser ullage (greater level) measurement:
Several threshold settings determine how the transmitter categorizes each received pulse. Threshold T1 for this particular radar instrument defines which pulse is the reference (fiducial). Thus, the first echo in time to exceed the value of threshold T1 is interpreted by the instrument to be the reference point. Threshold T2 defines the upper product level, so the first echo in time to exceed this threshold value is interpreted as the vapor/liquid interface point. Threshold T3 for this particular transmitter is used to define the echo generated by a liquid-liquid interface. However, threshold T3 does not appear in this echo plot because the interface measurement option was disabled during this experiment. The last threshold, T4, defines the end-of-probe detection. Set at a negative value (just like the reference threshold T1), threshold T4 looks for the first pulse in time to exceed that value and interprets that pulse as the one resulting from the signal reaching the probe’s end.
All along the echo curve you can see weak echo signals showing up as bumps. These echoes may be caused by discontinuities along the probe (solid deposits, vent holes, centering spacers, etc.), discontinuities in the process liquid (suspended solids, emulsions, etc.), or even discontinuities in the surrounding process vessel (for non-coaxial probes which exhibit varying degrees of sensitivity to surrounding objects). A challenge in configuring a radar level transmitter is to set the threshold values such that “false” echoes are not interpreted as real liquid or interface levels.
A simple way to eliminate false echoes near the reference point is to set a null zone where any echoes are ignored. The upper null zone (UNZ) setting on the Rosemount 3301 radar level transmitter whose screen capture image was shown previously was set to zero, meaning it would be sensitive to any and all echoes near the reference point. If a false echo from a tank nozzle or some other discontinuity near the probe’s entry point into the process vessel created a measurement problem, the upper null zone (UNZ) value could be set just beyond that point so the false echo would not be interpreted as a liquid level echo, regardless of the threshold value for T2. A “null zone” is sometimes referred to as a hold-off distance.
Some radar level instruments allow thresholds to be set as curves themselves rather than straight lines. Thus, thresholds may be set high during certain periods along the horizontal (time/distance) axis to ignore false echoes, and set low during other periods to capture legitimate echo signals.
Regardless of how null zones and thresholds are set for any guided-wave radar level transmitter, the technician must be aware of transition zones near each end of the probe. Measurements of liquid level or interface level within these zones may not be accurate or even linearly responsive. Thus, it is strongly advised to range the instrument in such a way that the lower- and upper-range values (LRV and URV) lie between the transition zones:
The size of these transition zones depends on both the process substances and the probe type. The instrument manufacturer will provide you with appropriate data for determining transition zone dimensions.
Laser level measurement
The least-common form of echo-based level measurement is laser, which uses pulses of laser light reflected off the surface of a liquid to detect the liquid level. Perhaps the most limiting factor with laser measurement is the necessity of having a sufficiently reflective surface for the laser light to “echo” off of. Many liquids are not reflective enough for this to be a practical measurement technique, and the presence of dust or thick vapors in the space between the laser and the liquid will disperse the light, weakening the light signal and making the level more difficult to detect.
However, lasers have been applied with great success in measuring distances between objects. Applications of this technology include motion control on large machines, where a laser points at a moving reflector, the laser’s electronics calculating distance to the reflector based on the amount of time it takes for the laser “echo” to return. The advent of mass-produced, precision electronics has made this technology practical and affordable for many applications. At the time of this writing (2008), it is even possible for the average American consumer to purchase laser “tape measures” for use in building construction.
Magnetostrictive level measurement
A variation on the theme of echo-based level instruments, where the level of some process material in a vessel is measured by timing the travel of a wave between the instrument and the material interface, is one applied to float-type instruments: magnetostriction.
In a magnetostrictive level instrument, liquid level is sensed by a lightweight, donut-shaped float containing a magnet. This float is centered around a long metal rod called a waveguide, hung vertically in the process vessel (or hung vertically in a protective cage like the type used for displacement-style level instruments) so that the float may rise and fall with process liquid level. The magnetic field from the float’s magnet at that point, combined with the magnetic field produced by an electric current pulse periodically sent through the rod, generates a torsional stress pulse at the precise location of the float. This torsional (twisting) stress travels at the speed of sound through the rod toward either end. At the bottom end is a dampener device designed to absorb the mechanical wave.
One might argue that a magnetostrictive instrument is not an “echo” technology in the strictest sense of the word. Unlike ultrasonic, radar, and laser instruments, we are not reflecting a wave off a discontinuous interface between materials. Instead, a mechanical wave (pulse) is generated at the location of a magnetic float in response to an electrical pulse. However, the principle of measuring distance by the wave’s travel time is the same. At the top end of the rod (above the process liquid level) is a sensor and electronics package designed to detect the arrival of the mechanical wave. A precision electronic timing circuit measures the time elapsed between the electric current pulse (called the interrogation pulse) and the received mechanical pulse. So long as the speed of sound through the metal waveguide rod remains fixed, the time delay is strictly a function of distance between the float and the sensor, which we already know is called ullage.
The following photograph (left) and illustration (right) show a magnetostrictive level transmitter propped up against a classroom wall and the same style of transmitter installed in a liquid-holding vessel, respectively:
The design of this instrument is reminiscent of a guided-wave radar transmitter, where a metal waveguide hangs vertically into the process liquid, guiding a pulse to the sensor head where the sensitive electronic components are located. The major difference here is that the pulse is a sonic vibration traveling through the metal of the waveguide rod, not an electromagnetic pulse as is the case with radar. Like all sound waves, the torsional pulse in a magnetostriction-based level transmitter is much slower-traveling than electromagnetic waves.
It is even possible to measure liquid-liquid interfaces with magnetostrictive instruments. If the waveguide is equipped with a float of such density that it floats on the interface between the two liquids (i.e. the float is denser than the light liquid and less dense than the heavy liquid), the sonic pulse generated in the waveguide by that float’s position will represent interface level. Magnetostrictive instruments may even be equipped with two floats: one to sense a liquid-liquid interface, and the other to sense the liquid-vapor interface, so that it may measure both the interface and total levels simultaneously just like a guided-wave radar transmitter:
With such an instrument, each electrical “interrogation” pulse returns two sonic pulses to the sensor head: the first pulse representing the total liquid level (upper, light float) and the second pulse representing the interface level (lower, heavy float). If the instrument has digital communication capability (e.g. HART, FOUNDATION Fieldbus, Profibus, etc.), both levels may be reported to the control system over the same wire pair, making it a “multivariable” instrument.
Perhaps the greatest limitation of magnetostrictive level instruments is mechanical interference between the float and the rod. In order for the magnetostrictive effect to be strong, the magnet inside the float must be in close proximity to the rod. This means the inside diameter of the donut-shaped float must fit closely to the outside diameter of the waveguide. Any fouling of the waveguide’s or float’s surfaces by suspended solids, sludge, or other semi-solid materials may cause the float to bind and therefore not respond to changes in liquid level.
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Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License
| 2020-04-01T21:09:35 |
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https://par.nsf.gov/biblio/10003014-measurement-zz-production-cross-section-limits-anomalous-neutral-triple-gauge-couplings-proton-proton-collisions-atlas-detector
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Measurement of the $ZZ$ Production Cross Section and Limits on Anomalous Neutral Triple Gauge Couplings in Proton-Proton Collisions at $s=7 TeV$ with the ATLAS Detector
| 2022-09-24T23:34:07 |
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https://pos.sissa.it/395/296/
|
Volume 395 - 37th International Cosmic Ray Conference (ICRC2021) - CRI - Cosmic Ray Indirect
Measurement of the Proton-Air Cross Section with Telescope Arrays Black Rock, Long Ridge, and Surface Array in Hybrid Mode.
R. Abbasi* and W. Hanlon
Full text: pdf
Pre-published on: July 31, 2021
Published on:
Abstract
Ultra High Energy Cosmic Ray (UHECR) detectors have been reporting on the proton-air cross section measurement beyond the capability of particle accelerators since 1984. The knowledge of this fundamental particle property is vital for our understanding of high energy particle interactions and could possibly hold the key to new physics. The data used in this work was collected over eight years using the hybrid events of Black Rock (BR) and Long Ridge (LR) fluorescence detectors as well as the Telescope Array Surface Detector (TASD). The proton-air cross section is determined at $\sqrt{s}=73$~TeV by fitting the exponential tail of the $X_{max}$ distribution of these events. The proton-air cross section is then inferred from the exponential tail fit and from the most updated high energy interaction models. $\sigma^{\mathrm{inel}}_{\mathrm{p-air}}$ is observed to
be $520.1 \pm 35.8$ [Stat.] $^{+25.3}_{-42.9}$[Sys.] mb. This is the second proton-air cross section work reported by the Telescope Array collaboration.
DOI: https://doi.org/10.22323/1.395.0296
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.
| 2021-08-03T03:09:06 |
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https://pos.sissa.it/256/323/
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Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Theoretical Developments
Nf = 1+2 mass dependence of the topological susceptibility
J. Frison,* R. Kitano, N. Yamada
*corresponding author
Full text: pdf
Pre-published on: February 18, 2017
Published on: March 24, 2017
Abstract
$m_u=0$ has long been proposed as a solution to the strong CP problem. While this solution is sometimes thought to have been excluded, it
is actually still ill-defined. In this work, we study the mass dependence of the physical observable $\chi_t$, the topological susceptibility.
Assigning an unphysically large value to the down mass allows to be more sensitive to the non-perturbative effects behind the $m_u=0$ ambiguity. Preliminary results are presented for four masses of clover fermions.
DOI: https://doi.org/10.22323/1.256.0323
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.
| 2020-12-02T10:30:24 |
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https://www.zbmath.org/authors/?q=ai%3Ajanko.zvonimir
|
# zbMATH — the first resource for mathematics
## Janko, Zvonimir
Compute Distance To:
Author ID: janko.zvonimir Published as: Janko, Z.; Janko, Zvonimir; Janko, Zvonivir External Links: MGP · Wikidata · GND
Documents Indexed: 128 Publications since 1959, including 7 Books Reviewing Activity: 53 Reviews
all top 5
#### Co-Authors
83 single-authored 19 Tran Van Trung 8 Berkovich, Yakov G. 5 Božikov, Zdravka 4 Tonchev, Vladimir D. 3 Kharaghani, Hadi 2 Thompson, John Griggs 1 Cigić, Vlado 1 Gagen, Terence Matthew 1 Newman, Mike Frederick 1 Wong, Seung Kai 1 Wong, Siu-kee
all top 5
#### Serials
20 Journal of Algebra 20 Glasnik Matematički. Serija III 14 Journal of Combinatorial Theory. Series A 8 Mathematische Zeitschrift 7 Periodicum Mathematico-Physicum et Astronomicum 6 Israel Journal of Mathematics 6 Journal of Group Theory 5 De Gruyter Expositions in Mathematics 4 Archiv der Mathematik 3 Acta Scientiarum Mathematicarum 3 Geometriae Dedicata 3 Journal für die Reine und Angewandte Mathematik 3 Journal of Algebra and its Applications 2 Discrete Mathematics 2 Studia Scientiarum Mathematicarum Hungarica 2 Journal of Combinatorial Designs 2 Journal of the Australian Mathematical Society 1 Canadian Journal of Mathematics 1 Radovi Matematički 1 Designs, Codes and Cryptography 1 Proceedings of the National Academy of Sciences of the United States of America
#### Fields
73 Group theory and generalizations (20-XX) 26 Combinatorics (05-XX) 17 Geometry (51-XX) 4 General and overarching topics; collections (00-XX)
#### Citations contained in zbMATH
80 Publications have been cited 669 times in 468 Documents Cited by Year
A new finite simple group with abelian Sylow 2-subgroups and its characterization. Zbl 0214.28003
Janko, Zvonimir
1966
Groups of prime power order. Vol. 2. Zbl 1168.20002
Berkovich, Yakov; Janko, Zvonimir
2008
Groups of prime power order. Vol. 3. Zbl 1229.20001
Berkovich, Yakov; Janko, Zvonimir
2011
On a class of finite simple groups of Ree. Zbl 0145.02702
Janko, Z.; Thompson, J. G.
1966
A new finite simple group of order 86,775,571,046,077,562,880 which possesses $$M_{24}$$ and the full covering group of $$M_{22}$$ as subgroups. Zbl 0344.20010
Janko, Zvonimir
1976
A characterization of the Mathieu simple groups. I, II. Zbl 0159.03101
Janko, Z.
1968
Structure of finite $$p$$-groups with given subgroups. Zbl 1108.20013
Berkovich, Yakov; Janko, Zvonimir
2006
Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen. Zbl 0104.24902
Janko, Zvonimir
1962
Coset enumeration in groups and construction of symmetric designs. Zbl 0773.05010
Janko, Zvonimir
1992
Nonsolvable finite groups all of whose 2-local subgroups are solvable. I. Zbl 0243.20013
Janko, Zvonimir
1972
Finite groups with invariant fourth maximal subgroups. Zbl 0118.26704
Janko, Z.
1963
A characterization of the Higman-Sims simple group. Zbl 0184.04602
Janko, Z.; Wong, S. K.
1969
Construction of a new symmetric block design for $$(78,22,6)$$ with the help of tactical decompositions. Zbl 0577.05011
Janko, Zvonimir; Tran van Trung
1985
Verallgemeinerung eines Satzes von B. Huppert und J. G. Thompson. Zbl 0099.01501
Janko, Zvonimir
1961
A classification of finite 2-groups with exactly three involutions. Zbl 1081.20025
Janko, Zvonimir
2005
A characterization of the finite simple group PSp$$_4(3)$$. Zbl 0178.02202
Janko, Z.
1967
Finite $$2$$-groups with small centralizer of an involution. Zbl 0988.20009
Janko, Zvonimir
2001
A complete classification of finite $$p$$-groups all of whose noncyclic subgroups are normal. Zbl 1194.20016
Božikov, Zdravka; Janko, Zvonimir
2009
Finite 2-groups with no normal elementary Abelian subgroups of order 8. Zbl 0992.20012
Janko, Zvonimir
2001
The existence of a Bush-type Hadamard matrix of order 324 and two new infinite classes of symmetric designs. Zbl 0987.05031
2001
A characterization of the McLaughlin’s simple group. Zbl 0225.20009
Janko, Zvonimir; Wong, S. K.
1972
The full collineation group of any projective plane of order 12 is a $$(2,3)$$-group. Zbl 0474.51007
Janko, Zvonimir; Tran van Trung
1982
On projective planes of order 12 with an automorphism of order 13. I: Kirkman designs of order 27. Zbl 0467.51010
Janko, Zvonimir; Tran van Trung
1981
Some new simple groups of finite order. I. Zbl 0182.35304
Janko, Z.
1969
A characterization of a simple group $$G_2(3)$$. Zbl 0177.04001
Janko, Z.
1969
On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4. Zbl 1127.20018
Janko, Zvonimir
2007
Finite 2-groups with exactly four cyclic subgroups of order $$2^n$$. Zbl 1037.20020
Janko, Zvonimir
2004
Bush-type Hadamard matrices and symmetric designs. Zbl 0973.05010
2001
The nonexistence of a certain type of finite simple group. Zbl 0219.20010
Janko, Z.
1971
Some new simple groups of finite order. Zbl 0182.35303
Janko, Z.
1969
Finite simple groups with short chains of subgroups. Zbl 0119.02802
Janko, Z.
1964
Finite 2-groups with exactly one nonmetacyclic maximal subgroup. Zbl 1157.20010
Janko, Zvonimir
2008
A new biplane of order 9 with a small automorphism group. Zbl 0656.05019
Janko, Zvonimir; Tran van Trung
1986
Projective planes of order 12 do not have a non-abelian group of order 6 as a collineation group. Zbl 0452.51008
Janko, Zvonimir; Tran van Trung
1981
A characterization of the smallest group of Ree associated with the simple Lie algebra of type $$(G_ 2)$$. Zbl 0145.02703
Janko, Z.
1966
A new finite simple group with abelian 2-Sylow subgroups. Zbl 0142.25903
Janko, Z.
1965
Groups of prime power order. Vol. 5. Zbl 1344.20002
Berkovich, Yakov G.; Janko, Zvonimir
2016
Minimal nonmodular finite $$p$$-groups. Zbl 1074.20013
Janko, Zvonimir
2004
A block negacyclic Bush-type Hadamard matrix and two strongly regular graphs. Zbl 1016.05019
2002
The classification of projective planes of order 9 which possess an involution. Zbl 0487.51010
Janko, Zvonimir; Tran van Trung
1982
Two new semibiplanes. Zbl 0485.05019
Janko, Zvonimir; Tran van Trung
1982
A generalization of a result of L. Baumert and M. Hall about projective planes of order 12. Zbl 0485.05018
Janko, Zvonimir; Tran van Trung
1982
Finite groups with a nilpotent maximal subgroup. Zbl 0135.05301
Janko, Z.
1964
On subgroups of finite $$p$$-groups. Zbl 1181.20017
Berkovich, Yakov; Janko, Zvonimir
2009
The existence of a Bush-type Hadamard matrix of order 36 and two new infinite classes of symmetric designs. Zbl 0995.05024
Janko, Zvonimir
2001
The existence of a symmetric block design for $$(70,24,8)$$. Zbl 0571.05005
Janko, Zvonimir; Tran van Trung
1984
Janko, Zvonimir; Tran van Trung
1984
Projective plane of order 12 do not have a four group as a collineation group. Zbl 0492.51014
Janko, Zvonimir; Tran van Trung
1982
On projective planes of order 12 with an automorphism of order 13. Zbl 0479.51008
Janko, Zvonimir; Tran van Trung
1982
Projective planes of order 12 do not possess an elation of order 3. Zbl 0488.05018
Janko, Zvonimir; Tran van Trung
1981
Projective planes of order 10 do not have a collineation of order 3. Zbl 0462.51010
Janko, Zvonimir; Tran van Trung
1981
On projective planes of order 12 which have a subplane of order 3. I. Zbl 0446.51006
Janko, Zvonimir; Tran van Trung
1980
Finite simple groups with nilpotent third maximal subgroups. Zbl 0166.02102
Gagen, T. M.; Janko, Z.
1966
On minimal non-Abelian subgroups in finite $$p$$-groups. Zbl 1203.20017
Janko, Zvonimir
2009
Some peculiar minimal situations by finite $$p$$-groups. Zbl 1153.20016
Janko, Zvonimir
2008
On maximal Abelian subgroups in finite 2-groups. Zbl 1133.20011
Janko, Zvonimir
2008
Finite $$p$$-groups with a uniqueness condition for non-normal subgroups. Zbl 1084.20016
Janko, Zvonivir
2005
Finite 2-groups $$G$$ with $$|\Omega_2(G)|=16$$. Zbl 1081.20024
Janko, Zvonimir
2005
Elements of order at most 4 in finite 2-groups. Zbl 1074.20012
Janko, Zvonimir
2004
Finite 2-groups with a self-centralizing elementary Abelian subgroup of order 8. Zbl 1036.20020
Janko, Zvonimir
2003
Finite $$2$$-groups with small centralizer of an involution. II. Zbl 0994.20018
Janko, Zvonimir
2001
New designs with block size 7. Zbl 0910.05012
1998
Cyclic 2-(91,6,1) designs with multiplier automorphisms. Zbl 0765.05009
1991
Finite $$p$$-groups with some isolated subgroups. Zbl 1354.20012
Janko, Zvonimir
2016
Finite $$p$$-groups all of whose maximal subgroups, except one, have its derived subgroup of order $$\leq p$$. Zbl 1263.20018
Janko, Zvonimir
2012
Finite $$p$$-groups with many minimal nonabelian subgroups. Zbl 1262.20022
Janko, Zvonimir
2012
Finite $$p$$-groups all of whose proper subgroups have its derived subgroup of order at most $$p$$. Zbl 1244.20014
Janko, Zvonimir
2011
Finite $$p$$-groups $$G$$ with $$p>2$$ and $$d(G)>2$$ having exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1231.20021
Janko, Zvonimir
2011
Finite $$p$$-groups $$G$$ with $$p>2$$ and $$d(G)=2$$ having exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1258.20015
Janko, Zvonimir
2010
Finite 2-groups with exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1198.20018
Božikov, Zdravka; Janko, Zvonimir
2010
Finite quaternion-free 2-groups. Zbl 1134.20015
Janko, Zvonimir
2006
Finite 2-groups all of whose nonabelian subgroups are generated with involutions. Zbl 1089.20007
Janko, Zvonimir
2006
Finite 2-groups $$G$$ with $$|\Omega_3(G)|\leqslant 2^5$$. Zbl 1040.20015
Božikov, Zdravka; Janko, Zvonimir
2004
The existence of symmetric designs with parameters (105, 40, 15). Zbl 0945.05010
Janko, Zvonimir
1999
On symmetric designs with parameters $$(176, 50, 14)$$. Zbl 0838.05010
Janko, Zvonimir
1995
On projective planes of order twelve and twenty. Zbl 0438.51009
Janko, Zvonimir; Tran van Trung
1980
On finite simple groups whose Sylow 2-subgroups have no normal elementary subgroups of order 8. Zbl 0176.30001
Janko, Zvonimir; Thompson, John G.
1969
On finite groups with p-nilpotent subgroups. Zbl 0118.26701
Janko, Z.; Newman, M. F.
1963
Eine Bemerkung über die $$\Phi$$-Untergruppe endlicher Gruppen. Zbl 0106.24502
Janko, Z.
1962
A theorem on nilpotent groups. Zbl 0108.02703
Janko, Z.
1960
Groups of prime power order. Vol. 5. Zbl 1344.20002
Berkovich, Yakov G.; Janko, Zvonimir
2016
Finite $$p$$-groups with some isolated subgroups. Zbl 1354.20012
Janko, Zvonimir
2016
Finite $$p$$-groups all of whose maximal subgroups, except one, have its derived subgroup of order $$\leq p$$. Zbl 1263.20018
Janko, Zvonimir
2012
Finite $$p$$-groups with many minimal nonabelian subgroups. Zbl 1262.20022
Janko, Zvonimir
2012
Groups of prime power order. Vol. 3. Zbl 1229.20001
Berkovich, Yakov; Janko, Zvonimir
2011
Finite $$p$$-groups all of whose proper subgroups have its derived subgroup of order at most $$p$$. Zbl 1244.20014
Janko, Zvonimir
2011
Finite $$p$$-groups $$G$$ with $$p>2$$ and $$d(G)>2$$ having exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1231.20021
Janko, Zvonimir
2011
Finite $$p$$-groups $$G$$ with $$p>2$$ and $$d(G)=2$$ having exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1258.20015
Janko, Zvonimir
2010
Finite 2-groups with exactly one maximal subgroup which is neither Abelian nor minimal nonabelian. Zbl 1198.20018
Božikov, Zdravka; Janko, Zvonimir
2010
A complete classification of finite $$p$$-groups all of whose noncyclic subgroups are normal. Zbl 1194.20016
Božikov, Zdravka; Janko, Zvonimir
2009
On subgroups of finite $$p$$-groups. Zbl 1181.20017
Berkovich, Yakov; Janko, Zvonimir
2009
On minimal non-Abelian subgroups in finite $$p$$-groups. Zbl 1203.20017
Janko, Zvonimir
2009
Groups of prime power order. Vol. 2. Zbl 1168.20002
Berkovich, Yakov; Janko, Zvonimir
2008
Finite 2-groups with exactly one nonmetacyclic maximal subgroup. Zbl 1157.20010
Janko, Zvonimir
2008
Some peculiar minimal situations by finite $$p$$-groups. Zbl 1153.20016
Janko, Zvonimir
2008
On maximal Abelian subgroups in finite 2-groups. Zbl 1133.20011
Janko, Zvonimir
2008
On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4. Zbl 1127.20018
Janko, Zvonimir
2007
Structure of finite $$p$$-groups with given subgroups. Zbl 1108.20013
Berkovich, Yakov; Janko, Zvonimir
2006
Finite quaternion-free 2-groups. Zbl 1134.20015
Janko, Zvonimir
2006
Finite 2-groups all of whose nonabelian subgroups are generated with involutions. Zbl 1089.20007
Janko, Zvonimir
2006
A classification of finite 2-groups with exactly three involutions. Zbl 1081.20025
Janko, Zvonimir
2005
Finite $$p$$-groups with a uniqueness condition for non-normal subgroups. Zbl 1084.20016
Janko, Zvonivir
2005
Finite 2-groups $$G$$ with $$|\Omega_2(G)|=16$$. Zbl 1081.20024
Janko, Zvonimir
2005
Finite 2-groups with exactly four cyclic subgroups of order $$2^n$$. Zbl 1037.20020
Janko, Zvonimir
2004
Minimal nonmodular finite $$p$$-groups. Zbl 1074.20013
Janko, Zvonimir
2004
Elements of order at most 4 in finite 2-groups. Zbl 1074.20012
Janko, Zvonimir
2004
Finite 2-groups $$G$$ with $$|\Omega_3(G)|\leqslant 2^5$$. Zbl 1040.20015
Božikov, Zdravka; Janko, Zvonimir
2004
Finite 2-groups with a self-centralizing elementary Abelian subgroup of order 8. Zbl 1036.20020
Janko, Zvonimir
2003
A block negacyclic Bush-type Hadamard matrix and two strongly regular graphs. Zbl 1016.05019
2002
Finite $$2$$-groups with small centralizer of an involution. Zbl 0988.20009
Janko, Zvonimir
2001
Finite 2-groups with no normal elementary Abelian subgroups of order 8. Zbl 0992.20012
Janko, Zvonimir
2001
The existence of a Bush-type Hadamard matrix of order 324 and two new infinite classes of symmetric designs. Zbl 0987.05031
2001
Bush-type Hadamard matrices and symmetric designs. Zbl 0973.05010
2001
The existence of a Bush-type Hadamard matrix of order 36 and two new infinite classes of symmetric designs. Zbl 0995.05024
Janko, Zvonimir
2001
Finite $$2$$-groups with small centralizer of an involution. II. Zbl 0994.20018
Janko, Zvonimir
2001
The existence of symmetric designs with parameters (105, 40, 15). Zbl 0945.05010
Janko, Zvonimir
1999
New designs with block size 7. Zbl 0910.05012
1998
On symmetric designs with parameters $$(176, 50, 14)$$. Zbl 0838.05010
Janko, Zvonimir
1995
Coset enumeration in groups and construction of symmetric designs. Zbl 0773.05010
Janko, Zvonimir
1992
Cyclic 2-(91,6,1) designs with multiplier automorphisms. Zbl 0765.05009
1991
A new biplane of order 9 with a small automorphism group. Zbl 0656.05019
Janko, Zvonimir; Tran van Trung
1986
Construction of a new symmetric block design for $$(78,22,6)$$ with the help of tactical decompositions. Zbl 0577.05011
Janko, Zvonimir; Tran van Trung
1985
The existence of a symmetric block design for $$(70,24,8)$$. Zbl 0571.05005
Janko, Zvonimir; Tran van Trung
1984
Janko, Zvonimir; Tran van Trung
1984
The full collineation group of any projective plane of order 12 is a $$(2,3)$$-group. Zbl 0474.51007
Janko, Zvonimir; Tran van Trung
1982
The classification of projective planes of order 9 which possess an involution. Zbl 0487.51010
Janko, Zvonimir; Tran van Trung
1982
Two new semibiplanes. Zbl 0485.05019
Janko, Zvonimir; Tran van Trung
1982
A generalization of a result of L. Baumert and M. Hall about projective planes of order 12. Zbl 0485.05018
Janko, Zvonimir; Tran van Trung
1982
Projective plane of order 12 do not have a four group as a collineation group. Zbl 0492.51014
Janko, Zvonimir; Tran van Trung
1982
On projective planes of order 12 with an automorphism of order 13. Zbl 0479.51008
Janko, Zvonimir; Tran van Trung
1982
On projective planes of order 12 with an automorphism of order 13. I: Kirkman designs of order 27. Zbl 0467.51010
Janko, Zvonimir; Tran van Trung
1981
Projective planes of order 12 do not have a non-abelian group of order 6 as a collineation group. Zbl 0452.51008
Janko, Zvonimir; Tran van Trung
1981
Projective planes of order 12 do not possess an elation of order 3. Zbl 0488.05018
Janko, Zvonimir; Tran van Trung
1981
Projective planes of order 10 do not have a collineation of order 3. Zbl 0462.51010
Janko, Zvonimir; Tran van Trung
1981
On projective planes of order 12 which have a subplane of order 3. I. Zbl 0446.51006
Janko, Zvonimir; Tran van Trung
1980
On projective planes of order twelve and twenty. Zbl 0438.51009
Janko, Zvonimir; Tran van Trung
1980
A new finite simple group of order 86,775,571,046,077,562,880 which possesses $$M_{24}$$ and the full covering group of $$M_{22}$$ as subgroups. Zbl 0344.20010
Janko, Zvonimir
1976
Nonsolvable finite groups all of whose 2-local subgroups are solvable. I. Zbl 0243.20013
Janko, Zvonimir
1972
A characterization of the McLaughlin’s simple group. Zbl 0225.20009
Janko, Zvonimir; Wong, S. K.
1972
The nonexistence of a certain type of finite simple group. Zbl 0219.20010
Janko, Z.
1971
A characterization of the Higman-Sims simple group. Zbl 0184.04602
Janko, Z.; Wong, S. K.
1969
Some new simple groups of finite order. I. Zbl 0182.35304
Janko, Z.
1969
A characterization of a simple group $$G_2(3)$$. Zbl 0177.04001
Janko, Z.
1969
Some new simple groups of finite order. Zbl 0182.35303
Janko, Z.
1969
On finite simple groups whose Sylow 2-subgroups have no normal elementary subgroups of order 8. Zbl 0176.30001
Janko, Zvonimir; Thompson, John G.
1969
A characterization of the Mathieu simple groups. I, II. Zbl 0159.03101
Janko, Z.
1968
A characterization of the finite simple group PSp$$_4(3)$$. Zbl 0178.02202
Janko, Z.
1967
A new finite simple group with abelian Sylow 2-subgroups and its characterization. Zbl 0214.28003
Janko, Zvonimir
1966
On a class of finite simple groups of Ree. Zbl 0145.02702
Janko, Z.; Thompson, J. G.
1966
A characterization of the smallest group of Ree associated with the simple Lie algebra of type $$(G_ 2)$$. Zbl 0145.02703
Janko, Z.
1966
Finite simple groups with nilpotent third maximal subgroups. Zbl 0166.02102
Gagen, T. M.; Janko, Z.
1966
A new finite simple group with abelian 2-Sylow subgroups. Zbl 0142.25903
Janko, Z.
1965
Finite simple groups with short chains of subgroups. Zbl 0119.02802
Janko, Z.
1964
Finite groups with a nilpotent maximal subgroup. Zbl 0135.05301
Janko, Z.
1964
Finite groups with invariant fourth maximal subgroups. Zbl 0118.26704
Janko, Z.
1963
On finite groups with p-nilpotent subgroups. Zbl 0118.26701
Janko, Z.; Newman, M. F.
1963
Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen. Zbl 0104.24902
Janko, Zvonimir
1962
Eine Bemerkung über die $$\Phi$$-Untergruppe endlicher Gruppen. Zbl 0106.24502
Janko, Z.
1962
Verallgemeinerung eines Satzes von B. Huppert und J. G. Thompson. Zbl 0099.01501
Janko, Zvonimir
1961
A theorem on nilpotent groups. Zbl 0108.02703
Janko, Z.
1960
all top 5
#### Cited by 435 Authors
38 Janko, Zvonimir 15 Berkovich, Yakov G. 13 Zhang, Qinhai 10 Crnković, Dean 9 Aschbacher, Michael George 9 Gorenstein, Daniel 9 Meng, Wei 8 Michler, Gerhard O. 7 Guo, Xiuyun 7 Pavčević, Mario-Osvin 7 Zhang, Junqiang 6 Lu, Jiakuan 6 Skiba, Alexander Nikolaevich 6 Stroth, Gernot 6 Tran Van Trung 5 Ćepulić, Vladimir 5 Golemac, Anka 5 Guo, Wenbin 5 Held, Dieter 5 Nakić, Anamari 5 Zhang, Lihua 4 An, Lijian 4 Ballester-Bolinches, Adolfo 4 Dempwolff, Ulrich 4 Harada, Koichiro 4 Kharaghani, Hadi 4 Lv, Heng 4 Maksimović, Marija 4 Rukavina, Sanja 4 Solomon, Ronald Mark 4 Suetake, Chihiro 4 Vučičić, Tanja 4 Zhang, Jiping 3 Abel, R. Julian R. 3 Belonogov, Vyacheslav Aleksandrovich 3 Burness, Timothy C. 3 Finkelstein, Larry A. 3 Griess, Robert L. jun. 3 Ivanov, Alexander A. 3 Li, Xianhua 3 Liao, Jun 3 Liu, Chiahsin 3 Lyons, Richard 3 Makhnëv, Aleksandr Alekseevich 3 Mandić, Joško 3 Mazurov, Viktor Danilovich 3 Montinaro, Alessandro 3 Niroomand, Peyman 3 Parrott, David 3 Previtali, Andrea 3 Qu, Haipeng 3 Reifart, Arthur 3 Rowley, Peter J. 3 Russo, Francesco Giuseppe 3 Ryba, Alexander J. E. 3 Sambale, Benjamin 3 Shalev, Aner 3 Weller, Michael 3 Zhou, Wei 2 Aivazidis, Stefanos 2 Akiyama, Kenzi 2 Asaad, Mohamed 2 Azizi, Abdelmalek 2 Bai, Pengfei 2 Beisiegel, Bert 2 Bluskov, Iliya 2 Božikov, Zdravka 2 Broshi, Aviad M. 2 Bruno, Brunella 2 Buchthal, David C. 2 Carlson, Jon Frederick 2 Cossey, John 2 Essert, Mario 2 Gagen, Terence Matthew 2 Gilman, Robert C. 2 Gollan, Holger Wolfgang 2 Gomi, Kensaku 2 Greig, Malcolm 2 Hartley, Michael Ian 2 Hayashi, Makoto 2 Heineken, Hermann 2 Hrabě de Angelis, Jörg Michael 2 Ionin, Yury J. 2 Kleidman, Peter B. 2 Kondrat’ev, Anatoliĭ Semenovich 2 Korchmáros, Gábor 2 Krčadinac, Vedran 2 Kutnar, Klavdija 2 Landrock, Peter 2 Leemans, Dimitri 2 Lempken, Wolfgang 2 Liebeck, Martin Walter 2 Liu, Heguo 2 Ma, Li 2 Mann, Avinoam 2 Marangunić, Ljubo 2 Marušič, Dragan 2 Mason, Geoffrey 2 Moorhouse, G. Eric 2 Muzychuk, Mikhail E. ...and 335 more Authors
all top 5
#### Cited in 83 Serials
130 Journal of Algebra 28 Communications in Algebra 22 Archiv der Mathematik 22 Journal of Algebra and its Applications 20 Discrete Mathematics 19 Journal of Combinatorial Theory. Series A 19 Mathematische Zeitschrift 14 Israel Journal of Mathematics 11 Journal of Group Theory 10 Journal of Combinatorial Designs 9 Designs, Codes and Cryptography 8 Mathematical Notes 8 Algebra and Logic 7 Rendiconti del Seminario Matematico della Università di Padova 7 European Journal of Combinatorics 6 Siberian Mathematical Journal 6 Bulletin of the American Mathematical Society. New Series 6 Journal of the Australian Mathematical Society 5 Transactions of the American Mathematical Society 4 Inventiones Mathematicae 4 Journal of Pure and Applied Algebra 4 Journal of Statistical Planning and Inference 4 Monatshefte für Mathematik 4 Proceedings of the American Mathematical Society 4 Acta Mathematica Sinica. English Series 4 Bulletin of the American Mathematical Society 3 Bulletin of the Australian Mathematical Society 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Algebra Colloquium 3 Science China. Mathematics 2 Periodica Mathematica Hungarica 2 Ukrainian Mathematical Journal 2 Acta Mathematica 2 Journal of Geometry 2 Journal of Soviet Mathematics 2 Mathematische Annalen 2 Results in Mathematics 2 Acta Mathematica Hungarica 2 Science in China. Series A 2 Glasnik Matematički. Serija III 2 Linear Algebra and its Applications 2 Journal of Algebraic Combinatorics 2 Frontiers of Mathematics in China 1 Indian Journal of Pure & Applied Mathematics 1 Mathematics of Computation 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 Journal of Combinatorial Theory. Series B 1 Journal of the Korean Mathematical Society 1 Memoirs of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Cybernetics 1 Chinese Annals of Mathematics. Series B 1 Graphs and Combinatorics 1 Journal of the American Mathematical Society 1 Acta Mathematica Sinica. New Series 1 The Australasian Journal of Combinatorics 1 Applied Mathematics. Series B (English Edition) 1 Acta Universitatis Matthiae Belii. Series Mathematics 1 Turkish Journal of Mathematics 1 Finite Fields and their Applications 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Contributions to Discrete Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Advances in Mathematics of Communications 1 European Journal of Pure and Applied Mathematics 1 Ars Mathematica Contemporanea 1 Acta Universitatis Sapientiae. Mathematica 1 Symmetry 1 International Journal of Group Theory 1 Problemy Fiziki, Matematiki i Tekhniki 1 Communications in Mathematics and Statistics 1 Open Mathematics 1 Journal of Algebra, Combinatorics, Discrete Structures and Applications 1 Algebraic Structures and their Applications 1 The Art of Discrete and Applied Mathematics
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#### Cited in 22 Fields
359 Group theory and generalizations (20-XX) 89 Combinatorics (05-XX) 35 Geometry (51-XX) 8 Algebraic topology (55-XX) 8 Information and communication theory, circuits (94-XX) 7 Associative rings and algebras (16-XX) 5 Number theory (11-XX) 5 Algebraic geometry (14-XX) 3 General and overarching topics; collections (00-XX) 3 Commutative algebra (13-XX) 3 Nonassociative rings and algebras (17-XX) 3 Functions of a complex variable (30-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) 2 Topological groups, Lie groups (22-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 1 $$K$$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX)
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http://mathonline.wikidot.com/line-integrals
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Line Integrals
# Line Integrals of Function of Two Variables
We will now introduce a new type of integral known as a line integral. Let $z = f(x, y)$ be a two variable real-valued function, and consider a curve $C$ given parametrically by the equations $x = x(t)$ and $y = y(t)$ for $a ≤ t ≤ b$ that is contained in the domain of $f$. We can merge these two parametric equations nicely into a vector equation $\vec{r}(t) = (x(t), y(t)) = x(t) \vec{i} + y(t) \vec{j}$. Suppose further that $C$ is a smooth curve, that is, $\vec{r'}(t) \neq 0$ and $\vec{r'}(t)$ is continuous for $a ≤ t ≤ b$.
Now we will take the interval $[a, b]$ for the parameter $t$ and divide it up into $n$ equal-width subintervals $[t_{i-1}, t_i]$. Then let $\vec{r}(t_i) = (x(t_i), y(t_i)) = (x_i, y_i)$ be the point $P_i(x_i, y_i)$ on $C$. The curve of $C$ is thus divided into $n$ sub arcs that are partitioned by the points $P_i$ on $C$. The lengths of each of these arcs will be $\Delta s_1, \Delta s_2, ...,\Delta s_n$. Now choose a sample number $t_i^* \in [t_{i-1}, t_i]$. This value $t_i^*$ corresponds to the point $P_i^*(x_i^*, y_i^*)$ on $C$ and between $P_{i-1}$ and $P_i$.
Now we evaluate $f$ at the point $(x_i^*, y_i^*)$ and multiply by the length $\Delta s_i$ then we get the area of of rectangle that is standing on the $xy$ plane with height $f(x_i^*, y_i^*)$ and length $\Delta s_i$. Thus the area of each of these rectangles is $f(x_i^*, y_i^*)$. We now sum up all of these rectangles:
(1)
\begin{align} \quad \sum_{i=1}^{n} f(x_i^*, y_i^*) \Delta s_i \end{align}
If $f(x, y) ≥ 0$ for points $(x, y)$ on $C$, then as $n \to \infty$, this sum represents the area of the upright "fence" standing on the $xy$-plane. We formally define this limit to be the line integral of $f$ along the curve $C$ which we define below.
Definition: Let $z = f(x, y)$ be a two variable real-valued function, and let $C$ be a smooth curve given by the parametric equations $x = x(t)$ and $y = y(t)$ for $a ≤ t ≤ b$. Then the Line Integral of $f$ Along $C$ is defined as $\int_C f(x, y) \: ds = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*, y_i^*) \Delta s_i$ provided that this limit exists.
Now recall that $\frac{ds}{dt}$ is precisely the speed function of $\vec{r}(t)$, that is:
(2)
\begin{align} \quad \frac{ds}{dt} = \| \vec{r'}(t) \| = \sqrt{ \left ( \frac{dx}{dt} \right )^2 + \left ( \frac{dy}{dt} \right )^2} \end{align}
Therefore $ds = \sqrt{ \left ( \frac{dx}{dt} \right )^2 + \left ( \frac{dy}{dt} \right )^2} \: dt$, and so we can evaluate a line integral with the following formula:
(3)
\begin{align} \quad \int_C f(x, y) \: ds = \int_a^b f(x(t), y(t)) \sqrt{ \left ( \frac{dx}{dt} \right )^2 + \left ( \frac{dy}{dt} \right )^2} \: dt = \int_a^b f(\vec{r}(t)) \| \vec{r'}(t) \| \: dt \end{align}
Furthermore, we have generalized the definite integral of a single variable function to a two variable function. Note that if we want to compute the line integral of $f$ from the point $(a, 0)$ to $(b, 0)$ then we have that this curve can be parameterized as $\vec{r}(t) = (x(t), y(t)) = (x, 0)$ and so $\frac{dx}{dt} = 1$ and $\frac{dy}{dt} = 0$ so:
(4)
\begin{align} \quad \int_C f(x, y) \: ds = \int_a^b f(x, 0) \sqrt{1} \: dx = \int_a^b f(x, 0) \: dx \end{align}
It is important to note that the value of the line integral of $f$ along $C$ does NOT depend of the parameterization of $C$. We prove this statement in the following proposition.
Proposition 1: If $z = f(x, y)$ is a two variable real-valued function and $C$ is a smooth plane curve contained in the domain of $f$ and parameterized as $\vec{r}(t) = (x(t), y(t))$ for $a ≤ t ≤ b$ and $\vec{r^*}(u)$ for $\alpha ≤ u ≤ \beta$ then $\int_a^b f(\vec{r}(t)) \| \vec{r'}(t) \| \: dt = \int_{\alpha}^{\beta} f(\vec{r^*}(u)) \| \vec{r^*{'}}(u) \| \: du$.
• Proof: Suppose that $\vec{r}(t) = (x(t), y(t))$ for $a ≤ t ≤ b$ and $\vec{r^*}(u)$ for $\alpha ≤ u ≤ \beta$ both represent the plane curve $C$. Then any point $\vec{r}(t)$ on the curve $C$ can be represented in terms of the parameterization $\vec{r^*}(u)$ where $u$ depends on $u$ depends on $t$, that is $u = u(t)$.
• Now there are two cases to consider. If $\vec{r^*}(u)$ traces $C$ in the same direction as $\vec{r}(t)$ then we have that $u(a) = \alpha$, $u(b) = \beta$, and $\frac{du}{dt} ≥ 0$. Thus:
(5)
\begin{align} \quad \int_a^b f(\vec{r}(t)) \biggr \| \frac{d \vec{r}}{dt} \biggr \| \: dt = \int_a^b f(\vec{r^*}(u(t)) \biggr \| \frac{d \vec{r^*}}{du} \frac{du}{dt} \biggr \| \: dt= \int_a^b f(\vec{r^*}(u(t)) \biggr \| \frac{d \vec{r^*}}{du} \biggr \| \frac{du}{dt} \: dt = \int_{\alpha}^{\beta} f(\vec{r^*}(u)) \biggr \| \frac{d \vec{r^*}}{du} \biggr \| \: du \end{align}
• Similarly, if $\vec{r^*}(u)$ traces $C$ in the opposite direction a $\vec{r}(t)$ then we have that $u(a) = \beta$ and $u(b) = \alpha$ and $\frac{du}{dt} ≤ 0$, so:
(6)
\begin{align} \quad \: \int_a^b f(\vec{r}(t)) \biggr \| \frac{d \vec{r}}{dt} \biggr \| \: dt = \int_a^b f(\vec{r^*}(u(t)) \biggr \| \frac{d \vec{r^*}}{du} \frac{du}{dt} \biggr \| \: dt= \int_a^b f(\vec{r^*}(u(t)) \biggr \| \frac{d \vec{r^*}}{du} \biggr \| \left ( -\frac{du}{dt} \right ) \: dt = -\int_{\beta}^{\alpha} f(\vec{r^*}(u)) \biggr \| \frac{d \vec{r^*}}{du} \biggr \| \: du = \int_{\alpha}^{\beta} f(\vec{r^*}(u)) \biggr \| \frac{d \vec{r^*}}{du} \biggr \| \: du \end{align}
• Thus our proof is complete. $\blacksquare$
We should also be weary of whether or not this curve is traversed once for $a ≤ t ≤ b$.
# Line Integrals of Functions of Three Variables
Definition: Let $w = f(x, y, z)$ be a three variable real-valued function, and let $C$ be a smooth space curve given by the parametric equations $x = x(t)$, $y = y(t)$, $z = z(t)$ for $a ≤ t ≤ b$. Then the Line Integral of $f$ Along $C$ is defined as $\int_C f(x, y) \: ds = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*, y_i^*, z_i^*) \Delta s_i$ provided that this limit exists.
Like with line integrals of functions of two variables, the following formula allows us to readily evaluate such line integrals:
(7)
\begin{align} \quad \int_C f(x, y, z) \: ds = \int_a^b f(x(t), y(t), z(t)) \sqrt{\left ( \frac{dx}{dt} \right )^2 + \left ( \frac{dy}{dt} \right )^2 + \left ( \frac{dz}{dt} \right )^2 } \: dt = \int_a^b f(\vec{r}(t)) \| \vec{r'}(t) \| \: dt \end{align}
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2020-01-28T11:18:52 |
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|
http://dlmf.nist.gov/22.5
|
# §22.5(i) Special Values of $z$
Table 22.5.1 gives the value of each of the 12 Jacobian elliptic functions, together with its $z$-derivative (or at a pole, the residue), for values of $z$ that are integer multiples of $K$, $iK^{\prime}$. For example, at $z=K+iK^{\prime}$, $\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)=1/k$, $\ifrac{d\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)}{dz}=0$. (The modulus $k$ is suppressed throughout the table.)
Table 22.5.2 gives $\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)$, $\mathop{\mathrm{cn}\/}\nolimits\left(z,k\right)$, $\mathop{\mathrm{dn}\/}\nolimits\left(z,k\right)$ for other special values of $z$. For example, $\mathop{\mathrm{sn}\/}\nolimits\left(\frac{1}{2}K,k\right)=(1+k^{\prime})^{-1/2}$. For the other nine functions ratios can be taken; compare (22.2.10).
# §22.5(ii) Limiting Values of $k$
If $k\to 0+$, then $K\to\pi/2$ and $K^{\prime}\to\infty$; if $k\to 1-$, then $K\to\infty$ and $K^{\prime}\to\pi/2$. In these cases the elliptic functions degenerate into elementary trigonometric and hyperbolic functions, respectively. See Tables 22.5.3 and 22.5.4.
Expansions for $K,K^{\prime}$ as $k\to 0$ or $1$ are given in §§19.5, 19.12.
For values of $K,K^{\prime}$ when $k^{2}=\frac{1}{2}$ (lemniscatic case) see §23.5(iii), and for $k^{2}=e^{i\pi/3}$ (equianharmonic case) see §23.5(v).
| 2014-08-28T03:12:30 |
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|
http://encyclopedia-magnetica.com/doku.php/skin_depth
|
skin_depth
# Skin depth
Stan Zurek, Skin depth, Encyclopedia-Magnetica.com, {accessed 2020-07-15}
Skin depth (often denoted by lower-case Greek letter delta δ) - such a depth of penetration of alternating current or electromagnetic field, at which the amplitude is reduced to a value of 1/e (around 37%), as compared to the amplitude at the surface of the conductor.
Skin depth is a function of frequency of current, as well as magnetic permeability and electric resistivity (or conductivity) of the conductor in question.
Support us with just $0.25 through PayPal or a credit card: For good conductors (like most metals) the function can be defined as:1) $\delta = \sqrt{\frac{2 · \rho }{\omega · \mu_r · \mu_0}} = \frac{1}{\sqrt{\pi · f · \mu_r · \mu_0 · \sigma}}\$ (m)
where: π - mathematical constant, f - frequency (Hz), μr - relative permeability of the conductor, μ0 - magnetic permeability of free space (H/m), σ - electric conductivity (S/m), ρ = 1 - electric resistivity (Ω·m), ω = 2·π·f - pulsation frequency (rad/s).
Skin depth vs. frequency for some materials (red line denotes 50 Hz):
by S. Zurek, Encyclopedia Magnetica™, CC-BY-3.0
| 2020-07-15T11:44:35 |
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https://indico.physics.lbl.gov/event/684/contributions/2927/
|
NorCal HEP-EXchange 2018
December 1, 2018
Lawrence Berkeley National Lab
US/Pacific timezone
Study of the rare decays of Bs0 and B0 into muon pairs from data collected during 2015 and 2016 with the ATLAS detector.
Dec 1, 2018, 1:15 PM
15m
Building 50 Auditorium (Lawrence Berkeley National Lab)
Speaker
Aidan Grummer (ATLAS Collaboration)
Description
A study of the decays $B^0_s→μ^+μ^−$ and $B^0→μ^+μ^−$ has been performed using 26.3$~$fb$^{−1}$ of 13 TeV LHC proton-proton collisions collected with the ATLAS detector in 2015 and 2016. For $B^0_s$, the branching fraction $BR(B^0_s→μ^+μ^−)=(3.2^{+1.1}_{−1.0})×10^{−9}$ is measured. For the $B^0$, an upper limit on the branching fraction is set at $BR(B^0→μ^+μ^−)<4.3×10^{−10}$ at 95 confidence level. The result is combined with the full Run 1 ATLAS result, yielding $BR(B^0_s→μ^+μ^−)=(2.8^{+0.8}_{−0.7})×10^{−9}$ and $BR(B^0→μ^+μ^−)<2.1×10^{−10}$. The combined result is consistent with the Standard Model within 2.4 standard deviations.
Session Works in Progress (15+5 min)
Primary author
Aidan Grummer (ATLAS Collaboration)
| 2023-02-05T13:34:01 |
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|
https://nbviewer.jupyter.org/github/barbagroup/CFDPython/blob/master/lessons/06_Array_Operations_with_NumPy.ipynb
|
Text provided under a Creative Commons Attribution license, CC-BY. All code is made available under the FSF-approved BSD-3 license. (c) Lorena A. Barba, Gilbert F. Forsyth 2017. Thanks to NSF for support via CAREER award #1149784.
# 12 steps to Navier–Stokes¶
This lesson complements the first interactive module of the online CFD Python class, by Prof. Lorena A. Barba, called 12 Steps to Navier–Stokes. It was written with BU graduate student Gilbert Forsyth.
## Array Operations with NumPy¶
For more computationally intensive programs, the use of built-in Numpy functions can provide an increase in execution speed many-times over. As a simple example, consider the following equation:
$$u^{n+1}_i = u^n_i-u^n_{i-1}$$
Now, given a vector $u^n = [0, 1, 2, 3, 4, 5]\ \$ we can calculate the values of $u^{n+1}$ by iterating over the values of $u^n$ with a for loop.
In [1]:
import numpy
In [2]:
u = numpy.array((0, 1, 2, 3, 4, 5))
for i in range(1, len(u)):
print(u[i] - u[i-1])
1
1
1
1
1
This is the expected result and the execution time was nearly instantaneous. If we perform the same operation as an array operation, then rather than calculate $u^n_i-u^n_{i-1}\$ 5 separate times, we can slice the $u$ array and calculate each operation with one command:
In [3]:
u[1:] - u[0:-1]
Out[3]:
array([1, 1, 1, 1, 1])
What this command says is subtract the 0th, 1st, 2nd, 3rd, 4th and 5th elements of $u$ from the 1st, 2nd, 3rd, 4th, 5th and 6th elements of $u$.
### Speed Increases¶
For a 6 element array, the benefits of array operations are pretty slim. There will be no appreciable difference in execution time because there are so few operations taking place. But if we revisit 2D linear convection, we can see some substantial speed increases.
In [4]:
nx = 81
ny = 81
nt = 100
c = 1
dx = 2 / (nx - 1)
dy = 2 / (ny - 1)
sigma = .2
dt = sigma * dx
x = numpy.linspace(0, 2, nx)
y = numpy.linspace(0, 2, ny)
u = numpy.ones((ny, nx)) ##create a 1xn vector of 1's
un = numpy.ones((ny, nx))
u[int(.5 / dy): int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2
With our initial conditions all set up, let's first try running our original nested loop code, making use of the iPython "magic" function %%timeit, which will help us evaluate the performance of our code.
Note: The %%timeit magic function will run the code several times and then give an average execution time as a result. If you have any figures being plotted within a cell where you run %%timeit, it will plot those figures repeatedly which can be a bit messy.
The execution times below will vary from machine to machine. Don't expect your times to match these times, but you should expect to see the same general trend in decreasing execution time as we switch to array operations.
In [5]:
%%timeit
u = numpy.ones((ny, nx))
u[int(.5 / dy): int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2
for n in range(nt + 1): ##loop across number of time steps
un = u.copy()
row, col = u.shape
for j in range(1, row):
for i in range(1, col):
u[j, i] = (un[j, i] - (c * dt / dx *
(un[j, i] - un[j, i - 1])) -
(c * dt / dy *
(un[j, i] - un[j - 1, i])))
u[0, :] = 1
u[-1, :] = 1
u[:, 0] = 1
u[:, -1] = 1
3.07 s ± 15.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
With the "raw" Python code above, the mean execution time achieved was 3.07 seconds (on a MacBook Pro Mid 2012). Keep in mind that with these three nested loops, that the statements inside the j loop are being evaluated more than 650,000 times. Let's compare that with the performance of the same code implemented with array operations:
In [6]:
%%timeit
u = numpy.ones((ny, nx))
u[int(.5 / dy): int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2
for n in range(nt + 1): ##loop across number of time steps
un = u.copy()
u[1:, 1:] = (un[1:, 1:] - (c * dt / dx * (un[1:, 1:] - un[1:, 0:-1])) -
(c * dt / dy * (un[1:, 1:] - un[0:-1, 1:])))
u[0, :] = 1
u[-1, :] = 1
u[:, 0] = 1
u[:, -1] = 1
7.38 ms ± 105 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
As you can see, the speed increase is substantial. The same calculation goes from 3.07 seconds to 7.38 milliseconds. 3 seconds isn't a huge amount of time to wait, but these speed gains will increase exponentially with the size and complexity of the problem being evaluated.
In [7]:
from IPython.core.display import HTML
def css_styling():
| 2021-02-27T18:25:36 |
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|
https://zbmath.org/authors/?q=ai%3Aeshelby.j-d
|
# zbMATH — the first resource for mathematics
## Eshelby, John Douglas
Compute Distance To:
Author ID: eshelby.j-d Published as: Eshelby, J. D. External Links: Wikidata · GND
Documents Indexed: 18 Publications since 1949, including 1 Book Biographic References: 2 Publications
#### Co-Authors
15 single-authored 1 Chou, Ye Tsang 1 Frank, F. C. 1 Nabarro, F. R. N. 1 Stroh, A. N.
all top 5
#### Serials
4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 3 The Philosophical Magazine, VII. Series 2 Journal of the Mechanics and Physics of Solids 2 Philosophical Transactions of the Royal Society of London. Ser. A 1 Journal of Elasticity 1 Journal of Applied Physics 1 Physical Review, II. Series 1 The Philosophical Magazine, VIII. Series 1 Solid Mechanics and Its Applications
#### Fields
4 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX)
#### Citations contained in zbMATH
18 Publications have been cited 1,609 times in 1,298 Documents Cited by Year
The determination of the elastic field of an ellipsoidal inclusion, and related problems. Zbl 0079.39606
Eshelby, J. D.
1957
The force on an elastic singularity. Zbl 0043.44102
Eshelby, J. D.
1951
The elastic energy-momentum tensor. Zbl 0323.73011
Eshelby, J. D.
1975
The elastic field outside an ellipsoidal inclusion. Zbl 0092.42001
Eshelby, J. D.
1959
Dislocations in visco-elastic materials. Zbl 0097.17602
Eshelby, J. D.
1961
The equilibrium of linear arrays of dislocations. Zbl 0042.22704
Eshelby, J. D.; Frank, F. C.; Nabarro, F. R. N.
1951
The equation of motion of a dislocation. Zbl 0051.23101
Eshelby, J. D.
1953
Aspects of the theory of dislocations. Zbl 0489.73118
Eshelby, J. D.
1982
The elastic field of a crack extending non-uniformly under general anti- plane loading. Zbl 0172.51302
Eshelby, J. D.
1969
Edge dislocations in anisotropic materials. Zbl 0033.04801
Eshelby, J. D.
1949
Dislocations as a cause of mechanical damping in metals. Zbl 0032.37901
Eshelby, J. D.
1949
The energy-momentum tensor of complex continua. Zbl 0555.73014
Eshelby, J. D.
1980
The interaction of kinks and elastic waves. Zbl 0106.44703
Eshelby, J. D.
1962
Distortion of a crystal by point imperfections. Zbl 0055.44208
Eshelby, J. D.
1954
Dislocations in thin plates. Zbl 0043.44005
Eshelby, J. D.; Stroh, A. N.
1951
Collected works of J. D. Eshelby. The mechanics of defects and inhomogeneities. Edited by X. Markenscoff and A. Gupta. Zbl 1099.01027
Eshelby, J. D.
2006
Dislocation theory for geophysical applications. Zbl 0254.73081
Eshelby, J. D.
1973
The energy and line tension of a dislocation in a hexagonal crystal. Zbl 0102.17902
Chou, Y. T.; Eshelby, J. D.
1962
Collected works of J. D. Eshelby. The mechanics of defects and inhomogeneities. Edited by X. Markenscoff and A. Gupta. Zbl 1099.01027
Eshelby, J. D.
2006
Aspects of the theory of dislocations. Zbl 0489.73118
Eshelby, J. D.
1982
The energy-momentum tensor of complex continua. Zbl 0555.73014
Eshelby, J. D.
1980
The elastic energy-momentum tensor. Zbl 0323.73011
Eshelby, J. D.
1975
Dislocation theory for geophysical applications. Zbl 0254.73081
Eshelby, J. D.
1973
The elastic field of a crack extending non-uniformly under general anti- plane loading. Zbl 0172.51302
Eshelby, J. D.
1969
The interaction of kinks and elastic waves. Zbl 0106.44703
Eshelby, J. D.
1962
The energy and line tension of a dislocation in a hexagonal crystal. Zbl 0102.17902
Chou, Y. T.; Eshelby, J. D.
1962
Dislocations in visco-elastic materials. Zbl 0097.17602
Eshelby, J. D.
1961
The elastic field outside an ellipsoidal inclusion. Zbl 0092.42001
Eshelby, J. D.
1959
The determination of the elastic field of an ellipsoidal inclusion, and related problems. Zbl 0079.39606
Eshelby, J. D.
1957
Distortion of a crystal by point imperfections. Zbl 0055.44208
Eshelby, J. D.
1954
The equation of motion of a dislocation. Zbl 0051.23101
Eshelby, J. D.
1953
The force on an elastic singularity. Zbl 0043.44102
Eshelby, J. D.
1951
The equilibrium of linear arrays of dislocations. Zbl 0042.22704
Eshelby, J. D.; Frank, F. C.; Nabarro, F. R. N.
1951
Dislocations in thin plates. Zbl 0043.44005
Eshelby, J. D.; Stroh, A. N.
1951
Edge dislocations in anisotropic materials. Zbl 0033.04801
Eshelby, J. D.
1949
Dislocations as a cause of mechanical damping in metals. Zbl 0032.37901
Eshelby, J. D.
1949
all top 5
#### Cited by 1,981 Authors
19 Markenscoff, Xanthippi 18 Sevostianov, Igor 18 Steinmann, Paul 18 Weng, George J. 16 Ponte Castañeda, Pedro 16 Wang, Xu 15 Novotny, Antonio André 12 Buryachenko, Valeriy A. 12 Hellmich, Christian 12 Schiavone, Peter 12 Shodja, Hossein M. 10 Lazar, Markus 10 Sokołowski, Jan 9 Chen, Yizhou 9 Feijóo, Raúl Antonino 9 Kushch, Volodymyr I. 9 Li, Shaofan 8 Chiang, Chun-Ron 8 Ma, Hang 8 Muller, Ralf 8 Yavari, Arash 8 Zou, Wennan 7 Acharya, Amit 7 Berveiller, Marcel 7 Epstein, Marcelo 7 Fried, Eliot 7 Gao, Huajian 7 Giraud, Albert 7 Gurtin, Morton Edward 7 Keer, Leon M. 7 Knops, Robin J. 7 Lubarda, Vlado A. 7 Zheng, Quanshui 6 Aderogba, K. V. 6 Barthelemy, Jean-Francois M. 6 Cheung, Ying Kuen K. 6 Dai, Ming 6 Freĭdin, Aleksandr Borisovich 6 Giusti, Sebastián M. 6 Gross, Dietmar 6 He, Qichang 6 Huang, Mojia 6 Korsunsky, Alexander M. 6 Levin, Valery M. 6 Liu, Liping 6 Ma, Lifeng 6 Maugin, Gérard A. 6 Ni, Luqun 6 Padra, Claudio 6 Sabar, Hafid 6 Taroco, Edgardo O. 6 Walpole, L. J. 6 Wang, Qian 6 Xu, Baixiang 5 Berbenni, Stephane 5 Bhattacharya, Kaushik 5 Bonnet, Guy 5 Brock, Louis M. 5 Clayton, John D. 5 Doghri, Issam 5 Gupta, Anurag P. 5 Kolling, Stefan 5 Kuhl, Ellen 5 Li, Qun 5 Liu, Wing Kam 5 Lopez-Pamies, Oscar 5 To, Quy-Dong 5 Trimarco, Carmine 5 Wang, Minzhong 5 Wang, Zhanjiang 5 Yu, Jianwu 4 Adam, Laurent 4 Aghdam, Mohammad Mohammadi 4 Agiasofitou, Eleni K. 4 Barnett, David M. 4 Chatzigeorgiou, George 4 Cherepanov, Genady P. 4 Crouch, Steven L. 4 Delfani, M. R. 4 Denda, Mitsunori 4 Dormieux, Luc 4 Duan, Huiling 4 Eberhardsteiner, Josef 4 Eshelby, John Douglas 4 Federico, Salvatore 4 Fish, Jacob 4 Foulk, James W. III 4 Franciosi, Patrick 4 Ganghoffer, Jean-François 4 Gao, Cun-Fa 4 Ghosh, Somnath 4 Giordano, Stefano 4 Idiart, Martín I. 4 Jin, Xiaoqing 4 Kaliske, Michael 4 Kalpakides, Vassilios K. 4 Lagoudas, Dimitris C. 4 Laws, Norman 4 Leugering, Günter 4 Liew, Kim Meow ...and 1,881 more Authors
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#### Cited in 109 Serials
201 Journal of the Mechanics and Physics of Solids 148 Acta Mechanica 89 International Journal of Engineering Science 78 Computer Methods in Applied Mechanics and Engineering 70 Journal of Elasticity 65 European Journal of Mechanics. A. Solids 59 International Journal of Solids and Structures 55 Mathematics and Mechanics of Solids 41 Computational Mechanics 31 International Journal for Numerical Methods in Engineering 30 Engineering Analysis with Boundary Elements 27 International Journal of Plasticity 24 ZAMP. Zeitschrift für angewandte Mathematik und Physik 23 Continuum Mechanics and Thermodynamics 23 International Journal of Fracture 22 Archive of Applied Mechanics 22 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 19 Archive for Rational Mechanics and Analysis 17 Journal of Applied Mathematics and Mechanics 12 Meccanica 12 Applied Mathematics and Mechanics. (English Edition) 8 Journal of Engineering Mathematics 8 Journal of Fluid Mechanics 8 Acta Mechanica Sinica 8 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 7 Wave Motion 7 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 7 Archives of Computational Methods in Engineering 6 Mechanics Research Communications 6 Applied Mathematical Modelling 5 Mathematical Methods in the Applied Sciences 5 Journal of Theoretical Biology 4 International Journal for Numerical and Analytical Methods in Geomechanics 4 Journal of Mathematical Physics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Journal of Computational and Applied Mathematics 4 Physica D 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Acta Mechanica Sinica. (English Edition) 4 Mathematical Problems in Engineering 4 The Philosophical Magazine, VIII. Series 3 Archives of Mechanics 3 Computers & Mathematics with Applications 3 Journal of Computational Physics 3 Prikladnaya Matematika i Mekhanika 3 Applied Mathematics and Computation 3 Proceedings of the National Academy of Sciences of the United States of America 3 SIAM Journal on Applied Mathematics 3 Communications in Numerical Methods in Engineering 3 Structural and Multidisciplinary Optimization 2 Applicable Analysis 2 International Journal of Heat and Mass Transfer 2 Physics Letters. A 2 Chaos, Solitons and Fractals 2 Journal of Geometry and Physics 2 Applied Mathematics and Optimization 2 Journal of Differential Equations 2 Quarterly of Applied Mathematics 2 European Journal of Applied Mathematics 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Journal of Nonlinear Science 2 Calculus of Variations and Partial Differential Equations 2 Physics of Fluids 2 Lobachevskii Journal of Mathematics 2 International Journal of Computational Methods 2 Journal of Applied Physics 2 Physical Review, II. Series 2 PAMM. Proceedings in Applied Mathematics and Mechanics 2 International Journal for Computational Methods in Engineering Science and Mechanics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Modern Physics Letters B 1 Computers and Fluids 1 Ingenieur-Archiv 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Physics of Fluids, A 1 Soviet Applied Mechanics 1 Anais da Academia Brasileira de Ciências 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of the Nigerian Mathematical Society 1 Journal of Scientific Computing 1 Applications of Mathematics 1 Journal of Non-Newtonian Fluid Mechanics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Vestnik St. Petersburg University. Mathematics 1 International Applied Mechanics 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Science in China. Series E 1 Computing and Visualization in Science 1 Journal of Applied Mechanics and Technical Physics 1 Computational Geosciences 1 Physical Review Letters 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Multiscale Modeling & Simulation 1 International Journal of Geometric Methods in Modern Physics 1 Foundations of Physics ...and 9 more Serials
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#### Cited in 30 Fields
1,225 Mechanics of deformable solids (74-XX) 66 Numerical analysis (65-XX) 60 Partial differential equations (35-XX) 58 Statistical mechanics, structure of matter (82-XX) 38 Fluid mechanics (76-XX) 31 Classical thermodynamics, heat transfer (80-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 17 Functions of a complex variable (30-XX) 16 Biology and other natural sciences (92-XX) 12 Optics, electromagnetic theory (78-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Differential geometry (53-XX) 7 Mechanics of particles and systems (70-XX) 7 Geophysics (86-XX) 6 Integral equations (45-XX) 4 Relativity and gravitational theory (83-XX) 3 History and biography (01-XX) 3 Ordinary differential equations (34-XX) 3 Statistics (62-XX) 3 Operations research, mathematical programming (90-XX) 3 Systems theory; control (93-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Information and communication theory, circuits (94-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.
| 2021-03-08T06:40:09 |
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https://alldimensions.fandom.com/wiki/Lightverse
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## FANDOM
1,815 Pages
Lightverse is a universe that there is no darkness, everything is bright. Everything put in Lightverse would be $abs(L+{\sqrt{L}})$ times more bright than its luminosity in our Universe.
But, the Lightversians are adapted to the Brightness. Also, the speed of light is VERY fast. It is 15,671 times faster than our universe (aproximately 300,000 km/s). And the equation to Energy is $E=mc^{15}$. (The speed of the light of Lightverse is 4,701,300,000 km/s)
The light on this universe is measured as litt.
Oh, and L=Luminosity of the object.
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-07-22T16:21:05 |
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http://sgovindarajan.wikidot.com/questions
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The integral
Evaluate the integral where $\Delta x$ is taken to be infinitesimal.
(1)
\begin{align} \int_{x}^{x+\Delta x} f(y) dy \end{align}
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2018-01-17T15:11:21 |
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https://pdglive.lbl.gov/DataBlock.action?node=B173M&home=sumtabB
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#### ${{\mathit \Omega}_{{c}}{(3000)}^{0}}$ MASS
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 3000.41 \pm0.22}$ OUR AVERAGE
$3000.7$ $\pm1.0$ $\pm0.2$ 38
2018 B
BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \Upsilon}{(4S)}}$
$3000.4$ $\pm0.2$ $\pm0.1$ 1.3k
2017 AH
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$2999.2$ $\pm0.9$ $\pm0.9$ ${}^{+0.19}_{-0.22}$ 24 1
2021 AC
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
1 Measured via ${{\mathit \Omega}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit \Omega}_{{c}}^{**0}}{{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{-}}$ . The third uncertainty is due to the uncertainty in the ${{\mathit \Xi}_{{c}}^{+}}$ mass.
References:
AAIJ 2021AC
PR D104 L091102
YELTON 2018B
PR D97 051102 Observation of Excited $\Omega_c$ Charmed Baryons in $e^+e^-$ Collisions
AAIJ 2017AH
PRL 118 182001 Observation of Five New Narrow ${{\mathit \Omega}_{{c}}^{0}}$ States Decaying to ${{\mathit \Xi}_{{c}}^{+}}{{\mathit K}^{-}}$
| 2022-10-06T19:58:34 |
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https://www.federalreserve.gov/econres/notes/feds-notes/monetary-policy-inflation-outlook-and-recession-probabilities-20220712.html
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July 12, 2022
Monetary Policy, Inflation Outlook, and Recession Probabilities1
Andrea Ajello, Luca Benzoni, Makena Schwinn, Yannick Timmer, and Francisco Vazquez-Grande
Introduction
An inverted yield curve—defined as an episode in which long-maturity Treasury yields fall below their short-maturity counterparts—is a powerful near-term predictor of recessions.2 While most previous studies focus on the predictive power of the spread between long- and short-maturity Treasury yields, Engstrom and Sharpe (2019) have recently shown that a measure of the nominal near-term forward spread (NTFS), given by the difference between the six-quarter-ahead forward Treasury yield and the current three-month Treasury bill rate, dominates long-term spreads as a leading indicator of economic activity.
Why does the NTFS predict recessions?
In this note we explore the economic forces that shape the NTFS dynamics and identify channels through which the NTFS forecasts recessions. In particular, we highlight the roles of the current stance of monetary policy and short-term inflation expectations in predicting downturns. Moreover, we examine the tradeoff between the Federal Reserve's ability to reduce inflation by increasing the federal funds rate and the effect of such intervention on the estimated likelihood of an upcoming recession.
The NTFS is an informative gauge of market-participants' expectations about future near-term monetary policy actions, such as the raising and lowering of the federal funds rate by the Federal Reserve. Thus, it carries information about current and near-term real interest rates, future expected inflation, and the interest rate forward risk premium (or term premium), which in turn are linked to expectations of future business cycle outcomes.
Building on these insights, we decompose the NTFS into four terms: the current and expected stance of monetary policy, measured as the policy gap between current or expected short-term real rates and their longer-run equilibrium level ($r^{\ast}$); the slope of inflation forecasts; and the term premium on the short-maturity forward yield. We explore the effect of these channels on the estimated probability of a recession and find that the power of the NTFS mostly lies in the information contained in the current real rate gap and the slope of short-run inflation expectations. In contrast, the near-term expected policy gap and the near-term premium contain little information that predicts downturns.
We perform the NTFS decomposition with the dynamic term structure model of Ajello, Benzoni, and Chyruk (2020, ABC), estimated on quarterly Treasury yields and inflation data from 1962Q2 to 2022Q2.3 The ABC model provides a good fit of the yield curve as well as core and headline inflation, both in and out of sample—an important requirement to decompose the sources of information contained in the NTFS that we exploit in this study.4 We focus on a long sample period that starts in the early 1960s to inform the analysis with data from the inflationary episodes from the 1960s through the early 1980s, as well as data from later years during which inflation realizations and expectations declined.
Using the variables from the NTFS decomposition, we estimate a probit model that predicts the probability of a recession in the U.S. economy over the next twelve months. We find that tighter current monetary policy relative to a neutral stance, i.e., a narrower current policy gap, and a downward near-term slope of the expected inflation path are significant predictors of recessions. In contrast, the near-term expected policy gap and the near-term premium contain little information that predicts downturns. Moreover, we show that the quality of fit and the predictive ability of our model is at par with other probit specifications that only include nominal yield spreads data.
Why does the NTFS predict that a recession is not imminent?
We use our framework to explore why, using data through the first quarter of 2022, Engstrom and Sharpe (2022) find that the NTFS predicts a low probability that the U.S. economy will transition into a recession over the next year. Our analysis has highlighted that the predictive power of the NTFS mostly stems from the information contained in the current monetary policy stance and the slope of expected inflation. Using data through early June 2022, we estimate a largely accommodative current policy gap that lowers the odds of an incipient economic downturn. We also find a downward sloping expected inflation curve. Historically a decrease in the slope of the expected inflation curve is associated with a higher likelihood of a recession. Of these two counter-acting effects the first one prevails, resulting in the low recession probability documented by Engstrom and Sharpe (2022). This is a rare combination of events that has not been observed prior to a U.S. recession over our sample period, extending back to the early 1960s.
What lies ahead as monetary policy continues to tighten?
While the NTFS is currently positive, market participants anticipate further monetary policy tightening in the upcoming months.5 If such interest rates hikes indeed materialize, they could result in a lower NTFS and thus an increase in recession probabilities. In the second part of this note, we use our NTFS decomposition to inform the channels that can lead to such a change in the economic outlook. We simulate future realizations of the policy gap and the slope of inflation forecasts from the ABC model from current initial conditions through 2023Q4. Through this analysis, we show that future inflation outcomes and the odds of a recession depend critically on both the pace of removal of monetary policy accommodation and on how restrictive the monetary policy stance will become over the medium term. In particular, we highlight two scenarios:
1. Baseline Case: The ABC model predicts that nominal and real yields will rise over the next six quarters, the current policy gap will narrow and become mildly restrictive in mid-2023, while core inflation will fall and remain around one percentage point above its model-implied longer-run expectations through 2023. The expected tightening of the policy gap and a downward-sloping expected inflation path combine to increase the one-year-ahead recession probability to about 35% by 2023, compared with the 16% unconditional estimate. Such a level is similar to the one estimated ahead of the 1994 monetary policy tightening cycle that was followed by a soft-landing scenario.
2. Tighter-Policy Scenario: We then consider an alternative scenario characterized by faster removal of monetary policy accommodation relative to the baseline forecasts. When we focus on model simulations in which the policy gap is markedly restrictive over 2023, we find that core inflation declines more rapidly than under the baseline, closing the gap with its model-implied longer-run expectations almost completely by the end of 2023. By that date, in this scenario the likelihood of a recession approaches 60%, a level that, based on our historical estimates, is generally followed by a recession in our sample.
In sum, our results highlight the role of the policy gap and the slope of near-term expected inflation as important predictors of U.S. recessions. Moreover, our analysis allows us to quantify the outcomes associated with monetary policy scenarios characterized by a different pace of removal of accommodation, and different degrees of overshooting of a model-consistent measure of the neutral long-run real rate. In our baseline case, the model expects the policy gap to close and become mildly restrictive, inflation to decline, and recession probability to increase to around 35% by 2023. However, we also identify a tighter-policy scenario for monetary policy in which the policy gap closes more rapidly and becomes more restrictive than under the baseline over the same time horizon. In this scenario inflation retreats more rapidly at the cost of a significantly higher recession risk. This analysis highlights the relationship between the potential risk of an economic contraction and the degree of monetary policy tightness that is enacted in response to inflationary pressures. Our results hinge on several modeling assumptions, e.g., we focus on the signal contained in the NTFS rather than the information in long-maturity yields. We discuss the reasons for these modeling choices and their implications for our results in the concluding section, leaving more work on this topic to future research.
1. A Decomposition of the Near-Term Slope of the Yield Curve
The NTFS is a measure of the short-run nominal yield curve slope, defined as:
$${\rm NTFS}_t={\rm fwd}_t^6-y_t^1,$$
Where ${\rm fwd}_t^6$ is the six-quarter ahead one-quarter Treasury rate and $y_t^1$ is the one-quarter Treasury rate at time $t$.
The NTFS closely mirrors market participants' expectations for the trajectory of the Federal Funds rate over the near future. Such expectations are influenced by views about the business cycle and monetary policy. For instance, if market participants anticipate a recession, they will also likely expect that monetary policymakers will lower the policy rate to provide accommodation. The expectation of lower future rates reduces forward rates, resulting in a negative NTFS. Thus, to the extent that markets' expectations are correct, a negative NTFS is associated with a heightened recession probability.
While the NTFS is an important measure of near-term monetary policy expectations, several underlying forces can affect its fluctuations. The spread embeds information about market participants' expectations about the path of real interest rates relative to their long-run equilibrium level. When real rates are at their neutral level, monetary policy is neither accommodative nor restrictive on the economy. In contrast, a negative policy gap indicates that the current, or future expected, monetary policy is accommodative, while a positive gap occurs when the Federal Reserve removes accommodation, to the point that the policy stance becomes restrictive. The NTFS also reflects market participants' expectations of future inflation outcomes and their attitudes toward interest rate risk, which all can carry information about the future evolution of the economy. Thus, movement in any of these components can drive fluctuations in the NTFS and help forecast downturn risk in their own right.
Motivated by these insights, we explore the distinct channels through which the NTFS predicts recessions. We decompose the NTFS in terms of (i) current and (ii) expected measures of the policy gap—an indicator of the degree of accommodation of the monetary policy stance, defined as the difference between the short-term real rate and a model-consistent estimate for the natural rate; (iii) the slope of the expected inflation path, and (iv) the term premium on short-maturity forward rates:6
(1) ${\rm NTFS}_t \approx \left(r_{t+6}^{e,1}-r_t^{\ast}\right) - \left(r_t^1-r_t^{\ast}\right) + (\pi_{t+7:t+10}^e-\pi_{t+1:t+4}^e) + (tp_t^{t+6})$.
The first two terms capture the slope of the policy gap over the next six quarters, defined as the distance of the expected and current real spot rates, $r_{t+6}^{e,1}$ and $r_t^1$, from the natural rate, denoted by $r_t^{\ast}$. The next term, $(\pi_{t+7:t+10}^e-\pi_{t+1:t+4}^e)$, reflects the slope of the times $t+6$ and $t$ one-year-ahead headline inflation forecasts computed using time $t$ information. The last term, $tp_t^{t+6}$, is the term premium that gauges the compensation for real and inflation risks embedded in the six-quarter forward nominal rate. All such variables respond over time to aggregate shocks to the outlook and to the conduct of monetary policy.
While the NTFS is easily measured with interest rate data, its constituents are not observable. To overcome this problem, in what follows we rely on the ABC model to estimate the expectation and risk premium components in term structure data. The ABC model jointly prices the real and nominal term structures using no-arbitrage restrictions. Estimation exploits a panel of nominal Treasury yields and CPI data on core, food, and energy inflation. In the model, the three inflation series have distinct dynamics that allow for a different degree of persistence and volatility of each inflation component. The three individual series recombine into a single headline inflation measure that ties nominal and real bond prices together. An important feature of the ABC model that we exploit in our analysis is that it can be estimated over a long historical sample of quarterly data starting in 1962Q2 and ending in 2022Q2.7 During this long window the U.S. economy has experienced alternating periods of inflationary pressure and easing, several monetary policy cycles, expansions, and recessions with different underlying drivers. These events will inform the ABC estimates of the terms in equation (1) and thus help us to identify the channels through which the NTFS predicts recessions. As a proxy for the natural rate $(r_t^{\ast})$, we use the ABC estimate of the level of real rates expected to prevail between five and ten years in the future. We interpret this measure as a market-based estimate of long-run equilibrium real rates, which serves as an approximation to the natural rate of interest.8 Finally, the proxy for expected inflation computed at quarters $t$ and $t+6$ is the average of quarterly ABC expected headline inflation over the following 4 quarters.
In the next section, we use the ABC estimates of the NTFS components to predict whether the U.S. economy will transition into a recession in the next four quarters. We compare these results to those from a model that relies on the NTFS alone as a leading indicator of economic activity.9
1.1 The Policy Gap, the Expected Inflation Slope, and Recession Probabilities
Table 1 shows estimates for the marginal effects of the explanatory variables of three probit models, on the probability that the U.S. will transition into a recession in any of the following four quarters.10 The first column displays the estimates for the benchmark model, in which the probability of a recession depends only on the NTFS. The second column displays the estimates for a probit specification estimated on the four NTFS components given on the right-hand side of equation (1): the six-quarters-slope of the expected inflation curve, the current policy gap, the six-quarter-ahead expected policy gap, and the term premium. The third column displays the estimates for our preferred probit model that excludes the six-quarter-ahead expected policy gap and the term premium, which are insignificant in model (2).
Table 1. Probit Models to Forecast Recessions
Model (1) Model (2) Model (3) -0.23*** n.a. n.a. (0.03) n.a. n.a. n.a. -0.29*** -0.27*** n.a. (0.04) (0.03) n.a. 0.15*** 0.13*** n.a. (0.02) (0.02) n.a. -0.05 n.a. n.a. (0.03) n.a. n.a. -0.06 n.a. n.a. (0.04) n.a. 0.74 0.75 0.72 147 137 136 237 237 237
Note: The dependent variable is an indicator variable that is equal to 1 if the U.S. economy is in a recession at any time over the next four quarters and is 0 otherwise. The entries in the table denote the marginal effect of one percentage point change the explanatory variables on the probability of recession over a 12-month horizon based on the coefficients from the probit regression. All specifications include a constant (not reported). Standard errors are reported in parentheses; * p < 0.05; ** p < 0.01; and *** p < 0.001. The pseudo-R2 values are computed according to McKelvey and Zavoina (1975). AIC refers to the Akaike information criterion. Expected inflation, real rates, and long-run r* estimates all come from the ABC model.
Model (1) confirms the finding of Engstrom and Sharpe (2019) that the NTFS is a significant predictor of economic downturns, with narrowing spreads pointing to a higher likelihood that the U.S. economy will transition into a recession in any of the next four quarters. Model (2) and model (3) show that an increase of the current policy gap, i.e., tighter policy today, is associated with higher probability of an upcoming recession. Moreover, lower future expected inflation relative to current expected inflation (a negative slope in the expected inflation curve) points to a higher likelihood of recession. This finding is mostly driven by the experience observed in the second part of the sample period, during which economic downturns have generally been accompanied by mild or even negative inflation.11 The marginal effect of the expected future policy gap and the term premium are not significant in model (2) and therefore we do not include these variables in model (3).12 Model (3) confirms that the bulk of predictive power in the NTFS comes from the current policy gap and the expected inflation slope, without loss of fit relative to model (1) and model (2) measured by the pseudo-R2 of McKelvey and Zavoina (1975) or by the Akaike information criterion.13
Figure 1 compares the fitted recession probability estimates based on model (1), the blue solid line, and (3), the green dashed line, as well as the 16% unconditional estimate of the recession-transition probability (the dotted line).14 While the signal that the probit models provide ahead of recessions is comparable across the two specifications, the fitted recession probability for model (3) features fewer false positives than the model that relies only on the NTFS as a leading indicator. This is visible in the mid-1960s and, more recently, in response to the taper tantrum episode of 2013.15
Figure 1. Probability of Recession Implied by NTFS, the Policy Gap, and Inflation Slope
Turning now to the current outlook, in model (1) a wide and positive NTFS predicts a near-zero probability that a recession will occur over the next four quarters. This evidence confirms the result highlighted by Engstrom and Sharpe (2022) for the first quarter of 2022 and extends it to 2022Q2. Model (3) helps us to interpret this finding. There are two opposing forces at play: On the one hand, the ABC estimate of the policy gap, $(r_t^1 – r_t^{\ast})$, is wide and negative in 2022Q1-2022Q2, pointing to a current high degree of monetary policy accommodation that is typically associated with a recovering economy. On the other hand, the expected inflation path is downward sloping, suggesting a higher likelihood of a downturn.16 On net, the large amount of monetary policy accommodation still at play in the U.S. economy outweighs the signal associated with a downward-sloping inflation curve, implying low odds of an incoming recession.
It is worth noting that the current combination of a wide and negative policy gap and downward expected inflation slope has not been observed ahead of any other recession over our sample period that extends back to the early 1960s.17 Figure 2 shows median (the solid lines) and interquartile ranges (the light blue shaded areas) of the current policy gap (left) and the near-term inflation slope (right) one to six quarters ahead of a historical contraction, and compares such realizations with the 2022Q2 estimates of the same two variables (the black dashed lines). The plots highlight that ahead of recessions the ABC estimates of the current policy gap are positive, while the near-term inflation slope tends to decline and, at times, turns negative. As of early June 2022, the ABC model estimates a negative expected inflation slope. However, the estimate of the current policy gap is wide and negative.
Figure 2. Policy Gap, Inflation Slope ahead of Recessions and Current Values
Looking forward, the Federal Reserve has signaled the possibility of additional federal funds rate increases; see, e.g., the estimates of the appropriate monetary policy path in the June 2022 Summary of Economic Projections. Consistent with such communications, market participants anticipate further monetary policy tightening in the coming months; for instance, the 2023 consensus forecasts of the federal funds rate in the July 2022 Blue Chip Survey of Financial Indicators are in the 3.4-3.5% range. If these expectations where to materialize, as the policy rate increases the NTFS could decrease or even turn negative, and the Engstrom and Sharpe (2019) model would then point to a much higher recession probability.
In the last part of this note, we turn to the NTFS decomposition to ask how the pace of future monetary policy tightening could influence recession risk and inflation outcomes.
2. What lies ahead as monetary policy continues to tighten?
An intuitive and key insight of our analysis is that the magnitude and sign of the current monetary policy gap has a significant impact on the likelihood of an upcoming recession. In this section, we quantify the impact of possible future monetary policy tightening on downturn risk and inflation outcomes. We simulate 100,000 samples of Treasury yields and inflation rates from the conditional density implied by our estimates of the ABC model, starting from 2022Q2 as our initial condition and going through 2023Q4. Along each of the simulated paths we construct future realizations of the current policy gap and the expected inflation slope and we use them to evaluate the recession probability predicted by our preferred probit model (3). We then compare outcomes across two scenarios: i) the baseline case, which reflects the ABC model forecasts or, equivalently, the average of the 100,000 simulated paths and ii) a tighter-policy scenario, characterized by faster removal of monetary policy accommodation and identified by the average of the simulated paths in which policy becomes restrictive by the end of 2022.18
Figure 3 compares the policy gap, the core inflation gap—defined as the difference between the annual rate of core inflation and its longer-run level expected by the ABC model—and recession probabilities for the baseline case (the blue lines), with the corresponding outcomes that would realize in the tighter-policy scenario (the red dashed lines). In the baseline case, real rates increase over the next year in response to monetary policy tightening and the policy gap shown in the left panel narrows and turns positive in the second quarter of 2023. As the inflation gap, shown in the middle panel, closes, the expected inflation slope (not shown) narrows and remains negative, approaching zero over the next few years. Accordingly, a narrowing policy gap and a persistent negative expected inflation slope increases the probability of recession implied by our preferred probit model (3) from its current near-zero estimate to about 25% percent in 2022Q4, reaching 35% by the end of 2023, as shown in the right panel. These probabilities are comparable to the levels estimated ahead of the 1994 monetary policy tightening that resulted in a soft-landing—i.e., a slowdown in inflation in the absence of an economic recession.
Figure 3. Expected Path of the Policy Gap, Core Inflation and Probability of Recession under Two Scenarios
By design, the policy gap closes more rapidly in the tighter-policy scenario. A faster removal of monetary policy accommodation leads inflation to decrease more rapidly than in the baseline scenario, and the one-year ahead recession probability increases to 35% by the end of 2022, compared to 25% in the baseline case. In this more restrictive scenario, the policy gap keeps tightening over 2023, and the core inflation gap closes by the end of 2023. By the end of 2023 the probability of recession implied by the model approaches 60% under the tighter-policy scenario, a level that in our historical estimates has generally been followed by a recession.
Conclusion
In this note, we use a dynamic term structure model to show that the current policy gap and the slope of the expected inflation path are the NTFS components that play the main role in predicting recessions. The decomposition helps us to explain why the NTFS does not currently forecast a recession, as shown by Engstrom and Sharpe (2022). We show that at present, the model estimates a wide and negative policy gap. Such high degree of monetary policy accommodation outweighs the signal coming from our estimate of a negative expected inflation slope, which points instead to a more likely contraction.
Going forward, however, the model expects monetary policy to become more restrictive, and thus it estimates a higher likelihood of a downturn. In our baseline case, we forecast increasing real rates, a narrowing policy gap, and a 35% recession probability by the end of 2023. Moreover, we illustrate a second, tighter-policy scenario in which policymakers tighten the stance of monetary policy more rapidly than expected by the model, pushing the real rate above neutral in the first quarter of 2023. In this alternative scenario, inflation declines more rapidly than in the baseline case, at the cost of a higher downside risk for economic activity, as the one-year ahead recession probability approaches 60% by the end of 2023.
Of course, our results hinge on several modeling assumptions. They are robust to many alternative choices that we have examined, but certainly not all. First, we rely on a specific dynamic term structure model to parse the expectations and risk premium NTFS components, and to infer the long-run equilibrium real rate $r^{\ast}$. The literature has provided a wide range of alternative $r^{\ast}$ estimates that are generally characterized by a high degree of uncertainty. In unreported checks, we verify that our main conclusions are robust to adopting such alternative measures.19 Second, and more importantly, our analysis focuses on the decomposition of the Engstrom and Sharpe (2019) NTFS, rather than long-term yield spreads. We focus on the NTFS because of both its success as a leading indicator of economic activity, and the desire to better understand the link between the short- and medium-term monetary policy stance and recessions. Usually, the information content of the NTFS is qualitatively similar to that of long-term spreads. However, current times are different. The recent decline in the ten- minus two-year spread, which has turned negative, has received considerable attention as it has already started to point toward a significantly higher probability of recession. Part of the signal from the long-term spread comes from the slope of long-term risk premia. For instance, Benzoni, Chyruk, and Kelley (2018) show that the slope in long-term inflation- and real-rate risk premia are significant predictors of incoming downturns. In particular, the ABC model estimates a recent increase in the real rate risk premium, which in Benzoni, Chyruk, and Kelley (2018) is associated with a significant increase in downturn risk.20 This discussion underscores that more work is warranted to better understand the link between the yield curve and the economy. We leave further analysis to future research.
References
Ajello, Andrea, Luca Benzoni, and Olena Chyruk (2020). "Core and 'Crust': Consumer Prices and the Term Structure of Interest Rates," Review of Financial Studies, Vol. 33, No. 8, pp. 3719–3765.
Ang, Andrew, Geert Bekaert, and Min Wei (2008). "The term structure of real rates and expected inflation," Journal of Finance, Vol. 63, No. 2, pp. 797-849
Bauer, Michael D., and Thomas M. Mertens (2018). "Economic forecasts with the yield curve," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, No. 2018-07, March 5.
Bauer, Michael D., and Thomas M. Mertens (2018). "Information in the yield curve about future recessions," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, No. 2018-20, August 27.
Benzoni, Luca, Olena Chyruk, and David Kelley (2018). "Why Does the Yield-Curve Slope Predict Recessions?" Chicago Fed Letter Number 404.
Cooper, Daniel H., Jeffrey C. Fuhrer, and Giovanni P. Olivei (2020). "Predicting Recessions Using the Yield Curve: The Role of the Stance of Monetary Policy," Current Policy Perspectives 87522, Federal Reserve Bank of Boston.
Engstrom, Eric C., and Steven A. Sharpe (2019). "The Near-Term Forward Yield Spread as a Leading Indicator: A Less Distorted Mirror," Financial Analysts Journal, 75:4, 37-49.
Engstrom, Eric C., and Steven A. Sharpe (2022). "(Don't Fear) The Yield Curve, Reprise," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, March 25, 2022
Estrella, Arturo, and Gikas A. Hardouvelis (1991). "The Term Structure as a Predictor of Real Economic Activity," The Journal of Finance 46(2): 555–576.
Estrella, Arturo, and Frederic S. Mishkin (1998). "Predicting U.S. recessions: Financial variables as leading indicators," Review of Economics and Statistics, Vol. 80, No. 1, February, pp. 45–61.
Fama, Eugene F. (1986). "Term premiums and default premiums in money markets," Journal of Financial Economics, Vol. 17, No. 1, pp. 175–196.
Favero, Carlo A., Iryna Kaminska, and Ulf Söderström (2005). "The predictive power of the yield spread: Further evidence and a structural interpretation," working paper, Università Bocconi.
Hamilton, James D., and Dong Heon Kim (2002). "A reexamination of the predictability of economic activity using the yield spread," Journal of Money, Credit and Banking, Vol. 34, No. 2, pp. 340–60.
Harvey, Campbell R. (1988). "The real term structure and consumption growth," Journal of Financial Economics, Vol. 22, No. 2, pp. 305–333.
Harvey, Campbell R. (1989). "Forecasts of Economic Growth from the Bond and Stock Markets," Financial Analysts Journal 45(5): 38–45.
Harvey, Campbell R. (1991). "The term structure and world economic growth," Journal of Fixed Income, Vol. 1, pp. 4–17.
Harvey, Campbell R. (1993). "The term structure forecasts economic growth," Financial Analysts Journal, May/June, pp. 6–8.
Holston, K., Laubach, T., & Williams, J. C. (2017). Measuring the natural rate of interest: International trends and determinants. Journal of International Economics, 108, S59–S75.
Kessel, Reuben A. (1965). "The cyclical behavior of the term structure of interest rates," National Bureau of Economic Research, occasional paper, No. 9.
McKelvey, Richard D., and William Zavoina (1975). "A statistical model for the analysis of ordinal level dependent variables," The Journal of Mathematical Sociology, 4:1, 103-120.
Rudebusch, Glenn D., Brian P. Sack, and Eric T. Swanson (2007). "Macroeconomic implications of changes in the term premium," Federal Reserve Bank of St. Louis, Review, July/August, Vol. 89, No. 4, pp. 241–269.
Rudebusch, Glenn D., and John C. Williams (2009). "Forecasting recessions: The puzzle of the enduring power of the yield curve," Journal of Business & Economic Statistics, Vol. 27, No. 4, pp. 492–503.
Stock, James H., and Mark W. Watson (1989). "New Indices of Coincident and Leading Indicators," in NBER Macroeconomic Annual 4, edited by Olivier J. Blanchard and Stanley Fischer, 351–394. Cambridge, MA: MIT Press
Wright, Jonathan H. (2006). "The yield curve and predicting recessions," Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series, No. 2006-7.
Appendix
The NTFS can be expressed as the difference between the expected one-quarter nominal Treasury yield that markets believe will prevail 6 quarters from now, $y_{t+6}^{e,1} = E_t[y_{t+6}^1]$, and the current one-quarter yield, plus the difference in term premium on the six-quarter-ahead forward rate and on the one-quarter Treasury yield, ($tp_t^{t+6} - tp_t^1$), where $tp_t^1 = 0$:
$${\rm NTFS}_t = y_{t+6}^{e,1} - y_t^1 + tp_t^{t+6}.$$
In the short run the Fisher equation holds in approximation, and the nominal short-term rate can be written as the sum of the real rate and expected inflation k-periods ahead, multiplied by a constant $0 \lt \delta \le 1$,
$$y_t^1 \approx r_t^1 + \delta\pi_{t+1:t+k}^1.$$
Hence, the NTFS can be further decomposed as the sum of the real forward spread, $(r_{t+6}^{e,1}-r_t^1)$, the slope of the expected inflation path $\delta(\pi_{t+7:t+6+k}^e - \pi_{t+1:t+k}^e)$, and the term premium term, $tp_t^{t+6}$. Using an annual expected rate of inflation, with $k$= 4, and setting $\delta$=1, we obtain
$${\rm NTFS}_t \approx (r_{t+6}^{e,1} - r_t^1) + (\pi_{t+7:t+10}^e - \pi_{t+1:t+4}^e) + (tp_t^{t+6}).$$
Adding and subtracting the natural rate $r_t^{\ast}$ on the right-hand side of the previous expression and rearranging terms, we obtain that the NTFS can be decomposed in three terms,
$${\rm NTFS}_t \approx \left(r_{t+6}^{e,1} - r_t^{\ast}\right) - \left(r_t^1 - r_t^{\ast}\right) + (\pi_{t+7:t+10}^e - \pi_{t+1:t+4}^e) + (tp_t^{t+6}),$$
which is equation (1) in the text.
1. Luca Benzoni is with the Federal Reserve Bank of Chicago; Andrea Ajello, Makena Schwinn, Yannick Timmer, and Francisco Vazquez-Grande are with the Board of Governors of the Federal Reserve System. We are grateful to Gene Amromin, Jim Clouse, Rochelle Edge, Eric Engstrom, Giovanni Favara, Spencer Krane, Trevor Reeve, David López-Salido, Steve Sharpe, and Min Wei for many insightful comments. All errors and omissions are our own. The views expressed in this note are solely those of the authors and should not be interpreted as reflecting the views of the Federal Open Market Committee, the Board of Governors of the Federal Reserve System, the Federal Reserve Bank of Chicago, or of anyone else associated with the Federal Reserve System. Return to text
2. Many studies have documented the predictive power of the term structure slope to forecast recessions. Early work by Kessel (1965) was followed by several influential articles, e.g., Fama (1986), Harvey (1988, 1989, 1991, and 1993), Stock and Watson (1989), Estrella and Hardouvelis (1991), Estrella and Mishkin (1998), Rudebusch and Williams (2009). Return to text
3. Data for 2022Q2 includes the CPI release of June 10th and Treasury yields through June 9th. Return to text
4. Ajello, Benzoni, and Chyruk (2020) document that the ABC model outperforms a wide array of statistical models in forecasting core and headline inflation as well as interest rates. Moreover, they show that the ABC prediction errors are systematically lower than those of professional survey forecasts, such as the Survey of Professional Forecasters and the Blue Chip Economic Indicators. Return to text
5. For instance, the consensus forecasts for the 2023 realization of the federal funds rate are in the 3.4-3.5% range in the Blue Chip Survey of Financial Indicators released on July 1, 2022. This forecast is slightly below the 3.6-4.1% central tendency projection for the 2023 federal funds rate associated with the appropriate monetary policy path in the Summary of Economic Projections (SEP) released in June 2022 by the Federal Open Market Committee. Return to text
6. See the Appendix below for more details on how we derive equation (1). Return to text
7. More specifically, we use inflation and Treasury yields data available through June 10, 2022. There is a trade off in the choice of the sample period. On the one hand, including the inflationary episodes of the 1960-70s is beneficial to study the recent, unusually high inflation realizations. On the other hand, this choice forces us to span a sample period characterized by multiple regimes of monetary policy that might be better captured by, e.g., a regime switching model (see, e.g., Ang, Bekaert, and Wei (2008)). Indeed, using data prior to the recent inflation outburst, ABC show that their model has a better out-of-sample performance when estimated on post-1985 data. Return to text
8. We define the natural rate of interest as the real short-term interest rate that would prevail absent transitory disturbances. Our proxy for the natural rate is the short-term real rate expected to prevail in the longer run as all transitory shocks have dissipated. This is different from shorter-run estimates of r* from dynamic general equilibrium models, in which the natural rate is the real rate that would prevail in an efficient equilibrium absent nominal frictions. See Holston, Laubach and Williams (2017) and references therein for more details on the distinction between natural and neutral rates. Return to text
9. This extends previous work by Ang, Piazzesi, and Wei (2006), Bauer and Mertens (2018a and b), Benzoni, Kelley, and Chyruk (2018), Favero, Kaminska, and Söderström (2005), Hamilton and Kim (2002), Rudebusch, Sack, and Swanson (2007), and Wright (2006), who exploit a term‐structure decomposition into its expected nominal rate path and risk premium terms. Return to text
10. We estimate probit models to forecast recession conditioned on whether the U.S. economy is currently in expansion or in recession. The dependent variable is an indicator variable that is equal to 1 if the U.S. economy is in a recession at any time over the next 4 quarters and is 0 otherwise. The dating of recessions follows the National Bureau of Economic Research (NBER) convention. We use the "NBER based Recession Indicators for the United States from the Peak through the Trough" from FRED (Federal Reserve Economic Data).
The recession probability implied by the specification of model (2) takes the following form:
$$P\left({NBER}_{t+1:t+4}=1|{NBER}_t\right) = \Phi \left(\alpha_{NBER_t}+\beta_{NBER_t}^{\pi}(\pi_{t+7:t+11}^e - \pi_{t+1:t+4}^e) + \beta_{NBER_t}^{gap} (r_t^1-r_t^{\ast}) + \beta_{NBER_t}^{gap^e}(r_{t+6}^{e,1}-r_t^{\ast}) + \\\\ + \beta_{NBER_t}^{tp}(tp_t^{t+6}) \right)$$
Where $\Phi$ represents the cumulative distribution function of a standard normal distribution. The model parameters take two values depending on whether the U.S. economy is assessed to be in an expansion ($NBER_t=0$) or in a recession ($NBER_t=1$). Table 1 only displays marginal effects and not model parameter estimates.Return to text
11. Indeed, we find that the marginal effect of the near-term inflation slope is even stronger when we estimate the probit model with the NTFS decomposition produced by the ABC model over the post-1985 period. Return to text
12. Ang, Piazzesi, and Wei (2006) also find that the term premium is insignificant in predicting economic activity. Return to text
13. Recent work by Cooper, Fuhrer and Olivei (2020) documents that the stance of monetary policy plays a determinant role in forecasting recessions. While they focus on the forecasting power of the policy gap as a complement to longer-term yield spreads, we document that the policy gap and the expected inflation slope drive the forecasting power of the near-term forward spread. Return to text
14. The unconditional estimate of the recession-transition probability is computed as the fraction of times, measured in quarters, during which the economy was in a recession since 1962. Return to text
15. Consistent with these findings, we document in unreported results that the variables in our NTFS decomposition predict real activity measures such as GDP growth in linear regressions. Return to text
16. Note that if inflation pressures were to decrease for reasons other than a weakening of the economic outlook—e.g., due to a normalization of the supply chain, and a resolution of geopolitical tensions in Europe—a negative expected inflation slope might be less informative about the probability of an upcoming contraction. Return to text
17. Univariate probit models (not shown) fitted to each NTFS component independently show that the negative values of expected inflation slope pointed to high recession probabilities before 1980—and especially in the 1970s. The contribution of the inflation slope predictor appears muted past 1980 when revisions in inflation expectations were less volatile and has started playing a more prominent role in pointing to a future downturn since the end of 2021. Return to text
18. As of June 10, 2022, the baseline ABC model predicts that nominal yields will rise to 2.5% in 2022 and peak at 2.8% in 2023. In the alternative more restrictive scenario, the nominal spot rate path peaks at 5.1% in 2023. (Note that in the June 2022 SEP, the ranges for the federal funds rate at the end of 2022 and 2023 were 3.1 to 3.9% and 2.9 to 4.4%, respectively.) Core CPI inflation in the baseline scenario declines to 3.8% by the end of 2023, and the longer-run core inflation expectation, defined as the 5-year-5-year-forward average core inflation rate, is 2.7%. In the alternative scenario core CPI inflation in 2023 is 3.1% and the longer-run expectation is 3.1%. Return to text
19. In unreported robustness checks, we have also considered $r^{\ast}$ estimates obtained from the models of Holston, Laubach and Williams (2017), Johannsen-Mertens (2016), Lewis and Vazquez-Grande (2017), Lubik and Matthes (2015), and Del Negro et al. (2017). We obtain qualitatively the same results for all the right hand-side variables except for the coefficients on the 6-quarter-ahead expected policy gap, which for some models is estimated to be negative and significant. Return to text
20. In probit model (2), the slope of the near-term premium is insignificant, while the risk-premia slopes are significant in Benzoni, Chyruk, and Kelley (2018). There are two reasons for this discrepancy. First, in this article we focus on a decomposition of the NTFS and therefore only consider the effect of the short-term premium, which is smaller and less cyclical than the premia estimated on longer-term yields. Second, Benzoni et al. decompose the term-premium slope into its inflation and real-rate components, which they find to have marginal effects of opposite sign. Return to text
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https://www.scstatehouse.gov/sess121_2015-2016/sj16/20160407.htm
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South Carolina General Assembly
121st Session, 2015-2016
Journal of the Senate
Thursday, April 7, 2016
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 11:00 A.M., 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:
In Exodus Moses declares:
"The Lord is my strength and my song; he has become my salvation." (Exodus 15:2a)
Join your heart with mine as we pray, if you will:
O loving God, we understand that in a city nearby a particular event begins today, a tournament requiring special skills, a contest demanding mental and physical strength. In some ways, of course, all that is also a description of what these leaders do in this Senate Chamber day by day: each of them working conscientiously to bring about "championship results" for South Carolina. Yet in this setting all of the efforts of these players are not a game, but instead a serious push to move our State forward in the very best ways possible. So, may it be, O God, that all South Carolinians will soon be able to cheer loudly -- and with good reason -- for solid, positive, and worthwhile results. In Your blessed name we pray, O Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
MESSAGE FROM THE GOVERNOR
The following appointment was transmitted by the Honorable Nikki Randhawa Haley:
Local Appointment
Initial Appointment, Darlington County Part-Time Magistrate, with the term to commence April 30, 2015, and to expire April 30, 2019
Craig L. LaCross, 716 Lee State Park Road, Lamar, SC 29069 VICE Cely A. Brigman
Doctor of the Day
Senator GROOMS introduced Dr. Marc New of North Charleston, S.C., Doctor of the Day.
Leave of Absence
At 10:59 A.M., Senator CAMPSEN requested a leave of absence for Senators CLEARY and CAMPBELL for the day.
Leave of Absence
At 11:08 A.M., Senator BENNETT requested a leave of absence for Senators HEMBREE and THURMOND for the day.
Leave of Absence
At 11:17 A.M., Senator ALLEN requested a leave of absence for Senator M.B. MATTHEWS for the day.
Leave of Absence
At 11:39 A.M., Senator NICHOLSON requested a leave of absence for Senator REESE for the day.
Expression of Personal Interest
Senator VERDIN rose for an Expression of Personal Interest.
Remarks by Senator VERDIN
Thank you, Mr. PRESIDENT, members of the Senate. I'm not nearly as disconcerted today as I was yesterday and for that, I apologize. When we get to the point in the Calendar where we have the opportunity to take up the animal welfare slate of Bills, I'll be moving for their carryover. So, I'm here this morning with the burden of my heart from yesterday.
I really want to talk about our daily bread. We are so privileged and so blessed... and I'm going to be more specific and direct my remarks to a Bill that is on the Calendar and of peculiar and unique interest to me. I will explain myself before I take my seat. If I take more than five minutes, I would ask for an extension.
This is just a gentle reminder to myself and to us of the source from which we derive our daily bread. As I practice my Christian faith and draw my counsel and my instruction from the Canon of Scripture, Old and New Testaments, I can't help but be rebuked when I sometimes fail to acknowledge the Source and Giver of our daily bread. "In the beginning..." As we find ourselves, as we consider ourselves, in Adam's race and we can look back and see ourselves in the Garden of Eden, we would then, once in our collective human lifetime, know what is, what we speak of sometimes flippantly as, a perfect world. We have only seen a perfect world for a short period, even though, in our daily endeavors, we are striving for a perfect world. We are striving for a new heaven and a new earth. As I've contemplated the reason we find ourselves with an expanded statutory code, with an expanded government -- as we all measure the intent of our hearts, I find myself always compelled to go back and find some basis in my faith. So, I am thankful that even after -- in the perfect world -- God's provision was profound and manifold. Even after the imperfection entered the world, I am thankful for His provision and I am thankful for His daily bread. We're thankful for every bountiful blessing, but we start with what is rudimentary. Our children can be thankful they have parents-- symbolized as our first parents Adam and Eve. Cain and Abel can be thankful for their parents that provided food, raiment and shelter. My faith teaches me that Cain and Abel were directed by their parents to the Giver of Life, hence, the source of the bread of life.
Even as further imperfection manifested itself in the world, after Adam was removed from the world of perfection into toil and labor for his daily sustenance, as his progeny came along with further imperfection and offered the fruits of their labor, which was not acceptable in the eyes of God, even then, was Cain mercifully dealt with by his Lord. He was directly preserved from the wrath and retribution of man and God was his Judge and part of his judgment was that his daily sustenance would be further impaired -- the land would no longer bring forth a great increase for him. In the annals of time and millennia, from the first family right on through the multiple generations, the historical record is abundantly clear that our daily bread, the very sustenance of life, was a spiritual matter. It was physical, but it was spiritual.
Even as our Lord was in His earthly ministry, he pointed back to Moses to remind that Moses was not the provider of our daily bread. Moses was the instrument of the Lord, for His people, in the provision of their daily bread, hence, a spiritual and a physical manifestation and a union.
Our Lord, Himself, again, millennia closer, really, not that too distant removed from us today, providentially, as His people followed Him into a remote location on the other side of the Sea of Galilee, once again used an instrument -- a young lad with five loaves and two fishes. A multitude, five thousand or more, and the young lad, faithful to his mission and his ministry, was in the role, used of the Lord to take care of His people. I'm going to extrapolate. I'm not going to use the USDA statistics but I will just say this: if that Israelite was an instrument in feeding that five thousand, it would take a thousand of him under the same demonstration of the Lord's mercy to feed five million.
The point is, whether it be God teaching Adam, God teaching Cain, God teaching His disciples or His followers; there are some things in life, life itself, the emblem of life -- the bread of life, that are about the relationship. The relationship is for time and for eternity. We deal in time.
I believe this rudimentary symbol of bread is inescapable to us. We've proven you can go without shelter and maintain life. Mankind has proven that. Mankind has proven you can go without raiment, sometimes embarrassingly. I'll bring it right here to the twenty-first century, across the steps of Europe and the plains of Asia, in our century, we have seen hundreds of millions of our fellow man, perish for the lack of provision -- instrument or the hand of God. We remove ourselves from even our recent history when we consider the bread of life -- that mana from heaven to the Israelites was to remind them... and us, subsequently.
I can't help but think of George Muller, even, two centuries before in the nineteenth, as he was doing the Lord's work ministering to the children and sometimes they would not eat the one piece of bread they had received that day. They would hold it in their hand over night, in faith, that God would provide the next day. Muller was the instrument; God used him.
I'll just say this, in closing -- God reigns supreme. He holds this world in His hands -- it wasn't global warming that put the anomaly in the Atlantic Ocean in October, the convergence of a northeastern storm, a cold front pressing across this country, the unprecedented twenty-seven inches of rain that flooded our State. Out of the thousand or more that were directly impacted in this peculiar and particular arena of being instruments for our daily bread, I can assure you, if they are familiar with Adam Smith or Milton Friedman, they're thankful that even those men can be instruments in the hands of God for being providers of our daily bread.
I'm intimately acquainted with scores of these families. I have commercial relationships in over a third of the counties of this State -- hence, my conflict and my anxiety yesterday -- not being able to engage the subject, not knowing the debate was really going to transpire yesterday. I'm abstaining from the debate; I'm recusing myself from the conversation and the floor work, if we get to it, or anything subsequent other actions of the House of Representatives or the Executive Branch, but I will pray for you and for everyone who truly can say it is all of the Lord that we sustain one day of life, one moment of life. If we have a particular opportunity to express some expression, I would pray that we seek it and find it -- whatever our walk of life is and whatever our course may carry us to. I appreciate your time.
On motion of Senator ALEXANDER, with unanimous consent, the remarks of Senator VERDIN were ordered printed in the Journal.
ACTING PRESIDENT PRESIDES
Senator CROMER assumed the Chair.
CO-SPONSORS ADDED
The following co-sponsors were added to the respective Bills:
S. 1016 (Word version) Sen. Alexander
S. 1064 (Word version) Sen. Rankin
S. 1136 (Word version) Sen. Campsen
S. 1203 (Word version) Sen. Fair
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 1211 (Word version) -- Senators Grooms and Campbell: A BILL TO AMEND SECTION 58-31-310 OF THE 1976 CODE, RELATING TO PROVIDING ELECTRIC SERVICE, TO PROVIDE DEFINITIONS; AND TO AMEND TITLE 31, CHAPTER 58, RELATING TO PROVIDING ELECTRIC SERVICE, BY ADDING SECTION 58-31-470 TO AUTHORIZE A PILOT PROGRAM REQUIRING THE PUBLIC SERVICE AUTHORITY TO SELL POWER TO ELECTROLYTIC PROCESSORS AT MARKET-BASED PRICES WHILE PROTECTING THE PUBLIC SERVICE AUTHORITY'S OTHER CUSTOMERS FROM ANY ADDITIONAL COSTS.
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Read the first time and referred to the Committee on Judiciary.
S. 1212 (Word version) -- Senator Bright: A BILL TO AMEND SECTION 7-7-490, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN SPARTANBURG COUNTY, SO AS TO ADD THE RIVER RIDGE PRECINCT, AND TO REDESIGNATE THE MAP NUMBER ON
WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE REVENUE AND FISCAL AFFAIRS OFFICE.
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Read the first time and referred to the Committee on Judiciary.
S. 1213 (Word version) -- Senator Coleman: A CONCURRENT RESOLUTION TO RECOGNIZE THE LIFE OF MRS. ELIZABETH TANT "LIBBY" THRAILKILL OF FORT LAWN, AND TO HONOR HER PASSION FOR, DEDICATION AND SERVICE TO, EVERYONE AROUND HER.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 1214 (Word version) -- Senators Jackson and Courson: A SENATE RESOLUTION TO RECOGNIZE AND HONOR THE DREHER HIGH SCHOOL GIRLS VARSITY BASKETBALL TEAM, COACHES, AND SCHOOL OFFICIALS FOR AN OUTSTANDING SEASON AND TO CONGRATULATE THEM FOR WINNING THE 2015-2016 CLASS AAA STATE CHAMPIONSHIP TITLE.
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The Senate Resolution was adopted.
S. 1215 (Word version) -- Senator Shealy: A SENATE RESOLUTION TO RECOGNIZE AND HONOR THE PELION HIGH SCHOOL MARCHING BAND FOR ITS OUTSTANDING SEASON AND TO CONGRATULATE THESE FINE MUSICIANS ON WINNING THE 2015 SOUTH CAROLINA BAND DIRECTORS ASSOCIATION CLASS AA STATE CHAMPIONSHIP TITLE.
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The Senate Resolution was adopted.
S. 1216 (Word version) -- Senator Coleman: A SENATE RESOLUTION TO RECOGNIZE AND HONOR METROPOLITAN AFRICAN METHODIST EPISCOPAL ZION CHURCH UPON THE OCCASION OF ITS ONE HUNDRED FIFTIETH ANNIVERSARY AND TO CONGRATULATE THE PASTOR, CONGREGATION, AND CHURCH STAFF FOR MORE THAN A CENTURY AND A HALF OF FAITHFUL SERVICE TO THEIR CONGREGANTS AND COMMUNITY.
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The Senate Resolution was adopted.
S. 1217 (Word version) -- Senators McElveen, Alexander, Allen, Bennett, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Corbin, Courson, Cromer, Davis, Fair, Gregory, Grooms, Hayes, Hembree, Hutto, Jackson, Johnson, Kimpson, Leatherman, Lourie, Malloy, L. Martin, S. Martin, Massey, J. Matthews, M. B. Matthews, Nicholson, Peeler, Rankin, Reese, Sabb, Scott, Setzler, Shealy, Sheheen, Thurmond, Turner, Verdin, Williams and Young: A SENATE RESOLUTION TO RECOGNIZE AND HONOR THE SOUTH CAROLINA AUTISM SOCIETY FOR ITS OUTSTANDING SERVICE TO CHILDREN AND OTHERS WHO ARE AFFECTED BY AUTISM AND TO DECLARE APRIL 2016 AS "AUTISM AWARENESS MONTH" IN THE PALMETTO STATE.
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The Senate Resolution was adopted.
S. 1218 (Word version) -- Senator Shealy: A SENATE RESOLUTION TO RECOGNIZE AND CONGRATULATE THE NORTH CAROLINA BUSINESS ASSOCIATION'S MISS SC PEARLS SCHOLARSHIP PAGEANT AND GALA.
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The Senate Resolution was adopted.
PRESIDENT PRESIDES
At 11:20 A.M., the PRESIDENT assumed the Chair.
REPORT OF STANDING COMMITTEE
Senator CLEARY from the Committee on Invitations polled out S. 991 favorable:
S. 991 (Word version) -- Senator Verdin: A CONCURRENT RESOLUTION DESIGNATING MAY 11, 2016, AS "DIFFUSE INTRINSIC PONTINE GLIOMA AWARENESS DAY" IN SOUTH CAROLINA.
Poll of the Invitations Committee
Polled 11; Ayes 10; Nays 0; Not Voting 1
AYES
Cleary Alexander Verdin
Campsen Cromer Malloy
Johnson Kimpson McElveen
Campbell
Total--10
NAYS
Total--0
NOT VOTING
Reese
Total--1
Ordered for consideration tomorrow.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
READ THE THIRD TIME
SENT TO THE HOUSE
The following Bill was read the third time and ordered sent to the House of Representatives:
S. 982 (Word version) -- Senators Peeler, Grooms and Bryant: A BILL TO AMEND SECTION 12-36-2120, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EXEMPTIONS FROM THE STATE SALES TAX, SO AS TO EXEMPT NATURAL GAS SOLD TO A PERSON WITH A MISCELLANEOUS FUEL USER FEE LICENSE WHO WILL PRODUCE COMPRESSED NATURAL GAS OR LIQUEFIED NATURAL GAS FOR USE AS MOTOR FUEL IN THEIR OWN MOTOR VEHICLES AND REMIT THE APPLICABLE MOTOR FUEL USER FEES.
READ THE SECOND TIME
S. 267 (Word version) -- Senators Young, Campsen, Hembree, Bennett, Turner, Thurmond, Davis, Bright, Bryant, L. Martin, S. Martin, Hayes, Campbell and Grooms: A BILL TO AMEND SECTION 2-1-180 OF THE 1976 CODE, RELATING TO ADJOURNMENT OF THE GENERAL ASSEMBLY, TO CHANGE THE DATE FOR THE MANDATORY ADJOURNMENT OF THE GENERAL ASSEMBLY FROM THE FIRST THURSDAY IN JUNE TO THE FIRST THURSDAY IN MAY, AND PROVIDE THAT IN ANY YEAR THAT THE HOUSE OF REPRESENTATIVES FAILS TO GIVE THIRD READING TO THE APPROPRIATIONS BILL BY MARCH FIRST, RATHER THAN MARCH THIRTY-FIRST, THE DATE OF ADJOURNMENT IS EXTENDED BY ONE STATEWIDE DAY FOR EACH STATEWIDE DAY AFTER MARCH FIRST, THAT THE HOUSE FAILS TO GIVE THE BILL THIRD READING.
The Senate proceeded to a consideration of the Bill.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 0
AYES
Alexander Allen Bennett
Bright Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Jackson Johnson Kimpson
Leatherman Martin, Larry Martin, Shane
Massey Matthews, John McElveen
Nicholson Peeler Rankin
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--35
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1178 (Word version) -- Fish, Game and Forestry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF NATURAL RESOURCES, RELATING TO ADDITIONAL REGULATIONS APPLICABLE TO SPECIFIC PROPERTIES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4634, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
The Senate proceeded to a consideration of the Resolution.
Senator CAMPSEN explained the Resolution.
The question being the second reading of the Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 1
AYES
Alexander Allen Bennett
Bryant Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Johnson Kimpson Leatherman
Malloy Martin, Larry Martin, Shane
Massey Matthews, John McElveen
Nicholson Peeler Sabb
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--35
NAYS
Bright
Total--1
The Resolution was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1179 (Word version) -- Fish, Game and Forestry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF NATURAL RESOURCES, RELATING TO WILDLIFE MANAGEMENT AREA REGULATIONS; AND TURKEY HUNTING RULES AND SEASONS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4635, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
The Senate proceeded to a consideration of the Resolution.
Senator CAMPSEN explained the Resolution.
The question being the second reading of the Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 1
AYES
Alexander Allen Bennett
Bryant Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Johnson Kimpson Leatherman
Malloy Martin, Larry Martin, Shane
Massey Matthews, John McElveen
Nicholson Peeler Sabb
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--35
NAYS
Bright
Total--1
The Resolution was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1180 (Word version) -- Fish, Game and Forestry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - BOARD OF REGISTRATION FOR FORESTERS, RELATING TO FEES FOR REGISTRATION AND RENEWAL, DESIGNATED AS REGULATION DOCUMENT NUMBER 4627, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
The Senate proceeded to a consideration of the Resolution.
The question being the second reading of the Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 1
AYES
Alexander Allen Bennett
Bryant Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Johnson Kimpson Leatherman
Malloy Martin, Larry Martin, Shane
Massey Matthews, John McElveen
Nicholson Peeler Sabb
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--35
NAYS
Bright
Total--1
The Resolution was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 689 (Word version) -- Senators Hembree and McElveen: A BILL TO AMEND SECTION 56-1-50(B)(2) AND (C) OF THE 1976 CODE, RELATING TO MOTOR VEHICLE BEGINNER'S PERMIT AND VEHICLE OPERATION, TO PROVIDE THAT A PERMITTEE MAY NOT OPERATE A MOTORCYCLE, MOTOR SCOOTER, OR LIGHT MOTOR-DRIVEN CYCLE AT ANY UNPERMITTED TIME UNLESS SUPERVISED BY A LICENSED MOTORCYCLE, MOTOR SCOOTER, OR LIGHT MOTOR-DRIVEN CYCLE OPERATOR AND TO PROVIDE THAT THE ACCOMPANYING DRIVER MUST BE WITHIN A SAFE VIEWING DISTANCE OF THE PERMITTEE WHEN THE PERMITTEE IS OPERATING A MOTORCYCLE OR A THREE-WHEEL VEHICLE.
The Senate proceeded to a consideration of the Bill.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 33; Nays 0
AYES
Alexander Allen Bennett
Bright Campsen Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hutto Johnson
Kimpson Leatherman Malloy
Martin, Larry Martin, Shane Massey
Matthews, John McElveen Nicholson
Peeler Scott Setzler
Shealy Sheheen Turner
Verdin Williams Young
Total--33
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
COMMITTEE AMENDMENT ADOPTED
READ THE SECOND TIME
S. 1073 (Word version) -- Senators Setzler and Alexander: A BILL TO AMEND SECTION 12-6-40, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE APPLICATION OF THE INTERNAL REVENUE CODE TO STATE INCOME TAX LAWS, SO AS TO UPDATE THE REFERENCE TO THE INTERNAL REVENUE CODE TO THE YEAR 2015 AND TO PROVIDE THAT IF THE INTERNAL REVENUE CODE SECTIONS ADOPTED BY THIS STATE ARE EXTENDED, THEN THESE SECTIONS ALSO ARE EXTENDED FOR SOUTH CAROLINA INCOME TAX PURPOSES.
The Senate proceeded to a consideration of the Bill.
The Committee on Finance proposed the following amendment (BBM\1073C001.BBM.DG16), which was adopted:
Amend the bill, as and if amended, by adding an appropriately numbered SECTION to read:
/ SECTION ___. A. Section 12-6-4970(B) of the 1976 Code is amended to read:
"(B)(1) Returns of 'S' corporations and partnerships must be filed on or before the fifteenth day of the third month following the taxable year.
(2) Returns for foreign corporations that do not maintain an office or place of business in the United States must be filed on or before the fifteenth day of the sixth month following the taxable year."
B. Section 12-8-590(C) of the 1976 Code is amended to read:
"(C) Partnerships are required to withhold income taxes at a rate of five percent on a nonresident partner's share of South Carolina taxable income of the partnership, whether distributed or undistributed, and pay the withheld amount to the department in the manner prescribed by the department. For a taxable year beginning after 1991, The partnership shall make a return and pay over the withheld funds on or before the fifteenth day of the fourth third month following the close of its tax year. Taxes withheld in the name of the nonresident partner must be used as credit against taxes due at the time the nonresident files income taxes for the taxable year."
C. Section 12-13-80 of the 1976 Code is amended to read:
"Section 12-13-80. Returns with respect to the income tax herein imposed shall be in such form as the department may prescribe. Returns shall be filed with the department on or before the fifteenth day of the third fourth month following the close of the accounting period of the association."
D. Section 12-20-20(B) of the 1976 Code is amended to read:
"(B) Unless otherwise provided, corporations shall file an annual report on or before the fifteenth day of the third fourth month following the close of the taxable year."
E. This SECTION takes effect upon approval by the Governor and first applies to tax years beginning after 2015. /
Renumber sections to conform.
Amend title to conform.
Senator CROMER explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 33; Nays 3
AYES
Alexander Allen Bennett
Campsen Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Jackson Johnson Kimpson
Leatherman Malloy Martin, Larry
Martin, Shane Massey Matthews, John
McElveen Nicholson Peeler
Sabb Scott Setzler
Shealy Sheheen Turner
Verdin Williams Young
Total--33
NAYS
Bright Bryant Corbin
Total--3
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
COMMITTEE AMENDMENT ADOPTED
READ THE SECOND TIME
S. 1075 (Word version) -- Senators Campbell, Hayes and Grooms: A BILL TO AMEND SECTION 12-28-110 OF THE 1976 CODE, RELATING TO DEFINITIONS PERTAINING TO MOTOR FUELS, TO AMEND CERTAIN DEFINITIONS; TO AMEND SECTION 56-5-4160 OF THE 1976 CODE, RELATING TO VEHICLE WEIGHTS AND LOADS, TO PROVIDE ADDITIONAL WEIGHT ALLOWANCES FOR MOTOR VEHICLES FUELED BY ALTERNATIVE FUEL; TO AMEND SECTION 12-37-2820, RELATING TO THE ASSESSMENT OF MOTOR VEHICLES, TO CLARIFY A DEFINITION AS IT RELATES TO MOTOR VEHICLES FUELED BY ALTERNATIVE FUEL; TO ADD SECTION 12-6-3695, RELATING TO INCOME TAX CREDITS, TO ALLOW AN INCOME TAX CREDIT TO A TAXPAYER WHO PURCHASES OR CONSTRUCTS AND INSTALLS AND PLACES IN SERVICE IN THIS STATE ELIGIBLE PROPERTY THAT IS USED FOR DISTRIBUTION, DISPENSING, OR STORING ALTERNATIVE FUEL AT A NEW OR EXISTING FUEL DISTRIBUTION OR DISPENSING FACILITY, AND TO SPECIFY THE AMOUNT OF THE CREDIT AND THE REQUIREMENTS OF THE CREDIT; AND TO ADD SECTION 12-6-3697, RELATING TO INCOME TAX CREDITS, TO ALLOW FOR AN INCOME TAX CREDIT FOR THE INCREMENTAL COSTS OR CONVERSION COSTS OF THE AMOUNT EXPENDED TO PURCHASE OR CONVERT AN ALTERNATIVE FUEL HEAVY-DUTY VEHICLE, ALTERNATIVE FUEL VEHICLE, AND A BI-FUEL ALTERNATIVE FUEL VEHICLE, AND TO SPECIFY THE AMOUNT OF THE CREDITS AND THE REQUIREMENTS OF THE CREDIT.
The Senate proceeded to a consideration of the Bill.
The Committee on Finance proposed the following amendment (BBM\1075C001.BBM.DG16), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. A. Section 12-28-110(1) of the 1976 Code is amended to read:
"(1) 'Alternative fuel' means a liquefied petroleum gas, liquefied natural gas, compressed natural gas product, or a combination of liquefied petroleum gas and a compressed natural gas product used in an internal combustion engine or motor to propel any form of vehicle, machine, or mechanical contrivance. It includes all forms of fuel commonly or commercially known or sold as butane, propane, liquefied natural gas, or compressed natural gas."
B. Section 12-28-110(39) of the 1976 Code is amended to read:
"(39) 'Motor fuel' means gasoline, diesel fuel, substitute fuel, renewable fuel, alternative fuel, and blended fuel."
C. Section 12-28-110(55) of the 1976 Code is amended to read:
"(55) 'Motor fuel subject to the user fee' means gasoline, diesel fuel, kerosene, blended fuel, substitute fuel, alternative fuel and blends of them and any other substance blended with them."
D. Section 12-28-110 of the 1976 Code is amended by adding two appropriately numbered items to read:
"( ) 'Diesel gallon equivalent' or 'DGE' means the amount of liquefied natural gas containing the same energy content as one gallon of diesel. For purposes of calculating the motor fuel user fee on liquefied natural gas that is used or consumed in this State in producing or generating power for propelling a motor vehicle, each 6.06 pounds of liquefied natural gas equals one gallon of motor fuel.
( ) 'Gasoline gallon equivalent' or 'GGE' means the amount of compressed natural gas or liquefied petroleum gas containing the same energy content as one gallon of gasoline. For purposes of calculating the motor fuel user fee on compressed natural gas or liquefied petroleum gas that is used or consumed in South Carolina in producing or generating power for propelling a motor vehicle, each 126.67 cubic feet of compressed natural gas, or 5.66 pounds if the compressed natural gas is dispensed via a mass flow meter, equals one gallon of motor fuel and each gallon of liquefied petroleum gas equals .73 of a gallon of motor fuel."
E. Article 1, Chapter 28, Title 12 of the 1976 Code is amended by adding:
"Section 12-28-120. For purposes of this chapter, any reference to the term gallon with respect to liquefied natural gas means diesel gallon equivalent (DGE) and any reference to the term gallon with respect to compressed natural gas or liquefied petroleum gas means gasoline gallon equivalent (GGE). For any gaseous product for which a conversion factor is not provided for in this chapter, based on the best information available, the department shall establish a temporary conversion factor to determine the gallon equivalent. The department shall subsequently submit to the General Assembly a recommended legislative change for this conversion factor."
F. Section 12-36-2120(15) of the 1976 Code is amended by adding two appropriately lettered subitems to read:
"( ) natural gas sold to a person with a miscellaneous motor fuel user fee license pursuant to Section 12-28-1139 who will compress it to produce compressed natural gas, or cool it to produce liquefied natural gas, for use as a motor fuel and remit the motor fuel user fees as required by law; and
( ) liquefied petroleum gas sold to a person with a miscellaneous motor fuel user fee license pursuant to Section 12-28-1139 who will use the liquefied petroleum gas as a motor fuel and remit the motor fuel user fees as required by law;"
G. Section 12-28-1125(A) of the 1976 Code is amended to read:
"(A) Each person who wishes to cause motor fuel subject to the user fee to be delivered into this State on his behalf, for his own account, or for resale to a purchaser in this State, from another state in a fuel transport truck or in a pipeline or barge shipment by any means into storage facilities other than a qualified terminal, shall apply and obtain an occasional importer's license or a bonded importer's license, at the discretion of the applicant."
SECTION 2. Section 56-5-4160 of the 1976 Code, as last amended by Act 234 of 2008, is further amended by adding an appropriately lettered subsection to read:
"( ) Any motor vehicle that is fueled primarily by natural gas may exceed the gross, single axle, tandem axle, or bridge formula weight limits, including tolerances, by no more than 2,000 pounds each individually weighed, up to a maximum gross vehicle weight of 82,000 pounds on the interstate, by an amount that is equal to the difference between: the weight of the vehicle attributable to the natural gas tank and fueling system carried by that vehicle and the weight of a comparable diesel tank and fueling system. This subsection only applies if the operator of the vehicle can demonstrate that the vehicle is a natural gas vehicle, a biofuel vehicle using natural gas, or a vehicle that has been converted to a natural gas vehicle. The operator shall provide documentation which certifies the difference between the weight of the vehicle attributable to the natural gas tank and fueling system carried by that vehicle and the weight of a comparable diesel tank and fueling system."
SECTION 3. A. Section 12-37-2820(B) of the 1976 Code is amended to read:
"(B) 'Gross capitalized cost', as used in this section, means the original cost upon acquisition for income tax purposes, not to include taxes, interest, or cab customizing. However, for a motor vehicle which is fueled wholly or partially by alternative fuel as defined in Section 12-28-110(1), and that was acquired after 2015 but before 2026, the gross capitalized cost is reduced by the differential costs of a comparable diesel or gasoline powered vehicle, not to exceed thirty percent of the total acquisition cost of the motor vehicle. This reduction shall apply for the first ten property tax years for which tax is due following the acquisition of the vehicle."
B. This SECTION first applies to property tax years beginning after 2015.
SECTION 4. A. Article 25, Chapter 6, Title 12 of the 1976 Code is amended by adding:
"Section 12-6-3695. (A)(1) A taxpayer who purchases or constructs and installs and places in service in this State eligible property that is used for distribution, dispensing, or storing alternative fuel specified in this subsection, at a new or existing fuel distribution or dispensing facility, is allowed an income tax credit equal to twenty-five percent of the cost to the taxpayer of purchasing, constructing, and installing the eligible property.
(2) The entire credit may not be taken in the taxable year in which the property is placed in service, but must be taken in three equal annual installments beginning with the taxable year in which the property is placed in service. If, in one of the years in which the installment of a credit accrues, property directly and exclusively used for distributing, dispensing, or storing alternative fuel is disposed of or taken out of service and is not replaced, the credit expires and the taxpayer may not claim any remaining installment of the credit.
(3) The unused portion of an unexpired credit may be carried forward for not more than ten succeeding taxable years.
(4) The taxpayer may transfer any applicable credit associated with this section. To the extent that the taxpayer transfers the credit, the taxpayer must notify the department of the transfer in the manner the department prescribes. Notwithstanding subsection (D), as used in this item, the term 'taxpayer' only applies to the State or any agency or instrumentality, authority, or political subdivision, including municipalities.
(5) A taxpayer who claims any other credit allowed pursuant to this article with respect to the costs of constructing and installing a facility may not take the credit allowed in this section with respect to the same costs.
(B) The Department of Revenue may require documentation that it considers necessary to administer the credit.
(C) To claim the credits allowed in this section, the taxpayer must place the property or facility in service before January 1, 2026.
(D) For purposes of this section:
(1) 'Eligible property' includes pumps, compressors, storage tanks, and related equipment that is directly and exclusively used for distribution, dispensing, or storing alternative fuel. The equipment used to store, distribute, or dispense alternative fuel must be labeled for this purpose and clearly identified as associated with alternative fuel.
(2) 'Alternative fuel' means compressed natural gas, liquefied natural gas, or liquefied petroleum gas, dispensed for use in motor vehicles and compressed natural gas, liquefied natural gas, or liquefied petroleum gas, dispensed by a distributor or facility.
(3) 'Taxpayer' means any sole proprietor, partnership, corporation of any classification, limited liability company, or association taxable as a business entity. Also, the word 'taxpayer' includes the State or any agency or instrumentality, authority, or political subdivision, including municipalities."
B. This SECTION first applies to tax years beginning after 2015.
SECTION 5. A. Article 25, Chapter 6, Title 12 of the 1976 Code is amended by adding:
"Section 12-6-3697. (A) For purposes of this section:
(1) 'Alternative fuel' means liquified petroleum gas, liquified natural gas, or compressed natural gas fuel.
(2) 'Alternative fuel heavy-duty vehicle' means a new or converted commercial vehicle, with a gross vehicle weight ratio equal to or more than 26,001 pounds, which is primarily fueled by an alternative fuel. As used in this paragraph, 'primarily fueled by an alternative fuel' means a vehicle that is produced by an original equipment manufacturer or converted by a third-party equipment manufacturer and operates on ninety percent or more alternative fuel and on ten percent or less gasoline or diesel fuel.
(3) 'Alternative fuel vehicle' means a new or converted commercial vehicle, with a gross vehicle weight ratio less than 26,001 pounds, that is fueled solely by an alternative fuel and that is produced by an original equipment manufacturer or converted by a third-party equipment manufacturer.
(4) 'Bi-fuel alternative fuel vehicle' means a new or converted commercial vehicle with a gross vehicle weight ratio less than 26,001 pounds, that has two separate fuel systems, one of which is fueled by an alternative fuel and the other by conventional gasoline and that is produced by an original equipment manufacturer or a third-party equipment manufacturer.
(5) 'Conversion cost' means the cost that results from modifying a motor vehicle which is propelled by gasoline or diesel to be propelled by an alternative fuel. In the case of a bi-fuel alternative fuel vehicle, cost conversion means the cost that results from modifying a motor vehicle to be partially propelled by an alternative fuel.
(6) 'Commercial vehicle' means any vehicle used for commercial or business purposes owned by a taxpayer.
(7) 'Incremental cost' means the cost that results from subtracting the manufacturer's list price of the motor vehicle operating on conventional gasoline or diesel fuel from the manufacturer's list price of the same model motor vehicle designed to operate on an alternative fuel.
(8) 'Taxpayer' means any sole proprietor, partnership, corporation of any classification, limited liability company, or association taxable as a business entity. Also, the word 'taxpayer' includes the State or any agency or instrumentality, authority, or political subdivision, including municipalities.
(B)(1) A taxpayer is allowed an income tax credit of fifty percent of the incremental costs or conversion costs of the amount expended to purchase or convert an alternative fuel heavy-duty vehicle. The credit may not exceed twelve thousand dollars for each vehicle.
(2) A taxpayer is allowed an income tax credit of fifty percent of the incremental costs or conversion costs of the amount expended to purchase or convert an alternative fuel vehicle. The credit may not exceed eight thousand dollars for each vehicle.
(3) A taxpayer is allowed an income tax credit of fifty percent of the incremental costs or conversion costs of the amount expended to purchase or convert a bi-fuel alternative fuel vehicle. The credit may not exceed six thousand dollars for each vehicle.
(C) The credit allowed by this section is limited in use to fifty percent of either:
(1) the taxpayer's income tax liability for the taxable year if taxpayer claims the credit allowed by this section as a credit against income tax imposed pursuant to Chapter 6; or
(2) the taxpayer's corporate license fees for the taxable year if the taxpayer claims the credit allowed by this section as a credit against license fees imposed pursuant to Chapter 20.
(D) The tax credit is nonrefundable but unused credits may be carried forward for seven years. The seven-year carry forward period must not be extended due to periods of noncompliance.
(E) The taxpayer may transfer any applicable credit associated with this section. To the extent that the taxpayer transfers the credit, the taxpayer must notify the department of the transfer in the manner the department prescribes. Notwithstanding subsection (A), as used in this subsection, the term 'taxpayer' only applies to the State or any agency or instrumentality, authority, or political subdivision, including municipalities.
(F) The department shall produce an appropriate form for the taxpayer to submit certifying the following:
(1) certification from the manufacturer that the vehicle is an alternative fuel heavy-duty vehicle, alternative fuel vehicle, a bi-fuel alternative fuel vehicle, or a third-party equipment manufacturer who possesses a current and legal Certificate of Conformity from the Environmental Protection Agency's Office of Transportation and Air Quality specific to the qualified alternative fuel vehicle;
(2) a sworn affidavit from the taxpayer certifying that the vehicle will accumulate at least fifty-one percent of its mileage in South Carolina in each year for a five-year period, and that the vehicle is registered in this State and will remain registered in South Carolina for no less than five years; and
(3) any other information requested by the department.
(G) The department may promulgate rules and regulations necessary to implement and administer the provisions of this section, including provisions for repayment of any credit in the event any of the certifications are or become untrue during the five-year period following the date of application.
(H) To the extent that the taxpayer is a partnership or a limited liability company taxed as a partnership, the credit may be passed through to the partners or members and may be allocated by the taxpayer among any of its partners or members on an annual basis including, without limitation, an allocation of the entire credit to any partner or member who was a member or partner at any time during the year in which the credit is allocated.
(I) The credit authorized by this section is allowed for purchases or conversions made after December 31, 2015, but before January 1, 2021."
B. This SECTION first applies to tax years beginning after 2015.
SECTION 6. This act takes effect upon approval by the Governor. /
Renumber sections to conform.
Amend title to conform.
Senator CROMER explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 36; Nays 1
AYES
Alexander Allen Bennett
Bryant Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Jackson Johnson Kimpson
Leatherman Malloy Martin, Larry
Martin, Shane Massey Matthews, John
McElveen Nicholson Peeler
Sabb Scott Setzler
Shealy Sheheen Turner
Verdin Williams Young
Total--36
NAYS
Bright
Total--1
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1125 (Word version) -- Senator Reese: A BILL TO AMEND SECTION 12-65-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE TEXTILES COMMUNITIES REVITALIZATION INCOME TAX CREDIT, SO AS TO DELETE A PROVISION THAT LIMITS THE CREDIT TO FIFTY PERCENT OF CERTAIN LIABILITY.
The Senate proceeded to a consideration of the Bill.
Senator CROMER explained the Bill.
The question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 32; Nays 1; Abstain 1
AYES
Alexander Allen Bennett
Campsen Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Jackson Johnson
Kimpson Leatherman Malloy
Martin, Larry Martin, Shane Massey
Matthews, John McElveen Nicholson
Peeler Sabb Shealy
Sheheen Turner Verdin
Williams Young
Total--32
NAYS
Bright
Total--1
ABSTAIN
Setzler
Total--1
The Bill was read the second time, passed and ordered to a third reading.
READ IN FULL
READ THE SECOND TIME, 'AYES' AND 'NAYS' TAKEN
S. 1136 (Word version) -- Senators Malloy and Campsen: A JOINT RESOLUTION PROPOSING AN AMENDMENT TO SECTION 3, ARTICLE XII OF THE CONSTITUTION OF SOUTH CAROLINA, 1895, RELATING TO THE REQUIREMENT THAT THE GENERAL ASSEMBLY PROVIDE FOR THE SEPARATE CONFINEMENT OF JUVENILE OFFENDERS FROM OLDER CONFINED PERSONS, SO AS TO CHANGE THE AGE FOR WHICH THE GENERAL ASSEMBLY SHALL PROVIDE FOR THE SEPARATE CONFINEMENT OF JUVENILE OFFENDERS FROM "UNDER THE AGE OF SEVENTEEN" TO "UNDER THE AGE OF EIGHTEEN".
Be it enacted by the General Assembly of the State of South Carolina:
SECTION 1. It is proposed that Section 3, Article XII of the Constitution of this State be amended to read:
"Section 3. The General Assembly shall provide for the separate confinement of juvenile offenders under the age of seventeen eighteen from older confined persons."
SECTION 2. The proposed amendment must be submitted to the qualified electors at the next general election for representatives. Ballots must be provided at the various voting precincts with the following words printed or written on the ballot:
"Must Section 3, Article XII of the Constitution of this State, relating to the requirement that the General Assembly provide for the separate confinement of juvenile offenders from older confined persons, be amended to change the age for which the General Assembly shall provide for the separate confinement of juvenile offenders from 'under the age of seventeen' to 'under the age of eighteen?'
Yes []
No []
Those voting in favor of the question shall deposit a ballot with a check or cross mark in the square after the word 'Yes', and those voting against the question shall deposit a ballot with a check or cross mark in the square after the word 'No'."
The Senate proceeded to a consideration of the Resolution.
Senator MASSEY explained the Resolution.
The question being the second reading of the Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 38; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campsen
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Jackson Johnson Kimpson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Massey
Matthews, John McElveen Nicholson
Peeler Rankin Sabb
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--38
NAYS
Total--0
The Resolution was read the second time, passed and ordered to a third reading.
COMMITTEE AMENDMENT ADOPTED
READ THE SECOND TIME
H. 4328 (Word version) -- Rep. White: A BILL TO AMEND SECTION 12-8-1530, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE QUARTERLY INCOME TAX WITHHOLDINGS, SO AS TO CHANGE THE DUE DATE OF THE FOURTH QUARTER RETURN FROM THE LAST DAY OF FEBRUARY TO THE LAST DAY OF JANUARY; AND TO AMEND SECTION 12-8-1550, RELATING TO THE DUE DATE FOR FILING STATEMENTS REGARDING INCOME TAX WITHHOLDINGS WITH THE DEPARTMENT OF REVENUE, SO AS TO CHANGE THE DUE DATE FROM THE LAST DAY OF FEBRUARY TO THE LAST DAY OF JANUARY.
The Senate proceeded to a consideration of the Bill.
The Committee on Finance proposed the following amendment (BBM\4328C004.BBM.DG16), which was adopted:
Amend the bill, as and if amended, by adding the following appropriately numbered SECTIONS to read:
/ SECTION ___. Section 12-6-40(A)(1)(a) and (c) of the 1976 Code, as last amended by Act 5 of 2015, is further amended to read:
"(a) Except as otherwise provided, 'Internal Revenue Code' means the Internal Revenue Code of 1986, as amended through December 31, 2014 2015, and includes the effective date provisions contained in it.
(c) If Internal Revenue Code sections adopted by this State which expired or portions thereof expired on December 31, 2014 2015, are extended, but otherwise not amended, by congressional enactment during 2015 2016, these sections or portions thereof also are extended for South Carolina income tax purposes in the same manner that they are extended for federal income tax purposes."
SECTION ___. A. Section 12-6-4970(B) of the 1976 Code is amended to read:
"(B)(1) Returns of 'S' corporations and partnerships must be filed on or before the fifteenth day of the third month following the taxable year.
(2) Returns for foreign corporations that do not maintain an office or place of business in the United States must be filed on or before the fifteenth day of the sixth month following the taxable year."
B. Section 12-8-590(C) of the 1976 Code is amended to read:
"(C) Partnerships are required to withhold income taxes at a rate of five percent on a nonresident partner's share of South Carolina taxable income of the partnership, whether distributed or undistributed, and pay the withheld amount to the department in the manner prescribed by the department. For a taxable year beginning after 1991, The partnership shall make a return and pay over the withheld funds on or before the fifteenth day of the fourth third month following the close of its tax year. Taxes withheld in the name of the nonresident partner must be used as credit against taxes due at the time the nonresident files income taxes for the taxable year."
C. Section 12-13-80 of the 1976 Code is amended to read:
"Section 12-13-80. Returns with respect to the income tax herein imposed shall be in such form as the department may prescribe. Returns shall be filed with the department on or before the fifteenth day of the third fourth month following the close of the accounting period of the association."
D. Section 12-20-20(B) of the 1976 Code is amended to read:
"(B) Unless otherwise provided, corporations shall file an annual report on or before the fifteenth day of the third fourth month following the close of the taxable year."
E. This SECTION takes effect upon approval by the Governor and first applies to tax years beginning after 2015.
SECTION __. Section 12-28-110 of the 1976 Code is amended by adding two appropriately numbered items to read:
"( ) 'Diesel gallon equivalent' or 'DGE' means the amount of liquefied natural gas containing the same energy content as one gallon of diesel. For purposes of calculating the motor fuel user fee on liquefied natural gas that is used or consumed in this State in producing or generating power for propelling a motor vehicle, each 6.06 pounds of liquefied natural gas equals one gallon of motor fuel.
( ) 'Gasoline gallon equivalent' or 'GGE' means the amount of compressed natural gas or liquefied petroleum gas containing the same energy content as one gallon of gasoline. For purposes of calculating the motor fuel user fee on compressed natural gas or liquefied petroleum gas that is used or consumed in South Carolina in producing or generating power for propelling a motor vehicle, each 126.67 cubic feet of compressed natural gas, or 5.66 pounds if the compressed natural gas is dispensed via a mass flow meter, equals one gallon of motor fuel and each gallon of liquefied petroleum gas equals .73 of a gallon of motor fuel."
SECTION __. Article 1, Chapter 28, Title 12 of the 1976 Code is amended by adding:
"Section 12-28-120. For purposes of this chapter, any reference to the term gallon with respect to liquefied natural gas means diesel gallon equivalent (DGE) and any reference to the term gallon with respect to compressed natural gas or liquefied petroleum gas means gasoline gallon equivalent (GGE). For any gaseous product for which a conversion factor is not provided for in this chapter, based on the best information available, the department shall establish a temporary conversion factor to determine the gallon equivalent. The department shall subsequently submit to the General Assembly a recommended legislative change for this conversion factor."
SECTION __. Section 12-36-2120(15) of the 1976 Code is amended by adding two appropriately lettered subitems to read:
"( ) natural gas sold to a person with a miscellaneous motor fuel user fee license pursuant to Section 12-28-1139 who will compress it to produce compressed natural gas, or cool it to produce liquefied natural gas, for use as a motor fuel and remit the motor fuel user fees as required by law; and
( ) liquefied petroleum gas sold to a person with a miscellaneous motor fuel user fee license pursuant to Section 12-28-1139 who will use the liquefied petroleum gas as a motor fuel and remit the motor fuel user fees as required by law;"
SECTION __. Section 12-28-1125(A) of the 1976 Code is amended to read:
"(A) Each person who wishes to cause motor fuel subject to the user fee to be delivered into this State on his behalf, for his own account, or for resale to a purchaser in this State, from another state in a fuel transport truck or in a pipeline or barge shipment by any means into storage facilities other than a qualified terminal, shall apply and obtain an occasional importer's license or a bonded importer's license, at the discretion of the applicant."
SECTION __. 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. /
Renumber sections to conform.
Amend title to conform.
Senator CROMER explained the Bill.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 2
AYES
Alexander Allen Bennett
Campsen Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hutto Jackson
Johnson Kimpson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey Matthews, John
McElveen Nicholson Peeler
Rankin Sabb Scott
Setzler Shealy Sheheen
Turner Verdin Williams
Young
Total--37
NAYS
Bright Bryant
Total--2
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
H. 3706 (Word version) -- Reps. Putnam, Gagnon, Yow, Thayer, Gambrell, Ridgeway, Norrell, Henderson, Fry and Bedingfield: A BILL TO AMEND CHAPTER 99, TITLE 44, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EMERGENCY TREATMENT FOR MEDICAL HAZARDS CAUSED BY INSECT STINGS, SO AS TO RENAME THE CHAPTER THE "EMERGENCY ANAPHYLAXIS TREATMENT ACT", TO ADD A DEFINITION FOR "EPINEPHRINE AUTO-INJECTOR", TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO DEVELOP A TRAINING AND CERTIFICATION PROGRAM FOR INDIVIDUALS WHO ADMINISTER EPINEPHRINE AUTO-INJECTORS, TO ALLOW CERTAIN ENTITIES TO OBTAIN A PRESCRIPTION FOR AN EPINEPHRINE AUTO-INJECTOR FROM PHYSICIANS, PHARMACISTS, AND OTHER AUTHORIZED INDIVIDUALS, TO ALLOW PHYSICIANS, PHARMACISTS, AND OTHER AUTHORIZED INDIVIDUALS TO PRESCRIBE OR SELL A PRESCRIPTION FOR AN EPINEPHRINE AUTO-INJECTOR TO CERTAIN ENTITIES, TO ALLOW APPROPRIATELY CERTIFIED EMPLOYEES OF CERTAIN ENTITIES TO USE AN EPINEPHRINE AUTO-INJECTOR, TO PROVIDE LIABILITY LIMITATIONS FOR CERTAIN INDIVIDUALS AND ENTITIES WHEN ADMINISTERING AN EPINEPHRINE AUTO-INJECTOR, AND FOR OTHER PURPOSES.
The Senate proceeded to a consideration of the Bill.
The question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 38; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campsen
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hutto
Jackson Johnson Kimpson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Massey
Matthews, John McElveen Nicholson
Peeler Rankin Sabb
Scott Setzler Shealy
Sheheen Turner Verdin
Williams Young
Total--38
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1028 (Word version) -- Senator Verdin: A BILL TO AMEND CHAPTER 3, TITLE 46 OF THE 1976 CODE, RELATING TO THE DEPARTMENT OF AGRICULTURE, SO AS TO ADD SECTION 46-3-280 TO PROVIDE FOR THE VETERANS AND WARRIORS TO AGRICULTURE PROGRAM AND FUND.
The Senate proceeded to a consideration of the Bill.
Senator VERDIN explained the Bill.
The question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campsen
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hutto Jackson Johnson
Kimpson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
Massey Matthews, John McElveen
Nicholson Peeler Rankin
Sabb Scott Setzler
Shealy Sheheen Turner
Verdin Williams Young
Total--39
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
H. 4141 (Word version) -- Reps. Gambrell, Sandifer and Pitts: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO ENACT THE "LIMITED LINES TRAVEL INSURANCE ACT" BY ADDING ARTICLE 6 TO CHAPTER 43, TITLE 38 SO AS TO PROVIDE A CITATION, TO DEFINE NECESSARY TERMS, TO PROVIDE REQUIREMENTS ONLY UNDER WHICH TRAVEL RETAILERS MAY OFFER AND DISSEMINATE TRAVEL INSURANCE UNDER A LIMITED LINES TRAVEL INSURANCE PRODUCER BUSINESS ENTITY LICENSE FOR COMPENSATION, TO PROVIDE THAT TRAVEL INSURANCE MAY BE PROVIDED UNDER AN INDIVIDUAL POLICY OR UNDER A GROUP OR MASTER POLICY, TO PROVIDE THAT LIMITED LINES TRAVEL INSURANCE PRODUCERS ACTING AS AN INSURANCE DESIGNEE ARE RESPONSIBLE FOR THE ACTS OF THE TRAVEL RETAILER AND SHALL USE REASONABLE MEANS TO ENSURE COMPLIANCE BY THE TRAVEL RETAILER WITH THIS ARTICLE, AND TO PROVIDE PENALTIES FOR VIOLATIONS.
The Senate proceeded to a consideration of the Bill.
Senator RANKIN explained the Bill.
The question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 36; Nays 1
AYES
Alexander Allen Bennett
Bryant Campsen Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Johnson Kimpson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey McElveen
Nicholson Peeler Rankin
Sabb Scott Setzler
Shealy Sheheen Turner
Verdin Williams Young
Total--36
NAYS
Bright
Total--1
The Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
H. 4662 (Word version) -- Rep. Gambrell: A BILL TO REENACT THE INTERSTATE INSURANCE PRODUCT REGULATION COMPACT AND RELATED PROVISIONS, ENACTED BY SECTIONS 1, 2, 3, AND 5, ACT 339 OF 2008, WHICH EXPIRED ON JUNE 1, 2014, AND TO MAKE THESE REENACTED PROVISIONS RETROACTIVE TO THIS EXPIRATION DATE, AND TO SPECIFICALLY NOT REENACT CERTAIN OBSOLETE PROVISIONS.
The Senate proceeded to a consideration of the Bill.
Senator RANKIN explained the Bill.
The question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campsen
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hutto Johnson Kimpson
Leatherman Malloy Martin, Larry
Martin, Shane Massey Matthews, John
McElveen Nicholson Peeler
Rankin Sabb Scott
Setzler Shealy Sheheen
Turner Verdin Williams
Young
Total--37
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
COMMITTEE AMENDMENT ADOPTED
READ THE SECOND TIME
S. 1064 (Word version) -- Senators Young and Rankin: A BILL TO AMEND SECTION 38-73-525 OF THE 1976 CODE, RELATING TO THE REQUIREMENT THAT AN INSURER WRITING A WORKERS' COMPENSATION POLICY SHALL FILE CERTAIN INFORMATION ON WHICH IT RELIES TO SUPPORT ITS RATE REQUEST, TO PROVIDE THAT THE INSURER MUST ADOPT THE MOST RECENT LOSS COST WITHIN ONE HUNDRED TWENTY DAYS OF APPROVAL OF THE LOSS COSTS; AND TO AMEND SECTION 38-73-1210, RELATING TO THE REQUIREMENT THAT ITS OBLIGATION TO MAKE CERTAIN FILINGS MAY BE SATISFIED BY MAKING FILINGS AS A MEMBER OF, OR SUBSCRIBER TO, A LICENSED RATING ORGANIZATION THAT MAKES FILINGS, TO REQUIRE THE FILINGS BE RULE AND FORM FILINGS AND NOT LOSS COST ADOPTION FILINGS, AND REQUIRE THE INSURER TO FILE FOR CERTAIN APPROVAL IF THE RATING ORGANIZATION TO WHICH IT SUBSCRIBES HAS A RATE INCREASE WITHIN TWELVE MONTHS AFTER THE INSURER BECOMES A MEMBER.
The Senate proceeded to a consideration of the Bill.
The Committee on Banking and Insurance proposed the following amendment (NBD\1064C001.NBD.CZ16), which was adopted:
Amend the bill, as and if amended, after the enacting words by striking the bill in its entirety and inserting:
/ SECTION 1. Section 38-73-525 of the 1976 Code is amended to read:
"Section 38-73-525. (A) Each insurer writing workers' compensation insurance shall adopt the most recent loss costs within sixty days after approval of these loss costs. This loss costs adoption must become effective no later than one hundred twenty days after the effective date of the approved loss costs. An insurer must notify the department of its adoption of the most recently approved loss costs by filing a notification on a form and in a manner prescribed by the director or his designee. The notification filing required by this subsection does not constitute a rate filing and is not subject to prior approval.
(B)(1) At least thirty sixty days prior to before using a new rates, every multiplier for expenses, assessments, profits, and contingencies, each insurer writing workers' compensation must shall file its multiplier for expenses, assessments, profit, and contingencies and any information relied upon by the insurer to support the multiplier and any modifications to loss costs. A copy of the filing must be provided simultaneously to the consumer advocate.
(2) The filing Filings submitted pursuant to item (1) must be filed on a form and in the manner prescribed by the director or his designee and must contain, at a minimum, the following information: commission expense; other acquisition expense; general expense; expenses associated with recoveries from the Second Injury Fund; guaranty fund assessments; other assessments; premium taxes; miscellaneous taxes, licenses, or fees; and a provision for profit and contingencies, and the date of approval of the loss costs to which the multiplier is applied, which must be the most recently approved loss costs.
(3) Rate Filings submitted pursuant to item (1) are subject to approval of the director or his designee and must be reviewed by an actuary employed or retained by the department who is a member of the American Academy of Actuaries or an associate or fellow of the Casualty Actuarial Society.
(4)(a) Within the thirty-day sixty-day period, if the director or his or her designee believes the information filed is not complete, the director or his or her designee must shall notify the insurer of additional information to be provided. Within fifteen days of receipt of the notification, the insurer must shall provide the requested information or file for a hearing challenging the reasonableness of the director's or his or her designee's request. The burden is on the insurer to justify the denial of the additional information.
(b) Unless a hearing has been is requested, upon expiration of the thirty-day sixty-day period or the fifteen-day period, whichever is later, the insurer may use the rates developed using the multiplier of expenses, assessments, profit, and contingencies multiplier for expenses, assessments, profit, and contingencies."
SECTION 2. Section 38-73-1210 of the 1976 Code is amended to read:
"Section 38-73-1210. (A)(1) This item applies to property and casualty insurance but does not apply to workers' compensation insurance. An insurer may satisfy its obligation to make required filings by becoming a member of, or a subscriber to, a licensed rating organization which makes filings and by authorizing the director or his designee to accept the filings on its behalf. However, notwithstanding any other provisions another provision of this article, no a member or subscriber may, within twelve months after its membership or subscribership, may not file to adopt any a rate approved for use for the rating organization if the rate is more than the rate in use by the member or subscriber prior to before its membership or subscribership in the rating organization. Further, notwithstanding the provisions of Sections 38-73-1300, and 38-73-1310, and 38-73-1320, no a member or subscriber, within twelve months after its membership or subscribership, may not be granted an upward deviation from its rate in use when becoming a member or subscriber. However, if a rate increase for the rating organization is approved within twelve months after an insurer becomes a member or subscriber, the member or subscriber may increase its rates by the same percentage of increase granted the rating organization. Nothing contained in this chapter may be construed as requiring any to require an insurer to become a member of or a subscriber to any a rating organization.
(2) This item applies to workers' compensation insurance. An insurer may satisfy its obligation to make required filings by becoming a member of, or a subscriber to, a licensed rating organization that makes filings and by authorizing the director or his designee to accept the filings on its behalf. However, a licensed rating organization may not satisfy the insurer's obligation to make filings required pursuant to Section 38-73-525.
(B)In addition to other activities not prohibited by this chapter, a rating organization may collect, compile, and disseminate to insurers
compilations of past and current premiums of insurers."
SECTION 3. This act takes effect upon approval by the Governor. /
Renumber sections to conform.
Amend title to conform.
Senator RANKIN explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campsen
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hutto Jackson Johnson
Kimpson Leatherman Malloy
Martin, Larry Martin, Shane Massey
Matthews, John Nicholson Peeler
Rankin Sabb Scott
Setzler Shealy Sheheen
Turner Verdin Williams
Young
Total--37
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
READ THE SECOND TIME
S. 1166 (Word version) -- Senators Leatherman, Setzler, Allen, J. Matthews, Jackson, M.B. Matthews, Malloy, Lourie, Williams, Sheheen, Nicholson, Johnson, Scott, Sabb, Hutto and Kimpson: A JOINT RESOLUTION TO PROVIDE FOR ANNUAL INSTALLMENT PAYMENTS BY SOUTH CAROLINA STATE UNIVERSITY ON OUTSTANDING LOANS MADE TO THE UNIVERSITY BY THE STATE OF SOUTH CAROLINA AND LIABILITIES INCURRED PURSUANT TO SECTION 2-65-70, TO PROVIDE FOR WHEN THE INSTALLMENT PAYMENTS ARE DUE, TO PROVIDE FOR THE AMOUNT OF THE INSTALLMENT PAYMENTS, TO PROVIDE FOR A PROCESS THROUGH WHICH THE DEBT INCURRED MAY BE RELIEVED, AND TO EXTEND FLEXIBILITY RELATED TO FURLOUGHS AS PROVIDED IN ACT 120 OF 2015.
The Senate proceeded to a consideration of the Resolution.
Senator COURSON explained the Resolution.
The question being the second reading of the Resolution.
The Resolution was read the second time, passed and ordered to a third reading.
Motion under Rule 26B
Senator MASSEY asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Recorded Vote
Senators BRIGHT, CORBIN, DAVIS, BRYANT, SHANE MARTIN and YOUNG desired to be recorded as voting against the second reading of the Resolution.
MINORITY REPORT REMOVED
H. 4548 (Word version) -- Reps. Sandifer, Forrester, Toole, Bales, Chumley, Burns, Hardee, Allison, Tallon, Henderson, Clemmons, Sottile, Crosby, V.S. Moss, Jefferson, Yow, Duckworth, H.A. Crawford, Jordan, Fry, Herbkersman, Lowe, Goldfinch, Hixon, Norman, Hiott, Taylor, McCoy, D.C. Moss, Collins, Rutherford, Anderson, Kirby, Pitts, Corley, Ballentine, Hamilton, Finlay, Huggins, Ott, Govan, Riley, Willis, Thayer, Felder, Hicks, Simrill, G.A. Brown, Bedingfield, Stringer, Ryhal, King, Loftis, Hayes, Mack, Rivers, Ridgeway, Clary, Brannon, Atwater, Daning, Bannister, Anthony, McEachern, Mitchell, Erickson, Weeks, Knight, Cole, George, Horne, G.R. Smith, G.M. Smith, Williams, Limehouse, Pope, Gambrell, Alexander, Stavrinakis, Newton, White, Spires, R.L. Brown, Gilliard, Dillard and Gagnon: A BILL TO AMEND SECTION 37-2-307, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO CLOSING FEES ASSESSED ON MOTOR VEHICLES SALES CONTRACTS, SO AS TO PROVIDE A MOTOR VEHICLE DEALER WHO MEETS CERTAIN STATUTORY REQUIREMENTS MAY CHARGE A CLOSING FEE, TO ESTABLISH DEFENSES FOR A MOTOR VEHICLE DEALER, AND TO AUTHORIZE THE DEPARTMENT OF CONSUMER AFFAIRS TO ADMINISTER AND ENFORCE MOTOR VEHICLE DEALER CLOSING FEES.
Senator HUTTO asked unanimous consent to remove his name from the minority report of the Bill.
There was no objection and proper notation was made on the Bill.
COMMITTEE AMENDMENT ADOPTED
AMENDMENT PROPOSED
CARRIED OVER
S. 650 (Word version) -- Senators Scott, Malloy, Williams and J. Matthews: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 23-3-90 SO AS TO GRANT THE SOUTH CAROLINA LAW ENFORCEMENT DIVISION SPECIFIC AND EXCLUSIVE JURISDICTION AND AUTHORITY TO CONDUCT AN INVESTIGATION OF ALL OFFICER-INVOLVED SHOOTINGS THAT RESULT, OR COULD HAVE RESULTED, IN BODILY INJURY OR DEATH, TO ALLOW FOR AN INVESTIGATION OF AN OFFICER-INVOLVED SHOOTING TO BE COMPLETED BY A SEPARATE LAW ENFORCEMENT AGENCY IN CERTAIN CIRCUMSTANCES, TO ESTABLISH A PROTOCOL FOR EVIDENCE COLLECTION AND PROCESSING IN CERTAIN CIRCUMSTANCES, TO GRANT AN INVESTIGATING OFFICER THE SAME AUTHORITY AS HE WOULD HAVE IN HIS HOME JURISDICTION FOR THE DURATION OF THE INVESTIGATION, TO ESTABLISH A PROCEDURE FOR THE FORWARDING OF THE EVIDENCE TO THE CIRCUIT SOLICITOR UPON COMPLETION OF THE INVESTIGATION, AND TO ESTABLISH PENALTIES FOR THE FAILURE TO COMPLETE AN INDEPENDENT INVESTIGATION PURSUANT TO THE PROVISIONS OF THIS SECTION.
The Senate proceeded to a consideration of the Bill.
The Committee on Judiciary proposed the following amendment (JUD0650.002), which was adopted:
Amend the bill, as and if amended, by striking SECTION 1 and inserting:
/ SECTION 1. Article 1, Chapter 3, Title 23 of the 1976 Code is amended by adding:
"Section 23-3-90. (A) Except as otherwise provided in this section, the South Carolina Law Enforcement Division (SLED) shall have specific and exclusive jurisdiction and authority in the investigation of:
(1) the shooting of or discharge of a weapon at a person by a law enforcement officer acting in the line of duty; and
(2) the unexpected death of an arrestee while in the care, custody, or control of a law enforcement officer or correctional officer; the unexpected death of an arrestee shortly after being in the care, custody, or control of a law enforcement officer or correctional officer; and the unexpected death of an intended arrestee during an arrest attempt by a law enforcement officer. For purposes of this section, 'unexpected death' includes all deaths which, before investigation, appear possibly to have been caused by trauma, suspicion, or obscure circumstances.
(B) If the officer is employed by SLED, the sheriff of the county in which the shooting, discharge, or unexpected death occurred shall investigate the shooting, discharge, or unexpected death, regardless of whether the shooting, discharge, or unexpected death occurred within an incorporated jurisdiction. If the sheriff does not employ a full-time unit that regularly processes crime scenes and conducts forensic and criminal investigations, the sheriff shall defer the investigation to a law enforcement agency that employs a full-time unit that regularly processes crime scenes and conducts forensic and criminal investigations and that possesses the expertise to conduct a proper investigation. All forensic evidence collected at the scene of the shooting, discharge, or unexpected death must be submitted to and analyzed by an accredited state law enforcement laboratory outside of South Carolina.
(C) If an officer employed by SLED and an officer employed by the sheriff of the county in which the shooting, discharge, or unexpected death occurred are both involved in the shooting, discharge, or unexpected death, the solicitor of the county in which the shooting, discharge, or unexpected death occurred shall defer the investigation to a law enforcement agency that employs a unit that regularly processes crime scenes and conducts forensic and criminal investigations and that possesses the expertise to conduct a proper investigation. All forensic evidence collected at the scene of the shooting, discharge, or unexpected death must be submitted to and analyzed by an accredited state law enforcement laboratory outside of South Carolina.
(D) An officer investigating the shooting, discharge, or unexpected death pursuant to this section has the same authority as the officer has in the officer's home jurisdiction for the duration of the investigation.
(E) Upon completion, all investigations must be forwarded to the solicitor's office in the jurisdiction where the shooting, discharge, or unexpected death occurred prior to the initiation or declination of any formal criminal action.
(F) A person who knowingly and willfully violates the provisions of subsection (A), (B), or (C) is subject to punishment as provided for in Section 8-1-80, even if the person's authority extends beyond a single election or judicial district."/
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the committee amendment.
Senator LOURIE proposed the following amendment (650R003.EB.JL):
Amend the bill, as and if amended, by striking subsections 23-3-90(A)-(C) and inserting:
/ "Section 23-3-90 (A) A law enforcement agency may choose the South Carolina Law Enforcement Division (SLED) or any other law enforcement agency, including the Federal Bureau of Investigation, to investigate incidents where one or more of its law enforcement officers were involved in the following:
(1) the shooting of or discharge of a weapon at a person by a law enforcement officer acting in the line of duty; and
(2) the unexpected death of an arrestee while in the care, custody, or control of a law enforcement officer or correctional officer; the unexpected death of an arrestee shortly after being in the care, custody, or control of a law enforcement officer or correctional officer; and the unexpected death of an intended arrestee during an arrest attempt by a law enforcement officer. For purposes of this section, 'unexpected death' includes all deaths which, before investigation, appear possibly to have been caused by trauma, suspicion, or obscure circumstances.
(B) The law enforcement agency may not choose an internal investigation pursuant to subsection (A) if one of its law enforcement officers was involved in the shooting, discharge, or unexpected death. /
Renumber sections to conform.
Amend title to conform.
Senator LOURIE explained the amendment.
On motion of Senator MASSEY, the Bill was carried over.
COMMITTEE AMENDMENT ADOPTED
CARRIED OVER
H. 4712 (Word version) -- Reps. White, Bannister, Rutherford, G.R. Smith, Lowe, Pitts, Hiott, Erickson, Clemmons, Loftis, G.M. Smith, Hayes, Sandifer, Whitmire, Cole, Simrill, Allison, Cobb-Hunter, Long, Huggins, Delleney, Pope and Bales: A BILL TO AMEND SECTION 12-43-230, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE TREATMENT OF AGRICULTURAL REAL PROPERTY, MOBILE HOME, AND LESSEE IMPROVEMENTS TO REAL PROPERTY, SO AS TO CLASSIFY OFF-PREMISES OUTDOOR ADVERTISING SIGNS AS PERSONAL PROPERTY AND TO PROVIDE THAT UNDER CERTAIN CIRCUMSTANCES AN OFF-PREMISES SIGN SITE MUST BE TAXED AT ITS VALUE WHICH EXISTED BEFORE THE ERECTION OF THE SIGN.
The Senate proceeded to a consideration of the Bill.
The Committee on Finance proposed the following amendment (BBM\4712C004.BBM.DG16), which was adopted:
Amend the bill, as and if amended, SECTION 1, by striking Section 12-43-230(e)(2) and inserting:
/ (2)(a) If an off-premises outdoor advertising sign site is one-quarter of an acre or less, or is otherwise limited to an area large enough only to accommodate the necessary building structure, foundation, and provide for service or maintenance, is leased from an unrelated third party, or the sign is owned by the owner of the site, and the sign owner has filed a business personal property tax return with the Department of Revenue, then the off-premises outdoor advertising sign site real property must be assessed to the site owner at its value before the lease or construction of the sign without regard to the structure, the lease, or lease income, and no separate assessment may be issued for the sign company's lease or ownership interest. The lease or construction of such property does not constitute an assessable transfer of interest pursuant to Article 25, Chapter 37, Title 12, and the real property constituting the sign site must maintain its same property tax classification as commercial, manufacturing, agricultural, or utility property as it had before the lease.
(b) The provisions of this item do not apply to:
(i) real property whose property tax classification is subject to change due to the addition of buildings, structures, or other improvements subsequent to the erection of the sign on the property; and
(ii) real property whose property tax classification was changed due to the erection of an on-premises outdoor advertising sign on existing buildings, structures, or other improvements unless the existing buildings, structures, or other improvements qualify within the same property tax classification pursuant to Chapter 43 of this title." /
Renumber sections to conform.
Amend title to conform.
Senator HAYES explained the committee amendment.
On motion of Senator YOUNG, the Bill was carried over.
CARRIED OVER
H. 3682 (Word version) -- Reps. Finlay, Bannister, Newton, Cole, Delleney, Weeks, Whipper, Robinson-Simpson and Bingham: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 4 TO TITLE 39 SO AS TO ENACT THE "BAD FAITH ASSERTION OF PATENT INFRINGEMENT ACT", TO PROVIDE THAT BAD FAITH ASSERTIONS OF PATENT INFRINGEMENTS ARE PROHIBITED, TO DEFINE TERMS, TO PROVIDE FOR A PRIVATE CAUSE OF ACTION IN STATE COURTS BY A RECIPIENT OF A BAD FAITH ASSERTION TO PATENT INFRINGEMENT, TO PROVIDE THAT ENFORCEMENT ACTIONS MAY BE BROUGHT BY THE ATTORNEY GENERAL AND WILLFUL AND KNOWING VIOLATIONS MAY RESULT IN CIVIL PENALTIES OF NOT MORE THAN FIFTY THOUSAND DOLLARS FOR EACH VIOLATION, TO PROVIDE FOR THE FACTORS THAT A COURT MAY CONSIDER WHEN MAKING A BAD FAITH DETERMINATION, AND TO PROVIDE EXCEPTIONS.
On motion of Senator MALLOY, the Bill was carried over.
H. 3768 (Word version) -- Reps. G.M. Smith, Johnson and Willis: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 3 TO CHAPTER 5, TITLE 11 SO AS TO ESTABLISH THE "SOUTH CAROLINA ABLE SAVINGS PROGRAM", TO ALLOW INDIVIDUALS WITH A DISABILITY AND THEIR FAMILIES TO SAVE PRIVATE FUNDS TO SUPPORT THE INDIVIDUAL WITH A DISABILITY, TO PROVIDE GUIDELINES TO THE STATE TREASURER FOR THE MAINTENANCE OF THESE ACCOUNTS, AND TO ESTABLISH THE SAVINGS PROGRAM TRUST FUND AND SAVINGS EXPENSE TRUST FUND; AND TO DESIGNATE THE EXISTING SECTIONS OF CHAPTER 5, TITLE 11 AS ARTICLE 1 AND ENTITLE THEM "GENERAL PROVISIONS".
On motion of Senator SHANE MARTIN, the Bill was carried over.
H. 4717 (Word version) -- Reps. White, Lucas, Hiott, Simrill, G.M. Smith, Lowe, Whitmire, Taylor, George, V.S. Moss, J.E. Smith, M.S. McLeod, Bowers, Corley, Parks, McKnight, Douglas, Knight, Erickson, Sandifer, Willis, Kirby, Clary, Cobb-Hunter, Hardee, Duckworth, Johnson, Limehouse, Clyburn, Bales, Horne, Stavrinakis, Hayes, Yow, Neal, Kennedy, Newton, Tinkler, Riley, Howard, King, Henegan, Williams, Anthony, Clemmons, Crosby, Cole, Daning, Dillard, Forrester, Funderburk, Gambrell, Herbkersman, Hixon, Hosey, Loftis, Long, Pitts, Rivers, Rutherford, Ryhal, G.R. Smith, Wells, W.J. McLeod, Ridgeway, G.A. Brown, Bamberg, Hodges, Alexander, Thayer, McEachern, Gagnon, Whipper, R.L. Brown, Jefferson, Anderson, Spires and Hicks: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 46-1-160 SO AS TO CREATE THE "SOUTH CAROLINA FARM AID FUND" TO ASSIST FARMERS WHO HAVE SUFFERED AT LEAST A FORTY PERCENT LOSS OF AGRICULTURAL COMMODITIES AS A RESULT OF A NATURAL DISASTER, TO CREATE THE FARM AID BOARD TO ADMINISTER THE FUND, AND TO SPECIFY ELIGIBILITY AND GRANT AMOUNTS.
Senator MASSEY spoke on the Bill.
On motion of Senator MASSEY, the Bill was carried over.
S. 1169 (Word version) -- Senators Gregory and Shealy: A BILL TO AMEND SECTION 20-3-130(B), CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE AWARD OF ALIMONY AND OTHER ALLOWANCES, SO AS TO PROVIDE FOR TWO NEW FORMS OF ALIMONY AND TO CHANGE THE DEFINITION OF COHABITATION; TO AMEND SECTION 20-3-150, RELATING TO SEGREGATION OF ALLOWANCE BETWEEN SPOUSE AND CHILDREN AND THE EFFECT OF REMARRIAGE OF A SPOUSE, SO AS TO CHANGE THE DEFINITION OF COHABITATION.
On motion of Senator SETZLER, the Bill was carried over.
H. 3147 (Word version) -- Reps. G.M. Smith, G.R. Smith, Huggins, Weeks, Taylor, Pope, Collins, Johnson, Stavrinakis, Yow, Clemmons, Goldfinch, Murphy, J.E. Smith and Mitchell: A BILL TO AMEND SECTION 12-6-1140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEDUCTIONS FROM SOUTH CAROLINA TAXABLE INCOME OF INDIVIDUALS FOR PURPOSES OF THE SOUTH CAROLINA INCOME TAX ACT, SO AS TO ALLOW THE DEDUCTION OF RETIREMENT BENEFITS ATTRIBUTABLE TO SERVICE ON ACTIVE DUTY IN THE ARMED FORCES OF THE UNITED STATES; AND TO AMEND SECTION 12-6-1170, AS AMENDED, RELATING TO THE RETIREMENT INCOME DEDUCTION, SO AS TO CONFORM THIS DEDUCTION TO THE MILITARY RETIREMENT DEDUCTION ALLOWED BY THIS ACT.
Senator CROMER explained the committee amendment.
Senator McELVEEN spoke on the Bill.
On motion of Senator SHEHEEN, the Bill was carried over.
H. 3313 (Word version) -- Reps. Pope, Simrill, Ballentine, Felder, Atwater, Bedingfield, Spires, Clary, Collins, Delleney, Hamilton, Hiott, Hixon, V.S. Moss, Norman, Stringer, Toole, W.J. McLeod and Newton: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-43-222 SO AS TO PROVIDE WHEN CALCULATING ROLL-BACK TAX DUE ON A PARCEL OF REAL PROPERTY CHANGED FROM AGRICULTURAL TO COMMERCIAL OR RESIDENTIAL USE THE VALUE USED FOR PLATTED GREEN SPACE OR OPEN SPACE USE OF THE PARCEL, IF SUCH USE IS TEN PERCENT OR MORE OF THE PARCEL, MUST BE VALUED BASED ON THE GREEN SPACE OR OPEN SPACE USE; AND TO AMEND SECTION 12-43-220, AS AMENDED, RELATING TO CLASSES OF PROPERTY AND APPLICABLE ASSESSMENT RATIOS FOR PURPOSES OF IMPOSITION OF THE PROPERTY TAX, SO AS TO MAKE A CONFORMING AMENDMENT, AND TO PROVIDE THAT AFTER A PARCEL OF REAL PROPERTY HAS UNDERGONE AN ASSESSABLE TRANSFER OF INTEREST, DELINQUENT PROPERTY TAX AND PENALTIES ASSESSED BECAUSE THE PROPERTY WAS IMPROPERLY CLASSIFIED AS OWNER-OCCUPIED RESIDENTIAL PROPERTY WHILE OWNED BY THE TRANSFEROR ARE SOLELY A PERSONAL LIABILITY OF THE TRANSFEROR AND DO NOT CONSTITUTE A LIEN ON THE PROPERTY AND ARE NOT ENFORCEABLE AGAINST THE PROPERTY AFTER THE ASSESSABLE TRANSFER OF INTEREST IF THE TRANSFEREE IS A BONA FIDE PURCHASER FOR VALUE WITHOUT NOTICE.
On motion of Senator SHANE MARTIN, the Bill was carried over.
H. 3685 (Word version) -- Reps. D.C. Moss and Pitts: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 14-1-219 SO AS TO PROVIDE THAT A FIVE DOLLAR SURCHARGE IS IMPOSED UPON ALL MONETARY PENALTIES IMPOSED BY CERTAIN COURTS FOR OFFENSES IN WHICH AN ELECTRONIC TICKET OR CITATION WAS ISSUED, AND TO PROVIDE FOR THE DISTRIBUTION OF THE SURCHARGE.
On motion of Senator MASSEY, the Bill was carried over.
H. 3710 (Word version) -- Reps. Hixon, Norman, Taylor, Wells, Hamilton, Atwater, Brannon, Gagnon, Corley, Ballentine, Southard, Clemmons, Delleney, Gambrell, Huggins, Kennedy, Kirby, Loftis, D.C. Moss, Pitts, Riley, Rivers, Simrill, Toole and Bedingfield: A BILL TO AMEND SECTION 12-43-225, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE MULTIPLE LOT DISCOUNT, SO AS TO PROVIDE FIVE ADDITIONAL YEARS OF ELIGIBILITY IN CERTAIN CIRCUMSTANCES.
Senator HAYES explained the committee amendment.
On motion of Senator HAYES, the Bill was carried over.
H. 3909 (Word version) -- Reps. Herbkersman, Jefferson, Bernstein, G.A. Brown, Funderburk, Hill, W.J. McLeod, J.E. Smith, Whitmire, Gagnon, Dillard and Bowers: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "BICYCLE AND PEDESTRIAN SAFETY ACT"; BY ADDING SECTION 56-5-3520 SO AS TO PROVIDE THAT BICYCLES WITH HELPER MOTORS SHALL BE SUBJECT TO ALL THE RIGHTS AND DUTIES OF BICYCLES; TO AMEND SECTION 56-1-1710, RELATING TO THE TERM "MOPED" AND ITS DEFINITION, SO AS TO PROVIDE THAT THIS SECTION DOES NOT APPLY TO MOTORCYCLES OR BICYCLES; TO AMEND SECTION 56-5-990, RELATING TO CERTAIN PEDESTRIAN CONTROL SIGNALS, SO AS TO PROVIDE THAT THIS SECTION ALSO APPLIES TO PEDESTRIAN CONTROL SIGNALS THAT EXHIBIT THE SYMBOLS FOR "WALK" OR "WAIT", AND TO PROVIDE THAT FOR PEDESTRIAN CROSSWALKS EQUIPPED WITH COUNTDOWN INDICATORS, A PEDESTRIAN MAY CROSS IF HE CAN COMPLETE THE CROSSING DURING THE REMAINING TIME; TO AMEND SECTION 56-5-3130, RELATING TO A PEDESTRIAN'S RIGHT-OF-WAY IN A CROSSWALK, SO AS TO PROVIDE THAT THE DRIVER OF A VEHICLE SHALL STOP TO YIELD TO A PEDESTRIAN CROSSING A ROADWAY UNDER CERTAIN CIRCUMSTANCES; TO AMEND SECTION 56-5-3230, RELATING TO A DRIVER'S DUTY TO EXERCISE DUE CARE WHEN OPERATING A VEHICLE, SO AS TO PROVIDE THAT THIS SECTION ALSO APPLIES TO A DRIVER'S DUTY TO AVOID COLLIDING WITH AN ELECTRIC PERSONAL ASSISTIVE MOBILITY DEVICE, A WHEELCHAIR, A FARM TRACTOR, OR A SIMILAR VEHICLE DESIGNED FOR FARM USE, AND TO PROVIDE PENALTIES FOR VIOLATIONS OF THIS SECTION; TO AMEND SECTION 56-5-3425, RELATING TO THE DEFINITION OF THE TERM "BICYCLE LANE" AND OPERATIONS OF MOTOR VEHICLES AND BICYCLES ALONG BICYCLE LANES, SO AS TO REVISE THE DEFINITION OF THE TERM "BICYCLE LANE" AND TO PROVIDE A DEFINITION FOR THE TERM "SUBSTANDARD-WIDTH LANE"; AND TO AMEND SECTION 56-16-10, RELATING TO CERTAIN TERMS AND THEIR DEFINITIONS REGARDING THE REGULATION OF MOTORCYCLE MANUFACTURERS, DISTRIBUTORS, DEALERS, AND WHOLESALERS, SO AS TO PROVIDE A DEFINITION FOR THE TERM "BICYCLES WITH HELPER MOTORS".
On motion of Senator BENNETT, the Bill was carried over.
S. 980 (Word version) -- Senators Sheheen and McElveen: A BILL TO AMEND CHAPTER 69, TITLE 40 OF THE 1976 CODE, RELATING TO VETERINARIANS, BY ADDING SECTION 40-69-305 TO REQUIRE ALL PRESCRIPTION DRUGS DISPENSED TO AN ANIMAL'S OWNER TO BE LABELED IN ACCORDANCE WITH STATE AND FEDERAL LAW; AND TO PROVIDE PENALTIES FOR VIOLATING THIS SECTION.
On motion of Senator VERDIN, the Bill was carried over.
S. 981 (Word version) -- Senator Sheheen: A BILL TO AMEND SECTION 56-3-9600 OF THE 1976 CODE, RELATING TO "NO MORE HOMELESS PETS" LICENSE PLATES, SO AS TO PROVIDE THAT THE SOUTH CAROLINA ANIMAL CARE AND CONTROL ASSOCIATION SHALL COORDINATE THE GRANT PROGRAM, BE ELIGIBLE TO RECEIVE REIMBURSEMENT, AND DISTRIBUTE GRANT MONEY; TO REQUIRE AN ANNUAL ACCOUNTING FOR THE PROGRAM; AND REQUIRE CERTAIN INFORMATION BEFORE A NONPROFIT ORGANIZATION CAN RECEIVE FUNDING UNDER THE GRANT PROGRAM.
On motion of Senator VERDIN, the Bill was carried over.
H. 3343 (Word version) -- Reps. Huggins, Toole, Long, McCoy, Knight, R.L. Brown, Pope, Collins, Bingham, Stavrinakis, Yow and Erickson: A BILL TO AMEND SECTION 47-3-420, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO METHODS OF EUTHANASIA THAT MAY BE USED TO KILL ANIMALS IMPOUNDED OR QUARANTINED IN ANIMAL SHELTERS, SO AS TO PROVIDE THAT THE USE OF BARBITURIC ACID DERIVATIVES, AND CARBON MONOXIDE GAS ARE NOT ALLOWABLE METHODS OF EUTHANASIA AND TO PROVIDE THAT THE USE OF SODIUM PENTOBARBITAL AND OTHER SUBSTANCES OR PROCEDURES THAT ARE HUMANE MAY BE USED TO PERFORM EUTHANASIA.
On motion of Senator J. MATTHEWS, the Bill was carried over.
S. 1192 (Word version) -- Education Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE STATE BOARD OF EDUCATION, RELATING TO DISTRICT AND SCHOOL PLANNING, DESIGNATED AS REGULATION DOCUMENT NUMBER 4605, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator HAYES, the Resolution was carried over.
S. 1193 (Word version) -- Education Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE STATE BOARD OF EDUCATION, RELATING TO TEST SECURITY, DESIGNATED AS REGULATION DOCUMENT NUMBER 4606, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator HAYES, the Resolution was carried over.
S. 1194 (Word version) -- Education Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE STATE BOARD OF EDUCATION, RELATING TO PROGRAM APPROVAL STANDARDS FOR SOUTH CAROLINA TEACHER EDUCATION INSTITUTIONS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4593, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator HAYES, the Resolution was carried over.
S. 1195 (Word version) -- Education Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE STATE BOARD OF EDUCATION, RELATING TO SPECIAL EDUCATION, EDUCATION OF STUDENTS WITH DISABILITIES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4586, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator HAYES, the Resolution was carried over.
ADOPTED
S. 1198 (Word version) -- Senators Peeler, Alexander, Hayes, Scott and Rankin: A CONCURRENT RESOLUTION TO FIX WEDNESDAY, APRIL 27, 2016, AT NOON, AS THE DATE AND TIME FOR THE HOUSE OF REPRESENTATIVES AND THE SENATE TO MEET IN JOINT SESSION IN THE HALL OF THE HOUSE OF REPRESENTATIVES FOR THE PURPOSE OF ELECTING MEMBERS OF THE BOARDS OF TRUSTEES FOR THE CITADEL, CLEMSON UNIVERSITY, COLLEGE OF CHARLESTON, FRANCIS MARION UNIVERSITY, LANDER UNIVERSITY, MEDICAL UNIVERSITY OF SOUTH CAROLINA, UNIVERSITY OF SOUTH CAROLINA, WINTHROP UNIVERSITY, AND WIL LOU GRAY OPPORTUNITY SCHOOL TO SUCCEED THOSE MEMBERS WHOSE TERMS EXPIRE ON JUNE 30, 2016, OR WHOSE POSITIONS OTHERWISE MUST BE FILLED; IMMEDIATELY FOLLOWING THE ELECTION OF MEMBERS OF BOARDS OF TRUSTEES, TO ELECT MEMBERS OF THE DEPARTMENT OF EMPLOYMENT AND WORKFORCE APPELLATE PANEL TO SUCCEED THOSE MEMBERS WHOSE TERMS EXPIRE OR WHOSE TERMS OTHERWISE MUST BE FILLED; AND TO ESTABLISH PROCEDURES REGARDING NOMINATIONS AND SECONDING SPEECHES FOR THE CANDIDATES FOR THESE OFFICES DURING THE JOINT SESSION.
The Resolution was adopted, ordered sent to the House.
S. 1191 (Word version) -- Senators Hembree and Kimpson: A CONCURRENT RESOLUTION TO DISAPPROVE AMENDMENTS TO THE SOUTH CAROLINA RULES OF CRIMINAL PROCEDURE, AS PROMULGATED BY THE SUPREME COURT OF SOUTH CAROLINA AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE.
Having received the necessary three-fifths vote, the Resolution was adopted, ordered sent to the House.
H. 4929 (Word version) -- Reps. Crosby, Daning, Jefferson, Merrill, Rivers and Southard: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE PORTION OF HIGHWAY IN BERKELEY COUNTY FROM THE INTERSECTION OF N.A.D. ROAD AND GOOSE CREEK ROAD TO THE INTERSECTION OF OLD STATE ROAD AND RED BANK ROAD "M.C. CANNON MEMORIAL HIGHWAY" AND ERECT APPROPRIATE MARKERS OR SIGNAGE ALONG THIS PORTION OF HIGHWAY THAT CONTAIN THIS DESIGNATION.
The Resolution was adopted, ordered return to the House.
Expression of Personal Interest
Senator KIMPSON rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator COURSON rose for an Expression of Personal Interest.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
MOTION ADOPTED
At 1:15 P.M., on motion of Senator CROMER, the Senate agreed to dispense with the balance of the Motion Period.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CARRIED OVER
S. 199 (Word version) -- Senators Grooms, Hembree, Bennett, Campbell, Verdin, Campsen, Gregory, Johnson, Setzler, Sabb, Nicholson and Scott: A BILL TO AMEND SECTION 56-5-1535 OF THE 1976 CODE, RELATING TO SPEEDING IN WORK ZONES AND PENALTIES ASSOCIATED WITH SPEEDING IN WORK ZONES, TO DELETE THIS PROVISION AND CREATE "PEANUT'S LAW", TO PROVIDE A DEFINITION FOR THE TERMS "HIGHWAY WORK ZONE" AND "HIGHWAY WORKER", TO CREATE THE OFFENSES OF "ENDANGERMENT OF A HIGHWAY WORKER", AND TO PROVIDE PENALTIES FOR THESE OFFENSES; TO AMEND SECTION 56-1-720, RELATING TO THE POINT SYSTEM ESTABLISHED FOR THE EVALUATION OF THE DRIVING RECORD OF PERSONS OPERATING MOTOR VEHICLES, TO PROVIDE THAT "ENDANGERMENT OF A HIGHWAY WORKER" VIOLATIONS RANGE BETWEEN TWO AND SIX POINTS; AND TO REPEAL SECTION 56-5-1536 RELATING TO DRIVING IN TEMPORARY WORK ZONES AND PENALTIES FOR UNLAWFUL DRIVING IN TEMPORARY WORK ZONES.
On motion of Senator LEATHERMAN, the Bill was carried over.
THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE.
COMMITTEE AMENDMENT OUT OF ORDER
AMENDMENT PROPOSED
DEBATE INTERRUPTED
H. 3184 (Word version) -- Reps. Pope, Cole, Anderson, Bales, G.A. Brown, R.L. Brown, Finlay, Funderburk, Hart, Knight, Lucas, Murphy, Newton, Norman, Norrell, Putnam, Rivers, Southard, Spires, Tallon, Taylor, Wells, Williams, Willis, Bernstein, Long, Douglas, Henderson, G.M. Smith, G.R. Smith, McCoy, McKnight, Clary, M.S. McLeod, Thayer, W.J. McLeod, Weeks, J.E. Smith and Stavrinakis: A BILL TO AMEND SECTION 8-13-310, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE STATE ETHICS COMMISSION AND ITS MEMBERSHIP, SO AS TO RECONSTITUTE THE MEMBERSHIP OF THE COMMISSION EFFECTIVE JULY 1, 2015, TO CONSIST OF FOUR MEMBERS APPOINTED BY THE GOVERNOR, FOUR MEMBERS ELECTED BY THE SUPREME COURT, TWO MEMBERS ELECTED BY THE HOUSE OF REPRESENTATIVES, AND TWO MEMBERS ELECTED BY THE SENATE, RESPECTIVELY, TO PROVIDE FOR THE QUALIFICATIONS OF THESE MEMBERS, TO PROVIDE FOR OFFICERS OF THE COMMISSION, AND TO PROVIDE FOR THE MEMBERS' TERMS OF OFFICE AND MANNER OF THEIR REMOVAL UNDER CERTAIN CONDITIONS; TO AMEND SECTION 8-13-320, AS AMENDED, RELATING TO THE DUTIES, POWERS, AND PROCEDURES OF THE STATE ETHICS COMMISSION, SO AS TO REVISE THESE DUTIES, POWERS, AND PROCEDURES INCLUDING PROVISIONS TO VEST WITH THE COMMISSION THE ADDITIONAL RESPONSIBILITY TO INITIATE OR RECEIVE COMPLAINTS AGAINST MEMBERS OF THE GENERAL ASSEMBLY, ITS STAFF, AND CANDIDATES FOR ELECTION TO THE GENERAL ASSEMBLY, TO INITIATE OR RECEIVE COMPLAINTS AGAINST JUDGES AND OTHER JUDICIAL OFFICIALS OF THE UNIFIED JUDICIAL SYSTEM AND THEIR STAFFS, TO PROVIDE FOR THE INVESTIGATION AND PROCESSING OF COMPLAINTS AGAINST GENERAL ASSEMBLY MEMBERS, STAFF, AND CANDIDATES PURSUANT TO SPECIFIED PROCEDURES AND FOR THE REFERRAL OF SUBSTANTIVE COMPLAINTS TO THE APPROPRIATE HOUSE OR SENATE ETHICS COMMITTEES FOR DISPOSITION TOGETHER WITH THE ETHICS COMMISSION'S RECOMMENDATION AS TO WHETHER OR NOT THERE IS PROBABLE CAUSE TO BELIEVE A VIOLATION HAS OCCURRED, TO PROVIDE FOR THE INVESTIGATION AND PROCESSING OF COMPLAINTS AGAINST JUDGES AND OTHER JUDICIAL OFFICIALS OR THEIR STAFF PURSUANT TO SPECIFIED PROCEDURES AND, AFTER INVESTIGATION, FOR THE REFERRAL OF SUBSTANTIVE COMPLAINTS TO THE COMMISSION ON JUDICIAL CONDUCT AND THE SUPREME COURT FOR DISPOSITION TOGETHER WITH THE ETHICS COMMISSION'S RECOMMENDATION AS TO WHETHER OR NOT THERE IS PROBABLE CAUSE TO BELIEVE A VIOLATION HAS OCCURRED; TO AMEND SECTIONS 8-13-530 AND 8-13-540, BOTH AS AMENDED, RELATING TO THE DUTIES, FUNCTIONS, AND PROCEDURES OF THE HOUSE AND SENATE ETHICS COMMITTEES, SO AS TO REVISE THESE DUTIES, FUNCTIONS, AND PROCEDURES IN ORDER TO BE CONSISTENT WITH THE ABOVE PROVISIONS AND TO MAKE OTHER CHANGES; BY ADDING SECTION 8-13-545 SO AS TO AUTHORIZE THE HOUSE OR SENATE ETHICS COMMITTEES TO ISSUE FORMAL ADVISORY OPINIONS AND PROVIDE FOR THEIR EFFECT AND APPLICABILITY; AND BY ADDING ARTICLE 6 TO CHAPTER 13, TITLE 8 SO AS TO PROVIDE FOR JUDICIAL COMPLAINT PROCEDURES IN REGARD TO THE ABOVE PROVISIONS.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Amendment No. P4
Senator SHEHEEN proposed the following amendment (3184R019.EB.LAR):
Amend the committee amendment, as and if amended, by adding appropriately numbered new SECTIONS to read:
/ SECTION __. Section 8-13-1300(6) of the 1976 Code is amended to read:
"(6) 'Committee' means an association, a club, an organization, or a group of persons which, to influence the outcome of an elective office, receives contributions or makes expenditures in excess of five hundred dollars in the aggregate during an election cycle. It also means a person who, to influence the outcome of an elective office, makes:
(a) contributions aggregating at least twenty-five thousand dollars during an election cycle to or at the request of a candidate or a committee, or a combination of them; or
(b) independent expenditures aggregating five hundred dollars or more during an election cycle for the election or defeat of a candidate. a person, two or more individuals, such as any person, association, organization, or other entity that makes or accepts anything of value to make contributions or expenditures, and has one or more of the following characteristics:
(a) is a political party or executive committee of a political party or is controlled by a political party or executive committee of a political party; or
(b) has the major purpose to support or oppose the nomination or election of one or more clearly identified candidates.
Supporting or opposing the election of clearly identified candidates includes supporting or opposing the candidates of a clearly identified political party.
If the entity qualifies as a 'committee' pursuant to this section, it continues to be a committee if it receives contributions or makes expenditures or maintains assets or liabilities. A committee ceases to exist when it winds up its operations, disposes of its assets, and files its final report.
'Committee' includes a party committee, a legislative caucus committee, a noncandidate committee, or a committee that is not a campaign committee for a candidate but that is organized for the purpose of influencing an election and has as the major purpose to support or oppose the nomination or election of a candidate to an elective office."
SECTION __. Section 8-13-1300(7) of the 1976 Code is amended to read:
"(7) 'Contribution' means a gift, subscription, loan, guarantee upon which collection is made, forgiveness of a loan, an advance, in-kind contribution or expenditure, a deposit of money, or anything of value made to a candidate or committee to influence an election; or payment or compensation for the personal service of another person which is rendered for any purpose to a candidate or committee without charge, whether any of the above are made or offered directly or indirectly. 'Contribution' does not include (a) volunteer personal services on behalf of a candidate or committee for which the volunteer or any person acting on behalf of or instead of the volunteer receives no compensation either in cash or in-kind, directly or indirectly, from any source; or (b) a gift, subscription, loan, guarantee upon which collection is made, forgiveness of a loan, an advance, in-kind contribution or expenditure, a deposit of money, or anything of value made to a committee, other than a candidate committee, and is used to pay for communications made not more than forty-five days before the election to influence the outcome of an elective office as defined in Section 8-13-1300(31)(c). These funds must be deposited in an account separate from a campaign account as required in Section 8-13-1312."
SECTION __. Section 8-13-1300(23) of the 1976 Code is amended to read:
"(23) 'Noncandidate committee' means a committee that is not a campaign committee for a candidate but is organized to influence an election or to support or oppose a candidate or public official, for the major purpose to support or oppose the nomination or election of a candidate to elective office, which receives contributions or makes expenditures in excess of five hundred dollars in the aggregate during an election cycle. 'Noncandidate committee' does not include political action committees that contribute solely to federal campaigns."
SECTION __. Section 8-13-1300(32) of the 1976 Code is amended to read:
"(32) 'Ballot measure committee' means:
(a) an association, club, an organization, or a group of persons which, to influence the outcome of a ballot measure, receives contributions or makes expenditures in excess of two thousand five hundred dollars in the aggregate during an election cycle;
(b) a person, other than an individual, who, to influence the outcome of a ballot measure, makes contributions aggregating at least fifty thousand dollars during an election cycle to or at the request of a ballot measure committee; or
(c) a person, other than an individual, who, to influence the outcome of a ballot measure, makes independent expenditures aggregating two thousand five hundred dollars or more during an election cycle.
a person, two or more individuals, such as any person, association, organization, or other entity that makes or accepts anything of value to make contributions or expenditures that has the major purpose to support or oppose the passage of a ballot measure."
SECTION __. Section 8-13-1300 of the 1976 Code is amended by adding an appropriately numbered subsection to read:
"( ) 'electioneering communication' means any broadcast, cable, or satellite communication or mass postal mailing or telephone bank that has the following characteristics:
(a) refers to a candidate for elected office;
(b) is publically aired or distributed within sixty days prior to a general election or within thirty days prior to a primary for that office; and
(c) may be received by either:
(i) fifty thousand or more individuals in the State in an election for statewide office, or seven thousand five hundred or more individuals in any other election if in the form of broadcast, cable, or satellite communication; or
(ii) twenty thousand or more households, cumulative per election, in a statewide election or two thousand five hundred households, cumulative per election, in any other election if in the form of mass mailing or telephone bank.
(d) The definition does not include:
(i) a communication appearing in a news story, commentary, or editorial distributed through the facilities of any broadcasting station, unless those facilities are owned or controlled by any political party, political committee, or candidate;
(ii) a communication that constitutes an expenditure or independent expenditure under this Article;
(iii) a communication that constitutes a candidate debate or forum conducted pursuant to rules adopted by a political party or that solely promotes that debate or forum and is made by or on behalf of the person sponsoring the debate or forum;
(iv) a communication made which, incidental to advocacy for or against a specific piece of legislation, ordinance, or local initiative pending before the General Assembly or governing body of a political subdivision, urges the audience to communicate with a member or members of the General Assembly or the governing body of a political subdivision, concerning that piece of legislation, ordinance, or local initiative; or
(v) a communication that meets all of the following criteria:
(1) does not mention any election, candidacy, political party, opposing candidate, or voting by the general public;
(2) does not take a position on the candidate's character or qualifications and fitness for office; and
(3) proposes a commercial transaction."
SECTION __. Section 8-13-1300 of the 1976 Code is amended by adding an appropriately numbered subsection to read:
"( ) 'Independent expenditure-only committee' means a committee that:
(a) is not made by, controlled by, coordinated with, requested by, or made in consultation with a candidate, an agent of a candidate, a political party, or an agent of a political party;
(b) does not make contributions to any candidate or other committee, with the exception of other independent expenditure-only committees;
(c) makes only independent expenditures as defined by Section 8-13-1300(17); and
(d) is organized for the major purpose to support or oppose the nomination or election of a candidate to elective office."
SECTION __. Chapter 13, Title 8 of the 1976 Code is amended by adding:
"Section 8-13-1301. For purposes of this article, factors that shall be considered to determine whether a committee, ballot measure committee, a party committee, a legislative caucus committee, a noncandidate committee, or independent expenditure-only committee has the major purpose of supporting or opposing one or more candidates or the passage of one or more ballot measures include, but are not limited to:
(A) any of the committee's organizational documents, including bylaws or articles of incorporation, identify advocacy to support or to oppose one or more candidates or the passage of one or more ballot measures as its major purpose;
(B) over fifty percent of the committee's disbursements made within the State in a calendar year are made to support or to oppose one or more candidates or the passage of one or more ballot measures; or
(C) over fifty percent of the committee's total disbursements made in a calendar year are made to support or to oppose one or more candidates or the passage of one or more ballot measures; or
(D) the committee's public statements, including statements made in oral or written fundraising solicitations, identify advocacy in support of or in opposition to one or more candidates or the passage of one or more ballot measures as its major purpose."
SECTION __. Chapter 13, Title 8 of the 1976 Code is amended by adding:
"Section 8-13-1311. Independent expenditure-only committees must:
(A) file a statement of organization with the State Ethics Commission no later than five days after receiving or expending more than five hundred dollars in the aggregate during an election cycle to influence the outcome of an elective office;
(B) under penalty of perjury, the chief executive officer or the controlling individual of the committee must file a certification that the independent expenditure-only committee is not made in cooperation, consultation, or concert, with, or at the request or suggestion of, any candidate or any authorized committee or agent of such candidate;
(C) only make independent expenditures as defined by Section 8-13-1300(17); and
(D) comply with all requirements, disclosures, and restrictions of committees under this Article except contribution limits under section 8-13-1322."
SECTION __. Chapter 13, Title 8 of the 1976 Code is amended by adding:
"Section 8-13-1313. A person who is not a committee required to file subject to Section 8-13-1304 and who makes an independent expenditure as defined by Section 8-13-1300(17), in an aggregate amount or value in excess of five hundred dollars during a calendar year or makes an electioneering communication must file a report of such expenditure or communication with the State Ethics Commission pursuant to Section 8-13-365. This report must be filed within thirty days of making the independent expenditure, or if the independent expenditure or electioneering communication is made within thirty days before an election, the report must be filed within forty-eight hours. The report must include:
(1) a detailed description of the use of the expenditure or communication and the amount of the expenditure or the cost of the communication;
(2) the full name, primary occupation, street address, and phone number of the reporting person;
(3) the identification of the chief executive officer, or for all controlling individuals if the reporting person is a business or another organization that is not an individual, to include name, title, employer, and address;
(4) the name of the candidate or ballot measure that is the target of the independent expenditure or electioneering communication and whether the expenditure or communication was made in support of, or opposition to, the candidate or ballot measure;
(5) the chief executive officer or controlling individual must file, under penalty of perjury, a certification that the independent expenditure is not made in cooperation, consultation, or concert, with, or at the request or suggestion of, any candidate or any authorized committee or agent of such candidate;
(6) the identification of the top five donors to the reporting person and for any donor who has donated more than ten thousand dollars to the committee within the previous twelve months, to include name, primary occupation, address, and amount of the donation; and
(7) if the donor is a business or another organization that is not an individual, then the identification must indicate the name and title of the chief executive officer or the controlling individual of the donor organization."
SECTION __. Section 8-13-1322 of the 1976 Code is amended to read:
"Section 8-13-1322. (A) A person may not contribute to a committee and a committee may not accept from a person contributions aggregating more than three thousand five hundred dollars in a calendar year.
(B) A person may not contribute to a committee and a committee may not accept from a person a cash contribution unless the cash contribution does not exceed twenty-five dollars for each election and is accompanied by a record of the amount of the contribution and the name and address of the contributor.
(C) The provisions of subsection (A) do not apply to independent expenditure-only committees registered with the State Ethics Commission." /
Renumber sections to conform.
Amend title to conform.
Senator SHEHEEN spoke on the perfecting amendment.
Senator MALLOY spoke on the perfecting amendment.
Point of Order
Senator MALLOY raised a Point of Order under Rule 24A that the amendment by the Committee on Judiciary was out of order inasmuch as it was not germane to the Bill.
Senator LARRY MARTIN spoke against the Point of Order.
Senator MALLOY spoke on the Point of Order.
RECESS
At 2:09 P.M., on motion of Senator MALLOY, the Senate receded from business not to exceed 10 minutes.
At 2:20 P.M., the Senate resumed.
The PRESIDENT sustained the Point of Order.
The committee amendment was ruled out of order.
Amendment No. 2
Senator L. MARTIN proposed the following amendment (JUD3184.011):
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 8-13-310 of the 1976 Code is amended to read:
"Section 8-13-310. (A) The State Ethics Commission as constituted under law in effect before July 1, 1992, is reconstituted to continue in existence with the appointment and qualification of the at-large members as prescribed in this section and with the changes in duties and powers as prescribed in this chapter. On July 1, 1993, when the duties and powers given to the Secretary of State in Chapter 17 of Title 2 are transferred to the State Ethics Commission, the Code Commissioner is directed to change all references to 'this chapter' in Article 3 of Chapter 13 of Title 8 to 'this chapter and Chapter 17 of Title 2'.
(B)(A)(1) There is created the State Ethics Commission composed of nine eight members of which:
(a) four members must be appointed by the Governor, upon the advice and consent of the General Assembly. no more than two of whom are members of the appointing Governor's political party;
(b) one member must be appointed by the legislative caucus of the majority political party in the Senate;
(c) one member must be appointed by the legislative caucus of the largest minority political party in the Senate;
(d) one member must be appointed by the legislative caucus of the majority political party in the House of Representatives; and
(e) one member must be appointed by the legislative caucus of the largest minority political party in the House of Representatives.
Each appointee must be appointed with the advice and consent of the General Assembly. One member shall represent each of the seven congressional districts, and two members must be appointed from the State at large.
(2) The terms of the members serving on the State Ethics Commission as of March 30, 2017 shall end on March 31, 2017. A member who is serving at that time and who has not completed a full five year term may be reappointed pursuant to this subsection. The initial appointments for service to begin on April 1, 2017, shall be made as follows:
(a) two members appointed by the Governor shall be appointed for a three year term;
(b) two members appointed by the Governor shall be appointed for a five year term;
(c) one member appointed by the legislative caucus of the majority political party of the Senate shall be appointed for a three year term;
(e) one member appointed by the legislative caucus of the largest minority political party of the Senate shall be appointed for a five year term;
(f) one member appointed by the legislative caucus of the majority political party of the House of Representatives shall be appointed for a five year term; and
(g) one member appointed by the legislative caucus of the largest minority political party of the House of Representatives shall be appointed for a three year term.
The initial members who have served terms that are less than five years are eligible to be reappointed for one full five-year term.
(B)(1) The qualifications the appointing authorities shall consider for the appointees include, but are not limited to:
(a) constitutional qualifications;
(b) ethical fitness;
(c) character;
(d) mental stability;
(e) experience; and
(f) judicial temperament.
(2) In addition to other information that may be requested, candidates for appointment must provide the following information to the appointing authority, which must be shared with the General Assembly during the confirmation process:
(a) The candidate's membership in any civic, charitable, or social groups within the previous four years;
(b) Any contribution made by the candidate to a candidate for Governor or any member of the General Assembly within the previous four years; and
(c) Any contribution made by the candidate to any committee, as defined by Section 8-13-1300(6), including a noncandidate committee, within the previous four years.
(3) The appointing authorities shall make their appointments based on merit. However, in making appointments to the commission, the appointing authorities shall ensure that race, color, gender, national origin, and other demographic factors are considered to ensure the geographic and political balance of the appointments, and shall strive to assure that the membership of the commission will represent, to the greatest extent possible, all segments of the population of the State.
(4) The following are not eligible to serve on the State Ethics Commission:
(a) a member of the General Assembly;
(b) a former member of the General Assembly within eight years following the termination of his service in the General Assembly;
(c) a family member, as defined by Section 8-13-100(15), of a member of the General Assembly or the Governor;
(d) a person who made a campaign contribution, as defined by Section 8-13-1300(7), within the previous four years to the individual who appointed the person to serve on the State Ethics Commission;
(e) a person who registered as a lobbyist within four years of being appointed to the State Ethics Commission;
(f) a person who is under the jurisdiction of the State Ethics Commission, House of Representatives Ethics Committee, or Senate Ethics Committee.
No member of the General Assembly or other public official must be eligible to serve on the State Ethics Commission.
The Governor shall make the appointments based on merit regardless of race, color, creed, or gender and shall strive to assure that the membership of the commission is representative of all citizens of the State of South Carolina.
(C) The terms of the members are for five years and until their successors are appointed and qualify. The members of the State Ethics Commission serving on this chapter's effective date may continue to serve until the expiration of their terms. These members may then be appointed to serve one full five-year term under the provisions of this chapter. Members representing the first, third, and sixth congressional districts on this chapter's effective date are eligible to be appointed for a full five-year term in or after 1991. Members currently representing the second, fourth, and fifth congressional districts on this chapter's effective date are eligible to be appointed for a full five-year term in or after 1993. The initial appointments for the at large members of the commission created by this chapter must be for a one-, two-, or three-year term, but these at-large members are eligible subsequently for a full five-year term. Under this section, the at-large members of the commission are to be appointed to begin service on or after July 1, 1992. Vacancies must be filled in the manner of the original appointment for the unexpired portion of the term only. Members of the commission who serve less than a full five-year term may be reappointed for one full five-year term. Members of the commission who have completed a full five-year term are not eligible for reappointment. A member shall not serve on the commission in hold-over status after the member's term expires. An appointee shall not serve on the commission, even in interim capacity, until he has been confirmed by the General Assembly.
(D) The commission shall elect a chairman, a vice-chairman, and such other officers as it considers necessary. Five members of the commission shall constitute a quorum. The commission must adopt a policy concerning the attendance of its members at commission meetings. The commission meets at the call of the chairman or a majority of its members. Members of the commission, while serving on business of the commission, receive per diem, mileage, and subsistence as is provided by law for members of state boards, committees, and commissions.
(E)(1) A commission member appointed by the Governor may be removed from office by the Governor for malfeasance, misfeasance, incompetency, absenteeism, conflicts of interest, misconduct, persistent neglect of duty in office, or incapacity, pursuant to Section 1-3-240.
(2) A commission member appointed by a legislative caucus of the Senate may be removed for malfeasance, misfeasance, incompetency, absenteeism, conflicts of interest, misconduct, persistent neglect of duty in office, or incapacity upon a finding by the Senate Ethics Committee, and the concurrence of two-thirds of the membership of the Senate.
(3) A commission member appointed by a legislative caucus of the House of Representatives may be removed for malfeasance, misfeasance, incompetency, absenteeism, conflicts of interest, misconduct, persistent neglect of duty in office, or incapacity upon a finding by the House Ethics Committee, and the concurrence of two-thirds of the membership of the House of Representatives."
SECTION 2. Section 8-13-320(9) of the 1976 Code is amended to read:
"(9) to initiate or receive complaints and make investigations, as provided in item (10), or as provided in Section 8-13-540, as appropriate, of statements filed or allegedly failed to be filed under the provisions of this chapter and Chapter 17 of Title 2 and, upon complaint by an individual, of an alleged violation of this chapter or Chapter 17 of Title 2 by a public official, public member, or public employee except members or staff, including staff elected to serve as officers of or candidates for the General Assembly unless otherwise provided for under House or Senate rules. Any person charged with a violation of this chapter or Chapter 17 of Title 2 is entitled to the administrative hearing process contained in this section or in Article 5 of this chapter, as appropriate.
(a) The commission may commence an investigation on the filing of a complaint by an individual or by the commission, as provided in item (10)(d), upon a majority vote of the total membership of the commission.
(b)(1) No complaint may be accepted by the commission concerning a candidate for elective office during the fifty-day period before an election in which he is a candidate. During this fifty-day period, any person may petition the court of common pleas alleging the violations complained of and praying for appropriate relief by way of mandamus or injunction, or both. Within ten days, a rule to show cause hearing must be held, and the court must either dismiss the petition or direct that a mandamus order or an injunction, or both, be issued. A violation of this chapter by a candidate during this fifty-day period must be considered to be an irreparable injury for which no adequate remedy at law exists. The institution of an action for injunctive relief does not relieve any party to the proceeding from any penalty prescribed for violations of this chapter. The court must award reasonable attorneys fees and costs to the nonpetitioning party if a petition for mandamus or injunctive relief is dismissed based upon a finding that the:
(i) petition is being presented for an improper purpose such as harassment or to cause delay;
(ii) claims, defenses, and other legal contentions are not warranted by existing law or are based upon a frivolous argument for the extension, modification, or reversal of existing law or the establishment of new law; and
(iii) allegations and other factual contentions do not have evidentiary support or, if specifically so identified, are not likely to have evidentiary support after reasonable opportunity for further investigation or discovery.
(2) Action on a complaint filed against a candidate which was received more than fifty days before the election but which cannot be disposed of or dismissed by the commission at least thirty days before the election must be postponed until after the election.
(c) If an alleged violation is found to be groundless by the commission, the entire matter must be stricken from public record. If the commission finds that the complaining party willfully filed a groundless complaint, the finding must be reported to the Attorney General. The willful filing of a groundless complaint is a misdemeanor and, upon conviction, a person must be fined not more than one thousand dollars or imprisoned not more than one year. In lieu of the criminal penalty provided by this item, a civil penalty of not more than one thousand dollars may be assessed against the complainant upon proof, by a preponderance of the evidence, that the filing of the complaint was willful and without just cause or with malice.
(d) Action may not be taken on a complaint filed more than four years after the violation is alleged to have occurred unless a person, by fraud or other device, prevents discovery of the violation. The Attorney General may initiate an action to recover a fee, compensation, gift, or profit received by a person as a result of a violation of the chapter no later than one year after a determination by the commission that a violation of this chapter has occurred;"
SECTION 3. Section 8-13-320(10)(g) of the 1976 Code is amended to read:
"(g) All investigations, inquiries, hearings, and accompanying documents must remain are confidential and may only be released pursuant to this section, unless otherwise required by law. until a finding of probable cause or dismissal unless the respondent waives the right to confidentiality.
(i) After a dismissal, except for dismissal pursuant to item (10)(b) or a technical violation pursuant to Section 8-13-1170 or 8-13-1372, the following documents become public record: the complaint, the response by the respondent, and the notice of dismissal.
(ii) After a finding of probable cause, except for a technical violation pursuant to Section 8-13-1170 or 8-13-1372, the following documents become public record: the complaint, the response by the respondent, and the notice of hearing. If a hearing is held on the matter, the final order and all exhibits introduced at the hearing shall become public record upon issuance of the final order by the commission. Exhibits introduced must be redacted prior to release to exclude personal information where the public disclosure would constitute an unreasonable invasion of personal privacy.
The respondent may waive the right to confidentiality. In the event a hearing is not held on a matter after a finding of probable cause, the final disposition of the matter becomes public record. The willful release of confidential information is a misdemeanor, and any person releasing such confidential information, upon conviction, must be fined not more than one thousand dollars or imprisoned not more than one year."
SECTION 4. Section 8-13-320(10)(j) of the 1976 Code is amended to read:
"(j) If a hearing is to be held, the respondent must be allowed to examine and make copies of all evidence in the commission's possession relating to the charges. The same discovery techniques which are available to the commission must be equally available to the respondent, including the right to request the commission to subpoena witnesses or materials and the right to conduct depositions as prescribed by subitem (f) A panel of three commissioners must conduct a hearing in accordance with Chapter 23 of Title 1 (Administrative Procedures Act), except as otherwise expressly provided. Panel action requires the participation of the three panel members. During a commission panel hearing conducted to determine whether a violation of the chapter has occurred, the respondent must be afforded appropriate due process protections, including the right to be represented by counsel, the right to call and examine witnesses, the right to introduce exhibits, and the right to cross-examine opposing witnesses. All evidence, including records the commission considers, must be offered fully and made a part of the record in the proceedings. The hearings must be held in executive session unless the respondent requests an open hearing open to the public."
SECTION 5. Section 8-13-530 of the 1976 Code is amended to read:
"Section 8-13-530. Each ethics committee shall:
(1) ascertain whether a person has failed to comply fully and accurately with the disclosure requirements of this chapter and promptly notify the person to file the necessary notices and reports to satisfy the requirements of this chapter;
(2) receive complaints filed by individuals and, upon a majority vote of the total membership of the committee, file complaints when alleged violations are identified;
(3) upon the filing of a complaint, investigate possible violations of breach of a privilege governing a member or staff of the appropriate house, the alleged breach of a rule governing a member of, legislative caucus committees for, or a candidate, or staff for the appropriate house, misconduct of a member or staff of, legislative caucus committees for, or a candidate for the appropriate house, or a violation of this chapter or Chapter 17 of Title 2 alleging a violation by a member or staff of the appropriate house, or a member or staff of a legislative caucus committee, or a candidate for the appropriate house, for a violation of this chapter or Chapter 17, Title 2, other than a violation of a rule of the appropriate house, the ethics committee shall refer the complaint to the State Ethics Commission for an investigation pursuant to Section 8-13-540;
(4) receive, investigate, and hear a complaint which alleges a possible violation of a breach of a privilege or a rule governing a member or staff of the appropriate house or legislative caucus committee, or candidate for the appropriate house, the alleged breach of a rule governing a member or staff of or candidate for the appropriate house, misconduct of a member or staff of or candidate for the appropriate house, or a violation of this chapter or Chapter 17 of Title 2.;
(5) no a complaint may not be accepted by the ethics committee concerning a member of or candidate for the appropriate house during the fifty-day period before an election in which the member or candidate is a candidate. During this fifty-day period, any person may petition the court of common pleas alleging the violations complained of and praying for appropriate relief by way of mandamus or injunction, or both. Within ten days, a rule to show cause hearing must be held, and the court must either dismiss the petition or direct that a mandamus order or an injunction, or both, be issued. A violation of this chapter by a candidate during this fifty-day period must be considered to be an irreparable injury for which no adequate remedy at law exists. The institution of an action for injunctive relief does not relieve any party to the proceeding from any penalty prescribed for violations of this chapter. The court must award reasonable attorney's fees and costs to the nonpetitioning party if a petition for mandamus or injunctive relief is dismissed based upon a finding that the:
(i) petition is being presented for an improper purpose such as harassment or to cause delay;
(ii) claims, defenses, and other legal contentions are not warranted by existing law or are based upon a frivolous argument for the extension, modification, or reversal of existing law or the establishment of new law; and
(iii) allegations and other factual contentions do not have evidentiary support or, if specifically so identified, are not likely to have evidentiary support after reasonable opportunity for further investigation or discovery.
Action on a complaint filed against a member or candidate which was received more than fifty days before the election but which cannot be disposed of or dismissed by the ethics committee at least thirty days before the election must be postponed until after the election;
(5)(6) obtain information, and investigate technical violation complaints, and hear complaints as provided in Section 8-13-540 with respect to any complaint filed pursuant to this chapter or Chapter 17, of Title 2 and to that end may compel by subpoena issued by a majority vote of the committee the attendance and testimony of witnesses and the production of pertinent books and papers;
(6)(7) administer or recommend sanctions appropriate to a particular member, or staff of, or candidate for, the appropriate house pursuant to Section 8-13-540, including the recovery of the value of anything transferred or received in breach of the ethical standards, or dismiss the charges; and
(7)(8) act as an advisory body to the General Assembly and to individual members of or candidates for the appropriate house on questions pertaining to the disclosure and filing requirements of members of or candidates for the appropriate house, and may issue, upon request from a member or staff of the appropriate house, or legislative caucus committee, or candidate for the appropriate house, and publish advisory opinions on the requirements of these chapters."
SECTION 6. Chapter 13, Title 8 of the 1976 Code is amended by adding Section 8-13-535 to read:
"Section 8-13-535. (A) The committee may issue a formal advisory opinion, based on real or hypothetical sets of circumstances. A formal advisory opinion issued by the committee is binding on the committee, until amended or revoked, in any subsequent charges concerning the person who requested the formal opinion and any other person who acted in reliance upon it in good faith, unless material facts were omitted or misstated by the person in the request for the opinion. A formal advisory opinion must be in writing and is considered rendered when approved by a majority of the committee members subscribing to the advisory opinion. Advisory opinions must be made available to the public unless the committee, by majority vote of the total membership of the committee, requires an opinion to remain confidential. However, the identities of the parties involved must be withheld upon request.
(B) Staff of the appropriate ethics committee may issue a written informal advisory opinion, based on a real or hypothetical set of circumstances, to a member upon that member's request. If raised in response to a complaint, the appropriate committee shall consider whether the member relied, in good faith, upon a written informal opinion prior to making a probable cause determination or concurring in a determination, as applicable. A written informal advisory opinion issued by the committee staff is binding on the committee, until amended or revoked, in any subsequent charges concerning the person who requested the informal opinion unless material facts were omitted or misstated by the person in the request for the opinion.
(C) The appropriate ethics committee must consider whether a person relied in good faith upon a formal advisory opinion or written informal opinion issued by the committee prior to the effective date of this act, unless amended or revoked prior to the action considered as a possible violation, prior to making a probable cause decision."
SECTION 7. Section 8-13-540 of the 1976 Code is amended to read:
"Section 8-13-540. Unless otherwise provided for by House or Senate rule, as appropriate, each ethics committee must conduct its investigation of a complaint filed pursuant to this chapter or Chapter 17 of Title 2 in accordance with this section.
(1) When a complaint is filed with or by the ethics committee, a copy must promptly be sent to the person alleged to have committed the violation. If the ethics committee determines the complaint does not allege facts sufficient to constitute a violation, the complaint must be dismissed and the complainant and respondent notified. If the ethics committee finds that the complaining party wilfully filed a groundless complaint, the finding must be reported to appropriate law enforcement authorities. The wilful filing of a groundless complaint is a misdemeanor and, upon conviction, a person must be fined not more than one thousand dollars or imprisoned not more than one year. In lieu of the criminal penalty provided by this subsection, a civil penalty of not more than one thousand dollars may be assessed against the complainant upon proof, by a preponderance of the evidence, that the filing of the complaint was wilful and without just cause or with malice. If the ethics committee determines the complaint alleges facts sufficient to constitute a violation, it shall promptly investigate the alleged violation and may compel by subpoena the attendance and testimony of witnesses and the production of pertinent books and papers.
If after such preliminary investigation, the ethics committee finds that probable cause exists to support an alleged violation, it shall, as appropriate:
(a) render an advisory opinion to the respondent and require the respondent's compliance within a reasonable time; or
(b) convene a formal hearing on the matter within thirty days of the respondent's failure to comply with the advisory opinion. All ethics committee investigations and records relating to the preliminary investigation are confidential. No complaint shall be accepted which is filed later than four years after the alleged violation occurred.
(2) If a hearing is to be held, the respondent must be allowed to examine and make copies of all evidence in the ethics committee's possession relating to the charges. At the hearing the charged party must be afforded appropriate due process protections, including the right to be represented by counsel, the right to call and examine witnesses, the right to introduce exhibits, and the right to cross-examine opposing witnesses. All hearings must be conducted in executive session.
(3) After the hearing, the ethics committee shall determine its findings of fact. If the ethics committee, based on competent and substantial evidence, finds the respondent has violated this chapter or Chapter 17 of Title 2, it shall:
(a) administer a public or private reprimand;
(b) determine that a technical violation as provided for in Section 8-13-1170 has occurred;
(c) recommend expulsion of the member; and/or,
(d) in the case of an alleged criminal violation, refer the matter to the Attorney General for investigation. The ethics committee shall report its findings in writing to the Speaker of the House or President Pro Tempore of the Senate, as appropriate. The report must be accompanied by an order of punishment and supported and signed by a majority of the ethics committee members. If the ethics committee finds the respondent has not violated a code or statutory provision, it shall dismiss the charges.
(4) An individual has ten days from the date of the notification of the ethics committee's action to appeal the action to the full legislative body.
(5) No ethics committee member may participate in any matter in which he is involved.
(6) The ethics committee shall establish procedures which afford respondents appropriate due process protections, including the right to be represented by counsel, the right to call and examine witnesses, the right to introduce exhibits, and the right to cross-examine opposing witnesses.
(A) Filing of Complaints
(1) A complaint alleging a member of the General Assembly, legislative caucus committees, candidates for the General Assembly, or staff of the General Assembly or legislative caucus committee has committed a violation of this chapter or Chapter 17, Title 2 must be in writing and state the name of the person alleged to have committed the violation and the particulars of the violation.
(2) When a complaint is filed with or by the ethics committee alleging a violation of this chapter or Chapter 17, Title 2, a copy must be sent to the person alleged to have committed the violation and to the State Ethics Commission, hereinafter referred to as "the commission" within thirty days from the date the complaint was filed, for an investigation as provided in this section. However, if the complaint only alleges a violation of a rule of the House of Representatives or of the Senate, the appropriate ethics committee must forward a copy of the complaint to the person alleged to have committed the violation, and the appropriate ethics committee shall investigate and make a determination for a complaint.
(3)(a) The commission, upon receipt of information, may initiate and file a complaint upon an affirmative vote of the commission. The commission shall accept complaints referred by the ethics committees and notarized complaints from individuals, whether personally or on behalf of an organization or governmental body.
(b) The commission shall forward a copy of the complaint, a general statement of the applicable law with respect to the complaint, and a statement explaining the due process rights of the respondent including, but not limited to, the right to counsel to the respondent within ten days of the filing of the complaint. Unless the complaint was referred by an ethics committee, the commission shall send a copy of the complaint to the appropriate ethics committee.
(4) Action may not be taken on a complaint filed more than four years after the violation is alleged to have occurred unless the person alleged to have committed the violation, by fraud or other device, prevents discovery of the violation.
(B) Actions by the State Ethics Commission
(1) Upon receiving a complaint filed pursuant to subsection (A), the commission must determine whether the complaint alleges only a violation of a rule of the House of Representatives or Senate or a technical violation pursuant to Section 8-13-1170 or Section 8-13-1372. If the commission determines the complaint alleges only a rule violation or technical violation, the complaint must be referred to the appropriate ethics committee for investigation and determination.
(2)(a) If the commission determines the complaint alleges more than a violation of a rule of the House of Representatives or Senate or a technical violation pursuant to Section 8-13-1170 or Section 8-13-1372, the commission must determine whether the complaint alleges facts sufficient to constitute a violation of this chapter or Chapter 17, Title 2.
(b) If the commission determines that the complaint either does not allege facts sufficient to constitute a violation or does not find probable cause that a violation occurred, a report must be provided to the appropriate ethics committee with the recommendation that the complaint be dismissed. The appropriate ethics committee may concur or nonconcur with the commission's recommendation, or within fifteen days from the committee's receipt of the finding, the committee may request the commission to continue the investigation and consider additional matters not considered by the commission. If the appropriate ethics committee concurs with the recommendation to dismiss the complaint, the committee must notify the complainant and respondent.
(c) If the commission finds that the complaining party wilfully filed a groundless complaint, the finding must be reported to the Attorney General. The wilful filing of a groundless complaint is a misdemeanor and, upon conviction, the person must be fined not more than one thousand dollars or imprisoned not more than one year. In lieu of the criminal penalty provided by this item, a civil penalty of not more than one thousand dollars may be assessed against the complainant upon proof by a preponderance of the evidence that the filing of the complaint was wilful and without just cause or with malice.
(d) If the commission determines that the complaint alleges facts sufficient to constitute a violation of this chapter or Chapter 17, Title 2, an investigation may be conducted into the alleged violation.
(3) If the commission finds evidence that the person alleged to have committed the violation wilfully violated a section of this chapter or Chapter 17 of Title 2 that imposes a criminal penalty, the commission must forward the complaint and accompanying materials to the Attorney General or circuit solicitor. This provision does not limit any authority of the Attorney General or circuit solicitor to initiate or conduct any criminal investigation within his jurisdiction.
(4) If the commission determines that it needs assistance in conducting an investigation, the commission shall request the assistance of appropriate agencies.
(5) In conducting its investigation, the commission may order testimony to be taken in any investigation or deposition before a person who is designated by the commission and has the power to administer oaths and, in these instances, to compel testimony. The commission may administer oaths and affirmation for the testimony of witnesses and issue subpoenas, by approval of the chairman and subject to judicial enforcement, for the procurement of witnesses and materials including books, papers, records, documents, or other tangible objects relevant to the agency's investigation. A person to whom a subpoena has been issued may move before a commission panel or the commission for an order quashing a subpoena issued pursuant to this section.
(6) Upon completing its investigation, the commission must provide a report to the appropriate ethics committee with a recommendation as to whether there is probable cause to believe a violation of this chapter or of Chapter 17, Title 2 has occurred. The report must include a copy of all relevant reports, evidence, and testimony considered by the commission.
(C) Release of complaint and information related to investigations
(1) All investigations and accompanying documents are confidential and may be released only pursuant to this section.
(2) If the committee concurs with a recommendation by the commission that a complaint should be dismissed due to the complaint either failing to allege facts sufficient to constitute a violation or did not find probable cause that a violation occurred, a notice of dismissal will be sent by the committee to the complainant and respondent. This notice and all materials regarding the matter are confidential.
(3)(a) If the commission determines the complaint only alleges a technical violation pursuant to Section 8-13-1170 or 8-13-1372, and the committee subsequently either dismisses the matter or determines a technical violation occurred, documents involving the matter shall remain confidential.
(b) If the commission's report to the committee recommends that there is probable cause to believe a violation of this chapter or Chapter 17, Title 2, other than a technical violation pursuant to Section 8-13-1170 or 8-13-1372, has occurred, and the committee does not request further investigation regarding the probable cause recommendation, the following documents become public thirty days after the commission issues its report to the committee: the complaint, the response by the respondent, the notice of hearing before the appropriate ethics committee, and the commission's recommendations.
(c) If the appropriate committee requests further investigation after receipt of the commission's report, documents may only be released if the commission's second report to the committee recommends a finding of probable cause. If the commission's second report recommends a finding of probable cause, the documents listed in (a) must be released either thirty days after the conclusion of the investigation or upon a finding of probable cause by the committee, whichever occurs earlier.
(d)(i) If the commission's report recommends that there is probable cause for a violation of this chapter or Chapter 17, Title 2, other than a technical violation pursuant to Section 8-13-1170 or 8-13-1372, but the appropriate committee nonconcurs and dismisses the matter, the notice of dismissal must be made public.
(ii) If the commission's report recommends that there is probable cause for a violation of this chapter or Chapter 17, Title 2, other than a technical violation pursuant to Section 8-13-1170 or 8-13-1372, but the appropriate committee nonconcurs and finds, prior to a public hearing, that only a technical violation occurred, the notice of the committee's findings must be made public.
(4) If the committee determines there is probable cause for a violation of this chapter or Chapter 17, Title 2, other than a technical violation pursuant to Section 8-13-1170 or 8-13-1372, and issues an advisory opinion to the respondent pursuant to this section, the advisory opinion becomes public.
(5) If the committee conducts a public hearing pursuant to this section, the final order and exhibits introduced at the hearing become public upon the issuance of the final order. Exhibits introduced must be redacted prior to release to exclude personal information where the public disclosure would constitute an unreasonable invasion of personal privacy.
(6) Documents released or made public must be redacted prior to release to exclude personal information where the public disclosure would constitute an unreasonable invasion of personal privacy. The respondent may waive the right to confidentiality. The wilful release of confidential information is a misdemeanor, and a person releasing confidential information, upon conviction, must be fined not more than one thousand dollars or imprisoned for not more than one year.
(D) Actions by ethics committees
(1) If the commission's report recommends that there is not probable cause to believe a violation of this chapter or Chapter 17, Title 2 has occurred, the appropriate ethics committee may concur or nonconcur with that recommendation, or within fifteen days from the committee's receipt of the report, request the commission to continue the investigation and consider additional matters not considered by the commission.
(2) If, after reviewing the commission's recommendation and relevant evidence, the ethics committee determines that probable cause does not exist to believe a violation of this chapter or of Chapter 17, Title 2 has occurred, the committee shall dismiss the complaint and send a written decision to the respondent and the complainant.
(3) If, after reviewing the commission's recommendation and relevant evidence, the ethics committee determines that the respondent has committed only a technical violation pursuant to Section 8-13-1170 or 8-13-1372, the provisions of the appropriate section apply, which may include subsection (C), if applicable.
(4) If, after reviewing the commission's recommendation and relevant evidence, the ethics committee determines that probable cause exists to believe a violation of this chapter or of Chapter 17, Title 2 has occurred, except for a technical violation of Section 8-13-1170 or Section 8-13-1372, the committee shall, as appropriate:
(a) render an advisory opinion to the respondent and require the respondent's compliance within a reasonable time; or
(b) convene a formal public hearing on the matter.
The ethics committee may obtain its own information, or request additional investigation by the State Ethics Commission, if it needs additional information to make a determination as to whether or not probable cause exists.
(5) If the ethics committee convenes a formal public hearing:
(a) the investigator or attorney handling the investigation for the State Ethics Commission shall present the evidence related to the complaint to the appropriate ethics committee;
(b) it is the duty of the investigator or attorney to further investigate the subject of the complaint and any related matters under the jurisdiction and at the direction of the ethics committee, to request assistance from appropriate state agencies as needed, to request authorization from the committee for funds for the hiring of auditors, investigators, or other assistance as necessary, to prepare subpoenas, and to present evidence to the committee at any public hearing. The appropriate committee shall maintain the authority to approve subpoenas, authorize expenditures, dismiss complaints, schedule hearings, grant continuances, and any other authority as provided for by their rules;
(c) the respondent must be allowed to examine and make copies of all evidence in the ethics committee's possession relating to the charges. At the hearing the respondent must be afforded appropriate due process protections, including the right to be represented by counsel, the right to call and examine witnesses, the right to introduce exhibits, and the right to cross-examine opposing witnesses.
(d) all hearings must be open to the public.
(6)(a) After the formal public hearing, the ethics committee shall determine its findings of fact and issue its final order.
(b) If the ethics committee, based on competent and substantial evidence, finds the respondent has not violated this chapter or Chapter 17, Title 2, the committee shall dismiss the complaint and send a written decision to the respondent and the complainant.
(c) If the ethics committee, based on competent and substantial evidence, finds the respondent has violated this chapter or Chapter 17, Title 2, the committee shall:
(i) administer a public reprimand;
(ii) determine that a technical violation as provided for in Section 8-13-1170 or 8-13-1372 has occurred;
(iii) require the respondent to pay a civil penalty not to exceed two thousand dollars for each nontechnical violation that is unrelated to the late filing of a required statement or report or failure to file a required statement or report;
(iv) require the forfeiture of gifts, receipts, or profits, or the value of each, obtained in violation of Chapter 13, Title 8 or Chapter 17, Title 2;
(v) recommend expulsion of the member;
(vi) provide a copy of the complaint and accompanying materials to the Attorney General if the committee finds that there is probable cause to believe the respondent wilfully violated a section of this chapter or Chapter 17 of Title 2 that imposes a criminal penalty; or
(vii) require a combination of subitems (i) though (vi) as necessary and appropriate.
(d) The ethics committee shall report its findings in writing to the Speaker of the House of Representatives or President Pro Tempore of the Senate, as appropriate. The report must be accompanied by an order of punishment or dismissal and supported and signed by a majority of the ethics committee members.
(e) Upon the issuance of the final order, the following documents become public record: exhibits introduced at the hearing, the committee's findings, and the final order. Exhibits introduced must be redacted prior to release to exclude personal information where the public disclosure would constitute an unreasonable invasion of personal privacy.
(E) If, after conducting a formal public hearing, the ethics committee finds the respondent has violated this chapter or Chapter 17, Title 2, the respondent has ten days from the date of receiving the committee's order of punishment to appeal the action to the full legislative body.
(F) No ethics committee member may participate in any matter in which he is involved.
(G) The ethics committees shall establish procedures which afford respondents appropriate due process protections, including the right to be represented by counsel, the right to call and examine witnesses, the right to introduce exhibits, and the right to cross-examine opposing witnesses."
SECTION 8. Subsection 8-13-550(B) of the 1976 Code is amended to read:
"(B) Upon consideration of an ethics committee report by the House or the Senate, whether in executive or open session, the results of the consideration, except in the case of the issuance of a private reprimand, are a matter of public record."
SECTION 9. The provisions of this act are severable. If any section, subsection, paragraph, subparagraph, item, subitem, 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 the act, the General Assembly hereby declaring that it would have passed each and every section, subsection, paragraph, subparagraph, item, subitem, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, items, subitems, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective.
SECTION 10. The provisions of this act are effective as of April 1, 2017 and shall apply to complaints filed on or after April 1, 2017. However, the provisions in Section 8-13-310 regarding the selection of the initial members to serve on the State Ethics Commission as of April 1, 2017 and the termination of terms of the members serving on the commission as of March 31, 2017 take effect after the date of the Governor's signature for the limited purpose of having the initial members of the reconstituted State Ethics Commission begin service on April 1, 2017. The State Ethics Commission, House Ethics Committee and Senate Ethics Committee shall maintain jurisdiction over all open complaints and investigations pending in the appropriate entity on or before March 31, 2017. The reconstituted State Ethics Commission shall have jurisdiction over open complaints and investigations pending within the State Ethics Commission as of March 31, 2017. /
Renumber sections to conform.
Amend title to conform.
Senator LARRY MARTIN spoke on the amendment.
Senator RANKIN spoke on the amendment.
Remarks by Senator RANKIN
Thank you, Mr. PRESIDENT. Thank you, my Chairman, who will bear with me for just a few moments. As we hopefully will work our way out of this situation that we are in, I would like to make a few closing remarks for this week, if I may, on the front of two subjects.
One general, that being ethics reform. It has been said, like Mark Twain in his death, or Harry Truman in his defeat, the statements of my position on ethics reform have been greatly exaggerated, in fact taken out of context and in fact misrepresented. But I am not up here to whine, I'm not up here to complain in this free democracy that we live in where you can say anything you want and be held accountable perhaps only in a court of law or in the ultimate court above. I'm not complaining about that. But I do want it said and heard that ethics reform is something we need. It is something that I support. Since 2013, in fact beyond, Senator HAYES, myself and others, at the stead of then PRESIDENT Pro Tem JOHN COURSON, put together a group. We labored in 2013. We generated a Bill, folks. We had a Bill in 2014, the House adopted a Bill, the Senate adopted a Bill and what did we do? We had a conference committee. Guess what was included in that very Bill but the subject we are talking about right now, and that subject being 'dark money'. We have been there, folks. We have done it before -- to do it again is not unprecedented and it's not something from a new group. It's the same makeup that's in this Senate right now. So, I urge you all as you go home and you think about what is, as Micah says, "What is required of you, to do justly, love mercy and walk humbly with thy God." Folks, this is not heretical. It is constitutional and before we get out of this subject, it will not be as has been written by some, you are either for ethics reform or you're not, it will be whether you are for transparency in South Carolina, whether you can put your money where your mouth is, but put your name on the dotted line like is required right now. Or, excuse me, that was required before 2010. The Krawcheck case created in South Carolina a wild, wild west of independent expenditures that can go into any Senate district, any House district and any Governor's race automatically, without restriction. Judge Wooten's decision in 2010, which has not been changed, totally opens this State up for the very things that are happening in Senator LEATHERMAN's district and others across this State who have challenges right now. Say what you want to say folks, but be man enough to come forward, put your name on a list, and tell us who you are. That's all that was required before, but what is happening right now, unless we do this -- it will continue to be the most wide open, free-ranging State without any law requiring them to do as we did six years ago and up until that point when we adopted this Ethics Reform Bill in 1991, you had to report. Right now, you don't. So, am I for ethics reform, Senator HAYES? Amen. Do I want this Bill to get passed, Senator LARRY MARTIN? Amen. My brother from Cherokee County? Yes, I want ethics reform. I want a clean Bill. But I want one with clean hands and a clean, clear conscience so I can sleep well at night, face my brothers and sisters in Horry County, and face my Maker when I'm done on this earth. Thank you, Mr. Chairman.
On motion of Senator JACKSON, with unanimous consent, the remarks of Senator RANKIN were ordered printed in the Journal.
Debate was interrupted by adjournment.
Motion Adopted
On motion of Senator LARRY MARTIN, the Senate agreed to stand adjourned.
LOCAL APPOINTMENT
Confirmation
Having received a favorable report from the Senate, the following appointment was confirmed in open session:
Initial Appointment, Darlington County Part-Time Magistrate, with the term to commence April 30, 2015, and to expire April 30, 2019
Craig L. LaCross, 716 Lee State Park Road, Lamar, SC 29069 VICE Cely A. Brigman
MOTION ADOPTED
On motion of Senator ALEXANDER, with unanimous consent, the Senate stood adjourned out of respect to the memory of Ms. Frances Sandifer of Westminster, S.C. Frances and Cecil, her husband, met as children at the Connie Maxwell Children's Home where they became childhood sweethearts and were married for over 74 years. Frances was a member of Westminster Baptist Church and had a wonderful sense of humor. Frances was a loving wife, devoted mother and doting grandmother who will be dearly missed.
ADJOURNMENT
At 2:30 P.M., on motion of Senator LARRY MARTIN, the Senate adjourned to meet tomorrow at 11:00 A.M. under the provisions of Rule 1 for the purpose of taking up local matters and uncontested matters which have previously received unanimous consent to be taken up.
* * *
This web page was last updated on Thursday, March 9, 2017 at 12:31 P.M.
| 2022-12-07T23:30:29 |
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|
https://mail.aimsciences.org/article/doi/10.3934/dcds.2010.28.665
|
Article Contents
Article Contents
# Sc-smoothness, retractions and new models for smooth spaces
• We present the concept of sc-smoothness for Banach spaces, which leads to new models of spaces having locally varying dimensions called M-polyfolds. We present detailed proofs of the technical results needed for the applications, in particular, to the Symplectic Field Theory. We also outline a very general Fredholm theory for bundles over M-polyfolds. The concepts are illustrated by holomorphic mappings between conformal cylinders which break apart as the modulus tends to infinity.
Mathematics Subject Classification: Primary: 58B99; Secondary: 58C99.
Citation:
Open Access Under a Creative Commons license
| 2023-02-04T22:38:28 |
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https://atb.nrel.gov/electricity/2022/utility-scale_pv
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# Utility-Scale PV
Units using capacity above represent kWAC.
2022 ATB data for utility-scale solar photovoltaics (PV) are shown above, with a Base Year of 2020. The Base Year estimates rely on modeled capital expenditures (CAPEX) and operation and maintenance (O&M) cost estimates benchmarked with industry and historical data. Capacity factor is estimated for 10 resource classes, binned by mean global horizontal irradiance (GHI) in the United States. The 2022 ATB presents capacity factor estimates that encompass a range associated with advanced, moderate, and conservative technology innovation scenarios across the United States. Future year projections are derived from bottom-up benchmarking of PV CAPEX and bottom-up engineering analysis of O&M costs.
The three scenarios for technology innovation are:
• Conservative Technology Innovation Scenario (Conservative Scenario): lower levels of R&D investment with minimal technology advancement and global module pricing consistent with the base year
• Moderate Technology Innovation Scenario (Moderate Scenario): R&D investment continuing at similar levels as today, with current industry technology road maps achieved, but no substantial innovations or new technologies introduced to the market
• Advanced Technology Innovation Scenario (Advanced Scenario): an increase in R&D spending that generates substantial innovation, allowing historical rates of development to continue.
A detailed description of the scenarios is below.
## Resource Categorization
The 2022 ATB provides the average capacity factor for 10 resource categories in the United States, binned by mean GHI. Average capacity factors are calculated using county-level capacity factor averages from the Renewable Energy Potential (reV) model for 1998–2019 (inclusive) of the National Solar Radiation Database (NSRDB). The NSRDB provides modeled spatiotemporal solar irradiance resource data at 4-km spatial and 0.5-hour temporal resolution. The county-level mean GHI is calculated by aggregating each individual NSRDB point’s multiyear mean GHI to provide a county’s mean GHI for all years included in the analysis. The U.S. average capacity factor for each resource category is weighted by the land area (square miles) of each county within the GHI resource category. The county estimated land area is provided by geospatial and tabular data from the U.S. Census. The map below shows average annual GHI in the United States.
The following table summarizes the estimated 2019 capacity factors (in the first year of operation) for resource category and each resource category's associated U.S. land area.
Utility-Scale PV Resource Classes
DOE’s Solar Energy Technologies Office sets its PV cost targets for a location centered geographically within the contiguous United States, in Resource Class 7, whereas the ATB benchmark is Class 5, representing the national-average solar resource.
## Scenario Descriptions
Summary of Technology Innovations by Scenario (2030)
1 Module efficiency improvements represent an increase in energy production over the same area, in this case, the dimensions of a PV module. Energy yield gain represents an improvement in capacity factor relative to the rated capacity of a PV system. In the case of bifacial modules, the increase in energy production between two modules with the same dimensions does not currently change the capacity rating of the module under standard test conditions, as the rating is based on light from one direction.
## Representative Technology
Utility-scale PV systems in the 2022 ATB are representative of one-axis tracking systems with performance and pricing characteristics in line with a DC-to-AC ratio, or inverter loading ratio (ILR), of 1.28 for the base year and future years (Ramasamy et al., 2021); this is a change from the 2021 ATB, which used an ILR of 1.34. We recognize that ILR is likely to change, particularly with the adoption of bifacial modules, and to greatly depend on location. However, allowing for this change would require the optimization of ILR and CAPEX by resource bin and year, causing a range of prices, independent of other regional factors. We believe this would create less transparency and more confusion with respect to the impact of technology changes on these individual levelized cost of energy (LCOE) categories.
## Methodology
This section describes the methodology to develop assumptions for CAPEX, O&M, and capacity factor. For standardized assumptions, see regional cost variationmaterials cost indexscale of industrypolicies and regulations, and inflation. The PV-specific and standardized assumptions for labor cost differ; the PV analysis assumes use of nonunion labor only.
PV projections in the 2022 ATB are driven primarily by CAPEX cost improvements but also by improvements in energy yield, operational cost, and cost of capital (for the Market + Policies Financial Assumptions Case).
Though CAPEX is one driver of lower costs, R&D efforts continue to focus on other areas to lower the cost of energy from utility-scale PV, such as longer system lifetime and improved performance. Three projections are developed for scenario modeling as bounding levels (see Scenario Descriptions above).
### Capital Expenditures (CAPEX)
Definitions: The rated capacity used to calculate CAPEX for PV systems is reported in terms of the aggregated capacity of either all its modules or all its inverters. PV modules are rated using standard test conditions and produce direct current (DC) energy; inverters convert DC energy/power to alternating current (AC) energy/power. Therefore, the capacity of a PV system is rated either in units of MWDC via the aggregation of all modules' rated capacities or in units of MWAC via the aggregation of all inverters' rated capacities. The ratio of these two capacities is referred to as the inverter loading ratio (ILR). The 2022 ATB assumes the base year estimates and future projections use an ILR of 1.28.
The PV industry typically refers to PV CAPEX in units of $/MWDC based on the aggregated module capacity. The electric utility industry typically refers to PV CAPEX in units of$/MWAC based on the aggregated inverter capacity; starting with the 2020 ATB, we use $/MWAC for utility-scale PV. Plant costs are represented with a single estimate per innovations scenario, because CAPEX does not correlate well with solar resource. For the 2022 ATB—and based on (EIA, 2016) and the National Renewable Energy Laboratory (NREL) PV cost model (Ramasamy et al., 2021)—the utility-scale PV plant envelope is defined to include items noted in the table (Components of CAPEX) below. Base Year: A system price of$1.30/WAC in 2020 is based on modeled pricing for a 100-MWDC, one-axis tracking system quoted in Q1 2020 as reported by (Feldman et al., 2021), adjusted from $/WDC to$/WAC by an ILR of 1.28. The 1.14/WAC price in 2021 is based on modeled pricing for a 100-MWDC, one-axis tracking system quoted in Q1 2021 as reported by (Ramasamy et al., 2021), adjusted by an ILR of 1.28. We focus on larger systems for the 2020 and 2021 values to better align with recent trends in utility-scale installations. (EIA, 2021a) reported 155 PV installations (greater than 5 MWAC in capacity) totaling 9.5 GWAC were placed in service in 2020 in the United States. Though this represents an average of approximately 61 MWAC, 85% of the installed capacity in 2020 came from systems greater than 50 MWAC and 42% came from systems greater than 100 MWAC. In the chart below, reported historical utility-scale PV plant CAPEX (Bolinger et al., 2021) is shown in box-and-whiskers format for comparison to the historical benchmarked and future CAPEX projections for utility-scale PV plants. (Bolinger et al., 2021) provide statistical representation of CAPEX for projects larger than 5 MWAC, which includes 91% of the U.S. utility-scale PV capacity installed in 2020. Historical Sources: (Bolinger et al., 2021) (Ramasamy et al., 2021) Future Projections: 2022 ATB All prices quoted in WDC are converted to WAC (1 WDC = ILR × WAC). Reported and benchmark prices can differ for a variety of reasons, as outlined by Barbose and Darghouth (Barbose et al., 2019) and Bolinger, Seel, and Robson (Bolinger et al., 2019), including: • Timing-Related Issues: For example, the time between power purchase agreement contract completion and project placement in service can vary, and a system can be reported as being installed in separate sections over time or when an entire complex is complete. For example, in 2014, the reported capacity-weighted average system price was higher than 80% of system prices in 2014 because very large systems with multiyear construction schedules were being installed that year. Developers of these large systems negotiated contracts and installed portions of their systems when module and other costs were higher. • System Variations: The size, technology, installer margin, and design of systems installed in a given year vary over time. • Cost Categories: There are variations in which cost categories are included in CAPEX (e.g., financing costs and initial O&M expenses). Federal investment tax credits provide an incentive to include costs in the upfront CAPEX to receive a higher tax credit, and these included costs might have otherwise been reported as operating costs. The bottom-up benchmarks are more reflective of an overnight capital cost, which is in-line with the ATB methodology of inputting overnight capital cost and calculating construction financing to derive CAPEX. Use the following table to view the components of CAPEX. Components of CAPEX Future Years Projections of utility-scale PV plant CAPEX for 2030 are based on bottom-up cost modeling, with 2021 values from (Ramasamy et al., 2021) and a straight-line change in price in the intermediate years between 2021 and 2030. ILR is assumed to remain at a constant 1.28. The system design and price changes made in the models are summarized and described in the Summary of Technology Innovations by Scenario table. See below for the details of changes to components of system price in the different ATB scenarios. Cost Details by Scenario We assume each scenario's CAPEX in 2050 is the equivalent of the CAPEX in 2030 but is one degree more aggressive, with a straight-line change in price in the years between 2030 and 2050. In the table below, asterisks and daggers indicate corresponding cells, where scenarios use the same values but are shifted in time. We also develop and model a scenario one degree more aggressive than the Advanced Scenario to estimate its 2050 CAPEX. The Advanced Scenario assumes: • Module efficiency of 30% achieved by 2050 • Further inverter simplification and manufacturing automation • 50% labor and hardware BOS cost improvements through automation and preassembly of module mounting and wiring efficiencies • Replacement of steel and aluminum with carbon fiber, which cuts material costs in half. More-Aggressive Scenarios Reach Given CAPEX Sooner More-aggressive scenarios reach given CAPEX sooner, as indicated by the asterisks and daggers. We compare the ATB CAPEX scenarios over time to projections from four sources, adjusted for inflation and ILR. The median of those projections is displayed in the figure below through 2030. CAPEX in the Conservative Scenario is higher than all analysts' projections, but otherwise the ATB scenarios are generally in line with the other projections. Two of the four analyst projections do not go beyond 2030, so data points with which to compare the ATB projections are limited; however, the Advanced Scenario is in line with the minimum analyst projection in 2050. Sources: 2022 ATB; (EIA, 2021b)(BNEF, 2019)(BNEF, 2021)(Cox, 2021) All prices quoted in WDC are converted to WAC (1 WAC = ILR × WDC). ### Operation and Maintenance (O&M) Costs Definition: Operation and maintenance (O&M) costs represent the annual fixed expenditures required to operate and maintain a PV plant over its lifetime, including items noted in the table below. Base Year: The O&M cost of23/kWAC-yr in 2020 is based on modeled pricing for a 100-MWDC, one-axis tracking system quoted in Q1 2020 as reported by (Feldman et al., 2021), adjusted from DC to AC. Lawrence Berkeley National Laboratory collected feedback on O&M costs from U.S. solar industry professionals (Wiser et al., 2020). The wide range in reported prices depends in part on the range in maintenance practices for various systems and on cost categories that include asset management (including compliance and reporting for incentive payments), insurance products, site security, cleaning, vegetation removal, and component failure. Not all these practices are performed for each system, and some factors depend on the quality of the parts and construction. NREL analysts estimate O&M costs can range from $0/kWDC-yr to$40/kWDC-yr ($0/kWAC-yr to$51/kWAC-yr at an ILR of 1.28).
Future Years: The fixed O&M (FOM) cost of $21/kWAC-yr for 2021 is based on pricing reported by (Ramasamy et al., 2021), which can be divided into system-related expenses ($13/kWAC-yr), property-related expenses ($5/kWAC-yr), and administration-related expenses ($2/kWAC-yr). From 2021 to 2050, system-related FOM is based on the ratio of system-related O&M costs ($/kW-yr) to CAPEX costs ($/kW) of 1.2:100 in 2021, as reported by (Ramasamy et al., 2021). This ratio is higher than the ratio of O&M costs to historically reported CAPEX costs of 0.8:100, which is derived from 2011–2018 historical data reported by Bolinger, Seel, and Robson (Bolinger et al., 2019), as well as the ratio of O&M costs to CAPEX costs of 1.0:100, which is derived from (IEA, 2018) and Lazard (Lazard, 2018). Historically reported data suggest O&M and CAPEX cost reductions are correlated; from 2011 to 2018, fleetwide average O&M and CAPEX costs fell 43% and 64% respectively, as reported by Bolinger, Seel, and Robson (Bolinger et al., 2019). From 2021 to 2050, property-related expenses are reduced by the inverse ratio of the increase in module efficiency, as less space will be required on a per watt basis. Administrative expenses are kept constant.
Components of O&M Costs
### Capacity Factor
Definition: The capacity factor represents the expected annual average energy production divided by the annual energy production assuming the plant operates at rated capacity for every hour of the year. It is intended to represent a long-term average over the lifetime of the plant; it does not represent interannual variation in energy production. Future-year estimates represent the estimated annual average capacity factor over the technical lifetime of a new plant installed in a given year.
PV system inverters, which convert DC energy/power to AC energy/power, have AC capacity ratings; therefore, the capacity of a PV system is rated in units of MWAC, or the aggregation of all inverters' rated capacities, or MWDC, or the aggregation of all modules' rated capacities. Other technologies' capacity factors are represented exclusively in AC units; however, in some previous editions of the ATB, PV pricing is represented in $/kWDC. In the 2022 ATB, utility-scale PV (though not commercial PV or residential PV) is represented in$/kWAC; for this reason, values in the 2022 ATB are not directly comparable to values in the 2019 ATB or earlier editions of the ATB without adjusting previous versions from WDC to WAC.
The capacity factor is influenced by the hourly solar profile, technology (e.g., thin-film or crystalline silicon), the bifaciality of the module, albedo, axis type (i.e., none, one, or two), shading, expected downtime, ILR, and inverter losses to transform from DC to AC power. The ILR (DC-to-AC ratio) is a design choice that influences the capacity factor. PV plant capacity factor incorporates an assumed degradation rate of 0.7%/yr in the annual average calculation. R&D could increase energy yield through bifaciality, improved albedo, better soil removal, improved cell temperature, lower system losses, O&M practices that improve uptime, and lower degradation rates of PV plant capacity factor; future projections assume energy yield gains of 0%–25% depending on the scenario.
From 2007 to 2019, the cumulative median AC capacity factor for utility-scale U.S. projects installed at the time (including fixed-tilt systems) was 24.0%, but individual project-level capacity factors exhibited a wide range (9.0%–36.0%) (Bolinger et al., 2021). The reported U.S. system capacity factors are consistent with the range of estimated capacity factors in the 2022 ATB (18%–31% in 2021) and the calculated U.S. area-weighted 30-year lifetime average capacity factor (24.5%). The figure below shows historical data for capacity factor as a function of ILR.
Cumulative net AC capacity factor of U.S. utility-scale PV projects
Source: (Bolinger et al., 2021)
Over time, PV plant output is reduced. This degradation is accounted for in ATB estimates of capacity factor (see table below). The 2022 ATB capacity factor estimates represent estimated annual average energy production over a 30-year lifetime.
These AC capacity factors are for a one-axis tracking system with a DC-to-AC ratio of 1.28, and therefore are not representative of the lower capacity factors reported by fixed-tilt systems.
Base Year: In the interactive data chart at the top of this page, select Technology Detail = All to add filters to display a range of capacity factors based on variation in solar resource in the contiguous United States. The range of the Base Year estimates illustrate the effect of locating a utility-scale PV plant in places with lower or higher solar irradiance. The ATB provides the average capacity factor for 10 resource categories in the United States, binned by mean GHI. Average capacity factors are calculated using county-level capacity factor averages from the reV model for years 1998–2019 (inclusive) of the NSRDB
The NSRDB provides modeled spatiotemporal solar irradiance resource data at 4-km spatial and 0.5-hour temporal resolution. The county-level mean GHI is calculated by aggregating each individual NSRDB point’s multiyear mean GHI to provide the county’s mean GHI for all years included in the analysis. U.S. average capacity factor for each resource category is weighted by the land area (square mileage) of each county within the GHI resource category. The county estimated land area is provided by geospatial and tabular data from the U.S. Census.
Because of the change in methodology in calculating capacity factors in the 2022 ATB, they are not directly comparable to those in previous editions of the ATB. In the 2022 ATB, we use capacity factors ranging from 18.4% for Class 10 (for locations with an average annual GHI less than 3.75) to 30.1% for Class 1 (for locations with an average annual GHI greater than 5.75) in 2020. The 2022 ATB capacity factor assumptions are based on ILR = 1.28.
Future Years: Projections of capacity factors for plants installed in future years increase over time because of an increase in energy yield from the module (better tracking, improved cell temperature, bifaciality, and better siting/practices to improve albedo), reduced system losses (improved soil removal, improved O&M uptime, and more-efficient inverters), and a reduction in degradation rates. The table below summarizes the technology improvements we used to calculate indicative improvements in capacity factor in each scenario.
2030 Technology Improvements Influencing Capacity Factor
* The year 2019 is used here because improvement assumptions were not changed from last year's ATB base year of 2019.
The technology improvements summarized above would not necessarily result in the estimated capacity factor improvements, given the 2022 ATB assumption of a constant ILR of 1.28. PV system ILR choice is based on an optimization exercise to maximize profits (or offer the lowest energy price), trading-off the extra cost and increased clipping losses of additional modules with improvements in inverter operation and a higher, flatter electricity production curve. All things being equal, the optimal ILR of PV systems in higher resource classes or for those that use bifacial modules will be lower than the optimal ILR of systems in lower resource classes or for those with monofacial modules, particularly without the use of energy storage.
Because of the complexity of optimizing CAPEX and ILR for each resource class for each year, and with and without storage, ATB PV system CAPEX and capacity factor benchmarks are calculated using a fixed ILR of 1.28, independent of system location, performance improvements over time, or the incorporation of storage. Also, we assume performance improvements over time are not location-dependent, even though a PV system with the same ILR in a higher resource area will experience more clipping and thus lower performance improvements. However, in reality, PV systems in those areas would reduce their clipping losses by installing fewer PV panels and would thus have a lower upfront cost (trading-off the marginally greater production with reduced CAPEX).
The following table summarizes the difference in average capacity factor in 2030 caused by these changes in the three technology innovation scenarios. Similar to our CAPEX assumptions, we assume each scenario's 2050 capacity factor is the equivalent of the 2030 capacity factor of the scenario but one degree more aggressive, with a straight-line change in price in the intermediate years between 2030 and 2050. The table below summarizes capacity factors for each ATB scenario by resource class.
2030 Utility PV AC Capacity Factors by Resource Location and Innovation Scenario
We also develop and model a scenario one degree more aggressive than the Advanced Scenario to estimate the capacity factor in 2050. In the Advanced Scenario, the capacity factor in 2050 is assumed to have a 23% improvement over 2020 capacity factors.
## References
The following references are specific to this page; for all references in this ATB, see References.
Feldman, David, Vignesh Ramasamy, Ran Fu, Ashwin Ramdas, Jal Desai, and Robert Margolis. “U.S. Solar Photovoltaic System and Energy Storage Cost Benchmark: Q1 2020.” Golden, CO: National Renewable Energy Laboratory, January 27, 2021. https://doi.org/10.2172/1764908.
Barbose, Galen, Naïm Darghouth, Salma Elmallah, Sydney Forrester, Kristina LaCommare, Dev Millstein, Joe Rand, Will Cotton, and Eric O’Shaughnessy. “Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States: 2019 Edition.” Tracking the Sun. Berkeley, CA: Lawrence Berkeley National Laboratory, October 30, 2019. https://escholarship.org/content/qt5422n7wm/qt5422n7wm.pdf.
Fuscher, Moritz, and Ehrler Bruno. “Efficiency Limit of Perovskite/Si Tandem Solar Cells.” ACS Energy Lett. 1, no. 4 (October 3, 2016): 863–68. https://doi.org/10.1021/acsenergylett.6b00405.
ITRPV. “ITRPV 2020: International Technology Roadmap for Photovoltaic (ITRPV).” VDMA, April 2020. https://www.vdma.org/international-technology-roadmap-photovoltaic.
Satpathy, Rabindra. “Additional Energy Yield Using Bifacial Solar PV Modules and Dependency on Albedo.” n.d. https://www.ises.org/sites/default/files/webinars/Presentation Rabi Satpathy_ISESWebinar_0.pdf.
Ramasamy, Vignesh, David Feldman, Jal Desai, and Robert Margolis. “U.S. Solar Photovoltaic System and Energy Storage Cost Benchmarks: Q1 2021.” Golden, CO: National Renewable Energy Laboratory, 2021. https://www.nrel.gov/docs/fy22osti/80694.pdf.
EIA. “Annual Energy Outlook 2016 Early Release: Annotated Summary of Two Cases.” Annual Energy Outlook. Washington, D.C.: U.S. Energy Information Administration, 2016. https://www.eia.gov/outlooks/archive/aeo16/er/.
EIA. “2020 Form EIA-860 Data,” 2021a. https://www.eia.gov/electricity/data/eia860/.
Bolinger, Mark, Joachim Seel, Cody Warner, and Dana Robson. “Utility-Scale Solar, 2021 Edition.” Utility-Scale Solar. Berkeley, CA: Lawrence Berkeley National Laboratory, 2021. https://doi.org/10.2172/1823604.
Bolinger, Mark, Joachim Seel, and Dana Robson. “Utility-Scale Solar: Empirical Trends in Project Technology, Cost, Performance, and PPA Pricing in the United States: 2019 Edition.” Utility-Scale Solar. Berkeley, CA: Lawrence Berkeley National Laboratory, December 2019. https://doi.org/10.2172/1581088.
EIA. “Annual Energy Outlook 2021.” Washington D.C.: U.S. Energy Information Administration, 2021b. https://www.eia.gov/outlooks/aeo/.
BNEF. “New Energy Outlook 2019.” Bloomberg New Energy Finance, 2019. https://about.bnef.com/new-energy-outlook/.
BNEF. “2H 2021 U.S. Renewable Energy Market Outlook.” BloombergNEF, October 2021.
Cox, Molly. “H1 2021 US Solar PV System Pricing.” Wood Mackenzie, 2021.
Wiser, Ryan, Mark Bolinger, and Joachim Seel. “Benchmarking Utility-Scale PV Operational Expenses and Project Lifetimes: Results from a Survey of U.S. Solar Industry Professionals.” Berkeley, CA: Lawrence Berkeley National Laboratory., June 2020. https://escholarship.org/content/qt2pd8608q/qt2pd8608q.pdf.
IEA. “World Energy Outlook 2018.” Paris, France: International Energy Agency, December 2018.
Lazard. “Lazard’s Levelized Cost of Energy Analysis: Version 12.0.” Lazard’s Levelized Cost of Energy Analysis. Lazard, November 2018. https://www.lazard.com/media/450784/lazards-levelized-cost-of-energy-version-120-vfinal.pdf.
| 2023-03-31T08:35:05 |
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https://bison.inl.gov/Documentation/source/executioners/Transient.aspx
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Transient
!syntax description /Executioner/Transient
Normal Usage
The Transient Executioner is the primary workhorse Executioner in MOOSE. Most simulations will use it.
At its most basic the Transient Executioner allows a simulation to step through multiple steps in _time_... doing one nonlinear solve per timestep. Most of the time this type of execution will utilize one or more TimeDerivative Kernels on the variables to solve for their time evolution.
Primary Parameters
The most important parameters for Transient (beyond what Steady already provides) are:
- dt: The initial timestep size - num_steps: Number of steps to do - end_time: Finish time for the simulation - scheme: The TimeIntegrator to use (see below) - defaults to Implicit/Backward Euler.
See down below for the full list of parameters for this class.
TimeIntegrators
It's important to note that transient simulations generally use a TimeIntegrator. As mentioned above, there is a scheme parameter that is shortcut syntax for selection of that TimeIntegrator. However, there is also a whole TimeIntegrator system for creating your own or specifying detailed parameters for time integration.
TimeSteppers
Similarly, the choice of how to move through time (the choice of timestep size) is important as well. The default TimeStepper is ConstantDT but many other choices can be made using the TimeStepper system.
Transient can also be used for simulations that don't necessarily need _time_. In this context a "transient" calculation can simply be thought of as a series of nonlinear solves. The time parameter will move forward - but what you do with it, or what it means is up to you.
One good example of this is doing "load steps" for a solid mechanics calculation. If the only thing that is desired is the final, steady state, solution, but getting to it is extremely difficult, then you might employ "load steps" to slowly ramp up a boundary condition so you can more easily solve from the initial state (the "initial condition") to the final configuration. In this case you would use "time" as a parameter to control how much of the force is applied (for instance, by using FunctionDirichletBC).
In this case you don't use any TimeDerivative Kernels. The "transient" behavior comes from changing a condition based on "time". What that "time" means is up to you to identify (generally, I like to just step through time = 1,2,3,4.. and define my functions so that at time = end_steps the full load is applied.
Quasi-Transient
Similarly to Load Steps, you can use Transient to do "Quasi-Transient" calculations. This is where some variables are evolving with time derivatives, while others are solved to steady state each step.
A classic example of this is doing coupled thermo-mechanics. It's very normal for the heat flow to move much more slowly than the solid mechanics. Therefore, classically, it is normal to have a time derivative for your heat conduction equation but none for the solid mechanics so that at each timestep the solid-mechanics is solved to a full steady state based on the current configuration of heat.
This idea works perfectly in MOOSE with Transient: just simply only apply TimeDerivative Kernels to the equations you want and leave them off for the others.
Another use-case is to use Transient to solve to a steady state. In this case there are a few built-in parameters to help detect steady state and stop the solve when it's reached. You can see them down below in the "Steady State Detection Parameters" section.
It is important to know that you must turn _on_ steady state detection using steady_state_detection = true before the other two parameters will do anything.
Input Parameters
• reset_dtFalseUse when restarting a calculation to force a change in dt.
Default:False
C++ Type:bool
Description:Use when restarting a calculation to force a change in dt.
• line_search_packagepetscThe solver package to use to conduct the line-search
Default:petsc
C++ Type:MooseEnum
Description:The solver package to use to conduct the line-search
• verboseFalsePrint detailed diagnostics on timestep calculation
Default:False
C++ Type:bool
Description:Print detailed diagnostics on timestep calculation
• update_xfem_at_timestep_beginFalseShould XFEM update the mesh at the beginning of the timestep
Default:False
C++ Type:bool
Description:Should XFEM update the mesh at the beginning of the timestep
• petsc_options_inameNames of PETSc name/value pairs
C++ Type:MultiMooseEnum
Description:Names of PETSc name/value pairs
• petsc_optionsSingleton PETSc options
C++ Type:MultiMooseEnum
Description:Singleton PETSc options
• max_xfem_update4294967295Maximum number of times to update XFEM crack topology in a step due to evolving cracks
Default:4294967295
C++ Type:unsigned int
Description:Maximum number of times to update XFEM crack topology in a step due to evolving cracks
• num_steps4294967295The number of timesteps in a transient run
Default:4294967295
C++ Type:unsigned int
Description:The number of timesteps in a transient run
• line_searchdefaultSpecifies the line search type (Note: none = basic)
Default:default
C++ Type:MooseEnum
Description:Specifies the line search type (Note: none = basic)
• splittingTop-level splitting defining a hierarchical decomposition into subsystems to help the solver.
C++ Type:std::vector
Description:Top-level splitting defining a hierarchical decomposition into subsystems to help the solver.
• contact_line_search_ltolThe linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
C++ Type:double
Description:The linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
• petsc_options_valueValues of PETSc name/value pairs (must correspond with "petsc_options_iname"
C++ Type:std::vector
Description:Values of PETSc name/value pairs (must correspond with "petsc_options_iname"
• end_time1e+30The end time of the simulation
Default:1e+30
C++ Type:double
Description:The end time of the simulation
• solve_typePJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
C++ Type:MooseEnum
Description:PJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
• mffd_typewpSpecifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
Default:wp
C++ Type:MooseEnum
Description:Specifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
• dt1The timestep size between solves
Default:1
C++ Type:double
Description:The timestep size between solves
• schemeimplicit-eulerTime integration scheme used.
Default:implicit-euler
C++ Type:MooseEnum
Description:Time integration scheme used.
• contact_line_search_allowed_lambda_cuts2The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
Default:2
C++ Type:unsigned int
Description:The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
Optional Parameters
• use_multiapp_dtFalseIf true then the dt for the simulation will be chosen by the MultiApps. If false (the default) then the minimum over the master dt and the MultiApps is used
Default:False
C++ Type:bool
Description:If true then the dt for the simulation will be chosen by the MultiApps. If false (the default) then the minimum over the master dt and the MultiApps is used
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• abort_on_solve_failFalseabort if solve not converged rather than cut timestep
Default:False
C++ Type:bool
Description:abort if solve not converged rather than cut timestep
• timestep_tolerance2e-14the tolerance setting for final timestep size and sync times
Default:2e-14
C++ Type:double
Description:the tolerance setting for final timestep size and sync times
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• no_fe_reinitFalseSpecifies whether or not to reinitialize FEs
Default:False
C++ Type:bool
Description:Specifies whether or not to reinitialize FEs
• dtmax1e+30The maximum timestep size in an adaptive run
Default:1e+30
C++ Type:double
Description:The maximum timestep size in an adaptive run
• dtmin2e-14The minimum timestep size in an adaptive run
Default:2e-14
C++ Type:double
Description:The minimum timestep size in an adaptive run
• n_startup_steps0The number of timesteps during startup
Default:0
C++ Type:int
Description:The number of timesteps during startup
• start_time0The start time of the simulation
Default:0
C++ Type:double
Description:The start time of the simulation
• l_abs_step_tol-1Linear Absolute Step Tolerance
Default:-1
C++ Type:double
Description:Linear Absolute Step Tolerance
• nl_abs_tol1e-50Nonlinear Absolute Tolerance
Default:1e-50
C++ Type:double
Description:Nonlinear Absolute Tolerance
• nl_max_its50Max Nonlinear Iterations
Default:50
C++ Type:unsigned int
Description:Max Nonlinear Iterations
• l_max_its10000Max Linear Iterations
Default:10000
C++ Type:unsigned int
Description:Max Linear Iterations
• compute_initial_residual_before_preset_bcsFalseUse the residual norm computed *before* PresetBCs are imposed in relative convergence check
Default:False
C++ Type:bool
Description:Use the residual norm computed *before* PresetBCs are imposed in relative convergence check
• nl_rel_tol1e-08Nonlinear Relative Tolerance
Default:1e-08
C++ Type:double
Description:Nonlinear Relative Tolerance
• l_tol1e-05Linear Tolerance
Default:1e-05
C++ Type:double
Description:Linear Tolerance
• nl_max_funcs10000Max Nonlinear solver function evaluations
Default:10000
C++ Type:unsigned int
Description:Max Nonlinear solver function evaluations
• nl_rel_step_tol1e-50Nonlinear Relative step Tolerance
Default:1e-50
C++ Type:double
Description:Nonlinear Relative step Tolerance
• nl_abs_step_tol1e-50Nonlinear Absolute step Tolerance
Default:1e-50
C++ Type:double
Description:Nonlinear Absolute step Tolerance
Solver Parameters
• picard_abs_tol1e-50The absolute nonlinear residual to shoot for during Picard iterations. This check is performed based on the Master app's nonlinear residual.
Default:1e-50
C++ Type:double
Description:The absolute nonlinear residual to shoot for during Picard iterations. This check is performed based on the Master app's nonlinear residual.
• picard_rel_tol1e-08The relative nonlinear residual drop to shoot for during Picard iterations. This check is performed based on the Master app's nonlinear residual.
Default:1e-08
C++ Type:double
Description:The relative nonlinear residual drop to shoot for during Picard iterations. This check is performed based on the Master app's nonlinear residual.
• relaxed_variablesList of variables to relax during Picard Iteration
C++ Type:std::vector
Description:List of variables to relax during Picard Iteration
• picard_max_its1Number of times each timestep will be solved. Mainly used when wanting to do Picard iterations with MultiApps that are set to execute_on timestep_end or timestep_begin
Default:1
C++ Type:unsigned int
Description:Number of times each timestep will be solved. Mainly used when wanting to do Picard iterations with MultiApps that are set to execute_on timestep_end or timestep_begin
• relaxation_factor1Fraction of newly computed value to keep.Set between 0 and 2.
Default:1
C++ Type:double
Description:Fraction of newly computed value to keep.Set between 0 and 2.
Restart Parameters
• steady_state_start_time0Minimum amount of time to run before checking for steady state conditions.
Default:0
C++ Type:double
Description:Minimum amount of time to run before checking for steady state conditions.
• steady_state_tolerance1e-08Whenever the relative residual changes by less than this the solution will be considered to be at steady state.
Default:1e-08
C++ Type:double
Description:Whenever the relative residual changes by less than this the solution will be considered to be at steady state.
Default:False
C++ Type:bool
Description:Whether or not to check for steady state conditions
• time_period_startsThe start times of time periods
C++ Type:std::vector
Description:The start times of time periods
• time_period_endsThe end times of time periods
C++ Type:std::vector
Description:The end times of time periods
• time_periodsThe names of periods
C++ Type:std::vector
Description:The names of periods
| 2020-11-28T02:56:45 |
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|
https://lammps.sandia.gov/doc/fix_bond_react.html
|
# fix bond/react command
## Syntax
fix ID group-ID bond/react common_keyword values ...
react react-ID react-group-ID Nevery Rmin Rmax template-ID(pre-reacted) template-ID(post-reacted) map_file individual_keyword values ...
react react-ID react-group-ID Nevery Rmin Rmax template-ID(pre-reacted) template-ID(post-reacted) map_file individual_keyword values ...
react react-ID react-group-ID Nevery Rmin Rmax template-ID(pre-reacted) template-ID(post-reacted) map_file individual_keyword values ...
...
• ID, group-ID are documented in fix command. Group-ID is ignored.
• bond/react = style name of this fix command
• zero or more common keyword/value pairs may be appended directly after ‘bond/react’
• these apply to all reaction specifications (below)
• common_keyword = stabilization
stabilization values = no or yes group-ID xmax
no = no reaction site stabilization
yes = perform reaction site stabilization
group-ID = user-assigned prefix for the dynamic group of non-reacting atoms
xmax = xmax value that is used by an internally-created nve/limit integrator
• react = mandatory argument indicating new reaction specification
• react-ID = user-assigned name for the reaction
• react-group-ID = only atoms in this group are considered for the reaction
• Nevery = attempt reaction every this many steps
• Rmin = bonding pair atoms must be separated by more than Rmin to initiate reaction (distance units)
• Rmax = bonding pair atoms must be separated by less than Rmax to initiate reaction (distance units)
• template-ID(pre-reacted) = ID of a molecule template containing pre-reaction topology
• template-ID(post-reacted) = ID of a molecule template containing post-reaction topology
• map_file = name of file specifying corresponding atom-IDs in the pre- and post-reacted templates
• zero or more individual keyword/value pairs may be appended to each react argument
• individual_keyword = prob or max_rxn or stabilize_steps or update_edges
prob values = fraction seed
fraction = initiate reaction with this probability if otherwise eligible
seed = random number seed (positive integer)
max_rxn value = N
N = maximum number of reactions allowed to occur
stabilize_steps value = timesteps
timesteps = number of timesteps to apply the internally-created nve/limit fix to reacting atoms
update_edges value = none or charges or custom
none = do not update topology near the edges of reaction templates
charges = update atomic charges of all atoms in reaction templates
custom = force the update of user-specified atomic charges
## Examples
molecule mol1 pre_reacted_topology.txt
molecule mol2 post_reacted_topology.txt
fix 5 all bond/react react myrxn1 all 1 0 3.25 mol1 mol2 map_file.txt
molecule mol1 pre_reacted_rxn1.txt
molecule mol2 post_reacted_rxn1.txt
molecule mol3 pre_reacted_rxn2.txt
molecule mol4 post_reacted_rxn2.txt
fix 5 all bond/react stabilization yes nvt_grp .03 &
react myrxn1 all 1 0 3.25 mol1 mol2 map_file_rxn1.txt prob 0.50 12345 &
react myrxn2 all 1 0 2.75 mol3 mol4 map_file_rxn2.txt prob 0.25 12345
fix 6 nvt_grp_REACT nvt temp 300 300 100 # set thermostat after bond/react
## Description
Initiate complex covalent bonding (topology) changes. These topology changes will be referred to as ‘reactions’ throughout this documentation. Topology changes are defined in pre- and post-reaction molecule templates and can include creation and deletion of bonds, angles, dihedrals, impropers, bond types, angle types, dihedral types, atom types, or atomic charges. In addition, reaction by-products or other molecules can be identified and deleted.
Fix bond/react does not use quantum mechanical (eg. fix qmmm) or pairwise bond-order potential (eg. Tersoff or AIREBO) methods to determine bonding changes a priori. Rather, it uses a distance-based probabilistic criteria to effect predetermined topology changes in simulations using standard force fields.
This fix was created to facilitate the dynamic creation of polymeric, amorphous or highly cross-linked systems. A suggested workflow for using this fix is: 1) identify a reaction to be simulated 2) build a molecule template of the reaction site before the reaction has occurred 3) build a molecule template of the reaction site after the reaction has occurred 4) create a map that relates the template-atom-IDs of each atom between pre- and post-reaction molecule templates 5) fill a simulation box with molecules and run a simulation with fix bond/react.
Only one ‘fix bond/react’ command can be used at a time. Multiple reactions can be simultaneously applied by specifying multiple react arguments to a single ‘fix bond/react’ command. This syntax is necessary because the ‘common keywords’ are applied to all reactions.
The stabilization keyword enables reaction site stabilization. Reaction site stabilization is performed by including reacting atoms in an internally-created fix nve/limit time integrator for a set number of timesteps given by the stabilize_steps keyword. While reacting atoms are being time integrated by the internal nve/limit, they are prevented from being involved in any new reactions. The xmax value keyword should typically be set to the maximum distance that non-reacting atoms move during the simulation.
The group-ID set using the stabilization keyword can be an existing static group or a previously-unused group-ID. It cannot be specified as ‘all’. If the group-ID is previously unused, the fix bond/react command creates a dynamic group that is initialized to include all atoms. If the group-ID is that of an existing static group, the group is used as the parent group of new, internally-created dynamic group. In both cases, this new dynamic group is named by appending ‘_REACT’ to the group-ID, e.g. nvt_grp_REACT. By specifying an existing group, you may thermostat constant-topology parts of your system separately. The dynamic group contains only non-reacting atoms at a given timestep, and therefore should be used by a subsequent system-wide time integrator such as nvt, npt, or nve, as shown in the second example above. The time integration command should be placed after the fix bond/react command due to the internal dynamic grouping performed by fix bond/react.
Note
If the group-ID is an existing static group, react-group-IDs should also be specified as this static group, or a subset.
Note
If the group-ID is previously unused, the internally-created group applies to all atoms in the system, i.e. you should generally not have a separate thermostat which acts on the ‘all’ group, or any other group.
The following comments pertain to each react argument (in other words, can be customized for each reaction, or reaction step):
A check for possible new reaction sites is performed every Nevery timesteps.
Two conditions must be met for a reaction to occur. First a bonding atom pair must be identified. Second, the topology surrounding the bonding atom pair must match the topology of the pre-reaction template. If both these conditions are met, the reaction site is modified to match the post-reaction template.
A bonding atom pair will be identified if several conditions are met. First, a pair of atoms I,J within the specified react-group-ID of type itype and jtype must be separated by a distance between Rmin and Rmax. It is possible that multiple bonding atom pairs are identified: if the bonding atoms in the pre-reacted template are 1-2 neighbors, i.e. directly bonded, the farthest bonding atom partner is set as its bonding partner; otherwise, the closest potential partner is chosen. Then, if both an atom I and atom J have each other as their bonding partners, these two atoms are identified as the bonding atom pair of the reaction site. Once this unique bonding atom pair is identified for each reaction, there could two or more reactions that involve a given atom on the same timestep. If this is the case, only one such reaction is permitted to occur. This reaction is chosen randomly from all potential reactions. This capability allows e.g. for different reaction pathways to proceed from identical reaction sites with user-specified probabilities.
The pre-reacted molecule template is specified by a molecule command. This molecule template file contains a sample reaction site and its surrounding topology. As described below, the bonding atom pairs of the pre-reacted template are specified by atom ID in the map file. The pre-reacted molecule template should contain as few atoms as possible while still completely describing the topology of all atoms affected by the reaction. For example, if the force field contains dihedrals, the pre-reacted template should contain any atom within three bonds of reacting atoms.
Some atoms in the pre-reacted template that are not reacting may have missing topology with respect to the simulation. For example, the pre-reacted template may contain an atom that would connect to the rest of a long polymer chain. These are referred to as edge atoms, and are also specified in the map file. When the pre-reaction template contains edge atoms, not all atoms, bonds, charges, etc. specified in the reaction templates will be updated. Specifically, topology that involves only atoms that are ‘too near’ to template edges will not be updated. The definition of ‘too near the edge’ depends on which interactions are defined in the simulation. If the simulation has defined dihedrals, atoms within two bonds of edge atoms are considered ‘too near the edge.’ If the simulation defines angles, but not dihedrals, atoms within one bond of edge atoms are considered ‘too near the edge.’ If just bonds are defined, only edge atoms are considered ‘too near the edge.’
Note that some care must be taken when a building a molecule template for a given simulation. All atom types in the pre-reacted template must be the same as those of a potential reaction site in the simulation. A detailed discussion of matching molecule template atom types with the simulation is provided on the molecule command page.
The post-reacted molecule template contains a sample of the reaction site and its surrounding topology after the reaction has occurred. It must contain the same number of atoms as the pre-reacted template. A one-to-one correspondence between the atom IDs in the pre- and post-reacted templates is specified in the map file as described below. Note that during a reaction, an atom, bond, etc. type may change to one that was previously not present in the simulation. These new types must also be defined during the setup of a given simulation. A discussion of correctly handling this is also provided on the molecule command page.
The map file is a text document with the following format:
A map file has a header and a body. The header of map file the contains one mandatory keyword and three optional keywords. The mandatory keyword is ‘equivalences’ and the optional keywords are ‘edgeIDs’ and ‘deleteIDs’ and ‘customIDs’:
N equivalences = # of atoms N in the reaction molecule templates
N edgeIDs = # of edge atoms N in the pre-reacted molecule template
N deleteIDs = # of atoms N that are specified for deletion
N customIDs = # of atoms N that are specified for a custom update
N constraints = # of specified reaction constraints N
The body of the map file contains two mandatory sections and four optional sections. The first mandatory section begins with the keyword ‘BondingIDs’ and lists the atom IDs of the bonding atom pair in the pre-reacted molecule template. The second mandatory section begins with the keyword ‘Equivalences’ and lists a one-to-one correspondence between atom IDs of the pre- and post-reacted templates. The first column is an atom ID of the pre-reacted molecule template, and the second column is the corresponding atom ID of the post-reacted molecule template. The first optional section begins with the keyword ‘EdgeIDs’ and lists the atom IDs of edge atoms in the pre-reacted molecule template. The second optional section begins with the keyword ‘DeleteIDs’ and lists the atom IDs of pre-reaction template atoms to delete. The third optional section begins with the keyword ‘Custom Edges’ and allows for forcing the update of a specific atom’s atomic charge. The first column is the ID of an atom near the edge of the pre-reacted molecule template, and the value of the second column is either ‘none’ or ‘charges.’ Further details are provided in the discussion of the ‘update_edges’ keyword. The fourth optional section begins with the keyword ‘Constraints’ and lists additional criteria that must be satisfied in order for the reaction to occur. Currently, there is one type of constraint available, as discussed below.
A sample map file is given below:
# this is a map file
2 edgeIDs
7 equivalences
BondingIDs
3
5
EdgeIDs
1
7
Equivalences
1 1
2 2
3 3
4 4
5 5
6 6
7 7
Any number of additional constraints may be specified in the Constraints section of the map file. Currently there is one type of additional constraint, of type ‘distance’, whose syntax is as follows:
distance ID1 ID2 rmin rmax
where ‘distance’ is the required keyword, ID1 and ID2 are pre-reaction atom IDs, and these two atoms must be separated by a distance between rmin and rmax for the reaction to occur. This constraint can be used to enforce a certain orientation between reacting molecules.
Once a reaction site has been successfully identified, data structures within LAMMPS that store bond topology are updated to reflect the post-reacted molecule template. All force fields with fixed bonds, angles, dihedrals or impropers are supported.
A few capabilities to note: 1) You may specify as many react arguments as desired. For example, you could break down a complicated reaction mechanism into several reaction steps, each defined by its own react argument. 2) While typically a bond is formed or removed between the bonding atom pairs specified in the pre-reacted molecule template, this is not required. 3) By reversing the order of the pre- and post- reacted molecule templates in another react argument, you can allow for the possibility of one or more reverse reactions.
The optional keywords deal with the probability of a given reaction occurring as well as the stable equilibration of each reaction site as it occurs.
The prob keyword can affect whether an eligible reaction actually occurs. The fraction setting must be a value between 0.0 and 1.0. A uniform random number between 0.0 and 1.0 is generated and the eligible reaction only occurs if the random number is less than the fraction. Up to N reactions are permitted to occur, as optionally specified by the max_rxn keyword.
The stabilize_steps keyword allows for the specification of how many timesteps a reaction site is stabilized before being returned to the overall system thermostat.
In order to produce the most physical behavior, this ‘reaction site equilibration time’ should be tuned to be as small as possible while retaining stability for a given system or reaction step. After a limited number of case studies, this number has been set to a default of 60 timesteps. Ideally, it should be individually tuned for each fix reaction step. Note that in some situations, decreasing rather than increasing this parameter will result in an increase in stability.
The update_edges keyword can increase the number of atoms whose atomic charges are updated, when the pre-reaction template contains edge atoms. When the value is set to ‘charges,’ all atoms’ atomic charges are updated to those specified by the post-reaction template, including atoms near the edge of reaction templates. When the value is set to ‘custom,’ an additional section must be included in the map file that specifies whether to update charges, on a per-atom basis. The format of this section is detailed above. Listing a pre-reaction atom ID with a value of ‘charges’ will force the update of the atom’s charge, even if it is near a template edge. Atoms not near a template edge are unaffected by this setting.
A few other considerations:
Many reactions result in one or more atoms that are considered unwanted by-products. Therefore, bond/react provides the option to delete a user-specified set of atoms. These pre-reaction atoms are identified in the map file. A deleted atom must still be included in the post-reaction molecule template, in which it cannot be bonded to an atom that is not deleted. In addition to deleting unwanted reaction by-products, this feature can be used to remove specific topologies, such as small rings, that may be otherwise indistinguishable.
Also, it may be beneficial to ensure reacting atoms are at a certain temperature before being released to the overall thermostat. For this, you can use the internally-created dynamic group named “bond_react_MASTER_group.” For example, adding the following command would thermostat the group of all atoms currently involved in a reaction:
fix 1 bond_react_MASTER_group temp/rescale 1 300 300 10 1
Note
This command must be added after the fix bond/react command, and will apply to all reactions.
Computationally, each timestep this fix operates, it loops over neighbor lists (for bond-forming reactions) and computes distances between pairs of atoms in the list. It also communicates between neighboring processors to coordinate which bonds are created and/or removed. All of these operations increase the cost of a timestep. Thus you should be cautious about invoking this fix too frequently.
You can dump out snapshots of the current bond topology via the dump local command.
Restart, fix_modify, output, run start/stop, minimize info:
No information about this fix is written to binary restart files, aside from internally-created per-atom properties. None of the fix_modify options are relevant to this fix.
This fix computes one statistic for each react argument that it stores in a global vector, of length ‘number of react arguments’, that can be accessed by various output commands. The vector values calculated by this fix are “intensive”.
These is 1 quantity for each react argument:
1. cumulative # of reactions occurred
No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
When fix bond/react is ‘unfixed,’ all internally-created groups are deleted. Therefore, fix bond/react can only be unfixed after unfixing all other fixes that use any group created by fix bond/react.
## Restrictions
This fix is part of the USER-MISC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
## Default
The option defaults are stabilization = no, prob = 1.0, stabilize_steps = 60, update_edges = none
(Gissinger) Gissinger, Jensen and Wise, Polymer, 128, 211 (2017).
| 2019-05-20T23:22:12 |
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|
https://logicgrimoire.wordpress.com/page/11/
|
How to calculate the circumference of a circle (without knowing pi)
Some time ago I posted the following little challenge to www.reddit.com/r/programming:
Dear Proggit: Imagine that you must devise a method to calculate the circumference of a circle of any radius. The catch? You are unaware of the existence of Pi.
The other catch? You must begin right now. You may use only what tools you have in front of you (text editor, calculator, pencil and paper with compass(!)), without looking anything up. That means no Google searches, no Wikipedia, no formulas in a book, nothing.
Once you have devised a method, please write a small program in the language of your choice that performs the calculation (the more accurate, the better). Bonus points will be awarded for brevity, cleverness, etc.
I will post my little solution sometime tomorrow. Enjoy!
One final note: If you are a total geometry/math wizard who thinks this is lame, please refrain from posting; I want this to be a fun problem for those of us who will get something out of it.
Below is my method for calculating (or rather, estimating) the circumference of a circle without using pi. This method involves summing the lengths of the hypotenuses of smaller and smaller triangles, as shown in the diagram above.
Begin by cutting the given circle into quarters. Using the radius r, find the hypotenuse of triangle A using Pythagoras’ method. Cut the hypotenuse in half; using that, and the radius, you can calculate the length of line segment Q. Subtract Q from r, and you have the length of line segment P, which is one side of the right triangle B. That, combined with half the hypotenuse of A, will allow you to calculate the hypotenuse of B. Continue, calculating the hypotenuses of smaller and smaller triangles. Sum as many lengths as are required to cover the quarter-circle arc, and multiply by 4 (or multiply the current length by 2^(n*+1), where *n is the number of iterations of the method you’ve performed).
Below I’ve provided an implementation in Perl. Note that the Perl interpreter doesn’t optimize away recursive function calls (that I know of), so you could in theory blow up the stack. In practice, it only takes a few iterations to arrive at a reasonable estimate, so it’s not a problem.
```#!/usr/bin/env perl
use strict;
use warnings;
use autodie;
use Math::Trig ':pi';
my \$iterations = 0;
sub main {
my (\$radius, \$a, \$b) = @_;
my \$hyp = hypotenuse(\$a, \$b);
\$iterations++;
die "Current hypotenuse is \$hyp after \$iterations iterations\n"
. "Estimated circumference: " . \$hyp * (2**(\$iterations+1)) . "\n"
. "Actual circumference: " . (\$radius*2) * pi . "\n"
if \$iterations == \$maxiter;
}
sub hypotenuse {
my (\$a, \$b) = @_;
return sqrt(\$a**2 + \$b**2);
}
```
As you can see, we pretty much mirror the textual description given above, but in code. We then compare our work to the “real” value of pi using the Perl core’s `Math::Trig` constant. Save the above into a file named circ.pl, and you can run it like so:
mel@foo:~\$ ./circ.pl 4 12 # Given a radius of 4, run through 12 iterations
Current hypotenuse is 0.00306796150057116 after 12 iterations
Estimated circumference: 25.132740612679
Actual circumference: 25.1327412287183
I might not want to try to calculate planetary orbits using this kind of rough estimation, but for 99% of real-world cases, it’s good enough.
Preamble
For a long time now, I’ve been looking to make my life more Lispy. As part of that transformation, I’ve begun porting some of my little Perl scripts over to Guile Scheme. Today I’m going to walk through a script that renames my files in a nice, *nix-friendly fashion. For example, if I download a file that someone has erroneously (if good-naturedly) called “My Cool Data.tar.gz”, this script will rename it to “my-cool-data.tar.gz”.
A note on filename style: I’ve never liked the common practice of naming files using underscores (`_’), so I use hyphens instead (`-‘). It’s more Lispy! Also, regular expressions usually recognize the underscore character as part of a word, such that `my_cool_data’ is considered one word, whereas `my-cool-data’ will be treated as three, and the latter is almost always what I’d prefer (since those are, in fact, three words).
Ok. So what about Guile then? It’s an R5RS-compatible scheme, so you get all of that goodness. If you’re an Emacs user, check out Geiser, which turns Emacs into an AWESOME Scheme hacking environment. You don’t need to be an Emacs weirdo like me to write programs in Guile, however. Vim works very nicely, as a matter of fact, and it also highlights Scheme source code beautifully.
Finally, not that it matters that much, but this short essay is also a literate program, thanks to Orgmode (a.k.a. “The Teal Unicorn”). Fun!
Just like any other *nix script, we need to declare a path to our interpreter, as well as any arguments to the interpreter itself. In Guile’s case, there are two things to notice: (1) The `guile` executable must be passed the `-s` argument to execute in script-mode, and (2) The opening `#!` in the interpreter path must be matched by a closing `!#` due to the way Scheme works (or at least, this particular Scheme).
Next, we declare the modules we’d like to use. In this case, it’s just the one: `ice-9 regex`. Please don’t ask me what the `ice-9` part means, but Guile has a whole bunch of functionality under the `ice-9` umbrella, such as regular expression support (which we’re using here), POSIX-related stuff, a `getopt-long` library, and more. For details see [the fine manual]. Or just type “C-h i C-s guile” as \$DEITY intended.
```#!/usr/local/bin/guile -s
!#
(use-modules (ice-9 regex))
```
Defining the `main` procedure
We’re ready to start writing our actual program! Because we’re exciting and creative folk, we’ll call our single procedure `main`.
We’ll go ahead and use a `let` statement to grab all but the first element of the `program-arguments` list and stick it in the `args` variable for brevity (the first element is the name of the executable file). This use of `let` isn’t really required in such a simple program, but I find that it makes things easier to read, and if I expand the program later, it’s easier to modify.
```(define (main)
(let ((args (cdr (program-arguments))))
```
We can’t just assume that the `args` list is going to have anything in it, however, so we’ll print a short message and exit the program if it’s empty. If it’s not empty, we travel on to the `else’ clause of the `if` expression.
```(if (null? args)
(begin (display "No arguments, exiting...")
(newline)
(exit))
```
Now that we’ve invoked the interpreter with the right incantations, loaded our required module, and checked the program arguments list to make sure that we have something there to process, we can write the part of the program that actually does something. Sweet!
In the `else’ clause of the `if` expression, we iterate over `args` using the `for-each` procedure. We use `for-each` in this case (rather than our beloved `map`) because we don’t want to build a new list by transforming each element of `args`, we just want to iterate over our list being all “side-effect-y” (a technical term that in this case means “affecting the state of stuff on disk”).
The best way to read Lisp code is usually “inside-out”. Begin with the innermost element, figure out what argument(s) it takes, and see what it passes along as a return value. That return value is then an input for something else. This is true in most computer languages, but in Lisp it becomes especially necessary to read things this way.
Therefore we’ll start inside the innermost expression, at `regexp-substitute/global`. The documentation says that it needs a port, a regular expression, and a string to match that regular expression against. Since `regexp-substitute/global` isn’t writing its output to a port, but passing its arguments out to `string-downcase`, we specify “no port” as `#f`. `Post` has to do with making `regexp-substitute/global` recur on any unmatched parts of the string in `arg`, and the literal `-` is what we’d like to replace our matches with. For more comprehensive information on `pre` and `post`, I actually needed to consult the documentation on `regexp-substitute`, since `regexp-substitute/global` is apparently a special case of the former (and is perhaps implemented using `regexp-substitute`? I didn’t check, but it would be easy enough to do so).
Let’s look at that regex, `[,'!_ \t]+`. In English, it means “match any commas, apostrophes, exclamation points, underscores, blank spaces or tabs”. As noted above, we want to replace any occurrences of these characters with `-`.
For example, a string like `Hey Kids I Have Spaces.txt` would become `Hey-Kids-I-Have-Spaces.txt`. We then pass it out to the `string-downcase` procedure, which transforms it into `hey-kids-i-have-spaces.txt`.
That value is then passed as the second argument to the `rename-file` procedure, which renames `arg` (our original, uncool filename) to `hey-kids-i-have-spaces.txt`.
It’s all wrapped in a `lambda` expression, which does the job of creating and invoking a one-argument procedure out of the several we’ve discussed; this procedure is then applied to every item in our argument list `args`.
```(for-each (lambda (arg)
(rename-file arg
(string-downcase
(regexp-substitute/global
#f "[,'!_ \t]+" arg
'pre "-" 'post))))
args))))
```
Invocation and Program Listing
In this way the file renaming operation that we’ve defined here is applied to each of our program’s arguments, and we invoke it like so (shown here operating on two files):
`\$ guile renamer.scm Hey\ Kids\ I\ Got\ Spaces.txt Oh_no_ugly_underscores.html`
A final note: even for a program as simple as this, I didn’t sit down and bang it out all in one go. Especially with the regex, I was testing little parts of it at the REPL the whole way, consulting the documentation for these functions via the relevant Geiser and Emacs commands. But that’s a story for another day…
Finally, here’s the complete program listing:
```#!/usr/local/bin/guile -s
!#
(use-modules (ice-9 regex))
(if (null? args)
(begin (display "No arguments, exiting...")
(newline)
(exit))
(for-each (lambda (arg)
(rename-file arg
(string-downcase
(regexp-substitute/global
#f "[,'!_ \t]+" arg
'pre "-" 'post))))
args))))
(main)
```
(Image courtesy Melisande under Creative Commons license.)
How often will a bus jam the Lincoln Tunnel?
I commute into Manhattan four or five days a week. Like a lot of people who ride the bus, I really really hate it when the Lincoln tunnel gets jammed. Even though there are tow trucks standing by at all times (from what I can tell), it seems to cost you about 30-60 minutes of commute time. Because it happens often enough to be a pain in the ass, I’ve been thinking lately about how the numbers play out.
As it turns out, there are statistics on bus usage in the lincoln tunnel available on the port authority website:
…in 2009, the XBL averaged 1,791 daily buses…
Since we’re talking averages, i’m going to assume that the weekday load is heavier than on weekends due to commuters. that should bring the average up a bit. The product of 1,791 buses * 7 days is 12,537 buses each week. Guesstimating that 85% of those buses pass through the tunnel Monday through Friday gives us 10,656 buses divided by 5 days for a weekday average of 2,131 buses.
That’s a lot of buses to push through a tunnel each day. But what about during peak commute times? The signage along the road says that the XBL is open from 6am to 10am. Since the statistics from the above website refer only to the XBL, we can infer that all of their measurements come from those morning commute hours. (There is no special commuter lane for buses leaving the city in the evenings that I’ve seen.) Therefore I’ll assume that these statistics refer only to the peak AM commute.
You might infer from the picture on the Port Authority website that there is only one lane leading up to and through the tunnel. I can confirm this. Not only is there only one bus lane, but it’s one lane that stretches quite a ways back from the tunnel and into New Jersey. Once inside the lane, you may not change into another lane, either (this is probably obvious, but worth noting).
What about bus reliability? How often do buses break down? Let’s be generous and assume that any given bus will make this trip successfully 99.9% of the time. This means that the bus will only break down once every 1,000 trips through the lane. I’d estimate that the XBL is ~3 miles long, measured beginning at the EZPASS out in Jersey and ending when the bus has entered normal city traffic around 40th street. Once inside the city proper, a bus can still stall and create problems in the tunnel, but we’ve got to end our measurement somewhere.
According to the multiplication rule 1, we can get the probability that none of the 2131 buses going through the XBL will stall (that is, that they will all make it) by taking our probability that any given bus will make it and raising it to the 2131 power. This gives us 0.999 ^ 2131, yielding 0.119. This means that there is only an 11.9% chance that all 2131 buses will get through the XBL on any given weekday morning without stalling or breaking down!
But is this true? My anecdotal experience over the past few months of commuting says yes. I’ve had to sit through a number of traffic jams coming into the city in the mornings. As a result, I’ve switched to an earlier bus in order to avoid most of the peak commuter buses.
(Image courtesy Melisande under Creative Commons license.)
Footnotes:
1 wonderfully described in John Paulos’ book Innumeracy
What is a Continuation?
This week we explore the continuation, that noble construct of the mind – O bright, shining tool in the aspiring wizard’s toolchest! Half of what you shall read here is paraphrase, half allegory, and the rest? Sprinkled with a few potent grains of Scheme code.
Continuations are constructs that give a programming language the ability to save the execution state at any point and return to that point at a later time in the program’s execution.
Note that continuations do not save program data, only execution context. Taking a function f as its only argument, `call/cc` takes the current continuation (i.e., a “snapshot” of the current control context or control state of the program) as an object and applies f to it.
As you might imagine, the Grand Wizards Sussman and Steele themselves (all hail!) were the first to bring this power to the hands of the humble. Since then continuations have been implemented in a number of other languages, though in my biased opinion Scheme is the most lovely of them all.
Yet another way to think of a continuation is as “that thing that is waiting for the current computation to finish.” When we say “computation,” we really just mean “function” or more loosely “whatever the program is doing at the moment.”
For the more magically inclined, the continuation can be imagined as a jump, or “non-local exit,” that allows the practitioner to teleport from one computational place to another (or from one computational palace to another, even!).
Suppose for example that you are a Sorceror’s Apprentice (as I am). You’ve been asked to clean the Master’s tower while he’s away, but it’s quite boring and will take a long time. Lazy apprentice (and aspiring wizard programmer) that you are, you’d much rather be writing on your obscure programming blog or doing logic proofs. Or even writing Scheme programs!
The state of the tower could best be described as “abysmal”. It turns out that he’s a total slob, though of course he’d probably describe himself as an eccentric genius who’s concerned with things other than housecleaning. Whatever the reasons, the place is a wreck.
How do continuations fit in? Let’s say you’re thinking about writing up a new post for your aforementioned obscure programming blog. You’d like to write about continuations, in part as a teaching exercise for yourself, and in part because it’s just good, clean fun. Now you take a continuation (i.e., save the current execution state of this little program we call “Life”1) – let’s call our saved program state “The Master’s Tower is a wreck and I’m thinking about a post on continuations for my obscure programming blog” for short (or long). Let’s call this time $T_1$.
Having thus taken the continuation, you merrily go about the business of cleaning the Master’s tower, or more precisely, attempting to write Scheme programs that will somehow result in the cleanliness of said tower. Hours later, you invoke the continuation you saved earlier, and you wake up to find yourself thinking about writing up a new post for your blog. You look around and see that the tower is clean (for the moment), leaving you free to go and procrastinate in front of your computer and call it blogging.
Are you tired from having cleaned (or taught Scheme to clean) the whole messy tower? No! Remember that we saved the current execution state at $T_1$, and you were feeling energetic then. Hours later, we’re at $T_2$, and you’re not so fresh anymore. However, you are a Sorceror’s Apprentice, tired or not, and you know a few tricks, such as how to jump back to the continuation you saved at $T_1$.
That’s how you come to find yourself sitting at your tiny desk in the corner of the Master’s tower, surrounded by orderliness, calm, and quiet. The tower is clean, you’re feeling refreshed, and you have an idea for something to write about. Ain’t life grand?
But wait! What the hell does this have to do with anything? Is there any actual code we can look at? Of course!
Our motivating example is taken from a couple of earlier posts regarding a little Scheme problem. (See here for details.) The following procedure was implemented the first time around using good-ol’-fashioned recursion. You can see its implementation and a trace of its output here. I thought it would be fun to play around a bit with continuations, and so I wrote the following:
```(define (gather-next-batch-cc pred seq)
(let ((result '()))
(call-with-current-continuation
(lambda (return)
(for-each (lambda (elem)
(if (pred elem)
(set! result (cons elem result))
(return (reverse result))))
seq)))))
```
As you can see, we’re doing a simple iteration over a list using `for-each`, but we’ve wrapped it in the `call-with-current-continuation` form. According to the venerable R5RS:
procedure: `(call-with-current-continuation /proc/)`
Proc must be a procedure of one argument. The procedure `call-with-current-continuation` packages up the current continuation (see the rationale below) as an “escape procedure” and passes it as an argument to proc.
In our example above, `call-with-current-continuation` (which I’ll refer to as “call/cc” from here on out) takes a `lambda` with one argument, return. We then iterate over seq, checking to see if elem matches our predicate. If it does, we push it onto result. Because we know the format of the list that `gather-next-batch-cc` will be dealing with, e.g.,
```'(1 2 3 b 4 5 c 6 7)
```
We know that, as we move down the list, we can jump to return as soon as we start seeing elements of the list that don’t match our predicate (`number?` in this case), rather than iterating down the whole thing.
But don’t take my word for it! Let’s trace that puppy! I must return once again to my lovely Scheme 48 REPL. First, we’ll run a trace using our recursive implementation of `gather-next-batch`:
> (plist->alist gather-next-batch L)
[Enter (gather-next-batch #{Procedure 585 number?} ‘(1 2 3 b 4 5 c 6 —))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(2 3 b 4 5 c 6 d —))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(3 b 4 5 c 6 d e))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(b 4 5 c 6 d e))
Leave gather-next-batch ‘()]
Leave gather-next-batch ‘(3)]
Leave gather-next-batch ‘(2 3)]
Leave gather-next-batch ‘(1 2 3)]
[Enter (gather-next-batch #{Procedure 585 number?} ‘(4 5 c 6 d e))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(5 c 6 d e))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(c 6 d e))
Leave gather-next-batch ‘()]
Leave gather-next-batch ‘(5)]
Leave gather-next-batch ‘(4 5)]
[Enter (gather-next-batch #{Procedure 585 number?} ‘(6 d e))
[Enter (gather-next-batch #{Procedure 585 number?} ‘(d e))
Leave gather-next-batch ‘()]
Leave gather-next-batch ‘(6)]
[Enter (gather-next-batch #{Procedure 585 number?} ‘(e))
Leave gather-next-batch ‘()]
[Enter (gather-next-batch #{Procedure 585 number?} ‘())
Leave gather-next-batch ‘()]
‘((a (1 2 3)) (b (4 5)) (c (6)) (d ()) (e ()))
As we expect, we’re recurring down through the list, banging on the empty list at the bottom, and then building back up from that. Easy-peasy.
Now let’s trace the version under discussion, the continuation-powered `gather-next-batch-cc`:
> (plist->alist gather-next-batch-cc L)
[Enter (gather-next-batch-cc #{Procedure 585 number?} ‘(1 2 3 b 4 5 c 6 —))
Leave gather-next-batch-cc ‘(1 2 3)]
[Enter (gather-next-batch-cc #{Procedure 585 number?} ‘(4 5 c 6 d e))
Leave gather-next-batch-cc ‘(4 5)]
[Enter (gather-next-batch-cc #{Procedure 585 number?} ‘(6 d e))
Leave gather-next-batch-cc ‘(6)]
[Enter (gather-next-batch-cc #{Procedure 585 number?} ‘(e))
Leave gather-next-batch-cc ‘()]
[Enter (gather-next-batch-cc #{Procedure 585 number?} ‘())
Leave gather-next-batch-cc #{Unspecific}]
‘((a (1 2 3)) (b (4 5)) (c (6)) (d ()) (e #{Unspecific}))
As you can see (and if the trace output is to be believed), we’re performing significantly fewer operations here. I count 5 procedure entries using this implementation, compared to 11 for the recursive version. I performed this same test using a list with 8 separate groups of numbers, totalling 28 numbers in all. The recursive version called itself 36 times, whereas the “call/cc’d” version came in at 8. In both these cases, `gather-next-batch-cc` is only called as many times as there are groups of numbers, since it only iterates until it runs out of numbers, and then jumps back.
(Image courtesy Melisande under Creative Commons license.)
Footnotes:
1 Yes, I know about Conway’s Game of Life.
A Scheme Code Kata, Explained (Part II)
Last time I walked you through the `gather-next-batch` procedure. Now let’s put it together with its caller. As I mentioned before, I was inspired by the Schemish stylings of the good Mr. Harvey to implement the ‘plist’ to ‘alist’ transformation using a higher-order procedure. `gather-next-batch` was that procedure.
One way I like to think about higher-order procedures is as follows: Imagine a man pushing a lawn-mower along on a beautiful Saturday morning. As he pushes the mower along, it lifts, slices, and ejects the grass that comes underneath its blade. In order for it to move along and do its work, it needs the man pushing, since the forward momentum is essential to its operation – otherwise there would be no grass underneath for it to cut!
It’s much the same with higher-order procedures: one procedure (the man) pushes another (the lawn-mower) across a data structure (the lawn). Of course, this is the simplest use case, but it’s where most of us start.
That might help you to understand how `gather-next-batch` works, at least in broad strokes. Coming back to our overall problem, we need to figure out how to use `gather-next-batch` to our advantage. We’ll call it from inside another procedure which will collect the entire ‘alist’ together, the cryptically-named `p->a`.
`p->a` will transform the given type of ‘property list’ into an ‘association list.’ Here it is:
```(define (p->a p)
(cond ((null? p) '())
((symbol? (car p))
(cons (list (car p)
(gather-next-batch number? (cdr p)))
(p->a (cdr p))))
(else (p->a (cdr p)))))
```
Let’s walk through it. We take a property list p as our only parameter. As is usual with Scheme, we walk the list recursively, checking first for `null?`, and returning an empty list in that case. If the first item is a symbol, we make a new, smaller list whose first item is the first item of p and whose other items are the result of calling `gather-next-batch` with `number?` as its predicate. `gather-next-batch` walks the rest of p (a.k.a., `(cdr p)`) and return the next group of numbers.
We then take the little list we’ve made (which will look something like `(a 1 2 3)` ) and push it onto the result of `p->a` when called with all but the first element of p.
If the first element of p is not a symbol, we just call `p->a` on the rest of p.
That’s rather more verbose in English than in Scheme, but I was able to write the English description much more quickly than I was able to write the initial solution in Scheme. See if you can step through the Scheme code in your mind, and use the English as an aid where necessary.
Note that Scheme and Lisp, more so than some other languages, require you to read the code “from the inside out.” The heart of a procedure will return a little data structure, which you’ll then pass to another procedure, and perhaps another, etc.
In closing, let’s look at the trace of `p->a` printed by my lovely assistant, Scheme 48. Ain’t recursion beautiful?
```> (p->a '(a 1 2 3 b 4 5 c 6 7 d e))
[Enter (p->a '(a 1 2 3 b 4 5 c ---))
[Enter (p->a '(1 2 3 b 4 5 c 6 ---))
[Enter (p->a '(2 3 b 4 5 c 6 7 ---))
[Enter (p->a '(3 b 4 5 c 6 7 d ---))
[Enter (p->a '(b 4 5 c 6 7 d e))
[Enter (p->a '(4 5 c 6 7 d e))
[Enter (p->a '(5 c 6 7 d e))
[Enter (p->a '(c 6 7 d e))
[Enter (p->a '(6 7 d e))
[Enter (p->a '(7 d e))
[Enter (p->a '(d e))
[Enter (p->a '(e))
[Enter (p->a '())
Leave p->a '()]
Leave p->a '((e ()))]
Leave p->a '((d ()) (e ()))]
Leave p->a '((d ()) (e ()))]
Leave p->a '((d ()) (e ()))]
Leave p->a '((c (6 7)) (d ()) (e ()))]
Leave p->a '((c (6 7)) (d ()) (e ()))]
Leave p->a '((c (6 7)) (d ()) (e ()))]
Leave p->a '((b (4 5)) (c (6 7)) (d ()) (e ()))]
Leave p->a '((b (4 5)) (c (6 7)) (d ()) (e ()))]
Leave p->a '((b (4 5)) (c (6 7)) (d ()) (e ()))]
Leave p->a '((b (4 5)) (c (6 7)) (d ()) (e ()))]
Leave p->a '((a (1 2 3)) (b (4 5)) (c (6 7)) (d ()) (e ()))]
'((a (1 2 3)) (b (4 5)) (c (6 7)) (d ()) (e ()))
```
(Image courtesy Mélisande* under Creative Commons license.)
A Scheme Code Kata, Explained (Part I).
A little while ago I dumped some Scheme code on you, without much in the way of context. Unless you clicked on those delicious links and spent time poring over the information therein, what I posted might not have made much sense. I intend to rectify that sad situation with this little post.
(BTW: If you want this code, it’s available at github, as is the entire source of this blog. Though I heartily recommend that you type it in for yourself, since that will probably force you to pay slightly closer attention to it. And attention is the name of the game, I think.)
I’ll begin by restating the problem in my own words. Suppose you are given a regular Lisp list of the form
```(a 1 2 3 b 4 5 c 6 d e).
```
Write code that will convert said list into a so-called “association list.” This is a very ancient Lisp structure that serves a function similar to a primitive hash table (though much, much slower).
```((a (1 2 3)) (b (4 5)) (c (6)) (d ()) (e ()))
```
This will allow us to get at the “values” associated with each symbol using the `assoc` procedure. In this case:
```scheme@(guile-user)> (assoc 'b (plist->alist foo))
\$397 = (b (3 4))
```
After wrestling with a few of my own failed solutions, I came across one by Brian Harvey in the comp.lang.scheme discussion surrounding this problem. He used a couple of higher-order procedures, as I recall. I didn’t fully grok his particular solution; I decided that I could write something a bit more concise.
His solution did inspire me to separate the act of gathering the next batch of non-symbols from the act of creating the alist.
Here I’ll define a procedure, `gather-next-batch`, which accepts two arguments: a predicate procedure and a sequence. The predicate will tell `gather-next-batch` what, exactly, to gather the next batch of:
```(define (gather-next-batch pred seq)
(cond ((null? seq) '())
((pred (car seq))
(cons (car seq)
(gather-next-batch pred (cdr seq))))
(else '())))
```
You can see that this is a pretty bog-standard recursive Scheme procedure. Let’s walk through it together. First, we test if our sequence `seq` is `null?`, or empty. If not, we check the first element of `seq` (a.k.a. `(car seq)`) against our `pred`, or predicate procedure, which will return true or false. If `pred` looks at `(car seq)` and returns `#t`, then we `cons` the aforementioned first element of `seq` onto a list created by recursively calling `gather-next-batch` on what’s left of `seq`, namely, all but the first element, which we’ve just processed.
(If you’re looking for a set of rules/patterns on how to write nice little recursive procedures like this, I can highly recommend a tome of great power known as The Little Schemer. Or should I say: a tome that deposits one, slightly bewildered, at the outer gateways of great power! But I digress…)
Let’s test out our awesome new procedure:
```scheme@(guile-user)> (gather-next-batch number? '(a 1 2 3 b 4 5 c 6 d e))
\$404 = ()
```
What happened? I was expecting to get back `(1 2 3)`! Well, as it turns out the first element of the list we passed to `gather-next-batch` didn’t match our supplied `number?` predicate. Therefore, we crashed through our conditional to the bottom (where `else` lives), and in this case we asked `else` to return the empty list, `()`. And so it did!
Let’s try this again, using a list whose first element matches our predicate:
```scheme@(guile-user)> (gather-next-batch number? (cdr '(a 1 2 3 b 4 5 c 6 d e)))
\$403 = (1 2 3)
```
In this case we asked for the `cdr` of our list, which does begin with a number. Therefore `gather-next-batch` was able to get going on its work of gathering up a list containing the next batch of numbers, `(1 2 3)`.
Next time we’ll look at how to integrate this procedure with our larger solution. For now I’ll leave you with the trace output of `gather-next-sequence` (helpfully drawn for us by Scheme 48). It should help visualize what this little procedure’s actually doing.
Until then, may you hack gracefully, friends!
```> (gather-next-batch number? (cdr foo))
'(1 2 3)
> ,trace gather-next-batch
> (gather-next-batch number? (cdr foo))
[Enter (gather-next-batch #{Procedure 585 number?} '(1 2 3 b 4 5 c 6 ---))
[Enter (gather-next-batch #{Procedure 585 number?} '(2 3 b 4 5 c 6 d ---))
[Enter (gather-next-batch #{Procedure 585 number?} '(3 b 4 5 c 6 d e))
[Enter (gather-next-batch #{Procedure 585 number?} '(b 4 5 c 6 d e))
Leave gather-next-batch '()]
Leave gather-next-batch '(3)]
Leave gather-next-batch '(2 3)]
Leave gather-next-batch '(1 2 3)]
'(1 2 3)
```
(Image courtesy Mélisande* under Creative Commons license.)
A Scheme Code Kata
Reader beware! This is a meta-creature, a post about a post about a post. By way of comp.lang.scheme, the musings of the great jao (who incidentally is the Wizard behind Geiser (which is the way to Scheme with Emacs these days)), and finally, this humble blag, I present my (straight R^5RS!) solution to the Scheme kata described in the above links:
```(define (plist->alist p)
(cond ((null? p) '())
((symbol? (car p))
(cons (list (car p)
(gather-next-batch number? (cdr p)))
(plist->alist (cdr p))))
(else (plist->alist (cdr p)))))
(define (gather-next-batch pred seq)
(cond ((null? seq) '())
((pred (car seq))
(cons (car seq)
(gather-next-batch pred (cdr seq))))
(else '())))
```
(Image courtesy Mélisande* under Creative Commons license.)
A Description of the Problem
We are given a triangle of numbers, and we are asked to write a program that computes the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base.
• Each step can go diagonally down to the left or the right.
• The number of rows in the triangle will be between 1 and 100, inclusive.
• The numbers that populate the triangle are integers between 0 and 99.
What are our Inputs and Outputs?
Our initial input data will live in a file called `triangle-input.txt`, which contains the following:
```5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
```
Note that the first line of the file is not part of the triangle itself; it’s there to tell us how many levels deep the triangle goes.
```30
```
We’ll place our output in a file called `triangle-output.txt`, which will contain a single integer. We’ll place the names of our input and output files in the program constants `INPUT_FILE` and `OUTPUT_FILE`, respectively.
Reading the Input, Writing the Output
First, we’ll need to get the values out of `triangle-input.txt` and store them in a convenient structure. In this case, an array of arrays should do.
We begin by creating an empty array, tmp, which will act as a temporary storage space for the lines of `triangle-input.txt`.
We’ll read the lines of the file one at a time. For each line, we `split` the string, e.g., “1 2 3 4 5\n”, into a list, and `push` that line onto our array `tmp`.
```tmp = []
File.open(INPUT_FILE, "r") do |f|
f.lines.each do |line|
tmp.push line.split
end
end
```
Unfortunately, we’re pushing an array of strings onto tmp, since
```"4 5 2 6 5\n".split
```
returns this:
```["4", "5", "2", "6", "5"]
```
Therefore, we’ll take a second pass through and convert those arrays of strings into arrays of numbers. The resulting array will allow us to – finally! – begin our real work. Notice that this is a nested call to `map`, best read from the inside out. The value returned by the inner `map` is returned to the outer, with the results stored in variable tri, since the return value of `map` is always an array.
```tri = tmp.map { |array| array.map { |elem| elem.to_i } }
```
We’ll wrap everything here up in a method, `read_triangle_input`, which will show up in the complete program listing below. We’ll also leave the `write_triangle_output` method for the listing; it requires little explanation.
Solving our Actual Problem
Now that the housekeeping chores are out of the way, we can jump in and begin the real work of finding the highest sum in our triangle.
We’d like to write a method, `triangle_sum`, which, given an array of arrays like the one we’ve just constructed, returns an integer representing the highest sum calculated on its imagined path “down through the triangle.”
Since our route through the triangle is restricted to “steps” that can “go diagonally down to the left or the right,” the most natural representation of this data is as a tree. We’ll simulate this in a crude way using an array of arrays.
The Inner Loop
Since our fundamental data structure is an array, we’ll need to choose a looping construct; we’ll stick with the “C-style” iterative constructs here since they map well onto this problem (no pun intended). We’ll use an `index` variable to keep track of where we are in the iteration.
Inside the loop, we want to know three things (among others):
• Where am I?
• Where is the element to my upper left?
• Where is the element to my upper right?
We’ll denote the answers to these questions with the variables `this`, `upleft`, and `upright` in our program listing below.
Remember the problem description: Starting at the root of the tree, we’ll keep a running sum of all the numbers we’ve seen thus far on this particular path through the tree.
Visualizing Our Movement Down the Triangle
In order to solve this problem, we started with some hand-simulation of what would eventually become the final algorithm. The example below shows how it works: given where we are in the array of arrays, we look “up and to the left” and “up and to the right” of where we are. In the following diagrams, we denote our position in the algorithm with a lovely text arrow.
```Index: 1
[7] <---
[3, 8]
[8, 1, 0]
[2, 7, 4, 4]
[4, 5, 2, 6, 5]
```
When `index` is 1, there isn’t anything to do, since we can’t look “up” at anything. Therefore, move on.
```Index: 2
[7]
[10, 15] <--- Was: [3, 8]
[8, 1, 0]
[2, 7, 4, 4]
[4, 5, 2, 6, 5]
```
When `index` is 2, we look up and to the left (7), and up and to the right (also 7). Each time through the loop, we create a new temporary array called `next_row`, in which to store the running sums. In this case, we create a new array `[10, 15]` by adding 7 to each of `[3, 8]`. We then replace the old array with the new.
```Index: 3
[7]
[10, 15]
[18, 11, 16, 15] <--- Was: [8, 1, 0]
[2, 7, 4, 4]
[4, 5, 2, 6, 5]
```
`index` is now 3. We perform the same operations as above: first, create an empty array. Then, for each element in the old array `[8, 1, 0]`, we add the value of the element (which we’ll call `this` in our program code) to the values of `upleft` and `upright` (these are obviously our variable names for the “up and to the left” and “up and to the right” values we’ve already mentioned). In each case we push the results of these additions onto the new temporary array. Once we’ve finished, we replace the existing array with the new, as before.
```Index: 4
[7]
[10, 15]
[18, 11, 16, 15]
[20, 25, 18, 15, 20, 20] <--- Was: [2, 7, 4, 4]
[4, 5, 2, 6, 5]
Index: 5
[7]
[10, 15]
[18, 11, 16, 15]
[20, 25, 18, 15, 20, 20]
[24, 25, 30, 27, 20, 24, 21, 20] <--- Was: [4, 5, 2, 6, 5]
Result: 30
```
Here we show two steps more of the process, and its completion. We can easily see that 30 is the largest sum in the last array, and our answer.
We notice that the “new” interior arrays we’re creating on each turn through the loop are longer than the originals they replace, so we’re not being as efficient with memory as we’d like. At least Array expansion is an O(n) operation!
The Complete Program Listing of `triangle.rb`
This essay is over 1200 words long already according to `wc -w`. Therefore, since this algorithm can be described very succinctly in code, I’ll break the rules of literate programming and simply end with the program listing itself. Note the temporary variables `next_row`, `this`, `upleft`, and `upright`, which are described in the section “Visualizing Our Movement Down the Triangle” above.
As always, the contents of this literate program are available at Github.
(Update: better solutions and discussion over at the Ruby Reddit)
```#!/usr/bin/env ruby
require 'test/unit'
INPUT_FILE = "triangle-input.txt"
OUTPUT_FILE = "triangle-output.txt"
tmp = []
File.open(INPUT_FILE, "r") do |f|
f.lines.each do |line|
tmp.push line.split
end
end
tri = tmp.map { |array| array.map { |elem| elem.to_i } }
end
def write_triangle_output(result)
File.open(OUTPUT_FILE, "w") do |f|
f.print result
end
end
def triangle_sum(tri)
a = Array.new(tri)
index = 1
len = a.shift[0]-1
while index <= len
next_row = []
for i in 0..index
this = a[index][i]
upleft = a[index-1][i-1]
upright = a[index-1][i]
if i == 0
next_row.push this + upright
elsif i == index
next_row.push this + upleft
else
next_row.push this + upleft
next_row.push this + upright
end
end
a[index] = next_row
index += 1
end
a[index-1].max
end
highest_sum = triangle_sum(tri)
write_triangle_output(highest_sum)
class TestTriangleSum < Test::Unit::TestCase
def test_01
expected = triangle_sum(tri)
assert_equal expected, 30
end
end
```
(Image courtesy Mélisande* under Creative Commons license.)
The Problem Description
A zero-indexed array A consisting of N integers is given. An
equilibrium index of this array is any integer P such that 0 <=
P < N and the sum of elements of lower indices is equal to the sum
of elements of higher indices, i.e.,
```A[0] + A[1] + ... + A[P-1] =
A[P+1] + ... + A[N-2] + A[N-1].
```
The sum of zero elements is assumed to be equal to 0.
Write a function that, given a zero-indexed array A consisting of
N integers, returns any of its equilibrium indices. The function
should return -1 if no equilibrium index exists.
• Expected worst-case time complexity is O(N)
• Expected worst-case space complexity is O(N), beyond input storage
(not counting the storage required for input arguments).
The above is taken from the problem description by Codility; they discuss one solution (written in C) here.
Notes on this Implementation
First things first: we’ll avoid the `return -1` “C-ism,” as it’s more natural to return `nil` in Ruby. In fact, Ruby sees -1 as `True`, so returning it will break many common predicates, whereas `nil` won’t.
Experienced programmers will observe that this implementation does not meet the `O(n)` time and space complexity requirements as listed above. Absolute simplicity of implementation is the focus right now, but that may change in a future version.
Finally, notice that this short essay is itself a literate program, implemented using the wonderful Org-mode capabilities which are included with the Emacs text editor.
The Inner Loop
Since most of the program’s work is done inside a single `while` loop, we’ll begin there.
Let A be the Ruby array
```[-7, 1, 5, 2, -4, 3, 0].
```
The equilibrium index of A can be computed by hand, so it’s a good place to start. It’s also our first test case (see below).
We’ve chosen to implement the iteration over A using a `while` loop rather than the more idiomatic `Array#each` method since we need to keep track of our current index into the array.
As we begin the loop, the variable `index` is initialized as the length of the array minus one. This is required because Ruby’s arrays are zero-based, but the value returned by its `Array#length` method is not.
```while index > 0
left = a[0..index-1].reduce(:+)
right = a[index+1..len].reduce(:+)
if left == right
return index
end
index -= 1
end
```
We’ll iterate backwards through the array from the end. At each value of `index`, we’ll split A into two smaller arrays, `left` and `right`. This requires allocating two new arrays in memory, reading the values of the desired “slices” of A, and copying them into `left` and `right`, respectively. This operation provides for an implementation that is simple to visualize and understand, but it’s also the reason why we fail to meet the requirements for `O(n)` space and time complexity. A more efficient implementation would avoid these unnecessary allocation and copying steps, and we might change this program at some point to achieve that.
Visualizing the Iteration
Let’s look at `left` and `right` at each stage of the iteration:
We can see that when we split A at `index`, we always leave a “gap” in between, and it’s this gap which will provide us with the answer we seek: the equilibrium index (provided that the equilibrium index is defined for the given array, that is). At every iteration in the diagram above, we sum the values within `left` and `right` using the `Array#reduce` method. If `left` and `right` are equal, `index` is defined as the equilibrium index, and we `return index`. Otherwise, we’ll end up escaping the loop and returning `nil`.
The `equi` Function
Looking briefly at the entire `equi` function, we can see that it’s just a wrapper for the `while` loop. First we set the value of `index` and `len` as bookkeeping measures. We then enter the `while` loop as described above. If the loop completes without returning a value, the program returns to the next outer context and returns the `nil` value, which lets our caller know that this array doesn’t have an equilibrium index.
```def equi(a)
index = a.length-1
len = a.length-1
while index > 0
left = a[0..index-1].reduce(:+)
right = a[index+1..len].reduce(:+)
if left == right
return index
end
index -= 1
end
nil
end
```
Test Cases
Over the course of developing the program, a number of test cases have come to mind. We’ll begin with the given array A that we started with.
```def test_random
sample_array = [-7, 1, 5, 2, -4, 3, 0]
expected = equi(sample_array)
assert_equal expected, 3
end
```
Here we’ve defined a trivial `pyramid’ array of values that ascend and descend symmetrically.
```def test_trivial_pyramid
sample_array = [1, 2, 3, 4, 3, 2, 1]
expected = equi(sample_array)
assert_equal expected, 3
end
```
This test checks the case where the first value is equal to the sum of all the rest (save the equilibrium index, of course).
``` def test_biggest_first
sample_array = [99, 0, 66, 32, 1]
expected = equi(sample_array)
assert_equal expected, 1
end
```
Similarly, we check for the case where the last value alone is equal to the sum of `left`.
```def test_biggest_last
sample_array = [66, 32, 1, 0, 99]
expected = equi(sample_array)
assert_equal expected, 3
end
```
We should return `nil` for an array with a single element, since the equilibrium index is not defined in that case.
```def test_single_element
sample_array = [0]
expected = equi(sample_array)
assert_equal expected, nil
end
```
The same is true of an array containing a single `nil`.
```def test_single_nil
sample_array = [nil]
expected = equi(sample_array)
assert_equal expected, nil
end
```
The Complete Program Listing
Finally, we have the complete program listing for the `tangle`‘d file `literate-equi.rb`. Since we’ve included our tests by subclassing the `Test::Unit` class, Ruby will run them for us when we invoke the program. Running `ruby literate-equi.rb` at the command shell should return the following output:
```~/Desktop/Dropbox/current/logicgrimoire \$ ruby literate-equi.rb
Started
......
Finished in 0.002195 seconds.
6 tests, 6 assertions, 0 failures, 0 errors
```
The program itself:
```#!/usr/bin/env ruby
require 'test/unit'
def equi(a)
index = a.length-1
len = a.length-1
while index > 0
left = a[0..index-1].reduce(:+)
right = a[index+1..len].reduce(:+)
if left == right
return index
end
index -= 1
end
nil
end
class TestEqui < Test::Unit::TestCase
def test_random
sample_array = [-7, 1, 5, 2, -4, 3, 0]
expected = equi(sample_array)
assert_equal expected, 3
end
def test_trivial_pyramid
sample_array = [1, 2, 3, 4, 3, 2, 1]
expected = equi(sample_array)
assert_equal expected, 3
end
def test_biggest_first
sample_array = [99, 0, 66, 32, 1]
expected = equi(sample_array)
assert_equal expected, 1
end
def test_biggest_last
sample_array = [66, 32, 1, 0, 99]
expected = equi(sample_array)
assert_equal expected, 3
end
def test_single_element
sample_array = [0]
expected = equi(sample_array)
assert_equal expected, nil
end
def test_single_nil
sample_array = [nil]
expected = equi(sample_array)
assert_equal expected, nil
end
end
```
First Post
“Imagination is more important than knowledge.”
— Albert Einstein
At the age of 30, I finally started learning Calculus. If that sounds crazy to you, you’re not alone. It sounded pretty crazy to me too. It still does, in fact. I was never much good at math in school, as my transcripts would show anyone who cared to look. I failed New York State’s Course II on geometry in tenth grade, and ended up taking it again the next year. I barely passed, even the second time around — with a 68, I believe. As for Course III in trigonometry, I failed outright. In short, I was not considered one of the bright mathematical lights at my high school.
It was some years later, in college, that I discovered computers. Up to that point, I’d used them mostly to write term papers for my classes, but as time went on, I became more interested in how they worked. In my travels on the web, I stumbled across a few message boards frequented by programmers, and discovered another world. It was amazing; there were people who actually just wrote computer programs all day long. In return, people paid them money. This seemed hard to believe at the time.
I soon found out what drove these people to do what they did: it was a whole lot of fun. Before long, I was writing my own little programs. There was something really neat about giving a computer a set of instructions and then standing back and seeing what happened. Sometimes, I could get it to do what I was imagining. Most of the time, I couldn’t. Slowly, I got better at talking to the computer in ways it could understand. In its own language.
There comes a point in the life of any programmer, however, when a lack of math skills starts to really hold her back. Once I reached that point, my historical disinterest in math disappeared. I couldn’t wait to get started. I bought a book from the local bookstore that promised to “demystify” trigonometry and worked on it almost every day after work, carefully reading through descriptions of terms like “vector” and “parallax,” all the while amazed that here I was, actually doing what I never thought I could: I was teaching myself the math I never learned in school, and what’s more, I began to look forward to those sessions as the best part of my day.
Why does any of this matter? It matters because I know that there are lots of kids out there like I was. They may think they aren’t any good at math, or that it’s boring. They may even believe that they hate it. What they’re lacking is a fun way to apply it. After all, memorizing trigonometric formulas is only fun if you have a reason.
That is exactly what I aim to do with this blog: give people a reason to care about math, and help them to understand that math isn’t just about some abstract notion of “intellectual enrichment,” but that it can help us do cool things, whether we’re interested in programming computers, experimenting with model rocketry, or building our own robots.
I don’t consider myself an expert in math or programming, of course. I’m just another PC hobbyist with an itch to scratch, and in many ways, I’ve spent the last few years learning just how little I really know. That doesn’t matter — if something I write here helps even one other person out there achieve their dream, I’ll consider the time well spent.
Bottom line: whatever this strange way of thinking that makes a computer programmer is, I’m determined to keep going until I master it. It doesn’t matter how long it takes me to get there, since I consider the journey itself to be a labor of love, and it’s something that I know I will enjoy for the rest of my life.
What activities can you say that about?
(Image courtesy Melisande under Creative Commons license.)
| 2023-02-09T03:23:47 |
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|
https://finalfantasy.fandom.com/wiki/Peninsula_of_Power?oldid=2508638
|
## FANDOM
37,451 Pages
The following article is based on a subject that has not been officially named in any official Square Enix material; the current title is merely a placeholder.
Final Fantasy games that use random encounters on a world map utilize a grid that separates the areas in which monsters appear. Depending on the location on the grid the player traversing the world map is standing on, different enemies will be encountered. Sometimes, due to a programming oversight, the player is allowed earlier access to monsters intended to be fought when the party reaches a certain part or area in the story. Many of these areas are in remote places where players have to go out of their way to reach. Players can exploit these areas to grind for experience and gil early.
The term Peninsula of Power was coined in an issue of Nintendo Power for the original Final Fantasy, where it was hinted the area can be used for easy experience and gil. Players have continued to call such similar areas as the Peninsula of Power within the series and in other video games.
## Appearances
### Final Fantasy
The Peninsula of Power is a term for a location in the original Final Fantasy. It is a peninsula northeast of Pravoka, accessible by ship. In that certain area around the peninsula, monsters usually encountered in the Lufenia area are encountered there as well, allowing for early access of these monsters.
This occurs because the world map is divided into an eight-by-eight grid, each containing 32-by-32 squares. The grid determines which enemies are fought in any location. Where the most northwest grid-square is $(0,0)$, from there to the east it will be $(1,0)$ and to the south it will be $(0,1)$; $(6,4)$ contains Pravoka, and to the east is $(7,4)$, the area south of the peninsula and including the southern part of the peninsula. $(7,4)$, $(7,5)$, and $(6,5)$ all contain the same enemy formations not much tougher than Pravoka's.
However, the northern part of the peninsula infringes on the square that covers a large section of the area surrounding Lufenia including the town itself. In this square, $(7,3)$, the enemies fought are built for the late stage of the game after the airship is obtained.
While not exactly a Peninsula of Power, in the NES version of Final Fantasy exists a short, 3 tiles-long area south of the mountains underneath the Yahnikurm Desert, consisting of only Goblins as enemies.
### Final Fantasy II
A few tiles to the south of Altair, the player can encounter Mysidian area monsters. The monsters can only be encountered on the three horizontal tiles in the shore.
### Final Fantasy III
This area can be accessed right after Goldor Manor. From Amur, the player must fly north. The area does not look like a peninsula, but is the same concept as the Peninsula of Power from Final Fantasy. The grid ends one tile after the mountainside, and this horizontal strip of land contains monsters from around the Crystal Tower area, which are monsters intended to be fought near the end of the game. This area does not apply to the 3D versions of Final Fantasy III.
### Final Fantasy IV
The monsters fought north of Mt. Ordeals are those from the Mythril and Troia areas. The grid tries to cover all the islands north of Mt. Ordeals, but has been done poorly resulting in early access to stronger monsters. This is still available in the Final Fantasy IV: The Complete Collection version of the game. This area does not apply to the 3D versions of Final Fantasy IV.
### Final Fantasy VI
Similar to the other examples, but not quite a Peninsula of Power. In the World of Ruin, there is a peninsula with six trees directly east of Kefka's Tower; its random encounters are set to default resulting in encounters that solely involve Leaf Bunnies and Darkwinds, one of the first enemies fought in the game found right outside Narshe.
## Gallery
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-04-08T01:50:44 |
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|
https://finalfantasy.fandom.com/wiki/Missing_Score
|
FANDOM
37,120 Pages
A kind of gun-arm, a type of weapon from another world, that greatly boosts physical and magical power when equipped. It is said that the leader of a resistance group used this gun-arm to fight against Shinra Inc, a corporation trying to use the planet's life force as energy.
Final Fantasy Brave Exvius description
Missing Score (ミシングスコア, Mishingu Sukoa?) is a recurring weapon in the series.
AppearancesEdit
Final Fantasy VIIEdit
Missing Score is Barret's ultimate weapon, obtained by finding it during the Raid on Midgar at the Sister Ray while Barret is in the party. It is permanently missable if not picked up.
It provides 98 Attack, 108 Atk%, 49 Magic, and 4 linked Materia slots with Nothing growth. It deals damage equal to the following formula, dealing more damage the more AP is on the weapon:
$[1 + ( Total AP on Weapon / 10,000 )] / 16$
This is then modified by the attack's power, for normal attacks, the multiplier is 1.0. Note that unlike most other damage modifiers, each character's ultimate weapon applies the damage modifier after all other modifiers, instead of modifying the attack strength of the weapon itself.
To achieve a base 1.0 damage multiplier, the weapon needs to have approximately 150,000 AP on it. To reach the 4x damage multiplier that most characters have with their ultimate weapons, the weapon needs to have approximately 630,000 AP on it.
Materia that do not add to the value are the Underwater, Master Magic, Master Command, Master Summon, and Enemy Skill Materia. Much like Vincent's Death Penalty, it is possible to induce the overflow glitch with this weapon if at least 8 mastered Knights of Round Materia are equipped on the weapon, among other conditions.
Final Fantasy Type-0Edit
Missing Score is a magicite pistol for Cater. It has attack power of 52 and is found in a treasure in Bethnel Caverns and sells for 2700 gil.
Pictlogica Final Fantasy ≒Edit
This section about equipment in Pictlogica Final Fantasy ≒ is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
This section about equipment in Final Fantasy Airborne Brigade is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
Final Fantasy Brave ExviusEdit
Missing Score is a Gun obtained as Barret's Trust Master. It provides 107 ATK, 98 MAG, and MP +10%.
EtymologyEdit
A missing score is an unidentified variable within algebraic mean equations used in analyzing mass consensus to determine a general average. The name reflects Missing Score being a weapon of variable power improved upon additions of customizable Materia, and as a weapon that stands out as its output exceeds average means.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-01-18T13:59:43 |
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|
https://lammps.sandia.gov/doc/angle_cosine_shift.html
|
# angle_style cosine/shift/omp command
## Syntax
angle_style cosine/shift
## Examples
angle_style cosine/shift
angle_coeff * 10.0 45.0
## Description
The cosine/shift angle style uses the potential
where theta0 is the equilibrium angle. The potential is bounded between -Umin and zero. In the neighborhood of the minimum E=- Umin + Umin/4(theta-theta0)^2 hence the spring constant is umin/2.
The following coefficients must be defined for each angle type via the angle_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:
• umin (energy)
• theta (angle)
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc page for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See the Speed packages doc page for more instructions on how to use the accelerated styles effectively.
## Restrictions
This angle style can only be used if LAMMPS was built with the USER-MISC package.
| 2019-04-25T12:10:47 |
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https://www.zbmath.org/authors/?q=ai%3Azudilin.wadim
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# zbMATH — the first resource for mathematics
Compute Distance To:
Author ID: zudilin.wadim Published as: Zudilin, Wadim; Zudilin, V. V.; Zudilin, W.; Zudilin, W. V. Homepage: http://www.math.ru.nl/~wzudilin/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp · GND
Documents Indexed: 139 Publications since 1995, including 3 Books Reviewing Activity: 62 Reviews
all top 5
#### Co-Authors
64 single-authored 6 Straub, Armin 6 Wan, James Gu Feng 5 Chan, Heng Huat 5 Guo, Victor J. W. 5 Väänänen, Keijo O. 4 Borwein, Jonathan Michael 3 Almkvist, Gert 3 Bundschuh, Peter 3 Cooper, Shaun 3 Fischler, Stéphane 3 Guillera, Jesús 3 Krattenthaler, Christian Friedrich 3 Rivoal, Tanguy 3 Warnaar, S. Ole 3 Zeilberger, Doron 2 Bertin, Marie-Jose 2 Bertrand, Daniel 2 Broadhurst, David John 2 Long, Ling 2 Matala-aho, Tapani 2 Ohno, Yasuo 2 Osburn, Robert 2 Rogers, Mathew D. 2 Sprang, Johannes 2 van Straten, Duco 2 Viola, Carlo 2 Yang, Yifan 1 Bailey, David Harold 1 Brent, Richard Peirce 1 Brunault, François 1 Chappell, Tom 1 Coons, Michael 1 Dauguet, Simon 1 Ekhad, Shalosh B. (computer) 1 Gallot, Yves 1 Haynes, Alan K. 1 Hessami Pilehrood, Khodabakhsh 1 Hessami Pilehrood, Tatiana 1 Lalín, Matilde N. 1 Lascoux, Alain 1 Luca, Florian 1 Marcovecchio, Raffaele 1 Moree, Pieter 1 Okuda, Jun-ichi 1 Pasol, Vicentiu 1 Polanco, Geremías 1 Rochev, Igor 1 Samart, Detchat 1 Shallit, Jeffrey O. 1 Shparlinski, Igor E. 1 Sondow, Jonathan D. 1 Tanigawa, Yoshio 1 Tu, Fang-Ting 1 van der Poorten, Alfred J. 1 Yui, Noriko
all top 5
#### Serials
12 Mathematical Notes 9 Russian Mathematical Surveys 6 Sbornik: Mathematics 5 Journal of Number Theory 4 Journal of Approximation Theory 3 Bulletin of the Australian Mathematical Society 3 Journal of Computational and Applied Mathematics 3 Journal de Théorie des Nombres de Bordeaux 3 Izvestiya: Mathematics 3 The Ramanujan Journal 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Mathematical Analysis and Applications 2 Mathematics of Computation 2 Acta Arithmetica 2 Advances in Mathematics 2 Compositio Mathematica 2 Journal of the London Mathematical Society. Second Series 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Proceedings of the American Mathematical Society 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 IMRN. International Mathematics Research Notices 2 Journal of Mathematical Sciences (New York) 2 The Electronic Journal of Combinatorics 2 Séminaire Lotharingien de Combinatoire 2 Journal of the Australian Mathematical Society 2 Chebyshevskiĭ Sbornik 2 Australian Mathematical Society Lecture Series 2 Annales Mathématiques du Québec 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of Combinatorial Theory. Series A 1 Manuscripta Mathematica 1 Mathematica Scandinavica 1 Mathematika 1 Results in Mathematics 1 Constructive Approximation 1 Aequationes Mathematicae 1 Kyushu Journal of Mathematics 1 Integral Transforms and Special Functions 1 Annals of Combinatorics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 International Journal of Number Theory 1 International Journal of Mathematics and Computer Science 1 Communications in Number Theory and Physics 1 Moscow Journal of Combinatorics and Number Theory 1 Springer Proceedings in Mathematics & Statistics 1 Mathematics 1 ICCM Notices 1 Research in the Mathematical Sciences 1 Research in Number Theory
all top 5
#### Fields
130 Number theory (11-XX) 82 Special functions (33-XX) 11 Combinatorics (05-XX) 8 Algebraic geometry (14-XX) 6 Approximations and expansions (41-XX) 5 Ordinary differential equations (34-XX) 5 Numerical analysis (65-XX) 4 Functions of a complex variable (30-XX) 2 Field theory and polynomials (12-XX) 2 $$K$$-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX)
#### Citations contained in zbMATH Open
115 Publications have been cited 983 times in 587 Documents Cited by Year
Ramanujan-type supercongruences. Zbl 1231.11147
2009
Zeta stars. Zbl 1228.11132
2008
Generalizations of Clausen’s formula and algebraic transformations of Calabi-Yau differential equations. Zbl 1223.33007
Almkvist, Gert; van Straten, Duco; Zudilin, Wadim
2011
Algebraic relations for multiple zeta values. Zbl 1171.11323
Zudilin, V. V.
2003
On the (K.2) supercongruence of Van Hamme. Zbl 1400.11062
2016
Arithmetic of linear forms involving odd zeta values. Zbl 1156.11327
2004
One of the numbers $$\zeta(5)$$, $$\zeta(7)$$, $$\zeta(9)$$, $$\zeta(11)$$ is irrational. Zbl 1047.11072
Zudilin, V. V.
2001
Ramanujan-type formulae for $$1/\pi$$: a second wind? Zbl 1159.11053
2008
From $$L$$-series of elliptic curves to Mahler measures. Zbl 1260.11062
2012
Densities of short uniform random walks. Zbl 1296.33011
Borwein, Jonathan M.; Straub, Armin; Wan, James; Zudilin, Wadim
2012
New analogues of Clausen’s identities arising from the theory of modular forms. Zbl 1234.33009
Chan, Heng Huat; Tanigawa, Yoshio; Yang, Yifan; Zudilin, Wadim
2011
Irrationality of values of the Riemann zeta function. Zbl 1114.11305
Zudilin, W.
2002
Diophantine properties of numbers related to Catalan’s constant. Zbl 1028.11046
Rivoal, T.; Zudilin, W.
2003
“Divergent” Ramanujan-type supercongruences. Zbl 1276.11027
2012
Congruences for $$q$$-binomial coefficients. Zbl 1431.11032
2019
Neverending fractions. An introduction to continued fractions. Zbl 1307.11001
Borwein, Jonathan; van der Poorten, Alf; Shallit, Jeffrey; Zudilin, Wadim
2014
New representations for Apéry-like sequences. Zbl 1275.11035
2010
Cyclic $$q$$-MZSV sum. Zbl 1268.11119
Ohno, Yasuo; Okuda, Jun-Ichi; Zudilin, Wadim
2012
On the Mahler measure of $$1+X+1/X+Y +1/Y$$. Zbl 1378.11091
2014
Basic hypergeometric series, $$q$$-analoges, of the values of the zeta function, and Eisenstein series. (Séries hypergéométriques basiques, $$q$$-analogues des valeurs de la fonction zêta et séries d’Eisenstein.) Zbl 1089.11038
Krattenthaler, C.; Rivoal, T.; Zudilin, W.
2006
On a $$q$$-deformation of modular forms. Zbl 1445.11014
Guo, Victor J. W.; Zudilin, Wadim
2019
Differential equations, mirror maps and zeta values. Zbl 1118.14043
2006
Dedekind’s $$\eta$$-function and Rogers-Ramanujan identities. Zbl 1234.05040
2012
Legendre polynomials and Ramanujan-type series for $$1/\pi$$. Zbl 1357.11123
Chan, Heng Huat; Wan, James; Zudilin, Wadim
2013
Regulator of modular units and Mahler measures. Zbl 1386.11129
2014
A common $$q$$-analogue of two supercongruences. Zbl 1439.33007
Guo, Victor J. W.; Zudilin, Wadim
2020
A refinement of Nesterenko’s linear independence criterion with applications to zeta values. Zbl 1206.11088
2010
Well-poised hypergeometric series for Diophantine problems of zeta values. Zbl 1156.11326
2003
Arithmetic hypergeometric series. Zbl 1225.33008
Zudilin, V. V.
2011
On three theorems of Folsom, Ono and Rhoades. Zbl 1311.11026
2015
The hypergeometric equation and Ramanujan functions. Zbl 1072.11052
Zudilin, W.
2003
Heine’s basic transform and a permutation group for $$q$$-harmonic series. Zbl 1052.11053
2004
Approximations to $$q$$-logarithms and $$q$$-dilogarithms, with applications to $$q$$-zeta values. Zbl 1088.11052
Zudilin, W.
2005
Ramanujan-type formulae for $$1/\pi: q$$-analogues. Zbl 1436.11024
Guo, Victor J. W.; Zudilin, Wadim
2018
More Ramanujan-type formulae for $$1/\pi^2$$. Zbl 1203.11088
Zudilin, V. V.
2007
Euler’s constant, $$q$$-logarithms, and formulas of Ramanujan and Gosper. Zbl 1132.11056
2006
Diophantine problems for $$q$$-zeta values. Zbl 1044.11066
Zudilin, V. V.
2002
Generating functions of Legendre polynomials: A tribute to Fred Brafman. Zbl 1242.33018
2012
Quadratic transformations and Guillera’s formulas for $$1/\pi^2$$. Zbl 1144.33002
Zudilin, V. V.
2007
An Apéry-like difference equation for Catalan’s constant. Zbl 1093.11075
Zudilin, W.
2003
Irrationality measures for certain $$q$$-mathematical constants. Zbl 1153.11034
2007
A $$q$$-rious positivity. Zbl 1234.11023
Warnaar, S. Ole; Zudilin, W.
2011
Many odd zeta values are irrational. Zbl 1430.11097
Fischler, Stéphane; Sprang, Johannes; Zudilin, Wadim
2019
Lower bounds for polynomials in the values of certain entire functions. Zbl 0878.11030
Zudilin, V. V.
1996
On the integrality of power expansions related to hypergeometric series. Zbl 1043.11060
Zudilin, V. V.
2002
On the irrationality measure for a $$q$$-analogue of $$\zeta(2)$$. Zbl 1044.11067
Zudilin, W. V.
2002
On the transcendence degree of the differential field generated by Siegel modular forms. Zbl 1130.11020
Bertrand, D.; Zudilin, W.
2003
An essay on the irrationality measure of $$\pi$$ and other logarithms. Zbl 1140.11036
Zudilin, V. V.
2004
Algebraic independence of Mahler functions via radial asymptotics. Zbl 1415.11104
Brent, Richard P.; Coons, Michael; Zudilin, Wadim
2016
Many values of the Riemann zeta function at odd integers are irrational. (Beaucoup de valeurs aux entiers impairs de la fonction zêta de Riemann sont irrationnelles.) Zbl 1398.11109
Fischler, Stéphane; Sprang, Johannes; Zudilin, Wadim
2018
New irrationality measures for $$q$$-logarithms. Zbl 1158.11033
Matala-aho, Tapani; Väänänen, Keijo; Zudilin, Wadim
2006
Period(d)ness of $$L$$-values. Zbl 1316.11038
2013
On the Mahler measure of a family of genus 2 curves. Zbl 1347.11076
2016
Multiple $$q$$-zeta brackets. Zbl 1312.11069
2015
One of the odd zeta values from $$\zeta(5)$$ to $$\zeta(25)$$ is irrational. By elementary means. Zbl 1445.11063
2018
Approximations to di- and tri-logarithms. Zbl 1220.65028
2007
Euler’s factorial series and global relations. Zbl 1444.11037
2018
A third-order Apéry-like recursion for $$\zeta(5)$$. Zbl 1041.11057
Zudilin, V. V.
2002
Well-poised hypergeometric transformations of Euler-type multiple integrals. Zbl 1065.11054
Zudilin, W.
2004
Very well-poised hypergeometric series and multiple integrals. Zbl 1229.33011
Zudilin, V. V.
2002
Ramanujan-type formulae and irrationality measures of some multiples of $$\pi$$. Zbl 1114.11064
Zudilin, V. V.
2005
Further explorations of Boyd’s conjectures and a conductor 21 elliptic curve. Zbl 1337.11072
Lalín, Matilde; Samart, Detchat; Zudilin, Wadim
2016
Ramanujan-type formulae for $$1/\pi$$: the art of translation. Zbl 1371.11162
2013
On the Mahler measure of hyperelliptic families. Zbl 1434.11211
2017
A supercongruence motivated by the Legendre family of elliptic curves. Zbl 1252.11017
Chan, Heng Huat; Long, Ling; Zudilin, V. V.
2010
The Erdős–Moser equation $$1^k+2^k+\cdots +(m-1)^k=m^k$$ revisited using continued fractions. Zbl 1231.11038
Gallot, Yves; Moree, Pieter; Zudilin, Wadim
2011
A modular supercongruence for $${}_6 F_5$$: an Apéry-like story. (Une supercongruence modulaire pour $${}_6 F_5$$: un conte à la Apéry.) Zbl 1429.11039
Osburn, Robert; Straub, Armin; Zudilin, Wadim
2018
Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds. Zbl 1443.11053
Long, Ling; Tu, Fang-Ting; Yui, Noriko; Zudilin, Wadim
2019
On theorems of Gelfond and Selberg concerning integral-valued entire functions. Zbl 1081.11051
2004
Baker-type estimates for linear forms in the values of $$q$$-series. Zbl 1064.11054
2005
Some remarks on linear forms containing Catalan’s constant. Zbl 1099.11036
Zudilin, V. V.
2002
On simultaneous Diophantine approximations to $$\zeta(2)$$ and $$\zeta(3)$$. Zbl 1315.11062
2014
Two hypergeometric tales and a new irrationality measure of $$\zeta (2)$$. Zbl 1307.11085
2014
On the non-quadraticity of values of the $$q$$-exponential function and related $$q$$-series. Zbl 1232.11080
Krattenthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, Wadim
2009
Experimental mathematics and mathematical physics. Zbl 1221.82006
2010
A new lower bound for $$\|(3/2)^k\|$$. Zbl 1127.11049
2007
Apéry’s theorem. Thirty years after. Zbl 1223.11089
2009
Difference equations and the irrationality measure of numbers. Zbl 0910.11032
Zudilin, V. V.
1997
One of the eight numbers $$\zeta(5),\zeta(7),\cdots,\zeta(17),\zeta(19)$$ is irrational. Zbl 1022.11035
Zudilin, V. V.
2001
On a combinatorial problem of Asmus Schmidt. Zbl 1126.11012
Zudilin, W.
2004
On the irrationality of the values of the zeta function at odd integer points. Zbl 1037.11048
Zudilin, V. V.
2001
Remarks on irrationality of $$q$$-harmonic series. Zbl 1044.11068
2002
Derivatives of Siegel modular forms and exponential functions. Zbl 1021.11013
Bertrand, D.; Zudilin, W.
2001
A generating function of the squares of Legendre polynomials. Zbl 1334.33022
2014
Rational approximations to a $$q$$-analogue of $$\pi$$ and some other $$q$$-series. Zbl 1213.11146
2008
A hypergeometric problem. Zbl 1178.33007
2009
On rational approximations of values of a certain class of entire functions. Zbl 0848.11031
Zudilin, V. V.
1995
Thetanulls and differential equations. Zbl 1021.11011
Zudilin, V. V.
2000
On a measure of irrationality for values of $$G$$-functions. Zbl 0931.11025
Zudilin, V. V.
1996
Binomial sums related to rational approximations to $$\zeta(4)$$. Zbl 1070.11029
Zudilin, V. V.
2004
Hankel determinants of zeta values. Zbl 1387.11054
2015
Apéry limits of differential equations of order 4 and 5. Zbl 1159.14019
Almkvist, Gert; van Straten, Duco; Zudilin, Wadim
2008
Lost in translation. Zbl 1285.33008
2013
Hypergeometry inspired by irrationality questions. Zbl 1450.11072
2019
On $$\mathrm{Sp}_4$$ modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds. Zbl 1283.11073
2010
An elementary proof of the irrationality of Tschakaloff series. Zbl 1204.11112
Zudilin, W.
2007
Hypergeometric transformations of linear forms in one logarithm. Zbl 1205.33008
2008
Crouching AGM, hidden modularity. Zbl 1437.11058
Cooper, Shaun; Guillera, Jesús; Straub, Armin; Zudilin, Wadim
2018
Recurrent sequences and the measure of irrationality of values of elliptic integrals. Zbl 0917.11031
Zudilin, V. V.
1997
Cancellation of factorials. Zbl 1030.11032
Zudilin, V. V.
2001
A common $$q$$-analogue of two supercongruences. Zbl 1439.33007
Guo, Victor J. W.; Zudilin, Wadim
2020
Congruences for $$q$$-binomial coefficients. Zbl 1431.11032
2019
On a $$q$$-deformation of modular forms. Zbl 1445.11014
Guo, Victor J. W.; Zudilin, Wadim
2019
Many odd zeta values are irrational. Zbl 1430.11097
Fischler, Stéphane; Sprang, Johannes; Zudilin, Wadim
2019
Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds. Zbl 1443.11053
Long, Ling; Tu, Fang-Ting; Yui, Noriko; Zudilin, Wadim
2019
Hypergeometry inspired by irrationality questions. Zbl 1450.11072
2019
Hypergeometric modular equations. Zbl 1428.33014
2019
Ramanujan-type formulae for $$1/\pi: q$$-analogues. Zbl 1436.11024
Guo, Victor J. W.; Zudilin, Wadim
2018
Many values of the Riemann zeta function at odd integers are irrational. (Beaucoup de valeurs aux entiers impairs de la fonction zêta de Riemann sont irrationnelles.) Zbl 1398.11109
Fischler, Stéphane; Sprang, Johannes; Zudilin, Wadim
2018
One of the odd zeta values from $$\zeta(5)$$ to $$\zeta(25)$$ is irrational. By elementary means. Zbl 1445.11063
2018
Euler’s factorial series and global relations. Zbl 1444.11037
2018
A modular supercongruence for $${}_6 F_5$$: an Apéry-like story. (Une supercongruence modulaire pour $${}_6 F_5$$: un conte à la Apéry.) Zbl 1429.11039
Osburn, Robert; Straub, Armin; Zudilin, Wadim
2018
Crouching AGM, hidden modularity. Zbl 1437.11058
Cooper, Shaun; Guillera, Jesús; Straub, Armin; Zudilin, Wadim
2018
A hypergeometric version of the modularity of rigid Calabi-Yau manifolds. Zbl 1456.11073
2018
A variation on the theme of Nicomachus. Zbl 1410.11079
Luca, Florian; Polanco, Geremías; Zudilin, Wadim
2018
Linear independence of dilogarithmic values. Zbl 1454.11131
2018
A study of elliptic gamma function and allies. Zbl 1440.11063
2018
On the Mahler measure of hyperelliptic families. Zbl 1434.11211
2017
A determinantal approach to irrationality. Zbl 1367.11062
2017
Holonomic alchemy and series for $$1/\pi$$. Zbl 1391.11165
Cooper, Shaun; Wan, James G.; Zudilin, Wadim
2017
On the (K.2) supercongruence of Van Hamme. Zbl 1400.11062
2016
Algebraic independence of Mahler functions via radial asymptotics. Zbl 1415.11104
Brent, Richard P.; Coons, Michael; Zudilin, Wadim
2016
On the Mahler measure of a family of genus 2 curves. Zbl 1347.11076
2016
Further explorations of Boyd’s conjectures and a conductor 21 elliptic curve. Zbl 1337.11072
Lalín, Matilde; Samart, Detchat; Zudilin, Wadim
2016
On the irrationality of generalized $$q$$-logarithm. Zbl 1415.11099
2016
On three theorems of Folsom, Ono and Rhoades. Zbl 1311.11026
2015
Multiple $$q$$-zeta brackets. Zbl 1312.11069
2015
Hankel determinants of zeta values. Zbl 1387.11054
2015
Positivity of rational functions and their diagonals. Zbl 1374.05023
2015
Neverending fractions. An introduction to continued fractions. Zbl 1307.11001
Borwein, Jonathan; van der Poorten, Alf; Shallit, Jeffrey; Zudilin, Wadim
2014
On the Mahler measure of $$1+X+1/X+Y +1/Y$$. Zbl 1378.11091
2014
Regulator of modular units and Mahler measures. Zbl 1386.11129
2014
On simultaneous Diophantine approximations to $$\zeta(2)$$ and $$\zeta(3)$$. Zbl 1315.11062
2014
Two hypergeometric tales and a new irrationality measure of $$\zeta (2)$$. Zbl 1307.11085
2014
A generating function of the squares of Legendre polynomials. Zbl 1334.33022
2014
Legendre polynomials and Ramanujan-type series for $$1/\pi$$. Zbl 1357.11123
Chan, Heng Huat; Wan, James; Zudilin, Wadim
2013
Period(d)ness of $$L$$-values. Zbl 1316.11038
2013
Ramanujan-type formulae for $$1/\pi$$: the art of translation. Zbl 1371.11162
2013
Lost in translation. Zbl 1285.33008
2013
Generating functions of Legendre polynomials: a tribute to Fred Brafman. Zbl 1282.33015
2013
From $$L$$-series of elliptic curves to Mahler measures. Zbl 1260.11062
2012
Densities of short uniform random walks. Zbl 1296.33011
Borwein, Jonathan M.; Straub, Armin; Wan, James; Zudilin, Wadim
2012
“Divergent” Ramanujan-type supercongruences. Zbl 1276.11027
2012
Cyclic $$q$$-MZSV sum. Zbl 1268.11119
Ohno, Yasuo; Okuda, Jun-Ichi; Zudilin, Wadim
2012
Dedekind’s $$\eta$$-function and Rogers-Ramanujan identities. Zbl 1234.05040
2012
Generating functions of Legendre polynomials: A tribute to Fred Brafman. Zbl 1242.33018
2012
Generalizations of Clausen’s formula and algebraic transformations of Calabi-Yau differential equations. Zbl 1223.33007
Almkvist, Gert; van Straten, Duco; Zudilin, Wadim
2011
New analogues of Clausen’s identities arising from the theory of modular forms. Zbl 1234.33009
Chan, Heng Huat; Tanigawa, Yoshio; Yang, Yifan; Zudilin, Wadim
2011
Arithmetic hypergeometric series. Zbl 1225.33008
Zudilin, V. V.
2011
A $$q$$-rious positivity. Zbl 1234.11023
Warnaar, S. Ole; Zudilin, W.
2011
The Erdős–Moser equation $$1^k+2^k+\cdots +(m-1)^k=m^k$$ revisited using continued fractions. Zbl 1231.11038
Gallot, Yves; Moree, Pieter; Zudilin, Wadim
2011
New representations for Apéry-like sequences. Zbl 1275.11035
2010
A refinement of Nesterenko’s linear independence criterion with applications to zeta values. Zbl 1206.11088
2010
A supercongruence motivated by the Legendre family of elliptic curves. Zbl 1252.11017
Chan, Heng Huat; Long, Ling; Zudilin, V. V.
2010
Experimental mathematics and mathematical physics. Zbl 1221.82006
2010
On $$\mathrm{Sp}_4$$ modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds. Zbl 1283.11073
2010
Ramanujan-type supercongruences. Zbl 1231.11147
2009
On the non-quadraticity of values of the $$q$$-exponential function and related $$q$$-series. Zbl 1232.11080
Krattenthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, Wadim
2009
Apéry’s theorem. Thirty years after. Zbl 1223.11089
2009
A hypergeometric problem. Zbl 1178.33007
2009
Zeta stars. Zbl 1228.11132
2008
Ramanujan-type formulae for $$1/\pi$$: a second wind? Zbl 1159.11053
2008
Rational approximations to a $$q$$-analogue of $$\pi$$ and some other $$q$$-series. Zbl 1213.11146
2008
Apéry limits of differential equations of order 4 and 5. Zbl 1159.14019
Almkvist, Gert; van Straten, Duco; Zudilin, Wadim
2008
Hypergeometric transformations of linear forms in one logarithm. Zbl 1205.33008
2008
Linear independence of values of Tschakaloff functions with different parameters. Zbl 1173.11044
2008
More Ramanujan-type formulae for $$1/\pi^2$$. Zbl 1203.11088
Zudilin, V. V.
2007
Quadratic transformations and Guillera’s formulas for $$1/\pi^2$$. Zbl 1144.33002
Zudilin, V. V.
2007
Irrationality measures for certain $$q$$-mathematical constants. Zbl 1153.11034
2007
Approximations to di- and tri-logarithms. Zbl 1220.65028
2007
A new lower bound for $$\|(3/2)^k\|$$. Zbl 1127.11049
2007
An elementary proof of the irrationality of Tschakaloff series. Zbl 1204.11112
Zudilin, W.
2007
Linear independence of values of Tschakaloff series. Zbl 1173.11043
Väänänen, K.; Zudilin, V. V.
2007
Basic hypergeometric series, $$q$$-analoges, of the values of the zeta function, and Eisenstein series. (Séries hypergéométriques basiques, $$q$$-analogues des valeurs de la fonction zêta et séries d’Eisenstein.) Zbl 1089.11038
Krattenthaler, C.; Rivoal, T.; Zudilin, W.
2006
Differential equations, mirror maps and zeta values. Zbl 1118.14043
2006
Euler’s constant, $$q$$-logarithms, and formulas of Ramanujan and Gosper. Zbl 1132.11056
2006
New irrationality measures for $$q$$-logarithms. Zbl 1158.11033
Matala-aho, Tapani; Väänänen, Keijo; Zudilin, Wadim
2006
Approximations to $$q$$-logarithms and $$q$$-dilogarithms, with applications to $$q$$-zeta values. Zbl 1088.11052
Zudilin, W.
2005
Ramanujan-type formulae and irrationality measures of some multiples of $$\pi$$. Zbl 1114.11064
Zudilin, V. V.
2005
Baker-type estimates for linear forms in the values of $$q$$-series. Zbl 1064.11054
2005
Well-poised generation of Apéry-like recursions. Zbl 1063.11026
2005
Computing powers of two generalizations of the logarithm. Zbl 1088.11015
2005
Arithmetic of linear forms involving odd zeta values. Zbl 1156.11327
2004
Heine’s basic transform and a permutation group for $$q$$-harmonic series. Zbl 1052.11053
2004
An essay on the irrationality measure of $$\pi$$ and other logarithms. Zbl 1140.11036
Zudilin, V. V.
2004
Well-poised hypergeometric transformations of Euler-type multiple integrals. Zbl 1065.11054
Zudilin, W.
2004
On theorems of Gelfond and Selberg concerning integral-valued entire functions. Zbl 1081.11051
2004
On a combinatorial problem of Asmus Schmidt. Zbl 1126.11012
Zudilin, W.
2004
Binomial sums related to rational approximations to $$\zeta(4)$$. Zbl 1070.11029
Zudilin, V. V.
2004
Algebraic relations for multiple zeta values. Zbl 1171.11323
Zudilin, V. V.
2003
Diophantine properties of numbers related to Catalan’s constant. Zbl 1028.11046
Rivoal, T.; Zudilin, W.
2003
Well-poised hypergeometric series for Diophantine problems of zeta values. Zbl 1156.11326
2003
The hypergeometric equation and Ramanujan functions. Zbl 1072.11052
Zudilin, W.
2003
An Apéry-like difference equation for Catalan’s constant. Zbl 1093.11075
Zudilin, W.
2003
On the transcendence degree of the differential field generated by Siegel modular forms. Zbl 1130.11020
Bertrand, D.; Zudilin, W.
2003
Irrationality of values of the Riemann zeta function. Zbl 1114.11305
Zudilin, W.
2002
Diophantine problems for $$q$$-zeta values. Zbl 1044.11066
Zudilin, V. V.
2002
On the integrality of power expansions related to hypergeometric series. Zbl 1043.11060
Zudilin, V. V.
2002
On the irrationality measure for a $$q$$-analogue of $$\zeta(2)$$. Zbl 1044.11067
Zudilin, W. V.
2002
A third-order Apéry-like recursion for $$\zeta(5)$$. Zbl 1041.11057
Zudilin, V. V.
2002
...and 15 more Documents
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#### Cited by 484 Authors
58 Zudilin, Wadim 45 Guo, Victor J. W. 18 Rivoal, Tanguy 15 Liu, Jicai 13 Fischler, Stéphane 11 Straub, Armin 10 Guillera, Jesús 10 He, Bing 10 Hessami Pilehrood, Khodabakhsh 10 Hessami Pilehrood, Tatiana 10 Wan, James Gu Feng 8 Borwein, Jonathan Michael 8 Chan, Heng Huat 8 Lalín, Matilde N. 8 Mao, Guo-Shuai 8 Matala-aho, Tapani 8 Rogers, Mathew D. 8 Väänänen, Keijo O. 7 Bachmann, Henrik 7 Cooper, Shaun 6 Bundschuh, Peter 6 Chu, Wenchang 6 Ebrahimi-Fard, Kurusch 6 Folsom, Amanda 6 Schlosser, Michael J. 6 Wang, Xiaoxia 6 Wei, Chuanan 5 Delaygue, Éric 5 Eie, Minking 5 Genčev, Marian 5 Kalita, Gautam 5 Long, Ling 5 Manchon, Dominique 5 Osburn, Robert 5 Samart, Detchat 5 Singer, Johannes Maria 5 Sun, Zhihong 5 Warnaar, S. Ole 5 Zhao, Jianqiang 5 Zhou, Yajun 4 Brunault, François 4 Coons, Michael 4 Krattenthaler, Christian Friedrich 4 Luca, Florian 4 Marcovecchio, Raffaele 4 Nesterenko, Yuriĭ Valentinovich 4 Pan, Hao 4 Pupyrev, Yuri A. 4 Sondow, Jonathan D. 4 Van Assche, Walter 4 van Straten, Duco 4 Ye, Dongxi 4 Zeng, Jiang 3 Berndt, Bruce Carl 3 Bouillot, Olivier 3 Bradley, David M. 3 Bringmann, Kathrin 3 Dixit, Atul 3 Guo, Li 3 Jana, Arijit 3 Jouhet, Frédéric 3 Machide, Tomoya 3 Maillard, Jean-Marie 3 Maji, Bibekananda 3 Movasati, Hossein 3 Murty, Maruti Ram 3 Ni, He-Xia 3 Ong, Yaolin 3 Pila, Jonathan 3 Roques, Julien 3 Sahu, Brundaban 3 Sprang, Johannes 3 Tachiya, Yohei 3 Wang, Su-Dan 3 Yang, Yifan 3 Yue, Mingbing 3 Zeilberger, Doron 3 Zlobin, S. A. 2 Allouche, Jean-Paul Simon 2 Almkvist, Gert 2 Bailey, David Harold 2 Baruah, Nayandeep Deka 2 Bell, Jason P. 2 Bertin, Marie-Jose 2 Bézivin, Jean-Paul 2 Blümlein, Johannes 2 Bostan, Alin 2 Cai, Tianxin 2 Calinescu, Corina 2 Castillo-Medina, Jaime 2 Chen, Shaoshi 2 Chen, William Yong-Chuan 2 Chen, Xiaojing 2 Chetry, Arjun Singh 2 Choi, Junesang 2 Cohl, Howard Saul 2 Dauguet, Simon 2 D’Aurizio, Jacopo 2 D’Hoker, Eric 2 Diamantis, Nikolaos ...and 384 more Authors
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#### Cited in 143 Serials
48 The Ramanujan Journal 42 Journal of Number Theory 36 International Journal of Number Theory 27 Journal of Mathematical Analysis and Applications 19 Proceedings of the American Mathematical Society 15 Mathematical Notes 14 Results in Mathematics 12 Journal de Théorie des Nombres de Bordeaux 12 Journal of Difference Equations and Applications 11 Advances in Applied Mathematics 11 Integral Transforms and Special Functions 11 Research in Number Theory 10 Advances in Mathematics 9 Bulletin of the Australian Mathematical Society 9 Journal of Approximation Theory 9 Journal of the Australian Mathematical Society 8 Compositio Mathematica 7 Israel Journal of Mathematics 7 Acta Arithmetica 7 Journal of Algebra 7 Journal of Mathematical Sciences (New York) 6 Journal of Computational and Applied Mathematics 6 Manuscripta Mathematica 6 Monatshefte für Mathematik 6 Transactions of the American Mathematical Society 6 Journal of Symbolic Computation 6 Journal of High Energy Physics 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Rocky Mountain Journal of Mathematics 5 Mathematics of Computation 5 Duke Mathematical Journal 5 Journal of Combinatorial Theory. Series A 5 Mathematische Zeitschrift 5 Integers 4 Functiones et Approximatio. Commentarii Mathematici 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Archiv der Mathematik 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the Japan Academy. Series A 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Experimental Mathematics 3 Journal of Integer Sequences 3 Proceedings of the Steklov Institute of Mathematics 3 Annales Mathématiques du Québec 3 Mathematics 3 Research in the Mathematical Sciences 3 Electronic Research Archive 2 American Mathematical Monthly 2 Journal of Mathematical Physics 2 Nuclear Physics. B 2 Problems of Information Transmission 2 Inventiones Mathematicae 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Annalen 2 Memoirs of the American Mathematical Society 2 Tokyo Journal of Mathematics 2 Constructive Approximation 2 International Journal of Mathematics 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Annales Mathématiques Blaise Pascal 2 Documenta Mathematica 2 Journal of Inequalities and Applications 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Communications in Contemporary Mathematics 2 Chebyshevskiĭ Sbornik 2 Journal of Physics A: Mathematical and Theoretical 1 Communications in Algebra 1 Computer Physics Communications 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Lithuanian Mathematical Journal 1 The Mathematical Gazette 1 Periodica Mathematica Hungarica 1 Journal of Geometry and Physics 1 Annales de l’Institut Fourier 1 Bulletin de la Société Mathématique de France 1 Colloquium Mathematicum 1 Functional Analysis and its Applications 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Journal of Applied Probability 1 Journal of Functional Analysis 1 Journal of the Mathematical Society of Japan 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Slovaca 1 Mathematika 1 Nagoya Mathematical Journal 1 Notre Dame Journal of Formal Logic 1 Rendiconti del Seminario Matematico della Università di Padova 1 Theoretical Computer Science 1 Transactions of the Moscow Mathematical Society 1 Tsukuba Journal of Mathematics ...and 43 more Serials
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#### Cited in 45 Fields
489 Number theory (11-XX) 265 Special functions (33-XX) 107 Combinatorics (05-XX) 45 Algebraic geometry (14-XX) 23 Approximations and expansions (41-XX) 19 Quantum theory (81-XX) 18 Ordinary differential equations (34-XX) 18 Numerical analysis (65-XX) 17 Functions of a complex variable (30-XX) 16 Sequences, series, summability (40-XX) 16 Computer science (68-XX) 14 Probability theory and stochastic processes (60-XX) 12 $$K$$-theory (19-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Nonassociative rings and algebras (17-XX) 9 Associative rings and algebras (16-XX) 9 Integral transforms, operational calculus (44-XX) 7 Mathematical logic and foundations (03-XX) 7 Real functions (26-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Field theory and polynomials (12-XX) 5 Partial differential equations (35-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Difference and functional equations (39-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Commutative algebra (13-XX) 3 Differential geometry (53-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX)
#### Wikidata Timeline
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https://zbmath.org/authors/?q=ai%3Acohen.jacob-willem
|
## Cohen, Jacob Willem
Compute Distance To:
Author ID: cohen.jacob-willem Published as: Cohen, J. W.; Cohen, Jacob Willem Further Spellings: Cohen, Wim External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 64 Publications since 1957, including 7 Books 1 Contribution as Editor · 3 Further Contributions Biographic References: 6 Publications Co-Authors: 6 Co-Authors with 9 Joint Publications 165 Co-Co-Authors
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### Co-Authors
50 single-authored 5 Boxma, Onno Johan 2 Rubinovitch, Michael 1 Bailey, Norman T. J. 1 Callaert, Herman 1 Chesson, Peter L. 1 deLange, S. J. 1 Disney, Ralph L. 1 Down, Douglas G. 1 Ewens, Warren J. 1 Frieze, Alan Michael 1 Gani, Joseph Mark 1 Greenber, I. 1 Hannan, Edward James 1 Hastings, Alan Matthew 1 Hooghiemstra, Gerard 1 Huffels, N. 1 Kareiva, P. M. 1 Keilson, Julian 1 Kendall, David George 1 Levin, Simon Asher 1 Matula, David W. 1 Neuts, Marcel Fernand 1 Okubo, Akira 1 Pack, Charles D. 1 Pimm, Stuart L. 1 Prabhu, Narahari Umanath 1 Slissenko, Anatol 1 Solomon, Herbert 1 Syski, Ryszard 1 Tweedie, Richard Lewis 1 van Marion, E. W. B. 1 Vere-Jones, David 1 Watson, Geoffrey S. 1 Whittle, Peter 1 Yodzis, Peter
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### Serials
11 Journal of Applied Probability 6 Queueing Systems 5 Stochastic Processes and their Applications 3 Mathematics of Operations Research 3 Statistica Neerlandica 3 Journal of Applied Mathematics and Stochastic Analysis 3 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 2 Advances in Applied Probability 2 Journal of Engineering Mathematics 2 Operations Research 2 Simon Stevin 1 Acta Informatica 1 Theory of Probability and its Applications 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Delft Progress Report 1 Communications in Statistics. Stochastic Models 1 Nieuw Archief voor Wiskunde. Derde Serie 1 Applied Probability 1 Lecture Notes in Economics and Mathematical Systems 1 North-Holland Mathematics Studies 1 Studies in Probability, Optimization and Statistics 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Applied Scientific Research, Section B
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### Fields
47 Probability theory and stochastic processes (60-XX) 23 Operations research, mathematical programming (90-XX) 5 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Integral equations (45-XX) 1 Biology and other natural sciences (92-XX)
### Citations contained in zbMATH Open
52 Publications have been cited 800 times in 531 Documents Cited by Year
The single server queue. Rev. ed. Zbl 0481.60003
Cohen, J. W.
1982
The single server queue. Zbl 0183.49204
Cohen, J. W.
1969
Boundary value problems in queueing system analysis. Zbl 0515.60092
Cohen, J. W.; Boxma, O. J.
1983
On up- an downcrossings. Zbl 0365.60108
Cohen, J. W.
1977
On regenerative processes in queueing theory. Zbl 0323.60083
Cohen, J. W.
1976
Some results on regular variation for distributions in queueing and fluctuation theory. Zbl 0258.60076
Cohen, J. W.
1973
Boundary value problems in queueing theory. Zbl 0662.60098
Cohen, J. W.
1988
Single server queues with restricted accessibility. Zbl 0186.24503
Cohen, J. W.
1969
The multiple phase service network with generalized processor sharing. Zbl 0396.68038
Cohen, J. W.
1979
A two-queue, one-server model with priority for the longer queue. Zbl 0655.60090
Cohen, J. W.
1987
Analysis of random walks. Zbl 0809.60081
Cohen, J. W.
1992
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions. Zbl 0997.60113
Boxma, O. J.; Cohen, J. W.
1999
Approximations of the mean waiting time in an M/G/s queueing system. Zbl 0439.60090
Boxma, O. J.; Cohen, J. W.; Huffels, N.
1979
Extreme value distribution for the M/G/1 and the G/M/1 queueing systems. Zbl 0162.49302
Cohen, J. W.
1968
The inadequacy of the classical stress-strain relations for the right helicoidal shell. Zbl 0151.38101
Cohen, J. W.
1960
On processor sharing and random service. Zbl 0562.60097
Cohen, J. W.
1984
Analysis of the asymmetrical shortest two-server queueing model. Zbl 0922.60084
Cohen, J. W.
1998
On level crossings and cycles in dam processes. Zbl 0389.60077
Cohen, J. W.; Rubinovitch, Michael
1977
On the optimal switching level for an M/G/1 queueing system. Zbl 0339.60085
Cohen, J. W.
1976
Brownian excursion, the M/M/1 queue and their occupation times. Zbl 0497.60073
Cohen, J. W.; Hooghiemstra, G.
1981
Asymptotic relations in queueing theory. Zbl 0258.60077
Cohen, J. W.
1973
Superimposed renewal processes and storage with gradual input. Zbl 0281.60107
Cohen, J. W.
1974
Single server queue with uniformly bounded virtual waiting time. Zbl 0164.48103
Cohen, J. W.
1968
The single server queue. 2nd impression of the 2nd revised ed. 1982. Zbl 0746.60093
Cohen, J. W.
1992
On the asymmetric clocked buffered switch. Zbl 0919.90062
Cohen, J. W.
1998
Properties of the process of level crossings during a busy cycle of the M/G/I queueing system. Zbl 0383.60089
Cohen, J. W.
1978
The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1. Zbl 0178.20804
Cohen, J. W.
1967
On a class of two-dimensional nearest-neighbour random walks. Zbl 0807.60065
Cohen, J. W.
1994
Level crossings and stationary distributions for general dams. Zbl 0437.60078
Rubinovitch, Michael; Cohen, J. W.
1980
Sensitivity and insensitivity. Zbl 0452.60092
Cohen, J. W.
1980
On the role of Rouché’s theorem in queueing analysis. Zbl 0879.60097
Cohen, J. W.; Down, D. G.
1996
A lemma on regular variation of a transient renewal function. Zbl 0237.60036
Callaert, H.; Cohen, J. W.
1972
On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue. Zbl 0238.60073
Cohen, J. W.
1972
On a single-server queue with group arrivals. Zbl 0348.60125
Cohen, J. W.
1976
On the busy periods for the M/G/1 queue with finite and with infinite waiting room. Zbl 0227.60053
Cohen, J. W.
1971
The suprema of the actual and virtual waiting times during a busy cycle of the $$K_m/K_n/1$$ queueing system. Zbl 0239.60090
Cohen, J. W.
1972
The Wiener-Hopf technique in applied probability. Zbl 0334.60030
Cohen, J. W.
1975
On the M/G/2 queueing model. Zbl 0482.60088
Cohen, J. W.
1982
The full availability group of trunks with an arbitrary distribution of the inter-arrival times and a negative exponential holding time distribution. Zbl 0129.10901
Cohen, J. W.
1957
On derived and nonstationary Markov chains. Zbl 0143.19901
Cohen, J. W.
1963
On two integral equations of queueing theory. Zbl 0153.20101
Cohen, J. W.
1967
Distribution of crossings of level $$K$$ in a busy cycle of the M/G/1 queue. Zbl 0162.49401
Cohen, J. W.; Greenber, I.
1968
The craft of probabilistic modelling. A collection of personal accounts. Zbl 0605.60006
1986
On periodic Pollaczek waiting time processes. Zbl 0858.60079
Cohen, J. W.
1996
Community ecology. A workshop held at Davis, CA, April 1986. Zbl 0696.92021
1988
Some ideas and models in reliability theory. Zbl 0278.60064
Cohen, J. W.
1974
Derived Markov chains. I, II, III. Zbl 0103.36401
Cohen, J. W.
1962
Boundary value problems in queueing system analysis. (Granichnye zadachi v teorii massovogo obsluzhivaniya). Transl. from English by A. D. Vajnshtejn and A. Ya. Krejnin. Transl. ed. and with a preface and notes by V. V. Kalashnikov. Zbl 0662.60097
Cohen, Jacob Willem; Boxma, Onno J.
1987
On the random walk with zero drifts in the first quadrant of $${\mathbb{R}{}}_ 2$$. Zbl 0761.60059
Cohen, J. W.
1992
A survey of the evolution of queueing theory. Zbl 0565.60076
Cohen, J. W.; Boxma, O. J.
1985
On the attained waiting time. Zbl 0729.60091
Cohen, J. W.
1991
Random walk with a heavy-tailed jump distribution. Zbl 0993.60096
Cohen, J. W.
2002
Random walk with a heavy-tailed jump distribution. Zbl 0993.60096
Cohen, J. W.
2002
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions. Zbl 0997.60113
Boxma, O. J.; Cohen, J. W.
1999
Analysis of the asymmetrical shortest two-server queueing model. Zbl 0922.60084
Cohen, J. W.
1998
On the asymmetric clocked buffered switch. Zbl 0919.90062
Cohen, J. W.
1998
On the role of Rouché’s theorem in queueing analysis. Zbl 0879.60097
Cohen, J. W.; Down, D. G.
1996
On periodic Pollaczek waiting time processes. Zbl 0858.60079
Cohen, J. W.
1996
On a class of two-dimensional nearest-neighbour random walks. Zbl 0807.60065
Cohen, J. W.
1994
Analysis of random walks. Zbl 0809.60081
Cohen, J. W.
1992
The single server queue. 2nd impression of the 2nd revised ed. 1982. Zbl 0746.60093
Cohen, J. W.
1992
On the random walk with zero drifts in the first quadrant of $${\mathbb{R}{}}_ 2$$. Zbl 0761.60059
Cohen, J. W.
1992
On the attained waiting time. Zbl 0729.60091
Cohen, J. W.
1991
Boundary value problems in queueing theory. Zbl 0662.60098
Cohen, J. W.
1988
Community ecology. A workshop held at Davis, CA, April 1986. Zbl 0696.92021
1988
A two-queue, one-server model with priority for the longer queue. Zbl 0655.60090
Cohen, J. W.
1987
Boundary value problems in queueing system analysis. (Granichnye zadachi v teorii massovogo obsluzhivaniya). Transl. from English by A. D. Vajnshtejn and A. Ya. Krejnin. Transl. ed. and with a preface and notes by V. V. Kalashnikov. Zbl 0662.60097
Cohen, Jacob Willem; Boxma, Onno J.
1987
The craft of probabilistic modelling. A collection of personal accounts. Zbl 0605.60006
1986
A survey of the evolution of queueing theory. Zbl 0565.60076
Cohen, J. W.; Boxma, O. J.
1985
On processor sharing and random service. Zbl 0562.60097
Cohen, J. W.
1984
Boundary value problems in queueing system analysis. Zbl 0515.60092
Cohen, J. W.; Boxma, O. J.
1983
The single server queue. Rev. ed. Zbl 0481.60003
Cohen, J. W.
1982
On the M/G/2 queueing model. Zbl 0482.60088
Cohen, J. W.
1982
Brownian excursion, the M/M/1 queue and their occupation times. Zbl 0497.60073
Cohen, J. W.; Hooghiemstra, G.
1981
Level crossings and stationary distributions for general dams. Zbl 0437.60078
Rubinovitch, Michael; Cohen, J. W.
1980
Sensitivity and insensitivity. Zbl 0452.60092
Cohen, J. W.
1980
The multiple phase service network with generalized processor sharing. Zbl 0396.68038
Cohen, J. W.
1979
Approximations of the mean waiting time in an M/G/s queueing system. Zbl 0439.60090
Boxma, O. J.; Cohen, J. W.; Huffels, N.
1979
Properties of the process of level crossings during a busy cycle of the M/G/I queueing system. Zbl 0383.60089
Cohen, J. W.
1978
On up- an downcrossings. Zbl 0365.60108
Cohen, J. W.
1977
On level crossings and cycles in dam processes. Zbl 0389.60077
Cohen, J. W.; Rubinovitch, Michael
1977
On regenerative processes in queueing theory. Zbl 0323.60083
Cohen, J. W.
1976
On the optimal switching level for an M/G/1 queueing system. Zbl 0339.60085
Cohen, J. W.
1976
On a single-server queue with group arrivals. Zbl 0348.60125
Cohen, J. W.
1976
The Wiener-Hopf technique in applied probability. Zbl 0334.60030
Cohen, J. W.
1975
Superimposed renewal processes and storage with gradual input. Zbl 0281.60107
Cohen, J. W.
1974
Some ideas and models in reliability theory. Zbl 0278.60064
Cohen, J. W.
1974
Some results on regular variation for distributions in queueing and fluctuation theory. Zbl 0258.60076
Cohen, J. W.
1973
Asymptotic relations in queueing theory. Zbl 0258.60077
Cohen, J. W.
1973
A lemma on regular variation of a transient renewal function. Zbl 0237.60036
Callaert, H.; Cohen, J. W.
1972
On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue. Zbl 0238.60073
Cohen, J. W.
1972
The suprema of the actual and virtual waiting times during a busy cycle of the $$K_m/K_n/1$$ queueing system. Zbl 0239.60090
Cohen, J. W.
1972
On the busy periods for the M/G/1 queue with finite and with infinite waiting room. Zbl 0227.60053
Cohen, J. W.
1971
The single server queue. Zbl 0183.49204
Cohen, J. W.
1969
Single server queues with restricted accessibility. Zbl 0186.24503
Cohen, J. W.
1969
Extreme value distribution for the M/G/1 and the G/M/1 queueing systems. Zbl 0162.49302
Cohen, J. W.
1968
Single server queue with uniformly bounded virtual waiting time. Zbl 0164.48103
Cohen, J. W.
1968
Distribution of crossings of level $$K$$ in a busy cycle of the M/G/1 queue. Zbl 0162.49401
Cohen, J. W.; Greenber, I.
1968
The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1. Zbl 0178.20804
Cohen, J. W.
1967
On two integral equations of queueing theory. Zbl 0153.20101
Cohen, J. W.
1967
On derived and nonstationary Markov chains. Zbl 0143.19901
Cohen, J. W.
1963
Derived Markov chains. I, II, III. Zbl 0103.36401
Cohen, J. W.
1962
The inadequacy of the classical stress-strain relations for the right helicoidal shell. Zbl 0151.38101
Cohen, J. W.
1960
The full availability group of trunks with an arbitrary distribution of the inter-arrival times and a negative exponential holding time distribution. Zbl 0129.10901
Cohen, J. W.
1957
all top 5
### Cited by 570 Authors
54 Boxma, Onno Johan 18 Adan, Ivo J. B. F. 18 Perry, David 13 Knessl, Charles 13 Stadje, Wolfgang 12 van Leeuwaarden, Johan S. H. 11 Cohen, Jacob Willem 10 Mandjes, Michel Robertus Hendrikus 10 Zwart, Bert P. 9 Borst, Sem C. 9 Landriault, David 9 Whitt, Ward 8 Vlasiou, Maria 8 Walraevens, Joris 7 Asmussen, Søren 7 Bekker, René 7 Bruneel, Herwig 7 Dimitriou, Ioannis 7 He, Qi-Ming 7 Kella, Offer 7 Resing, Jacques A. C. 6 Abate, Joseph 6 Boucherie, Richard J. 6 Chaudhry, Mohan L. 6 Guillemin, Fabrice M. 6 Kapodistria, Stella 6 Kempa, Wojciech M. 6 Winands, Erik M. M. 6 Zacks, Shelemyahu 6 Zhao, Yiqiang Q. 5 Boon, Marko A. A. 5 Matsak, Ivan K. 5 Minkevičius, Saulius 5 Raschel, Kilian 5 Sivazlian, B. D. 5 van Ommeren, Jan-Kees C. W. 5 Yao, Haishen 4 Agarwal, Manju Lata 4 Albrecher, Hansjörg 4 Badila, E. S. 4 Blanc, Johannes Pieter Cornelis 4 Fiems, Dieter 4 Gakis, K. G. 4 Hooghiemstra, Gerard 4 Kovalenko, Igor Mykolaĭovych 4 Li, Hui 4 Núñez-Queija, Rudesindo 4 Parthasarathy, Panamalai Ramarao 4 Shi, Tianxiang 4 Wessels, Jaap 4 Willmot, Gordon E. 3 Andersen, Lars Nørvang 3 Bae, Jongho 3 Buzacott, John Alan 3 Claeys, Dieter 3 Down, Douglas G. 3 El-hady, El-sayed 3 Fackrell, Mark 3 Gittenberger, Bernhard 3 Glynn, Peter W. 3 Grassmann, Winfried K. 3 Hanbali, Ahmad Al 3 Harris, Carl M. 3 Ivanovs, Jevgeņijs 3 Janssen, Augustus Josephus Elizabeth Maria 3 Jonckheere, Matthieu 3 Kadankov, Viktor F. 3 Kadankova, Tat’yana V. 3 Kosiński, Kamil Marcin 3 Li, Shuanming 3 Löpker, Andreas H. 3 Louchard, Guy 3 Morrison, John A. 3 Nain, Philippe 3 Palmowski, Zbigniew 3 Serfozo, Richard F. 3 Shanthikumar, Jeyaveerasingam George 3 Shneer, Vsevolod Vladislavovich 3 Templeton, James G. C. 3 Tijms, Henk C. 3 Veraverbeke, Noël 3 Yashkov, Sergei Fedorovich 3 Yechiali, Uri 2 Abramov, Vyacheslav M. 2 Altiok, Tayfur 2 Barbe, Philippe 2 Brill, Percy H. 2 Brito, Margarida 2 Brzdęk, Janusz 2 Chae, Kyung Chul 2 Chen, Yanting 2 Chydzinski, Andrzej 2 Daduna, Hans 2 De Turck, Koen 2 De Vuyst, Stijn 2 Dębicki, Krzysztof 2 Denisov, Denis E. 2 Drmota, Michael 2 Embrechts, Paul 2 Fayolle, Guy ...and 470 more Authors
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### Cited in 114 Serials
99 Queueing Systems 33 Operations Research Letters 32 Stochastic Processes and their Applications 31 Stochastic Models 30 European Journal of Operational Research 24 Probability in the Engineering and Informational Sciences 19 Annals of Operations Research 16 Insurance Mathematics & Economics 15 Journal of Applied Probability 12 Computers & Operations Research 10 Advances in Applied Probability 9 Statistica Neerlandica 7 Applied Mathematics and Computation 7 Mathematical Methods of Operations Research 6 Stochastic Analysis and Applications 6 Applied Mathematical Modelling 5 Acta Informatica 5 Computers & Mathematics with Applications 5 Journal of Mathematical Analysis and Applications 5 Naval Research Logistics 5 Naval Research Logistics Quarterly 4 Journal of Computational and Applied Mathematics 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 4 Cybernetics and Systems Analysis 3 Journal of Soviet Mathematics 3 Scandinavian Actuarial Journal 3 Theoretical Computer Science 3 Acta Applicandae Mathematicae 3 Annales Scientifiques de l’Université de Clermont-Ferrand II. Probabilités et Applications 3 Sequential Analysis 3 The Annals of Applied Probability 3 Communications in Statistics. Theory and Methods 3 Top 3 Scandinavian Actuarial Journal 3 Journal of Systems Science and Complexity 2 Studies in Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Optimization 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 European Journal of Applied Mathematics 2 Aequationes Mathematicae 2 International Journal of Computer Mathematics 2 SIAM Journal on Applied Mathematics 2 Zeitschrift für Operations Research. Serie A: Theorie 2 Theory of Probability and Mathematical Statistics 2 Journal of Mathematical Sciences (New York) 2 Parallel Algorithms and Applications 2 Methodology and Computing in Applied Probability 2 ASTIN Bulletin 2 Journal of the Korean Statistical Society 2 Advances in Operations Research 2 Stochastic Systems 1 Bulletin of the Australian Mathematical Society 1 International Journal of Mathematical Education in Science and Technology 1 International Journal of Systems Science 1 Journal of Engineering Mathematics 1 Lithuanian Mathematical Journal 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Metrika 1 Physica A 1 Stochastics 1 The Annals of Probability 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Computing 1 Information Sciences 1 International Journal of Computer & Information Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Mathematische Nachrichten 1 Mathematics of Operations Research 1 Proceedings of the American Mathematical Society 1 Trabajos de Estadistica y de Investigacion Operativa 1 European Journal of Combinatorics 1 OR Spektrum 1 Journal of Information & Optimization Sciences 1 Systems & Control Letters 1 Statistics & Probability Letters 1 Journal of Time Series Analysis 1 Probability and Mathematical Statistics 1 American Journal of Mathematical and Management Sciences 1 Applied Stochastic Models and Data Analysis 1 Annales Scientifiques de l’Université Blaise Pascal Clermont-Ferrand II. Probabilités et Applications 1 Journal of Applied Mathematics and Stochastic Analysis 1 Random Structures & Algorithms 1 Discrete Event Dynamic Systems 1 Automation and Remote Control 1 Linear Algebra and its Applications 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 ZOR. Zeitschrift für Operations Research 1 Potential Analysis 1 Applied Mathematics. Series B (English Edition) 1 Georgian Mathematical Journal 1 The Electronic Journal of Combinatorics 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings ...and 14 more Serials
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### Cited in 29 Fields
423 Probability theory and stochastic processes (60-XX) 329 Operations research, mathematical programming (90-XX) 64 Computer science (68-XX) 32 Statistics (62-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Functions of a complex variable (30-XX) 14 Numerical analysis (65-XX) 10 Systems theory; control (93-XX) 8 Combinatorics (05-XX) 4 Ordinary differential equations (34-XX) 4 Difference and functional equations (39-XX) 4 Integral equations (45-XX) 4 Biology and other natural sciences (92-XX) 4 Information and communication theory, circuits (94-XX) 3 History and biography (01-XX) 3 Special functions (33-XX) 3 Approximations and expansions (41-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Partial differential equations (35-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-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.
| 2022-10-01T18:04:44 |
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https://finalfantasy.fandom.com/wiki/Comet_(Final_Fantasy_VII_ability)
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## FANDOM
37,202 Pages
Non-elemental attack
Description
Comet is a magic spell in Final Fantasy VII granted by the Comet Materia. It is the first-tier Comet spell below Comet2. It is a powerful non-elemental spell that summons a comet to attack a target for heavy damage.
## StatsEdit
Magic Materia Comet, Master Magic Major non-elemental damage. 70 Added Cut, Final Attack, HP Absorb, Magic Counter, MP Absorb, MP Turbo, Quadra Magic, Sneak Attack, Steal as Well No
Comet deals damage in the following formula:
$(80 / 16) * [ (Level + Magical Attack) * 6 ]$
where "Level" is the caster's current level and "Magical Attack" is their Magic atk stat. This is effectively 5x the base magic damage.
## UseEdit
Comet can be used by characters with the Comet Materia at level 1. It deals heavy non-elemental magic damage to a target and cannot be reflected making it useful against any enemy and in any situation. Though it cannot exploit a vulnerability to an element, it cannot be resisted by an elemental resistance either.
Comet should be amplified by pairing the Comet Materia with Support Materia. Since it is good against all enemies, it is a great choice to link with Magic Counter. MP Absorb can also mitigate its high MP cost, while HP Absorb can provide durability to spellcasters. MP Turbo or Quadra Magic can amplify its already strong damage to single targets. Unlike most magic, Comet cannot be paired with All.
Comet is one of the strongest spells in the game. Though spells from the Contain Materia are slightly more powerful, they are also elemental, meaning they are easier to resist. Comet is outclassed by Ultima, a non-elemental spell that deals more damage and also hits all targets.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-02-21T19:59:16 |
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https://par.nsf.gov/biblio/10305476-every-positive-integer-order-ordinary-abelian-variety-over-mathbb-_2
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Every positive integer is the order of an ordinary abelian variety over $${{\mathbb {F}}}_2$$
Abstract
We show that for every integer$$m > 0$$$m>0$, there is an ordinary abelian variety over $${{\mathbb {F}}}_2$$${F}_{2}$that has exactlymrational points.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10305476
Journal Name:
Research in Number Theory
Volume:
7
Issue:
4
ISSN:
2522-0160
Publisher:
Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$$\left({10}^{-7}\lesssim \mathrm{Re}\lesssim {10}^{-3}\right)$. Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$$\mathrm{Re}=\frac{{v}_{0}{x}_{0}}{\nu }$, wherev0corresponds to the maximum wetting speed on a flat, dry surface andx0is the extension length of the liquidmore »
We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000$$\hbox {cm}^2\,\hbox {V}^{-1}\,\hbox {s}^{-1}$$${\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}{\text{V}}^{-1}\phantom{\rule{0ex}{0ex}}{\text{s}}^{-1}$), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of anin-planeelectric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from$$\lambda =3$$$\lambda =3$to 12$$\upmu$$$\mu$m by adjusting themore »
The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropics-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_{m}\right)$and show that its angular dependence strongly varies below$${T}_{{\rm{c}}}$$${T}_{c}$. We show that this variation is a signature of QC pairing and comes about because there are multiples-wave pairing instabilities with closely spaced transition temperatures$${T}_{{\rm{c}},n}$$${T}_{c,n}$. Taken alone, each instability would produce a gap$$\Deltamore »$\Delta \left(\theta ,{\omega }_{m}\right)$that changes sign$$8n$$$8n$times along the Fermi surface. We show that the equilibrium gap$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_{m}\right)$is a superposition of multiple components that are nonlinearly induced below the actual$${T}_{{\rm{c}}}={T}_{{\rm{c}},0}$$${T}_{c}={T}_{c,0}$, and get resonantly enhanced at$$T={T}_{{\rm{c}},n}\ <\ {T}_{{\rm{c}}}$$$T={T}_{c,n}\phantom{\rule{0ex}{0ex}}<\phantom{\rule{0ex}{0ex}}{T}_{c}$. This gives rise to strong temperature variation of the angular dependence of$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_{m}\right)$. This variation progressively disappears away from a QC point. 4. Abstract We evaluate the$$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$${a}_{1}\left(1260\right)\to \pi \sigma \left({f}_{0}\left(500\right)\right)$decay width from the perspective that the$$a_1(1260)$$${a}_{1}\left(1260\right)$resonance is dynamically generated from the pseudoscalar–vector interaction and the$$\sigma $$$\sigma$arises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with$$a_1(1260) \rightarrow \rho \pi $$${a}_{1}\left(1260\right)\to \rho \pi$followed by$$\rho \rightarrow \pi \pi $$$\rho \to \pi \pi$and a fusion of two pions within the loop to produce the$$\sigma $$$\sigma$provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decaymore » 5. Abstract We study the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries, which is referred to as the$$\ell _0$$${\ell }_{0}$-norm of the vector. Our main results are new improved bounds on the minimal$$\ell _0$$${\ell }_{0}$-norm of solutions to systems$$A\varvec{x}=\varvec{b}$$$Ax=b$, where$$A\in \mathbb {Z}^{m\times n}$$$A\in {Z}^{m×n}$,$${\varvec{b}}\in \mathbb {Z}^m$$$b\in {Z}^{m}$and$$\varvec{x}$$$x$is either a general integer vector (lattice case) or a non-negative integer vector (semigroup case). In certain cases, we give polynomial time algorithms for computing solutions with$$\ell _0${\ell }_{0}$-norm satisfying the obtained bounds. We show that our bounds aremore »
| 2022-08-16T03:50:17 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/4868/2897
|
Finite Element Magnetostatic Analysis of Magnetostrictive (Tb<sub>0.3</sub>Dy<sub>0.7</sub>Fe<sub>1.95</sub>) Actuator with Different Housing Materials
The nanocomposite of TiO2-MWCNTs has been synthesised by simple hydrothermal route showing significant enhancement in the photocatalytic activity for the degradation of methyl orange dye (MO). Several characterisations employed were X-ray diffraction (XRD), Scanning electron microscopy (SEM), Energy-dispersive X-ray spectroscopy (EDX), Transmission electron microscopy (TEM), Raman spectroscopy.XRD pattern shows the formation of anatase phase in prepared TiO2 which was retained in TiO2-MWCNTs composite as well. The Raman spectrum of prepared TiO2-MWCNT shows the interface integration of TiO2 and MWCNTs which is further supported by TEM data. Complete decolorisation and degradation of dye using TiO2-MWCNTs nanocomposite has been observed only in 45 minutes of UV irradiation. 65 per cent reduction in chemical oxygen demand (COD) value of treated dye shows substantial mineralisation of dye by composite catalyst. Dye degradation reactions were found to follow first order kinetics.
The intensity and uniformity of a magnetic field are the key factors that influence the performance of a giant magnetostrictive actuator. These factors govern the sensitivity and linearity of the output motion. Moreover, the domain of drive current to meet design requirement and linear working domain of a magnetostrictive actuator can be effectively computed by analysing the magnetic field. In magnetic field analysis the common methods existing in practice to find associated magnetic field parameters like B, H and f are reluctance method, finite difference method and finite element method. The effective rate of flux transfer to the Terfenol-D rod depends on the permeability of housing material. An insight in to flux density distribution could be perceived by magnetostatic analysis using finite element method. Studies have been carried out with different types of magnetic circuits to understand the magnetic field distribution along the magnetostrictive rod using FEA1 and COSMOSM2. Theoretically magnetic field parameters for the given strain and force requirement3 and the effect of magnetic circuit components like gap’s magnetic permeability, evenness of driving magnetic field4 has been analysed. Magnetic circuit of magnetostrictive actuator developed for different applications like undersea propagation5, precise controlled flow6, low machining precision problem affected due to vibration disturbance7 and precise machining of non-cylinder pin-hole of a piston8 has been analysed. Comparison of experimental and numerical results of magnetic flux density obtained with FEMM9,10 has shown good agreement. FEA analysis using Ansoft has been proved effective and dose support theoretically the design of GMM actuator and GMM motor11. Radial distribution rules of internal magnetic field intensity and internal stress and strain in a high frequency driven Terfenol-D rod provided theoretical guidance for the development of magnetostrictive application devices using ANSYS software12,13. In all these studies the emphasis is made for the optimisation of magnetic circuit of an actuator to enhance the intensity and uniformity of magnetic field intensity. The output displacement and force of the Terfenol-D linear actuator is mainly decided by the distribution of the magnetic field in Terfenol-D rod. In order to gain a magnetic field which meets the drive requirements, the relationship between the current supplied to actuator’s coils and magnetic field intensity in Terfenol-D rod should be analysed in the process of electromagnetic design. The objective of the present paper is to provide a detailed overview involved in magnetic field analysis, under direct current input for a giant magnetostrictive actuator with different housing materials having different permeabilities namely mild steel, cast iron and aluminium, using finite element method.
The design of actuator has been carried out based on magnetic field requirements. Terfenol-D rod surrounded by coils (TC layout) is chosen for analysing the actuator. This layout consists of two co-axially placed coils namely coil 1 and coil 2. By providing DC input to coil 1, a bias magnetic field will be generated and helps to achieve linear response and over which is superimposed the magnetic field strength produced by coil 2 due to direct current or alternating current input. The Terfenol-D rod and co-axially placed coils are enclosed in a housing made up of different housing materials namely mild steel, cast iron and aluminium respectively. The magnetic circuit of an actuator is composed of other components like plunger and aluminium bobbins as shown in Fig. 1(a). Since the axial length and diameter of co-axial coils is finite, end effect and magnetic leakage are unavoidable. Hence the driving magnetic field is inhomogeneous. Therefore, the lengths of co-axially placed coils are chosen slightly longer than that of the Terfenol-D rod, which results in the rod being surrounded by homogeneous magnetic field. A close magnetic circuit structure is adopted to reduce the leakage of flux. A work out on the number of turns for coil 1 and coil 2 has been arrived at using the ampere’s law and reluctance approach. The number of turns for coil 1 is 560 and coil 2 is 440. Length of coil is 80 mm. Maximum amperage of the copper wires used for the coils is 4 A. The solenoid coils are capable of providing 50 kA/m of magnetic field. Terfenol-D rod of diameter 28 mm and length 80 mm are chosen in the present work. The Terfenol-D actuator proposed here is used for operating the friction pads of a disc brake system.
Magnetic flux density has been measured using Lakeshore guassmeter-410 with hall probes HT5891 (Transverse Probe) and HA3863 (Axial Probe) as shown in Fig. 1(b). Transverse probe has a hall sensor mounted parallel to the probe axis and measures magnetic fields perpendicular to the probe axis. Axial probe has a hall sensor mounted perpendicular to the probe axis and measures magnetic fields parallel to the probe axis. APLAB-LD6405 power supply is used for varying DC input to coils from 0A to 4A in a step of 0.25 A. The distance between the coils and the probe is maintained constant 5 mm during measurement.
Figure 1. (a) Layout and structure of a terfenol-D actuator, (b) Experimental setup.
Under static magnetic fields the energy input due to magnetic field should be equal to the magnetic energy stored in the material provided there is no power loss14 hence
${W}_{in}={W}_{stored}$ (1)
Input energy in magnetic fields is a function of current density J and the corresponding energy. $1}{2}\int J.Adv$ and the energy stored is a function of magnetic induction B and the corresponding energy is. Therefore Eqn. (1) can be written as
$1}{2}\int J.Adv=\int \frac{{B}^{2}}{2\mu }dv$ (2)
The magnetic vector potential A is related to the magnetic flux density as follows
$B=\nabla ×A$ (3)
The energy functional is the difference between stored energy and input energyfor linear magnetic fields.
$F={W}_{\text{stored}}-{W}_{\text{input}}$ (4)
$F=\left[\int \frac{{B}^{2}}{2\mu }dv-\frac{1}{2}\int J.Adv\right]$ (5)
The law of energy conversation requires the functional F to be zero. In finite element method the functional F is minimized to obtain the magnetic vector potential A and magnetic flux density B, i.e.$\frac{\partial F}{\partial A}=0$
i.e. $\frac{\partial }{\partial A}\left(\int \frac{{B}^{2}}{2\mu }dv-\frac{1}{2}\int Jdv\right)=0$ (6)
Eqn. (6) is the basis for finite element analysis of linear magnetostatic problems.
5.1 Magnetic Flux Density Distribution from the Coil in Free Air
The axial magnetic flux density distribution at the center of coaxial coils can be calculated using the analytical expression15.
$B z = μ 0 J 2 [ ( b−z )ln a 2 + a 2 2 + ( b−z ) 2 a 1 + a 1 2 + ( b−z ) 2 +( b+z )ln a 2 + a 2 2 + ( b+z ) 2 a 1 + a 1 2 + ( b+z ) 2 ] MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWG6baabeaakiabg2da9maalaaabaaccaGae8hVd02aaSba aSqaaiaaicdaaeqaaOGaamOsaaqaaiaaikdaaaWaamWaaeaadaqada qaaiaadkgacqGHsislcaWG6baacaGLOaGaayzkaaGaciiBaiaac6ga daWcaaqaaGqaciaa+fgadaWgaaWcbaGaaGOmaaqabaGccqGHRaWkda GcaaqaaiaadggadaqhaaWcbaGaaGOmaaqaaiaaikdaaaGccqGHRaWk daqadaqaaiaadkgacqGHsislcaWG6baacaGLOaGaayzkaaWaaWbaaS qabeaacaaIYaaaaaqabaaakeaacaWGHbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSYaaOaaaeaacaWGHbWaa0baaSqaaiaaigdaaeaacaaIYa aaaOGaey4kaSYaaeWaaeaacaWGIbGaeyOeI0IaamOEaaGaayjkaiaa wMcaamaaCaaaleqabaGaaGOmaaaaaeqaaaaakiabgUcaRmaabmaaba GaamOyaiabgUcaRiaadQhaaiaawIcacaGLPaaaciGGSbGaaiOBamaa laaabaGaamyyamaaBaaaleaacaaIYaaabeaakiabgUcaRmaakaaaba GaamyyamaaDaaaleaacaaIYaaabaGaaGOmaaaakiabgUcaRmaabmaa baGaamOyaiabgUcaRiaadQhaaiaawIcacaGLPaaadaahaaWcbeqaai aaikdaaaaabeaaaOqaaiaadggadaWgaaWcbaGaaGymaaqabaGccqGH RaWkdaGcaaqaaiaadggadaqhaaWcbaGaaGymaaqaaiaaikdaaaGccq GHRaWkdaqadaqaaiaadkgacqGHRaWkcaWG6baacaGLOaGaayzkaaWa aWbaaSqabeaacaaIYaaaaaqabaaaaaGccaGLBbGaayzxaaaaaa@7AB0@$ (7)
where ${\mu }_{0}$ = permeability of material in free space, 4π×10-7 T-m/A,$J=\frac{NI}{A}$ , Current density in A/m2, 2b= height of the coil, 2 = Inner diameter of coil, 2=outer diameter of coil, = axial distance along the axis. The cross-section and other parameters of a coil in the present work are = 16.5 mm, = 57.5 mm, b = 41.5 mm and current density is J = 3.75×104 A/m2. The axial magnetic flux density distribution has been calculated using the Eqn. (7) along the length of the Terfenol-D rod in steps of 10 mm on either side of mid-plane. Co-axial coils in free air are energised with direct current to analyse the magnetic flux density using the finite element analysis in Maxwell 2D solver. Figure 2 summarizes the results on magnetic flux density obtained for co-axial coils alone in free air. The comparison of analytical, numerical and experimental results obtained for co-axial coils in free air shows good agreement with each other. It may be concluded that this study gave scope for analysing magnetic field for a whole actuator assembly with and without Terfenol-D. Figure 3 shows the comparison of experimental and Ansoft simulated axial magnetic flux density distribution along the length of Terfenol-D rod for different housings with a co-axially placed coils. It is observed that the axial flux density values are in close agreement with each other and small deviations are observed due to varying experimental conditions. The magnitude of axial magnetic flux density has been observed 32.3 mT in mild steel housing with coils compared to cast iron and aluminium housing with 31.1 mT and 26.9 mT respectively.
Figure 2.Axial magnetic flux density of coaxial coils in free air.
5.2 Distribution of Axial and Radial Magnetic Flux Density Distribution in Actuator
Figures 4 (a), 4 (b) and 5 (a), 5 (b) shows the comparison of axial and radial magnetic flux density distribution with and without Terfenol-D in an actuator with mild steel and cast iron housing.
Figure 3.Axial magnetic flux density of coaxial coils in different housing materials.
Figure 4.Axial and radial magnetic flux density distribution in a mild steel housing (a) without Terfenol-D (b) with Terfenol-D.
Figure 5.Axial and radial magnetic flux density distribution in cast iron housing (a) without Terfenol-D (b) with Terfenol-D.
The current density input to the coil 1 and coil 2 are 2.7×106 amp-turns/m2 and 1.18×106 amp-turns/m2 for 4 A , respectively. It is observed that the magnetic flux density increases from either ends and remains uniform within the coil with Terfenol-D rod and without Terfenol-D. The radial magnetic flux distribution has discontinuities due to the presence of various materials. The radial magnetic flux density is uniform in air and in presence of Terfenol-D, decreases linearly due to presence of coils, bobbin material and wall of the housing as shown in Figs. 4 and 5. The profile of axial and radial magnetic flux density distribution is almost same compared to aluminium housing. This may be because of relative permeability of aluminium material which is almost equal to relative permeability of free space.
Figures 6 (a) and 6(b) shows the comparison of axial and radial magnetic flux density distribution with and without Terfenol-D in an actuator with aluminium housing. It is observed that the magnitude of axial magnetic flux density is more at the center of coils with and without Terfenol-D. The radial distribution of magnetic flux density is almost same compared to both mild steel and cast iron housing.
Figure 6.Axial and radial magnetic flux density distribution in aluminium housing (a) without Terfenol-D (b) with Terfenol-D.
5.3 Comparison of Flux Distribution in an Actuator
The comparison of distribution of flux in an assembly of actuator having mild steel, cast iron and aluminium housing with and without Terfenol-D rod has been discussed. According to Lenz’s law the rate of flux transfer from the housing material will be effective and faster whenever the magnetic permeability of housing material is more compared to Terfenol-D rod. With and without Terfenol-D, the intensity and magnitude of a flux lines in an actuator assembly contained with mild steel housing are dense and high compared to cast iron and aluminium housing have been observed. This is due to high relative permeability of mild steel compared to cast iron and aluminium. The flux in an actuator assembly enclosed with aluminium housing was more in the absence of Terfenol-D compared to the presence of Terfenol-D. This may be due to high magnetic permeability of Terfenol-D compared to aluminium housing material.
Table 1. Percentage of flux in an actuator assembly with different housing materials.
Maximum flux of 4.5778×10-5 Wb/m2, 4.5059×10-5 Wb/m2, 2.7312×10-5 Wb/m2 and 1.1123×10-4 Wb/m2, 1.09×10-4 Wb/m2, 4.62×10-5 Wb/m2 is observed in a mild steel, cast iron and aluminium housing without and with Terfenol-D rod respectively with an input supply of 4 A. Table 1 shows the percentage of variation in flux for an actuator assembly with different housing materials. The increase in flux was 58.8 per cent and 58.6 per cent with mild steel and cast iron housing in the presence of Terfenol-D. The decrease in flux was around 41 per cent in the presence of Terfenol-D with an actuator containing aluminium housing. The percentage of increase in the flux was around 58.46 per cent and 57.6 per cent in an actuator assembly with mild steel and cast iron housing compared to aluminium housing in the presence of Terfenol-D rod.
An insight into flux density distribution provides good support for the design distribution provided theoretically good support for the design of Terfenol-D actuator. Also, it is clear that the performance of actuator depends on driving magnetic field and the magnetic properties of materials used more importantly housing materials. A uniform axial magnetic flux density distribution in the actuator assembly with mild steel housing has been observed with and without Terfenol-D compared to actuator with cast iron and aluminium housing. It is observed that the magnetic flux distribution is stronger by 58.8 per cent with mild steel, 58.6 per cent with cast iron and weaker by 40.8 per cent with aluminium when the actuator is contained with Terfenol-D. It is summarized that the magnetic field distribution on Terfenol-D is influenced due to magnetic permeability of housing material, hence a suitable housing material like mild steel is preferable for the effective magnetic field distribution and to improve the performance of actuator.
The research activity reported here was funded by the Ministry of Human Resource and Development (MHRD) R and D projects (No.26-11/2004- TS V, Dated 31-03-05), New Delhi, India. The authors thank Defense Metallurgical Research Laboratory (DMRL), Hyderabad for providing Terfenol-D specimen.
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4. Dehui, L.; Quanguo, L. & Yuyun, Z. Magnetic circuit optimisation design of giant magnetostrictive actuator. In the 9th International Conference on Computer Aided Industrial Design and Conceptual Design, Kunming, 2008, pp. 688-692. [Full text via CrossRef]
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9. Olabi, A.G. & Grunwald, A. Computation of magnetic field in an actuator. Simul. Model. Practice Theory, 2008, 16(1), 1728-1736. [Full text via CrossRef]
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11. Han, H.; Xin, Q. & Wang, S. Finite element analysis on magnetic field in the actuator of giant magnetostrictive linear motor with Ansoft. In the IEEE International Conference on Industrial Technology, Chengdu, 2008, pp.1-5. [Full text via CrossRef]
12. Wang, J.; Li, G.; Wang, C. & Liu, C. Finite element analysis of internal magnetic field on Terfenol-D rod in high frequency driven. In the 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce, Deng Leng, 2011, pp. 5572-5575. [Full text via CrossRef]
13. Wang, C. & Wang, J. Finite element analysis of internal stress and strain on Terfenol-D rod in high frequency driven. In the 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce, Deng Leng, 2011, pp. 5576-5579. [Full text via CrossRef]
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*, and
Mr Raghavendra Joshi obtained his MTech (Machine Design) from Jawaharlal Nehru Technological University, Hyderabad. Presently, he is a research scholar in the Department of Mechanical Engineering, NIT, Surathkal. His areas of research are: Hysteresis modeling and applications of magnetostrictive materials, vibration and conditioning monitoring. Mr Subba Rao M. obtained his MTech (Manufacturing Engineering) from National Institute of Technology, Surathkal and is involved in the development of actuator using magneostrictive material. Presently, he is working as Assistant Professor in the Department of Mechanical Engineering, Madanapalle Institute of Technology & Science, Madanapalle. His area of research is applications of magnetostrictive materials. Dr Ravikiran Kadoli obtained his PhD from Indian Institute of Technology, Madras. Presently he is a Professor in the Department of Mechancial Engineering, NIT, Surathkal. He is actively involved in the research activities and guided one PhD and many UG and PG Projects. His areas of research are: Structural mechancis, magnetostrictive technology, computational fluid dynamics, heat transfer, thermally induced vibrations.
| 2020-01-27T01:45:14 |
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|
https://www.usgs.gov/center-news/volcano-watch-shhh-dont-tell-there-eruption-eruption-1942
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# Volcano Watch — Shhh! Don't tell there is an eruption - Eruption of 1942
Release Date:
The eruption of 1942 was noteworthy for several reasons. (1) It was declared a secret so the press was not allowed to publicize the event. (2) This was the second time lava diversion was tried on an eruption of Mauna Loa. (3) The volcanologists were able to predict the timing and place of the eruption.
The eruption of 1942 was noteworthy for several reasons. (1) It was declared a secret so the press was not allowed to publicize the event. (2) This was the second time lava diversion was tried on an eruption of Mauna Loa. (3) The volcanologists were able to predict the timing and place of the eruption.
World War II was four months old when the eruption began. Hawaii was observing war-time restrictions that imposed a night-time blackout. Pele was having none of this, and the eruptions began on April 26, 1942, at 5:05 p.m. Government officials felt that advertising the eruption would permit the Japanese military to use the bright glow as a means to guide their warplanes under cover of darkness to wreak havoc upon Hawaii.
The eruption, heralded by three months of elevated seismic activity, started when fissures opened along the western rim of Mokuaweoweo, and lava cascaded into the caldera. By early morning April 27, the summit activity began to wane. Eventually, seismic activity migrated toward the northeast rift zone. New fissures then opened at the junction between the summit caldera and northeast rift on April 27. Here the dike stopped advancing at the 3,658-m (12,000 ft) level. A line of spatter ramparts issued an aa flow that traveled in a north-northeasterly direction 7 km (4 mi) away from the rift. all this activity had ended by the early morning of April 28.
However On April 28, activity jumped far down the northeast rift zone. This new vent system opened at 4:40 a.m., creating a 1-km-long (0.6 mi) fissure at an elevation of 2,850 m (9,350 ft), 14.5 km (9 mi) from Mauna Loa's summit. Lava fountains propelled 70 to 90 meters (230 to 295 ft) high, producing small flows. Meanwhile the summit activity continued to fade as the flank activity expanded. Eventually, the summit activity ceased altogether.
By 3 p.m., the 1-km-long (0.6 mi) fissure lengthened an additional 0.5 km (0.3 mi). Fountains then were visible only from the distal ends of the fissure system; the central vents were drowned by lava moving in from the margins.
At 8 p.m., the eruption appeared to have begun in earnest as lava fountains reached heights of 150 m (500 ft). The fountains fed a rapidly moving aa lava flow headed in the general direction of Waiakea Uka. Gradually, eruptive activity condensed to a few spatter ramparts at the center of this fissure system. These vents were responsible for the bulk of the lava production.
A few hours later, the dike propagated another 4.6 km (2.9 mi) northeast. Here the dike changed orientation from northeast to north. Lava issuing from these lower elevation vents appeared to be gas-poor and more dense in character. The character of the lava caused scientists to speculate that these "new vents" were really sites where upslope lava entered an old tube or fracture system, only to reemerge at this lower elevation.
On May 1, the flow front was moving at 100 to 150 m (328 to 492 ft) per hour in the direction of Waiakea Uka. The advancing flow threatened the Olaa flume, Mountain View's water source, and would ultimately endanger the circum-island road. It was at this time that the decision was made to utilize aerial bombing to influence the course of the lava flows.
Aerial bombing was selected as the most efficient means of emplacing explosives at the optimal sites. The points of contact were lava tubes and channels that fed the flow front. The Army Air Force conducted the bombing missions and selected the sites. In all, 16 bombs weighing between 300 to 600 pounds each were dropped. Though most appeared to hit their mark, the bombs had little or no impact on the eruption or on the flow's direction.
On May 4, mauka activity became more restricted to a single, large cone edifice with vents producing lava at its center. The cone grew to a height of 30 meters (100 ft) and lava fountains stretched to heights of 200 m (650 ft). Later in the day, lava flows accomplished what bombs could not. These lava flows caused the central cone to collapse, resulting in the creation of secondary flows. These secondary flows diverted the lava from the flow front, slowing its advance, and resulted in the stagnation of the main flow on May 7. When the eruption ended on May 9, the lava flow extended 26 km from the main vents at 2,850 m (9,350 ft) and came within 11 km (6.8 mi) of Upper Waiakea Uka.
### Volcano Activity Update
Activity within Puu Oo increased during the past week, and lava covered the floor of the crater. The light from the lava cast a bright glow onto the fume clouds. Lava continued to flow through a network of tubes down to the seacoast, where it entered the ocean at two locations - Waha`ula and Kamokuna. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying frequent collapses of the lava delta. The steam cloud is highly acidic and laced with glass particles.
There were no earthquakes reported felt during the past week.
| 2020-12-03T01:23:20 |
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|
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/22%3A_Magnetism/22.02_Magnets
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$$\require{cancel}$$
# 22.1: Magnets
Figure $$\PageIndex{1}$$: Magnets come in various shapes, sizes, and strengths. All have both a north pole and a south pole. There is never an isolated pole (a monopole).
All magnets attract iron, such as that in a refrigerator door. However, magnets may attract or repel other magnets. Experimentation shows that all magnets have two poles. If freely suspended, one pole will point toward the north. The two poles are thus named the north magnetic pole and the south magnetic pole (or more properly, north-seeking and south-seeking poles, for the attractions in those directions).
UNIVERSAL CHARACTERISTICS OF MAGNETS AND MAGNET POLES
It is a universal characteristic of all magnets that like poles repel and unlike poles attract. (Note the similarity with electrostatics: unlike charges attract and like charges repel.)
Further experimentation shows that it is impossible to separate north and south poles in the manner that + and − charges can be separated.
Figure $$\PageIndex{2}$$: One end of a bar magnet is suspended from a thread that points toward north. The magnet’s two poles are labeled N and S for north-seeking and south-seeking poles, respectively.
MISCONCEPTION ALERT: EARTH'S GEOGRAPHIC NORTH POLE HIDES AN S
The Earth acts like a very large bar magnet with its south-seeking pole near the geographic North Pole. That is why the north pole of your compass is attracted toward the geographic north pole of the Earth—because the magnetic pole that is near the geographic North Pole is actually a south magnetic pole! Confusion arises because the geographic term “North Pole” has come to be used (incorrectly) for the magnetic pole that is near the North Pole. Thus, “North magnetic pole” is actually a misnomer—it should be called the South magnetic pole.
Figure $$\PageIndex{3}$$: Unlike poles attract, whereas like poles repel.
Figure $$\PageIndex{4}$$: North and south poles always occur in pairs. Attempts to separate them result in more pairs of poles. If we continue to split the magnet, we will eventually get down to an iron atom with a north pole and a south pole—these, too, cannot be separated.
The fact that magnetic poles always occur in pairs of north and south is true from the very large scale—for example, sunspots always occur in pairs that are north and south magnetic poles—all the way down to the very small scale. Magnetic atoms have both a north pole and a south pole, as do many types of subatomic particles, such as electrons, protons, and neutrons.
MAKING CONNECTIONS: TAKE-HOME EXPERIMENT -- REFRIGERATOR MAGNETS
We know that like magnetic poles repel and unlike poles attract. See if you can show this for two refrigerator magnets. Will the magnets stick if you turn them over? Why do they stick to the door anyway? What can you say about the magnetic properties of the door next to the magnet? Do refrigerator magnets stick to metal or plastic spoons? Do they stick to all types of metal?
### Summary
• Magnetism is a subject that includes the properties of magnets, the effect of the magnetic force on moving charges and currents, and the creation of magnetic fields by currents.
• There are two types of magnetic poles, called the north magnetic pole and south magnetic pole.
• North magnetic poles are those that are attracted toward the Earth’s geographic north pole.
• Like poles repel and unlike poles attract.
• Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
### Glossary
north magnetic pole
the end or the side of a magnet that is attracted toward Earth’s geographic north pole
south magnetic pole
the end or the side of a magnet that is attracted toward Earth’s geographic south pole
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-05-20T13:30:31 |
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https://pdglive.lbl.gov/DataBlock.action?node=Q007ST7
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#### t-channel Single ${{\mathit t}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
Direct probe of the ${{\mathit t}}{{\mathit b}}{{\mathit W}}$ coupling and possible new physics at $\sqrt {s }$ = 7 TeV.
VALUE (pb) DOCUMENT ID TECN COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$67.5$ $\pm5.7$ 1
2019 R
LHC combination of ATLAS+CMS
$68$ $\pm2$ $\pm8$ 2
2014 BI
ATLS ${{\mathit \ell}}$ + $\not E_T$ + 2j or 3j
$83$ $\pm4$ ${}^{+20}_{-19}$ 3
2012 CH
ATLS ${{\mathit t}}$ -channel ${{\mathit \ell}}$ + $\not E_T$+ (2,3)j (1${{\mathit b}}$ )
$67.2$ $\pm6.1$ 4
2012 BQ
CMS ${{\mathit t}}$ -channel ${{\mathit \ell}}$ + $\not E_T$+ ${}\geq{}$2j (1${{\mathit b}}$ )
$83.6$ $\pm29.8$ $\pm3.3$ 5
2011 R
CMS ${{\mathit t}}$ -channel
1 AABOUD 2019R based on 1.17 to 5.1 fb${}^{-1}$ of data from ATLAS and CMS at 7 TeV.
2 Based on 4.59 fb${}^{-1}$ of data, using neural networks for signal and background separation. ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}$ = $46$ $\pm1$ $\pm6$ pb and ${\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$ = $23$ $\pm1$ $\pm3$ pb are separately measured, as well as their ratio ${{\mathit R}}$ = ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}/{\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$ = $2.04$ $\pm0.13$ $\pm0.12$. The results are for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV, and those for other ${\mathit m}_{{{\mathit t}}}$ values are given by eq.(4) and Table IV. The measurements give $\vert V_{tb}\vert$ = $1.02$ $\pm0.07$ or $\vert V_{tb}\vert$ $>$ 0.88 (95$\%$ CL).
3 Based on 1.04 fb${}^{-1}$ of data. The result gives $\vert V_{tb}\vert$ = $1.13$ ${}^{+0.14}_{-0.13}$ from the ratio ${\mathit \sigma (}$exp${)}/{\mathit \sigma (}$th${)}$, where ${\mathit \sigma (}$th${)}$ is the SM prediction for $\vert V_{tb}\vert$ = 1. The 95$\%$ CL lower bound of $\vert V_{tb}\vert$ $>$ 0.75 is found if $\vert V_{tb}\vert$ $<$ 1 is assumed. ${\mathit \sigma (}{{\mathit t}}{)}$ = $59$ ${}^{+18}_{-16}$ pb and ${\mathit \sigma (}{{\overline{\mathit t}}}{)}$ = $33$ ${}^{+13}_{-12}$ pb are found for the separate single ${{\mathit t}}$ and ${{\overline{\mathit t}}}$ production cross sections, respectively. The results assume ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV for the acceptance.
4 Based on 1.17 fb${}^{-1}$ of data for ${{\mathit \ell}}$ = ${{\mathit \mu}}$ , 1.56 fb${}^{-1}$ of data for ${{\mathit \ell}}$ = ${{\mathit e}}$ at 7 TeV collected during 2011. The result gives $\vert V_{tb}\vert$ = $1.020$ $\pm0.046$(meas)$\pm0.017$(th). The 95$\%$ CL lower bound of $\vert V_{tb}\vert$ $>$ 0.92 is found if $\vert V_{tb}\vert$ $<$ 1 is assumed. The results assume ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV for the acceptance.
5 Based on 36 pb${}^{-1}$ of data. The first error is statistical + systematic combined, the second is luminosity. The result gives $\vert V_{tb}\vert$ = $1.114$ $\pm0.22$(exp)$\pm0.02$(th) from the ratio ${\mathit \sigma (}$exp${)}/{\mathit \sigma (}$th${)}$, where ${\mathit \sigma (}$th${)}$ is the SM prediction for $\vert V_{tb}\vert$ = 1. The 95$\%$ CL lower bound of $\vert V_{tb}\vert$ $>$ 0.62 (0.68) is found from the 2D (BDT) analysis under the constraint 0 $<$ $\vert V_{tb}\vert ^2$ $<$ 1.
References:
AABOUD 2019R
JHEP 1905 088 Combinations of single-top-quark production cross-section measurements and |f$_{LV}$V$_{tb}$| determinations at $\sqrt{s}$ = 7 and 8 TeV with the ATLAS and CMS experiments
PR D90 112006 Comprehensive Measurements of ${\mathit {\mathit t}}$-Channel Single Top-Quark Production Cross Sections at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
PL B717 330 Measurement of the $\mathit t$-Channel Single Top-Quark Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
JHEP 1212 035 Measurement of the Single-Top-Quark $\mathit t$-Channel Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
PRL 107 091802 Measurement of the $\mathit t$-Channel Single Top Quark Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
| 2023-03-25T05:43:29 |
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|
http://dlmf.nist.gov/30.3
|
# §30.3 Eigenvalues
## §30.3(i) Definition
With , the spheroidal wave functions are solutions of Equation (30.2.1) which are bounded on , or equivalently, which are of the form where is an entire function of . These solutions exist only for eigenvalues , , of the parameter .
## §30.3(iii) Transcendental Equation
If is an even nonnegative integer, then the continued-fraction equation
30.3.5
where , , are defined by
30.3.6
has the solutions , . If is an odd positive integer, then Equation (30.3.5) has the solutions , . If or , the finite continued-fraction on the left-hand side of (30.3.5) equals 0; if its last denominator is or .
In equation (30.3.5) we can also use
## §30.3(iv) Power-Series Expansion
For values of see Meixner et al. (1980, p. 109).
30.3.9
30.3.11
30.3.12
Further coefficients can be found with the Maple program SWF9; see §30.18(i).
| 2013-05-26T04:18:54 |
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|
https://zbmath.org/authors/?q=ai%3Avan-de-geer.sara-a
|
## Van de Geer, Sara Anna
Compute Distance To:
Author ID: van-de-geer.sara-a Published as: van de Geer, Sara; Van de Geer, Sara; van de Geer, Sara A.; Van De Geer, Sara; van de Geer, S. A.; Van de Geer, Sara A.; Van De Geer, Sara A.; van de Geer, S. more...less Homepage: http://stat.ethz.ch/~vsara/ External Links: MGP · Wikidata · ResearchGate · GND · IdRef · theses.fr
Documents Indexed: 98 Publications since 1987, including 6 Books 5 Contributions as Editor Co-Authors: 55 Co-Authors with 75 Joint Publications 1,406 Co-Co-Authors
all top 5
### Co-Authors
28 single-authored 15 Bühlmann, Peter 6 Nickl, Richard 5 Janková, Jana 5 Kolchinskiĭ, Vladimir I’ich 5 Ortelli, Francesco 4 Wellner, Jon August 3 Elsener, Andreas 3 Lederer, Johannes 3 Mammen, Enno 3 Meier, Lukas 3 Müller, Patric 3 Stucky, Benjamin 3 Tsybakov, Alexandre B. 2 Goeman, Jelle J. 2 Muro, Alan 2 Reiß, Markus 2 Rütimann, Philipp 2 Städler, Nicolas 2 Stougie, Leen 2 Tarigan, Bernadetta 2 Wainwright, Martin J. 2 Wegkamp, Marten H. 2 Zhang, Cun-Hui 1 Baatenburg de Jong, R. J. 1 Bartlett, Peter L. 1 Belitser, Eduard 1 Deheuvels, Paul 1 del Barrio, Eustasio 1 Dezeure, Ruben 1 Dümbgen, Lutz 1 Györfi, László 1 Haccou, Patsy 1 Hebiri, Mohamed 1 Hinz, Peter 1 Klaassen, Chris A. J. 1 Le Cessie, Saskia 1 Linton, Oliver Bruce 1 Loubes, Jean-Michel 1 Lounici, Karim 1 Lugosi, Gábor 1 Maathuis, Marloes H. 1 Marchetti-Spaccamela, Alberto 1 Meelis, Evert 1 Mitchell, Charles 1 Mohammadi, Leila 1 Nielsen, Jens Perch 1 Pontil, Massimiliano 1 Rhee, Wansoo T. 1 Ritov, Ya’acov 1 Schelldorfer, Jürg 1 Steinwart, Ingo 1 van Houwelingen, Hans C. 1 van Zwet, Willem Rutger 1 Veraar, Mark C. 1 Wang, Sven 1 Zhou, Shuheng
all top 5
### Serials
20 The Annals of Statistics 10 Electronic Journal of Statistics 8 Journal of Statistical Planning and Inference 5 Journal of Machine Learning Research (JMLR) 4 Test 4 Oberwolfach Reports 3 IEEE Transactions on Information Theory 3 Scandinavian Journal of Statistics 3 Stochastic Processes and their Applications 2 Statistica Neerlandica 2 Mathematical Methods of Statistics 2 Bernoulli 2 Journal of the Royal Statistical Society. Series B. Statistical Methodology 2 Cambridge Series in Statistical and Probabilistic Mathematics 2 Sankhyā. Series A 1 American Mathematical Monthly 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Journal of Multivariate Analysis 1 Statistics & Probability Letters 1 Operations Research Letters 1 Probability Theory and Related Fields 1 Statistical Science 1 IEEE Transactions on Signal Processing 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 Journal of Nonparametric Statistics 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Butlletí de la Societat Catalana de Matemàtiques 1 CWI Tracts 1 Lecture Notes in Mathematics 1 Information and Inference 1 Springer Series in Statistics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Transactions of A. Razmadze Mathematical Institute 1 Mathematical Statistics and Learning 1 EMS Series of Lectures in Mathematics
all top 5
### Fields
91 Statistics (62-XX) 23 Probability theory and stochastic processes (60-XX) 6 Computer science (68-XX) 5 History and biography (01-XX) 4 General and overarching topics; collections (00-XX) 4 Numerical analysis (65-XX) 4 Operations research, mathematical programming (90-XX) 2 Combinatorics (05-XX) 2 Information and communication theory, circuits (94-XX) 1 Partial differential equations (35-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Systems theory; control (93-XX)
### Citations contained in zbMATH Open
89 Publications have been cited 2,625 times in 1,813 Documents Cited by Year
Statistics for high-dimensional data. Methods, theory and applications. Zbl 1273.62015
Bühlmann, Peter; van de Geer, Sara
2011
The group Lasso for logistic regression. Zbl 1400.62276
Meier, Lukas; van de Geer, Sara; Bühlmann, Peter
2008
On asymptotically optimal confidence regions and tests for high-dimensional models. Zbl 1305.62259
van de Geer, Sara; Bühlmann, Peter; Ritov, Ya’acov; Dezeure, Ruben
2014
High-dimensional generalized linear models and the lasso. Zbl 1138.62323
van de Geer, Sara A.
2008
On the conditions used to prove oracle results for the Lasso. Zbl 1327.62425
van de Geer, Sara A.; Bühlmann, Peter
2009
Applications of empirical process theory. Zbl 0953.62049
Van de Geer, Sara A.
2000
High-dimensional additive modeling. Zbl 1360.62186
Meier, Lukas; van de Geer, Sara; Bühlmann, Peter
2009
Locally adaptive regression splines. Zbl 0871.62040
Mammen, Enno; van de Geer, Sara
1997
Empirical processes in M-estimation. Reprint of the 2000 hardback ed. Zbl 1179.62073
van de Geer, Sara A.
2010
Oracle inequalities and optimal inference under group sparsity. Zbl 1306.62156
Lounici, Karim; Pontil, Massimiliano; van de Geer, Sara; Tsybakov, Alexandre B.
2011
Hellinger-consistency of certain nonparametric maximum likelihood estimators. Zbl 0779.62033
Van de Geer, Sara
1993
$$\ell_{1}$$-penalization for mixture regression models. Zbl 1203.62128
Städler, Nicolas; Bühlmann, Peter; Van de Geer, Sara
2010
Estimating a regression function. Zbl 0709.62040
van de Geer, Sara
1990
Penalized quasi-likelihood estimation in partial linear models. Zbl 0906.62033
Mammen, Enno; van de Geer, Sara
1997
Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes. Zbl 0852.60019
van de Geer, Sara
1995
Testing against a high dimensional alternative. Zbl 1110.62002
Goeman, Jelle J.; van de Geer, Sara A.; van Houwelingen, Hans C.
2006
Confidence sets in sparse regression. Zbl 1288.62108
Nickl, Richard; Van De Geer, Sara
2013
Estimation for high-dimensional linear mixed-effects models using $$\ell_1$$-penalization. Zbl 1246.62161
Schelldorfer, Jürg; Bühlmann, Peter; van de Geer, Sara
2011
The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso). Zbl 1274.62471
van de Geer, Sara; Bühlmann, Peter; Zhou, Shuheng
2011
$$\ell_{0}$$-penalized maximum likelihood for sparse directed acyclic graphs. Zbl 1267.62037
van de Geer, Sara; Bühlmann, Peter
2013
Estimation and testing under sparsity. École d’Été de Probabilités de Saint-Flour XLV – 2015. Zbl 1362.62006
Van de Geer, Sara
2016
Confidence intervals for high-dimensional inverse covariance estimation. Zbl 1328.62458
Janková, Jana; van de Geer, Sara
2015
Classifiers of support vector machine type with $$\ell_1$$ complexity regularization. Zbl 1118.62067
Tarigan, Bernadetta; van de Geer, Sara A.
2006
The smooth-Lasso and other $$\ell _{1}+\ell _{2}$$-penalized methods. Zbl 1274.62443
Hebiri, Mohamed; van de Geer, Sara
2011
Nemirovski’s inequalities revisited. Zbl 1213.60039
Dümbgen, Lutz; van de Geer, Sara A.; Veraar, Mark C.; Wellner, Jon A.
2010
A new approach to least-squares estimation, with applications. Zbl 0625.62046
van de Geer, Sara
1987
Square root penalty: Adaption to the margin in classification and in edge estimation. Zbl 1080.62047
Tsybakov, A. B.; van de Geer, S. A.
2005
Rates of convergence for the maximum likelihood estimator in mixture models. Zbl 0872.62039
van de Geer, Sara
1996
Least squares estimation with complexity penalties. Zbl 1005.62043
van de Geer, Sara
2001
The likelihood ratio test for the change point problem for exponentially distributed random variables. Zbl 0671.62019
Haccou, Patsy; Meelis, Evert; van de Geer, Sara
1987
Correlated variables in regression: clustering and sparse estimation. Zbl 1278.62103
Bühlmann, Peter; Rütimann, Philipp; van de Geer, Sara; Zhang, Cun-Hui
2013
Estimating multiplicative and additive hazard functions by kernel methods. Zbl 1040.62089
Linton, Oliver B.; Nielsen, Jens Perch; van de Geer, Sara
2003
Lectures on empirical processes. Theory and statistical applications. Zbl 1132.62001
del Barrio, Eustasio; Deheuvels, Paul; van de Geer, Sara
2007
Adaptive estimation with soft thresholding penalties. Zbl 1090.62534
Loubes, Jean-Michel; van de Geer, Sara
2002
Consistency for the least squares estimator in nonparametric regression. Zbl 0867.62027
van de Geer, Sara; Wegkamp, Marten
1996
The Bernstein-Orlicz norm and deviation inequalities. Zbl 1284.60060
van de Geer, Sara; Lederer, Johannes
2013
The partial linear model in high dimensions. Zbl 1364.62196
Müller, Patric; van de Geer, Sara
2015
High-dimensional inference in misspecified linear models. Zbl 1327.62420
Bühlmann, Peter; van de Geer, Sara
2015
Asymptotic theory for maximum likelihood in nonparametric mixture models. Zbl 1429.62117
van de Geer, Sara
2003
The method of sieves and minimum contrast estimators. Zbl 0831.62029
van de Geer, S.
1995
On Hoeffding’s inequality for dependent random variables. Zbl 1027.60013
van de Geer, Sara A.
2002
On higher order isotropy conditions and lower bounds for sparse quadratic forms. Zbl 1308.62148
van de Geer, Sara; Muro, Alan
2014
Weakly decomposable regularization penalties and structured sparsity. Zbl 1349.62325
van de Geer, Sara
2014
M-estimation using penalties or sieves. Zbl 1030.62026
van de Geer, Sara
2002
Honest confidence regions and optimality in high-dimensional precision matrix estimation. Zbl 1368.62204
Janková, Jana; Van de Geer, Sara
2017
On the uniform convergence of empirical norms and inner products, with application to causal inference. Zbl 1348.62152
van de Geer, Sara
2014
The Lasso, correlated design, and improved oracle inequalities. Zbl 1327.62426
van de Geer, Sara; Lederer, Johannes
2013
Regression analysis and empirical processes. Zbl 0641.62041
van de Geer, S. A.
1988
Robust low-rank matrix estimation. Zbl 1412.62068
Elsener, Andreas; van de Geer, Sara
2018
New concentration inequalities for suprema of empirical processes. Zbl 1355.60026
Lederer, Johannes; Van De Geer, Sara
2014
On concentration for (regularized) empirical risk minimization. Zbl 1380.62085
Van de Geer, Sara; Wainwright, Martin J.
2017
Discussion of: “Grouping strategies and thresholding for high dimension linear models”. Zbl 1432.62112
van de Geer, Sara
2013
Convergence rates for penalized least squares estimators in PDE constrained regression problems. Zbl 1436.62163
Nickl, Richard; van de Geer, Sara; Wang, Sven
2020
Probabilistic analysis of the minimum weighted flowtime scheduling problem. Zbl 0761.90063
Marchetti Spaccamela, Alberto; Rhee, Wan Soo; Stougie, Leen; van de Geer, Sara
1992
Asymptotic normality in mixture models. Zbl 0867.62026
van de Geer, Sara
1995
Semiparametric efficiency bounds for high-dimensional models. Zbl 1420.62308
Janková, Jana; van de Geer, Sara
2018
Statistics for big data: a perspective. Zbl 06892162
Bühlmann, Peter; van de Geer, Sara
2018
On rates of convergence and asymptotic normality in the multiknapsack problem. Zbl 0753.90045
van de Geer, Sara; Stougie, Leen
1991
Quasi-likelihood and/or robust estimation in high dimensions. Zbl 1331.62354
van de Geer, Sara; Müller, Patric
2012
On the total variation regularized estimator over a class of tree graphs. Zbl 1411.62208
Ortelli, Francesco; van de Geer, Sara
2018
Penalized least squares estimation in the additive model with different smoothness for the components. Zbl 1328.62256
van de Geer, Sara; Muro, Alan
2015
Worst possible sub-directions in high-dimensional models. Zbl 1334.62133
Van de Geer, Sara
2016
On tight bounds for the Lasso. Zbl 1467.62127
van de Geer, Sara
2018
Sharp oracle inequalities for square root regularization. Zbl 1441.62188
Stucky, Benjamin; Van de Geer, Sara
2017
Asymptotic confidence regions for high-dimensional structured sparsity. Zbl 1415.94240
Stucky, Benjamin; van de Geer, Sara
2018
On non-asymptotic bounds for estimation in generalized linear models with highly correlated design. Zbl 1176.62071
van de Geer, Sara A.
2007
Rejoinder to the comments on: $$\ell _{1}$$-penalization for mixture regression models. Zbl 1203.62129
Städler, Nicolas; Bühlmann, Peter; Van de Geer, Sara
2010
Adaptive rates for total variation image denoising. Zbl 07306926
Ortelli, Francesco; van de Geer, Sara
2020
Discussion: “A significance test for the lasso”. Zbl 1305.62248
Bühlmann, Peter; Meier, Lukas; van de Geer, Sara
2014
$$\chi^{2}$$-confidence sets in high-dimensional regression. Zbl 1384.62251
Van de Geer, Sara; Stucky, Benjamin
2016
Oracle inequalities for square root analysis estimators with application to total variation penalties. Zbl 1475.62211
Ortelli, Francesco; van de Geer, Sara
2021
De-biased sparse PCA: inference for eigenstructure of large covariance matrices. Zbl 1473.62204
Janková, Jana; van de Geer, Sara
2021
$$\ell _{1}$$-regularization in high-dimensional statistical models. Zbl 05971198
van de Geer, Sara
2011
Censored linear model in high dimensions. Penalised linear regression on high-dimensional data with left-censored response variable. Zbl 1341.62218
Müller, Patric; Van de Geer, Sara
2016
Sparse recovery problems in high dimensions: statistical inference and learning theory. Abstracts from the mini-workshop held March 15th – March 21st, 2009. Zbl 1177.62001
2009
Asymptotics in empirical risk minimization. Zbl 1222.68267
Mohammadi, Leila; Van De Geer, Sara
2005
On the asymptotic variance of the debiased Lasso. Zbl 1429.62311
van de Geer, Sara
2019
Worst possible sub-directions in high-dimensional models. Zbl 1430.62162
van de Geer, Sara
2014
Logistic regression with total variation regularization. Zbl 1458.62153
van de Geer, Sara
2020
Prediction bounds for higher order total variation regularized least squares. Zbl 1486.62205
Ortelli, Francesco; van de Geer, Sara
2021
On robust recursive nonparametric curve estimation. Zbl 0958.62035
Belitser, Eduard; van de Geer, Sara
2000
A moment bound for multi-hinge classifiers. Zbl 1225.68218
Tarigan, Bernadetta; Van De Geer, Sara A.
2008
Predicting survival using disease history: a model combining relative survival and frailty. Zbl 1090.62571
Goeman, J. J.; Le Cessie, S.; Baatenburg de Jong, R. J.; van de Geer, S. A.
2004
Oracle inequalities for local and global empirical risk minimizers. Zbl 1443.62148
Elsener, Andreas; van de Geer, Sara
2019
The mathematical work of Evarist Giné. Zbl 1376.01013
Koltchinskii, Vladimir; Nickl, Richard; Van de Geer, Sara; Wellner, Jon A.
2016
Generic chaining and the $$\ell _{1}$$-penalty. Zbl 1428.62335
Van de Geer, Sara
2013
General oracle inequalities for model selection. Zbl 1326.62076
Mitchell, Charles; van de Geer, Sara
2009
Sharp oracle inequalities for stationary points of nonconvex penalized M-estimators. Zbl 1432.62062
Elsener, Andreas; van de Geer, Sara
2019
Inference in high-dimensional graphical models. Zbl 1442.62143
Janková, Jana; van de Geer, Sara
2019
Oracle inequalities for square root analysis estimators with application to total variation penalties. Zbl 1475.62211
Ortelli, Francesco; van de Geer, Sara
2021
De-biased sparse PCA: inference for eigenstructure of large covariance matrices. Zbl 1473.62204
Janková, Jana; van de Geer, Sara
2021
Prediction bounds for higher order total variation regularized least squares. Zbl 1486.62205
Ortelli, Francesco; van de Geer, Sara
2021
Convergence rates for penalized least squares estimators in PDE constrained regression problems. Zbl 1436.62163
Nickl, Richard; van de Geer, Sara; Wang, Sven
2020
Adaptive rates for total variation image denoising. Zbl 07306926
Ortelli, Francesco; van de Geer, Sara
2020
Logistic regression with total variation regularization. Zbl 1458.62153
van de Geer, Sara
2020
On the asymptotic variance of the debiased Lasso. Zbl 1429.62311
van de Geer, Sara
2019
Oracle inequalities for local and global empirical risk minimizers. Zbl 1443.62148
Elsener, Andreas; van de Geer, Sara
2019
Sharp oracle inequalities for stationary points of nonconvex penalized M-estimators. Zbl 1432.62062
Elsener, Andreas; van de Geer, Sara
2019
Inference in high-dimensional graphical models. Zbl 1442.62143
Janková, Jana; van de Geer, Sara
2019
Robust low-rank matrix estimation. Zbl 1412.62068
Elsener, Andreas; van de Geer, Sara
2018
Semiparametric efficiency bounds for high-dimensional models. Zbl 1420.62308
Janková, Jana; van de Geer, Sara
2018
Statistics for big data: a perspective. Zbl 06892162
Bühlmann, Peter; van de Geer, Sara
2018
On the total variation regularized estimator over a class of tree graphs. Zbl 1411.62208
Ortelli, Francesco; van de Geer, Sara
2018
On tight bounds for the Lasso. Zbl 1467.62127
van de Geer, Sara
2018
Asymptotic confidence regions for high-dimensional structured sparsity. Zbl 1415.94240
Stucky, Benjamin; van de Geer, Sara
2018
Honest confidence regions and optimality in high-dimensional precision matrix estimation. Zbl 1368.62204
Janková, Jana; Van de Geer, Sara
2017
On concentration for (regularized) empirical risk minimization. Zbl 1380.62085
Van de Geer, Sara; Wainwright, Martin J.
2017
Sharp oracle inequalities for square root regularization. Zbl 1441.62188
Stucky, Benjamin; Van de Geer, Sara
2017
Estimation and testing under sparsity. École d’Été de Probabilités de Saint-Flour XLV – 2015. Zbl 1362.62006
Van de Geer, Sara
2016
Worst possible sub-directions in high-dimensional models. Zbl 1334.62133
Van de Geer, Sara
2016
$$\chi^{2}$$-confidence sets in high-dimensional regression. Zbl 1384.62251
Van de Geer, Sara; Stucky, Benjamin
2016
Censored linear model in high dimensions. Penalised linear regression on high-dimensional data with left-censored response variable. Zbl 1341.62218
Müller, Patric; Van de Geer, Sara
2016
The mathematical work of Evarist Giné. Zbl 1376.01013
Koltchinskii, Vladimir; Nickl, Richard; Van de Geer, Sara; Wellner, Jon A.
2016
Confidence intervals for high-dimensional inverse covariance estimation. Zbl 1328.62458
Janková, Jana; van de Geer, Sara
2015
The partial linear model in high dimensions. Zbl 1364.62196
Müller, Patric; van de Geer, Sara
2015
High-dimensional inference in misspecified linear models. Zbl 1327.62420
Bühlmann, Peter; van de Geer, Sara
2015
Penalized least squares estimation in the additive model with different smoothness for the components. Zbl 1328.62256
van de Geer, Sara; Muro, Alan
2015
On asymptotically optimal confidence regions and tests for high-dimensional models. Zbl 1305.62259
van de Geer, Sara; Bühlmann, Peter; Ritov, Ya’acov; Dezeure, Ruben
2014
On higher order isotropy conditions and lower bounds for sparse quadratic forms. Zbl 1308.62148
van de Geer, Sara; Muro, Alan
2014
Weakly decomposable regularization penalties and structured sparsity. Zbl 1349.62325
van de Geer, Sara
2014
On the uniform convergence of empirical norms and inner products, with application to causal inference. Zbl 1348.62152
van de Geer, Sara
2014
New concentration inequalities for suprema of empirical processes. Zbl 1355.60026
Lederer, Johannes; Van De Geer, Sara
2014
Discussion: “A significance test for the lasso”. Zbl 1305.62248
Bühlmann, Peter; Meier, Lukas; van de Geer, Sara
2014
Worst possible sub-directions in high-dimensional models. Zbl 1430.62162
van de Geer, Sara
2014
Confidence sets in sparse regression. Zbl 1288.62108
Nickl, Richard; Van De Geer, Sara
2013
$$\ell_{0}$$-penalized maximum likelihood for sparse directed acyclic graphs. Zbl 1267.62037
van de Geer, Sara; Bühlmann, Peter
2013
Correlated variables in regression: clustering and sparse estimation. Zbl 1278.62103
Bühlmann, Peter; Rütimann, Philipp; van de Geer, Sara; Zhang, Cun-Hui
2013
The Bernstein-Orlicz norm and deviation inequalities. Zbl 1284.60060
van de Geer, Sara; Lederer, Johannes
2013
The Lasso, correlated design, and improved oracle inequalities. Zbl 1327.62426
van de Geer, Sara; Lederer, Johannes
2013
Discussion of: “Grouping strategies and thresholding for high dimension linear models”. Zbl 1432.62112
van de Geer, Sara
2013
Generic chaining and the $$\ell _{1}$$-penalty. Zbl 1428.62335
Van de Geer, Sara
2013
Quasi-likelihood and/or robust estimation in high dimensions. Zbl 1331.62354
van de Geer, Sara; Müller, Patric
2012
Statistics for high-dimensional data. Methods, theory and applications. Zbl 1273.62015
Bühlmann, Peter; van de Geer, Sara
2011
Oracle inequalities and optimal inference under group sparsity. Zbl 1306.62156
Lounici, Karim; Pontil, Massimiliano; van de Geer, Sara; Tsybakov, Alexandre B.
2011
Estimation for high-dimensional linear mixed-effects models using $$\ell_1$$-penalization. Zbl 1246.62161
Schelldorfer, Jürg; Bühlmann, Peter; van de Geer, Sara
2011
The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso). Zbl 1274.62471
van de Geer, Sara; Bühlmann, Peter; Zhou, Shuheng
2011
The smooth-Lasso and other $$\ell _{1}+\ell _{2}$$-penalized methods. Zbl 1274.62443
Hebiri, Mohamed; van de Geer, Sara
2011
$$\ell _{1}$$-regularization in high-dimensional statistical models. Zbl 05971198
van de Geer, Sara
2011
Empirical processes in M-estimation. Reprint of the 2000 hardback ed. Zbl 1179.62073
van de Geer, Sara A.
2010
$$\ell_{1}$$-penalization for mixture regression models. Zbl 1203.62128
Städler, Nicolas; Bühlmann, Peter; Van de Geer, Sara
2010
Nemirovski’s inequalities revisited. Zbl 1213.60039
Dümbgen, Lutz; van de Geer, Sara A.; Veraar, Mark C.; Wellner, Jon A.
2010
Rejoinder to the comments on: $$\ell _{1}$$-penalization for mixture regression models. Zbl 1203.62129
Städler, Nicolas; Bühlmann, Peter; Van de Geer, Sara
2010
On the conditions used to prove oracle results for the Lasso. Zbl 1327.62425
van de Geer, Sara A.; Bühlmann, Peter
2009
High-dimensional additive modeling. Zbl 1360.62186
Meier, Lukas; van de Geer, Sara; Bühlmann, Peter
2009
Sparse recovery problems in high dimensions: statistical inference and learning theory. Abstracts from the mini-workshop held March 15th – March 21st, 2009. Zbl 1177.62001
2009
General oracle inequalities for model selection. Zbl 1326.62076
Mitchell, Charles; van de Geer, Sara
2009
The group Lasso for logistic regression. Zbl 1400.62276
Meier, Lukas; van de Geer, Sara; Bühlmann, Peter
2008
High-dimensional generalized linear models and the lasso. Zbl 1138.62323
van de Geer, Sara A.
2008
A moment bound for multi-hinge classifiers. Zbl 1225.68218
Tarigan, Bernadetta; Van De Geer, Sara A.
2008
Lectures on empirical processes. Theory and statistical applications. Zbl 1132.62001
del Barrio, Eustasio; Deheuvels, Paul; van de Geer, Sara
2007
On non-asymptotic bounds for estimation in generalized linear models with highly correlated design. Zbl 1176.62071
van de Geer, Sara A.
2007
Testing against a high dimensional alternative. Zbl 1110.62002
Goeman, Jelle J.; van de Geer, Sara A.; van Houwelingen, Hans C.
2006
Classifiers of support vector machine type with $$\ell_1$$ complexity regularization. Zbl 1118.62067
Tarigan, Bernadetta; van de Geer, Sara A.
2006
Square root penalty: Adaption to the margin in classification and in edge estimation. Zbl 1080.62047
Tsybakov, A. B.; van de Geer, S. A.
2005
Asymptotics in empirical risk minimization. Zbl 1222.68267
Mohammadi, Leila; Van De Geer, Sara
2005
Predicting survival using disease history: a model combining relative survival and frailty. Zbl 1090.62571
Goeman, J. J.; Le Cessie, S.; Baatenburg de Jong, R. J.; van de Geer, S. A.
2004
Estimating multiplicative and additive hazard functions by kernel methods. Zbl 1040.62089
Linton, Oliver B.; Nielsen, Jens Perch; van de Geer, Sara
2003
Asymptotic theory for maximum likelihood in nonparametric mixture models. Zbl 1429.62117
van de Geer, Sara
2003
Adaptive estimation with soft thresholding penalties. Zbl 1090.62534
Loubes, Jean-Michel; van de Geer, Sara
2002
On Hoeffding’s inequality for dependent random variables. Zbl 1027.60013
van de Geer, Sara A.
2002
M-estimation using penalties or sieves. Zbl 1030.62026
van de Geer, Sara
2002
Least squares estimation with complexity penalties. Zbl 1005.62043
van de Geer, Sara
2001
Applications of empirical process theory. Zbl 0953.62049
Van de Geer, Sara A.
2000
On robust recursive nonparametric curve estimation. Zbl 0958.62035
Belitser, Eduard; van de Geer, Sara
2000
Locally adaptive regression splines. Zbl 0871.62040
Mammen, Enno; van de Geer, Sara
1997
Penalized quasi-likelihood estimation in partial linear models. Zbl 0906.62033
Mammen, Enno; van de Geer, Sara
1997
Rates of convergence for the maximum likelihood estimator in mixture models. Zbl 0872.62039
van de Geer, Sara
1996
Consistency for the least squares estimator in nonparametric regression. Zbl 0867.62027
van de Geer, Sara; Wegkamp, Marten
1996
Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes. Zbl 0852.60019
van de Geer, Sara
1995
The method of sieves and minimum contrast estimators. Zbl 0831.62029
van de Geer, S.
1995
Asymptotic normality in mixture models. Zbl 0867.62026
van de Geer, Sara
1995
Hellinger-consistency of certain nonparametric maximum likelihood estimators. Zbl 0779.62033
Van de Geer, Sara
1993
Probabilistic analysis of the minimum weighted flowtime scheduling problem. Zbl 0761.90063
Marchetti Spaccamela, Alberto; Rhee, Wan Soo; Stougie, Leen; van de Geer, Sara
1992
On rates of convergence and asymptotic normality in the multiknapsack problem. Zbl 0753.90045
van de Geer, Sara; Stougie, Leen
1991
Estimating a regression function. Zbl 0709.62040
van de Geer, Sara
1990
Regression analysis and empirical processes. Zbl 0641.62041
van de Geer, S. A.
1988
A new approach to least-squares estimation, with applications. Zbl 0625.62046
van de Geer, Sara
1987
The likelihood ratio test for the change point problem for exponentially distributed random variables. Zbl 0671.62019
Haccou, Patsy; Meelis, Evert; van de Geer, Sara
1987
all top 5
### Cited by 2,692 Authors
56 Van de Geer, Sara Anna 45 Bühlmann, Peter 25 Lian, Heng 24 Huang, Jian 23 Fan, Jianqing 23 Tsybakov, Alexandre B. 18 Ma, Shuangge 17 Cheng, Guang 17 Mammen, Enno 17 Nickl, Richard 16 Zhang, Cun-Hui 13 Bradic, Jelena 13 Cui, Hengjian 13 Li, Runze 13 Wainwright, Martin J. 12 Dalalyan, Arnak S. 12 Liu, Han 12 Wellner, Jon August 11 Chernozhukov, Victor 11 Kolchinskiĭ, Vladimir I’ich 11 Lecué, Guillaume 11 Liang, Hua 11 Samworth, Richard J. 10 Wasserman, Larry Alan 10 Wegkamp, Marten H. 10 Zhu, Lixing 9 Guntuboyina, Adityanand 9 Lederer, Johannes 9 Lv, Jinchi 9 Meinshausen, Nicolai 9 Mendelson, Shahar 9 Munk, Axel 9 Sen, Bodhisattva 9 Tutz, Gerhard E. 9 Vieu, Philippe 9 Yuan, Ming 8 Alquier, Pierre 8 Cai, Tony Tony 8 Fan, Yingying 8 Kock, Anders Bredahl 8 Kohler, Michael 8 Liu, Yufeng 8 Raskutti, Garvesh 8 Shojaie, Ali 7 Aneiros-Pérez, Germán 7 Bellec, Pierre C. 7 Belloni, Alexandre 7 Bunea, Florentina 7 Candès, Emmanuel J. 7 Chatterjee, Sabyasachi 7 Claeskens, Gerda 7 Ghosal, Subhashis 7 Groeneboom, Piet 7 Honda, Toshio 7 Jiao, Yuling 7 Klopp, Olga 7 Kosorok, Michael R. 7 Kovac, Arne 7 Li, Hongzhe 7 Linton, Oliver Bruce 7 Loubes, Jean-Michel 7 Shang, Zuofeng 7 Suzuki, Taiji 7 Taylor, Jonathan E. 7 Tibshirani, Robert John 7 Tibshirani, Ryan J. 7 Zhang, Tong 7 Zheng, Zemin 7 Zou, Hui 6 Antoniadis, Anestis 6 Baraud, Yannick 6 Bartlett, Peter L. 6 Birgé, Lucien 6 Chetverikov, Denis 6 Fan, Xiequan 6 Gaïffas, Stéphane 6 Guo, Zijian 6 Hall, Peter Gavin 6 Han, Qiyang 6 Jordan, Michael Irwin 6 Kolar, Mladen 6 Koo, Ja-Yong 6 Lahiri, Soumendra Nath 6 Lei, Jing 6 Liao, Yuan 6 Meier, Lukas 6 Rigollet, Philippe 6 Rinaldo, Alessandro 6 Shah, Rajen Dinesh 6 Sun, Qiang 6 Van der Vaart, Adrianus Willem 6 Yu, Bin 6 Zhu, Ji 5 Carpentier, Alexandra 5 Davies, Patrick Laurie 5 Fadili, Jalal M. 5 Fang, Kuangnan 5 Foygel Barber, Rina 5 Guilloux, Agathe 5 Horowitz, Joel L. ...and 2,592 more Authors
all top 5
### Cited in 217 Serials
274 The Annals of Statistics 156 Electronic Journal of Statistics 84 Computational Statistics and Data Analysis 71 Journal of Multivariate Analysis 65 Bernoulli 63 Journal of Statistical Planning and Inference 61 Journal of the American Statistical Association 48 Journal of Machine Learning Research (JMLR) 41 Journal of Econometrics 31 Statistics and Computing 28 Statistics & Probability Letters 27 Statistical Science 25 Annals of the Institute of Statistical Mathematics 25 Communications in Statistics. Theory and Methods 24 Journal of Nonparametric Statistics 24 The Annals of Applied Statistics 21 Mathematical Programming. Series A. Series B 20 Probability Theory and Related Fields 20 Journal of Statistical Computation and Simulation 20 Test 20 Statistica Sinica 19 Biometrics 19 Statistics 19 Stochastic Processes and their Applications 18 Journal of Applied Statistics 17 Scandinavian Journal of Statistics 17 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 16 Computational Statistics 16 Communications in Statistics. Simulation and Computation 15 Journal of Computational and Graphical Statistics 14 Machine Learning 14 Statistical Papers 11 Metrika 11 Econometric Theory 10 Science China. Mathematics 9 Psychometrika 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Journal of the Royal Statistical Society. Series B. Statistical Methodology 9 SIAM Journal on Mathematics of Data Science 8 Neural Computation 7 The Canadian Journal of Statistics 7 Biometrical Journal 7 Journal of Optimization Theory and Applications 7 Econometric Reviews 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Statistical Applications in Genetics and Molecular Biology 7 Journal of the Korean Statistical Society 7 Advances in Data Analysis and Classification. ADAC 6 European Journal of Operational Research 6 Mathematical Methods of Statistics 6 Acta Mathematica Sinica. English Series 6 Statistical Methods and Applications 6 Sankhyā. Series A 5 Inverse Problems 5 Journal of Complexity 5 SIAM Journal on Optimization 5 Journal of Mathematical Imaging and Vision 5 Computational Optimization and Applications 5 Applied and Computational Harmonic Analysis 5 Lifetime Data Analysis 5 AStA. Advances in Statistical Analysis 5 SIAM Journal on Imaging Sciences 5 Journal of the Operations Research Society of China 4 Journal of the Franklin Institute 4 The Annals of Probability 4 Acta Mathematicae Applicatae Sinica. English Series 4 Journal of Theoretical Probability 4 The Annals of Applied Probability 4 Journal of Global Optimization 4 Journal of the European Mathematical Society (JEMS) 4 Analysis and Applications (Singapore) 4 Mathematical Statistics and Learning 4 Japanese Journal of Statistics and Data Science 3 Journal of Mathematical Analysis and Applications 3 Automatica 3 Operations Research 3 Statistica Neerlandica 3 Operations Research Letters 3 Constructive Approximation 3 Annals of Operations Research 3 Pattern Recognition 3 SIAM Journal on Scientific Computing 3 Electronic Communications in Probability 3 Optimization Methods & Software 3 Foundations of Computational Mathematics 3 Journal of Systems Science and Complexity 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Computational & Mathematical Methods in Medicine 3 Journal of Statistical Theory and Practice 3 Statistics Surveys 3 Sankhyā. Series B 3 SIAM/ASA Journal on Uncertainty Quantification 2 International Journal of Control 2 Lithuanian Mathematical Journal 2 Mathematical Biosciences 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Chinese Annals of Mathematics. Series B 2 International Journal of Approximate Reasoning 2 Mathematical and Computer Modelling ...and 117 more Serials
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### Cited in 32 Fields
1,588 Statistics (62-XX) 212 Numerical analysis (65-XX) 198 Probability theory and stochastic processes (60-XX) 160 Computer science (68-XX) 128 Operations research, mathematical programming (90-XX) 51 Biology and other natural sciences (92-XX) 40 Information and communication theory, circuits (94-XX) 35 Functional analysis (46-XX) 31 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 19 Combinatorics (05-XX) 15 Approximations and expansions (41-XX) 15 Systems theory; control (93-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 11 Operator theory (47-XX) 10 Partial differential equations (35-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 7 Convex and discrete geometry (52-XX) 5 General and overarching topics; collections (00-XX) 5 Integral equations (45-XX) 4 History and biography (01-XX) 4 Ordinary differential equations (34-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Real functions (26-XX) 3 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Special functions (33-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-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.
| 2022-08-11T02:01:18 |
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http://gams.cam.nist.gov/28.9
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# §28.9 Zeros
For real $q$ each of the functions $\mathrm{ce}_{2n}\left(z,q\right)$, $\mathrm{se}_{2n+1}\left(z,q\right)$, $\mathrm{ce}_{2n+1}\left(z,q\right)$, and $\mathrm{se}_{2n+2}\left(z,q\right)$ has exactly $n$ zeros in $0. They are continuous in $q$. For $q\to\infty$ the zeros of $\mathrm{ce}_{2n}\left(z,q\right)$ and $\mathrm{se}_{2n+1}\left(z,q\right)$ approach asymptotically the zeros of $\mathit{He}_{2n}\left(q^{1/4}(\pi-2z)\right)$, and the zeros of $\mathrm{ce}_{2n+1}\left(z,q\right)$ and $\mathrm{se}_{2n+2}\left(z,q\right)$ approach asymptotically the zeros of $\mathit{He}_{2n+1}\left(q^{1/4}(\pi-2z)\right)$. Here $\mathit{He}_{n}\left(z\right)$ denotes the Hermite polynomial of degree $n$18.3). Furthermore, for $q>0$ $\mathrm{ce}_{m}\left(z,q\right)$ and $\mathrm{se}_{m}\left(z,q\right)$ also have purely imaginary zeros that correspond uniquely to the purely imaginary $z$-zeros of $J_{m}\left(2\sqrt{q}\cos z\right)$10.21(i)), and they are asymptotically equal as $q\to 0$ and $\left|\Im z\right|\to\infty$. There are no zeros within the strip $\left|\Re z\right|<\tfrac{1}{2}\pi$ other than those on the real and imaginary axes.
For further details see McLachlan (1947, pp. 234–239) and Meixner and Schäfke (1954, §§2.331, 2.8, 2.81, and 2.85).
| 2017-07-24T10:49:05 |
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https://ftp.aimsciences.org/article/doi/10.3934/proc.2009.2009.385
|
Article Contents
Article Contents
Periodic solutions and their stability of a differential-difference equation
• Existence, stability, and shape of periodic solutions are derived for the differential-difference equation $\varepsilon\dot x(t)+x(t)=f(x([t-1])), 0<\varepsilon\<\<1,$ where $[\cdot]$ is the integer part function. The equation can be viewed as a special discretization (discrete version) of the singularly perturbed differential delay equation $\varepsilon\dot x(t)+x(t)=f(x(t-1))$. The principal analysis is based on reduction to the two-dimensional map $F: (u,v)\to (v, f(u)+ [v-f(u)]e^{-1/\varepsilon}),$ many relevant properties of which follow from those of the one-dimensional map $f$.
Mathematics Subject Classification: Primary: 34K13, 34K26; Secondary: 37E05.
Citation:
Open Access Under a Creative Commons license
| 2022-11-27T16:37:46 |
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http://tanb.agenziafunebretassoni.it/solve-matrix-in-python.html
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Text on GitHub with a CC-BY-NC-ND license Code on GitHub with a MIT license. A tridiagonal system for n unknowns may be written as. Square matrix – The matrix in which the number of rows is equal to the number of columns. The Linear Algebra module of NumPy offers various methods to apply linear algebra on any numpy array. Extended Capabilities. Tridiagonal Matrix Algorithm solver in Python. Smith-McMillan Form of a polynomial matrix. factorized (A) Return a function for solving a sparse linear system, with A pre-factorized. Below it is assumed that NumPy and SciPy are installed in your Python installation. GitHub Gist: instantly share code, notes, and snippets. The first row can be selected as X[0]. Solving equations and inverting matrices. In Matlab you would. See the first article in this series Solving linear equations using matrices and Python. "for a brief description. How can I solve a non-linear algebraic equation in ArcGIS python over multiple rasters. Each elementary row operation will be printed. Remember that a recursive algorithm has at least 2 parts: Base case(s) that determine when to stop. v0 = ps0,0 * rs0,0 + ps0,1 * rs0,1 + ps0,2 * rs0,2 + y(ps0,0 * v0 + ps0,1 * v1 + ps0,2 *v2) I am solving for v0,v1,v2. , each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the "magic constant. Introduction. Singular value decomposition (SVD). It is the lists of the list. The SVD decomposition is a factorization of a matrix, with many useful applications in signal processing and statistics. Mathematical Operations. If A is an m by n matrix of rank r, we know r ≤ m and r ≤ n. We've already looked at some other numerical linear algebra implementations in Python, including three separate matrix decomposition methods: LU Decomposition, Cholesky Decomposition and QR Decomposition. In linear algebra , Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. array, which only handles one-dimensional arrays and offers less functionality. Algorithm to solve a rat in a maze. The modern way to solve a system of linear equations is to transform the problem from one about numbers and ordinary algebra into one about matrices and matrix algebra. If A is the original matrix, then A = (L*U). First, we will find inverse of matrix A that we defined in the previous section. You can also find the dimensional of the matrix. It can be easily integrated with big data frameworks such as Spark and Hadoop. linalg as spla. PEP 465, a new matrix multiplication operator: a @ b. Thanks a lot, it was very very useful, if you have another tricks in python, please post it!!!. Inverse of a Matrix can be calculated by “inv” method of numpy’s linalg module. It contains more than 200 coding problem and will provide you. solve_undetermined_coeffs (equ, coeffs, sym, **flags) [source] ¶ Solve equation of a type p(x; a_1, …, a_k) == q(x) where both p, q are univariate polynomials and f depends on k parameters. See the Sage Constructions documentation for more examples. FEniCS is a popular open-source ( LGPLv3) computing platform for solving partial differential equations (PDEs). append(r1) M. The function accept the A matrix and the b vector (or matrix !) as input. The list example below shows another way to loop over a string or list using index numbers. Arrays are sequence types and behave very much like lists, except that the type of objects stored in them is constrained. This takes at least one argument: the left-hand-side of an equation to be solved. Dependencies and Setup. As it turns out, this is way too slow for this kind of problems, probably due to the fact that PuLP calls solvers externally via the command line. The matrix objects are a subclass of the numpy arrays (ndarray). Recursion¶. Singular values are important properties of a matrix. This is implemented below. To solve this regression problem we will use the random forest algorithm via the Scikit-Learn Python library. While the Cholesky decomposition only works for symmetric, positive definite matrices, the more general LU decomposition works for any square matrix. OpenCV comes with two methods, we will see both. It works just like the solve() function in R. 5x (or more) faster than numpy. If lower is True then the strictly upper triangular part of each inner-most matrix is assumed to be zero and not accessed. LinAlgError: Singular matrix Does anyone know what I am doing wrong? -Kenny. Inverse of an identity [I] matrix is an identity matrix [I]. We can treat each element as a row of the matrix. I wouldn't say it's thoroughly debugged yet, so let me know if you run into a problem. An option for entering a symmetrix matrix is offered which can speed up the processing when applicable. solve(A,B) It uses a LU decomposition method for solving (not inversion). For practice, I've written the following code, which uses Gaussian reduction to solve a system of linear equations. Then, if you want to solve multicollinearity reducing number of variables with a transformation, you could use a multidimensional scaling using some distance that remove redundancies. Equation Solver Gui Using Python Tkinter Sajeewa Pemasinghe. The Matrix Solution. Your function should take $$A$$ and $$b$$ as input and return $$x$$. First, we will find inverse of matrix A that we defined in the previous section. so you must provide the matrix with the zero values. array([4, 5, 6]) # linalg. Note: This is not how the la. Smith-McMillan Form of a polynomial matrix. Recursive part(s) that call the same algorithm (i. We have got what we were trying. solve (a, b) [source] ¶ Solve a linear matrix equation, or system of linear scalar equations. However, In this tutorial, we will be solving multiplication of two matrices in the Python programming language. izip is equivalent to the newer Python 3 zip function. Full column rank If r = n, then from the previous lecture we know that the nullspace has dimen sion n − r = 0 and contains only the zero vector. Check If Matrix Is Symmetric Python. of an array. The -matrices immediately give a number of important Fibonacci identities, including. You are encouraged to solve this task according to the task description, using any language you may know. We're living in the era of large amounts of data, powerful computers, and artificial intelligence. The operator. There is a sudoku solver included with the constraint package, but it's less flexible. Use this text box to input your dirty-formatted python code, and get a nice, well ordered file. Dataset: In this Confusion Matrix in Python example, the data set that we will be using is a subset of famous Breast Cancer Wisconsin (Diagnostic) data set. Join over 8 million developers in solving code challenges on HackerRank, one of the best ways to prepare for programming interviews. Python programming uses object-oriented concepts, such as class inheritance and operator overloading, to maintain a distinct separation between the problem formulation and the optimization. " Python calculates the square root and displays it on the next line. n1 = n1 self. See the code below. Write a Python program to calculate magic square. With help of this calculator you can: find the matrix determinant, the rank, raise the matrix to a power, find the sum and the multiplication of matrices, calculate the inverse matrix. The matrix rank will tell us that. The transpose of matrix A is written A T. Q: Create an algorithm for a menu based program that uses a switch-case statement to include the. The function accept the A matrix and the b vector (or matrix !) as input. If the state change is not dependent on the current state, A will be the zero matrix. The matrices are an important part of linear algebra as matrices is something we use to represent Vector mappings as well. 0 License , and code samples are licensed under the Apache 2. If the b matrix is a matrix, the result will be the solve function apply to all dimensions. To solve this regression problem we will use the random forest algorithm via the Scikit-Learn Python library. For example, to construct a numpy array that corresponds to the matrix. The advantage to using Python, is that we can create a dynamic function that would solve our equation, no matter the grid size. For sparse inputs, inv (X) creates a sparse identity matrix and uses backslash, X\speye (size (X)). matlab Showing 1-45 of 45 messages. Below are examples that show how to solve differential equations with (1) GEKKO Python, (2) Euler's method, (3) the ODEINT function from Scipy. The matrix objects inherit all the attributes and methods of ndarry. of an array. Among them, the equations at junior high school, the quadratic curve at high school and the calculus at university level are the most troublesome topics. CVXOPT supplies its own matrix object; all arguments given to its solvers must be in this matrix type. While the Cholesky decomposition only works for symmetric, positive definite matrices, the more general LU decomposition works for any square matrix. Consider a square matrix A of size n×n, elements of which may be either real or complex numbers. Is there any way to solve it faster in Python? My code is something like that, to solve a for the equation BT * UT = BT*B a, where m is the number of test cases (in my case over 5000), B is a data matrix m*17956, and u is 1*m. (Python 3 uses the range function, which acts like xrange). Now, you know both, so go and apply your newfound mastery of the Python square root function!. This Python exercise is a FREE course that will help you become more familiar with Python. choice() function for selecting a random password from word-list, Selecting a random item from the available data. Project: synthetic-data-tutorial Author: theodi File: PrivBayes. Type "print sqrt (root)" then press "Enter. 6, 12 Solve system of linear equations, using matrix method. solve() which solves a linear matrix equation, or system of linear scalar equation. Python array module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. Operation on Matrix : 1. A matrix that is easy to invert has a small condition number. Python's numerical library NumPy has a function numpy. Solve Linear Equations in Matrix Form. Diagonalize the matrix. Diagonal matrix – A matrix with all the non-diagonal elements equal to 0 is called a diagonal matrix. LinAlgError: Singular matrix Does anyone know what I am doing wrong? -Kenny. This command expects an input matrix and a right-hand-side vector. The idea is to perform elementary row operations to reduce the system to its row echelon form and then solve. A Python Program for Solving Schrödinger's Equation in Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming once students aim to make to construct a matrix representation of the Laplacian differential operator. Do that by eliminating one of the unknowns from two pairs of equations: either from equations 1) and 2), or 1) and 3), or 2) and 3). See the guide: Math > Matrix Math Functions Solves systems of linear equations. The Python programming language has no built-in support for linear algebra, but it is fairly straightforward to write code which will implement as much as you need. 2%; Makefile 3. SciPy also pronounced as "Sigh Pi. linalg as la NumPy Arrays. Solve a linear matrix equation, or system of linear scalar equations. , itself) to assist in solving the problem. linalg module; Solving linear systems: A x = b with A as a matrix and x, b as vectors. This module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. Python has awesome robust libraries for machine learning, natural language processing, deep learning, big data and artificial Intelligence. The following ultra-compact Python function performs in-place Gaussian elimination for given matrix, putting it into the Reduced Row Echelon Form. Normal equations¶. It means that we can find the values of x, y and z (the X matrix) by multiplying the inverse of the A matrix by the B matrix. Python is a simple, general purpose, high level, and object-oriented programming language. choice() function returns a random element from the non-empty sequence. When the first tank overflows, the liquid is lost and does not enter tank 2. There are many factors that play into this: Python's simple syntax, the fantastic PyData ecosystem, and of course buy-in from Python's BDFL. we can use the random. For simple application our data may only consist of 1 row or 1 column, so we don't consider it as a matrix. For example, "print sqrt (49. x − y + z = 4 2x + y − 3z = 0 x + y + z = 2 The system of equations is x − y + z = 4 2x + y − 3z = 0 x + y + z = 2 Step 1 Write equation as AX = B 1−1121−3111 𝑥𝑦𝑧 = 402 Hence A = 1−1. 02142857) and the 3x3 covariance matrix. Project: synthetic-data-tutorial Author: theodi File: PrivBayes. Solving a quadratic program¶. Redis with Python NumPy array basics A NumPy Matrix and Linear Algebra Pandas with NumPy and Matplotlib Celluar Automata Batch gradient descent algorithm Longest Common Substring Algorithm Python Unit Test - TDD using unittest. if you make an initial guess solution x0, an improved solution is x1 = inverse(D) * (b - Rx) where all multiplications are matrix-vector multiplication and inverse(D) is the matrix inverse. If the state change is not dependent on the current state, A will be the zero matrix. In this post we will see how to compute the SVD decomposition of a matrix A using numpy, how to compute the inverse of A using the matrices computed by the decomposition,. optimize import fsolve , newton_krylov import matplotlib. A is the 3x3 matrix of x, y and z coefficients; X is x, y and z, and ; B is 6, −4 and 27; Then (as shown on the Inverse of a Matrix page) the solution is this:. solve (a, b) [source] ¶ Solve a linear matrix equation, or system of linear scalar equations. Forming matrix from latter, gives the additional functionalities for performing various operations in matrix. The result x will be the same shape and size as b (that is, 1D, 2D row, or 2D column). they are n-dimensional. This module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. Boolean values are the two constant objects False and True. 2x + 5y - z = 27. And what is Linear Programming? See "What is Linear Programming?"and "Oh, and we also want to solve it as an integer program. – A matrix with 0 on all entries is the 0–matrix and is often written simply as 0. solve() function. About Python. leastsq ¶ Scipy provides a method called leastsq as part of its optimize package. The process is then iterated until it converges. This website is intended to host a variety of resources and pointers to information about Deep Learning. linalg as spla. I think changing #if 1 to #if 0 is designed to get lpsolve to accept numpy arrays or matrices without the convert tolist. The result will be a (mxl. This lecture discusses different numerical methods to solve ordinary differential equations, such as forward Euler, backward Euler, and central difference methods. Python Algebra. PHP is one of the best languages for the website development. The two matrices must be the same size, i. Data Science and Linear Algebra Fundamentals with Python, SciPy, & NumPy Math is relevant to software engineering but it is often overshadowed by all of the exciting tools and technologies. One can regard a column vector of length r as an r × 1 matrix and a row vector of length c as a 1×c matrix. The same loop as above, for num in nums:, will loop over all the values in a list. What included in these Python Exercises? Each exercise contains specific Python topic questions you need to practice and solve. If you are a python beginner and want to start learning the python programming, then keep your close attention in this tutorial as I am going to share a Python program to rotate a matrix with the output. Solving an optimization problem in Python. Project: synthetic-data-tutorial Author: theodi File: PrivBayes. First, we need to find the inverse of the A matrix (assuming it exists!) Using the Matrix Calculator we get this: (I left the 1/determinant outside the matrix to make the numbers simpler). From DataCamp's NumPy tutorial, you will have gathered that this library is one of the core libraries for scientific computing in Python. a i x i − 1 + b i x i + c i x i + 1 = d i. 0 x fun(x) Figure 1: Root found with uniroot The package was created to solve the steady-state and stability analysis examples in the book. Success! A_M has morphed into an Identity matrix, and I_M has become the inverse of A. As it turns out, this is way too slow for this kind of problems, probably due to the fact that PuLP calls solvers externally via the command. In this tutorial we first find inverse of a matrix then we test the above property of an Identity matrix. Sum Root to Leaf Numbers(Java and Python) Given a binary tree containing digits from 0-9 only, each root-to-leaf path could represent a number. So, I decided to write a solver for 3 x 3 systems in Python. Note that numpy:rank does not give you the matrix rank, but rather the number of dimensions of the array. Solve Equations in Python The following tutorials are an introduction to solving linear and nonlinear equations with Python. Let's first create the matrix A in Python. If the b matrix is a matrix, the result will be the solve function apply to all dimensions. [X,R] = linsolve (A,B) also returns the reciprocal of the condition number of A if A is a square matrix. You programmers that are into Big O thinking are cringing right now, and you should be!. Linear Algebra Operations¶. Solve Quadratic Equation in Python. Anyway, after reading Solving Sudoku in the Autumn 2005 issue of Warwick the Magazine (catchy title!) by Psychology lecturer Dr Neil Stewart, I finally got round to trying to solve Sudoku with Python. Forming matrix from latter, gives the additional functionalities for performing various operations in matrix. I have a system of coupled differential equations, one of which is second-order. Python has awesome robust libraries for machine learning, natural language processing, deep learning, big data and artificial Intelligence. read_csv (“/home/user/data1”) for row in df. I have created a python script that runs an OD cost matrix over five years from 1999 to 2004. In this article, you learn how to do algebraic mathematics computation in Python with SymPy module. Please note that MicroPython is different from the Python that runs on a computer. spsolve_triangular (A, b[, lower, …]) Solve the equation A x = b for x, assuming A is a triangular matrix. The sum of the infinite series is called the matrix exponential and denoted as etA:. svd function for that. coreascfc The computation is initialized by defining the topology matrix Edof, containing element numbers and global element. Simplex Method: It is one of the solution method used in linear programming problems that involves two variables or a large number of constraint. Determinant is calculated by reducing a matrix to row echelon form and multiplying its main diagonal elements. Python-Tesseract is a python wrapper that helps you use Tesseract-OCR engine to convert images to the accepted format from Python. The result of this functions is a dictionary with symbolic values of those parameters with respect to coefficients in q. You can also find the dimensional of the matrix. Do that by eliminating one of the unknowns from two pairs of equations: either from equations 1) and 2), or 1) and 3), or 2) and 3). Consider a set of equations in a matrix form , where A is a lower triangular matrix with non-zero diagonal elements. #!/usr/bin/env python from sympy import Symbol, solve x = Symbol('x') sol = solve(x**2 - x, x) print(sol) In SymPy, we can work with matrixes. The matrix for the maze shown above is: 0 1. To find the solution in Python, we type in the right hand side as a vector and the matrix. Please wait until "Ready!" is written in the 1,1 entry of the spreadsheet. linalg module; Solving linear systems: A x = b with A as a matrix and x, b as vectors. c and rebuild the interface. Transpose Matrix: If you change the rows of a matrix with the column of the same matrix, it is known as transpose of a matrix. Linear equations such as A*x=b are solved with NumPy in Python. Most probably because you're using a 32 bit version of Python. The SVD decomposition is a factorization of a matrix, with many useful applications in signal processing and statistics. , each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the "magic constant. Linear equations such as A*x=b are solved with NumPy in Python. where A is a square matrix, b is the right-hand side vector, and x is the vector to be found. Otherwise, linsolve returns the rank of A. To construct a matrix in numpy we list the rows of the matrix in a list and pass that list to the numpy array constructor. where is the identity matrix. linalg or numpy. From now on you will win all Sudoku challenges. Our Python tutorial is designed for beginners and professionals. vabr is 2 x 3 because it is the matrix product of a 2 x 2 and a 2 x 3. The following program demonstrates how two matrices can be added in python using the list data structure. Defining problems. The first code segment contains the equations explicitly entered as an array. The rst is to de ne the matrix directly with (potentially nested) lists: from cvxopt import matrix P = matrix([[1. Linear regression is a method for modeling the relationship between one or more independent variables and a dependent variable. choice() random. Solving Nar Algebraic Equations Springerlink. Solve this system of linear equations in matrix form by using linsolve. "100x" -> "100x", add some input validation, in particular check whether the equation is actually linear and not quadratic or cubic, and finally add a GUI to solve and plot multiple linear functions using different colors and get a nice tool for use in elementary mathematical education. The steps to solve the system of linear equations with np. When you venture into machine learning one of the fundamental aspects of your learning would be to understand “Gradient Descent”. Z3 can solve and crunch formulas. Years ago, I wrote a couple of short math books. The function accept the A matrix and the b vector (or matrix !) as input. C is a 3×2 matrix and D is a 2×4 matrix, so first I'll look at the dimension product for CD: So the product CD is defined (that is, I can do the multiplication); also, I can tell that I'm going to get a 3×4 matrix for my answer. With two standardized variables, our regression equation is. 0 Python API supports matrix-oriented modeling with NumPy and SciPy matrices. Let's now see how to solve a system of linear equations with the Numpy library. A matrix equation is Ax = b. Python's numerical library NumPy has a function numpy. linalg which builds on NumPy. Python is an interpreted, object-oriented, high-level programming language with dynamic semantics. Your function should take $$A$$ and $$b$$ as input and return $$x$$. The online course for beginners with more than 100 problems that turn you into a developer. A matrix that is easy to invert has a small condition number. Sage can perform various computations related to basic algebra and calculus: for example, finding solutions to equations, differentiation, integration, and Laplace transforms. SCS solves convex cone problems via operator splitting and it has a Python interface. In Matlab you would. However, we can treat list of a list as a matrix. func = fun self. It can be easily integrated with big data frameworks such as Spark and Hadoop. SfePy: Simple Finite Elements in Python¶ SfePy is a software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D. In fact, the general rule says that in order to perform the multiplication AB, where A is a (mxn) matrix and B a (kxl) matrix, then we must have n=k. SciPy is an Open Source Python-based library, which is used in mathematics, scientific computing, Engineering, and technical computing. For practice, I've written the following code, which uses Gaussian reduction to solve a system of linear equations. We can treat each element as a row of the matrix. But once the matrix is factored, solving Ax = b takes only O(n 2) operations. Write a Python program to calculate magic square. That's actually my background - well, mathematical physics, anyway. Unfortunately, many of the vector operations you learn in 151 cannot be done on lists, but we can convert them to type "Matrix" using the Matrix command. These are implemented under the hood using the same industry-standard Fortran libraries used in. This website is intended to host a variety of resources and pointers to information about Deep Learning. You are encouraged to solve this task according to the task description, using any language you may know. Numpy is a Python library which provides various routines for operations on arrays such as mathematical, logical, shape manipulation and many more. We can think of a 1D NumPy array as a list of numbers. Video of the Day. See the Sage Constructions documentation for more examples. Click to share on Twitter (Opens in new window) Click to share on Facebook (Opens in new window). Solving Problems Using Code. The first array represents the row indices, the second array represents column indices and the third array represents non-zero data in the element. A magic square is an arrangement of distinct numbers (i. Is there someone who can show me how I can do this with a loop in python (arcpy) instead of setting up the OD cost matrix for each year?. multiply () − multiply elements of two matrices. The row and column indices specify the location of non-zero element and the data array specifies the actual non-zero data in it. Transpose Matrix: If you change the rows of a matrix with the column of the same matrix, it is known as transpose of a matrix. Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4. Gradient Descent in Python. Extended Capabilities. There are various techniques for handling data in Python such as using Dictionaries, Tuples, Matrices, etc. Number Crunching and Related Tools. b can either be 1D or 2D -- and in fact if 2D it can be a row or a column! Some math packages that solve linear algebra problems would require that b be a 2D column, but not Python. Some of us even bet on this game but did you know that you can use python to make a Sudoku solver ? In this post I am going to share with you a Sudoku solver written in python. Python is a simple, general purpose, high level, and object-oriented programming language. Solving Banded Matrix Equations • To solve a set of equations with a banded coefficient matrix we use the scipy. Python is an interpreted scripting language also. Try this code. A random puzzle from the Internet. There are 7 different types of sparse matrices available. leastsq ¶ Scipy provides a method called leastsq as part of its optimize package. iterrows (): print (row) answered Mar 28, 2019 by Shri. We will also discuss different performance metrics classification accuracy, sensitivity, specificity, recall, and F1 score. Let's begin with a quick review of NumPy arrays. For those who are confused by the Python 2: First input asks for the matrix size (n). com homepage. Gradient Descent in Python. Below are simple examples of how to implement these methods in Python, based on formulas given in the lecture note (see lecture 7 on Numerical Differentiation above). Sudoku is a 9x9 matrix filled with numbers 1 to 9 in such a way that every row, column and sub-matrix (3x3) has each of the digits from 1 to 9. Pycalculix – Build FEA Models in Python Pycalculix is a tool I wrote which lets users build, solve, and query mechanical engineering models of parts. #!/usr/bin/env python from sympy import Symbol, solve x = Symbol('x') sol = solve(x**2 - x, x) print(sol) In SymPy, we can work with matrixes. Transformations is a Python library for calculating 4x4 matrices for translating, rotating, reflecting, scaling, shearing, projecting, orthogonalizing, and superimposing arrays of 3D homogeneous coordinates as well as for converting between rotation matrices, Euler angles, and quaternions. if you make an initial guess solution x0, an improved solution is x1 = inverse(D) * (b - Rx) where all multiplications are matrix-vector multiplication and inverse(D) is the matrix inverse. The process is then iterated until it converges. I wouldn't say it's thoroughly debugged yet, so let me know if you run into a problem. Extended Capabilities. The rst is to de ne the matrix directly with (potentially nested) lists: from cvxopt import matrix P = matrix([[1. The first row can be selected as X[0]. Order of matrix – If a matrix has 3 rows and 4 columns, order of the matrix is 3*4 i. So let's go ahead and do that. Module pywraplp from sys import version_info as _swig_python_version_info if _swig_python_version_info < (2, 7, 0): raise RuntimeError("Python 2. Without the conversion, you're in $$\mathcal{O}(1)$$. To create a matrix, the array method of the Numpy module can be used. And, today we will use Python to solve the equations, and do calculus and matrix. Let's now see how to solve a system of linear equations with the Numpy library. Created by experts, Khan Academy’s library of trusted, standards-aligned practice and lessons covers math K-12 through early college, grammar, science, history, AP®, SAT®, and more. Reproduce textbook content on a calculator!. Learn Statistical Analysis, Data Mining And Visualization. Also see Formulation of an lp problem in. Inverse of a Matrix can be calculated by “inv” method of numpy’s linalg module. The code below is modified for Python 3. NumPy arrays are designed to handle large data sets efficiently and with a minimum of fuss. A matrix product between a 2D array and a suitably sized 1D array results in a 1D array: In [199]: np. Mr325 Demo. If our set of linear equations has constraints that are deterministic, we can represent the problem as matrices and apply matrix algebra. It can be easily integrated with big data frameworks such as Spark and Hadoop. [X,R] = linsolve (A,B) also returns the reciprocal of the condition number of A if A is a square matrix. Solve Differential Equations in Python source Differential equations can be solved with different methods in Python. plotting import plot plot(1/x) The example plots a 2d graph of a 1/x function. In this tutorial, we will make use of NumPy's numpy. But before that, we can refine the camera matrix based on a free scaling parameter using cv2. Diagonal matrix – A matrix with all the non-diagonal elements equal to 0 is called a diagonal matrix. MatrixRankWarning. For example, a Sudoku problem is given below. Below are simple examples of how to implement these methods in Python, based on formulas given in the lecture note (see lecture 7 on Numerical Differentiation above). For example, "print sqrt (49. divide() − divide elements of two matrices. choice(sequence) Here sequence can be a list, string, tuple. ) or 0 (no, failure, etc. Solving Matrix Equation. leastsq ¶ Scipy provides a method called leastsq as part of its optimize package. Now, you know both, so go and apply your newfound mastery of the Python square root function!. The non-zero and non-diagonal elements of the lower triangular matrix are the factors we used to arrive at our Gaussian matrix. I1 = [1], I2 = [1 0 0 1], I3 = [1 0. Arrays are sequence types and behave very much like lists, except that the type of objects stored in them is constrained. This is the way we keep it in this chapter of our. In this tutorial, we will make use of NumPy's numpy. If you have a list of items (a list of car names, for example), storing the cars in single variables could look like this: However, what if you want to loop through the cars. Linear Regression In Python Towards Data Science. It’s easy to create well-maintained, Markdown or rich text documentation alongside your code. Defining problems. Inverse Matrix in Python. For example, I will create three lists and will pass it the matrix () method. For a solution, see the post “ Quiz 13 (Part 1) Diagonalize a matrix. A Markov chain is a discrete-time stochastic process that progresses from one state to another with certain probabilities that can be represented by a graph and state transition matrix P as indicated below: Such chains, if they are first-order Markov Chains, exhibit the Markov property, being that the next state is only dependent on the current. Please note that MicroPython is different from the Python that runs on a computer. The cross-shore component of wavenumber is found as the gradient in phase of the first complex empirical orthogonal function of this matrix. The cheapest price from city 0 to city 2 with at most 1 stop costs 200, as marked red in the picture. Solve the sparse linear system Ax=b, where b may be a vector or a matrix. The Jacobi method is a matrix iterative method used to solve the equation Ax = b for a. Below are simple examples of how to implement these methods in Python, based on formulas given in the lecture note (see lecture 7 on Numerical Differentiation above). For example: A = [[1, 4, 5], [-5, 8, 9]] We can treat this list of a list as a matrix having 2 rows and 3 columns. Evaluation of Matrix Exponential Using Fundamental Matrix: In the case A is not diagonalizable, one approach to obtain matrix exponential is to use Jordan forms. To avoid this problem, we […]. Let us rst de ne the above parameters in Python. Using python to solve simultaneous equations relies on matrix linear algebra and can be done by using a built-in function (method 1) or manually (method 2) manually manipulating the matrices to solve. Additional information is provided on using APM Python for parameter estimation with dynamic models and scale-up […]. 1) Just put the funtion in a file called linsolve. Anyway, after reading Solving Sudoku in the Autumn 2005 issue of Warwick the Magazine (catchy title!) by Psychology lecturer Dr Neil Stewart, I finally got round to trying to solve Sudoku with Python. These operations and array are defines in module " numpy ". PHP (recursive acronym for PHP: Hypertext Preprocessor) is a widely-used open source general-purpose scripting language that is especially suited for web development and can be embedded into HTML. lstsq(F,E). About Python. Matrix can be expanded to a graph related problem. Evaluate expressions with arbitrary precision. Quadratic Programming in Python Quadratic programs are a particular class of numerical optimization problems with several applications such as in statistics for curve fitting, in machine learning to compute support vector machines (SVMs) , in robotics to solve inverse kinematics , etc. As Windows (and most other OSes as well) limits. Recursive parts. Description. Solving Ax=B by inverting matrix A can be lot more computationally intensive than solving directly. Python's numerical library NumPy has a function numpy. 8-Puzzle is an interesting game which requires a player to move blocks one at a time to solve a picture or a particular pattern. You are encouraged to solve this task according to the task description, using any language you may know. It aims to be an alternative to systems such as Mathematica or Maple while keeping the code as simple as possible and easily extensible. Import the array from numpy inside matrix. You can use decimal (finite and periodic) fractions: 1/3, 3. PHP (recursive acronym for PHP: Hypertext Preprocessor) is a widely-used open source general-purpose scripting language that is especially suited for web development and can be embedded into HTML. The quadratic equation is defined as below :. Notes-----This module is a lite version of the linalg. If you call gj_Solve(A) — i. While ode is more versatile, odeint (ODE integrator) has a simpler Python interface works very well for most problems. If you don't know about backtracking, then just brush through the previous post. linalg or numpy. solve(): Solve a linear matrix equation, or system of linear scalar equations. The code below is modified for Python 3. • The format for this function is slin. A small perturbation of a singular matrix is non-singular, but the condition number will be large. we can calculate the matrices. NumPy has a function to solve linear equations. 1 will represent the blocked cell and 0 will represent the cells in which we can move. An assignment at school required me to write a Python program for this task: In the matrix-chain multiplication problem, we are given a sequence of matrices A(1), A(2), …, A(n). The user will enter the values of the equation, our program will solve it and print out the result. Video of the Day. pandas is a NumFOCUS sponsored project. append(r2) [/code]And now you have a list of lists, nested list, multidimensional list,. choice(sequence) Here sequence can be a list, string, tuple. In python matrix can be implemented as 2D list or 2D Array. ePythoGURU is a platform for those who want ot learn programming related to python and cover topics related to calculus, Multivariate Calculus, ODE, Numericals Methods Concepts used in Python Programming. solve_undetermined_coeffs (equ, coeffs, sym, **flags) [source] ¶ Solve equation of a type p(x; a_1, …, a_k) == q(x) where both p, q are univariate polynomials and f depends on k parameters. From the DSP implementation point of view, computation of requires one FLoating Point Operation per Second (FLOPS) - only one. Free matrix equations calculator - solve matrix equations solver step-by-step This website uses cookies to ensure you get the best experience. In this article I am going to attempt to explain the fundamentals of gradient descent using python code. Leave extra cells empty to enter non-square matrices. I think it's difficult to see space complexity in python programs. In numerical linear algebra, the Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. PHP is one of the best languages for the website development. Delegates to x. If A is the original matrix, then A = (L*U). In computational physics, with Numpy and also Scipy (numeric and scientific library for Python), we can solve many complex problems because it provides matrix solver (eigenvalue and eigenvector solver), linear algebra operation, as well as signal processing, Fourier transform, statistics, optimization, etc. The example above uses two variables x and y, and three constraints. (In retrospect, we all think PEP 225 was a bad idea too -- or at least far more complex than it needed to be. The idea is to perform elementary row operations to reduce the system to its row echelon form and then solve. Using Python to Solve Partial Differential Equations This article describes two Python modules for solving partial differential equations (PDEs): PyCC is designed as a Matlab-like environment for writing algorithms for solving PDEs, and SyFi creates matrices based on symbolic mathematics, code generation, and the finite element method. Actually, conducting a numerical studies either with Python, Matlab or C++ is alike that you should understand physical incident, find appropriate mathematical model, carry out discretization studies, and apply a matrix solver in case problem is differential equation. The solution to linear equations is through matrix operations while sets of nonlinear equations require a solver to numerically find a solution. You make a list: [code]M = list() [/code]You make a second and third list: [code]r1 = [1,2,3] r2 = [4,5,6] [/code]You put both lists in M: [code]M. array([[1,2],[3,4]]) # Solution Array B= np. linalg documentation for details. – A matrix with 0 on all entries is the 0–matrix and is often written simply as 0. sqrt(a) Square root: log(a) math. First, we need to find the inverse of the A matrix (assuming it exists!) Using the Matrix Calculator we get this: (I left the 1/determinant outside the matrix to make the numbers simpler). NumPy arrays are designed to handle large data sets efficiently and with a minimum of fuss. The determinant of a matrix is a numerical value computed that is useful for solving for other values of a matrix such as the inverse of a matrix. Python calls vectors and matrices "arrays", You can create a vector with array([1. eig returns a tuple (eigvals,eigvecs) where eigvals is a 1D NumPy array of complex numbers giving the eigenvalues of. I do love Jupyter notebooks, but I want to use this in scripts now too. In this tutorial, you will learn: SciPy contains varieties of sub packages which help to solve the most common issue related to Scientific. Using python to solve simultaneous equations relies on matrix linear algebra and can be done by using a built-in function (method 1) or manually (method 2) manually manipulating the matrices to solve. That is, all the non-zero elements are in the lower triangle: Write a C program to find whether a given matrix is a lower triangular matrix or not. linalg): import scipy x_qr2 = scipy. A matrix can be considered as a list. Created by experts, Khan Academy’s library of trusted, standards-aligned practice and lessons covers math K-12 through early college, grammar, science, history, AP®, SAT®, and more. Introduction. bsr_matrix: Block Sparse Row matrix; coo_matrix: COOrdinate format matrix; csc_matrix: Compressed Sparse Column matrix; csr_matrix: C ompressed Sparse R ow matrix. Solve Differential Equations in Python source Differential equations can be solved with different methods in Python. Perform algebraic manipulations on symbolic expressions. A computer program was created in Python to read the muon flux rate and atmospheric pressure sensor readings from the detector's data acquisition board. n1 = n1 self. An identity matrix of size n is denoted by In. As it turns out, this is way too slow for this kind of problems, probably due to the fact that PuLP calls solvers externally via the command. solve is the function of NumPy to solve a system of linear scalar equations print "Solutions:\n",np. When you venture into machine learning one of the fundamental aspects of your learning would be to understand “Gradient Descent”. Using Python environments in VS Code. They are from open source Python projects. 6%; Branch: master. The example above uses two variables x and y, and three constraints. I would be extremely grateful for any advice on how can I do that!. Read the instructions. In Python, we can implement a matrix as nested list (list inside a list). The first row can be selected as X [0]. ) or 0 (no, failure, etc. Check If Matrix Is Symmetric Python. Evaluate expressions with arbitrary precision. iterrows (): print (row) answered Mar 28, 2019 by Shri. Andrew Mao • 2 years ago. Python's NumPy has linalg. Python's numerical library NumPy has a function numpy. To install a package, use the pkg command from the Octave prompt by typing: pkg install -forge package_name, where package_name is the name of the package you want to install. Python array module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. Solve this system of linear equations in matrix form by using linsolve. We're going to use the identity matrix I in the process for inverting a matrix. In eq 2, h is some small number and represents a. In Matlab you would. If you have made syntax mistakes, It will complain and don't give you the cookie ;). Data Science and Linear Algebra Fundamentals with Python, SciPy, & NumPy Math is relevant to software engineering but it is often overshadowed by all of the exciting tools and technologies. See the code below. I guess nice try would be making a matrix in x,y coordinates and solve the schroedinger equation in odeint() with two variables. Solving Matrix Equations with Sympy solve. I would be extremely grateful for any advice on how can I do that!. First, I write down the entries the matrix A, but I write them in a double-wide matrix:. Using Python environments in VS Code. Sympy has a sophisticated ability to solve systems of equations. Write a function in Python to solve a system $Ax = b$ using SVD decomposition. The dividing matrices operation M1/M2 M 1 / M 2 consist in the multiplication of the matrix M1 M 1 by the. solve() which solves a linear matrix equation, or system of linear scalar equation. Evaluate expressions with arbitrary precision. Do that by eliminating one of the unknowns from two pairs of equations: either from equations 1) and 2), or 1) and 3), or 2) and 3). Python Matrices and NumPy Arrays In this article, we will learn about Python matrices using nested lists, and NumPy package. solve() function. Machine learning and data science method for Netflix challenge, Amazon ratings, +more. I attribute obtains the inverse of a matrix. The following ultra-compact Python function performs in-place Gaussian elimination for given matrix, putting it into the Reduced Row Echelon Form. A matrix is a two-dimensional data structure where numbers are arranged into rows and columns. Note: Python does not have built-in support for Arrays, but Python Lists can be used instead. Using numpy to solve the system import numpy as np # define matrix A using Numpy arrays A = np. solve_triangular(R, Qb, check_finite=False) This is 5. Solving Banded Matrix Equations • To solve a set of equations with a banded coefficient matrix we use the scipy. In this series, we will show some classical examples to solve linear equations Ax=B using Python, particularly when the dimension of A makes it computationally expensive to calculate its inverse. In this Python article, we are going to learn how to create a BMI (stands for - Body Mass Index) calculator? Submitted by Anoop Nair, on November 09, 2017. In particular, I will discuss finding the inverse matrix in Python, solving the linear system, finding determinant, computing norms, solving linear least-squares problems and pseudo-inverses, as well as decompositions of eigenvalues and eigenvectors. Build projects and get yourselves out there!! EDIT: Thanks everyone. It’s easy to create well-maintained, Markdown or rich text documentation alongside your code. These are implemented under the hood using the same industry-standard Fortran libraries used in. I have the following system of 3 nonlinear equations that I need to solve in python: 7 = -10zt + 4yzt - 5yt + 4tz^2 3 = 2yzt + 5yt 1 = - 10t + 2yt + 4zt Therefore I need to solve for y,z, and t. The steps are. Solving a quadratic program¶. We start off by writing a function to check if a given word…. array is not the same as the Standard Python Library class array. The strategy is to reduce this to two equations in two unknowns. In addition to its use in. Python has a number of built-in functions that you may be familiar with, including: Function names include parentheses and may include parameters. One entry for each variable. Created by experts, Khan Academy’s library of trusted, standards-aligned practice and lessons covers math K-12 through early college, grammar, science, history, AP®, SAT®, and more. The function accept the A matrix and the b vector (or matrix !) as input. vabs is 2 x 1 because it is the matrix product of a 2 x 3 and a 3 x 1. SOLVE IN PYTHON: Exercise #1: Develop a PYTHON program (name it SumArrayColumns) that prints out the sum of each column of a two-dimensional array. pyplot as plt class ImpRK4 : def __init__(self, fun , t0, tf, dt , y0): self. How do I solve this problem in Python using matrices? I've already solved the problem by hand using my textbook, but I can't figure out how to convert it into matrices and solve using python. Whilst I agree with the general consensus of responders that this is not the best way to solve the minimisation problem in the question, I have now resolved the challenge and can answer my own question to share the way one might overcome similar issues in using penalty methods to resolve optimisation problems in Python. Python-Tesseract is a python wrapper that helps you use Tesseract-OCR engine to convert images to the accepted format from Python. In this article we will present a NumPy/SciPy listing, as well as a pure Python listing, for the LU Decomposition method, which is used in certain quantitative finance algorithms. This could be especially handy if, as in our example above, we decided to add more repairs, or get more contractor quotes. The diffusion equations: Assuming a constant diffusion coefficient, D, we use the Crank-Nicolson methos (second order accurate in time and space): u[n+1,j]-u[n,j] = 0. solve_triangular(R, Qb, check_finite=False) This is 5. ePythonGURU -Python is Programming language which is used today in Web Development and in schools and colleges as it cover only basic concepts. This turns out to be a very powerful idea but we will first need to know some basic facts about matrices before we can understand how they help to solve linear equations. To install a package, use the pkg command from the Octave prompt by typing: pkg install -forge package_name, where package_name is the name of the package you want to install. log10(a) Logarithm, base 10. , the characteristic polynomial, echelon form, trace, decomposition, etc. The right-hand-side is assumed to be zero. Create a matrix. Steps to Solve Problems. Arrays are sequence types and behave very much like lists, except that the type of objects stored in them is constrained. 0/(10**10)): """Puts given matrix (2D array) into the Reduced Row Echelon Form. Python array module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. choice() function returns a random element from the non-empty sequence. solve_banded((l,u), cm, rhs) • (l, u) is a tuple where l is the number of nonzero lower diagonals, and u is the number of nonzero upper diagonals. The function accept the A matrix and the b vector (or matrix !) as input. In the example above, the expression x + 2*y == 7 is a Z3 constraint. This flag allows objects which occupy more than 2gb of memory, but it does not permit a single-dimensional array to contain more than 2^31 entries. To find the solution in Python, we type in the right hand side as a vector and the matrix. This website is intended to host a variety of resources and pointers to information about Deep Learning. solve(): Solve a linear matrix equation, or system of linear scalar equations. numerical and administrative tasks. Include the entire matrix in this. Solving equations and inverting matrices. Quadratic programs can be solved via the solvers. solve is the function of NumPy to solve a system of linear scalar equations print "Solutions:\n",np. Here's the multiplication: Since the inner dimensions don't match, I can't do the multiplication. I originally looked at the Wikipedia pseudocode and tried to essentially rewrite that in Python, but that was more trouble than it was worth so I just redid it from scratch. b can either be 1D or 2D -- and in fact if 2D it can be a row or a column! Some math packages that solve linear algebra problems would require that b be a 2D column, but not Python. Python is a programming language in addition that lets you work quickly and integrate systems more efficiently. SCS solves convex cone problems via operator splitting and it has a Python interface. The above shown matrices are generated by the Element class shown below:. Simple Markov chain weather model. It is the lists of the list. The matrix rank will tell us that. In Python, we can implement a matrix as nested list (list inside a list). spsolve_triangular (A, b[, lower, …]) Solve the equation A x = b for x, assuming A is a triangular matrix. dot: If both a and b are 1-D (one dimensional) arrays -- Inner product of two vectors (without complex conjugation) If both a and b are 2-D (two dimensional) arrays -- Matrix multiplication. Matrix can be expanded to a graph related problem. Learn to use NumPy for Numerical Data. Boolean values are the two constant objects False and True.
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https://www.zbmath.org/authors/?q=ai%3Aschuster.thomas
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# zbMATH — the first resource for mathematics
## Schuster, Thomas
Compute Distance To:
Author ID: schuster.thomas Published as: Schuster, T.; Schuster, Th.; Schuster, Thomas Homepage: http://www.num.uni-sb.de/schuster/index.php/en/ External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 49 Publications since 1996, including 2 Books
all top 5
#### Co-Authors
8 single-authored 12 Schöpfer, Frank 7 Louis, Alfred Karl 6 Derevtsov, Evgeny Yurievich 6 Rieder, Andreas 3 Wöstehoff, Arne 2 Binder, Franz 2 Dietz, Rainer 2 Kaltenbacher, Barbara 2 Katsevich, Alexander I. 2 Kazantsev, Sergeĭ Gavrilovich 2 Kazimierski, Kamil S. 2 Quinto, Eric Todd 2 Seydel, Julia 2 Volkov, Yuriĭ Stepanovich 2 Wald, Anne 1 Bonesky, Thomas 1 Burger, Martin 1 Efimov, Anton V. 1 Hahn, Bernadette Nadine 1 Haltmeier, Markus 1 Heber, Frederik 1 Hofmann, Bernd 1 Littau, Benjamin 1 Maass, Peter 1 Pfitzenreiter, Tim 1 Rothermel, Dimitri 1 Scherzer, Otmar 1 Schröder, Udo 1 Svetov, Ivan Evgenyevich 1 Tepe, Jens 1 Weickert, Joachim
all top 5
#### Serials
18 Inverse Problems 10 Journal of Inverse and Ill-Posed Problems 3 Mathematical Methods in the Applied Sciences 1 Applicable Analysis 1 Mathematics of Computation 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 SIAM Journal on Applied Mathematics 1 Mathematical Problems in Engineering 1 Abstract and Applied Analysis 1 Inverse Problems in Science and Engineering 1 Lecture Notes in Mathematics 1 Inverse Problems and Imaging 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 SIAM Journal on Imaging Sciences 1 Radon Series on Computational and Applied Mathematics
all top 5
#### Fields
42 Numerical analysis (65-XX) 20 Integral transforms, operational calculus (44-XX) 15 Biology and other natural sciences (92-XX) 13 Operator theory (47-XX) 11 Partial differential equations (35-XX) 5 Mechanics of deformable solids (74-XX) 4 Integral equations (45-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 Special functions (33-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH
42 Publications have been cited 455 times in 311 Documents Cited by Year
Regularization methods in Banach spaces. Zbl 1259.65087
Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S.
2012
An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Zbl 1153.46308
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Zbl 1088.65052
Schöpfer, F.; Louis, A. K.; Schuster, T.
2006
Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems. Zbl 1176.65070
Kaltenbacher, Barbara; Schöpfer, Frank; Schuster, Thomas
2009
Filtered backprojection for thermoacoustic computed tomography in spherical geometry. Zbl 1085.65092
Haltmeier, M.; Schuster, T.; Scherzer, O.
2005
Fast regularizing sequential subspace optimization in Banach spaces. Zbl 1165.47010
Schöpfer, F.; Schuster, T.
2009
Local inversion of the sonar transform regularized by the approximate inverse. Zbl 1214.65066
Quinto, Eric Todd; Rieder, Andreas; Schuster, Thomas
2011
Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods. Zbl 1160.46048
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
The approximate inverse in action with an application to computerized tomography. Zbl 0961.65112
Rieder, Andreas; Schuster, Thomas
2000
Minimization of Tikhonov functionals in Banach spaces. Zbl 1357.49135
Bonesky, Thomas; Kazimierski, Kamil S.; Maass, Peter; Schöpfer, Frank; Schuster, Thomas
2008
An efficient mollifier method for three-dimensional vector tomography: Convergence analysis and implementation. Zbl 0988.65121
Schuster, Thomas
2001
The approximate inverse in action II: convergence and stability. Zbl 1022.65066
Rieder, Andreas; Schuster, Thomas
2003
The approximate inverse in action. III: 3D-Doppler tomography. Zbl 1071.65178
Rieder, Andreas; Schuster, Thomas
2004
Sequential subspace optimization for nonlinear inverse problems. Zbl 1355.65147
Wald, Anne; Schuster, Thomas
2017
Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography. Zbl 1279.33015
Derevtsov, Evgeny Y.; Efimov, Anton V.; Louis, Alfred K.; Schuster, Thomas
2011
Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions. Zbl 1124.33015
Derevtsov, E. Yu.; Kazantsev, S. G.; Schuster, Th.
2007
The 3D Doppler transform: Elementary properties and computation of reconstruction kernels. Zbl 1017.44005
Schuster, Thomas
2000
An iterative method to reconstruct the refractive index of a medium from time-of-flight measurements. Zbl 1388.35226
Schröder, Udo; Schuster, Thomas
2016
An exact inversion formula for cone beam vector tomography. Zbl 1273.45010
Katsevich, Alexander; Schuster, Thomas
2013
The method of approximate inverse: Theory and applications. Zbl 1171.65001
Schuster, Thomas
2007
Tomographic reconstruction of the curl and divergence of 2D vector fields taking refractions into account. Zbl 1208.65179
Pfitzenreiter, Tim; Schuster, Thomas
2011
On a regularization scheme for linear operators in distribution spaces with an application to the spherical Radon transform. Zbl 1081.65122
Schuster, Thomas; Quinto, Eric Todd
2005
A novel filter design technique in 2D computerized tomography. Zbl 0863.65085
Louis, A. K.; Schuster, Th.
1996
On the identifiability of the stored energy function of hyperelastic materials from sensor data at the boundary. Zbl 1304.35771
Schuster, Thomas; Wöstehoff, Arne
2014
On the application of projection methods for computing optical flow fields. Zbl 1147.68817
Schuster, Thomas; Weickert, Joachim
2007
Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the method. Zbl 1078.65123
Schuster, Thomas
2005
Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem. Zbl 0961.65113
Derevtsov, E. Yu.; Dietz, R.; Louis, A. K.; Schuster, T.
2000
Acceleration of sequential subspace optimization in Banach spaces by orthogonal search directions. Zbl 06950464
Heber, Frederik; Schöpfer, Frank; Schuster, Thomas
2019
Tomographic terahertz imaging using sequential subspace optimization. Zbl 1401.78007
Wald, Anne; Schuster, Thomas
2018
An improved exact inversion formula for solenoidal fields in cone beam vector tomography. Zbl 1370.65073
Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas
2017
Asymptotic inversion formulas in 3D vector field tomography for different geometries. Zbl 1279.42028
Kazantsev, Sergey G.; Schuster, Thomas
2011
A stable inversion scheme for the Laplace transform using arbitrarily distributed data scanning points. Zbl 1032.65140
Schuster, T.
2003
Preface: Dynamic inverse problems: modelling-regularization-numerics. Zbl 1395.00048
Schuster, Thomas (ed.); Hahn, Bernadette (ed.); Burger, Martin (ed.)
2018
A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography. Zbl 1398.65363
Tepe, Jens; Schuster, Thomas; Littau, Benjamin
2017
Identifying the stored energy of a hyperelastic structure by using an attenuated Landweber method. Zbl 1394.74047
Seydel, Julia; Schuster, Thomas
2017
On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field. Zbl 1366.35243
Seydel, J.; Schuster, T.
2017
Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials. Zbl 1326.35207
Wöstehoff, A.; Schuster, T.
2015
Defect localization in fibre-reinforced composites by computing external volume forces from surface sensor measurements. Zbl 1333.35338
Binder, F.; Schöpfer, F.; Schuster, T.
2015
Solving linear operator equations in Banach spaces non-iteratively by the method of approximate inverse. Zbl 1218.47023
Schuster, Thomas; Schöpfer, Frank
2010
Error estimates for defect correction methods in Doppler tomography. Zbl 1099.65131
Schuster, T.
2006
Two approaches to the problem of defect correction in vector field tomography solving boundary value problems. Zbl 1099.65101
Derevtsov, E. Yu.; Louis, A. K.; Schuster, T.
2004
Approximate inverse meets local tomography. Zbl 0966.65109
Rieder, Andreas; Dietz, Rainer; Schuster, Thomas
2000
Acceleration of sequential subspace optimization in Banach spaces by orthogonal search directions. Zbl 06950464
Heber, Frederik; Schöpfer, Frank; Schuster, Thomas
2019
Tomographic terahertz imaging using sequential subspace optimization. Zbl 1401.78007
Wald, Anne; Schuster, Thomas
2018
Preface: Dynamic inverse problems: modelling-regularization-numerics. Zbl 1395.00048
Schuster, Thomas (ed.); Hahn, Bernadette (ed.); Burger, Martin (ed.)
2018
Sequential subspace optimization for nonlinear inverse problems. Zbl 1355.65147
Wald, Anne; Schuster, Thomas
2017
An improved exact inversion formula for solenoidal fields in cone beam vector tomography. Zbl 1370.65073
Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas
2017
A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography. Zbl 1398.65363
Tepe, Jens; Schuster, Thomas; Littau, Benjamin
2017
Identifying the stored energy of a hyperelastic structure by using an attenuated Landweber method. Zbl 1394.74047
Seydel, Julia; Schuster, Thomas
2017
On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field. Zbl 1366.35243
Seydel, J.; Schuster, T.
2017
An iterative method to reconstruct the refractive index of a medium from time-of-flight measurements. Zbl 1388.35226
Schröder, Udo; Schuster, Thomas
2016
Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials. Zbl 1326.35207
Wöstehoff, A.; Schuster, T.
2015
Defect localization in fibre-reinforced composites by computing external volume forces from surface sensor measurements. Zbl 1333.35338
Binder, F.; Schöpfer, F.; Schuster, T.
2015
On the identifiability of the stored energy function of hyperelastic materials from sensor data at the boundary. Zbl 1304.35771
Schuster, Thomas; Wöstehoff, Arne
2014
An exact inversion formula for cone beam vector tomography. Zbl 1273.45010
Katsevich, Alexander; Schuster, Thomas
2013
Regularization methods in Banach spaces. Zbl 1259.65087
Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S.
2012
Local inversion of the sonar transform regularized by the approximate inverse. Zbl 1214.65066
Quinto, Eric Todd; Rieder, Andreas; Schuster, Thomas
2011
Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography. Zbl 1279.33015
Derevtsov, Evgeny Y.; Efimov, Anton V.; Louis, Alfred K.; Schuster, Thomas
2011
Tomographic reconstruction of the curl and divergence of 2D vector fields taking refractions into account. Zbl 1208.65179
Pfitzenreiter, Tim; Schuster, Thomas
2011
Asymptotic inversion formulas in 3D vector field tomography for different geometries. Zbl 1279.42028
Kazantsev, Sergey G.; Schuster, Thomas
2011
Solving linear operator equations in Banach spaces non-iteratively by the method of approximate inverse. Zbl 1218.47023
Schuster, Thomas; Schöpfer, Frank
2010
Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems. Zbl 1176.65070
Kaltenbacher, Barbara; Schöpfer, Frank; Schuster, Thomas
2009
Fast regularizing sequential subspace optimization in Banach spaces. Zbl 1165.47010
Schöpfer, F.; Schuster, T.
2009
An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Zbl 1153.46308
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods. Zbl 1160.46048
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
Minimization of Tikhonov functionals in Banach spaces. Zbl 1357.49135
Bonesky, Thomas; Kazimierski, Kamil S.; Maass, Peter; Schöpfer, Frank; Schuster, Thomas
2008
Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions. Zbl 1124.33015
Derevtsov, E. Yu.; Kazantsev, S. G.; Schuster, Th.
2007
The method of approximate inverse: Theory and applications. Zbl 1171.65001
Schuster, Thomas
2007
On the application of projection methods for computing optical flow fields. Zbl 1147.68817
Schuster, Thomas; Weickert, Joachim
2007
Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Zbl 1088.65052
Schöpfer, F.; Louis, A. K.; Schuster, T.
2006
Error estimates for defect correction methods in Doppler tomography. Zbl 1099.65131
Schuster, T.
2006
Filtered backprojection for thermoacoustic computed tomography in spherical geometry. Zbl 1085.65092
Haltmeier, M.; Schuster, T.; Scherzer, O.
2005
On a regularization scheme for linear operators in distribution spaces with an application to the spherical Radon transform. Zbl 1081.65122
Schuster, Thomas; Quinto, Eric Todd
2005
Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the method. Zbl 1078.65123
Schuster, Thomas
2005
The approximate inverse in action. III: 3D-Doppler tomography. Zbl 1071.65178
Rieder, Andreas; Schuster, Thomas
2004
Two approaches to the problem of defect correction in vector field tomography solving boundary value problems. Zbl 1099.65101
Derevtsov, E. Yu.; Louis, A. K.; Schuster, T.
2004
The approximate inverse in action II: convergence and stability. Zbl 1022.65066
Rieder, Andreas; Schuster, Thomas
2003
A stable inversion scheme for the Laplace transform using arbitrarily distributed data scanning points. Zbl 1032.65140
Schuster, T.
2003
An efficient mollifier method for three-dimensional vector tomography: Convergence analysis and implementation. Zbl 0988.65121
Schuster, Thomas
2001
The approximate inverse in action with an application to computerized tomography. Zbl 0961.65112
Rieder, Andreas; Schuster, Thomas
2000
The 3D Doppler transform: Elementary properties and computation of reconstruction kernels. Zbl 1017.44005
Schuster, Thomas
2000
Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem. Zbl 0961.65113
Derevtsov, E. Yu.; Dietz, R.; Louis, A. K.; Schuster, T.
2000
Approximate inverse meets local tomography. Zbl 0966.65109
Rieder, Andreas; Dietz, Rainer; Schuster, Thomas
2000
A novel filter design technique in 2D computerized tomography. Zbl 0863.65085
Louis, A. K.; Schuster, Th.
1996
all top 5
#### Cited by 433 Authors
19 Hofmann, Bernd 16 Schuster, Thomas 15 Scherzer, Otmar 11 Han, Bo 11 Jin, Qinian 9 Burger, Martin 9 Shehu, Yekini 8 Haltmeier, Markus 8 Quinto, Eric Todd 7 Kaltenbacher, Barbara 7 Trương Minh Tuyên 6 Kazantsev, Sergeĭ Gavrilovich 6 Louis, Alfred Karl 6 Rieder, Andreas 5 Derevtsov, Evgeny Yurievich 5 Gerth, Daniel 5 Gu, Ruixue 5 Mewomo, Oluwatosin Temitope 5 Reich, Simeon 5 Ren, Kui 5 Schöpfer, Frank 5 Svetov, Ivan Evgenyevich 5 Wang, Wei 5 Zou, Jun 4 Albani, Vinicius V. L. 4 Chen, Dehan 4 Cholamjiak, Prasit 4 Estatico, Claudio 4 Flemming, Jens 4 Hahn, Bernadette Nadine 4 Iyiola, Olaniyi Samuel 4 Kazimierski, Kamil S. 4 Klibanov, Michael V. 4 Maass, Peter 4 Margotti, Fábio 4 Mathé, Peter 4 Mishra, Rohit Kumar 4 Nguyen Viet Linh 4 Polyakova, Anna Petrovna 4 Qiu, Lingyun 4 Resmerita, Elena 4 Shi, Luoyi 4 Tong, Shanshan 4 Wald, Anne 4 Wu, Yujing 3 Ammari, Habib M. 3 Arridge, Simon R. 3 Balandin, A. L. 3 Beckmann, Matthias 3 Bredies, Kristian 3 Chen, Rudong 3 Clason, Christian 3 De Cezaro, Adriano 3 Dixit, Sharad Kumar 3 Grathwohl, Christine 3 Hein, Torsten 3 Jin, Bangti 3 Jolaoso, Lateef Olakunle 3 Krishnan, Venkateswaran P. 3 Kunstmann, Peer Christian 3 Lechleiter, Armin 3 Lorenz, Dirk Alfred 3 Lu, Xiliang 3 Mahale, Pallavi 3 Maltseva, Svetlana Vasilevna 3 Moon, Sunghwan 3 Neubauer, Andreas 3 Suantai, Suthep 3 Taiwo, Adeolu 3 Wang, Fenghui 3 Wang, Jinping 3 Zubelli, Jorge P. 2 Ambartsoumian, Gaik 2 Anzengruber, Stephan W. 2 Benning, Martin 2 Boţ, Radu Ioan 2 Brianzi, Paola 2 Bukhgeim, Alexander A. 2 Che, Haitao 2 Cuomo, Salvatore 2 D’Amore, Luisa 2 de Hoop, Maarten V. 2 Di Benedetto, Fabio 2 Ding, Liang 2 Dong, Qiaoli 2 Felea, Raluca 2 Frikel, Jürgen 2 Fu, Chuli 2 Fu, Zhenwu 2 Giordano, Matteo 2 Giri, Ankik Kumar 2 Grasmair, Markus 2 Hegland, Markus 2 Hofmann, Christopher 2 Holler, Martin 2 Iske, Armin 2 Jiao, Yuling 2 Kindermann, Stefan 2 Kirisits, Clemens 2 Kokurin, Mikhail Yur’evich ...and 333 more Authors
all top 5
#### Cited in 83 Serials
49 Inverse Problems 28 Journal of Inverse and Ill-Posed Problems 15 Inverse Problems and Imaging 11 Applicable Analysis 10 Journal of Computational and Applied Mathematics 10 Numerical Functional Analysis and Optimization 8 Numerische Mathematik 7 Journal of Mathematical Analysis and Applications 7 Optimization 7 Inverse Problems in Science and Engineering 7 SIAM Journal on Imaging Sciences 6 Numerical Algorithms 6 SIAM Journal on Mathematical Analysis 5 SIAM Journal on Numerical Analysis 5 Journal of Mathematical Imaging and Vision 5 Abstract and Applied Analysis 4 Mathematics of Computation 4 SIAM Journal on Optimization 4 Mathematical Problems in Engineering 4 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 4 Journal of Fixed Point Theory and Applications 4 Journal of Nonlinear Science and Applications 3 Mathematical Methods in the Applied Sciences 3 Applied Numerical Mathematics 3 Journal of Integral Equations and Applications 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Applied Mathematics 3 Computational Optimization and Applications 3 ETNA. Electronic Transactions on Numerical Analysis 3 GEM - International Journal on Geomathematics 2 Computers & Mathematics with Applications 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Calcolo 2 Quaestiones Mathematicae 2 Journal of Scientific Computing 2 European Journal of Applied Mathematics 2 Mathematical Programming. Series A. Series B 2 Computational and Applied Mathematics 2 Acta Numerica 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 SIAM/ASA Journal on Uncertainty Quantification 1 Advances in Applied Probability 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Physics Letters. A 1 Computing 1 Journal of Differential Equations 1 Journal of the Korean Mathematical Society 1 Journal of Optimization Theory and Applications 1 Le Matematiche 1 Mathematics and Computers in Simulation 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Acta Applicandae Mathematicae 1 Computational Mathematics and Mathematical Physics 1 Bulletin of the American Mathematical Society. New Series 1 SIAM Journal on Scientific Computing 1 Journal of Mathematical Sciences (New York) 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Finance and Stochastics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Optimization Methods & Software 1 Journal of Inequalities and Applications 1 International Journal of Theoretical and Applied Finance 1 Nonlinear Analysis. Real World Applications 1 Computational Methods in Applied Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya: Matematika, Mekhanika, Informatika 1 Communications on Pure and Applied Analysis 1 International Journal of Computational Methods 1 GAMM-Mitteilungen 1 Complex Variables and Elliptic Equations 1 Electronic Journal of Statistics 1 Algorithms 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Symmetry 1 Analysis and Mathematical Physics 1 Frontiers of Computer Science 1 Advances in Operator Theory 1 Ural Mathematical Journal
all top 5
#### Cited in 36 Fields
206 Numerical analysis (65-XX) 116 Operator theory (47-XX) 70 Partial differential equations (35-XX) 49 Calculus of variations and optimal control; optimization (49-XX) 43 Integral transforms, operational calculus (44-XX) 36 Biology and other natural sciences (92-XX) 34 Operations research, mathematical programming (90-XX) 33 Information and communication theory, circuits (94-XX) 17 Integral equations (45-XX) 14 Functional analysis (46-XX) 12 Statistics (62-XX) 11 Differential geometry (53-XX) 10 Computer science (68-XX) 10 Mechanics of deformable solids (74-XX) 10 Optics, electromagnetic theory (78-XX) 7 Special functions (33-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Functions of a complex variable (30-XX) 6 Approximations and expansions (41-XX) 6 Geophysics (86-XX) 4 General and overarching topics; collections (00-XX) 4 General topology (54-XX) 4 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Abstract harmonic analysis (43-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-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.
| 2021-04-16T23:37:14 |
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|
https://mooseframework.inl.gov/docs/doxygen/modules/classPowerLawSoftening.html
|
PowerLawSoftening Class Reference
PowerLawSoftening is a smeared crack softening model that uses a power law equation to soften the tensile response. More...
#include <PowerLawSoftening.h>
Inheritance diagram for PowerLawSoftening:
[legend]
## Public Member Functions
PowerLawSoftening (const InputParameters ¶meters)
virtual void computeCrackingRelease (Real &stress, Real &stiffness_ratio, const Real strain, const Real crack_initiation_strain, const Real crack_max_strain, const Real cracking_stress, const Real youngs_modulus) override
Compute the effect of the cracking release model on the stress and stiffness in the direction of a single crack. More...
void resetQpProperties () final
Retained as empty methods to avoid a warning from Material.C in framework. These methods are unused in all inheriting classes and should not be overwritten. More...
void resetProperties () final
## Protected Attributes
const Real & _stiffness_reduction
Reduction factor applied to the initial stiffness each time a new crack initiates. More...
## Detailed Description
PowerLawSoftening is a smeared crack softening model that uses a power law equation to soften the tensile response.
It is for use with ComputeSmearedCrackingStress.
Definition at line 26 of file PowerLawSoftening.h.
## ◆ PowerLawSoftening()
PowerLawSoftening::PowerLawSoftening ( const InputParameters & parameters )
Definition at line 30 of file PowerLawSoftening.C.
31 : SmearedCrackSofteningBase(parameters),
32 _stiffness_reduction(getParam<Real>("stiffness_reduction"))
33 {
34 }
const Real & _stiffness_reduction
Reduction factor applied to the initial stiffness each time a new crack initiates.
SmearedCrackSofteningBase(const InputParameters ¶meters)
## ◆ computeCrackingRelease()
void PowerLawSoftening::computeCrackingRelease ( Real & stress, Real & stiffness_ratio, const Real strain, const Real crack_initiation_strain, const Real crack_max_strain, const Real cracking_stress, const Real youngs_modulus )
overridevirtual
Compute the effect of the cracking release model on the stress and stiffness in the direction of a single crack.
Parameters
stress Stress in direction of crack stiffness_ratio Ratio of damaged to original stiffness in cracking direction strain Strain in the current crack direction crack_initiation_strain Strain in crack direction when crack first initiated crack_max_strain Maximum strain in crack direction cracking_stress Threshold tensile stress for crack initiation youngs_modulus Young's modulus
Implements SmearedCrackSofteningBase.
Definition at line 37 of file PowerLawSoftening.C.
44 {
45 if (stress > cracking_stress)
46 {
47 // This is equivalent to k = k_0 * (stiffness_reduction)^n, where n is the number of cracks
48 stiffness_ratio *= _stiffness_reduction;
49 stress = stiffness_ratio * youngs_modulus * strain;
50 }
51 }
const Real & _stiffness_reduction
Reduction factor applied to the initial stiffness each time a new crack initiates.
## ◆ resetProperties()
void SmearedCrackSofteningBase::resetProperties ( )
inlinefinalinherited
Definition at line 57 of file SmearedCrackSofteningBase.h.
57 {}
## ◆ resetQpProperties()
void SmearedCrackSofteningBase::resetQpProperties ( )
inlinefinalinherited
Retained as empty methods to avoid a warning from Material.C in framework. These methods are unused in all inheriting classes and should not be overwritten.
Definition at line 56 of file SmearedCrackSofteningBase.h.
56 {}
## ◆ _stiffness_reduction
const Real& PowerLawSoftening::_stiffness_reduction
protected
Reduction factor applied to the initial stiffness each time a new crack initiates.
Definition at line 41 of file PowerLawSoftening.h.
Referenced by computeCrackingRelease().
The documentation for this class was generated from the following files:
| 2019-04-19T07:29:55 |
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|
https://large-numbers.fandom.com/wiki/Expansion
|
## FANDOM
1,128 Pages
Expansion refers to the function $$a \{\{1\}\} b = a \{a \{\cdots \{a\} \cdots\}a\}a$$, where there are b a's from the center out.[1] It is $$\{a,b,1,2\}$$ in BEAF and a{X+1}b in X-Sequence Hyper-Exponential Notation. The notation a{c}b means {a,b,c}, which is a "c + 2"-ated to b, using the bracket operator.
The function eventually dominates any hyper-operator, such as tetration, pentation or even centation.
Graham's number is defined using a very close variant of expansion. It is $$3 \{\{1\}\} 65$$ with the central 3 replaced with a 4.
a{{1}}b is exactly equal to [a,a,a,b-1] in the Graham Array Notation.
By Bird's Proof, $$a \{\{1\}\} b > a \rightarrow a \rightarrow (b-1) \rightarrow 2$$ using chained arrow notation.
## Examples Edit
• $$2\ \{\{1\}\}\ 2$$ = 4
• $$2\ \{\{1\}\}\ 3 = 2\{2\{2\}2\}2 = 2\{4\}2 = 2\{3\}2 = 2\{2\}2 = 2\{1\}2 = 4$$
• In fact, if the base is equal to 2 and prime is ≥ 2, then the result will always be 4.
• $$3\ \{\{1\}\}\ 2 = \{3,2,1,2\} = 3 \{3\} 3 = 3\uparrow\uparrow\uparrow 3$$ (tritri)
• $$a\ \{\{1\}\}\ 2 = \{a,2,1,2\} = a \{a\} a = a\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{a}a$$
• $$3\ \{\{1\}\}\ 3 = \{3,3,1,2\} = 3 \{3 \{3\} 3\} 3 = 3\{\text{tritri}\}3 = 3\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\text{tritri}}3$$
• $$4\ \{\{1\}\}\ 3 = \{4,3,1,2\} = 4 \{4 \{4\} 4 \}4 = 4 \{$$Template:Mathlink$$\} 4 = 4\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\text{tritet}}4$$
• $$a\ \{\{1\}\}\ 3 = \{a,3,1,2\} = a \{a \{a\} a\} a = a\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{a\{a\}a}a$$
• $$3\ \{\{1\}\}\ 4 = \{3,4,1,2\} = 3 \{3 \{3 \{3\} 3\} 3 \}3 = 3 \{3 \{\text{tritri}\} 3\} 3 = 3\{\ \{3,3,1,2\}\ \}3 = 3\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\{3,3,1,2\} }3$$ = $$3 \uparrow^{3 \uparrow^{3 \uparrow^{3}3}3}3$$
• $$a\ \{\{1\}\}\ 4 = \{a,4,1,2\} = a \{a \{a \{a\} a\} a \}a = a\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{a\{a\{a\}a\}a}a$$
• $$10 \{\{1\}\} 100 = \{10,100,1,2\} = \{10,10,\{10,99,1,2 \}\} = 10 \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\{10,99,1,2 \} }10$$ (corporal)
• $$a \{\{1\}\} b = \{a,b,1,2\} = \{a,a,\{a,b-1,1,2 \}\} = a \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\{a,b-1,1,2\} }a$$
## Pseudocode Edit
Below is an example of pseudocode for expansion.
function expansion(a, b):
result := a
repeat b - 1 times:
result := hyper(a, a, result + 2)
return result
function hyper(a, b, n):
if n = 1:
return a + b
result := a
repeat b - 1 times:
result := hyper(a, result, n - 1)
return result
## Sources Edit
1. Array Notation by Jonathan Bowers
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-07-12T23:07:25 |
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|
https://mfix.netl.doe.gov/doc/tracker/19.1.0/userguide/visualization.html
|
# Visualization¶
The visualization tab provides a series of options for visualizing the object tracks. The color of each track can be based on:
1. Constant - Constant color for all tracks, selected with the Constant color button.
2. Track - A random color from the Color Map is chosen for each track.
3. Velocity - A color based on the x velocity, y velocity, or magnitude of the velocity, the selected Color Map, and the selected Range.
The number of points of each track can be changed with the Point history spinner. To show every point of every track, no matter what frame is currently displayed, un-check the Only show tracks with point in frame check box.
The points of the track can be displayed by selecting the Show points check-box. The size of the point can be changed using the Point radius spinner. The edge of the points can be changed using the Edge width spinner where a value of -1 will remove the edge. The points can be filled by selecting the Fill check-box. Finally, the points can fade out as the point gets further away from the current frame by selecting the Fade out check-box.
Lines can be drawn through points by selecting the Show Lines check-box. The width of the lines can be changed using the Line width spinner.
To see the search areas (radius) of the poly-projection algorithm, select the Show search check-box. The width of the line and the style of the line ( solid, dash, or dot) can be changed using the Edge width spinner and Edge style drop-down list.
When using multi-threading or multi-processing with more than 1 worker, the domain decomposition can be displayed by selecting the Show domain decomposition check-box. The color and transparency of the tile edges can be changed by using the Color button and the Transparency spinner.
Finally, images of the currently displayed frame can be saved by selecting the Save image stack check-box. As the frames are traversed, by either pressing play or the forward and backward buttons, the frames will automatically be saved in the directory specified in the Path line-edit. The Browse button can be used to browse to a directory. The name of the saved images can be changed using the Prefix line-edit. A zero-padded integer corresponding to the frame will be automatically added after the prefix. The saved images can be scaled using the Scale spinner, which is a multiplier on the number of pixels. See ffmpeg Commands for turning the image stack into a video using FFMPEG.
| 2021-06-14T02:47:44 |
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|
https://lammps.sandia.gov/doc/Modify_compute.html
|
11.6. Compute styles
Classes that compute scalar and vector quantities like temperature and the pressure tensor, as well as classes that compute per-atom quantities like kinetic energy and the centro-symmetry parameter are derived from the Compute class. New styles can be created to add new calculations to LAMMPS.
Compute_temp.cpp is a simple example of computing a scalar temperature. Compute_ke_atom.cpp is a simple example of computing per-atom kinetic energy.
Here is a brief description of methods you define in your new derived class. See compute.h for details.
init perform one time setup (required) init_list neighbor list setup, if needed (optional) compute_scalar compute a scalar quantity (optional) compute_vector compute a vector of quantities (optional) compute_peratom compute one or more quantities per atom (optional) compute_local compute one or more quantities per processor (optional) pack_comm pack a buffer with items to communicate (optional) unpack_comm unpack the buffer (optional) pack_reverse pack a buffer with items to reverse communicate (optional) unpack_reverse unpack the buffer (optional) remove_bias remove velocity bias from one atom (optional) remove_bias_all remove velocity bias from all atoms in group (optional) restore_bias restore velocity bias for one atom after remove_bias (optional) restore_bias_all same as before, but for all atoms in group (optional) pair_tally_callback callback function for tally-style computes (optional). memory_usage tally memory usage (optional)
Tally-style computes are a special case, as their computation is done in two stages: the callback function is registered with the pair style and then called from the Pair::ev_tally() function, which is called for each pair after force and energy has been computed for this pair. Then the tallied values are retrieved with the standard compute_scalar or compute_vector or compute_peratom methods. The USER-TALLY package provides examples_compute_tally.html for utilizing this mechanism.
| 2020-08-10T11:56:00 |
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|
https://pos.sissa.it/091/245/
|
Volume 091 - The XXVII International Symposium on Lattice Field Theory (LAT2009) - Weak Decays and Matrix Elements
$B^0$-$\bar{B}^0$ mixing with Fermilab heavy quarks
E. Gamiz, R. Evans, A.X. El-Khadra and A. Kronfeld*
Full text: pdf
Published on: June 23, 2010
DOI: https://doi.org/10.22323/1.091.0245
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-ShareAlike.
| 2023-04-01T14:06:08 |
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|
https://par.nsf.gov/biblio/10272507-search-feebly-interacting-particle-decay-k+-+x
|
Search for a feebly interacting particle X in the decay K+ → π+X
A bstract A search for the K + → π + X decay, where X is a long-lived feebly interacting particle, is performed through an interpretation of the K + → $${\pi}^{+}\nu \overline{\nu}$$ π + ν ν ¯ analysis of data collected in 2017 by the NA62 experiment at CERN. Two ranges of X masses, 0–110 MeV /c 2 and 154–260 MeV /c 2 , and lifetimes above 100 ps are considered. The limits set on the branching ratio, BR( K + → π + X ), are competitive with previously reported searches in the first mass range, and improve on current limits in the second mass range by more than an order of magnitude.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10272507
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
3
ISSN:
1029-8479
2. A bstract We present a search for the dark photon A ′ in the B 0 → A ′ A ′ decays, where A ′ subsequently decays to e + e − , μ + μ − , and π + π − . The search is performed by analyzing 772 × 10 6 $$B\overline{B}$$ B B ¯ events collected by the Belle detector at the KEKB e + e − energy-asymmetric collider at the ϒ(4 S ) resonance. No signal is found in the dark photon mass range 0 . 01 GeV /c 2 ≤ m Amore »
3. Abstract A search for heavy resonances decaying into a pair of Z bosons leading to $$\ell ^+\ell ^-\ell '^+\ell '^-$$ ℓ + ℓ - ℓ ′ + ℓ ′ - and $$\ell ^+\ell ^-\nu {{\bar{\nu }}}$$ ℓ + ℓ - ν ν ¯ final states, where $$\ell$$ ℓ stands for either an electron or a muon, is presented. The search uses proton–proton collision data at a centre-of-mass energy of 13 TeV collected from 2015 to 2018 that corresponds to the integrated luminosity of 139 $$\mathrm {fb}^{-1}$$ fb - 1 recorded by the ATLAS detector during Run 2 of the Largemore »
4. A bstract The NA62 experiment reports an investigation of the $${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$$ K + → π + ν ν ¯ mode from a sample of K + decays collected in 2017 at the CERN SPS. The experiment has achieved a single event sensitivity of (0 . 389 ± 0 . 024) × 10 − 10 , corresponding to 2.2 events assuming the Standard Model branching ratio of (8 . 4 ± 1 . 0) × 10 − 11 . Two signal candidates are observed with an expected background of 1.5 events. Combined with the result of amore »
5. Abstract The production of $$\pi ^{\pm }$$ π ± , $$\mathrm{K}^{\pm }$$ K ± , $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\mathrm{K}^{*}(892)^{0}$$ K ∗ ( 892 ) 0 , $$\mathrm{p}$$ p , $$\phi (1020)$$ ϕ ( 1020 ) , $$\Lambda$$ Λ , $$\Xi ^{-}$$ Ξ - , $$\Omega ^{-}$$ Ω - , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV at midrapidity ( $$|y|<0.5$$ | y | < 0.5 ) as a function of transverse momentum ( $$p_{\mathrm{T}}$$ p T ) using the ALICE detector at the CERNmore »
| 2022-06-26T21:04:16 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/fiscal-implications-of-the-federal-reserve-balance-sheet-normalization-20180109.htm
|
January 09, 2018
Fiscal implications of the Federal Reserve’s Balance Sheet Normalization
Michele Cavallo, Marco Del Negro (Federal Reserve Bank of New York), W. Scott Frame (Federal Reserve Bank of Atlanta), Jamie Grasing (University of Maryland), Benjamin Malin (Federal Reserve Bank of Minneapolis), and Carlo Rosa1
In the wake of the global financial crisis, the Federal Reserve dramatically increased the size of its balance sheet--from about $900 billion at the end of 2007 to about$4.5 trillion today. At its September 2017 meeting, the Federal Open Market Committee (FOMC) announced that--effective October 2017--it would initiate the balance sheet normalization program described in the June 2017 addendum to the FOMC's Policy Normalization Principles and Plans.
This Note summarizes analysis conducted in our recent FEDS working paper (PDF) that seeks to understand the fiscal implications of the Federal Reserve's balance sheet normalization program. Of course, monetary policy always has fiscal implications since it influences interest rates paid on government debt. But changes in the Federal Reserve's balance sheet have additional fiscal consequences related to the central bank's net income that is remitted to the U.S. Treasury. While the level and volatility of remittances do not prevent the FOMC from conducting monetary policy in conformity with its mandate and are thus not the focus of monetary policy decisions, they can potentially be associated with political-economy concerns (see, for example, Dudley).
In the paper, we assess the fiscal implications of different longer-run sizes of the balance sheet. We conduct simulations that leverage two models maintained by the Federal Reserve Board: The System Open Market Account (SOMA) model that generates detailed projections of the evolution of the balance sheet and associated net income; and the public version of the FRB/US model, a large-scale macroeconomic model, which we use to generate future paths for interest rates as well as government revenues, expenditures, and debt.
We explore how different longer-run sizes of the Federal Reserve's balance sheet affect the average size and variability of remittances and the likelihood of net losses. We consider four scenarios tied to longer-run levels of reserve balances: $100 billion (which is intended to represent a return to a pre-crisis "scarce-reserves" balance sheet),$2.3 trillion (which roughly corresponds to the current level of reserves), and two levels in-between, namely $500 billion and$1 trillion. The $2.3 trillion longer-run reserve balance scenario means that reserves would remain at their currently elevated level. This implies, in turn, that the balance sheet would immediately start growing at a pace mostly in line with the expansion in key liabilities such as the value of Federal Reserve notes and capital paid-in. It is important to stress that this scenario is neither consistent with the current FOMC's balance sheet normalization program nor an indication of any potential future Federal Reserve policy. We present this counterfactual, illustrative scenario only to understand the fiscal implications that could arise with reserve balances close to current levels. The other scenarios, which feature a gradual reduction in securities holdings through the medium term, are in line with the FOMC's balance sheet normalization program. All other assumptions needed are based on publicly available information (such as the June 2017 addendum to the FOMC's Policy Normalization Principles and Plans and the June 2017 Summary of Economic Projections forecast). Given these assumptions, for each scenario, we run stochastic simulations of the FRB/US model and compute summary statistics for Federal Reserve net income and remittances to the Treasury. Specifically, for each of our four scenarios we generate paths for interest rates and other financial and macroeconomic variables using the March 2017 public version of FRB/US. Then, for each path, we derive the implications for remittances and other variables of interest. A key feature of our approach is that it allows us to consider the effects of changing the longer-run size of the balance sheet on interest rates, asset prices, economic activity, and inflation. For instance, in the context of the model, larger holdings of longer-term securities by the central bank put downward pressure on longer-term interest rates and stimulate the economy. In response, short-term interest rates increase (in accordance with the monetary policy rule in FRB/US). These changes in short- and longer-term interest rates have important feedback effects on remittances. We start by looking at the evolution of average remittances from the Federal Reserve to the Treasury. The chart below displays, for each of the four scenarios, the average annual remittances (across the simulations) for the next twenty years. In each case, average remittances decline over the next four or five years and increase thereafter. This initial decrease is largely driven by an increase in interest expense paid on reserves, which rises sharply since short-term interest rates are projected to increase at a faster pace than the decline in the level of reserve balances. The larger the balance sheet the larger the increase in expenses. In addition, under the largest balance sheet scenario, interest expense is further boosted owing to the more accommodative financial conditions, which lead to higher inflation and short-term interest rates. By contrast, interest income is less responsive to the current level of interest rates through the medium term because it mostly reflects fixed coupon interest produced by long-term legacy assets. Of course, interest income will initially decline in scenarios in which securities mature and roll off the portfolio. After normalization of the size of the balance sheet, income starts to move up, as the Federal Reserve resumes purchases of securities at higher prevailing market yields, mostly to keep up with currency demand. All in all, remittances decline more in the short run under the$2.3 billion of reserves scenario through the medium term. In the longer-run, remittances are increasing, and more so for scenarios with a larger balance-sheet size, since expected future term premiums are, on average, positive.
Figure 1. Projected Average Annual Remittances
The next chart shows the standard deviation (across simulations) of annual remittances for each of the four scenarios. The volatility of remittances increases for all scenarios for the first few years because, as the modal path for the interest rate on excess reserves (IOER) moves away from the effective lower bound, there is more scope for volatility in IOER and thus for volatility in interest expense. For the scenarios featuring declines in securities holdings over the next few years (that is, the three smaller reserve-balances scenarios), the volatility of remittances falls as the size of the balance sheet shrinks. On the contrary, volatility does not fall for the large balance sheet scenario because reserve balances never decrease. Eventually, volatility increases for all scenarios as the balance sheet grows in line with Federal Reserve notes.
Figure 2. Projected Standard Deviation of Annual Remittances
In the event that the Federal Reserve's earnings net of expenses are negative, no remittances occur and a deferred asset is booked as a negative liability on its balance sheet. We use our stochastic simulations to compute the likelihood of recording a deferred asset. The analysis shows that it is only when short-term interest rates are driven to exceptionally high levels--which occurs very rarely in our simulations--that interest expense on reserve balances more than offsets interest income from the Federal Reserve's securities holdings. The next chart plots the share of simulations for each scenario featuring a deferred asset in any quarter prior to and including that quarter. Overall, for the scenarios which exhibit a reduction in the securities portfolio of the Federal Reserve, the probability of recording a deferred asset is low. In fact, only in the scenario in which longer-run reserve balances remain at $2.3 trillion is the likelihood of booking a deferred asset significant, at about 30 percent. This likelihood falls under 5 percent with longer-run reserve balances below$1 trillion.
Figure 3. Projected Likelihood of Deferred Asset
Our analysis shows that the FOMC's balance sheet normalization program should lead to a reduction in both the volatility of remittances and the likelihood of the Federal Reserve recording a deferred asset. We stress that remittances are an outcome of the proper conduct of monetary policy and that the FOMC's actions are designed to achieve its dual mandate of maximum employment and price stability. However, these simulations are informative for understanding the possible evolution of remittances based on different longer-run size of the Federal Reserve's balance sheet. As noted in previous research (Carpenter et al. and Rosengren), the fiscal implications of balance sheet policies go well beyond the effects on remittances. More generally, when short-term interest rates are constrained by the effective lower bound, unconventional policy measures such as large-scale asset purchases can provide necessary stimulus to the economy (as shown in Engen, Laubach and Reifschneider), allowing the Federal Reserve to meet its dual mandate.
Note: This post is running in the Federal Reserve Bank of New York's Liberty Street Economics blog today also.
Disclaimer
The views expressed in this post are those of the authors and not necessarily those of their employers or any other entity within the Federal Reserve System. Any errors or omissions are the responsibility of the authors.
Michele Cavallo is chief in the Federal Reserve Board's Division of Monetary Affairs, heading the money market analysis section.
Marco Del Negro is a vice president in the Federal Reserve Bank of New York's Research and Statistics Group.
W. Scott Frame is a financial economist and senior adviser in the Research Department of the Federal Reserve Bank of Atlanta.
Jamie Grasing, a former research assistant at the Federal Reserve Board, is a graduate student at the University of Maryland.
Benjamin A. Malin is a senior economist in the Research Division of the Federal Reserve Bank.
Carlo Rosa worked on this analysis when employed as a senior economist in the Federal Reserve Bank of New York's Markets Group, and is currently working for a financial institution.
1. We thank Jane Ihrig and Larry Mize for helpful comments and Khalela Francis, Margaret Sauer, and James Trevino for excellent research assistance. Return to text
| 2018-01-21T05:16:02 |
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|
https://par.nsf.gov/biblio/10288206-efficient-algorithm-routing-recharging-electric-vehicles
|
An Efficient Algorithm for Routing and Recharging of Electric Vehicles
In this paper, we address the routing and recharging problem for electric vehicles, where charging nodes have heterogeneous prices and waiting times, and the objective is to minimize the total recharging cost. We prove that the problem is NP-hard and propose two algorithms to solve it. The first, is an algorithm which obtains the optimal solution in pseudo-polynomial time. The second, is a polynomial time algorithm that obtains a solution with the total cost of recharging not greater than the optimal cost for a more constrained instance of the problem with the maximum waiting time of (1−ϵ)⋅W , where W is the maximum allowable waiting time.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10288206
Journal Name:
COCOA 2020: Combinatorial Optimization and Applications
2. We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi-)streaming algorithm that uses roughly $O(k / \varepsilon^2)$ memory, where $k$ is the size constraint. At the end of the stream, our algorithm post-processes its data structure using any offline algorithm for submodular maximization, and obtains a solution whose approximation guarantee is $\frac{\alpha}{1+\alpha}-\varepsilon$, where $\alpha$ is the approximation of the offline algorithm. If we use an exact (exponential time) post-processing algorithm, this leads to $\frac{1}{2}-\varepsilon$ approximation (which is nearly optimal). If we post-process with the algorithm of \cite{buchbinder2019constrained}, that achieves the state-of-the-art offline approximation guarantee of $\alpha=0.385$, we obtain $0.2779$-approximation in polynomial time, improving over the previously best polynomial-time approximation of $0.1715$ due to \cite{feldman2018less}. It is also worth mentioning that our algorithm is combinatorial and deterministic, which is rare for an algorithm for non-monotone submodular maximization, and enjoys a fast update time of $O(\frac{\log k + \log (1/\alpha {\varepsilon^2})$ per element.
4. We present an $m^{4/3}+o(1) \log W$ -time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where W is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known running time for this problem and, by well-known reductions, also implies improved running times for the shortest path problem with negative weights, minimum cost bipartite $b$-matching when $\|b\|_1 = O(m)$, and recovers the running time of the currently fastest algorithm for maximum flow in graphs with unit capacities (Liu-Sidford, 2020). Our algorithm relies on developing an interior point method–based framework which acts on the space of circulations in the underlying graph. From the combinatorial point of view, this framework can be viewed as iteratively improving the cost of a suboptimal solution by pushing flow around circulations. These circulations are derived by computing a regularized version of the standard Newton step, which is partially inspired by previous work on the unit-capacity maximum flow problem (Liu-Sidford, 2019), and subsequently refined based on the very re- cent progress on this problem (Liu-Sidford, 2020). The resulting step problem can then be computed efficiently using the recent work on $l_p$-norm minimizing flows (Kyng-Peng-Sachdeva- Wang, 2019).more »
| 2022-10-04T20:49:17 |
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https://www.usgs.gov/news/volcano-watch-frozen-time-ice-and-snow-yield-secrets-past
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Volcano Watch — Frozen in time: ice and snow yield secrets from the past
December 8, 2005
Hawaii Island residents and visitors eagerly awaiting the season's first snowfall were rewarded this past week. By Wednesday morning, a light dusting of snow was visible on the upper slopes of Mauna Kea and Mauna Loa.
The seasonal ritual of transporting snow from the summit of Mauna Kea will likely begin soon, and occasionally an ephemeral snowman will appear in front of a Hilo home. Once or twice each winter, depending on conditions, ski and snowboard competitions are hastily organized on Mauna Kea and provide short-lived recreational opportunities for snow sport enthusiasts.
In colder environments with persistent snow, the novelty of a Hawaiʻian winter wonderland may be lacking, but the enduring snow and ice can yield secrets from the past. For instance, long records of global climate are buried in glaciers and in the polar ice sheets of Greenland and Antarctica.
In areas where temperatures are generally below freezing, each year's snow is added on top of the previous years' unmelted layers. Material in the atmosphere, including dust, ash, gases, and particles are washed out of the air and remain behind in that year's snow layer. As more snow piles up, it is compacted into layers of ice, a layer for each year, with the deposited atmospheric material preserved in each layer.
Samples are collected from the ice sheets by driving a hollow tube deep into the sheet and removing a long cylinder of ice. These ice cores, which can be as much as 3.2 km (2 miles) long, provide a systematic record of the composition and temperature of the Earth's atmosphere over the past million years.
Tiny bubbles of ancient air trapped within the ice provide a direct look at the atmosphere's abundance of greenhouse gases through the ages. Ice core studies provide evidence of the dramatic impact that human activity has had on the planet since the industrial revolution, when greenhouse gases and pollutants, such as sulfates and nitrates, increased significantly.
Some of the events that can be discerned in the ice core record include the leveling off of sulfate and nitrate levels after the 1972 clean air act went into effect; a radioactive signature from the Chernobyl nuclear accident in 1986; the beginning of atomic-bomb testing in the mid-1950s; an increase in sea storminess that occurred toward the end of the 14th century (as indicated by the sea salt signature); and periods of rapid climate change. One example shows that around 12,000 years ago average temperatures plunged approximately 27 degrees F., possibly in less than a five year period.
Volcanic eruptions also leave a distinct marker within ice cores. Ash, sulfate particles, gases, and acidity can all be measured. The resulting time series is the most reliable means of developing continuous records of past volcanic activity and assessing the impact of global volcanism on climate and the environment.
Ice core studies have revealed that volcanic eruptions have shaped human history in unsuspected ways. For example, one researcher identified that the timing of the seven largest volcanic eruptions of the last 2,000 years were followed by known outbreaks of plague (except for one eruption, which occurred while a plague pandemic was already underway). Plague pandemics and major volcanic eruptions are both so rare that the odds of them occurring together by chance are very small.
However, major volcanic eruptions can drastically alter global climate by producing a vast aerosol haze that blocks sunlight and lowers temperatures worldwide. This causes an increase in clouds and rainfall, which can result in crop failures and famines. A starving, weakened population is more susceptible to illness, and hungry rats are driven from the failed fields into human food supplies. The rats bring diseases, such as the plague bacteria, which thrive in the cool, moist conditions created by major volcanic eruptions.
A volcanologist's fantasy might include the presence of ice cores on Mauna Kea. The information they could provide about significant eruptions in the early history of Hawaiʻian volcanoes might help reveal how the human and natural environment have been shaped by volcanism here in Hawaii.
Volcano Activity Update
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater and on the southwest side of the cone. Lava continues to flow through the PKK lava tube from its source on the flank of Puu Oo to the ocean, with a few surface flows breaking out of the tube. In the past week, flows were active on the steep slopes of Pulama pali, above the coastal plain. Surface flows on the pali are visible at night (weather permitting) from the end of Chain of Craters Road.
As of December 8, lava is entering the ocean at East Laeapuki, in Hawaii Volcanoes National Park. A new bench continues to grow in the embayment created during the large bench collapse on November 28. The truncated lava tube, initially hosting a fire hose-like stream of lava freefalling into the water, has crusted over to form a steep ramp leading down to the bench. Most of the lava is passively entering the ocean with little fanfare. A few littoral explosions from the front of the rapidly growing bench, however, have been large enough to bombard the top of the sea cliff behind the ocean entry with spatter.
During the week ending December 7, there were no felt earthquakes reported on Hawaii Island. A magnitude-4.7 earthquake occurred at 1:42 a.m. on Wednesday, December 7 and was located 8 km (5 miles) east of Loihi seamount. This earthquake occurred a few hours after a flurry of earthquakes began in the Lo`ihi region early in the evening on December 6.
Mauna Loa is not erupting. During the past week, six earthquakes were located beneath the volcano. Inflation continues but has slowed over the past several weeks.
| 2022-05-17T19:13:27 |
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|
http://dlmf.nist.gov/4.24
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§4.24 Inverse Trigonometric Functions: Further Properties
§4.24(i) Power Series
4.24.1.
4.24.2.
4.24.3, .
4.24.4, .
4.24.5,
which requires to lie between the two rectangular hyperbolas given by
4.24.6
§4.24(ii) Derivatives
4.24.10.
4.24.11.
4.24.13
4.24.14
4.24.15
4.24.16
4.24.17
The above equations are interpreted in the sense that every value of the left-hand side is a value of the right-hand side and vice versa. All square roots have either possible value.
| 2013-05-25T09:41:43 |
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https://www.usgs.gov/center-news/volcano-watch-what-will-happen-when-eruption-ends
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# Volcano Watch — What will happen when the eruption ends?
Release Date:
Kīlauea has been erupting for nearly 18 years, and there is no sign of it stopping anytime soon. But all previous Kīlauea eruptions ended, and there's no reason to think this one is any different. What can we expect when the curtain finally falls?
Kīlauea has been erupting for nearly 18 years, and there is no sign of it stopping anytime soon. But all previous Kīlauea eruptions ended, and there's no reason to think this one is any different. What can we expect when the curtain finally falls?
We can look at what we know about the past and make educated guesses. The guesses range widely and depend on whether the supply of magma will continue into the volcano, whether the summit or a rift zone will be the next point of weakness, and whether the current eruption will last for a few years or a few decades longer.
Obviously the eruption will end if magma stops rising into the volcano, and nothing will happen at the surface until supply resumes. This is unlikely but possible. A more likely scenario is that magma entering the volcano will be stored somewhere in it, perhaps deep in the east rift zone or below the summit. This is what may have happened between 1924 and 1952, when Kīlauea was, for all intents and purposes, quiet. During the first half of 1924, the lava lake in Halemaumau drained, a large area near Kapoho opened and dropped, and explosions burst from Halemaumau. Apparently these events made room in the volcano to store incoming magma, and it wasn't until 1952 that the volcano was full and Kīlauea had to erupt.
Without such drastic events, we can expect more eruptions, either at the summit or along one of the two rift zones. In fact, this could even happen before the Puu Oo eruption ends. Many people believe that extrusion at Puu Oo removes pressure from the rest of the volcano, so that no eruption can occur elsewhere. During the Mauna Ulu eruptions (1969-71 and 1972-74), however, four other outbreaks did in fact take place, two in 1971 and two in 1973. Just after the Mauna Ulu eruption ended, two summit eruptions, and one in the upper southwest rift zone, occurred between July and December 1974.
The Mauna Ulu events show that, if the volcano remains pressurized, eruptions can take place during and soon after a long-lived eruption. And, the eruptions can be at the summit, anywhere in the rift zones, or both. Currently a barrier blocks the east rift zone near Puu Oo and keeps magma from moving into lower Puna. How long this barrier will last, and how it will respond to the end of the Puu Oo eruption, are anybody's guesses.
Perhaps the most striking scenario of all is suggested by the 15th-century eruption of Kīlauea and its aftermath. This summit or upper east-rift-zone eruption, named the Ailaau eruption by geologists, lasted from about 1410 to about 1470, according to work by Dave Clague and associates. It is the longest rift eruption known at Kīlauea. By 1500, only 30 years later, a new caldera had formed at Kīlauea's summit. This close association in time suggests that the long-lasting Ailaau eruption somehow led to the collapse of the caldera, perhaps by milking magma from the summit reservoir faster than it could be replenished. The collapse of the caldera ushered in nearly three centuries of episodic explosive activity.
If the current eruption continues several decades longer, could it result in renewed caldera collapse? Of interest in this regard is that the caldera has been sinking at a rate of nearly 10 cm (4 inches) per year since the eruption began in 1983. Is this sagging a prelim before the main event?
The bottom line is that the end of the current eruption could result in prolonged quiet, frequent new outbreaks, or caldera collapse and explosions. This complete spectrum of outcomes is not surprising. It reflects the exceedingly complex and dynamic nature of one of Earth's most active volcanoes.
### Volcano Activity Update
The 81 cm (32 inches) of rain recorded at Puu Oo on Thursday was not enough to douse the eruption. Eruptive activity of Kīlauea Volcano continued unabated during the past week. Lava is erupting from Puu Oo and flowing southeast through a tube system down to the flats below Pulama pali and beyond to the ocean. Breakouts from the tube system are feeding small flows at the top of Pulama pali. Lava in the tube system is entering the ocean at Kamokuna located 1.6 km (1 mi) west-southwest of Waha`ula. The public is reminded that the ocean-entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The active lava flows are hot and have places with very thin crust. The steam clouds are highly acidic and laced with glass particles.
There were no earthquakes reported felt during the week ending on November 3.
| 2020-11-28T19:13:01 |
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|
https://www.itl.nist.gov/div898/handbook/pri/section5/pri5993.htm
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5. Process Improvement
5.5.9. An EDA approach to experimental design
5.5.9.9. Cumulative residual standard deviation plot
## Motivation: How do we Construct a Good Model?
Models for 2k and 2k-p designs Given that we have a statistic to measure the quality of a model, any model, we move to the question of how to construct reasonable models for fitting data from 2k and 2k-p designs.
Initial simple model The simplest such proposed model is
$$Y = c + \epsilon$$
that is, the response Y = a constant + random error. This trivial model says that all of the factors (and interactions) are in fact worthless for prediction and so the best-fit model is one that consists of a simple horizontal straight line through the body of the data. The least squares estimate for this constant c in the above model is the sample mean $$\bar{Y}$$. The prediction equation for this model is thus
$$\hat{Y} = \bar{Y}$$
The predicted values $$\small \hat{Y}$$ for this fitted trivial model are thus given by a vector consisting of the same value (namely $$\bar{Y}$$) throughout. The residual vector for this model will thus simplify to simple deviations from the mean:
$$Y - \bar{Y}$$
Since the number of fitted coefficients in this model is 1 (namely the constant c), the residual standard deviation is the following:
$$s_{res} = \sqrt{\frac{\sum_{i=1}^{n}{(Y_{i} - \bar{Y})^2}}{n - 1}}$$
which is of course the familiar, commonly employed sample standard deviation. If the residual standard deviation for this trivial model were "small enough", then we could terminate the model-building process right there with no further inclusion of terms. In practice, however, this trivial model does not yield a residual standard deviation that is small enough (because the common value $$\bar{Y}$$ will not be close enough to some of the raw responses Y) and so the model must be augmented--but how?
Next-step model The logical next-step proposed model will consist of the above additive constant plus some term that will improve the predicted values the most. This will equivalently reduce the residuals the most and thus reduce the residual standard deviation the most.
Using the most important effects As it turns out, it is a mathematical fact that the factor or interaction that has the largest estimated effect
$$\hat{E} = \bar{Y}(+) - \bar{Y}(-)$$
will necessarily, after being included in the model, yield the "biggest bang for the buck" in terms of improving the predicted values toward the response values Y. Hence at this point the model-building process and the effect estimation process merge.
In the previous steps in our analysis, we developed a ranked list of factors and interactions. We thus have a ready-made ordering of the terms that could be added, one at a time, to the model. This ranked list of effects is precisely what we need to cumulatively build more complicated, but better fitting, models.
Step through the ranked list of factors Our procedure will thus be to step through, one by one, the ranked list of effects, cumulatively augmenting our current model by the next term in the list, and then compute (for all n design points) the predicted values, residuals, and residual standard deviation. We continue this one-term-at-a-time augmentation until the predicted values are acceptably close to the observed responses Y (and hence the residuals and residual standard deviation become acceptably close to zero).
Starting with the simple average, each cumulative model in this iteration process will have its own associated residual standard deviation. In practice, the iteration continues until the residual standard deviations become sufficiently small.
Cumulative residual standard deviation plot The cumulative residual standard deviation plot is a graphical summary of the above model-building process. On the horizontal axis is a series of terms (starting with the average, and continuing on with various main effects and interactions). After the average, the ordering of terms on the horizontal axis is identical to the ordering of terms based on the half-normal probability plot ranking based on effect magnitude.
On the vertical axis is the corresponding residual standard deviation that results when the cumulative model has its coefficients fitted via least squares, and then has its predicted values, residuals, and residual standard deviations computed. The first residual standard deviation (on the far left of the cumulative residual standard deviation plot) is that which results from the model consisting of
1. the average.
The second residual standard deviation plotted is from the model consisting of
1. the average, plus
2. the term with the largest |effect|.
The third residual standard deviation plotted is from the model consisting of
1. the average, plus
2. the term with the largest |effect|, plus
3. the term with the second largest |effect|.
and so forth.
| 2018-05-26T00:05:32 |
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|
https://www.zbmath.org/authors/?q=ai%3Akurusa.arpad
|
# zbMATH — the first resource for mathematics
## Kurusa, Árpád
Compute Distance To:
Author ID: kurusa.arpad Published as: Kurusa, Arpád; Kurusa, Á.; Kurusa, Árpád Homepage: http://www.math.u-szeged.hu/tagok/kurusa/ External Links: MGP · Wikidata · ORCID · ResearchGate
Documents Indexed: 40 Publications since 1990
all top 5
#### Co-Authors
30 single-authored 3 Kozma, József 2 Ódor, Tibor 2 Vígh, Viktor 1 Berenstein, Carlos Alberto 1 Casadio Tarabusi, Enrico 1 Czédli, Gábor 1 Fodor, Ferenc 1 Kincses, János 1 Zsolt, Lángi
all top 5
#### Serials
6 Beiträge zur Algebra und Geometrie 5 Journal of Geometry 4 Acta Scientiarum Mathematicarum 3 Geometriae Dedicata 2 Archiv der Mathematik 2 Proceedings of the American Mathematical Society 2 Mathematica Balkanica. New Series 1 Journal of Mathematical Analysis and Applications 1 Periodica Mathematica Hungarica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Duke Mathematical Journal 1 Mathematica Scandinavica 1 Publicationes Mathematicae 1 Acta Mathematica Hungarica 1 Radovi Matematički 1 Discrete & Computational Geometry 1 Aequationes Mathematicae 1 Advances in Geometry 1 Mediterranean Journal of Mathematics 1 International Electronic Journal of Geometry 1 International Journal of Geometry 1 Categories and General Algebraic Structures with Applications
all top 5
#### Fields
20 Convex and discrete geometry (52-XX) 18 Integral transforms, operational calculus (44-XX) 12 Differential geometry (53-XX) 9 Geometry (51-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX)
#### Citations contained in zbMATH
24 Publications have been cited 86 times in 44 Documents Cited by Year
Support theorems for totally geodesic Radon transforms on constant curvature spaces. Zbl 0852.44001
Kurusa, Árpád
1994
Radon transform on spaces of constant curvature. Zbl 0860.44003
Berenstein, Carlos A.; Tarabusi, Enrico Casadio; Kurusa, Árpád
1997
Can you recognize the shape of a figure from its shadows? Zbl 0828.52001
Kincses, J.; Kurusa, Á.
1995
The Radon transform on hyperbolic space. Zbl 0803.44002
Kurusa, Á.
1991
The invertibility of the Radon transform on abstract rotational manifolds of real type. Zbl 0755.44004
Kurusa, Árpád
1992
Inequalities for hyperconvex sets. Zbl 1386.52005
Fodor, Ferenc; Kurusa, Árpád; Vígh, Viktor
2016
You can recognize the shape of a figure from its shadows! Zbl 0846.52001
Kurusa, Árpád
1996
Is a convex plane body determined by an isoptic? Zbl 1235.52005
Kurusa, Árpád
2012
The shadow picture problem for nonintersecting curves. Zbl 0846.52002
Kurusa, Árpád
1996
Can you see the bubbles in a foam? Zbl 1399.52006
Kurusa, Árpád
2016
Ceva’s and Menelaus’ theorems characterize the hyperbolic geometry among Hilbert geometries. Zbl 06516363
Kozma, József; Kurusa, Árpád
2015
Isoptic characterization of spheres. Zbl 1320.52009
Kurusa, Árpád; Ódor, Tibor
2015
Visual distinguishability of segments. Zbl 1308.52005
Kurusa, Árpád
2013
A characterization of the Radon transform and its dual on Euclidean space. Zbl 0732.44001
Kurusa, Á.
1990
Characterizations of balls by sections and caps. Zbl 1330.52013
Kurusa, Árpád; Ódor, Tibor
2015
Visual distinguishability of polygons. Zbl 1279.52004
Kurusa, Árpád
2013
Orbital integrals on the Lorentz space of curvature $$-1$$. Zbl 0970.44002
Kurusa, Árpád
2000
The Radon transform on half sphere. Zbl 0792.44003
Kurusa, Árpád
1993
A characterization of the Radon transform’s range by a system of PDEs. Zbl 0754.44001
Kurusa, Á.
1991
Hyperbolic is the only Hilbert geometry having circumcenter or orthocenter generally. Zbl 1336.53022
Kozma, József; Kurusa, Árpád
2016
The shadow picture problem for parallel straight lines. Zbl 1266.52005
Kurusa, Árpád
2012
The totally geodesic Radon transform on the Lorentz space of curvarture $$-1$$. Zbl 0872.44003
Kurusa, Árpád
1997
Generalized $$X$$-ray pictures. Zbl 1274.52005
Kurusa, Árpád
1996
Support curves of invertible Radon transforms. Zbl 0783.44001
Kurusa, Árpád
1993
Inequalities for hyperconvex sets. Zbl 1386.52005
Fodor, Ferenc; Kurusa, Árpád; Vígh, Viktor
2016
Can you see the bubbles in a foam? Zbl 1399.52006
Kurusa, Árpád
2016
Hyperbolic is the only Hilbert geometry having circumcenter or orthocenter generally. Zbl 1336.53022
Kozma, József; Kurusa, Árpád
2016
Ceva’s and Menelaus’ theorems characterize the hyperbolic geometry among Hilbert geometries. Zbl 06516363
Kozma, József; Kurusa, Árpád
2015
Isoptic characterization of spheres. Zbl 1320.52009
Kurusa, Árpád; Ódor, Tibor
2015
Characterizations of balls by sections and caps. Zbl 1330.52013
Kurusa, Árpád; Ódor, Tibor
2015
Visual distinguishability of segments. Zbl 1308.52005
Kurusa, Árpád
2013
Visual distinguishability of polygons. Zbl 1279.52004
Kurusa, Árpád
2013
Is a convex plane body determined by an isoptic? Zbl 1235.52005
Kurusa, Árpád
2012
The shadow picture problem for parallel straight lines. Zbl 1266.52005
Kurusa, Árpád
2012
Orbital integrals on the Lorentz space of curvature $$-1$$. Zbl 0970.44002
Kurusa, Árpád
2000
Radon transform on spaces of constant curvature. Zbl 0860.44003
Berenstein, Carlos A.; Tarabusi, Enrico Casadio; Kurusa, Árpád
1997
The totally geodesic Radon transform on the Lorentz space of curvarture $$-1$$. Zbl 0872.44003
Kurusa, Árpád
1997
You can recognize the shape of a figure from its shadows! Zbl 0846.52001
Kurusa, Árpád
1996
The shadow picture problem for nonintersecting curves. Zbl 0846.52002
Kurusa, Árpád
1996
Generalized $$X$$-ray pictures. Zbl 1274.52005
Kurusa, Árpád
1996
Can you recognize the shape of a figure from its shadows? Zbl 0828.52001
Kincses, J.; Kurusa, Á.
1995
Support theorems for totally geodesic Radon transforms on constant curvature spaces. Zbl 0852.44001
Kurusa, Árpád
1994
The Radon transform on half sphere. Zbl 0792.44003
Kurusa, Árpád
1993
Support curves of invertible Radon transforms. Zbl 0783.44001
Kurusa, Árpád
1993
The invertibility of the Radon transform on abstract rotational manifolds of real type. Zbl 0755.44004
Kurusa, Árpád
1992
The Radon transform on hyperbolic space. Zbl 0803.44002
Kurusa, Á.
1991
A characterization of the Radon transform’s range by a system of PDEs. Zbl 0754.44001
Kurusa, Á.
1991
A characterization of the Radon transform and its dual on Euclidean space. Zbl 0732.44001
Kurusa, Á.
1990
all top 5
#### Cited by 47 Authors
13 Kurusa, Árpád 8 Rubin, Boris 2 Bezdek, Károly 2 Ishikawa, Satoshi 2 Kozma, József 2 Ódor, Tibor 2 Vígh, Viktor 1 Al-Omari, Shrideh Khalaf Qasem 1 Bal, Guillaume 1 Bray, William O. 1 Carroll, Emily 1 Castro, Jesús Jerónimo 1 Chernov, Roman 1 Drach, Kostiantyn 1 Estrada, Ricardo 1 Faulkner, Thomas 1 Fodor, Ferenc 1 García-Jiménez, Magdalena 1 Ghosh, Arka Prasanna 1 González-Arreola, Edgar 1 Guica, Monica 1 Hartman, Thomas E. 1 Kiliçman, Adem 1 Kincses, János 1 Krishnan, Venkateswaran P. 1 Lukacs, Peter 1 Michalska, Małgorzata 1 Mikkonen, Yrjö 1 Mozgawa, Witold 1 Myers, Robert C. 1 Myroshnychenko, Sergii 1 Naszódi, Márton 1 Nguyen Viet Linh 1 Nguyen, Xuan Hien 1 Palamodov, Victor Pavlovitch 1 Quinto, Eric Todd 1 Roitershtein, Alexander 1 Roopkumar, Rajakumar 1 Rouvière, François 1 Savost’yanova, Irina Mikhaĭlovna 1 Tatarko, Kateryna 1 Van Raamsdonk, Mark 1 Volchkov, Valeriĭ Vladimirovich 1 Volchkov, Vitaliĭ Vladimirovich 1 Yaskin, Vladyslav 1 Zhang, Ning 1 Zsolt, Lángi
all top 5
#### Cited in 27 Serials
5 Beiträge zur Algebra und Geometrie 4 Advances in Mathematics 4 Discrete & Computational Geometry 3 Journal of Geometry 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 2 The Journal of Fourier Analysis and Applications 1 International Journal of General Systems 1 Israel Journal of Mathematics 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Journal of Applied Probability 1 Journal of Functional Analysis 1 Monatshefte für Mathematik 1 Rendiconti del Seminario Matematico della Università di Padova 1 Transactions of the American Mathematical Society 1 Aequationes Mathematicae 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Applied and Computational Harmonic Analysis 1 Doklady Mathematics 1 Abstract and Applied Analysis 1 Journal for Geometry and Graphics 1 Journal of High Energy Physics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Mediterranean Journal of Mathematics 1 International Electronic Journal of Geometry 1 Analysis and Mathematical Physics
all top 5
#### Cited in 22 Fields
19 Integral transforms, operational calculus (44-XX) 19 Convex and discrete geometry (52-XX) 10 Differential geometry (53-XX) 5 Geometry (51-XX) 3 Probability theory and stochastic processes (60-XX) 3 Numerical analysis (65-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-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.
| 2021-04-16T21:31:26 |
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https://www.zbmath.org/authors/?q=ai%3Apier.jean-paul
|
# zbMATH — the first resource for mathematics
## Pier, Jean-Paul
Compute Distance To:
Author ID: pier.jean-paul Published as: Pier, J.-P.; Pier, Jean-Paul External Links: Wikidata
Documents Indexed: 39 Publications since 1961, including 13 Books Reviewing Activity: 113 Reviews
#### Co-Authors
35 single-authored 2 Li, Bingren 1 Dhombres, Jean G. 1 Eymard, Pierre
all top 5
#### Serials
2 Historia Mathematica 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Janus 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Advances in Mathematics 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Cahiers d’Histoire et de Philosophie des Sciences. Nouvelle Série 1 Cahiers du Séminaire d’Histoire des Mathématiques. 2e Série 1 Lecture Notes in Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Revue d’Histoire des Sciences et de leurs Applications
all top 5
#### Fields
23 History and biography (01-XX) 15 Abstract harmonic analysis (43-XX) 11 Topological groups, Lie groups (22-XX) 9 General and overarching topics; collections (00-XX) 5 Measure and integration (28-XX) 4 Functional analysis (46-XX) 3 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX)
#### Citations contained in zbMATH Open
11 Publications have been cited 197 times in 174 Documents Cited by Year
Amenable locally compact groups. Zbl 0597.43001
Pier, Jean-Paul
1984
Amenable locally compact groups. Zbl 0621.43001
Pier, Jean-Paul
1984
Amenable Banach algebras. Zbl 0676.46036
Pier, Jean-Paul
1988
Mathematical analysis during the 20th century. Zbl 0983.01011
Pier, Jean-Paul
2001
Amenability with respect to a closed subgroup of a product group. Zbl 0763.43002
Li, Bingren; Pier, Jean-Paul
1992
Quasi-invariance interieure sur les groupes localement compacts. Zbl 0487.43002
Pier, Jean-Paul
1982
Historique de la notion de compacite. Zbl 0451.01005
Pier, Jean-Paul
1980
Integration and measure 1900–1950. Zbl 0806.01017
Pier, Jean-Paul
1994
Development of mathematics 1900-1950. Based on a symposium organized by the Luxembourg Mathematical Society in June 1992, at Château Bourglinster, Luxembourg. Zbl 0796.00016
Pier, Jean-Paul (ed.)
1994
Marc Krasner. Zbl 0572.01017
Pier, Jean-Paul
1986
Genese et évolution de l’idee de compact. Zbl 0124.37902
Pier, J.-P.
1961
Mathematical analysis during the 20th century. Zbl 0983.01011
Pier, Jean-Paul
2001
Integration and measure 1900–1950. Zbl 0806.01017
Pier, Jean-Paul
1994
Development of mathematics 1900-1950. Based on a symposium organized by the Luxembourg Mathematical Society in June 1992, at Château Bourglinster, Luxembourg. Zbl 0796.00016
Pier, Jean-Paul (ed.)
1994
Amenability with respect to a closed subgroup of a product group. Zbl 0763.43002
Li, Bingren; Pier, Jean-Paul
1992
Amenable Banach algebras. Zbl 0676.46036
Pier, Jean-Paul
1988
Marc Krasner. Zbl 0572.01017
Pier, Jean-Paul
1986
Amenable locally compact groups. Zbl 0597.43001
Pier, Jean-Paul
1984
Amenable locally compact groups. Zbl 0621.43001
Pier, Jean-Paul
1984
Quasi-invariance interieure sur les groupes localement compacts. Zbl 0487.43002
Pier, Jean-Paul
1982
Historique de la notion de compacite. Zbl 0451.01005
Pier, Jean-Paul
1980
Genese et évolution de l’idee de compact. Zbl 0124.37902
Pier, J.-P.
1961
all top 5
#### Cited by 171 Authors
18 Lau, Anthony To-Ming 8 Ghaffari, Ali 8 Kaniuth, Eberhard 8 Nasr-Isfahani, Rasoul 7 Bekka, Mohammed el Bachir 6 Runde, Volker 4 Akbarbaglu, Ibrahim 4 Lin, Michael 4 Nemati, Mehdi 4 Paterson, Alan L. T. 4 Schlichting, Günter 4 Woess, Wolfgang 4 Yuan, Chuankuan 3 Derighetti, Antoine 3 Dorofaeff, Brian 3 Kaimanovich, Vadim A. 3 Ludwig, Jean 3 Maghsoudi, Saeid 3 McMullen, Curtis Tracy 3 Miao, Tianxuan 3 Nowak, Piotr W. 3 Pham, Hung Le 3 Pourmahmood-Aghababa, Hasan 3 Ulger, Ali 3 Zhang, Yong 2 Akhtari, Fatemeh 2 Amini, Massoud 2 Bédos, Erik 2 Conti, Roberto 2 Filali, Mahmoud 2 Fozouni, Mohammad 2 Knudby, Søren 2 Lasser, Rupert 2 Lust-Piquard, Françoise 2 Müller, Detlef 2 Nemesh, Norbert T. 2 Neufang, Matthias 2 Pavel, Liliana 2 Pier, Jean-Paul 2 Sady, Fereshteh 2 Takahashi, Yuji 2 Wittmann, Rainer 2 Wong, James C. S. 2 Yousefi, Marzieh Shams 1 Aita, Marco 1 Alaghmandan, Mahmood 1 Anderson, Michael T. 1 Anker, Jean-Philippe 1 Arendt, Wolfgang 1 Arhancet, Cédric 1 Badora, Roman 1 Bami, Mahmood Lashkarizadeh 1 Bandyopadhyay, Choiti 1 Barnes, Bruce A. 1 Baudier, Florent P. 1 Beiglböck, Mathias 1 Bellow, Alexandra 1 Bergelson, Vitaly 1 Bergmann, Wolfgang R. 1 Burger, Marc 1 Chen, Xiao 1 Chou, Ching 1 Chung, Nhan-Phu 1 Cohen, Guy 1 Conti, Roberto 1 Cowling, Michael G. 1 Croft, T. Nicholas 1 Cross, Mark 1 Cuny, Christophe 1 Dales, H. Garth 1 Daws, Matthew 1 Dawson, John W. jun. 1 de Jeu, Marcel 1 de la Peña, José Antonio 1 Delmonico, Cédric 1 Derriennic, Yves 1 Desaulniers, Shawn 1 Dirbák, Matúš 1 Douglas, Ronald George 1 El Harti, Rachid 1 Farhadi, Hamid-Reza 1 Feinstein, Joel Francis 1 Fish, Alexander 1 Forrest, Brian E. 1 Galindo, Johan F. 1 García-Ramos, Felipe 1 Gerl, Peter 1 Ghaffari, Asma 1 Ghanei, Mohammad Reza 1 Głąb, Szymon 1 Glasner, Yair 1 Gourdeau, Frédéric 1 Gournay, Antoine 1 Grundling, Hendrik B. G. S. 1 Harper, John F. 1 Hebisch, Waldemar 1 Hofmann, Michael H. 1 Hösel, Volker 1 Izzo, Alexander John 1 Jackson, Frances Y. ...and 71 more Authors
all top 5
#### Cited in 70 Serials
14 Journal of Mathematical Analysis and Applications 12 Transactions of the American Mathematical Society 11 Journal of Functional Analysis 10 Proceedings of the American Mathematical Society 8 Mathematische Annalen 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Monatshefte für Mathematik 5 Israel Journal of Mathematics 5 Mathematische Zeitschrift 4 Bulletin of the Australian Mathematical Society 4 Rocky Mountain Journal of Mathematics 4 Advances in Mathematics 4 Journal of Theoretical Probability 3 Inventiones Mathematicae 3 Semigroup Forum 3 Indagationes Mathematicae. New Series 3 Acta Mathematica Sinica. English Series 3 Mediterranean Journal of Mathematics 2 Discrete Mathematics 2 Archiv der Mathematik 2 Bulletin of the London Mathematical Society 2 Functional Analysis and its Applications 2 Integral Equations and Operator Theory 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Ergodic Theory and Dynamical Systems 2 Linear Algebra and its Applications 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Expositiones Mathematicae 2 Acta Mathematica Sinica. New Series 2 Journal of the Australian Mathematical Society 2 Journal of Topology and Analysis 2 Sahand Communications in Mathematical Analysis 1 Archive for History of Exact Sciences 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Indian Journal of Pure & Applied Mathematics 1 Journal d’Analyse Mathématique 1 Studia Mathematica 1 Journal of Geometry and Physics 1 Annales de l’Institut Fourier 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Journal of Pure and Applied Algebra 1 Mathematische Nachrichten 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Quaestiones Mathematicae 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 History and Philosophy of Logic 1 Acta Mathematica Hungarica 1 Statistical Science 1 Revista Matemática Iberoamericana 1 International Journal of Mathematics 1 Aequationes Mathematicae 1 Historia Mathematica 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Dynamics and Differential Equations 1 Potential Analysis 1 Topological Methods in Nonlinear Analysis 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Positivity 1 Algebraic & Geometric Topology 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Fixed Point Theory 1 BSHM Bulletin 1 Annals of Functional Analysis 1 ISRN Geometry
all top 5
#### Cited in 34 Fields
110 Abstract harmonic analysis (43-XX) 57 Topological groups, Lie groups (22-XX) 55 Functional analysis (46-XX) 29 Operator theory (47-XX) 16 Group theory and generalizations (20-XX) 16 Probability theory and stochastic processes (60-XX) 10 Dynamical systems and ergodic theory (37-XX) 8 Measure and integration (28-XX) 8 General topology (54-XX) 7 Combinatorics (05-XX) 7 Manifolds and cell complexes (57-XX) 6 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Number theory (11-XX) 3 Differential geometry (53-XX) 2 Associative rings and algebras (16-XX) 2 $$K$$-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Partial differential equations (35-XX) 2 Difference and functional equations (39-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX)
#### Wikidata Timeline
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