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http://www-spires.fnal.gov/spires/hep/refs/helpus.shtml
|
## Checking your file before sending to arXiv.org
You can now check your reference list before you send your paper to arXiv.org when you use the SPIRES LaTeX formats. Simply send your tex file to:
To: [email protected]
Subject: references
The script works by extracting the %%CITATION= tags. You'll then be sent back a url with your reference list as it will appear in SPIRES format.
## Eprint format considerations
If you are preparing a large paper with many separate .tex files our extraction will be more accurate and efficient if you combine the references into one file when you submit to arXiv. This file should have the
\begin{thebibliography}
command in it, and should be named
bib*.tex
or
ref*.tex
where the * is the usual wildcard, so you are free to use
bib_for_worlds_best_paper.tex
if you wish.
useless_filename.tex
## Getting LaTeX format of SPIRES output
A display format can produce output as plain LaTeX For example:
EFFICIENT GLUEBALL SIMULATIONS ON ANISOTROPIC LATTICES.
By Colin J. Morningstar (UC, San Diego), Mike Peardon (Kentucky U.). UCSD-PTH-97-05, UK-97-02, Apr 1997. 43pp.
Published in Phys.Rev.D56:4043-4061,1997
e-Print Archive: hep-lat/9704011
TOPCITE 50+
References | LaTeX(US) | LaTeX(EU) | BibTeX | Keywords | Citation Search
Abstract and Postscript from arXiv.org: (mirrors:au br cn de es fr il in it jp kr ru tw uk aps)
Phys. Rev. D Server
Clicking on "LaTeX(US)" will produce:
%\cite{Morningstar:1997ff}
\bibitem{Morningstar:1997ff}
C.J.~Morningstar and M.~Peardon,
%Efficient glueball simulations on anisotropic lattices,"
Phys. Rev. {\bf D56}, 4043 (1997)
hep-lat/9704011.
%%CITATION = PHRVA,D56,4043;%%
Just cut-and-paste this into your LaTeX file!! Choosing LaTeX(EU) will give Phys. Rev. {\bf D56} (1997) 4043.
Our program looks for the %%CITATION tag in your tex file (which, of course, will not show up in the printed copy of your paper), none of the other lines matters, so you can change them as you want. However, using the \bibitem{Morningstar:1997ff} will make it easier for you to update your reference list using our database should you wish to do so in future.
## What to do when you want to cite a paper we don't have in SPIRES
Obviously you'll also want to cite papers we don't have. We can only track citations of either eprints (say cond-mat/9711200) or papers published in journals with unique volume/page structure (e.g. Zeit. Phys. C31 (1986) 634). We cannot, for example, handle books (e.g. "Quantum Field Theory" by Itzykson and Zuber) or Talk given at 23rd Conference on Physics in Kyancutta." In this case you can make your own CITATION tag. For the eprints this is easy:
%%CITATION = COND-MAT 9711200;%% (note the "/" is missing and the ";" is very important)
For journals we need to know the journal CODEN:
%%CITATION = CODEN,volume,first page;%%
For the example above you would have:
%%CITATION = ZEPYA,C31,634;%%
You can find the coden using the CODEN search form. However, if this is too complicated, you can just put
%%CITATION = NONE;%%
and we'll fix for you.
If you feel the missing paper should be included in the HEP database, please use this form.
## Using BibTeX
Everything you need to know is mostly covered here, but there are some issues that are of special relevance to BibTeX.
SPIRES HEP is a joint project of SLAC, DESY & FNAL as well as the worldwide HEP community.
Mirrors: DESY (Germany), Fermilab (US), IHEP (Russia), Durham U. (UK), SLAC (US), YITP (Japan); LIPI (Indonesia);
Last Updated: 01/31/2005
| 2017-01-18T07:55:15 |
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|
https://gea.esac.esa.int/archive/documentation/GDR1/datamodel/Ch2/rrlyrae.html
|
2.4 rrlyrae
This table describes the RRLyrae stars identified in table VariableSummary as classification="RRLYR". In the analyses only observations with rejectedByVariabilityProcessing=false are included, as found in table PhotVariableTimeSeriesGfov.
Columns description:
best_classification : Best RR Lyrae classification estimate out of: ”RRC”, ”RRAB” (string, Dimensionless[see description])
Classification of an RR Lyrae star according to the pulsation mode: RRc (”RRC”) for first overtone and RRab (”RRAB”) for fundamental mode, obtained using the period-amplitude diagram in the G-band and the plots of the Fourier parameters R21 and Phi2 vs period.
solution_id : Solution Identifier (long)
The data in the MDB will be described by means of a ”Solution identifier” parameter. This will be a numeric field attached to each table row that can be used to unequivocally identify the version of all the subsystems that where used in the generation of the data as well as the input data used. Each DPC generating the data will have the freedom to choose the Solution identifier number, but they must ensure that given the Solution identifier they can provide detailed information about the ”conditions” used to generate the data: versions of the software, version of the data used…
source_id : Unique source identifier (long)
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id)
p1 : Period corresponding to the maximum power peak in the periodogram of G band time series (double, Time[day])
This parameter is filled with the period of the maximum power peak in the frequencygram obtained from the modeling of the time series. The light curve of the target star is modeled with a truncated Fourier series ($mag(t_{j})=zp+\sum[A_{i}sin(i\times 2\pi\nu_{max}t_{j}+\phi_{i})]$). Zero-point (zp), period (1/$\nu_{max}$), number of harmonics ($i$), amplitudes ($A_{i}$), and phases ($\phi_{i}$) of the harmonics, for the G-band light curve are determined using the Levenberg-Marquardt non linear fitting algorithm.
p1_error : Uncertainty on the p1 period (double, Time[day])
This parameter is filled with the uncertainty value of the p1 parameter. Its value is derived with Monte Carlo simulations that generate several (100) time series with the same time path as the data points but with magnitudes generated randomly around the corresponding data value. For each of these time series the period is derived from the non linear modeling with a truncated Fourier series of the light curve. The mean of all the periods found and its standard deviation are then computed, and the latter value is kept as value to fill the p1_error parameter.
epoch_g : Epoch of the maximum of the light curve in the G band (double, Time[Barycentric JD in TCB - 2455197.5 (day)])
The epoch of maximum light for the Gaia integrated $G$ band. It corresponds to the Baricentric Julian day (BJD) of the maximum value of the light curve model which is closest to the BJD of the first observations -3$\times$p1.
The mentioned BJD is offset by JD 2455197.5 (= J2010.0).
epoch_g_error : Uncertainty on the epoch parameter epoch_g (double, Time[day])
The uncertainty value of the epoch_g parameter. Its value is three times the error on the p1.
int_average_g : Intensity-averaged magnitude in the G band (double, Magnitude[mag])
The intensity-averaged magnitude in the $G$-band. The intensity-averaged magnitude is obtained by computing the average flux and then converting the average flux to magnitude.
int_average_g_error : Uncertainty on int_average_g parameter (double, Magnitude[mag])
This parameter is filled with the uncertainty value of the int_average_g parameter. The uncertainty is computed as the $error(zp)$, where $zp$ is the zero point obtained by the non linear Fourier modeling of the light curve.
peak_to_peak_g : Peak-to-peak amplitude of the G band light curve (double, Magnitude[mag])
This parameter is filled with the peak-to-peak amplitude value of the $G$ band light curve. The peak-to-peak amplitude is calculated as the (maximum) - (minimum) of the folded modeled light curve in the $G$ band. The light curve of the target star is modeled with a truncated Fourier series ($mag(t_{j})=zp+\sum[A_{i}sin(i\times 2\pi\nu_{max}t_{j}+\phi_{i})]$). Zero-point (zp), period (1/$\nu_{max}$), number of harmonics ($i$), amplitudes ($A_{i}$), and phases ($\phi_{i}$) of the harmonics, for the $G$-band light curve are determined using the Levenberg-Marquardt non linear fitting algorithm.
peak_to_peak_g_error : Uncertainty on the peak_to_peak_g parameter (double, Magnitude[mag])
This parameter is filled with the uncertainty value of the peak_to_peak_g parameter. The uncertainty is computed as the $\sqrt{2}\times error(zp)$, where $zp$ is the zero point obtained by the non linear Fourier modeling of the light curve.
num_harmonics_for_p1 : Number of harmonics used to model P1 of the light curve (int, Dimensionless[see description])
This parameter is filled with the number of harmonics used to model P1 of the light curve. The light curve of the target star is modeled with a truncated Fourier series ($mag(t_{j})=zp+\sum[A_{i}sin(i\times 2\pi\nu_{max}t_{j}+\phi_{i})]$). Zero-point (zp), period (1/$\nu_{max}$), number of harmonics ($i$), amplitudes ($A_{i}$), and phases ($\phi_{i}$) of the harmonics are determined using the Levenberg-Marquardt non linear fitting algorithm.
r21_g : Fourier decomposition parameter r21_g: A2/A1 (for G band) (double, Dimensionless[see description])
This parameter is filled with the Fourier decomposition parameter $R_{21}=A_{2}/A_{1}$, where $A_{2}$ is the amplitude of the 2nd harmonic and $A_{1}$ is the amplitude of the fundamental harmonic of the truncated Fourier series defined hereafter. The light curve of the target star is modeled with a truncated Fourier series ($mag(t_{j})=zp+\sum[A_{i}sin(i\times 2\pi\nu_{max}t_{j}+\phi_{i})]$). Zero-point ($zp$), period (1/$\nu_{max}$), number of harmonics ($i$), amplitudes ($A_{i}$), and phases ($\phi_{i}$) of the harmonics, are determined using the Levenberg-Marquardt non linear fitting algorithm.
r21_g_error : Uncertainty on the r21_g parameter: A2/A1 (for G band) (double, Dimensionless[see description])
This parameter is filled with the uncertainty value on the r21_g parameter. Its value isderived by propagation of the errors in the A2 and A1 parameters. Errors in A1,A2 are computed from Monte Carlo simulations that generate several (100) time series with the same time path as the data points but with magnitudes generated randomly around the corresponding data value. The mean for each of these values and their standard deviations are then computed, and the latter values are kept as value to fill the uncertainty of the A1, A2 parameters.
phi21_g : Fourier decomposition parameter phi21_g: phi2 - 2*phi1 (for G band) (double, Dimensionless[see description])
This parameter is filled with the Fourier decomposition parameter $\phi_{21}$: $\phi_{2}-2\phi_{1}$ value. The light curve of the target star is modeled with a truncated Fourier series ($mag(t_{j})=zp+\sum[A_{i}sin(i\times 2\pi\nu_{max}t_{j}+\phi_{i})]$). Zero-point ($zp$), period (1/$\nu_{max}$), number of harmonics ($i$), amplitudes ($A_{i}$), and phases ($\phi_{i}$) of the harmonics, for the $G$-band light curve are determined using the Levenberg-Marquardt non linear fitting algorithm.
phi21_g_error : Uncertainty on the phi21_g parameter: phi2 - 2*phi1 (for G band) (double, Dimensionless[see description])
This parameter is filled with the uncertainty of the phi21_g parameter. Its value is derived by propagation of the errors in the phi1 and phi2 parameters. Errors in phi1,phi2 are computed from Monte Carlo simulations that generate several (100) time series with the same time path as the data points but with magnitudes generated randomly around the corresponding data value. For each of these time series the phi1, phi2 values are computed. The mean for each of these values and their standard deviation are then computed, and the latter values are kept as value to fill the uncertainty of the phi1 and phi2 parameters.
| 2021-08-02T03:55:44 |
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|
https://www.usgs.gov/publications/estimating-species-misclassification-occupancy-dynamics-and-encounter-rates-semi
|
# Estimating species misclassification with occupancy dynamics and encounter rates: A semi-supervised, individual-level approach
April 5, 2022
1. Large-scale, long-term biodiversity monitoring is essential to conservation, land management, and identifying threats to biodiversity. However, multispecies surveys are prone to various types of observation error, including false positive/negative detection, and misclassification, where a species is thought to have been encountered but not correctly identified. Previous methods assume an imperfect classifier produces species-level classifications, but in practice, particularly with human observers, we may end up with extraspecific classifications including unknown', morphospecies designations, and taxonomic identifications coarser than species. Disregarding these types of species misclassification in biodiversity monitoring datasets can bias estimates of ecologically important quantities such as demographic ratess, occurrence, and species richness.
2. Here we present a joint classification-occupancy model that accounts for species non-detection and misclassification. Our framework accommodates extinction and colonization dynamics, allows for additional uncertain morphospecies' designations, and makes use of individual specimens with known species identities in a semi-supervised setting. We compare the performance of our model to a classification-only model that discards information about occupancy and encounter rate. We illustrate our model with an empirical case study of the carabid beetle (Carabidae) community at the National Ecological Observatory Network Niwot Ridge Mountain Research Station, near Boulder, CO, USA. We also use simulations to evaluate model performance through validation metrics where varying fractions of the data are confirmed.
3. The model supported imperfect classifier accuracy and favored certain true species classifications strongly for some morphospecies. The model outperformed (e.g., precision) the reduced model that discarded occupancy information, and these differences were most pronounced for abundant species.
4. Spatial and temporal dynamics from modeled occupancy and encounter rates may inform species misclassification probability, but this idea has not yet been tested. Our statistical framework explores this opportunity, and can be applied to datasets with imperfect species detection and classification, limited verification data, and non-species classifications.
| 2022-05-17T02:33:00 |
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|
https://par.nsf.gov/biblio/10097662
|
Near Field Cosmology: Translating Galaxy Properties to Lyman-alpha and Lyman-continuum escape fractions
We present our analyses of 39 selected star-forming low- to intermediate-mass low-redshift galaxies from the KISSR survey. These galaxies were selected as being representative in the local volume of the kinds of early galaxies that might have hosted the first stars, and span a range of galaxy properties (EWHA, reddening, metallicity, stellar mass). The KISSR systems contain a population, in appearance resembling "purple peas", with potentially steep UV slopes and high equivalent widths in H-alpha. Using archival GALEX data and theoretical models of radiation transport in dusty galaxies with clumpy gas media, we translate measurements of the UV slopes of these low-mass low-z KISSR galaxies to their escape fractions in Ly-alpha (LyA) and Ly-continuum (LyC) radiation, confirming a relationship between a galaxy's steep UV spectral slope and a significant (> 0.1) LyA escape fraction. This relationship is seen in existing data of low- to intermediate-mass galaxies in the local volume (please see accompanying poster by Pilon et al. at this meeting). We also translate measured LyA escape fractions in the literature for 14 LARS galaxies and a few dozen green pea galaxies to their LyC escape fractions using similar modeling. This work was supported by the University of San Francisco more »
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10097662
Journal Name:
American Astronomical Society, AAS Meeting
Volume:
233
Page Range or eLocation-ID:
383.05
4. ABSTRACT We measure the Lyman continuum (LyC) escape fraction in 54 faint Lyman-alpha emitters (LAEs) at $z$ ≃ 3.1 in the GOODS-South field. With the average magnitude of R = 26.7 AB (MUV = −18.8 and L ≃ 0.1L*), these galaxies represent a population of compact young dwarf galaxies. Their properties are likely to resemble those in the galaxies responsible for reionizing the Universe at $z$ > 6. We do not detect LyC emission in any individual LAEs in the deep HST F336W images, which covers the rest-frame 820 Å. We do not detect the LyC emission of these LAEs in the stacked F336W images either. The 3σ upper limit of LyC escape fractions is $f_{\rm esc}\lt 14\!-\!32{{\ \rm per\ cent}}$. However, the high Ly α rest-frame equivalent width (EW), low stellar mass, and UV luminosity of these LAEs suggest that they should have $f_{\rm esc}\gt 50{{\ \rm per\ cent}}$. The low LyC escape fraction from this work and other stacking analyses suggests that the LyC-leaking galaxies with $f_{\rm esc}\gt 50{{\ \rm per\ cent}}$ at $z$ = 2–3 do not follow the relation between fesc and UV luminosity and Ly α EW derived from typical galaxies at similar redshifts. Therefore, the UV luminositymore »
We report the discovery of a double-peaked Lyman-α (Ly α) emitter (LAE) at z = 3.2177 ± 0.0001 in VLT/MUSE data. The galaxy is strongly lensed by the galaxy cluster RXC J0018.5+1626 recently observed in the RELICS survey, and the double-peaked Ly α emission is clearly detected in the two counter images in the MUSE field of view. We measure a relatively high Ly α rest-frame equivalent width (EW) of EWLy α, 0 = (63 ± 2) Å. Additional spectroscopy with Gemini/GNIRS in the near-infrared (NIR) allows us to measure the H β, [O iii] λ4959 Å, and [O iii] λ5007 Å emission lines, which show moderate rest-frame EWs of the order of a few ∼10–100 Å, an [O iii] λ5007 Å/H β ratio of 4.8 ± 0.7, and a lower limit on the [O iii]/[O ii] ratio of >9.3. The galaxy has very blue UV-continuum slopes of βFUV = −2.23 ± 0.06 and βNUV = −3.0 ± 0.2, and is magnified by factors μ ∼ 7–10 in each of the two images, thus enabling a view into a low-mass ($M_{\star }\simeq 10^{7.5}\, \mathrm{M}_{\odot }$) high-redshift galaxy analogue. Notably, the blue peak of the Ly α profile is significantly stronger than the red peak, which suggests an inflow of matter and possibly very low H i column densities in its circumgalactic gas. To the best of our knowledge, this is the first detection of suchmore »
| 2023-03-24T15:32:27 |
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|
https://warframe.fandom.com/wiki/Heavy_Caliber
|
## FANDOM
5,920 Pages
Heavy Caliber increases damage of Primary Weapons (excluding Shotguns) at the cost of reduced accuracy by 15% and -5% per rank, at a maximum of 165% and -55% at rank 10, respectively.
## StatsEdit
Rank Damage Accuracy Cost
0 +15% -5% 6
1 +30% -10% 7
2 +45% -15% 8
3 +60% -20% 9
4 +75% -25% 10
5 +90% -30% 11
6 +105% -35% 12
7 +120% -40% 13
8 +135% -45% 14
9 +150% -50% 15
10 +165% -55% 16
## NotesEdit
• Instead of reducing the accuracy by 5% per rank, each rank increases spread by a specific percent per rank depending on the weapon. This effectively reduces accuracy but may reduce it by greater than 5% per rank (according to the Arsenal UI).
• Damage increase value of this mod stacks additively with that of to a total of +330% base damage.
• Since the two stack additively and Heavy Caliber costs 2 more mod capacity for the same bonus, combining the two is slightly less efficient in terms of damage per capacity cost. Maxed Serration grants +11.79% bonus damage per 1 mod capacity, while maxed Heavy Caliber grants +10.31% bonus damage per mod capacity. Combining the two, Serration and Heavy Caliber grant +11% bonus damage per 1 mod capacity, which is +0.79% less bonus damage per capacity than Serration alone.
• The bonus damage from using Heavy Caliber with Serration is double that of using Serration by itself, though it comes at the cost of an additional mod slot and Heavy Caliber's slightly higher "base" drain of 6.
• For example, if base damage is 100 then Serration adds 165% bonus damage and Heavy Caliber adds an additional 165% bonus damage, for a total of 430 damage. Thus, bonus damage is doubled for roughly double (+114%) the drain cost.
• Accuracy reduction varies by weapon, even for those with 100 accuracy. For example, (which has 100 accuracy, decreased to 1.7 at max rank) rockets fly very far outside of the reticule, while (which has 28.6 accuracy, decreased to 15.5 at max rank) spreads bullets considerably but don't stray too far from the reticule.
• With the exception of Ogris, the final accuracy after installing Heavy Caliber can be found by the following formula:
$\text{Resultant Accuracy} = \frac{100}{(100 / \text{Base Accuracy}) + 0.27 * (\text{Heavy Caliber's rank} + 1)}$
• can counter the accuracy reduction.
• The following weapons are unaffected or barely affected by the accuracy penalty:
• (Alternate Fire)
• Gaze
• ()
• () (Helps somewhat due to a wider attack radius)
• ()
• ()
• () (Primary Fire)
• (Cannonball mode)
• While the center beam of all continuous weapons will noticeably wobble, they will stay within the reticle, making them more accurate than most other weapons.
## TriviaEdit
• When it was first released, Heavy Caliber's original penalty was an increase in recoil as well as damage. However the recoil penalty did not affect recoil-less weapons (, , , bows and among others), effectively acting as another instance of . This was confirmed to be unintentional in Warframe Prime Time - Episode 2 (9:40). The mod's penalty was changed in Update 10.4.
## Patch HistoryEdit
Update 20.0
• Fixed the Ferrox not being affected by Heavy Caliber.
• Fixed extra stat appended to end of Heavy Caliber description.
• Fixed Mirage’s Hall of Mirrors not being affected by some mods (Heavy Caliber).
• Fixed an issue with certain Mods (i.e Heavy Caliber) not working correctly with Hall of Mirror clones.
• Weapon and Mod conclave tweaks – increased the rating on the Heavy Caliber mod.
• Recoil penalty changed to accuracy penalty.
• Introduced along with Orokin Vaults.
• , the normal variant of this mod.
• , the pistol counterpart of this mod.
• , the shotgun counterpart of this mod.
• , the melee counterpart of this mod.
## Start a Discussion Discussions about Heavy Caliber
• #### Buying MAXED HEAVY CALIBER
32 messages
• Does anyone have an unranked one on the xbox one?
• Yes I do 100 Gt stewedlearner01
• #### WTB - Heavy Caliber on Xbox One
• I'm getting tired of running vault runs ran them a good 100 times and now im just getting dupes it would be awesome if some one would tr...
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-08-14T02:43:52 |
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|
https://par.nsf.gov/biblio/10002736-measurement-bs0-lifetime-fully-partially-reconstructed-bs0ds-decays-pp-collisions
|
Measurement of the $Bs0$ Lifetime in Fully and Partially Reconstructed $Bs0→Ds−(ϕπ−)X$ Decays in $p¯p$ Collisions at $s=1.96 TeV$
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10002736
Journal Name:
Physical Review Letters
Volume:
107
Issue:
27
ISSN:
0031-9007
Publisher:
American Physical Society
| 2022-08-15T03:49:55 |
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https://pos.sissa.it/358/411/
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Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
The muon component of extensive air showers above 10$^{17.5}$ eV measured with the Pierre Auger Observatory
F.A. Sánchez
Full text: pdf
Pre-published on: 2019 July 22
Published on:
Abstract
The muon densities at 450m from the core for showers above $10^{17.5}$eV and zenith angle between $0^\circ$ and $45^\circ$ are presented. Results are based on 1 year of calibrated data collected by the engineering array of the Auger Muons and Infill for Ground Array (AMIGA) detector. Taking into account systematic uncertainties as well as attenuation effects, the observations suggest that the current hadronic interaction models fail in reproducing the measured number of muons with energies ${>}1$GeV. Simulations at $10^{17.5}$eV and $10^{18.0}$eV show that for EPOS-LHC an increase of 38% is required at both energies, while for QGSJET an increment of 50% and 53% is needed at respective energies. Data have been combined with previous results on muon densities at higher energies showing the match in the evolution of the composition derived with the measurements of depth of the maximum development of the showers in the atmosphere ($X_\text{max}$). The current AMIGA observations show that the variation of the primary masses has no sudden changes in the
energy range $10^{17.5}$ to $10^{18.0}$eV.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2019-08-25T15:33:42 |
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https://www.usgs.gov/special-topics/bipartisan-infrastructure-law-investments/news/bipartisan-infrastructure-law-funds-2
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January 25, 2023
RESTON, Va. — The U.S. Geological Survey (USGS) and the Colorado Geological Survey are investing $300,000 to map four 7.5-minute quadrangles (Rampant Hills, La Plata, Monument Hills, and Thompson Park) in the historic La Plata mining district along the southwest edge of the San Juan Mountains and eastern portion of the Colorado Plateau in southwestern Colorado. The study area is southwest of the San Juan volcanic field and consists of marine and non-marine sedimentary rocks of Late Paleozoic to Late Mesozoic age. Past mineral production in the district included gold, silver, copper, lead and zinc; critical minerals are associated with these precious and base metal deposits. Potential critical minerals in the project area: palladium, platinum, tellurium, vanadium and zinc. The grants for the geologic mapping come from a$74 million investment allocated earlier this year to the USGS Mineral Resources Program’s Earth Mapping Resources Initiative (Earth MRI), provided through annual appropriations and investments from the Administration’s Bipartisan Infrastructure Law. Overall, the Infrastructure Law is providing an appropriated \$510.7 million investment to the USGS to advance scientific innovation and map critical minerals.
The objectives of this project are to complete new mapping, at a scale of 1:24,000, or more detailed; fill in data gaps among previous maps that partially cover the study area; and provide higher resolution in areas where existing mapping is generalized or unclear. Concurrent geochemical and mineralogical studies are also being conducted. The goal is to better define the surface geology associated with mineral deposits in the La Plata polymetallic district.
The new geologic maps will refine our understanding of the geologic framework of mineral areas of interest. In addition to helping identify mineral potential, these maps also support both decisions about the use of land, water, energy and minerals, and understanding the potential impact of geologic hazards on communities.
Earth MRI is a partnership between the USGS and state geological surveys across America to modernize our understanding of the Nation’s fundamental geologic framework and mineral resources through new geologic maps, geophysical and topographic surveys, and geochemical sampling. The 2022 Bipartisan Infrastructure Law provided additional funding that has accelerated this new mapping in areas with potential for hosting critical mineral resources both still in the ground and in mine wastes.
| 2023-01-27T18:11:55 |
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|
https://theory.pppl.gov/news/seminars.php?scid=9&n=heliophysics-seminars
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# Heliophysics Seminars
The Heliophysics seminars are intended to allow guests and local members of the plasma physics community to present heliophysics related research and foster collaborations; to facilitate development of theoretical tools for understanding fundamental physical processes such as reconnection, turbulence, waves, and transport that control the dynamics in the context of the heliosphere; and to provide a forum to facilitate cross-fertilization between laboratory plasma physics, astrophysics, and heliospheric science.
### Upcoming
• Title: TBA
Prof. Steve Cranmer
#s1622, Tuesday, 28 Mar 2023, 2:00pm
### Past
• Frequency-resolved local measurements of phase-space energization **This will be a hybrid seminar on zoom and in person at the CCA in NYC**
E. Lichko, U. Chicago , abstract
[#s1619, 24 Jan 2023]
In order to disentangle the competing kinetic-scale energy dissipation processes that are intrinsic to space and astrophysical plasmas it is critical to be able to diagnose the energy transfer that is occurring locally in both time and space. A relatively recent technique to resolve the local rate of energy transfer between the fields and particles is the field-particle correlation (Klein & Howes APJL 2016), which has resolved local energy transfer at a single point in space for a large variety of systems and physical processes. This work details an updated version of the field-particle correlation that includes for the first time a breakdown of the energy transfer in frequency space, as well as time and velocity space. In addition to the increase in available information, this new method more cleanly separates magnitude and phase information of the signal, resulting in an improvement of the temporal resolution. This new method is applied to Gkeyll simulations of electron Landau damping as a proof of concept.
• Physical Regimes of Electrostatic Wave-Wave nonlinear interactions generated by an Electron Beam Propagation in Background Plasma
Haomin Sun [PPPL], abstract
[#s1611, 17 Jan 2023]
Electron-beam plasma interaction has long been a topic of great interest. Despite the success of Quasi-Linear (QL) theory and Weak Turbulence (WT) theory, their validities are limited by the requirement of sufficiently dense mode spectrum and small wave amplitude. In this paper, by performing a large number of high resolution two-dimensional (2D) particle-in-cell (PIC) simulations and using analytical theories, we extensively studied the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma. We confirm that initial two-stream instability between the beam and background cold electrons is saturated by wave trapping. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the different regimes are analyzed in detail. For the first time, we identified a new regime in strong Langmuir turbulence featured by what we call Electron Modulational Instability (EMI) that could create a local Langmuir wave packet growing faster than ion frequency. Ions do not respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually the beam-plasma wave interaction stops being resonant due to strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction is a periodic burst (intermittent) process. The beams are strongly scattered, and the Langmuir wave spectrum is significantly broadened, which gives rise to the strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa distribution and a energy spectrum observed in the strong turbulent regime are also discussed. This work was supported by the US Department of Energy, Office of Fusion Energy Science under contract # DE-AC02-09CH11466 as a part of the Princeton Collaborative Low Temperature Plasma Research Facility.
• Turbulent plasma wind tunnel studies on the Bryn Mawr Experiment (BMX) , Video
Prof. David Schaffner, Bryn Mawr
[#s1573, 19 Dec 2022]
• Intermittency and electron heating in kinetic-Alfven-wave turbulence video
Dr. Muni Zhou, IAS, abstract
[#s1572, 05 Dec 2022]
We report analytical and numerical investigations of sub-ion-scale turbulence in low-beta plasmas, focusing on the spectral properties of the fluctuations and electron heating. In the isothermal limit, the numerical results strongly support a description of the turbulence as a critically-balanced Kolmogorov-like cascade of kinetic Alfven wave fluctuations, as amended by Boldyrev & Perez (Astrophys. J. Lett. 758, L44 (2012)) to include intermittent effects. When the constraint of isothermality is removed (i.e., with the inclusion of electron kinetic physics), the energy spectrum is found to steepen due to electron Landau damping, which is enabled by the local weakening of advective nonlinearities around current sheets, and yields significant energy dissipation via a velocity-space cascade. The use of a Hermite-polynomial representation to express the velocity-space dependence of the electron distribution function allows us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.
• Laboratory Study of Residual Energy Generation in Strong Alfvén Wave Interactions video
Dr. Mel Abler, Space Science Institute, abstract
[#s1571, 21 Nov 2022]
Plasmas confined by a dipole magnetic field exhibit interchange and entropy mode turbulence causing bursty intermittent transport of particles and energy [1]. On the Collisionless Terrella Experiment (CTX), this turbulence is dominated by low-frequency, long-wavelength modes with amplitudes and phases that vary chaotically in time [2]. We present a new paradigm for characterizing this turbulence by measuring the time-evolution of the fluctuation power spectrum and the instantaneous bispectrum using the continuous wavelet transform [3,4] and computing the statistical properties of turbulent wave kinetics. We observe that both the fluctuation power and the energy transfer by three-wave coupling between these fluctuations can be intermittent. When antenna are used to actively launch waves into the turbulence, the intermittency of the driven waves decreases, while the intermittency of other waves increases. Similarly, application of active feedback [5] to amplify the turbulence decreases the intermittency of the wave energy, while suppressing feedback increases this intermittency. Measurements based on this new paradigm show that the transfer of wave energy to larger and smaller scales in a turbulent plasma is not steady but occurs in short and intense bursts, analogous to the better-known short bursts of particle transport in magnetized plasma. [1] B.A. Grierson, et al, Phys Rev Lett 105, 205004 (2010). [2] B.A. Grierson, et al, Phys Plasmas 16, 055902 (2009). [3] C. Torrence and G.P. Compo, Bulletin of the American Meteorological Society, 61-78 (1998). [4] B.P. Van Milligen, et al, Phys Rev Lett 74, 395 (1995). [5] T.M. Roberts, et al, Phys Plasmas 22, 055702 (2015).
• SCALED SOLAR EJECTION EXPERIMENTS ON THE BIG RED BALL video
Dr. Rachel Young, University of Michigan, abstract
[#s1570, 14 Nov 2022]
At the Center for Laboratory Astrophysics at the University of Michigan, we specialize in laboratory experiments scaled to be relevant to astrophysics. How do we design laboratory experiments to answer questions about astrophysics? And what do we mean by “scaled” in terms of an experiment? This talk will explain how we go from an astrophysical system to a laboratory experiment by focusing on one project currently underway at the University of Michigan: studying solar ejections on the Big Red Ball machine at the University of Wisconsin. These are systems of magnetized plasma that the Sun ejects frequently and when they reach Earth cause geomagnetic storms. These storms are responsible for the aurora borealis (the northern lights) but they can also damage electrical equipment and cause power outages, and there is great interest in being able to understand and predict them better. Our Big Red Ball experiments are designed to address open questions about how these solar ejections react to external magnetic fields. Our experiments launch a compact torus of plasma (the scaled analog of the ejected coronal material) into background plasma inside the Big Red Ball (the scaled analog of the interplanetary medium, the diffuse plasma that fills the Solar System). I will discuss how the experiment was designed, how we went about “scaling” it, results of our first round of experiments, and plans for future work. This work is funded by the U.S. Department of Energy NNSA Center of Excellence under cooperative agreement number DE-NA0003869.
• Electron Energization during Electron-Only Magnetic Reconnection in PHASMA video
Dr. Peiyun Shi, West Virginia University, abstract
[#s1566, 07 Nov 2022]
Electron-only reconnection is a variant of magnetic reconnection without significant ion involvement. Such reconnection has recently been observed in the terrestrial magnetosheath and has received considerable attention due to its likely role in the energy cascade of turbulent magnetized plasmas. Different electron energization mechanisms usually favor electron acceleration along different directions and occur in different regions of reconnection. Therefore, spatially resolved electron velocity distribution function (EVDF) measurements along specific directions are required to elucidate the underlying electron energization mechanisms during electron-only reconnection. In the PHAse Space MApping (PHASMA) facility, a first-of-its-kind multi-dimensional incoherent Thomson scattering system enables 3D EVDF measurements by employing two injection paths and two collection paths. In this seminar, I will present 3D local electron heating measurement around the separatrix during reconnection. The measured heating corresponds to 70% of the incoming Poynting flux [Shi et al., Phys. Rev. Lett. 128, 025002 (2022)]. The electron temperature is clearly anisotropic, with the ratio between parallel and perpendicular electron temperature Te|| / Te⟂ ~ 1.5. This preferential parallel electron heating reveals the important role of the reconnecting electric field in electron energization for strong guide field reconnection. In addition, non-Maxwellian EVDFs, composed of a warm bulk population and a cold beam, were measured. Oppositely directed electron beams that appear on either side of the X-point are clear evidence of electron acceleration in magnetic reconnection. Interestingly, parallel EVDFs with either a flat top or beam component are also observed around two separatrices, reflecting the removal or enhancement of some electron portion of the electron velocity phase space. This agrees well with the field-particle correlation signatures reported in gyrokinetic numerical simulations [McCubbin et al., Phys. Plasmas 29, 052105 (2022)].
• Plasma-Physics Problems Operating an Accelerator in Space video
Joe Borovsky, Gian Luca Delzanno and Vadim Roytershteyn, abstract
[#s1563, 24 Oct 2022]
There is interest in operating a 1-MeV 1-kWatt electron accelerator on a spacecraft in the tenuous plasma of the Earth’s distant magnetosphere. The desire is to fire the electron beam into the atmospheric loss cone to optically excite the atmosphere at the magnetic footpoint of the accelerator. A NASA-funded engineering mission design was just completed for this mission concept. To bring the concept to reality, several plasma-physics problems had to be overcome. This talk will focus on 6 of those problems. (1) Designing an electron beam with a divergence smaller than the loss cone. (2) Knowing where the loss cone is located when there are finite-gyroradii effects. (3) Overcoming electron-beam-driven spacecraft charging. (4) Checking beam-plasma stability. (5) Examining whether ambient magnetospheric plasma waves will scatter the beam electrons. (6) Detecting the optical beamspot with ground-based imagers. Five out of six of these problems were difficult.
• A survey on recent problems in ionospheric plasma physics: Instabilities and parameter estimation video
Dr. Kike (Enrique) Rojas Villalba, Cornell, abstract
[#s1561, 10 Oct 2022]
The ionosphere is a weakly ionized plasma where electrostatic phenomena dominate. This plasma constantly interacts with the neutral atmosphere through particle collisions and dynamo-generated fields, and various free energy sources often drive it unstable, which can cause density irregularities and even storms. Nevertheless, despite its complexity and taking advantage of its response to radio waves, we can measure it with great precision using radars and other instruments. In this talk, I will present some of the ionospheric plasma physics projects I have been involved with recently, emphasizing potential commonalities with other plasma communities. First, I am going to describe the experimental characteristics of the collar-shaped echoes found at 150 km in the equatorial region, recent progress in understanding their origin, and how to use them to measure electron densities. Then, I will present some new results in modeling Farley-Buneman instabilities using fluid models and how these can capture various features measured with experiments and reproduced using PIC simulations. Next, I describe recent measurements of lower-hybrid waves in the topside of the ionosphere and a potential mechanism for their production. Finally, I will outline a method we are developing to estimate electron density distributions by fitting the computer estimations of radio wave refraction to local radar measurements. I will highlight open questions and potential solutions for each presented problem.
• Prof. David Schaffner, Bryn Mawr
[#s1471, 20 Jun 2022]
• Charging of dust grains in a plasma video
Prof. John Goree, University of Iowa, abstract
[#s1470, 06 Jun 2022]
A solid object immersed in a plasma collects electrons and ions unequally, so that its surface is at a floating potential, and the object as a whole gains an electric charge. This charging occurs for solid objects of all sizes, from moons to nanoparticles. When exposed to ultraviolet light or energetic electrons, the object can charge positively due to electron emission. On the other hand, a negative charge was almost always thought to develop in a low-temperature plasma, for a micron-size dust grain, until recently when it was discovered that a large positive charge can develop in an afterglow plasma. In this talk I review the basics of dust-grain charging, including for space-physics and industrial applications. I also present some recent experimental results with positive charging in an afterglow. Work supported by: Army Research Office under MURI Grant No. W911NF-18-1-0240, NASA-JPL subcontract 1672641, NSF grant 1740379-001, and U.S. Department of Energy Grant DE-SC0014566.
• Shocks Under the Microscope: Examining the Microphysics of Collisionless Shocks with High Resolution, Multi-point Space Plasma Measurements video
Prof. Katy Goodrich, University of West Virginia, abstract
[#s1469, 16 May 2022]
Collisionless shocks are an important and universal phenomenon in astrophysical plasmas. Shocks form when a supersonic plasma flow interacts with an impermeable obstacle. Examples of such interactions include galactic jets or supernova remnants interacting with the interstellar medium, or plasma wind from stars encountering stellar system bodies, such as planets, comets and moons. The shock performs the necessary function of converting kinetic energy to thermal energy, heating the originally supersonic plasma flow until its speed is reduced and it can flow around the obstacle. The energy conversion processes that take place inside collisionless shocks, however, are not not well established and have thus been a subject of interest for several decades. The closest and perhaps the most relevant collisionless shock to us humans, is the Earth’s bow shock. This shock forms 10-12 Earth radii upstream of our planet when supersonic plasma ejected from the sun, called the solar wind, meets the Earth’s intrinsic magnetosphere. The bow shock has been observed by multiple spacecraft such as ISEE, Cluster, WIND, and THEMIS over three decades. These missions have provided us with a wealth of information on plasma conditions both upstream and downstream of the shock, however, limited instrument capabilities have prevented us from resolving the physical processes active at the shock itself. The energy conversion processes active within shocks are expected to occur at primarily electron spatial and time scales (milliseconds to seconds), which up until recently were beyond the reach of our particle observations. While we can rely on highly time resolved magnetic and electric field measurements from these missions, they provide an incomplete view of the inner workings of the shock. Observations from the Magnetospheric Multiscale (MMS) mission (launched in 2014) provide particle observations on the order of 10s of milliseconds, providing an unprecedented opportunity to directly observe microscale processes inside collisionless shocks. In this talk, we’ll take a first look at the direct connection between electric and magnetic field signals with electron and ion dynamics in the Earth’s bow shock. We find that energy conversion can occur from multiple processes, some unexpected, within varied areas of the shock. The new dataset provided by MMS enables a new age of collisionless shock analysis as well as motivation for future space missions dedicated to the shock, signaling an exciting time for space physicists!
• Laboratory evidence for proton energization by collisionless shocks video
Dr. Weipeng Yao, Ecole Polytechnique, abstract
[#s1468, 09 May 2022]
Collisionless shocks are ubiquitously in the Universe and are held responsible for the production of non-thermal particles and high-energy radiation. Without particle collisions, theoretical works show that microscopic instabilities are able to mediate energy dissipation and allow for shock formation. Using our platform where we couple high-powerful lasers (JLF/Titan at LLNL and LULI2000) with high-strength magnetic fields, we have investigated the generation of magnetized collisionless shock and the associated particle energization [1]. We have diagnosed the plasma density, temperature, as well as the electromagnetic field structures and particle energization in the experiments, under various conditions of ambient plasma and B-field [2]. We have also modelled the formation and interpenetration of the shocks using both macroscopic hydrodynamic simulations and kinetic particle-in-cell simulations [3]. By varying the parameters of the expanding plasma launched in the ambient gas, as well as those of the background magnetic field, we investigate the bridge between the simulated dissipation mechanisms and observed particle energization, as will be reported here. [1] W. Yao, A. Fazzini, et al., Nat. Phys. 17, 1177–1182 (2021) [2] W. Yao, A. Fazzini, et al., MRE 7, 014402 (2021) [3] A. Fazzini, W. Yao, et al., arXiv:2202.03465 (2022)
• The Modifications of Collisionless Shock Hydrodynamics by Nonthermal Particles in Kinetic Simulations video
Prof. Colby Haggerty, University of Hawaii, abstract
[#s1467, 25 Apr 2022]
Earth’s bow shock, and collisionless plasma shocks more generally, are efficient accelerators of energetic, nonthermal particles. Shocks can deposit a significant fraction of their ram energy into non-thermal populations, yet despite this, much of our understanding of shock hydrodynamics is derived assuming the plasma behavies as a collisional fluid. With this in mind, we reconsider the theory of shock hydrodynamics including the effects of both the self generated, non-thermal, energetic population and the associated enhanced magnetic fields, amplified by the non-thermal particles. Using hybrid simulations of parallel collisionless shocks for a range of Mach numbers, it is shown that the non-thermal particles diffuse away from the shock in the downstream at an enhanced rate, increasing the compressibility and decreasing the speed of the shock. This nonlinear feedback process limits the fraction of shock energy deposited into the non-thermal particles and changes the slope of the associated power-law distribution function. These hydrodynamic modifications have important implications for our understanding of heliospheric shocks and how the sun and solar wind affect Earth’s magnetosphere as well as collisionless astrophysical shocks more generally.
• Enhanced Thomson scattering in super-Alfvenic, pulsed power driven magnetic reconnection experiments video
Dr. Lee Suttle, Imperial College London, abstract
[#s1466, 11 Apr 2022]
Pulsed-power driven exploding wire arrays have been used to demonstrate long-lived laboratory magnetic reconnection events in a quasi-2D geometry of colliding magnetized plasma flows [1]. The platform allows detailed measurements of reconnection layer structure and of the properties of the in- and out- flowing plasma, and provides control over the reconnecting plasma parameters (e.g. drive strength and radiative cooling time-scale) through the choice of the wire array material, enabling different non-idealized aspects of reconnection physics to be studied [2]. In this talk I will be discussing experiments carried out at the MAGPIE generator, using aluminum wire arrays which produce a reconnection layer with super-Alfvenic inflows (MA ~ 3, βdyn ~10). Thomson scattering (TS) measurements of the plasma temperatures and flow velocity components in the reconnection plane have shown a fast outflow of material along the layer consistent with the generalized Sweet-Parker model [3], and a preferential heating of ions inside the layer, reaching an energy partition of Ti ~ ZTe. Spitzer resistivity appears sufficient to balance Ohm’s law in this scenario, however it is unclear what mechanism is driving the ion heating. Further investigation was made using a TS geometry which is sensitive only to the out-of-plane component of plasma velocity – aligned with the reconnection electric field. This shows consistent plasma temperatures and electron drift velocities greater than the local sound speed of the plasma: a criterion for ion acoustic turbulence (IAT). An assessment of the spectrally integrated TS signal inside the current sheet also shows an enhancement in the scattered intensity, above the expected level of thermally-driven ion acoustic waves (IAWs), which is only present for current-aligned K vectors. However, the spectral shape of the observed IAWs is not consistent with previous observations of IAT [4]. We discuss and analyse potential implications of these measurements.
• Cross-scale energy transfer processes in weakly collisional plasmas video
Dr. Yan Yang, University of Delaware, abstract
[#s1462, 28 Mar 2022]
Space plasmas are frequently taken to be weakly collisional or collisionless. Therefore, an explicit form of viscous dissipation as in collisional (e.g., MHD) cases cannot be easily defined. A variety of approaches have attempted to characterize specific mechanisms (e.g., magnetic reconnection, wave-particle interaction and turbulent-driven intermittency) and to quantify the dissipation. However, the community has not come to a consensus solution applicable to all systems. Turbulence enters into space plasmas in many guises. The complexity and variability of the behavior of plasma turbulence is in large part due to the involvement of dynamics at many scales, ranging from macroscopic fluid to sub-electron scales. Observed turbulence in space is expected to involve cross-scale energy transfer and subsequent dissipation and heating. Instead of identifying specific mechanisms, we discuss how to disentangle multiscale properties, how plasma dynamics bridges multiple scales, what new ingredients are introduced in cross-scale transfer as models progress from fluid to kinetic, and how to identify key steps in energy transfer. This motivates several surrogates, arising from the energy transfer process, to estimate energy dissipation rate in weakly collisional plasmas. We investigate in detail the cross-scale energy transfer process and discuss unresolved issues (e.g., entropy and reversibility) that may be addressed by future studies. Where feasible, examples are given from MHD, Particle in Cell, and hybrid Vlasov-Maxwell simulations, and from Magnetospheric Multiscale (MMS) observations.
• Modeling CME-driven Solar/Stellar Energetic Particle Events at Solar-like Stars
Dr. Junxiang Hu, Center for Space Plasma and Aeronomic Research (CSPAR) / University of Alabama in Huntsville (UAH), abstract
[#s1460, 14 Mar 2022]
Coronal mass ejections (CMEs) and solar flares are arguably the two most energetic phenomena in the solar system. Large gradual solar energetic particle (SEP) events are primarily associated with coronal mass ejections (CME) driven shocks. The Discovery of frequent superflares on active cool stars opened a new avenue in understanding the properties of eruptive events and their impact on exoplanetary environments. Solar data suggest that CMEs should be associated with superflares on active solar-like planet hosts and produce Stellar Energetic Particle (StEP) events that could be orders of magnitude stronger than solar events. The improved Particle Acceleration and Transport in the Heliosphere (iPATH) model is a physics-based MHD SEP model developed at CSPAR. The iPATH model simulates diffusive shock acceleration (DSA) at CME-driven shocks and follows the subsequent transport of energetic particles through the inner heliosphere. Our recent work applies previous modeling efforts using iPATH for SEP events in the solar system to the stellar energetic particle events at young solar-like stars. We derive the scaling of StEP’s fluence and hardness of energy spectra with CME speed and associated flare energy. This study focuses on the very high energy (~hundreds of MeVs to GeVs) particles and their impact on erosion and chemistry of exoplanetary atmospheres. These results will have crucial implications for the prebiotic chemistry and expected biosignatures from atmospheres of early Earth and young rocky exoplanets, as well as the chemistry and isotopic composition of circumstellar disks around infant Suns.
• ParkerSolar Probe Observations of the Prevalence of Magnetic Reconnection in the near-Sun Heliospheric Current Sheet video
Tai Phan (UC Berkeley) and the PSP Team, abstract
[#s1433, 31 Jan 2022]
During its first eight orbits around the Sun, Parker Solar Probe (PSP) crossed the large-scale Heliospheric Current Sheet (HCS) multiple times and provided unprecedented detailed plasma and field observations of the near-Sun HCS. We report thecommon detections by PSP of reconnection exhaust signatures in the HCS at heliocentric distances of 16-107 solar radii. Both sunward and antisunward-directedreconnection exhausts were observed. In the sunward reconnection exhausts, PSP detected counter streaming strahl electrons, indicating that HCS reconnection resulted in the formation of closed magnetic field lines with both ends connected to the Sun. In the anti sunward exhausts, PSP observed dropouts of strahl electrons, consistent with the reconnected HCS field lines being disconnected from the Sun. Ion and electron signatures of the reconnection separatrix layers are also observed adjacent to some exhausts. The commondetection of reconnection in the HCS suggests that reconnection is almost always active in the HCS near the Sun. Furthermore, the occurrence of multiple long-duration partial crossings of the HCS suggests that HCS reconnection could produce chains of large bulges with spatial dimensions of up to several solar radii. The finding of the prevalence of reconnection in the HCS is somewhat surprising since PSP has revealed that the HCS is much thicker than the kinetic scales required for reconnection onset. Thus, the PSP findings suggest that large-scale dynamics either locally in the solar wind or within the coronal source of the HCS (e.g., at the tip of helmet streamers) plays a critical role in triggering reconnection onset.
• Exploring driven magnetic reconnection in the laboratory video
Dr. Joe Olson, University of Wisconsin, abstract
[#s1371, 13 Dec 2021]
In this talk, I'll discuss our recent work on the Terrestrial Reconnection Experiment (TREX) where magnetic reconnection is explored with asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. We find that magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed, helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Given the small system size relative to the ions, the observed normalized reconnection rate is consistent with a range of previous numerical results indicating a possible transition to "electron only" reconnection. These experimental results have also been corroborated through the use of PIC simulations utilizing the specialized TREX geometry and driving mechanism, showing similar scaling of the reconnection rate with system size. Finally, I'll touch on recent ongoing work to upgrade the reconnection drive system in an effort to reach more kinetic regimes of reconnection where effects such as electron pressure anisotropy are expected.
• Laboratory Simulation of Basic Space Plasma Phenomena video
Prof. Bill Amatucci, West Virginia University, abstract
[#s1370, 06 Dec 2021]
A rich variety of wave phenomena exist in virtually every region of the geospace environment. Understanding of the various wave signatures and driving mechanisms provided insight into the local conditions, not only at the instant that the waves are observed, but also into how the conditions may evolve in time. Comprehensive, controlled investigations of the detailed microphysics associated with these waves are difficult to accomplish through in situ methods alone. Space-based measurements typically offer a statistical picture, built up over long periods of time and under varying conditions. Consequently, properly scaled laboratory experiments performed under controlled, repeatable conditions can offer an important complementary approach to investigating the space plasma wave dynamics. We present an overview of several key wave modes found in the various regions with a particular emphasis on significant contributions of laboratory investigations toward the present understanding of the wave dynamics, validation of theoretical models, and interpretation of the in situ observations.
• An unexpected encounter in the inner Heliosphere: Solar Orbiter crossing through the ion tail of comet ATLAS. Structure of magnetic field draping and signatures from cometary pick-up ion waves close to the Sun. video
Prof. Lorenzo Matteini, Imperial College, abstract
[#s1369, 29 Nov 2021]
Soon after the launch of the ESA Solar Orbiter in February 2020 it was suggested that the spacecraft would have flown through the ion and dust tails of comet C/2019 Y4 (ATLAS) just after perihelion, while its nucleus was at 0.25 Astronomical Units from the Sun. The encounter is expected to have taken place when Orbiter was also close to its first perihelion at 0.5 AU, then offering us the first opportunity to study the tail of a comet inside 1AU. Moreover, comet ATLAS fragmented just before perihelion, making such an unusual near-Sun encounter even more interesting and a unique event. In this talk, I will briefly review some of the main plasma processes that characterise the interaction of an active comet with the surrounding solar wind, namely the draping of the interplanetary magnetic field around the nucleus, the pick-up of cometary ions and the generation of plasma waves by associated instabilities. Then, I will present joint observations from all in-situ instruments onboard Solar Orbiter about this event and will discuss identified signatures of magnetic field draping and ion-scale waves. Despite fragmentation and the fact that the encounter took place at a significant distance downstream of the nucleus, the overall structure observed at large scale is consistent with that of a comet magnetotail - 2 magnetic lobes of opposite polarity surrounding a central dense and almost unmagnetised plasma sheet - and qualitatively in agreement with past comet-tail crossings. Moreover, at smaller scale, we identified several intervals of ion waves likely associated to instabilities driven by cometary Oxygen ions picked-up by the solar wind and whose polarisation properties are in good agreement with predictions from numerical simulations. These results suggest that the spacecraft has indeed crossed the ion-tail of comet ATLAS at 0.5 AU and that events of this type could become more common in the near future thanks to the presence of Solar Orbiter, Parker Solar Probe and BepiColombo in the inner Heliosphere.
• Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasmat
Dr. Vadim Roytershteyn, Space Science Institute, abstract
[#s1368, 15 Nov 2021]
Whistler waves play a major role in the dynamics of the Earth’s magnetosphere, where they are associated with local electron energization as well as precipitation in the form of aurora. Naturally occurring chorus waves are primarily generated by an instability driven by temperature anisotropy of hot (~keV) electrons which are injected during substorms. In addition, cold plasma populations (~eV) originating from ionosphere are often present and may in fact be the dominant population by density. In this presentation, I will describe our recent kinetic simulations and theory demonstrating that in the presence of cold populations whistler waves can excite oblique, short-wavelength electrostatic turbulence through a nonlinear process involving secondary drift instabilities. Depending on the parameters, the secondary modes are related to electron Bernstein and/or oblique whistler modes near the resonance cone. They lead to heating of the cold plasma, damping of the primary whistler waves, and may contribute to the excitation of the oblique chorus. The new mechanism can play a significant role in controlling amplitude of of whistlers in the regions of the Earth’s magnetosphere where cold background plasma of sufficient density is present. In addition to affecting the naturally occurring waves, this process may also be of importance to the efforts on so-called radiation belt remediation, i.e. attempts to enhance losses of dangerous energetic electrons from radiation belts by artificially injecting whistler waves.
• Space Physics in the PHAse SPace MApping (PHASMA) Experiment video
Prof. Earl Scime, West Virginia University , abstract
[#s1367, 01 Nov 2021]
A new experiment, called the PHAse Space MApping (PHASMA) experiment, features laser induced fluorescence diagnostics for ion measurements, Thomson scattering diagnostics for electron velocity distribution function measurements, and a microwave scattering system for turbulence measurements. PHASMA is designed to enable the direct measurement of ion and electron vdfs in space-relevant plasma phenomena including reconnection, shocks, and turbulence. To create the conditions necessary for different experimental regimes, PHASMA employs a 1 kW, steady-state helicon source capable of generating variable-density background hydrogen, helium, argon, krypton, and xenon plasmas with controllable plasma pressure (relative to the magnetic pressure), collisionality, and azimuthal flow shear. Reconnecting flux ropes arise through the merging of discharges from two pulsed plasma guns that operate in argon, helium, and hydrogen. In this talk I will describe results from two recent, space-relevant, experimental campaigns. The first campaign explored the stability of non-line-tied flux ropes. Similar boundary conditions exist for flus ropes observed in space and the solar corona. The measurements confirm the theoretically predicted stability threshold for the ropes and indicate that the m = 1 kink instability triggered for large currents in the flux rope drives an additional Alfvénic mode that propagates along the flux rope. In the second campaign, the merger of two flux ropes through electron-only reconnection is investigated at the kinetic, sub-gyroradius, scale. We find that the majority of the incoming magnetic energy appears as electron thermal energy and that Ohmic processes are unlikely to be responsible for the measured increase in electron enthalpy. The electron distribution function measurements include non-Maxwellian features, including beams that jet out from the X-point in both outflow directions. The electron beam speed scales with the local electron Alfvén speed.
• Dust in Space Plasmas: Investigations of Orbital Debris and Asteroid Evolution video
Prof. Christine Hartzell,University of Maryland , abstract
[#s1366, 25 Oct 2021]
The interaction of charged particles with the local plasma environment is of interest in a variety of space applications. This talk will focus on two specific applications: 1. the design of new technologies to detect orbital debris and 2. the evolution of asteroid surfaces. Small (sub-cm) orbital debris poses a serious hazard to functional spacecraft, but is very difficult to detect (and impossible to track) using conventional technologies. Our simulations predict that many of these debris objects will produce solitons in the ionospheric plasma environment. We will present the characteristics of the debris that are predicted to produce solitons and the characteristics of the resulting solitons. Detection of debris-produced solitons may provide a new technique to monitor the highly uncertain sub-cm debris environment. Our second topic concerns the removal of small particles from the surfaces of asteroids. The regolith of many small asteroids is coarse compared to other solar system bodies like the Moon. It has been hypothesized that small regolith particles may be removed from asteroids due to the interaction of the charged particles with the local plasma environment. We will present predictions of the sizes of particles that can be lofted from asteroid surfaces (considering two leading particle charging models) and the subsequent trajectories (including escape) of those particles. Electrostatic lofting, combined with solar radiation pressure, may be an active loss mechanism on asteroids.
• The helicity barrier: how low-frequency turbulence triggers high-frequency heating of the solar wind video
Prof. Jono Squire, University of Otago , abstract
[#s1365, 11 Oct 2021]
Low-frequency Alfvénic turbulence is a leading candidate to explain the heating of the solar corona and launching of the fast solar wind. A sufficiently energetic source of such motions is observed near the coronal base and in-situ measurements reveal that the solar wind is filled with Alfvénic fluctuations. However, a persistent difficulty with the scenario has been explaining the observed dominance of perpendicular ion heating, since theories predict a variety of outcomes, with electron heating dominating in the highly anisotropic, low-beta limit that seems most relevant to the low solar wind. Ion cyclotron wave (ICW) heating, in contrast, can readily explain the observed heating properties (including those of alpha particles and other minor ions); but, given the small parallel scale of ICWs, it has proved difficult to explain their source. In this work, using six-dimensional hybrid-kinetic simulations, we show how imbalanced Alfvénic turbulence can drive ICW heating of the solar wind. The effect is enabled by the recently discovered “helicity barrier,” which stops turbulent energy from cascading to scales below the ion gyroradius, thus inhibiting electron heating. Instead, the turbulent energy hits the “barrier” and is stuck, building up in time until the parallel scales decrease sufficiently to generate ICWs and perpendicular ion heating. The resulting turbulence bears detailed resemblance to a wide array of in-situ measurements from the solar wind, capturing the steep “transition range,” observed magnetic-helicity signatures, and key features of the ion distribution function. Based on the predicted dependence of the ion-to-electron heating ratio on imbalance, we suggest that fast- and slow-wind streams are driven by similar physical effects with the helicity barrier playing an important role. Preprint https://arxiv.org/abs/2109.03255
• Overview of plasma wave studies using the Basic Plasma Science Facility video
Troy Carter, UCLA, abstract, slides
[#s1354, 20 Sep 2021]
The Basic Plasma Science Facility (BaPSF) at UCLA is a US national collaborative research facility sponsored by DOE and NSF for studies of fundamental processes in magnetized plasmas. The centerpiece of the facility is the Large Plasma Device (LAPD), a 20m long, magnetized linear plasma device. LAPD has been utilized to study a number of fundamental processes, including: collisionless shocks, dispersion and damping of kinetic and inertial Alfvén waves, compressional Alfvén waves for ion-cyclotron range of frequencies heating, flux ropes and magnetic reconnection, three-wave interactions and parametric instabilities of Alfvén waves, turbulence and transport and interactions of energetic ions and electrons with plasma waves. An overview of research using the facility will be given, followed by a more detailed discussion of studies of the nonlinear physics of Alfvén waves and the physics of high power ICRF waves in LAPD. Recent experiments have resulted in the first laboratory observation of the parametric instability of shear Alfvén waves. Shear waves with sufficiently high ω/Ωc,i (> 0.6) and above a threshold wave amplitude are observed to decay into co-propagating daughter waves; one a shear Alfvén wave and the other a low-frequency quasimode. The observed process is similar to the modulational decay instability. Another series of experiments using LAPD have studied high power (~ 200kW) fast wave excitation (ω ∼ 2−10Ωci). Highlights of this work include documenting: the structure and scaling of RF sheaths, the formation of convective cells and associated density modification, and parasitic coupling to the slow mode in the low density plasma in front of the antenna.
• WIND Observations of Magnetic Reconnection Exhausts in the Solar Wind video
Dr. Stefan Eriksson, LASP University of Colorado, abstract
[#s1328, 30 Aug 2021]
The WIND satellite has been collecting magnetic fields at 92-ms and plasma moments at 3-s cadence in the pristine solar wind over nearly two full solar cycles, since it was launched on 1 Nov 1994. We report on the statistical properties in and around magnetic reconnection jets in the solar wind during a nearly 10-year period of continuous observations from 1 July 2004 to 31 Dec 2014. The conservative criteria of the external variability of the magnetic field and plasma velocity that we applied in the automatic surveys for jets across current sheets of variable durations resulted in a total of 4451 candidate exhaust events over this period. We have analyzed the Walen relation manually across all candidate events, and this exercise resulted in a subset of 3374 confirmed reconnection exhausts. This particular WIND data survey applied six running windows with time durations Δt=[12-s, 18-s, 2-m, 4-m, 10-m, 20-m] to the solar wind observations of magnetic field and bulk velocity. We present and discuss the histograms of several important parameters associated with these periods of current sheets with reconnection exhausts. We will also discuss some initial comparisons with the intensity of solar wind turbulence inside the exhausts and how this compares with the intensity of the external solar wind turbulence ahead of the current sheets.
• Concerted simulations and laser-driven laboratory experiments of fundamental astrophysical processes in turbulent magnetized plasmas
Prof. Petros Tzeferacos, University of Rochester, abstract
[#s1327, 23 Aug 2021]
I present an overview of the exciting fundamental science in magnetized astrophysical plasmas that the TDYNO team is accomplishing through concerted application of the FLASH code and laboratory plasma astrophysics experiments. Our international collaboration has conducted breakthrough experiments in the study of turbulent dynamo. This ubiquitous astrophysical mechanism is thought to be responsible for present-day magnetization of numerous celestial objects but had eluded laboratory plasma physicists for decades. The experiments have enabled us to explore dynamo in various regimes, providing us with novel insights and a new tool to validate or falsify our theoretical understanding. I will also describe how these experiments are enabling laboratory investigations of cosmic ray (CR) acceleration, the diffusive transport of extragalactic and ultra-high energy CRs, and the strong suppression of heat conduction in galaxy clusters.
• Flare simulations with the MURaM radiative MHD code video
Dr. Matthias Rempel High Altitude Observatory, National Center for Atmospheric Research, abstract
[#s1326, 16 Aug 2021]
Over the past few years, the MURaM radiative MHD code was expanded for its capability to simulate the coupled solar atmosphere from the upper convection zone into the lower solar corona. The code includes the essential physics to synthesize thermal emission ranging from the visible spectrum in the photosphere to EUV and soft X-ray from transition region and corona. A more sophisticated treatment of the chromosphere is currently under development. After a brief review of the code's capabilities and limitations I present a few recent examples of solar flare simulations computed with the MURaM code. Specifically, I present data inspired simulations that do capture 2 scenarios that have been proven to be flare productive in solar observations: emergence of new magnetic flux into an existing active region and compact collisional polarity inversion lines (cPILs) that result from the collision of sunspots. We compute synthetic observables including photospheric emission and coronal EUV and X-ray emission and study specifically observables that diagnose the pre-eruptive flux rope structure and highlight the location of reconnection sites leading to the destabilization of the flux system, which will be available from the Multi-slit Solar Explorer (MUSE), a mission undergoing a phase A study. In the simulated flares we find energy releases in the 5x1030 – 2x1031 erg range corresponding on the sun to flares of mid C to lower M class, leading to a multi-thermal plasma with temperatures exceeding 100 million K. While our current models cannot distinguish between thermal and non-thermal plasma, I discuss implications from the presence of a multi-thermal plasma for the interpretation of coronal observations.
• Using kinetic entropy to study energy conversion and dissipation in space plasmas video
Prof. Paul Cassak, University of West Virginia, abstract
[#s1325, 02 Aug 2021]
A recurring theme in the fundamental plasma physics of heliospheric, planetary, and astrophysical plasmas is the ultimate fate of large scale energy when it reaches small scales. This is certainly topical for magnetic reconnection, turbulence, and shocks which underly many physical processes of importance to these settings. In collisional plasmas, the fate of the energy is relatively straight-forward — it is irreversibly dissipated into heat at small-scale structures. In weakly collisional or collisionless plasmas, it is much less clear. This presentation will discuss our recent efforts to investigate entropy in the kinetic theory description as a possible tool. Recent theoretical developments have included a kinetic entropy-based non-Maxwellianity parameter and its applications. Numerically, we show kinetic entropy measures in fully-kinetic particle-in-cell (PIC) simulations of magnetic reconnection. We also show a comparison of a collection of measures that have been used to investigate kinetic-scale energy conversion in simulations of reconnection and turbulence using a suite of PIC, hybrid-Vlasov, and full Vlasov simulations. Finally, we show results of measuring kinetic entropy using the Magnetospheric Multiscale (MMS) satellites and discuss potential comparisons with laboratory plasma experiments.
• Can electromagnetic ion cyclotron waves propagate to the ground? 2D Full-wave simulations,video
Eun-Hwa Kim, PPPL, abstract
[#s1324, 19 Jul 2021]
This presentation numerically examines electromagnetic ion cyclotron (EMIC) wave propagation in the magnetosphere using the full-wave simulation tool, Petra-M. The Petra-M code is a state-of-the- art generic electromagnetic simulation tool for modeling RF wave propagation based on MFEM [http://mfem.org] and successfully examined wave properties by adopting realistic antenna geometry in tokamaks. This presentation adopts Earth’s dipole magnetic field geometry with a realistic density profile into the Petra-M and examines EMIC wave properties when waves have various wave normal angles (WNAs) and background heavy-ion densities. The EMIC waves are low-frequency waves typically in the Pc 1-2 frequency range that are excited below the proton gyrofrequency. The existing instability theories and ray tracing suggest that only left-hand polarized EMIC waves are generated near the magnetic equator and propagate along the field line toward the Earth. EMIC waves are predicted to reflect at the Buchsbaum resonance in the higher magnetic field region and not reach the ground. However, these results are inconsistent with observations. A1D full-wave analysis found that EMIC waves can tunnel through the evanescent region between cutoff and ion cyclotron resonance locations and reach the ground, but 1D modeling cannot include 2D magnetic curvature effects. 2D full-wave simulations enable us to overcome these shortcomings of ray tracing or 1D full-wave simulations using an approach that describes wave propagation, mode conversion, tunneling with 2D magnetic curvature effect for arbitrary plasma and magnetic field configurations. Previous 2D simulations using FW2D wave code showed excellent agreement with previous calculations, such as wave cutoff at the Buchsbaum resonance, polarization reversal, and mode conversion at the crossover locations. They also showed that equatorially generated EMIC waves could propagate into the inner or outer magnetosphere depending on the WNA, and thus suggested that WNAs could be one of the critical parameters to control EMIC wave propagation to the ground. However, since the previous work only focuses on wave properties near the ion cyclotron frequency, they did not provide a global picture of wave propagation. Here, we provide a global structure of the EMIC wave propagation from the source to the ground along the WNAs in various heavy ion compositions and densities. He-mode EMIC waves with small WNA cannot penetrate through the critical frequencies near the He gyrofrequencies; however, obliquely propagate He-mode EMIC waves can reach lower altitude and lower L-shell having right-handed polarization. Interestingly, the secondary mode conversion from the right- handed polarization EMIC waves to the linearly polarized Alfvenic wave occurs in the inner magnetosphere, and these waves can finally reach the ground.
• Alfvénic turbulence in the solar wind: An overview
Prof. Anna Tenerani, UT Austin, abstract, slides
[#s1321, 12 Jul 2021]
The solar wind carries a broadband of fluctuations in density, velocity and magnetic fields that, at the large scales, have been interpreted in terms of an ongoing magnetohydrodynamic turbulent cascade of Alfvénic fluctuations. These fluctuations carry sufficient energy to explain the non-adiabatic temperature gradients in the wind, and they may be a remnant of the flux responsible for coronal heating and solar wind acceleration close to the sun. However, a complete understanding of the origin and nonlinear evolution of Alfvénic turbulence in the solar wind still remains elusive. Parker Solar Probe (PSP), launched in 2018, will be the first spacecraft to fly into the sun’s corona, to within about 10 solar radii from the sun’s surface, with the goal to understand what heats the corona and accelerates the solar wind. Early measurements from PSP have already provided us with a wealth of data from regions of space never explored before. Measurements from the first orbits have shown the ubiquitous and persistent presence of the so-called switchbacks. These are magnetic field lines which are strongly perturbed to the point that they produce local inversions of the radial magnetic field. Switchbacks are embedded in the continuous flux of turbulent fluctuations emanating from the sun, and may be the remnant of coronal processes leading to solar wind formation – but their origin is still open to debate. In this seminar, we will review the main properties of Alfvénic fluctuations and switchbacks in the solar wind and discuss how their evolution is affected by parametric instabilities, kinetic effects and solar wind expansion. We will conclude by discussing the implications of our numerical and observational work for models of switchback generation and related open questions.
• Trigger Shy? A “Rosetta-Stone” Solar Eruption, video
Dr. Emily Mason, NASA Goddard, abstract, slides
[#s1279, 26 Apr 2021]
Coronal mass ejections, jets, prominence eruptions: solar eruptions are an active field with a broad range of accepted phenomena, and an even broader range of proposed mechanisms that cause the phenomena. This talk reports the observations of an event that connects the major eruption classes, and could provide a holistic explanation for all of them. The event originated in a filament channel overlying a circular polarity inversion line (PIL) and occurred on 2013 March 13 during the extended decay phase of the active region designated (sequentially) NOAA 12488/12501. This event was especially well-observed by multiple spacecraft and was seen to have the well-studied null-point topology. We analyze all aspects of the eruption using SDO AIA and HMI, STEREO-A, and SOHO LASCO imagery. One section of the filament undergoes a classic failed eruption with cool plasma subsequently draining onto the section that did not erupt, but a complex structured CME/jet is clearly observed by SOHO LASCO C2 shortly after the failed filament eruption. We describe in detail the long, slow buildup to eruption; the lack of an obvious trigger; and the immediate reappearance of the filament after the event. The unique mixture of major eruption properties that are observed in this event places severe constraints on the structure of the filament channel field and, consequently, on the possible eruption mechanism.
• Magnetohydrodynamics with embedded particle-in-cell model (MHD-EPIC) and its applications, video
Yuxi Chen, University of Michigan, abstract, slides
[#s1278, 19 Apr 2021]
It is challenging to capture kinetic phenomena in global simulations due to the significant difference between the kinetic scales and global scales. The magnetohydrodynamics with embedded particle-in-cell model (MHD-EPIC) is developed to incorporate kinetic physics into global simulations. It combines the physics capability of a particle-in-cell (PIC) code and the efficiency of an MHD model by coupling a semi-implicit PIC code with the global MHD model BATS-R-US. The PIC code is used to cover the regions where kinetic effects are important and the MHD model handles the rest part of the simulation domain.
We have improved the robustness of the PIC code by introducing the Gauss’s Law satisfying Energy Conserving Semi-Implicit Method (GL-ECSIM), which conserves energy and satisfies Gauss’s law numerically. Instead of modifying the electric field to satisfy Gauss’s law like the classical methods, we invented a new alternative approach: correcting the particle positions to satisfy the restriction. The simulation results demonstrate that the GL-ECSIM algorithm is accurate and robust. The capability of the MHD-EPIC model is further improved by using a new PIC code, the FLexible Exascale Kinetic Simulator (FLEKS). FLEKS allows PIC simulation domains of any shape so that it is more flexible to choose PIC regions in MHD-EPIC simulations. We have also designed particle resampling algorithms to further improve the accuracy and efficiency of FLEKS.
The MHD-EPIC model has been successfully applied to simulate planetary magnetospheres. We will present the simulation results of Earth’s and Mercury’s magnetospheres. The PIC region covers the dayside magnetopause in the simulation of Earth’s magnetosphere, and we studied the evolution of flux transfer events (FTEs) and compared the simulation results with observations. The MHD-EPIC model has also been applied to study the dawn-dusk asymmetry of Mercury’s magnetotail dynamics. It shows the asymmetries of the current sheet thickness, plasma density, reconnection site and reconnection jets.
• Using topology to locate the position where fully three dimensional reconnection occurs, video
Walter Gekelman, Department of Physics, UCLA , abstract, slides
[#s1277, 09 Apr 2021]
Magnetic flux ropes are bundles of twisted magnetic fields and their associated currents. They are common on the surface of the sun (and presumably all other stars) and are observed to have a large range of sizes and lifetimes. Two “kink” unstable ropes are generated in a background plasma in the Large Plasma Device at UCLA. When they collide fully 3D magnetic reconnection occurs. In a reconnection process magnetic energy is transformed to heat, energized particles and waves. In two dimensional magnetic reconnection, involving neutral sheets and magnetic islands it is generally a straightforward task to recognize reconnection sites when detailed data sets or simulations are available. In fully three dimensional reconnection their analogues can be challenging to identify. In this experiment the time dependent magnetic fields, plasma flows, electron temperature, plasma density, space charge and inductive electric fields were measured at over 42,000 spatial positions, 16,000 times steps requiring several million rope collision experiments. Magnetic field lines are followed in 3D and used to derive quasi-seperatrix layers (QSL), extended surfaces within which reconnection occurs. It turns out that QSL’s do not fully capture areas of reconnection. We have used additional topological quantities : the winding number (which measures the entanglement of pairs of field lines), magnetic twist, writhe and helicity to calculate a new quantity, the reconnection activity (RA). The RA identifies sub- regions of magnetic field lines which are reconnecting. It is demonstrated that the regions with the highest reconnective activity do not always coincide with the largest QSL signatures are, thus indicating this is a more complete methodology for quantifying reconnective activity than standard methods. This framework can serve as a model for reconnection analysis in future studies, in combination with established methods for identifying the specific form of reconnection once its location is established.
T. DeHass1 C. Prior2, A Yeates2
1 Tri Alpha Energy, Irvine Ca. 2 Durham University, United Kingdom
• The Tandem Reconnection and Cusp Electrodynamics Reconnaissance Satellites Mission, video
Prof. Craig Kletzing, University of Iowa, abstract, slides
[#s1276, 02 Apr 2021]
The TRACERS mission consists of two identically instrumented satellites in the same low-Earth, sun-synchronous orbit with the spacecraft separated by 10-120s along the orbital track. The mission was selected for implementation in June, 2019 by NASA as a Small Explorer class investigation. The overarching mission goal of the TRACERS mission is: Connecting the magnetospheric cusp to the magnetopause – discovering how spatial or temporal variations in magnetic reconnection drive cusp dynamics. To address this goal, the TRACERS mission has three major scientific objectives: * Determine whether magnetopause reconnection is primarily spatially or temporally variable for a range of solar wind conditions. * For temporally varying reconnection, determine how the reconnection rate evolves. * Determine to what extent dynamic structures in the cusp are associated with temporal versus spatial reconnection. To accomplish this scientific research, TRACERS makes field and particle observations in the cusp in a Sun Synchronous Orbit at 500 km. Statistical analysis of the orbit shows that TRACERS will have more than 3250 cusp encounters in a one year mission lifetime. Well-proven instruments and good understanding of orbital characteristics allows for simple mission operations coupled with proven data analysis techniques backed by high-fidelity simulations. The instrumentation consists of ion and electron spectrometers, DC electric and magnetic field and AC wave measurements. We discuss the mission concept and relevance to space weather as well as presenting details of the spacecraft instruments, engineering challenges, and operational plan.
• Magnetic Reconnection Rate in Collisionless Plasmas, video
Prof. Yi-Hsin Liu, Dartmouth University, abstract, slides
[#s1275, 26 Mar 2021]
Magnetic reconnection is the process whereby the change in the magnetic field lines' connectivity allows for a rapid release of magnetic energy into the thermal and kinetic energy of the surrounding plasma. The magnitude of the reconnection electric field parallel to the reconnection x-line (where magnetic field lines break and rejoin) not only determines how fast reconnection processes magnetic flux, but can also be crucial for generating super-thermal particles. Observations and numerical simulations have revealed that collisionless magnetic reconnection in the steady-state tends to proceed with a normalized reconnection rate of an order of 0.1 in disparate systems. However, the explanation of fast reconnection remains an open question. In this talk, I will present a series of theory, modeling, and MMS (Magnetospheric Multiscale mission) observational studies on this issue. We propose that this value 0.1 is essentially an upper bound value constrained by the force-balance at the upstream and downstream regions, independent of the dissipation-scale physics, independent of the mechanism that localizes the x-line. The prediction from this model compares favorably to particle-in-cell simulations of magnetic reconnection in both the non-relativistic and extremely relativistic limits, from symmetric to asymmetric reconnection. Lately, we have included thermal pressure effects in our model to predict the rate in the high-beta limit. We also extend our study from 2D to the 3D system, studying the impact of a short x-line extent in the out-of-plane direction. Finally, we show that the maximum plausible reconnection rate could determine some of the 3D nature of magnetic reconnection, particularly the orientation of the x-line. These results could be interesting to researchers who study solar, magnetospheric, astrophysical, and laboratory plasmas.
• Parallel shock experiments on the Big Red Ball: Understanding the role of non-linear whistler waves, video
Doug Endrizzi, U. Wisconsin, abstract, slides
[#s1220, 12 Mar 2021]
Whistler waves are a common feature of space plasmas, notably present upstream of shocklets, SLAMS, and switchbacks in the solar wind. In the laboratory, they have been studied for at least 60 years, being easily generated from RF antennas, electron beams, and in pulsed power experiments. On the Big Red Ball vacuum vessel, strong whistler waves appeared in recent parallel shock experiments, where a supersonic high-density plasma piston was launched parallel to the magnetic field. These experiments explored a large range in plasma beta (from 0.04 up to above 1.0) and had diagnostic coverage allowing for 2D views of the interaction. Results will be presented showing the generation of dispersive whistler waves from an abrupt nonlinear ramp at the leading edge of the piston. Analysis of the whistler electric and magnetic fields will show how they mediate shock-like behavior in the cylindrical geometry.
• Ion Wakes: Modeling Dust Plasma Interactions, video
Prof. Lorin Matthews, Baylor University, abstract
[#s1252, 05 Mar 2021]
The interaction of an object within a streaming fluid is a phenomenon widely encountered in physics, spanning a range of length scales, from the familiar meter- to cm-sized wakes observed behind rocks in flowing streams (Fig. 1a), the kilometers-long wakes observed in cloud patterns as air flows past ocean islands (Fig. 1b), to the wakes produced in the bow shock of a speeding neutron star covering distances on the order of a parsecs (Fig. 1c). Plasma, a gas consisting of electrons, ions, and neutral molecules, can also be considered as a fluid. When plasma is moving with respect to an immersed object (such as a micron-sized dust grain), the object becomes charged and the trajectories of the ions in the plasma are altered as they flow past the charged body. Depending on flow velocity and the magnitude of the perturbing potential, ions can be focused into a region downstream of the object, creating an ion wakefield (Fig. 1d). Here we report results of coupled numerical models of the plasma discharge, ion wakefield and particle interactions in ground-based lab experiments and in microgravity experiments onboard the ISS.
• Alfven Wave Damping and Heating in the Solar Corona, video
Dr. Michael Hahn, Columbia, abstract, slides
[#s1219, 26 Feb 2021]
Understanding the mechanism by which the solar corona is heated to over a million Kelvin has been an unresolved problem in astrophysics for over 80 years. One theory is that energy is carried by Alfven waves into the corona where the waves are damped, thereby converting their energy into plasma heating. Using spectroscopic observations, we have found evidence that Alfven waves do carry enough energy for the heating and are indeed damped at low heights in the corona, as required by wave heating models. However, the physical processes that cause the wave damping are unknown. We are now investigating the cause of this damping through both observations and laboratory experiments. Recently, we studied intensity fluctuations in EUV images obtained by the Sun Watcher with Active Pixels (SWAP) instrument on the Proba2 satellite. These intensity fluctuations are proportional to density fluctuations, and show that density fluctuations grow in amplitude at heights similar to where the Alfven waves are damped. The density fluctuations change the local Alfven speed and are expected to cause reflection of the Alfven waves. Thus, the density fluctuations may help trap Alfven wave energy and promote dissipation through turbulence between the outward and reflected waves. We have also been carrying out laboratory experiments using the Large Plasma Device at the University of California Los Angeles. There, we have studied the propagation of Alfven waves through Alfven-speed gradients similar to those in the corona. Our results confirm that the transmission of Alfven wave energy is significantly reduced by the gradient. Surprisingly, though, we have not observed any reflection of the Alfven waves, which is the mechanism predicted by theory to be responsible for the reduced transmittance.
• Flux Ropes, Turbulence, and Collisionless Perpendicular Shock Waves: High Plasma Beta Case, video
Prof. Gary Zank, U. Alabama, abstract, slides
[#s1218, 12 Feb 2021]
With the onset of solar maximum and the likely increased prevalence of interplanetary shock waves, Parker Solar Probe is likely to observe numerous shocks in the next few years. An outstanding question that has received surprisingly little attention has been how turbulence interacts with collisionless shock waves. Turbulence in the supersonic solar wind is described frequently as a superposition of a majority 2D and a minority slab component. We formulate a collisional perpendicular shock-turbulence transmission problem in a way that enables investigation of the interaction and transmission of quasi-perpendicular fluctuations such as magnetic flux ropes/islands and vortices as well as entropy and acoustic modes in the large plasma beta regime. We focus on the transmission of an upstream spectrum of these modes, finding that the downstream spectral amplitude is typically increased significantly (a factor of 10 or more), and that the upstream spectral index of the inertial range, and indeed the general spectral shape, is unchanged for the downstream magnetic variance, kinetic energy, and density variance. A comparison of the theoretically predicted downstream magnetic variance, kinetic energy, and destiny variance spectra with those observed at 1 au, 5 au, and 84 au by Wind, Ulysses, and Voyager 2 shows excellent agreement. The overall theoretically predicted characteristics of the transmission of turbulence across shocks observed in the solar wind appear to be largely consistent with recent observational studies by Pitna et al. 2016, Pitna et al. 2020, and Borovsky 2020.
• Dynamic, Astrophysically- and Solar-Relevant MHD Plasma Experiments, video
Paul M. Bellan, Caltech, abstract
[#s1217, 05 Feb 2021]
Dynamics relevant to solar and astrophysical plasmas is being investigated using MHD-regime lab experiments. High-speed imaging resolves sub-Alfven time scales and reveals unexpected phenomena. Images show that highly collimated MHD-driven, finite-beta plasma flows occur and can be considered a lab ‘replica’ of an astrophysical jet. Having both axial and azimuthal magnetic fields, the jet can be considered to be a flux rope, i.e., a plasma-confining flux tube with embedded helical magnetic field. The jet velocity is proportional to axial electric current and the jet flows axially from where the flux tube radius is small to where it is large. Jet stagnation compresses embedded azimuthal magnetic flux resulting in self-collimation. An expanding solar coronal loop is effectively two jets pointing at each other carrying a common current and axial flux. Jets kink when they breach the Kruskal-Shafranov stability limit. Lateral acceleration of a sufficiently strong kink produces a substantial effective gravity that provides the environment for a spontaneously developing fine-scale, fast Rayleigh-Taylor instability. This instability involves ‘heavy’ plasma interchanging with ‘light’ plasma in a series of ripples that choke the current channel to less than the ion skin depth. This cascade from the MHD scale to the ion skin depth scale can result in a fast magnetic reconnection whereby the jet breaks off. Several distinct abrupt phenomena are observed when this happens. These include: radiation of a hard X-ray burst, emission of a whistler wave burst, localized EUV emission, and dimming of visible light
• Using magnetic fields and microgravity to explore the physics of dusty plasmas, video
Prof. Ed Thomas, Auburn, abstract
[#s1171, 18 Dec 2020]
Over the last three decades plasma scientists have learned how to control a new type of plasma system known as a “complex” or “dusty” plasma. These are four-component plasma systems that consist of electrons, ions, neutral atoms, and charged, solid, nanometer- to micrometer-sized particles. The presence of these microparticles allow us to “tune” the plasma to have solid-like, fluid-like, or gas-like properties. This means that dusty plasmas are not just a fourth state of matter – they can take on the properties of all four states of matter. From star-forming regions to planetary rings to fusion experiments, charged microparticles can be found in many naturally occurring and man-made plasma systems. Therefore, understanding the physics of dusty plasmas can provide new insights into a broad range of astrophysical and technological problems. This presentation introduces the physical properties of dusty plasmas – focusing on how the small charge-to-mass ratio of the charged microparticles gives rise to many of the characteristics of the system. In particular, dusty plasmas can be used to study a variety of processes in non-equilibrium or dissipative systems such as self-organization and energy cascade as well as a variety of transport and instability mechanisms. This presentation will discuss results from our studies of dusty plasmas in high (B ≥ 1 T) magnetic fields using the Magnetized Dusty Plasma Experiment (MDPX) device at Auburn University and in microgravity experiments using the Plasmakristall-4 (PK-4) laboratory on the International Space Station.
• Solar Wind Turbulence: in-situ observations from magneto-fluid to kinetic plasma scales, video
Dr. Olga Alexandrova, Observatorie de Paris, LESIA, abstract, slides
[#s1170, 04 Dec 2020]
This seminar is devoted to solar wind turbulence from MHD to kinetic plasma scales. Solar wind turbulence was mostly studied at MHD scales: there, magnetic fluctuations follow the Kolmogorov spectrum. The fluctuations are mostly incompressible and they have non-Gaussian statistics (intermittency), due to the presence of coherent structures in the form of current sheets, as it is widely accepted. Kinetic range of scales is less known and the subject of debates. We study the transition from Kolmogorov inertial range to small kinetic scales with a number of space missions. It becomes evident that if at ion scales (100-1000 km) turbulent spectra are variable, at smaller scales they follow a general shape. Thanks to Cluster/STAFF, the most sensitive instrument to measure magnetic fluctuations by today, we could resolve electron scales (1 km, at 1 AU) and smaller (up to 300 m) and show that the end of the electromagnetic turbulent cascade happens at electron Larmor radius scale, i.e., we could establish the dissipation scale in collisionless plasma. Recently, we have confirmed these results closer to the Sun (at 0.3 AU). Furthermore, we show that intermittency is not only related to current sheets, but also to cylindrical magnetic vortices, which are present within the inertial range as well as in the kinetic range. This result is in conflict with the classical picture of turbulence at kinetic scales, consisting of a mixture of kinetic Alfven waves. The dissipation of these waves via Landau damping may explain the turbulent dissipation. How does this picture change if turbulence is not only a mixture of waves but also filled with coherent structures such as magnetic vortices? These vortices seem to be an important ingredient in other instances, such as astrophysical shocks: for example, they are observed downstream of Earth's and Saturn's bow-shocks. With the new data of Parker Solar Probe and Solar Orbiter we hope to study these vortices closer to the Sun to better understand their origin, stability and interaction with charged particles
• Relativistic electron-ion shocks in gamma-ray bursts: What about pair loading?
Dr. Daniel Groselj, Columbia, abstract
[#s1169, 20 Nov 2020]
In the external gamma-ray burst (GRB) collisionless shocks, intense radiation gives rise to abundant production of electron-positron pairs in two-photon collisions. The upstream medium is thus transformed into a mixed composition electron-ion-positron plasma. How exactly the pair loading affects the structure, and the resulting particle acceleration, of external GRB shocks is largely unknown. Here, I present a set of first-principles kinetic simulations to elucidate the microscale physics of relativistic pair-plasma-loaded, weakly magnetized shocks. I will show that even moderate changes in the plasma composition can significantly impact the shock dynamics. More specifically, I will demonstrate that (i) the transition from a Weibel-mediated to a magnetized type shock becomes a function of the pair loading factor Z, (ii) the energy fraction transferred from ions to pairs is only weakly dependent on Z, and (iii) pair-loaded shocks are efficient particle accelerators in the limit of vanishing magnetization. These findings have important implications for the modeling of the early afterglow emission of GRBs.
• Experimental evidence of detached bow shock formation in the interaction of a laser-produced plasma with a magnetized obstacle
Dr. Joseph Levesque, LANL, abstract
[#s1179, 06 Nov 2020]
The magnetic field produced by planets with active dynamos, like the Earth, can exert sufficient pressure to oppose supersonic stellar wind plasmas, leading to a standing bow shock upstream of the pressure-balance surface, known as the magnetopause. Scaled laboratory experiments studying the interaction of an inflowing solar wind analog with a strong, external magnetic field can provide another way to study magnetospheric physics and complement existing models. In this talk I present experimental evidence of the formation of a magnetized bow shock in the interaction of a supersonic, super-Alfvenic plasma with a strongly magnetized obstacle at the OMEGA laser facility. The plasma source for these experiments is generated by the simultaneous laser-irradiation of two thin carbon discs, the resulting counter-propagating plasma plumes collide and subsequently expand outward toward the magnetized obstacle, which is a thin, current-carrying wire. We measure the plasma number density in the interaction region using Spatially resolved, optical Thomson scattering, from which we infer the presence of what appears to be a fast magnetosonic shock far upstream of the obstacle. Proton images additionally provide a measurement of large-scale features of the magnetic field topology based on proton deflections, and further suggest the formation of a bow shock by an inferred compression of the magnetic field in our system. From these images we determine the shock standoff distance and analyze the evolution of the bow shock for two applied field strengths.
• The Earth's Ion Foreshock: A natural laboratory for ion beam-generated waves and non-linear wave processes
Dr. Seth Dorfman, SRI, abstract
[#s1168, 30 Oct 2020]
Waves generated by accelerated particles are important throughout our heliosphere. These particles often gain their energy at shocks via Fermi acceleration. At the Earth's bow shock, this mechanism accelerates ion beams back into the solar wind; the beams can then generate ultra low frequency (ULF) waves below the ion cyclotron frequency via an ion-ion right hand resonant instability. These ULF waves influence the shock structure and particle acceleration, lead to coherent structures in the magnetosheath, and are ideal for non-linear interaction studies relevant to turbulence. We report the first satellite measurement of the ultralow frequency (ULF) wave growth rate in the upstream region of the Earth's bow shock [1]. This is made possible by employing the two ARTEMIS spacecraft orbiting the moon at ∼60 Earth radii from Earth to characterize crescent-shaped reflected ion beams and relatively monochromatic ULF waves. Using ARTEMIS data, the ULF wave growth rate is estimated and found to fall within dispersion solver predictions during the initial growth time. Observed frequencies and wave numbers are within the predicted range. Other ULF wave properties such as the phase speed, obliquity, and polarization are consistent with expectations from resonant beam instability theory and prior satellite measurements. Building on this result, new work is underway to determine the statistical properties of the ULF waves at the location of ARTEMIS and make comparisons with the global hybrid-Vlasov code Vlasiator. For example, an analysis of all foreshock events observed by ARTEMIS from 2011-2019 shows a clear preference for the left-hand polarized waves (in the spacecraft frame) expected from the ion-ion right hand resonant instability. However, unlike a 2.5-D Vlasiator simulation in which the waves are entirety left-hand polarized, ARTEMIS data shows a significant right-hand component that is unlikely to be directly generated by the ion beam. This component may therefore result from non-linear processes that are 3-D in nature with potential applications to turbulence and dissipation in the heliosphere.
• Understanding Our Heliospheric Shield: Laying the Groundwork to Predict Habitable Astrospheres
Prof. Merav Opher, Boston University, abstract
[#s1167, 23 Oct 2020]
The heliosphere is an immense shield that protects the solar system from harsh, galactic radiation. This radiation affects not only life on Earth, but human space exploration as well. In order to understand the evolution of the heliosphere’s shielding properties, we need to understand its structure and large-scale dynamics. The heliosphere is a template for all other astrospheres, enabling predictions about the conditions necessary to create habitable planets. Space science is at a pivotal point in generating new understandings of the heliosphere due to the flood of new in situ data from the Voyager 1 (V1), Voyager 2 (V2), and New Horizon spacecraft, combined with the energetic neutral atom (ENA) maps generated by IBEX and Cassini. I this talk I will review some of the most pressing aspects that need understanding in the heliosphere. Among them, the shape of the heliosphere. The canonical view of the structure of the heliosphere is that it has a long comet-like tail. This view is not universally accepted and there is vigorous debate as to whether it possesses a long comet-like structure, is bubble shaped, or is “croissant”-like, a debate that is driven by observations and modeling. Opher et al. (2015) suggest a heliosphere with two lobes, described as “croissant”-like. An extension of the single ion global 3D MHD model that treats PUIs created in the supersonic solar wind as a fluid separate and distinct from the thermal solar wind plasma yields a heliosphere that is reduced in size and rounder in shape (Opher et al. 2020). In contrast, Izmodenov et al. 2020 argue that a long/extended tail confines the plasma. One direct way to probe the structure of the tail is through energetic neutral atom (ENA) maps. ENA images of the tail by Interstellar Boundary Explorer (IBEX) at energies of 0.5-6keV exhibit a multi-lobe structure. These lobes are attributed to signatures of slow and fast wind within the extended heliospheric tail as part of the 11-year solar cycle (McComas et al. 2013; Zirnstein et al. 2017). Higher energy ENA observations (>5.2 keV) from the Cassini spacecraft, in conjunction with >28 keV in-situ ions from V1&2/LECP (Dialynas et al. 2017), in contrast, support the interpretation of bubble-like heliosphere. Regardless of the shape of the heliotail, there is an agreement between models that the solar magnetic field in the inner heliosheath (IHS) possesses a “slinky-like” structure (Opher et al. 2015; Pogorelov et al. 2015; Izmodenov et al. 2015) that helps confine the plasma in the IHS. I will review some of the recent discoveries and challenges as part of the recently funded NASA Science Center SHIELD (Solar-wind with Hydrogen Ion Exchange and Large-scale Dynamics).
• Kinetic physics of the electrons in the solar wind
Prof. Daniel Verscharen, University College London, abstract
[#s1118, 09 Oct 2020]
The electron distribution function in the solar wind consists of three main populations: a thermal core, a suprathermal, quasi-isotropic halo, and a field-aligned beam called “strahl”. In contrast to the protons, the electrons are a sub-sonic particle population, and due to their small mass, they contribute little to the overall momentum flux of the solar wind. However, their unique kinetic properties supply the solar wind with a significant heat flux. We investigate the regulation of this heat flux by kinetic microinstabilities. I will present a mathematical framework for the description of electron-driven instabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fast-magnetosonic/whistler (FM/W) mode is the best candidate for a microinstability that regulates the strahl heat flux by scattering strahl electrons into the halo population, consistent with spacecraft measurements. We derive approximate analytic expressions for the FM/W instability thresholds and confirm their accuracy through comparison with numerical solutions to the hot-plasma dispersion relation. The comparison of our theoretical results with a large statistical dataset from the Wind spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. In addition, we find a good agreement between our theoretical results and numerical solutions to the quasilinear diffusion equation. I will present our results in the context of the latest measurements from Parker Solar Probe and Solar Orbiter.
• Interplay among Arched Plasma Eruptions, Global Oscillations, and Broad Spectra of Alfvén Waves
Dr. Shreekrishna Tripathi, UCLA, abstract
[#s1117, 18 Sep 2020]
Arched magnetized structures that carry electrical current ubiquitously exist in solar and heliospheric plasmas. Varieties of plasma waves and current-driven instabilities (e.g., fast waves, kink, sausage, and Kelvin-Helmholtz instabilities) have been at the forefront of contemporary research in solar and heliospheric physics. After introducing key concepts related to eruptive processes in solar physics, results from a laboratory experiment on arched magnetized plasmas (plasma β ≈ 10-3, Lundquist number ≈ 102–105, plasma radius/ion-gyroradius ≈ 20, B ≈ 1000 Gauss at footpoints, 1/2 Hz repetition rate) will be presented. The arched plasma is created using a lanthanum hexaboride plasma source and it evolves in an ambient magnetized plasma produced by another source. The plasma and wave parameters are recorded with a good resolution using movable Langmuir and three-axis magnetic-loop probes in 3D. Images of the plasma are recorded using a CCD camera. In the upgraded experiment, the main focus is on the direct measurement of propagation and damping characteristics of global kink-mode oscillations and fast waves. These waves are frequently observed after eruptive events on the Sun. Recent results reveal fascinating interplay among global oscillations of the arched plasma and fast waves. Transverse gradients in Alfvén speed across the arched plasma have been observed to excite a broad spectra of fast Alfvén waves that carry away energy from large scale oscillations in the arched plasma. These observations are consistent with predictions of the phase mixing of fast waves in an inhomogeneous magnetized plasma that effectively enhances damping of large scale oscillations. Phase-mixing of these waves is likely to play important role in affecting the energetic of the solar atmosphere.
• Study the Alfvén-wave acceleration of auroral electrons in the laboratory using field-particle correlations
Prof. Jim Schroeder, Wheaton College, abstract
[#s1119, 11 Sep 2020]
The acceleration of auroral electrons is primarily attributed to quasistatic field-aligned currents in the magnetosphere. However, dispersive Alfvén waves in inertial plasmas (vA > vte) have an electric field parallel to B0 and are frequently detected in the auroral magnetosphere traveling earthward with sufficient Poynting flux to produce auroras. Test particle simulations in relevant plasma conditions show inertial Alfvén waves can resonantly accelerate electrons to auroral energies. Satellite surveys find that inertial Alfvén waves deposit an amount of energy in the lower magnetosphere capable of accounting for one-third of all auroral luminosity. Despite these results supporting the hypothesis that inertial Alfvén waves accelerate a significant fraction of auroral electrons, the limitations of spacecraft data have so far prevented direct evidence of the acceleration process from being found. Laboratory experiments in UCLA’s Large Plasma Device seek to provide insight by launching inertial Alfvén waves and simultaneously measuring the parallel electron velocity distribution. The electron distribution is measured using wave absorption, a technique where a small-amplitude probe wave is absorbed in proportion to the number of resonant electrons. Alfvénic perturbations to the electron distribution have been detected, and, using a field-particle correlation, energy transfer to electrons from the launched Alfvén waves has been found. Experimental results are interpreted using kinetic theory and numerical simulations.
• A Laboratory Model for Magnetized Stellar Winds
Dr. Ethan Peterson, MIT, abstract
[#s1116, 21 Aug 2020]
Eugene Parker developed the first theory of how the solar wind interacts with the dynamo-generated magnetic field of the Sun. He showed that the wind carries the magnetic field lines away from the star, while their footpoints are frozen into the corona and twisted into an Archimedean spiral by stellar rotation. The resulting magnetic topology is now known as the Parker spiral and is the largest magnetic structure in the heliosphere. The transition between magnetic field co-rotating with a star and the field advected by the wind is thought to occur near the so-called Alfv\'en surface - where inertial forces in the wind can stretch and bend the magnetic field. According to the governing equations of magnetohydrodynamics, this transition in a magnetic field like the Sun's is singular in nature and therefore suspected to be highly dynamic. However, this region has yet to be observed in-situ by spacecraft or in the laboratory, but is presently the primary focus of the Parker Solar Probe mission. Here we show, in a synergistic approach to studying solar wind dynamics, that the large-scale magnetic topology of the Parker spiral can also be created and studied in the laboratory. By generating a rotating magnetosphere with Alfv\'enic flows, magnetic field lines are advected into an Archimedean spiral, giving rise to a dynamic current sheet that undergoes magnetic reconnection and plasmoid ejection. These plasmoids are born at the tip of the streamer cusp, driven by non-equilibrium pressure gradients, and carry blobs of plasma outwards at super-Alfv\'enic speeds, mimicking the observed dynamics of coronal helmet streamers. Further more, a simple heuristic model based on a critical plasmoid length scale and sonic expansion time is presented. This model explains the frequencies observed in the experiment and simulations (10s of KHz) and is consistent with the 90 minute plasmoid ejection period of full-scale coronal streamers as observed by the LASCO and SECCHI instrument suites.
• Constructing a Rosetta Stone for Plasma Heating and Particle Acceleration in Kinetic Plasma Physics
Prof. Gregory Howes, University of Iowa, abstract
[#s1115, 14 Aug 2020]
The general question of how plasmas are heated and particles accelerated underlies many key challenges at the frontier of heliophysics and astrophysics, including solar coronal heating, particle acceleration in solar flares and supernova remnants, and auroral electron acceleration. The hot and diffuse plasmas in many space and astrophysical environments lead to weakly collisional conditions, so plasma kinetic theory is essential to understand both how particles are energized and whether that leads to heating of the bulk plasma or the directed energization of accelerated particles. The field-particle correlation technique is an innovative method to understand how the electromagnetic fields energize particles in weakly collisional plasmas, yielding a velocity-space signature that is characteristic of a given mechanism of energization. These signatures can be used both to distinguish and identify the mechanism at play and to determine the net rate of particle energization. I will present the construction of a "Rosetta Stone" of these velocity-space signatures that can be used to identify the mechanisms of energization in kinetic plasma turbulence, collisionless magnetic reconnection, and collisionless shocks.
• Proton temperature anisotropy, Alfven waves, and the turbulence heating problem in the solar wind
Prof. Robert Wicks, University of Northumbria, abstract
[#s1114, 07 Aug 2020]
Over the last 10 years many different studies have shown different and related forms of anisotropy about the magnetic field in the solar wind plasma. Protons have anisotropic temperature, the turbulent fluctuations have different amplitudes, polarisations, and frequency-dependent scaling, and instabilities and coherent waves propagate, grow and damp at different rates depending on their relative direction to the magnetic field. The big problem with this is that measurements made by single spacecraft rely on the solar wind flow to provide different measurement directions relative to the magnetic field. This means that our perception of what is happening is heavily biased by what occurs in the direction of flow of the plasma (radially away from the Sun). In this talk, I will review results investigating anisotropy and describe a novel method to leverage the Taylor hypothesis to identify the field-parallel and -perpendicular components of wavevectors measured by a single spacecraft. Comparing these results to proton temperature anisotropy then allows us to show that instabilities growing in the field-parallel direction are primarily cyclotron waves and associated with strong proton beams, and in the perpendicular direction are firehose instabilities (although these are rarer). Furthermore, we can associate the polarisation of the magentic field waves routinely observed close to the gyrofrequency to the different branches of the Alfven wave dispersion relation, confirming that the modes are at least somewhat similar to linear waves with left-handed polarisation in the parallel direction and right-handed in the perpendicular. When we sample the proton temperature anisotropy in this space a strong pattern emerges, with high perpendicular temperature where left-handed parallel modes and proton beams exist, and high parallel temperature where the right-handed perpendicular modes exist. This important result shows that cyclotron and landau damping play important roles in heating the solar wind, but also throws out a big problem. The polarisation of the wave measured is critically dependent on the sampling direction of the spacecraft (radial) and so it seems that the modes present in the radial direction have a disproportionately large effect on proton temperature. I will discuss a few ideas for why this might be true.
• Magnetic Reconnection and Turbulence in Stellar-Convection-Zone-Relevant Laboratory Plasmas
Dr. Jack Hare, Imperial College London, abstract, slides
[#s1113, 17 Jul 2020]
Magnetic reconnection and magnetised turbulence are ubiquitous phenomena in our magnetised universe. These processes have been carefully studied in the photosphere of the sun, in the solar wind, and in laboratory experiments which can recreate these collisionless or weakly collisional conditions. However, these phenomena are also important strongly collisional plasmas, in which the mean free path is shorter than the ion and electron skin depths. One example is the convection zone of the sun, the opaque region beneath the photosphere which is difficult to study through observations. Ryutov noted that this regime is also present in dense z-pinches (Ryutov, 2015), which combine intense magnetic fields with high temperatures and densities. In this talk, I will discuss experiments which use mega-ampere currents to ablate, accelerate and sculpt plasma from initially solid-density targets, creating geometries such as a quasi-two-dimensional reconnection layer in which plasmoids form, or a column of turbulent plasma confined at the axis of an imploding wire-array z-pinch. I will describe new diagnostics for studying the spectrum of turbulent fluctuations in the density, velocity, temperature and magnetic field, and I will present a new pulsed-power facility for studying magnetised high-energy-density plasmas which will be built at MIT. [Ryutov, 2015]: "Characterizing the Plasmas of Dense Z-Pinches." IEEE TPS
• Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock
Dr. Emily Lichko, U. Arizona, seminar, abstract, slides
[#s1112, 10 Jul 2020]
Energetic particle generation is an important component of a variety of astrophysical systems, from seed particle generation in shocks to the heating of the solar wind. It has been shown that magnetic pumping is an efficient mechanism for heating thermal particles, using the largest-scale magnetic fluctuations. Here we show that when magnetic pumping is extended to a spatially-varying magnetic flux tube, magnetic trapping of superthermal particles renders pumping an effective energization method for particles moving faster than the speed of the waves and naturally generates power-law distributions. We validated the theory by spacecraft observations of the strong, compressional magnetic fluctuations near the Earth’s bow shock from the Magnetospheric Multiscale mission. Given the ubiquity of magnetic fluctuations in different astrophysical systems, this mechanism has the potential to be transformative to our understanding of how the most energetic particles in the universe are generated.
• Testing the Physics of Solar and Stellar Flares with NASA’s Solar Dynamics Observatory and Radiative MHD Simulations
Dr. Mark Cheung, Lockheed Martin, abstract, slides
[#s1088, 11 Nov 2019]
Solar and stellar flares are the most intense emitters of X-rays and extreme ultraviolet radiation in planetary systems. On the Sun, strong flares are usually found in newly emerging sunspot regions. The emergence of these magnetic sunspot groups leads to the accumulation of magnetic energy in the corona. Following magnetic reconnection, the energy released powers coronal mass ejections and heats plasma to temperatures beyond tens of millions of Kelvins. In part one of this talk, we show how extreme UV images of the solar corona taken by NASA’s Solar Dynamics Observatory can be used to quantify the thermal structure and evolution of magnetically active regions on the Sun. The thermal structures inferred from extreme UV observations are consistent with their soft X-ray counterparts. Lessons learned from such studies guide the development of models of flares and eruptions. In the second part of this talk, we present radiative MHD simulations of flares and eruptions with sufficient realism for the synthesis of remote sensing measurements at visible, UV and X-ray wavelengths. These models allow us to explain a number of well-known observational features, including the time profile of the X-ray flux, chromospheric evaporation and condensation, the sweeping of flare ribbons in the lower atmosphere, global coronal waves, and the non-thermal spectral shape of coronal X-ray sources. Implications for how we interpret X-ray spectra from other astrophysical sources will be discussed.
• Plasma astrophysics of neutron stars and black holes
Dr. Sasha Philippov, Center for Computational Astrophysics, slides
[#s1070, 13 Sep 2019]
• Nonthermal particle energization in relativistic plasma turbulence
Dr. Vladimir Zhdankin, Princeton University, abstract, slides
[#s982, 02 May 2019]
I will describe recent numerical progress on understanding turbulence in relativistic collisionless plasmas, as found in high-energy astrophysical systems such as pulsar wind nebulae, black-hole accretion flows, and jets. I will present results from first-principles particle-in-cell simulations of driven turbulence. One main outcome is the confirmation that turbulence can be an efficient and viable astrophysical particle accelerator, producing nonthermal energy distributions with extended power laws, supporting decades-old theoretical ideas. I will also discuss intriguing results on electron-ion energy partition, showing that the dissipation of turbulence naturally produces a two-temperature plasma (with ions much hotter than electrons, as required by models of radiatively inefficient accretion flows). Finally, I will describe recent results on turbulence with strong radiative cooling through inverse Compton scattering, which allows a rigorous statistical steady state to be maintained. I will show that radiative cooling thermalizes the particle distribution and allows intermittent beaming of particles, possibly explaining rapid flares in various astrophysical systems.
• Magnetic turbulence in a plasma wind tunnel at the Bryn Mawr Plasma Laboratory
Prof. David Schaffner, Bryn Mawr College, abstract, slides
[#s984, 25 Apr 2019]
A newly commissioned device at the Bryn Mawr Plasma Laboratory (BMPL) is the first experiment specifically designed to be a magnetically turbulent plasma wind tunnel. Called the Bryn Mawr Magnetohydrodynamic Experiment (BMX), the experiment consists of a plasma gun generated magnetized plasma that is launched down a flux conserving chamber. A high density magnetic pickup probe array and high bit-depth data acquisition system allows for a through exploration of spatial and temporal magnetic fluctuations. This talk presents the first results from the experiment including time and spatial correlation features, magnetic turbulent spectra, and bulk velocity. Plans for upcoming experiments and goals will be discussed.
• Electron energy partition across interplanetary shocks near 1 AU
Dr. Lynn Wilson, NASA Goddard, abstract, slides
[#s983, 18 Apr 2019]
Analysis of 15,314 electron velocity distribution functions (VDFs) within ±2 hours of 52 interplanetary (IP) shocks observed by the Wind spacecraft near 1 AU are presented. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The halo and beam/strahl are always modeled as bi-kappa VDFs but the core is found to be best modeled by a bi-self-similar, not bi-Maxwellian, for nearly all cases and a bi-kappa for a small fraction of the events. The self-similar distribution deviation from a Maxwellian is a measure of inelasticity in particle scattering from waves and/or turbulence. The range of values defined by the lower and upper quartiles for the kappa exponents are k_ec ~ 5.40--10.2 for the core, k_eh ~ 3.58--5.34 for the halo, and k_eb ~ 3.40--5.16 for the beam/strahl. The lower-to-upper quartile range of symmetric bi-self-similar core exponents are s_ec ~ 2.00--2.04, and asymmetric bi-self-similar core exponents are p_ec ~ 2.20--4.00 for the parallel exponent, and q_ec ~ 2.00--2.46 for the perpendicular exponent. The rest of the parameters will be summarized as well during the talk.
• The interplay of plasma turbulence and magnetic reconnection in producing nonthermal particles
Dr. Luca Comisso, Columbia University, abstract, slides
[#s991, 12 Apr 2019]
Due to its ubiquitous presence, turbulence is often invoked to explain the origin of nonthermal particles in astrophysical sources of high-energy emission. With particle-in-cell simulations, we study decaying turbulence in magnetically-dominated (or equivalently, “relativistic”) pair plasmas. We find that the generation of a power-law particle energy spectrum is a generic by-product of magnetically-dominated turbulence. The power-law slope is harder for higher magnetizations and stronger turbulence levels. In large systems, the slope attains an asymptotic, system-size-independent value, while the high-energy spectral cutoff increases linearly with system size; both the slope and the cutoff do not depend on the dimensionality of our domain. By following a large sample of particles, we show that particle injection happens at reconnecting current sheets; the injected particles are then further accelerated by stochastic interactions with turbulent fluctuations. Our results have important implications for the origin of non-thermal particles in high-energy astrophysical sources.
• Instabilities and Plasma Heating in the Inner Heliosphere: Thermodynamics far from Equilibrium
Prof. Kris Klein, University of Arizona, abstract, slides
[#s981, 28 Mar 2019]
One key feature of the solar wind, a diffuse and high-temperature plasma, is that generally the Coulomb collision frequency is low compared to other dynamic timescales, enabling the plasma to maintain significant deviations from local thermodynamic equilibrium. These departures from LTE, characterized for instance by temperature anisotropies as well as temperature disequilibrium and relative drifts between components, can drive unstable wave growth. In this talk, we discuss recent results that use observations of non-equilibrium distributions at 1 au to determine how frequently unstable waves are driven. Using an automated implementation of Nyquist's instability criterion, we find that half of the intervals from a statistical set of ion velocity distributions support linear instabilities, a much larger fraction than previous estimates. Departures from LTE can also serve as signatures of processes that occurred at an earlier time, before the solar wind was advected to the point of measurement. Using a model of Coulomb relaxation and solar wind expansion, coupled with decades of observations of Hydrogen and Helium temperatures at 1 au, we are able to identify a region within tens of Solar radii of the Sun where strong preferential heating of minor ions is active, producing the observed temperature disequilibrium. The existence and characteristics of this predicted region will be tested by Parker Solar Probe, which will provide in situ plasma and electromagnetic field measurements within 10 Solar radii from the Sun, closer than any previous mission.
• Turbulent "heating" in kinetic plasmas
Dr. Tulasi Parashar, University of Delaware *CANCELLED*, abstract
[#s980, 14 Mar 2019]
Many naturally occurring plasmas are weakly collisional. Examples include Solar Wind, planetary magnetospheres, black hole accretion disks, and intracluster medium. Most of these systems are either observed or believed to be in a turbulent state. Nonlinear interactions cascade fluctuations to kinetic scales where energy is converted from turbulent fluctuations to internal energy. The kinetic nature of these systems makes traditional viscous closure inapplicable. We discuss possible route to increasing the internal energy in kinetic plasma turbulence. Average energy equations for the Vlasov-Maxwell system provide valuable insights into how a collisionless generalization of viscosity is responsible for this conversion into internal energy. Evidence from kinetic simulations as well as multi-spacecraft observations is presented.
• Large-scale solar eruptions and induced small-scale magnetic reconnection
Prof. Xin Cheng, Nanjing University , abstract, slides
[#s979, 08 Mar 2019]
Coming Coronal mass ejections (CMEs) and solar flares are the large-scale and most energetic eruptive phenomena in our solar system and able to release a large quantity of plasma and magnetic flux into the solar wind. When these high-speed magnetized plasmas along with the energetic particles arrive at the Earth, they may interact with the magnetosphere and ionosphere, and seriously affect the safety of human high-tech activities in outer space. To predict CMEs/flares caused space weather effects, we need to elucidate some fundamental but still puzzled questions including in particular the origin and early evolution of CMEs/flares. Theoretically, magnetic flux rope is defined as a coherent magnetic structure with all magnetic field lines wrapping around its central axis. It is believed to be the fundamental structure of CMEs/flares, however, its existence has been lack of direct evidence. In my talk, I will present recent observations, in which the flux rope is found to appear as a coherent plasma channel with a temperature up to 10 million degree. It even pre-exists prior to the eruption. I then show the evolution of the hot channel toward CMEs/flares. Finally, I plan to talk about the properties of magnetic reconnection that takes place in the stretched long current sheet in the wake of the erupting CMEs. Some interesting features including significant heating and nonthermal velocity within the current sheet, intermittent outflows at two ends of the current sheet, and large length-to-width ratio suggest that magnetic reconnection during CMEs/flares may proceed in fragmented and turbulent way.
• Probing Magnetic Reconnection in Solar Flares with Radio Spectral Imaging
Prof. Bin Chen, New Jersey Institute of Technology , abstract
[#s978, 01 Mar 2019]
Flares on the Sun, thanks to their proximity, serve as an outstanding laboratory to test our understanding on magnetic reconnection and the associated magnetic energy release and particle acceleration processes. Flare-accelerated nonthermal electrons in the low solar corona emit radio waves in decimeter-centimeter wavelengths. Observations of these radio waves provide excellent means for tracing the accelerated electrons, and in turn, for probing a variety of physical processes and plasma properties in and around the magnetic reconnection site. The newly available radio spectral imaging capability from recently commissioned telescope arrays opens up a new window for such investigations. I will discuss our recent results of this kind based on observations from the Karl G. Jansky Very Large Array and NJIT’s Expanded Owens Valley Solar Array.
• Magnetic Reconnection Drivers of Solar Eruptions
Dr. Joel Dahlin, NASA Goddard, abstract, slides
[#s977, 14 Feb 2019]
Eruptive solar activity such as coronal mass ejections, eruptive flares, and coronal jets are understood to be powered by highly stressed magnetic fields in the solar corona. It is generally agreed that a key role is played by magnetic reconnection, a fundamental plasma process that drives explosive magnetic energy release via large-scale topological reconfiguration. We report on 3D MHD simulations that definitively demonstrate three distinct roles of magnetic reconnection in the genesis of a coronal mass ejection. The system is initialized with a simple, current-free null point configuration, and energy and structure are injected via small-scale boundary flows. The evolution proceeds as follows: (1) A reconnection-mediated inverse helicity cascade rapidly reconfigures the magnetic fields to form a circular, highly sheared magnetic arcade. (2) The resulting magnetic pressure deforms the coronal null into a horizontal current sheet that reconnects and destabilizes quasi-static force balance by removing restraining tension. (3) The configuration expands, stretching magnetic fields to form a vertical current sheet that reconnects to expel the accumulated shear and drive rapid energy release. We discuss observational signatures of these three forms of reconnection and discuss implications for particle acceleration and solar eruption prediction.
• Mercury‘s Dynamic Magnetosphere
Prof. James Slavin, University of Michigan, abstract, slides
[#s743, 06 Dec 2018]
MESSENGER’s exploration of Mercury has led to many important discoveries and a global perspective on its magnetosphere, exosphere, and interior as a coupled system. Mercury’s proximity to the Sun, weak planetary magnetic field, electrically conducting core, and sodium-dominated exosphere give rise to a highly dynamic magnetosphere unlike that of any other planet. The strong interplanetary magnetic fields so close to the Sun result in a high rate of energy transfer from the solar wind into Mercury’s magnetosphere. Surprisingly, direct solar wind impact on the surface during coronal mass ejection impact has been found to be infrequent. Electric currents induced in Mercury’s highly conducting interior buttress the weak planetary magnetic field against direct impact for all but the strongest solar events. Kinetic effects associated with the large orbits of planetary ions about the magnetic field and the small dimensions of the magnetosphere are observed to significantly affect some fluid instabilities such as Kelvin-Helmholtz waves along the magnetopause. As at Earth, magnetic reconnection, dipolarization fronts, and plasmoid ejection are closely associated with substorms in Mercury’s magnetosphere, and MESSENGER frequently observed energetic electrons with energies of tens to several hundred thousand electron volts. However, no “Van Allen” radiation belts with durable trapping are present.
• The lunar plasma wake and electron phase-space holes
Prof. Ian Hutchinson, MIT, abstract, slides
[#s926, 30 Nov 2018]
Wakes of plasma flowing past unmagnetized bodies like probes, moons, or large particles are usually unsteady. Detailed theory and simulations show instabilities excited by the velocity distribution distortions give rise to electron holes (soliton-like BGK modes). We have recently discovered from spacecraft observations that the solar wind wake of the moon is full of electron holes, in agreement with predictions. Transverse instability of these holes determines their evolution and persistence and how they eventually merge into the background plasma.
2 related papers:
"Prediction and Observation of Electron Instabilities and Phase Space Holes Concentrated in the Lunar Plasma Wake", Ian H. Hutchinson, David M. Malaspina, Geophysical Res. Lett. 2018
"Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas", I. H. Hutchinson J. Plasma Phys. 2018
• On the role of magnetic reconnection in kinetic-range turbulence and the existence of cascades in the entire phase space from hybrid-Vlasov-Maxwell simulations
Silvio Cerri, Princeton University , abstract, slides
[#s735, 30 May 2018]
Understanding the properties of turbulent fluctuations and how turbulent energy is dissipated in weakly collisional plasmas is a fundamental step towards understanding how turbulence feeds back on the evolution of several astrophysical systems. In this context, space plasmas are probably the best laboratory for the study of plasma turbulence in a weakly collisional regime, as the Earth’s environment has become accessible to increasingly accurate direct measurements. In situ observations of the solar wind and the terrestrial magnetosheath have indeed provided relevant constraints on the turbulent energy spectra, determining the typical values of their slopes and revealing the presence of breaks in the electromagnetic fluctuation cascade at kinetic scales. A first break in the turbulent spectrum is indeed encountered at the proton kinetic scales and separates the so-called “MHD inertial range” spectrum from the kinetic spectrum that arises at scales smaller than the proton gyroradius (also referred to as the “dissipation” or “dispersion” range). Such transition is a clear evidence of a change in the physics underlying the cascade process, and its understanding is today a matter of a strong debate. Very high resolution measurements by MMS have also recently pointed out the presence of structures in the particle (electron) distribution function that can be interpreted as a cascade in velocity space.
In this talk I will present some recent developments in the investigation of the properties of kinetic-range turbulence via high-resolution hybrid-kinetic (fully-kinetic ions and fluid electrons) simulations both in 2D and 3D. In particular, I will show the first numerical evidence that has led to the suggestion of a link between magnetic reconnection, ion break and turbulent energy transfer in the sub-ion-gyroradius cascade[1,2] (also known as “reconnection-mediated scenario” for plasma turbulence). Finally, I will show the first evidence for a six-dimensional (“dual”) phase-space cascade of ion-entropy fluctuations in a 3D3V simulation of electromagnetic turbulence: such phase-space cascade is shown to be anisotropic with respect to the background magnetic fleld in both real and velocity space and suggests that both linear and non-linear phase mixing are simultanously at work[3].
[1] S. S. Cerri & F. Califano, New J. Phys. 19, 025007 (2017)
[2] Luca Franci, Silvio Sergio Cerri et al., Astrophys. J. Lett. 850, L16 (2017)
[3] S. S. Cerri, M. W. Kunz & F. Califano, Astrophys. J. Lett. 856, L13 (2018)
• Magnetic Reconnection during Turbulence and the Role it Plays in Dissipation and Heating
Mike Shay, U. Delaware , abstract, slides
[#s707, 09 May 2018]
Turbulence plays an important role in many plasmas, including those in accretion disks, in the heliosphere, and in the laboratory. In plasmas with low collisionality, such as those in the heliosphere, exactly how this turbulent energy damps away is an open question, with ramifications for the heating of the solar corona and the solar wind. Magnetic reconnection, where magnetic field lines break and reform in a plasma, is one possible mechanism for damping this turbulent energy and heating the plasma, but the role it may play is uncertain. Recently, however, significant progress has been made in understanding plasma heating in isolated reconnection sites. Can this new knowledge shed light on the properties of plasma heating during turbulence?
In this talk, after reviewing our understanding of heating due to reconnection, I will lay out a framework for applying reconnection heating predictions to turbulent systems, and show initial results for testing this framework using fully kinetic PIC simulations. In addition, I will discuss recent MMS observations of reconnection in Earth's turbulent magnetosheath. I will then explore the statistics of magnetic reconnection in kinetic simulations of turbulence. By statistics, I mean the number of x-lines, the spread of reconnection rates, and how these quantities vary in time. How these statistics vary in different turbulence regimes and its impact on reconnection heating will be discussed.
• Collisionless damping of slow magnetosonic waves (and related compressional fluctuations)
Bill Dorland, University of Maryland , abstract
[#s663, 30 Mar 2018]
Compressional perturbations are observed in the solar wind even when the collision time is much longer than an inferred wave period. This is puzzling. Lithwick & Goldreich argued that the parallel wavenumbers of the slow modes would be inherited from the Alfvén cascade, which would itself be well-described as being in critical balance. For most parameters, this argument favors rapid damping of compressional fluctuations, $\gamma \sim k_\parallel v_A \sim k_\perp v_\perp$. Schekochihin et al. argued instead that the compressional perturbations would evolve in Lagrangian fashion, maintaining their original (possibly very long) wavelengths along the magnetic field, even as the field itself developed ever-shorter parallel wavelengths. Although compressional waves would still experience Landau and/or Barnes damping in this picture, the rate could be very small. Kanekar et al. observed that stochastic echoes could “fluidize” the compressional fluctuations, allowing them to evade collisionless damping altogether. It remains unclear which mechanism is dominant, if any. I will present recent work on this problem by R. Meyrand, A. Kanekar, A. Schekochihin, and myself.
• Magnetic Reconnection in MHD and Kinetic Turbulence
Nuno Loureiro, MIT , abstract
[#s631, 21 Feb 2018]
Recent works have revisited the current understanding of Alfvénic turbulence to account for the role of magnetic reconnection [1-3]. Theoretical arguments suggest that reconnection inevitably becomes important in the inertial range, at the scale where it becomes faster than the eddy turn over time. This leads to a transition to a new sub-inertial interval, suggesting a route to energy dissipation that is fundamentally different from that envisioned in the usual Kolmogorov-like phenomenology.
These concepts can be extended to weakly collisional plasmas, where reconnection is enabled by electron inertia rather than resistivity [4,5]. Although several different cases must then be considered (whether the eddies themselves are on MHD or kinetic scales, whether the plasma beta is large or small, etc.), a common result to all of them is that the energy spectrum exhibits a scaling with the perpendicular wave number that scales between $k_\perp^{−8/3}$ and $k_\perp^{−3}$, in favourable agreement with many numerical results and observations.
This talk aims to review these results, and discuss their implications.
[1] Nuno F. Loureiro & Stanislav Boldyrev, Phys. Rev. Lett. 118, 245101 (2017)
[2] A. Mallet, A. A. Schekochihin & B.D.G. Chandran, Mon. Not. R. Astron. Soc. 468, 4862 (2017)
[3] Stanislav Boldyrev & Nuno F. Loureiro, Astrophys. J. 844, 125 (2017)
[4] Nuno F. Loureiro & Stanislav Boldyrev, Astrophys. J. 850, 182 (2017)
[5] Alexander A. Schekochihin & Benjamin D. G. Chandran, J. Plasma Phys. 83, 905830609 (2017)
| 2023-02-02T14:28:56 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1430/4613
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Accuracy Analysis of Attitude Computation-based on Optimal Coning Algorithm
To accurately evaluate the applicability of optimal coning algorithms, the direct influence of their periodic components on attitude accuracy is investigated. The true value of the change of the rotation vector is derived from the classical coning motion for analytic comparison. The analytic results show that the influence of periodic components is mostly dominant in two types of optimal coning algorithms. Considering that the errors of periodic components cannot be simply neglected, these algorithms are categorized with simplified forms. A variety of simulations are done under the classical coning motion. The numerical results are in good agreement with the analytic deductions. Considering their attitude accuracy, optimal coning algorithms of the 4-subinterval and 5-subinterval algorithms optimized with angular increments are not recommended for use for real application.
Attitude computation is a critical issue in the strapdown inertial navigation system (SINS). In the principal software function of the SINS, attitude computation is necessary for the transformation of acceleration which is twice integrated into velocity and position. Furthermore, noncommutativity of finite rotations is an inevitable phenomenon in the process of attitude computation. Therefore, how to design a special and efficient algorithm has been attracted over the past decades.
Many works appeared in the literatures describing the attitude computation based on the rotation vector proposed by Bortz1. In 1983, Miller2 firstly developed an approach which updated the attitude quaternion with the change of the rotation vector during the updating period. The change of the rotation vector consisting of the outputs of incremental gyros was optimized under the classical coning motion2 (called the optimal coning algorithm). Afterward, Ignagni3-5 provided a convenient method to simplify Miller’s derivation and made an assessment of the error inherent in the simplified form of the Bortz equation1. Several improved algorithms were also presented, additionally using the current and previous accumulated gyro outputs6 or a higher-order term when the angular rates were known analytically7. To obtain the incremental signals involved in Miller’s algorithm from the rate outputs of some modern-day gyros, hardware-based integrators are imperative. Addressing this issue, Huang and Deng8 presented an improved form including angular increments and angular rates. But in these cases, the use of hardware-based integrators has contributed to increase the cost and complexity of system. To overcome this problem, Zeng9, et al. stated a coning algorithm optimized with angular rates, which included a polynomial fitting procedure and a solution for coning compensation coefficients. Generalized method for this algorithm was detailedly introduced by Ben10, et al.
Although the mentioned kinds of algorithm worked well to minimize the residual error of one nonperiodic component, the accuracy of attitude computation in the case of multi-subinterval was rarely discussed. In this study, we analyze the influence of periodic components in the optimal coning algorithms, mainly aiming to evaluate the accuracy of attitude computation based on each algorithm.
The classical coning motion is a typical environment for the optimization and effectiveness test of the coning algorithm, which can be characterized by the unit vector
$\frac{a\left(t\right)}{a}=\left[\begin{array}{c}0\\ \mathrm{cos}\left(\gamma t\right)\\ \mathrm{sin}\left(\gamma t\right)\end{array}\right]$ (1)
where a is the coning half-angle equaling the module of the vector a, i.e., a = (a.a)1/2, γ = 2πf, and f is the coning frequency1. Based on the classical coning motion, the attitude quaternion q(t) for coordinate transformation can be formulated as
$q\left(t\right)=\left[\begin{array}{c}\mathrm{cos}\left(\frac{a}{2}\right)\\ \mathrm{sin}\left(\frac{a}{2}\right)a\left(t\right)\end{array}\right]=\left[\begin{array}{c}\mathrm{cos}\left(\frac{a}{2}\right)\\ 0\\ \mathrm{sin}\left(\frac{a}{2}\right)\mathrm{cos}\left(\gamma t\right)\\ \mathrm{sin}\left(\frac{a}{2}\right)\mathrm{sin}\left(\gamma t\right)\end{array}\right]$ (2)
and the angular rate ω(t) representing the relative angular rate between two coordinate frames can be derived as 2
$\omega \left(t\right)=2{q}^{\ast }\left(t\right)\circ \stackrel{˙}{q}\left(t\right)=\left[\begin{array}{c}-2\gamma {\mathrm{sin}}^{2}\left(\frac{a}{2}\right)\\ -\gamma \mathrm{sin}a\mathrm{sin}\left(\gamma t\right)\\ \gamma \mathrm{sin}a\mathrm{cos}\left(\gamma t\right)\end{array}\right]$ (3)
If only angular motion is considered, attitude quaternion can be simply updated as follows
$q\left(t+\Delta T\right)=q\left(t\right)\circ q\left(\Delta T\right)$ (4)
where $\circ$ denotes quaternion multiplication,q(t+ΔT) and q(t) are the attitude quaternions at time t+ΔT and time t, respectively, ΔT is the updating period of attitude quaternion, and q(ΔT) is the quaternion representing the change of the attitude quaternion during time interval [t, t+ΔT], which can be obtained by2
$q\left(\Delta T\right)=\left[\begin{array}{c}\mathrm{cos}\left(\frac{\Delta \sigma }{2}\right)\\ \frac{\Delta \sigma }{\Delta \sigma }\mathrm{sin}\left(\frac{\Delta \sigma }{2}\right)\end{array}\right]$ (5)
where Δσ is the change of the rotation vector during time interval [t, t+ΔT] with module Δσ = (Δσ.Δσ)1/2. When Δσ is near zero, power series expansions should be applied to the trigonometric function coefficients of Eqn (5) to avoid singularity. In this study, a fourth-order truncation is utilized
$\begin{array}{c}\mathrm{cos}\left(\frac{\Delta \sigma }{2}\right)=1-\frac{{\left(\Delta \sigma \right)}^{2}}{8}+\frac{{\left(\Delta \sigma \right)}^{4}}{384}\\ \frac{1}{\Delta \sigma }\mathrm{sin}\left(\frac{\Delta \sigma }{2}\right)=\frac{1}{2}-\frac{{\left(\Delta \sigma \right)}^{2}}{48}\end{array}$ (6)
The theoretical value of Δσ can be derived as Eqn (7) by integrating the Bortz equation1 from time t to time t+ΔT and making some simplifications3
$\begin{array}{cc}\Delta \overline{\sigma }=\alpha +\frac{1}{2}{\int }_{t}^{t+\Delta T}\alpha \left(\tau \right)×\omega d\tau ,& \alpha \left(\tau \right)={\int }_{t}^{\tau }\omega \left(\upsilon \right)d\upsilon \end{array}$ (7)
where ω is similar to the angular rate described in Eqn (3), α(τ) is the instantaneous integration of ω from time t, and α = α(t+ΔT). Considering the classical coning environment,Eqn (7) can be rewritten as
$\begin{array}{c}\Delta \overline{\sigma }=\left[\begin{array}{c}\Delta {\overline{\sigma }}_{x}\\ \Delta {\overline{\sigma }}_{y}\\ \Delta {\overline{\sigma }}_{z}\end{array}\right]\\ =\left[\begin{array}{c}-2\gamma \Delta T{\mathrm{sin}}^{2}\left(\frac{a}{2}\right)+\frac{1}{2}{\mathrm{sin}}^{2}a\left(\gamma \Delta T-\mathrm{sin}\left(\gamma \Delta T\right)\right)\\ -2\mathrm{sin}a\mathrm{sin}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\left(\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)+{\mathrm{sin}}^{2}\left(\frac{a}{2}\right)\left(-\gamma \Delta T\mathrm{cos}\left(\frac{\gamma \Delta T}{2}\right)+2\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\right)\right)\\ 2\mathrm{sin}a\mathrm{cos}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\left(\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)+{\mathrm{sin}}^{2}\left(\frac{a}{2}\right)\left(-\gamma \Delta T\mathrm{cos}\left(\frac{\gamma \Delta T}{2}\right)+2\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\right)\right)\end{array}\right]\end{array}$ (8)
On the other hand, the quaternion q(ΔT) can be calculated from Eqns (4) and (2)
$q\left(\Delta T\right)={q}^{\ast }\left(t\right)\circ q\left(t+\Delta T\right)\text{=}\left[\begin{array}{c}1-2{\mathrm{sin}}^{2}\left(\frac{a}{2}\right){\mathrm{sin}}^{2}\left(\frac{\gamma \Delta T}{2}\right)\\ -{\mathrm{sin}}^{2}\left(\frac{a}{2}\right)\mathrm{sin}\left(\gamma \Delta T\right)\\ -\mathrm{sin}a\mathrm{sin}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\\ \mathrm{sin}a\mathrm{cos}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\end{array}\right]$ (9)
where * denotes conjugate operator2 For brevity, our discussions are confined to the single-speed-N-subinterval coning algorithm. Thus dividing time interval [t, t+ΔT] into N subintervals of equal width Δt = ΔT/N, angular increments αi (i = 1, 2, …, N) and angular rates ωi (i = 0, 1, …, N) can be acquired from Eqn (3) to optimize the following coning algorithms. Here Δt is just the sampling time.
3.1 Coning Algorithms Optimized with Angular Increments
Under a simplified coning motion, Ignagni3 validated that the value of the cross product of two angular increments depended only on their spacing. A similar property can be derived under the classical coning motion, just referring to the nonperiodic component of αi×αj. Using this property, the change of the rotation vector during time interval [t, t+ΔT] is approximated
Eqn (10) $\Delta \stackrel{˜}{\sigma }=\sum _{i=1}^{N}{\alpha }_{i}+\sum _{i=1}^{N-1}{K}_{i}\left({\alpha }_{i}×{\alpha }_{N}\right)$ (10)
where Ki (i = 1, 2, …, N−1) are constant coefficients. If γΔT < 1, the coefficients Ki can be optimized by using power series expansions and minimizing the error of the nonperiodic component between Eqns (8) and (10).
The optimal coning algorithms in the form of Eqn (10) are listed in Table 1, where N = 1, 2, 3, 4, 5. In this study, the absolute value of the residual error along nonperiodic component is defined as the error drift of algorithm (EDOA).
3.2 Coning Algorithms Optimized with Angular Rates
Considering the given rate signals, the definite integral of a fitted polynomial is used to determine the accumulated angular increment αs during time interval [t, t+ΔT]. Furthermore, noticing that ωi×ωj under the classical coning motion has a property similar to αi×αj, the change of the rotation vector is approximately assumed as follows
$\Delta \stackrel{˜}{\sigma }={\alpha }_{s}+{\left(\Delta T\right)}^{2}\sum _{i=0}^{N-1}{M}_{i}\left({\omega }_{i}×{\omega }_{N}\right)$ (11)
where Mi (i = 0, 1,..., N−1) are constant coefficients. Finally, taking the same as what has been done in the derivation of Ki, the coefficients Mi can be optimally solved.9,10
The coning algorithms in the optimal expression of Eqn (11) and the corresponding EDOAs are shown in Table 2, where N = 1, 2, 3, 4.
Comparing the EDOAs in Table 2 with those in Table 1 indicates that the coning algorithms optimized with angular rates may be superior in the accuracy of attitude computation on condition γΔT < 1. This conjecture is based on the conventional assumption6 that the errors of periodic components in the optimal coning algorithms are negligible. However, almost no attention has been paid to examining this negligibility up till now.
4.1 Change of Rotation Vector
Based on Eqns (5) and (9), the true value of the change of the rotation vector can be deduced as
$\Delta \sigma =\left[\begin{array}{c}\Delta {\sigma }_{x}\\ \Delta {\sigma }_{y}\\ \Delta {\sigma }_{z}\end{array}\right]=\left(1+\xi \right)\Delta \Phi$ (12)
Where
$\Delta \Phi =\left[\begin{array}{c}\Delta {\Phi }_{x}\\ \Delta {\Phi }_{y}\\ \Delta {\Phi }_{z}\end{array}\right]=\left[\begin{array}{c}-2{\mathrm{sin}}^{2}\left(\frac{a}{2}\right)\mathrm{sin}\left(\gamma \Delta T\right)\\ -2\mathrm{sin}a\mathrm{sin}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\\ 2\mathrm{sin}a\mathrm{cos}\left(\gamma \left(t+\frac{\Delta T}{2}\right)\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\end{array}\right]$ (13)
$\xi =\frac{\frac{\Delta \sigma }{2}}{\mathrm{sin}\left(\frac{\Delta \sigma }{2}\right)}-1=\frac{{\mathrm{sin}}^{-1}\left(\mathrm{sin}\left(\frac{a}{2}\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\right)}{\mathrm{sin}\left(\frac{a}{2}\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\sqrt{1-{\left(\mathrm{sin}\left(\frac{a}{2}\right)\mathrm{sin}\left(\frac{\gamma \Delta T}{2}\right)\right)}^{2}}}-1$ (14)
Yan13, et al. took the vector ΔΦ denoted by Eqn (13) as the true value of the change of the rotation vector to analyze the residual error along nonperiodic component of Miller’s algorithm. This approximation seems necessary for further derivation in this case. However, in the accuracy analysis of attitude computation, the difference between the vectors Δσ and ΔΦ in Eqn (12) (i.e., the coefficient ξ) cannot be ignored.
As described in Eqn (14), the coefficient ξ is a function of the coning frequency f = γ/(2π) and the coning half-angle a when the updating period ΔT is invariant. This functional relation is illustrated in Fig. 1, where f varies in a wide range from 0.1 Hz to 10 Hz, a changes from 0.1° to 15°, and ΔT is 0.01 s. The surface in Fig. 1 shows that the coefficient ξ increases rapidly, and reaches its maximum value of 1.05098×10−3 as the coning frequency and coning half-angle grow. To a great extent, it demonstrates that the coefficient ξ is non-ignorable.
4.2 Categorization of Algorithms
Equation (8) is used to express the theoretical limit of the change of the rotation vector under the classical coning motion. As shown in Eqns (8) and (12), there is a difference between the theoretical value and the true value. To clarify this difference, we take advantage of the vector ΔΦ denoted by Eqn (13) and define the following parameters
${\overline{\xi }}_{x}=\frac{\Delta {\overline{\sigma }}_{x}}{\Delta {\Phi }_{x}}-1$, ${\overline{\xi }}_{y}=\frac{\Delta {\overline{\sigma }}_{y}}{\Delta {\Phi }_{y}}-1$, ${\overline{\xi }}_{z}=\frac{\Delta {\overline{\sigma }}_{z}}{\Delta {\Phi }_{z}}-1$ (15)
Substituting Eqn (15) into Eqn (8) yields
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\stackrel{˜}{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\overline{\xi }}_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\overline{\xi }}_{z}\right)\Delta {\Phi }_{z}\end{array}\right]$ (16)
Equation (16) shows that$\nabla \stackrel{-}{\sigma }$ can be written in a form similar to Eqn (12). So the deviation of$\nabla \stackrel{-}{\sigma }$ from the true value Δσ can be substantiated by comparing the parameters ${\overline{\xi }}_{x}$ , ${\overline{\xi }}_{y}$ and ${\overline{\xi }}_{z}$ with the coefficient ξ. For example, in an ideal coning environment where f = 2 Hz, a = 1°, and ΔT = 0.01 s, the approximate results can be obtained that ${\overline{\xi }}_{x}=2.00795×{10}^{-7}$ , ${\overline{\xi }}_{y}={\overline{\xi }}_{z}=2.00478×{10}^{-7}$ , and $\xi =2.00162×{10}^{-7}$ . It can be seen that the order of magnitude of the deviations along all three axes is 10−10.
This procedure can also be used to analyze the algorithms listed in Tables 1 and 2. For the convenience of further discussion, these algorithms are uniformly denoted by
$\Delta \stackrel{˜}{\sigma }=\alpha +\Delta {\sigma }_{s}$ (17)
Where
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\Delta {\stackrel{˜}{\sigma }}_{x}\\ \Delta {\stackrel{˜}{\sigma }}_{y}\\ \Delta {\stackrel{˜}{\sigma }}_{z}\end{array}\right]$, $\alpha$, α=[ α x $\Delta {\sigma }_{s}=\left[\begin{array}{c}\Delta {\sigma }_{sx}\\ \Delta {\sigma }_{sy}\\ \Delta {\sigma }_{sz}\end{array}\right]$ (18)
and Δσs and α are the sum of all cross products and the rest, respectively. Furthermore, five parameters are defined as follows
${\eta }_{y}=\frac{{\alpha }_{y}}{\Delta {\Phi }_{y}}-1$ (19)
${\eta }_{y}=\frac{{\alpha }_{y}}{\Delta {\Phi }_{y}}-1$, ${\eta }_{z}=\frac{{\alpha }_{z}}{\Delta {\Phi }_{z}}-1$ (20)
${\mu }_{y}=\frac{\Delta {\sigma }_{sy}}{{\alpha }_{y}}$, ${\mu }_{z}=\frac{\Delta {\sigma }_{sz}}{{\alpha }_{z}}$ (21)
Substituting Eqns (19-21) into Eqn (17), the relationship between$∇ σ −$ and ΔΦ can be described as
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\stackrel{˜}{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\eta }_{y}+{\mu }_{y}+{\eta }_{y}{\mu }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\eta }_{z}+{\mu }_{z}+{\eta }_{z}{\mu }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]$ (22)
So comparing the parameters ${\stackrel{˜}{\xi }}_{x}$ ,${\eta }_{y}+{\mu }_{y}+{\eta }_{y}{\mu }_{y}$ and ${\eta }_{z}+{\mu }_{z}+{\eta }_{z}{\mu }_{z}$ of each algorithm with the coefficient ξ, we can find its deviation from the true value Δσ.
As shown in Table 3 ${\stackrel{˜}{\xi }}_{x}$ , gradually approaches the parameter ${\overline{\xi }}_{x}$ calculated above as the number of subintervals increases, for both two types of algorithms. This result proves that the limit of the parameter ${\stackrel{˜}{\xi }}_{x}$ is not ξ but ${\stackrel{˜}{\xi }}_{x}$ . At the same time, low-magnitude oscillations occur in the parameters μy and μz, and the absolute values of the parameters ηy and ηz of the second type decline rapidly. Note that the deviations of the coning algorithms along y and z axes are determined by these four parameters.
Taking the limit denoted by Eqn (8) into account, the algorithms involved in Table 3 can be categorized into four groups as compared with the true value Δσ:
1) ${\stackrel{˜}{\xi }}_{x}-\xi \gg \left({\eta }_{y}+{\mu }_{y}+{\eta }_{y}{\mu }_{y}\right)-\xi$ and ${\stackrel{˜}{\xi }}_{x}-\xi \gg \left({\eta }_{z}+{\mu }_{z}+{\eta }_{z}{\mu }_{z}\right)-\xi$ .The 1-subinterval and 2-subinterval algorithms optimized with angular increments are ascribed to this group. Accordingly, Eqn (22) can be simplified as
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\stackrel{˜}{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\overline{\xi }}_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\overline{\xi }}_{z}\right)\Delta {\Phi }_{z}\end{array}\right]=\left[\begin{array}{c}\Delta {\stackrel{˜}{\sigma }}_{x}\\ \Delta {\overline{\sigma }}_{y}\\ \Delta {\overline{\sigma }}_{z}\end{array}\right]$ (23)
2)${\eta }_{y}\gg {\mu }_{y}$ and ${\eta }_{z}\gg {\mu }_{z}$ . This refers to the 1-subinterval algorithm optimized with angular rates. The corresponding approximation of Eqn (22) is
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\overline{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\eta }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\eta }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]=\left[\begin{array}{c}\Delta {\overline{\sigma }}_{x}\\ \left(1+{\eta }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\eta }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]$ (24)
3) The parameters ηy and μy are not negligible as compared with ηz and μz, respectively. The 2-subinterval and 3-subinterval algorithms optimized with angular rates are included in this group, where the simplified form of Eqn (22) can be expressed as
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\overline{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\eta }_{y}+{\mu }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\eta }_{z}+{\mu }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]=\left[\begin{array}{c}\Delta {\overline{\sigma }}_{x}\\ \left(1+{\eta }_{y}+{\mu }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\eta }_{z}+{\mu }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]$ (25)
4) ${\eta }_{y}\ll {\mu }_{y}$ and ${\eta }_{z}\ll {\mu }_{z}$ . This group is composed of the 3-subinterval, 4-subinterval, and 5-subinterval algorithms optimized with angular increments, and the 4-subinterval algorithm optimized with angular rates. In this case, the approximated expression for Eqn (22) is
$\Delta \stackrel{˜}{\sigma }=\left[\begin{array}{c}\left(1+{\overline{\xi }}_{x}\right)\Delta {\Phi }_{x}\\ \left(1+{\mu }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\mu }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]=\left[\begin{array}{c}\Delta {\overline{\sigma }}_{x}\\ \left(1+{\mu }_{y}\right)\Delta {\Phi }_{y}\\ \left(1+{\mu }_{z}\right)\Delta {\Phi }_{z}\end{array}\right]$ (26)
As shown in Eqns (24-26), the difference between the optimal coning algorithm and the theoretical value $\Delta \overline{\sigma }$ is not revealed by its component on x axis any longer. In other words, the influence of periodic components in these algorithms is dominant. It should be noted that all algorithms optimized with angular rates are included in the last three groups.
To validate the influence of periodic components, a variety of pitch-error simulations are carried out based on the two types of algorithms and their simplified forms denoted by Eqns (23-26).
In the simulation, the pitch error is defined as $\delta \theta =|\theta -\stackrel{˜}{\theta }|$ , where θ and $\stackrel{˜}{\theta }$ are the pitches calculated from
In the simulation, the pitch error is defined as , where θ and are the pitches calculated from Eqns (2) and (4) at the same time, respectively. Table 4 shows the ideal coning environments for simulation. The updating period of attitude quaternion is 0.01 s, and the duration of simulation is 36 s.
The numerical results in the coning environment 3# are illustrated in Figs. 2 and 3. For brevity’s sake, we omit the results in the other coning environments because of their high degree of similarity to those in the environment3.
Figure 2. Pitch errors (semilog plot in vertical axis) based on the coning algorithms optimized with angular increments (CAOWAI) and their simplified forms (SF) for: (a) N = 1, b) N = 2, (c) N = 3, (d) N = 4, and (e) N = 5.
In Fig. 2, the pitch errors based on the simplified forms (SF) are close to those based on the coning algorithms optimized with angular increments (CAOWAI), except for the case N = 3. This discrepancy is related to the corresponding parameter ${\stackrel{˜}{\xi }}_{x}$
in Table 3, which reveals that the optimization of nonperiodic component in the 3-subinterval algorithm is inadequate. In contrast, the curves in Fig. 3 show good agreement between the pitch errors based on the coning algorithms optimized with angular rates (CAOWAR) and their simplified forms (SF).
Fig. 2 reveals that when N exceeds 3
the CAOWAIs do not have substantial improvement in pitch accuracy any longer. Thus the 4-subinterval and 5-subinterval algorithms are not recommended on the consideration of their complex structures (see Table 1). On the other hand, comparing with Fig. 2, the CAOWAR with identical N is not obviously superior in pitch accuracy. This is not consistent with the conjecture stated at the end of section 3. The explanation for this phenomenon is that the periodic components in CAOWARs are dominant factors, just as what has been discussed in section 4. So it is necessary to further optimize these periodic components.
conjecture stated at the end of section 3. The explanation for this phenomenon is that the periodic components in CAOWARs are dominant factors, just as what has been discussed earlier. So it is necessary to further optimise these periodic components.
This study analyzes the accuracy of attitude computation based on two types of optimal coning algorithms under the classical coning motion. After deriving the true value of the change of the rotation vector, we explore the influence of periodic components in these algorithms using analytical comparison and categorization. Analytical results indicate that the influence of periodic components is dominant in these algorithms except for the 1-subinterval and 2-subinterval ones optimized with angular increments. Moreover, numerical tests are constructed, and the results agree well with the analyses. Allowing for the comparison of accuracy, the 4-subinterval and 5-subinterval algorithms optimized with angular increments are not recommended for use. To improve the accuracy of attitude computation, future work will concentrate on the optimization of periodic components in existing coning algorithms.
This work was supported in part by the National Basic Research Program of China (973 Program) (2009CB724002), the National Natural Science Foundation of China (50975049), the Specialized Research Fund for the Doctoral Program of Higher Education (20110092110039) and Ocean special funds for scientific research on public causes (201205035-09) and the Aeronautical Science Fund of China (20090869008). The authors would like to thank Tianhong Pan for his insightful comments and constructive suggestions. Thanks also to Feng Li for his help in partial work of the numerical simulations.
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3. Ignagni, M.B. Optimal strapdown attitude integration algorithms. J. Guid. Control Dyn., 1990, 13(2), 363-9.
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5. Ignagni, M.B. On the orientation vector differential equation in strapdown inertial systems. IEEE Trans. Aerosp. Electron. Syst., 1994, 30(4), 1076-81.
6. Jiang, Y.F. & Lin, Y.P. Improved strapdown coning algorithms. IEEE Trans. Aerosp. Electron. Syst., 1992,28(2), 484-90.
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8. Huang, H. & Deng, Z.L. A new expression for rotation vector attitude algorithm. Journal Astronautics, 2001, 22(3), 92-8. (in Chinese)
9. Zeng, Q.H.; Liu, J.Y.; Xiong, Z. & Zhao, W. A high-accuracy attitude algorithm of ring laser gyro strapdown inertial navigation system with pure angle rate output. J. Shanghai Jiaotong Uni., 2006, 40(12), 2159-63. (in Chinese)
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| 2019-10-14T03:50:44 |
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http://law.epa.gov.tw/en/laws/844578960.html
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Regulations, Current, Last revision on September 4 2009
# Noise Control Standards
Original six articles promulgated by EPA Order Huan-Shu-Kong-Tzu No. 016755 on June 29, 1992.
Revisions to Article 6 and Article 7 promulgated by EPA Order Huan-Shu-Kong-Tzu No. 49488 on September 11, 1996.
Revisions to Article 3 and Article 7 promulgated by EPA Order Huan-Shu-Kong-Tzu No. 0940007620 on January 31, 2005.
Revisions promulgated by EPA Order Huan-Shu-Kong-Tzu No. 0950087606 on November 8, 2006.
Revisions to Articles 2 and 4, and amended Article 6-1 promulgated by EPA Order Huan-Shu-Kong-Tzu No. 0970013826 on February 25, 2008.
Full text in 11 articles revised and promulgated in Environmental Protection Administration, Executive Yuan Order Huan-Shu-Kung-Tzu No. 0980078173 on September 4, 2009.
Article 1 [正體中文]
These Standards are determined pursuant to Article 9, Paragraph 2 of the Noise Control Act.
Article 2 [正體中文]
The terms used in these Standards are defined as follows.
1. Control zone: Refers to Class 1-4 noise control zones as specified in the Noise Control Zone Delineation Operating Standards.
2. Noise level: Use of decibels adjusted (dB (A)) means the A-weighted value of the noise level.
3. Background noise level: Refers to the noise level apart from the noise source to be measured.
4. Peripheral boundary: Refers to the boundary lines managed or used by premises or facilities. When a premise or facility is isolated by an obvious surrounding wall, the wall shall serve as the boundary; when there is no physical separation, the property scope or scope within which the members of the public do not commonly enter shall be the boundary.
5. Time periods
1. Daytime: Refers to from 6:00 a.m. to 8:00 p.m. in Class 1 and 2 control zones, and from 7:00 a.m. to 8:00 p.m. in Class 3 and 4 control zones.
2. Evening: Refers to from 8:00 p.m. to 10:00 p.m. in Class 1 and 2 control zones, and from 8:00 p.m. to 11:00 p.m. in Class 3 and 4 control zones.
3. Nighttime: Refers to from 10:00 p.m. to 6:00 a.m. on the following day in Class 1 and 2 control zones, and from 11:00 p.m. to 7:00 a.m. on the following day in Class 3 and 4 control zones.
6. Equivalent sound level: Refers to the average energy value of the measured noise level during a specific time period. Equivalent sound level of from 20 Hz up to 20 kHz is expressed as Leq, and from 20 Hz up to 200 Hz is expressed as Leq,LF; the following calculation formula is used:
1. $L_{\mathrm{eq}}=10\lg (\frac{1}{T}\int_{0}^{T} \left(\frac{P_{t}}{P_{0}}\right)^{2}\,d t)$[Formula description]
• T: Measurement time, expressed in seconds.
• P1: Measured sound pressure, in units of Pascals () .
• P0: Baseline sound pressure of 20 μ㎩.
2. $L_{\mathrm{eq}, \mathrm{LF}}=10\lg \sum_{n=20 Hz}^{200 Hz} \mathrm{10}^{(\mathrm{0.1}L_{\mathrm{eq}, n})}$[Formula description]
• Leq,n: 1/3 octave band filters are used to measure the equivalent sound level of each 1/3 octave band.
• n: Center frequency of the 1/3 octave band from 20 Hz up to 200 Hz.
7. Maximum noise level （Lmax）: The maximum noise level value measured during the measurement period.
8. The combined sound level: Means the sound level of a measured location in which the sound level is created and by two or more facilities.
Article 3 [正體中文]
Noise noise level measurements must comply with the following regulations:
1. Measurement instruments:
Measurement of noise from 20 Hz up to 20 kHz shall be conducted with any type of sound meter complying with CNS No. No.7129 specifications; measurement of noise from 20 Hz up to 200 Hz shall be conducted with any type of sound meter complying with CNS No.7129 specifications ; the said meter shall also comply with the IEC 61260 (1995) Class 1 standard. IEC 61260（1995）Class 1.
2. Measurement height:
1. When the measurement location is outdoors, the sound sensor should be from 1.2 m to 1.5 m above the ground or an extension of the floor slab of the floor on which measurements are performed.
2. When the measurement location is indoors, the sound sensor should be from 1.2 m to 1.5 m above the ground or floor slab.
3. Dynamic response:
In general, a noise meter with fast dynamic response should be used. However, a noise meter with slow dynamic response may be employed when the noise from a noise source has little variation, such as the noise from a motor.
4. Correction for the background noise level:
1. The background noise level in a premise where measurements are being performed should differ from the noise level of the noise source being measured by at least 10 dB(A). If the difference is less than 10 dB(A), the background must be corrected on the basis of the following table.
2. Correction of background noise level:
1. L1: measured value including background noise level.
2. L2: measured value of background noise level.
3. L1-L2 3 4 5 6 7 8 9
Corrected value -3 -2 -1
3. The statutory responsible persons or on-site personnel at premises and facilities must cooperate with the measurement of the background noise level, and their influence on the background noise level should be corrected for. When background noise level measurements are performed, and the statutory responsible person or on-site personnel cannot cooperate, then there is no need to correct for the background noise level, and the situation should be noted.
4. When it is desired to measure the overall noise level of a premise, but the difference from the background noise level is less than 3dB(A), the measurement should be discontinued, and either another suitable measurement location found or the noise from other sources eliminated or reduced before measurements are performed.
5. When a premise to be measured is a factory (facility) with equipment operating 24 hours a day, and the equipment cannot be stopped to accommodate measurement of background noise level at any time apart from annual maintenance, an annual maintenance background noise level monitoring plan may be submitted to the special municipality, county, or city competent authority; after the special municipality, county, or city competent authority has granted its approval, measurement of the noise level at a location outside the premise's peripheral boundary approved by the special municipality, county, or city competent authority should be performed for a continuous period of from 24 hours to 72 hours during annual maintenance. The results should be reported to the special municipality, county, or city competent authority for approval, and shall provide a basis for correction for the background noise level when measurements of noise within a frequency range of from 20 Hz up to 20 kHz are performed at any place outside the peripheral boundary of the factory (facility) within two years of the date of approval.
5. Testing time period:
Perform measurements at times when the emission of noise is most representative or that have been designated by the complainant.
6. Testing location:
1. When measuring noise in a frequency range of from 20 Hz up to 20 kHz at sources that are not public address facilities, apart from measurements at locations designated by a complainant as his or her living place, the measurements should be performed at any place specified by the competent authority outside the peripheral boundary of a factory (facility), entertainment premise, business premise, construction project, or other premises or facilities announced by the competent authority; measurements shall be taken at points at least one meter from the wall of the nearest building.
2. When measuring noise in a frequency range of from 20 Hz up to 200 Hz at sources that are not public address facilities, if measurements are performed at indoor points within a complainant's designated living place the measurements shall be conducted at points at least one meter from the nearest indoor wall line; however, this restriction shall not apply if it is desired to perform measurements with no obstructions between the noise source and sound sensor. Indoor doors and windows should be kept shut; other noise sources that will influence measurement results should be temporarily turned off.
3. When measuring noise at a public address facility, if the noise source at the public address facility has a horizontal projection distance of three meters or more, the measurements should be performed at a location designated by the competent authority. If a mobile public address facility is moving at the time, the measurements should be performed at a location designated by the competent authority and no less than three meters from the mobile noise source at its closest approach.
7. Assessment method:
1. When a noise source is not a public address facility, the equivalent sound level (Leq or Leq,LF) or maximum noise level (Lmax) shall be calculated on the basis of the following noise source emission characteristics, and the results may not exceed the values in the noise control standards table:
1. If the needle of a noise meter exhibits regular variation of a periodic or intermittent nature, but the maximum value is generally constant, the maximum value (Lmax) should be taken as the average of readings over the course of five consecutive changes. For example, Diagram 1 shows a regularly changing sound, with a constant period of variation. In addition, Diagram 2 shows an intermittent, regularly changing sound with a constant maximum value. In these examples, the average of five maximum values is taken.
2. Other situations are expressed using equivalent sound level. Continuous measurement sampling time must be at least two minutes, and sampling intervals may not be greater than two seconds. For instance, in Diagram 3, when the noise meter's reading is constant, or the needle only changes by 1-2dB(A), the results are expressed using equivalent sound level. In Diagram 4, when the sound volume and interval of occurrence are irregular, the results are also expressed using equivalent sound level.
Diagram 1
Diagram 2
Diagram 3
Diagram 4
2. With regard to assessment methods for noise from public address facilities, the equivalent sound level (Leq) or maximum noise level (Lmax) shall be calculated on the basis of the following noise source emission characteristics, and the results may not exceed the noise control standard value:
1. In the case of mobile public address facilities, the maximum value (Lmax) at the time the facility passes shall determine noise level.
2. In the case of stationary or currently stopped public address facilities, the noise level shall be expressed as equivalent sound level (Leq) . Continuous measurement sampling time must be at least two minutes, and sampling intervals may not be greater than two seconds.
Article 4 [正體中文]
Noise control standards for factory plants or sites are as follows:
Control zones 20 Hz up to 200 Hz, 20 Hz up to 20 kHz
Daytime Evening Nighttime Daytime Evening Nighttime
Equivalent sound level (Leq) Category 1 42 42 39 50 45 40
Category 2 42 42 39 60 55 50
Category 3 47 47 44 70 60 55
Category 4 47 47 44 80 70 65
Article 5 [正體中文]
The following are noise control standard values for entertainment and business premises:
Control zones 20 Hz up to 200 Hz 20 Hz up to 20 kHz
Daytime Evening Nighttime Daytime Evening Nighttime
Category 1 35 35 30 55 50 40
Category 2 40 35 30 60 55 50
Category 3 40 40 35 70 60 55
Category 4 40 40 35 80 70 65
Article 6 [正體中文]
Noise control standards for construction sites are as follows:
Control zones 20 Hz up to 200 Hz 20 Hz up to 20 kHz
Daytime Evening Nighttime Daytime Evening Nighttime
Equivalent sound level (Leq) Category 1 47 47 42 70 50 50
Category 2 47 47 42 70 60 50
Category 3 49 49 44 75 70 65
Category 4 49 49 44 80 70 65
Maximum noise level (Lmax) Categories 1 and 2 - 100 80 70
Categories 3 and 4 100 85 75
Article 7 [正體中文]
Noise control standards for amplifying facilities are as follows:
Control zones Daytime Evening Nighttime
Category 1 60 50 40
Category 2 75 60 50
Category 3 80 65 55
Category 4 85 75 65
Article 8
The following are noise control standard values for premises and facilities announced by the competent authority:
Control zones 20 Hz up to 200 Hz 20 Hz up to 20 kHz
Daytime Evening Nighttime Daytime Evening Nighttime
Category 1 35 35 30 55 50 35
Category 2 40 35 30 60 55 45
Category 3 40 40 35 70 60 50
Category 4 40 40 35 80 70 60
Article 9
When the combined sound level created by facilities not belonging to one person, juridical person or non-juridical person that exceed the values for noise control standards of the foregoing articles, all such facilities shall equally comply with the values for post-correction noise control standards in the following table:
Value of sound source not belonging to one person, juridical person, or non-juridical person. Corrected value for noise control standards with which all facilities shall comply
2 -3
3 -4
4 -6
5 -7
Over 6 -8
Article 10 [正體中文]
Special municipality, county, and city competent authorities shall announce specific noise control zones on the basis of the noise control zone types in the Noise Control Zone Delineation Operating Standards; the noise control standard values in such noise control zones shall be five decibels lower than the noise control standard values prescribed Articles 4 through 8.
When a measurement location has two or more noise control zone boundaries, the noise level may not exceed the noise control standard value for any internal area.
Article 11 [正體中文]
These Standards shall take effect from the date of promulgation.
| 2013-05-22T06:17:55 |
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|
https://www.usgs.gov/media/images/large-scale-map-june-27th-flow-k-laueas-erz-26
|
# Large-scale map of June 27th flow in Kīlauea's ERZ
## Detailed Description
This large-scale map shows the distal part of the June 27th flow in relation to nearby Puna communities. The area of the flow on November 12 and 13 is shown in pink, while widening and advancement of the flow as mapped on November 14 at 1:40 PM is shown in red. Surface activity continues along the north margin of the flow between 230 meters (250 yards) upslope of the flow tip and 2.7 kilometers (1.7 miles) mauka of AP‘A‘ā Street. The most active flow over the past few days is approximately 230 meters (250 yards) from AP‘A‘ā Street. Also, above where the flow enters the crack there was a small breakout 260 meters (285 yards) in length along the flow margin. The blue lines show steepest-descent paths calculated from a 1983 digital elevation model (DEM; for calculation details, see http://pubs.usgs.gov/of/2007/1264/). Steepest-descent path analysis is based on the assumption that the DEM perfectly represents the earth's surface. DEMs, however, are not perfect, so the blue lines on this map can be used to infer only approximate flow paths.
## Details
Image Dimensions: 1056 x 816
Date Taken:
| 2019-10-19T20:31:32 |
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http://www.bnl.gov/events/details.php?q=9171
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1. Nuclear Physics Seminar
"Status of W Boson Production Measurements at PHENIX"
Presented by Mikhail Stepanov, UMass Amherst
Tuesday, May 28, 2013, 11 am
Small Seminar Room, Bldg. 510
Hosted by: Oleg Eyser
The measurement of $W^{\pm}$ production in polarized proton-proton collisions at RHIC is an important probe of the proton's polarized sea quark distributions which are poorly constrained at present compared to the valence quarks distributions. Parity-violating single-spin asymmetries, $A_{L}$, measured in $W^{\pm}$ production in longitudinally polarized $p+p$ collisions provide access to the flavor-separated light quark and anti-quark polarized parton distribution functions. The PHENIX experiment observes $W^{\pm}$ through their leptonic decay to $e^{\pm}$ at mid-rapidity ($|\eta|<0.35|$) and to $\mu^{\pm}$ at forward/backward rapidities ($1.2<|\eta|<2.2$). These complementary measurements give access to the sea quark polarizations over different ranges in partonic momentum of a quark/antiquark. In succession to the first measurements performed in 2009 (mid-rapidity) and in 2011 (forward/backward rapidities), in 2012 PHENIX recorded data at $\sqrt{s}$ = 510 GeV with an integrated luminosity of $\approx$50 pb$^{-1}$ which is about twice the size of previous data sets and also takes an advantage of improved beam polarization ($P\approx$ 55$\%$). The parity-violating single-spin asymmetries for $W$ production from the 2012 dataset will be presented; as well as, details and status of the recent analyses and future prospects will be reported.
| 2013-12-13T09:47:01 |
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|
https://pos.sissa.it/336/236/
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Volume 336 - XIII Quark Confinement and the Hadron Spectrum (Confinement2018) - H. Statistical Methods for Physics Analysis in the XXI Century
Bayesian unfolding of charged particle $p_{\mathrm{T}}$ spectra with ALICE at the LHC
M. Krüger* on behalf of the ALICE collaboration
Full text: pdf
Pre-published on: September 12, 2019
Published on: September 26, 2019
Abstract
The study of the Quark-Gluon Plasma created in ultrarelativistic heavy-ion collisions at the CERN-LHC is complemented by reference measurements in proton-lead (p--Pb) and proton-proton (pp) collisions, where the effects of multiple-parton interactions and hadronization beyond independent string fragmentation can be investigated. In these proceedings, we present a Bayesian unfolding procedure to reconstruct the correlation between transverse momentum ($p_{\mathrm{T}}$) spectra of charged particles and the corresponding charged-particle multiplicities $N_{\mathrm{ch}}$. The unfolded spectra are presented in single multiplicity ($\Delta N_{\mathrm{ch}}$ = 1) bins and are used to derive moments of the $p_{\mathrm{T}}$ distributions. We illustrate the unfolding procedure of the $p_{\mathrm{T}}$ spectra with a Monte Carlo simulation for pp collisions at a centre-of-mass energy of $\sqrt{\mathrm{s}}= 5.02$ TeV.
DOI: https://doi.org/10.22323/1.336.0236
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.
| 2023-02-09T13:35:51 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/5460/4582
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Registration of Airborne Infrared Images using Platform Attitude Information
In current warfare scenario stealth and passive threat detection capabilities are considered as prime requirements to accomplish desired mission by the fighter aircrafts. To improve the stealth of an aircraft, the trend is towards detecting threats with the help of passive sensors (electro optic or infrared). Current situation caters for systems like infrared search and track (IRST) and Passive missile warning systems (PMWS). Both IRST and PMWS systems detect targets of interest by processing IR images acquired in mid-IR region. The prime challenge in IRST system or PMWS is detecting a moving target of size typically 1~2 pixels in acquired image sequences. The temporal change caused by moving target in consecutive frames can be considered as one important factor to detect them. The temporal change caused by moving target is identified through absolute frame differencing of successive frames. This principle has limitation in application to IRST and PMWS as the imaging sensor with the aircraft is moving. This motion also imparts temporal change in the acquired images. In this paper authors are proposing a method for removing the temporal change caused by the platform motion in two consequently acquired frames using registration process. The proposed method uses the platform attitude information at frame sampling times. Authors have analyzed the sensitivity of registration process to noisy platform attitude information.
In current warfare scenario, detection of threats by passive systems is of great importance for the fighters to accomplish their intended mission. These capabilities can be incorporated into aircraft using systems like infrared search and track (IRST)1 and passive missile warning system (PMWS)2 respectively. Both of these systems share common similarities among them, as far as the detection phase of target or threat concerned. IRST and PMWS exploit the thermal radiation of the scene for detecting the target of interest. Both the systems process acquired infrared (IR) imagery for identifying the targets of size 1~2 pixels in wide field of view sensor against background clutter. This low spatial extent, low signal to noise ratio (SNR) target is called dim target in research community. In this paper authors are referring to both IRST, PMWS with a common name as ‘passive target detection system (PTDS)’.
Commonly a PTDS consists of data processing stages3: Clutter rejection, tracking and association, and discrimination.
(a) Clutter rejection stage converts large amount of pixel data into few number of pixel data that may contain targets.
(b) Tracking and association stage associates the detections from same spatial source into a track.
(c) Discrimination stage discriminates tracks into true target tracks or false target tracks by extracting various features.
The data processing in clutter rejection stage is further elaborated below, as the registration algorithm that authors are proposing is part of it
1.1 Clutter Rejection
Clutter rejection stage operates on preprocessed images for rejecting clutter (radiation from background, natural or man-made sources). The main goal of clutter rejection stage is to attenuate the clutter level to zero without affecting the true target signal. The observation of random image embedded with dim small target could be modeled as4,5,
I(i,j,k) = S(i,j,k) + Ib(i,j,k) + N(i,j,k) (1)
k = 0,1,2….
where I denote an image embedded with small target, S represents the signal intensity of target, and Ib is clutter background. N is noise induced by the detector elements present in the sensor. An image consists of target and noise could be obtained after subtracting the clutter background from original image. This can be modeled as,
It (i,j,k) = S(i,j,k) + N(i,j,k) (2)
k = 0,1,2….
where It denotes an image containing target signal intensity and noise induced by the detector elements. This mathematical model in Eqn. (2) indicates that, ideally the target could be correctly detected if image background could be estimated accurately and the noise in image could be excluded.
Limited literature available for the problem of detecting weak point targets in Infrared clutter. The background estimation algorithms in IR images can be categorized into spatial filtering6,7, temporal filtering8,9, spatio-temporal filtering10,11, hypothesis testing12,13, track before detect14,15, image morphology based16, multi spectral image fusion methods17, wavelet decomposition18,19, and super resolution reconstruction methods20.
Two primary challenges in developing algorithm for dim target detection are:
(i) The algorithm should well distinguish the target and clutter.
(ii) To fast detect the target, the algorithm should be simple and real time implementable.
Of the various methods referred for background estimation, temporal filtering methods are gaining more attention in PTDS, being simple and real time implementable nature. PTDS uses imaging sensors with typical frame rate in range 60Hz to 120Hz. Temporal filtering methods analyses the moving property of target. The principle is ‘if two successive images are generated at slightly different times from the same point in space, they should exhibit almost exactly the same backgrounds, pixel for pixel’. If a moving target is present in the field of view, its signature will be different in the two images. Subtraction of one image from the other should therefore result in nearly complete cancellation of background clutter with much less cancellation of target. The main challenge in temporal filtering method is two consecutively sampled images to be aligned before frame differencing in order to nullify the platform motion. Consider the two images presented in Fig. 1., which are captured at two different time instants with a time gap of 30 ms. Upon comparison of two images one can observe that background content is same in both images, but the same background content is appearing in different pixel positions of the images due to platform motion.
The registration process geometrically aligns previously sampled image (previous image) with current sampled reference image (current image). In PTDS, Current image is the one sampled recently by the imaging sensor. Whereas previous image is, one sampled previously to the current image. Registration process is achieved by maximizing the normalized cross-correlation for two images, given by
$corr\text{\hspace{0.17em}}\left(f,g\right)=\frac{\sum {}_{x,y}\left(f\left(x,y\right)-\overline{f}\right)\left(g\left(x,y\right)-\overline{g}\right)}{\sqrt{\sum {}_{x,y}{\left(f\left(x,y\right)-\overline{f}\right)}^{2}{\left(g\left(x,y\right)-\overline{g}\right)}^{2}}}$
D
where f(x, y) and g(x, y) are the two images to be registered, and $\overline{f}$ ,$\overline{g}$ are the mean values for the respective images. Based on the assumption that ground is approximately flat (or aircraft is sufficiently high above the ground any terrain effects are negligible), a three dimensional affine or projective transformation can be used to describe the transformation from one frame to next21. The registration process merely finds the transformation that maximizes the cross correlation.
Nevertheless majority of registration methods consists of primarily four stages presented in Fig. 2.
(i) Feature detection stage identifies salient and distinctive features like closed boundary regions, edges, contours, line intersections, corners, in current and previous images. These feature points are called control points in literature22. The important consideration in selection of feature or control points is invariance of same under scaling, rotation and translation.
(ii) In Feature matching step, the correspondence between the features detected in current image and features detected in previous image is established.
(iii) In Transformation model estimation, the transformation or parameters of the transformation that best describes the established feature correspondence is estimated. The transformation model that describes the correspondence can be local or global. Typically in airborne imaging systems the transformation model assumed is affine transform, which is local.
(iv) After obtaining the transformation model and its parameters, it is applied on the base image to align to current image. Image values in non integer coordinates are found by appropriate interpolation techniques23.
The difficulties involved in using this conventional registration process, for registration of IR images are:
• PTDS shall require the completion of registration process on subsequent frames at frame rate for real time operation. But the conventional registration process involves computation intensive tasks like feature extraction, feature matching, transform model estimation. This may limit the real time performance of PTDS.
• For good registration accuracy there should be enough of the ground features to be common between current image and previous image. The low resolution and noisy nature of IR imagery poses more problems for conventional registration algorithms.
• IR imagers tend to generate a lot of fixed pattern noise (dead and saturated pixels) and other non- uniformities. This can cause false correlations and other registration difficulties.
To overcome these difficulties authors are proposing a method to find the registration transformation between current frame and previous frame using platform attitude. The details of the proposed approach are presented in next Section.
The proposed registration method uses following information.
• Sensor installation angles to the platform.
• Pixel’s line of sight (LOS) vectors.
• Platform attitude information (Yaw, Pitch, Roll, velocities in inertial coordinate system) available at each frame sampling time.
Inertial coordinate system also known as NED coordinate system is a geographical coordinate system for representing the state vectors that is commonly used in aviation24. It consists of three numbers: one represents the position along the northern axis, one along the eastern axis, and one represents vertical position. Down is chosen as opposed to up in order to comply with the right-hand rule. The origin of this coordinate system is usually chosen to be the aircraft’s center of gravity.
The pictorial representation of registration process for aligning two frames sampled at two different time instants is presented in Fig. 3.
Figure 3. Figure demonstrating the process for identification of registration transformation for a pixel in current image to previous image.
In proposed approach registration of a pixel in current image into previous image is carried out in three steps.
1. The inertial coordinates (NED coordinates) of point imaged into current image pixel is obtained using pixel’s unit inertial LOS vector and range to the 3-D point in space. The range to 3-D point in space is obtained with assumption of ground is approximately flat by,
$R=\frac{H}{\mathrm{cos}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(el\right)}$
H is platform altitude above ground level. el is inertial elevation angle of 3-D world point. The steps involved for identifying the Line of sight vector of a pixel in inertial coordinate system is presented in Fig. 4.
Figure 4. Transformations involved for representing the pixel’s line of sight in inertial coordinates.
2. LOS vector $\overline{C}$ of 3-D world point into the previous image coordinates is obtained in triangulation with platform translational vector $\overline{B}$ and current image pixel LOS vector $\overline{A}$ . From Fig. 3.
$\overline{C}=\overline{A}+\overline{B}$
Platform translational vector is obtained by [XN YE ZD] = [VN VE VD] * T
[VN VE VD] is inertial velocity vector of the platform. T is the time gap between the frames. Using the LOS vector $\overline{C}$ , pixel location in previous image is obtained through consecutive rotations depicted in Fig. 5.
3. Registration map obtained from current image to previous image consists of non integer locations. Intensity values at non integer locations of previous image are obtained through interpolation.
Figure 5. Transformations involved for reprojecting the 3-D world point into the previous frame.
The proposed approach is evaluated on video recordings obtained from a sensor mounted on airborne platform.
4.1 Experimental Data set
The proposed approach is evaluated on three different scenarios of video recordings NR01, NR02, NR03. These video recordings are collected from an IR sensor (operating in mid IR region of Electromagnetic spectrum) mounted on commercial aircraft. The IR sensor samples the picture of thermal scene at 30 frames per second. Platform attitude information is recorded from an inertial navigation sensor. Recorded platform attitude information is synchronized to frame sampling time using interpolation or extrapolation. The details about video recordings are presented in Table 1 and Fig.6.
Table 1. Details of video recordings used for evaluation of the proposed approach .
Figure 6. Figures demonstrating the background features present in each of video recordings (a) NR01, (b) NR02, (c) NR03, respectively.
4.2 Performance Analysis
The goal of registration process is to maximize the normalized cross correlation between two images. The performance measure used for evaluating proposed registration process is normalized cross correlation coefficient. The proposed approach is evaluated on three video recordings, and the results are presented in Table 2. Correlation coefficient for a video recording mentioned in Table 2 is obtained by averaging the correlation coefficient value of every frame with its corresponding previous frame. One can observe from Table 2, with registration process the correlation coefficient values of video recording increased. Video recordings NR01, NR02 are exhibiting high correlation coefficient values even without registration of frames. The reason for this is homogeneous background content present in video frames. With registration process correlation between frames in NR01, NR02 improved by 2%, which is a significant improvement in PTDS for effectively removing the clutter. In case of NR03 without registration the correlation between frames is very less, because of heterogeneous background content. With registration process the correlation between frames is improved by 20%. Even with registration the correlation between frames in NR03 is quite less compared to NR01, NR02. The reason for this is mainly due to registration inaccuracies contributed from height measurement errors. In case of NR03, platform is flying at low altitudes so the assumption of ground is approximately flat is failing and further contributing to registration errors.
Table 2. Performance comparison of the registration process on three experimental data sets.
4.3 Effect of Noisy attitude information on Registration accuracy
The proposed registration process identifies the registration map using platform attitude information. The accuracy of the registration process is analyzed with respect to noisy attitude information. Known amounts of additive Gaussian noise is added to the platform attitude variables Yaw, Pitch, Roll and NED plane velocities. The registration performance in terms of cross correlation coefficient for three video recordings is analyzed varying the noise levels in attitude information. Results are presented in Fig. 7, and Fig. 8. Registration performance is decreasing rapidly with increase in noise for Yaw, Pitch, Roll variables. Whereas the performance fall in registration process is very minimal with increase in noise for NED plane velocities. The reason for less sensitivity of registration process towards noisy NED plane velocities is less time gap between the frames (in order of msec). Due to less time gap between frames, the error contributed by NED plane velocities in finding platform translational vector ($\stackrel{-}{\beta }$ ) is negligible.
Figure 7. Sensitivity of registration process with respect to noise in inertial velocities.
Figure 8. Sensitivity of registration process with respect to noise in platform’s Yaw, Pitch, Roll measurements.
A novel method for registering air borne images using platform own ship motion is presented. The performance of the proposed approach is evaluated on video recordings with correlation coefficient as performance metric. The performance of the proposed approach is also evaluated for sensitivity towards noisy platform attitude information. It is observed that proposed approach is more sensitive to the noise in Yaw, Pitch, Roll parameters than inertial plane velocities. The performance of proposed approach is to be improved by accurately estimating the range to the 3-D world point, under low altitude flying scenarios of platform.
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Mr Ravi Shankar Chekuri obtained his BE (Electronics & Communication) from Andhra University, in 2008 and ME (Computer Vision & Embedded System Design) from IIT Kharagpur, in 2010. He is currently working at Defence Avionics Research Establishment, Banglore. His areas of interest include: Image processing, pattern classification, deep belief networks, hyper spectral image processing, automatic target recognition, automatic topographic map understanding and geographical information systems. Ms R. Anand Raji obtained her BE (Computer Science & Engineering) from Madras University. She is currently working as Team Leader for Algorithm Group in Avionics Division, Defence Avionics Research Establishment, Banglore. She is currently working for the Mission Management System for UAV and Algorithm development for dual color missile approach warning system. Her contributions were mainly on software development for mission computer, display processor and EW systems.
| 2020-06-04T14:30:01 |
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https://zbmath.org/authors/?q=ai%3Amalchiodi.andrea
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# zbMATH — the first resource for mathematics
## Malchiodi, Andrea
Compute Distance To:
Author ID: malchiodi.andrea Published as: Malchiodi, Andrea; Malchiodi, A. External Links: MGP · ORCID · Wikidata · GND · IdRef · theses.fr
Documents Indexed: 106 Publications since 1999, including 4 Books Reviewing Activity: 5 Reviews
all top 5
#### Co-Authors
31 single-authored 15 Ambrosetti, Antonio 6 Djadli, Zindine 5 Jevnikar, Aleks 5 Mahmoudi, Fethi 5 da Silva Montenegro, Marcelo 5 Ni, Wei-Ming 5 Ruiz, David 4 Gursky, Matthew J. 4 Ould Ahmedou, Mohameden 4 Wu, Ruijun 4 Yang, Paul C. P. 3 Battaglia, Luca 3 Cheng, Jih-Hsin 3 Ikoma, Norihisa 3 Li, YanYan 3 Mondino, Andrea 3 Wei, Juncheng 2 Bartolucci, Daniele 2 Carlotto, Alessandro 2 Felli, Veronica 2 Garcia-Azorero, Jesús 2 Hwang, Jenn-Fang 2 Lamm, Tobias 2 Micallef, Mario J. 2 Montoro, Luigi 2 Peral Alonso, Ireneo 2 Rizzi, Matteo 1 Berti, Massimiliano 1 Borrelli, William 1 Braides, Andrea 1 Caldiroli, Paolo 1 Chanillo, Sagun 1 de Marchis, Francesca 1 Farina, Alberto 1 Gazzola, Filippo 1 Gui, Changfeng 1 Kallel, Sadok 1 Lanconelli, Ermanno 1 Mandel, Rainer 1 Martinazzi, Luca 1 Mayer, Martin 1 Ndiaye, Cheikh Birahim 1 Novaga, Matteo 1 Pagliardini, Dayana 1 Secchi, Simone 1 Struwe, Michael 1 Tarantello, Gabriella 1 Uguzzoni, Francesco 1 Wang, Xu-Jia 1 Wei, Jungcheng 1 Xu, Haoyuan
all top 5
#### Serials
7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Communications in Mathematical Physics 4 Advances in Mathematics 4 Journal of Differential Equations 4 Journal of Functional Analysis 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Archive for Rational Mechanics and Analysis 3 Communications on Pure and Applied Mathematics 3 Discrete and Continuous Dynamical Systems 3 Journal of the European Mathematical Society (JEMS) 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Journal of Differential Geometry 2 Journal für die Reine und Angewandte Mathematik 2 Proceedings of the American Mathematical Society 2 Geometric and Functional Analysis. GAFA 2 Communications in Partial Differential Equations 2 Lecture Notes in Mathematics 2 Journal of Fixed Point Theory and Applications 2 Analysis & PDE 1 Journal d’Analyse Mathématique 1 American Journal of Mathematics 1 Duke Mathematical Journal 1 Indiana University Mathematics Journal 1 Mathematische Annalen 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Ricerche di Matematica 1 Transactions of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Asymptotic Analysis 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 Advances in Differential Equations 1 Matemática Contemporânea 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Journal of Mathematical Study 1 Annals of Mathematics. Second Series 1 Interfaces and Free Boundaries 1 Communications in Contemporary Mathematics 1 Advanced Nonlinear Studies 1 Analysis in Theory and Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Cambridge Studies in Advanced Mathematics 1 Progress in Mathematics 1 Frontiers of Mathematics in China 1 RIMS Kôkyûroku Bessatsu 1 Pure and Applied Functional Analysis 1 Bollettino dell’Unione Matematica Italiana
all top 5
#### Fields
88 Partial differential equations (35-XX) 52 Differential geometry (53-XX) 35 Global analysis, analysis on manifolds (58-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 7 Operator theory (47-XX) 7 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Fluid mechanics (76-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX)
#### Citations contained in zbMATH Open
91 Publications have been cited 2,270 times in 1,225 Documents Cited by Year
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1064.35175
Ambrosetti, Antonio; Felli, Veronica; Malchiodi, Andrea
2005
Perturbation methods and semilinear elliptic problems on $$\mathbb R^n$$. Zbl 1115.35004
Ambrosetti, Antonio; Malchiodi, Andrea
2006
Multiplicity results for some nonlinear Schrödinger equations with potentials. Zbl 1040.35107
Ambrosetti, A.; Malchiodi, A.; Secchi, S.
2001
Nonlinear analysis and semilinear elliptic problems. Zbl 1125.47052
Ambrosetti, Antonio; Malchiodi, Andrea
2007
Existence of conformal metrics with constant $$Q$$-curvature. Zbl 1186.53050
2008
Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I. Zbl 1072.35019
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2003
Boundary concentration phenomena for a singularly perturbed elliptic problem. Zbl 1124.35305
Malchiodi, Andrea; Montenegro, Marcelo
2002
Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. II. Zbl 1081.35008
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2004
Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1142.35082
Ambrosetti, A.; Malchiodi, A.; Ruiz, D.
2006
Multidimensional boundary layers for a singularly perturbed Neumann problem. Zbl 1065.35037
Malchiodi, Andrea; Montenegro, Marcelo
2004
Minimal surfaces in pseudohermitian geometry. Zbl 1158.53306
Hwang, Jenn-Fang; Cheng, Jih-Hsin; Malchiodi, Andrea; Yang, Paul
2005
Morse theory and a scalar field equation on compact surfaces. Zbl 1175.53052
Malchiodi, Andrea
2008
Supercritical conformal metrics on surfaces with conical singularities. Zbl 1254.30066
Bartolucci, Daniele; De Marchis, Francesca; Malchiodi, Andrea
2011
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains. Zbl 1087.35010
Malchiodi, A.
2005
Topological methods for an elliptic equation with exponential nonlinearities. Zbl 1144.35372
Malchiodi, Andrea
2008
Multiple clustered layer solutions for semilinear Neumann problems on a ball. Zbl 1207.35141
Malchiodi, A.; Ni, Wei-Ming; Wei, Juncheng
2005
Concentration on minimal submanifolds for a singularly perturbed Neumann problem. Zbl 1160.35011
Mahmoudi, Fethi; Malchiodi, Andrea
2007
New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces. Zbl 1235.35094
Malchiodi, Andrea; Ruiz, David
2011
Prescribing a fourth order conformal invariant on the standard sphere. II. Blow up analysis and applications. Zbl 1150.53012
Malchiodi, Andrea; Djadli, Zindine; Ould Ahmedou, Mohameden
2002
Some existence results for the Toda system on closed surfaces. Zbl 1148.35021
Malchiodi, Andrea; Ndiaye, Cheikh Birahim
2007
A perturbation result for the Webster scalar curvature problem on the CR sphere. Zbl 1042.53025
Malchiodi, Andrea; Uguzzoni, Francesco
2002
A general existence result for the Toda system on compact surfaces. Zbl 1327.35098
Battaglia, Luca; Jevnikar, Aleks; Malchiodi, Andrea; Ruiz, David
2015
Prescribing a fourth order conformal invariant on the standard sphere. I: A perturbation result. Zbl 1023.58020
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2002
Weighted barycentric sets and singular Liouville equations on compact surfaces. Zbl 1232.53035
Carlotto, Alessandro; Malchiodi, Andrea
2012
A variational analysis of the Toda system on compact surfaces. Zbl 1275.35095
Malchiodi, Andrea; Ruiz, David
2013
Critical points of the Moser-Trudinger functional on a disk. Zbl 1304.49011
Malchiodi, Andrea; Martinazzi, Luca
2014
$$Q$$-curvature flow on $$S^4$$. Zbl 1099.53034
Malchiodi, Andrea; Struwe, Michael
2006
Concentration phenomena for nonlinear Schrödinger equations: recent results and new perspectives. Zbl 1200.35106
Ambrosetti, Antonio; Malchiodi, Andrea
2007
On the Yamabe problem and the scalar curvature problems under boundary conditions. Zbl 1005.53034
Ambrosetti, Antonio; Li, YanYan; Malchiodi, Andrea
2002
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations. Zbl 1276.58005
Bartolucci, Daniele; Malchiodi, Andrea
2013
A strong maximum principle for the Paneitz operator and a non-local flow for the $$\mathcal Q$$-curvature. Zbl 1330.35053
Gursky, Matthew J.; Malchiodi, Andrea
2015
Compactness of solutions to some geometric fourth-order equations. Zbl 1098.53032
Malchiodi, Andrea
2006
Non-compactness and multiplicity results for the Yamabe problem on $$S^n$$. Zbl 0979.53038
Berti, Massimiliano; Malchiodi, Andrea
2001
Prescribing scalar and boundary mean curvature on the three dimensional half sphere. Zbl 1092.53028
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2003
Some new entire solutions of semilinear elliptic equations on $$\mathbb R^n$$. Zbl 1178.35186
Malchiodi, Andrea
2009
A multiplicity result for the Yamabe problem on $$S^n$$. Zbl 0949.53028
Ambrosetti, Antonio; Malchiodi, Andrea
1999
Some remarks on the equation $$-\Delta u=\lambda(1+u)^p$$ for varying $$\lambda,p$$ and varying domains. Zbl 1010.35042
Gazzola, Filippo; Malchiodi, Andrea
2002
The prescribed boundary mean curvature problem on $$\mathbb B^4$$. Zbl 1108.35070
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2004
A positive mass theorem in three dimensional Cauchy-Riemann geometry. Zbl 1360.32031
Cheng, Jih-Hsin; Malchiodi, Andrea; Yang, Paul
2017
A topological join construction and the Toda system on compact surfaces of arbitrary genus. Zbl 1336.35152
Jevnikar, Aleks; Kallel, Sadok; Malchiodi, Andrea
2015
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve. Zbl 1180.35485
Mahmoudi, Fethi; Montenegro, Marcelo; Malchiodi, Andrea
2009
Boundary interface for the Allen-Cahn equation. Zbl 1144.35326
Malchiodi, A.; Wei, Jungcheng
2007
A Codazzi-like equation and the singular set for $$C^1$$ smooth surfaces in the Heisenberg group. Zbl 1255.53026
Cheng, Jih-Hsin; Hwang, Jenn-Fang; Malchiodi, Andrea; Yang, Paul
2012
Solutions concentrating at curves for some singularly perturbed elliptic problems. Zbl 1081.35044
Malchiodi, Andrea
2004
Transition layer for the heterogeneous Allen-Cahn equation. Zbl 1148.35030
Mahmoudi, Fethi; Malchiodi, Andrea; Wei, Juncheng
2008
Boundary-clustered interfaces for the Allen-Cahn equation. Zbl 1221.35150
Malchiodi, Andrea; Ni, Wei-Ming; Wei, Juncheng
2007
A Moser-Trudinger inequality for the singular Toda system. Zbl 1295.35372
Battaglia, Luca; Malchiodi, Andrea
2014
Existence and non-existence results for the $$SU(3)$$ singular Toda system on compact surfaces. Zbl 1338.35156
Battaglia, Luca; Malchiodi, Andrea
2016
On the symmetric scalar curvature problem on $$S^n$$. Zbl 1006.35044
Ambrosetti, Antonio; Malchiodi, Andrea
2001
The scalar curvature problem on $$S^n$$: An approach via Morse theory. Zbl 1012.53035
Malchiodi, Andrea
2002
Asymptotic Morse theory for the equation $$\Delta v- 2v_x\wedge v_y$$. Zbl 1175.35049
Chanillo, Sagun; Malchiodi, Andrea
2005
Singular elliptic problems with critical growth. Zbl 1072.35527
Caldiroli, Paolo; Malchiodi, Andrea
2002
Concentration of solutions for some singularly perturbed mixed problems: asymptotics of minimal energy solutions. Zbl 1194.35037
Azorero, Jesus Garcia; Malchiodi, Andrea; Montoro, Luigi; Peral, Ireneo
2010
Axial symmetry of some steady state solutions to nonlinear Schrödinger equations. Zbl 1211.35115
Gui, Changfeng; Malchiodi, Andrea; Xu, Haoyuan
2011
Concentration of solutions for some singularly perturbed mixed problems: existence results. Zbl 1214.35024
Azorero, Jesus Garcia; Malchiodi, Andrea; Montoro, Luigi; Peral, Ireneo
2010
Conformal metrics with constant $$Q$$-curvature. Zbl 1135.35304
Malchiodi, Andrea
2007
On the Leray-Schauder degree of the Toda system on compact surfaces. Zbl 1315.35086
Malchiodi, Andrea; Ruiz, David
2015
Adiabatic limits of closed orbits for some Newtonian systems in $$\mathbb{R}^n$$. Zbl 0988.37076
Malchiodi, Andrea
2001
A class of existence results for the singular Liouville equation. Zbl 1216.35067
Carlotto, Alessandro; Malchiodi, Andrea
2011
Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem. Zbl 1223.35035
Mahmoudi, Fethi; Malchiodi, Andrea
2006
Construction of multidimensional spike-layers. Zbl 1220.35050
Malchiodi, Andrea
2006
A fourth order uniformization theorem on some four manifolds with large total $$Q$$-curvature. Zbl 1076.53046
2005
Solutions, concentrating on spheres, to symmetric singularly perturbed problems. Zbl 1072.35068
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2002
Curvature theory of boundary phases: The two-dimensional case. Zbl 1029.49039
Braides, Andrea; Malchiodi, Andrea
2002
Scalar curvature under boundary conditions. Zbl 0969.58005
Ambrosetti, Antonio; Li, Yan Yan; Malchiodi, Andrea
2000
Multiple positive solutions of some elliptic equations in $$\mathbb{R}^N$$. Zbl 0965.35047
Malchiodi, Andrea
2001
Symmetry properties of some solutions to some semilinear elliptic equations. Zbl 1378.35134
Farina, Alberto; Malchiodi, Andrea; Rizzi, Matteo
2016
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II: Morse theory. Zbl 1380.35094
Ikoma, Norihisa; Malchiodi, Andrea; Mondino, Andrea
2017
Existence results for a super-Liouville equation on compact surfaces. Zbl 1456.58016
Jevnikar, Aleks; Malchiodi, Andrea; Wu, Ruijun
2020
Variational analysis of Toda systems. Zbl 1379.35089
Malchiodi, Andrea
2017
Variational methods for singular Liouville equations. Zbl 1206.35038
Malchiodi, Andrea
2010
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: minimization. Zbl 1378.35121
Ikoma, Norihisa; Malchiodi, Andrea; Mondino, Andrea
2017
Non-uniqueness results for critical metrics of regularized determinants in four dimensions. Zbl 1251.53059
Gursky, Matthew; Malchiodi, Andrea
2012
Prescribing Morse scalar curvatures: subcritical blowing-up solutions. Zbl 1432.53056
Malchiodi, Andrea; Mayer, Martin
2020
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1225.35213
Ambrosetti, Antonio; Felli, Veronica; Malchiodi, Andrea
2004
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve. Zbl 1135.35076
Mahmoudi, Fethi; Malchiodi, Andrea; Montenegro, Marcelo
2008
Minimal surfaces in three dimensional pseudo-Hermitian manifolds. Zbl 1144.53324
Malchiodi, Andrea
2007
New classes of entire solutions for semilinear elliptic problems in $$\mathbb R^{n}$$. Zbl 1187.35090
Malchiodi, Andrea
2010
Entire solutions of autonomous equations on $$\mathbb{R}^n$$ with nontrivial asymptotics. Zbl 1223.35071
Malchiodi, Andrea
2008
Concentration of solutions for some singularly perturbed Neumann problems. Zbl 1184.35024
Malchiodi, Andrea
2009
Some existence results for the scalar curvature problem via Morse theory. Zbl 1021.53022
Malchiodi, Andrea
1999
On conformal metrics with constant $$Q$$-curvature. Zbl 1438.53069
Malchiodi, Andrea
2019
On singular Liouville equations and systems. Zbl 1364.35010
Malchiodi, Andrea
2017
A variational approach to Liouville equations. Zbl 1367.35031
Malchiodi, Andrea
2017
Boundary layers of arbitrary dimension for a singularly perturbed Neumann problem. Zbl 1236.35006
Malchiodi, Andrea; Montenegro, Marcelo
2004
Concentrating solutions of some singularly perturbed elliptic equations. Zbl 1149.35311
Malchiodi, Andrea
2008
Construction of multidimensional spike-layers. Zbl 1182.35121
Malchiodi, Andrea
2005
Variational theory for Liouville equations with singularities. Zbl 1206.35037
Malchiodi, Andrea
2009
A note on the scalar curvature problem in the presence of symmetries. Zbl 1008.53038
Ambrosetti, Antonio; Li, Yan Yan; Malchiodi, Andrea
2000
Ground state Dirac bubbles and Killing spinors. Zbl 1464.53064
Borrelli, William; Malchiodi, Andrea; Wu, Ruijun
2021
Existence results for super-Liouville equations on the sphere via bifurcation theory. Zbl 07366232
Jevnikar, Aleks; Malchiodi, Andrea; Wu, Ruijun
2021
Ground state Dirac bubbles and Killing spinors. Zbl 1464.53064
Borrelli, William; Malchiodi, Andrea; Wu, Ruijun
2021
Existence results for super-Liouville equations on the sphere via bifurcation theory. Zbl 07366232
Jevnikar, Aleks; Malchiodi, Andrea; Wu, Ruijun
2021
Existence results for a super-Liouville equation on compact surfaces. Zbl 1456.58016
Jevnikar, Aleks; Malchiodi, Andrea; Wu, Ruijun
2020
Prescribing Morse scalar curvatures: subcritical blowing-up solutions. Zbl 1432.53056
Malchiodi, Andrea; Mayer, Martin
2020
On conformal metrics with constant $$Q$$-curvature. Zbl 1438.53069
Malchiodi, Andrea
2019
A positive mass theorem in three dimensional Cauchy-Riemann geometry. Zbl 1360.32031
Cheng, Jih-Hsin; Malchiodi, Andrea; Yang, Paul
2017
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II: Morse theory. Zbl 1380.35094
Ikoma, Norihisa; Malchiodi, Andrea; Mondino, Andrea
2017
Variational analysis of Toda systems. Zbl 1379.35089
Malchiodi, Andrea
2017
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: minimization. Zbl 1378.35121
Ikoma, Norihisa; Malchiodi, Andrea; Mondino, Andrea
2017
On singular Liouville equations and systems. Zbl 1364.35010
Malchiodi, Andrea
2017
A variational approach to Liouville equations. Zbl 1367.35031
Malchiodi, Andrea
2017
Existence and non-existence results for the $$SU(3)$$ singular Toda system on compact surfaces. Zbl 1338.35156
Battaglia, Luca; Malchiodi, Andrea
2016
Symmetry properties of some solutions to some semilinear elliptic equations. Zbl 1378.35134
Farina, Alberto; Malchiodi, Andrea; Rizzi, Matteo
2016
A general existence result for the Toda system on compact surfaces. Zbl 1327.35098
Battaglia, Luca; Jevnikar, Aleks; Malchiodi, Andrea; Ruiz, David
2015
A strong maximum principle for the Paneitz operator and a non-local flow for the $$\mathcal Q$$-curvature. Zbl 1330.35053
Gursky, Matthew J.; Malchiodi, Andrea
2015
A topological join construction and the Toda system on compact surfaces of arbitrary genus. Zbl 1336.35152
Jevnikar, Aleks; Kallel, Sadok; Malchiodi, Andrea
2015
On the Leray-Schauder degree of the Toda system on compact surfaces. Zbl 1315.35086
Malchiodi, Andrea; Ruiz, David
2015
Critical points of the Moser-Trudinger functional on a disk. Zbl 1304.49011
Malchiodi, Andrea; Martinazzi, Luca
2014
A Moser-Trudinger inequality for the singular Toda system. Zbl 1295.35372
Battaglia, Luca; Malchiodi, Andrea
2014
A variational analysis of the Toda system on compact surfaces. Zbl 1275.35095
Malchiodi, Andrea; Ruiz, David
2013
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations. Zbl 1276.58005
Bartolucci, Daniele; Malchiodi, Andrea
2013
Weighted barycentric sets and singular Liouville equations on compact surfaces. Zbl 1232.53035
Carlotto, Alessandro; Malchiodi, Andrea
2012
A Codazzi-like equation and the singular set for $$C^1$$ smooth surfaces in the Heisenberg group. Zbl 1255.53026
Cheng, Jih-Hsin; Hwang, Jenn-Fang; Malchiodi, Andrea; Yang, Paul
2012
Non-uniqueness results for critical metrics of regularized determinants in four dimensions. Zbl 1251.53059
Gursky, Matthew; Malchiodi, Andrea
2012
Supercritical conformal metrics on surfaces with conical singularities. Zbl 1254.30066
Bartolucci, Daniele; De Marchis, Francesca; Malchiodi, Andrea
2011
New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces. Zbl 1235.35094
Malchiodi, Andrea; Ruiz, David
2011
Axial symmetry of some steady state solutions to nonlinear Schrödinger equations. Zbl 1211.35115
Gui, Changfeng; Malchiodi, Andrea; Xu, Haoyuan
2011
A class of existence results for the singular Liouville equation. Zbl 1216.35067
Carlotto, Alessandro; Malchiodi, Andrea
2011
Concentration of solutions for some singularly perturbed mixed problems: asymptotics of minimal energy solutions. Zbl 1194.35037
Azorero, Jesus Garcia; Malchiodi, Andrea; Montoro, Luigi; Peral, Ireneo
2010
Concentration of solutions for some singularly perturbed mixed problems: existence results. Zbl 1214.35024
Azorero, Jesus Garcia; Malchiodi, Andrea; Montoro, Luigi; Peral, Ireneo
2010
Variational methods for singular Liouville equations. Zbl 1206.35038
Malchiodi, Andrea
2010
New classes of entire solutions for semilinear elliptic problems in $$\mathbb R^{n}$$. Zbl 1187.35090
Malchiodi, Andrea
2010
Some new entire solutions of semilinear elliptic equations on $$\mathbb R^n$$. Zbl 1178.35186
Malchiodi, Andrea
2009
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve. Zbl 1180.35485
Mahmoudi, Fethi; Montenegro, Marcelo; Malchiodi, Andrea
2009
Concentration of solutions for some singularly perturbed Neumann problems. Zbl 1184.35024
Malchiodi, Andrea
2009
Variational theory for Liouville equations with singularities. Zbl 1206.35037
Malchiodi, Andrea
2009
Existence of conformal metrics with constant $$Q$$-curvature. Zbl 1186.53050
2008
Morse theory and a scalar field equation on compact surfaces. Zbl 1175.53052
Malchiodi, Andrea
2008
Topological methods for an elliptic equation with exponential nonlinearities. Zbl 1144.35372
Malchiodi, Andrea
2008
Transition layer for the heterogeneous Allen-Cahn equation. Zbl 1148.35030
Mahmoudi, Fethi; Malchiodi, Andrea; Wei, Juncheng
2008
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve. Zbl 1135.35076
Mahmoudi, Fethi; Malchiodi, Andrea; Montenegro, Marcelo
2008
Entire solutions of autonomous equations on $$\mathbb{R}^n$$ with nontrivial asymptotics. Zbl 1223.35071
Malchiodi, Andrea
2008
Concentrating solutions of some singularly perturbed elliptic equations. Zbl 1149.35311
Malchiodi, Andrea
2008
Nonlinear analysis and semilinear elliptic problems. Zbl 1125.47052
Ambrosetti, Antonio; Malchiodi, Andrea
2007
Concentration on minimal submanifolds for a singularly perturbed Neumann problem. Zbl 1160.35011
Mahmoudi, Fethi; Malchiodi, Andrea
2007
Some existence results for the Toda system on closed surfaces. Zbl 1148.35021
Malchiodi, Andrea; Ndiaye, Cheikh Birahim
2007
Concentration phenomena for nonlinear Schrödinger equations: recent results and new perspectives. Zbl 1200.35106
Ambrosetti, Antonio; Malchiodi, Andrea
2007
Boundary interface for the Allen-Cahn equation. Zbl 1144.35326
Malchiodi, A.; Wei, Jungcheng
2007
Boundary-clustered interfaces for the Allen-Cahn equation. Zbl 1221.35150
Malchiodi, Andrea; Ni, Wei-Ming; Wei, Juncheng
2007
Conformal metrics with constant $$Q$$-curvature. Zbl 1135.35304
Malchiodi, Andrea
2007
Minimal surfaces in three dimensional pseudo-Hermitian manifolds. Zbl 1144.53324
Malchiodi, Andrea
2007
Perturbation methods and semilinear elliptic problems on $$\mathbb R^n$$. Zbl 1115.35004
Ambrosetti, Antonio; Malchiodi, Andrea
2006
Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1142.35082
Ambrosetti, A.; Malchiodi, A.; Ruiz, D.
2006
$$Q$$-curvature flow on $$S^4$$. Zbl 1099.53034
Malchiodi, Andrea; Struwe, Michael
2006
Compactness of solutions to some geometric fourth-order equations. Zbl 1098.53032
Malchiodi, Andrea
2006
Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem. Zbl 1223.35035
Mahmoudi, Fethi; Malchiodi, Andrea
2006
Construction of multidimensional spike-layers. Zbl 1220.35050
Malchiodi, Andrea
2006
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1064.35175
Ambrosetti, Antonio; Felli, Veronica; Malchiodi, Andrea
2005
Minimal surfaces in pseudohermitian geometry. Zbl 1158.53306
Hwang, Jenn-Fang; Cheng, Jih-Hsin; Malchiodi, Andrea; Yang, Paul
2005
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains. Zbl 1087.35010
Malchiodi, A.
2005
Multiple clustered layer solutions for semilinear Neumann problems on a ball. Zbl 1207.35141
Malchiodi, A.; Ni, Wei-Ming; Wei, Juncheng
2005
Asymptotic Morse theory for the equation $$\Delta v- 2v_x\wedge v_y$$. Zbl 1175.35049
Chanillo, Sagun; Malchiodi, Andrea
2005
A fourth order uniformization theorem on some four manifolds with large total $$Q$$-curvature. Zbl 1076.53046
2005
Construction of multidimensional spike-layers. Zbl 1182.35121
Malchiodi, Andrea
2005
Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. II. Zbl 1081.35008
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2004
Multidimensional boundary layers for a singularly perturbed Neumann problem. Zbl 1065.35037
Malchiodi, Andrea; Montenegro, Marcelo
2004
The prescribed boundary mean curvature problem on $$\mathbb B^4$$. Zbl 1108.35070
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2004
Solutions concentrating at curves for some singularly perturbed elliptic problems. Zbl 1081.35044
Malchiodi, Andrea
2004
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. Zbl 1225.35213
Ambrosetti, Antonio; Felli, Veronica; Malchiodi, Andrea
2004
Boundary layers of arbitrary dimension for a singularly perturbed Neumann problem. Zbl 1236.35006
Malchiodi, Andrea; Montenegro, Marcelo
2004
Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I. Zbl 1072.35019
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2003
Prescribing scalar and boundary mean curvature on the three dimensional half sphere. Zbl 1092.53028
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2003
Boundary concentration phenomena for a singularly perturbed elliptic problem. Zbl 1124.35305
Malchiodi, Andrea; Montenegro, Marcelo
2002
Prescribing a fourth order conformal invariant on the standard sphere. II. Blow up analysis and applications. Zbl 1150.53012
Malchiodi, Andrea; Djadli, Zindine; Ould Ahmedou, Mohameden
2002
A perturbation result for the Webster scalar curvature problem on the CR sphere. Zbl 1042.53025
Malchiodi, Andrea; Uguzzoni, Francesco
2002
Prescribing a fourth order conformal invariant on the standard sphere. I: A perturbation result. Zbl 1023.58020
Djadli, Zindine; Malchiodi, Andrea; Ahmedou, Mohameden Ould
2002
On the Yamabe problem and the scalar curvature problems under boundary conditions. Zbl 1005.53034
Ambrosetti, Antonio; Li, YanYan; Malchiodi, Andrea
2002
Some remarks on the equation $$-\Delta u=\lambda(1+u)^p$$ for varying $$\lambda,p$$ and varying domains. Zbl 1010.35042
Gazzola, Filippo; Malchiodi, Andrea
2002
The scalar curvature problem on $$S^n$$: An approach via Morse theory. Zbl 1012.53035
Malchiodi, Andrea
2002
Singular elliptic problems with critical growth. Zbl 1072.35527
Caldiroli, Paolo; Malchiodi, Andrea
2002
Solutions, concentrating on spheres, to symmetric singularly perturbed problems. Zbl 1072.35068
Ambrosetti, Antonio; Malchiodi, Andrea; Ni, Wei-Ming
2002
Curvature theory of boundary phases: The two-dimensional case. Zbl 1029.49039
Braides, Andrea; Malchiodi, Andrea
2002
Multiplicity results for some nonlinear Schrödinger equations with potentials. Zbl 1040.35107
Ambrosetti, A.; Malchiodi, A.; Secchi, S.
2001
Non-compactness and multiplicity results for the Yamabe problem on $$S^n$$. Zbl 0979.53038
Berti, Massimiliano; Malchiodi, Andrea
2001
On the symmetric scalar curvature problem on $$S^n$$. Zbl 1006.35044
Ambrosetti, Antonio; Malchiodi, Andrea
2001
Adiabatic limits of closed orbits for some Newtonian systems in $$\mathbb{R}^n$$. Zbl 0988.37076
Malchiodi, Andrea
2001
Multiple positive solutions of some elliptic equations in $$\mathbb{R}^N$$. Zbl 0965.35047
Malchiodi, Andrea
2001
Scalar curvature under boundary conditions. Zbl 0969.58005
Ambrosetti, Antonio; Li, Yan Yan; Malchiodi, Andrea
2000
A note on the scalar curvature problem in the presence of symmetries. Zbl 1008.53038
Ambrosetti, Antonio; Li, Yan Yan; Malchiodi, Andrea
2000
A multiplicity result for the Yamabe problem on $$S^n$$. Zbl 0949.53028
Ambrosetti, Antonio; Malchiodi, Andrea
1999
Some existence results for the scalar curvature problem via Morse theory. Zbl 1021.53022
Malchiodi, Andrea
1999
all top 5
#### Cited by 1,006 Authors
65 Wei, Juncheng 46 Malchiodi, Andrea 20 Bartolucci, Daniele 20 Chtioui, Hichem 19 Lin, Chang-Shou 19 Pistoia, Angela 17 Jevnikar, Aleks 17 Yang, Wen 16 Bonheure, Denis 15 Ho, Pak Tung 15 Musso, Monica 15 Ould Ahmedou, Mohameden 15 Tang, Zhongwei 15 Yang, Minbo 13 Figueiredo, Giovany Malcher 13 Mahmoudi, Fethi 13 Peng, Shuangjie 13 Yang, Paul C. P. 12 Alves, Claudianor Oliveira 12 Ao, Weiwei 12 D’Aprile, Teresa 12 Del Pino, Manuel A. 11 Battaglia, Luca 11 Byeon, Jaeyoung 11 Ding, Yanheng 11 Wang, Zhi-Qiang 11 Yan, Shusen 11 Zhang, Jihui 10 Abdelhedi, Wael 10 Lee, Youngae 10 Li, YanYan 10 Liang, Sihua 10 Secchi, Simone 10 Van Schaftingen, Jean 10 Zou, Wenming 9 Ben Ayed, Mohamed 9 Chen, Haibo 9 Gover, Ashwin Rod 9 Martinazzi, Luca 9 Miyagaki, Olimpio Hiroshi 9 Ritoré, Manuel 9 Wang, Liping 9 Yang, Yunyan 8 Albuquerque, Francisco S. B. Albuquerque 8 Cao, Daomin 8 Cheng, Jih-Hsin 8 Chiu, Hung-Lin 8 de Marchis, Francesca 8 Do Ó, João M. Bezerra 8 Gamara, Najoua 8 He, Xiaoming 8 Kowalczyk, Michał 8 Lu, Guozhen 8 Rosales, César 8 Santra, Sanjiban 8 Wang, Jun 8 Xu, Xingwang 8 Zhang, Lei 7 Castéras, Jean-baptiste 7 Chen, Xuezhang 7 Cingolani, Silvia 7 El Mehdi, Khalil O. 7 Gui, Changfeng 7 Maalaoui, Ali 7 Mercuri, Carlo 7 Ruiz, David 7 Servadei, Raffaella 7 Tanaka, Kazunaga 7 Vaira, Giusi 7 Zhao, Chunyi 6 Ambrosetti, Antonio 6 Caldiroli, Paolo 6 Citti, Giovanna 6 Clapp, Mónica 6 Esposito, Pierpaolo 6 Gladiali, Francesca 6 Guo, Yuxia 6 Ianni, Isabella 6 Jeanjean, Louis 6 Jiao, Yujuan 6 Leung, Man Chun 6 Li, Gongbao 6 Musina, Roberta 6 Ndiaye, Cheikh Birahim 6 Pacard, Frank 6 Rădulescu, Vicenţiu D. 6 Sourdis, Christos 6 Squassina, Marco 6 Srikanth, P. N. 6 Struwe, Michael 6 Wei, Suting 6 Yacoub, Ridha 6 Zhu, Maochun 5 Badiale, Marino 5 Djadli, Zindine 5 Felli, Veronica 5 Ghimenti, Marco G. 5 Guida, Michela 5 Hurtado, Ana 5 Hyder, Ali ...and 906 more Authors
all top 5
#### Cited in 176 Serials
118 Journal of Differential Equations 118 Calculus of Variations and Partial Differential Equations 59 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 55 Journal of Functional Analysis 52 Journal of Mathematical Analysis and Applications 35 Discrete and Continuous Dynamical Systems 30 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 29 Advances in Mathematics 26 Communications in Contemporary Mathematics 24 Advanced Nonlinear Studies 23 Communications on Pure and Applied Analysis 22 Journal of Mathematical Physics 18 Communications in Partial Differential Equations 18 Journal of the European Mathematical Society (JEMS) 17 Mathematische Annalen 16 Archive for Rational Mechanics and Analysis 16 The Journal of Geometric Analysis 16 NoDEA. Nonlinear Differential Equations and Applications 16 Comptes Rendus. Mathématique. Académie des Sciences, Paris 14 Annali di Matematica Pura ed Applicata. Serie Quarta 14 Transactions of the American Mathematical Society 13 Journal de Mathématiques Pures et Appliquées. Neuvième Série 13 Complex Variables and Elliptic Equations 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 Proceedings of the American Mathematical Society 12 Boundary Value Problems 11 Applicable Analysis 11 Manuscripta Mathematica 11 Applied Mathematics Letters 11 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 10 Communications on Pure and Applied Mathematics 10 Annals of Global Analysis and Geometry 9 Mathematische Zeitschrift 9 Revista Matemática Iberoamericana 8 Differential Geometry and its Applications 8 Topological Methods in Nonlinear Analysis 8 Milan Journal of Mathematics 8 Journal of Fixed Point Theory and Applications 8 Science China. Mathematics 7 Communications in Mathematical Physics 7 Mathematical Methods in the Applied Sciences 7 Applied Mathematics and Computation 7 Mathematische Nachrichten 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Advances in Nonlinear Analysis 6 Journal of Geometry and Physics 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Bulletin des Sciences Mathématiques 6 Acta Mathematica Sinica. English Series 5 Journal d’Analyse Mathématique 5 Duke Mathematical Journal 5 Pacific Journal of Mathematics 5 Chinese Annals of Mathematics. Series B 5 SIAM Journal on Mathematical Analysis 5 Abstract and Applied Analysis 5 Nonlinear Analysis. Real World Applications 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Annales de l’Institut Fourier 4 Indiana University Mathematics Journal 4 Journal für die Reine und Angewandte Mathematik 4 Acta Applicandae Mathematicae 4 Geometric and Functional Analysis. GAFA 4 Differential Equations 4 Mediterranean Journal of Mathematics 4 Advances in Calculus of Variations 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Nonlinearity 3 Archiv der Mathematik 3 Illinois Journal of Mathematics 3 Inventiones Mathematicae 3 Memoirs of the American Mathematical Society 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 International Journal of Mathematics 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal of Dynamics and Differential Equations 3 Taiwanese Journal of Mathematics 3 Journal of Inequalities and Applications 3 Frontiers of Mathematics in China 3 Discrete and Continuous Dynamical Systems. Series S 3 Arabian Journal of Mathematics 2 Computers & Mathematics with Applications 2 Rocky Mountain Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Reviews in Mathematical Physics 2 Journal of the Korean Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Quarterly of Applied Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Zeitschrift für Analysis und ihre Anwendungen 2 Asymptotic Analysis 2 SIAM Journal on Applied Mathematics 2 Opuscula Mathematica 2 Vietnam Journal of Mathematics 2 Journal of Dynamical and Control Systems 2 Annales Henri Poincaré 2 Discrete and Continuous Dynamical Systems. Series B 2 Advances in Difference Equations 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 2 Bulletin of Mathematical Sciences 2 Analysis and Geometry in Metric Spaces ...and 76 more Serials
all top 5
#### Cited in 42 Fields
1,008 Partial differential equations (35-XX) 292 Differential geometry (53-XX) 225 Global analysis, analysis on manifolds (58-XX) 77 Calculus of variations and optimal control; optimization (49-XX) 51 Quantum theory (81-XX) 47 Several complex variables and analytic spaces (32-XX) 47 Functional analysis (46-XX) 42 Operator theory (47-XX) 36 Ordinary differential equations (34-XX) 24 Dynamical systems and ergodic theory (37-XX) 17 Integral equations (45-XX) 17 Biology and other natural sciences (92-XX) 16 Functions of a complex variable (30-XX) 15 Real functions (26-XX) 15 Fluid mechanics (76-XX) 14 Statistical mechanics, structure of matter (82-XX) 11 Optics, electromagnetic theory (78-XX) 8 Numerical analysis (65-XX) 7 Potential theory (31-XX) 7 Mechanics of deformable solids (74-XX) 6 Topological groups, Lie groups (22-XX) 6 Manifolds and cell complexes (57-XX) 6 Mechanics of particles and systems (70-XX) 6 Relativity and gravitational theory (83-XX) 5 Abstract harmonic analysis (43-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Algebraic topology (55-XX) 3 Probability theory and stochastic processes (60-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-12-01T12:22:43 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S044ETP
|
# AVERAGE PARTICLE MULTIPLICITIES IN HADRONIC ${{\boldsymbol Z}}$ DECAY
Summed over particle and antiparticle, when appropriate.
# $\langle{}\boldsymbol N_{{{\boldsymbol \eta}^{\,'}}}\rangle{}$ INSPIRE search
VALUE DOCUMENT ID TECN COMMENT
$\bf{ 0.17 \pm0.05}$ OUR AVERAGE Error includes scale factor of 2.4.
$0.14$ $\pm0.01$ $\pm0.02$
1998 A
OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
$0.25$ $\pm0.04$ 1
1997 D
L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.068$ $\pm0.018$ $\pm0.016$ 2
1992 D
ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
1 ACCIARRI 1997D obtain this value averaging over the two decay channels ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \rho}^{0}}{{\mathit \gamma}}$ .
2 BUSKULIC 1992D obtain this value for $\mathit x>0.1$.
References:
ACKERSTAFF 1998A
EPJ C5 411 Photon and Light Meson Production in Hadronic ${{\mathit Z}^{0}}$ Decays
ACCIARRI 1997D
PL B393 465 Measurement of Inclusive ${{\mathit \omega}}$ and ${{\mathit \eta}^{\,'}}$ Production in Hadronic ${{\mathit Z}}$ Decays
BUSKULIC 1992D
PL B292 210 Measurement of the Production Rates of ${{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ in Hadronic ${{\mathit Z}^{0}}$ Decays
| 2019-03-19T16:57:05 |
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|
http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd132.htm
|
4. Process Modeling
4.1. Introduction to Process Modeling
4.1.3. What are process models used for?
## Prediction
More on Prediction As mentioned earlier, the goal of prediction is to determine future value(s) of the response variable that are associated with a specific combination of predictor variable values. As in estimation, the predicted values are computed by plugging the value(s) of the predictor variable(s) into the regression equation, after estimating the unknown parameters from the data. The difference between estimation and prediction arises only in the computation of the uncertainties. These differences are illustrated below using the Pressure/Temperature example in parallel with the example illustrating estimation.
Example Suppose in this case the predictor variable value of interest is a temperature of 47 degrees. Computing the predicted value using the equation $$\hat{P} = 7.749695 + 3.930123T$$ yields a predicted pressure of 192.4655.
Of course, if the pressure/temperature experiment were repeated, the estimates of the parameters of the regression function obtained from the data would differ slightly each time because of the randomness in the data and the need to sample a limited amount of data. Different parameter estimates would, in turn, yield different predicted values. The plot below illustrates the type of slight variation that could occur in a repeated experiment.
Predicted Value from a Repeated Experiment
Prediction Uncertainty A critical part of prediction is an assessment of how much a predicted value will fluctuate due to the noise in the data. Without that information there is no basis for comparing a predicted value to a target value or to another prediction. As a result, any method used for prediction should include an assessment of the uncertainty in the predicted value(s). Fortunately it is often the case that the data used to fit the model to a process can also be used to compute the uncertainty of predictions from the model. In the pressure/temperature example a prediction interval for the value of the regresion function at 47 degrees can be computed from the data used to fit the model. The plot below shows a 99 % prediction interval produced using the original data. This interval gives the range of plausible values for a single future pressure measurement observed at a temperature of 47 degrees based on the parameter estimates and the noise in the data.
99 % Prediction Interval for Pressure at T=47
Length of Prediction Intervals Because the prediction interval is an interval for the value of a single new measurement from the process, the uncertainty includes the noise that is inherent in the estimates of the regression parameters and the uncertainty of the new measurement. This means that the interval for a new measurement will be wider than the confidence interval for the value of the regression function. These intervals are called prediction intervals rather than confidence intervals because the latter are for parameters, and a new measurement is a random variable, not a parameter.
Tolerance Intervals Like a prediction interval, a tolerance interval brackets the plausible values of new measurements from the process being modeled. However, instead of bracketing the value of a single measurement or a fixed number of measurements, a tolerance interval brackets a specified percentage of all future measurements for a given set of predictor variable values. For example, to monitor future pressure measurements at 47 degrees for extreme values, either low or high, a tolerance interval that brackets 98 % of all future measurements with high confidence could be used. If a future value then fell outside of the interval, the system would then be checked to ensure that everything was working correctly. A 99 % tolerance interval that captures 98 % of all future pressure measurements at a temperature of 47 degrees is 192.4655 $$\pm$$ 14.5810. This interval is wider than the prediction interval for a single measurement because it is designed to capture a larger proportion of all future measurements. The explanation of tolerance intervals is potentially confusing because there are two percentages used in the description of the interval. One, in this case 99 %, describes how confident we are that the interval will capture the quantity that we want it to capture. The other, 98 %, describes what the target quantity is, which in this case that is 98% of all future measurements at T=47 degrees.
| 2017-10-20T14:31:15 |
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|
https://linkeddata.tern.org.au/viewer/tern/id/http:/linked.data.gov.au/def/tern-cv/3eab0df3-4995-45e0-9674-331e67d77194
|
URI: http://linked.data.gov.au/def/tern-cv/3eab0df3-4995-45e0-9674-331e67d77194
Date created: 2020-07-09
Date modified: 2020-07-09
##### Definition
Grade of pedality is the degree of development and distinctness of peds. In virtually all material that has structure, the surface of individual peds will differ in some way from the interior of peds. The degree of development expresses the relative difference between the strength of cohesion within peds and the strength of adhesion between adjacent peds. Determination of grade of structure in the field depends on the proportion of peds that hold together as entire peds when displaced and also on the ease with which the soil separates into discrete peds. Grade of pedality varies with the soil water status. It is important to record the soil water status of the described profile, and it is desirable that the grade of pedality be described at the soil water status most common for the horizon.
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| 2022-07-04T12:38:49 |
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https://par.nsf.gov/biblio/10225109-dealer-end-end-model-marketplace-differential-privacy
|
Dealer: an end-to-end model marketplace with differential privacy
Data-driven machine learning has become ubiquitous. A marketplace for machine learning models connects data owners and model buyers, and can dramatically facilitate data-driven machine learning applications. In this paper, we take a formal data marketplace perspective and propose the first en D -to-end mod e l m a rketp l ace with diff e rential p r ivacy ( Dealer ) towards answering the following questions: How to formulate data owners' compensation functions and model buyers' price functions? How can the broker determine prices for a set of models to maximize the revenue with arbitrage-free guarantee, and train a set of models with maximum Shapley coverage given a manufacturing budget to remain competitive ? For the former, we propose compensation function for each data owner based on Shapley value and privacy sensitivity, and price function for each model buyer based on Shapley coverage sensitivity and noise sensitivity. Both privacy sensitivity and noise sensitivity are measured by the level of differential privacy. For the latter, we formulate two optimization problems for model pricing and model training, and propose efficient dynamic programming algorithms. Experiment results on the real chess dataset and synthetic datasets justify the design of Dealer and verify the efficiency more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10225109
Journal Name:
Proceedings of the VLDB Endowment
Volume:
14
Issue:
6
Page Range or eLocation-ID:
957 to 969
ISSN:
2150-8097
2. We develop a new nonparametric approach for discrete choice and use it to analyze the demand for health insurance in the California Affordable Care Act marketplace. The model allows for endogenous prices and instrumental variables, while avoiding parametric functional form assumptions about the unobserved components of utility. We use the approach to estimate bounds on the effects of changing premiums or subsidies on coverage choices, consumer surplus, and government spending on subsidies. We find that a $10 decrease in monthly premium subsidies would cause a decline of between 1.8% and 6.7% in the proportion of subsidized adults with coverage. The reduction in total annual consumer surplus would be between$62 and $74 million, while the savings in yearly subsidy outlays would be between$207 and \$602 million. We estimate the demand impacts of linking subsidies to age, finding that shifting subsidies from older to younger buyers would increase average consumer surplus, with potentially large impacts on enrollment. We also estimate the consumer surplus impact of removing the highly‐subsidized plans in the Silver metal tier, where we find that a nonparametric model is consistent with a wide range of possibilities. We find that comparable mixed logit models tend to yield pricemore »
| 2023-03-25T17:07:57 |
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|
https://www.khronos.org/registry/vulkan/specs/1.2-extensions/man/html/VkCommandPool.html
|
## C Specification
Command pools are opaque objects that command buffer memory is allocated from, and which allow the implementation to amortize the cost of resource creation across multiple command buffers. Command pools are externally synchronized, meaning that a command pool must not be used concurrently in multiple threads. That includes use via recording commands on any command buffers allocated from the pool, as well as operations that allocate, free, and reset command buffers or the pool itself.
Command pools are represented by VkCommandPool handles:
// Provided by VK_VERSION_1_0
VK_DEFINE_NON_DISPATCHABLE_HANDLE(VkCommandPool)
## Document Notes
For more information, see the Vulkan Specification
This page is extracted from the Vulkan Specification. Fixes and changes should be made to the Specification, not directly.
Copyright (c) 2014-2020 The Khronos Group Inc.
SPDX-License-Identifier: CC-BY-4.0
| 2020-07-08T02:55:06 |
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|
https://supernova.lbl.gov/~evlinder/umass/neu.html
|
## Massive Neutrinos
In June 1998 an experimental group working at SuperKamiokande in Japan released evidence for neutrino oscillations and hence that at least one species of neutrino has mass. Here is a very basic description of the effect and its significance.
What was detected?
They detected an asymmetry in the neutrino signal in the detector arriving from above the detector (downward going) and from below (upward going). The counts arise from neutrinos produced in Earth's atmosphere from cosmic ray events and are not related to solar neutrinos produced by thermonuclear reactions in the Sun. The origins of the neutrinos are thus in the Earth's atmosphere above the detector and on the far side of the Earth respectively; thus they have different path lengths to travel.
How is this interpreted?
While the electron neutrinos did not show the asymmetry, the muon neutrinos did. The detector is not sensitive to tau neutrinos or (by definition) sterile neutrinos. The interpretation is that some muon neutrinos oscillated or changed species to an undetected sort (tau or sterile) neutrino. These oscillations are expected to be dependent on path length and on neutrino mass.
The oscillations are called vacuum oscillations because they occur due to the internal properties of the neutrinos and not the environment through which they propagate. The cross section for neutrinos to interact with matter is so low that to them passing through the Earth is like passing through vacuum. On the other hand, the solution to the solar neutrino puzzle is thought to be matter dependent MSW oscillations (see below).
Why oscillations?
When we detect particles what we are doing in a quantum mechanical sense is hitting them with some operator, e.g. some Hamiltonian applied to their wave function. The detected properties or normal modes depend on what sort of operator, i.e. what we are measuring. When we talk about neutrino species, we are talking about their flavor eigenstates, those of the weak interaction Hamiltonian. Here the normal modes (eigenstates) are electron neutrino, muon neutrino, tau neutrino, etc. However, it is possible that when we ask their mass (hit the wave functions with the free Hamiltonian) that we obtain different eigenstates - the flavor states are superpositions of the mass eigenstates. This is only possible if the masses of the species are different, i.e. they cannot all have zero mass. It then opens up the possibility of oscillation between flavor states - a given mass state is partly one species and partly another and so the species can change with time or oscillate.
Mass and path length dependence of oscillations
We know how this change with time proceeds: Heisenberg taught us that wave functions evolve as \psi \sim \exp {(i/\hbar)\Delta E t}. Even if they have masses these are small compared to their energies, so the neutrinos move nearly at the speed of light and the time t and path length L are related by t = L/c. To find the wavelength of the oscillation we ask when the phase difference adds up to 2\pi: \Delta\phi = L \Delta E = L (\Delta m2 / 2E) where we have used that E2 = m2 + p2. One finds that the wavelength is Losc = 4\pi E/\Delta m2 = 800 (E/GeV) (\Delta m2 / 10-3eV2)-1 km.
One can measure the energy of the neutrinos received and one knows the path length difference of those arising from the near and the far side of the Earth, so one can relate the different proportions of muon neutrinos received upward going and downward going to the mass difference \Delta m. The SuperKamiokande results point to \Delta m = 0.07 eV. But they cannot detect what the muon neutrinos oscillate into, so they don't know if these are tau neutrinos or a new species of sterile neutrinos (they do know they are not electron neutrinos).
How is this different from the solar neutrino puzzle?
Just about completely. These are neutrinos produced in the Earth's atmosphere with energies of order GeV and undergo vacuum oscillations. The solar neutrinos are produced in the Sun's core with energies of order MeV and are thought to undergo MSW oscillations. These oscillations, also called matter resonant oscillations, involve interactions of electron neutrinos (not the muon neutrinos of SuperKamiokande) with the electrons in the solar matter. These interactions give the neutrinos an effective mass and can cause species oscillations to be resonantly enhanced for certain values of the electron density. MSW solutions tend to give \Delta m = 0.002 eV between electron neutrinos and another species, possibly muon neutrinos. It is possible that MSW oscillations turn electron neutrinos into muon neutrinos and vacuum oscillations are turning muon neutrinos into tau neutrinos. Many experiments are underway to understand exactly which oscillations are occuring, and what they imply for all the neutrino masses.
What impact does this have cosmologically?
The Cowsik-McClelland bound implies that the cosmological energy density of an equilibrium species of massive neutrino is \Omega = (M / 92 eV). All the oscillations results give is the mass difference between species so we do not know from these if the two masses are 1 eV and 1.07 eV or 30 eV and 30.07 eV, say. There are bounds on the masses, however, from other laboratory experiments, particle physics theory, and astrophysical observations, making it unlikely that neutrinos are large enough to give critical energy density though possibly enough to be an appreciable (\Omega = 0.3) component, in the form of hot dark matter.
| 2022-08-10T07:34:24 |
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|
https://zbmath.org/authors/cochran.william-gemmell
|
## Cochran, William Gemmell
Compute Distance To:
Author ID: cochran.william-gemmell Published as: Cochran, W. G.; Cochran, William G.; Cochran, W.; Cochran, Williams G.; Kochran, William G.; Cochran, William more...less External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 69 Publications since 1934, including 9 Books 3 Further Contributions Biographic References: 6 Publications Co-Authors: 24 Co-Authors with 18 Joint Publications 410 Co-Co-Authors
all top 5
### Co-Authors
52 single-authored 2 Bliss, Chester I. 2 Cox, Gertrude Mary 2 Hansen, Morris Howard 2 Hartley, Hermann Otto 2 Kempthorne, Oscar 2 Owen, Donald B. 2 Rao, Jonnagadda Nalini Kanth 2 Rubin, Donald Bruce 2 Tukey, John Wilder 1 Alexander, Philipp 1 Antoniak, Charles E. 1 Bakkestrøm, Eskild 1 Bartlett, Maurice Stevenson 1 Box, George Edward Pelham 1 Brillinger, David R. 1 Bryant, Edward C. 1 Chernoff, Herman 1 Christiansen, Karl O. 1 Cochran, R. S. 1 Crick, F. H. C. 1 D’Agostino, Ralph B. jun. 1 Darling, Donald A. 1 David, Herbert Aron 1 Dinkel, John J. 1 Doksum, Kjell A. 1 Doob, Joseph Leonard 1 Douglas, Andrew S. 1 Downs, B. W. 1 Dyer, H. B. 1 Efron, Bradley 1 Ferguson, Thomas S. 1 Fiedler, Robert 1 Gentle, James E. 1 Goodenough, Donald R. 1 Guoy, Damrong 1 Haas, Roy W. 1 Hackney, O. P. 1 Harshbarger, Boyd 1 Hemmerle, William J. 1 Hill, Jennifer L. 1 Hirschhorn, Kurt 1 Hocking, R. N. 1 Holland, Paul W. 1 Hopkins, Carl E. 1 Jiao, Xiangmin 1 John, Peter W. M. 1 Kaplan, Jack S. 1 Kiefer, Jack Carl 1 Kshirsagar, Anant M. 1 Kuo, Hui-Hsiung 1 Lipson, Henry 1 Lundsteen, Claes 1 Machover Reinisch, June 1 Madow, William G. 1 Mantel, Nathan 1 McIntosh, Martin W. 1 Mednick, Sarnoff A. 1 Moore, David S. 1 Mortensen, Erik Lykke 1 Mosteller, Frederick 1 Neyman, Jerzy 1 Owen, David Roger Jones 1 Pfaffenberger, Roger C. 1 Philip, John R. 1 Puri, Prem S. 1 Rao, Poduri S. R. S. 1 Rigby, Fred D. 1 Rosenbaum, Paul Richard 1 Sampford, Michael Robert 1 Sanders, Stephanie A. 1 Schulsinger, Fini 1 Scott, Elizabeth L. 1 Searle, Shayle Robert 1 Sengupta, Ambar N. 1 Shaffer, Eric 1 Shu, V. S. 1 Smith, William Boyce 1 Snedecor, George Waddel 1 Sonvico, V. 1 Stocking, Martha L. 1 Suriyamongkol, Pornput 1 Tepping, Benjamin J. 1 Thomas, Neal 1 Tiao, George C. 1 Traxler, Robert H. 1 Vand, V. 1 Williams, W. H. 1 Wilmarth, Terry 1 Witkin, Herman A.
all top 5
### Serials
8 Annals of Mathematical Statistics 7 Journal of the American Statistical Association 5 Supplement to the Journal of the Royal Statistical Society 5 Acta Crystallographica 4 Biometrics 3 Proceedings of the Cambridge Philosophical Society 2 Biometrika 2 Sankhyā. Series A. Methods and Techniques 2 Technometrics 2 Bulletin de l’Institut International de Statistique 2 Journal of the Royal Statistical Society 2 Annals of Eugenics 1 Annals of the Institute of Statistical Mathematics 1 Journal of the Royal Statistical Society. Series B 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Statistics: Textbooks and Monographs 1 Trabajos de Estadística 1 Wiley Series in Probability and Mathematical Statistics
all top 5
### Fields
15 Statistics (62-XX) 2 History and biography (01-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Functional analysis (46-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX)
### Citations contained in zbMATH Open
54 Publications have been cited 1,755 times in 1,646 Documents Cited by Year
Sampling techniques. 3rd ed. Zbl 0353.62011
Cochran, William G.
1977
Sampling techniques. Zbl 0051.10707
Cochran, W. G.
1953
Some methods for strengthening the common $$\chi^2$$ tests. Zbl 0059.12803
Cochran, William G.
1954
Statistical methods. 8th ed. Zbl 0727.62003
Snedecor, George W.; Cochran, William G.
1989
Experimental designs. 2nd ed. Zbl 0077.13205
Cochran, William G.; Cox, Gertrude M.
1957
The flow due to a rotating disc. JFM 60.0729.08
Cochran, W. G.
1934
The $$\chi^ 2$$-test of goodness of fit. Zbl 0047.13105
Cochran, William G.
1952
Errors of measurement in statistics. Zbl 0177.46503
Cochran, W. G.
1968
The combination of estimates from different experiments. Zbl 0059.12505
Kochran, William G.
1954
On a simple procedure of unequal probability sampling without replacement. Zbl 0112.10901
Rao, J. N. K.; Hartley, H. O.; Cochran, W. G.
1962
Controlling bias in observational studies: a review. Zbl 0291.62012
Cochran, William G.; Rubin, Donald B.
1973
Relative accuracy of systematic and stratified random samples for a certain class of populations. Zbl 0063.00940
Cochran, W. G.
1946
The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. Zbl 0009.12004
Cochran, W. G.
1934
The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. JFM 60.0465.04
Cochran, W. G.
1934
The comparison of percentages in matched samples. Zbl 0040.22203
Cochran, W. G.
1950
Estimators for the one-way random effects model with unequal error variances. Zbl 0463.62065
Rao, Poduri S. R. S.; Kaplan, Jack; Cochran, William G.
1981
Matched sampling for causal effects. Zbl 1118.62113
Rubin, Donald B.
2006
Problems arising in the analysis of a series of similar experiments. Zbl 0019.13003
Cochran, W. G.
1937
The omission or addition of an independent variate in multiple linear regression. Zbl 0019.31902
Cochran, W. G.
1938
Experimental designs. 2nd ed. 1st corr. printing. Zbl 0850.62005
Cochran, Williams G.; Cox, Gertrude M.
1992
Discriminant functions with covariance. Zbl 0031.37103
Cochran, W. G.; Bliss, C. I.
1948
A new class of white noise generalized functions. Zbl 0918.60027
Cochran, W. G.; Kuo, H.-H.; Sengupta, A.
1998
The distribution of the largest of a set of estimated variances as a fraction of their total. Zbl 0063.00936
Cochran, W. G.
1941
Comparison of two methods of handling covariates in discriminatory analysis. Zbl 0223.62076
Cochran, William G.
1964
Problems arising in the analysis of a series of similar experiments. JFM 63.1101.01
Cochran, W. G.
1937
Sampling theory when the sampling-units are of unequal sizes. Zbl 0063.00937
Cochran, W. G.
1942
The use of the analysis of variance in enumeration by sampling. Zbl 0023.14901
Cochran, W. G.
1939
The analysis of variance when experimental errors follow the Poisson or binomial laws. Zbl 0023.34104
Cochran, W. G.
1940
Some classification problems with multivariate qualitative data. Zbl 0099.13901
Cochran, William G.; Hopkins, Carl E.
1961
Approximate significance levels of the Behrens-Fisher test. Zbl 0119.35301
Cochran, William G.
1964
Note on an approximate formula for the significance levels of $$z$$. Zbl 0063.00935
Cochran, W. G.
1940
Contributions to survey sampling and applied statistics. Papers in honor of H. O. Hartley. Zbl 0437.62001
1978
Recent advances in mathematical statistics. Recent work on the analysis of variance. Zbl 0018.32104
Cochran, W. G.
1938
The structure of synthetic polypeptides. I: The transform of atoms on a helix. Zbl 0049.43702
Cochran, W.; Crick, F. H. C.; Vand, V.
1952
The comparison of different scales of measurement for experimental results. Zbl 0060.31610
Cochran, W. G.
1943
A test of a linear function of the deviations between observed and expected numbers. Zbl 0064.38801
Cochran, William G.
1955
The omission or addition of an independent variate in multiple linear regression. JFM 64.1214.02
Cochran, W. G.
1938
The present status of biometry. Zbl 0041.26506
Cochran, William G.
1950
The determination of crystal structures. Zbl 0053.18003
Lipson, H.; Cochran, W.
1953
The $$\chi^2$$ correction for continuity. Zbl 0063.00938
Cochran, W. G.
1942
Analysis of variance for percentages based on unequal numbers. Zbl 0063.00939
Cochran, W. G.
1943
Some effects of errors of measurement in multiple correlation. Zbl 0184.42802
Cochran, W. G.
1970
The efficiencies of the binomial series tests of significance of a mean and of a correlation coefficient. JFM 63.1108.03
Cochran, W. G.
1937
The $$\chi^2$$ distribution for the binomial and Poisson series, with small expectations. JFM 62.1344.02
Cochran, W. G.
1936
Recent developments in sampling theory in the United States. Zbl 0041.25805
Cochran, W. G.
1947
The symmetry of real periodic two-dimensional functions. Zbl 0049.43602
Cochran, W.
1952
Some practical applications of generalized crystal-structure projections. Zbl 0049.43701
Cochran, W.; Dyer, H. B.
1952
A rejection criterion based upon the range. Zbl 0074.13101
Bliss, C. I.; Cochran, W. G.; Tukey, John. W.
1956
On the performance of the linear discriminant function. Zbl 0124.34804
Cochran, William G.
1964
On the performance of the linear discriminant functions. Zbl 0201.52402
Cochran, William G.
1962
The statistical analysis of field counts of diseased plants. JFM 63.1101.02
Cochran, W. G.
1936
Parallel mesh adaptation for highly evolving geometries with application to solid propellant rockets. Zbl 1134.65319
Guoy, Damrong; Wilmarth, Terry; Alexander, Philipp; Jiao, Xiangmin; Campbell, Michael; Shaffer, Eric; Fiedler, Robert; Cochran, William; Suriyamongkol, Pornput
2008
Crystal stability and the theory of ferroelectricity. Zbl 0108.44904
Cochran, W.
1960
Contributions to statistics. With a foreword by Frederick Mosteller. Zbl 0584.01024
Cochran, William G.
1982
Parallel mesh adaptation for highly evolving geometries with application to solid propellant rockets. Zbl 1134.65319
Guoy, Damrong; Wilmarth, Terry; Alexander, Philipp; Jiao, Xiangmin; Campbell, Michael; Shaffer, Eric; Fiedler, Robert; Cochran, William; Suriyamongkol, Pornput
2008
Matched sampling for causal effects. Zbl 1118.62113
Rubin, Donald B.
2006
A new class of white noise generalized functions. Zbl 0918.60027
Cochran, W. G.; Kuo, H.-H.; Sengupta, A.
1998
Experimental designs. 2nd ed. 1st corr. printing. Zbl 0850.62005
Cochran, Williams G.; Cox, Gertrude M.
1992
Statistical methods. 8th ed. Zbl 0727.62003
Snedecor, George W.; Cochran, William G.
1989
Contributions to statistics. With a foreword by Frederick Mosteller. Zbl 0584.01024
Cochran, William G.
1982
Estimators for the one-way random effects model with unequal error variances. Zbl 0463.62065
Rao, Poduri S. R. S.; Kaplan, Jack; Cochran, William G.
1981
Contributions to survey sampling and applied statistics. Papers in honor of H. O. Hartley. Zbl 0437.62001
1978
Sampling techniques. 3rd ed. Zbl 0353.62011
Cochran, William G.
1977
Controlling bias in observational studies: a review. Zbl 0291.62012
Cochran, William G.; Rubin, Donald B.
1973
Some effects of errors of measurement in multiple correlation. Zbl 0184.42802
Cochran, W. G.
1970
Errors of measurement in statistics. Zbl 0177.46503
Cochran, W. G.
1968
Comparison of two methods of handling covariates in discriminatory analysis. Zbl 0223.62076
Cochran, William G.
1964
Approximate significance levels of the Behrens-Fisher test. Zbl 0119.35301
Cochran, William G.
1964
On the performance of the linear discriminant function. Zbl 0124.34804
Cochran, William G.
1964
On a simple procedure of unequal probability sampling without replacement. Zbl 0112.10901
Rao, J. N. K.; Hartley, H. O.; Cochran, W. G.
1962
On the performance of the linear discriminant functions. Zbl 0201.52402
Cochran, William G.
1962
Some classification problems with multivariate qualitative data. Zbl 0099.13901
Cochran, William G.; Hopkins, Carl E.
1961
Crystal stability and the theory of ferroelectricity. Zbl 0108.44904
Cochran, W.
1960
Experimental designs. 2nd ed. Zbl 0077.13205
Cochran, William G.; Cox, Gertrude M.
1957
A rejection criterion based upon the range. Zbl 0074.13101
Bliss, C. I.; Cochran, W. G.; Tukey, John. W.
1956
A test of a linear function of the deviations between observed and expected numbers. Zbl 0064.38801
Cochran, William G.
1955
Some methods for strengthening the common $$\chi^2$$ tests. Zbl 0059.12803
Cochran, William G.
1954
The combination of estimates from different experiments. Zbl 0059.12505
Kochran, William G.
1954
Sampling techniques. Zbl 0051.10707
Cochran, W. G.
1953
The determination of crystal structures. Zbl 0053.18003
Lipson, H.; Cochran, W.
1953
The $$\chi^ 2$$-test of goodness of fit. Zbl 0047.13105
Cochran, William G.
1952
The structure of synthetic polypeptides. I: The transform of atoms on a helix. Zbl 0049.43702
Cochran, W.; Crick, F. H. C.; Vand, V.
1952
The symmetry of real periodic two-dimensional functions. Zbl 0049.43602
Cochran, W.
1952
Some practical applications of generalized crystal-structure projections. Zbl 0049.43701
Cochran, W.; Dyer, H. B.
1952
The comparison of percentages in matched samples. Zbl 0040.22203
Cochran, W. G.
1950
The present status of biometry. Zbl 0041.26506
Cochran, William G.
1950
Discriminant functions with covariance. Zbl 0031.37103
Cochran, W. G.; Bliss, C. I.
1948
Recent developments in sampling theory in the United States. Zbl 0041.25805
Cochran, W. G.
1947
Relative accuracy of systematic and stratified random samples for a certain class of populations. Zbl 0063.00940
Cochran, W. G.
1946
The comparison of different scales of measurement for experimental results. Zbl 0060.31610
Cochran, W. G.
1943
Analysis of variance for percentages based on unequal numbers. Zbl 0063.00939
Cochran, W. G.
1943
Sampling theory when the sampling-units are of unequal sizes. Zbl 0063.00937
Cochran, W. G.
1942
The $$\chi^2$$ correction for continuity. Zbl 0063.00938
Cochran, W. G.
1942
The distribution of the largest of a set of estimated variances as a fraction of their total. Zbl 0063.00936
Cochran, W. G.
1941
The analysis of variance when experimental errors follow the Poisson or binomial laws. Zbl 0023.34104
Cochran, W. G.
1940
Note on an approximate formula for the significance levels of $$z$$. Zbl 0063.00935
Cochran, W. G.
1940
The use of the analysis of variance in enumeration by sampling. Zbl 0023.14901
Cochran, W. G.
1939
The omission or addition of an independent variate in multiple linear regression. Zbl 0019.31902
Cochran, W. G.
1938
Recent advances in mathematical statistics. Recent work on the analysis of variance. Zbl 0018.32104
Cochran, W. G.
1938
The omission or addition of an independent variate in multiple linear regression. JFM 64.1214.02
Cochran, W. G.
1938
Problems arising in the analysis of a series of similar experiments. Zbl 0019.13003
Cochran, W. G.
1937
Problems arising in the analysis of a series of similar experiments. JFM 63.1101.01
Cochran, W. G.
1937
The efficiencies of the binomial series tests of significance of a mean and of a correlation coefficient. JFM 63.1108.03
Cochran, W. G.
1937
The $$\chi^2$$ distribution for the binomial and Poisson series, with small expectations. JFM 62.1344.02
Cochran, W. G.
1936
The statistical analysis of field counts of diseased plants. JFM 63.1101.02
Cochran, W. G.
1936
The flow due to a rotating disc. JFM 60.0729.08
Cochran, W. G.
1934
The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. Zbl 0009.12004
Cochran, W. G.
1934
The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. JFM 60.0465.04
Cochran, W. G.
1934
all top 5
### Cited by 2,438 Authors
31 Singh, Garib Nath 28 Singh, Housila Prasad 16 Singh, Sarjinder 15 Vishwakarma, Gajendra Kumar 13 Kadılar, Cem 13 Rayner, John Charles Wi 12 Shabbir, Javid 11 Turkyilmazoglu, Mustafa 10 Best, D. John 10 Chaudhuri, Arijit 9 Bailey, Rosemary A. 9 Rao, Jonnagadda Nalini Kanth 9 Wright, Tommy 7 Arnab, Raghunath 7 Çıngı, Hülya 7 Ding, Peng 7 Ji, Un Cig 7 Khetan, Mukti 7 Kim, Jongmin 7 Maurya, Shweta 7 Solanki, Ramkrishna S. 6 Ahsan, Mohammad Jameel 6 Bennett, Bruce M. 6 Bouza Herrera, Carlos Narciso 6 Khan, M. G. M. 6 Kumar, Sunil 6 Lui, Kung-Jong 6 Pal, Surya Kant 6 Rubin, Donald Bruce 6 Ruiz Espejo, Mariano 6 Saha, Amitava 6 Sen, Pranab Kumar 6 Singh, Neha 6 Wong, Chi Song 5 Ariel, P. Donald 5 Attia, Hazem Ali 5 Bellhouse, David Richard 5 Böhning, Dankmar 5 Bolfarine, Heleno 5 Chandra, Hukum 5 Gil, María Angeles 5 Gupta, Sat Narian 5 Hartung, Joachim G. 5 Hayat, Tasawar 5 Kumar, Manish 5 Makambi, Kepher Henry 5 Mukerjee, Rahul 5 Mukhopadhyay, Nitis 5 Obata, Nobuaki 5 Sedory, Stephen Andrew 5 Šemrl, Peter 5 Son, Chang Kyoon 5 Tang, Manlai 5 Usman, Mahamood 5 Varshney, Rahul 5 Wermuth, Nanny 4 Al-saedi, Ahmed Eid Salem 4 Brien, C. J. 4 Buonaccorsi, John P. 4 Causeur, David J. 4 Cox, David Roxbee 4 Federer, Walter Theodore 4 Fienberg, Stephen Elliot 4 Jensen, Donald R. 4 Karna, Jaishree Prabha 4 Keele, Luke John 4 Lee, Gi Sung 4 Leung, Chi-Ying 4 Marchetti, Giovanni Maria 4 Meeden, Glen D. 4 Muttlak, Hassen A. 4 Ouerdiane, Habib 4 Park, Junyong 4 Ramirez, Donald E. 4 Rukhin, Andrew L. 4 Saavedra-Nieves, Alejandro 4 Sahoo, Bikash 4 Singh, Ravindra Pratap 4 Skinner, Chris J. 4 Subramani, J. 4 Zou, Guohua 3 Asai, Nobuhiro 3 Bahl, Shashi 3 Bandyopadhyay, Arnab 3 Bari, Abdul 3 Bhushan, Shashi 3 Binder, Harald 3 Booth, James G. 3 Bose, Mausumi 3 Breidt, F. Jay 3 Bretthauer, Kurt M. 3 Chakraborty, Subrata 3 Chang, Kuang-Chao 3 Chen, Zhongxue 3 Das Peddada, Shyamal 3 Das, Kalyan 3 Dasgupta, Tirthankar 3 Dihidar, Kajal 3 El Bassiouni, Mohamed Y. 3 Guo, Jianhua ...and 2,338 more Authors
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### Cited in 277 Serials
177 Communications in Statistics. Theory and Methods 141 Journal of Statistical Planning and Inference 77 Computational Statistics and Data Analysis 70 Communications in Statistics. Simulation and Computation 52 Statistics & Probability Letters 51 Journal of Statistical Computation and Simulation 48 Annals of the Institute of Statistical Mathematics 40 Psychometrika 35 Metrika 29 Statistical Science 29 Journal of Applied Statistics 28 Biometrics 27 Journal of Statistical Theory and Practice 24 Biometrical Journal 22 Statistical Papers 19 Applied Mathematics and Computation 19 European Journal of Operational Research 18 Journal of Econometrics 18 The Annals of Applied Statistics 17 The Annals of Statistics 17 Linear Algebra and its Applications 15 Journal of Multivariate Analysis 15 Statistics 12 Journal of Agricultural, Biological, and Environmental Statistics 11 The Canadian Journal of Statistics 10 Journal of the American Statistical Association 10 Test 10 Revista Investigación Operacional 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 9 Computational Statistics 8 Mathematical Biosciences 8 Physica A 8 American Journal of Mathematical and Management Sciences 8 Annals of Operations Research 8 Mathematical Population Studies 8 Statistical Methodology 8 AStA. Advances in Statistical Analysis 8 Statistics and Computing 7 Computers and Fluids 7 Mathematics and Computers in Simulation 7 Statistica Neerlandica 7 Computers & Operations Research 7 Applied Mathematical Modelling 7 Journal of the Korean Statistical Society 7 Journal of Probability and Statistics 7 Sankhyā. Series B 6 Acta Mechanica 6 Journal of Engineering Mathematics 6 Hacettepe Journal of Mathematics and Statistics 6 Thailand Statistician 6 Applied Scientific Research, Section A 6 International Journal of Applied and Computational Mathematics 5 The American Statistician 5 Computers & Mathematics with Applications 5 International Journal of Engineering Science 5 Linear and Multilinear Algebra 5 Scandinavian Journal of Statistics 5 Bulletin of Mathematical Biology 5 International Statistical Review 5 Meccanica 5 Metron 5 Theoretical Population Biology 5 Acta Applicandae Mathematicae 5 European Journal of Mechanics. B. Fluids 5 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Computational and Applied Mathematics 4 Statistica 4 Journal of Information & Optimization Sciences 4 International Journal of Approximate Reasoning 4 Science in China. Series A 4 Pattern Recognition 4 Mathematical Problems in Engineering 4 Journal of the Royal Statistical Society. Series B. Statistical Methodology 4 Lobachevskii Journal of Mathematics 4 Brazilian Journal of Probability and Statistics 4 Journal of the Australian Mathematical Society 4 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 4 Statistical Methods and Applications 4 Statistics Surveys 4 Sankhyā. Series A 4 Journal of Theoretical Biology 4 Communications in Mathematics and Statistics 3 Journal of Computational Physics 3 Rheologica Acta 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 3 Fuzzy Sets and Systems 3 Journal of Mathematical Psychology 3 Trabajos de Estadistica y de Investigacion Operativa 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 Mathematical Social Sciences 3 Operations Research Letters 3 Sequential Analysis 3 Econometric Reviews 3 Mathematical and Computer Modelling 3 Trabajos de Estadistica 3 Machine Learning 3 Economics Letters 3 International Journal of Computer Mathematics 3 Journal of Nonparametric Statistics ...and 177 more Serials
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### Cited in 43 Fields
1,300 Statistics (62-XX) 168 Numerical analysis (65-XX) 89 Fluid mechanics (76-XX) 70 Operations research, mathematical programming (90-XX) 64 Biology and other natural sciences (92-XX) 62 Probability theory and stochastic processes (60-XX) 49 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 47 Computer science (68-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 25 Combinatorics (05-XX) 21 Classical thermodynamics, heat transfer (80-XX) 19 History and biography (01-XX) 15 Functional analysis (46-XX) 13 Partial differential equations (35-XX) 11 Statistical mechanics, structure of matter (82-XX) 8 Systems theory; control (93-XX) 7 Mechanics of deformable solids (74-XX) 6 Geophysics (86-XX) 6 Information and communication theory, circuits (94-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Operator theory (47-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Convex and discrete geometry (52-XX) 4 Quantum theory (81-XX) 3 General and overarching topics; collections (00-XX) 3 Nonassociative rings and algebras (17-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Optics, electromagnetic theory (78-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Ordinary differential equations (34-XX) 2 Integral transforms, operational calculus (44-XX) 2 Relativity and gravitational theory (83-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-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.
| 2023-01-31T19:57:50 |
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https://par.nsf.gov/biblio/10127415-subaru-high-exploration-low-luminosity-quasars-shellqs-viii-less-biased-view-early-co-evolution-black-holes-host-galaxies
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Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). VIII. A less biased view of the early co-evolution of black holes and host galaxies
Abstract
We present ALMA [C ii] line and far-infrared (FIR) continuum observations of three $z \gt 6$ low-luminosity quasars ($M_{\rm 1450} \gt -25$ mag) discovered by our Subaru Hyper Suprime-Cam (HSC) survey. The [C ii] line was detected in all three targets with luminosities of $(2.4\mbox{--}9.5) \times 10^8\, L_{\odot }$, about one order of magnitude smaller than optically luminous ($M_{\rm 1450} \lesssim -25$ mag) quasars. The FIR continuum luminosities range from $\lt 9 \times 10^{10}\, L_{\odot }$ (3 $\sigma$ limit) to ${\sim } 2 \times 10^{12}\, L_{\odot }$, indicating a wide range in star formation rates in these galaxies. Most of the HSC quasars studied thus far show [C ii]/ FIR luminosity ratios similar to local star-forming galaxies. Using the [C ii]-based dynamical mass ($M_{\rm dyn}$) as a surrogate for bulge stellar mass ($M_{\rm\, bulge}$), we find that a significant fraction of low-luminosity quasars are located on or even below the local $M_{\rm\, BH}$–$M_{\rm\, bulge}$ relation, particularly at the massive end of the galaxy mass distribution. In contrast, previous studies of optically luminous quasars have found that black holes are overmassive relative to the local relation. Given the low luminosities of our targets, we are exploring the nature of the early co-evolution of supermassive black holes and more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10127415
Journal Name:
Publications of the Astronomical Society of Japan
Volume:
71
Issue:
6
ISSN:
0004-6264
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. ABSTRACT We report the serendipitous discovery of a dust-obscured galaxy observed as part of the Atacama Large Millimeter Array (ALMA) Large Program to INvestigate [C ii] at Early times (ALPINE). While this galaxy is detected both in line and continuum emissions in ALMA Band 7, it is completely dark in the observed optical/near-infrared bands and only shows a significant detection in the UltraVISTA Ks band. We discuss the nature of the observed ALMA line, that is [C ii] at $z$ ∼ 4.6 or high-J CO transitions at $z$ ∼ 2.2. In the first case, we find a [C ii]/FIR luminosity ratio of $\mathrm{log}{(L_{[\mathrm{more » 2. ABSTRACT The past decade has seen significant progress in understanding galaxy formation and evolution using large-scale cosmological simulations. While these simulations produce galaxies in overall good agreement with observations, they employ different sub-grid models for galaxies and supermassive black holes (BHs). We investigate the impact of the sub-grid models on the BH mass properties of the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA simulations, focusing on the MBH − M⋆ relation and the BH mass function. All simulations predict tight MBH − M⋆ relations, and struggle to produce BHs of$M_{\rm BH}\leqslant 10^{7.5}\, \rm M_{\odot }$in galaxies of$M_{\starmore »
3. ABSTRACT Previous studies of fueling black holes in galactic nuclei have argued (on scales ${\sim}0.01{-}1000\,$pc) accretion is dynamical with inflow rates $\dot{M}\sim \eta \, M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass Mgas, dynamical time tdyn, and some η. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency fwind = Mejected/Mtotal scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim \bar{a}_{\rm grav}/\langle \dot{p}/m_{\ast }\rangle \sim \Sigma _{\rm eff}/\Sigma _{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\, M_{\rm tot}(\ltmore » 4. ABSTRACT The James Webb Space Telescope will have the power to characterize high-redshift quasars at z ≥ 6 with an unprecedented depth and spatial resolution. While the brightest quasars at such redshift (i.e. with bolometric luminosity$L_{\rm bol}\geqslant 10^{46}\, \rm erg/s$) provide us with key information on the most extreme objects in the Universe, measuring the black hole (BH) mass and Eddington ratios of fainter quasars with$L_{\rm bol}= 10^{45}-10^{46}\, \rm erg\,s^{ -1}\$ opens a path to understand the build-up of more normal BHs at z ≥ 6. In this paper, we show that the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE,more »
5. ABSTRACT In large-scale hydrodynamical cosmological simulations, the fate of massive galaxies is mainly dictated by the modelling of feedback from active galactic nuclei (AGNs). The amount of energy released by AGN feedback is proportional to the mass that has been accreted on to the black holes (BHs), but the exact subgrid modelling of AGN feedback differs in all simulations. While modern simulations reliably produce populations of quiescent massive galaxies at z ≤ 2, it is also crucial to assess the similarities and differences of the responsible AGN populations. Here, we compare the AGN populations of the Illustris, TNG100, TNG300, Horizon-AGN,more »
| 2022-06-28T00:59:38 |
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http://dergipark.gov.tr/konuralpjournalmath/issue/28490/343519
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## DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$
#### HAŞİM ÇAYIR [1] , MOHAMMAD NAZRUL ISLAM KHAN [2]
##### 80 66
In this paper, we define the Cheeger-Gromoll metric in the $(1,1)$ $-$tensor bundle $T_{1}^{1}(M)$, which is completely determined by its action on vector fields of type $X^{H}$ and $\omega ^{V}$. Later, we obtain the covarient and Lie derivatives applied to the Cheeger-Gromoll metric with respect to the horizontal and vertical lifts of vector and kovector fields, respectively.
(1 1)-tensor bundle,Covarient Derivative,Lie Derivative,Cheeger-Gromoll metric,Horizontal Lift,Vertical Lift
• [1] Akyol, M. A., Sarı, R. and Aksoy, E., Semi-invariant -Riemannian submersions from almost contact metric manifolds, Int. J. Geom. Methods Mod. Phys. 14, 175007 4 (2017) DOI:http://dx.doi.org/10.1142/S0219887817500748.
• [2] Akyol, M. A., Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat. 46(2017), no.2, 177-192.
• [3] Çakmak, A. and Tarakç, Ö., Surfaces at a constant distance from the edge of regression on a surface of revolution in . Applied Mathematical Sciences, 10(2016), no.15, 707-719.
• [4] Çakmak, A., Karacan, M.K., Kiziltug, S. and Yoon, D.W., Translation surfaces in the 3-dimensional Gallean space satisfying . Bull. Korean Math. Soc. https://doi.org/10.4134/BKMS.b160442.
• [5] Çayır, H. and Akdağ, K., Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle, New Trends in Mathematical Sciences, 4(2016), no.4, 42-50.
• [6] Çayır, H. and Köseoğlu, G., Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4(2016), no.1, 153-159.
• [7] Cengiz, N. and Salimov, A. A., Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana (3) 8(2002), no.1, 75-82.
• [8] Gancarzewicz, J. and Rahmani, N., Relevent horizontal des connexions linearies au bre vectoriel associe avec le bre principal des repres lineaires, Annales Polinici Math., 48(1988), 281-289.
• [9] Gezer, A. and Altunbas, M., On the (1; 1)-tensor bundle with Cheeger-Grommol type metric, Proc. Indian Acad. Sci.(Math Sci.) 125(2015), no.4, 569-576.
• [10] Gunduzalp, Y., Slant submersions from almost paracontact Riemannian manifolds, product Riemannian manifolds, Kuwait Journal of Science, 42(2015), no.1, 17-29.
• [11] Gunduzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, DEMONSTRATIO MATHEMATICA, 49(2016), no.4.
• [12] Khan, M. N. I., and Jun, J.B., Lorentzian Almost r-para-contact Structure in Tangent Bundle, Journal of the Chungcheong Mathematical Society, 27(2014), no.1, 29-34.
• [13] Kobayashi, S. and Nomizu, K., Foundations of Di erential Geometry-Volume I, John Wiley & Sons, Inc, New York, 1963.
• [14] Lai, K. F. and Mok, K. P., On the differential geometry of the (1; 1)-tensor bundle, Tensor (New Series), 63(2002), no.1, 15-27.
• [15] Ledger, A. J. and Yano, K., Almost complex structures on the tensor bundles, J. Diff. Geom., 1(1967), 355-368.
• [16] Salimov, A.A., Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
• [17] Salimov, A. and Gezer, A., On the geometry of the (1,1) -tensor bundle with Sasaki type metric, Chin. Ann. Math. Ser. B 32(2011), no.3, 369-386.
• [18] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973.
Konular Mühendislik ve Temel Bilimler Articles Yazar: HAŞİM ÇAYIRE-posta: [email protected]Ülke: Turkey Yazar: MOHAMMAD NAZRUL ISLAM KHANE-posta: [email protected]Ülke: Saudi Arabia
Bibtex @araştırma makalesi { konuralpjournalmath343519, journal = {Konuralp Journal of Mathematics}, issn = {}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {78 - 86}, doi = {}, title = {DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC \$\^\{CG\}g\$ ON THE \$(1,1)-\$TENSOR BUNDLE \$T\_\{1\}\^\{1\}(M)\$}, key = {cite}, author = {KHAN, MOHAMMAD NAZRUL ISLAM and ÇAYIR, HAŞİM} } APA ÇAYIR, H , KHAN, M . (2017). DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$. Konuralp Journal of Mathematics, 5 (2), 78-86. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/343519 MLA ÇAYIR, H , KHAN, M . "DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$". Konuralp Journal of Mathematics 5 (2017): 78-86 Chicago ÇAYIR, H , KHAN, M . "DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$". Konuralp Journal of Mathematics 5 (2017): 78-86 RIS TY - JOUR T1 - DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ AU - HAŞİM ÇAYIR , MOHAMMAD NAZRUL ISLAM KHAN Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 78 EP - 86 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ %A HAŞİM ÇAYIR , MOHAMMAD NAZRUL ISLAM KHAN %T DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U
| 2018-03-21T12:48:24 |
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https://www.usgs.gov/news/volcano-watch-how-long-will-current-eruption-last
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# Volcano Watch — How long will the current eruption last?
March 10, 2005
The current eruption at Kīlauea is 22 years old and counting. Residents in the down-wind direction have probably become tired of the vog and would like the eruption to end. How long can an eruption last?
The longest historical eruption of Kīlauea prior to the current eruption was of lava lake activity at the summit, which lasted for nearly 20 years in the early 1800s. In more recent times, the activity at Mauna Ulu, from 1969 to 1974, dominated Kīlauea's landscape until the current eruption at Puu Oo.
USGS colleagues have studied the prehistoric record of Kīlauea and found that a summit eruption near Nahuku (Thurston lava tube) may have lasted 50 to 60 years! The eruption originated just east of Kīlauea Iki and sent flows downslope until it reached the sea at Kaloli point in Hawaiʻian Paradise Park. An estimated volume of 5.2 cubic kilometers (1.25 cubic miles) of lava was erupted, and the area covered is roughly 430 square kilometers (166 square miles).
What can we learn from Kīlauea's older and larger sibling, Mauna Loa? According to historical record, Mauna Loa has had summit activity that lasted for 6 years and flank activity for over one year.
Our research into the prehistoric record reveals that eruptions at Mauna Loa could have lasted more than a century! Radiocarbon age-dating of lava flows from the summit of Mauna Loa suggests sustained activity from 1,000 to 1,500 years before the present, or calendar dates of A.D. 1100 to 650. This period coincides with the arrival of Hawaiʻians to the islands. Furthermore, our geologic mapping shows that both the summit and rift zones were simultaneously active.
The area impacted by the prehistoric summit activity includes the east and west flanks of Mauna Loa directly downslope of Mokuaweoweo, Mauna Loa's summit caldera. In addition, the flows inundated the northwest flank, Kapapala Ranch and Forest Reserve to the east, Pohakuloa Training Area to the northwest, and Devils Country, or Keauhou 2, to the west, otherwise known as the saddle between Mauna Loa and Hualālai.
Lava flows from the summit also reached the sea at Kamehame on Kīlauea's southeast coast, 47 kilometers (29 miles) away. Another summit flow, traveling in the direction of Puako (Mauna Lani), is 57 kilometers (35 miles), one of the longest flows on record. By comparison, Mauna Loa's 1880 flow, the source of Kaumana Cave (above Hilo), is 47 kilometers (29 miles) long.
The area covered during the prehistoric period is 640 square kilometers (247 square miles) and constitutes an estimated volume of between 5.6 to 7.7 cubic kilometers (1.3 to 1.8 cubic miles). For some residents of Hawaii, the eruption has become tiresome, and they wish the activity would stop. One has to be careful of what one wishes for, however. The current eruptive activity is in a rather benign place in Hawaii Volcanoes National Park; the lava flows are not threatening any developments. Based on long-term monitoring, we know that the magma supply to Kīlauea is fairly constant over the long term.
If the eruption were to shut off, the magma supply to the volcano would continue. Eventually the influx of magma into the volcano would create pressure and result in a new outbreak. This outbreak could be in a remote location or migrate to where it threatens communities on the flanks of the volcano. So how long will the current eruption last? Well, if we rely on the geologic record, it could last several more decades or even a century!
### Volcano Activity Update
Eruptive activity at Puu Oo continues. All vents inside Puu Oo crater were incandescent this past week, producing bright glow on clear nights.
The PKK flow continues to host substantial breakouts from atop Pulama pali to the coastal plain. A "gorgeous" open channel lava flow on the east branch of the PKK flow was widely visible between 1,400 and 800 feet elevation on March 8. Two ocean entries are currently active at East Laeapuki and Kailiili; the West Highcastle entry ceased activity earlier this week. East Laeapuki and Kailiili entries are about 3.5 km (2 miles) and 7 km (4.5 miles) respectively from the ranger shed. Expect a 2-to-3 hour walk each way and remember to bring lots of water. Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Heed the National Park warning signs.
During the week ending March 10, four earthquakes were felt on the island. The first was a magnitude-3.1 quake at 4:20 pm on March 5. It was located 4 km (3 miles) southeast of Puu Oo vent at a depth of 9 km (5.7 miles), and was felt in Hilo and Sea View Estates. Two earthquakes northwest of Loihi Seamount on March 8 were felt on the southern part of Hawaiʻi island. A magnitude-4.2 quake 16 km (10 miles) northwest of Lo`ihi at 7:26 am was followed by a magnitude-3.3 quake at 7:27 am. The events occurred at a depth between 17 and 19 km (11-12 miles). A magnitude-3 quake at 6:45 am on March 10 was located 8 km (5 miles) north of Kalapana at a depth of 2.4 km (1.5 miles). It was felt by residents at Black Sands, Leilani Estates, and Sea View Estates.
Mauna Loa is not erupting. The summit region abruptly stopped inflating at the end of January and then started inflating again in mid to late February. Since July 2004, the rate of inflation and number of deep earthquakes has increased. Weekly earthquake counts have varied from 5 to over 150 in the last half of 2004 but have been less than 10 since the beginning of 2005. During the week ending March 10, only five earthquakes were recorded beneath the volcano.
| 2022-01-27T07:04:46 |
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https://zbmath.org/authors/?q=ai%3Adeninger.christopher
|
# zbMATH — the first resource for mathematics
## Deninger, Christopher
Compute Distance To:
Author ID: deninger.christopher Published as: Deninger, C.; Deninger, Ch.; Deninger, Christopher Homepage: https://www.uni-muenster.de/Arithm/deninger/ External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 73 Publications since 1984, including 1 Book
all top 5
#### Co-Authors
44 single-authored 6 Singhof, Wilhelm 5 Werner, Annette 3 Cuntz, Joachim 2 Nart, Enric 2 Scholl, Anthony James 2 Wingberg, Kay 1 Baldassarri, Francesco 1 Besser, Amnon 1 Deitmar, Anton 1 Laca, Marcelo 1 Lange, Herbert 1 Mellit, Anton S. 1 Murre, Jacob P. 1 Naumann, Niko 1 Schmidt, Klaus 1 Schneider, Peter 1 Schröter, Martin 1 Wegner, Dimitri
all top 5
#### Serials
8 Journal für die Reine und Angewandte Mathematik 5 Inventiones Mathematicae 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Documenta Mathematica 3 Münster Journal of Mathematics 2 Journal of Pure and Applied Algebra 2 Mathematische Annalen 2 Rendiconti del Seminario Matematico della Università di Padova 2 Journal of the American Mathematical Society 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin de la Société Mathématique de France 1 Collectanea Mathematica 1 Commentarii Mathematici Helvetici 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Mathematische Zeitschrift 1 Tokyo Journal of Mathematics 1 Ergodic Theory and Dynamical Systems 1 Annals of Global Analysis and Geometry 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Geometry 1 Annals of Mathematics. Second Series 1 Oberwolfach Reports 1 Groups, Geometry, and Dynamics
all top 5
#### Fields
46 Algebraic geometry (14-XX) 41 Number theory (11-XX) 15 Dynamical systems and ergodic theory (37-XX) 9 $$K$$-theory (19-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Functional analysis (46-XX) 5 Topological groups, Lie groups (22-XX) 4 Measure and integration (28-XX) 4 Differential geometry (53-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Algebraic topology (55-XX) 3 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX)
#### Citations contained in zbMATH
54 Publications have been cited 510 times in 389 Documents Cited by Year
Motivic decomposition of abelian schemes and the Fourier transform. Zbl 0745.14003
Deninger, Christopher; Murre, Jacob
1991
Deligne periods of mixed motives, $$K$$-theory and the entropy of certain $$\mathbb Z^n$$-actions. Zbl 0913.11027
Deninger, Christopher
1997
Local $$L$$-factors of motives and regularized determinants. Zbl 0762.14015
Deninger, Christopher
1992
Fuglede-Kadison determinants and entropy for actions of discrete amenable groups. Zbl 1104.22010
Deninger, Christopher
2006
Expansive algebraic actions of discrete residually finite amenable groups and their entropy. Zbl 1128.22003
Deninger, Christopher; Schmidt, Klaus
2007
$$C^*$$-algebras of Toeplitz type associated with algebraic number fields. Zbl 1273.22008
Cuntz, Joachim; Deninger, Christopher; Laca, Marcelo
2013
On the $$\Gamma$$-factors attached to motives. Zbl 0739.14010
Deninger, Christopher
1991
On the analogue of the formula of Chowla and Selberg for real quadratic fields. Zbl 0527.12009
Deninger, Christopher
1984
Higher regulators and Hecke $$L$$-series of imaginary quadratic fields. I. Zbl 0721.14004
Deninger, Christopher
1989
Motivic $$L$$-functions and regularized determinants. Zbl 0816.14010
Deninger, Christopher
1994
Higher regulators and Hecke $$L$$-series of imaginary quadratic fields. II. Zbl 0721.14005
Deninger, Christopher
1990
Vector bundles on $$p$$-adic curves and parallel transport. Zbl 1087.14026
Deninger, Christopher; Werner, Annette
2005
Some analogies between number theory and dynamical systems on foliated spaces. Zbl 0899.14001
Deninger, Christopher
1998
On the cohomology of nilpotent Lie algebras. Zbl 0653.17006
Deninger, Ch.; Singhof, W.
1988
A note on arithmetic topology and dynamical systems. Zbl 1077.14022
Deninger, Christopher
2002
The Beilinson conjectures. Zbl 0729.14002
Deninger, Christopher; Scholl, Anthony J.
1991
On the Beilinson conjectures for elliptic curves with complex multiplication. Zbl 0721.14006
Deninger, Christopher; Wingberg, Kay
1988
The e-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Zbl 0558.55010
Deninger, Ch.; Singhof, W.
1984
Witt vector rings and the relative de Rham Witt complex. Zbl 1326.13014
Cuntz, Joachim; Deninger, Christopher
2015
Higher order operations in Deligne cohomology. Zbl 0847.55014
Deninger, Christopher
1995
Formal groups and $$L$$-series. Zbl 0741.14026
Deninger, Christopher; Nart, Enric
1990
Mahler measures and Fuglede-Kadison determinants. Zbl 1245.11107
Deninger, Christopher
2009
On dynamical systems and their possible significance for arithmetic geometry. Zbl 1159.11310
Deninger, Christopher
2000
Lefschetz trace formulas and explicit formulas in analytic number theory. Zbl 0782.11034
Deninger, Christopher
1993
Analogies between analysis on foliated spaces and arithmetic geometry. Zbl 1163.37006
Deninger, Christopher
2008
Real polarizable Hodge structures arising from foliations. Zbl 1011.53026
Deninger, Christopher; Singhof, Wilhelm
2002
Number theory and dynamical systems on foliated spaces. Zbl 1003.11029
Deninger, Christopher
2001
$$p$$-adic Mahler measures. Zbl 0937.11056
Besser, Amnon; Deninger, Christopher
1999
Extensions of motives associated to symmetric powers of elliptic curves and to Hecke characters of imaginary quadratic fields. Zbl 0888.14002
Deninger, Christopher
1997
Duality in the étale cohomology of one-dimensional proper schemes and generalizations. Zbl 0607.14011
Deninger, Christopher
1987
Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents. Zbl 1220.46038
Deninger, Christopher
2011
On the nature of the “explicit formulas” in analytic number theory – a simple example. Zbl 1132.11347
Deninger, Christopher
2002
A distribution theoretic proof of Guinand’s functional equation for Cramér’s $$V$$-function and generalizations. Zbl 0847.11041
Deninger, Christopher; Schröter, Martin
1995
A proper base change theorem for non-torsion sheaves in étale cohomology. Zbl 0672.14010
Deninger, Ch.
1988
Artin-Verdier duality for $$n$$-dimensional local fields involving higher algebraic K-sheaves. Zbl 0608.12016
Deninger, Christopher; Wingberg, Kay
1986
On Artin-Verdier duality for function fields. Zbl 0585.14014
Deninger, Christopher
1984
An alternative to Witt vectors. Zbl 1320.13024
Cuntz, Joachim; Deninger, Christopher
2014
$$p$$-adic entropy and a $$p$$-adic Fuglede-Kadison determinant. Zbl 1208.37004
Deninger, Christopher
2009
Line bundles and $$p$$-adic characters. Zbl 1100.11019
Deninger, Christopher; Werner, Annette
2005
Exchanging the places $$p$$ and $$\infty$$ in the Leopoldt conjecture. Zbl 1087.11066
Deninger, Christopher
2005
Evidence for a cohomological approach to analytic number theory. Zbl 0838.11002
Deninger, Christopher
1994
An extension of Artin-Verdier duality to non-torsion sheaves. Zbl 0599.14017
Deninger, Christopher
1986
Vector bundles on $$p$$-adic curves and parallel transport. II. Zbl 1255.14023
Deninger, Christopher; Werner, Annette
2010
A note on dynamical trace formulas. Zbl 1211.58016
Deninger, Christopher; Singhof, Wilhelm
2001
$$L$$-functions of mixed motives. Zbl 0812.14001
Deninger, Christopher
1994
Regulators, entropy and infinite determinants. Zbl 1318.19005
Deninger, Christopher
2012
Representations attached to vector bundles on curves over finite and $$p$$-adic fields, a comparison. Zbl 1310.14035
Deninger, Christopher
2010
The Hilbert-Polya strategy and height pairings. Zbl 1225.14018
Deninger, Christopher
2010
A motivic version of Pellikaan’s two variable zeta function. Zbl 1151.14017
Baldassarri, Francesco; Deninger, Christopher; Naumann, Niko
2007
Two-variable zeta functions and regularized products. Zbl 1130.11327
Deninger, Christopher
2003
On the $$\Gamma$$-factors of motives. II. Zbl 1024.11048
Deninger, Christopher
2001
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas. Zbl 0997.58017
Deninger, Christopher; Singhof, Wilhelm
2001
How to recover an $$L$$-series from its values at almost all positive integers. Some remarks on a formula of Ramanujan. Zbl 1054.11046
Deninger, Christopher
2000
On extensions of mixed motives. Zbl 0890.14001
Deninger, Christopher
1997
Witt vector rings and the relative de Rham Witt complex. Zbl 1326.13014
Cuntz, Joachim; Deninger, Christopher
2015
An alternative to Witt vectors. Zbl 1320.13024
Cuntz, Joachim; Deninger, Christopher
2014
$$C^*$$-algebras of Toeplitz type associated with algebraic number fields. Zbl 1273.22008
Cuntz, Joachim; Deninger, Christopher; Laca, Marcelo
2013
Regulators, entropy and infinite determinants. Zbl 1318.19005
Deninger, Christopher
2012
Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents. Zbl 1220.46038
Deninger, Christopher
2011
Vector bundles on $$p$$-adic curves and parallel transport. II. Zbl 1255.14023
Deninger, Christopher; Werner, Annette
2010
Representations attached to vector bundles on curves over finite and $$p$$-adic fields, a comparison. Zbl 1310.14035
Deninger, Christopher
2010
The Hilbert-Polya strategy and height pairings. Zbl 1225.14018
Deninger, Christopher
2010
Mahler measures and Fuglede-Kadison determinants. Zbl 1245.11107
Deninger, Christopher
2009
$$p$$-adic entropy and a $$p$$-adic Fuglede-Kadison determinant. Zbl 1208.37004
Deninger, Christopher
2009
Analogies between analysis on foliated spaces and arithmetic geometry. Zbl 1163.37006
Deninger, Christopher
2008
Expansive algebraic actions of discrete residually finite amenable groups and their entropy. Zbl 1128.22003
Deninger, Christopher; Schmidt, Klaus
2007
A motivic version of Pellikaan’s two variable zeta function. Zbl 1151.14017
Baldassarri, Francesco; Deninger, Christopher; Naumann, Niko
2007
Fuglede-Kadison determinants and entropy for actions of discrete amenable groups. Zbl 1104.22010
Deninger, Christopher
2006
Vector bundles on $$p$$-adic curves and parallel transport. Zbl 1087.14026
Deninger, Christopher; Werner, Annette
2005
Line bundles and $$p$$-adic characters. Zbl 1100.11019
Deninger, Christopher; Werner, Annette
2005
Exchanging the places $$p$$ and $$\infty$$ in the Leopoldt conjecture. Zbl 1087.11066
Deninger, Christopher
2005
Two-variable zeta functions and regularized products. Zbl 1130.11327
Deninger, Christopher
2003
A note on arithmetic topology and dynamical systems. Zbl 1077.14022
Deninger, Christopher
2002
Real polarizable Hodge structures arising from foliations. Zbl 1011.53026
Deninger, Christopher; Singhof, Wilhelm
2002
On the nature of the “explicit formulas” in analytic number theory – a simple example. Zbl 1132.11347
Deninger, Christopher
2002
Number theory and dynamical systems on foliated spaces. Zbl 1003.11029
Deninger, Christopher
2001
A note on dynamical trace formulas. Zbl 1211.58016
Deninger, Christopher; Singhof, Wilhelm
2001
On the $$\Gamma$$-factors of motives. II. Zbl 1024.11048
Deninger, Christopher
2001
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas. Zbl 0997.58017
Deninger, Christopher; Singhof, Wilhelm
2001
On dynamical systems and their possible significance for arithmetic geometry. Zbl 1159.11310
Deninger, Christopher
2000
How to recover an $$L$$-series from its values at almost all positive integers. Some remarks on a formula of Ramanujan. Zbl 1054.11046
Deninger, Christopher
2000
$$p$$-adic Mahler measures. Zbl 0937.11056
Besser, Amnon; Deninger, Christopher
1999
Some analogies between number theory and dynamical systems on foliated spaces. Zbl 0899.14001
Deninger, Christopher
1998
Deligne periods of mixed motives, $$K$$-theory and the entropy of certain $$\mathbb Z^n$$-actions. Zbl 0913.11027
Deninger, Christopher
1997
Extensions of motives associated to symmetric powers of elliptic curves and to Hecke characters of imaginary quadratic fields. Zbl 0888.14002
Deninger, Christopher
1997
On extensions of mixed motives. Zbl 0890.14001
Deninger, Christopher
1997
Higher order operations in Deligne cohomology. Zbl 0847.55014
Deninger, Christopher
1995
A distribution theoretic proof of Guinand’s functional equation for Cramér’s $$V$$-function and generalizations. Zbl 0847.11041
Deninger, Christopher; Schröter, Martin
1995
Motivic $$L$$-functions and regularized determinants. Zbl 0816.14010
Deninger, Christopher
1994
Evidence for a cohomological approach to analytic number theory. Zbl 0838.11002
Deninger, Christopher
1994
$$L$$-functions of mixed motives. Zbl 0812.14001
Deninger, Christopher
1994
Lefschetz trace formulas and explicit formulas in analytic number theory. Zbl 0782.11034
Deninger, Christopher
1993
Local $$L$$-factors of motives and regularized determinants. Zbl 0762.14015
Deninger, Christopher
1992
Motivic decomposition of abelian schemes and the Fourier transform. Zbl 0745.14003
Deninger, Christopher; Murre, Jacob
1991
On the $$\Gamma$$-factors attached to motives. Zbl 0739.14010
Deninger, Christopher
1991
The Beilinson conjectures. Zbl 0729.14002
Deninger, Christopher; Scholl, Anthony J.
1991
Higher regulators and Hecke $$L$$-series of imaginary quadratic fields. II. Zbl 0721.14005
Deninger, Christopher
1990
Formal groups and $$L$$-series. Zbl 0741.14026
Deninger, Christopher; Nart, Enric
1990
Higher regulators and Hecke $$L$$-series of imaginary quadratic fields. I. Zbl 0721.14004
Deninger, Christopher
1989
On the cohomology of nilpotent Lie algebras. Zbl 0653.17006
Deninger, Ch.; Singhof, W.
1988
On the Beilinson conjectures for elliptic curves with complex multiplication. Zbl 0721.14006
Deninger, Christopher; Wingberg, Kay
1988
A proper base change theorem for non-torsion sheaves in étale cohomology. Zbl 0672.14010
Deninger, Ch.
1988
Duality in the étale cohomology of one-dimensional proper schemes and generalizations. Zbl 0607.14011
Deninger, Christopher
1987
Artin-Verdier duality for $$n$$-dimensional local fields involving higher algebraic K-sheaves. Zbl 0608.12016
Deninger, Christopher; Wingberg, Kay
1986
An extension of Artin-Verdier duality to non-torsion sheaves. Zbl 0599.14017
Deninger, Christopher
1986
On the analogue of the formula of Chowla and Selberg for real quadratic fields. Zbl 0527.12009
Deninger, Christopher
1984
The e-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Zbl 0558.55010
Deninger, Ch.; Singhof, W.
1984
On Artin-Verdier duality for function fields. Zbl 0585.14014
Deninger, Christopher
1984
all top 5
#### Cited by 381 Authors
18 Kurokawa, Nobushige 16 Deninger, Christopher 12 Laterveer, Robert 11 Lalín, Matilde N. 9 Wakayama, Masato 8 Li, Hanfeng 7 Brunault, François 7 Li, Xin 7 Schmidt, Klaus 5 Tanaka, Hidekazu 4 an Huef, Astrid 4 Bowen, Lewis Phylip 4 Hayes, Ben 4 Kings, Guido 4 Morin, Baptiste 4 Mukhamedov, Farruh Maksutovich 4 Raeburn, Iain 4 Samart, Detchat 4 Verbitskiy, Evgeny A. 4 Vial, Charles 3 Bars Cortina, Francesc 3 Brownlowe, Nathan 3 Cairns, Grant 3 Connes, Alain 3 Consani, Caterina 3 Cuntz, Joachim 3 Geisser, Thomas H. 3 Giordano Bruno, Anna 3 Grushevsky, Samuel 3 Jessup, Barry 3 Kakariadis, Evgenios T. A. 3 Kaledin, Dmitry B. 3 Kanemitsu, Shigeru 3 Koyama, Shin-ya 3 Künnemann, Klaus 3 Laca, Marcelo 3 Lagarias, Jeffrey C. 3 Larsen, Nadia S. 3 Lind, Douglas A. 3 Lorscheid, Oliver 3 Ludsteck, Thomas 3 Marcolli, Matilde 3 Nart, Enric 3 Ramagge, Jacqui 3 Rogers, Mathew D. 3 Tirao, Paulo 3 Ueki, Jun 3 Wildeshaus, Jörg 3 Zaharescu, Alexandru 2 Afsar, Zahra 2 Akatsuka, Hirotaka 2 Akhtar, Reza 2 Ancona, Giuseppe 2 Antieau, Benjamin 2 Berndt, Bruce Carl 2 Björklund, Michael 2 Borwein, Jonathan Michael 2 Boyd, David William 2 Bunke, Ulrich 2 Ceccherini-Silberstein, Tullio G. 2 Chung, Nhan-Phu 2 Colombo, Elisabetta 2 Coornaert, Michel 2 Diaz, Humberto A. 2 Dikranjan, Dikran N. 2 Everest, Graham Robert 2 Fish, Alexander 2 Gerasimov, Anton A. 2 Göll, Martin 2 Goncharov, Alexander Borisovich 2 Hanamura, Masaki 2 Huang, Xiaojun 2 Iyer, Jaya N. N. 2 Katsurada, Masanori 2 Keller, Timo 2 Kerr, David 2 Khakimov, Otabek N. 2 Kim, Sun Hyung 2 Kimura, Shun-ichi 2 Lan, Guitang 2 Lang, Serge 2 Lapidus, Michel L. 2 Lebedev, Dimitri R. 2 Lemma, Francesco 2 Liu, Jinsong 2 Mahanta, Snigdhayan 2 Masdeu, Marc 2 Masri, Riad 2 Mellit, Anton S. 2 Moonen, Ben 2 Murre, Jacob P. 2 Naumann, Niko 2 Oblezin, Sergey 2 Otsubo, Noriyuki 2 Pisolkar, Supriya 2 Pouseele, Hannes 2 Sairaiji, Fumio 2 Scholbach, Jakob 2 Seveso, Marco Adamo 2 Sheng, Mao ...and 281 more Authors
all top 5
#### Cited in 115 Serials
22 Journal of Number Theory 16 Advances in Mathematics 15 Proceedings of the American Mathematical Society 13 Duke Mathematical Journal 13 Transactions of the American Mathematical Society 12 Inventiones Mathematicae 10 Compositio Mathematica 9 Journal of Functional Analysis 9 Mathematische Annalen 9 Ergodic Theory and Dynamical Systems 7 Journal of Geometry and Physics 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Journal of Algebra 7 Journal für die Reine und Angewandte Mathematik 7 Journal of Algebraic Geometry 7 Documenta Mathematica 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Annales de l’Institut Fourier 6 Journal of Pure and Applied Algebra 6 Manuscripta Mathematica 6 Mathematische Zeitschrift 6 Indagationes Mathematicae. New Series 6 Journal de Théorie des Nombres de Bordeaux 6 The Ramanujan Journal 6 International Journal of Number Theory 5 Proceedings of the Japan Academy. Series A 5 International Journal of Mathematics 4 Communications in Mathematical Physics 4 Results in Mathematics 4 Journal of the American Mathematical Society 3 Communications in Algebra 3 Journal of Mathematical Analysis and Applications 3 Letters in Mathematical Physics 3 Mathematics of Computation 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Nagoya Mathematical Journal 3 Forum Mathematicum 3 Bulletin of the American Mathematical Society. New Series 3 Bulletin des Sciences Mathématiques 3 Geometry & Topology 3 Forum of Mathematics, Sigma 3 Annales Mathématiques du Québec 3 Research in Number Theory 2 Archiv der Mathematik 2 Geometriae Dedicata 2 Glasgow Mathematical Journal 2 Journal of the Mathematical Society of Japan 2 Memoirs of the American Mathematical Society 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 Tohoku Mathematical Journal. Second Series 2 Tokyo Journal of Mathematics 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Experimental Mathematics 2 Discrete and Continuous Dynamical Systems 2 Mathematical Physics, Analysis and Geometry 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 Journal of the Institute of Mathematics of Jussieu 2 Journal of Homotopy and Related Structures 2 Journal of $$K$$-Theory 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Research in the Mathematical Sciences 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Studia Mathematica 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Acta Arithmetica 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Dissertationes Mathematicae 1 Functiones et Approximatio. Commentarii Mathematici 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Theoretical Computer Science 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 $$K$$-Theory 1 Sugaku Expositions 1 Geometric and Functional Analysis. GAFA 1 Elemente der Mathematik 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Vestnik St. Petersburg University. Mathematics 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Selecta Mathematica. New Series 1 Annals of Combinatorics ...and 15 more Serials
all top 5
#### Cited in 39 Fields
196 Number theory (11-XX) 164 Algebraic geometry (14-XX) 46 Dynamical systems and ergodic theory (37-XX) 44 $$K$$-theory (19-XX) 34 Topological groups, Lie groups (22-XX) 34 Functional analysis (46-XX) 29 Special functions (33-XX) 18 Group theory and generalizations (20-XX) 17 Algebraic topology (55-XX) 16 Abstract harmonic analysis (43-XX) 15 Commutative algebra (13-XX) 15 Global analysis, analysis on manifolds (58-XX) 11 Nonassociative rings and algebras (17-XX) 11 Category theory; homological algebra (18-XX) 10 Operator theory (47-XX) 9 Associative rings and algebras (16-XX) 9 Measure and integration (28-XX) 9 Differential geometry (53-XX) 8 Manifolds and cell complexes (57-XX) 8 Quantum theory (81-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Field theory and polynomials (12-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Partial differential equations (35-XX) 5 General topology (54-XX) 3 Combinatorics (05-XX) 3 Functions of a complex variable (30-XX) 3 Difference and functional equations (39-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
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|
https://mooseframework.inl.gov/source/userobjects/AdvectiveFluxCalculatorConstantVelocity.html
|
## Information and Tools
The AdvectiveFluxCalculatorConstantVelocity computes , and that are used in the Kuzmin-Turek (Kuzmin and Turek, 2004) numerical stabilization scheme, when the velocity is constant and uniform over the mesh. is a measure of advective flux between neighbouring nodes, while and quantify how much antidiffusion to allow around the nodes. See A worked example of Kuzmin-Turek stabilization for many explicit details, and numerical diffusion for example of how the Kuzmin-Turek scheme compares with other numerical schemes.
## Input Parameters
• velocityVelocity vector
C++ Type:libMesh::VectorValue
Options:
Description:Velocity vector
• uThe variable that is being advected
C++ Type:std::vector
Options:
Description:The variable that is being advected
### Required Parameters
• execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
• flux_limiter_typeVanLeerType of flux limiter to use. 'None' means that no antidiffusion will be added in the Kuzmin-Turek scheme
Default:VanLeer
C++ Type:MooseEnum
Options:MinMod VanLeer MC superbee None
Description:Type of flux limiter to use. 'None' means that no antidiffusion will be added in the Kuzmin-Turek scheme
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
| 2019-03-24T01:10:43 |
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|
https://par.nsf.gov/biblio/10273259-broadband-ultraviolet-visible-frequency-combs-from-cascaded-high-harmonic-generation-quasi-phase-matched-waveguides
|
High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to the ninth order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable$≤<#comment/>12nJ$, 100 fs pulses at 3 µm with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, among an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex highly nonlinear process. Accommodating the extreme spectral bandwidth, numerical simulations based on a single broadband envelope equation with only quadratic nonlinearity give estimates for the conversion efficiency within approximately 1 order of magnitude over a wide range of experimental parameters. From this comparison between theory and experiment, we identify a dimensionless parameter capturing the competition between three-wave mixing and group-velocity walk-off of the harmonics that governs the cascaded HHG physics. We also gain insights into spectral optimization via tuning the waveguide poling profile and pump pulse parameters. These results can inform cascaded HHG in a range of different platforms.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10273259
Journal Name:
Journal of the Optical Society of America B
Volume:
38
Issue:
8
Page Range or eLocation-ID:
Article No. 2252
ISSN:
0740-3224; JOBPDE
Publisher:
Optical Society of America
1. Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of$∼<#comment/>40meV$. In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust$∼<#comment/>10W$fiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.
2. Quasi-phase-matched interactions in waveguides with quadratic nonlinearities enable highly efficient nonlinear frequency conversion. In this paper, we demonstrate the first generation of devices that combine the dispersion engineering available in nanophotonic waveguides with quasi-phase-matched nonlinear interactions available in periodically poled lithium niobate (PPLN). This combination enables quasi-static interactions of femtosecond pulses, reducing the pulse energy requirements by several orders of magnitude compared to conventional devices, from picojoules to femtojoules. We experimentally demonstrate two effects associated with second harmonic generation (SHG). First, we observe efficient quasi-phase-matched SHG with$<<#comment/>100fJ$of pulse energy. Second, in the limit of strong phase-mismatch, we observe spectral broadening of both harmonics with as little as 2 pJ of pulse energy. These results lay a foundation for a new class of nonlinear devices, in which coengineering of dispersion with quasi-phase-matching enables efficient nonlinear optics at the femtojoule level.
3. Thin-film lithium-niobate-on-insulator (LNOI) has emerged as a superior integrated-photonics platform for linear, nonlinear, and electro-optics. Here we combine quasi-phase-matching, dispersion engineering, and tight mode confinement to realize nonlinear parametric processes with both high efficiency and wide wavelength tunability. On a millimeter-long, Z-cut LNOI waveguide, we demonstrate efficient ($1900±<#comment/>500%<#comment/>W−<#comment/>1cm−<#comment/>2$) and highly tunable ($−<#comment/>1.71nm/K$) second-harmonic generation from 1530 to 1583 nm by type-0 quasi-phase-matching. Our technique is applicable to optical harmonic generation, quantum light sources, frequency conversion, and many other photonic information processes across visible to mid-IR spectral bands.
4. An optical parametric oscillator (OPO) is developed and characterized for the simultaneous generation of ultraviolet (UV) and near-UV nanosecond laser pulses for the single-shot Rayleigh scattering and planar laser-induced-fluorescence (PLIF) imaging of methylidyne (CH) and nitric oxide (NO) in turbulent flames. The OPO is pumped by a multichannel, 8-pulse Nd:YAG laser cluster that produces up to 225 mJ/pulse at 355 nm with pulse spacing of 100 µs. The pulsed OPO has a conversion efficiency of 9.6% to the signal wavelength of$∼<#comment/>430nm$when pumped by the multimode laser. Second harmonic conversion of the signal, with 3.8% efficiency, is used for the electronic excitation of the A-X (1,0) band of NO at$∼<#comment/>215nm$, while the residual signal at 430 nm is used for direct excitation of the A-X (0,0) band of the CH radical and elastic Rayleigh scattering. The section of the OPO signal wavelength for simultaneous CH and NO PLIF imaging is performed with consideration of the pulse energy, interference from the reactant and product species, and the fluorescence signal intensity. The excitation wavelengths of 430.7 nm and 215.35 nm are studied in a laminar, premixed–air flame. Single-shot CH and NO PLIF and Rayleigh scatter imaging is demonstrated in a turbulent$CH4−<#comment/>H2−<#comment/>NH3$diffusion flame using a high-speed intensified CMOS camera. Analysis of the complementary Rayleigh scattering and CH and NO PLIF enables identification and quantification of the high-temperature flame layers, the combustion product zones, and the fuel-jet core. Considerations for extension to simultaneous, 10-kHz-rate acquisition are discussed.
5. Optical nonlinearity plays a pivotal role in quantum information processing using photons, from heralded single-photon sources and coherent wavelength conversion to long-sought quantum repeaters. Despite the availability of strong dipole coupling to quantum emitters, achieving strong bulk optical nonlinearity is highly desirable. Here, we realize quantum nanophotonic integrated circuits in thin-film InGaP with, to our knowledge, a record-high ratio of$1.5%<#comment/>$between the single-photon nonlinear coupling rate ($g/2π<#comment/>=11.2MHz$) and cavity-photon loss rate. We demonstrate second-harmonic generation with an efficiency of$71200±<#comment/>10300%<#comment/>/W$in the InGaP photonic circuit and photon-pair generation via degenerate spontaneous parametric downconversion with an ultrahigh rate exceeding 27.5 MHz/µW—an order of magnitude improvement of the state of the art—and a large coincidence-to-accidental ratio up to$1.4×<#comment/>104$. Our work shows InGaP as a potentially transcending platform for quantum nonlinear optics and quantum information applications.
| 2023-03-31T13:27:00 |
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|
http://dlmf.nist.gov/5.12
|
# §5.12 Beta Function
In this section all fractional powers have their principal values, except where noted otherwise. In (5.12.1)–(5.12.4) it is assumed $\realpart{a}>0$ and $\realpart{b}>0$.
# Euler’s Beta Integral
5.12.1 $\mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right)=\int_{0}^{1}t^{a-1}(1-t)^{b-1% }dt=\frac{\mathop{\Gamma\/}\nolimits\!\left(a\right)\mathop{\Gamma\/}\nolimits% \!\left(b\right)}{\mathop{\Gamma\/}\nolimits\!\left(a+b\right)}.$ Defines: $\mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right)$: beta function Symbols: $\mathop{\Gamma\/}\nolimits\!\left(z\right)$: gamma function, $dx$: differential of $x$, $\int$: integral, $a$: real or complex variable and $b$: real or complex variable A&S Ref: 6.2.1 and 6.2.2 Referenced by: §10.22(ii), §10.43(iii), §19.20(i), §19.20(iv), §2.6(iii), §5.12, §5.12, §7.7(ii) Permalink: http://dlmf.nist.gov/5.12.E1 Encodings: TeX, pMML, png
5.12.2 $\int_{0}^{\pi/2}{\mathop{\sin\/}\nolimits^{2a-1}}\theta{\mathop{\cos\/}% \nolimits^{2b-1}}\theta d\theta=\tfrac{1}{2}\mathop{\mathrm{B}\/}\nolimits\!% \left(a,b\right).$
5.12.3 $\int_{0}^{\infty}\frac{t^{a-1}dt}{(1+t)^{a+b}}=\mathop{\mathrm{B}\/}\nolimits% \!\left(a,b\right).$
5.12.4 $\int_{0}^{1}\frac{t^{a-1}(1-t)^{b-1}}{(t+z)^{a+b}}dt=\mathop{\mathrm{B}\/}% \nolimits\!\left(a,b\right)(1+z)^{-a}z^{-b},$ $|\mathop{\mathrm{ph}\/}\nolimits z|<\pi$.
5.12.5 $\int_{0}^{\pi/2}(\mathop{\cos\/}\nolimits t)^{a-1}\mathop{\cos\/}\nolimits\!% \left(bt\right)dt=\frac{\pi}{2^{a}}\frac{1}{a\mathop{\mathrm{B}\/}\nolimits\!% \left(\frac{1}{2}(a+b+1),\frac{1}{2}(a-b+1)\right)},$ $\realpart{a}>0$.
5.12.6 $\int_{0}^{\pi}(\mathop{\sin\/}\nolimits t)^{a-1}e^{ibt}dt=\frac{\pi}{2^{a-1}}% \frac{e^{i\pi b/2}}{a\mathop{\mathrm{B}\/}\nolimits\!\left(\frac{1}{2}(a+b+1),% \frac{1}{2}(a-b+1)\right)},$ $\realpart{a}>0$.
5.12.7 $\int_{0}^{\infty}\frac{\mathop{\cosh\/}\nolimits\!\left(2bt\right)}{(\mathop{% \cosh\/}\nolimits t)^{2a}}dt=4^{a-1}\mathop{\mathrm{B}\/}\nolimits\!\left(a+b,% a-b\right),$ $\realpart{a}>|\realpart{b}|$.
5.12.8 ${\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{dt}{(w+it)^{a}(z-it)^{b}}=\frac{(w% +z)^{1-a-b}}{(a+b-1)\mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right)}},$ $\realpart{(a+b)}>1$, $\realpart{w}>0$, $\realpart{z}>0$.
In (5.12.8) the fractional powers have their principal values when $w>0$ and $z>0$, and are continued via continuity.
5.12.9 ${\frac{1}{2\pi i}\int_{c-\infty i}^{c+\infty i}t^{-a}(1-t)^{-1-b}dt=\frac{1}{b% \mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right)}},$ $0, $\realpart{(a+b)}>0$.
5.12.10 ${\frac{1}{2\pi i}\int_{0}^{(1+)}t^{a-1}(t-1)^{b-1}dt=\frac{\mathop{\sin\/}% \nolimits\!\left(\pi b\right)}{\pi}\mathop{\mathrm{B}\/}\nolimits\!\left(a,b% \right)},$ $\realpart{a}>0$,
with the contour as shown in Figure 5.12.1.
In (5.12.11) and (5.12.12) the fractional powers are continuous on the integration paths and take their principal values at the beginning.
5.12.11 $\frac{1}{e^{2\pi ia}-1}\int_{\infty}^{(0+)}t^{a-1}(1+t)^{-a-b}dt=\mathop{% \mathrm{B}\/}\nolimits\!\left(a,b\right),$
when $\realpart{b}>0$, $a$ is not an integer and the contour cuts the real axis between $-1$ and the origin. See Figure 5.12.2.
# Pochhammer’s Integral
When $a,b\in\Complex$
5.12.12 $\int_{P}^{(1+,0+,1-,0-)}t^{a-1}(1-t)^{b-1}dt=-4e^{\pi i(a+b)}\mathop{\sin\/}% \nolimits\!\left(\pi a\right)\mathop{\sin\/}\nolimits\!\left(\pi b\right)% \mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right),$
where the contour starts from an arbitrary point $P$ in the interval $(0,1)$, circles $1$ and then $0$ in the positive sense, circles $1$ and then $0$ in the negative sense, and returns to $P$. It can always be deformed into the contour shown in Figure 5.12.3.
| 2014-12-20T17:16:00 |
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|
https://math.wikia.org/wiki/System_of_linear_equations
|
1,183 Pages
Given the A linear equation is an equation with variables (commonly with two variables and with three) that can be written in the form
where and are real or complex numbers which are usually known beforehand.
A system of linear equations is a collection of linear equations using the same variables. For example, the equations
are not a system of linear equations because the two equations do not share any variables, whereas adding the equation
makes the collection a system of equation because variables are shared between equations.
A solution to a system of linear equations is a list of values that can be exchanged with the variables such that every equation becomes true. A system of linear equations may have no solution, exactly one solution, or infinitely many solutions.
## Solving systems of equations
When solving a system of equations, there are several ways to go about solving it.
### Matrix Notation
For a given system of equations, each equation can be written as a row in a matrix. For a coefficient matrix, each of the coefficients is written in aligned columns. For example, the system
would be written as the coefficient matrix
An augmented matrix shows the coefficient matrix with an additional column for the values of . The augmented matrix for the above system is
The goal of solving by a matrix is to produce a matrix of the form
so that each variable is paired with a solution value. This is known as reduced row-echelon form. The matrix can be put into this form by the use of elementary row operations. Matrices are said to be row-equivalent if one matrix may be transformed into the other using only elementary row operations. The three elementary row operations are:
• Replacement - replacing one row by a sum of itself and a multiple of another row.
• Interchange - exchange two rows
• Scaling - multiply a row by a non-zero constant.
The standard way, also known as the Gauss-Jordon Elimination Method, of solving using row operations is to work from left to right and attempt to make the value in the appropriate row (for example, the first row in the first column) equal to 1, then bring all the other values to 0. This has the advantage of never undoing work previously done. To solve the augmented matrix:
Interchange the first and second rows to get 1 in
Replace with
Scale by
Replace with
Replace with
Replace with
Replace with
Thus, the solution to the system is (29, 16, 3).
Another way is Cramer's rule, which states that in a system of linear equations, xn = Dxn/D, Where D is the determinant of the coefficient matrix and Dxn is the coefficient determinant with the coefficients of xn replaced with the constants on the right of the equations. However, this only works in a square matrix, and each equation must be in the form ax1+ax2+...=C.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-12-04T21:22:48 |
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|
https://zbmath.org/authors/?q=P%2A+Holod
|
# zbMATH — the first resource for mathematics
## Holod, Petro I.
Compute Distance To:
Author ID: holod.petro-i Published as: Holod, P.; Holod, P. I.; Holod, Petro; Holod, Petro I. External Links: Wikidata
Documents Indexed: 16 Publications since 1985
all top 5
#### Co-Authors
0 single-authored 7 Bernatska, Julia 3 Skrypnyk, Taras Volodymyrovych 1 Bezvershenko, Yulia V. 1 Kisilevich, A. 1 Kisilevych, O. V. 1 Klimyk, Anatoliy Ul’yanovich 1 Kondratiuk, S. 1 Kondratyuk, S. 1 Pakuliak, Stanislav Z.
all top 5
#### Serials
2 Theoretical and Mathematical Physics 1 Communications in Mathematical Physics 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Journal of Physics A: Mathematical and General 1 Journal of Nonlinear Mathematical Physics 1 Journal of Physical Studies 1 Journal of Geometry and Symmetry in Physics 1 Journal of Physics A: Mathematical and Theoretical
all top 5
#### Fields
11 Dynamical systems and ergodic theory (37-XX) 7 Partial differential equations (35-XX) 5 Quantum theory (81-XX) 3 Topological groups, Lie groups (22-XX) 2 Nonassociative rings and algebras (17-XX) 2 Differential geometry (53-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX)
#### Citations contained in zbMATH Open
7 Publications have been cited 31 times in 27 Documents Cited by Year
Geometry and topology of coadjoint orbits of semisimple Lie groups. Zbl 1208.22009
Bernatska, Julia; Holod, Petro
2008
On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014
Holod, P. I.; Klimyk, A. U.
1985
A generalized Landau-Lifshitz equation for an isotropic SU(3) magnet. Zbl 1157.82047
Bernatska, J.; Holod, P.
2009
Topological excitations in a two-dimensional spin system with high spin $$s \geq 1$$. Zbl 1177.82022
Bernatska, J. N.; Holod, P. I.
2009
Hierarchies of integrable equations associated with hyperelliptic Lie algebras. Zbl 1001.37075
Skrypnyk, T.; Holod, P.
2001
On separation of variables for integrable equations of soliton type. Zbl 1170.35506
Bernatska, Julia; Holod, Petro
2007
Resonance in a driven two-level system: analytical results without the rotating wave approximation. Zbl 1254.81106
Bezvershenko, Yulia V.; Holod, Petro I.
2011
Resonance in a driven two-level system: analytical results without the rotating wave approximation. Zbl 1254.81106
Bezvershenko, Yulia V.; Holod, Petro I.
2011
A generalized Landau-Lifshitz equation for an isotropic SU(3) magnet. Zbl 1157.82047
Bernatska, J.; Holod, P.
2009
Topological excitations in a two-dimensional spin system with high spin $$s \geq 1$$. Zbl 1177.82022
Bernatska, J. N.; Holod, P. I.
2009
Geometry and topology of coadjoint orbits of semisimple Lie groups. Zbl 1208.22009
Bernatska, Julia; Holod, Petro
2008
On separation of variables for integrable equations of soliton type. Zbl 1170.35506
Bernatska, Julia; Holod, Petro
2007
Hierarchies of integrable equations associated with hyperelliptic Lie algebras. Zbl 1001.37075
Skrypnyk, T.; Holod, P.
2001
On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014
Holod, P. I.; Klimyk, A. U.
1985
all top 5
#### Cited by 39 Authors
4 Skrypnyk, Taras Volodymyrovych 3 Kovalevskii, M. Yu. 2 Bernatska, Julia 2 Holod, Petro I. 2 Prykarpatsky, Anatoliy Karolevych 1 Amari, Yuki 1 Anderson, Louise 1 Bogolyubov, Nikolaĭ Nikolaevich jun. 1 Cahen, Benjamin 1 Cruz y Cruz, Sara 1 Enríquez, Marco 1 Ercolessi, Elisa 1 Fan, Yale 1 Glushchenko, Anatoliy V. 1 Gromov, Nikolai A. 1 Hanany, Amihay 1 Igonin, Sergeĭ Aleksandrovich 1 Kirwin, William D. 1 Le, Sook Teck 1 Loke, Hung Yean 1 Man’ko, Vladimir Ivanovich 1 Manno, Gianni 1 Meng, Guowu 1 Mihaylov, Georgi 1 Peletminskii, A. S. 1 Peletminskii, Sergey V. 1 Prykarpatsky, Yarema Anatoliyovych 1 Ramgoolam, Sanjaye 1 Rodríguez-Gómez, Diego 1 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Sawado, Nobuyuki 1 Schiavina, Michele 1 Slyusarenko, Yurii V. 1 Trushkov, Vladimir 1 van de Leur, Johan W. 1 Vlasii, Nadiia D. 1 von Rütte, F. 1 Wang, Yicao 1 Wiese, Uwe-Jens
all top 5
#### Cited in 16 Serials
3 Theoretical and Mathematical Physics 3 Journal of Geometry and Physics 3 Journal of High Energy Physics 2 Journal of Mathematical Physics 2 Nuclear Physics. B 2 Physics Letters. A 2 Geometriae Dedicata 2 Annals of Physics 1 Communications in Mathematical Physics 1 Israel Journal of Mathematics 1 Physics Letters. B 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Physica D 1 Foundations of Physics 1 Symmetry
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#### Cited in 16 Fields
13 Quantum theory (81-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Topological groups, Lie groups (22-XX) 6 Differential geometry (53-XX) 5 Nonassociative rings and algebras (17-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Algebraic geometry (14-XX) 3 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-05-16T14:32:53 |
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|
https://mfix.netl.doe.gov/doc/mfix/20.1.0/model_setup/solids.html
|
# 4.6. Solids¶
The solids pane is used to set solids phases material properties. The “Materials” tab sets material properties shared by most models (TFM, DEM and PIC). Specific settings for each model are accessed through their respective tabs (TFM, DEM, or PIC).
## 4.6.1. Creating a Solids phase¶
A new solids phase is created by clicking the add button, , at the top of the solids table. This will create a new entry in the table. The table summarizes all defined solids phases by listing the name, model, particle diameter and density. A blank entry in the density means the particle density is variable (it depends on its chemical composition).
Name
The name used to refer to the solids phase in the GUI. By default, the solids phase is called “Solid” followed by its assigned phase number. The phase number is incremented every time the button is pressed. The solids phase name may be renamed for convenience (optional). This name will appear in other panes or tabs when referring to the solids phase (say while setting initial or boundary conditions).
The modeling approach used to represent the solids phase. Available options include TFM (Two-Fluid Model), DEM (Discrete Element Model) and PIC (Particle in Cell). The setting is currently locked (the same solid model must be used for all solids phases), and mirrors the solver selection in the Model Setup pane.
## 4.6.2. Deleting a Solids phase¶
A solids phase can be deleted by selecting it (click on its name in the solids table) and clicking the remove button, , at the top of the solids table. If the solids phase is used in the model with a non-zero solids fraction (say in an initial or boundary condition), the deletion will need to be confirmed by the user. If confirmed, the deleted solids volume fraction will be assigned back to the fluid phase.
## 4.6.3. General Solid Model Options¶
Solve momentum equation (TFM only)
By default, all momentum equations are solved. Individual momentum equations may be disabled by toggling the check box.
Solve species equations
By default, species transport equations are not solved for the solids phase. If species equations are enabled, species will need to be added to the solids phase using the solids species tool. ADD REF
## 4.6.4. Solids phase Material Properties¶
Some material properties are only needed for a specific solid model or when the energy or species equation is solved.
Diameter $$(m)$$
The initial particle diameter. It will remain constant for non-reactive flows, and for reactive flows with a variable density. If the density is constant, and chemical reactions take place, the particle diameter will vary to reflect particle mass gain/loss.
Density $$(kg \mathbin{/} m^3)$$
The particle density can be set as:
• Constant:
• A positive (non-zero) number must be provided.
• The diameter may change due to chemical reactions.
• Variable:
• The density is computed from particle’s mass and volume.
• The particle mass is function of the particle’s chemical composition.
• A variable density can only be used if species equations are solved.
Viscosity $$(Pa \cdot s)$$ TFM only
It may be specified using one of the following approaches:
• Constant:
• A positive (non-zero) number must be provided.
• Continuum Solids stress Theory
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Molecular weight $$(\frac{kg}{kmol})$$
It may only be specified using the following approach, and is only used when Energy and solids species equations are solved:
• Mixture
• Requires species be used to defined the solid.
• Requires species mass fractions be specified for the whole domain and all flow boundary conditions
Specific heat $$(\frac{J}{kg \cdot K})$$
It may be specified using one of the following approaches (only used when Energy and species equations are solved):
• Constant:
• A positive (non-zero) number must be provided.
• Mixture
• Requires species be used to defined the fluid.
• Requires species mass fractions be specified for the whole domain and all flow boundary conditions
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Thermal conductivity $$(\frac{W}{m \cdot K})$$
It may be specified using one of the following approaches:
• Constant:
• A non-negative number must be provided.
• Temperature-Dependent
• Option available for TFM only.
• Requires solids phase temperature be specified for the whole domain and all flow boundary conditions.
• User-Defined Function (UDF)
• Option available for TFM only.
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Emissivity $$(-)$$ DEM only
The emissivity of the DEM solids phase. Leaving it blank or setting a zero value turns radiation off.
Parcel weight $$(-)$$ PIC only
A default parcel weight (number of particles per parcel) may be specified for convenience (default value of one). it is used to define a default statistical weight for parcels in initial conditions regions and mass inflows. Instead of defining the same parcel weight in every initial condition and mass inflow, this default value is automatically applied. The default value can be overwritten where needed.
## 4.6.5. Solids Model Species¶
Specie that comprise the solid phase are summarized in the species overview table. New species are added by clicking the add button, , at the top of the species table.
Disable close pack (TFM only)
Options to enable/disable a TFM phase from forming a packed bed. This is typically used to make the solids phase behave as a liquid phase.
Enable added mass force (TFM only)
Options to enable/disable the added (or virtual) mass force in a TFM phase. This tends to stabilize bubbly gas/liquid flows.
## 4.6.7. TFM Settings¶
Specific Two-Fluid Model settings are accessed from the TFM tab.
Packed bed void fraction $$(-)$$
The void fraction at close pack.
Viscous stress model
The solids phase stress model. Options include the algebraic formulation or various kinetic theories requiring solving a Partial Differential Equation for the granular energy:
• Algebraic Formulation [DEFAULT]
• Lun et al, 1984
• Iddir & Arastoopour, 2005
• Simonin, 1996 (requires k-ε turbulence enabled)
• Cao & Ahmadi, 1995 (requires k-ε turbulence enabled)
• Garzo and Dufty, 1999 (monodisperse system only)
• Garzo, Tenneti, Subramaniam, Hrenya, 2012 (monodisperse system only)
• Garzo, Hrenya and Dufty, 2007 - Requires at most two solids phases - Requires Wen-Yu or HYS drag model - Selection not available with added mass force
Frictional stress model
• Schaeffer model [DEFAULT]
• Srivastava and Sundaresan
• Only solids pressure
Solids volume fraction at onset of friction $$(-)$$
The minimum solids fraction above which the Srivastava and Sundaresan model sets in.
Particle-particle restitution coefficient $$(-)$$ :
The coefficient of restitution for particle-particle collision.
Interphase friction coefficient $$(-)$$ :
The coefficient of friction between particles of two solids phases.
Angle of internal friction $$(\deg)$$ :
The angle of internal friction. The plastic regime stress can be turned off by setting this value to zero.
• Carnahan-Startling (only option for monodisperse systems)
• Lebowitz (default for polydisperse system)
• Mansoori (polydisperse system)
• Modified Lebowitz (polydisperse system)
• Modified Mansoori (polydisperse system)
Stress blending
The blending function used to smooth transition around the packed bed volume fraction. It requires the Schaeffer frictional stress model.
• None [DEFAULT]
• Hyperbolic Tangent
• Sigmodial
Segregation slope coefficient $$(-)$$
Coefficient used in calculating the initial slope in segregation for polydisperse systems.
Max packing correlation
The correlation used to compute the maximum packing for polydisperse systems:
• Constant [DEFAULT]
• Yu & Standish
• Fedors & Landel (only with two solids phases)
Excluded volume in Boyle-Massoudi stress $$(?)$$
The excluded volume in Boyle-Massoudi stress. It is only used with the algebraic formulation of viscous stress model (optional).
## 4.6.8. DEM Settings¶
Specific Discrete Element Model settings are accessed from the DEM tab.
Enable automatic particle generation
Initialize particle location and velocity based on information from Initial Condition regions. If this option is disabled and any initial condition uses a non-zero solids volume fraction, the user will be prompted to turn on this option. Disabling this option will read initial particle location and velocity from a user generated text file (particle_input.dat) that must be saved in the project directory.
Data file particle count $$(-)$$
The number of particles read from particle_input.dat file when the automatic particle generation is turned off. This number must be smaller or equal to the number of lines in the file.
Integration method
The DEM time stepping scheme when integrating the particle trajectories (acceleration to velocity and velocity to position):
• Euler [DEFAULT]
Collision model
The soft-sphere collision model:
• Linear Spring Dashpot (LSD)
• Hertzian
Coupling method
The level of coupling between the gas phase and the solids phase:
• One-way coupled
• Fully coupled
Interpolation
The direction of interpolation between field and particle data:
• No interpolation
• field-to-particle and particle-to-field
• field-to-particle only
• particle-to-field only
Scheme
The interpolation scheme:
• None (centroid method)
• Garg, 2012 (interpolation width is dictated by grid spacing)
• Square DPVM (Divided Particle Volume Method), requires an interpolation width.
Width $$(m)$$
The square DPVM interpolation width.
Enable mean field diffusion
Smooths the disperse phase average fields by solving a diffusion equation.
Width $$(m)$$
The diffusion length scale.
Enable explicit coupling of interphase quantities
Option to explicitly couple the fluid and solids hydrodynamics.
Friction coefficient $$(-)$$
The particle-particle and particle-wall Coulomb friction coefficient. This is required for both the LSD and Hertzian collision models.
Normal spring constant $$(\frac{N}{m})$$
The particle-particle and particle-wall normal spring constant (LSD collision model).
Spring norm/tan ratio $$(-)$$
The ratio of normal to tangential spring constants for particle-particle and particle-wall (LSD collision model).
Damping norm/tan ratio $$()$$
The ratio of normal to tangential damping factors for particle-particle and particle-wall (LSD collision model).
Young’s modulus $$(Pa)$$
The wall and particles (one entry per phase) Young’s modulus (Hertzian collision model).
Poisson’s ratio $$(-)$$
The wall and particles (one entry per phase) Poisson’s ratio (Hertzian collision model).
Restitution coefficients (normal) $$(-)$$
The list of normal restitution coefficients for particle-wall and particle-particle interaction. The particle-particle entries are arranged into a symmetrical matrix. The diagonal terms and the upper side of the matrix need to be filled. There is one entry per phase for the particle-wall coefficient. This settings is required for both the LSD and Hertzian collision models.
Restitution coefficients (tangential) $$(-)$$
The list of tangential restitution coefficients for particle-wall and particle-particle interaction. The particle-particle entries are arranged into a symmetrical matrix. The diagonal terms and the upper side of the matrix need to be filled. There is one entry per phase for the particle-wall coefficient. This settings is only required for the Hertzian collision model.
Cohesion model
Toggles the van der Waals cohesion model. When turned on, additional parameters need to be set (see below):
Hamaker constant $$(J)$$
The particle-particle and particle-wall Hamaker constant used in the van der Waals cohesion model.
Outer cutoff $$(m)$$
The particle-particle and particle-wall maximum separation distances above which the van der Waals cohesion forces are set to zero.
Inner cutoff $$(-)$$
The particle-particle and particle-wall minimum separation distances below which the van der Waals cohesion forces are computed using a surface adhesion model.
Asperities $$(-)$$
The mean radius of surface asperities used in the cohesive force model.
Minimum fluid volume fraction $$(-)$$
Threshold used to clip the fluid phase volume fraction (to avoid non-physical values, typically when a particle size is near a small cut cell).
Neighbor search method
The neighbor search algorithm:
• Grid-based
• N-Square
Max steps between neighbor search $$(-)$$
The maximum number of DEM iterations between two neighbor searches. The neighbor search may be called earlier if the particle moves a distance greater than a defined quantity (see below).
Factor defining particle neighborhood $$(-)$$
A multiplying factor applied to the particle’s radius to define the region where particle neighbors are searched from.
Distance/diameter triggering search $$(-)$$
The distance a particle can travel before triggering an automatic neighbor search.
Search grid partition $$(-)$$
The number of DEM grid cells in each direction used for the neighbor search. This is an optional setting. If left undefined, the number of cells is computed so that the DEM grid size is three times the maximum particle diameter.
Enable user scalar tracking
Turns on the tracking of user-defined scalars attached to each particle. When the tracking is enables, the number of scalars (positive integer) needs to be set.
Minimum conduction distance $$(m)$$
The minimum separation distance between particles (used in the particle-fluid-particle conduction model to remove singularity).
Fluid lens proportionality constant $$(-)$$
Constant used to calculate the fluid lens radius that surrounds the particle (used in the particle-fluid-particle conduction model).
Young’s modulus used to correct DEM conduction $$(Pa)$$
The wall and particles (one entry per phase) Young’s modulus used to correct the DEM conduction. These optional input are used with both LSD and Hertzian collision models. Particles are typically made softer to increase the DEM time step. This may lead to inaccurate conduction. If defined, this Young’s modulus will be used to correct the DEM conduction model.
Poisson’s ratio used to correct DEM conduction $$(-)$$
The wall and particles (one entry per phase) Poisson’s ratio used to correct the DEM conduction. These optional input are used with both LSD and Hertzian collision models.
## 4.6.9. PIC Settings¶
Specific Particle in Cell settings are accessed from the PIC tab.
Many of the PIC settings refer to the PIC solids stress model, which influences parcel motion:
$$\tau_p=\frac{P_p \epsilon_p^\gamma}{\max[\epsilon_{cp} - \epsilon_p , \delta(1-\epsilon_p)]}$$
Void fraction at close pack $$(-)$$
The void fraction $$(\epsilon_{cp})$$ at maximum packing.
Volume fraction exponential scale factor $$(-)$$
The empirical exponent $$(\gamma)$$ on solids fraction in the solids stress model. Typical values are between 2.0 to 5.0.
Pressure linear scale factor $$(Pa)$$
The empirical pressure $$(P_p)$$ constant in the solids stress model. Typical values are 10 to 1000 Pa.
Empirical dampening factor $$(-)$$
A factor in a restitution coefficient for comparing solids stress with slip velocity. Typical value is 0.85.
Non-singularity constant $$(-)$$
The constant $$(\delta)$$ to prevent division by zero in solids stress model. Typical value is 1.0E-8.
Wall normal restitution coefficient $$(-)$$
The parcel-wall restitution coefficient for normal velocity component after wall collision.
Wall tangential restitution coefficient $$(-)$$
The parcel-wall restitution coefficient for tangential velocity component after wall collision.
Solids slip velocity scale factor $$(-)$$
A damping coefficient on slip velocity. Typical value is 1.0.
| 2022-05-18T15:31:37 |
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http://blog.case.edu/ajc30/free_software/index.html
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## August 01, 2007
### Spread Open Media vs PlayOgg
Xiph.org and Creative Commons seem to be behind a new open format advocacy campaign called Spread Open Media at the same time the Free Software Foundation called PlayOgg.
Spread Open Media or SOM which they call themselves for short looks pretty unprofessional. It is a word press blog with a narrow column of text. It doesn't seem to have any links on how to play any of the formats it supports. It doesn't have any sort of badge, button, or logo. they accuse PlayOgg of using "threat tactics, desinformation [sic], and ignorancy." That brings me to spelling I know I'm not a great speller but if I were running some sort of public campaign I'd be sure to have some sort of proof reader. Spread Open Media says to "avoid MP3, AAC, H.264, Xvid, and OOXML like the plague" but it doesn't say why. The truth is that MP3, AAC, H.264, and Xvid are open formats I have specifications for all of them, and anyone can buy the specs at the iso store for a fee. They are an inferior kind of open format because they are patent encumbered. Their name also seems a little bit too long. Spread Open Media is twice as long as PlayOgg, it's long enough that they call themselves SOM for short but unfortunately that don't own som.org.
PlayOgg may not look like a work of art wither but it looks a lot more professional than spread open media. It has a button that you can put near Ogg links, and conveniently PlayOgg.org points to the playOgg site. I disagree with PlayOgg's statement "Microsoft had to pay $1.5 billion after being sued for using MP3 without a license. With Ogg Vorbis, they would have been safe" because the patent in question was thought to be a non issue because it wasn't disclosed during development but was then brought out in the open much later now that MP3 is ubiquitous. In theory there could be several patents on which Vorbis/Theora potentially infringe where the holder may be waiting for popularity to increase before acting. It happened to MP3 and GIF. One blogger blasts PlayOgg saying: "This is the perfect example of how not to be an open source advocate; promoting a free audio format by suggesting to users that they .... download an entirely new media player." But at least PlayOgg gives some way to play these files unlike Spread Open Media. I do agree it would be good for PlayOgg to also link the Illiminable Ogg DirectShow Filters and XiphQT but i think that VLC should be displayed first because it is free software and it runs on any platform. Posted by ajc30 at 06:39 PM | Comments (0) | TrackBack ## April 09, 2007 ### In honor of etch... new feisty backports It's been a big day for Debian with the release of Etch and a new project leader being elected. In honor of these events I've made some bleeding edge backports from debian experimental, NEW, and unstable to Ubuntu feisty. The packages: * GNU Octave 2.9.10 (and related packages) - A MATLAB like tool for numerical computations * linuxdcpp 0.0.1.cvs20070330 - a GTK+ port of DC++ * zzuf 0.8.1 - a tool for fuzzing input files to expose buffer overflows (written by the new DPL) * audacity 1.3.2 - The beta release, this is built against gtk+ 2 All packages are available at http://filer.case.edu/ajc30/pub/debs/feisty/ Posted by ajc30 at 03:32 AM | Comments (1) | TrackBack ## November 08, 2006 ### Unofficial Sid backports for Edgy I'm now using Ubuntu 6.10 Edgy Eft on my laptop. However some package versions were frozen earlier than I would have wished. I have backports of gaim-2.0.0beta4 and octave-2.9.9 as well as a port of linuxdcpp from Debian sid. I've posted them at http://filer.case.edu/ajc30/pub/debs/edgy/. More will probably come along until feisty gets usable. Posted by ajc30 at 01:14 AM | Comments (0) | TrackBack ## July 04, 2006 ### Bits and Bytes I found two articles to follow up my previous post on Google's shortcomings. The first is a sixth grader's essay on why Google is great, and the second is a listing of webservices marketshares with commentary comparing Google to MSN. I found some really sweet Facebook userscripts at facebookWithBenefits. The best are post2faceBook which adds a quick post feature and inYOfaceBook which magnifies user picture thumbnails on mouse over. Mugshot for Windows still leaves a lot ot be desired. It ignores the users browser prefrence (probably to maintain the login session between the tray icon and the browser) and it only supports iTunes and YME. Digging into the source it looks like it uses two different sets of classes to abstract them. I made some new mugshot and loudmouth packages for dapper as jdub's mugshot packages are now out of date and the dapper loudmout packages crash on the mugshot out of date notification. The Gnome desktop has made steady progress lately but sometimes the developers seem so focused on visible changes that they forget about their backend stated goals. For instance they want to migrate from popt to GOption but the patch for gnome-terminal has been sitting for three months now. They have already recognized patch rot as a barrier to participation. Patch rot means that patches are lees likely to cleanly apply and is also frustrating to patch writers. What they really need is a Patch Marshall to make sure that submitted patches either get accepted or denied in a reasonable amount of time. Posted by ajc30 at 11:16 PM | Comments (0) | TrackBack ## June 03, 2006 ### Cool new social and collaboration tools from RedHat Two new interesting collaboration/social networking websites have been released from Red Hat. Unlike what you might expect from a company like Red Hat these sites focus on communication and discussion rather than source code or bug tracking. First is the more technically orientedRed Hat 108. . Second is the more entertainment oriented Mugshot. You can hear about both of them in Szulik's keynote at the 2006 Red Hat Summit. I really don't think I can give a more accurate description of either of these because I'm still learning about them, so you should check them out for yourself. Posted by ajc30 at 12:21 AM | Comments (0) | TrackBack ## April 19, 2006 ### Getting Right Shift to Work in Olin 404.5 Some of you have probably noticed that right shift doesn't work on under GNOME on the Sun Rays in Olin 404.5. The solution is to go to System > Prefrences > Keyboard Shortcuts, scroll down to E-mail click on it and hit backspace. Or you can run this command gconftool-2 --type string --set /apps/gnome_settings_daemon/keybindings/email disabled I found this from the Ubuntu on Sun Ray guide. It also has instructions on how to fix the Alt keys. Another good GNOME on Sun Ray guide is This blog post by a Sun employee. I recommend turning off wallpaper gconftool-2 --type string --set /desktop/gnome/background/picture_options none gconftool-2 --type string --set /desktop/gnome/background/primary_color \#037AD6 gconftool-2 --type string --set /desktop/gnome/background/color_shading_type solid and the desktop gconftool-2 --type bool --set /apps/nautilus/preferences/show_desktop false Posted by ajc30 at 10:51 AM | Comments (4) | TrackBack ## March 03, 2006 ### WebDAV and Windows Yesterday I had to manage some files over WebDAV. Explorer on Windows XP refused to open the share. The easiest way seemed to be to run konqueror over a remote X11 ssh tunnel from volatile.case.edu. Is functional WebDAV support slated for Windows Vista? P.S. Windows web developers, this is probably a good way to see how khtml renders your pages. Posted by ajc30 at 11:33 AM | Comments (1) | TrackBack ## March 01, 2006 ### UNIX software and the Free desktops Has else anyone noticed that despite growth and popularity of Free desktops like GNOME, KDE, and XFCE on X11 that traditional UNIX Software vendors like Mentor Graphics, Mathworks, and Synopsys continue to stick with old technology (Motif, etc.)? I know the EDA world has been much more centered on proprietary UNIXes in the past than on BSDs and Linux. But the open UNIXes are becoming more popular and the proprietary UNIXes are becoming more open. Even Sun has already open sourced Solaris and replaced CDE with JDS (re-branded GNOME) on Solaris. But the expensive UNIX software continues to ancient toolkits. These expensive programs are really starting to look dated. Now I'll admit the versions of Synopsys and Mentor Graphics software that I use a re a few years old but even then the advantages of a modern toolkit should have been clear and I am using the current version of MATLAB. I see a few posts relating to Gtk+ and Qt on DeepChip.com but nothing big, there seems to be no serious movement toward modern toolkits. There also doesn't seem to be any word coming from synopsys.com of a move toward modern toolkits though there are a few job postings that mention Qt. I realize that the majority of the time people don't use the GUIs for these tools but maintaining one that really sucks seems to be a waste of energy. Is this just a case of "if it ain't broke don't fix it" where they see no need to migrate existing tools or are the vendors actively avoiding these technologies? Posted by ajc30 at 12:00 PM | Comments (0) | TrackBack ## February 17, 2006 ### Free/Gratis Software round-up I thought I'd share some links to some software I've been using lately all of it is Free Software except for LTSpice/SwitcherCAD III which is gratis (freeware). • LTSpice/SwitcherCAD III - A circuit design tool and by far the nicest SPICE GUI I've ever used. • Cygwin/X - A port of X11 and Unix shells and utilities to Windows. It's prefect for connecting to remote Unis machines. It is so much nicer than the (ancient) version of Exceed that I've been forced to use from time to time. With such nice free software why is WinaXe still on the software center? Are we paying for it? • Maxima - A symbolic math tool similar to Mathematica. While being not as complete or polished or easy to use, it does have the advanteage of not having to jump through any license hoops. I gave up on Mathematica when it told me that my license was expired and to visit the website to generate a new one but the website wouldn't let me. • x264 - Because MPEG-4 ASP (Divx, Xvid) is so last year, the best H.264 video encoder. Winner of the Doom9 CODEC shootout. If you are going to use a patent encumbered CODEC it should be H.264 and this is THE H.264 encoder. • ffdshow - ffmpeg as ported to a direct show filter. Supports virtualy every video and audio format including H.264. Posted by ajc30 at 01:32 PM | Comments (0) | TrackBack ## September 11, 2005 ### It's like eTerm for Windows Today I came across one of those Programs I just feel compelled to share. It's a terminal emulator for windows called Console. It's much more configurable than the built in one and it uses native themes. It supports transparency, multiple configurations, z-order, system tray mode, focused and unfocused settings, and a few other things. Posted by ajc30 at 12:05 AM | Comments (1) | TrackBack ## August 16, 2005 ### Thank You Dr. Fourier Recently, I noticed that there don't seem to be any Free (as in GNU) Fourier/Laplace/Z tables. Wikipedia has Integral Tables and (Wikipedia also has Fourier Tables (which aren't particularity useful because they use different normalization constants than I need) but what I envision is even more than that. I'd like to see Free tables where you can select specific and specific types of entries and export to LaTeX, MathML, PDF, PS, or rasterize to PNG at a given size. This would be a great tool for students. Does any one know of any free tables or have any thoughts on this? As a final thought: u(t)\overset \mathcal{F} \longleftrightarrow \frac{1}{{j\omega }} + \pi \delta (\omega ) (and that too far to long to set) Posted by ajc30 at 08:02 PM | Comments (2) | TrackBack ## July 01, 2005 ### Bug Report for the Month of June 2005 I slacked off a little this month. Also this only includes bugs from public bug tracking systems, i.e. not work. Bug Report for the Month of June 2005 BTS ID Date Filed Summary Status Comments Ubuntu 7454 2005-03-11 About Ubuntu (from gnome panel) missing a section title RESOLVED FIXED Fixed in June Ubuntu 11516 2005-06-05 replace debian package search with ubuntu package search NEW GNOME 307398 2005-06-12 blank IMAP warning messages RESOLVED FIXED Thanks NotZed Mozilla 297869 2005-06-16 Objects slide on middle click NEW Try it on my main blog summary Ubuntu 11918 2005-06-17 gdm has runtime dependency on ksh not reflected in package deps RESOLVED FIXED Vim is real nice, but I really need some good visual XML/XSLT tools. Posted by ajc30 at 10:46 PM | Comments (0) | TrackBack ## May 29, 2005 ### Tar Wars Or Is the FSF the Microsoft of UNIX? Friday at work, I had to unpack a gzipped tarball... in Solaris. This ordinarily is quite a mundane task that I've done thousands of times. But this time something was rotten in the state of UNIX. Normally with gnu tar, tar xf file.tar.gz does the task. I wasn't surprised when this didn't work though as this feature was added to gnu tar quite recently. so i tried what I used to do when I first started using Linux, tar xzf filename.tar.gz, again this didn't work. Then I remembered that I had heard that the compression flags were a gnu extension to tar and not supported by many implementations of tar. I also remembered seeing pipe instructions come with many gzipped tar balls. I quickly found on gzip.org: gunzip < file.tar.gz | /usr/bin/tar xvf -. Now I've never had problems with this on EECS's sun boxen. This appears to be because we actually have tar in four different places on them. In PATH order we have: ajc30@bender ~$ /usr/pkg/bin/tar
usage: tar [-]{crtux}[-befhjlmopqvwzHLOPXZ014578] [archive] [blocksize]
[-C directory] [-T file] [-s replstr] [file ...]
ajc30@bender ~ $/usr/local/bin/tar /usr/local/bin/tar: You must specify one of the -Acdtrux' options Try /usr/local/bin/tar --help' for more information. ajc30@bender ~$ /usr/bin/tar
Usage: tar {txruc@}[vfbFXhiBDEelmopwnq[0-7]] [-k size] [tapefile] [blocksize] [exclude-file] [-I include-file] files ...
ajc30@bender ~ \$ /bin/tar
Usage: tar {txruc@}[vfbFXhiBDEelmopwnq[0-7]] [-k size] [tapefile] [blocksize] [exclude-file] [-I include-file] files ...
In order they appear to be NetBSD's tar, Gnu tar 1.13, Sun's tar, and Sun's tar not on PATH. NetBSD's tar seems to support the compression flags like gnu tar but not auto detection of compression. Gnu tar 1.13 also lacks auto detect. And obviously Sun's tar doesn't support either.
Now command line incompatibility is one thing but apparently there are problems with opening tar files themselves. It seems that OpenBSD's tar could not properly unpack Zope, which apparently used gnu extensions to tar to support long file names. Now it appears that since then OpenBSD tar has become compatible (based on unpacking with both tars on OpenBSD 3.6 and comparing with diff -r).
Another example is m4. The tex build system uses m4 -P yet according to tex-live mailing list m4 -P is a GNUism and not supported by IRIX's m4.
More familiar to people is the bash issue. Bash (maintained by out very own Chet Ramey) is a POSIX compatible shell and also adds a variety of use features that we desire from a more modern shell. Some systems (such as Debian) use bash as their /bin/sh. Then in these systems shell scripts assuming /bin/sh is bash creep in. And voilà incompatibility with other POSIX shells. Of course the shell world is compatibility is a nightmare. To quote the autoconf documentation: "there are some corner cases in the Bourne shell that are not completely compatible with a POSIX shell.... While most (at least most System V's) do have a Bourne shell that accepts shell functions most vendor /bin/sh programs are not the POSIX shell. So while most modern systems do have a shell somewhere that meets the POSIX standard, the challenge is to find it." And Bash even has it's own list of incompatibilities with it's own 1.x series (despite that bash is still my favorite shell)
Now it seems to me that in these examples GNU "embraced and extended" existing standards. For this very same behavior we vilify Microsoft. In this era of of GNU/Linux's rapid growth it seems like this might hurt competing UNIX like systems and cause unintentional GNU/Linux lock-in.
## May 09, 2005
### Confessions of an Ex-Linux User
At the beginning of the summer of 2000 my family got a new computer, this freed up our previous machine for my grand GNU/Linux experiment. After playing around with Phat Linux to test the waters and then Linux Mandrake I settled on Red Hat. From that point I used Red Hat Linux exclusively until the summer of 2003 where I started dual booting on my new college computer.
These days I'm back to using Windows almost exclusively now. Windows XP is far stabler than the Windows 98 that I dumped in 2000. Firefox is also nice enough that I can use it in place of IE and not have to worry about taking down the whole shell (though the Linux/X11 port is fairly horrible). And Thunderbird protects me from those nasty Outlook (Express) worms. It's nice being able to almost properly view documents that people have decided to typeset in MS Word (for the love for god, why?). The Windows Gaim port is in a good enough condition that I can use it in place of that add-ridden AOL client. And Media Player Classic has made multimedia a pleasure on windows. I'm also enjoying the excellent Nero suite, both their video tools and their burning tools. Gaming on Windows allows for more choices; Linux has some big title games like Doom 3 and UT2004 and lots of older games running on ported VMs but doesn't have nearly as many games as Windows. As a Linux user, I did (and still do) tend to play more console games though.
MATLAB is another reason. Though there is a Linux (with optional very ugly X11 support) port, I can't use the features I need the most. I need to use the fdatool quite a bit but it just isn't usable on the X11 port and I don't mean the Havoc Pennington it still has features unusable, I mean the gui is so horribly skewed and illegible that it is a real pain to use.
Windows can still really could use a few things though. I'd love to be able to have a tabbed terminal in windows. I'd like to see better out of the box archive support. I'd really like standard tar, gzip, bzip2, rar, and possibly 7z support, with tight shell integration. I'd also like to see a Direct Show Ogg demuxer, Vorbis decoder, and full MPEG 4 support (ASP/AVC/mp4). In the more likely to actually happen arena, windows should shorten the names of its default system folder location for those who have the misfortune to use it in the command line "cd c:\Documents and Settings\Username\My Documents" us a mouthful as is "cd c:\Program Files\Common Files" I realize that there are the tilde names like c:\docume~1\Username\mydocu~1" but that is also awkward. I also know about command completion but in some situations its not feasible. the My Documents, My Pictures, My Music, etc. folders should have the My lopped off, of course they are yours, and "C:\Program Files\Common Files" can become c:\programs\common, of course they store files, and "Documents and Settings" can become "profiles" because it is easier to type.
There are a few things on the Linux side that could win it massive amounts of points. It would be sweet to have a grub menu item or boot up key combination to not start gdm/kdm/xdm. Native Eclipse would also be sweet. Ubuntu got close I could smell it but progress mysteriously stopped over a month ago. I good audio player would also be awesome. Despite the fact that I am currently using Winamp on Windows I don't like the Beep/XMMS Winamp-cloned bitmap interface. Rhythmbox is pretty nice but could really use a plug-in system, right now rbscrobbler is such a hack. Firefox also needs a serious clean up. You shouldn't need to be root to install search plug-ins.
Maybe someday I will return but for now I am content with Windows.
EDIT 5/11/05: I added some stuff, I didn't mean to take the entry live earlier
## April 01, 2005
### New Operating System Experiences
Lately I've had the opportunity to work with some operating systems that are new to me.
The fist is Ubuntu hoary. I've worked with Debian on the server before so it wasn't totally foreign to me. I moved from Gentoo to Ubuntu because I was sick of waiting for slow compiles. All around it seems pretty decent but there are some things I'm not satisfied about:
1. There aren't any fast North American mirrors (chod's Gentoo mirror spoiled me)
2. It still has many of the standard gnome annoyances. For instance you need to edit an esoteric config file to edit the default file type handlers.
3. No packages for some really useful apps like eclipse. (It appears that they are working on this one.)
4. No packages for useful gratis non-free software like Java and recent versions of RealPlayer (the seem to have RealPlayer 8 though). This may come as a shock to you windows users but realplayer for X11 is really nice. And yes I do have the multiverse repository enabled.
5. I find dpkg really awkward I've heard for years about how rpm is allegedly inferior but I completely disagree. I love that rpm doesn't require me to poke around in the tarball, allows multiple single issue patches, allows command line build options, and has a single build macro/metadata file.
One thing that I really do like about Ubuntu is their choice to drop ESound in favor of polypaudio. Polypaudio seems to just work. I also like that they ship the non-free but super useful nVidia kernel drivers.
I 'm not sure about Ubuntu's unique color scheme. They a color scheme that they call human which really is brown. Some call it diarrhea brown others seem to love it. I haven't made up my mind yet.
In general Ubuntu just failed to impress me. I've heard their firefox desktop integration patches are pretty good but I don't use firefox. I know it seems to have a lot buzz it doesn't seem all that great.
While all of this is going on I've also been using OpenBSD on the Tau Beta Pi webserver. We chose OpenBSD because of its excellent security record. I made it my goal not to over gnuize the system but I did choose to install nano (I've always had problems with vi(m) over ssh) and gtar (I've grown dependent on gtar's special features) which I've made my default tar.
I had problems setting up apache to use mysql because of chroot consequences. I highly recommend that anyone setting up an OpenBSD system that you put /var/run and /var/www on the same partition. This is because the mysql socket requires a hardlink inside the apache chroot jail. I also had problems with the mysql init script or lack there of (I couldn't find one).
Ports came pretty naturally to me being an ex-gentoo user but I have no idea how to check for updates (etc.) without emerge, yum, or apt.
| 2014-11-24T15:08:15 |
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|
https://dlmf.nist.gov/15.4
|
# §15.4 Special Cases
## §15.4(i) Elementary Functions
The following results hold for principal branches when $|z|<1$, and by analytic continuation elsewhere. Exceptions are (15.4.8) and (15.4.10), that hold for $|z|<\ifrac{\pi}{4}$, and (15.4.12), (15.4.14), and (15.4.16), that hold for $|z|<\ifrac{\pi}{2}$.
15.4.1 $\displaystyle F\left(1,1;2;z\right)$ $\displaystyle=-z^{-1}\ln\left(1-z\right),$ 15.4.2 $\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};z^{2}\right)$ $\displaystyle=\frac{1}{2z}\ln\left(\frac{1+z}{1-z}\right),$ 15.4.3 $\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};-z^{2}\right)$ $\displaystyle=z^{-1}\operatorname{arctan}z,$ 15.4.4 $\displaystyle F\left(\tfrac{1}{2},\tfrac{1}{2};\tfrac{3}{2};z^{2}\right)$ $\displaystyle=z^{-1}\operatorname{arcsin}z,$ 15.4.5 $\displaystyle F\left(\tfrac{1}{2},\tfrac{1}{2};\tfrac{3}{2};-z^{2}\right)$ $\displaystyle=z^{-1}\ln\left(z+\sqrt{1+z^{2}}\right).$
15.4.6 $\displaystyle F\left(a,b;a;z\right)$ $\displaystyle=(1-z)^{-b},$ $\displaystyle F\left(a,b;b;z\right)$ $\displaystyle=(1-z)^{-a},$ ⓘ Symbols: $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$: $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $z$: complex variable, $a$: real or complex parameter and $b$: real or complex parameter Notes: See §15.2(ii) for treatment of the case when the third parameter is a nonpositive integer. Referenced by: §10.22(iv), §15.2(ii), §15.4(i), Erratum (V1.0.16) for Subsections 15.4(i), 15.4(ii) Permalink: http://dlmf.nist.gov/15.4.E6 Encodings: TeX, TeX, pMML, pMML, png, png Addition (effective with 1.0.16): This equation was expanded by adding the formula $F\left(a,b;a;z\right)=(1-z)^{-b}$. See also: Annotations for §15.4(i), §15.4 and Ch.15
where the limit interpretation (15.2.6), rather than (15.2.5), has to be taken when the third parameter is a nonpositive integer. See the final paragraph in §15.2(ii).
15.4.7 $F\left(a,\tfrac{1}{2}+a;\tfrac{1}{2};z^{2}\right)=\tfrac{1}{2}\left((1+z)^{-2a% }+(1-z)^{-2a}\right),$
15.4.8 $F\left(a,\tfrac{1}{2}+a;\tfrac{1}{2};-{\tan}^{2}z\right)=(\cos z)^{2a}\cos% \left(2az\right).$
15.4.9 $F\left(a,\tfrac{1}{2}+a;\tfrac{3}{2};z^{2}\right)=\frac{1}{(2-4a)z}\left((1+z)% ^{1-2a}-(1-z)^{1-2a}\right),$
15.4.10 $F\left(a,\tfrac{1}{2}+a;\tfrac{3}{2};-{\tan}^{2}z\right)=(\cos z)^{2a}\frac{% \sin\left((1-2a)z\right)}{(1-2a)\sin z}.$
15.4.11 $F\left(-a,a;\tfrac{1}{2};-z^{2}\right)=\tfrac{1}{2}\left(\left(\sqrt{1+z^{2}}+% z\right)^{2a}+\left(\sqrt{1+z^{2}}-z\right)^{2a}\right),$
15.4.12 $F\left(-a,a;\tfrac{1}{2};{\sin}^{2}z\right)=\cos\left(2az\right).$
15.4.13 $F\left(a,1-a;\tfrac{1}{2};-z^{2}\right)=\frac{1}{2\sqrt{1+z^{2}}}\left(\left(% \sqrt{1+z^{2}}+z\right)^{2a-1}+\left(\sqrt{1+z^{2}}-z\right)^{2a-1}\right),$
15.4.14 $F\left(a,1-a;\tfrac{1}{2};{\sin}^{2}z\right)=\frac{\cos\left((2a-1)z\right)}{% \cos z}.$
15.4.15 $F\left(a,1-a;\tfrac{3}{2};-z^{2}\right)=\frac{1}{(2-4a)z}\left(\left(\sqrt{1+z% ^{2}}+z\right)^{1-2a}-\left(\sqrt{1+z^{2}}-z\right)^{1-2a}\right),$
15.4.16 $F\left(a,1-a;\tfrac{3}{2};{\sin}^{2}z\right)=\frac{\sin\left((2a-1)z\right)}{(% 2a-1)\sin z}.$
15.4.17 $F\left(a,\tfrac{1}{2}+a;1+2a;z\right)=\left(\tfrac{1}{2}+\tfrac{1}{2}\sqrt{1-z% }\right)^{-2a},$ ⓘ Symbols: $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$: $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $z$: complex variable and $a$: real or complex parameter Notes: See §15.2(ii) for treatment of the case when the third parameter is a nonpositive integer. Referenced by: §15.4(i), §15.4(i) Permalink: http://dlmf.nist.gov/15.4.E17 Encodings: TeX, pMML, png See also: Annotations for §15.4(i), §15.4 and Ch.15
15.4.18 $F\left(a,\tfrac{1}{2}+a;2a;z\right)=\frac{1}{\sqrt{1-z}}\left(\tfrac{1}{2}+% \tfrac{1}{2}\sqrt{1-z}\right)^{1-2a},$ ⓘ Symbols: $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$: $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $z$: complex variable and $a$: real or complex parameter Notes: See §15.2(ii) for treatment of the case when the third parameter is a nonpositive integer. Referenced by: §15.4(i), §15.4(i) Permalink: http://dlmf.nist.gov/15.4.E18 Encodings: TeX, pMML, png See also: Annotations for §15.4(i), §15.4 and Ch.15
15.4.19 $F\left(a+1,b;a;z\right)=\left(1-(1-(\ifrac{b}{a}))z\right)(1-z)^{-1-b}.$ ⓘ Symbols: $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$: $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $z$: complex variable, $a$: real or complex parameter and $b$: real or complex parameter Notes: See §15.2(ii) for treatment of the case when the third parameter is a nonpositive integer. Referenced by: §15.4(i), §15.4(i) Permalink: http://dlmf.nist.gov/15.4.E19 Encodings: TeX, pMML, png See also: Annotations for §15.4(i), §15.4 and Ch.15
In (15.4.17), (15.4.18) and (15.4.19) when the third entry is a nonpositive integer one has to use the limit interpretation (15.2.6), rather than (15.2.5). Compare the final paragraph in §15.2(ii).
For an extensive list of elementary representations see Prudnikov et al. (1990, pp. 468–488).
## §15.4(ii) Argument Unity
If $\Re\left(c-a-b\right)>0$, then
15.4.20 $F\left(a,b;c;1\right)=\frac{\Gamma\left(c\right)\Gamma\left(c-a-b\right)}{% \Gamma\left(c-a\right)\Gamma\left(c-b\right)}.$
If $c=a+b$, then
15.4.21 $\lim_{z\to 1-}\frac{F\left(a,b;a+b;z\right)}{-\ln\left(1-z\right)}=\frac{% \Gamma\left(a+b\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}.$
If $\Re\left(c-a-b\right)=0$ and $c\neq a+b$, then
15.4.22 $\lim_{z\to 1-}(1-z)^{a+b-c}\left(F\left(a,b;c;z\right)-\frac{\Gamma\left(c% \right)\Gamma\left(c-a-b\right)}{\Gamma\left(c-a\right)\Gamma\left(c-b\right)}% \right)=\frac{\Gamma\left(c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a% \right)\Gamma\left(b\right)}.$
If $\Re\left(c-a-b\right)<0$, then
15.4.23 $\lim_{z\to 1-}\frac{F\left(a,b;c;z\right)}{(1-z)^{c-a-b}}=\frac{\Gamma\left(c% \right)\Gamma\left(a+b-c\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}.$
### Chu–Vandermonde Identity
15.4.24 $F\left(-n,b;c;1\right)=\frac{{\left(c-b\right)_{n}}}{{\left(c\right)_{n}}},$ $n=0,1,2,\dots$.
### Dougall’s Bilateral Sum
This is a generalization of (15.4.20). If $a,b$ are not integers and $\Re\left(c+d-a-b\right)>1$, then
15.4.25 $\sum_{n=-\infty}^{\infty}\frac{\Gamma\left(a+n\right)\Gamma\left(b+n\right)}{% \Gamma\left(c+n\right)\Gamma\left(d+n\right)}=\frac{\pi^{2}}{\sin\left(\pi a% \right)\sin\left(\pi b\right)}\*\frac{\Gamma\left(c+d-a-b-1\right)}{\Gamma% \left(c-a\right)\Gamma\left(d-a\right)\Gamma\left(c-b\right)\Gamma\left(d-b% \right)}.$
## §15.4(iii) Other Arguments
15.4.26 $F\left(a,b;a-b+1;-1\right)=\frac{\Gamma\left(a-b+1\right)\Gamma\left(\tfrac{1}% {2}a+1\right)}{\Gamma\left(a+1\right)\Gamma\left(\tfrac{1}{2}a-b+1\right)}.$
15.4.27 $F\left(1,a;a+1;-1\right)=\tfrac{1}{2}a\left(\psi\left(\tfrac{1}{2}a+\tfrac{1}{% 2}\right)-\psi\left(\tfrac{1}{2}a\right)\right).$
15.4.28 $F\left(a,b;\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{2};\tfrac{1}{2}\right)=\sqrt{% \pi}\frac{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{2}\right)}{\Gamma% \left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}b+\tfrac{1}{2}% \right)}.$
15.4.29 $F\left(a,b;\tfrac{1}{2}a+\tfrac{1}{2}b+1;\tfrac{1}{2}\right)=\frac{2\sqrt{\pi}% }{a-b}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b+1\right)\*\left(\frac{1}{\Gamma% \left(\tfrac{1}{2}a\right)\Gamma\left(\tfrac{1}{2}b+\tfrac{1}{2}\right)}-\frac% {1}{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}b% \right)}\right).$
15.4.30 $F\left(a,1-a;b;\tfrac{1}{2}\right)=\frac{2^{1-b}\sqrt{\pi}\Gamma\left(b\right)% }{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b\right)\Gamma\left(\tfrac{1}{2}b-% \tfrac{1}{2}a+\tfrac{1}{2}\right)}.$
15.4.31 $F\left(a,\tfrac{1}{2}+a;\tfrac{3}{2}-2a;-\tfrac{1}{3}\right)=\left(\frac{8}{9}% \right)^{-2a}\frac{\Gamma\left(\tfrac{4}{3}\right)\Gamma\left(\tfrac{3}{2}-2a% \right)}{\Gamma\left(\tfrac{3}{2}\right)\Gamma\left(\tfrac{4}{3}-2a\right)}.$
15.4.32 $F\left(a,\tfrac{1}{2}+a;\tfrac{5}{6}+\tfrac{2}{3}a;\tfrac{1}{9}\right)=\sqrt{% \pi}\left(\frac{3}{4}\right)^{a}\frac{\Gamma\left(\tfrac{5}{6}+\tfrac{2}{3}a% \right)}{\Gamma\left(\tfrac{1}{2}+\tfrac{1}{3}a\right)\Gamma\left(\tfrac{5}{6}% +\tfrac{1}{3}a\right)}.$
15.4.33 $F\left(3a,\tfrac{1}{3}+a;\tfrac{2}{3}+2a;e^{\ifrac{\mathrm{i}\pi}{3}}\right)=% \sqrt{\pi}e^{\ifrac{\mathrm{i}\pi a}{2}}\left(\frac{16}{27}\right)^{(3a+1)/6}% \frac{\Gamma\left(\frac{5}{6}+a\right)}{\Gamma\left(\frac{2}{3}+a\right)\Gamma% \left(\frac{2}{3}\right)},$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$: $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit and $a$: real or complex parameter Notes: See §15.2(ii) for treatment of the case when the third parameter is a nonpositive integer. Referenced by: §15.4(iii) Permalink: http://dlmf.nist.gov/15.4.E33 Encodings: TeX, pMML, png See also: Annotations for §15.4(iii), §15.4 and Ch.15
where the limit interpretation (15.2.6), rather than (15.2.5), has to be taken when $a=-\frac{1}{3},-\frac{4}{3},-\frac{7}{3},\dots$. Compare the final paragraph in §15.2(ii).
| 2021-02-24T18:25:40 |
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|
https://www.usgs.gov/center-news/volcano-watch-k-lauea-volcano-and-hvo-spotlight
|
# Volcano Watch — Kīlauea Volcano and HVO in the spotlight
Release Date:
This past week, the U.S. Geological Survey's Hawaiian Volcano Observatory (HVO) hosted 68 Japan Broadcasting Company (NHK) personnel and associates. NHK is scheduled to transmit a live 90-minute program from HVO to Japan on Saturday, February 20. Kīlauea Volcano and HVO are featured to demonstrate the quality of high definition TV and to attract a large audience.
This past week, the U.S. Geological Survey's Hawaiian Volcano Observatory (HVO) hosted 68 Japan Broadcasting Company (NHK) personnel and associates. NHK is scheduled to transmit a live 90-minute program from HVO to Japan on Saturday, February 20. Kīlauea Volcano and HVO are featured to demonstrate the quality of high definition TV and to attract a large audience.
Standing on the rim of Kīlauea Caldera, the host asks HVO Scientist-in-Charge Don Swanson a series of questions. Students of Floyd McCoy's geology classes, who use this column for information, may be interested in the answers.
The first question was, "Why is there a caldera?" The answer is that a caldera is a large collapse feature which forms over a magma storage area. When there is a rapid and massive withdrawal of magma from the storage area, the roof of the chamber is left unsupported and falls. The extent of the surface area affected by the roof collapse is dependent upon the size and depth of the magma body. The last caldera-forming event at Kīlauea Volcano was sometime before an explosive eruption in 1790.
The next question was, "With HVO located next to the caldera, is there any danger?" The answer is a qualified "yes." If an event similar to the 1790 eruption occurred today, HVO would be destroyed. However, these events are very infrequent, and if one were to happen, we would be able to predict it and evacuate.
Another question was, "Why are Kīlauea eruptions different from those in Japan?" The answer is that the chemical compositions of the Hawaiian and Japanese magmas are different, and this causes a difference in physical properties. Hawaiian basaltic magmas are very fluid and allow volatiles (gases) to escape readily. Japanese andesitic magmas are more viscous and tend to retain the volatiles. The higher gas content produces a higher pressure which results in more explosive eruptions.
The program moved indoors into the observatory to show the various volcano monitoring techniques. One of the questions posed by the host was, "Why are earthquakes important in the monitoring of the volcano?" The answer given is that earthquakes can indicate the expansion or overpressurization of a magma body or track the movement of magma within the volcano.
The scene shifts to the caldera floor near the 1982 spatter ramparts. Looking at the 1982 lava flow, Don is asked, "Why is lava black?" The answer is that the dark color of the shiny surface of the flow is from the glassy layer that forms when molten lava is chilled rapidly. If the melt were allowed to cool very slowly, minerals would be able to form and grow. The resulting color of the rock would be much lighter.
Another question was, "What causes the older rock surfaces to turn white?" The answer is that the action of hot, sulfurous liquids and gases alters the glassy surfaces, and secondary white (sulfide) minerals are formed.
The line of spatter ramparts on the caldera floor resemble the outline of the back of a giant stegosaurus. The question was asked, "How was this feature formed?" The answer is that this is the trace of the fissure that was active in 1982. The eruption was short-lived and, toward the end of the eruption, activity became sporadic and was confined to a few vents, but did not include the entire fissure. Occasionally, blobs of molten material were thrown out from the vents, and they coalesced to form the small cones.
The host asked, "How far down below our feet is the magma?" The answer is that seismic and deformationdata suggest that the magma is two to four kilometers (1.2 to 2.4 miles) below the caldera floor, but on occasion, it can intrude up to a depth of only a few hundred meters (yards).
The show will be seen live in Japan and, it is hoped, will be rebroadcast in a format that can be viewed in Hawaii.
### Volcano Activity Update
The eruption of Kīlauea Volcano continued unabated during the past week. Lava flows from the Puu O`o vent to the ocean near Kamokuna in a network of tubes. Breakouts from the tube system continue to occur occasionally. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying frequent collapses of the new land. The steam clouds are highly acidic and laced with glass particles.
No felt earthquakes were reported during the week ending on February 18.
| 2019-11-18T09:31:12 |
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|
https://pdglive.lbl.gov/Particle.action?init=0&node=M073&home=MXXX025
|
${\boldsymbol {\boldsymbol c}}$ ${\boldsymbol {\overline{\boldsymbol c}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search
${{\boldsymbol \psi}{(4415)}}$ $I^G(J^{PC})$ = $0^-(1^{- -})$
${{\mathit \psi}{(4415)}}$ MASS $4421 \pm4$ MeV
${{\mathit \psi}{(4415)}}$ WIDTH $62 \pm20$ MeV
Due to the complexity of the ${{\mathit c}}{{\overline{\mathit c}}}$ threshold region, in this listing, seen'' (not seen'') means that a cross section for the mode in question has been measured at effective $\sqrt {s }$ near this particle's central mass value, more (less) than 2${{\mathit \sigma}}$ above zero, without regard to any peaking behavior in $\sqrt {s }$ or absence thereof. See mode listing(s) for details and references.
| 2021-07-24T19:39:55 |
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|
https://par.nsf.gov/biblio/10299056
|
This content will become publicly available on October 1, 2022
Experimental study of the nature of the ${1}^{-}$ and ${2}^{-}$ excited states in ${}^{10}\mathrm{Be}$ using the ${}^{11}\mathrm{Be}\left(p,d\right)$ reaction in inverse kinematics
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10299056
Journal Name:
Physical Review C
Volume:
104
Issue:
4
ISSN:
2469-9985
| 2022-08-17T17:08:21 |
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https://en.m.wikipedia.org/wiki/Star_product
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Star product
In mathematics, the star product is a method of combining graded posets with unique minimal and maximal elements, preserving the property that the posets are Eulerian.
Definition
The star product of two graded posets ${\displaystyle (P,\leq _{P})}$ and ${\displaystyle (Q,\leq _{Q})}$ , where ${\displaystyle P}$ has a unique maximal element ${\displaystyle {\widehat {1}}}$ and ${\displaystyle Q}$ has a unique minimal element ${\displaystyle {\widehat {0}}}$ , is a poset ${\displaystyle P*Q}$ on the set ${\displaystyle (P\setminus \{{\widehat {1}}\})\cup (Q\setminus \{{\widehat {0}}\})}$ . We define the partial order ${\displaystyle \leq _{P*Q}}$ by ${\displaystyle x\leq y}$ if and only if:
1. ${\displaystyle \{x,y\}\subset P}$ , and ${\displaystyle x\leq _{P}y}$ ;
2. ${\displaystyle \{x,y\}\subset Q}$ , and ${\displaystyle x\leq _{Q}y}$ ; or
3. ${\displaystyle x\in P}$ and ${\displaystyle y\in Q}$ .
In other words, we pluck out the top of ${\displaystyle P}$ and the bottom of ${\displaystyle Q}$ , and require that everything in ${\displaystyle P}$ be smaller than everything in ${\displaystyle Q}$ .
Example
For example, suppose ${\displaystyle P}$ and ${\displaystyle Q}$ are the Boolean algebra on two elements.
Then ${\displaystyle P*Q}$ is the poset with the Hasse diagram below.
Properties
The star product of Eulerian posets is Eulerian.
References
• Stanley, R., Flag ${\displaystyle f}$ -vectors and the ${\displaystyle \mathbf {cd} }$ -index, Math. Z. 216 (1994), 483-499.
This article incorporates material from star product on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
| 2021-06-23T03:56:10 |
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|
https://math.wikia.org/wiki/Riemann_zeta_function
|
## FANDOM
1,168 Pages
The Riemann zeta function (also known as the Euler–Riemann zeta function), notated as $\zeta(s)$, is a function used in complex analysis and number theory. It is defined as the analytic continuation of the series
$\zeta(s) = \sum_{n = 1}^\infty \frac{1}{n^s} = \frac{1}{1^s} + \frac{1}{2^s} + \frac{1}{3^s} + \frac{1}{4^s} + \cdots$
which converges for all s such that $\mathrm{Re}(s) > 1$.
The Riemann hypothesis states that $\zeta(s) = 0$ iff s is a negative even integer or the imaginary part of s is 1/2.
## Representation as an integral
The Riemann zeta function can be expressed as an improper integral. Consider the improper integral,
$\int_{0}^{\infty} \frac{t^{z-1}}{e^t - 1} \mathrm{d}t$
One may multiply through $\frac{e^{-t}}{e^{-t}}$ to obtain,
$\int_{0}^{\infty} \frac{e^{-t}t^{z-1}}{1 - e^{-t}} \mathrm{d}t$
From which point, considering,
$\frac{1}{1-e^{-t}} = \sum_{n \geq 0} (e^{-t})^n$
One may rewrite the integrand as,
$\int_{0}^{\infty} e^{-t}t^{z-1} \sum_{n \geq 0} e^{-nt} \mathrm{d}t$
Which can be written as, by changing the order of the operators
$\int_{0}^{\infty} \sum_{n \geq 1} e^{-nt}t^{z-1} \mathrm{d}t$
By using a substitution of, say, $x = nt$ $\left(\implies \mathrm{d}x = n\mathrm{d}t \implies \mathrm{d}t = \frac{1}{n}\mathrm{d}x\right)$, one can write this as
$\int_{0}^{\infty} \sum_{n \geq 1} \frac{1}{n} e^{-x} \left(\frac{x}{n}\right)^{z-1} \mathrm{d}x$
$\int_{0}^{\infty} \sum_{n \geq 1} \frac{1}{n} e^{-x} \left(\frac{x^{z-1}}{n^{z-1}}\right)\mathrm{d}x$
$\int_{0}^{\infty} \sum_{n \geq 1} \frac{1}{n^z} e^{-x} x^{z-1} \mathrm{d}x$
Notice that $\frac{1}{n^z}$ is independent of x, and $e^{-x}x^{z-1}$ is independent of n, meaning that our integral can be written as,
$\sum_{n \geq 1} \frac{1}{n^z} \int_{0}^{\infty} e^{-x}x^{z-1} \mathrm{d}x$.
Using the definitions of both the zeta and the gamma function, we finally have,
$\int_{0}^{\infty} \frac{t^{z-1}}{e^t - 1} \mathrm{d}t = \zeta(z)\Gamma(z)$
Finally,
$\zeta(z) = \frac{1}{\Gamma(z)} \int_{0}^{\infty} \frac{t^{z-1}}{e^t - 1} \mathrm{d}t$
## Riemann Hypothesis
This is one of the unsolved problems throughout the 6 unsolved problems on the Millennium Prize Problem, which grants $1,000,000 to any person that could solve them correctly. The zeta function has no zeros where s is greater than or equal to one. When s is less than or equal to zero, the function has zeros on even integers known as trivial zeros. The remaining zeros are between zero and one; this is known as the critical strip. The Riemann hypothesis is that all non-trivial zeros lie on the line$ 1/2 + it $as$ t \$ ranges over all real numbers. Whether or not this is true is known as the Riemann Hypothesis, the challenge is to prove that the Riemann Hypothesis is true or false.
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-12-12T03:23:13 |
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|
https://zbmath.org/authors/?q=ai%3Aharris.joseph-daniel
|
# zbMATH — the first resource for mathematics
## Harris, Joseph Daniel
Compute Distance To:
Author ID: harris.joseph-daniel Published as: Harris, Joe; Harris, Joseph; Harris, J. External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 95 Publications since 1977, including 13 Books 4 Contributions as Editor Biographic References: 2 Publications
all top 5
#### Co-Authors
16 single-authored 29 Eisenbud, David 13 Griffiths, Phillip Augustus 9 Starr, Jason Michael 6 Mazur, Barry 4 Caporaso, Lucia 4 Ciliberto, Ciro 4 Graber, Tom 4 Green, Mark Lee 4 Gross, Benedict Hyman 3 Arbarello, Enrico 3 Cornalba, Maurizio 3 Diaz, Steven P. 3 Schreyer, Frank-Olaf 3 Tu, Loring W. 2 Coskun, Izzet 2 Fulton, William 2 Hulek, Klaus 2 Miranda, Rick 2 Morrison, Ian 2 Roth, Mike 1 Abramovich, Dan 1 Bryant, Robert L. 1 Brylinski, Ranee Kathryn 1 Buhler, Joe P. 1 Carlson, James A. 1 Clemens, C. Herbert 1 Danilov, Vladimir I. 1 Elkies, Noam David 1 Iskovskikh, Vasiliĭ Alekseevich 1 Lazarsfeld, Robert Kendall 1 Morrison, David R. 1 Mumford, David Bryant 1 Pandharipande, Rahul 1 Riehl, Emily 1 Schmid, Wilfried 1 Shokurov, Vyacheslav Vladimirovich 1 Silverman, Joseph Hillel 1 Speiser, Robert 1 Teixidor i Bigas, Montserrat 1 Tschinkel, Yuri 1 Vakil, Ravi
all top 5
#### Serials
13 Inventiones Mathematicae 8 Compositio Mathematica 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Duke Mathematical Journal 4 Mathematische Annalen 4 Graduate Texts in Mathematics 3 Transactions of the American Mathematical Society 3 Bulletin of the American Mathematical Society. New Series 3 Oberwolfach Reports 2 Proceedings of the American Mathematical Society 2 Journal of the American Mathematical Society 2 Journal of Algebraic Geometry 1 Communications in Algebra 1 Rocky Mountain Journal of Mathematics 1 Advances in Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Journal of Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Topology 1 L’Enseignement Mathématique. 2e Série 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Grundlehren der Mathematischen Wissenschaften
all top 5
#### Fields
95 Algebraic geometry (14-XX) 6 Several complex variables and analytic spaces (32-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 4 Number theory (11-XX) 4 Commutative algebra (13-XX) 4 Geometry (51-XX) 3 Manifolds and cell complexes (57-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 2 Mathematics education (97-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Quantum theory (81-XX)
#### Citations contained in zbMATH Open
91 Publications have been cited 7,524 times in 6,123 Documents Cited by Year
Principles of algebraic geometry. Zbl 0408.14001
Griffiths, Phillip; Harris, Joseph
1978
Representation theory. A first course. Zbl 0744.22001
Fulton, William; Harris, Joe
1991
Geometry of algebraic curves. Volume I. Zbl 0559.14017
Arbarello, E.; Cornalba, M.; Griffiths, P. A.; Harris, J.
1985
Principles of algebraic geometry. 2nd ed. Zbl 0836.14001
Griffiths, Phillip; Harris, Joseph
1994
Algebraic geometry. A first course. Zbl 0779.14001
Harris, Joe
1992
Moduli of curves. Zbl 0913.14005
Harris, Joe; Morrison, Ian
1998
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
1982
Families of rationally connected varieties. Zbl 1092.14063
Graber, Tom; Harris, Joe; Starr, Jason
2003
The geometry of schemes. Zbl 0960.14002
Eisenbud, David; Harris, Joe
2000
Limit linear series: Basic theory. Zbl 0598.14003
Eisenbud, David; Harris, Joe
1986
Cayley-Bacharach theorems and conjectures. Zbl 0871.14024
Eisenbud, David; Green, Mark; Harris, Joe
1996
The Kodaira dimension of the moduli space of curves of genus $$\geq 23$$. Zbl 0631.14023
Eisenbud, David; Harris, Joe
1987
3264 and all that. A second course in algebraic geometry. Zbl 1341.14001
Eisenbud, David; Harris, Joe
2016
Curves in projective space. With the collaboration of David Eisenbud. Zbl 0511.14014
Harris, Joe
1982
Algebraic geometry and local differential geometry. Zbl 0426.14019
Griffiths, Phillip; Harris, Joseph
1979
Real algebraic curves. Zbl 0533.14011
Gross, Benedict H.; Harris, Joe
1981
On the variety of special linear systems on a general algebraic curve. Zbl 0446.14011
Griffiths, Phillip; Harris, Joseph
1980
Infinitesimal variations of Hodge structure. I. Zbl 0531.14006
Carlson, James; Green, Mark; Griffiths, Phillip; Harris, Joe
1983
Divisors on general curves and cuspidal rational curves. Zbl 0527.14022
Eisenbud, D.; Harris, J.
1983
Galois groups of enumerative problems. Zbl 0433.14040
Harris, Joe
1979
On the Severi problem. Zbl 0596.14017
Harris, Joe
1986
Divisor classes associated to families of stable varieties with applications to the moduli space of curves. Zbl 0674.14006
Cornalba, Maurizio; Harris, Joe
1988
On symmetric and skew-symmetric determinantal varieties. Zbl 0534.55010
Harris, Joe; Tu, Loring W.
1984
A bound on the geometric genus of projective varieties. Zbl 0467.14005
Harris, Joe
1981
Developments in algebraic geometry. Zbl 0932.14001
Harris, Joe
1992
On Cayley’s explicit solution to Poncelet’s porism. Zbl 0384.14009
Griffiths, Phillip; Harris, Joseph
1978
Existence, decomposition, and limits of certain Weierstrass points. Zbl 0606.14014
Eisenbud, David; Harris, Joe
1987
Counting plane curves of any genus. Zbl 0934.14040
Caporaso, Lucia; Harris, Joe
1998
The genus of space curves. Zbl 0449.14006
Harris, Joe
1980
Residues and zero-cycles on algebraic varieties. Zbl 0423.14001
Griffiths, Phillip; Harris, Joseph
1978
Theta-characteristics on algebraic curves. Zbl 0513.14025
Harris, Joe
1982
Uniformity of rational points. Zbl 0872.14017
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1997
On the Noether-Lefschetz theorem and some remarks on codimension-two cycles. Zbl 0552.14011
Griffiths, Phillip; Harris, Joe
1985
On varieties of minimal degree. (A centennial account). Zbl 0646.14036
Eisenbud, David; Harris, Joe
1987
Vector spaces of matrices of low rank. Zbl 0657.15013
Eisenbud, David; Harris, Joe
1988
A Poncelet theorem in space. Zbl 0358.50009
Griffiths, Phillip; Harris, Joe
1977
Ideals associated to deformations of singular plane curves. Zbl 0707.14022
Diaz, Steven; Harris, Joe
1988
On the surjectivity of the Wahl map. Zbl 0684.14009
Ciliberto, Ciro; Harris, Joe; Miranda, Rick
1988
A simpler proof of the Gieseker-Petri theorem on special divisors. Zbl 0533.14012
Eisenbud, D.; Harris, J.
1983
Slopes of effective divisors on the moduli space of stable curves. Zbl 0705.14026
Harris, J.; Morrison, I.
1990
Bielliptic curves and symmetric products. Zbl 0727.11023
Harris, Joe; Silverman, Joseph H.
1991
Abelian varieties and curves in $$W_ d (C)$$. Zbl 0748.14010
Abramovich, Dan; Harris, Joe
1991
Higher Castelnuovo theory. Zbl 0819.14001
Eisenbud, David; Green, Mark; Harris, Joe
1993
Irreducibility of some families of linear series with Brill-Noether number $$-1$$. Zbl 0691.14006
Eisenbud, David; Harris, Joe
1989
Rational curves on hypersurfaces of low degree. Zbl 1052.14027
Harris, Joe; Roth, Mike; Starr, Jason
2004
Irreducibility and monodromy of some families of linear series. Zbl 0625.14013
Eisenbud, David; Harris, Joe
1987
Infinitesimal variations of Hodge structure. II: An infinitesimal invariant of Hodge classes. Zbl 0576.14008
Griffiths, Phillip; Harris, Joe
1983
General components of the Noether-Lefschetz locus and their density in the space of all surfaces. Zbl 0671.14017
Ciliberto, Ciro; Harris, Joe; Miranda, Rick
1988
On the Kodaira dimension of the moduli space of curves. II: The even-genus case. Zbl 0542.14014
Harris, J.
1984
Hypersurfaces of low degree. Zbl 0991.14018
Harris, Joe; Mazur, Barry; Pandharipande, Rahul
1998
Finite projective schemes in linearly general position. Zbl 0804.14002
Eisenbud, David; Harris, Joe
1992
Excess linear series on an algebraic curve. Zbl 0549.14004
Fulton, William; Harris, Joe; Lazarsfeld, Robert
1984
Chern numbers of kernel and cokernel bundles. Appendix to ”On the Kodaira dimension of the moduli space of curves. II. The even-genus case” by J. Harris. Zbl 0542.14015
Harris, J.; Tu, L.
1984
Rational points on quartics. Zbl 0982.14013
Harris, Joe; Tschinkel, Yuri
2000
Powers of ideals and fibers of morphisms. Zbl 1226.13012
Eisenbud, David; Harris, Joe
2010
Principles of algebraic geometry. Vol. 1, 2. Transl. from the English by V. I. Danilov, G. B. Shabat and V. V. Shokurov. (Printsipy algebraicheskoj geometrii. Tom 1, 2.) Zbl 0531.14002
Griffiths, Phillip; Harris, Joseph
1982
On some geometric constructions related to theta characteristics. Zbl 1072.14032
Gross, Benedict H.; Harris, Joe
2004
Geometry of the Severi variety. Zbl 0677.14003
Diaz, Steven; Harris, Joe
1988
On the Hurwitz scheme and its monodromy. Zbl 0726.14022
Eisenbud, David; Elkies, Noam; Harris, Joe; Speiser, Robert
1991
Schemes: The language of modern algebraic geometry. Zbl 0745.14002
Eisenbud, David; Harris, Joe
1992
Canonical curves and quadrics of rank 4. Zbl 0494.14011
Arbarello, Enrico; Harris, Joseph
1981
Parameter spaces for curves on surfaces and enumeration of rational curves. Enumerating rational curves: The rational fibration method. Zbl 0930.14036
Caporaso, Lucia; Harris, Joe
1998
Isotropic subspaces for skewforms and maximal abelian subgroups of $$p$$-groups. Zbl 0612.20009
Buhler, Joe; Gupta, Ranee; Harris, Joe
1987
How many rational points can a curve have? Zbl 0862.14012
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1995
Rational curves on hypersurfaces of low degree. II. Zbl 1083.14003
Harris, Joe; Starr, Jason
2005
Curves of small degree on cubic threefolds. Zbl 1080.14008
Harris, Joe; Roth, Mike; Starr, Jason
2005
Rational connectivity and sections of families over curves. Zbl 1092.14062
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2005
Families of smooth curves. Zbl 0548.14009
Harris, Joe
1984
When ramification points meet. Zbl 0606.14008
Eisenbud, David; Harris, Joe
1987
The effective cone of the Kontsevich moduli space. Zbl 1213.14022
Coskun, Izzet; Harris, Joe; Starr, Jason
2008
The ample cone of the Kontsevich moduli space. Zbl 1206.14050
Coskun, Izzet; Harris, Joe; Starr, Jason
2009
The monodromy of Weierstrass points. Zbl 0632.14014
Eisenbud, David; Harris, Joe
1987
The dimension of the Chow variety of curves. Zbl 0780.14003
Eisenbud, David; Harris, Joe
1992
On the Brill-Noether theorem. Zbl 0512.14016
Eisenbud, D.; Harris, J.
1983
On the normal bundle of curves on complete intersection surfaces. Zbl 0497.14025
Harris, Joe; Hulek, Klaus
1983
An intersection bound for rank 1 loci, with applications to Castelnuovo and Clifford theory. Zbl 0798.14029
Eisenbud, David; Harris, Joe
1992
Geometry of Severi varieties. II: Independence of divisor classes and example. Zbl 0677.14004
Diaz, Steven; Harris, Joe
1988
Arithmetic questions related to rationally connected varieties. Zbl 1071.14053
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2004
Limit linear series, the irrationality of $$M_ g$$, and other applications. Zbl 0533.14013
Eisenbud, David; Harris, Joe
1984
Curves and their moduli. Zbl 0646.14019
Harris, Joe
1987
Interpolation. Zbl 1259.14004
Harris, Joe
2012
Jumps in Mordell-Weil rank and arithmetic surjectivity. Zbl 1075.14021
Graber, Tom; Harris, Joseph; Mazur, Barry; Starr, Jason
2004
Surfaces of low degree containing a general canonical curve. Zbl 0970.14019
Ciliberto, C.; Harris, J.
1999
On the endomorphisms of $$\text{Jac}(W_ d^ 1(C))$$ when $$\rho=1$$ and $$C$$ has general moduli. Zbl 0787.14018
Ciliberto, Ciro; Harris, Joe; Teixidor i Bigas, Montserrat
1992
Recent work on $${\mathcal M}_ g$$. Zbl 0575.14008
Harris, Joe
1984
The connectedness of symmetric degeneracy loci: Odd ranks. Appendix to “The connectedness of degeneracy loci” by Loring W. Tu. Zbl 0744.14011
Harris, Joe; Tu, Loring W.
1990
Progress in the theory of complex algebraic curves. Zbl 0703.14016
Eisenbud, David; Harris, Joe
1989
Selected works of Phillip A. Griffiths with commentary. Part 1: Analytic geometry. Part 2: Algebraic geometry. Part 3: Variations of Hodge structures. Part 4: Differential systems. Edited by Maurizio Cornalba, Mark L. Green, Wilfried Schmid, Enrico Arbarello, Joe Harris, C. Herbert Clemens, David R. Morrison and Robert L. Bryant. Zbl 1045.01012
Griffiths, Phillip A.
2003
Recent progress in the study of Weierstrass points. Zbl 0581.14020
Eisenbud, David; Harris, Joe
1985
An introduction to the moduli space of curves. Zbl 0672.14014
Harris, Joe
1987
Parameter spaces of curves. Zbl 1322.14005
Harris, Joe
2013
3264 and all that. A second course in algebraic geometry. Zbl 1341.14001
Eisenbud, David; Harris, Joe
2016
Parameter spaces of curves. Zbl 1322.14005
Harris, Joe
2013
Interpolation. Zbl 1259.14004
Harris, Joe
2012
Powers of ideals and fibers of morphisms. Zbl 1226.13012
Eisenbud, David; Harris, Joe
2010
The ample cone of the Kontsevich moduli space. Zbl 1206.14050
Coskun, Izzet; Harris, Joe; Starr, Jason
2009
The effective cone of the Kontsevich moduli space. Zbl 1213.14022
Coskun, Izzet; Harris, Joe; Starr, Jason
2008
Rational curves on hypersurfaces of low degree. II. Zbl 1083.14003
Harris, Joe; Starr, Jason
2005
Curves of small degree on cubic threefolds. Zbl 1080.14008
Harris, Joe; Roth, Mike; Starr, Jason
2005
Rational connectivity and sections of families over curves. Zbl 1092.14062
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2005
Rational curves on hypersurfaces of low degree. Zbl 1052.14027
Harris, Joe; Roth, Mike; Starr, Jason
2004
On some geometric constructions related to theta characteristics. Zbl 1072.14032
Gross, Benedict H.; Harris, Joe
2004
Arithmetic questions related to rationally connected varieties. Zbl 1071.14053
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2004
Jumps in Mordell-Weil rank and arithmetic surjectivity. Zbl 1075.14021
Graber, Tom; Harris, Joseph; Mazur, Barry; Starr, Jason
2004
Families of rationally connected varieties. Zbl 1092.14063
Graber, Tom; Harris, Joe; Starr, Jason
2003
Selected works of Phillip A. Griffiths with commentary. Part 1: Analytic geometry. Part 2: Algebraic geometry. Part 3: Variations of Hodge structures. Part 4: Differential systems. Edited by Maurizio Cornalba, Mark L. Green, Wilfried Schmid, Enrico Arbarello, Joe Harris, C. Herbert Clemens, David R. Morrison and Robert L. Bryant. Zbl 1045.01012
Griffiths, Phillip A.
2003
The geometry of schemes. Zbl 0960.14002
Eisenbud, David; Harris, Joe
2000
Rational points on quartics. Zbl 0982.14013
Harris, Joe; Tschinkel, Yuri
2000
Surfaces of low degree containing a general canonical curve. Zbl 0970.14019
Ciliberto, C.; Harris, J.
1999
Moduli of curves. Zbl 0913.14005
Harris, Joe; Morrison, Ian
1998
Counting plane curves of any genus. Zbl 0934.14040
Caporaso, Lucia; Harris, Joe
1998
Hypersurfaces of low degree. Zbl 0991.14018
Harris, Joe; Mazur, Barry; Pandharipande, Rahul
1998
Parameter spaces for curves on surfaces and enumeration of rational curves. Enumerating rational curves: The rational fibration method. Zbl 0930.14036
Caporaso, Lucia; Harris, Joe
1998
Uniformity of rational points. Zbl 0872.14017
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1997
Cayley-Bacharach theorems and conjectures. Zbl 0871.14024
Eisenbud, David; Green, Mark; Harris, Joe
1996
How many rational points can a curve have? Zbl 0862.14012
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1995
Principles of algebraic geometry. 2nd ed. Zbl 0836.14001
Griffiths, Phillip; Harris, Joseph
1994
Higher Castelnuovo theory. Zbl 0819.14001
Eisenbud, David; Green, Mark; Harris, Joe
1993
Algebraic geometry. A first course. Zbl 0779.14001
Harris, Joe
1992
Developments in algebraic geometry. Zbl 0932.14001
Harris, Joe
1992
Finite projective schemes in linearly general position. Zbl 0804.14002
Eisenbud, David; Harris, Joe
1992
Schemes: The language of modern algebraic geometry. Zbl 0745.14002
Eisenbud, David; Harris, Joe
1992
The dimension of the Chow variety of curves. Zbl 0780.14003
Eisenbud, David; Harris, Joe
1992
An intersection bound for rank 1 loci, with applications to Castelnuovo and Clifford theory. Zbl 0798.14029
Eisenbud, David; Harris, Joe
1992
On the endomorphisms of $$\text{Jac}(W_ d^ 1(C))$$ when $$\rho=1$$ and $$C$$ has general moduli. Zbl 0787.14018
Ciliberto, Ciro; Harris, Joe; Teixidor i Bigas, Montserrat
1992
Representation theory. A first course. Zbl 0744.22001
Fulton, William; Harris, Joe
1991
Bielliptic curves and symmetric products. Zbl 0727.11023
Harris, Joe; Silverman, Joseph H.
1991
Abelian varieties and curves in $$W_ d (C)$$. Zbl 0748.14010
Abramovich, Dan; Harris, Joe
1991
On the Hurwitz scheme and its monodromy. Zbl 0726.14022
Eisenbud, David; Elkies, Noam; Harris, Joe; Speiser, Robert
1991
Slopes of effective divisors on the moduli space of stable curves. Zbl 0705.14026
Harris, J.; Morrison, I.
1990
The connectedness of symmetric degeneracy loci: Odd ranks. Appendix to “The connectedness of degeneracy loci” by Loring W. Tu. Zbl 0744.14011
Harris, Joe; Tu, Loring W.
1990
Irreducibility of some families of linear series with Brill-Noether number $$-1$$. Zbl 0691.14006
Eisenbud, David; Harris, Joe
1989
Progress in the theory of complex algebraic curves. Zbl 0703.14016
Eisenbud, David; Harris, Joe
1989
Divisor classes associated to families of stable varieties with applications to the moduli space of curves. Zbl 0674.14006
Cornalba, Maurizio; Harris, Joe
1988
Vector spaces of matrices of low rank. Zbl 0657.15013
Eisenbud, David; Harris, Joe
1988
Ideals associated to deformations of singular plane curves. Zbl 0707.14022
Diaz, Steven; Harris, Joe
1988
On the surjectivity of the Wahl map. Zbl 0684.14009
Ciliberto, Ciro; Harris, Joe; Miranda, Rick
1988
General components of the Noether-Lefschetz locus and their density in the space of all surfaces. Zbl 0671.14017
Ciliberto, Ciro; Harris, Joe; Miranda, Rick
1988
Geometry of the Severi variety. Zbl 0677.14003
Diaz, Steven; Harris, Joe
1988
Geometry of Severi varieties. II: Independence of divisor classes and example. Zbl 0677.14004
Diaz, Steven; Harris, Joe
1988
The Kodaira dimension of the moduli space of curves of genus $$\geq 23$$. Zbl 0631.14023
Eisenbud, David; Harris, Joe
1987
Existence, decomposition, and limits of certain Weierstrass points. Zbl 0606.14014
Eisenbud, David; Harris, Joe
1987
On varieties of minimal degree. (A centennial account). Zbl 0646.14036
Eisenbud, David; Harris, Joe
1987
Irreducibility and monodromy of some families of linear series. Zbl 0625.14013
Eisenbud, David; Harris, Joe
1987
Isotropic subspaces for skewforms and maximal abelian subgroups of $$p$$-groups. Zbl 0612.20009
Buhler, Joe; Gupta, Ranee; Harris, Joe
1987
When ramification points meet. Zbl 0606.14008
Eisenbud, David; Harris, Joe
1987
The monodromy of Weierstrass points. Zbl 0632.14014
Eisenbud, David; Harris, Joe
1987
Curves and their moduli. Zbl 0646.14019
Harris, Joe
1987
An introduction to the moduli space of curves. Zbl 0672.14014
Harris, Joe
1987
Limit linear series: Basic theory. Zbl 0598.14003
Eisenbud, David; Harris, Joe
1986
On the Severi problem. Zbl 0596.14017
Harris, Joe
1986
Geometry of algebraic curves. Volume I. Zbl 0559.14017
Arbarello, E.; Cornalba, M.; Griffiths, P. A.; Harris, J.
1985
On the Noether-Lefschetz theorem and some remarks on codimension-two cycles. Zbl 0552.14011
Griffiths, Phillip; Harris, Joe
1985
Recent progress in the study of Weierstrass points. Zbl 0581.14020
Eisenbud, David; Harris, Joe
1985
On symmetric and skew-symmetric determinantal varieties. Zbl 0534.55010
Harris, Joe; Tu, Loring W.
1984
On the Kodaira dimension of the moduli space of curves. II: The even-genus case. Zbl 0542.14014
Harris, J.
1984
Excess linear series on an algebraic curve. Zbl 0549.14004
Fulton, William; Harris, Joe; Lazarsfeld, Robert
1984
Chern numbers of kernel and cokernel bundles. Appendix to ”On the Kodaira dimension of the moduli space of curves. II. The even-genus case” by J. Harris. Zbl 0542.14015
Harris, J.; Tu, L.
1984
Families of smooth curves. Zbl 0548.14009
Harris, Joe
1984
Limit linear series, the irrationality of $$M_ g$$, and other applications. Zbl 0533.14013
Eisenbud, David; Harris, Joe
1984
Recent work on $${\mathcal M}_ g$$. Zbl 0575.14008
Harris, Joe
1984
Infinitesimal variations of Hodge structure. I. Zbl 0531.14006
Carlson, James; Green, Mark; Griffiths, Phillip; Harris, Joe
1983
Divisors on general curves and cuspidal rational curves. Zbl 0527.14022
Eisenbud, D.; Harris, J.
1983
A simpler proof of the Gieseker-Petri theorem on special divisors. Zbl 0533.14012
Eisenbud, D.; Harris, J.
1983
Infinitesimal variations of Hodge structure. II: An infinitesimal invariant of Hodge classes. Zbl 0576.14008
Griffiths, Phillip; Harris, Joe
1983
On the Brill-Noether theorem. Zbl 0512.14016
Eisenbud, D.; Harris, J.
1983
On the normal bundle of curves on complete intersection surfaces. Zbl 0497.14025
Harris, Joe; Hulek, Klaus
1983
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
1982
Curves in projective space. With the collaboration of David Eisenbud. Zbl 0511.14014
Harris, Joe
1982
Theta-characteristics on algebraic curves. Zbl 0513.14025
Harris, Joe
1982
Principles of algebraic geometry. Vol. 1, 2. Transl. from the English by V. I. Danilov, G. B. Shabat and V. V. Shokurov. (Printsipy algebraicheskoj geometrii. Tom 1, 2.) Zbl 0531.14002
Griffiths, Phillip; Harris, Joseph
1982
Real algebraic curves. Zbl 0533.14011
Gross, Benedict H.; Harris, Joe
1981
A bound on the geometric genus of projective varieties. Zbl 0467.14005
Harris, Joe
1981
Canonical curves and quadrics of rank 4. Zbl 0494.14011
Arbarello, Enrico; Harris, Joseph
1981
On the variety of special linear systems on a general algebraic curve. Zbl 0446.14011
Griffiths, Phillip; Harris, Joseph
1980
The genus of space curves. Zbl 0449.14006
Harris, Joe
1980
Algebraic geometry and local differential geometry. Zbl 0426.14019
Griffiths, Phillip; Harris, Joseph
1979
Galois groups of enumerative problems. Zbl 0433.14040
Harris, Joe
1979
Principles of algebraic geometry. Zbl 0408.14001
Griffiths, Phillip; Harris, Joseph
1978
On Cayley’s explicit solution to Poncelet’s porism. Zbl 0384.14009
Griffiths, Phillip; Harris, Joseph
1978
Residues and zero-cycles on algebraic varieties. Zbl 0423.14001
Griffiths, Phillip; Harris, Joseph
1978
A Poncelet theorem in space. Zbl 0358.50009
Griffiths, Phillip; Harris, Joe
1977
all top 5
#### Cited by 5,548 Authors
116 Ballico, Edoardo 43 Biswas, Indranil 42 Ciliberto, Ciro 41 Geng, Xianguo 41 Harris, Joseph Daniel 28 Farkas, Gavril 27 Pirola, Gian Pietro 26 Eisenbud, David 26 Martens, Gerriet 25 Keem, Changho 24 Coppens, Marc 19 Ran, Ziv 18 Geramita, Anthony Vito 18 Shustin, Eugenii Isaakovich 17 Sturmfels, Bernd 17 Verra, Alessandro 16 Chen, Dawei 16 Fontanari, Claudio 16 Lange, Herbert 16 Lanteri, Antonio 15 Coskun, Izzet 15 Kim, Seonja 15 Previato, Emma 15 Sommese, Andrew John 15 Teixidor i Bigas, Montserrat 15 Zuo, Kang 14 Beltrametti, Mauro C. 14 Dragović, Vladimir 14 Kollár, János 14 Osserman, Brian 14 Radnović, Milena 14 Sottile, Frank 13 Castorena, Abel 13 Chipalkatti, Jaydeep V. 13 Debarre, Olivier 13 Di Gennaro, Vincenzo 13 Dimca, Alexandru 13 Flamini, Flaminio 13 Hassett, Brendan 13 Lopez, Angelo Felice 13 Peternell, Thomas Martin 13 Schreyer, Frank-Olaf 12 Donagi, Ron Y. 12 Eelbode, David 12 Katz, Sheldon 12 Landsberg, Joseph Montague 12 Migliore, Juan Carlos 12 Pandharipande, Rahul 12 Spera, Mauro 12 Vafa, Cumrun 12 Voisin, Claire 11 Colombo, Elisabetta 11 Lazarsfeld, Robert Kendall 11 LeBrun, Claude R. 11 Möller, Martin 11 Ottaviani, Giorgio Maria 11 Pardini, Rita 11 Sernesi, Edoardo 11 Xue, Bo 11 Zeng, Xin 10 Blekherman, Grigoriy 10 Caporaso, Lucia 10 Diaz, Steven P. 10 Esteves, Eduardo 10 Fioresi, Rita 10 Frediani, Paola 10 Hurtubise, Jacques C. 10 Knutsen, Andreas Leopold 10 Lesfari, Ahmed 10 Manivel, Laurent 10 Pacini, Marco 10 Qiao, Youming 10 Sharpe, Eric R. 10 Torres, Fernando 10 Villarreal, Rafael Heraclio 10 Zelditch, Steve 9 Alzati, Alberto 9 Casnati, Gianfranco 9 Choi, Youngook 9 Ellia, Philippe 9 Friedland, Shmuel 9 Kaji, Hajime 9 Matsutani, Shigeki 9 Miranda, Rick 9 Newstead, Peter E. 9 Prokhorov, Yuriĭ Gennad’evich 9 Sam, Steven V. 9 Snowden, Andrew W. 9 van Geemen, Bert 9 Weyman, Jerzy M. 9 Yger, Alain 9 Zinger, Aleksey 8 Bastianelli, Francesco 8 Brivio, Sonia 8 Carlini, Enrico 8 Chen, Jinbing 8 Chiantini, Luca 8 Cotterill, Ethan 8 Dickenstein, Alicia M. 8 Franco, Davide ...and 5,448 more Authors
all top 5
#### Cited in 448 Serials
255 Transactions of the American Mathematical Society 222 Mathematische Annalen 220 Journal of Algebra 179 Advances in Mathematics 171 Communications in Mathematical Physics 168 Proceedings of the American Mathematical Society 166 Journal of Pure and Applied Algebra 162 Duke Mathematical Journal 160 Inventiones Mathematicae 135 Mathematische Zeitschrift 131 Manuscripta Mathematica 116 Communications in Algebra 113 Journal of Geometry and Physics 111 Compositio Mathematica 108 Journal of High Energy Physics 100 Annales de l’Institut Fourier 87 Journal of Algebraic Geometry 84 Nuclear Physics. B 82 Geometriae Dedicata 61 Journal of Mathematical Physics 60 Israel Journal of Mathematics 58 Michigan Mathematical Journal 57 International Journal of Mathematics 56 Linear Algebra and its Applications 51 Annali di Matematica Pura ed Applicata. Serie Quarta 50 The Journal of Geometric Analysis 48 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 48 Archiv der Mathematik 44 Journal of the American Mathematical Society 40 Journal of Symbolic Computation 39 Bulletin of the American Mathematical Society. New Series 39 Journal of Algebraic Combinatorics 37 Rendiconti del Circolo Matemàtico di Palermo. Serie II 34 Differential Geometry and its Applications 33 Journal of Number Theory 33 Journal für die Reine und Angewandte Mathematik 33 Journal of the European Mathematical Society (JEMS) 31 Tohoku Mathematical Journal. Second Series 30 Letters in Mathematical Physics 30 Indagationes Mathematicae. New Series 30 Journal of Mathematical Sciences (New York) 30 Geometry & Topology 29 Collectanea Mathematica 26 Functional Analysis and its Applications 26 Mathematische Nachrichten 26 Nagoya Mathematical Journal 26 Annals of Global Analysis and Geometry 26 Discrete & Computational Geometry 26 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 26 Selecta Mathematica. New Series 26 Comptes Rendus. Mathématique. Académie des Sciences, Paris 25 Mathematics of Computation 25 Geometric and Functional Analysis. GAFA 25 Transformation Groups 25 Science China. Mathematics 24 Publications Mathématiques 24 Journal of Combinatorial Theory. Series A 24 European Journal of Mathematics 23 Journal of Functional Analysis 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Annals of Mathematics. Second Series 22 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 22 Communications in Contemporary Mathematics 20 Bulletin de la Société Mathématique de France 20 Topology and its Applications 20 Finite Fields and their Applications 20 Bulletin of the Brazilian Mathematical Society. New Series 19 Acta Mathematica 19 Algebras and Representation Theory 19 Foundations of Computational Mathematics 18 Theoretical and Mathematical Physics 18 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 17 Mathematical Notes 17 Rocky Mountain Journal of Mathematics 17 Results in Mathematics 17 Bulletin des Sciences Mathématiques 17 Documenta Mathematica 17 Algebraic & Geometric Topology 17 Central European Journal of Mathematics 17 Journal of the Institute of Mathematics of Jussieu 16 Memoirs of the American Mathematical Society 16 Rendiconti del Seminario Matematico della Università di Padova 16 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 15 Mathematical Proceedings of the Cambridge Philosophical Society 15 Journal of Differential Equations 15 Publications of the Research Institute for Mathematical Sciences, Kyoto University 15 Advances in Geometry 14 Discrete Mathematics 14 Linear and Multilinear Algebra 14 Beiträge zur Algebra und Geometrie 14 Representation Theory 13 Osaka Journal of Mathematics 13 The Electronic Journal of Combinatorics 13 Proceedings of the Steklov Institute of Mathematics 13 Journal of Commutative Algebra 13 SIAM Journal on Applied Algebra and Geometry 12 Proceedings of the Japan Academy. Series A 12 Advances in Applied Mathematics 12 Revista Matemática Iberoamericana 12 Applicable Algebra in Engineering, Communication and Computing ...and 348 more Serials
all top 5
#### Cited in 63 Fields
3,782 Algebraic geometry (14-XX) 940 Several complex variables and analytic spaces (32-XX) 737 Differential geometry (53-XX) 500 Quantum theory (81-XX) 441 Number theory (11-XX) 411 Commutative algebra (13-XX) 381 Group theory and generalizations (20-XX) 363 Dynamical systems and ergodic theory (37-XX) 322 Global analysis, analysis on manifolds (58-XX) 290 Combinatorics (05-XX) 278 Nonassociative rings and algebras (17-XX) 270 Manifolds and cell complexes (57-XX) 212 Linear and multilinear algebra; matrix theory (15-XX) 196 Functions of a complex variable (30-XX) 163 Topological groups, Lie groups (22-XX) 162 Partial differential equations (35-XX) 126 Associative rings and algebras (16-XX) 119 Computer science (68-XX) 115 Convex and discrete geometry (52-XX) 110 Algebraic topology (55-XX) 109 Geometry (51-XX) 109 Relativity and gravitational theory (83-XX) 78 Field theory and polynomials (12-XX) 78 Numerical analysis (65-XX) 76 Ordinary differential equations (34-XX) 75 Mechanics of particles and systems (70-XX) 72 Functional analysis (46-XX) 69 Probability theory and stochastic processes (60-XX) 68 Operator theory (47-XX) 67 Category theory; homological algebra (18-XX) 64 Information and communication theory, circuits (94-XX) 58 Statistical mechanics, structure of matter (82-XX) 48 Special functions (33-XX) 44 $$K$$-theory (19-XX) 30 Abstract harmonic analysis (43-XX) 27 Operations research, mathematical programming (90-XX) 25 Systems theory; control (93-XX) 24 History and biography (01-XX) 23 Mathematical logic and foundations (03-XX) 21 Approximations and expansions (41-XX) 16 Statistics (62-XX) 15 Potential theory (31-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 13 Difference and functional equations (39-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 12 Real functions (26-XX) 11 Measure and integration (28-XX) 11 Integral transforms, operational calculus (44-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 General and overarching topics; collections (00-XX) 9 Biology and other natural sciences (92-XX) 7 Fluid mechanics (76-XX) 6 General topology (54-XX) 4 Mechanics of deformable solids (74-XX) 3 General algebraic systems (08-XX) 3 Optics, electromagnetic theory (78-XX) 2 Integral equations (45-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Sequences, series, summability (40-XX) 1 Classical thermodynamics, heat transfer (80-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.
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https://www.usgs.gov/data/waveform-data-and-metadata-used-national-earthquake-information-center-deep-learning-models
|
# Waveform Data and Metadata used to National Earthquake Information Center Deep-Learning Models
August 18, 2021
These data were used to train the Machine Learning models supporting the USGS software release "NEIC Machine Learning Applications Software" (https://doi.org/10.5066/P9ICQPUR), and its companion publication in Seismological Research Letters "Leveraging Deep Learning in Global 24/7 Real-Time Earthquake Monitoring at the National Earthquake Information Center" (https://doi.org/XXXXX). These data are formatted as python numpy arrays and readable by the python code used to generate deep-learning models that classify waveform phases, refine automatic pick timings, and estimate source distances.
The cataloged picks and associated metadata were obtained from the USGS PDE catalog (https://earthquake.usgs.gov/data/pde.php). Waveform segments were obtained from the IRIS Data Management Center using their readily available web-services (https://ds.iris.edu/ds/nodes/dmc/). IRIS Data Services are funded through the Seismological Facilities for the Advancement of Geoscience (SAGE) Award of the National Science Foundation under Cooperative Support Agreement EAR-1851048.
Each numpy array file is a tar zip file of a numpy array. Large files were split into separate files, where the extension '.parta[.]' is a alphabetical listing of the order of the split. In order to extract these files, it is necessary to run cat name.tar.gz.parta* name.tar.gz prior to uncompressing the file. To uncompress the .tar.gz files run tar xvzf name.tar.gz. Each numpy file contains a single array. The file names describe the data in the array. The files are named first with the phase type (P or S), then the data type, then if the data belongs to the training or testing dataset. The training and testing datasets are ordered so that the index of each array corresponds to the index of all the other P or S wave training / testing arrays. The data types include Dist (distance in degrees), Azi (back azimuth in degrees), EQID (PDE EQ ID), Mag (the preferred PDE earthquake magnitude), or WF (seismic waveform data). Waveform data is 60 seconds of 40 sample a second data centered on the arrival time, with rows corresponding to vertical component, north / 1 component, and east / 2 component.
| 2022-01-17T19:39:23 |
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https://zbmath.org/authors/?q=ai%3Areed.bruce-a
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# zbMATH — the first resource for mathematics
## Reed, Bruce Alan
Compute Distance To:
Author ID: reed.bruce-a Published as: Reed, B.; Reed, B. A.; Reed, Bruce; Reed, Bruce A. Homepage: http://cgm.cs.mcgill.ca/~breed/ External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 217 Publications since 1985, including 4 Books
all top 5
#### Co-Authors
20 single-authored 23 McDiarmid, Colin J. H. 22 Molloy, Michael S. O. 15 Kawarabayashi, Ken-ichi 13 Addario-Berry, Louigi 12 Frieze, Alan Michael 11 Seymour, Paul D. 9 Wood, David Ronald 8 King, Andrew D. 8 Vetta, Adrian R. 7 de Figueiredo, Celina M. Herrera 7 Havet, Frédéric 7 Klein, Sulamita 7 Linhares-Sales, Claudia 7 Maffray, Frédéric 6 Everett, Hazel 5 Li, Zhentao 4 Chudnovsky, Maria 4 Dalal, Ketan 4 Fiorini, Samuel 4 Hardy, Nadia 4 Hoàng, Chính T. 4 Kennedy, William Sean 4 Rautenbach, Dieter 4 Thomason, Andrew G. 3 Birmele, Etienne 3 Bondy, J. Adrian 3 Cooper, Colin 3 Devroye, Luc P. J. A. 3 Fountoulakis, Nikolaos 3 Lee, Orlando 3 Loebl, Martin 3 Meagher, Conor 3 Mohar, Bojan 3 Perarnau, Guillem 3 Perković, Ljubomir 3 Scott, Alexander D. 3 Sudakov, Benny 2 Alon, Noga M. 2 Avis, David M. 2 Berge, Claude Jacques Roger 2 Broutin, Nicolas 2 Calinescu, Gruia 2 Corneil, Derek Gordon 2 Dujmović, Vida 2 Fernandes, Cristina G. 2 Fertin, Guillaume 2 Habib, Michel A. 2 Hind, Hugh R. 2 Kilakos, Kyriakos 2 Kohayakawa, Yoshiharu 2 Lanlignel, Jean-Marc 2 Monma, Clyde L. 2 Nešetřil, Jaroslav 2 Norin, Sergey 2 Porto, Oscar 2 Ramírez Alfonsín, Jorge Luis 2 Raspaud, André 2 Robertson, Neil 2 Rotics, Udi 2 Schrijver, Alexander 2 Sereni, Jean-Sébastien 2 Shepherd, Bryan E. 2 Thomas, Robin 2 Thomassé, Stéphan 2 Trotter, William T. jun. 2 Wollan, Paul 1 Albert, Michael Henry 1 Aldred, Robert E. L. 1 Amini, Omid 1 Bang-Jensen, Jørgen 1 Berschi, M. 1 Bollobás, Béla 1 Bondy, Adrian 1 Cai, Xinshan 1 Cerioli, Márcia R. 1 Chattopadhyay, Arkadev 1 Chvátal, Vašek 1 Cook, William John 1 Cornuéjols, Gérard P. 1 Dantas, Simone 1 De Simone, Caterina 1 DeVos, Matthew 1 Ding, Guoli 1 Faria, Luerbio 1 Farzad, Babak 1 Ferreira, Talita O. 1 Gamble, B. 1 Gasparian, Grigor S. 1 Geelen, Jim 1 Gerards, Bert 1 González Hermosillo de la Maza, Sebastián 1 Gravier, Sylvain 1 Grohe, Martin 1 Habib, Michael 1 Harvey, Daniel J. 1 Hayward, Rayn B. 1 Hayward, Ryan B. 1 Hosseini, Seyyed Aliasghar 1 Hougardy, Stefan 1 Ito, Takehiro ...and 36 more Co-Authors
all top 5
#### Serials
26 Journal of Combinatorial Theory. Series B 13 Discrete Mathematics 13 Combinatorica 12 Journal of Graph Theory 12 Combinatorics, Probability and Computing 11 Discrete Applied Mathematics 11 Random Structures & Algorithms 6 SIAM Journal on Discrete Mathematics 5 Graphs and Combinatorics 4 SIAM Journal on Computing 4 European Journal of Combinatorics 3 Journal of Algorithms 3 Operations Research Letters 3 The Electronic Journal of Combinatorics 2 Theoretical Computer Science 2 Probability Theory and Related Fields 2 Mathematical Programming. Series A. Series B 2 Algorithms and Combinatorics 1 Annales de l’Institut Fourier 1 The Annals of Probability 1 Ars Combinatoria 1 Journal of Combinatorial Theory. Series A 1 Networks 1 CWI Quarterly 1 International Journal of Foundations of Computer Science 1 The Australasian Journal of Combinatorics 1 Congressus Numerantium 1 Journal of the ACM 1 RAIRO. Theoretical Informatics and Applications 1 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 ACM Transactions on Algorithms
all top 5
#### Fields
197 Combinatorics (05-XX) 51 Computer science (68-XX) 20 Operations research, mathematical programming (90-XX) 16 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 2 Convex and discrete geometry (52-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Numerical analysis (65-XX)
#### Citations contained in zbMATH Open
190 Publications have been cited 2,880 times in 2,101 Documents Cited by Year
A critical point for random graphs with a given degree sequence. Zbl 0823.05050
Molloy, Michael; Reed, Bruce
1995
Graph colouring and the probabilistic method. Zbl 0987.05002
Molloy, Michael; Reed, Bruce
2002
The size of the giant component of a random graph with a given degree sequence. Zbl 0916.05064
Molloy, Michael; Reed, Bruce
1998
Acyclic coloring of graphs. Zbl 0735.05036
Alon, Noga; McDiarmid, Colin; Reed, Bruce
1991
Finding odd cycle transversals. Zbl 1052.05061
Reed, Bruce; Smith, Kaleigh; Vetta, Adrian
2004
Further algorithmic aspects of the local lemma. Zbl 1028.68105
Molloy, Michael; Reed, Bruce
1998
Mick gets some (the odds are on his side). Zbl 0977.68538
Chvátal, V.; Reed, B.
1992
Tree width and tangles: A new connectivity measure and some applications. Zbl 0895.05034
Reed, B. A.
1997
Paths, stars and the number three. Zbl 0857.05052
Reed, Bruce
1996
A bound on the strong chromatic index of a graph. Zbl 0880.05036
Molloy, Michael; Reed, Bruce
1997
Degree constrained subgraphs. Zbl 1147.05055
Addario-Berry, L.; Dalal, K.; Reed, B. A.
2008
Minima in branching random walks. Zbl 1196.60142
2009
Vertex-colouring edge-weightings. Zbl 1127.05034
Addario-Berry, Louigi; Dalal, Ketan; McDiarmid, Colin; Reed, Bruce A.; Thomason, Andrew
2007
Star coloring of graphs. Zbl 1055.05051
Fertin, Guillaume; Raspaud, André; Reed, Bruce
2004
Vertex colouring edge partitions. Zbl 1074.05031
Addario-Berry, L.; Aldred, R. E. L.; Dalal, K.; Reed, B. A.
2005
$$\omega, \Delta$$ and $$\chi$$. Zbl 0980.05026
Reed, B.
1998
Channel assignment and weighted coloring. Zbl 0971.90100
McDiarmid, Colin; Reed, Bruce
2000
Polynomial time recognition of clique-width $$\leq 3$$ graphs (extended abstract). Zbl 0961.05062
Corneil, Derek G.; Habib, Michel; Lanlignel, Jean-Marc; Reed, Bruce; Rotics, Udi
2000
Some classes of perfectly orderable graphs. Zbl 0676.05071
Hoàng, C. T.; Reed, B. A.
1989
Perfect graphs. Zbl 0972.00015
Ramírez Alfonsín, Jorge L. (ed.); Reed, Bruce A. (ed.)
2001
The disjoint paths problem in quadratic time. Zbl 1298.05296
Kawarabayashi, Ken-Ichi; Kobayashi, Yusuke; Reed, Bruce
2012
Finding skew partitions efficiently. Zbl 0964.68107
de Figueiredo, Celina M. H.; Klein, Sulamita; Kohayakawa, Yoshiharu; Reed, Bruce A.
2000
Colouring a graph frugally. Zbl 0910.05023
Hind, Hugh; Molloy, Michael; Reed, Bruce
1997
Excluding any graph as a minor allows a low tree-width 2-coloring. Zbl 1042.05036
DeVos, Matt; Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Reed, Bruce; Seymour, Paul; Vertigan, Dirk
2004
Computing crossing number in linear time. Zbl 1232.90339
Kawarabayashi, Ken-ichi; Reed, Bruce
2007
Mangoes and blueberries. Zbl 0928.05059
Reed, Bruce
1999
List colouring squares of planar graphs. Zbl 1341.05073
Havet, Frédéric; van den Heuvel, Jan; McDiarmid, Colin; Reed, Bruce
2007
Multicoloured Hamilton cycles. Zbl 0817.05028
Albert, Michael; Frieze, Alan; Reed, Bruce
1995
Probabilistic methods for algorithmic discrete mathematics. Zbl 0898.00019
Habib, Michael (ed.); McDiarmid, Colin (ed.); Ramírez Alfonsín, Jorge (ed.); Reed, Bruce (ed.)
1998
Packing directed circuits. Zbl 0881.05050
Reed, B.; Robertson, N.; Seymour, P.; Thomas, R.
1996
On the odd-minor variant of Hadwiger’s conjecture. Zbl 1213.05079
Geelen, Jim; Gerards, Bert; Reed, Bruce; Seymour, Paul; Vetta, Adrian
2009
The Erdős-Pósa property for long circuits. Zbl 1136.05028
Birmelé, Etienne; Bondy, J. Adrian; Reed, Bruce A.
2007
A bound on the total chromatic number. Zbl 0921.05033
Molloy, Michael; Reed, Bruce
1998
Recognizing bull-free perfect graphs. Zbl 0832.05039
Reed, Bruce; Sbihi, Najiba
1995
A description of claw-free perfect graphs. Zbl 0933.05062
Maffray, Frédéric; Reed, Bruce A.
1999
A semi-strong perfect graph theorem. Zbl 0647.05052
Reed, B.
1987
$$L(2,1)$$-labelling of graphs. Zbl 1192.05135
Havet, Frédéric; Reed, Bruce; Sereni, Jean-Sébastien
2008
Polychromatic Hamilton cycles. Zbl 0803.05036
Frieze, Alan; Reed, Bruce
1993
The height of a random binary search tree. Zbl 1325.68076
Reed, Bruce
2003
Polynomial-time recognition of clique-width $$\leq 3$$ graphs. Zbl 1237.05147
Corneil, Derek G.; Habib, Michel; Lanlignel, Jean-Marc; Reed, Bruce; Rotics, Udi
2012
Bisimplicial vertices in even-hole-free graphs. Zbl 1205.05119
Addario-Berry, Louigi; Chudnovsky, Maria; Havet, Frédéric; Reed, Bruce; Seymour, Paul
2008
List colouring when the chromatic number is close to the order of the graph. Zbl 1063.05049
Reed, Bruce; Sudakov, Benny
2005
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width. Zbl 1079.68069
Călinescu, Gruia; Fernandes, Cristina G.; Reed, Bruce
2003
Graph colouring via the probabilistic method. Zbl 0926.05018
Molloy, M.; Reed, B.
1999
Star arboricity. Zbl 0780.05043
Alon, Noga; McDiarmid, Colin; Reed, Bruce
1992
The Erdős-Pósa property for odd cycles in highly connected graphs. Zbl 0981.05066
Rautenbach, Dieter; Reed, Bruce
2001
An improved algorithm for finding tree decompositions of small width. Zbl 1320.05128
Perković, Ljubomir; Reed, Bruce
2000
Building heaps fast. Zbl 0681.68069
McDiarmid, C. J. H.; Reed, B. A.
1989
Ballot theorems, old and new. Zbl 1151.91412
2008
Hadwiger’s conjecture for line graphs. Zbl 1050.05056
Reed, Bruce; Seymour, Paul
2004
The evolution of the mixing rate of a simple random walk on the giant component of a random graph. Zbl 1147.60316
Fountoulakis, N.; Reed, B. A.
2008
$$\beta$$-perfect graphs. Zbl 0857.05038
Markossian, S. E.; Gasparian, G. S.; Reed, B. A.
1996
Griggs and Yeh’s conjecture and $$L(p,1)$$-labelings. Zbl 1245.05110
Havet, Frédéric; Reed, Bruce; Sereni, Jean-Sébastien
2012
The edge-density for $$K_{2,t}$$ minors. Zbl 1231.05244
Chudnovsky, Maria; Reed, Bruce; Seymour, Paul
2011
Bounding $$\chi$$ in terms of $$\omega$$ and $$\Delta$$ for quasi-line graphs. Zbl 1184.05045
King, Andrew D.; Reed, Bruce A.
2008
On star coloring of graphs. Zbl 1042.68628
Fertin, Guillaume; Raspaud, André; Reed, Bruce
2001
Introducing directed tree width. Zbl 1072.05579
Reed, B.
1999
A strengthening of Brooks’ theorem. Zbl 0935.05045
Reed, Bruce
1999
The dominating number of a random cubic graph. Zbl 0839.05085
Molloy, Michael; Reed, Bruce
1995
An (almost) linear time algorithm for odd cycles transversal. Zbl 1288.05280
Kawarabayashi, Ken-ichi; Reed, Bruce
2010
Colouring graphs when the number of colours is nearly the maximum degree. Zbl 1323.05052
Molloy, Michael; Reed, Bruce
2001
Perfect matchings in random $$r$$-regular, $$s$$-uniform hypergraphs. Zbl 0857.05075
Cooper, Colin; Frieze, Alan; Molloy, Michael; Reed, Bruce
1996
On the variance of the height of random binary search trees. Zbl 0845.68027
Devroye, Luc; Reed, Bruce
1995
Finding disjoint trees in planar graphs in linear time. Zbl 0791.05092
Reed, B. A.; Robertson, N.; Schrijver, A.; Seymour, P. D.
1993
An extremal function for the achromatic number. Zbl 0787.05053
Bollobás, Béla; Reed, Bruce; Thomason, Andrew
1993
Fast skew partition recognition. Zbl 1162.05359
Kennedy, William S.; Reed, Bruce
2008
On the maximum degree of a random planar graph. Zbl 1160.05018
McDiarmid, Colin; Reed, Bruce
2008
Concentration for self-bounding functions and an inequality of Talagrand. Zbl 1120.60015
McDiarmid, Colin; Reed, Bruce
2006
Algorithmic aspects of tree width. Zbl 1035.05090
Reed, B. A.
2003
Even pairs. Zbl 0990.05053
Everett, Hazel; de Figueiredo, Celina M. H.; Linhares Sales, Cláudia; Maffray, Frédéric; Porto, Oscar; Reed, Bruce A.
2001
A proof of a conjecture of Ohba. Zbl 1320.05045
Noel, Jonathan A.; Reed, Bruce A.; Wu, Hehui
2015
Highly parity linked graphs. Zbl 1212.05143
Kawarabayashi, Ken-Ichi; Reed, Bruce
2009
Faster mixing and small bottlenecks. Zbl 1113.60073
Fountoulakis, N.; Reed, B. A.
2007
Threshold tolerance graphs. Zbl 0652.05059
Monma, Clyde L.; Reed, Bruce; Trotter, William T. jun.
1988
Odd cycle packing. Zbl 1293.05177
Kawarabayashi, Ken-ichi; Reed, Bruce
2010
A weaker version of Lovász’ path removal conjecture. Zbl 1171.05028
Kawarabayashi, Ken-Ichi; Lee, Orlando; Reed, Bruce; Wollan, Paul
2008
An upper bound for the chromatic number of line graphs. Zbl 1125.05039
King, A. D.; Reed, B. A.; Vetta, A.
2007
Channel assignment on graphs of bounded treewidth. Zbl 1029.05150
McDiarmid, Colin; Reed, Bruce
2003
The list colouring constants. Zbl 0926.05019
Reed, Bruce
1999
Fractional colouring and Hadwiger’s conjecture. Zbl 1029.05060
Reed, Bruce; Seymour, Paul
1998
Edge coloring regular graphs of high degree. Zbl 0902.05030
Perkovic, L.; Reed, B.
1997
List colouring of graphs with at most $$(2-o(1))\chi$$ vertices. Zbl 0997.05031
Reed, Bruce; Sudakov, Benny
2002
Near-optimal list colorings. Zbl 0971.05047
Molloy, Michael; Reed, Bruce
2000
Fractionally colouring total graphs. Zbl 0795.05056
Kilakos, K.; Reed, B.
1993
$$P_ 4$$-comparability graphs. Zbl 0675.05067
Hoàng, C. T.; Reed, B. A.
1989
Forcing a sparse minor. Zbl 1372.05211
Reed, Bruce; Wood, David R.
2016
Oriented trees in digraphs. Zbl 1262.05066
Addario-Berry, Louigi; Havet, Frédéric; Sales, Cláudia Linhares; Reed, Bruce; Thomassé, Stéphan
2013
Connectivity for Bridge-addable monotone graph classes. Zbl 1253.05089
Addario-Berry, L.; McDiarmid, C.; Reed, B.
2012
A linear-time algorithm to find a separator in a graph excluding a minor. Zbl 1298.05308
Reed, Bruce; Wood, David R.
2009
Partition into cliques for cubic graphs: Planar case, complexity and approximation. Zbl 1144.05049
Cerioli, M. R.; Faria, L.; Ferreira, T. O.; Martinhon, C. A. J.; Protti, F.; Reed, B.
2008
Degree constrained subgraphs. Zbl 1203.05032
Addario-Berry, L.; Dalal, K.; Reed, B. A.
2005
On the mixing rate of the triangulation walk. Zbl 0918.60060
Molloy, Michael; Reed, Bruce; Steiger, William
1999
On total colourings of graphs. Zbl 0725.05036
McDiarmid, Colin; Reed, Bruce
1993
A note on short cycles in digraphs. Zbl 0626.05021
Hoàng, C. T.; Reed, B.
1987
Polynomial treewidth forces a large grid-like-minor. Zbl 1234.05223
Reed, Bruce A.; Wood, David R.
2012
Recognizing a totally odd $$K_{4}$$-subdivision, parity 2-disjoint rooted paths and a parity cycle through specified elements. Zbl 1288.05279
Kawarabayashi, Ken-ichi; Li, Zhentao; Reed, Bruce
2010
Critical random graphs and the structure of a minimum spanning tree. Zbl 1214.05154
Addario-Berry, L.; Broutin, N.; Reed, B.
2009
Skew partitions in perfect graphs. Zbl 1147.05035
Reed, Bruce
2008
On six problems posed by Jarik Nešetřil. Zbl 1116.05081
Bang-Jensen, Jørgen; Reed, Bruce; Schacht, Mathias; Šámal, Robert; Toft, Bjarne; Wagner, Uli
2006
Random regular graphs of non-constant degree: Connectivity and Hamiltonicity. Zbl 1005.05039
Cooper, Colin; Frieze, Alan; Reed, Bruce
2002
A variant of the Erdős-Sós conjecture. Zbl 07202780
Havet, Frédéric; Reed, Bruce; Stein, Maya; Wood, David R.
2020
How to determine if a random graph with a fixed degree sequence has a giant component. Zbl 1379.05102
Joos, Felix; Perarnau, Guillem; Rautenbach, Dieter; Reed, Bruce
2018
Acyclic edge colourings of graphs with large girth. Zbl 1368.05045
Cai, X. S.; Perarnau, G.; Reed, B.; Watts, A. B.
2017
Existence of spanning $$\mathcal{F}$$-free subgraphs with large minimum degree. Zbl 1371.05146
Perarnau, G.; Reed, B.
2017
Colourings with bounded monochromatic components in graphs of given circumference. Zbl 1375.05102
Mohar, Bojan; Reed, Bruce; Wood, David R.
2017
Forcing a sparse minor. Zbl 1372.05211
Reed, Bruce; Wood, David R.
2016
A short proof that $$\chi$$ can be bounded $$\epsilon$$ away from $$\Delta + 1$$ toward $$\omega$$. Zbl 1330.05070
King, Andrew D.; Reed, Bruce A.
2016
A proof of a conjecture of Ohba. Zbl 1320.05045
Noel, Jonathan A.; Reed, Bruce A.; Wu, Hehui
2015
Claw-free graphs, skeletal graphs, and a stronger conjecture on $$\omega$$, $$\Delta$$, and $$\chi$$. Zbl 1309.05076
King, Andrew D.; Reed, Bruce A.
2015
Excluding a substar and an antisubstar. Zbl 1408.05090
Chudnovsky, Maria; Norin, Sergey; Reed, Bruce; Seymour, Paul
2015
Colouring graphs when the number of colours is almost the maximum degree. Zbl 1301.05130
Molloy, Michael; Reed, Bruce
2014
For most graphs $$H$$, most $$H$$-free graphs have a linear homogeneous set. Zbl 1302.05116
Kang, Ross J.; McDiarmid, Colin; Reed, Bruce; Scott, Alex
2014
Oriented trees in digraphs. Zbl 1262.05066
Addario-Berry, Louigi; Havet, Frédéric; Sales, Cláudia Linhares; Reed, Bruce; Thomassé, Stéphan
2013
Digraph girth via chromatic number. Zbl 1272.05065
Keevash, Peter; Li, Zhentao; Mohar, Bojan; Reed, Bruce
2013
Asymptotics of the chromatic number for quasi-line graphs. Zbl 1269.05037
King, Andrew D.; Reed, Bruce
2013
A simple algorithm for the graph minor decomposition – logic meets structural graph theory. Zbl 1423.05159
Grohe, Martin; Kawarabayashi, Ken-ichi; Reed, Bruce
2013
A linear-time algorithm for finding a complete graph minor in a dense graph. Zbl 1285.05164
Dujmović, Vida; Harvey, Daniel J.; Joret, Gwenaël; Reed, Bruce; Wood, David R.
2013
The disjoint paths problem in quadratic time. Zbl 1298.05296
Kawarabayashi, Ken-Ichi; Kobayashi, Yusuke; Reed, Bruce
2012
Polynomial-time recognition of clique-width $$\leq 3$$ graphs. Zbl 1237.05147
Corneil, Derek G.; Habib, Michel; Lanlignel, Jean-Marc; Reed, Bruce; Rotics, Udi
2012
Griggs and Yeh’s conjecture and $$L(p,1)$$-labelings. Zbl 1245.05110
Havet, Frédéric; Reed, Bruce; Sereni, Jean-Sébastien
2012
Connectivity for Bridge-addable monotone graph classes. Zbl 1253.05089
Addario-Berry, L.; McDiarmid, C.; Reed, B.
2012
Polynomial treewidth forces a large grid-like-minor. Zbl 1234.05223
Reed, Bruce A.; Wood, David R.
2012
The edge-density for $$K_{2,t}$$ minors. Zbl 1231.05244
Chudnovsky, Maria; Reed, Bruce; Seymour, Paul
2011
The graph minor algorithm with parity conditions. Zbl 1292.68127
Kawarabayashi, Ken-ichi; Reed, Bruce; Wollan, Paul
2011
An (almost) linear time algorithm for odd cycles transversal. Zbl 1288.05280
Kawarabayashi, Ken-ichi; Reed, Bruce
2010
Odd cycle packing. Zbl 1293.05177
Kawarabayashi, Ken-ichi; Reed, Bruce
2010
Recognizing a totally odd $$K_{4}$$-subdivision, parity 2-disjoint rooted paths and a parity cycle through specified elements. Zbl 1288.05279
Kawarabayashi, Ken-ichi; Li, Zhentao; Reed, Bruce
2010
Finding a maximum-weight induced $$k$$-partite subgraph of an $$i$$-triangulated graph. Zbl 1216.05152
Addario-Berry, Louigi; Kennedy, W. S.; King, Andrew D.; Li, Zhentao; Reed, Bruce
2010
Asymptotically optimal frugal colouring. Zbl 1211.05046
Molloy, Michael; Reed, Bruce
2010
Almost all $$H$$-free graphs have the Erdős-Hajnal property. Zbl 1219.05124
Loebl, Martin; Reed, Bruce; Scott, Alex; Thomason, Andrew; Thomassé, Stéphan
2010
Corrigendum to “Asymptotically optimal frugal colouring” [J. Comb. Theory, Ser. B 100, No. 2, 226–246 (2010)]. Zbl 1211.05047
Molloy, Michael; Reed, Bruce
2010
Minima in branching random walks. Zbl 1196.60142
2009
On the odd-minor variant of Hadwiger’s conjecture. Zbl 1213.05079
Geelen, Jim; Gerards, Bert; Reed, Bruce; Seymour, Paul; Vetta, Adrian
2009
Highly parity linked graphs. Zbl 1212.05143
Kawarabayashi, Ken-Ichi; Reed, Bruce
2009
A linear-time algorithm to find a separator in a graph excluding a minor. Zbl 1298.05308
Reed, Bruce; Wood, David R.
2009
Critical random graphs and the structure of a minimum spanning tree. Zbl 1214.05154
Addario-Berry, L.; Broutin, N.; Reed, B.
2009
Hadwiger’s conjecture is decidable. Zbl 1304.05047
Kawarabayashi, Ken-ichi; Reed, Bruce
2009
A general critical condition for the emergence of a giant component in random graphs with given degrees. Zbl 1273.05201
Fountoulakis, Nikolaos; Reed, Bruce
2009
A characterization of graphs with fractional total chromatic number equal to $$\Delta +2$$. Zbl 1268.05075
Ito, Takehiro; Kennedy, W. Sean; Reed, Bruce A.
2009
Coloring Artemis graphs. Zbl 1165.05027
Lévêque, Benjamin; Maffray, Frédéric; Reed, Bruce; Trotignon, Nicolas
2009
A nearly linear time algorithm for the half integral parity disjoint paths packing problem. Zbl 1423.68349
Kawarabayashi, Ken-Ichi; Reed, Bruce
2009
Asymptotically optimal frugal colouring. Zbl 1423.05073
Molloy, Michael; Reed, Bruce
2009
Tree-width of graphs without a $$3\times 3$$ grid minor. Zbl 1231.05243
Birmelé, E.; Bondy, J. A.; Reed, B. A.
2009
Removable cycles in non-bipartite graphs. Zbl 1176.05041
Kawarabayashi, Ken-Ichi; Reed, Bruce; Lee, Orlando
2009
Degree constrained subgraphs. Zbl 1147.05055
Addario-Berry, L.; Dalal, K.; Reed, B. A.
2008
$$L(2,1)$$-labelling of graphs. Zbl 1192.05135
Havet, Frédéric; Reed, Bruce; Sereni, Jean-Sébastien
2008
Bisimplicial vertices in even-hole-free graphs. Zbl 1205.05119
Addario-Berry, Louigi; Chudnovsky, Maria; Havet, Frédéric; Reed, Bruce; Seymour, Paul
2008
Ballot theorems, old and new. Zbl 1151.91412
2008
The evolution of the mixing rate of a simple random walk on the giant component of a random graph. Zbl 1147.60316
Fountoulakis, N.; Reed, B. A.
2008
Bounding $$\chi$$ in terms of $$\omega$$ and $$\Delta$$ for quasi-line graphs. Zbl 1184.05045
King, Andrew D.; Reed, Bruce A.
2008
Fast skew partition recognition. Zbl 1162.05359
Kennedy, William S.; Reed, Bruce
2008
On the maximum degree of a random planar graph. Zbl 1160.05018
McDiarmid, Colin; Reed, Bruce
2008
A weaker version of Lovász’ path removal conjecture. Zbl 1171.05028
Kawarabayashi, Ken-Ichi; Lee, Orlando; Reed, Bruce; Wollan, Paul
2008
Partition into cliques for cubic graphs: Planar case, complexity and approximation. Zbl 1144.05049
Cerioli, M. R.; Faria, L.; Ferreira, T. O.; Martinhon, C. A. J.; Protti, F.; Reed, B.
2008
Skew partitions in perfect graphs. Zbl 1147.05035
Reed, Bruce
2008
A nearly linear time algorithm for the half integral disjoint paths packing. Zbl 1192.05161
Kawarabayashi, Ken-ichi; Reed, Bruce
2008
Optimization and recognition for $$K _{5}$$-minor free graphs in linear time. Zbl 1136.90492
Reed, Bruce; Li, Zhentao
2008
Domination in cubic graphs of large girth. Zbl 1162.05341
Rautenbach, Dieter; Reed, Bruce
2008
Planar graph bipartization in linear time. Zbl 1163.05052
2008
On planar quasi-parity graphs. Zbl 1165.68057
Sales, Cláudia Linhares; Maffray, Frédéric; Reed, Bruce
2008
Fractional coloring and the odd Hadwiger’s conjecture. Zbl 1142.05027
Kawarabayashi, Ken-Ichi; Reed, Bruce
2008
List colouring constants of triangle free graphs. Zbl 1341.05060
Amini, Omid; Reed, Bruce
2008
Vertex-colouring edge-weightings. Zbl 1127.05034
Addario-Berry, Louigi; Dalal, Ketan; McDiarmid, Colin; Reed, Bruce A.; Thomason, Andrew
2007
Computing crossing number in linear time. Zbl 1232.90339
Kawarabayashi, Ken-ichi; Reed, Bruce
2007
List colouring squares of planar graphs. Zbl 1341.05073
Havet, Frédéric; van den Heuvel, Jan; McDiarmid, Colin; Reed, Bruce
2007
The Erdős-Pósa property for long circuits. Zbl 1136.05028
Birmelé, Etienne; Bondy, J. Adrian; Reed, Bruce A.
2007
Faster mixing and small bottlenecks. Zbl 1113.60073
Fountoulakis, N.; Reed, B. A.
2007
An upper bound for the chromatic number of line graphs. Zbl 1125.05039
King, A. D.; Reed, B. A.; Vetta, A.
2007
Brambles, prisms and grids. Zbl 1120.05087
Birmelé, E.; Bondy, J. A.; Reed, B. A.
2007
Approximate min-max relations for odd cycles in planar graphs. Zbl 1113.05054
2007
Asymptotics of the chromatic number for quasi-line graphs. Zbl 1341.05078
King, Andrew D.; Reed, Bruce
2007
Concentration for self-bounding functions and an inequality of Talagrand. Zbl 1120.60015
McDiarmid, Colin; Reed, Bruce
2006
On six problems posed by Jarik Nešetřil. Zbl 1116.05081
Bang-Jensen, Jørgen; Reed, Bruce; Schacht, Mathias; Šámal, Robert; Toft, Bjarne; Wagner, Uli
2006
The diameter of the minimum spanning tree of a complete graph. Zbl 1190.05042
Addario-Berry, Louigi; Broutin, Nicolas; Reed, Bruce
2006
Vertex colouring edge partitions. Zbl 1074.05031
Addario-Berry, L.; Aldred, R. E. L.; Dalal, K.; Reed, B. A.
2005
List colouring when the chromatic number is close to the order of the graph. Zbl 1063.05049
Reed, Bruce; Sudakov, Benny
2005
Degree constrained subgraphs. Zbl 1203.05032
Addario-Berry, L.; Dalal, K.; Reed, B. A.
2005
Fast separation in a graph with an excluded minor. Zbl 1192.05082
Reed, Bruce; Wood, David R.
2005
($$\Delta-k$$)-critical graphs. Zbl 1062.05056
Farzad, Babak; Molloy, Michael; Reed, Bruce
2005
Planar graph bipartization in linear time. Zbl 1203.05153
2005
Approximate min-max relations for odd cycles in planar graphs. Zbl 1119.90360
2005
On the fractional chromatic index of a graph and its complement. Zbl 1090.90134
Avis, David; De Simone, Caterina; Reed, Bruce
2005
An upper bound for the chromatic number of line graphs. Zbl 1192.05052
King, Andrew D.; Reed, Bruce A.; Vetta, Adrian R.
2005
Heap building bounds. Zbl 1161.68400
Li, Zhentao; Reed, Bruce A.
2005
On the Co-$$P_{3}$$-structure of perfect graphs. Zbl 1069.05034
Hoàng, Chính T.; Reed, Bruce
2005
The perfection and recognition of bull-reducible Berge graphs. Zbl 1063.05055
Everett, Hazel; de Figueiredo, Celina M. H.; Klein, Sulamita; Reed, Bruce
2005
Finding odd cycle transversals. Zbl 1052.05061
Reed, Bruce; Smith, Kaleigh; Vetta, Adrian
2004
Star coloring of graphs. Zbl 1055.05051
Fertin, Guillaume; Raspaud, André; Reed, Bruce
2004
Excluding any graph as a minor allows a low tree-width 2-coloring. Zbl 1042.05036
DeVos, Matt; Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Reed, Bruce; Seymour, Paul; Vertigan, Dirk
2004
Hadwiger’s conjecture for line graphs. Zbl 1050.05056
Reed, Bruce; Seymour, Paul
2004
Stable skew partition problem. Zbl 1053.05058
Dantas, Simone; de Figueiredo, Celina M. H.; Klein, Sulamita; Gravier, Sylvain; Reed, Bruce A.
2004
The height of a random binary search tree. Zbl 1325.68076
Reed, Bruce
2003
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width. Zbl 1079.68069
Călinescu, Gruia; Fernandes, Cristina G.; Reed, Bruce
2003
Algorithmic aspects of tree width. Zbl 1035.05090
Reed, B. A.
2003
Channel assignment on graphs of bounded treewidth. Zbl 1029.05150
McDiarmid, Colin; Reed, Bruce
2003
A note on random homomorphism from arbitrary graphs to $$\mathbb{Z}$$. Zbl 1035.05085
Loebl, Martin; Nešetřil, Jaroslav; Reed, Bruce
2003
Graph colouring and the probabilistic method. Zbl 0987.05002
Molloy, Michael; Reed, Bruce
2002
List colouring of graphs with at most $$(2-o(1))\chi$$ vertices. Zbl 0997.05031
Reed, Bruce; Sudakov, Benny
2002
Random regular graphs of non-constant degree: Connectivity and Hamiltonicity. Zbl 1005.05039
Cooper, Colin; Frieze, Alan; Reed, Bruce
2002
Random regular graphs of non-constant degree: Independence and chromatic number. Zbl 0997.05089
Cooper, Colin; Frieze, Alan; Reed, Bruce; Riordan, Oliver
2002
...and 90 more Documents
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#### Cited by 2,661 Authors
59 Reed, Bruce Alan 35 Kawarabayashi, Ken-ichi 30 Maffray, Frédéric 30 Saurabh, Saket 26 Wood, David Ronald 25 Przybyło, Jakub 24 de Figueiredo, Celina M. Herrera 24 Havet, Frédéric 22 McDiarmid, Colin J. H. 22 Rautenbach, Dieter 22 Thilikos, Dimitrios M. 22 Wang, Wei-Fan 21 Kang, Ross J. 20 van der Hofstad, Remco W. 18 Brandstädt, Andreas 18 Lokshtanov, Daniel 18 Paulusma, Daniël 18 Zhu, Xuding 17 Chudnovsky, Maria 17 Frieze, Alan Michael 17 Henning, Michael Anthony 17 Raspaud, André 17 Wang, Guanghui 16 Marx, Dániel 15 Dantas, Simone 15 Nešetřil, Jaroslav 15 Sudakov, Benny 15 Wu, Jian-Liang 14 Addario-Berry, Louigi 14 Fomin, Fedor V. 14 Hell, Pavol 14 Hoàng, Chính T. 13 Klein, Sulamita 13 Vušković, Kristina 12 Alon, Noga M. 12 Bhamidi, Shankar 12 Heggernes, Pinar 12 Joos, Felix Claudius 12 Kobayashi, Yusuke 12 Kostochka, Aleksandr Vasil’evich 12 Král’, Daniel 12 Krivelevich, Michael 12 Kwon, Ojoung 12 Liu, Guizhen 12 Sau, Ignasi 11 Chandran, L. Sunil 11 Cranston, Daniel W. 11 Hou, Jianfeng 11 Karthick, T. 11 Kratochvíl, Jan 11 Lozin, Vadim Vladislavovich 11 Molloy, Michael S. O. 11 Niedermeier, Rolf 11 Ossona de Mendez, Patrice 11 Perarnau, Guillem 11 Pilipczuk, Marcin 11 Sereni, Jean-Sébastien 11 Seymour, Paul D. 11 Spirakis, Paul G. 11 Wang, Yiqiao 10 Joret, Gwenaël 10 Mohar, Bojan 10 Pilipczuk, Michał 10 Raman, Venkatesh 10 Schiermeyer, Ingo 9 Achlioptas, Dimitris 9 Britton, Tom 9 Dujmović, Vida 9 Janson, Svante 9 Kreutzer, Stephan 9 Miao, Lianying 9 Oum, Sang-Il 9 Raymond, Jean-Florent 9 Shu, Qiaojun 9 Trotignon, Nicolas 9 Wong, Tsai-Lien 9 Zeitouni, Ofer 9 Žerovnik, Janez 8 Amini, Omid 8 Bensmail, Julien 8 Bodlaender, Hans L. 8 Creignou, Nadia 8 Daudé, Hervé 8 Ding, Jian 8 Feder, Tomás 8 Golovach, Petr A. 8 Grytczuk, Jarosław 8 Kakimura, Naonori 8 King, Andrew D. 8 Lê Văn Băng 8 Lévêque, Benjamin 8 Linhares-Sales, Claudia 8 Subramanian, C. R. 8 Thomassé, Stéphan 8 Van Leeuwen, Erik Jan 8 van ’t Hof, Pim 8 Yu, Gexin 7 Adler, Isolde 7 Bernshteyn, Anton 7 Chen, Jian-er ...and 2,561 more Authors
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#### Cited in 220 Serials
209 Discrete Applied Mathematics 203 Discrete Mathematics 124 Theoretical Computer Science 119 Journal of Combinatorial Theory. Series B 83 Journal of Graph Theory 79 European Journal of Combinatorics 70 Graphs and Combinatorics 63 Random Structures & Algorithms 59 Information Processing Letters 56 Algorithmica 54 SIAM Journal on Discrete Mathematics 39 Journal of Combinatorial Optimization 29 Combinatorics, Probability and Computing 27 Journal of Computer and System Sciences 26 The Electronic Journal of Combinatorics 25 Journal of Statistical Physics 24 Combinatorica 22 The Annals of Applied Probability 18 Probability Theory and Related Fields 17 The Annals of Probability 17 SIAM Journal on Computing 17 Theory of Computing Systems 14 Discussiones Mathematicae. Graph Theory 13 Advances in Applied Probability 13 Journal of Discrete Algorithms 11 Journal of Mathematical Biology 11 Physica A 11 Applied Mathematics and Computation 11 Journal of Statistical Mechanics: Theory and Experiment 10 Information and Computation 10 Discrete Mathematics, Algorithms and Applications 10 Journal of Theoretical Biology 9 Advances in Mathematics 9 Stochastic Processes and their Applications 8 Journal of Applied Probability 8 Physica D 8 Acta Mathematicae Applicatae Sinica. English Series 8 Acta Mathematica Sinica. English Series 8 Discrete Optimization 8 Computer Science Review 7 Mathematical Biosciences 7 Discrete & Computational Geometry 7 International Journal of Computer Mathematics 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Israel Journal of Mathematics 6 Journal of Combinatorial Theory. Series A 6 Computational Geometry 6 Linear Algebra and its Applications 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Chaos 6 The European Physical Journal B. Condensed Matter and Complex Systems 5 Communications in Mathematical Physics 5 Statistics & Probability Letters 5 Electronic Journal of Probability 5 RAIRO. Theoretical Informatics and Applications 5 Internet Mathematics 4 Bulletin of Mathematical Biology 4 Czechoslovak Mathematical Journal 4 Networks 4 Proceedings of the American Mathematical Society 4 Advances in Applied Mathematics 4 Journal of Theoretical Probability 4 Applied Mathematics Letters 4 International Journal of Foundations of Computer Science 4 Bernoulli 4 Journal of Graph Algorithms and Applications 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Frontiers of Mathematics in China 4 Science China. Mathematics 3 Artificial Intelligence 3 Nuclear Physics. B 3 Chaos, Solitons and Fractals 3 Theoretical Population Biology 3 Operations Research Letters 3 Discrete Mathematics and Applications 3 European Journal of Operational Research 3 Proceedings of the National Academy of Sciences of the United States of America 3 Mathematical Programming. Series A. Series B 3 Journal of Mathematical Sciences (New York) 3 Complexity 3 New Journal of Physics 3 Journal of Applied Mathematics and Computing 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Journal of Physics A: Mathematical and Theoretical 3 Stochastic Systems 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics 2 Indian Journal of Pure & Applied Mathematics 2 Periodica Mathematica Hungarica 2 Physics Reports 2 Canadian Journal of Mathematics 2 Journal of Economic Theory 2 Journal of Statistical Planning and Inference 2 Mathematics of Operations Research 2 Transactions of the American Mathematical Society 2 Order 2 Journal of Automated Reasoning 2 Journal of the American Mathematical Society 2 Science in China. Series A 2 International Journal of Computational Geometry & Applications ...and 120 more Serials
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#### Cited in 39 Fields
1,686 Combinatorics (05-XX) 578 Computer science (68-XX) 219 Probability theory and stochastic processes (60-XX) 133 Operations research, mathematical programming (90-XX) 79 Biology and other natural sciences (92-XX) 64 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Statistical mechanics, structure of matter (82-XX) 28 Information and communication theory, circuits (94-XX) 25 Mathematical logic and foundations (03-XX) 18 Statistics (62-XX) 15 Dynamical systems and ergodic theory (37-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Numerical analysis (65-XX) 10 Ordinary differential equations (34-XX) 9 Systems theory; control (93-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 5 Number theory (11-XX) 5 Group theory and generalizations (20-XX) 5 Measure and integration (28-XX) 5 Convex and discrete geometry (52-XX) 5 Manifolds and cell complexes (57-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 General topology (54-XX) 2 Commutative algebra (13-XX) 2 Partial differential equations (35-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 2 Fluid mechanics (76-XX) 2 Quantum theory (81-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX)
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https://zbmath.org/authors/?q=ai%3Arybakov.vladimir-vladimirovich
|
# zbMATH — the first resource for mathematics
## Rybakov, Vladimir Vladimirovich
Compute Distance To:
Author ID: rybakov.vladimir-vladimirovich Published as: Rybakov, V.; Rybakov, V. V.; Rybakov, Vladimir; Rybakov, Vladimir V.; Rybakov, Vladimir Vladimirovich Homepage: http://math.sfu-kras.ru/node/303 External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp
Documents Indexed: 123 Publications since 1975, including 1 Book Reviewing Activity: 29 Reviews
all top 5
#### Co-Authors
90 single-authored 7 Terziler, Mehmet 5 Babenyshev, Sergey 5 Gencer, Çigdem 4 Kiyatkin, Vladimir R. 4 Odintsov, Sergei P. 4 Oner, Tahsin 3 Kosheleva, Anna Vladimirovna 2 Bashmakov, Stepan Igorevich 2 Calardo, Erica 2 Golovanov, Mikhail I. 2 Maksimova, Larisa L’vovna 2 Rimatskij, V. V. 1 Alaev, Pavel Evgenievich 1 Bogopol’skiĭ, O. V. 1 Churkin, Valerii Avdeevich 1 Ershov, Yuriĭ Leonidovich 1 Fedorishin, B. R. 1 Filyurin, A. S. 1 Goncharov, Sergeĭ Savost’yanovich 1 Khramtsov, D. G. 1 Luk’yanchuk, A. N. 1 Mazurov, Viktor Danilovich 1 Moor, Michael Alexandrovich 1 Morozov, Andreĭ Sergeevich 1 Pal’chunov, Dimitriĭ Evgen’evich 1 Puzarenko, Vadim G. 1 Remazki, Vitaliy 1 Rimatksi, V. V. 1 Ryaskin, A. N. 1 Rychkov, K. L. 1 Schmidt, Renate A. 1 Taimanov, Iskander Asanovich 1 Terziller, M. 1 Tishkovsky, Dmitry 1 Vasil’ev, Andreĭ Viktorovich 1 Yurasova, E. M.
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#### Serials
12 Algebra and Logic 11 Bulletin of the Section of Logic 9 Logic Journal of the IGPL 8 Algebra i Logika 8 Sibirskie Èlektronnye Matematicheskie Izvestiya 6 Journal of Logic and Computation 5 Siberian Mathematical Journal 4 Studia Logica 4 Annals of Pure and Applied Logic 4 Mathematical Logic Quarterly (MLQ) 3 Mathematical Notes 3 The Journal of Symbolic Logic 3 Mathematics of the USSR. Izvestiya 3 Soviet Mathematics. Doklady 3 Journal of Applied Non-Classical Logics 2 Matematicheskie Zametki 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Archive for Mathematical Logic 1 Information Sciences 1 Notre Dame Journal of Formal Logic 1 Theoretical Computer Science 1 Siberian Advances in Mathematics 1 Mathematics of the USSR, Sbornik 1 Theory of Computing Systems 1 Fundamenta Informaticae 1 Lobachevskii Journal of Mathematics 1 Logic and Logical Philosophy 1 Semiotika i Informatika 1 Studies in Logic and the Foundations of Mathematics 1 Logica Universalis
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#### Fields
121 Mathematical logic and foundations (03-XX) 18 Computer science (68-XX) 8 General algebraic systems (08-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX)
#### Citations contained in zbMATH
79 Publications have been cited 456 times in 157 Documents Cited by Year
Admissibility of logical inference rules. Zbl 0872.03002
Rybakov, V. V.
1997
A criterion for admissibility of rules in the modal system S4 and intuitionistic logic. Zbl 0598.03013
Rybakov, V. V.
1984
A lattice of normal modal logics. Zbl 0315.02027
Maksimova, L. L.; Rybakov, V. V.
1975
Rules of inference with parameters for intuitionistic logic. Zbl 0788.03007
Rybakov, Vladimir V.
1992
Logical consecutions in discrete linear temporal logic. Zbl 1110.03010
Rybakov, V. V.
2005
Unification and admissible rules for paraconsistent minimal Johanssons’ logic J and positive intuitionistic logic $$\mathbf{IPC}^+$$. Zbl 1323.03029
Odintsov, Sergei; Rybakov, Vladimir
2013
Linear temporal logic with until and next, logical consecutions. Zbl 1147.03008
Rybakov, V.
2008
Linear temporal logic LTL: basis for admissible rules. Zbl 1233.03026
Babenyshev, Sergey; Rybakov, Vladimir
2011
Bases of admissible rules of the logics S4 and Int. Zbl 0598.03014
Rybakov, V. V.
1985
Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus. Zbl 0709.03009
Rybakov, V. V.
1990
Construction of an explicit basis for rules admissible in modal system S4. Zbl 0992.03027
Rybakov, Vladimir V.
2001
Non-transitive linear temporal logic and logical knowledge operations. Zbl 1403.03028
Rybakov, Vladimir V.
2016
Linear temporal logic $${\mathcal{LTL}}_K$$ extended by multi-agent logic $$\text{K}_n$$ with interacting agents. Zbl 1208.03023
Rybakov, Vladimir
2009
Multi-modal and temporal logics with universal formula – reduction of admissibility to validity and unification. Zbl 1149.03017
Rybakov, V.
2008
A tableau method for checking rule admissibility in S4. Zbl 1345.03033
Babenyshev, Sergey; Rybakov, Vladimir; Schmidt, Renate A.; Tishkovsky, Dmitry
2010
Linear temporal logic with until and before on integer numbers, deciding algorithms. Zbl 1185.03022
Rybakov, V.
2006
On finite model property for admissible rules. Zbl 0938.03033
Rybakov, Vladimir V.; Kiyatkin, Vladimir R.; Oner, Tahsin
1999
Admissible rules of pretabular modal logics. Zbl 0489.03005
Rybakov, V. V.
1981
Logic of knowledge and discovery via interacting agents – decision algorithm for true and satisfiable statements. Zbl 1179.68151
Rybakov, Vladimir
2009
Logical consecutions in intransitive temporal linear logic of finite intervals. Zbl 1091.03002
Rybakov, Vladimir
2005
Logical equations and admissible rules of inference with parameters in modal provability logics. Zbl 0729.03012
Rybakov, V. V.
1990
Unification in linear temporal logic LTL. Zbl 1241.03014
Babenyshev, Sergey; Rybakov, Vladimir
2011
Refined common knowledge logics or logics of common information. Zbl 1030.03015
Rybakov, V. V.
2003
An essay on unification and inference rules for modal logics. Zbl 0952.03019
Rybakov, V. V.; Terziler, M.; Gencer, C.
1999
Hereditarily structurally complete modal logics. Zbl 0836.03014
Rybakov, V. V.
1995
Decidability of admissibility in the modal system Grz and in intuitionistic logic. Zbl 0624.03009
Rybakov, V. V.
1987
Admissible rules for logics containing S4.3. Zbl 0582.03009
Rybakov, V. V.
1984
Noncompact extensions of the logic S4. Zbl 0406.03039
Rybakov, V. V.
1977
Multiagent temporal logics with multivaluations. Zbl 06976648
Rybakov, V. V.
2018
Decidability of hybrid logic with local common knowledge based on linear temporal logic LTL. Zbl 1142.03323
Babenyshev, Sergey; Rybakov, Vladimir
2008
Logics with the universal modality and admissible consecutions. Zbl 1186.03048
Rybakov, Vladimir
2007
A basis in semi-reduced form for the admissible rules of the intuitionistic logic IPC. Zbl 0955.03037
Rybakov, Vladimir V.; Terziler, Mehmet; Remazki, Vitaliy
2000
Bases of admissible rules of the modal system Grz and of intuitionistic logic. Zbl 0617.03007
Rybakov, V. V.
1987
Temporal multi-valued logic with lost worlds in the past. Zbl 1436.03154
Rybakov, Vladimir Vladimirovich
2018
Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms. Zbl 1420.03060
Rybakov, Vladimir V.
2017
Writing out unifiers for formulas with coefficients in intuitionistic logic. Zbl 1277.03004
Rybakov, Vladimir V.
2013
Rules admissible in transitive temporal logic $$\mathrm{T}_{\mathrm{S}4}$$, sufficient condition. Zbl 1209.03011
Rybakov, Vladimir
2010
Branching time logics $$\mathcal {BTL}^{\text{U,S}}_{\text{N},\text{N}^{-1}}(\mathcal {Z})_{\alpha }$$ with operations Until and Since based on bundles of integer numbers, logical consecutions, deciding algorithms. Zbl 1148.03011
Rybakov, V.
2008
An axiomatisation for the multi-modal logic of knowledge and linear time LTK. Zbl 1134.03011
Calardo, Erica; Rybakov, Vladimir V.
2007
Until-since temporal logic based on parallel time with common past. Deciding algorithms. Zbl 1132.03324
Rybakov, V.
2007
Unification and passive inference rules for modal logics. Zbl 1040.03014
Rybakov, V. V.; Terziler, M.; Gencer, C.
2000
A modal analog for Glivenko’s theorem and its applications. Zbl 0788.03020
Rybakov, V. V.
1992
Equations in free topoboolean algebra. Zbl 0624.03007
Rybakov, V. V.
1986
Decidability of the admissibility problem in layer-finite logics. Zbl 0576.03012
Rybakov, V. V.
1984
Bases of quasiidentities of finite modal algebras. Zbl 0507.08005
Rybakov, V. V.
1982
Linear temporal logic with non-transitive time, algorithms for decidability and verification of admissibility. Zbl 1429.03074
Rybakov, Vladimir V.
2018
Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility. Zbl 06751250
Rybakov, Vladimir
2016
Inference rules in Nelson’s logics, admissibility and weak admissibility. Zbl 1336.03036
Odintsov, Sergei; Rybakov, Vladimir
2015
Unifiers in transitive modal logics for formulas with coefficients (meta-variables). Zbl 1278.03050
Rybakov, Vladimir
2013
Writing out unifiers in linear temporal logic. Zbl 1259.03029
Rybakov, Vladimir V.
2012
Combining time and knowledge, semantic approach. Zbl 1117.03021
Calardo, E.; Rybakov, V.
2005
Unification in common knowledge logics. Zbl 1036.03012
Rybakov, V. V.
2002
Quasi-characteristic inference rules for modal logics. Zbl 0887.03014
Rybakov, Vladimir V.
1997
Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property. Zbl 0807.03016
Rybakov, Vladimir V.
1994
Problems of admissibility and substitution, logical equations and restricted theories of free algebras. Zbl 0691.03012
Rybakov, V. V.
1989
Elementary theories of free topo-Boolean and pseudo-Boolean algebras. Zbl 0593.03041
Rybakov, V. V.
1985
Admissible rules for pretable modal logics. Zbl 0496.03008
Rybakov, V. V.
1982
Modale Logiken mit LM-Axiomen. Zbl 0417.03007
Rybakov, V. V.
1978
Noncompact extensions of the logic S4. Zbl 0413.03013
Rybakov, V. V.
1978
Hereditarily finitely axiomatizable extensions of logic S4. Zbl 0358.02022
Rybakov, V. V.
1977
Branching time agents logics, satisfiability problem by rules in reduced form. Zbl 1436.03126
Rybakov, Vladimir Vladimirovich
2019
Projective formulas and unification in linear temporal logic $$\mathrm{LTL}_{U}$$. Zbl 1342.03017
Rybakov, Vladimir
2014
Temporal logic with interacting agents. Decidability: theorems and admissible rules. Zbl 1181.03016
Rybakov, Vladimir
2008
Discrete linear temporal logic with current time point clusters, deciding algorithms. Zbl 1298.03063
Rybakov, V.
2008
Logic of visibility, perception, and knowledge and admissible inference rules. Zbl 1083.03021
Golovanov, M. I.; Kosheleva, A. V.; Rybakov, V.
2005
Residual finiteness for admissible inference rules. Zbl 0989.03015
Rybakov, V. V.; Kiyatkin, V. R.; Oner, T.
2001
On self-admissible quasi-characterizing inference rules. Zbl 0969.03032
Rybakov, V. V.; Terziler, M.; Gencer, C.
2000
An explicit basis for rules admissible in modal system S4. Zbl 0961.03021
Rybakov, Vladimir V.
1999
Independent bases for rules admissible in pretabular logics. Zbl 0956.03024
Rybakov, V.; Kiyatkin, V.; Terziler, M.
1999
The structure of rigid frames of restricted depth 2. Zbl 0965.03025
Rybakov, V. V.; Oner, T.
1998
Modal logics preserving admissible for S4 inference rules. Zbl 1044.03515
Rybakov, Vladimir V.
1995
Even tabular modal logics sometimes do not have independent base for admissible rules. Zbl 0847.03014
Rybakov, Vladimir V.
1995
Intermediate logics preserving admissible inference rules of Heyting calculus. Zbl 0807.03017
Rybakov, Vladimir V.
1993
Solvability of logical equations in the modal system Grz and in intuitionistic logic. Zbl 0729.03014
Rybakov, V. V.
1991
Semantic criteria for admissible inference rules in the logics S4 and Int. Zbl 0729.03013
Rybakov, V. V.
1991
Equations in a free topoboolean algebra and the substitution problem. Zbl 0607.06008
Rybakov, V. V.
1986
A criterion for admissibility of rules of inference in modal and intuitionistic logic. Zbl 0596.03025
Rybakov, V. V.
1985
Modal logics with LM-axioms. Zbl 0427.03013
Rybakov, V. V.
1979
A decidable noncompact extension of the logic S4. Zbl 0415.03012
Rybakov, V. V.
1979
Branching time agents logics, satisfiability problem by rules in reduced form. Zbl 1436.03126
Rybakov, Vladimir Vladimirovich
2019
Multiagent temporal logics with multivaluations. Zbl 06976648
Rybakov, V. V.
2018
Temporal multi-valued logic with lost worlds in the past. Zbl 1436.03154
Rybakov, Vladimir Vladimirovich
2018
Linear temporal logic with non-transitive time, algorithms for decidability and verification of admissibility. Zbl 1429.03074
Rybakov, Vladimir V.
2018
Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms. Zbl 1420.03060
Rybakov, Vladimir V.
2017
Non-transitive linear temporal logic and logical knowledge operations. Zbl 1403.03028
Rybakov, Vladimir V.
2016
Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility. Zbl 06751250
Rybakov, Vladimir
2016
Inference rules in Nelson’s logics, admissibility and weak admissibility. Zbl 1336.03036
Odintsov, Sergei; Rybakov, Vladimir
2015
Projective formulas and unification in linear temporal logic $$\mathrm{LTL}_{U}$$. Zbl 1342.03017
Rybakov, Vladimir
2014
Unification and admissible rules for paraconsistent minimal Johanssons’ logic J and positive intuitionistic logic $$\mathbf{IPC}^+$$. Zbl 1323.03029
Odintsov, Sergei; Rybakov, Vladimir
2013
Writing out unifiers for formulas with coefficients in intuitionistic logic. Zbl 1277.03004
Rybakov, Vladimir V.
2013
Unifiers in transitive modal logics for formulas with coefficients (meta-variables). Zbl 1278.03050
Rybakov, Vladimir
2013
Writing out unifiers in linear temporal logic. Zbl 1259.03029
Rybakov, Vladimir V.
2012
Linear temporal logic LTL: basis for admissible rules. Zbl 1233.03026
Babenyshev, Sergey; Rybakov, Vladimir
2011
Unification in linear temporal logic LTL. Zbl 1241.03014
Babenyshev, Sergey; Rybakov, Vladimir
2011
A tableau method for checking rule admissibility in S4. Zbl 1345.03033
Babenyshev, Sergey; Rybakov, Vladimir; Schmidt, Renate A.; Tishkovsky, Dmitry
2010
Rules admissible in transitive temporal logic $$\mathrm{T}_{\mathrm{S}4}$$, sufficient condition. Zbl 1209.03011
Rybakov, Vladimir
2010
Linear temporal logic $${\mathcal{LTL}}_K$$ extended by multi-agent logic $$\text{K}_n$$ with interacting agents. Zbl 1208.03023
Rybakov, Vladimir
2009
Logic of knowledge and discovery via interacting agents – decision algorithm for true and satisfiable statements. Zbl 1179.68151
Rybakov, Vladimir
2009
Linear temporal logic with until and next, logical consecutions. Zbl 1147.03008
Rybakov, V.
2008
Multi-modal and temporal logics with universal formula – reduction of admissibility to validity and unification. Zbl 1149.03017
Rybakov, V.
2008
Decidability of hybrid logic with local common knowledge based on linear temporal logic LTL. Zbl 1142.03323
Babenyshev, Sergey; Rybakov, Vladimir
2008
Branching time logics $$\mathcal {BTL}^{\text{U,S}}_{\text{N},\text{N}^{-1}}(\mathcal {Z})_{\alpha }$$ with operations Until and Since based on bundles of integer numbers, logical consecutions, deciding algorithms. Zbl 1148.03011
Rybakov, V.
2008
Temporal logic with interacting agents. Decidability: theorems and admissible rules. Zbl 1181.03016
Rybakov, Vladimir
2008
Discrete linear temporal logic with current time point clusters, deciding algorithms. Zbl 1298.03063
Rybakov, V.
2008
Logics with the universal modality and admissible consecutions. Zbl 1186.03048
Rybakov, Vladimir
2007
An axiomatisation for the multi-modal logic of knowledge and linear time LTK. Zbl 1134.03011
Calardo, Erica; Rybakov, Vladimir V.
2007
Until-since temporal logic based on parallel time with common past. Deciding algorithms. Zbl 1132.03324
Rybakov, V.
2007
Linear temporal logic with until and before on integer numbers, deciding algorithms. Zbl 1185.03022
Rybakov, V.
2006
Logical consecutions in discrete linear temporal logic. Zbl 1110.03010
Rybakov, V. V.
2005
Logical consecutions in intransitive temporal linear logic of finite intervals. Zbl 1091.03002
Rybakov, Vladimir
2005
Combining time and knowledge, semantic approach. Zbl 1117.03021
Calardo, E.; Rybakov, V.
2005
Logic of visibility, perception, and knowledge and admissible inference rules. Zbl 1083.03021
Golovanov, M. I.; Kosheleva, A. V.; Rybakov, V.
2005
Refined common knowledge logics or logics of common information. Zbl 1030.03015
Rybakov, V. V.
2003
Unification in common knowledge logics. Zbl 1036.03012
Rybakov, V. V.
2002
Construction of an explicit basis for rules admissible in modal system S4. Zbl 0992.03027
Rybakov, Vladimir V.
2001
Residual finiteness for admissible inference rules. Zbl 0989.03015
Rybakov, V. V.; Kiyatkin, V. R.; Oner, T.
2001
A basis in semi-reduced form for the admissible rules of the intuitionistic logic IPC. Zbl 0955.03037
Rybakov, Vladimir V.; Terziler, Mehmet; Remazki, Vitaliy
2000
Unification and passive inference rules for modal logics. Zbl 1040.03014
Rybakov, V. V.; Terziler, M.; Gencer, C.
2000
On self-admissible quasi-characterizing inference rules. Zbl 0969.03032
Rybakov, V. V.; Terziler, M.; Gencer, C.
2000
On finite model property for admissible rules. Zbl 0938.03033
Rybakov, Vladimir V.; Kiyatkin, Vladimir R.; Oner, Tahsin
1999
An essay on unification and inference rules for modal logics. Zbl 0952.03019
Rybakov, V. V.; Terziler, M.; Gencer, C.
1999
An explicit basis for rules admissible in modal system S4. Zbl 0961.03021
Rybakov, Vladimir V.
1999
Independent bases for rules admissible in pretabular logics. Zbl 0956.03024
Rybakov, V.; Kiyatkin, V.; Terziler, M.
1999
The structure of rigid frames of restricted depth 2. Zbl 0965.03025
Rybakov, V. V.; Oner, T.
1998
Admissibility of logical inference rules. Zbl 0872.03002
Rybakov, V. V.
1997
Quasi-characteristic inference rules for modal logics. Zbl 0887.03014
Rybakov, Vladimir V.
1997
Hereditarily structurally complete modal logics. Zbl 0836.03014
Rybakov, V. V.
1995
Modal logics preserving admissible for S4 inference rules. Zbl 1044.03515
Rybakov, Vladimir V.
1995
Even tabular modal logics sometimes do not have independent base for admissible rules. Zbl 0847.03014
Rybakov, Vladimir V.
1995
Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property. Zbl 0807.03016
Rybakov, Vladimir V.
1994
Intermediate logics preserving admissible inference rules of Heyting calculus. Zbl 0807.03017
Rybakov, Vladimir V.
1993
Rules of inference with parameters for intuitionistic logic. Zbl 0788.03007
Rybakov, Vladimir V.
1992
A modal analog for Glivenko’s theorem and its applications. Zbl 0788.03020
Rybakov, V. V.
1992
Solvability of logical equations in the modal system Grz and in intuitionistic logic. Zbl 0729.03014
Rybakov, V. V.
1991
Semantic criteria for admissible inference rules in the logics S4 and Int. Zbl 0729.03013
Rybakov, V. V.
1991
Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus. Zbl 0709.03009
Rybakov, V. V.
1990
Logical equations and admissible rules of inference with parameters in modal provability logics. Zbl 0729.03012
Rybakov, V. V.
1990
Problems of admissibility and substitution, logical equations and restricted theories of free algebras. Zbl 0691.03012
Rybakov, V. V.
1989
Decidability of admissibility in the modal system Grz and in intuitionistic logic. Zbl 0624.03009
Rybakov, V. V.
1987
Bases of admissible rules of the modal system Grz and of intuitionistic logic. Zbl 0617.03007
Rybakov, V. V.
1987
Equations in free topoboolean algebra. Zbl 0624.03007
Rybakov, V. V.
1986
Equations in a free topoboolean algebra and the substitution problem. Zbl 0607.06008
Rybakov, V. V.
1986
Bases of admissible rules of the logics S4 and Int. Zbl 0598.03014
Rybakov, V. V.
1985
Elementary theories of free topo-Boolean and pseudo-Boolean algebras. Zbl 0593.03041
Rybakov, V. V.
1985
A criterion for admissibility of rules of inference in modal and intuitionistic logic. Zbl 0596.03025
Rybakov, V. V.
1985
A criterion for admissibility of rules in the modal system S4 and intuitionistic logic. Zbl 0598.03013
Rybakov, V. V.
1984
Admissible rules for logics containing S4.3. Zbl 0582.03009
Rybakov, V. V.
1984
Decidability of the admissibility problem in layer-finite logics. Zbl 0576.03012
Rybakov, V. V.
1984
Bases of quasiidentities of finite modal algebras. Zbl 0507.08005
Rybakov, V. V.
1982
Admissible rules for pretable modal logics. Zbl 0496.03008
Rybakov, V. V.
1982
Admissible rules of pretabular modal logics. Zbl 0489.03005
Rybakov, V. V.
1981
Modal logics with LM-axioms. Zbl 0427.03013
Rybakov, V. V.
1979
A decidable noncompact extension of the logic S4. Zbl 0415.03012
Rybakov, V. V.
1979
Modale Logiken mit LM-Axiomen. Zbl 0417.03007
Rybakov, V. V.
1978
Noncompact extensions of the logic S4. Zbl 0413.03013
Rybakov, V. V.
1978
Noncompact extensions of the logic S4. Zbl 0406.03039
Rybakov, V. V.
1977
Hereditarily finitely axiomatizable extensions of logic S4. Zbl 0358.02022
Rybakov, V. V.
1977
A lattice of normal modal logics. Zbl 0315.02027
Maksimova, L. L.; Rybakov, V. V.
1975
all top 5
#### Cited by 98 Authors
39 Rybakov, Vladimir Vladimirovich 13 Iemhoff, Rosalie 9 Maksimova, Larisa L’vovna 8 Citkin, Alex 6 Zakharyaschev, Michael Viktorovich 5 Bezhanishvili, Nick 5 Goudsmit, Jeroen P. 4 Gencer, Çigdem 4 Ghilardi, Silvio 4 Jeřábek, Emil 4 Metcalfe, George 4 Rimatskij, V. V. 3 Balbiani, Philippe 3 Bezhanishvili, Guram 3 Chagrov, Aleksandr Vasil’evich 3 de Jongh, Dick H. J. 3 Schmidt, Renate A. 3 Tishkovsky, Dmitry 3 Wolter, Frank 3 Yun, Veta Fëdorovna 2 Babenyshev, S. V. 2 Babenyshev, Sergey 2 Cabrer, Leonardo Manuel 2 Dzik, Wojciech 2 Hartonas, Chrysafis 2 Kiyatkin, Vladimir R. 2 Luk’yanchuk, A. N. 2 Moraschini, Tommaso 2 Odintsov, Sergei P. 2 Oner, Tahsin 2 Pigozzi, Don Leonard 2 Rozière, Paul 2 Stronkowski, Michał Marek 2 Visser, Albert 2 Wojtylak, Piotr 1 Andréka, Hajnal 1 Baader, Franz 1 Baltazar, Pedro 1 Beklemishev, Lev D. 1 Beyersdorff, Olaf 1 Blok, Wim J. 1 Borgwardt, Stefan 1 Calardo, Erica 1 Cintula, Petr 1 Citkin, Alexander 1 Colacito, Almudena 1 Conradie, Willem J. 1 Czelakowski, Janusz 1 Darnière, Luck 1 Dziobiak, Wiesław 1 Fagin, Ronald 1 Font, Josep Maria 1 Franks, Curtis 1 Gabelaia, David 1 Gispert, Joan 1 Groszek, Marcia J. 1 Halpern, Joseph Yehuda 1 Ilin, Julia 1 Jibladze, Mamuka A. 1 Junker, Markus 1 Kharchenko, Vladislav K. 1 Khodadadi, Mohammad 1 Kostrzycka, Zofia 1 Kutz, Oliver 1 Lempp, Steffen 1 Martins, Manuel António 1 Moor, Michael Alexandrovich 1 Morawska, Barbara 1 Mundici, Daniele 1 Muravitsky, Alexei Yu. 1 Németi, István 1 Palmigiano, Alessandra 1 Pohlers, Wolfram 1 Priestley, Hilary A. 1 Pudlák, Pavel 1 Rabe, Florian 1 Raftery, James G. 1 Rasga, João 1 Rathjen, Michael 1 Rautenberg, Wolfgang 1 Rotolo, Antonino 1 Schwichtenberg, Helmut 1 Sernadas, Amilcar C. 1 Sernadas, Cristina S. 1 Shen, Weina 1 Shkatov, Dmitry 1 Sutcliffe, Geoff 1 Świrydowicz, Katarzyna 1 Terziler, Mehmet 1 Vakarelov, Dimiter 1 van Alten, Clint J. 1 Vardi, Moshe Y. 1 Vargas, Ana Lucia 1 Venema, Yde 1 Yang, Eunsuk 1 Yang, Fan 1 Yashin, Aleksandr D. 1 Zhao, Zhiguang
all top 5
#### Cited in 31 Serials
22 Algebra and Logic 18 Studia Logica 15 Annals of Pure and Applied Logic 11 The Journal of Symbolic Logic 7 Siberian Mathematical Journal 7 Journal of Applied Non-Classical Logics 7 The Bulletin of Symbolic Logic 6 Archive for Mathematical Logic 5 Sibirskie Èlektronnye Matematicheskie Izvestiya 5 Logica Universalis 5 The Review of Symbolic Logic 4 Notre Dame Journal of Formal Logic 3 Algebra Universalis 3 Journal of Philosophical Logic 3 Mathematical Logic Quarterly (MLQ) 2 Mathematical Notes 2 Theoretical Computer Science 2 Transactions of the American Mathematical Society 2 Bulletin of the Section of Logic 2 Logical Methods in Computer Science 1 Fuzzy Sets and Systems 1 Information Sciences 1 Journal of Pure and Applied Algebra 1 History and Philosophy of Logic 1 MSCS. Mathematical Structures in Computer Science 1 Theory of Computing Systems 1 Soft Computing 1 Lobachevskii Journal of Mathematics 1 Logic and Logical Philosophy 1 Journal of Applied Logic 1 Axioms
all top 5
#### Cited in 10 Fields
151 Mathematical logic and foundations (03-XX) 20 Computer science (68-XX) 15 General algebraic systems (08-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 5 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-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.
| 2021-01-21T06:10:03 |
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|
http://wpts.wikidot.com/astronauts-vs-cosmonauts
|
Astronauts Vs Cosmonauts
(1)
$$insert LaTeX equation here$$
We put the RAD in RAD-IO
page revision: 1, last edited: 22 Feb 2007 04:40
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Share Alike 2.5 License.
| 2017-10-23T09:49:31 |
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|
https://learnmathnow.fandom.com/wiki/Triangles
|
## FANDOM
37 Pages
A triangle is any polygon with three sides.
## PropertiesEdit
The sum of the angles in any triangle must always be equal to 180°. Radians are not used to measure triangle angles, since they only apply to circles.
The area of any given triangle is described in this formula:
$A = \frac{1}{2}bh$
where b is the base of the triangle and h is the height of the triangle.
Hero of Alexandria is credited with the following formula. If a triangle has sides a, b, and c:
$A = \sqrt{s(s-a)(s-b)(s-c)}$
where s is the semiperimeter of the triangle, i.e. the sum of the sides divided by 2. This formula does not require knowledge of the triangle's height.
## Triangle Classifications Based On AnglesEdit
### RightEdit
A right triangle is any triangle with an angle of 90°.
#### Special Right TrianglesEdit
##### 45-45-90Edit
A 45-45-90 triangle is a triangle whose angles measure only 90° and 45°. Shortcuts to finding the lengths of missing sides can be found here.
$2x^2 = c^2$,
so therefore,
$x = \frac{c}{\sqrt{2}\,}\,$, or
$x = \frac{c\sqrt{2}\,}{2}\,$
##### 30-60-90Edit
A 30-60-90 triangle is a triangle whose angles measure only 30°, 60°, and 90°. Shortcuts to finding the lengths of missing sides can be found here.
$a^2 + x^2 = 4a^2$,
so therefore,
$x = a\sqrt{3}\,$
$a = \frac{x}{\sqrt{3}\,}\,$, or
$a = \frac{x\sqrt{3}\,}{3}\,$
### AcuteEdit
An acute triangle is any triangle where all the angles measure less than 90°.
#### EquiangularEdit
An equiangular triangle is an acute triangle in which all sides and angles are the same. The angles in equiangular triangles always measure 60°. This is true because 180° ÷ 3 = 60°.
### ObtuseEdit
An obtuse triangle is any triangle where one angle measures more than 90°.
## Triangle Classification Based On SidesEdit
### EquilateralEdit
An equilateral (Latin aequalis "equal" + latus "side") triangle, also called an equiangular triangle, is an acute triangle in which all sides and angles are the same. The angles in equilateral triangles always measure 60°. This is true because 180° ÷ 3 = 60°.
### IsoscelesEdit
An isosceles (Greek ίσος ísos "same" + σκελες skeles "legs") triangle is any triangle where 2 sides are congruent, leaving the base angles congruent as well.
### ScaleneEdit
A scalene triangle is any triangle where no sides are congruent.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-11-29T20:12:32 |
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|
https://www.health-ni.gov.uk/publications/equality-scheme-department-health-social-services-and-public-safety
|
# Equality scheme for the Department of Health
Date published: 28 March 2012
Section 75 of the Northern Ireland Act 1998 (the Act) requires
public authorities, in carrying out their functions relating to
Northern Ireland, to have due regard to the need to promote
equality of opportunity and regard to the desirability of promoting
good relations across a range of categories outlined in the Act
## Details
This equality scheme sets out how the Department of Health,
Social Services and Public Safety (the Department) proposes to fulfil the Section 75 statutory duties (the Duties).
| 2020-11-28T14:24:26 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=B180W&home=sumtabB
|
#### ${{\mathit \Xi}_{{b}}{(6227)}^{-}}$ WIDTH
VALUE (MeV) DOCUMENT ID TECN COMMENT
$19.9$ $\pm2.1$ $\pm1.5$ 1
2021
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$18.1$ $\pm5.4$ $\pm1.8$ 2
2018 H
LHCB Repl. by AAIJ 2021
1 Uses ${{\mathit \Lambda}_{{b}}^{0}}{{\mathit K}^{-}}$ decays.
2 Uses ${{\mathit \Lambda}_{{b}}^{0}}{{\mathit K}^{-}}$ and ${{\mathit \Xi}_{{b}}^{0}}{{\mathit \pi}^{-}}$ modes.
References:
AAIJ 2021
PR D103 012004 Observation of a new $\Xi_b^0$ state
AAIJ 2018H
PRL 121 072002 Observation of a new $\Xi_b^-$ resonance
| 2022-09-29T19:56:02 |
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|
https://www.usgs.gov/center-news/volcano-watch-reginald-t-okamura-a-personal-recollection
|
# Volcano Watch — Reginald T. Okamura: A personal recollection
Release Date:
Reggie and the Hawaiian Volcano Observatory were inextricably associated for 34 years. I was privileged to be part of the relationship for much of this time.
Tom Wright, former Scientist-in-Charge of the Hawaiian Volcano Observatory (HVO), wrote the following tribute to the late Reginald T. Okamura, retired long-time staff member, who passed away on January 16.
Reggie and the Hawaiian Volcano Observatory were inextricably associated for 34 years. I was privileged to be part of the relationship for much of this time. I was assigned to work with Reg when I arrived in 1964 as a young staff geologist. Reg and I were the same age, and we became professional colleagues and personal friends. He introduced me to Island ways, and when I left HVO in 1969, I could count Hawaii as my second home.
I'll never forget the vision of Reg on Chain of Craters Road during the beginning of the March 1965 eruption in Makaopuhi Crater--catching falling pumice in his hard hat for a visiting scientist who desired volcanic samples untouched by rain! In that moment I realized that HVO was not just a local facility but one literally connected to the greater scientific world through the accessibility of the observatory and its information. HVO has built a reputation established equally by the locally hired staff and by the scientists who came from the mainland to temporarily staff it. The eruption formed a deep "lava lake" ponded in the crater. Reg and I collaborated on all aspects of what became a classic study of the cooling of basaltic lava. Climbing down 200 m (700 feet) into a crater, sometimes several times a week, creates unbreakable bonds, and so it was between Reg and the many others who participated in the lava lake study. As driller, Reg took responsibility for equipment checks before making the descent, and he kept all the notebooks in which data were recorded. Back at HVO we worked together to plan the experiments and interpret the data. We authored a USGS Professional Paper on the results of our studies.
Before computers, when hand calculators were barely introduced, Reg was record keeper for the growing studies of ground deformation. He maintained the entire early record of Kīlauea and Mauna Loa surveys and calculated the surveying results quickly after the field data were acquired, often staying long after pau hana time to finish the job. His speed with mental arithmetic is legendary and provided a quick reality check to eager young Ph.D.s, who couldn't begin to keep up.
Reggie was Chief of Operations at HVO when I was chosen as Scientist-in-Charge in 1984. In this role he handled the day-to-day responsibility for making HVO work, and again Reg and I collaborated on the scientific program. His job was made especially challenging by the long-awaited approval of a new building, coming about, in part, through Reg's contacts within Hawaii's Congressional delegation. He was instrumental in ensuring a graceful transition from our old facility to the new. Reg was in charge during times when I was on the Mainland, with no thought of any disruption in the decision-making associated with HVO's work. I still treasure a photograph of the two of us taken in 1965 in front of a newly installed X-ray diffraction unit, labeling it "Who ever thought these guys could run a volcano observatory?"
Reg was present at the initiation of the Minority Participation in Earth Sciences (MPES) program. This program matured to become essential to HVO, not only providing summer help but also identifying several future staff members. Reg was the vital connection between the Scientist-in-Charge and the permanent staff, summer students, and the many volunteers, and he also worked with State and County officials as Scientists-in-Charge changed. I was moved, at his funeral service, to see the many people whose lives Reg had personally touched. His contributions to HVO and the Big Island community will be long remembered.
### Volcano Activity Update
Lava continued to erupt from Puu O`o and flow through a network of tubes from the vent to the sea. No surface flows from breakouts of the tube system were observed on the coastal flats. Lava is entering the ocean near Kamokuna and forming a new bench. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying frequent collapses of the new land. The steam clouds are highly acidic and laced with glass particles.
No felt earthquakes were reported during the week ending on January 28. The public is invited to learn more about earthquakes at a natural hazard educational symposium on Saturday, February 6, 1999 from 9:00 a.m. until noon in room 306 of the UHH Campus Center. The symposium is organized by the University of Hawaii at Hilo (UHH) Center for the Study of Active Volcanoes (CSAV) and sponsored by the Federal Emergency Management Agency (FEMA). Speakers include seismologists Paul Okubo and Carl Johnson, Hawaii County Civil Defense director Harry Kim, structural engineer Afaq Sarwar, and architect Virginia Macdonald. Attendees will have an opportunity to ask questions of the speakers, obtain literature and educational materials, and visit the American Red Cross resource booth.
| 2020-11-27T06:48:52 |
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|
https://www.madisoncounty.in.gov/election-results
|
# Election Results
#### 2020 Election Results
REMEMBER TO REFRESH YOUR BROWSER FOR THE MOST UPDATED RESULTS!
******* OFFICIAL ***** OFFICIAL ***** OFFICIAL ***** OFFICIAL ***** OFFICIAL *******
******* UNOFFICIAL ***** UNOFFICIAL ***** UNOFFICIAL ***** UNOFFICIAL ***** UNOFFICIAL *******
``` ```
SUMMARY REPORT Madison County, IN Unofficial Results
Run Date:05/03/22 Primary Election
RUN TIME:07:57 PM May 3, 2022
STATISTICS
PRECINCTS COUNTED (OF 112). . . . . 112 100.00
REGISTERED VOTERS - TOTAL . . . . . 89,892
BALLOTS CAST - TOTAL. . . . . . . 14,840
BALLOTS CAST - REPUBLICAN . . . . . 10,077 67.90
BALLOTS CAST - DEMOCRATIC . . . . . 4,763 32.10
BALLOTS CAST - NONPARTISAN. . . . . 0
BALLOTS CAST - BLANK. . . . . . . 9 .06
VOTER TURNOUT - TOTAL . . . . . . 16.51
VOTER TURNOUT - BLANK . . . . . . .01
********** (REPUBLICAN) **********
US SENATOR
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
TODD YOUNG . . . . . . . . . . 8,984 100.00
US REPRESENTATIVE
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
VICTORIA SPARTZ . . . . . . . . 9,174 100.00
STATE SENATOR DIST 25
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
MIKE GASKILL . . . . . . . . . 5,489 55.55
EVAN MCMULLEN . . . . . . . . . 4,393 44.45
STATE REPRESENTATIVE DIST 31
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
ANDY LYONS . . . . . . . . . . 108 32.63
ANN VERMILION . . . . . . . . . 223 67.37
STATE REPRESENTATIVE DIST 35
(VOTE FOR) 1
(WITH 35 OF 35 PRECINCTS COUNTED)
ELIZABETH ROWRAY . . . . . . . . 3,232 100.00
STATE REPRESENTATIVE DIST 36
(VOTE FOR) 1
(WITH 58 OF 58 PRECINCTS COUNTED)
KYLE PIERCE. . . . . . . . . . 4,123 100.00
STATE REPRESENTATIVE DIST 53
(VOTE FOR) 1
(WITH 10 OF 10 PRECINCTS COUNTED)
ROBERT W. CHERRY . . . . . . . . 959 100.00
STATE REPRESENTATIVE DIST 88
(VOTE FOR) 1
(WITH 5 OF 5 PRECINCTS COUNTED)
CHRIS JETER. . . . . . . . . . 261 64.13
CHRYSTAL SISSON . . . . . . . . 146 35.87
JUDGE CIRCUIT COURT COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
MARK DUDLEY. . . . . . . . . . 9,089 100.00
ATTORNEY COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
RODNEY CUMMINGS . . . . . . . . 8,732 100.00
CLERK CIRCUIT COURT COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
LINDA S. SMITH. . . . . . . . . 9,067 100.00
RECORDER COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
ANGELA (ANGIE) ABEL . . . . . . . 5,563 59.25
SUSAN ODOM . . . . . . . . . . 3,826 40.75
TREASURER COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
DAN GIRT. . . . . . . . . . . 9,022 100.00
SHERIFF COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
JOHN L. BEEMAN. . . . . . . . . 3,832 39.05
ANTHONY EMERY . . . . . . . . . 2,758 28.11
KIMBERLY S. STIGALL . . . . . . . 3,223 32.84
ASSESSOR COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
LARRY D. DAVIS. . . . . . . . . 9,078 100.00
COMMISSIONER DIST 1 COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
KELLY GASKILL . . . . . . . . . 4,390 44.47
OLIVIA PRATT . . . . . . . . . 5,482 55.53
COUNCIL DIST 1
(VOTE FOR) 1
(WITH 34 OF 34 PRECINCTS COUNTED)
JERRY ALEXANDER . . . . . . . . 1,273 40.68
BETHANY KELLER. . . . . . . . . 1,856 59.32
COUNCIL DIST 2
(VOTE FOR) 1
(WITH 26 OF 26 PRECINCTS COUNTED)
DIANA LIKENS . . . . . . . . . 1,271 50.10
DEVIN T. NORRICK . . . . . . . . 1,266 49.90
COUNCIL DIST 3
(VOTE FOR) 1
(WITH 28 OF 28 PRECINCTS COUNTED)
PETE HEUER . . . . . . . . . . 817 49.31
JODI L. NORRICK . . . . . . . . 840 50.69
COUNCIL DIST 4
(VOTE FOR) 1
(WITH 24 OF 24 PRECINCTS COUNTED)
KAELE ALBERT . . . . . . . . . 863 35.60
ROB STEELE . . . . . . . . . . 1,561 64.40
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
JILL FESLER. . . . . . . . . . 400 100.00
(VOTE FOR) 3
(WITH 4 OF 4 PRECINCTS COUNTED)
NANCY L. LOWE . . . . . . . . . 375 33.54
RANDY TWEEDY . . . . . . . . . 375 33.54
MARILEA A. WYATT . . . . . . . . 368 32.92
TOWNSHIP TRUSTEE ANDERSON
(VOTE FOR) 1
(WITH 47 OF 47 PRECINCTS COUNTED)
MIKE SHIVELY . . . . . . . . . 2,894 100.00
TOWNSHIP BOARD MEMBERS ANDERSON
(VOTE FOR) 3
(WITH 47 OF 47 PRECINCTS COUNTED)
JOHN AUKERMAN . . . . . . . . . 2,593 53.74
PHIL HERBIG. . . . . . . . . . 2,232 46.26
TOWNSHIP TRUSTEE BOONE
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
LISA A. SCHWINN . . . . . . . . 93 100.00
TOWNSHIP BOARD MEMBERS BOONE
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
JOHN R. HIATT . . . . . . . . . 90 33.71
RYAN J. PATTISON . . . . . . . . 89 33.33
RANDY WILLIAMS. . . . . . . . . 88 32.96
TOWNSHIP TRUSTEE DUCK CREEK
(VOTE FOR) 1
(WITH 2 OF 2 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS DUCK CREEK
(VOTE FOR) 3
(WITH 2 OF 2 PRECINCTS COUNTED)
LINDA SUE FLOYD . . . . . . . . 69 32.70
STEPHANIE TATE. . . . . . . . . 68 32.23
ANDREW WILLIAMS . . . . . . . . 74 35.07
TOWNSHIP TRUSTEE FALL CREEK
(VOTE FOR) 1
(WITH 10 OF 10 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS FALL CREEK
(VOTE FOR) 3
(WITH 10 OF 10 PRECINCTS COUNTED)
DAVID L. MARTIN . . . . . . . . 938 100.00
TOWNSHIP TRUSTEE GREEN
(VOTE FOR) 1
(WITH 5 OF 5 PRECINCTS COUNTED)
GREG VALENTINE. . . . . . . . . 394 100.00
TOWNSHIP BOARD MEMBERS GREEN
(VOTE FOR) 3
(WITH 5 OF 5 PRECINCTS COUNTED)
JERRY A. MANGES . . . . . . . . 359 33.84
SHARON K. ROBINSON . . . . . . . 354 33.36
FARRELL J. SMITH . . . . . . . . 348 32.80
TOWNSHIP TRUSTEE JACKSON
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
JOSHUA MILLER . . . . . . . . . 259 100.00
TOWNSHIP BOARD MEMBERS JACKSON
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
HAROLD MILLER . . . . . . . . . 247 34.02
RONALD G. NEESE . . . . . . . . 240 33.06
FRANK L. SHETTERLY . . . . . . . 239 32.92
TOWNSHIP TRUSTEE LAFAYETTE
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
CHRIS BURRIS . . . . . . . . . 213 49.08
KOREY HUGHES . . . . . . . . . 221 50.92
TOWNSHIP BOARD MEMBERS LAFAYETTE
(VOTE FOR) 3
(WITH 4 OF 4 PRECINCTS COUNTED)
DAVID WISE . . . . . . . . . . 410 100.00
TOWNSHIP TRUSTEE MONROE
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
GEORGE (CHIP) MCFERRAN . . . . . . 765 100.00
TOWNSHIP BOARD MEMBERS MONROE
(VOTE FOR) 3
(WITH 8 OF 8 PRECINCTS COUNTED)
SARAH COLLIS . . . . . . . . . 684 32.39
VALERIE JERRILS . . . . . . . . 708 33.52
JENNIFER WARD . . . . . . . . . 720 34.09
TOWNSHIP TRUSTEE PIPE CREEK
(VOTE FOR) 1
(WITH 12 OF 12 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS PIPE CREEK
(VOTE FOR) 3
(WITH 12 OF 12 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE RICHLAND
(VOTE FOR) 1
(WITH 6 OF 6 PRECINCTS COUNTED)
DOUGLAS STEIN . . . . . . . . . 502 100.00
TOWNSHIP BOARD MEMBERS RICHLAND
(VOTE FOR) 3
(WITH 6 OF 6 PRECINCTS COUNTED)
DALE RUSSELL COOK. . . . . . . . 427 32.62
MICHELLE DAVIS. . . . . . . . . 449 34.30
H. BILL ENGLAND . . . . . . . . 433 33.08
TOWNSHIP TRUSTEE STONY CREEK
(VOTE FOR) 1
(WITH 3 OF 3 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS STONY CREEK
(VOTE FOR) 3
(WITH 3 OF 3 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE UNION
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
TIM DUNHAM . . . . . . . . . . 602 65.51
MEGAN GREEN. . . . . . . . . . 317 34.49
TOWNSHIP BOARD MEMBERS UNION
(VOTE FOR) 3
(WITH 8 OF 8 PRECINCTS COUNTED)
DENNIS ADAMS . . . . . . . . . 674 27.74
LLOYD BROWN. . . . . . . . . . 594 24.44
WALTER A. CARTER . . . . . . . . 527 21.69
JACK ODLE . . . . . . . . . . 635 26.13
TOWNSHIP TRUSTEE VAN BUREN
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
DENISE (DEE) AMOS. . . . . . . . 152 100.00
TOWNSHIP BOARD MEMBERS VAN BUREN
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
RALPH GORDON . . . . . . . . . 150 100.00
COUNCIL AT LRG LAPEL
(VOTE FOR) 2
(WITH 3 OF 3 PRECINCTS COUNTED)
NOAH BOZELL. . . . . . . . . . 207 100.00
COUNCIL AT LRG INGALLS
(VOTE FOR) 2
(WITH 4 OF 4 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
COUNCIL DIST 3 PENDLETON
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
JENNIFER ROBERTS . . . . . . . . 351 100.00
COUNCIL AT LRG DIST 4 PENDLETON
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
MARISSA SKAGGS. . . . . . . . . 351 100.00
STATE DELEGATES DIST 1
(VOTE FOR) 12
(WITH 30 OF 30 PRECINCTS COUNTED)
JERRY ALEXANDER . . . . . . . . 2,267 7.47
DEBORAH DUNHAM. . . . . . . . . 2,383 7.85
VIVIEN LEE DYER . . . . . . . . 2,018 6.65
BENJAMIN EVANS. . . . . . . . . 2,239 7.38
JILL HUPFER. . . . . . . . . . 2,392 7.88
KYLE HUPFER. . . . . . . . . . 2,422 7.98
KELLY GASKILL . . . . . . . . . 1,918 6.32
MIKE GASKILL . . . . . . . . . 1,978 6.52
CHRISTINA L. ORGAN . . . . . . . 2,031 6.69
MICHAEL ORGAN . . . . . . . . . 2,026 6.68
ROY E. ORGAN . . . . . . . . . 1,829 6.03
ROB STEELE . . . . . . . . . . 2,536 8.36
DENA WILLIS. . . . . . . . . . 2,127 7.01
RUSS WILLIS. . . . . . . . . . 2,173 7.16
STATE DELEGATES DIST 2
(VOTE FOR) 12
(WITH 48 OF 48 PRECINCTS COUNTED)
CHLOE ANAGNOS . . . . . . . . . 1,538 4.89
JOHN AUKERMAN . . . . . . . . . 2,302 7.32
JENNIFER CULP . . . . . . . . . 2,572 8.18
TODD CULP . . . . . . . . . . 2,317 7.37
RODNEY CUMMINGS . . . . . . . . 2,475 7.87
CONNIE GARDNER. . . . . . . . . 2,184 6.95
RICK GARDNER . . . . . . . . . 2,474 7.87
KRISTI A. GRABOWSKI . . . . . . . 1,958 6.23
JONI HARVEY. . . . . . . . . . 2,023 6.43
KELLI HEUER. . . . . . . . . . 2,159 6.87
PETE N. HEUER . . . . . . . . . 2,223 7.07
MICHAEL MILLER. . . . . . . . . 2,061 6.56
KYLE PIERCE. . . . . . . . . . 2,056 6.54
HEATHER PROPHET . . . . . . . . 1,539 4.90
KEVIN A. SULC . . . . . . . . . 1,557 4.95
STATE DELEGATES DIST 3
(VOTE FOR) 12
(WITH 34 OF 34 PRECINCTS COUNTED)
TROY A. ABBOTT. . . . . . . . . 2,341 20.47
DAVID ABERNATHY . . . . . . . . 2,339 20.46
LARRY DAVIS. . . . . . . . . . 2,446 21.39
SEAN SMITH . . . . . . . . . . 2,104 18.40
LAUREEN WHITE . . . . . . . . . 2,204 19.28
********** (DEMOCRATIC) **********
US SENATOR
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
THOMAS M. MCDERMOTT, JR. . . . . . 4,074 100.00
US REPRESENTATIVE
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
MATTHEW L. HALL . . . . . . . . 1,846 41.75
JEANNINE LEE LAKE. . . . . . . . 2,576 58.25
STATE SENATOR DIST 25
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
TAMIE DIXON-TATUM. . . . . . . . 2,875 62.04
AARON HIGGINS . . . . . . . . . 1,759 37.96
STATE REPRESENTATIVE DIST 31
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
STATE REPRESENTATIVE DIST 35
(VOTE FOR) 1
(WITH 35 OF 35 PRECINCTS COUNTED)
BRAD SOWINSKI . . . . . . . . . 1,057 100.00
STATE REPRESENTATIVE DIST 36
(VOTE FOR) 1
(WITH 58 OF 58 PRECINCTS COUNTED)
TERRI JO AUSTIN . . . . . . . . 2,680 100.00
STATE REPRESENTATIVE DIST 53
(VOTE FOR) 1
(WITH 10 OF 10 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
STATE REPRESENTATIVE DIST 88
(VOTE FOR) 1
(WITH 5 OF 5 PRECINCTS COUNTED)
DONNA L. GRIFFIN . . . . . . . . 105 78.95
CRAIG M. HIRSTY . . . . . . . . 28 21.05
JUDGE CIRCUIT COURT COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
ATTORNEY COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
CLERK CIRCUIT COURT COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
JOE SPENCER. . . . . . . . . . 4,235 100.00
RECORDER COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
WENDI CARTER-HOPKINS. . . . . . . 4,329 100.00
TREASURER COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
DEVIN SCROGGINS . . . . . . . . 4,055 100.00
SHERIFF COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
JOEY COLE . . . . . . . . . . 4,284 100.00
ASSESSOR COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
COMMISSIONER DIST 1 COUNTY
(VOTE FOR) 1
(WITH 112 OF 112 PRECINCTS COUNTED)
STEPHEN GAISER. . . . . . . . . 2,173 50.22
LATISHA GUINN . . . . . . . . . 2,154 49.78
COUNCIL DIST 1
(VOTE FOR) 1
(WITH 34 OF 34 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
COUNCIL DIST 2
(VOTE FOR) 1
(WITH 26 OF 26 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
COUNCIL DIST 3
(VOTE FOR) 1
(WITH 28 OF 28 PRECINCTS COUNTED)
FRED REESE . . . . . . . . . . 1,384 100.00
COUNCIL DIST 4
(VOTE FOR) 1
(WITH 24 OF 24 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
(VOTE FOR) 3
(WITH 4 OF 4 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE ANDERSON
(VOTE FOR) 1
(WITH 47 OF 47 PRECINCTS COUNTED)
NORMAN D. ANDERSON, JR.. . . . . . 881 36.34
ASAUHN A. DIXON-TATUM . . . . . . 989 40.80
STEPHANY MAE STENNIS. . . . . . . 554 22.85
TOWNSHIP BOARD MEMBERS ANDERSON
(VOTE FOR) 3
(WITH 47 OF 47 PRECINCTS COUNTED)
MEREDITH (COCO) ARMSTRONG . . . . . 1,625 26.00
JANNETTE MANSFIELD-STITH . . . . . 1,874 29.98
LARRY RUSSELL . . . . . . . . . 1,322 21.15
LEO WILLIAMS . . . . . . . . . 1,429 22.86
TOWNSHIP TRUSTEE BOONE
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS BOONE
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE DUCK CREEK
(VOTE FOR) 1
(WITH 2 OF 2 PRECINCTS COUNTED)
CHAD KELICH. . . . . . . . . . 20 100.00
TOWNSHIP BOARD MEMBERS DUCK CREEK
(VOTE FOR) 3
(WITH 2 OF 2 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE FALL CREEK
(VOTE FOR) 1
(WITH 10 OF 10 PRECINCTS COUNTED)
FRED GASKILL . . . . . . . . . 311 100.00
TOWNSHIP BOARD MEMBERS FALL CREEK
(VOTE FOR) 3
(WITH 10 OF 10 PRECINCTS COUNTED)
TIM PRITCHARD . . . . . . . . . 328 100.00
TOWNSHIP TRUSTEE GREEN
(VOTE FOR) 1
(WITH 5 OF 5 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS GREEN
(VOTE FOR) 3
(WITH 5 OF 5 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE JACKSON
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS JACKSON
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
LOU ANNE JENNINGS. . . . . . . . 42 100.00
TOWNSHIP TRUSTEE LAFAYETTE
(VOTE FOR) 1
(WITH 4 OF 4 PRECINCTS COUNTED)
TERRY R. BAILEY . . . . . . . . 161 100.00
TOWNSHIP BOARD MEMBERS LAFAYETTE
(VOTE FOR) 3
(WITH 4 OF 4 PRECINCTS COUNTED)
JEFFREY J. JARRELL . . . . . . . 121 44.32
PATRICIA A. MAUCK. . . . . . . . 152 55.68
TOWNSHIP TRUSTEE MONROE
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
AMIE L. HOOD . . . . . . . . . 211 100.00
TOWNSHIP BOARD MEMBERS MONROE
(VOTE FOR) 3
(WITH 8 OF 8 PRECINCTS COUNTED)
DON SWEGMAN. . . . . . . . . . 196 50.65
RICHARD E. THOMPSON . . . . . . . 191 49.35
TOWNSHIP TRUSTEE PIPE CREEK
(VOTE FOR) 1
(WITH 12 OF 12 PRECINCTS COUNTED)
MARIAN DUNNICHAY . . . . . . . . 362 100.00
TOWNSHIP BOARD MEMBERS PIPE CREEK
(VOTE FOR) 3
(WITH 12 OF 12 PRECINCTS COUNTED)
LISA A. HOBBS . . . . . . . . . 332 30.46
SHEILA MCPHEARSON. . . . . . . . 296 27.16
DEBRA SERES. . . . . . . . . . 263 24.13
KEVIN SIPE . . . . . . . . . . 199 18.26
TOWNSHIP TRUSTEE RICHLAND
(VOTE FOR) 1
(WITH 6 OF 6 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS RICHLAND
(VOTE FOR) 3
(WITH 6 OF 6 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE STONY CREEK
(VOTE FOR) 1
(WITH 3 OF 3 PRECINCTS COUNTED)
DIANE LAWTHER . . . . . . . . . 99 100.00
TOWNSHIP BOARD MEMBERS STONY CREEK
(VOTE FOR) 3
(WITH 3 OF 3 PRECINCTS COUNTED)
PATRICIA FIELDS . . . . . . . . 95 35.32
STEPHEN N. PRISER. . . . . . . . 86 31.97
TERRY A. WILSON . . . . . . . . 88 32.71
TOWNSHIP TRUSTEE UNION
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS UNION
(VOTE FOR) 3
(WITH 8 OF 8 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP TRUSTEE VAN BUREN
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
TOWNSHIP BOARD MEMBERS VAN BUREN
(VOTE FOR) 3
(WITH 1 OF 1 PRECINCTS COUNTED)
DIX ANN CAMPBELL . . . . . . . . 44 46.81
STEPHEN A. WALLER. . . . . . . . 50 53.19
COUNCIL AT LRG LAPEL
(VOTE FOR) 2
(WITH 3 OF 3 PRECINCTS COUNTED)
NO CANDIDATE FILED . . . . . . . 0
COUNCIL AT LRG INGALLS
(VOTE FOR) 2
(WITH 4 OF 4 PRECINCTS COUNTED)
GEORGIA PARKER. . . . . . . . . 29 100.00
COUNCIL DIST 3 PENDLETON
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
JOE NOEL. . . . . . . . . . . 139 100.00
COUNCIL AT LRG DIST 4 PENDLETON
(VOTE FOR) 1
(WITH 8 OF 8 PRECINCTS COUNTED)
JOSHUA RING. . . . . . . . . . 135 100.00
PRCT COMMITTEEMAN 5 - 6
5 - 6 (Prec-0037)
(VOTE FOR) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
JEFF BARRANCO . . . . . . . . . 31 29.25
JOHN E. ETCHISON . . . . . . . . 75 70.75
```
```
| 2022-05-17T16:36:06 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/somas-unrealized-loss-what-does-it-mean-20180813.htm
|
August 13, 2018
SOMA's Unrealized Loss: What does it mean?
Brian Bonis, Lauren Fiesthumel, and Jamie Noonan1
In May 2018, the Federal Reserve published its Federal Reserve Banks Combined Quarterly Financial Report for the first quarter of 2018.2 For the first time since 2013, the report showed the System Open Market Account (SOMA) portfolio having an unrealized loss position. In particular, SOMA displayed an unrealized loss position of $462 million. What does it mean for the Fed to have an unrealized loss position on its securities holdings? This Note discusses the various valuation measures of the Fed's securities holdings, what these values mean, and the expected evolution of the value of the SOMA portfolio. Importantly, as discussed below, the SOMA portfolio's unrealized position has no effect on the ability of the Federal Reserve, as a central bank, to meet its financial obligations and pursue its statutory goals of price stability and maximum employment; in addition, it has no implications for the evolution of the Federal Reserve's earnings remittances to the U.S. Treasury or, ultimately, for U.S. taxpayers when, as expected, securities are held to maturity. 1. Differences Between GAAP and Federal Reserve Accounting Principles The Federal Reserve follows distinct accounting principles, which include a specific approach to report the value of the securities held in the SOMA portfolio (see the technical appendix for more information about the basis of the Reserve Bank accounting policies). On the Federal Reserve's weekly H.4.1 release, securities held outright in the SOMA are reported at face value, while unamortized premiums and discounts associated with those securities are reported on separate line items.3 In the Federal Reserve Banks Combined Quarterly Financial Report, SOMA securities are reported on an amortized cost basis, a valuation that is based on the face value of a security, adjusted in turn for any discounts or premiums associated with the purchase of the security.4 The premium or discount is amortized over the expected life of the security, and the security's value on an amortized cost basis is equal to the total purchase price paid less the amount of the premium or discount that has already been written down. At maturity, the Federal Reserve receives the face value, which at that point equals the security's amortized cost. Publicly traded companies as well as many private companies in the United States follow GAAP (generally accepted accounting principles) for their financial reporting. Under GAAP, in certain circumstances securities are reported at "fair value."5 Fair value represents the market price that would be received in selling an asset in an orderly transaction between market participants at the measurement date, which is the date reported in the statements. As such, fair value for a fixed-income security is a function of future expected interest rates, which are used to discount the flow of future coupon and principal payments. Under fair value accounting, changes in the market value of a security are recognized as income or loss and affect the income and capital position of a company. For a private company, whose equity holders have a claim on the value of a company's assets, fair value accounting ensures that the financial statements are a reflection of the expected value of a company. The Federal Reserve is a unique non-profit entity created by the Congress. Any income received in excess of the amount needed to pay expenses and dividends and to maintain surplus at the level of$6.825 billion is, by law, remitted to Treasury and does not affect the capital position or value of the Federal Reserve.6 Member banks hold shares of the Federal Reserve Banks, are paid a fixed dividend, and do not have a claim on the value of Federal Reserve assets, unlike in the case of a private company. Use of fair value accounting would create considerable volatility in Federal Reserve income as the value of its securities portfolio fluctuates over time. This is especially true because the values of Federal Reserve liabilities are not tied to interest rates to a similar degree. While the fair value of securities fluctuates with changes in interest rates, the valuation of a substantial portion of Federal Reserve liabilities does not. Consider, among various items, the case of reserve balances that depository institutions hold with the Federal Reserve. The value of this item, which accounts for a large share of the overall value of Federal Reserve liabilities and, at the same time, plays an important role in the conduct of monetary policy, does not depend on interest rates. Its level, instead, changes when, among other things, SOMA securities are purchased, sold, or eventually reach their maturity. Reporting the securities at amortized cost is more meaningful for the central bank because it provides a more transparent link between the amount of securities held for monetary policy purposes and the corresponding reserve balances.
2. Interest Rates and Unrealized Gains and Losses
Although the Federal Reserve reports its SOMA securities holdings at amortized cost, it also reports, for informational purposes, the fair value of the SOMA portfolio and the resulting unrealized gain or loss position, which is calculated as the difference between the fair value of the portfolio and its amortized cost.7 As noted above, the fair value of securities in SOMA fluctuates with changes in interest rates. Currently, the SOMA portfolio includes primarily Treasury securities and agency mortgage-backed securities (MBS).8 Because market prices of Treasury securities and MBS move inversely with respect to interest rates, when interest rates rise, all else equal, the value of SOMA securities holdings decreases. The resulting decline in the fair value of SOMA securities holdings means that the unrealized gain or loss position will also deteriorate, leading to a smaller unrealized gain or a larger unrealized loss. The converse is true when interest rates fall.
The figure below shows the inverse relationship between the 10-year Treasury yield and the SOMA's unrealized gain/loss position. Generally speaking, during the years following the financial crisis the SOMA portfolio displayed large unrealized gains that were driven by both the historically large portfolio size and the fact that longer-term interest rates had declined after many of the SOMA securities were purchased. Subsequently, as a result of an increase in longer-term interest rates, the SOMA exhibited an unrealized loss position in 2013 and, as indicated at the beginning of this note, most recently in the first quarter of 2018.
Figure 1: 10-year Treasury Yield and SOMA Unrealized Gain/Loss Position
In general, calculating the fair value of a portfolio of securities and the resulting unrealized gain or loss position can require some degree of estimation of the expected payment stream of the underlying securities. As Treasury securities are very liquid assets, market pricing is readily available for every CUSIP. However, to calculate the fair value of agency MBS holdings in the SOMA portfolio, model-based valuation is required due to the embedded prepayment options in the underlying mortgages. Different prepayment model structures and assumptions can lead to different model-based estimates. This means that the fair values calculated by different sources can differ.
3. Monetary Policy and SOMA Gains and Losses
When securities are sold or prepayments from MBS are received, the gains or losses resulting from these transactions become realized and affect the Reserve Banks' net income and remittances to the Treasury. Any realized gains and losses are recorded in the non-interest income portion of the Combined Statements of Operations on the Federal Reserve's Financial Reports. In recent years, the only SOMA securities sales conducted by the Desk were for small-value testing purposes and any gains or losses that were realized did not have a meaningful impact on net income. There are cases, however, in which a significant number of SOMA securities were sold before maturity, and the sales affected the Federal Reserve's net income and remittances to the Treasury. One such circumstance was the Maturity Extension Program (MEP), under which the Federal Reserve sold or redeemed nearly $700 billion of shorter-term Treasury securities between the end of September 2011 and the end of 2012. As interest rates at that time were lower than when the securities were originally purchased, the Federal Reserve, as a result of this program, recorded net gains of$2.3 billion in 2011 and $13.3 billion in 2012. Looking forward, the FOMC has indicated that securities sales are not anticipated to be part of the balance sheet normalization program. In particular, in the 2014 Policy Normalization Principles and Plans, the Committee announced that it intends to "reduce the Federal Reserve's securities holdings in a gradual and predictable manner primarily by ceasing to reinvest repayments of principal on securities held in the SOMA." This strategy, therefore, implies that the Federal Reserve's Treasury securities will be held until maturity, at which point the Federal Reserve will receive the par values for the securities, thus not realizing any gains or losses. Differently from holdings of Treasury securities, the Federal Reserve's holdings of MBS are subject to prepayment risk. Prepayments of MBS principal can result in small realized gains or losses and have, therefore, analogous implications to those of small-value sales of the securities in the SOMA portfolio. In a declining interest rate environment, principal prepayments are likely to increase, but it would be highly unlikely that the realized losses stemming from prepayments could significantly affect the overall net income result for the Federal Reserve. In an increasing interest rate environment, prepayments would be depressed, leading to muted realized losses on MBS, even as the fair value of MBS would decline. However, these Principles and Plans also note that for agency MBS, "limited sales might be warranted in the longer run to reduce or eliminate residual holdings." If sales were to occur in this situation, then associated realized gains or losses with any sales would affect net income. Even under the very unlikely hypothetical scenario in which the Fed sold a large amount of securities prior to maturity and incurred a sizable realized loss as a result, the Federal Reserve would still be able to meet its responsibilities and financial obligations. In particular, from a monetary policy standpoint, the losses alone would not affect the amount of depository institutions' reserves held with Federal Reserve Banks and would have no effect on the conduct of monetary policy. Moreover, in the unlikely scenario in which realized losses were sufficiently large enough to result in an overall net income loss for the Reserve Banks, the Federal Reserve would still meet its financial obligations to cover operating expenses. In that case, remittances to the Treasury would be suspended and a deferred asset would be recorded on the Federal Reserve's balance sheet, representing a claim on future net earnings that the Reserve Banks would need to realize before remittances to the Treasury would resume.9 Given that a large portion of the Federal Reserve's liabilities are comprised of Federal Reserve notes, which have no interest expense and are mostly collateralized by interest-earning Treasury and agency mortgage-backed securities, it is unlikely that the Federal Reserve Banks would be in an overall net loss position for very long. Importantly, we conclude by stressing that there is no reason to believe that policy actions would be affected by their impact on the Federal Reserve's net income. In fact, the fair value of the Federal Reserve's portfolio as well as its earnings, gains, or losses do not affect the ability to carry out its responsibilities as the nation's central bank, which is to conduct monetary policy to achieve its statutory goals of maximum employment and stable prices. Technical Appendix GAAP accounting principles are established by accounting standard-setting bodies, such as the Financial Accounting Standards Board. However, accounting principles for entities with the unique powers and responsibilities of the nation's central bank have not been formulated by these bodies. In light of this, the Board of Governors has developed specialized accounting principles and practices that it considers appropriate for the central bank. These accounting principles and practices are documented in the Financial Accounting Manual for Federal Reserve Banks (FAM) which is issued by the Board of Governors (The Financial Accounting Manual for Federal Reserve Banks is available at https://www.federalreserve.gov/aboutthefed/financial-accounting-manual-for-federal-reserve-banks.htm). All 12 regional Reserve Banks are required to adopt and apply accounting policies and practices that are consistent with the FAM. The individual Reserve Bank financial statements are combined to create the Combined Federal Reserve Bank financial statements. The 12 Reserve Banks operate independently but under the supervision of the Board of Governors of the Federal Reserve System. 1. We thank Gurubala Kotta for excellent assistance. Return to text 2. Federal Reserve Banks Combined Quarterly Financial Reports (Unaudited) are available at https://www.federalreserve.gov/aboutthefed/combined-quarterly-financial-reports-unaudited.htm. Federal Reserve System Audited Annual Financial Statements are available at https://www.federalreserve.gov/aboutthefed/audited-annual-financial-statements.htm. Return to text 3. When the Federal Reserve purchases a security, the market price paid generally differs from the security's face value. If the security is purchased for more (less) than its face value, the difference between the purchase price and the face value--the premium (the discount) on that security--is recorded as a separate asset (contra-asset) on the H.4.1 release. Return to text 4. The amortized cost valuation is, in turn, adjusted for credit impairment, if any. In the Supplemental Financial Information of the Quarterly Financial Report, there are tables that disclose the par values of the securities. Return to text 5. Under the Financial Accounting Standards Board's Accounting Standards Codification (FASB ASC), securities holdings are classified into three categories: held-to-maturity securities, trading securities, and available-for-sale securities. Trading securities and available-for-sale securities are reported at fair value. Return to text 6. The Board of Governors requires the Reserve Banks to transfer excess earnings to the Treasury as interest on Federal Reserve notes after providing for the costs of operations, payment of dividends, and surplus funds that exceed the aggregate limitation of$6.825 billion. The \$6.825 billion surplus limitation is required by the Federal Reserve Act, as amended by the Economic Growth, Regulatory Relief, and Consumer Protection Act, which was enacted on May 24, 2018. Return to text
7. These are presented in Table 2 of the Supplemental Financial Information section in Combined Quarterly Financial Report and in Section 5.d. of the Notes to Combined Financial Statements section in the annual Reserve Bank Combined Financial Statements. Return to text
8. SOMA also contains agency debt securities as well as foreign currency denominated securities held for the purpose of managing the Federal Reserve's foreign exchange reserves, although these components make up a much smaller fraction of the portfolio. Return to text
9. From time to time, some individual Reserve Banks have reported a deferred asset. For more information, see section 11.96 Accrued Remittances to Treasury / Deferred Asset in the January 2018 Financial Accounting Manual for Federal Reserve Banks: https://www.federalreserve.gov/aboutthefed/files/BSTfinaccountingmanual.pdf Return to text
| 2021-03-07T21:21:07 |
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|
https://par.nsf.gov/biblio/10209949-enhancing-cognitive-assessment-through-multimodal-sensing-case-study-using-block-design-test
|
Enhancing cognitive assessment through multimodal sensing: A case study using the block design test
Many cognitive assessments are limited by their reliance on relatively sparse measures of performance, like per-item accuracy or reaction time. Capturing more detailed behavioral measurements from cognitive assessments will enhance their utility in many settings, from individual clinical evaluations to large-scale research studies. We demonstrate the feasibility of combining scene and gaze cameras with supervised learning algorithms to automatically measure key behaviors on the block design test, a widely used test of visuospatial cognitive ability. We also discuss how this block-design measurement system could enhance the assessment of many critical cognitive and meta-cognitive functions such as attention, planning, progress monitoring, and strategy selection.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10209949
Journal Name:
Proceedings of the 42nd Annual Meeting of the Cognitive Science Society
Page Range or eLocation-ID:
2546-2552
1. The block design test (BDT), in which a person has to recreate a visual design using colored blocks, is notable among cognitive assessments because it makes so much of a person's problem-solving strategy visible'' through their ongoing manual actions. While, for decades, numerous pockets of research on the BDT have identified certain behavioral variables as being important for certain cognitive or neurological hypotheses, there is no unifying framework for bringing together this spread of variables and hypotheses. In this paper, we identify 25 independent and dependent variables that have been examined as part of published BDT studies across many areas of cognitive science and present a sample of the research on each one. We also suggest variables of interest for future BDT research, especially as made possible with the advent of advanced recording technologies like wearable eye trackers.
| 2022-11-29T18:00:11 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M248M%2B&home=sumtabM
|
#### ${{\mathit B}_{{J}}{(5970)}^{+}}$ MASS
OUR FIT uses ${\mathit m}_{{{\mathit B}^{0}}}$ and ${\mathit m}_{{{\mathit B}_{{J}}{(5970)}^{+}}}–{\mathit m}_{{{\mathit B}^{0}}}$ to determine ${\mathit m}_{{{\mathit B}_{{J}}{(5970)}^{+}}}$.
VALUE (MeV)
$\bf{ 5964 \pm5}$ OUR FIT
| 2023-02-08T20:40:50 |
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|
https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1716/4665
|
Deterministic Polynomial-time Equivalence of Computing the CRT-RSA Secret Keys and Factoring
Let N = pq be the product of two large primes. Consider Chinese remainder theorem-Rivest, Shamir, Adleman (CRT-RSA) with the public encryption exponent e and private decryption exponents dp, dq. It is well known that given any one of dp or dq (or both) one can factorise N in probabilistic poly(log N) time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice-based deterministic poly(log N) time algorithm that uses both dp, dq (in addition to the public information e, N) to factorise N for certain ranges of dp, dq. We like to stress that proving the equivalence for all the values of dp, dq may be a nontrivial task.
Keywords: CRT-RSAcryptanalysisfactorisationLLL algorithmRSA
RSA17 is one of the most popular cryptosystems in the history of cryptology. Let us briefly describe the idea of RSA as follows:
• primes p, q, with q<p< 2q,
• N = pq, φ(N) = (p − 1)(q − 1),
• e, d are such that ed =1+ k φ(N), k ≥ 1,
• N, e are publicly available and plaintext M is encrypted as CMe mod N,
• The secret key d is required to decrypt the ciphertext as
MCd mod N.
The study of RSA is one of the most attractive areas in cryptology research as evident from many excellent works1,10,15. Rivest17, et al. itself presents a probabilistic polynomial time algorithm that on input N, e, d provides the factorisation of N; this is based on the technique provided by Miller16,18. It has been proved7,14 that given N, e, d, one can factor N in deterministic poly(log N) time provided edN2 .
Speeding up RSA encryption and decryption is of serious interest and for large N as both e, d cannot be small at the same time. For fast encryption, it is possible to use smaller e, e.g., the value as small as 216 + 1 is widely believed to be a good candidate. For fast decryption, the value of d needs to be small. However, Wiener19 showed that for $d<\frac{1}{3}{N}^{\frac{1}{4}}$ , N can be factorised easily. Later, Boneh-Durfee2 increased this bound up to d<N0.292. Thus, use of smaller d is in general not recommended. In this direction, an alternative approach has been proposed by Wiener19 exploiting the Chinese Remainder Theorem (CRT) for faster decryption. The idea is as follows:
• the public exponent e and the private CRT exponents dp and dq are used satisfying edp ≡ 1 mod (p − 1) and edq ≡ 1 mod (q − 1),
• the encryption is same as standard RSA,
• to decrypt a ciphertext C one needs to compute ${M}_{\text{1}}\equiv {C}^{{d}_{p}}$ mod p and ${M}_{\text{2}}\equiv {C}^{{d}_{q}}$ mod q,
• using CRT, one can get the plain text $M\in {ℤ}_{N}$ such that MM1 mod p and MM2 mod q.
This variant of RSA is popularly known as CRT-RSA. One may refer to Jochemsz & May12 and the references therein for state-of-the-art analysis on CRT-RSA.
Let us now outline the organization of this paper. Some preliminaries required in this area are discussed in section 1.1 and 1.2. A lattice-based technique was used to show that one can factorise N in deterministic polynomial time from the knowledge of N, e, dp , dq for certain ranges of dp , dq. Section 3 concludes the paper.
1.1 Probabilistic Polynomial Time Algorithm
Given N, e and any one of dp , dq (or both), there exists a well known solution to factorise N in probabilistic poly(log N) time with probability almost 1. An important work in this direction shows that with the availability of decryption oracle under a fault model, one can factorise N in poly(log N) time [3,Section 2,2] and the idea has been improved by Lenstra13.
Without loss of generality, consider that dp is available. One can pick any random integer W in [2, N − 1]. If gcd(W, N) ≠ 1, then we already have one of the factors. Else, we consider gcd (${W}^{e{d}_{p}-1}-1$ , N). First note that p divides. This is because, edp ≡ 1 mod (p − 1), i.e., edp − 1= k(p − 1) for some positive integer k and hence ${W}^{e{d}_{p}-1}-1$ =Wk(p−1)−1 is divisible by ${W}^{e{d}_{p}-1}-1$ p. Thus if q does not divide ${W}^{e{d}_{p}-1}-1$ then
gcd(${W}^{e{d}_{p}-1}-1$ , N) = p (this happens with probability almost equal to 1). If q too divides ${W}^{e{d}_{p}-1}-1$ , then gcd(${W}^{e{d}_{p}-1}-1$ , N) = N and the factorisation is not possible (this happens with a very low probability).
Thus, when both dp, dq are available, one can calculate both gcd(${W}^{e{d}_{p}-1}-1$ , N) and gcd(${W}^{e{d}_{q}-1}-1$ , N). If both of them are N (which happens with a very low probability) then the factorisation is not possible by this method.
Given e, dp, dq and N, let us define,
T e,dp ,dq ,N = {W $\in$ [2, N − 1]| gcd(W, N)=1,
gcd(${W}^{e{d}_{p}-1}-1$ , N) = N and gcd(${W}^{e{d}_{p}-1}-1$ , N) = N}
T e,dp,N = {W$\in$ [2, N − 1]| gcd(W, N)=1,
gcd(${W}^{e{d}_{p}-1}-1$ , N) = N} and
T e,dq,N = {W $\in$ [2, N − 1]|
gcd(W, N)=1, gcd(${W}^{e{d}_{p}-1}-1$ , N) = N}.
Table 1.Cardinality of Te,dp,dq,N : some toy examples
It is easy to note that Te,dp,dq,N = Te,dp,NTe,dq,N . Let us now provide some examples in Table 1. It is clear that while |Te,dp,dq,N | is quite large for one prime-pair, it is very small for the other.
Proposition 1
Consider CRT-RSA with N = pq, encryption exponent e and decryption exponents dp and dq. Let g1 = gcd(p−1, q −1),
gp=gcd(edp−1, q−1), gq = gcd(edq −1, p−1) and ge = gcd(edp − 1, edq − 1). Then |Te,dp,N| = gp(p − 1) − 1, |Te,dq,N| = gq(q − 1) − 1 and |Te,dp ,dq ,N| = gp gq − 1. Further, ${g}_{1}^{2}$ − 1 ≤|Te,dp,dq,N|≤ ${g}_{e}^{2}$ − 1.
Proof
We have gp = gcd(edp − 1, q − 1). Then there exists a subgroup Sq of order gp in ${ℤ}_{q}^{*}$ such that for any $w\in {S}_{q}$ , we have q|wgp − 1. Now consider any ${w}_{1}\in {ℤ}_{p}^{*}$ and w2 from Sq. By CRT, there exists a unique $W\in {ℤ}_{N}^{*}$ such that Ww1 mod p and
Ww2 mod q, and vice versa. Thus the number of such W’s is gp(p − 1). It is evident that for all these W’s, we have
gcd(W, N) = 1 and N|W edp−1 − 1. We can also observe that any $W\in {T}_{e,{d}_{p},N}$ can be obtained in this way. Discarding the case
W = 1, we get | Te,dp,N | = gp(p − 1) – 1.
Similarly, we have gq = gcd(edq − 1, p − 1). Then there exists a subgroup Sp of order gq in ${ℤ}_{p}^{*}$ such that for any $w\in {S}_{p}$ , we have p|wgq − 1. In the same manner, we get
|Te,dq,N | = gq(q − 1) – 1.
Now consider any ${w}_{1}\in {S}_{p}$ and ${w}_{2}\in {S}_{q}$ . By CRT, there exists a unique $W\in {ℤ}_{N}^{*}$ such that Ww1 mod p and Ww2 mod q, and vice versa. Thus the number of such W’s is gpgq. It is evident that for all these W’s, we have gcd(W, N) = 1,
N|W edp−1 − 1 and N|W edq−1 − 1. One may observe that any
W ÎTe,dp,dq,N can be obtained in this manner. Discarding the case W = 1, we get |Te,dp,dq,N | = gpgq − 1.
Consider edp − 1= k(p − 1) and edq − 1= l(q − 1). Then we get |Te,dp,dq,N |≥ ${g}_{1}^{2}$ − 1, as g1 divides both gp and gq. Since ge = gcd(edp − 1, edq − 1) = gcd(k(p − 1), l(q − 1)), each of gp, gq divides ge. Thus the bounds on |Te,dp,dq,N | follow.
Given e, N, dp, dq, one can get ge easily, and thus the upper bound of |Te,dp,dq,N | is immediately known. If ge is bounded by poly(log N), then it is enough to try ${g}_{e}^{2}$ many distinct W’s to factorise N in poly(log N) time. However, from proposition 1, it is clear that |Te,dp,dq,N | may not be bounded by poly(log N) as gp,gq may not be bounded by poly(log N) in all the cases. Thus we have the following question, where an affirmative answer will transform the probabilistic algorithm to a deterministic one. Is it possible to identify a W $\in$ [2,N − 1] \ Te,dp,dq,N in poly(log N) time?
To our knowledge, an affirmative answer to the above question is not known. Thus, from theoretical point of view, getting a deterministic polynomial time algorithm for factorising N with the knowledge of N, e, dp,dq is important. We solve it using lattice-based technique.
1.2 Preliminaries on Lattices
Let us present some basics on lattice reduction techniques. Consider the linearly independent vectors u1,..., , $\in {ℤ}^{n}$ where ω ≤ n. A lattice, spanned by {u1,...,}, is the set of all linear combinations of u1,...,, i.e., ω is the dimension of the lattice. A lattice is called full rank when ω = n. Let L be a lattice spanned by the linearly independent vectors u1,...,, where u1,..., $\in {ℤ}^{n}$ . By ${u}_{1}^{*}$ ,......,${u}_{w}^{*}$ , we denote the vectors obtained by applying the Gram-Schmidt process to the vectors u1,...,uω.
The determinant of L is defined as $\mathrm{det}\left(L\right)={\prod }_{i=1}^{w}\parallel {u}_{i}^{*}\parallel$ , where ||.|| denotes the Euclidean norm on vectors. Given a polynomial $g\left(x,y\right)=\sum {a}_{i,j}{x}^{i}{y}^{j}$ , we define the Euclidean norm as $\parallel g\left(x,y\right)\parallel =\sqrt{{\sum }_{i,j}{a}_{i,j}^{2}}$ and infinity norm as $\parallel g\left(x,y\right)\parallel \infty ={\mathrm{max}}_{i,j}|{a}_{i,j}|$ .
It is known that given a basis u1,...,uω of a lattice L, the LLL algorithm13 can find a new basis b1,...,bω of L with the following properties.
$‖{b}_{i}^{*}‖{}^{2}\le 2{‖{b}_{i+1}^{*}‖}^{2}$, for 1 ≤ i < ω.
– For all i, if ${b}_{i}={b}_{i}^{*}+{\sum }_{j=1}^{i-1}{\mu }_{i,j}{b}_{j}^{*}$ then $|{\mu }_{i,j}|\le \frac{1}{2}$ for all j.
– $‖{b}_{i}‖\le {2}^{\frac{w\left(w-1\right)+\left(i-1\right)\left(i-2\right)}{4\left(w-i+1\right)}}\mathrm{det}{\left(L\right)}^{\frac{1}{w-i+1}}$ for i =1,...,ω.
Deterministic polynomial time algorithms has been presented by Coppersmith4 to find small integer roots of (i) polynomials in a single variable mod N, and of (ii) polynomials in two variables over the integers. The idea of Coppersmith4 extends to more than two variables also, but in that event, the method becomes heuristic.
A simpler algorithm by Coron5, than Coppersmith4 has been presented in this direction, but it was asymptotically less efficient. Later, a simpler idea by Coron6 than Coppersmith4 has been presented with the same asymptotic bound as in Coppersmith4. Both the works of Coron5,6 depends on the result of Howgrave-Graham8.
The results of May14, in finding the deterministic polynomial time algorithm to factorise N from the knowledge of e, d, uses the techniques presented by Coppersmith4 & Coron5. Further, the work of Coron and May7 exploits the technique presented in Howgrave-Graham9.
2. DETERMINISTIC POLYNOMIAL TIME ALGORITHM
In this section we consider that both dp, dq are known apart from the public information N, e. We start with the following lemma. In the following results, we consider $p\approx {N}^{{\gamma }_{1}}$ as the bit size of p can be correctly estimated in log N many attempts.
Lemma 1
Let ,${d}_{p}\le {N}^{{\delta }_{1}}$ ,${d}_{q}\le {N}^{{\delta }_{2}}$ . Suppose p > q and $p\approx {N}^{{\gamma }_{1}}$ . If both dp, dq. are known then one can factor N in deterministic poly(log N) time if 2α + δ1 + δ2 ≤ 2 − γ1.
Proof
We have edp − 1= k(p − 1), edq − 1= l(q − 1) for some positive integers k, l.
So,$kl=\frac{\left(e{d}_{p}-1\right)\left(e{d}_{q}-1\right)}{\left(p-1\right)\left(q-1\right)}$
Let $A=\frac{\left(e{d}_{p}-1\right)\left(e{d}_{q}-1\right)}{N}$. Now $|kl-A|=\left(e{d}_{p}-1\right)\left(e{d}_{q}-1\right)\frac{N-\left(p-1\right)\left(q-1\right)}{N\left(p-1\right)\left(q-1\right)}\approx \frac{e{d}_{p}e{d}_{p}\left(p+q\right)}{{N}^{2}}\le {N}^{2\alpha +{\delta }_{1}+{\delta }_{2}+{\gamma }_{1}-2}$ (neglecting the small constant).
So, as long as, 2α + δ1 + δ2 ≤ 2 − γ1, we have $kl=⌈A⌉$ . After finding kl, one gets (p − 1)(q − 1) and hence p + q can be obtained immediately, which factorises N. In the next result, we use the idea of Coppersmith4.
Theorem 1
Let ,${d}_{p}\le {N}^{{\delta }_{1}}$ ,${d}_{q}\le {N}^{{\delta }_{2}}$ . Suppose p is estimated as ${N}^{{\gamma }_{1}}$ . Further consider that an approximation p0 of p is known such that $|p-{p}_{0}|<{N}^{\beta }$ .
Let ${k}_{0}=⌊\frac{e{d}_{p}}{{p}_{0}}⌋,{q}_{0}=⌊\frac{N}{{p}_{0}}⌋,{l}_{0}=⌊\frac{e{d}_{p}}{{q}_{0}}⌋$ and
g = gcd(N –1,edq–1 + l0–l0N, edp–1 + k0k0 N) = Nη
If both dp , dq are known then one can factor N in deterministic poly(log N) time if
α2 + αδ1 +2αβ +δ1β −2αγ1${\gamma }_{1}^{2}$ +αδ21δ2
+βδ2 −2γ1δ2 −2βη +2γη –η2 −α−δ1 +β +2η −1 < 0
provided 1+3γ1 − 2β − δ1 − α − η ≥ 0.
Proof
We have edp = 1+ k(p − 1) and edq = 1+ l(q − 1). So $k=\frac{e{d}_{p}-1}{p-1}$ . We also have${k}_{0}=\frac{e{d}_{p}}{{p}_{0}}$
then,
$|k-{k}_{0}|=|\frac{e{d}_{p}-1}{p-1}-\frac{e{d}_{p}}{{p}_{0}}|\approx |\frac{e{d}_{p}}{p}-\frac{e{d}_{p}}{{p}_{0}}|=\frac{e{d}_{p}|p-{p}_{0}|}{p{p}_{0}}\le {N}^{\alpha +{\delta }_{1}+\beta -2{\gamma }_{1}}$ Considering ${q}_{0}=\frac{N}{{p}_{0}}$ , it can be shown that,|qq0| <N1+β-2γ1, neglecting the small constant. Assume, $q={N}^{{\gamma }_{\text{2}}}$ , where γ2 =1–γ1 . So if we take ${l}_{0}=\frac{e{d}_{p}}{{p}_{0}}$ .
then $|k-{k}_{0}|=|\frac{e{d}_{p}-1}{p-1}-\frac{e{d}_{p}}{{p}_{0}}|\approx |\frac{e{d}_{p}}{p}-\frac{e{d}_{p}}{{p}_{0}}|=\frac{e{d}_{p}|p-{p}_{0}|}{p{p}_{0}}\le {N}^{\alpha +{\delta }_{1}+\beta -2{\gamma }_{1}}$
Considering ${q}_{0}=\frac{N}{{p}_{0}}$,it can be shown that $|q-{q}_{0}|<{N}^{1+\beta -2{\gamma }_{1}}$, neglecting the small constant. Assume, $q={N}^{{\gamma }_{\text{2}}}$ , where γ2 =1- γ1 . So if we take ${l}_{0}=\frac{e{d}_{p}}{{p}_{0}}$ then$\begin{array}{l}|l-{l}_{0}|=|\frac{e{d}_{q}-1}{q-1}-\frac{e{d}_{q}}{{q}_{0}}|\approx |\frac{e{d}_{q}}{q}-\frac{e{d}_{q}}{{q}_{0}}|\\ =\frac{e{d}_{q}|q-{q}_{0}|}{q{q}_{0}}\le {N}^{\alpha +{\delta }_{2}+1+\beta -2{\gamma }_{1}-2{\gamma }_{2}}={N}^{\alpha +{\delta }_{2}+\beta -1}\end{array}$
Let k1 = k k0 and l1 = ll0. We have edp + k1= kp. So edp + k0 + k1 − 1= (k0 + k1)p. Similarly, edq+l0+l1−1=(l0 + l1)q. Now multiplying these equations, we get
(edp − 1+ k0)(edq − 1+ l0)+ k1(edq − 1+ l0)
+ l1(edp − 1+ k0)+ k1l1 =(k0 + k1)p(l0 + l1)q
Now if we substitute k1, l1 by x, y respectively, then
(edp − 1+ k0)( edp − 1+ l0)+ x(edq − 1+ l0)
+ y(edp − 1+ k0)+ xy =( k0 + x)p(l0 + y)q
Hence we have to find the solution k1, l1 of
(edp − 1+ k0)( edq − 1+ l0)+ x(edq− 1+ l0)
+ y(edp − 1+ k0)+ xy =( k0 + x)p(l0 + y)q
i.e., we have to find the roots of ${f}^{\prime }$ (x, y) = 0, where
${f}^{\prime }$ (x, y) = (1 − N)xy + x(edq − 1+ l0 − l0N)
+ y(edp−1+k0k0N)+( edp− 1+ k0)( edq− 1+ l0) − k0 l0 N.
We have
g = gcd(1 − N, edq − 1+ l0l0 N, edp − 1+ k0k0N)= Nη .
Let $f\left(x,y\right)=\frac{{f}^{\prime }\left(x,y\right)}{g}$ , X = ${N}^{\alpha +{\delta }_{1}+\beta -2{\gamma }_{1}}$ and Y = ${N}^{\alpha +{\delta }_{2}+\beta -1}$ . Clearly X, Y are the upper bounds of (k1,l1), the root of f
Thus,
Then from Coppersmith4 we need $XY<{W}^{\frac{2}{3}}$ , which implies 2α + δ1 + δ2 +2η< 3 + 4(γ1 − β) (1)
If one of the variables x, y is significantly smaller than the other, we give some extra shifts on x or y. Without loss of generality, let us assume that k1 is significantly smaller than l1. Following the ‘extended strategy’ of Jochemsz and May11,we know that these polynomials can be found by lattice reduction if for ${s}_{j}=\sum {}_{{x}^{{i}_{\text{\hspace{0.17em}}1}}{y}^{{i}_{\text{\hspace{0.17em}}2}}\in M/{S}^{{i}_{j}}}$
where$s=|S|$ , j=1, 2. One can check that
${s}_{1}=\frac{3}{2}{m}^{2}+\frac{7}{2}m+\frac{{t}^{2}}{2}+\frac{5}{2}t+2mt+2$
,${s}_{2}=\frac{3}{2}{m}^{2}+\frac{7}{2}m+t+mt+2$
,
and s =(m + 1)2 + mt + ts = (m + 1)2 + mt + t
Let t = τm. Neglecting the lower order terms we get that is satisfied when
i.e., when
In this case the value of τ for which the left hand side of the above inequality is minimum is $\tau =\frac{1+3{\gamma }_{1}-2\beta -{\delta }_{1}-\alpha -\eta }{\alpha +{\delta }_{1}+\beta -2{\gamma }_{1}}$ . As $\tau \ge 0$ , we need $1+3{\gamma }_{1}-2\beta -{\delta }_{1}-\alpha -\eta \ge 0$ . Putting this optimal value of τ we get the required condition as ${\alpha }^{2}+\alpha {\delta }_{1}+2\alpha \beta +{\delta }_{1}\beta -2\alpha {\gamma }_{1}-\gamma \frac{2}{1}+\alpha {\delta }_{2}+{\delta }_{1}{\delta }_{2}+\beta {\delta }_{2}-2{\gamma }_{1}{\delta }_{2}-2\beta \eta -{\eta }^{2}-\alpha -{\delta }_{1}+\beta +2\eta -1<0.$
The strategy presented by Jochemsz and May11 works in polynomial time in log N. As we follow the same strategy, N can be factored from the knowledge of N, e, dp, dq in deterministic polynomial time in log N.
As the condition given in Theorem 1 is quite involved, we present a few numerical values in Table 2.
Table 2. Numerical values of α, δ1, δ2, β, γ1, η following Theorem 1 for which N can be factored in poly(log N) time.
Corollary 1
Let ,${d}_{p}<{N}^{{\delta }_{1}}$ ,${d}_{q}<{N}^{{\delta }_{2}}$ .
Let g = gcd(N − 1, edp − 1, edq − 1) = Nη .
If N, e, dp, dq are known then N can be factored in deterministic polynomial time in log N when
2α + δ1 + δ2 +2η< 3.
Proof
Since in this case we do not consider any approximation of p, q, we take β = γ. Putting this value of β in Inequality 1, we get the desired result.
For practical purposes, p, q are same bit size and if we consider that no information about the bits of p is known, then we have . In this case, we require as well as .
As discussed in Section 1.1, if |Te,dp,dq,N | is small, then one can easily prove the deterministic polynomial time equivalence. However, this idea cannot be applied when |Te,dp,dq,N | is large. In such an event, our lattice based technique provides a solution for certain ranges of dp, dq. In all our experiments we start with large g1, e.g., of the order of 100 bits. In such cases, |Te,dp,dq,N | is large as $g\frac{2}{1}-1$ ≤|Te,dp,dq,N | following Proposition 1. One may note that the g1 in Proposition 1 divides the g in Theorem 1.
Let us now present some experimental results in Table 3. Our experiments are based on the strategy of Coron5 as it is easier to implement. We have written the programs in SAGE 3.1.1 over Linux Ubuntu 8.04 on a computer with Dual CORE Intel(R) Pentium(R) D 1.83 GHz CPU, 2 GB RAM and 2 MB Cache. We take large primes p, q such that N is of 1000 bits. We like to point out that the experimental results cannot reach the theoretical bounds due to the small lattice dimensions.
Table 3. Experimental results corresponding to Theorem 1.
Towards theoretical interest, we have presented a deterministic poly(log N) time algorithm that can factorise N given e, dp and dq for certain ranges of dp , dq. This algorithm is based on lattice reduction techniques.
The authors like to thank Dr A Venkateswarlu for pointing out Proposition 1 and Mr Sourav Sen Gupta for presenting detailed comments on this version.
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| 2020-02-24T21:20:19 |
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https://www.federalreserve.gov/econres/notes/feds-notes/monitoring-risk-from-collateral-runs-20200731.htm
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July 31, 2020
### Monitoring Risk From Collateral Runs
Executive Summary
We present an estimate of the total amount of funds primary dealers can access from the intermediation of cash and securities through secured funding transactions (SFTs). 1 We highlight how this activity can introduce an additional source of risk: the abrupt withdrawal of cash borrowers, which we call collateral runs. This fragility arises because primary dealers are able to intermediate funds through SFTs by using the same underlying collateral posted by the end cash borrower, a process known as reuse or rehypothecation. The reuse of counterparties' collateral puts cash borrowers at risk of losing it, creating incentives for them to withdraw their collateral. Using the Federal Reserve Bank of New York's (FRBNY's) primary dealer survey (FR 2004) we provide an estimate of the amount of liquidity dealers can extract through reuse across different collateral classes, which we call the relative reuse windfall (RRW). The RRW is a measure of cash borrowers' exposure to a dealer, and thus, it captures the likelihood of a collateral run.
We find that the liquidity windfall stemming from collateral reuse accounts for up to 10% of a primary dealer's total secured funding. This windfall varies across collateral classes, with Agency MBS exhibiting the largest exposure to a collateral run. However, in absolute terms, the windfall from US Treasury repo is sizable and may pose a high degree of collateral run risk. This last finding underscores that the risk of a collateral run is independent of the risk profile of the underlying collateral class.
This article highlights the importance of not only monitoring dealers' secured borrowing, but also their secured lending. It also shows that contrary to how SFTs are typically characterized, cash borrowers' risk of losing their collateral is directly proportional to the amount of overcollateralization (e.g., repo haircut) on their SFTs. These insights suggest that regulatory framework's designed to increase the resiliency of short-term funding markets must also consider possible risks posed by short-term lending. Although the RRW is merely an estimate of cash borrowers' exposure, it is a useful tool to monitor additional sources of risk primary dealers may face.
Background
The systemic impact of a large broker-dealer's default was a key lesson from the 2007-09 financial crisis. These firms are at the heart of the U.S. financial system, providing a number of services that enhance market functioning. To provide these services, dealers rely heavily on short-term SFTs, for example repurchase agreements (repo). The short-term nature of these contracts makes them a fragile source of funding. In effect, financial crises are often characterized by the loss in confidence from short-term creditors. Therefore, it is no surprise that many post-crisis regulatory initiatives have been geared towards regulating and monitoring dealers' use of short-term funding. For example, leverage regulations disincentive firms to increase the size of their balance sheet using SFTs and liquidity regulations penalize excessively short liabilities. Other proposed reforms have directly targeted these markets, like for example, a proposal on minimum haircut requirements (also known as haircut floors) for repo.2
However, recent research has identified another possible source of fragility: excessive short-term lending financed with collateral reuse.3 Dealers are active intermediaries in secured funding markets, bringing together end borrowers with initial cash lenders.4 In addition, dealers rely on SFTs to source and distribute securities for market making. Thus, the amount of funds dealers lend through SFTs (also known as incoming SFTs) which are borrowed through SFTs (also known as outgoing SFTs) is sizable.5
Consequently, different contracting terms between incoming SFTs and outgoing SFTs can be an important source of liquidity for a dealer, which can evaporate if the end borrower decides to withdraw their collateral. This type of fragility, called collateral runs, is markedly different from traditional bank runs as they are triggered by a contraction of dealers' assets.
What is a collateral run?
A collateral run is the abrupt withdrawal of securities posted to a dealer through SFTs. Cash borrowers have incentives to withdraw their securities because they risk losing them if the dealer defaults, which may be more valuable than what they owe. These incentives increase with the degree of overcollateralization in borrowers' SFTs. Infante and Vardoulakis (2020) have identified three ingredients that lead to this type of fragility. First, dealers must extend SFTs by reusing the underlying collateral. If the collateral is reused and leaves the dealer, the risk that the cash borrower may lose it in bankruptcy is higher, as the dealer would not have direct access to it. Second, dealers need some degree of market power to set different contracting terms between borrowers and lenders. Specifically, when reusing collateral dealers may lend less than what they borrow which in the context of repo means that a dealer's reverse repo haircut is larger than its repo haircut.6 Finally, dealers must have the flexibility to use any excess funds they reap from reuse for their own benefit. This underscores that the risk of a collateral run does not have to be related to the riskiness of the collateral itself, but rather to how the intermediary uses any excess funds from reuse.
Under these three conditions, cash borrowers are exposed to losing the overcollateralization of their SFTs. Moreover, because of the dealer's discretion to use said overcollateralization, borrowers' claims may be pooled with the claims of others, creating a first mover advantage to withdraw collateral, resulting in a run.
In today's financial markets, two of the three conditions are already met. In effect, an important part of primary dealers' activity involves the reuse of collateral, and much of this activity is done through repos, which gives dealers the flexibility to use any windfall they acquire.7 However, it is unclear to what degree dealers have the ability to set different contracting terms between borrowers and lenders to reap liquidity from reuse. Our proposed measure attempts to capture this difference in contracting terms, and can be a useful tool to monitor collateral-run risk.
Monitoring collateral run risk
The FRBNY's weekly primary dealer survey asks respondents to report their long and short securities positions and the amount of funds received and extended through outgoing and incoming SFTs. The difference between funds that come in from sales and outgoing SFTs, and funds that go out from purchases and incoming SFTs is a measure of dealers' liquidity windfall from reuse.
To understand this measure, Figure 1 shows the balance sheet of two stylized dealers for a given collateral class. In this example, balance sheet entries can come in one of four forms: outright security positions (green diamonds), SFTs (blue squares), equity or other unsecured liabilities (yellow ovals), and excess cash (orange triangles). Although it is typically treacherous to match specific assets with liabilities, because the focus is on collateralized transactions, we can identify corresponding assets and liabilities per collateral class. The balance sheet on the left illustrates a dealer that is not reaping any additional funds from reuse. All of its long positions and SFTs are wholly backed by either short positions, SFTs, or other liabilities. The balance sheet on the right, however, illustrates a dealer extending less funds than it receives, resulting in an additional cash windfall. Note that in this latter case, the dealer does not need any unsecured liabilities to finance its activity; its short positions and secured funding are large enough to finance its long positions and secured financing, within a collateral class.
##### Figure 1.
With this concept in mind, we can use the FR 2004---weekly survey of primary dealers' market activities which includes their positions and funding---to have an estimate of a dealer's windfall from reuse.8 It is simply the sum of a dealer's short position and outgoing SFT minus the sum of their long position and incoming SFT lending
$$\text{RRW} = \frac{{Short\ Postion} + {Outgoing\ SFT} - ({Long\ Position} + {Incoming\ SFT})}{{Outgoing\ SFT}}$$
In order to understand the order of magnitude of the liquidity windfall, we normalize itby the total amount of secured financing, that is, outgoing SFTs. This calculation results in the relative reuse windfall measure. A large and positive value suggests that a significant amount of a dealer's available liquidity comes from different contracting terms between borrowers and lenders. In this case, their cash borrowers are at greater risk of losing their collateral, and thus, the dealer is more exposed to a collateral run. We expect these risks to be more salient if the total volume of activity is large, creating more of a coordination problem; and if the underlying market is relatively uncompetitive, giving dealers more market power to increase cash borrowers' haircuts.
Infante and Vardoulakis (2020) calculate the RRW for Bear Stearns, and the average of the remaining dealers in the period leading up to the Financial Crisis, across all collateral classes. They find that before Bear Stearns demise, their RRW reached up to 30% whereas the average of the dealer sector was close to zero. This suggests that part of Bear Stearns' liquidity problems came from the withdrawal of their cash borrowers.
What we find
Figure 1 shows the RRW quartiles across all primary dealers for all the SFTs reported in the FR 2004. We find that on aggregate, across all securities, the 75th percentile of RRW fluctuates between 0 and 10%. In relative terms, this may seem small, but given the size of some primary dealers' repo book, the dollar amount could be sizable. We see important differences when looking across collateral classes. The RRW for U.S. Treasuries is small, which is likely due to the smaller likelihood of there being significant dealer market power in the US Treasury market, and the different economic motives to intermediate repo.9 We find significantly larger values for RRW in the Agency MBS, suggesting that cash borrowers have a high exposure to losing their collateral. This is concentrated in firms that are relatively more active in the Agency MBS market, consistent with Infante (2019) prediction that cash borrowers accept larger haircuts for collateral classes that are more correlated with an intermediary's default. There are also specific contracting types in the Agency MBS market, which could produce a high RRW without necessarily implying a high windfall, but still capturing a higher risk exposure (see the Caveats section for details). Curiously, for corporate securities, the riskiest asset class we consider, the RRW is relatively small, suggesting that an important fraction of dealers' corporate security activity is financed through non-SFTs.
##### Figure 2.
Figure 2 shows the RRW quartiles across all primary dealers focusing only on repos. The reason behind separating the analysis is that there are less regulatory and contractual restrictions on repo, which could possibly alter dealers' behavior. Given that the use of repo is ubiquitous in fixed income markets the repo measure still captures a significant portion of dealers' activity. The figure provides a similar qualitative message, but underscores the important role of repo. Here the windfall of the 75th percentile is higher across all collateral classes except for Agency MBS. It is particularly interesting to see that 75th precentral of the RRW for US Treasuries is larger than 10%, which is a sizable amount given the size of the Treasury repo market. It is important to note that even though the collateral may be safe the risks of a collateral run may still be large. In effect, the RRW estimates the amount of excess cash the dealer extracts from its reuse activity that, in principle, could be used for any type of risky activity.
##### Figure 3.
Concluding Remarks:
Primary dealers' high degree of securities reuse through SFTs exposes them to a relatively unexplored source of risk: a withdrawal from their secured borrowers, i.e., a collateral run. We propose a measure to gauge primary dealers' exposure to collateral runs, which may be an important tool to monitor dealers' resiliency. Collateral runs are markedly different from traditional banks runs (or other liability driven runs) and call for different regulatory initiatives to mitigate them. Future work studying dealer market resiliency should consider these risks.
Caveats
The RRW is designed to capture the amount of funds the dealer receives, but does not distribute, when it reuses collateral. However, there are a few issues regarding data that may affect the measure's interpretation:
• The RRW is a lower bound: The left-hand-side of Figure 1 illustrates how unsecured funding liabilities may alter the interpretation of the RRW. For example, a firm with a large amount of equity outstanding would appear to have a negative RRW. This certainly makes the firm safer. However, there could still by significant differences in contracting terms between cash borrowers and lenders, which put cash borrowers at risk and gives them incentives to withdraw.
• Forward positions: The FR 2004 asks respondents to also report their long and short forward positions. This alters the interpretation of the RRW as these positions are promises to exchange cash and securities in the future, and thus, do not affect the amount of cash or securities the dealer has today.
This issue might be particularly acute for Agency MBS. In effect, a large amount of trading in this market is through the to-be-announced (TBA) forward market and dollar rolls, which are essentially two offsetting forward contracts of the cheapest to deliver MBS, one front month and one future month.10 Dealers trading forwards may take offsetting positions before settlement, eliminating the exchange of cash and securities, and thus, the RRW. In the specific context of dollar rolls, if a dealer were to sell a large amount of dollar rolls of them, without engaging in an offsetting trade, once the front month matures the dealer would have to take position of the underlying MBS. It is reasonable to think that this purchase would be finance through an SFT. Thus, in the data, we would observe a small net position along with a large repo position. This would increase the RRW.
• SFTs to intermediate collateral: The standing assumption of this memo is that the economic motive behind these SFTs are to intermediate cash, which imply positive haircuts. If the economic motive were to source collateral, haircuts would be negative.11 Infante (2019) shows that intermediating repo to source assets would imply a positive windfall for the dealer, as the outgoing SFT haircut would be "less negative". However, this would reduce RRW.
It is important to note that irrespective of these three caveats, a larger RRW is still evidence of a riskier position as it may be due to either less equity or a larger short position in forwards. Thus, regardless of the interpretation, a higher RRW indicates more risk taking.
References
Duffie, D. (2013), "Replumbing our financial system: Uneven progress," International Journal of Central Banking 9 (1), 251–279.
Baklanova V., Caglio, C., Cipriani, M., and Copeland, A. (2019), "The use of collateral in bilateral repurchase and securities lending agreements," Review of Economic Dynamics 33: 228-249.
Financial Stability Board (2014), "Strengthening Oversight and Regulation of Shadow Banking: Regulatory framework for haircuts on non-centrally cleared securities financing transactions,'' October 14, 2014, http://www.fsb.org/wp-content/uploads/r_141013a.pdf.
Gao, P., Schultz, P., and Song, Z. (2017), "Liquidity in a Market for Unique Assets: Specified Pool and To‐Be‐Announced Trading in the Mortgage‐Backed Securities Market," The Journal of Finance 72(3), pp.1119-1170.
Infante, S. (2019), "Liquidity windfalls: The consequences of repo rehypothecation," Journal of Financial Economics 133 (1), 42–63.
Infante, S., Press, C., and Saravay, Z. (2020), "Understanding collateral reuse in the U.S. financial system," AEA Papers and Proceedings (forthcoming)
Infante, S., Press, C., and Strauss, J. (2018), "The ins and outs of collateral reuse," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, December 21, 2018, https://doi.org/10.17016/2380-7172.2298.
Infante, S. and Vardoulakis, A.P. (2018), "Collateral Runs", FEDS WP 2018-022.
1. Secured funding transactions include repurchase agreements (repos), securities lending contracts, and collateral swaps. These transactions are economically equivalent to secured loans backed by financial assets. Return to text
3. For example, Duffie (2013) describes how the withdrawal of cash borrowers was a potential risk that materialized during the crisis. Infante and Vardoulakis (2020) theoretically show how this type of fragility can arise. Infante (2019) shows how different contracting terms can arise across markets because of dealers' reuse of collateral. Return to text
4. Intermediating funds between cash lenders and cash borrowers overcomes regulatory and institutional restrictions that can bar counterparties from interacting with each other directly. Return to text
5. See Infante, Press, Saravay (2020) for a discussion of the magnitude of collateral reuse in the U.S. financial system, and of its possible drivers. Return to text
6. In a frictionless bankruptcy regime, the cash borrowers would have access to the cash lender's overcollateralization in case of a dealer default. However, in practice, it is more likely that the cash borrower's claim would be pooled with the rest of the dealer's unsecured claims, suggesting that the real exposure is closer to the cash borrower's overcollateralization of their SFT. Return to text
7. Importantly, the windfall acquired is considered to be encumbered and, thus, does not qualify as a High Quality Liquid Asset (HQLA) to ease liquidity regulations. As a result, the incentive to use the windfall for proprietary purposes is not mitigated by liquidity regulation. See Infante, Press, Strauss (2018) for the different types of SFTs dealers use and the relative importance of repo. Return to text
8. The RRW is not a precise measure of the liquidity windfall because 1) we cannot account for the dealers other funding liabilities, 2) long and short positions include forward contracts, and 3) if the economic motive for reuse is to source securities, haircuts can be negative. Irrespective of these caveats, we argue that a high RRW is still an indication of relatively riskier dealer activity. See section Caveats to understand the limitations, and alternative interpretations, of this measure. Return to text
9. Specifically, when the economic motive is to source specific collateral repo haircuts can be negative. See the Caveats section for more details. Return to text
| 2020-09-22T14:50:51 |
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https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.10.005
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• •
### 基于高维波动率网络模型的股票市场风险特征研究
• 出版日期:2019-10-25 发布日期:2019-10-25
### Research on Stock Market Risk Features Based on High-Dimensional Volatility Network Model
Ning Hanwen & Tu Xueyong
• Online:2019-10-25 Published:2019-10-25
Abstract: Volatility is crucial in financial risk management research. This paper proposes a high-dimensional volatility network model for the stock market based on complex network theory and data mining technology. Firstly, the theory of mutual information is utilized to measure the correlation of stock price fluctuations. Secondly, we design the network topological indicators such as the degree centralization, average distance and power law distribution for different periods of the stock market. With these indicators, the Prim algorithm and the Newman-Girvan algorithm are used to construct the highdimensional volatility network models and stratify the correlation of the volatility respectively. Compared with the conventional models, our new model can overcome the difficulties of high dimensional settings, explore the relationship among different financial market entities, and reflect the risk features and network topology of financial markets based on just a few hypotheses. The empirical results demonstrate that in contrast to Pearson correlation coefficient, the mutual information is a better measure for the nonlinear correlations of stock price volatility. The market volatility and price volatility correlation move in opposite directions, and the portfolio decentralization effect is more obvious in the period of high market volatility. The effects of industry agglomeration are significant. There exist a small number of key nodes and central nodes in the network, and the risk quickly spreads to the entire market through these nodes. The network stratification further shows the characteristics of risk transmission between layers and corresponding industrial characteristics. The high-dimensional volatility network model provides a novel tool for exploring the risk features in stock market and managing financial risks.
| 2023-02-02T20:45:12 |
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http://www.popflock.com/learn?s=Dispersion_(water_waves)
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Dispersion (water Waves)
Get Dispersion Water Waves essential facts below. View Videos or join the Dispersion Water Waves discussion. Add Dispersion Water Waves to your PopFlock.com topic list for future reference or share this resource on social media.
Dispersion Water Waves
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium.
For a certain water depth, surface gravity waves - i.e. waves occurring at the air-water interface and gravity as the only force restoring it to flatness - propagate faster with increasing wavelength. On the other hand, for a given (fixed) wavelength, gravity waves in deeper water have a larger phase speed than in shallower water.[1] In contrast with the behavior of gravity waves, capillary waves (i.e. only forced by surface tension) propagate faster for shorter wavelengths.
Besides frequency dispersion, water waves also exhibit amplitude dispersion. This is a nonlinear effect, by which waves of larger amplitude have a different phase speed from small-amplitude waves.
## Frequency dispersion for surface gravity waves
This section is about frequency dispersion for waves on a fluid layer forced by gravity, and according to linear theory. For surface tension effects on frequency dispersion, see surface tension effects in Airy wave theory and capillary wave.
### Wave propagation and dispersion
Sinusoidal wave.
The simplest propagating wave of unchanging form is a sine wave. A sine wave with water surface elevation ?( x, t ) is given by:[2]
${\displaystyle \eta (x,t)=a\sin \left(\theta (x,t)\right),\,}$
where a is the amplitude (in metres) and ? = ?( x, t ) is the phase function (in radians), depending on the horizontal position ( x , in metres) and time ( t , in seconds):[3]
${\displaystyle \theta =2\pi \left({\frac {x}{\lambda }}-{\frac {t}{T}}\right)=kx-\omega t,}$ with ${\displaystyle k={\frac {2\pi }{\lambda }}}$ and ${\displaystyle \omega ={\frac {2\pi }{T}},}$
where:
Characteristic phases of a water wave are:
• the upward zero-crossing at ? = 0,
• the wave crest at ? = ½ ?,
• the downward zero-crossing at ? = ? and
• the wave trough at ? = 1½ ?.
A certain phase repeats itself after an integer m multiple of 2?: sin(?) = sin(?+mo2?).
Essential for water waves, and other wave phenomena in physics, is that free propagating waves of non-zero amplitude only exist when the angular frequency ? and wavenumber k (or equivalently the wavelength ? and period T ) satisfy a functional relationship: the frequency dispersion relation[4][5]
${\displaystyle \omega ^{2}=\Omega ^{2}(k).\,}$
The dispersion relation has two solutions: ? = +?(k) and ? = -?(k), corresponding to waves travelling in the positive or negative x-direction. The dispersion relation will in general depend on several other parameters in addition to the wavenumber k. For gravity waves, according to linear theory, these are the acceleration by gravity g and the water depth h. The dispersion relation for these waves is:[6][5]
${\displaystyle \omega ^{2}=g\,k\,\tanh(k\,h)}$ or ${\displaystyle \displaystyle \lambda ={\frac {g}{2\pi }}\,T^{2}\,\tanh \left(2\pi \,{\frac {h}{\lambda }}\right),}$
an implicit equation with tanh denoting the hyperbolic tangent function.
An initial wave phase ? = ?0 propagates as a function of space and time. Its subsequent position is given by:
${\displaystyle x={\frac {\lambda }{T}}\,t+{\frac {\lambda }{2\pi }}\,\theta _{0}={\frac {\omega }{k}}\,t+{\frac {\theta _{0}}{k}}.}$
This shows that the phase moves with the velocity:[2]
${\displaystyle c_{p}={\frac {\lambda }{T}}={\frac {\omega }{k}}={\frac {\Omega (k)}{k}},}$
which is called the phase velocity.
### Phase velocity
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity as a function of relative depth h / λ.Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity valid in shallow water.Drawn lines: dispersion relation valid in arbitrary depth.Dashed lines (blue and red): deep water limits. Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by deep-water phase velocity as a function of relative depth h / λ.Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity valid in shallow water.Drawn lines: dispersion relation valid in arbitrary depth.Dashed lines (blue and red): deep water limits.
A sinusoidal wave, of small surface-elevation amplitude and with a constant wavelength, propagates with the phase velocity, also called celerity or phase speed. While the phase velocity is a vector and has an associated direction, celerity or phase speed refer only to the magnitude of the phase velocity. According to linear theory for waves forced by gravity, the phase speed depends on the wavelength and the water depth. For a fixed water depth, long waves (with large wavelength) propagate faster than shorter waves.
In the left figure, it can be seen that shallow water waves, with wavelengths ? much larger than the water depth h, travel with the phase velocity[2]
${\displaystyle c_{p}={\sqrt {gh}}\qquad \scriptstyle {\text{(shallow water),}}\,}$
with g the acceleration by gravity and cp the phase speed. Since this shallow-water phase speed is independent of the wavelength, shallow water waves do not have frequency dispersion.
Using another normalization for the same frequency dispersion relation, the figure on the right shows that for a fixed wavelength ? the phase speed cp increases with increasing water depth.[1] Until, in deep water with water depth h larger than half the wavelength ? (so for h/? > 0.5), the phase velocity cp is independent of the water depth:[2]
${\displaystyle c_{p}={\sqrt {\frac {g\lambda }{2\pi }}}={\frac {g}{2\pi }}T\qquad \scriptstyle {\text{(deep water),}}}$
with T the wave period (the reciprocal of the frequency f, T=1/f ). So in deep water the phase speed increases with the wavelength, and with the period.
Since the phase speed satisfies cp = ?/T = ?f, wavelength and period (or frequency) are related. For instance in deep water:
${\displaystyle \lambda ={\frac {g}{2\pi }}T^{2}\qquad \scriptstyle {\text{(deep water).}}}$
The dispersion characteristics for intermediate depth are given below.
### Group velocity
Frequency dispersion in bichromatic groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity.
Interference of two sinusoidal waves with slightly different wavelengths, but the same amplitude and propagation direction, results in a beat pattern, called a wave group. As can be seen in the animation, the group moves with a group velocity cg different from the phase velocity cp, due to frequency dispersion.
The group velocity is depicted by the red lines (marked B) in the two figures above. In shallow water, the group velocity is equal to the shallow-water phase velocity. This is because shallow water waves are not dispersive. In deep water, the group velocity is equal to half the phase velocity: cg = ½ cp.[7]
The group velocity also turns out to be the energy transport velocity. This is the velocity with which the mean wave energy is transported horizontally in a narrow-band wave field.[8][9]
In the case of a group velocity different from the phase velocity, a consequence is that the number of waves counted in a wave group is different when counted from a snapshot in space at a certain moment, from when counted in time from the measured surface elevation at a fixed position. Consider a wave group of length ?g and group duration of ?g. The group velocity is:[10]
${\displaystyle c_{g}={\frac {\Lambda _{g}}{\tau _{g}}}.}$
The number of waves per group as observed in space at a certain moment (upper blue line), is different from the number of waves per group seen in time at a fixed position (lower orange line), due to frequency dispersion.
North Pacific storm waves as seen from the NOAA M/V Noble Star, Winter 1989.
The number of waves in a wave group, measured in space at a certain moment is: ?g / ?. While measured at a fixed location in time, the number of waves in a group is: ?g / T. So the ratio of the number of waves measured in space to those measured in time is:
${\displaystyle {\tfrac {\text{No. of waves in space}}{\text{No. of waves in time}}}={\frac {\Lambda _{g}/\lambda }{\tau _{g}/T}}={\frac {\Lambda _{g}}{\tau _{g}}}\cdot {\frac {T}{\lambda }}={\frac {c_{g}}{c_{p}}}.}$
So in deep water, with cg = ½ cp,[11] a wave group has twice as many waves in time as it has in space.[12]
The water surface elevation ?(x,t), as a function of horizontal position x and time t, for a bichromatic wave group of full modulation can be mathematically formulated as:[11]
${\displaystyle \eta =a\,\sin \left(k_{1}x-\omega _{1}t\right)+a\,\sin \left(k_{2}x-\omega _{2}t\right),}$
with:
• a the wave amplitude of each frequency component in metres,
• k1 and k2 the wave number of each wave component, in radians per metre, and
• ?1 and ?2 the angular frequency of each wave component, in radians per second.
Both ?1 and k1, as well as ?2 and k2, have to satisfy the dispersion relation:
${\displaystyle \omega _{1}^{2}=\Omega ^{2}(k_{1})\,}$ and ${\displaystyle \omega _{2}^{2}=\Omega ^{2}(k_{2}).\,}$
Using trigonometric identities, the surface elevation is written as:[10]
${\displaystyle \eta =\left[2\,a\,\cos \left({\frac {k_{1}-k_{2}}{2}}x-{\frac {\omega _{1}-\omega _{2}}{2}}t\right)\right]\;\cdot \;\sin \left({\frac {k_{1}+k_{2}}{2}}x-{\frac {\omega _{1}+\omega _{2}}{2}}t\right).}$
The part between square brackets is the slowly varying amplitude of the group, with group wave number ½ ( k1 - k2 ) and group angular frequency ½ ( ?1 - ?2 ). As a result, the group velocity is, for the limit k1 -> k2 :[10][11]
${\displaystyle c_{g}=\lim _{k_{1}\,\to \,k_{2}}{\frac {\omega _{1}-\omega _{2}}{k_{1}-k_{2}}}=\lim _{k_{1}\,\to \,k_{2}}{\frac {\Omega (k_{1})-\Omega (k_{2})}{k_{1}-k_{2}}}={\frac {{\text{d}}\Omega (k)}{{\text{d}}k}}.}$
Wave groups can only be discerned in case of a narrow-banded signal, with the wave-number difference k1 - k2 small compared to the mean wave number ½ (k1 + k2).
### Multi-component wave patterns
Frequency dispersion of surface gravity waves on deep water. The superposition (dark blue line) of three sinusoidal wave components (light blue lines) is shown.
The effect of frequency dispersion is that the waves travel as a function of wavelength, so that spatial and temporal phase properties of the propagating wave are constantly changing. For example, under the action of gravity, water waves with a longer wavelength travel faster than those with a shorter wavelength.
While two superimposed sinusoidal waves, called a bichromatic wave, have an envelope which travels unchanged, three or more sinusoidal wave components result in a changing pattern of the waves and their envelope. A sea state - that is: real waves on the sea or ocean - can be described as a superposition of many sinusoidal waves with different wavelengths, amplitudes, initial phases and propagation directions. Each of these components travels with its own phase velocity, in accordance with the dispersion relation. The statistics of such a surface can be described by its power spectrum.[13]
### Dispersion relation
In the table below, the dispersion relation ?2 = [?(k)]2 between angular frequency ? = 2? / T and wave number k = 2? / ? is given, as well as the phase and group speeds.[10]
Frequency dispersion of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory
quantity symbol units deep water
( h > ½ ? )
shallow water
( h < 0.05 ? )
intermediate depth
( all ? and h )
dispersion relation ${\displaystyle \displaystyle \Omega (k)}$ rad / s ${\displaystyle {\sqrt {gk}}={\sqrt {\frac {2\pi \,g}{\lambda }}}}$ ${\displaystyle k{\sqrt {gh}}={\frac {2\pi }{\lambda }}{\sqrt {gh}}}$ {\displaystyle {\begin{aligned}&{\sqrt {gk\,\tanh \left(kh\right)}}\,\\[1.2ex]&={\sqrt {{\frac {2\pi g}{\lambda }}\tanh \left({\frac {2\pi h}{\lambda }}\right)}}\,\end{aligned}}}
phase velocity ${\displaystyle \displaystyle c_{p}={\frac {\lambda }{T}}={\frac {\omega }{k}}}$ m / s ${\displaystyle {\sqrt {\frac {g}{k}}}={\frac {g}{\omega }}={\frac {g}{2\pi }}T}$ ${\displaystyle {\sqrt {gh}}}$ ${\displaystyle {\sqrt {{\frac {g}{k}}\tanh \left(kh\right)}}}$
group velocity ${\displaystyle \displaystyle c_{g}={\frac {\partial \Omega }{\partial k}}}$ m / s ${\displaystyle {\frac {1}{2}}{\sqrt {\frac {g}{k}}}={\frac {1}{2}}{\frac {g}{\omega }}={\frac {g}{4\pi }}T}$ ${\displaystyle {\sqrt {gh}}}$ ${\displaystyle {\frac {1}{2}}c_{p}\left(1+{\frac {2kh}{\sinh \left(2kh\right)}}\right)}$
ratio ${\displaystyle \displaystyle {\frac {c_{g}}{c_{p}}}}$ - ${\displaystyle \displaystyle {\frac {1}{2}}}$ ${\displaystyle \displaystyle 1}$ ${\displaystyle {\frac {1}{2}}\left(1+{\frac {2kh}{\sinh \left(2kh\right)}}\right)}$
wavelength ${\displaystyle \displaystyle \lambda }$ m ${\displaystyle {\frac {g}{2\pi }}T^{2}}$ ${\displaystyle T{\sqrt {gh}}}$ for given period T, the solution of:
${\displaystyle \displaystyle \left({\frac {2\pi }{T}}\right)^{2}={\frac {2\pi g}{\lambda }}\tanh \left({\frac {2\pi h}{\lambda }}\right)}$
Deep water corresponds with water depths larger than half the wavelength, which is the common situation in the ocean. In deep water, longer period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water, for wavelengths larger than twenty times the water depth,[14] as found quite often near the coast, the group velocity is equal to the phase velocity.
## History
The full linear dispersion relation was first found by Pierre-Simon Laplace, although there were some errors in his solution for the linear wave problem. The complete theory for linear water waves, including dispersion, was derived by George Biddell Airy and published in about 1840. A similar equation was also found by Philip Kelland at around the same time (but making some mistakes in his derivation of the wave theory).[15]
The shallow water (with small h / ?) limit, ?2 = gh k2, was derived by Joseph Louis Lagrange.
## Surface tension effects
Dispersion of gravity-capillary waves on the surface of deep water. Phase and group velocity divided by ${\displaystyle \scriptstyle {\sqrt[{4}]{g\sigma /\rho }}}$ as a function of inverse relative wavelength ${\displaystyle \scriptstyle {\frac {1}{\lambda }}{\sqrt {\sigma /(\rho g)}}}$.
Blue lines (A): phase velocity, Red lines (B): group velocity.
Drawn lines: dispersion relation for gravity-capillary waves.
Dashed lines: dispersion relation for deep-water gravity waves.
Dash-dot lines: dispersion relation valid for deep-water capillary waves.
In case of gravity-capillary waves, where surface tension affects the waves, the dispersion relation becomes:[5]
${\displaystyle \omega ^{2}=\left(gk+{\frac {\sigma }{\rho }}k^{3}\right)\tanh(kh),}$
with ? the surface tension (in N/m).
For a water-air interface (with and ) the waves can be approximated as pure capillary waves - dominated by surface-tension effects - for wavelengths less than 0.4 cm (0.2 in). For wavelengths above 7 cm (3 in) the waves are to good approximation pure surface gravity waves with very little surface-tension effects.[16]
## Interfacial waves
Wave motion on the interface between two layers of inviscid homogeneous fluids of different density, confined between horizontal rigid boundaries (at the top and bottom). The motion is forced by gravity. The upper layer has mean depth h' and density ?', while the lower layer has mean depth h and density ?. The wave amplitude is a, the wavelength is denoted by ?.
For two homogeneous layers of fluids, of mean thickness h below the interface and h? above - under the action of gravity and bounded above and below by horizontal rigid walls - the dispersion relationship ?2 = ?2(k) for gravity waves is provided by:[17]
${\displaystyle \Omega ^{2}(k)={\frac {g\,k(\rho -\rho ')}{\rho \,\coth(kh)+\rho '\,\coth(kh')}},}$
where again ? and are the densities below and above the interface, while coth is the hyperbolic cotangent function. For the case is zero this reduces to the dispersion relation of surface gravity waves on water of finite depth h.
When the depth of the two fluid layers becomes very large (h->?, h?->?), the hyperbolic cotangents in the above formula approaches the value of one. Then:
${\displaystyle \Omega ^{2}(k)={\frac {\rho -\rho '}{\rho +\rho '}}\,g\,k.}$
## Nonlinear effects
### Shallow water
Amplitude dispersion effects appear for instance in the solitary wave: a single hump of water traveling with constant velocity in shallow water with a horizontal bed. Note that solitary waves are near-solitons, but not exactly - after the interaction of two (colliding or overtaking) solitary waves, they have changed a bit in amplitude and an oscillatory residual is left behind.[18] The single soliton solution of the Korteweg-de Vries equation, of wave height H in water depth h far away from the wave crest, travels with the velocity:
${\displaystyle c_{p}=c_{g}={\sqrt {g(h+H)}}.}$
So for this nonlinear gravity wave it is the total water depth under the wave crest that determines the speed, with higher waves traveling faster than lower waves. Note that solitary wave solutions only exist for positive values of H, solitary gravity waves of depression do not exist.
### Deep water
The linear dispersion relation - unaffected by wave amplitude - is for nonlinear waves also correct at the second order of the perturbation theory expansion, with the orders in terms of the wave steepness (where a is wave amplitude). To the third order, and for deep water, the dispersion relation is[19]
${\displaystyle \omega ^{2}=gk\left[1+(ka)^{2}\right],}$ so ${\displaystyle c_{p}={\sqrt {\frac {g}{k}}}\,\left[1+{\tfrac {1}{2}}\,(ka)^{2}\right]+{\mathcal {O}}\left((ka)^{4}\right).}$
This implies that large waves travel faster than small ones of the same frequency. This is only noticeable when the wave steepness is large.
## Waves on a mean current: Doppler shift
Water waves on a mean flow (so a wave in a moving medium) experience a Doppler shift. Suppose the dispersion relation for a non-moving medium is:
${\displaystyle \omega ^{2}=\Omega ^{2}(k),\,}$
with k the wavenumber. Then for a medium with mean velocity vector V, the dispersion relationship with Doppler shift becomes:[20]
${\displaystyle \left(\omega -\mathbf {k} \cdot \mathbf {V} \right)^{2}=\Omega ^{2}(k),}$
where k is the wavenumber vector, related to k as: k = |k|. The dot product koV is equal to: koV = kV cos ?, with V the length of the mean velocity vector V: V = |V|. And ? the angle between the wave propagation direction and the mean flow direction. For waves and current in the same direction, koV=kV.
## Notes
1. ^ a b Pond, S.; Pickard, G.L. (1978), Introductory dynamic oceanography, Pergamon Press, pp. 170-174, ISBN 978-0-08-021614-0
2. ^ a b c d See Lamb (1994), §229, pp. 366-369.
3. ^ See Whitham (1974), p.11.
4. ^ This dispersion relation is for a non-moving homogeneous medium, so in case of water waves for a constant water depth and no mean current.
5. ^ a b c See Phillips (1977), p. 37.
6. ^ See e.g. Dingemans (1997), p. 43.
7. ^ See Phillips (1977), p. 25.
8. ^ Reynolds, O. (1877), "On the rate of progression of groups of waves and the rate at which energy is transmitted by waves", Nature, 16 (408): 343-44, Bibcode:1877Natur..16R.341., doi:10.1038/016341c0
Lord Rayleigh (J. W. Strutt) (1877), "On progressive waves", Proceedings of the London Mathematical Society, 9: 21-26, doi:10.1112/plms/s1-9.1.21 Reprinted as Appendix in: Theory of Sound 1, MacMillan, 2nd revised edition, 1894.
9. ^ See Lamb (1994), §237, pp. 382-384.
10. ^ a b c d See Dingemans (1997), section 2.1.2, pp. 46-50.
11. ^ a b c See Lamb (1994), §236, pp. 380-382.
12. ^ Henderson, K. L.; Peregrine, D. H.; Dold, J. W. (1999), "Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation", Wave Motion, 29 (4): 341-361, CiteSeerX 10.1.1.499.727, doi:10.1016/S0165-2125(98)00045-6
13. ^ See Phillips (1977), p. 102.
14. ^ See Dean and Dalrymple (1991), page 65.
15. ^ See Craik (2004).
16. ^ See Lighthill (1978), pp. 224-225.
17. ^ Turner, J. S. (1979), Buoyancy effects in fluids, Cambridge University Press, p. 18, ISBN 978-0521297264
18. ^ See e.g.: Craig, W.; Guyenne, P.; Hammack, J.; Henderson, D.; Sulem, C. (2006), "Solitary water wave interactions", Physics of Fluids, 18 (57106): 057106-057106-25, Bibcode:2006PhFl...18e7106C, doi:10.1063/1.2205916
19. ^ See Lamb (1994), §250, pp. 417-420.
20. ^ See Phillips (1977), p. 24.
## References
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.
| 2020-11-27T17:53:44 |
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|
https://drupal.star.bnl.gov/STAR/book/export/html/3086
|
# 2006 di-jet Sivers PRL paper
Measurement of Transverse Single-Spin Asymmetries for Di-Jet Production in Proton-Proton Collisions at sqrt(s) of 200 GeV
Target Journal: PRL
Principal Authors (PA): J.Balewski, I.Qattan, and S.Vigdor
Abstract+summary+figures (ver 1.2) : link to protected/spin area
Status:
presented to PWGC on December 01,
pwg approved to request GPC, Decmeber 14,
GPC phone conference , January 4
1. Draft of the PRL paper version 1.2 (posted November 16, 2006)
* from Carl , received on Nov 16
* from Hal ,received on Nov 27
*
3. Revised ver 1.3 (ps) , posted December 12,
1. Akio,Les: I guess the biggest question I had was east BEMC "problem" and your measurement on Nov 30
The 2% of the off-line data have be reanalyzed with the new (electron based) BTOW gains to verify the previous conclusions hold, as posted on Issam's summary page, spin-hn, on January 11, 2007
4. Comments from GPC are listed below
• Peter J., Jan 4, 2007
5. Revised draft ver 2.0 (January 29, 2007)
• Comments from Mike, Feb 2,2006, below
# Mike M., Feb 02, 2007
<pre>
Hi all,
1) Overall, I really like the way the first page reads -- well done.
2) I think it's lacking a crisp explanation of why online jets are used instead of offline, perhaps I missed it.
3) I think that Figure 2 should clearly be labeled as "Simulation". It's in the caption, but the minute the figure gets clipped into a presentation the caption (and that info) are gone.
4) I would prefer the use of "Fast Monte Carlo" instead of "toy model," for various reasons. First, anyone in particle physics will probably understand that Fast MC implies not doing full simulation/ reconstruction, but a quick smearing. Furthermore, there's enough info in the MC that you believe the results, whereas the phrase "toy" makes it sound otherwise. Second, anybody outside of particle physics won't know the difference between a fast MC and a full slow simulation.
5) Personally I find Figure 3 fairly confusing, especially when dumped to BW. I realize this comes down to matters of taste, but I personally prefer to show the model calculations as binned histograms (TH1::Draw("hist")). The markers are in my mind too easily confused with the data (given that this is really 6 plots). Further, the "hist" option will clearly show that the models were binned the same as the data, and makes a nice distinction between data/theory. By a clever choice of line styles, you can probably even make this fairly clear in BW.
6) In Figure 3 and in the text, would it be possible to use some english to differentiate between A_N(>pi) vs A_N(<pi). Maybe introduce the phrases "quark-like" and "gluon-like"? If you can find a smooth way, it would sure make the p4 text smoother, and give some intuition to fig 3.
I realize it'sa little tricky because Fig3b is kind of an orphan. Do you really need it? They're straight lines , and you could quote 4 numbers in the text in a single sentence, even cutting down on some space. Then you could have a "quark-like" left panel and a "gluon- like" right panel.
But, again, I really like the draft.
-Mike
# Peter J., Jan 4, 2007
Hi GPC and PAs,
Here are some first comments on the paper draft:
(i) physics intro, 1st para: I find the physics intro to be a bit confusing. I looked briefly at refs [6,7] (Brodsky et al and Collins). Within my distinctly limited understanding of them I don't think the last sentence of the first paragraph is accurate, and the main physics point of interest in this measurement is missed.
Evidently, the SSA arises due to interference of left- and right-handed quark polarization states, and thus is sensitive to chiral symmertry breaking. If correct, this is important and should be featured prominently in the intro.
On the other hand, I am confused by the various claims about factorization in this process. Brodsky et al claim that the process cannot be factored into PDF and FF, while Collins claims that factorization holds but then derives a pdf $f_{1T}^\perp$ whose sign is opposite for DIS and DY (eq 3), i.e. a pdf whose value is process-dependent, which doesn't sound to me like factorization. The only thing I know for sure is that I am confused on this point and could use some guidance. I suspect that most non-experts will be similarly confused. The physics intro should be precise and clear about what the theory says.
(ii) p 1 left col 2nd para bottom: what is the specific relevance to this measurement of the inclusive jet cross section being described by (factorized) pQCD? I guess if it didn't work for the inclusive yields one could stop immediately. Is that the only point to be made here? Can one say more about constraints on PDFs and FFs?
(iii) p 1 right col line 9: I know nothing about Siberian snakes. What are the limits on possible non-vertical polarization states?
(iv) End of that para: give errors on polarization: 59\pm{xx}\% (57\pm{yy}\%).
(v) jet reconstruction: nowhere do you actually describe what "jet reconstruction" you do. P 2 left col line 6 talks about "jet clusters at level 2" and the caption of Fig 1 talks about "full jet reconstrcution" but the reader is left hanging about how a jet is actually defined. Is there some peak-finding with a cut-off radius, or what? I know that you use EMC energy only but the non-expert reader will not know what this implies, i.e. all of the EMC energy plus perhaps 30% of the charged hadronic energy, with some charged-track dispersion in the magnetic field that is not corrected for. You need a couple of paragraphs defining the jet finding used for the analysis and giving its comparison to full jet reco, justifying why this technique is adequate for this measurement (there is currently some of that later in the text but it should be consolidated).
(vi) Fig 1d: why only 2% of the data? I think I know the answer: that's what was reconstructed at the time you were in the thick of this analysis, but evidently more has been done in the meantime. Not usable?
(vii) p 2 left col middle: I printed the paper in B&W and don't see the 6-fold L0 peaks in fig 1a. Am I missing them?
(viii) p 2 right col 2nd para: the "favoring" of qg vs gg at forward vs midrapidity is qualitative. Can this be made quantitative, e.g using PYTHIA? What is the magnitude of the variation of the two contributions?
(ix) p 2 right col middle: "while we away the time-consuming replay of the full dataset including TPC..." is a STAR detail of little interest to others, and has a limited shelf-life. I suggest simply describing what was done, saying that this rapid analysis technique (in contrast to full jet reco) is sufficient for present purposes.
(x) Fig 1b and discussion of tails in p2 right col bottom: "might reflect moderately hard gluon emission" is weak. Can this be studied with a model calculation? But I also find it confusing because I don't know how the jet finding was done. Hard gluon emission will generate an acoplanarity only if it pushes some of the energy flow out of the jet cone, otherwise momentum is conserved. So I suspect that this tail depends on how the jet is defined. Needs more discussion.
I also wonder about tails being generated by the combination of relatively low multiplicity in low energy jets and only partial jet reco (EM plus ~30% hadronic, with some funny spread in the latter due to the field). Could unfavorable, perhaps rare, fluctuations in charged vs neutral pions generate such apparent tails which are not present for full jet reco? Perhaps a model study would help here. Anyway, the toy model in which you just fit with a Gaussian with an exponential seems inadequate - can you do a more meaningful study based on PYTHIA or HERWIG?
(xi) p 3 left col top: is there a jet energy dependence to <kT^2>? More generally, the distribution shown in Fig 1d goes out to ~50 GeV if I jack it up by eye by a factor 50. Can you make a few coarse energy bins to look at the dependence of the asymmetry on jet energy? You say somewhere that you expect the ET dependence of the Sivers effect to be small, but surely it would be good to test this.
(xii) definitions of A_N and r_\pm (eq 1 and 2): it's late in the evening and I am a bit tired, but frankly these formulas are not speaking to me at the moment. A_N is defined as the ratio of ratios, which is OK, but I am not getting the purpose of the sqrt. There are too many +- and -+ subscripts and zeta>pi vs zeta<pi which are hard to distinguish. Can you find a more transparent notation, or explain the structure of the definitions a bit better?
That's all for now. I didn't read the last third as carefully, I'll do that next time.
Hope these are helpful, talk to you tomorrow.
Peter
| 2020-08-05T05:40:40 |
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|
https://cnls.lanl.gov/~ebn/pubs/inel/inel.html
|
## Nontrivial Velocity Distributions in Inelastic Gases,
### P.L. Krapivsky and E. Ben-Naim
We study spatially homogeneous inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient \epsilon. In the unforced case, we find that the velocity distribution decays algebraically, P(v,t)~ v^{-sigma}\$, for sufficiently large velocities. The exponent \sigma(d,epsilon) exhibits nontrivial dependence on the spatial dimension and the dissipation coefficient.
source, ps, pdf
| 2019-08-22T13:55:51 |
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|
https://par.nsf.gov/biblio/10361773
|
Experimental realization of linearly polarized x-ray detected ferromagnetic resonance
Abstract
We present the first theoretical and experimental evidence of time-resolved dynamic x-ray magnetic linear dichroism (XMLD) measurements of GHz magnetic precessions driven by ferromagnetic resonance in both metallic and insulating thin films. Our findings show a dynamic XMLD in both ferromagnetic Ni80Fe20and ferrimagnetic Ni0.65Zn0.35Al0.8Fe1.2O4for different measurement geometries and linear polarizations. A detailed analysis of the observed signals reveals the importance of separating different harmonic components in the dynamic signal in order to identify the XMLD response without the influence of competing contributions. In particular, RF magnetic resonance elicits a large dynamic XMLD response at the fundamental frequency under experimental geometries with oblique x-ray polarization. The geometric range and experimental sensitivity can be improved by isolating the 2ωFourier component of the dynamic response. These results illustrate the potential of dynamic XMLD and represent a milestone accomplishment toward the study of GHz spin dynamics in systems beyond ferromagnetic order.
Authors:
; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10361773
Journal Name:
New Journal of Physics
Volume:
24
Issue:
1
Page Range or eLocation-ID:
Article No. 013030
ISSN:
1367-2630
Publisher:
IOP Publishing
National Science Foundation
##### More Like this
1. Many technologically useful magnetic oxides are ferrimagnetic insulators, which consist of chemically distinct cations. Here, we examine the spin dynamics of different magnetic cations in ferrimagnetic NiZnAl-ferrite (Ni0.65Zn0.35Al0.8Fe1.2O4) under continuous microwave excitation. Specifically, we employ time-resolved x-ray ferromagnetic resonance to separately probe Fe2+/3+and Ni2+cations on different sublattice sites. Our results show that the precessing cation moments retain a rigid, collinear configuration to within [Formula: see text]2°. Moreover, the effective spin relaxation is identical to within <10% for all magnetic cations in the ferrite. Thus, we validate the oft-assumed “ferromagnetic-like” dynamics in the resonantly driven ferrimagnetic oxide: the magnetic moments from different cations precess as a coherent, collective magnetization, despite the high contents of nonmagnetic Zn2+and Al3+diluting the exchange interactions.
2. Abstract
The emergence of ferromagnetism in materials where the bulk phase does not show any magnetic order demonstrates that atomically precise films can stabilize distinct ground states and expands the phase space for the discovery of materials. Here, the emergence of long-range magnetic order is reported in ultrathin (111) LaNiO3(LNO) films, where bulk LNO is paramagnetic, and the origins of this phase are explained. Transport and structural studies of LNO(111) films indicate that NiO6octahedral distortions stabilize a magnetic insulating phase at the film/substrate interface and result in a thickness-dependent metal–insulator transition att = 8 unit cells. Away from this interface, distortions relax and bulk-like conduction is regained. Synchrotron x-ray diffraction and dynamical x-ray diffraction simulations confirm a corresponding out-of-plane unit-cell expansion at the interface of all films. X-ray absorption spectroscopy reveals that distortion stabilizes an increased concentration of Ni2+ions. Evidence of long-range magnetic order is found in anomalous Hall effect and magnetoresistance measurements, likely due to ferromagnetic superexchange interactions among Ni2+–Ni3+ions. Together, these results indicate that long-range magnetic ordering and metallicity in LNO(111) films emerges from a balance among the spin, charge, lattice, and orbital degrees of freedom.
3. Abstract
This report is on studies directed at the nature of magneto-electric (ME) coupling by ferromagnetic resonance (FMR) under an electric field in a coaxial nanofiber of nickel ferrite (NFO) and lead zirconate titanate (PZT). Fibers with ferrite cores and PZT shells were prepared by electrospinning. The core–shell structure of annealed fibers was confirmed by electron- and scanning probe microscopy. For studies on converse ME effects, i.e., the magnetic response of the fibers to an applied electric field, FMR measurements were done on a single fiber with a near-field scanning microwave microscope (NSMM) at 5–10 GHz by obtaining profiles of both amplitude and phase of the complex scattering parameterS11as a function of bias magnetic field. The strength of the voltage-ME couplingAvwas determined from the shift in the resonance fieldHrfor bias voltage ofV = 0–7 V applied to the fiber. The coefficientAvfor the NFO core/PZT shell structure was estimated to be − 1.92 kA/Vm (− 24 Oe/V). A model was developed for the converse ME effects in the fibers and the theoretical estimates are in good agreement with the data.
4. Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enablemore »
5. Abstract
We present a strategy for the design of ferromagnetic materials with exceptionally low magnetic hysteresis, quantified by coercivity. In this strategy, we use a micromagnetic algorithm that we have developed in previous research and which has been validated by its success in solving the “Permalloy Problem”—the well-known difficulty of predicting the composition 78.5% Ni of the lowest coercivity in the Fe–Ni system—and by the insight it provides into the “Coercivity Paradox” of W. F. Brown. Unexpectedly, the design strategy predicts that cubic materials with large saturation magnetizationmsand large magnetocrystalline anisotropy constantκ1will have low coercivity on the order of that of Permalloy, as long as the magnetostriction constantsλ100, λ111are tuned to special values. The explicit prediction for a cubic material with low coercivity is the dimensionless number$$({c}_{11}-{c}_{12}){\lambda }_{100}^{2}/(2{\kappa }_{1})=81$$$\left({c}_{11}-{c}_{12}\right){\lambda }_{100}^{2}/\left(2{\kappa }_{1}\right)=81$for 〈100〉 easy axes. The results would seem to have broad potential application, especially to magnetic materials of interest in energy research.
| 2023-04-01T02:39:39 |
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|
https://large-numbers.fandom.com/wiki/Legion%27s_number_of_the_first_kind?oldid=4983
|
## FANDOM
1,138 Pages
Legion's number of the first kind is equal to $$666^{666} \approx 2.71541759288712\times10^{1,880}$$.[1]
## Decimal expansion Edit
271541759288712855826087455170021786027838521065016987178223004696578367534784603688013417861287317081040369394618136925376390776734814142359269954981438585309058005792575777286547766974032030622709400636076630337695472357344193883258618859601636747029392705682480231361672383305593666601292142319787714400226324514478109346054646257736974663071867802948304106037331337648245560659985653200111117423345076820028856039271697478224170953365430292002540313209626985629026842226720098365723596644589192169647865964771608482657447815673166354263425761875056075351412658924918167675222004537186685221728745459415025183608088786527610184833513790116757654287910149888366373032818151480800952809005528561125366155648578375191671516389923637068612545908928591509856524061271778433035659907099937099027157651275866007333020305683709128393004786162164158503634595479326165593895852888778701548580946457862112993933286295883107151254097505408450243425177831253342079786634358573748818965808816613570280697021834844832652027344442640175038787842736503395375213097324598270999348133857903750526167553966478796074667482527451958013385703152678559571864116226566032365908052857936209172690002387460244899885396862691793991738773357078062613492707085820369352745180327438422889555512909451485998615969501470146470402649889349212006778573387292851099036349527469520676832881968856724904460084994793476708042987577163193492415961223417659787157202545333783334777830218014905077675699766649698676892834587204825046787698439067298022983708693783338395078457245428904542657506873425865596233432542160135568886423752229229562648133533088569487318295430287726946641649809356760113688980954104973336888392785547924780056268147894207107543052594542403021659363655062233931413319416693234844064515946449947016545969427094539246444208735559647539174640853111520180776757872042024272504000286839563050880598016
### Sources Edit
1. Legion's Numbers from Wolfram MathWorld
### See also Edit
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-08-05T16:51:55 |
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https://pdglive.lbl.gov/DataBlock.action?node=S067UDE
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# $\boldsymbol N_{{\mathrm {up}}}({{\boldsymbol e}})/\boldsymbol N_{{\mathrm {down}}}({{\boldsymbol e}}$) INSPIRE search
VALUE DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.961$ ${}^{+0.086}_{-0.079}$ $\pm0.016$ 1
2005
SKAM multi-GeV
1 ASHIE 2005 results are based on an exposure of 92 kton yr during the complete Super-Kamiokande I running period. The analyzed data sample consists of fully-contained single-ring ${{\mathit e}}$-like events with visible energy $>$ 1.33 GeV. Upward-going events are those with $-1$ $<$ cos(zenith angle) $<$ $-0.2$ and downward-going events are those with 0.2 $<$ cos(zenith angle) $<$ 1. The ${{\mathit e}}$-like up-down ratio for the multi-GeV data is consistent with 1 (the expectation for no atmospheric ${{\mathit \nu}_{{e}}}$ oscillations).
References:
ASHIE 2005
PR D71 112005 Measurement of Atmospheric Neutrino Oscillation Parameters by Super-Kamiokande I
| 2020-11-29T16:38:38 |
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https://pdglive.lbl.gov/Particle.action?init=0&node=S041&home=MXXX045
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BOTTOM MESONS($\mathit B$ = $\pm1$) ${{\mathit B}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit b}}}$, ${{\mathit B}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit b}}}$, ${{\overline{\mathit B}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit b}}$, ${{\mathit B}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit b}}$, similarly for ${{\mathit B}^{*}}$ 's
#### ${{\mathit B}^{\pm}}$
$I(J^P)$ = $1/2(0^{-})$
Quantum numbers not measured. Values shown are quark-model predictions. See also the ${{\mathit B}^{\pm}}$ /${{\mathit B}^{0}}$ ADMIXTURE and ${{\mathit B}^{\pm}}$ /${{\mathit B}^{0}}$ /${{\mathit B}_{{s}}^{0}}$ /${{\mathit b}}$ -baryon ADMIXTURE sections.
${{\mathit B}^{\pm}}$ MASS $5279.34 \pm0.12$ MeV
${{\mathit B}^{\pm}}$ MEAN LIFE $(1638 \pm4) \times 10^{-15}$ s
${\mathit \tau}_{{{\mathit B}^{+}}}/{\mathit \tau}_{{{\mathit B}^{-}}}$ $1.002 \pm0.004$
A$_{P}({{\mathit B}^{+}}$ ) = [${\mathit \sigma (}{{\mathit B}^{-}}{)}$ $−$ ${\mathit \sigma (}{{\mathit B}^{+}}{)}$] $/$ [${\mathit \sigma (}{{\mathit B}^{-}}{)}$ $+$ ${\mathit \sigma (}{{\mathit B}^{+}}{)}$] $-0.0052 \pm0.0019$
${{\mathit B}^{-}}$ modes are charge conjugates of the modes below. Modes which do not identify the charge state of the ${{\mathit B}}$ are listed in the ${{\mathit B}^{\pm}}$ /${{\mathit B}^{0}}$ ADMIXTURE section.
The branching fractions listed below assume 50$\%$ ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ and 50$\%$ ${{\mathit B}^{+}}{{\mathit B}^{-}}$ production at the ${{\mathit \Upsilon}{(4S)}}$ . We have attempted to bring older measurements up to date by rescaling their assumed ${{\mathit \Upsilon}{(4S)}}$ production ratio to 50:50 and their assumed ${{\mathit D}}$ , ${{\mathit D}_{{s}}}$ , ${{\mathit D}^{*}}$ , and ${{\mathit \psi}}$ branching ratios to current values whenever this would affect our averages and best limits significantly.
Indentation is used to indicate a subchannel of a previous reaction. All resonant subchannels have been corrected for resonance branching fractions to the final state so the sum of the subchannel branching fractions can exceed that of the final state.
For inclusive branching fractions, $\mathit e.g.,$ ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}^{\pm}}{{\mathit X}}$ , the values usually are multiplicities, not branching fractions. They can be greater than one.
FOOTNOTES
| 2023-03-21T00:32:14 |
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https://pos.sissa.it/282/516/
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Volume 282 - 38th International Conference on High Energy Physics (ICHEP2016) - Neutrino Physics
Recent Results of Electron-Neutrino Appearance Measurement at NOvA
J. Bian* On behalf of the NOvA collaboration
*corresponding author
Full text: pdf
Pre-published on: April 18, 2017
Published on: April 19, 2017
Abstract
NOvA is a long-baseline accelerator-based neutrino oscillation experiment that is optimized for NuE measurements. It uses the upgraded NuMI beam from Fermilab and measures electron-neutrino appearance and muon-neutrino disappearance at its Far Detector in Ash River, Minnesota. The NuE appearance analysis at NOvA aims to resolve the neutrino mass hierarchy problem and to constrain the CP-violating phase. The first measurement of electron-neutrino appearance in NOvA based on its first year's data was produced in 2015, providing solid evidence of NuE oscillation with the NuMI beam line and some hints on mass-hierarchy and CP. This talk will discuss the second $\nu_e$ oscillation analysis at NOvA, which is based on 2 years of data.
DOI: https://doi.org/10.22323/1.282.0516
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.
| 2020-12-05T03:14:46 |
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https://indico.fnal.gov/event/15949/contributions/34973/
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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
## Renormalization group properties of scalar field theories using gradient flow
Jul 27, 2018, 5:10 PM
20m
104 (Kellogg Hotel and Conference Center)
### 104
#### Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Theoretical Developments
### Speaker
Andrea Carosso (University of Colorado, Boulder)
### Description
Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations on the lattice, distinct from the usual blocking techniques in spin models and gauge theories. In this talk, we discuss two approaches to define an RG transformation which incorporate gradient flow: (1) the correlator ratio method, and (2) Langevin exact RG. We present preliminary numerical results for the critical exponents at the Wilson-Fisher fixed point of three-dimensional scalar $\phi^4$ theory from both methods.
### Primary author
Andrea Carosso (University of Colorado, Boulder)
### Co-authors
Prof. Anna Hasenfratz (University of Colorado) Prof. Ethan Neil (University of Colorado, Boulder)
Slides
| 2021-10-20T23:48:43 |
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https://tjyj.stats.gov.cn/CN/abstract/abstract4442.shtml
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• 论文 •
### 外汇储备币种结构风险测度及优化
• 出版日期:2014-03-15 发布日期:2014-03-10
### Risk Measurement of Currency Composition of Foreign Exchange Reserves and Optimization
Guangyou Zhou & Sijie Zhao
• Online:2014-03-15 Published:2014-03-10
Abstract: With the scale of Chinese foreign exchange reserves are expanding continuously, so they are the risk of the foreign exchange reserves. And the risk caused by the currency composition is extremely important. This paper selects the daily interest rate data, from 2008 to 2012, of the U.S. dollar, euro, Japanese yen and British pound assets, which are the four most important reserved currencies, as the analysis objects, and uses the GARCH Model and VaR Method to estimate the yield and the volatility of each reserve currency. Besides, it also calculates the optimal currency composition with different expected returns. According to the result, the yields and the volatilities of the U.S. dollar and British pound assets are relatively tiny, while the yields of the euro and Japanese yen assets are relatively great. Therefore, it is suggested that appropriately reducing the proportion of the U.S. dollar or adjusting the structure of the U.S. dollar asset, and increasing the proportion of euro and Japanese yen.
| 2022-08-19T20:33:02 |
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https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/01%3A_The_Basics_of_Physics/1.5%3A_Units_and_Measurement_Redux/Estimates_and_Fermi_Calculations
|
$$\require{cancel}$$
# Estimates and Fermi Calculations
Learning Objectives
• Estimate the values of physical quantities.
On many occasions, physicists, other scientists, and engineers need to make estimates for a particular quantity. Other terms sometimes used are guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. (The physicist Enrico Fermi mentioned earlier was famous for his ability to estimate various kinds of data with surprising precision.) Will that piece of equipment fit in the back of the car or do we need to rent a truck? How long will this download take? About how large a current will there be in this circuit when it is turned on? How many houses could a proposed power plant actually power if it is built? Note that estimating does not mean guessing a number or a formula at random. Rather, estimation means using prior experience and sound physical reasoning to arrive at a rough idea of a quantity’s value. Because the process of determining a reliable approximation usually involves the identification of correct physical principles and a good guess about the relevant variables, estimating is very useful in developing physical intuition. Estimates also allow us perform “sanity checks” on calculations or policy proposals by helping us rule out certain scenarios or unrealistic numbers. They allow us to challenge others (as well as ourselves) in our efforts to learn truths about the world.
Many estimates are based on formulas in which the input quantities are known only to a limited precision. As you develop physics problem-solving skills (which are applicable to a wide variety of fields), you also will develop skills at estimating. You develop these skills by thinking more quantitatively and by being willing to take risks. As with any skill, experience helps. Familiarity with dimensions (see Table 1.3) and units (see Table 1.1 and Table 1.2), and the scales of base quantities (see Figure 1.4) also helps.
To make some progress in estimating, you need to have some definite ideas about how variables may be related. The following strategies may help you in practicing the art of estimation:
• Get big lengths from smaller lengths. When estimating lengths, remember that anything can be a ruler. Thus, imagine breaking a big thing into smaller things, estimate the length of one of the smaller things, and multiply to get the length of the big thing. For example, to estimate the height of a building, first count how many floors it has. Then, estimate how big a single floor is by imagining how many people would have to stand on each other’s shoulders to reach the ceiling. Last, estimate the height of a person. The product of these three estimates is your estimate of the height of the building. It helps to have memorized a few length scales relevant to the sorts of problems you find yourself solving. For example, knowing some of the length scales in Figure 1.4 might come in handy. Sometimes it also helps to do this in reverse—that is, to estimate the length of a small thing, imagine a bunch of them making up a bigger thing. For example, to estimate the thickness of a sheet of paper, estimate the thickness of a stack of paper and then divide by the number of pages in the stack. These same strategies of breaking big things into smaller things or aggregating smaller things into a bigger thing can sometimes be used to estimate other physical quantities, such as masses and times.
• Get areas and volumes from lengths. When dealing with an area or a volume of a complex object, introduce a simple model of the object such as a sphere or a box. Then, estimate the linear dimensions (such as the radius of the sphere or the length, width, and height of the box) first, and use your estimates to obtain the volume or area from standard geometric formulas. If you happen to have an estimate of an object’s area or volume, you can also do the reverse; that is, use standard geometric formulas to get an estimate of its linear dimensions.
• Get masses from volumes and densities. When estimating masses of objects, it can help first to estimate its volume and then to estimate its mass from a rough estimate of its average density (recall, density has dimension mass over length cubed, so mass is density times volume). For this, it helps to remember that the density of air is around 1 kg/m3, the density of water is 103 kg/m3, and the densest everyday solids max out at around 104 kg/m3. Asking yourself whether an object floats or sinks in either air or water gets you a ballpark estimate of its density. You can also do this the other way around; if you have an estimate of an object’s mass and its density, you can use them to get an estimate of its volume.
• If all else fails, bound it. For physical quantities for which you do not have a lot of intuition, sometimes the best you can do is think something like: Well, it must be bigger than this and smaller than that. For example, suppose you need to estimate the mass of a moose. Maybe you have a lot of experience with moose and know their average mass offhand. If so, great. But for most people, the best they can do is to think something like: It must be bigger than a person (of order 102 kg) and less than a car (of order 103 kg). If you need a single number for a subsequent calculation, you can take the geometric mean of the upper and lower bound—that is, you multiply them together and then take the square root. For the moose mass example, this would be $$\left(10^{2} \times 10^{3}\right)^{0.5} = 10^{2.5} = 10^{0.5} \times 10^{2} \approx 3 \times 10^{2}\; kg \ldotp$$The tighter the bounds, the better. Also, no rules are unbreakable when it comes to estimation. If you think the value of the quantity is likely to be closer to the upper bound than the lower bound, then you may want to bump up your estimate from the geometric mean by an order or two of magnitude.
• One “sig. fig.” is fine. There is no need to go beyond one significant figure when doing calculations to obtain an estimate. In most cases, the order of magnitude is good enough. The goal is just to get in the ballpark figure, so keep the arithmetic as simple as possible.
• Ask yourself: Does this make any sense? Last, check to see whether your answer is reasonable. How does it compare with the values of other quantities with the same dimensions that you already know or can look up easily? If you get some wacky answer (for example, if you estimate the mass of the Atlantic Ocean to be bigger than the mass of Earth, or some time span to be longer than the age of the universe), first check to see whether your units are correct. Then, check for arithmetic errors. Then, rethink the logic you used to arrive at your answer. If everything checks out, you may have just proved that some slick new idea is actually bogus.
Example $$\PageIndex{1}$$: Mass of Earth’s Oceans
Estimate the total mass of the oceans on Earth.
Strategy
We know the density of water is about 103 kg/m3, so we start with the advice to “get masses from densities and volumes.” Thus, we need to estimate the volume of the planet’s oceans. Using the advice to “get areas and volumes from lengths,” we can estimate the volume of the oceans as surface area times average depth, or V = AD. We know the diameter of Earth from Figure 1.4 and we know that most of Earth’s surface is covered in water, so we can estimate the surface area of the oceans as being roughly equal to the surface area of the planet. By following the advice to “get areas and volumes from lengths” again, we can approximate Earth as a sphere and use the formula for the surface area of a sphere of diameter d—that is, A = $$\pi d^{2}$$, to estimate the surface area of the oceans. Now we just need to estimate the average depth of the oceans. For this, we use the advice: “If all else fails, bound it.” We happen to know the deepest points in the ocean are around 10 km and that it is not uncommon for the ocean to be deeper than 1 km, so we take the average depth to be around (103 x 104)0.5 ≈ 3 x 103m. Now we just need to put it all together, heeding the advice that “one ‘sig. fig.’ is fine.”
Solution
We estimate the surface area of Earth (and hence the surface area of Earth’s oceans) to be roughly
$$A = \pi d^{2} = \pi \left(10^{7}\; m\right)^{2} \approx 3 \times 10^{14}\; m^{2} \ldotp$$
Next, using our average depth estimate of D = 3 x 103m, which was obtained by bounding, we estimate the volume of Earth’s oceans to be
$$V = AD = \left(3 \times 10^{14}\; m^{2}\right)\left(3 \times 10^{3}\; m\right) = 9 \times 10^{17}m^{3} \ldotp$$
Last, we estimate the mass of the world's oceans to be
$$M = \rho V = \left(10^{3}\; kg/m^{3}\right) \left(9 \times 10^{17}\; m^{3}\right) = 9 \times 10^{20}\; kg \ldotp$$
Thus, we estimate that the order of magnitude of the mass of the planet’s oceans is 1021 kg.
Significance
To verify our answer to the best of our ability, we first need to answer the question: Does this make any sense? From Figure 1.4, we see the mass of Earth’s atmosphere is on the order of 1019 kg and the mass of Earth is on the order of 1025 kg. It is reassuring that our estimate of 1021 kg for the mass of Earth’s oceans falls somewhere between these two. So, yes, it does seem to make sense. It just so happens that we did a search on the Web for “mass of oceans” and the top search results all said 1.4 x 1021 kg, which is the same order of magnitude as our estimate. Now, rather than having to trust blindly whoever first put that number up on a website (most of the other sites probably just copied it from them, after all), we can have a little more confidence in it.
Exercise$$\PageIndex{1}$$
Figure 1.4 says the mass of the atmosphere is 1019 kg. Assuming the density of the atmosphere is 1 kg/m3, estimate the height of Earth’s atmosphere. Do you think your answer is an underestimate or an overestimate? Explain why.
How many piano tuners are there in New York City? How many leaves are on that tree? If you are studying photosynthesis or thinking of writing a smartphone app for piano tuners, then the answers to these questions might be of great interest to you. Otherwise, you probably couldn’t care less what the answers are. However, these are exactly the sorts of estimation problems that people in various tech industries have been asking potential employees to evaluate their quantitative reasoning skills. If building physical intuition and evaluating quantitative claims do not seem like sufficient reasons for you to practice estimation problems, how about the fact that being good at them just might land you a high-paying job?
Phet Simulation: Estimation
For practice estimating relative lengths, areas, and volumes, check out this PhET simulation, titled “Estimation.”
## Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2020-01-24T22:54:50 |
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http://www.scstatehouse.gov/sess121_2015-2016/sj16/20160428.htm
|
South Carolina General Assembly
121st Session, 2015-2016
Journal of the Senate
Thursday, April 28, 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 the writings of Ezekiel we read this:
"A new heart I will give you, and a new spirit I will put within you " (Ezekiel 36:26a)
Holy God, as we draw near the close of this fourth month of this 2016 Senate Session, we call upon You to grant a fresh spirit of hope and promise to these leaders and to the people they serve. O God, as these Senators and their dedicated staff members continue with their efforts to move South Carolina forward on so many fronts, grant to each of them the resolve and determination to bring about positive, long-lasting and meaningful results that will truly improve life for every citizen in this State. May it be so, and to You be the glory, Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Statement by Senator COLEMAN
Yesterday, I was required to be out of the Chamber on business working for the constituents of Senate District 17. Had I been present, I would have voted in favor of the Ethics Reform Bills, H. 3184 and H. 3186.
Doctor of the Day
Senator CAMPSEN introduced Dr. Radwan Hallaba of Charleston, S.C., Doctor of the Day.
Leave of Absence
At 11:12 A.M., Senator YOUNG requested a leave of absence for Senator SHEALY for the day.
Leave of Absence
At 11:43 A.M., Senator SHANE MARTIN requested leave of absence on Thursday, April 28, 2016, beginning at 1:27 P.M. until Wednesday, May 4, 2016, at 1:17 P.M.
Leave of Absence
At 12:23 P.M., Senator CAMPBELL requested a leave of absence for Senator CLEARY for the day.
Leave of Absence
At 12:36 P.M., Senator VERDIN requested a leave of absence for Senator GROOMS until 1:00 P.M.
Leave of Absence
At 12:36 P.M., Senator LARRY MARTIN requested a leave of absence for Senator HAYES for the day.
Expression of Personal Interest
Senator DAVIS rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator BRYANT rose for an Expression of Personal Interest.
S. 719 (Word version) Sen. Peeler
Privilege of the Floor
On motion of Senator CLEARY, on behalf of Senator LOURIE, with unanimous consent, the Privilege of the Floor was extended to members of the Lady Gamecocks team in recognition of their outstanding accomplishments in their second straight SEC tournament title and on making it into the 2016 NCAA Tournament's "Sweet Sixteen."
RECALLED
H. 5225 (Word version) -- Rep. Hayes: A CONCURRENT RESOLUTION TO REQUEST THE DEPARTMENT OF TRANSPORTATION NAME NORTH 9TH AVENUE IN THE TOWN OF DILLON "ROBERT MCRAE MEMORIAL AVENUE" AND TO ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS AVENUE THAT CONTAIN THIS DESIGNATION.
Senator WILLIAMS asked unanimous consent to make a motion to recall the Concurrent Resolution from the Committee on Transportation.
The Concurrent Resolution was recalled from the Committee on Transportation and ordered placed on the Calendar for consideration tomorrow.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 1278 (Word version) -- Senators Courson and Scott: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE COLUMBIA MUSEUM OF ART AND TO CONGRATULATE THE MUSEUM'S ADMINISTRATORS AND STAFF UPON BEING NAMED A RECIPIENT OF THE INSTITUTE OF MUSEUM AND LIBRARY SERVICES' NATIONAL MEDAL FOR MUSEUM AND LIBRARY SERVICE.
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S. 1279 (Word version) -- Senator Allen: A SENATE RESOLUTION TO RECOGNIZE PATRICK J. KENNEDY II, FORMER U.S. REPRESENTATIVE FOR RHODE ISLAND'S 1ST CONGRESSIONAL DISTRICT, FOR HIS MANY YEARS OF DEDICATED PUBLIC SERVICE AND TO EXTEND TO HIM A CORDIAL WELCOME TO THE PALMETTO STATE UPON THE OCCASION OF HIS ADDRESS AT THE NATIONAL ALLIANCE ON MENTAL ILLNESS/MICHELIN LUNCHEON, TO BE HELD MAY 7, 2016, IN GREENVILLE.
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S. 1280 (Word version) -- Senator Verdin: A CONCURRENT RESOLUTION TO CONGRATULATE MR. BILLY R. STRICKLAND, SUPERINTENDENT OF LAURENS COUNTY SCHOOL DISTRICT 55, UPON THE OCCASION OF HIS RETIREMENT, AND TO HONOR AND RECOGNIZE HIS MANY YEARS OF DEDICATED SERVICE TO LAURENS COUNTY SCHOOL DISTRICT 55.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 1281 (Word version) -- Senators Hutto, Lourie and Fair: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 4 TO CHAPTER 101, TITLE 59 SO AS TO ENACT THE "DISCIPLINARY PROCEDURE DUE PROCESS ACT"; TO DEFINE NECESSARY TERMS; TO ESTABLISH THE REQUIREMENTS OF A PROCEEDING, TO ENUMERATE THE RIGHTS OF A STUDENT WHO IS SUBJECT TO A PROCEEDING, TO ESTABLISH STANDARDS FOR THE DISCLOSURE OF EVIDENCE RELATING TO THE PROCEEDING, TO REQUIRE WRITTEN STATEMENTS ENTERED AS EVIDENCE TO BE NOTARIZED, TO PROHIBIT CERTAIN DOCUMENTS FROM BEING USED AS EVIDENCE WITHOUT THE CONSENT OF BOTH PARTIES, TO ALLOW FOR THE INFORMAL DISPOSITION OF A PROCEEDING IN CERTAIN CIRCUMSTANCES, TO PROHIBIT IRRELEVANT, IMMATERIAL, OR UNDULY REPETITIVE EVIDENCE FROM BEING ADMITTED, TO APPLY THE STANDARDS FOR PRIVILEGE OF THE STATE TO A PARTY IN A PROCEEDING, TO ALLOW THE SUBMISSION OF EVIDENCE IN WRITTEN FORM IN CERTAIN CIRCUMSTANCES, TO REQUIRE A RECORD OF THE PROCEEDING BE MADE AND TO ENUMERATE THE REQUIRED CONTENTS OF THE RECORD, TO ALLOW A PARTY TO REQUEST A RECORDING OF THE PROCEEDING FOR TRANSCRIPTION, TO REQUIRE THE PRESIDING PERSON TO BE IMPARTIAL, TO ESTABLISH STANDARDS FOR THE PRESIDING PERSON TO MAKE A DECISION, TO REQUIRE AN INSTITUTION TO PROVIDE A STUDENT THE INTERNAL APPEALS PROCEDURE IF THE DECISION OF THE INSTITUTION IS ADVERSE TO THE STUDENT, TO ALLOW THE STUDENT OR INSTITUTION TO APPEAL TO THE CIRCUIT COURT OR ADMINISTRATIVE LAW COURT, TO ESTABLISH A PRESUMPTION OF NONVIOLATION FOR THE STUDENT AND THE BURDEN OF PROOF FOR THE INSTITUTION, TO REQUIRE ANY PUNISHMENT TO BE REASONABLE AND PROPORTIONATE TO THE VIOLATION, TO ALLOW THE CIRCUIT COURT OR ADMINISTRATIVE LAW COURT TO ISSUE AN INJUNCTION AND ALLOW FOR THE AWARD OF ATTORNEYS' FEES AND COSTS; AND TO ALLOW AN INSTITUTION TO IMMEDIATELY SUSPEND A STUDENT FOR ALLEGED MISCONDUCT IN CERTAIN CIRCUMSTANCES.
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Read the first time and referred to the Committee on Education.
H. 3084 (Word version) -- Reps. Jefferson, Southard, McKnight, Weeks, Whipper, Robinson-Simpson, Mitchell and W. J. McLeod: A BILL TO AMEND SECTION 7-15-380, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE OATH OF THE ABSENTEE BALLOT APPLICANT, SO AS TO ELIMINATE THE REQUIREMENT THAT THE ABSENTEE BALLOT APPLICANT'S OATH BE WITNESSED.
Read the first time and referred to the Committee on Judiciary.
H. 3167 (Word version) -- Reps. Tallon, Long, G. R. Smith, Pitts, Toole, Pope, Simrill, Johnson, Felder, Kennedy, Jordan, Goldfinch, Clemmons, Duckworth, Fry, Hardee, Ryhal, Yow, Gagnon, Willis, Rutherford, Hixon, Taylor, Hill, Howard, Williams, Douglas, Dillard, Hayes, Daning, Crosby, George, Bales, Bradley, Murphy, Bannister, Delleney, Bingham, McKnight and Kirby: A BILL TO AMEND SECTION 7-13-710, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ACCEPTABLE FORMS OF IDENTIFICATION REQUIRED OF A PERSON WHEN HE PRESENTS HIMSELF TO VOTE, SO AS TO INCLUDE A VALID AND CURRENT SOUTH CAROLINA RESIDENT CONCEALED WEAPON PERMIT AS AN AUTHORIZED FORM OF IDENTIFICATION.
Read the first time and referred to the Committee on Judiciary.
H. 3449 (Word version) -- Rep. Bales: A BILL TO AMEND SECTION 50-13-675, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO NONGAME FISHING DEVICES AND GEAR THAT ARE PERMITTED TO BE USED IN CERTAIN BODIES OF FRESHWATER, SO AS TO PROVIDE THAT THE DEPARTMENT OF NATURAL RESOURCES MAY ISSUE RECREATIONAL LICENSES FOR THE USE OF HOOP NETS ALONG THE WATEREE RIVER.
Read the first time and referred to the Committee on Fish, Game and Forestry.
H. 4029 (Word version) -- Reps. Norman, Govan, King, Corley, Hixon, Simrill, Thayer, Alexander and Willis: A BILL TO AMEND SECTION 20-3-130, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ALIMONY AWARDS, SO AS TO CREATE A PRESUMPTION FOR THE AWARD OF LUMP-SUM OR REIMBURSEMENT ALIMONY AND AGAINST THE AWARD OF PERIODIC OR REHABILITATIVE ALIMONY, TO ESTABLISH GUIDELINES FOR AWARDING ALIMONY BASED ON THE DURATION OF THE MARRIAGE, TO PROVIDE THAT THE COURT MAY FIND COHABITATION EVEN IF A PARTY MAINTAINS A RESIDENCE OR DWELLING IN ADDITION TO THE RESIDENCE OR DWELLING WHERE THE PARTY IS COHABITING, TO PROHIBIT THE COURT FROM TAKING INTO CONSIDERATION CERTAIN EARNINGS OR PROPERTIES WHEN DETERMINING A SUPPORTING SPOUSE'S ABILITY TO PAY, TO ALLOW THE COURT TO CONSIDER THE EXTENT TO WHICH ALIMONY PAID TO A PARTY WHO IS COHABITING IS USED TO CONTINUE OR SUPPORT THE COHABITATION, TO REQUIRE THE COURT TO CONSIDER SOCIAL SECURITY SPOUSAL RETIREMENT BENEFITS AND OTHER RETIREMENT INCOME TO WHICH A SUPPORTED SPOUSE IS ENTITLED WHEN MAKING OR MODIFYING AN ALIMONY AWARD, TO PROHIBIT THE COURT FROM TAKING INTO CONSIDERATION INCOME OR BENEFITS RELATED TO AN INJURY OR DISABILITY OF THE SUPPORTING SPOUSE WHEN DETERMINING THE SUPPORTING SPOUSE'S ABILITY TO PAY; AND TO AMEND SECTION 20-3-170, RELATING TO MODIFICATION, CONFIRMATION, AND TERMINATION OF ALIMONY, SO AS TO CREATE A PRESUMPTION THAT RETIREMENT IS A CHANGE OF CIRCUMSTANCE JUSTIFYING TERMINATION OF ALIMONY WHEN THE SUPPORTING SPOUSE IS ELIGIBLE TO RECEIVE SOCIAL SECURITY RETIREMENT BENEFITS, TO PROVIDE THAT THE COURT SHOULD DECREASE AN ALIMONY AWARD IF A SUPPORTED SPOUSE IS ENTITLED TO RECEIVE CERTAIN SPOUSAL SOCIAL SECURITY RETIREMENT BENEFITS, AND TO PROVIDE THAT THE COURT HAS THE DISCRETION TO MODIFY AN ALIMONY AWARD AT WHATEVER AGE THE SUPPORTING SPOUSE RETIRES.
Read the first time and referred to the Committee on Judiciary.
H. 4215 (Word version) -- Reps. Finlay, McCoy, Delleney, Lucas, Newton, Pitts, Limehouse, Loftis and Burns: A BILL TO AMEND SECTION 48-39-150, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE APPROVAL OF PERMITS TO ALTER CRITICAL AREAS, SO AS TO ENACT THE "MANAGED TIDAL IMPOUNDMENT PRESERVATION ACT", BY EXEMPTING PROPERTY THAT IS DEEMED ELIGIBLE UNDER A UNITED STATES ARMY CORP OF ENGINEERS' GENERAL PERMIT FROM PERMITTING REQUIREMENTS IN CERTAIN CIRCUMSTANCES AND GRANTING ENFORCEMENT AUTHORITY TO THE COASTAL DIVISION OF THE SOUTH CAROLINA DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL.
Read the first time and referred to the Committee on Agriculture and Natural Resources.
H. 4387 (Word version) -- Reps. Bamberg, Henegan, Clyburn, Pitts, Cobb-Hunter and Whipper: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 23-1-245 SO AS TO PROVIDE THAT A LAW ENFORCEMENT AGENCY, DEPARTMENT, OR DIVISION MAY NOT REQUIRE ITS OFFICERS TO ISSUE A SPECIFIC AMOUNT OR MEET A QUOTA FOR THE NUMBER OF CITATIONS THEIR OFFICERS ISSUE DURING A DESIGNATED PERIOD OF TIME, TO PROVIDE THAT A LAW ENFORCEMENT AGENCY, DEPARTMENT, OR DIVISION MAY NOT COMPARE THE NUMBER OF CITATIONS ISSUED BY ITS OFFICERS FOR THE PURPOSE OF EVALUATING AN OFFICER'S JOB PERFORMANCE, TO PROVIDE THAT "POINT OF CONTACT" MAY BE USED TO EVALUATE AN OFFICER'S PERFORMANCE, TO PROVIDE THAT AN EMPLOYEE WHO FILES A REPORT THAT ALLEGES A VIOLATION OF THIS SECTION IS PROTECTED BY THE "WHISTLE BLOWER ACT", AND TO PROVIDE DEFINITIONS.
Read the first time and referred to the Committee on Judiciary.
H. 4416 (Word version) -- Reps. Felder, Pope, Merrill, Burns, V. S. Moss and Pitts: A BILL TO AMEND SECTION 6-1-970, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE EXEMPTIONS FROM IMPACT FEES, SO AS TO ADD EXEMPTIONS FOR CERTAIN SCHOOLS AND VOLUNTEER FIRE DEPARTMENTS.
Read the first time and referred to the Committee on Finance.
H. 4546 (Word version) -- Reps. Putnam, Clyburn, Robinson-Simpson, Thayer, Collins, Clary, Erickson, Long, Ryhal, Herbkersman, Newton, Jordan, Hicks, McCoy, M. S. McLeod, Douglas, Henegan, Allison, Quinn, Funderburk, Finlay, Jefferson, Willis and Bedingfield: A BILL TO AMEND SECTION 63-7-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS USED IN THE CHILDREN'S CODE, SO AS TO ADD DEFINITIONS FOR "AGE-APPROPRIATE ACTIVITY", "CAREGIVER", AND "STANDARD OF CARE OF A REASONABLE AND PRUDENT PARENT"; TO AMEND SECTION 63-7-1700, AS AMENDED, RELATING TO PERMANENCY PLANNING, SO AS TO PROVIDE FOR COURT CONSIDERATION OF LOCAL FOSTER CARE REVIEW BOARD RECOMMENDATIONS, TO REQUIRE THE COURT TO TAKE INTO CONSIDERATION RECOMMENDATIONS OF THE DEPARTMENT OF SOCIAL SERVICES, THE LOCAL FOSTER CARE REVIEW BOARD, AND THE GUARDIAN AD LITEM BEFORE APPROVING A PLACEMENT PLAN, AND TO REQUIRE THE COURT TO REVIEW THE DEPARTMENT'S EFFORTS TO ENSURE A FOSTER CHILD HAS THE OPPORTUNITY TO ENGAGE IN AGE-APPROPRIATE ACTIVITIES; TO AMEND SECTION 63-7-2310, RELATING TO THE FOSTER CARE SYSTEM, SO AS TO REQUIRE THE DEPARTMENT TO MAKE EFFORTS TO NORMALIZE THE LIVES OF CHILDREN IN FOSTER CARE BY ENABLING PARTICIPATION IN AGE-APPROPRIATE ACTIVITIES; TO AMEND SECTION 63-11-720, RELATING TO FUNCTIONS AND POWERS OF LOCAL FOSTER CARE REVIEW BOARDS, SO AS TO CHANGE THE FREQUENCY WITH WHICH THESE BOARDS MUST REVIEW CASES OF CHILDREN IN FOSTER CARE AND CERTAIN REPORTING REQUIREMENTS; TO AMEND SECTION 63-11-750, RELATING THE FOSTER CARE REVIEW BOARD'S RIGHT TO PARTICIPATE IN CHILD ABUSE AND NEGLECT JUDICIAL PROCEEDINGS, SO AS TO ALLOW THE BOARD TO INTRODUCE, EXAMINE, AND CROSS-EXAMINE WITNESSES; AND FOR OTHER PURPOSES.
Read the first time and referred to the Committee on Judiciary.
H. 4547 (Word version) -- Reps. Rutherford, Hosey and Alexander: A BILL TO AMEND SECTION 63-19-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF "CHILD" AND "JUVENILE" IN THE JUVENILE JUSTICE CODE, SO AS TO CHANGE THE AGE TO A PERSON UNDER TWENTY-ONE YEARS OF AGE, WITH EXCEPTIONS; TO AMEND SECTIONS 63-19-1030, 63-19-1210, 63-19-1410, 63-19-1420, 63-19-1440, AS AMENDED, 63-19-1650, AND 63-19-2050, AS AMENDED, ALL RELATING TO JUVENILE JUSTICE, SO AS TO MAKE CONFORMING CHANGES.
Read the first time and, on motion of Senator MALLOY, with unanimous consent, ordered placed on the Calendar without reference.
H. 4661 (Word version) -- Reps. Forrester, Sandifer, Clemmons, Loftis, Stringer, Norman, Ballentine, Rivers and Hicks: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SUBARTICLE 7 TO ARTICLE 9, CHAPTER 35, TITLE 11 SO AS TO PROVIDE REQUIREMENTS CONCERNING ACCEPTABLE PIPING MATERIAL IN THE STATE PROCUREMENT CODE, AND TO DEFINE NECESSARY TERMS.
Read the first time and referred to the Committee on Finance.
H. 4728 (Word version) -- Reps. Long, Erickson, Douglas, Ridgeway, Hixon, Jefferson, Whitmire, Tallon, Daning, Anthony, Hiott, Ballentine, Allison, Bowers, Spires, W. J. McLeod, Williams, Bales, Nanney, Knight, Southard, V. S. Moss, Gagnon, Willis, Huggins, Corley, Taylor, Herbkersman, King, Felder, Hicks, Loftis, Simrill, Pope, Riley, McCoy, Henderson, Hosey, D. C. Moss and Brannon: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 45 TO TITLE 44 TO ENACT THE "EYE CARE CONSUMER PROTECTION LAW" SO AS TO ESTABLISH REQUIREMENTS FOR A PERSON WHO SELLS SPECTACLES OR CONTACT LENSES USING REFRACTIVE DATA OR INFORMATION GENERATED BY AN AUTOMATED TESTING DEVICE.
Read the first time and referred to the Committee on Medical Affairs.
H. 4762 (Word version) -- Reps. Anthony, Yow and W. J. McLeod: A BILL TO AMEND SECTION 6-1-320, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE LIMITATION ON MILLAGE RATE INCREASES AND EXCEPTIONS TO THIS LIMITATION, SO AS TO REVISE THE EXCEPTION TO THIS LIMITATION FOR THE PURCHASE OF CAPITAL EQUIPMENT AND OTHER EXPENDITURES IN A COUNTY HAVING A POPULATION OF LESS THAN ONE HUNDRED THOUSAND PERSONS AND HAVING AT LEAST FORTY THOUSAND ACRES OF STATE FOREST LAND BY CHANGING THE TERM "STATE FOREST LAND" IN THIS EXCEPTION TO THE TERM "STATE OR NATIONAL FOREST LAND".
Read the first time and referred to the Committee on Finance.
H. 4765 (Word version) -- Reps. G. R. Smith, Parks, D. C. Moss, Cobb-Hunter, Jefferson, Duckworth, Daning, Kirby, R. L. Brown, Burns, Douglas, Brannon, Anthony, Mitchell, Ridgeway, Robinson-Simpson, Clyburn, Ryhal, Johnson, Yow, G. A. Brown, Riley, Taylor, Limehouse, Williams, Simrill, Bedingfield, Chumley, Dillard, Herbkersman, Hicks, Hill, Loftis, Long, V. S. Moss, Pope, Rivers, Thayer, Wells, Crosby and King: A BILL TO AMEND SECTION 12-6-5060, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO VOLUNTARY CONTRIBUTIONS MADE BY AN INDIVIDUAL BY MEANS OF THE INCOME TAX RETURN CHECK OFF, SO AS TO ADD HABITAT FOR HUMANITY.
Read the first time and referred to the Committee on Finance.
H. 4776 (Word version) -- Reps. Allison, Erickson, Crosby, Yow, Gagnon, Duckworth, Clary, Govan, Neal, George, Anthony, Willis, Bannister, Bingham, R. L. Brown, Daning, Hayes, Henderson, Hixon, Long, Lucas, V. S. Moss, Murphy, Pope, Simrill, Tallon, Wells, W. J. McLeod, Kennedy, White and Whipper: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 158 TO TITLE 59 SO AS TO ENACT THE "SOUTH CAROLINA EDUCATION SCHOOL FACILITIES ACT" TO PROVIDE FINANCIAL ASSISTANCE TO SCHOOL DISTRICTS IN ORDER TO ACQUIRE SCHOOL FACILITIES BY USING GENERAL OBLIGATION BONDS, AND OTHER FORMS OF ASSISTANCE, TO PROVIDE THAT THE STATE BOARD OF EDUCATION SHALL DETERMINE AND SELECT ON A PRIORITY BASIS, QUALIFIED SCHOOL PROJECTS WHICH SHALL RECEIVE FINANCIAL ASSISTANCE FROM THE STATE, TO PROVIDE FOR THE POWERS AND DUTIES OF THE STATE BOARD OF EDUCATION AND STATE DEPARTMENT OF EDUCATION IN THIS REGARD, AND TO PROVIDE FOR OTHER RELATED PROVISIONS IN CONNECTION WITH THE CONSTRUCTION OR RENOVATION OF SCHOOL FACILITIES; AND TO REPEAL CHAPTER 146, TITLE 59 RELATING TO THE STATE SCHOOL FACILITIES BONDS ACT WHICH AUTHORIZED THE ISSUANCE OF SPECIFIC DOLLAR AMOUNTS OF STATE SCHOOL FACILITIES BONDS WITHIN A SPECIFIED TIME PERIOD.
Read the first time and referred to the Committee on Finance.
H. 4835 (Word version) -- Reps. Erickson, Johnson, Delleney, Loftis, Finlay, Brannon, M. S. McLeod, Pope, Thayer, Long, Atwater, Knight, McCoy, Henegan, Douglas, Allison, Goldfinch, Gambrell, Newton, Riley, Collins, Clemmons, Duckworth, Funderburk, Gagnon, Henderson, Hicks, D. C. Moss and G. R. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 7 TO CHAPTER 15, TITLE 63 SO AS TO ENACT THE "SUPPORTING AND STRENGTHENING FAMILIES ACT" TO ALLOW PARENTS AND PERSONS WITH LEGAL CUSTODY OF A CHILD TO DELEGATE CAREGIVING AUTHORITY FOR THE CHILD TEMPORARILY TO AN ADULT BY EXECUTION OF A POWER OF ATTORNEY, TO PROVIDE FOR THE REQUIREMENTS AND LIMITATIONS OF THE DELEGATION OF CAREGIVING AUTHORITY AND THE RIGHT TO REVOKE THE POWER OF ATTORNEY, AND FOR OTHER PURPOSES; TO AMEND SECTION 63-7-920, AS AMENDED, RELATING TO INVESTIGATIONS OF SUSPECTED CHILD ABUSE OR NEGLECT, SO AS TO REQUIRE THE DEPARTMENT OF SOCIAL SERVICES TO PROVIDE CERTAIN INFORMATION ABOUT COMMUNITY SUPPORTIVE SERVICES TO A PARENT WHEN THE INVESTIGATION DOES NOT RESULT IN PLACEMENT OF THE CHILD OUTSIDE OF THE HOME; AND TO AMEND SECTION 63-13-20, RELATING TO THE DEFINITION OF A CHILDCARE FACILITY, SO AS TO EXCLUDE AN ADULT DESIGNATED AS AN ATTORNEY-IN-FACT FOR A CHILD IN A POWER OF ATTORNEY EXECUTED PURSUANT TO ARTICLE 7, CHAPTER 15, TITLE 63.
Read the first time and referred to the Committee on Judiciary.
H. 4845 (Word version) -- Reps. King and Parks: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 40-19-105 SO AS TO PROVIDE A FUNERAL HOME, FUNERAL DIRECTOR, OR EMBALMER MAY REFUSE TO RELEASE A DEAD HUMAN BODY TO THE CUSTODY OF THE PERSON OR ENTITY WHO HAS THE LEGAL RIGHT TO EFFECT A RELEASE UNTIL ALL FINANCIAL OBLIGATIONS RELATED TO SERVICES PROVIDED BY THE FUNERAL HOME, FUNERAL DIRECTOR, OR EMBALMER WITH RESPECT TO THE DEAD HUMAN BODY HAVE BEEN FULLY SATISFIED; AND TO AMEND SECTION 40-19-110, RELATING TO UNPROFESSIONAL CONDUCT OF A FUNERAL DIRECTOR OR EMBALMER, SO AS TO PROVIDE THAT REFUSING TO PROPERLY RELEASE A DEAD HUMAN BODY TO THE CUSTODY OF THE PERSON OR ENTITY WHO HAS THE LEGAL RIGHT TO EFFECT A RELEASE CONSTITUTES UNPROFESSIONAL CONDUCT EXCEPT WHEN THE REFUSAL IS FOR FAILURE TO SATISFY RELATED FINANCIAL OBLIGATIONS.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
H. 4970 (Word version) -- Rep. R. L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-5-1040 SO AS TO PROVIDE THAT THE DEPARTMENT OF TRANSPORTATION SHALL ERECT SIGNS ALONG THE STATE'S INTERSTATE HIGHWAYS THAT INFORM MOTORISTS THAT CERTAIN VEHICLES MUST TRAVEL IN THE FARTHEST RIGHT LANE, AND TO PROVIDE A PENALTY.
Read the first time and referred to the Committee on Transportation.
H. 5006 (Word version) -- Reps. Lucas, Pope, Merrill, Bradley, Finlay, Stringer, Norman, Ballentine, Felder, Mitchell, King and W. J. McLeod: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 9-16-100 SO AS TO PROHIBIT LOBBYISTS AND PLACEMENT AGENTS FROM CONTACTING CERTAIN INDIVIDUALS CONNECTED WITH THE RETIREMENT SYSTEM INVESTMENT COMMISSION; TO AMEND SECTION 9-4-10, RELATING TO THE PUBLIC EMPLOYEE BENEFIT AUTHORITY, SO AS TO CLARIFY THE BOARD OF THE AUTHORITY IS THE SOLE GOVERNING BODY OF THE AUTHORITY, TO PROVIDE FOR A FIVE-YEAR TERM AND STAGGERED TERMS OF BOARD MEMBERS, TO PRESCRIBE MEETING REQUIREMENTS, TO PROVIDE FOR AN EXECUTIVE DIRECTOR, AND TO PROVIDE CERTAIN FIDUCIARY DUTIES; TO AMEND SECTION 9-16-10, AS AMENDED, RELATING TO DEFINITIONS, SO AS TO REVISE CERTAIN DEFINITIONS; TO AMEND SECTION 9-16-315, AS AMENDED, RELATING TO THE RETIREMENT SYSTEM INVESTMENT COMMISSION, SO AS TO ADD A GUBERNATORIAL APPOINTMENT TO THE COMMISSION, TO LIMIT A MEMBER TO TWO TERMS, TO PROVIDE FURTHER QUALIFICATIONS FOR MEMBERS, TO PROVIDE FOR AN EXECUTIVE DIRECTOR, AND TO ALLOW THE COMMISSION TO ENGAGE ATTORNEYS ON A FEE BASIS; TO AMEND SECTION 9-16-380, RELATING TO THE AUDIT OF THE RETIREMENT SYSTEM INVESTMENT COMMISSION, SO AS TO REQUIRE THE AUDIT FIRM BE SELECTED USING THE PROCUREMENT CODE; TO AMEND SECTION 9-16-340, AS AMENDED, RELATING TO THE INVESTMENT OF RETIREMENT SYSTEM FUNDS, SO AS TO REQUIRE A REDUCTION IN THE TOTAL AMOUNT OF FEES PAID; BY ADDING ARTICLE 4 TO CHAPTER 16, TITLE 9 SO AS TO ESTABLISH THE REVIEW AND OVERSIGHT COMMISSION ON THE RETIREMENT SYSTEM INVESTMENT COMMISSION, TO PROVIDE FOR ITS MEMBERSHIP, AND TO PROVIDE FOR ITS SCREENING DUTIES; TO AMEND SECTION 9-1-1310, AS AMENDED, RELATING TO THE ASSETS OF THE RETIREMENT SYSTEM AND INVESTMENT OF RETIREMENT SYSTEM FUNDS, SO AS TO REQUIRE THE PUBLIC EMPLOYEE BENEFIT AUTHORITY TO HOLD THE ASSETS OF THE RETIREMENT SYSTEM IN A GROUP TRUST, AND TO PROHIBIT INVESTMENTS IN CERTAIN MONEY MORTGAGES AND REAL ESTATE INVESTMENT TRUSTS; AND TO AMEND SECTION 1-3-240, AS AMENDED, RELATING TO THE REMOVAL OF OFFICERS BY THE GOVERNOR, SO AS TO ADD THE MEMBERS OF THE RETIREMENT SYSTEM INVESTMENT COMMISSION TO THE LIST OF OFFICERS OR ENTITIES THE GOVERNING BOARD OF WHICH MAY BE REMOVED BY THE GOVERNOR ONLY FOR CERTAIN REASONS CONSTITUTING CAUSE.
Read the first time and referred to the Committee on Finance.
H. 5007 (Word version) -- Reps. Lucas, Pope, Merrill, Bradley, Finlay, Stringer, Norman, Ballentine, Felder, Mitchell, King and W. J. McLeod: A BILL TO AMEND SECTION 9-16-335, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ASSUMED RATE OF RETURN FOR RETIREMENT SYSTEM FUNDS, SO AS TO PROVIDE THAT THE ASSUMED RATE OF RETURN EXPIRES EVERY FOUR YEARS UNLESS ACTION IS TAKEN BY THE GENERAL ASSEMBLY, AND IF NOT, THE RATE IS SET BY THE STATE FISCAL ACCOUNTABILITY AUTHORITY; AND TO AMEND SECTION 9-1-1085, RELATING TO EMPLOYER AND EMPLOYEE CONTRIBUTION RATES FOR PURPOSES OF THE RETIREMENT SYSTEM, SO AS TO REDUCE THE AMORTIZATION SCHEDULE FROM THIRTY YEARS TO TWENTY YEARS.
Read the first time and referred to the Committee on Finance.
H. 5009 (Word version) -- Reps. Cole, Tallon, Hicks, Brannon, Allison, Chumley, Clary, Forrester, Mitchell, King and W. J. McLeod: 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.
Senator S. MARTIN spoke on the Bill.
Read the first time and ordered placed on the Calendar without reference.
H. 5011 (Word version) -- Reps. Clemmons, Fry, Johnson, Duckworth, Hardee, Anderson, Goldfinch, George, Hayes, H. A. Crawford and Ryhal: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 4-10-980 SO AS TO PROVIDE FOR THE REIMPOSITION OF THE LOCAL OPTION TOURISM DEVELOPMENT FEE.
Read the first time and referred to the Committee on Finance.
H. 5021 (Word version) -- Reps. Collins, Clary and Felder: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO ENACT THE "ADULT STUDENTS WITH DISABILITIES EDUCATIONAL RIGHTS CONSENT ACT" BY ADDING ARTICLE 3 TO CHAPTER 33, TITLE 59 SO AS TO PROVIDE PROCEDURES AND POLICIES THROUGH WHICH STUDENTS WHO ARE ELIGIBLE FOR SPECIAL EDUCATION UNDER THE INDIVIDUALS WITH DISABILITIES ACT AND WHO HAVE NOT BEEN DETERMINED TO BE INCAPACITATED IN PROBATE COURT MAY BE IDENTIFIED AS UNABLE TO PROVIDE INFORMED CONSENT WITH RESPECT TO HIS EDUCATIONAL PROGRAM AND DELEGATE THE AUTHORITY TO MAKE SUCH DECISIONS TO AN AGENT OR REPRESENTATIVE; AND TO DESIGNATE THE EXISTING SECTIONS OF CHAPTER 33, TITLE 59 AS ARTICLE 1 ENTITLED "GENERAL PROVISIONS".
Read the first time and referred to the Committee on Education.
H. 5034 (Word version) -- Rep. White: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-21-4320 SO AS TO REQUIRE THE DEPARTMENT OF REVENUE TO ESTABLISH AN INFORMATIONAL CHARITABLE BINGO WEBPAGE ON ITS WEBSITE; TO AMEND SECTION 12-21-3920, RELATING TO DEFINITIONS FOR PURPOSES OF THE BINGO TAX ACT, SO AS TO REDEFINE "BUILDING"; TO AMEND SECTION 12-21-3940, RELATING TO APPLICATIONS FOR A BINGO LICENSE BY NONPROFIT ORGANIZATIONS AND PROMOTERS, SO AS TO EXTEND THE TIME BY WHICH THE DEPARTMENT MUST RESPOND; TO AMEND SECTION 12-21-3990, RELATING TO THE MANNER OF PLAYING BINGO, SO AS TO PROVIDE THE MANNER IN WHICH CERTAIN DEVICES MUST BE OPERATED; TO AMEND SECTION 12-21-4000, RELATING TO PROCEDURES APPLICABLE TO THE CONDUCT OF BINGO, SO AS TO INCREASE THE ALLOWANCE FOR PROMOTIONS; TO AMEND SECTION 12-21-4005, RELATING TO THE OPERATION OF BINGO GAMES, SO AS TO EXCLUDE CERTAIN RAFFLES; TO AMEND SECTION 12-21-4090, RELATING TO BINGO CHECKING AND SAVINGS ACCOUNTS, SO AS TO ALLOW THE PROMOTER TO MAKE CERTAIN CONTRIBUTIONS AND TO ALLOW FOR ELECTRONIC PAYMENTS; AND TO AMEND SECTION 12-21-4190 RELATING TO THE DISTRIBUTION OF BINGO REVENUES, SO TO INCREASE THE PERCENTAGE THAT IS DISTRIBUTED TO CHARITY.
Read the first time and referred to the Committee on Finance.
H. 5066 (Word version) -- Reps. Herbkersman, Erickson, Bowers, Bradley, Newton and Hodges: A BILL TO AMEND ACT 589 OF 1986, AS AMENDED, RELATING TO THE BEAUFORT COUNTY BOARD OF EDUCATION, SO AS TO REQUIRE CANDIDATES SEEKING ELECTION TO SUBMIT A STATEMENT OF CANDIDACY RATHER THAN SUBMIT SIGNED PETITIONS.
Read the first time and ordered placed on the Local and Uncontested Calendar.
H. 5077 (Word version) -- Rep. White: A BILL TO AMEND SECTION 6-25-113, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PAYMENT OF BONDS BY A JOINT AUTHORITY WATER AND SEWER SYSTEM, SO AS TO ALLOW A LIEN TO BE PLACED ON THE AUTHORITY'S PROPERTY IN ACCORDANCE WITH THE REVENUE BOND ACT FOR UTILITIES.
Read the first time and referred to the Committee on Finance.
H. 5078 (Word version) -- Reps. White and Cobb-Hunter: A BILL TO AMEND SECTION 4-10-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO VARIOUS LOCAL SALES AND USE TAXES, SO AS TO DEFINE "GENERAL ELECTION"; TO AMEND SECTIONS 4-10-330 AND 4-10-340, BOTH AS AMENDED, RELATING TO THE CAPITAL PROJECTS SALES TAX ACT, SO AS TO PROVIDE THAT THE TAX MUST TERMINATE ON APRIL THIRTIETH OF AN ODD- OR EVEN-NUMBERED YEAR.
Read the first time and referred to the Committee on Finance.
H. 5089 (Word version) -- Rep. Daning: A BILL TO AMEND SECTION 56-19-10, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TERMS AND THEIR DEFINITIONS REGARDING THE PROTECTION OF TITLES TO AND INTEREST IN MOTOR VEHICLES, SO AS TO ADD ADDITIONAL TERMS AND THEIR DEFINITIONS TO THIS SECTION; AND TO AMEND SECTION 56-19-265, AS AMENDED, RELATING TO LIENS RECORDED AGAINST MOTOR VEHICLES AND MOBILE HOMES, SO AS TO PROVIDE THAT A LIEN OR ENCUMBRANCE ON A MOTOR VEHICLE OR TITLED MOBILE HOME MUST BE NOTED ON THE PRINTED TITLE OR ELECTRONICALLY THROUGH THE DEPARTMENT OF MOTOR VEHICLES' ELECTRONIC TITLE AND LIEN SYSTEM, TO PROVIDE THAT THE TRANSMITTAL MUST BE DONE ELECTRONICALLY FOR BUSINESS ENTITIES, TO MAKE TECHNICAL CHANGES, TO PROVIDE THAT BUSINESS ENTITIES ARE SUBJECT TO CERTAIN FEES, TO PROVIDE THAT THE TRANSMITTAL AND RETRIEVAL OF DATA FEES ARE "OFFICIAL FEES", TO PROVIDE THAT CERTAIN BUSINESSES AND COMMERCIAL LIENHOLDERS MUST UTILIZE THE ELECTRONIC LIEN SYSTEM TO TRANSMIT AND RECEIVE ELECTRONIC LIEN INFORMATION, TO PROVIDE THE EFFECTIVE DATE AND LAPSE DATE FOR CERTAIN LIENS, TO PROVIDE THAT THE DEPARTMENT SHALL PUBLISH FORMS FOR THE PURPOSE OF FILING A LIEN CONTINUATION STATEMENT, AND TO PROVIDE THE PROCESS FOR FILING A LIEN CONTINUATION STATEMENT AND THE PERIOD FOR WHICH THE LIEN REMAINS IN EFFECT.
Read the first time and referred to the Committee on Transportation.
H. 5118 (Word version) -- Reps. Herbkersman and Newton: A BILL TO AMEND SECTION 56-2-105, AS AMENDED, RELATING TO THE ISSUANCE OF GOLF CART DECALS, THE REGISTRATION OF GOLF CARTS, AND THE OPERATION OF GOLF CARTS ALONG THE STATE'S HIGHWAYS, SO AS TO PROVIDE THAT CERTAIN MUNICIPALITIES AND COUNTIES MAY ADOPT ORDINANCES THAT ALLOW GOLF CARTS TO BE OPERATED AT NIGHT.
Read the first time and referred to the Committee on Transportation.
H. 5119 (Word version) -- Reps. Goldfinch, Putnam, Clemmons, Quinn, Fry, H. A. Crawford, Johnson, Burns, Collins, Merrill, Yow, Hamilton, McCoy, Jordan, Robinson-Simpson, Finlay, Kennedy, Spires, Ballentine, Bannister, Bedingfield, R. L. Brown, Delleney, Dillard, Duckworth, Felder, Funderburk, Gambrell, Hardee, Henderson, Hill, Lowe, Lucas, D. C. Moss, Nanney, Pitts, Ryhal, Sandifer, G. R. Smith, J. E. Smith, Stringer, Toole, Williams and Willis: A BILL TO AMEND SECTION 12-6-1140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEDUCTIONS FROM INDIVIDUAL TAXABLE INCOME, SO AS TO REQUIRE A MEMBER OF THE STATE GUARD TO COMPLETE A MINIMUM OF ONE HUNDRED NINETY-TWO HOURS OF TRAINING OR DRILL EACH YEAR IN ORDER TO QUALIFY FOR THE DEDUCTION; TO AMEND SECTION 25-1-635, AS AMENDED, RELATING TO LEGAL ASSISTANCE SERVICES FOR GUARD MEMBERS AND IMMEDIATE FAMILY MEMBERS, SO AS TO AUTHORIZE SOUTH CAROLINA STATE GUARD JUDGE ADVOCATES TO PROVIDE THESE SERVICES AND TO INCLUDE THEM WITHIN THE PERSONAL LIABILITY EXEMPTION; TO AMEND SECTIONS 25-3-20 AND 25-3-130, BOTH RELATING TO THE GOVERNOR'S AUTHORITY TO CALL THE STATE GUARD INTO DUTY, SO AS TO CLARIFY THE CIRCUMSTANCES AUTHORIZING THE GOVERNOR TO CALL THE STATE GUARD INTO DUTY AND TO PROVIDE THAT CIRCUMSTANCES INVOLVING A NATURAL OR MANMADE DISASTER, EMERGENCY, OR EMERGENCY PREPAREDNESS MAY WARRANT CALLING THE STATE GUARD INTO SERVICE; AND TO AMEND SECTION 25-3-140, RELATING TO PAY OF STATE GUARD MEMBERS ON ACTIVE DUTY, SO AS TO PROVIDE THAT STATE GUARD MEMBERS MAY RECEIVE A DAILY STIPEND OR PER DIEM PAY FOR REASONABLE EXPENSES, OR BOTH, IF APPROVED BY THE ADJUTANT GENERAL.
Read the first time and referred to the Committee on Finance.
H. 5172 (Word version) -- Reps. Fry, Henegan, Erickson, Long, Funderburk, Bernstein, Allison, Nanney, Robinson-Simpson, Norrell, Tinkler, H. A. Crawford, Cobb-Hunter, Ott, M. S. McLeod, Thayer, Whitmire, Johnson, Felder, Hardee, Goldfinch, Lowe, Jordan, Sandifer, Yow, Hill, Finlay, Gagnon, Jefferson, Williams, Knight, Govan, Rivers, Herbkersman, Bales, Ridgeway, Henderson, Duckworth, Dillard, Huggins, Atwater, Hicks, Gilliard, G. A. Brown, Whipper and Clemmons: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 16-3-2110 SO AS TO ENACT THE "SAFE HARBOR FOR EXPLOITED MINORS ACT", TO PROVIDE FOR PROTECTION OF THE IDENTITY OF MINOR VICTIMS OF TRAFFICKING IN PERSONS AND PROVIDE CERTAIN PROTECTIONS TO MINORS CHARGED WITH CERTAIN CRIMES INVOLVING PROSTITUTION AND COERCED INVOLVEMENT IN SUCH CRIMES, AMONG OTHER THINGS.
Read the first time and referred to the Committee on Judiciary.
H. 5218 (Word version) -- Reps. Gilliard, Anderson, Limehouse, Mack, Hosey, Whipper and R. L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 53-3-117 SO AS TO PROVIDE THAT THE MONTH OF MAY EVERY YEAR IS DECLARED "WATER SAFETY AWARENESS MONTH" IN THE STATE OF SOUTH CAROLINA; TO PROMOTE AN UNDERSTANDING OF WATER SAFETY PRACTICES AND THE CRITICAL IMPORTANCE OF WATER SAFETY IN AN EFFORT TO REDUCE DROWNING DEATHS AMONG CHILDREN IN THIS STATE; TO CREATE THE "WATER SAFETY AWARENESS IN SCHOOLS STUDY COMMITTEE"; TO EXAMINE THE ISSUE OF DROWNING DEATHS AMONG SCHOOL-AGED CHILDREN IN SOUTH CAROLINA; AND TO IDENTIFY A CURRICULUM TO
PROVIDE SWIMMING INSTRUCTION IN OUR PUBLIC SCHOOLS AS A MEASURE TO HELP PREVENT CHILD DROWNING DEATHS.
Read the first time and, on motion of Senator THURMOND, with unanimous consent, ordered placed on the Calendar without reference.
H. 5270 (Word version) -- Reps. Tallon, Bernstein and Pope: A BILL TO AMEND SECTION 8-11-83, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PAYROLL DEDUCTION FOR STATE EMPLOYEES' ASSOCIATION DUES, SO AS TO ALLOW MEMBERSHIP DUES FOR THE SOCIETY OF FORMER AGENTS OF THE STATE LAW ENFORCEMENT DIVISION TO BE DEDUCTED FROM THE COMPENSATION OF STATE RETIREES AND PAID OVER TO THE ASSOCIATION IN THE SAME MANNER OTHER MEMBERSHIP DUES ARE DEDUCTED AND PAID.
Read the first time and referred to the Committee on Finance.
H. 5278 (Word version) -- Rep. Bingham: A JOINT RESOLUTION TO AUTHORIZE THE DEPARTMENT OF EDUCATION TO CARRY FORWARD CERTAIN FUNDS APPROPRIATED IN THE 2015-2016 GENERAL APPROPRIATIONS ACT REGARDING SUPPLEMENTAL SUPPORT OF PROGRAMS AND SERVICES FOR STUDENTS WITH DISABILITIES SO AS TO MEET THE ESTIMATED MAINTENANCE OF EFFORT FOR THE INDIVIDUALS WITH DISABILITIES ACT (IDEA).
Read the first time and referred to the Committee on Finance.
H. 5279 (Word version) -- Reps. Stavrinakis, McCoy, Merrill, Sottile, Daning, Gilliard, Limehouse, Crosby, Tinkler, Whipper and R. L. Brown: A BILL TO AMEND ACT 340 OF 1967, AS AMENDED, RELATING TO THE CHARLESTON COUNTY SCHOOL DISTRICT, SO AS TO REVISE PROCEDURES CONCERNING THE ANNUAL DISTRICT BUDGET BY PROVIDING THE SCHOOL BOARD SHALL OBTAIN CERTIFICATION OF PROPERTY TAX REVENUE EXPECTED FOR THE BUDGET FROM THE COUNTY AUDITOR BEFORE THE BOARD MAY GIVE THE BUDGET SECOND READING, TO PROVIDE THAT WITHIN SIXTY DAYS FOLLOWING ENACTMENT OF THE ANNUAL STATE BUDGET, THE BOARD SHALL REVIEW AND, IF NEEDED TO AVOID OPERATING WITH A DEFICIT, AMEND THE ANNUAL DISTRICT BUDGET TO REFLECT FUNDS ACTUALLY APPROPRIATED BY THE GENERAL ASSEMBLY, TO PROVIDE THAT BEFORE JANUARY FIRST ANNUALLY THE BOARD SHALL REVIEW THE STATUS OF ITS FISCAL YEAR REVENUES AND EXPENDITURES TO DETERMINE THE EXTENT TO WHICH, IF ANY, THE DISTRICT IS OPERATING WITH A DEFICIT, AND TO PROVIDE IF THE DISTRICT DETERMINES THAT IT IS OPERATING WITH A DEFICIT, IT MUST AMEND ITS BUDGET TO ELIMINATE THE DEFICIT WITHIN SIXTY DAYS.
Read the first time and ordered placed on the Local and Uncontested Calendar.
H. 5292 (Word version) -- Rep. R. L. Brown: A CONCURRENT RESOLUTION TO COMMEND MARGARET PRESTON BLACKMER OF CHARLESTON FOR HER MANY YEARS OF DEDICATED SERVICE TO HER COMMUNITY AND TO WISH HER MANY BLESSINGS IN THE DAYS AHEAD.
The Concurrent Resolution was adopted, ordered returned to the House.
REPORT OF STANDING COMMITTEE
Senator VERDIN from the Committee on Agriculture and Natural Resources submitted a favorable with amendment report on:
S. 680 (Word version) -- Senators Rankin and Hembree: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 47-1-145, TO ENACT THE "PROVISIONS FOR COST OF ANIMAL CARE ACT OF 2015", TO PROVIDE THAT THE CUSTODIAN OF AN ANIMAL TAKEN INTO CUSTODY DUE TO CIVIL OR CRIMINAL VIOLATIONS BY ITS OWNER MAY PETITION THE COURT FOR EXPENSES RELATED TO PROVIDING CARE TO THE ANIMAL, TO ESTABLISH PROCEDURES FOR HEARING SUCH PETITIONS AND FOR THE COLLECTION AND USE OF FUNDS ORDERED TO BE PAID, TO PROVIDE THAT A PERSON WHO FAILS TO PAY SUCH FUNDS FORFEITS RIGHTS OF OWNERSHIP TO THE ANIMAL, TO PROVIDE FOR THE DISPOSITION OF SUCH AN ANIMAL, AND TO PROVIDE FOR THE RETURN OF FUNDS WHEN A PERSON IS NOT FOUND TO BE IN VIOLATION; TO AMEND SECTION 47-1-130, AS AMENDED, RELATING TO CRUELTY TO ANIMALS, TO PROVIDE THAT AGENTS OF THE SOUTH CAROLINA SOCIETY FOR THE PREVENTION OF CRUELTY TO ANIMALS, OR ANY OTHER SOCIETY DULY INCORPORATED FOR THAT PURPOSE, MAY ASSIST WITH A LAWFUL INVESTIGATION OF THIS CHAPTER, BUT MAY ONLY EFFECTUATE AN ARREST OF A PERSON IF THEY HAVE BEEN VESTED WITH THE POWER TO ARREST BY A SHERIFF OR THE GOVERNING BODY OF A COUNTY OR MUNICIPALITY; AND TO AMEND SECTION 47-1-140, AS AMENDED, RELATING TO NOTICE PROVIDED TO THE OWNER OF ANIMALS WHICH HAVE BEEN SEIZED FROM OTHERS UPON ARREST, TO REMOVE SPECIAL PROVISIONS FOR AGENTS OF THE SOUTH CAROLINA SOCIETY FOR THE PREVENTION OF CRUELTY TO ANIMALS, OR ANY OTHER SOCIETY DULY INCORPORATED FOR THAT PURPOSE.
Ordered for consideration tomorrow.
On motion of Senator VERDIN, with unanimous consent, the Bill was taken up for immediate consideration.
S. 680 (Word version) -- Senators Rankin and Hembree: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 47-1-145, TO ENACT THE "PROVISIONS FOR COST OF ANIMAL CARE ACT OF 2015", TO PROVIDE THAT THE CUSTODIAN OF AN ANIMAL TAKEN INTO CUSTODY DUE TO CIVIL OR CRIMINAL VIOLATIONS BY ITS OWNER MAY PETITION THE COURT FOR EXPENSES RELATED TO PROVIDING CARE TO THE ANIMAL, TO ESTABLISH PROCEDURES FOR HEARING SUCH PETITIONS AND FOR THE COLLECTION AND USE OF FUNDS ORDERED TO BE PAID, TO PROVIDE THAT A PERSON WHO FAILS TO PAY SUCH FUNDS FORFEITS RIGHTS OF OWNERSHIP TO THE ANIMAL, TO PROVIDE FOR THE DISPOSITION OF SUCH AN ANIMAL, AND TO PROVIDE FOR THE RETURN OF FUNDS WHEN A PERSON IS NOT FOUND TO BE IN VIOLATION; TO AMEND SECTION 47-1-130, AS AMENDED, RELATING TO CRUELTY TO ANIMALS, TO PROVIDE THAT AGENTS OF THE SOUTH CAROLINA SOCIETY FOR THE PREVENTION OF CRUELTY TO ANIMALS, OR ANY OTHER SOCIETY DULY INCORPORATED FOR THAT PURPOSE, MAY ASSIST WITH A LAWFUL INVESTIGATION OF THIS CHAPTER, BUT MAY ONLY EFFECTUATE AN ARREST OF A PERSON IF THEY HAVE BEEN VESTED WITH THE POWER TO ARREST BY A SHERIFF OR THE GOVERNING BODY OF A COUNTY OR MUNICIPALITY; AND TO AMEND SECTION 47-1-140, AS AMENDED, RELATING TO NOTICE PROVIDED TO THE OWNER OF ANIMALS WHICH HAVE BEEN SEIZED FROM OTHERS UPON ARREST, TO REMOVE SPECIAL PROVISIONS FOR AGENTS OF THE SOUTH CAROLINA SOCIETY FOR THE PREVENTION OF CRUELTY TO ANIMALS, OR ANY OTHER SOCIETY DULY INCORPORATED FOR THAT PURPOSE.
The Senate proceeded to the consideration of the Bill.
The Committee on Agriculture and Natural Resources proposed the following amendment (680R001.DR.VAS), which was adopted:
Amend the bill, as and if amended, by striking SECTION 2 and inserting:
/ SECTION 2. Chapter 1, Title 47 of the 1976 Code is amended by adding:
"Section 47-1-145. (A) Any person, organization, or other entity that is awarded custody of an animal under the provisions of Section 47-1-150 because of the arrest of a defendant for a violation of any provision of Chapter 1, Title 47 or Chapter 24, Title 16 and that provides services to the animal without compensation, may file a petition with the court requesting that the defendant, if found guilty, be ordered to deposit funds in an amount sufficient to secure payment of all the reasonable expenses incurred by the custodian in caring for and providing for the animal pending the disposition of the litigation. In the absence of a conviction, the county or municipality making the arrest shall pay the reasonable expenses of the custodian. For purposes of this section, 'court' refers to municipal or magistrate's court and 'reasonable expenses' includes the cost of providing food, water, shelter, and care, including medical care, but does not include extraordinary medical procedures.
(B) The court shall, at the time of adjudication, determine the actual cost of care for the animal the custodian incurred pursuant to subsection (A). Either party may demand that the trial be given priority over other cases.
(C)(1) If the court makes a final determination of the charges or claims against the defendant in his favor, then the defendant may recover custody of his animal.
(2) If the defendant is found guilty, the custodian of the animal may then determine whether the animal is suitable for adoption and whether adoption can be arranged for the animal. The animal may not be adopted by the defendant or by any person residing in the defendant's household if the defendant was found guilty. If no adoption can be arranged after the forfeiture, or the animal is unsuitable for adoption, the custodian shall humanely euthanize the animal.
(D) Within thirty days of an animal's impoundment, the animal's custodian must provide a good faith estimate, pursuant to subsection (A), of the daily custodial cost of the impounded animal. Upon receipt of the good faith estimate, the court shall then issue a notice to the defendant about his impounded animal that includes:
(1) an estimate of the daily custodial costs required to care for the animal;
(2) a statement that the defendant, if found guilty, shall be required to pay for the animal's care during impoundment; and
(3) a statement that the defendant at any time prior to final adjudication, has the right to forfeit ownership of the animal and avoid all accrued custodial costs related to the animal's care.
(E) The remedy provided for in this section is in addition to any other remedy provided by law." /
Amend the bill further, as and if amended, by striking SECTIONS 3 and 4 in their entirety.
Renumber sections to conform.
Amend title to conform.
The question then was 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 Campbell
Campsen Coleman Corbin
Courson Cromer Davis
Fair Grooms Hembree
Hutto Johnson Kimpson
Leatherman Malloy Martin, Larry
Martin, Shane Massey Matthews, John
Matthews, Margie McElveen Nicholson
Peeler Rankin Reese
Sabb Scott Setzler
Sheheen Thurmond Turner
Verdin Williams Young
Total--39
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 680--Ordered to a Third Reading
On motion of Senator VERDIN, with unanimous consent, S. 680 was ordered to receive a third reading on the next legislative day.
Senator VERDIN from the Committee on Agriculture and Natural Resources submitted a favorable with amendment report on:
S. 923 (Word version) -- Senator Bryant: A BILL TO AMEND SECTION 47-3-630 OF THE 1976 CODE, RELATING TO POLICE DOGS AND HORSES, TO PROVIDE THAT A PERSON WHO TORTURES, MUTILATES, INJURES, DISABLES, POISONS, OR KILLS A POLICE DOG OR HORSE MAY BE FINED UP TO THIRTY THOUSAND DOLLARS, MAY BE IMPRISONED FOR UP TO TEN YEARS, MUST PAY RESTITUTION TO COVER THE COST OF RESTORING OR REPLACING THE DOG OR HORSE INJURED OR KILLED, AND MUST PARTICIPATE IN ANIMAL-RELATED COMMUNITY SERVICE FOR ONE YEAR IN ADDITION TO OTHER PENALTIES.
Ordered for consideration tomorrow.
Senator GROOMS from the Committee on Transportation submitted a favorable report on:
S. 1243 (Word version) -- Senator Bennett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 138 TO CHAPTER 3, TITLE 56 SO AS TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ISSUE "CHASE AWAY CHILDHOOD CANCER" SPECIAL LICENSE PLATES.
Ordered for consideration tomorrow.
Message from the House
Columbia, S.C., April 28, 2016
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Concurrent Resolution to the Senate with amendments:
S. 950 (Word version) -- Senators Grooms and Thurmond: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE INTERSECTION LOCATED AT THE JUNCTION OF SOUTH CAROLINA HIGHWAY 162 AND SOUTH CAROLINA HIGHWAY 165 IN CHARLESTON COUNTY "CHARLESTON COUNTY POLICEMAN STEVEN BUIST HIOTT, JR. MEMORIAL HIGHWAY" AND ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS PORTION OF HIGHWAY THAT CONTAIN THE WORDS "CHARLESTON COUNTY POLICEMAN STEVEN BUIST HIOTT, JR. MEMORIAL HIGHWAY".
Very respectfully,
Speaker of the House
Placed on Calendar for consideration tomorrow.
HOUSE CONCURRENCE
S. 1277 (Word version) -- Senator Setzler: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR MRS. FRANKIE NEWMAN FOR HER MANY YEARS OF DEDICATED SERVICE TO THE WIL LOU GRAY OPPORTUNITY SCHOOL.
Returned with concurrence.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
AMENDED
HOUSE BILL RETURNED
The following Bill was amended, read the third time and ordered returned to the House with amendments.
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.
The Senate proceeded to the consideration of the Bill.
Senators YOUNG, MASSEY and SETZLER proposed the following amendment (4717R006.EB.TRY), which was adopted:
Amend the bill, as and if amended, SECTION 2, by striking subsection 46-1-160(B)(1) and inserting:
/ (B)(1) The Department of Agriculture shall administer the grant program authorized by this section. The Department of Revenue shall assist the Department of Agriculture in the administration of the grant program by providing auditing services, accounting services, and review and oversight of all financial aspects of the grant program. There is created the Farm Aid Advisory Board to make recommendations to the department regarding the duties of the department in administering the grant program. The Commissioner of Agriculture, or his designee, shall serve ex officio, as chairman of the board. Also, the Director of the Department of Revenue, or his designee, the Vice President for Public Service and Agriculture of Clemson Public Service Activities, or his designee, and the Vice President for Land Grant Services of South Carolina State Public Service Activities, or his designee, shall serve on the board. Finally, the following additional members shall be appointed to the board:
(a) the Commissioner of Agriculture shall appoint one member representing South Carolina Farm Bureau;
(b) the Commissioner of Agriculture shall appoint one member representing a farm credit association;
(c) the Director of the Department of Revenue shall appoint one member representing the crop insurance industry; and
(d) the Director of the Department of Revenue shall appoint one member who is an agricultural commodities producer. /
Amend the bill further, as and if amended, SECTION 2, by striking subsections 46-1-160(D)-(E) and inserting:
/ (D)(1) If the department determines that a person who received a grant provided inaccurate information, then the person shall refund the entire amount of the grant. If the department determines that a person who received a grant used the funds for ineligible expenses, then the person must refund the amount of the ineligible expenses. If the person does not refund the appropriate amount, the Department of Revenue shall utilize the provisions of the Setoff Debt Collection Act to collect the money from the person.
(2) If the department determines that a person knowingly provided false information to obtain a grant pursuant to this section or knowingly used funds for ineligible expenses, the person shall be subject to prosecution pursuant to Section 16-13-240.
(E)(1) From the 2014-2015 Contingency Reserve Fund, there is appropriated \$40,000,000 to the South Carolina Farm Aid Fund.
(2) Within forty-five days of the completion of the awarding of grants, but no later than June 30, 2017, the Farm Aid Advisory Board is dissolved. Any funds remaining in the fund upon dissolution shall lapse to the general fund. /
Renumber sections to conform.
Amend title to conform.
Senator SETZLER explained the amendment.
The question then was third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 33; Nays 3; Abstain 1
AYES
Alexander Allen Bennett
Bryant Campbell Campsen
Coleman Corbin Courson
Cromer Fair Hembree
Hutto Johnson Kimpson
Leatherman Malloy Martin, Larry
Martin, Shane Massey Matthews, John
Matthews, Margie McElveen Nicholson
Peeler Rankin Reese
Sabb Scott Setzler
Turner Williams Young
Total--33
NAYS
Bright Davis Thurmond
Total--3
ABSTAIN
Verdin
Total--1
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House.
S. 944 (Word version) -- Senators Peeler and Hembree: A BILL TO AMEND SECTION 10-1-30 OF THE 1976 CODE, RELATING TO USE OF STATE HOUSE LOBBIES, STEPS, AND OTHER PUBLIC BUILDINGS AND GROUNDS, TO REQUIRE THAT THE DEPARTMENT OF ADMINISTRATION CREATE A PERMIT PROCESS FOR EVENTS AND DEMONSTRATIONS ON THE STATE HOUSE GROUNDS; TO AMEND SECTION 10-11-310 OF THE 1976 CODE, RELATING TO THE DEFINITION OF CAPITOL GROUNDS, TO ADD PENDLETON STREET TO THE DEFINITION; AND TO AMEND SECTION 10-11-330 OF THE 1976 CODE, RELATING TO UNAUTHORIZED ENTRY INTO THE CAPITOL BUILDING, TO MAKE IT UNLAWFUL TO INCITE PHYSICAL VIOLENCE OR ENGAGE IN ACTIVITIES THAT ENCOURAGE UNLAWFUL CONDUCT, AND TO ALLOW LAW ENFORCEMENT TO REMOVE AND DISBURSE PERSONS THAT CAUSE A THREAT TO PUBLIC SECURITY, HEALTH, OR WELL-BEING.
The Senate proceeded to the consideration of the Bill.
The question being the third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 16; Nays 22
AYES
Alexander Campbell Courson
Cromer Fair Grooms
Hembree Johnson Leatherman
Martin, Larry Massey Matthews, John
Peeler Reese Turner
Young
Total--16
NAYS
Allen Bennett Bright
Bryant Campsen Coleman
Corbin Davis Hutto
Kimpson Malloy Martin, Shane
Matthews, Margie McElveen Nicholson
Rankin Sabb Scott
Setzler Thurmond Verdin
Williams
Total--22
SENT TO THE HOUSE
The following Bills and Resolution were read the third time and ordered sent to the House of Representatives:
S. 916 (Word version) -- Senators Malloy, Fair and M.B. Matthews: A BILL TO AMEND SECTION 63-19-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO JUVENILE JUSTICE CODE DEFINITIONS, SO AS TO PROVIDE THAT A "CHILD" OR "JUVENILE" MEANS A PERSON LESS THAN EIGHTEEN YEARS OF AGE, DOES NOT MEAN A PERSON SEVENTEEN YEARS OF AGE OR OLDER WHO IS CHARGED WITH A VIOLENT CRIME, AND THAT A PERSON SIXTEEN YEARS OF AGE WHO IS CHARGED WITH A CLASS A, B, C, OR D FELONY OR A FELONY WHICH PROVIDES FOR A MAXIMUM TERM OF IMPRISONMENT OF FIFTEEN YEARS OR MORE MUST BE PROVIDED THE RIGHT TO HAVE THE CASE REMANDED TO FAMILY COURT; AND TO AMEND SECTION 63-19-1210, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO JURISDICTION OVER A CASE INVOLVING A CHILD, SO AS TO PROVIDE THAT IF A CHILD WAS UNDER THE AGE OF EIGHTEEN YEARS AT THE TIME OF COMMITTING AN ALLEGED OFFENSE, THE CIRCUIT COURT SHALL TRANSFER THE CASE TO FAMILY COURT, THAT IF A CHILD BELOW EIGHTEEN YEARS OF AGE IS CHARGED WITH AN OFFENSE WHICH, IF COMMITTED BY AN ADULT, WOULD BE A VIOLENT CRIME, THE COURT MAY RETAIN JURISDICTION, AND THAT IF A CHILD UNDER THE AGE OF EIGHTEEN IS CHARGED WITH CERTAIN OFFENSES, THE COURT MAY BIND OVER THE CHILD TO A COURT WHICH WOULD HAVE TRIAL JURISDICTION OF THE OFFENSES IF COMMITTED BY AN ADULT.
S. 1272 (Word version) -- Senator Hayes: A JOINT RESOLUTION TO AUTHORIZE THE DEPARTMENT OF EDUCATION TO CARRY FORWARD CERTAIN FUNDS APPROPRIATED IN THE 2015-2016 GENERAL APPROPRIATIONS ACT REGARDING SUPPLEMENTAL SUPPORT OF PROGRAMS AND SERVICES FOR STUDENTS WITH DISABILITIES SO AS TO MEET THE ESTIMATED MAINTENANCE OF EFFORT FOR THE INDIVIDUALS WITH DISABILITIES ACT (IDEA).
CARRIED OVER
H. 4510 (Word version) -- Reps. Thayer, Hosey, Nanney, Hamilton, Erickson, Long, Hicks, McCoy, McEachern and Bedingfield: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 63-7-2400 SO AS TO ESTABLISH LIMITATIONS ON THE NUMBER OF FOSTER CHILDREN WHO MAY BE PLACED IN A FOSTER HOME.
On motion of Senator DAVIS, the Bill was carried over.
H. 3560 (Word version) -- Reps. Limehouse, Sottile, McCoy and Spires: A BILL TO AMEND SECTION 59-25-460, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE REQUIRED NOTICE AND HEARINGS FOR DISMISSAL OF A TEACHER, SO AS TO PROVIDE THAT THE BOARD MAY DESIGNATE A HEARING OFFICER TO CONDUCT A DISMISSAL HEARING AND ISSUE A REPORT WITH RECOMMENDATIONS, TO PROVIDE RELATED REQUIREMENTS OF A HEARING OFFICER, TO PROVIDE A HEARING MUST BE PRIVATE UNLESS THE TEACHER REQUESTS IN WRITING THAT THE HEARING BE PUBLIC, TO PROVIDE THAT A NOTICE OF DISMISSAL MUST BE GIVEN BY THE SUPERINTENDENT OR HIS DESIGNEE INSTEAD OF THE SCHOOL BOARD, TO SPECIFY USE OF A COURT REPORTER TO RECORD THE PROCEEDINGS, AND TO PROVIDE AN APPEALS PROCESS.
On motion of Senator LEATHERMAN, the Bill was 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 WILFUL 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 LEATHERMAN, the Bill was carried over.
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.
On motion of Senator LEATHERMAN, 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.
On motion of Senator LEATHERMAN, 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 LEATHERMAN, 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 LEATHERMAN, 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.
On motion of Senator LEATHERMAN, 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 LEATHERMAN, 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 LEATHERMAN, the Bill was carried over.
H. 3799 (Word version) -- Reps. Hixon, Simrill, Taylor, Loftis, Burns, Brannon, Spires, Yow, Clemmons, Riley, Corley, Collins, Clary, Hosey, Clyburn, King, Hicks, Knight, Bradley, Jefferson, Kirby, Huggins, Duckworth, Kennedy, Hamilton, Hardee, Johnson, Murphy, Felder, Alexander, Atwater, Ballentine, Bedingfield, Bowers, Cobb-Hunter, Daning, Delleney, Dillard, Forrester, Funderburk, Gagnon, Gambrell, Hiott, Howard, Lowe, W.J. McLeod, V.S. Moss, Nanney, Norman, Ott, Pitts, Pope, Ridgeway, Ryhal, G.R. Smith, Tallon, Thayer, Toole, Weeks, Wells, White, Willis, Chumley and Rivers: A BILL TO AMEND SECTION 23-31-215, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ISSUANCE OF CONCEALED WEAPON PERMITS, SO AS TO PROVIDE THAT SOUTH CAROLINA SHALL RECOGNIZE CONCEALED WEAPON PERMITS ISSUED BY GEORGIA AND NORTH CAROLINA UNDER CERTAIN CIRCUMSTANCES.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 3848 (Word version) -- Reps. Huggins, J.E. Smith, McKnight, Jefferson, Hosey, Atwater, Toole, Burns, Herbkersman, Ridgeway, Simrill, Kennedy, Ballentine and Henegan: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "SOUTH CAROLINA FOUNDING PRINCIPLES ACT" BY ADDING SECTION 59-29-155 SO AS TO REQUIRE THE COMPLETION OF A SEPARATE, FULL SEMESTER COURSE CONSISTING ONLY OF INSTRUCTION IN CERTAIN FOUNDING PRINCIPLES OF THE UNITED STATES OF AMERICA, TO REQUIRE A PASSING GRADE IN THE COURSE AND ON THE NATURALIZATION TEST FOR UNITED STATES CITIZENSHIP AS A CONDITION FOR GRADUATION FROM HIGH SCHOOL, AND TO PROVIDE RELATED REQUIREMENTS OF THE STATE BOARD OF EDUCATION AND THE LOCAL SCHOOL DISTRICTS.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 3891 (Word version) -- Reps. Toole, Long, Bedingfield, J.E. Smith, Anderson, Forrester, Rutherford and Sandifer: A BILL TO AMEND SECTION 56-31-50, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO SURCHARGES ON RENTAL OR PRIVATE PASSENGER MOTOR VEHICLES FOR THIRTY-ONE DAYS OR LESS, SO AS TO DEFINE NECESSARY TERMS, TO DELETE EXISTING SURCHARGE PROVISIONS, TO INSTEAD PROVIDE RENTAL COMPANIES ENGAGED IN THE BUSINESS OF RENTING VEHICLES FOR PERIODS OF NINETY DAYS OR LESS MAY CHARGE SEPARATELY STATED FEES WHICH MAY INCLUDE CERTAIN FEES AND TAXES, TO PROVIDE THE AMOUNT OF THE CHARGE MUST REPRESENT THE GOOD FAITH ESTIMATE BY THE MOTOR VEHICLE RENTAL COMPANY OF ITS DAILY CHARGE CALCULATED TO RECOVER ITS ACTUAL TOTAL ANNUAL RECOVERABLE COSTS, TO PROVIDE REQUIREMENTS FOR WHEN THE TOTAL AMOUNT OF THE VEHICLE LICENSE FEES COLLECTED BY A MOTOR VEHICLE RENTAL COMPANY IN ANY CALENDAR YEAR EXCEEDS THE ACTUAL COSTS OF THE CAR RENTAL COMPANY DURING THAT PERIOD, TO REQUIRE A CERTAIN DESCRIPTION OF VEHICLE LICENSE FEES IN THE VEHICLE RENTAL AGREEMENTS, AND TO PROVIDE THAT VEHICLE LICENSE FEES ARE SUBJECT TO CERTAIN SALES AND USE TAXES.
On motion of Senator LEATHERMAN, the Bill was carried over.
On motion of Senator LEATHERMAN, the Bill was carried over.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4931 (Word version) -- Reps. Gambrell, Gagnon, Bannister, Mitchell and Thayer: A BILL TO AMEND SECTION 38-53-85, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EDUCATION AND CONTINUING EDUCATION REQUIREMENTS FOR PROFESSIONAL BONDSMEN, SURETY BONDSMEN, AND RUNNERS, SO AS TO INCREASE THE NUMBER OF HOURS OF EDUCATION REQUIRED FOR LICENSURE AND FOR CONTINUING EDUCATION; AND TO AMEND SECTION 38-53-320, RELATING TO VISITING AND EXAMINING PROFESSIONAL BONDSMEN BY THE DEPARTMENT OF INSURANCE, SO AS TO SUBJECT SURETIES TO THESE VISITS AND EXAMINATIONS, AND TO REQUIRE BONDSMEN TO MAINTAIN A PROPERLY ZONED OFFICE IN THIS STATE THAT IS ACCESSIBLE TO THE GENERAL PUBLIC AND DEPARTMENT DURING NORMAL BUSINESS HOURS, AND TO REQUIRE THE BONDSMAN TO PROVIDE CERTAIN CONTACT INFORMATION.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4936 (Word version) -- Education and Public Works Committee: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-1-50 SO AS TO PROVIDE FOR EDUCATIONAL GOALS FOR ALL SOUTH CAROLINA HIGH SCHOOL GRADUATES AND THE STANDARDS AND AREAS OF LEARNING BY WHICH THESE GOALS ARE MEASURED.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4937 (Word version) -- Education and Public Works Committee: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-59-175 SO AS TO ESTABLISH THE SOUTH CAROLINA EDUCATION AND ECONOMIC DEVELOPMENT COORDINATING COUNCIL AND TO PROVIDE FOR ITS MEMBERSHIP, DUTIES, AND FUNCTIONS.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4938 (Word version) -- Education and Public Works Committee: A JOINT RESOLUTION TO PROVIDE THAT THE STATE DEPARTMENT OF EDUCATION, WITH THE ASSISTANCE OF OTHER ENTITIES, SHALL SURVEY STUDENTS ENROLLED IN THE STATE'S COLLEGES OF EDUCATION AND INCLUDE QUESTIONS INQUIRING AS TO WHETHER THE STUDENTS HAVE EVER CONSIDERED TEACHING IN A RURAL AND ECONOMICALLY CHALLENGED SCHOOL DISTRICT AND WHAT INCENTIVES, IF ANY, WOULD CAUSE THEM TO CONSIDER WORKING IN SUCH A DISTRICT.
On motion of Senator LEATHERMAN, the Resolution was carried over.
H. 4939 (Word version) -- Education and Public Works Committee: A BILL TO ESTABLISH A COMMITTEE COMPOSED OF SPECIFIED MEMBERS TO REVIEW ALL EXISTING STATE EDUCATION STATUTES AND REPORT TO THE GENERAL ASSEMBLY THOSE WHICH ARE OBSOLETE OR NO LONGER APPLICABLE; AND TO PROVIDE THAT THE STATE DEPARTMENT OF EDUCATION SHALL DEVELOP THE SYSTEM FOR PROVIDING SERVICES AND TECHNICAL ASSISTANCE FOR SCHOOL DISTRICTS ON A REGIONAL BASIS TO INCLUDE ACADEMIC ASSISTANCE AND ASSISTANCE WITH FINANCES, AND TO PROVIDE THAT THE SUPERINTENDENT OF EDUCATION SHALL REPORT THE DESIGN OF THE SYSTEM TO THE GENERAL ASSEMBLY NO LATER THAN DECEMBER 31, 2016, AND EVERY YEAR THEREAFTER REPORT THE PROGRESS OF THE SYSTEM IN REGARD TO ASSISTANCE PROVIDED TO LOCAL SCHOOL DISTRICTS, AND ALSO TO REQUIRE THAT THE DEPARTMENT OF EDUCATION SHALL MONITOR THE OPERATIONS OF SCHOOL BOARDS IN UNDERPERFORMING DISTRICTS TO DETERMINE IF THEY ARE OPERATING EFFICIENTLY AND EFFECTIVELY AND TO PROVIDE THAT THE DEPARTMENT SHALL MONITOR THE PROFESSIONAL DEVELOPMENT OF TEACHERS, STAFF, AND ADMINISTRATORS IN DISTRICTS IT DETERMINES ARE UNDERPERFORMING TO ASCERTAIN WHAT IMPROVEMENTS AND CHANGES ARE NECESSARY.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4940 (Word version) -- Education and Public Works Committee: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-3-110 SO AS TO PROVIDE FOR THE DUTIES, FUNCTIONS, AND RESPONSIBILITIES OF THE OFFICE OF TRANSFORMATION WITHIN THE SOUTH CAROLINA DEPARTMENT OF EDUCATION.
On motion of Senator LEATHERMAN, the Bill was carried over.
S. 1245 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF STATE FIRE MARSHAL, RELATING TO HYDROGEN FACILITIES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4621, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
S. 1246 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF STATE FIRE MARSHAL, RELATING TO FIRE PREVENTION AND LIFE SAFETY FOR SPECIAL OCCUPANCIES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4619, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
S. 1247 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF STATE FIRE MARSHAL, RELATING TO FIREWORKS AND PYROTECHNICS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4620, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
S. 1248 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF STATE FIRE MARSHAL, RELATING TO PORTABLE FIRE EXTINGUISHERS AND FIXED FIRE EXTINGUISHING SYSTEMS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4623, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4941 (Word version) -- Education and Public Works Committee: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-20-90 SO AS TO REQUIRE THE STATE DEPARTMENT OF EDUCATION TO DEVELOP AND ADOPT A STATEWIDE PROGRAM FOR IDENTIFYING FISCAL PRACTICES AND BUDGETARY CONDITIONS THAT, IF UNCORRECTED, COULD COMPROMISE THE FISCAL INTEGRITY OF A SCHOOL DISTRICT AND FOR ADVISING THE DISTRICT ON HOW TO TAKE APPROPRIATE CORRECTIVE ACTIONS, AND TO DIRECT THE DEPARTMENT TO PROMULGATE EMERGENCY REGULATIONS TO CARRY OUT THE PROVISIONS OF THIS SECTION; AND BY ADDING SECTION 59-20-95 SO AS TO REQUIRE THE STATE AUDITOR TO ADOPT THE STATEWIDE PROGRAM CREATED BY THE DEPARTMENT OF EDUCATION IN SECTION 59-20-90 AND USE IT TO IDENTIFY FISCAL PRACTICES AND BUDGETARY CONDITIONS THAT, IF UNCORRECTED, COULD COMPROMISE THE FISCAL INTEGRITY OF A STATE AGENCY THAT IS ALSO A LOCAL EDUCATION AGENCY AND TO ADVISE THE STATE AGENCY THAT IS ALSO A LOCAL EDUCATION AGENCY ON HOW TO TAKE APPROPRIATE CORRECTIVE ACTIONS, AND TO PROVIDE EXCEPTIONS TO ENABLE THE STATE AUDITOR TO DIRECT THE DEPARTMENT TO IMMEDIATELY ASSUME EMERGENCY MANAGEMENT OF THE STATE AGENCY THAT IS ALSO A LOCAL EDUCATION AGENCY FOR WHICH IT HAS MADE A DECLARATION OF FISCAL CAUTION OR FISCAL EMERGENCY, TO CONTINUE THIS EMERGENCY MANAGEMENT OF THE LOCAL EDUCATION AGENCY UNTIL THE STATE AUDITOR RELEASES THE STATE AGENCY THAT IS ALSO A LOCAL EDUCATION AGENCY FROM THE DECLARATION OF FISCAL CAUTION OR FISCAL EMERGENCY, AS APPLICABLE, AND TO DIRECT THE STATE AUDITOR TO PROMULGATE EMERGENCY REGULATIONS TO CARRY OUT THE PROVISIONS OF THIS SECTION.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4877 (Word version) -- Reps. Delleney, Pitts, Lucas, Bannister and Whipper: A BILL TO AMEND SECTION 63-3-40, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FAMILY COURT JUDGES ELECTED FROM EACH JUDICIAL CIRCUIT, SO AS TO ADD TWO ADDITIONAL FAMILY COURT JUDGES WHO SHALL BE AT LARGE AND MUST BE ELECTED WITHOUT REGARD TO THEIR COUNTY OR CIRCUIT OF RESIDENCE.
On motion of Senator LEATHERMAN, the Bill was carried over.
S. 1162 (Word version) -- Senators Peeler and McElveen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-61-55 SO AS TO REQUIRE THE SOUTH CAROLINA DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO CREATE PRIMARY AND SECONDARY CALL LISTS FOR AIR AMBULANCE SERVICE PROVIDERS, PROVIDE THE LISTS AND AIR AMBULANCE FEE SCHEDULES TO CERTAIN PERSONS AND ENTITIES, AND ESTABLISH AIR AMBULANCE SERVICE RESPONSE ZONES AND PROTOCOL FOR RESPONDING TO REQUESTS FOR AIR AMBULANCE SERVICES, TO REQUIRE AIR AMBULANCE SERVICE PROVIDERS TO PROVIDE FEE SCHEDULES UPON REQUEST, AND TO REQUIRE HOSPITALS TO MAKE REASONABLE EFFORTS TO INFORM PATIENTS OF AIR AMBULANCE FEES BEFORE REFERRAL, WITH EXCEPTIONS; TO AMEND SECTION 44-61-30, AS AMENDED, RELATING TO STANDARDS AND REGULATIONS TO IMPROVE EMERGENCY MEDICAL SERVICES, SO AS TO REQUIRE REGULATIONS FOR AIR AMBULANCE SERVICE PROVIDERS; AND BY ADDING SECTIONS 38-71-295 AND 42-5-75 SO AS TO DEFINE CERTAIN TERMS PERTAINING TO CLASSIFICATION OF EMERGENCY SERVICES FOR PURPOSES OF ACCIDENT AND HEALTH INSURANCE POLICIES AND WORKERS' COMPENSATION INSURANCE POLICIES.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4743 (Word version) -- Reps. Bedingfield, Dillard, Robinson-Simpson and Henderson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 50-11-935 SO AS TO PROVIDE THAT THE LAND OWNED AND MANAGED BY THE CONESTEE FOUNDATION AND KNOWN AS LAKE CONESTEE NATURE PARK IS DECLARED TO BE A WILDLIFE SANCTUARY.
On motion of Senator LEATHERMAN, the Bill was carried over.
H. 4786 (Word version) -- Regulations and Administrative Procedures Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE OFFICE OF THE GOVERNOR, RELATING TO LOCAL EMERGENCY PREPAREDNESS STANDARDS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4563, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
H. 5002 (Word version) -- Ways and Means Committee: A JOINT RESOLUTION TO APPROPRIATE MONIES FROM THE CAPITAL RESERVE FUND FOR FISCAL YEAR 2015-2016, AND TO ALLOW UNEXPENDED FUNDS APPROPRIATED TO BE CARRIED FORWARD TO SUCCEEDING FISCAL YEARS AND EXPENDED FOR THE SAME PURPOSES.
On motion of Senator LEATHERMAN, the Resolution was carried over.
S. 1175 (Word version) -- Senator L. Martin: A SENATE RESOLUTION TO AUTHORIZE THE GREENVILLE YOUNG MEN'S CHRISTIAN ASSOCIATION TO USE THE CHAMBER OF THE SOUTH CAROLINA SENATE AND ANY AVAILABLE COMMITTEE HEARING ROOMS IN THE GRESSETTE BUILDING FOR ITS YOUTH IN GOVERNMENT PROGRAM ON WEDNESDAY, NOVEMBER 16 THROUGH SATURDAY, NOVEMBER 19, 2016. HOWEVER, THE CHAMBER MAY NOT BE USED IF THE SENATE IS IN SESSION OR THE CHAMBER IS OTHERWISE UNAVAILABLE.
On motion of Senator LEATHERMAN, the Resolution was carried over.
THE SENATE PROCEEDED TO A CONSIDERATION OF H. 5001--GENERAL APPROPRIATIONS BILL
REPORT OF THE SENATE FINANCE COMMITTEE ADOPTED
DEBATE INTERRUPTED
H. 5001 (Word version) -- Ways and Means Committee: A BILL TO MAKE APPROPRIATIONS AND TO PROVIDE REVENUES TO MEET THE ORDINARY EXPENSES OF STATE GOVERNMENT FOR THE FISCAL YEAR BEGINNING JULY 1, 2016, TO REGULATE THE EXPENDITURE OF SUCH FUNDS, AND TO FURTHER PROVIDE FOR THE OPERATION OF STATE GOVERNMENT DURING THIS FISCAL YEAR AND FOR OTHER PURPOSES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Finance.
Senator LEATHERMAN spoke on the report.
Report of the Committee on Finance Adopted
Senator LEATHERMAN asked unanimous consent to make a motion that the Report of the Committee on Finance be adopted, with all members reserving the right to raise any Points of Order and to offer amendments without regard to questions of degree.
There was no objection and the motion was adopted.
The Report of the Committee on Finance was adopted.
On motion of Senator LEATHERMAN, with unanimous consent, staff members from the Revenue and Fiscal Affairs Office were authorized as necessary to be in that area behind the rail and, further, that Finance Committee staff and other staff designated by the President Pro Tempore were admitted to the floor of the Senate Chamber while debate was in progress on H. 5100, the General Appropriations Bill.
There was no objection and the motion was adopted.
On motion of Senator LEATHERMAN, with unanimous consent, the Senate agreed to proceed immediately to debate on the General Appropriations Bill upon conclusion of the morning hour on each day that it is in masthead status.
Report of the Subcommittee on K-12 Education
Senator DAVIS was recognized to report to the Senate regarding the work of the of the Subcommittee on K-12 Education.
Report of the Subcommittee on Higher Education
Senator COURSON, Chairman of the Subcommittee on Higher Education, was recognized to report to the Senate regarding the work of the subcommittee.
Report of the Subcommittee on
Judicial and Criminal Justice
Senator FAIR, Chairman of the Subcommittee on Judicial and Criminal Justice, was recognized to report to the Senate regarding the work of the subcommittee.
Report of the Subcommittee on
Health and Human Services
Senator ALEXANDER, Chairman of the Subcommittee on Health and Human Services, was recognized to report to the Senate regarding the work of the subcommittee.
Report of the Subcommittee on
Natural Resources and Economic Development
Senator SETZLER, Chairman of the Subcommittee on Natural Resources and Economic Development, was recognized to report to the Senate regarding the work of the subcommittee.
Report of the Subcommittee on
Transportation and Regulatory Laws
Senator J. MATTHEWS, Chairman of the Subcommittee on Transportation and Regulatory Laws, was recognized to report to the Senate regarding the work of the subcommittee.
Report of the Subcommittee on
Senator CROMER, on behalf of the Chairman of the Subcommittee on Constitutional and Administrative Laws, was recognized to report to the Senate regarding the work of the subcommittee.
THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CONCURRENCE
S. 1238 (Word version) -- Senators Leatherman and Williams: A BILL TO AMEND ACT 806 OF 1952, AS AMENDED, RELATING TO THE ANNUAL BUDGET FOR FLORENCE COUNTY SCHOOL DISTRICT TWO, SO AS TO ONLY REQUIRE A SEPARATE MEETING OF THE CITIZENS IF THE PROPOSED BUDGET REQUIRES A MILLAGE INCREASE.
The House returned the Bill with amendments.
The question being concurrence in the House amendments.
Senator LEATHERMAN explained the amendments.
On motion of Senator LEATHERMAN, the Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification.
On motion of Senator LEATHERMAN, the Senate agreed to stand adjourned to meet Tuesday, May 3, 2016, at 10:00 A.M.
On motion of Senators BRYANT, ALEXANDER, ALLEN, BENNETT, BRIGHT, CAMPBELL, CAMPSEN, CLEARY, COLEMAN, CORBIN, COURSON, CROMER, DAVIS, FAIR, GREGORY, GROOMS, HAYES, HEMBREE, HUTTO, JACKSON, JOHNSON, KIMPSON, LEATHERMAN, LOURIE, MALLOY, LARRY MARTIN, SHANE MARTIN, MASSEY, JOHN MATTHEWS, MARGIE BRIGHT MATTHEWS, McELVEEN, NICHOLSON, PEELER, RANKIN, REESE, SABB, SCOTT, SETZLER, SHEALY, SHEHEEN, THURMOND, TURNER, VERDIN, WILLIAMS and YOUNG, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Joshua "Josh" Michael Bedingfield of Belton, S.C. Josh was the son of Representative Eric Bedingfield. He was a graduate of Wren High School, attended Greenville Technical College and was working with Averitt Express. He was a member of Cedar Shoals Baptist Church. Josh enjoyed going to the lake, Clemson football and spending time with his family and friends. Josh was a loving son and brother, devoted fiancé and doting father who will be dearly missed.
and
| 2017-12-17T00:29:18 |
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|
http://legisquebec.gouv.qc.ca/en/showversion/cr/R-5,%20r.%201?code=se:5&pointInTime=20201022
|
### R-5, r. 1 - Regulation respecting contributions to the Québec Health Insurance Plan
5. The proportion referred to in the seventh paragraph of section 34.1.6 of the Act is the proportion determined in accordance with sections 22R1 to 22R21 of the Regulation respecting the Taxation Act (chapter I-3, r. 1).
O.C. 778-94, s. 5; O.C. 1463-2001, s. 3; O.C. 1116-2007, s. 2; O.C. 1303-2009, s. 2; O.C. 1182-2017, s. 1.
5. The proportion referred to in the fifth paragraph of section 34.1.6 of the Act is the proportion determined in accordance with sections 22R1 to 22R21 of the Regulation respecting the Taxation Act (chapter I-3, r. 1).
O.C. 778-94, s. 5; O.C. 1463-2001, s. 3; O.C. 1116-2007, s. 2; O.C. 1303-2009, s. 2.
| 2020-12-02T19:47:22 |
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|
https://pdglive.lbl.gov/Particle.action?node=B198&home=sumtabB
|
BOTTOM BARYONS($\boldsymbol B$ = $-1$) ${{\mathit \Lambda}_{{b}}^{0}}$ = ${{\mathit u}}{{\mathit d}}{{\mathit b}}$ , ${{\mathit \Xi}_{{b}}^{0}}$ = ${{\mathit u}}{{\mathit s}}{{\mathit b}}$ , ${{\mathit \Xi}_{{b}}^{-}}$ = ${{\mathit d}}{{\mathit s}}{{\mathit b}}$ , ${{\mathit \Omega}_{{b}}^{-}}$ = ${{\mathit s}}{{\mathit s}}{{\mathit b}}$ INSPIRE search
| 2021-06-19T04:15:51 |
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|
http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMDASetPreallocationCenterDimension.html
|
petsc-3.5.2 2014-09-08
Report Typos and Errors
DMDASetPreallocationCenterDimension
Determine the topology used to determine adjacency
Synopsis
#include "petscdmda.h"
PetscErrorCode DMDASetPreallocationCenterDimension(DM dm, PetscInt preallocCenterDim)
Input Parameters
dm - The DM object preallocCenterDim - The dimension of points which connect adjacent entries
Notes
FEM: Two points p and q are adjacent if q \in closure(star(p)), preallocCenterDim = dim
FVM: Two points p and q are adjacent if q \in star(cone(p)), preallocCenterDim = dim-1
FVM++: Two points p and q are adjacent if q \in star(closure(p)), preallocCenterDim = 0
| 2014-11-26T18:09:11 |
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|
http://abuse.wikia.com/wiki/International_Standard_Book_Number
|
## FANDOM
4,017 Pages
IMPORTANT:This page has used Creative Commons Licensed content from Wikipedia in either a refactored, modified, abridged, expanded, built on or 'strait from' text content! (view authors)
The International Standard Book Number (ISBN) is a unique[1][2] numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin,[3] for the booksellers and stationers W.H. Smith and others in 1966.[4]
The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO 2108.[4] (However, the 9-digit SBN code was used in the United Kingdom until 1974.) Currently, the ISO’s TC 46/SC 9 is responsible for the ISBN. The ISO on-line facility only refers back to 1978.[5]
Since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland EAN-13s.[6]
Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure; however, this is usually later rectified.[7]
A similar numeric identifier, the International Standard Serial Number (ISSN), identifies periodical publications such as magazines.
## OverviewEdit
An ISBN is assigned to each edition and variation (except reprintings) of a book.[8] The ISBN is 13 digits long if assigned after January 1, 2007, and 10 digits long if assigned before 2007. An International Standard Book Number consists of 4 or 5 parts:
1. for a 13 digit ISBN, a GS1 prefix: 978 or 979 (indicating the industry; in this case, 978 denotes book publishing)[9]
2. the group identifier, (language-sharing country group)[10]
3. the publisher code,[11]
4. the item number, (title of the book)[11] and
5. a checksum character or check digit.[11]
The ISBN separates its parts (group, publisher, title and check digit) with either a hyphen or a space. Other than the check digit, no part of the ISBN will have a fixed number of digits.[12]
### Group identifierEdit
The group identifier is a 1 to 5 digit number. The single digit group identifiers are: 0 or 1 for English-speaking countries; 2 for French-speaking countries; 3 for German-speaking countries; 4 for Japan; 5 for Russian-speaking countries, 7 for People's Republic of China. An example 5 digit group identifier is 99936, for Bhutan. The allocated group IDs are: 0–5, 600-617, 7, 80–94, 950–989, 9927–9989, and 99901–99967.[13] Some catalogs include books that were published with no ISBN but add a non-standard number with an as-yet unallocated 5-digit group such as 99985; this practice is not part of the standard. Books published in rare languages typically have longer group identifiers.[9]
The original standard book number (SBN) had no group identifier, but affixing a zero (0) as prefix to a 9-digit SBN creates a valid 10-digit ISBN. Group identifiers form a prefix code; compare with country calling codes.
### Publisher codeEdit
The national ISBN agency assigns the publisher number (cf. the category:ISBN agencies); the publisher selects the item number. Generally, a book publisher is not required to assign an ISBN, nor is it necessary for a book to display its number (except in China; see below). However, most book stores only handle ISBN-bearing merchandise.
A listing of all the 628,000 assigned publisher codes is published, and can be ordered in book form (558, US$915.46). The web site of the ISBN agency does not offer any free method of looking up publisher codes.[14] Partial lists have been compiled (from library catalogs) for the English-language groups: identifier 0 and identifier 1. Publishers receive blocks of ISBNs, with larger blocks allotted to publishers expecting to need them; a small publisher may receive ISBNs of one or more digits for the group identifier code, several digits for the publisher, and a single digit for the individual items. Once that block of ISBNs is used, the publisher may receive another block of ISBNs, with a different publisher number. Consequently, a publisher may have different allotted publisher numbers. There also may be more than one group identifier used in a country. This might occur if a popular identifier has used up all of its numbers. The cited list of identifiers shows this has happened in China and in more than a dozen other countries. By using variable block lengths, a large publisher will have few digits allocated for the publisher number and many digits allocated for titles; likewise countries publishing much will have few allocated digits for the group identifier, and many for the publishers and titles.[15] Here are some sample ISBN-10 codes, illustrating block length variations. ISBN Country or area Publisher 99921-58-10-7 Qatar NCCAH, Doha 9971-5-0210-0 Singapore World Scientific 960-425-059-0 Greece Sigma Publications 80-902734-1-6 Czech Republic; Slovakia Taita Publishers 85-359-0277-5 Brazil Companhia das Letras 1-84356-028-3 English-speaking area Simon Wallenberg Press 0-684-84328-5 English-speaking area Scribner 0-8044-2957-X English-speaking area Frederick Ungar 0-85131-041-9 English-speaking area J. A. Allen & Co. 0-943396-04-2 English-speaking area Willmann–Bell 0-9752298-0-X English-speaking area KT Publishing #### PatternEdit English-language publisher codes follow a systematic pattern, which allows their length to be easily determined, as follows:[16] Item number length 0- group identifier 1- group identifier Total From To Publishers From To Publishers 6 digits 0-00-xxxxxx-x 0-19-xxxxxx-x 20 1-00-xxxxxx-x 1-09-xxxxxx-x 10 30 5 digits 0-200-xxxxx-x 0-699-xxxxx-x 500 1-100-xxxxx-x 1-399-xxxxx-x 300 800 4 digits 0-7000-xxxx-x 0-8499-xxxx-x 1,500 1-4000-xxxx-x 1-5499-xxxx-x 1,500 3,000 3 digits 0-85000-xxx-x 0-89999-xxx-x 5,000 1-55000-xxx-x 1-86979-xxx-x 31,980 36,980 2 digits 0-900000-xx-x 0-949999-xx-x 50,000 1-869800-xx-x 1-998999-xx-x 129,200 179,200 1 digit 0-9500000-x-x 0-9999999-x-x 500,000 1-9990000-x-x 1-9999999-x-x 10,000 510,000 Total 557,020 Total 172,990 730,010 ## Check digitsEdit A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. It consists of a single digit computed from the other digits in the message. ### ISBN-10Edit The 2001 edition of the official manual of the International ISBN Agency says that the ISBN-10 check digit[17] — which is the last digit of the ten-digit ISBN — must range from 0 to 10 (the symbol X is used instead of 10) and must be such that the sum of all the ten digits, each multiplied by the integer weight, descending from 10 to 1, is a multiple of the number 11. Modular arithmetic is convenient for calculating the check digit using modulus 11. Each of the first nine digits of the ten-digit ISBN — excluding the check digit, itself — is multiplied by a number in a sequence from 10 to 2, and the remainder of the sum, with respect to 11, is computed. The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is 11 minus the remainder of the sum of the products. For example, the check digit for an ISBN-10 of 0-306-40615-? is calculated as follows:$ \begin{align} s &= 0\times 10 + 3\times 9 + 0\times 8 + 6\times 7 + 4\times 6 + 0\times 5 + 6\times 4 + 1\times 3 + 5\times 2 \\ &= 0 + 27 + 0 + 42 + 24 + 0 + 24 + 3 + 10 \\ &= 130 = 11\times 11 + 9\\ \end{align} $Thus the remainder is 9, the check digit is 2, and the complete sequence is ISBN 0-306-40615-2. Formally, the check digit calculation is:$ 10x_1 + 9x_2 + 8x_3 + 7x_4 + 6x_5 + 5x_6 + 4x_7 + 3x_8 + 2x_9 + x_{10} \equiv 0 \pmod{11}. $The value$ x_{10} $required to satisfy this condition might be 10; if so, an 'X' should be used. The two most common errors in handling an ISBN (e.g., typing or writing it) are an altered digit or the transposition of adjacent digits. Since 11 is a prime number, the ISBN check digit method ensures that these two errors will always be detected. However, if the error occurs in the publishing house and goes undetected, the book will be issued with an invalid ISBN.[18] #### Alternative calculationEdit The simplest way to verify an ISBN number is to compute a running sum of a running sum: bool is_isbn_valid(char digits[10]) { int i, a = 0, b = 0; for (i = 0; i < 10; i++) { a += digits[i]; // Assumed already converted from ASCII to 0..9 b += a; } return b % 11 == 0; } The ISBN-10 check-digit can also be calculated in a slightly easier way:$ x_{10} = ( 1x_1 + 2x_2 + 3x_3 + 4x_4 + 5x_5 + 6x_6 + 7x_7 +8x_8 + 9x_9 )\, \bmod\;11. $This is simply replacing 11 with 0, and each subtraction with its complement:$ -10 \equiv 1 \mod 11, $etc. For example, the check digit for an ISBN-10 of 0-306-40615-? is calculated as follows:$ (1 \times 0 + 2 \times 3 + 3 \times 0 + 4 \times 6 + 5 \times 4 + 6 \times 0 + 7 \times 6 + 8 \times 1 + 9 \times 5) \, \bmod\; 11 = 145 \, \bmod\; 11 = 2 $### ISBN-13Edit The 2005 edition of the International ISBN Agency's official manual[19] covering some ISBNs issued from January 2007, describes how the 13-digit ISBN check digit is calculated. The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed modulo 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero (0) replaces a ten (10), so, in all cases, a single check digit results. For example, the ISBN-13 check digit of 978-0-306-40615-? is calculated as follows: s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3 = 9 + 21 + 8 + 0 + 3 + 0 + 6 + 12 + 0 + 18 + 1 + 15 = 93 93 / 10 = 9 remainder 3 10 – 3 = 7 Thus, the check digit is 7, and the complete sequence is ISBN 978-0-306-40615-7. Formally, the ISBN-13 check digit calculation is:$ x_{13} = 10 - \big(x_1 + 3x_2 + x_3 + 3x_4 + \cdots + x_{11} + 3x_{12}\big) \,\bmod\, 10. \$
This check system — similar to the UPC check digit formula — does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes 3×6+1×1 = 19 to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be 3×1+1×6 = 9. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0-9 to express the check digit.
Additionally, If you triple the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits and then add them to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e. end in 0).
### Errors in usageEdit
Publishers and libraries have varied policies about the use of the ISBN check digit. Publishers sometimes fail to check the correspondence of a book title and its ISBN before publishing it; that failure causes book identification problems for libraries, booksellers, and readers.[20]
Most libraries and booksellers display the book record for an invalid ISBN issued by the publisher. The Library of Congress catalogue contains books published with invalid ISBNs, which it usually tags with the phrase "Cancelled ISBN".[21] However, book-ordering systems such as Amazon.com will not search for a book if an invalid ISBN is entered to its search engine.
## EAN format used in barcodes, and upgradingEdit
Currently, the barcodes on a book's back cover (or inside a mass-market paperback book's front cover) are EAN-13; they may have a separate barcode encoding five digits for the currency and the recommended retail price.[22] The number "978", the Bookland "country code", is prefixed to the ISBN in the barcode data, and the check digit is recalculated according to the EAN13 formula (modulo 10, 1x, and 3x weighting on alternate digits).
Partly because of a pending shortage in certain ISBN categories, the International Organization for Standardization (ISO) migrated to a thirteen-digit ISBN (ISBN-13); the process began January 1, 2005 and was to conclude January 1, 2007.[23] Thirteen-digit ISBNs are prefixed with "978" (and the check digit recalculated); as the "978" ISBN supply is exhausted, the "979" prefix will be introduced. This is expected to occur more rapidly outside the United States; originally, "979" was the "Musicland" code for musical scores with an ISMN, however, ISMN codes will differ visually as they begin with an "M" letter; the bar code represents the "M" as a zero (0), and for checksum purposes it will count as a 3.
Publisher identification code numbers are unlikely to be the same in the "978" and "979" ISBNs, like-wise, there is no guarantee that language area code numbers will be the same. Moreover, the ten-digit ISBN check digit generally is not the same as the thirteen-digit ISBN check digit. Because the EAN/UCC-13 is part of the Global Trade Item Number (GTIN) system (that includes the EAN/UCC-14, the UPC-12, and the EAN-8), it is expected that ISBN-generating software should accommodate fourteen-digit ISBNs.[24]
Barcode format compatibility is maintained, because (aside from the group breaks) the ISBN-13 barcode format is identical to the EAN barcode format of existing ISBN-10s. So, migration to an EAN-based system allows booksellers the use of a single numbering system for both books and non-book products that is compatible with existing ISBN-based data, with only minimal changes to information technology systems. Hence, many booksellers (e.g. Barnes & Noble) migrated to EAN barcodes as early as March 2005. Although many American and Canadian booksellers have been able to read EAN-13 barcodes before 2005, most general retailers could not read them. The upgrading of the UPC barcode system to full EAN-13, in 2005, eased migration to the ISBN-13 in North America. Moreover, by January 2007, most large book publishers added ISBN-13 barcodes alongside the ten-digit ISBN barcodes of books published before January 2007.[25]
• ESTC (English Short Title Catalogue)
• ISSN (International Standard Serial Number)
• VD 16 (Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des 16. Jahrhunderts)
• VD 17 (Verzeichnis der im deutschen Sprachraum erschienenen Drucke des 17. Jahrhunderts)
• LCCN (Library of Congress Control Number)
• OCLC number (Online Computer Library Center number [1])
• CODEN (serial publication identifier currently used by libraries; replaced by the ISSN for new works)
• SICI (Serial Item and Contribution Identifier)
• ASIN (Amazon Standard Identification Number)
• DOI (Digital Object Identifier)
• ISAN (International Standard Audiovisual Number)
• ISMN (International Standard Music Number)
• ISRC (International Standard Recording Code)
• ISWC (International Standard Musical Work Code)
• ISWN (International Standard Wine Number)
• List of group-0 ISBN publisher codes
• List of group-1 ISBN publisher codes
• Registration authority
## NotesEdit
1. Occasionally, publishers erroneously assign an ISBN to more than one title — the first edition of The Ultimate Alphabet and The Ultimate Alphabet Workbook have the same ISBN, 0-8050-0076-3. Conversely, books are published with several ISBNs: A German, second-language edition of Emil und die Detektive has the ISBNs 87-23-90157-8 (Denmark), 0-8219-1069-8 (United States), 91-21-15628-X (Sweden), 0-85048-548-7 (England) and 3-12-675495-3 (Germany).
2. in some cases, books sold only as sets share ISBNs. For example the Vance Integral Edition used only 2 ISBNs for 44 books.
3. Gordon Fosters original 1966 report can be found at Informaticsdevelopmentinstitute.net
4. 4.0 4.1 See discussion of the history at isbn.org.
7. 9.0 9.1 Hailman, Jack Parker (2008). Coding and redundancy: man-made and animal-evolved signals. Harvard University Press. p. 209. ISBN 978-0674027954.
8. Some books have several codes in the first block (A.M. Yaglom's Correlation Theory..., published by Springer Verlag, has two ISBNs, 0-387-96331-6 and 3-540-96331-6. Though Springer's 387 and 540 codes are different for English (0) and German (3); the same item number 96331 produces the same check digit: 6. Springer uses 431 as their publisher code for Japanese (4) and 4-431-96331-? would also have check digit ? = 6. Other Springer books in English have publisher code 817, and 0-817-96331-? would also get check digit ? = 6. This suggests special considerations were made for assigning Springer's publisher codes, as random assignments of different publisher codes would not lead the same item number to get the same check digit every time. Finding publisher codes for English and German, say, with this effect amounts to solving a linear equation in modular arithmetic.
9. 11.0 11.1 11.2 Reed, Kennette (2008). From Idea to Author: How to Become Successfully Published. KRA Publications. p. 47. ISBN 978-0971371842.
10. The international ISBN agency's ISBN User's Manual says: "The ten-digit number is divided into four parts of variable length, which must be separated clearly, by hyphens or spaces" although permitting their omission for internal data processing, as the prefix code ensures that no two codes begin the same way. If present, hyphens must be correctly placed; See hyphenation instructions at the isbn.org web site.
11. See a complete list of group identifiers. The web site at www.isbn.org now sometimes calls them group numbers. Their table of identifiers now refers to ISBN prefix ranges, which must be assumed to be group identifier ranges.
12. Splane, Lily (2002). The Book Book: A Complete Guide to Creating a Book on Your Computer. Anaphase II Publishing. p. 37. ISBN 978-0945962144.
13. Hyphenation Instructions. ISBN.org.
| 2018-09-22T01:08:26 |
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|
https://pos.sissa.it/396/003/
|
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Plenary presentation
Aspects of finite temperature QCD towards the chiral limit
A. Lahiri
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
QCD under extreme conditions has been studied for a long time, and the chiral limit has been a grey area mostly.
In this write-up of my talk, I review some of the recent developments made by the community to unveil various features of QCD
towards the chiral limit, which includes calculation of the chiral critical temperature and determination of the order
of chiral phase transition for various numbers of flavors. Acknowledging the importance of the studies regarding the
effective restoration of $U_A(1)$, I try to give a comprehensive overview about the various studies done in the last
few years in a comparative manner to realize the current status of the community in this regard. I also discuss
very recent efforts about the relevance of various energy-like observables w.r.t. the chiral phase transition.
DOI: https://doi.org/10.22323/1.396.0003
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2022-06-28T11:45:30 |
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https://zbmath.org/authors/?q=ai%3Ahardt.robert-m
|
## Hardt, Robert M.
Compute Distance To:
Author ID: hardt.robert-m Published as: Hardt, Robert; Hardt, Robert M.; Hardt, R.; Hardt, R. M. more...less Further Spellings: Hardt, Robert Miller Homepage: https://math.rice.edu/~hardt/ External Links: MGP · Wikidata · ResearchGate · dblp · GND · IdRef · theses.fr
Documents Indexed: 85 Publications since 1972, including 2 Books 2 Contributions as Editor Reviewing Activity: 3 Reviews Co-Authors: 49 Co-Authors with 64 Joint Publications 931 Co-Co-Authors
all top 5
### Co-Authors
23 single-authored 23 Lin, Fang Hua 10 Kinderlehrer, David 6 Simon, Leon Melvin 5 De Pauw, Thierry 5 Wolf, Michael 4 Rivière, Tristan 3 Han, Qing 2 dos Santos, Pedro F. 2 Lima-Filho, Paulo 2 Mou, Libin 2 Poon, Chicheung 2 Wang, Changyou 1 Allard, William K. 1 Alper, Onur 1 Caffarelli, Luis Ángel 1 Chen, Bin 1 Cox, Dennis D. 1 Cox, Steven J. 1 Digilov, Yan 1 Eggert, William 1 Fleming, Wendell Helms 1 Forman, Robin 1 Funk, Quentin 1 Hart, James B. 1 Hoffmann-Ostenhof, Maria 1 Hoffmann-Ostenhof, Thomas 1 Jauch, Michael 1 Jones, B. Frank jun. 1 Keyfitz, Barbara Lee 1 Klouček, Petr 1 Lambrechts, Pascal 1 Lau, Chiping 1 Lewis, James D. 1 Lewis, Rob 1 Loftis, Conor 1 Luskin, Mitchell 1 McCrory, Clint G. 1 Mehta, Aneesh 1 Morgan, Frank 1 Nadirashvili, Nikolai S. 1 Parks, Harold R. 1 Perez, Hector E. 1 Pfeffer, Washek Frank 1 Pitts, Jon T. 1 Rosales, Leobardo 1 Rosenberg, Harold 1 Shah, Anand 1 Sullivan, Dennis Parnell 1 Tonegawa, Yoshihiro 1 Turchin, Victor Éduardovich 1 Vaaler, Leslie 1 Volić, Ismar 1 Wermer, John 1 Zhou, Xiaodong 1 Ziemer, William Paul
all top 5
### Serials
7 Communications on Pure and Applied Mathematics 5 Indiana University Mathematics Journal 5 Manuscripta Mathematica 4 Communications in Partial Differential Equations 4 Calculus of Variations and Partial Differential Equations 3 Inventiones Mathematicae 3 Journal of Differential Geometry 2 Acta Mathematica 2 American Journal of Mathematics 2 Transactions of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 1 Communications in Mathematical Physics 1 Journal of Mathematical Analysis and Applications 1 Annales de l’Institut Fourier 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Publications Mathématiques 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 The Journal of Geometric Analysis 1 SIAM Journal on Mathematical Analysis 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Communications in Analysis and Geometry 1 Séminaire Équations aux Dérivées Partielles 1 Annals of Mathematics. Second Series 1 Algebraic & Geometric Topology 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bulletin of the American Mathematical Society 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 DMV Seminar 1 IAS/Park City Mathematics Series 1 Student Mathematical Library 1 Involve
all top 5
### Fields
36 Calculus of variations and optimal control; optimization (49-XX) 32 Global analysis, analysis on manifolds (58-XX) 23 Partial differential equations (35-XX) 16 Several complex variables and analytic spaces (32-XX) 13 Differential geometry (53-XX) 9 Measure and integration (28-XX) 9 Algebraic topology (55-XX) 7 Algebraic geometry (14-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Manifolds and cell complexes (57-XX) 4 Functions of a complex variable (30-XX) 3 Functional analysis (46-XX) 3 Fluid mechanics (76-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX)
### Citations contained in zbMATH Open
71 Publications have been cited 1,264 times in 921 Documents Cited by Year
Existence and partial regularity of static liquid crystal configurations. Zbl 0611.35077
Hardt, Robert; Kinderlehrer, David; Lin, Fang-Hua
1986
Mappings minimizing the $$L^ p$$ norm of the gradient. Zbl 0646.49007
Hardt, Robert; Lin, Fanghua
1987
Nodal sets for solutions of elliptic equations. Zbl 0692.35005
Hardt, Robert; Simon, Leon
1989
Boundary regularity and embedded solutions for the oriented Plateau problem. Zbl 0457.49029
Hardt, Robert; Simon, Leon
1979
Stratification of real analytic mappings and images. Zbl 0298.32003
Hardt, Robert M.
1975
Semi-algebraic local-triviality in semi-algebraic mappings. Zbl 0465.14012
Hardt, Robert M.
1980
A remark on $$H^ 1$$ mappings. Zbl 0618.58015
Hardt, Robert; Lin, Fang-Hua
1986
Stable defects of minimizers of constrained variational principles. Zbl 0657.49018
Hardt, R.; Kinderlehrer, D.; Lin, Fang-Hua
1988
Topological properties of subanalytic sets. Zbl 0303.32008
Hardt, Robert M.
1975
Minimal surfaces with isolated singularities. Zbl 0568.53033
Caffarelli, Luis; Hardt, Robert; Simon, Leon
1984
Critical sets of solutions to elliptic equations. Zbl 1144.35370
Hardt, R.; Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Nadirashvili, N.
1999
Area minimizing hypersurfaces with isolated singularities. Zbl 0577.49031
Hardt, Robert; Simon, Leon
1985
Geometric measure of singular sets of elliptic equations. Zbl 0940.35065
Han, Qing; Hardt, Robert; Lin, Fanghua
1998
Rectifiable and flat $$G$$ chains in a metric space. Zbl 1252.49070
De Pauw, Thierry; Hardt, Robert
2012
Partially constrained boundary conditions with energy minimizing mappings. Zbl 0686.35035
Hardt, Robert; Lin, Fang Hua
1989
Elastic plastic deformation. Zbl 0522.73029
Hardt, Robert; Kinderlehrer, David
1983
Triangulation of subanalytic sets and proper subanalytic maps. Zbl 0331.32006
Hardt, Robert M.
1977
An evolution problem for linear growth functionals. Zbl 0811.35061
Hardt, Robert; Zhou, Xiaodong
1994
Slicing and intersection theory for chains associated with real analytic varieties. Zbl 0234.32005
Hardt, Robert M.
1972
Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space. Zbl 0633.49020
Hardt, Robert; Lin, Fang-Hua
1987
Connecting topological Hopf singularities. Zbl 1150.58004
Hardt, Robert; Riviére, Tristan
2003
Mathematical questions of liquid crystal theory. Zbl 0704.76005
Hardt, R.; Kinderlehrer, D.
1988
Strong convergence of $$p$$-harmonic mappings. Zbl 0833.35038
Hardt, R.; Lin, F. H.; Mou, L.
1994
Singularities of harmonic maps. Zbl 0871.58026
Hardt, Robert M.
1997
Size minimization and approximating problems. Zbl 1022.49026
De Pauw, Thierry; Hardt, Robert
2003
Stability of singularities of minimizing harmonic maps. Zbl 0673.58016
Hardt, Robert; Lin, Fanghau
1989
Singularities for $$p$$-energy minimizing unit vector fields on planar domains. Zbl 0828.58008
Hardt, Robert; Lin, Fanghua
1995
The $$p$$-energy minimality of $$x/| x|$$. Zbl 0922.58015
Hardt, Robert; Lin, Fanghua; Wang, Changyou
1998
Axially symmetric harmonic maps minimizing a relaxed energy. Zbl 0769.58012
Hardt, Robert; Lin, Fang-Hua; Poon, Chi-Cheung
1992
Harmonic maps into round cones and singularities of nematic liquid crystals. Zbl 0790.58010
Hardt, Robert; Lin, Fang Hua
1993
Connecting rational homotopy type singularities. Zbl 1148.58003
Hardt, Robert; Rivière, Tristan
2008
Harmonic extensions of quasiconformal maps to hyperbolic space. Zbl 0881.30015
Hardt, Robert; Wolf, Michael
1997
On boundary regularity for integral currents or flat chains modulo two minimizing the integral of an elliptic integrand. Zbl 0385.49025
Hardt, Robert M.
1977
Seminar on geometric measure theory. (Schloss Mickeln, Düsseldorf, June 11–15, 1984). Zbl 0601.49029
Hardt, R.; Simon, L.
1986
The variety of configurations of static liquid crystals. Zbl 0723.58018
Hardt, Robert; Kinderlehrer, David; Lin, Fang Hau
1990
Singularities of $$p$$-energy minimizing maps. Zbl 0880.58006
Hardt, Robert; Lin, Fanghua; Wang, Changyou
1997
Some regularity results in ferromagnetism. Zbl 0958.35136
Hardt, Robert; Kinderlehrer, David
2000
The singular set of an energy minimizing map from $$B^ 4$$ to $$S^ 2$$. Zbl 0713.58006
Hardt, Robert; Lin, Fang-Hua
1990
Real homotopy theory of semi-algebraic sets. Zbl 1254.14066
Hardt, Robert; Lambrechts, Pascal; Turchin, Victor; Volić, Ismar
2011
Homology theory for real analytic and semianalytic sets. Zbl 0309.32004
Hardt, Robert M.
1975
Point and line singularities in liquid crystals. Zbl 0752.49018
Hardt, Robert M.
1990
Some basic theorems on flat $$G$$ chains. Zbl 1347.49073
De Pauw, Thierry; Hardt, Robert
2014
Harmonic maps with fixed singular sets. Zbl 0777.58013
Hardt, Robert; Mou, Libin
1992
Singular sets of higher order elliptic equations. Zbl 1290.35065
Han, Qing; Hardt, Robert; Lin, Fanghua
2003
Slicing and intersection theory for chains modulo $$\nu$$ associated with real analytic varieties. Zbl 0267.28010
Hardt, Robert M.
1973
Homology of normal chains and cohomology of charges. Zbl 1382.46059
De Pauw, Th.; Hardt, R. M.; Pfeffer, W. F.
2017
Prescribing singularities for $$p$$-harmonic maps. Zbl 0843.58029
Hardt, Robert; Chen, Bin
1995
Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053
Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell
1988
Uniqueness of nonparametric area minimizing currents. Zbl 0333.49043
Hardt, Robert M.
1977
Defects of liquid crystals with variable degree of orientation. Zbl 1418.58005
Alper, Onur; Hardt, Robert; Lin, Fang-Hua
2017
Application of scans and fractional power integrands. Zbl 1076.49021
De Pauw, Thierry; Hardt, Robert
2004
Variation of the Green function on Riemann surfaces and Whitney’s holomorphic stratification conjecture. Zbl 0735.30039
Hardt, Robert; Sullivan, Dennis
1988
Steenrod operations in subanalytic homology. Zbl 0424.55016
Hardt, Robert M.; McCrory, Clint G.
1979
Sullivan’s local Euler characteristic theorem. Zbl 0281.32005
Hardt, Robert M.
1974
Homology and images of semianalytic sets. Zbl 0291.32011
Hardt, Robert M.
1974
Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents. Zbl 0598.49028
Hardt, Robert M.; Pitts, Jon T.
1986
Boundary regularity and embedded solutions for the oriented plateau problem. Zbl 0421.49042
Hardt, Robert; Simon, Leon
1979
Some analytic bounds for subanalytic sets. Zbl 0547.32003
Hardt, Robert M.
1983
Variational principles with linear growth. Zbl 0706.49001
Hardt, Robert; Kinderlehrer, David
1989
Partial regularity for evolution problems with discontinuity. Zbl 0854.35020
Hardt, Robert; Tonegawa, Yoshihiro
1996
Axially symmetric harmonic maps minimizing a relaxed energy. Zbl 0769.58013
Hardt, Robert; Lin, Fang-Hua; Poon, Chi-Cheung
1992
Continuite locale Hölder de la tranche d’une chaîne sous-analytique par une application sous-analytique. Zbl 0445.32006
Hardt, Robert M.
1978
Some regularity results in plasticity. Zbl 0591.73047
Hardt, Robert M.; Kinderlehrer, David
1986
Tangential regularity near the $${\mathcal C}^ 1$$-boundary. Zbl 0598.49027
Hardt, Robert M.; Lin, Fang-Hua
1986
Existence et régularité des configurations statiques des cristaux liquides. (Existence and smoothness of static liquid crystal configurations). Zbl 0614.35072
Hardt, Robert; Kinderlehrer, David; Lin, Fang-Hua
1985
Axially symmetric harmonic maps. Zbl 0738.58014
Hardt, Robert M.
1991
Topological singular sets in functional spaces between manifolds. (Ensembles singuliers topologiques dans les espaces fonctionnels entre variétés.) Zbl 1057.58003
Hardt, Robert; Rivière, Tristan
2001
Convergence of Gibbs measures associated with simulated annealing. Zbl 1148.60051
Cox, Dennis D.; Hardt, Robert M.; Klouček, Petr
2008
Stratification via corank one projections. Zbl 0525.32011
Hardt, Robert M.
1983
Sequential weak approximation for maps of finite Hessian energy. Zbl 1455.46035
Hardt, Robert; Rivière, Tristan
2015
Slicing and intersection theory for the chains modulo $$\nu$$ associated with real analytic varieties. Zbl 0248.28018
Hardt, Robert M.
1973
Homology of normal chains and cohomology of charges. Zbl 1382.46059
De Pauw, Th.; Hardt, R. M.; Pfeffer, W. F.
2017
Defects of liquid crystals with variable degree of orientation. Zbl 1418.58005
Alper, Onur; Hardt, Robert; Lin, Fang-Hua
2017
Sequential weak approximation for maps of finite Hessian energy. Zbl 1455.46035
Hardt, Robert; Rivière, Tristan
2015
Some basic theorems on flat $$G$$ chains. Zbl 1347.49073
De Pauw, Thierry; Hardt, Robert
2014
Rectifiable and flat $$G$$ chains in a metric space. Zbl 1252.49070
De Pauw, Thierry; Hardt, Robert
2012
Real homotopy theory of semi-algebraic sets. Zbl 1254.14066
Hardt, Robert; Lambrechts, Pascal; Turchin, Victor; Volić, Ismar
2011
Connecting rational homotopy type singularities. Zbl 1148.58003
Hardt, Robert; Rivière, Tristan
2008
Convergence of Gibbs measures associated with simulated annealing. Zbl 1148.60051
Cox, Dennis D.; Hardt, Robert M.; Klouček, Petr
2008
Application of scans and fractional power integrands. Zbl 1076.49021
De Pauw, Thierry; Hardt, Robert
2004
Connecting topological Hopf singularities. Zbl 1150.58004
Hardt, Robert; Riviére, Tristan
2003
Size minimization and approximating problems. Zbl 1022.49026
De Pauw, Thierry; Hardt, Robert
2003
Singular sets of higher order elliptic equations. Zbl 1290.35065
Han, Qing; Hardt, Robert; Lin, Fanghua
2003
Topological singular sets in functional spaces between manifolds. (Ensembles singuliers topologiques dans les espaces fonctionnels entre variétés.) Zbl 1057.58003
Hardt, Robert; Rivière, Tristan
2001
Some regularity results in ferromagnetism. Zbl 0958.35136
Hardt, Robert; Kinderlehrer, David
2000
Critical sets of solutions to elliptic equations. Zbl 1144.35370
Hardt, R.; Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Nadirashvili, N.
1999
Geometric measure of singular sets of elliptic equations. Zbl 0940.35065
Han, Qing; Hardt, Robert; Lin, Fanghua
1998
The $$p$$-energy minimality of $$x/| x|$$. Zbl 0922.58015
Hardt, Robert; Lin, Fanghua; Wang, Changyou
1998
Singularities of harmonic maps. Zbl 0871.58026
Hardt, Robert M.
1997
Harmonic extensions of quasiconformal maps to hyperbolic space. Zbl 0881.30015
Hardt, Robert; Wolf, Michael
1997
Singularities of $$p$$-energy minimizing maps. Zbl 0880.58006
Hardt, Robert; Lin, Fanghua; Wang, Changyou
1997
Partial regularity for evolution problems with discontinuity. Zbl 0854.35020
Hardt, Robert; Tonegawa, Yoshihiro
1996
Singularities for $$p$$-energy minimizing unit vector fields on planar domains. Zbl 0828.58008
Hardt, Robert; Lin, Fanghua
1995
Prescribing singularities for $$p$$-harmonic maps. Zbl 0843.58029
Hardt, Robert; Chen, Bin
1995
An evolution problem for linear growth functionals. Zbl 0811.35061
Hardt, Robert; Zhou, Xiaodong
1994
Strong convergence of $$p$$-harmonic mappings. Zbl 0833.35038
Hardt, R.; Lin, F. H.; Mou, L.
1994
Harmonic maps into round cones and singularities of nematic liquid crystals. Zbl 0790.58010
Hardt, Robert; Lin, Fang Hua
1993
Axially symmetric harmonic maps minimizing a relaxed energy. Zbl 0769.58012
Hardt, Robert; Lin, Fang-Hua; Poon, Chi-Cheung
1992
Harmonic maps with fixed singular sets. Zbl 0777.58013
Hardt, Robert; Mou, Libin
1992
Axially symmetric harmonic maps minimizing a relaxed energy. Zbl 0769.58013
Hardt, Robert; Lin, Fang-Hua; Poon, Chi-Cheung
1992
Axially symmetric harmonic maps. Zbl 0738.58014
Hardt, Robert M.
1991
The variety of configurations of static liquid crystals. Zbl 0723.58018
Hardt, Robert; Kinderlehrer, David; Lin, Fang Hau
1990
The singular set of an energy minimizing map from $$B^ 4$$ to $$S^ 2$$. Zbl 0713.58006
Hardt, Robert; Lin, Fang-Hua
1990
Point and line singularities in liquid crystals. Zbl 0752.49018
Hardt, Robert M.
1990
Nodal sets for solutions of elliptic equations. Zbl 0692.35005
Hardt, Robert; Simon, Leon
1989
Partially constrained boundary conditions with energy minimizing mappings. Zbl 0686.35035
Hardt, Robert; Lin, Fang Hua
1989
Stability of singularities of minimizing harmonic maps. Zbl 0673.58016
Hardt, Robert; Lin, Fanghau
1989
Variational principles with linear growth. Zbl 0706.49001
Hardt, Robert; Kinderlehrer, David
1989
Stable defects of minimizers of constrained variational principles. Zbl 0657.49018
Hardt, R.; Kinderlehrer, D.; Lin, Fang-Hua
1988
Mathematical questions of liquid crystal theory. Zbl 0704.76005
Hardt, R.; Kinderlehrer, D.
1988
Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053
Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell
1988
Variation of the Green function on Riemann surfaces and Whitney’s holomorphic stratification conjecture. Zbl 0735.30039
Hardt, Robert; Sullivan, Dennis
1988
Mappings minimizing the $$L^ p$$ norm of the gradient. Zbl 0646.49007
Hardt, Robert; Lin, Fanghua
1987
Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space. Zbl 0633.49020
Hardt, Robert; Lin, Fang-Hua
1987
Existence and partial regularity of static liquid crystal configurations. Zbl 0611.35077
Hardt, Robert; Kinderlehrer, David; Lin, Fang-Hua
1986
A remark on $$H^ 1$$ mappings. Zbl 0618.58015
Hardt, Robert; Lin, Fang-Hua
1986
Seminar on geometric measure theory. (Schloss Mickeln, Düsseldorf, June 11–15, 1984). Zbl 0601.49029
Hardt, R.; Simon, L.
1986
Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents. Zbl 0598.49028
Hardt, Robert M.; Pitts, Jon T.
1986
Some regularity results in plasticity. Zbl 0591.73047
Hardt, Robert M.; Kinderlehrer, David
1986
Tangential regularity near the $${\mathcal C}^ 1$$-boundary. Zbl 0598.49027
Hardt, Robert M.; Lin, Fang-Hua
1986
Area minimizing hypersurfaces with isolated singularities. Zbl 0577.49031
Hardt, Robert; Simon, Leon
1985
Existence et régularité des configurations statiques des cristaux liquides. (Existence and smoothness of static liquid crystal configurations). Zbl 0614.35072
Hardt, Robert; Kinderlehrer, David; Lin, Fang-Hua
1985
Minimal surfaces with isolated singularities. Zbl 0568.53033
Caffarelli, Luis; Hardt, Robert; Simon, Leon
1984
Elastic plastic deformation. Zbl 0522.73029
Hardt, Robert; Kinderlehrer, David
1983
Some analytic bounds for subanalytic sets. Zbl 0547.32003
Hardt, Robert M.
1983
Stratification via corank one projections. Zbl 0525.32011
Hardt, Robert M.
1983
Semi-algebraic local-triviality in semi-algebraic mappings. Zbl 0465.14012
Hardt, Robert M.
1980
Boundary regularity and embedded solutions for the oriented Plateau problem. Zbl 0457.49029
Hardt, Robert; Simon, Leon
1979
Steenrod operations in subanalytic homology. Zbl 0424.55016
Hardt, Robert M.; McCrory, Clint G.
1979
Boundary regularity and embedded solutions for the oriented plateau problem. Zbl 0421.49042
Hardt, Robert; Simon, Leon
1979
Continuite locale Hölder de la tranche d’une chaîne sous-analytique par une application sous-analytique. Zbl 0445.32006
Hardt, Robert M.
1978
Triangulation of subanalytic sets and proper subanalytic maps. Zbl 0331.32006
Hardt, Robert M.
1977
On boundary regularity for integral currents or flat chains modulo two minimizing the integral of an elliptic integrand. Zbl 0385.49025
Hardt, Robert M.
1977
Uniqueness of nonparametric area minimizing currents. Zbl 0333.49043
Hardt, Robert M.
1977
Stratification of real analytic mappings and images. Zbl 0298.32003
Hardt, Robert M.
1975
Topological properties of subanalytic sets. Zbl 0303.32008
Hardt, Robert M.
1975
Homology theory for real analytic and semianalytic sets. Zbl 0309.32004
Hardt, Robert M.
1975
Sullivan’s local Euler characteristic theorem. Zbl 0281.32005
Hardt, Robert M.
1974
Homology and images of semianalytic sets. Zbl 0291.32011
Hardt, Robert M.
1974
Slicing and intersection theory for chains modulo $$\nu$$ associated with real analytic varieties. Zbl 0267.28010
Hardt, Robert M.
1973
Slicing and intersection theory for the chains modulo $$\nu$$ associated with real analytic varieties. Zbl 0248.28018
Hardt, Robert M.
1973
Slicing and intersection theory for chains associated with real analytic varieties. Zbl 0234.32005
Hardt, Robert M.
1972
all top 5
### Cited by 904 Authors
34 Lin, Fang Hua 31 Hardt, Robert M. 14 Wang, Changyou 12 Duzaar, Frank 12 Rivière, Tristan 11 Hong, Minchun 10 Canevari, Giacomo 9 Pan, Xingbin 8 Giaquinta, Mariano 8 Marchese, Andrea 8 White, Brian Cabell 7 Ambrosio, Luigi 7 Basu, Saugata 7 Bethuel, Fabrice 7 Coskunuzer, Baris 7 Dutertre, Nicolas 7 Isobe, Takeshi 7 Orlandi, Giandomenico 7 Trélat, Emmanuel 6 Brézis, Haïm 6 Goresky, Robert Mark 6 Grotowski, Joseph F. 6 Lei, Yutian 6 Meeks, William Hamilton III 6 Millot, Vincent 6 Minicozzi, William Philip II 6 Modica, Giuseppe 6 Simon, Leon Melvin 6 Van Schaftingen, Jean 6 Wang, Dehua 6 Wei, Shihshu Walter 6 Zheng, Shenzhou 5 Bierstone, Edward 5 Bousquet, Pierre 5 Colding, Tobias Holck 5 De Lellis, Camillo 5 De Pauw, Thierry 5 Frehse, Jens 5 Jiang, Ning 5 Mazzieri, Lorenzo 5 Milman, Pierre D. 5 Mironescu, Petru 5 Morgan, Frank 5 Mucci, Domenico 5 Parusiński, Adam 5 Petrache, Mircea 5 Soucek, Jiri 5 Strzelecki, Paweł 5 Stuvard, Salvatore 5 Szafraniec, Zbigniew 5 Valette, Guillaume 5 Veronelli, Giona 5 Wunderli, Thomas 5 Zarnescu, Arghir Dani 5 Zheng, Yuxi 4 Agostiniani, Virginia 4 Alouges, François 4 Bögelein, Verena 4 Chen, Geng 4 Dávila, Juan 4 Fardoun, Ali 4 Fuchs, Martin 4 Golovaty, Dmitry 4 Hoffman, David A. 4 Huang, Tao 4 Jost, Jürgen 4 Kukavica, Igor 4 Lamy, Xavier 4 Liu, Chun 4 Liu, Hairong 4 Luo, Yi-Long 4 Majumdar, Apala 4 Massaccesi, Annalisa 4 McCrory, Clint G. 4 Mingione, Giuseppe 4 Mou, Libin 4 Onninen, Jani 4 Peralta-Salas, Daniel 4 Pollack, Richard M. 4 Privat, Yannick 4 Rosales, Leobardo 4 Roy, Marie-Françoise 4 Scheven, Christoph 4 Sire, Yannick 4 Tian, Long 4 Tonegawa, Yoshihiro 4 Valette-Stasica, Anna 4 Valtorta, Daniele 4 Wang, Wei 4 Wei, Juncheng 4 Wickramasekera, Neshan 4 Yang, Xiaoping 4 Zhu, Jiuyi 3 Alama, Stan 3 Bertsch, Michiel 3 Bourgoin, Jean-Christophe 3 Bronsard, Lia 3 Brunovský, Pavol 3 Campos, Ricardo 3 Caraballo, David G. ...and 804 more Authors
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### Cited in 188 Serials
70 Calculus of Variations and Partial Differential Equations 41 Archive for Rational Mechanics and Analysis 35 Manuscripta Mathematica 34 The Journal of Geometric Analysis 32 Communications in Partial Differential Equations 28 Transactions of the American Mathematical Society 26 Journal of Differential Equations 26 Journal of Functional Analysis 24 Journal of Mathematical Analysis and Applications 23 Inventiones Mathematicae 21 Mathematische Zeitschrift 19 Communications in Mathematical Physics 19 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 Advances in Mathematics 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 Mathematische Annalen 13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 12 Proceedings of the American Mathematical Society 12 SIAM Journal on Mathematical Analysis 11 Annales de l’Institut Fourier 10 Communications on Pure and Applied Mathematics 10 Acta Mathematica 10 Bulletin of the American Mathematical Society. New Series 9 Duke Mathematical Journal 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Geometriae Dedicata 8 Annals of Global Analysis and Geometry 8 Annals of Mathematics. Second Series 8 Advances in Calculus of Variations 7 Journal d’Analyse Mathématique 7 Discrete and Continuous Dynamical Systems 7 Acta Mathematica Sinica. English Series 7 Nonlinear Analysis. Theory, Methods & Applications 6 Journal of the American Mathematical Society 5 Journal of Computational Physics 5 Journal of Mathematical Physics 5 Publications Mathématiques 5 Journal für die Reine und Angewandte Mathematik 5 Memoirs of the American Mathematical Society 5 Revista Matemática Iberoamericana 5 Geometric and Functional Analysis. GAFA 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 NoDEA. Nonlinear Differential Equations and Applications 5 Communications in Contemporary Mathematics 4 Applied Mathematics and Optimization 4 Numerische Mathematik 4 Zeitschrift für Analysis und ihre Anwendungen 4 Journal of Symbolic Computation 4 Science in China. Series A 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Geometry & Topology 4 Journal of the European Mathematical Society (JEMS) 4 Foundations of Computational Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Israel Journal of Mathematics 3 Mathematical Methods in the Applied Sciences 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Compositio Mathematica 3 Journal of Differential Geometry 3 Tohoku Mathematical Journal. Second Series 3 Physica D 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Optimization 3 Journal of Mathematical Fluid Mechanics 3 Advances in Geometry 3 Nonlinear Analysis. Real World Applications 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Bulletin of the American Mathematical Society 3 Science China. Mathematics 3 Analysis and Geometry in Metric Spaces 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Mathematics of Computation 2 Journal of Geometry and Physics 2 Automatica 2 Glasgow Mathematical Journal 2 Indiana University Mathematics Journal 2 Journal of Algebra 2 Journal of Mathematical Economics 2 Nagoya Mathematical Journal 2 SIAM Journal on Numerical Analysis 2 Tokyo Journal of Mathematics 2 Topology and its Applications 2 Chinese Annals of Mathematics. Series B 2 Asymptotic Analysis 2 Forum Mathematicum 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Games and Economic Behavior 2 Linear Algebra and its Applications 2 Journal of Dynamics and Differential Equations 2 Journal of Mathematical Sciences (New York) 2 Selecta Mathematica. New Series 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Journal of Dynamical and Control Systems 2 Communications on Pure and Applied Analysis 2 Journal of Fixed Point Theory and Applications 2 Journal of Singularities 2 Journal of Spectral Theory ...and 88 more Serials
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### Cited in 54 Fields
384 Partial differential equations (35-XX) 254 Global analysis, analysis on manifolds (58-XX) 244 Calculus of variations and optimal control; optimization (49-XX) 207 Differential geometry (53-XX) 115 Fluid mechanics (76-XX) 70 Algebraic geometry (14-XX) 66 Several complex variables and analytic spaces (32-XX) 60 Statistical mechanics, structure of matter (82-XX) 41 Manifolds and cell complexes (57-XX) 35 Functional analysis (46-XX) 34 Mechanics of deformable solids (74-XX) 32 Measure and integration (28-XX) 30 Numerical analysis (65-XX) 28 Algebraic topology (55-XX) 23 Real functions (26-XX) 19 Quantum theory (81-XX) 18 Functions of a complex variable (30-XX) 18 Potential theory (31-XX) 16 Systems theory; control (93-XX) 15 Dynamical systems and ergodic theory (37-XX) 12 Mathematical logic and foundations (03-XX) 12 Operator theory (47-XX) 12 Computer science (68-XX) 10 Operations research, mathematical programming (90-XX) 9 Ordinary differential equations (34-XX) 9 Optics, electromagnetic theory (78-XX) 9 Information and communication theory, circuits (94-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Relativity and gravitational theory (83-XX) 5 Category theory; homological algebra (18-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 General topology (54-XX) 4 Combinatorics (05-XX) 4 Topological groups, Lie groups (22-XX) 4 Geometry (51-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Convex and discrete geometry (52-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistics (62-XX) 3 Biology and other natural sciences (92-XX) 2 History and biography (01-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Nonassociative rings and algebras (17-XX) 2 $$K$$-theory (19-XX) 2 Group theory and generalizations (20-XX) 2 Mechanics of particles and systems (70-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)
### Wikidata Timeline
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| 2022-06-28T20:52:19 |
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http://itl.nist.gov/div898/handbook/pmc/section3/pmc323.htm
|
6. Process or Product Monitoring and Control
6.3. Univariate and Multivariate Control Charts
6.3.2. What are Variables Control Charts?
## CUSUM Control Charts
CUSUM is an efficient alternative to Shewhart procedures CUSUM charts, while not as intuitive and simple to operate as Shewhart charts, have been shown to be more efficient in detecting small shifts in the mean of a process. In particular, analyzing ARL's for CUSUM control charts shows that they are better than Shewhart control charts when it is desired to detect shifts in the mean that are 2 sigma or less.
CUSUM works as follows: Let us collect $$m$$ samples, each of size $$n$$, and compute the mean of each sample. Then the cumulative sum (CUSUM) control chart is formed by plotting one of the following quantities:
Definition of cumulative sum $$S_{m} = \sum_{i=1}^{m}(\bar{x}_{i} - \hat{\mu}_{0}) \,\,\,\,\,\,\, \mbox{or} \,\,\,\,\,\,\, S_{m}' = \frac{1}{\sigma_{\bar{x}}} \sum_{i=1}^{m}(\bar{x}_{i} - \hat{\mu}_{0})$$
against the sample number $$m$$, where $$\hat{\mu}_0$$ is the estimate of the in-control mean and $$\sigma_{\bar{x}}$$ is the known (or estimated) standard deviation of the sample means. The choice of which of these two quantities is plotted is usually determined by the statistical software package. In either case, as long as the process remains in control centered at $$\hat{\mu}_0$$, the CUSUM plot will show variation in a random pattern centered about zero. If the process mean shifts upward, the charted CUSUM points will eventually drift upwards, and vice versa if the process mean decreases.
V-Mask used to determine if process is out of control A visual procedure proposed by Barnard in 1959, known as the V-Mask, is sometimes used to determine whether a process is out of control. More often, the tabular form of the V-Mask is preferred. The tabular form is illustrated later in this section.
A V-Mask is an overlay shape in the form of a V on its side that is superimposed on the graph of the cumulative sums. The origin point of the V-Mask (see diagram below) is placed on top of the latest cumulative sum point and past points are examined to see if any fall above or below the sides of the V. As long as all the previous points lie between the sides of the V, the process is in control. Otherwise (even if one point lies outside) the process is suspected of being out of control.
Sample V-Mask demonstrating an out of control process
Interpretation of the V-Mask on the plot In the diagram above, the V-Mask shows an out of control situation because of the point that lies above the upper arm. By sliding the V-Mask backwards so that the origin point covers other cumulative sum data points, we can determine the first point that signaled an out-of-control situation. This is useful for diagnosing what might have caused the process to go out of control. From the diagram it is clear that the behavior of the V-Mask is determined by the distance $$k$$ (which is the slope of the lower arm) and the rise distance $$h$$. These are the design parameters of the V-Mask. Note that we could also specify $$d$$ and the vertex angle (or, as is more common in the literature, $$\theta = 1/2$$ of the vertex angle) as the design parameters, and we would end up with the same V-Mask. In practice, designing and manually constructing a V-Mask is a complicated procedure. A CUSUM spreadsheet style procedure shown below is more practical, unless you have statistical software that automates the V-Mask methodology. Before describing the spreadsheet approach, we will look briefly at an example of a V-Mask in graph form. V-Mask Example An example will be used to illustrate the construction and application of a V-Mask. The 20 data points 324.925, 324.675, 324.725, 324.350, 325.350, 325.225, 324.125, 324.525, 325.225, 324.600, 324.625, 325.150, 328.325, 327.250, 327.825, 328.500, 326.675, 327.775, 326.875, 328.350 are each the average of samples of size 4 taken from a process that has an estimated mean of 325. Based on process data, the process standard deviation is 1.27 and therefore the sample means have a standard deviation of $$1.27 / (4^{1/2}) = 0.635$$. We can design a V-Mask using $$h$$ and $$k$$ or we can use an $$\alpha$$ and $$\beta$$ design approach. For the latter approach we must specify $$\alpha$$: the probability of a false alarm, i.e., concluding that a shift in the process has occurred, while in fact it did not, $$\beta$$: the probability of not detecting that a shift in the process mean has, in fact, occurred, and $$\delta$$ (delta): the amount of shift in the process mean that we wish to detect, expressed as a multiple of the standard deviation of the data points (which are the sample means). Note: Technically, $$\alpha$$ and $$\beta$$ are calculated in terms of one sequential trial where we monitor $$S_m$$ until we have either an out-of-control signal or $$S_m$$ returns to the starting point (and the monitoring begins, in effect, all over again). The values of $$h$$ and $$k$$ are related to $$\alpha$$, $$\beta$$, and $$\delta$$ based on the following equations (adapted from Montgomery, 2000). $$\begin{eqnarray} k & = & \frac{\delta \sigma_{x}}{2} \\ \hspace{.2in} \\ d & = & \frac{2}{\delta^2}\mbox{ln } \left( \frac{1-\beta}{\alpha} \right) \\ \hspace{.2in} \\ h & = & d k \end{eqnarray}$$ In our example we choose $$\alpha = 0.0027$$ (equivalent to the plus or minus 3 sigma criteria used in a standard Shewhart chart), and $$\beta = 0.01$$. Finally, we decide we want to quickly detect a shift as large as 1 sigma, which sets $$\delta = 1$$. CUSUM Chart with V-Mask When the V-Mask is placed over the last data point, the mask clearly indicates an out of control situation. CUSUM chart after moving V-Mask to first out of control point We next move the V-Mask and back to the first point that indicated the process was out of control. This is point number 14, as shown below.
Rule of thumb for choosing $$h$$ and $$k$$ Note: A general rule of thumb (Montgomery) if one chooses to design with the $$h$$ and $$k$$ approach, instead of the $$\alpha$$ and $$\beta$$ method illustrated above, is to choose $$k$$ to be half the $$\delta$$ shift (0.5 in our example) and $$h$$ to be around 4 or 5.
To generate the tabular form we use the $$h$$ and $$k$$ h and k parameters expressed in the original data units. It is also possible to use sigma units.
The following quantities are calculated: $$\begin{eqnarray} S_{hi}(i) & = & \mbox{max}(0,S_{hi}(i-1) + x_i - \hat{\mu}_0 - k) \\ S_{lo}(i) & = & \mbox{max}(0,S_{lo}(i-1) + \hat{\mu}_0 - k - x_i) \, , \end{eqnarray}$$ where $$S_{hi}(0)$$ and $$S_{lo}(0)$$ are 0. When either $$S_{hi}(i)$$ and $$S_{lo}(i)$$ exceeds $$h$$, the process is out of control.
Example of spreadsheet calculations We will construct a CUSUM tabular chart for the example described above. For this example, the parameter are $$h = 4.1959$$ and $$k = 0.3175$$. Using these design values, the tabular form of the example is
$$\hat{\mu}_0$$ $$h$$ $$k$$ 325 4.1959 0.3175
Increase in mean Decrease in mean Group $$x$$ $$x - 325$$ $$x - 325 - k$$ $$S_{hi}$$ $$325 - k - x$$ $$S_{lo}$$ CUSUM 1 324.93 -0.07 -0.39 0.00 -0.24 0.00 -0.007 2 324.68 -0.32 -0.64 0.00 0.01 0.01 -0.40 3 324.73 -0.27 -0.59 0.00 -0.04 0.00 -0.67 4 324.35 -0.65 -0.97 0.00 0.33 0.33 -1.32 5 325.35 0.35 0.03 0.03 -0.67 0.00 -0.97 6 325.23 0.23 -0.09 0.00 -0.54 0.00 -0.75 7 324.13 -0.88 -1.19 0.00 0.56 0.56 -1.62 8 324.53 -0.48 -0.79 0.00 0.16 0.72 -2.10 9 325.23 0.23 -0.09 0.00 0.54 0.17 -1.87 10 324.60 -0.40 -0.72 0.00 0.08 0.25 -2.27 11 324.63 -0.38 -0.69 0.00 0.06 0.31 -2.65 12 325.15 0.15 -0.17 0.00 0.47 0.00 -2.50 13 328.33 3.32 3.01 3.01 -3.64 0.00 0.83 14 327.25 2.25 1.93 4.94* -0.57 0.00 3.08 15 327.83 2.82 2.51 7.45* -3.14 0.00 5.90 16 328.50 3.50 3.18 10.63* -3.82 0.00 9.40 17 326.68 1.68 1.36 11.99* -1.99 0.00 11.08 18 327.78 2.77 2.46 14.44* -3.09 0.00 13.85 19 326.88 1.88 1.56 16.00* -2.19 0.00 15.73 20 328.35 3.35 3.03 19.04* -3.67 0.00 19.08
| 2016-02-09T03:03:27 |
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|
http://slideviewer.herokuapp.com/github/yoavram/ipython-notebooks/blob/master/simulation%20frameworks.ipynb
|
# Comparing different approaches to evolutionary simulations¶
## 4 Feb 2013¶
http://www.yoavram.com/
# Moran vs. Wright-Fisher¶
## Moran process¶
The simplest approach to model the change in frequency of alleles (i.e., evolution) is described by the Moran process, which can be explained as a type of a ball and urn game.
There is an urn with yellow blue balls. At each turn we draw two balls from the urn. The one in our right hand we replace by two balls of the same color, and the one in our left hand we discard.
Of course, in half of the cases the number of balls of each color doesn't change (when we draw two balls of the same color) and therefore we focus on cases in which we draw two different balls. The game can be rephrased as we draw a ball, replace it by two balls of the same color, and discard a ball of the opposite color.
The game ends when all balls are of the same color.
Denoting the number of yellow balls by x and the number of blue balls by y we can write a code for this game.
In [4]:
def moran_draw(x, y):
r = randint(1, x + y + 1)
if r <= x:
return x + 1, y - 1
else:
return x - 1, y + 1
In [5]:
def game(x, y, draw):
count = 0
while x != 0 and y != 0:
x, y = draw(x, y)
count += 1
return y == 0, count
We can run this game multiple times to check, for example, how the number of draws required to finish the game are distributed:
In [6]:
def repeat(x, y, repeats, draw):
return [game(x, y, draw)[1] for _ in range(repeats)]
In [7]:
num_balls = [10, 50, 100, 200, 500, 800, 1000, 1250, 1400, 1500]
def run_and_summarize(draw, n_repeats=100):
results = array([repeat(n, n, n_repeats, draw) for n in num_balls])
means = results.mean(axis=1)
stds = results.std(axis=1)
return results, means, stds
moran_results, moran_means, moran_stds = run_and_summarize(moran_draw)
In [8]:
plot_summary(num_balls, moran_means, moran_stds, game_name="Moran process")
In [9]:
plot_histograms(moran_results, num_balls, game_name="Moran process")
### Markov Chain¶
A moran process can be described by a Markov chain. Denote the total number of balls by $n$ and use this probability matrix (for n=2):
in which $A_{i,j}$ is the probablity to transition from j yellow balls to i yellow balls where there is a total of n=2 balls in the game.
### Evolutionary model¶
From an evolutionary perspective, this setup models genetic drift, but it can be expanded is much the same way to include mutation and selection (although adding selection will disrupt the linearity of the above model), and even recombination in a multi-locous model.
## Wright-Fisher process¶
In the Wirght-Fisher (WF) process, we replace the entire contents of the urn at each step of the game, drawing the next generation of balls from the current urn with replacement.
At first, this sounds the same as the Moran process if we zoom out and look at a generation as n draws, where n is the total number of balls. But in effect the processes are different, because in the WF process the draws within the generation are independent, but in the Moran process they are not. This leads to stronger drift and faster extinctions in the Moran process, as we will soon see.
The WF process can be modeled by using a binomial random function (or a multinomial, if there are multiple types/loci):
In [10]:
def wf_draw(x, y):
n = x + y
x = binomial(n, x / float(n))
y = n - x
return x, y
Note that we only changed the drawing function, but now a draw is a whole generation, whereas in the Moran process it was a single reproduction and death step, so that a generation was regarded as n draws, where n is the total number of balls.
In [11]:
wf_results, wf_means, wf_stds = run_and_summarize(wf_draw)
plot_summary(num_balls, wf_means, wf_stds, "Wright-Fisher process")
Note that the time scales (on the y-axis) are different from those of the Moran process because in the WF process the entire population is replaced on each tick, whereas in the Moran process a single individual is replaced on each tick.
The fact that the sacles, although different, are on the same order of magnitude suggests that the time for extinction of an allele in the Moran process is much shorter, as it requires several thousands of reproductions instead of several thousands of generations. This is a result of the fact that in the Moran process the sampling is without replacement whereas in the WF process the sampling is with replacement.
In [12]:
plot_histograms(wf_results, num_balls)
## Computational comparison¶
In the WF model we use one random function call per generation, whereas in the Moran process we use n calls, where n is the total number of balls. On the other hand, the Moran process tends to finish in a smaller number of generations because drift is stronger. I therefore compare the running time of both processes for a small population and a large one:
In [13]:
%timeit game(100, 100, moran_draw)
%timeit game(100, 100, wf_draw)
1000 loops, best of 3: 365 us per loop
1000 loops, best of 3: 458 us per loop
In [15]:
%timeit -n 100 game(10**6, 10**6, moran_draw)
%timeit -n 100 game(10**6, 10**6, wf_draw)
100 loops, best of 3: 8.4 s per loop
100 loops, best of 3: 4.56 s per loop
For the small population the Moran process was slightly faster. For the large population, the WF model was slightly faster.
So if I were to require 25,000 games to produce a good dataset for a research project, the Moran process would take
In [17]:
print "%.2f seconds for a small population" % (25000*365.0*10**-6)
print "%.2f days for a large population" % (25000*8.4/(24*60*60))
9.12 seconds for a small population
2.43 days for a large population
and the WF process would take
In [16]:
print "%.2f seconds for a small population" % (25000*458.0*10**-6)
print "%.2f days for a large population" % (25000*4.56/(24*60*60))
11.45 seconds for a small population
1.32 days for a large population
# Individual-based vs. Density-based simulation¶
## Individual-based simulation¶
In individual-based simulations (also called agent-based simulations) all the attributes of every individual, such as fitness, genome and modifiers, are explicitly modeled.
To illustrate an example of an individual-based simulation, the following code implements a Wright-Fisher process with drift, selection and mutation. The genome is represented by the number of mutations accumulated, and all mutations are deleterious with a constant effect on fitness.
We start from a mutation-free constant size population and proceed for a pre-defined number of generations, en route to a mutation-selection balance in which the mean number of deleterious mutations in the population is stable around $\mu/s$, where $\mu$ is the mutation rate and $s$ is the selection coefficient.
In [5]:
class Organism:
def __init__(self, mutations, mutation_rate, selection_cofficient):
self.mutations = mutations
self.mutation_rate = mutation_rate
self.selection_cofficient = selection_cofficient
self.fitness = self._fitness()
def reproduce(self):
child = Organism(self.mutations, self.mutation_rate, self.selection_cofficient)
child.mutations += poisson(self.mutation_rate)
child.fitness = self._fitness()
return child
def _fitness(self):
return (1 - self.selection_cofficient) ** self.mutations
def __repr__(self):
return "*"+str(self.mutations)
In [6]:
import random
def selection_mutation_IBS(population):
fitness = array([o.fitness for o in population])
fitness = fitness/fitness.sum()
count = multinomial(len(population), fitness)
i = 0
for o,n in zip(population, count):
while n > 0:
population[i] = o.reproduce()
n -= 1
i += 1
return population
def drift_IBS(population):
return random.sample(population, len(population))
In [7]:
def mutation_selection_balance_IBS(ticks, population_size, mutation_rate, selection_coefficient):
population = [Organism(0, mutation_rate, selection_coefficient) for i in range(population_size)]
for t in range(ticks):
population = drift_IBS(population)
population = selection_mutation_IBS(population)
mutation_load[t] = mean([o.mutations for o in population])
In []:
generations, population_size, mu, s = 100, 10**5, 0.003, 0.1
population_IBS, mutation_load_IBS = mutation_selection_balance_IBS(generations, population_size, mu, s)
In [54]:
plot_mutation_load(mutation_load_IBS, mu, s, "Individual-based simulation")
## Density-based simulation¶
In a density-based simulation (and also in frequency-based simulations, which are only slightly different) the population is divided into types or classes of individuals that share the same set of attributes (alleles, modifiers, etc.). Then, these types are explicitly modeled, and the individuals are only implicitly modeled via the types they belong to.
This framework is very efficient because it allows the use of general algorithms, such as mutlinomial random number sampling.
Here is the code for a density-based simulation based on the same assumptions as the individual-based simulation above:
In [10]:
def selection_DBS(population, population_size, selection_coefficient):
fitness = array([(1 - selection_coefficient) ** i for i in range(len(population))]) * population
fitness = fitness/fitness.sum()
return multinomial(population_size, fitness)
def drift_DBS(population, population_size):
population = population/float(population.sum())
return multinomial(population_size, population)
def mutation_DBS(population, mutation_rate):
mutations = poisson(mutation_rate * population)
population[:-1] = population[:-1] - mutations[:-1]
population[1:] = population[1:] + mutations[:-1]
return population
In [11]:
def mutation_selection_balance_DBS(ticks, population_size, max_num_mutations, mutation_rate, selection_coefficient):
population = array([0] * max_num_mutations)
population[0] = population_size
for t in range(ticks):
population = drift_DBS(population, population_size)
population = selection_DBS(population, population_size, selection_coefficient)
population = mutation_DBS(population, mutation_rate)
mutation_load[t] = sum([i * x for i,x in enumerate(population) if x > 0])/float(population.sum())
In []:
population_DBS, mutation_load_DBS = mutation_selection_balance_DBS(generations, population_size, 100, mu, s)
In [55]:
plot_mutation_load(mutation_load_DBS, mu, s, "Density-based simulation")
## Computational comparison¶
### Running time¶
In individual-based simulations, because each individual is explicitly modeled, it is easier to write and test the simulation code, but it will likely be slow, because at every generation the complexity is O(n), as the simulation code must process each and every individual.
In a density-based simulations every type/class of individuals is explicitly modeled, and therefore the code is expected to run much faster, as long as the number of types is smaller than the number of individuals. This is expected to occur when the mutation and recombination rates are low and the population is large (i.e., in asexual populations). This gain in performance is paid by a more complex code which requires a minimal understanding of probability theory.
The below performance comparison shows that the density-based simulation is ~3800 times faster!
In [14]:
%timeit mutation_selection_balance_IBS(10, population_size, mu, s)
%timeit mutation_selection_balance_DBS(10, population_size, 100, mu, s)
1 loops, best of 3: 14.6 s per loop
100 loops, best of 3: 3.78 ms per loop
### Memory use¶
If the population size is, say, $10^5$ individuals, and each has 1,000 loci in his genome, then the population will occupy ~100 megabytes of memory. If the population size increases to $10^7$, then the population will occupy 10 gigabytes of memory, which is already not feasible on most machines and not efficient when it is feasible.
The following prints the memory footpring of the individual-based and density-based populations:
In [40]:
import sys
print "Individual-based population: %d bytes" % sys.getsizeof(population_IBS)
print "Density-based population: %d bytes" % sys.getsizeof(population_DBS)
Individual-based population: 800064 bytes
Density-based population: 80 bytes
The individual-based population is 10,000 times larger than the density-based population.
# Fin¶
This presentation was written using the IPython notebook.
The code for this presentation is available on GitHub.
The presentation can be viewed online on slideviewer, or you could install the latest versions of IPython (0.14.dev) and nbconvert - follow this recipe.
The presentation is published under a a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
In []:
| 2019-07-22T09:58:51 |
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|
https://mooseframework.inl.gov/source/bcs/DisplacementAboutAxis.html
|
# Displacement About Axis
Implements a boundary condition that enforces rotationaldisplacement around an axis on a boundary
## Description
The boundary condition class DisplacementAboutAxis applies a rotating displacement to the specified mesh surface according to the user defined rotation function. The boundary condition is always applied to the displaced mesh. The rotation function can be given in either radians or in angles, and an axis of rotation can be specified with the axis_origin and axis_direction parameters.
The rotating displacement value at the current node is calculated according to Eq. (1): (1) where is the translation matrix for axes of rotation not centered at the coordinate system origin, and , , and are rotation matrices about the , , and coordinate system axes, respectively.
## Example Input File Syntax
[./top_x]
type = DisplacementAboutAxis
boundary = 2
function = rampConstantAngle
angle_units = degrees
axis_origin = '10. 10. 10.'
axis_direction = '0 -1.0 1.0'
component = 0
variable = disp_x
[../]
(modules/tensor_mechanics/test/tests/torque_reaction/torque_reaction_cylinder.i)
A Function is required to prescribe the rate of the DisplacementAboutAxis boundary condition application to the mesh. Note that the name of the Function is used as the argument for the function input parameter in the DisplacementAboutAxis block.
[./rampConstantAngle]
type = PiecewiseLinear
x = '0. 1.'
y = '0. 1.'
scale_factor = 0.1
[../]
(modules/tensor_mechanics/test/tests/torque_reaction/torque_reaction_cylinder.i)
## Input Parameters
• functionThe function providing the angle of rotation.
C++ Type:FunctionName
Options:
Description:The function providing the angle of rotation.
• angle_unitsThe units of the angle of rotation. Choices are:degrees radians
C++ Type:MooseEnum
Options:degrees radians
Description:The units of the angle of rotation. Choices are:degrees radians
• axis_directionDirection of the axis of rotation
C++ Type:libMesh::VectorValue
Options:
Description:Direction of the axis of rotation
• componentThe component for the rotational displacement
C++ Type:int
Options:
Description:The component for the rotational displacement
• variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
• axis_originOrigin of the axis of rotation
C++ Type:libMesh::VectorValue
Options:
Description:Origin of the axis of rotation
### Required Parameters
• save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
### Optional Parameters
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
• use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:True
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
### Advanced Parameters
• vector_tagsresidualThe tag for the vectors this Kernel should fill
Default:residual
C++ Type:MultiMooseEnum
Options:nontime time residual
Description:The tag for the vectors this Kernel should fill
• extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
• matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime system time
Description:The tag for the matrices this Kernel should fill
• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill
| 2018-12-10T13:22:36 |
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|
http://dlmf.nist.gov/1.10
|
# §1.10 Functions of a Complex Variable
## §1.10(i) Taylor’s Theorem for Complex Variables
Let be analytic on the disk . Then
The right-hand side is the Taylor series for at , and its radius of convergence is at least .
### ¶ Examples
1.10.4.
Again, in these examples and have their principal values; see §§4.2(i) and 4.2(iv).
### ¶ Zeros
An analytic function has a zero of order (or multiplicity) () at if the first nonzero coefficient in its Taylor series at is that of . When the zero is simple.
## §1.10(ii) Analytic Continuation
Let be analytic in a domain . If , analytic in , equals on an arc in , or on just an infinite number of points with a limit point in , then they are equal throughout and is called an analytic continuation of . We write , to signify this continuation.
Suppose , , is an arc and . Suppose the subarc , is contained in a domain , . The function on is said to be analytically continued along the path , , if there is a chain , .
Analytic continuation is a powerful aid in establishing transformations or functional equations for complex variables, because it enables the problem to be reduced to: (a) deriving the transformation (or functional equation) with real variables; followed by (b) finding the domain on which the transformed function is analytic.
### ¶ Schwarz Reflection Principle
Let be a simple closed contour consisting of a segment of the real axis and a contour in the upper half-plane joining the ends of . Also, let be analytic within , continuous within and on , and real on . Then can be continued analytically across by reflection, that is,
1.10.5
## §1.10(iii) Laurent Series
Suppose is analytic in the annulus , , and . Then
1.10.6
where
and the integration contour is described once in the positive sense. The series (1.10.6) converges uniformly and absolutely on compact sets in the annulus.
Let , so that the annulus becomes the punctured neighborhood : , and assume that is analytic in , but not at . Then is an isolated singularity of . This singularity is removable if for all , and in this case the Laurent series becomes the Taylor series. Next, is a pole if for at least one, but only finitely many, negative . If is the first negative integer (counting from ) with , then is a pole of order (or multiplicity) . Lastly, if for infinitely many negative , then is an isolated essential singularity.
The singularities of at infinity are classified in the same way as the singularities of at .
An isolated singularity is always removable when exists, for example at .
The coefficient of in the Laurent series for is called the residue of at , and denoted by , , or (when there is no ambiguity) .
A function whose only singularities, other than the point at infinity, are poles is called a meromorphic function. If the poles are infinite in number, then the point at infinity is called an essential singularity: it is the limit point of the poles.
### ¶ Picard’s Theorem
In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception.
## §1.10(iv) Residue Theorem
If is analytic within a simple closed contour , and continuous within and on —except in both instances for a finite number of singularities within —then
Here and elsewhere in this subsection the path is described in the positive sense.
### ¶ Phase (or Argument) Principle
If the singularities within are poles and is analytic and nonvanishing on , then
where and are respectively the numbers of zeros and poles, counting multiplicity, of within , and is the change in any continuous branch of as passes once around in the positive sense. For examples of applications see Olver (1997b, pp. 252–254).
each location again being counted with multiplicity equal to that of the corresponding zero or pole.
### ¶ Rouché’s Theorem
If and are analytic on and inside a simple closed contour , and on , then and have the same number of zeros inside .
## §1.10(v) Maximum-Modulus Principle
### ¶ Analytic Functions
If is analytic in a domain , and for all , then is a constant in .
Let be a bounded domain with boundary and let . If is continuous on and analytic in , then attains its maximum on .
### ¶ Harmonic Functions
If is harmonic in , , and for all , then is constant in . Moreover, if is bounded and is continuous on and harmonic in , then is maximum at some point on .
### ¶ Schwarz’s Lemma
In , if is analytic, , and , then
1.10.11
Equalities hold iff , where is a constant such that .
## §1.10(vi) Multivalued Functions
Functions which have more than one value at a given point are called multivalued (or many-valued) functions. Let be a multivalued function and be a domain. If we can assign a unique value to at each point of , and is analytic on , then is a branch of .
### ¶ Example
is two-valued for . If and , then one branch is , the other branch is , with in both cases. Similarly if , then one branch is , the other branch is , with in both cases.
A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed. Each contour is called a cut. A cut neighborhood is formed by deleting a ray emanating from the center. (Or more generally, a simple contour that starts at the center and terminates on the boundary.)
Suppose is multivalued and is a point such that there exists a branch of in a cut neighborhood of , but there does not exist a branch of in any punctured neighborhood of . Then is a branch point of . For example, is a branch point of .
Branches can be constructed in two ways:
(a) By introducing appropriate cuts from the branch points and restricting to be single-valued in the cut plane (or domain).
(b) By specifying the value of at a point (not a branch point), and requiring to be continuous on any path that begins at and does not pass through any branch points or other singularities of .
If the path circles a branch point at , times in the positive sense, and returns to without encircling any other branch point, then its value is denoted conventionally as .
### ¶ Example
Let and be real or complex numbers that are not integers. The function is many-valued with branch points at . Branches of can be defined, for example, in the cut plane obtained from by removing the real axis from 1 to and from −1 to ; see Figure 1.10.1. One such branch is obtained by assigning and their principal values (§4.2(iv)).
Figure 1.10.1: Domain .
Alternatively, take to be any point in and set where the logarithms assume their principal values. (Thus if is in the interval , then the logarithms are real.) Then the value of at any other point is obtained by analytic continuation.
Thus if is continued along a path that circles times in the positive sense and returns to without circling , then . If the path also circles times in the clockwise or negative sense before returning to , then the value of becomes .
## §1.10(vii) Inverse Functions
### ¶ Lagrange Inversion Theorem
Suppose is analytic at , , and . Then the equation
1.10.12
has a unique solution analytic at , and
1.10.13
in a neighborhood of , where is the residue of at . (In other words is the coefficient of in the Laurent expansion of in powers of ; compare §1.10(iii).)
Furthermore, if is analytic at , then
where is the residue of at .
### ¶ Extended Inversion Theorem
Suppose that
1.10.15
where , , and the series converges in a neighborhood of . (For example, when is an integer has a zero of order at .) Let . Then (1.10.12) has a solution , where
in a neighborhood of , being the residue of at .
It should be noted that different branches of used in forming in (1.10.16) give rise to different solutions of (1.10.12). Also, if in addition is analytic at , then
where is the residue of at .
## §1.10(viii) Functions Defined by Contour Integrals
Let be a domain and be a closed finite segment of the real axis. Assume that for each , is an analytic function of in , and also that is a continuous function of both variables. Then
1.10.18
is analytic in and its derivatives of all orders can be found by differentiating under the sign of integration.
This result is also true when , or when has a singularity at , with the following conditions. For each , is analytic in ; is a continuous function of both variables when and ; the integral (1.10.18) converges at , and this convergence is uniform with respect to in every compact subset of .
The last condition means that given () there exists a number that is independent of and is such that
for all and all ; compare §1.5(iv).
### ¶ -test
If for and converges, then the integral (1.10.18) converges uniformly and absolutely in .
## §1.10(ix) Infinite Products
Let . If for some , as , then we say that the infinite product converges. (The integer may be greater than one to allow for a finite number of zero factors.) The convergence of the product is absolute if converges. The product , with for all , converges iff converges; and it converges absolutely iff converges.
Suppose , , a domain. The convergence of the infinite product is uniform if the sequence of partial products converges uniformly.
### ¶ -test
Suppose that are analytic functions in . If there is an , independent of , such that
and
1.10.21
then the product converges uniformly to an analytic function in , and only when at least one of the factors is zero in . This conclusion remains true if, in place of (1.10.20), for all , and again .
### ¶ Weierstrass Product
If is a sequence such that is convergent, then
is an entire function with zeros at .
## §1.10(x) Infinite Partial Fractions
Suppose is a domain, and
1.10.23,
where is analytic for all , and the convergence of the product is uniform in any compact subset of . Then is analytic in .
If, also, when and , then on and
1.10.24
### ¶ Mittag-Leffler’s Expansion
If and are sequences such that () and is convergent, then
1.10.25
is analytic in , except for simple poles at of residue .
| 2013-05-25T23:24:54 |
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|
https://indico.bnl.gov/event/15775/
|
High Energy / Nuclear Theory / RIKEN seminars
# Mikko Laine, "[NT/RBRC hybrid seminar] Heavy quark kinetic equilibration from the lattice"
US/Eastern
https://bnl.zoomgov.com/j/1617203107?pwd=MUpFWHdtT2hYUjk1RTVPN3U1bnBHUT09
#### https://bnl.zoomgov.com/j/1617203107?pwd=MUpFWHdtT2hYUjk1RTVPN3U1bnBHUT09
Description
After summarizing basic motivations for considering the heavy quark kinetic equilibration rate in thermal QCD, we discuss recent progress in estimating this quantity from the lattice. In particular, corrections suppressed by O(T/M), relevant particularly for charm quarks and originating from the magnetic part of a coloured Lorentz force, are extracted.
Organized by
Yacine Mehtar-Tani
| 2022-10-02T00:14:12 |
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|
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2010.28.845
|
Article Contents
Article Contents
# A Neumann eigenvalue problem for fully nonlinear operators
• We prove the existence of the principal eigenvalues for the Pucci operators in bounded domains with boundary condition $\frac{\partial u}{\partial\vec n}=\alpha u$ corresponding respectively to positive and negative eigenfunctions and study their asymptotic behavior when $\alpha$ goes to $+\infty$.
Mathematics Subject Classification: Primary: 35D40, 35J25; Secondary: 35P30.
Citation:
Open Access Under a Creative Commons license
• on this site
/
| 2023-03-26T22:58:10 |
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|
https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/2999/4592
|
Collision-free Multiple Unmanned Combat Aerial Vehicles Cooperative Trajectory Planning for Time-critical Missions using Differential Flatness Approach
This paper investigates the cooperative trajectory planning for multiple unmanned combat aerial vehicles in performing autonomous cooperative air-to-ground target attack missions. Firstly, the collision-free cooperative trajectory planning problem for time-critical missions is formulated as a cooperative trajectory optimal control problem (CTP-OCP), which is based on an approximate allowable attack region model, several constraints model, and a multi-criteria objective function. Next, a planning algorithm based on the differential flatness, B-spline curves and nonlinear programming is designed to solve the CTP-OCP. In particular, the notion of the virtual time is introduced to deal with the temporal constraints. Finally, the proposed approach is validated by two typical scenarios and the simulation results show the feasibility and effectiveness of the proposed planning approach.
Keywords: Cooperative trajectory planning, unmanned combat aerial vehicle, differential flatness, B-spline curve, allowable attack region
Nowadays, it is an active research area to perform autonomous cooperative air-to-ground target attack (CA/GTA) missions by multiple unmanned combat aerial vehicles (multi-UCAV)1 . However, it is quite difficult to coordinate the strike operation of multi-UCAV, especially for time-critical missions that require precise timing and sequencing of tasks and operations. In order to accomplish the mission successfully, UCAVs need to generate detailed cooperative execution plans to lead themselves well to penetrate through enemy threat areas, avoid the collisions with obstacles or each other, fly into the allowable attack regions (AARs) simultaneously or in sequence, and then perform weapon delivery operations. The cooperative trajectory planning for CA/GTA is vital to achieve the mission goals. It is really one of the key challenging technologies, due to its high dimensionality, severe equality and inequality constraints involved, and the requirement of spatial-temporal cooperation of multi-UCAV, and has recently received extensive attentions2 .
To date, various algorithms3 - 7 have been developed to solve this cooperative planning problem, including several collision-avoidance techniques and time adjustment strategies. McLain3 , et al. used coordination variables and coordination functions based strategies to achieve cooperative timing among teams of vehicles, by coordinating the velocity and path length of each vehicle. Kaminer4 , et al. proposed a solution to the problem of coordinated control of multiple unmanned aerial vehicles (multi-UAV) to ensure collision-free maneuvers under strict spatial and temporal constraints. Bollino5 , et al. addressed the optimal path planning of UAVs in obstacle-rich environments and proposed the collision-free path planning for multi-UAV using optimal control techniques and pseudospectral methods. Lian6 introduced a differential flatness based approach to optimally formulate the cooperative path planning for multi-agent dynamical systems considering spatial and temporal constraints, and parameterized the curves by B-spline representations. Kuwata7 , et al. presented a cooperative distributed robust trajectory optimization approach, using RH-MILP with independent dynamics but coupled objectives and hard constraints. The above investigations have given several valuable strategies in the cooperative planning, but they failed to tackle the point-to-region cooperative trajectory planning for CA/GTA missions under consideration directly, which needs to integrate both the spatial and temporal constraints on the level of the trajectory planning. To address the trajectory planning, a novel cooperative trajectory planning algorithm for multi-UCAV in performing the CA/GTA missions is presented
Given a set of stationary ground targets in a terrain region, the mission objective is to plan several cooperative optimal or suboptimal, dynamically feasible flight trajectories from the initial points (IPs) into the AARs, such that multi-UCAV can effectively attack the targets with minimum time, maximum survivability and target destruction effectiveness. Therefore, many factors need to be considered synthetically in the cooperative trajectory planning. In this section, the cooperative trajectory planning problem is formulated after the modelling of AAR, constraints and the objective function.
2.1 Allowable Attack Region Model
For the point-to-region trajectory planning problem, the AARs of targets are defined as the areas where UCAVs can effectively perform weapon delivery operations. So, in order to plan the accurate and optimal attack trajectories for weapon delivery, the AARs and the delivery parameters need to be obtained. The AAR of the ith target TARi, denoted as R(TARi), is such a set of all feasible release states that TARi can be effectively attacked whenever the aircraft is in that states. R(TARi) can be formulated as an abstract 6-dimensional space8
$R\left(TA{R}_{i}\right)=\left\{x,y,h,v,\gamma ,\psi \right\}\subset {ℝ}^{6}\text{.}$ (1)
Obviously, R(TARi) is high-dimensional nonlinear space, which will make the problem solving much difficult. By presetting an appropriate weapon release speed, vr and the flight-path angle, ${\gamma }_{\text{r}}$ based on estimating the weapon impact effects and destruction requirements to the target, and predetermining release heading ${{\psi }^{\prime }}_{\text{r}}$ ,it can be reduced to a 3-dimensional space
(2)
2.2 Constraint Model
2.2.1 Maneuverability Constraints of UCAVs
The maneuverability constraints impact every phase during target attack missions, so they should be met for an executable plan. The constraints can be denoted as
(3)
where v is the aircraft velocity;$\gamma$ denotes the flight-path angle; denotes the heading angle$\psi$ ; denotes the roll angle $\mu$ ; nx and nh are the longitudinal and normal components of the load factor. and ${\left(\cdot \right)}_{\mathrm{min}}$ and ${\left(\cdot \right)}_{\mathrm{max}}$ represent the minimum and maximum boundary values of the value $\left(\cdot \right)$ .
2.2.2 Battlefield Environment Constraints
(a) Threat avoidance: without loss of generality, the threat impact range can be assumed as hemispheres approximately, thus threat avoidance constraint can be defined as
(4)
where the norm ${‖\cdot ‖}_{2}$ denotes the Euclidean distance between two points and$\left({x}_{i}^{\text{o}},{y}_{i}^{\text{o}},{h}_{i}^{\text{o}}\right)$ and ${R}_{i}^{\text{o}}$ denote the origin coordinates and the detection radius of the ith threat, respectively.
(b) No-fly zones (NFZs): herein, an infinite-length cylinder is used to describe the NFZs:
(5)
where $\left({x}_{i}^{\text{w}},{y}_{i}^{\text{w}}\right)$ and ${R}_{i}^{\text{w}}$ denote the origin coordinates and the radius of the ith NFZ.
2.2.3 Terminal Constraints
In the point-to-region trajectory planning, weapon delivery point (WDPt) as the trajectory terminal of CA/GTA needs to be in the AAR, i.e. satisfying the terminal constraints. The formula can be denoted as ${\text{WDPt}}_{i}\in R\text{(}TA{R}_{i}\text{)}$, that is
(6)
where tf is the terminal time, (xa, ya, ha) and (x(tf), y(tf), h(tf)) are the coordinates of AAR’s center point and WDPt, are the thresholds of errors.
2.2.4 Cooperative Constraints
During the mission, multi-UCAV should maintain a safe distance to avoid collision with each other, i.e. satisfying spatial constraint. The model can be denoted as
(7)
where ${\rho }^{j}\left({t}_{i}\right)=\left\{{x}^{j}\left({t}_{i}\right),{y}^{j}\left({t}_{i}\right),{h}^{j}\left({t}_{i}\right)\right\}$ is the spatial position of UCAVj at the time ti, is the minimum safety radius of UCAVj, and Nv is the total number of UCAVs.
The temporal constraints considered here include simultaneous arrival constraint and tight-sequencing constraint, which can be described as
(8)
where ${t}_{\text{f}}^{j}$ is the terminal time of UCAVj, ${\Delta }_{jk}$ is the arrival interval between UCAVs.
2.3 Objective Function
The objective function of each UCAVj can be defined by the weighted sum of the three separate running cost terms with appropriate weighting factors ${w}_{\text{t}}^{j}$ ${w}_{\text{r}}^{j}$ and ${w}_{\text{d}}^{j}$ , where ${w}_{\text{t}}^{j}+{w}_{\text{r}}^{j}+{w}_{\text{d}}^{j}=1$ . And the objective function of the entire team can defined as:
$J=\mathrm{min}\sum _{j=1}^{{N}_{v}}{J}^{j}=\mathrm{min}\sum _{j=1}^{{N}_{v}}\left({w}_{\text{t}}^{j}{J}_{\text{t}}^{j}+{w}_{\text{r}}^{j}{J}_{\text{prd}}^{j}+{w}_{\text{d}}^{j}{J}_{\text{dest}}^{j}\right),$ (9)
and three separate running cost terms can be respectively defined as
${J}_{\text{t}}^{j}=\frac{1}{{\Gamma }^{j}}{\int }_{{t}_{0}^{j}}^{{t}_{\text{f}}^{j}}dt=\frac{1}{{\Gamma }^{j}}\left({t}_{\text{f}}^{j}-{t}_{0}^{j}\right),$ (10)
(11)
${J}_{\text{dest}}^{j}={f}_{dest}\left({x}^{j}\left({t}_{\text{f}}^{j}\right)\right)=1-\sum _{i}^{{n}_{s}}{D}_{i}^{j}\left({x}^{j}\left({t}_{\text{f}}^{j}\right)\right)/{n}_{s},$ (12)
where ${t}_{0}^{j}$ and ${t}_{\text{f}}^{j}$ denote the initial and terminal time of UCAVj. The first term, ${J}_{\text{t}}^{j}$ denotes the total fight time of UCAVj $\Gamma =L/{v}_{\mathrm{min}}$ . is maximum flight time along the straight line (L denotes its length) from the IP to the center of AARs. The value is predetermined, and can be used to insure the first cost term consistent with others. The second term ${J}_{\text{prd}}^{j}$ , describes the average detection-probability of the nr-radar system to UCAVj, where ${P}_{\text{d}}^{j}\left(t,r\right)$ is the radar detection probability model between the trajectory point of UCAVj at the time t and the rth radar9. And the third term ${J}_{dest}^{j}$ , is the minimal form of the target damage probability, where ${D}_{i}^{j}\left({x}^{j}\left({t}_{\text{f}}^{j}\right)\right)$ denotes the target damage probability of UCAVj from the ith Monte Carlo simulation, and ns is the total simulation times.
2.4 Cooperative Trajectory Planning Problem Formulation
After establishing the above three models, the cooperative trajectory planning problem is formulated in the subsection. The problem under consideration is a cooperative scenario, consisting of Nv similar UCAVs, and the dynamics of UCAVj is given by
(13)
where $x={\left[x,y,h,v,\gamma ,\psi \right]}^{\text{T}}\in {ℝ}^{6}$ and $u={\left[\mu ,{n}_{\text{x}},{n}_{\text{h}}\right]}^{\text{T}}\in {ℝ}^{3}$ denote the state and control vectors, which are in accordance with the following UCAV kinematic and dynamics equations10
(14)
(15)
where x, y, h are the east, north, and up components of the earth-fixed reference frame, and denote longitude, latitude and altitude respectively; g denotes the gravity acceleration.Fig 1. shows the spatial relation of the states.
As mentioned above, to generate optimal or suboptimal cooperative trajectories, the trajectory planning problem for the CA/GTA missions can be formulated as a cooperative trajectory optimal control problem (CTP-OCP).
Figure 1. Relation of aircraft position, velocity, flight-path and heading angels.
2.4.1 Problem 1 (CTP-OCP)
Find the trajectories, which drive the system from given initial conditions to desired final conditions over time horizons [t0, tf], while the cooperative objective function is minimized as follows
$\begin{array}{l}\mathrm{min}J=\sum _{j=1}^{{N}_{\text{v}}}{J}^{j}\left(x,u\right)=\sum _{j=1}^{{N}_{\text{v}}}\left[{w}_{\text{t}}^{j}\left({t}_{\text{f}}^{j}-{t}_{0}^{j}\right)/\Gamma +{w}_{\text{r}}^{j}{\int }_{{t}_{0}^{j}}^{{t}_{\text{f}}^{j}}{\text{PRD}}^{j}\left(t\right)dt/\left({t}_{\text{f}}^{j}-{t}_{0}^{j}\right)+\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{w}_{\text{d}}^{j}{f}_{dest}\left({x}^{j}\left({t}_{\text{f}}^{j}\right)\right)\right]\end{array}$ (16)
subject to the dynamics equation (i.e., Eqn (13)) and the boundary constraints (i.e., the initial and terminal states (i.e., Eqn (6))
$\begin{array}{l}{\Phi }_{0}\left[{x}^{j}\left({t}_{0}^{j}\right),{u}^{j}\left({t}_{0}^{j}\right),{t}_{0}^{j}\right]=0,\\ {\Phi }_{1}\left[{x}^{j}\left({t}_{\text{f}}^{j}\right),{u}^{j}\left({t}_{\text{f}}^{j}\right),{t}_{\text{f}}^{j}\right]\le \text{0,}\end{array}$ (17)
and several inequality and equality constraints, the individual and cooperative constraints, including the state and control (i.e., Eqns (3)-(5) and Eqns (7)-(8)), are denoted as:
(18)
Note that, the terminal time tf is free. Thus the problem is a free terminal time problem. In addition, it is important in the problem formulation to scale the variables. The choice of scaling will balance the equations for numerical analysis, thus improving the accuracy of the solution and the computation time11.
To solve the previous CTP-OCP as quickly as possible, an efficient numerically cooperative trajectory planning algorithm is introduced, which combines several classical techniques, including differential flatness theory, B-spline curves, and nonlinear programming. In addition, for the time-critical cooperative missions, a novel strategy is proposed to handle the temporal constraints.
3.1 Time Cooperative Strategy
The time factor of trajectories is an argument of the state and control. To deal with temporal constraints, the time along the trajectories should be considered separately. In the work, the independent intermediate variable (called virtual time here $\tau \in \left[0,1\right]$ ) is introduced and described as
$\tau \triangleq \left(t-{t}_{0}\right)/\left({t}_{\text{f}}-{t}_{0}\right).$ (19)
Such that the trajectories can be generated in the virtual time domain from ${\tau }_{0}=0$ to ${\tau }_{\text{f}}=1$ .
For UCAVs are required to takeoff at the same time, it is assumed that the initial time of all UCAVs is zero (i.e.${t}_{\text{0}}=0$ ). Thus, the terminal time ${t}_{\text{f}}$ can be written as ${t}_{\text{f}}=t/\tau$ . That is ${t}_{\text{f}}$ , denotes the ratio between the true time variable and the newly defined virtual time variable. To coordinate the arrival time of all UCAVs, the terminal time can be defined as an argument in the dynamics to be optimized, designated as ${T}_{\text{f}}$ . Then, the following relationship between the virtual time and true time domain can be obtained for an arbitrary variable $\chi$
$\stackrel{˙}{\chi }\left(t\right)=\frac{d\chi \left(t\right)}{dt}=\frac{d\chi \left(t\right)}{{T}_{\text{f}}d\tau }={\chi }^{\prime }\left(\tau \right)/{T}_{\text{f}}.$ (20)
Especially, the derivative of the speed variable can be denoted as
$v\left(t\right)=\sqrt{\stackrel{˙}{x}{\left(t\right)}^{2}+\stackrel{˙}{y}{\left(t\right)}^{2}+\stackrel{˙}{h}{\left(t\right)}^{2}}=\sqrt{{\left({x}^{\prime }\right)}^{2}+{\left({y}^{\prime }\right)}^{2}+{\left({h}^{\prime }\right)}^{2}}/{T}_{\text{f}}=v\left(\tau \right)/{T}_{\text{f}}$ (21)
where the superscript () represents the derivative with respect to the virtual time.
According to Eqns (13) and (19), the dynamics can be rewritten as
(22)
Hence, the Problem 1 can be reformulated in virtual time domain (VTD) as Problem 2.
3.1.1 Problem 2 (CTP-OCP-VTD)
Minimize the cooperative cost function (Eqn (16)) of all UCAVs represented with respect to the new independent variable $\tau$ as:
$J=\sum _{j=1}^{{N}_{\text{v}}}{J}^{j}\left(x,u,{T}_{\text{f}}\right)=\sum _{j=1}^{{N}_{\text{v}}}\left[{w}_{\text{t}}^{j}{T}_{\text{f}}^{j}/\Gamma +{w}_{\text{r}}^{j}{\int }_{0}^{1}{\text{PRD}}^{j}\left(\tau \right)d\tau /{T}_{\text{f}}^{j}+{w}_{\text{d}}^{j}{f}_{dest}\left({x}^{j}\left(1\right)\right)\right]$ (23)
subject to the dynamics in Eqn (22), and the boundary constraints in Eqn (17), written as:
$\begin{array}{l}{\stackrel{˜}{\Phi }}_{0}\left[{x}^{j}\left(0\right),{u}^{j}\left(0\right)\right]=0\\ {\stackrel{˜}{\Phi }}_{1}\left[{x}^{j}\left(1\right),{u}^{j}\left(1\right),{T}_{\text{f}}^{j}\right]\le \text{0}\end{array}$ (24)
and the inequality and equality constraints (Eqn (18)), and additional temporal constraints
(25)
3.2 Problem Formulation in the Output Space
Due to the complexity in solving this higher dimensional space system, the differential flatness approach is introduced to transform the system dynamics to a lower dimensional space12. To confirm that the dynamics system is differentially flat, the spatial trajectory $\rho \left(\tau \right)$ in virtual time domain and the terminal time ${T}_{\text{f}}$ as the flat output vector can be defined as
$z=\left[\rho \left(\tau \right),{T}_{\text{f}}\right]={\left[x\left(\tau \right),y\left(\tau \right),h\left(\tau \right),{T}_{\text{f}}\right]}^{T}$ (26)
The original state x and control u can be recovered from the flat outputs and their derivatives as follows13
(27)
According to the kinematics equations in Eqn (14), the remaining three states using the flatness outputs in virtual time domain can be easily described as below
(28)
Thus, according to Eqn (15), the control variables can be determined as
(29)
Obviously, the dynamics constraints of this system (i.e. Eqns (14-15)) can be automatically satisfied. And the system of cooperative planning of UCAVs, including the objective function and the constraints, is mapped to a lower dimensional output space. Hence, Problem 2 can be modified as problem 3.
3.2.1 Problem 3 (CTP-OCP-VTD in Output Space)
Solving the problem
$\begin{array}{l}\mathrm{min}J=\sum _{j=1}^{{N}_{\text{v}}}{J}^{j}\left(\xi \left(\tau \right)\right)=\sum _{j=1}^{{N}_{\text{v}}}\left[{\varphi }^{j}\left(\phi \left({\xi }^{j}\left(0\right)\right),\alpha \left({\xi }^{j}\left(0\right)\right),\phi \left({\xi }^{j}\left(1\right)\right),\alpha \left({\xi }^{j}\left(1\right)\right),{T}_{\text{f}}^{j}\right)+\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\int }_{0}^{1}{L}^{j}\left(\phi \left({\xi }^{j}\left(\tau \right)\right),\alpha \left({\xi }^{j}\left(\tau \right)\right),{T}_{\text{f}}^{j}\right)d\tau \right)\right]\end{array}$ (30)
subject to
(31)
3.3 Parameterization of the Spatial Trajectory
To generate feasible trajectories in a finite parameter space, flatness outputs are parameterized in terms of B-spline curves, which have been used to represent the trajectory of UCAV to minimize computation loads and successfully applied to path/trajectory planning14. Without loss of generality, to decrease the computational time, the 3-degree B-spline curves are chosen to represent the trajectory, whose order equals to 4. Therefore, choosing every four neighboring points from the point set as control points, a 3-degree B-spline curve can be defined, which is a trajectory segment. In addition, it is clearly seen from Eqn (19) that the non-decreasing variable $\tau$ can be the knot sequence of B-spline. Consequently, the ith trajectory segment can be described as follows
${B}_{i}\left(\tau \right)={b}_{1,4}^{i}\left(\tau \right){C}_{1}^{i}+{b}_{2,4}^{i}\left(\tau \right){C}_{2}^{i}+{b}_{3,4}^{i}\left(\tau \right){C}_{3}^{i}+{b}_{4,4}^{i}\left(\tau \right){C}_{4}^{i}$ (32)
Obviously, as is known, once the control point serial ${C}_{m}^{i}$ is determined, the ith trajectory segment can be generated by Eqn (32). Thus, the trajectory of UCAV is mapped into the control point serial of B-spline curves.
As is previously stated, the spatial trajectory segment ${B}_{i}\left(\tau \right)$ can be replaced by flatness output variables, ${\left[{x}_{i}\left(\tau \right),{y}_{i}\left(\tau \right),{h}_{i}\left(\tau \right)\right]}^{\text{T}}$ and simplified as
(33)
where ${a}_{i}^{m-1}$, ${b}_{i}^{m-1}$, ${c}_{i}^{m-1}$ are the evaluation coefficients determined by the coefficients of the B-spline basis functions.
Once all control points are obtained, the spatial trajectory, i.e., the flatness outputs will be generated. Such that, the original control variables and remaining state variables, as well as the objective function and the constraints, can be parameterized (i.e., discretized) by the control point serial. Thus, the trajectory will be mapped to control point serial, and the complex trajectory planning is transformed into a parameter optimization problem.
3.4 Transformation into a Nonlinear Programming Problem
After the flatness outputs have been parameterized in terms of B-spline curves, the coefficients of the B-spline basis functions can be found by nonlinear programming.
First of all, the virtual time horizon of UCAVj denoted by $\tau \in \left[0,1\right]$ need be uniformity discretized as the $\text{(}{N}_{\text{c}}^{j}\text{+1)}$ collocation points below
(34)
And the coordinates of collocation points can be written as , which can be calculated by the Eqn (33). Thus, the continuous-spline curves can be discretized in $\text{(}{N}_{\text{c}}^{j}\text{+1)}$ points, and the constraints on the B-spline curves will be enforced at collocation points.
For the 3-degree B-spline curve under consideration, B-spline coefficients of UCAVj for all position outputs can be denoted as
${\zeta }_{j}:=\left[\begin{array}{l}\left({C}_{1}^{1j},{C}_{2}^{1j},\dots ,{C}_{{p}_{1j}}^{1j},{C}_{1}^{2j},{C}_{2}^{2j},\\ \text{\hspace{0.17em}}\dots ,{C}_{{p}_{2j}}^{2j},\dots ,{C}_{1}^{qj},{C}_{2}^{qj},\dots ,{C}_{{p}_{qj}}^{qj}\right)\end{array}\right]\in {ℝ}^{{M}_{j}}$ (35)
where ${M}_{j}=\sum _{i=1}^{q}{p}_{ij}$ Pij is the number of the control points for the ith position output of UCAVj , and these coefficients are used as the decision variables in the NLP problem.
Thus, the multi-UCAV trajectory planning problem in optimal control framework is transformed into a NLP problem, i.e. CTP-NLP, given by Problem 4.
3.4.1 Problem 4 (CTP-NLP)
Solving the problem
(36)
where $\zeta$ is a decision vector of cooperative planning, described as $\zeta :=\left({\zeta }_{1},{\zeta }_{2},\dots ,{\zeta }_{{N}_{\text{v}}}\right)$, ${r}_{n}$ and ${s}_{n}$ are the total number of the inequality and equality constraints of all UCAVs, respectively.
Then the resulting CTP-NLP problem can be solved through well developed algorithms, such as the sequential quadratic programming. In the paper, the SNOPT software toolbox is used due to its advantages in solution effectiveness for the large-scale NLP problems15.
The basic ideas presented in this paper are illustrated in the following two scenarios. The common parameters of models in our simulations are listed in Table 1. .
Table 1. State and control constraints of UCAVs
The experimental test environment is a rectangle area of 30 × 40 km2, as shown in Fig 2. and Fig. 4 All the results presented below are generated using TOMLAB/SNOPT software toolbox on a 2.4-GHz Core 2 CPU, 2G RAM computer running with MATLAB R2009b. The weighting factors, ${w}_{\text{t}}^{j}$ , ${w}_{\text{r}}^{j}$ , and ${w}_{\text{d}}^{j}$ are set as 0.4, 0.3, and 0.3, by using trail and error. And the minimum safety radius of each UCAV dsafe is set as 500 m. The first initial guesses of the optimization parameters can be generated by using the B-spline interpolation of the lines from the IPs to the AARs of the targets. Then, the multiresolution-based iterative strategy8 is used to generate some ‘good’ initial guesses to the solver, which can reduce the number of iterations required to solve the NLP problem. The specified maximum number of collocation points is set as. ${N}_{\text{c,max}}=100$ Moreover, it is assumed that the target assignment is already completed before.
Figure 2. Two collision-free UCAV trajectories with arriving simultaneously.
4.1 Scenario 1: Cooperative Trajectories of Two UCAVs Arriving Simultaneously
In this scenario, two UCAVs cooperatively attack two stationary ground targets while avoiding a series of static obstacles/threats detected and collision en route, and satisfying aircraft dynamics constraint, especially simultaneous arrival constraint. UCAV1 and UCAV2 start at each IP, i.e., IP1 (10 km, 2 km, 2 km) and IP2 (17 km, 2 km, 2 km). Then they fly into the AARs of two targets: Target 1 (4.2 km, 34 km, 0 km) and Target 2 (14 km, 40 km, 0 km), respectively. The other three initial states and control inputs are given by and. Thus and . The collision-free trajectories of the UCAVs and their arrival time, i.e. the total flight time, are shown in Fig 2. In addition, the approximate weapon trajectories are drawn to simulate the attack process. The time histories of the UCAVs’ states ( ) and control inputs are shown in Fig. 3 The average detection-probabilities of UCAVs are 0.12 and 0.17, and the target damage probabilities of UCAVs are 0.851 and 0.762, respectively. It is clear that the resulting trajectories are smooth, and the constraints on these variables, especially the cooperative constraints are all satisfied (Table 1.), which means the resulting trajectories are feasible and safe.
Figure 3. State and control time histories of the two UCAVs.
4.2 Scenario 2: Cooperative Trajectories of Multi-UCAV Arriving in Sequence
In this scenario, three UCAVs attack two stationary ground targets cooperatively. The only additional requirement is that the UCAVs arrive at their AARs in sequence rather than simultaneously, and the intervals between UCAVs are equal, denoted as . The coordinates of IP1, IP2 and two targets are the same as Scenario 1, and the third IP is IP3 (4 km, 2 km, 2 km). The result of the previous finished target assignment is that the UCAV1 and UCAV2 attack Target 1 and UCAV3 attacks the other one. The initial remaining three states and control inputs of the UCAV3 are preset as and . Thus , and Fig. 4 shows the overall collision-free attack trajectories of multi-UCAV and their arrival time. It can be clearly demonstrated that the UCAVs can avoid all obstacles or threats and successfully fly into the AARs in sequence to perform weapon delivery. Fig. 5 shows the distance between each pair UCAVs. From it, one can find that the minimum distance is more than the minimum safety radius of dsafe = 500 m. Fig. 6 shows the time histories of the UCAVs’ states ( ) and control inputs . The average detection-probabilities of UCAVs are 0.133, 0.092 and 0.12, and the target damage probabilities of UCAVs are 0.813, 0.901 and 0.724, respectively. Obviously, the resulting trajectories are feasible and safe for all the constraints listed in Table 1. are satisfied.
Figure 4. Three collision-free UCAV trajectories with arriving in sequence.
Figure 5. Distance between each pair UCAVs.
Figure 6. State and control time histories of the three UCAVs.
This paper is devoted to exploring the cooperative collision-free trajectory planning for multi-UCAV performing the CA/GTA missions. A novel cooperative planning approach is proposed in optimal control framework, based on differential flatness, B-spline curves and nonlinear programming. To integrate weapon delivery constraints in the problem formulation, an approximate AAR model is established. Moreover, the notion of the virtual time is introduced to handle the temporal constraint. Instead of solving an OCP over a high-dimensional continuous space, the NLP problem of very low dimension has been solved successfully, over a much smaller space. The proposed approach can efficiently solve the point-to-region trajectory planning problem with integrating the spatial and temporal constraints on the trajectory level, whose validity is illustrated with some simulation results finally. Further efforts may be made to analyse some uncertain factors in the true battlefield environment and carry out the research on the real-time cooperative trajectory planning.
1. Murray, R.M. Recent research in cooperative control of multi-vehicle systems. J. Dyn. Syst.-T. ASME, 2007, 129(5), 571-583.
2. Hurni, M. A.; Sekhavat, P.; Karpenko, M. & Ross, I. M. A pseudospectral optimal motion planner for autonomous unmanned vehicles. In American Control Conference. Baltimore, MD, USA. 2010.[Full text via CrossRef]
3. McLain, T.W. & Beard, R.W. Coordination variables, coordination functions, and cooperative-timing missions. J. Guid. Control Dynam., 2005, 28(1), 150-161.[Full text via CrossRef]
4. Kaminer, I.; Yakimenko, O.; Dobrokhodov, V.; A. Pascoal; Hovakimyan, N.; Cao, C.; Young, A. & Patel, V. Coordinated path pollowing for time-critical missions of multiple UAVs via L1 adaptive output feedback controllers. In AIAA Guidance, Navigation and Control Conference and Exhibit. Hilton Head, South Carolina, USA. 2007, pp.1-23.[Full text via CrossRef]
5. Bollino, K.P. & Lewis, L.R. Collision-free multi-UAV optimal path planning and cooperative control for tactical applications. In AIAA Guidance, Navigation and Control Conference and Exhibit. Honolulu, Hawaii, USA. 2008, pp.1-18.[Full text via CrossRef]
6. Lian, F.-L. Cooperative path planning of dynamical multi-agent systems using differential flatness approach. Int. J. Control Autom., 2008, 6(3), 401-412.
7. Kuwata, Y. & How, J.P. Cooperative distributed robust trajectory optimization using receding horizon MILP. IEEE T. Contr. Syst. T., 2011, 19(2), 423-431.[Full text via CrossRef]
8. Zhang, Y.; Chen, J. & Shen, L. Hybrid hierarchical trajectory planning for a fixed-wing UCAV performing air-to-surface multi-target attack. J. Syst. Eng. Electron., 2012, 23(4), 256-264.[Full text via CrossRef]
9. Besada-Portas, E.; Torre, L.d.l.; Cruz, J.M.d.l. & Andres-Toro, B.d. Evolutionary trajectory planner for multiple UAVs in realistic scenarios. IEEE Trans.. Robot., 2010, 26(4), 619-634.[Full text via CrossRef]
10. Stevens, B.L. & Lewis, F.L. Aircraft control and simulation. John Wiley & Sons, Inc. Ed 2, New Jersey, 2003. 680 p.
11. Lewis, L.-P.R. Rapid motion planning and autonomous obstacle avoidance for unmanned vehicles. Naval Postgraduate School, Monterey, California, USA, 2006. MA Thesis.
12. Michel, F. Flatness and defect of nonlinear systems: Introductory theory and examples. Int. J. Control, 1995, 61(6), 1327-1361.[Full text via CrossRef]
13. Zhang, Y.; Chen, J. & Shen, L. Real-time trajectory planning for UCAV air-to-surface attack using inverse dynamics optimization method and receding horizon control. Chinese J. Aeronaut., 2013, 26(4), 1038-1056.[Full text via CrossRef]
14. Foo, J.L.; Knutzon, J.; Kalivarapu, V.; Oliver, J. & Winer, E. Path planning of unmanned aerial vehicles using B-splines and particle swarm optimization. J. Aeros. Comp. Inf. Com., 2009, 6, 271-290.[Full text via CrossRef]
15. E. Rutquist, P. & M. Edvall, M. PROPT - Matlab optimal control software. TOMLABoptimization. 2010.
Dr Xueqiang Gu is a PhD scholar in College of Mechatronic Engineering and Automation, National University of Defense Technology (NUDT), Changsha, Hunan, China. His current research interests included: combat vehicle mission planning and intelligence control. Dr Yu Zhang received his PhD in control science and engineering from NUDT, Changsha, Hunan, China in 2012. He is a Docent of College of Mechatronic Engineering and Automation in NUDT. His current research interests included: combat vehicle mission planning and artificial intelligence Dr Jing Chen obtained his PhD in control science and engineering from NUDT in 1999. He is a Professor of College of Mechatronic Engineering and Automation in NUDT, Changsha, Hunan, China. His current research interests included: artificial intelligence and mission planning of aircraft Mr Lincheng Shen is the Dean and Professor of College of Mechatronic Engineering and Automation in NUDT, Changsha, Hunan, China. He has published over 100 technical papers in refereed international journals and academic conferences. His current research interests included: mission planning, SAR image processing, biomimetic robotics, automation and control engineering.
| 2022-10-07T05:03:52 |
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|
https://par.nsf.gov/biblio/10334893-bridging-gap-categorizing-gravitational-wave-events-transition-between-neutron-stars-black-holes
|
This content will become publicly available on May 31, 2023
Bridging the Gap: Categorizing Gravitational-wave Events at the Transition between Neutron Stars and Black Holes
Abstract We search for features in the mass distribution of detected compact binary coalescences which signify the transition between neutron stars (NSs) and black holes (BHs). We analyze all gravitational-wave (GW) detections by the LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration (LVK) made through the end of the first half of the third observing run, and find clear evidence for two different populations of compact objects based solely on GW data. We confidently (99.3%) find a steepening relative to a single power law describing NSs and low-mass BHs below 2.4 − 0.5 + 0.5 M ⊙ , which is consistent with many predictions for the maximum NS mass. We find suggestions of the purported lower mass gap between the most massive NSs and the least massive BHs, but are unable to conclusively resolve it with current data. If it exists, we find the lower mass gap’s edges to lie at 2.2 − 0.5 + 0.7 M ⊙ and 6.0 − 1.4 + 2.4 M ⊙ . We reexamine events that have been deemed “exceptional” by the LVK collaborations in the context of these features. We analyze GW190814 self-consistently in the context of the full population of compact more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10334893
Journal Name:
The Astrophysical Journal
Volume:
931
Issue:
2
Page Range or eLocation-ID:
108
ISSN:
0004-637X
National Science Foundation
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2. Abstract
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4. ABSTRACT The progenitor system of the compact binary merger GW190425 had a total mass of $3.4^{+0.3}_{-0.1}$ M⊙ (90th-percentile confidence region) as measured from its gravitational wave signal. This mass is significantly different from the Milky Way (MW) population of binary neutron stars (BNSs) that are expected to merge in a Hubble time and from that of the first BNS merger, GW170817. Here, we explore the expected electromagnetic (EM) signatures of such a system. We make several astrophysically motivated assumptions to further constrain the parameters of GW190425. By simply assuming that both components were NSs, we reduce the possible component masses significantly, finding $m_{1}=1.85^{+0.27}_{-0.19}$ M⊙ and $m_{2}=1.47^{+0.16}_{-0.18}$ M⊙. However, if the GW190425 progenitor system was an NS–black hole (BH) merger, we find best-fitting parameters $m_{1}=2.19^{+0.21}_{-0.17}$ M⊙ and $m_{2}=1.26^{+0.10}_{-0.08}$ M⊙. For a well-motivated BNS system where the lighter NS has a mass similar to the mass of non-recycled NSs in MW BNS systems, we find $m_{1}=2.03^{+0.15}_{-0.14}$ M⊙ and m2 = 1.35 ± 0.09 M⊙, corresponding to only 7 per cent mass uncertainties. For all scenarios, we expect a prompt collapse of the resulting remnant to a BH. Examining detailed models with component masses similar to our best-fitting results, we find the EM counterpart to GW190425 is expected to be significantly redder and fainter thanmore »
5. Abstract
The LIGO–Virgo–KAGRA Collaboration recently detected gravitational waves (GWs) from the merger of black hole–neutron star (BHNS) binary systems GW200105 and GW200115. No coincident electromagnetic (EM) counterparts were detected. While the mass ratio and BH spin in both systems were not sufficient to tidally disrupt the NS outside the BH event horizon, other, magnetospheric mechanisms for EM emission exist in this regime and depend sensitively on the NS magnetic field strength. Combining GW measurements with EM flux upper limits, we place upper limits on the NS surface magnetic field strength above which magnetospheric emission models would have generated an observable EM counterpart. We consider fireball models powered by the black hole battery mechanism, where energy is output in gamma rays over ≲1 s. Consistency with no detection by Fermi-GBM or INTEGRAL SPI-ACS constrains the NS surface magnetic field to ≲1015G. Hence, joint GW detection and EM upper limits rule out the theoretical possibility that the NSs in GW200105 and GW200115, and the putative NS in GW190814, retain dipolar magnetic fields ≳1015G until merger. They also rule out formation scenarios where strongly magnetized magnetars quickly merge with BHs. We alternatively rule out operation of the BH-battery-powered fireball mechanism in these systems.more »
| 2022-11-28T01:40:21 |
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|
https://indico.fnal.gov/event/21423/
|
Macarena Lagos, "Cosmology in the multi-messenger era"
Tuesday, October 15, 2019 from to (US/Central)
at Bldg 362 ( F-108 )
Description Abstract: We have great certainty on how gravity works around our Solar System, but on large scales we still have a considerable lack of understanding about the constituents of our universe. Furthermore, observational tensions are starting to arise as we enter the era of precision cosmology. In this talk, I will mention how we can learn more about cosmology with future gravitational wave data. In particular, I will focus on the use of standard sirens for testing cosmology beyond the ΛCDM model. I will show how new physics can change the way gravitational waves propagate, and discuss forecasts for binary neutron star mergers with Advanced LIGO. I will show that new physics can bias constraints on the current Hubble rate H0 from standard sirens, and thus it is crucial that we search for these new effects in order to make robust prediction on sensitive cosmological parameters. Finally, I will discuss the role that Lunar Laser Ranging and Binary Pulsar data play on the outlook of standard sirens. Material:
Go to day
| 2019-12-07T20:07:00 |
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https://docs.nersc.gov/performance/io/lustre/
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# Lustre
## NERSC File Striping Recommendations¶
NERSC has provided striping command shortcuts based on file size and I/O pattern to simplify optimization on Cori.
• Shared file I/O: Either one processor does all the I/O for a simulation in serial or multiple processors write to a single shared file as with MPI-IO and parallel HDF5 or NetCDF
• File per process: Each process writes to its own file resulting in as many files as number of processes
Single Shared-File I/O File per Process
File size (GB) command
< 1 keep default striping keep default striping
1 - 10 stripe_small keep default striping
10 - 100 stripe_medium keep default striping
> 100 stripe_large keep default striping
> 1000 stripe_large stripe_large
These helper scripts will set the number of OSTs to stripe across to 8, 24, and 72 for stripe_small, stripe_medium and stripe_large, respectively. In all cases, the stripe size is 1MB.
Warn
Files larger than 1 TB should be striped with the stripe_large script.
Striping must be set on a file before is written. For example, one could simultaneously create an empty file which will later be 10-100 GB in size and set its striping appropriately with the command:
nersc$stripe_medium output_file This could be done before running a job which will later populate this file. Striping of a file cannot be changed once the file has been written to, aside from copying the existing file into a newly created (empty) file with the desired striping. Files inherit the striping configuration of the directory in which they are created. Again, the desired striping must be set on the directory before creating the files (later changes of the directory striping are not inherited). When copying an existing striped file into a striped directory, the new copy will inherit the directory's striping configuration. This provides another approach to changing the striping of an existing file. Inheritance of striping provides a convenient way to set the striping on multiple output files at once, if all such files are written to the same output directory. For example, if a job will produce multiple 10-100 GB output files in a known output directory, the striping of the latter can be configured before job submission: nersc$ mkdir output_directory
nersc$stripe_medium output_directory ### Restriping an Existing File¶ Currently the only way to restripe an existing file is to make a copy of it. nersc$ stripe_large tmp_my_big_file
nersc$cp my_big_file tmp_my_big_file nersc$ mv tmp_my_big_file my_big_file
If there are multiple files, you could create a directory with the desired striping and copy the files into it to avoid doing the above procedure multiple times.
## Custom Lustre Striping¶
To set striping for a file or directory use the command lfs setstripe.
Each file and directory can have a separate striping pattern and a directory's striping setting can be overridden for a particular file by issuing the lfs setstripe command for individual files within that directory. However, as noted above, striping settings for a file must be set before it is created. If the settings for an existing file are changed, it will only get the new striping setting if the file is recreated. If the settings for an existing directory are changed, the files need to be copied elsewhere and then copied back to the directory in order to inherit the new settings. The lfs setstripe syntax is:
nersc\$ lfs setstripe --size [stripe-size] --index [OST-start-index]
--count [stripe-count] filename
Option Description Default
stripe-size Number of bytes write on one OST before cycling to the next. Use multiples of 1MB. Default has been most successful. 1MB
stripe-count Number of OSTs a file exists on 1 on Cori
OST-start-index Starting OST. Default highly recommended -1 (System follows a round robin procedure to optimize creation of files by all users.)
| 2019-11-17T09:55:16 |
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|
https://lammps.sandia.gov/doc/Modify_contribute.html
|
# 11.2. Submitting new features for inclusion in LAMMPS
We encourage users to submit new features or modifications for LAMMPS to the core developers so they can be added to the LAMMPS distribution. The preferred way to manage and coordinate this is via the LAMMPS project on GitHub. Please see the GitHub Tutorial for a demonstration on how to do that. An alternative is to contact the LAMMPS developers or the indicated developer of a package or feature directly and send in your contribution via e-mail, but that can add a significant delay on getting your contribution included, depending on how busy the developer is you contact, how complex a task it would be to integrate that code, and how many - if any - changes are required before the code can be included.
For any larger modifications or programming project, you are encouraged to contact the LAMMPS developers ahead of time, in order to discuss implementation strategies and coding guidelines, that will make it easier to integrate your contribution and result in less work for everybody involved. You are also encouraged to search through the list of open issues on GitHub and submit a new issue for a planned feature, so you would not duplicate the work of others (and possibly get scooped by them) or have your work duplicated by others.
For informal communication with (some of) the LAMMPS developers you may ask to join the LAMMPS developers on Slack. This slack work space is by invitation only. Thus for access, please send an e-mail to [email protected] explaining what part of LAMMPS you are working on. Only discussions related to LAMMPS development are tolerated, so this is NOT for people that look for help with compiling, installing, or using LAMMPS. Please contact the lammps-users mailing list for those purposes instead.
How quickly your contribution will be integrated depends largely on how much effort it will cause to integrate and test it, how much it requires changes to the core codebase, and of how much interest it is to the larger LAMMPS community. Please see below for a checklist of typical requirements. Once you have prepared everything, see the Using GitHub with LAMMPS Howto doc page for instructions on how to submit your changes or new files through a GitHub pull request. If you prefer to submit patches or full files, you should first make certain, that your code works correctly with the latest patch-level version of LAMMPS and contains all bug fixes from it. Then create a gzipped tar file of all changed or added files or a corresponding patch file using ‘diff -u’ or ‘diff -c’ and compress it with gzip. Please only use gzip compression, as this works well on all platforms.
If the new features/files are broadly useful we may add them as core files to LAMMPS or as part of a standard package. Else we will add them as a user-contributed file or user package. Examples of user packages are in src sub-directories that start with USER. The USER-MISC package is simply a collection of (mostly) unrelated single files, which is the simplest way to have your contribution quickly added to the LAMMPS distribution. All the standard and user packages are listed and described on the Packages details doc page.
Note that by providing us files to release, you are agreeing to make them open-source, i.e. we can release them under the terms of the GPL, used as a license for the rest of LAMMPS. See the Open source page on the LAMMPS website for details.
With user packages and files, all we are really providing (aside from the fame and fortune that accompanies having your name in the source code and on the Authors page of the LAMMPS WWW site), is a means for you to distribute your work to the LAMMPS user community, and a mechanism for others to easily try out your new feature. This may help you find bugs or make contact with new collaborators. Note that you’re also implicitly agreeing to support your code which means answer questions, fix bugs, and maintain it if LAMMPS changes in some way that breaks it (an unusual event).
Note
If you prefer to actively develop and support your add-on feature yourself, then you may wish to make it available for download from your own website, as a user package that LAMMPS users can add to their copy of LAMMPS. See the Offsite LAMMPS packages and tools page of the LAMMPS web site for examples of groups that do this. We are happy to advertise your package and web site from that page. Simply email the developers with info about your package and we will post it there.
The previous sections of this doc page describe how to add new “style” files of various kinds to LAMMPS. Packages are simply collections of one or more new class files which are invoked as a new style within a LAMMPS input script. If designed correctly, these additions typically do not require changes to the main core of LAMMPS; they are simply add-on files. If you think your new feature requires non-trivial changes in core LAMMPS files, you should communicate with the developers, since we may or may not want to include those changes for some reason. An example of a trivial change is making a parent-class method “virtual” when you derive a new child class from it.
Here is a checklist of steps you need to follow to submit a single file or user package for our consideration. Following these steps will save both you and us time. Please have a look at the existing files in packages in the src directory for examples. If you are uncertain, please ask.
• All source files you provide must compile with the most current version of LAMMPS with multiple configurations. In particular you need to test compiling LAMMPS from scratch with -DLAMMPS_BIGBIG set in addition to the default -DLAMMPS_SMALLBIG setting. Your code will need to work correctly in serial and in parallel using MPI.
• For consistency with the rest of LAMMPS and especially, if you want your contribution(s) to be added to main LAMMPS code or one of its standard packages, it needs to be written in a style compatible with other LAMMPS source files. This means: 2-character indentation per level, no tabs, no lines over 80 characters. I/O is done via the C-style stdio library (mixing of stdio and iostreams is generally discouraged), class header files should not import any system headers outside of <cstdio>, STL containers should be avoided in headers, system header from the C library should use the C++-style names (<cstdlib>, <cstdio>, or <cstring>) instead of the C-style names <stdlib.h>, <stdio.h>, or <string.h>), and forward declarations used where possible or needed to avoid including headers. All added code should be placed into the LAMMPS_NS namespace or a sub-namespace; global or static variables should be avoided, as they conflict with the modular nature of LAMMPS and the C++ class structure. Header files must not import namespaces with using. This all is so the developers can more easily understand, integrate, and maintain your contribution and reduce conflicts with other parts of LAMMPS. This basically means that the code accesses data structures, performs its operations, and is formatted similar to other LAMMPS source files, including the use of the error class for error and warning messages.
• If you want your contribution to be added as a user-contributed feature, and it’s a single file (actually a *.cpp and *.h file) it can rapidly be added to the USER-MISC directory. Send us the one-line entry to add to the USER-MISC/README file in that dir, along with the 2 source files. You can do this multiple times if you wish to contribute several individual features.
• If you want your contribution to be added as a user-contribution and it is several related features, it is probably best to make it a user package directory with a name like USER-FOO. In addition to your new files, the directory should contain a README text file. The README should contain your name and contact information and a brief description of what your new package does. If your files depend on other LAMMPS style files also being installed (e.g. because your file is a derived class from the other LAMMPS class), then an Install.sh file is also needed to check for those dependencies. See other README and Install.sh files in other USER directories as examples. Send us a tarball of this USER-FOO directory.
• Your new source files need to have the LAMMPS copyright, GPL notice, and your name and email address at the top, like other user-contributed LAMMPS source files. They need to create a class that is inside the LAMMPS namespace. If the file is for one of the USER packages, including USER-MISC, then we are not as picky about the coding style (see above). I.e. the files do not need to be in the same stylistic format and syntax as other LAMMPS files, though that would be nice for developers as well as users who try to read your code.
• You must also create a documentation file for each new command or style you are adding to LAMMPS. For simplicity and convenience, the documentation of groups of closely related commands or styles may be combined into a single file. This will be one file for a single-file feature. For a package, it might be several files. These are text files with a .rst extension using the reStructuredText markup language, that are then converted to HTML and PDF using the Sphinx documentation generator tool. Running Sphinx with the included configuration requires Python 3.x. Configuration settings and custom extensions for this conversion are included in the source distribution, and missing python packages will be transparently downloaded into a virtual environment via pip. Thus, if your local system is missing required packages, you need access to the internet. The translation can be as simple as doing “make html pdf” in the doc folder. As appropriate, the text files can include inline mathematical expression or figures (see doc/JPG for examples). Additional PDF files with further details (see doc/PDF for examples) may also be included. The doc page should also include literature citations as appropriate; see the bottom of doc/fix_nh.rst for examples and the earlier part of the same file for how to format the cite itself. Citation labels must be unique across all .rst files. The “Restrictions” section of the doc page should indicate if your command is only available if LAMMPS is built with the appropriate USER-MISC or USER-FOO package. See other user package doc files for examples of how to do this. Please run at least “make html” and “make spelling” and carefully inspect and proofread the resulting HTML format doc page before submitting your code. Upon submission of a pull request, checks for error free completion of the HTML and PDF build will be performed and also a spell check, a check for correct anchors and labels, and a check for completeness of references all styles in their corresponding tables and lists is run. In case the spell check reports false positives they can be added to the file doc/utils/sphinx-config/false_positives.txt
• For a new package (or even a single command) you should include one or more example scripts demonstrating its use. These should run in no more than a couple minutes, even on a single processor, and not require large data files as input. See directories under examples/USER for examples of input scripts other users provided for their packages. These example inputs are also required for validating memory accesses and testing for memory leaks with valgrind
• If there is a paper of yours describing your feature (either the algorithm/science behind the feature itself, or its initial usage, or its implementation in LAMMPS), you can add the citation to the *.cpp source file. See src/USER-EFF/atom_vec_electron.cpp for an example. A LaTeX citation is stored in a variable at the top of the file and a single line of code that references the variable is added to the constructor of the class. Whenever a user invokes your feature from their input script, this will cause LAMMPS to output the citation to a log.cite file and prompt the user to examine the file. Note that you should only use this for a paper you or your group authored. E.g. adding a cite in the code for a paper by Nose and Hoover if you write a fix that implements their integrator is not the intended usage. That kind of citation should just be in the doc page you provide.
Finally, as a general rule-of-thumb, the more clear and self-explanatory you make your documentation and README files, and the easier you make it for people to get started, e.g. by providing example scripts, the more likely it is that users will try out your new feature.
| 2020-07-12T20:23:36 |
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|
http://www-spires.fnal.gov/spires/find/books/www?keyword=%22Dark+energy+Astronomy%22
|
Fermilab Core Computing Division
Library Home | Ask a Librarian [email protected] | Book Catalog | Library Journals | Requests | SPIRES | Fermilab Documents |
Fermilab Library
SPIRES-BOOKS: FIND KEYWORD DARK ENERGY ASTRONOMY *END*INIT* use /tmp/qspiwww.webspi1/23593.266 QRY 131.225.70.96 . find keyword "dark energy astronomy" ( in books using www
Call number: 3527409416:ONLINE Show nearby items on shelf Title: Dark Energy Author(s): Wang Date: 2010 Publisher: Wiley-VCH Size: 1 online resource (257 p.) ISBN: 9783527409419 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Astronomy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642293382:ONLINE Show nearby items on shelf Title: Simulations of Dark Energy Cosmologies [electronic resource] Author(s): Elise Jennings Date: 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642293382 Series: Springer Theses Series: e-books Keywords: Cosmology , Theoretical, Mathematical and Computational Physics , Elementary Particles, Quantum Field Theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2001-9780306471162:ONLINE Show nearby items on shelf Title: The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Elementary Particle Physics Author(s): Date: 2001 Size: 1 online resource (261 p.) Note: 10.1007/b114707 Contents: The Cosmological Constant is not Really a Constant -- Recent Developments in Gravitational Theory and an Intrinsic Cosmological Parameter -- Quintessence and Cosmic Microwave Background -- Cosmic Acceleration and a Natural Solution to the Cosmological Constant Problem -- Beyond the Standard Model -- Spontaneous Violation of Lorentz and CPT Symmetry -- Topics in Lorentz and CPT Violation -- Dark Matter Caustics -- Manifest Supersymmetry and Background Ramond FLux -- Neutrino Physics and Cosmology -- Supernova II Neutrino Bursts and Neutrino Massive Mixing -- A Neutrino Component of Ultra High Energy Cosmic Rays? -- Probing the Nature of Neutrinos at Pion Factories -- Inclusive Neutrino and Antineutrino Reactions in Iron and an Interesting Relation -- Nature’s Highest Energy Particle Accelerators -- Nature’s Highest Energy Particle Accelerators -- The Origin of all Cosmic Rays: A Space-Filling Mechanism -- Primordial Black Holes and the Asymmetrical Distribution of Short GRB Events -- Exploring the Extreme Universe with the Gamma-Ray Large Area Space Telescope -- The Latest Developments in High Energy Physics and Cosmology -- Comments on Supersymmetry Extra Dimensions and the Accelerating Universe -- Field Theory Correlators and String Theory -- A Microscopic Basis for the Entropy of AdS3 Black Hole -- CP-Violation in B—Decays Status and Prospects of $$\bar B$$ -- New Experiment on Spinning Protons’ Violent Collisions -- The Grand Unified Theory of Classical Quantum Mechanics ISBN: 9780306471162 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Physics , Gravitation , Observations, Astronomical , Astronomy , Nuclear physics , Heavy ions , Hadrons , Elementary particles (Physics) , Quantum field theory , Physics , Elementary Particles, Quantum Field Theory , Particle and Nuclear Physics , Theoretical, Mathematical and Computational Physics , Nuclear Physics, Heavy Ions, Hadrons , Classical and Quantum Gravitation, Relativity Theory , Astronomy, Observations and Techniques Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: QC793.5.N42C87::2001 Show nearby items on shelf Title: Current Aspects of neutrino physics Author(s): David O. Caldwell (ed.) Date: 2001 Publisher: Springer: New York Size: 335 pgs. Contents: 1. Pauli's Ghotst: The Conception and Discovery of Neutrinos, 2. The Nature of Massive Neutrinos, 3. Direct Measurements of Neutrino Mass, 4. Neutrino Oscillations and the Solar Neutrino Problem, 5. The Atmospheric Neutrino Anomaly: Muon Neutrino Disappearance, 6. Studies of Neutrino Oscillations at Reactors, 7. Sutdies of Neutrino Oscillations at Accelerators, 8. Double Beta Decay: Theory, Experiment and Implications, 9. Neutrino Mixing Schemes, 10. Theories of Neutrino Masses and Mixings, 11. Neutrino Flavor Transformation in Supernovae and the Early Universe, 12. Hot Dark Matter in Cosmology, 13. High Energy Neutrino Astronomy: Towards Kilometer-Scale Detectors ISBN: 3540410023 Keywords: Neutrinos. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QB981.A38::2012 Show nearby items on shelf Title: Adventures in cosmology Author(s): (ed.) David Goodstein Date: 2012 Publisher: Hackensack, NJ : World Scientific Size: 410 p. Contents: Galaxy formation : from start to finish / Andrew Benson -- The reionization of cosmic hydrogen by the first galaxies / Abraham Loeb -- Clusters of galaxies / Elena Pierpaoli -- Reionizing the universe with the first sources of light / Volker Bromm -- Mapping the cosmic dawn / Steven Furlanetto -- Neutrino masses from cosmology / Ofer Lahav and Shaun Thomas -- Measuring the expansion rate of the universe / Laura Ferrarese Particles as dark matter / Dan Hooper -- Detection of WIMP dark matter / Sunil Golwala and Dan McKinsey -- The accelerating universe / Dragan Huterer -- Frontiers of dark energy / Eric V. Linder -- The first supermassive black holes in the universe / Xiaohui Fan. ISBN: 9789814313858 Keywords: Cosmology , Galaxies , Dark matter (Astronomy) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QB813.S95K57::2002 Show nearby items on shelf Title: The Extravagant universe Exploding stars, dark energy and the accelerating cosmos Author(s): Robert P. Kirshner 1949- Date: 2002 Publisher: Princeton, N.J. : Princeton University Press Note: 282 p. ISBN: 0691058628 Keywords: Supernovae , Dark energy (Astronomy) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QB791.3.L53::2015 Show nearby items on shelf Title: Dark energy Author(s): Miao Li Xiao-Dong Li Shuang Wang Yi Wang Publisher: World Scientific Size: 268 p. ISBN: 9789814619707 Keywords: Dark energy (Astronomy) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: SUGGESTIONS (email [email protected] if you would like this title added to the Library collection.)
Call number: QB791.3.G38::2009 Show nearby items on shelf Title: Einstein's Telescope : The Hunt for Dark Matter and Dark Energy in the Universe Author(s): Evalyn Gates Date: 2009 Publisher: W.W. Norton & Co. ISBN: 9780393062380 Keywords: Einstein, Albert, 1879-1955 - Influence , Dark Matter (Astronomy) , Dark Energy (Astronomy) , Graviatational Waves , Relativity (Physics) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: POP
Call number: QB791.3.F75::2014 Show nearby items on shelf Title: The cosmic cocktail : three parts dark matter Author(s): Katherine Freese Date: 2014 Publisher: Princeton, New Jersey : Princeton University Press Size: 250 p Contents: The golden era of particle cosmology or how I joind the Chicago mafia -- How do cosmologists know dark matter exists -- The big picture of the universe Einstein and the Big Bang -- What is dark matter -- The discovery of the Higgs Boson -- The exper imental hunt for dark matter particles -- claims of detection are the real -- Dark energy and the fate of the universe ISBN: 9780691153353 Series: Science essentials Keywords: Cosmology : fast , Dark matter (Astronomy) : fast Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QB791.3.D43::2008 Show nearby items on shelf Title: A Decade of dark energy [DVD] Conference: STSI Spring Symposium 2008, A Decade of Dark Energy, Baltimore Md., 5-8 May 2008 Author(s): Norbert Pirzkal (ed.) Henry Ferguson (ed.) Date: 2008 Publisher: Baltimore, MD : Space Telescope Sci.Inst. Size: 2 DVD Contents: Dark Energy Dichotomies by R. Bean Constraining Dark Energy by P. Steinhardt Piecing Together Current Supernova Constraints on Dark Energy by S. Perlmutter Dark Energy and the Hubble Constant from HST, Version 2.0 by A. Riess The Megamaser Cosmology Project by J. Braatz Models of Dark Energy by E. Witten Dark Energy Constraints on Modified Gravities by I. Neupane Cosmological Post-Newtonian Approximation with Dark Energy by J. Hwang Neutrino Clustering in Interacting Dark Energy Cosmologies by V. Pettorino Supernovae by W. Freedman Baryon Acoustic Oscillations : A Robust and Precise Route to the Cosmological Distance Scale by D. Eisenstein Magnification Distortion of the Galaxy Correlation Function : Opportunities and Challenges by L. Hui Figures of Merit for Dark Energy Experiments by D. Huterer What Figure of Merit Should We Use to Evaluate Dark Energy Projects by Y. Wang What Can We Learn from Future Dark Energy Probes by A. Albrecht Recent Results from Weak Gravitational Lensing by Large Scale Structure by H. Hoekstra WMAP : Recent Resluts and Dark Energy by L. Page Cosmological Constraints from X-Ray Studies of Galaxy Clusters by S. Allen Cosmic Shear : Potential and Prospects by S. Bridle First Results from the WiggleZ Galaxy Redshift Survey by C. Blake The Dark Energy Indicator : A Measure of Deviations of w from -1 by R. Daly TOC = Uncorrelated Estimates of Dark Energy Equation of State by A. Cooray Overview of the dark Energy Survey by B. Flaugher The SDSS Supernova Survey : Results and Prospects by S. Jha How Can CMB Help Constraining Dark Energy by L. Verde The Large Synoptic Survey Telescope by T. Tyson Inflation and Dark Energy : Is There a Connection by S. Watson Dark Energy Constraits from the Superrnova Legacy Survey by M. Sullivan Latest Results from Large - Scale Structure and Baryon Acoustic Oscillation Observations by W. Percival Improving the Low -Redshift Foundations : Resluts from the Lick Observatory Supernova Search by A. Filippenko The Cosmology of f(R) Models for Acceleration by W. Hu Testing Gravity with Lensing and Large-Scale Structure by B. Jain EUCLID : ESA's Proposed Dark Energy Mission by J.Peacock DESTINY, The Dark Energy Space Telescope by T. Lauer SNAP - An overview of the Supernova Acceleration Probe (SNAP) Mission by G. Bernstein ADEPT - Advanced Dark Energy Physics Telescope by C. Bennett Dark Energy : Hopes and Expectations by M. Livio Dark Conclusions by J. Peacock Series: Symposium (series) : 22 Keywords: Dark energy (Astronomy) Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Location: DVD COLLECTION
Call number: QB791.3.D37::2007 Show nearby items on shelf Title: Dark matter, dark energy : the dark side of the universe Author(s): Sean Carroll Date: 2007 Publisher: Chantilly, VA: Teaching Co. Size: 2 videodiscs + 1 course guidebook Note: 4 DVDs (Part 1 and Part 2) and course guidebook Note: Science & mathematics course no. 1272 Contents: Pt. 1. Disc 1. Lecture 1. Fundamental building blocks, Lecture 2. The smooth, expanding universe , Lecture 3. Space, time and gravity, Lecture 4. Cosmology in Einstein's universe, Lecture 5. Galaxies and clusters, Lecture 6. Gravitational lensing -- Disc 2. Lecture 7. Atoms and particles, Lecture 8. The standard model of particle physics, Lecture 9. Relic particles from the Big Bang, Lecture 10. Primordial nucleosynthesis , Lecture 11. The cosmic microwave background, Lecture 12. Dark stars and black holes. ISBN: 1598033506 Series: Great courses Keywords: Dark matter (Astronomy) , Dark energy (Astronomy) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: AV-CROSS-WALK
Call number: QB471.A1W77::2007 Show nearby items on shelf Title: Proceedings of the fifth International Workshop on Science With the New Generation High-Energy Gamma-Ray Experiments Villa Mondragone, Monteporzio, June 18-20, 2007 Conference: 5th Workshop on Science with the New Generation High Energy Gamma-Ray Experiments (SciNe-GHE07): The Light of the Dark: Solving the Mysteries of the Universe 18-20 Jun 2007, Frascati, Rome, Italy [C07-06-18.3] Author(s): A. Lionetto (ed.) A. Morselli (ed.) (INFN, Rome)(Rome U., Tor Vergata) Date: 2007 Publisher: Frascati : INFN Size: 328 p ISBN: 9788886409540 Series: Frascati physics series : v. 45 Keywords: Gamma ray astronomy Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QB464.2.N46::2017 Show nearby items on shelf Title: Neutrino astronomy current status, future prospects Author(s): Thomas Gaisser (ed.) Albrecht Karle (ed.) Date: 2017 Publisher: World Scientific Size: 242 p Note: This review volume is motivated by the recent discovery of high-energy astrophysical neutrinos by IceCube -- back cover Contents: Gamma ray bursts as neutrino sources / Peter Mészáros -- Active galactic nuclei as high-energy neutrino sources / Kohta Murase -- The origin of IceCube's neutrinos: cosmic ray accelerators embedded in star forming calorimeters / E. Waxman -- Galactic neutrino sources / Markus Ahlers -- Observations of diffuse fluxes of cosmic neutrinos / Christopher H. Wiebusch -- IceCube and astrophysical neutrinos: the search for sources / Chad Finley -- Recent results from the ANTARES neutrino telescope / Paschal Coyle and Clancy A. James -- The baikal neutrino project / V.M. Aynutdinov and Zh. A.M. Dzhilkibaev -- The dawn of multi-messenger astronomy / Marcos Santander -- Neutrinos from core-collapse supernovae / Marek Kowalski -- The quest for dark matter with neutrino telescopes / Carlos Pérez de los Heros -- KM3NeT: astroparticle and oscillations research with cosmics in the abyss / M. de Jong -- A next generation IceCube -- the IceCube-Gen2 facility for high energy neutrino astronomy / Erik Blaufuss and Albrecht Karle -- Neutrino physics with very large volume neutrino telescopes / Tyce DeYoung and Antoine Kouchner -- Radio detection of high-energy neutrinos / Amy Connolly and Abigail Vieregg ISBN: 9814759406 Keywords: Neutrino astrophysics , Astronomy Observations Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QB464.T8::2004 Show nearby items on shelf Title: A 21st century frontier of discovery: The physics of the universe a strategic plan for federal research at the intersection of physics and astronomy : a report of the Interagency Working Group on the Physics of the Universe. Author(s): National Science and Technology Council (U.S.)., Interagency Working Group on the Physics of the Universe Date: 2004 Publisher: [Washington, D.C.] : National Science and Technology Council, Committee on Science Size: 70 p. Contents: What is dark matter? -- What is the nature of dark energy? -- How did the universe begin? -- Did Einstein have the last word on gravity? -- What are the masses of the neutrinos and how have they shaped the evolution of the universe? How do cosmic accelerators work and what are they accelerating? -- Are protons unstable? -- What are the new states of matter at exceedingly high density and temperature? -- Are there additional space-time dimensions? -- How were the elements from iron to uranium made ? -- Is a new theory of matter and light needed at the highest energies? Corp. Author: National Science and Technology Council (U.S.)., Interagency Working Group on the Physics of the Universe Keywords: Physics Research United States , Astrophysics Research United States Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Full Text: Click here Location: POP
Call number: NUPHZ:V194 Show nearby items on shelf Title: GGI--Dark Matter and Dark Energy 2009 New Horizons for Modern Cosmology : Proceedings of the Galileo Galilei Institute Conferences on Dark Matter and Dark Energy, Florence, Italy, 19th January -- 13th March 2009 Conference: New Horizons For Modern Cosmology 19 Jan - 13 Mar 2009, Arcetri, Florence, Italy [C09-01-19] Author(s): M. Kamionkowski (ed.) C. Martins (ed.) A. Melchiorri (ed.) A. Polosa (ed.) L. Verde (ed.) Galileo Galilei Institute Conferences on Dark Matter and Dark Energy (2009 : Florence, Italy) Date: 2009 Publisher: Amsterdam : Elsevier Size: 360 p Series: Nucl.Phys.Proc.Suppl.194 Corp. Author: Galileo Galilei Institute Conferences on Dark Matter and Dark Energy (2009 : Florence, Italy) Keywords: Dark matter (Astronomy) Congresses , Dark energy (Astronomy) Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Full Text: Click here Location: ONLINE
Call number: NUPHZ:V173 Show nearby items on shelf Title: Dark matter 2006 Proceedings of the 7th UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe, Marina del Rey, CA, USA, 22-24 February 2006 Conference: 7th UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe 22-24 Feb 2006, Marina de Rey, California [C06-02-22.1] Author(s): David B. Cline (ed.) International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (7th : 2006 : Marina del Rey, Calif.) Date: 2007 Publisher: Amsterdam : Elsevier Size: 183 p Series: Nucl.Phys.Proc.Suppl.173 Corp. Author: International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (7th : 2006 : Marina del Rey, Calif.) Keywords: Dark matter (Astronomy) Congresses , Dark energy (Astronomy) Congresses , Detectors Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Full Text: Click here Location: ONLINE
Call number: NUPHZ:V124 Show nearby items on shelf Title: Dark matter 2002 Proceedings of the 5th International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe, Marina del Rey, CA, USA, 20-22 February 2002 Conference: 5th International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (DM 2002) 20-22 Feb 2002, Marina del Rey, California [C02-02-20] Author(s): International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (5th : 2002 : Marina del Rey, Calif.) Date: 2003 Publisher: Amsterdam : North-Holland Size: 276 p Series: Nucl.Phys.Proc.Suppl.124 Corp. Author: International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (5th : 2002 : Marina del Rey, Calif.) Keywords: Dark matter (Astronomy) Congresses , Dark energy (Astronomy) Congresses , Detectors Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Full Text: Click here Location: ONLINE
Call number: APCPC:V672 Show nearby items on shelf Title: Short distance behavior of fundamental interactions 31st Coral Gables Conference on High Energy Physics and Cosmology, Fort Lauderdale, Florida, 11-14 December 2002 Conference: 31st Coral Gables Conference on High-Energy Physics and Cosmology: Short Distance Behavior of Fundamental Interactions 11-14 Dec 2002, Fort Lauderdale, Florida [C02-12-11.2] Author(s): B.N. Kursunoglu Coral Gables Conference on High-Energy Physics and Cosmology (31st : 2002 : Fort Lauderdale, Florida) Date: 2003 Publisher: Melville, N.Y. : AIP Size: 227 p. Note: AIP Conference Proceedings eBook platform ISBN: 073540139X Series: AIP Conf.Proc.672 Series: e-Books Corp. Author: Coral Gables Conference on High-Energy Physics and Cosmology (31st : 2002 : Fort Lauderdale, Florida) Keywords: Particles (Nuclear physics) Congresses , Cosmology Congresses , Dark energy (Astronomy) Congresses , Conference proceedings , Conferences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Full Text: Click here Location: ONLINE
| 2019-03-25T21:44:54 |
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|
https://simpsonstappedout.fandom.com/wiki/Penny_Fountain
|
## FANDOM
5,418 Pages
The Penny Fountain is a limited-time building released on January 3, 2016, as part of the Homer the Heretic 2017 Event. It was awarded for free upon start of Homer the Heretic Pt. 2.
Whilst Mr. Burns goes shopping he finds a penny in a water fountain and reaches in to grab it; while doing so he falls in. The rushing water nearly drowns him, but Homer arrives and pulls him out of the water, saving Mr. Burns' life. To reward him, Mr. Burns offers to take Homer out to dinner. Homer says he likes Chicago deep dish pizza, so Mr. Burns takes him to Chicago on his private plane. On the plane, Homer is treated with luxury and gets serenaded by Lionel Richie.
## Jobs Involved Edit
### Regular Jobs
• Fall into the Fountain - 60m
## Tiered Reward Edit
A feature introduced with this item, and currently unique to it, is the tiered reward. The item's reward increases in pre-set milestones and it can be collected at any moment once the first milestone is reached. Whenever a collection of the item is made, the timer completely resets.
### Event Edit
During the Homer the Heretic 2017 Event, the Penny Fountain rewarded 1 Karma every five minutes as shown in the table below.
Time Reward
5 minutes 1
$5n$ minutes, $1<n<60$ $n$
300 minutes
(5 hours)
60
### Event expired or completed Edit
The Penny Fountain rewards Cash every hours up to five hours as shown in the table below
Time Reward
60 minutes 40
2 hours 80
3 hours 120
4 hours 160
5 hours 200
## Trivia Edit
• Only one can be obtained.
• It can be placed on grass, pavement, or dirt.
## Gallery Edit
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-09-23T00:54:32 |
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|
http://dlmf.nist.gov/30.8
|
# §30.8(i) Functions of the First Kind
30.8.1 $\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits\!\left(x,\gamma^{2}\right)=\sum_{k=-R}% ^{\infty}(-1)^{k}a^{m}_{n,k}(\gamma^{2})\mathop{\mathsf{P}^{m}_{n+2k}\/}% \nolimits\!\left(x\right),$
where $\mathop{\mathsf{P}^{m}_{n+2k}\/}\nolimits\!\left(x\right)$ is the Ferrers function of the first kind (§14.3(i)), $R=\left\lfloor\frac{1}{2}(n-m)\right\rfloor$, and the coefficients $a^{m}_{n,k}(\gamma^{2})$ are given by
30.8.2 $a^{m}_{n,k}(\gamma^{2})=(-1)^{k}\left(n+2k+\tfrac{1}{2}\right)\frac{(n-m+2k)!}% {(n+m+2k)!}\*\int_{-1}^{1}\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits\!\left(x,% \gamma^{2}\right)\mathop{\mathsf{P}^{m}_{n+2k}\/}\nolimits\!\left(x\right)dx.$
Let
30.8.3 $\displaystyle A_{k}$ $\displaystyle=-\gamma^{2}\frac{(n-m+2k-1)(n-m+2k)}{(2n+4k-3)(2n+4k-1)},$ $\displaystyle B_{k}$ $\displaystyle=(n+2k)(n+2k+1)-2\gamma^{2}\frac{(n+2k)(n+2k+1)-1+m^{2}}{(2n+4k-1% )(2n+4k+3)},$ $\displaystyle C_{k}$ $\displaystyle=-\gamma^{2}\frac{(n+m+2k+1)(n+m+2k+2)}{(2n+4k+3)(2n+4k+5)}.$
Then the set of coefficients $a^{m}_{n,k}(\gamma^{2})$, $k=-R,-R+1,-R+2,\dots$ is the solution of the difference equation
30.8.4 $A_{k}f_{k-1}+\left(B_{k}-\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}% \right)\right)f_{k}+C_{k}f_{k+1}=0,$
(note that $A_{-R}=0$) that satisfies the normalizing condition
30.8.5 $\sum_{k=-R}^{\infty}a_{n,k}^{m}(\gamma^{2})a_{n,k}^{-m}(\gamma^{2})\frac{1}{2n% +4k+1}=\frac{1}{2n+1},$
with
30.8.6 $a_{n,k}^{-m}(\gamma^{2})=\frac{(n-m)!(n+m+2k)!}{(n+m)!(n-m+2k)!}a_{n,k}^{m}(% \gamma^{2}).$
Also, as $k\to\infty$,
30.8.7 $\frac{k^{2}a^{m}_{n,k}(\gamma^{2})}{a^{m}_{n,k-1}(\gamma^{2})}=\frac{\gamma^{2% }}{16}+\mathop{O\/}\nolimits\!\left(\frac{1}{k}\right),$
and
30.8.8 $\frac{\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)-B_{k}}{A_{k% }}\frac{a^{m}_{n,k}(\gamma^{2})}{a^{m}_{n,k-1}(\gamma^{2})}=1+\mathop{O\/}% \nolimits\!\left(\frac{1}{k^{4}}\right).$
# §30.8(ii) Functions of the Second Kind
30.8.9 $\mathop{\mathsf{Qs}^{m}_{n}\/}\nolimits\!\left(x,\gamma^{2}\right)=\sum_{k=-% \infty}^{-N-1}(-1)^{k}{a^{\prime}}^{m}_{n,k}(\gamma^{2})\mathop{\mathsf{P}^{m}% _{n+2k}\/}\nolimits\!\left(x\right)+\sum_{k=-N}^{\infty}(-1)^{k}a^{m}_{n,k}(% \gamma^{2})\mathop{\mathsf{Q}^{m}_{n+2k}\/}\nolimits\!\left(x\right),$
where $\mathop{\mathsf{P}^{m}_{n}\/}\nolimits$ and $\mathop{\mathsf{Q}^{m}_{n}\/}\nolimits$ are again the Ferrers functions and $N=\left\lfloor\frac{1}{2}(n+m)\right\rfloor$. The coefficients $a^{m}_{n,k}(\gamma^{2})$ satisfy (30.8.4) for all $k$ when we set $a^{m}_{n,k}(\gamma^{2})=0$ for $k<-N$. For $k\geq-R$ they agree with the coefficients defined in §30.8(i). For $k=-N,-N+1,\dots,-R-1$ they are determined from (30.8.4) by forward recursion using $a^{m}_{n,-N-1}(\gamma^{2})=0$. The set of coefficients ${a^{\prime}}^{m}_{n,k}(\gamma^{2})$, $k=-N-1,-N-2,\dots$, is the recessive solution of (30.8.4) as $k\to-\infty$ that is normalized by
30.8.10 $A_{-N-1}{a^{\prime}}^{m}_{n,-N-2}(\gamma^{2})+{\left(B_{-N-1}-\mathop{\lambda^% {m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)\right){a^{\prime}}^{m}_{n,-N-1}(% \gamma^{2})}+C^{\prime}a^{m}_{n,-N}(\gamma^{2})=0,$
with
30.8.11 $C^{\prime}=\begin{cases}\dfrac{\gamma^{2}}{4m^{2}-1},&\mbox{n-m even},\\ -\dfrac{\gamma^{2}}{(2m-1)(2m-3)},&\mbox{n-m odd}.\end{cases}$ Symbols: $m$: nonnegative integer, $n\geq m$: integer degree, $\gamma^{2}$: real parameter and $C^{\prime}$ Permalink: http://dlmf.nist.gov/30.8.E11 Encodings: TeX, pMML, png
It should be noted that if the forward recursion (30.8.4) beginning with $f_{-N-1}=0$, $f_{-N}=1$ leads to $f_{-R}=0$, then $a^{m}_{n,k}(\gamma^{2})$ is undefined for $n<-R$ and $\mathop{\mathsf{Qs}^{m}_{n}\/}\nolimits\!\left(x,\gamma^{2}\right)$ does not exist.
| 2014-10-21T02:15:22 |
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|
https://pos.sissa.it/316/041/
|
Volume 316 - XXVI International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2018) - WG2: Small-x and Diffraction
Exclusive vector meson photoproduction at Run 2 LHC energies: Color dipole predictions
V.P. Goncalves*, M. Machado, B.D. Moreira, F.S. Navarra and G. Santos
Full text: pdf
Pre-published on: September 20, 2018
Published on: November 23, 2018
Abstract
The theoretical uncertainty on the Color Dipole predictions for the $\rho$ and $J/\Psi$ photoproduction in nucleus-nucleus collisions at Run 2 LHC energies is investigated. The results for rapidity distributions and total cross sections are presented. Moreover, the predictions are compared with the recent preliminary data from ALICE collaboration for the $\rho$ photoproduction in $PbPb$ collisions at central rapidities.
DOI: https://doi.org/10.22323/1.316.0041
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.
| 2023-02-05T18:17:10 |
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|
https://www.zbmath.org/authors/?q=ai%3Alamport.leslie
|
## Lamport, Leslie
Compute Distance To:
Author ID: lamport.leslie Published as: Lamport, Leslie; Lamport, L. External Links: MGP · Wikidata · dblp · GND · IdRef Awards: Turing Award (2013)
Documents Indexed: 75 Publications since 1970, including 2 Books 2 Further Contributions Biographic References: 3 Publications Co-Authors: 29 Co-Authors with 21 Joint Publications 425 Co-Co-Authors
all top 5
### Co-Authors
54 single-authored 4 Gafni, Eli M. 3 Pease, Marshall C. III 3 Shostak, Robert E. 2 Abadi, Martín 2 Aguilera, Marcos Kawazoe 2 Dijkstra, Edsger Wybe 2 Johnson, James E. 2 Langworthy, David E. 2 Scholten, Carel S. 2 Steffens, Elisabeth F. M. 2 Vogt, Friedrich H. 1 Cousineau, Denis 1 Doligez, Damien 1 Joshi, Rajeev 1 Ladkin, Peter B. 1 Lynch, Nancy Ann 1 Malkhi, Dahlia 1 Melliar-Smith, P. Michael 1 Merz, Stephan 1 Olivier, Bryan 1 Owicki, Susan S. 1 Perl, Sharon 1 Ricketts, Daniel 1 Roegel, Denis 1 Schneider, Fred B. 1 Tasiran, Serdar 1 Tuttle, Mark R. 1 Vanzetto, Hernán 1 Weihl, William E. 1 Yu, Yuan 1 Ziegler, Günter Matthias
all top 5
### Serials
12 Distributed Computing 8 Communications of the ACM 5 Journal of the Association for Computing Machinery 5 ACM Transactions on Programming Languages and Systems 3 Theoretical Computer Science 2 Acta Informatica 1 American Mathematical Monthly 1 Information Processing Letters 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 IEEE Transactions on Computers 1 Science of Computer Programming 1 IEEE Transactions on Software Engineering 1 Formal Methods in System Design 1 Bulletin of the European Association for Theoretical Computer Science EATCS 1 The Journal of Logic and Algebraic Programming 1 Foundations of Physics 1 Bulletin of the American Mathematical Society 1 Journal of Fixed Point Theory and Applications 1 ACM Books
all top 5
### Fields
70 Computer science (68-XX) 4 General and overarching topics; collections (00-XX) 3 Mathematical logic and foundations (03-XX) 2 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Partial differential equations (35-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
60 Publications have been cited 1,548 times in 1,187 Documents Cited by Year
Time, clocks, and the ordering of events in a distributed system. Zbl 0378.68027
Lamport, Leslie
1978
Reaching agreement in the presence of faults. Zbl 0434.68031
Pease, M.; Shostak, R.; Lamport, L.
1980
The Byzantine generals problem. Zbl 0483.68021
Lamport, Leslie; Shostak, Robert; Pease, Marshall
1982
The existence of refinement mappings. Zbl 0728.68083
1991
On interprocess communication. I: Basic formalism. Zbl 0598.68022
Lamport, Leslie
1986
How to make a microprocessor computer that correctly executes multiprocess programs. Zbl 0419.68045
Lamport, Leslie
1979
Proving liveness properties of concurrent programs. Zbl 0483.68013
Owicki, Susan; Lamport, Leslie
1982
A new solution of Dijkstra’s concurrent programming problem. Zbl 0281.68004
Lamport, Leslie
1974
Proving the correctness of multiprocess programs. Zbl 0349.68006
Lamport, Leslie
1977
On interprocess communication. II: Algorithms. Zbl 0598.68023
Lamport, Leslie
1986
The parallel execution of DO loops. Zbl 0273.68012
Lamport, Leslie
1974
Specifying concurrent program modules. Zbl 0516.68010
Lamport, Leslie
1983
The mutual exclusion problem. II: Statement and solutions. Zbl 0627.68018
Lamport, Leslie
1986
The mutual exclusion problem. I: A theory of interprocess communication. Zbl 0627.68017
Lamport, Leslie
1986
On-the-fly garbage collection: An exercise in cooperation. Zbl 0386.68024
Dijkstra, Edsger W.; Lamport, Leslie; Martin, A. J.; Scholten, C. S.; Steffens, E. F. M.
1978
Synchronizing clocks in the presence of faults. Zbl 0629.68025
Lamport, Leslie; Melliar-Smith, P. M.
1985
How to write a proof. Zbl 0877.00005
Lamport, Leslie
1995
Fast Paxos. Zbl 1266.68218
Lamport, Leslie
2006
The weak Byzantine Generals Problem. Zbl 0627.68026
Lamport, L.
1983
Specifying concurrent systems with TLA$$^+$$. Zbl 0959.68080
Lamport, Leslie
1999
The ”Hoare logic” of CSP, and all that. Zbl 0536.68017
Lamport, Leslie; Schneider, Fred B.
1984
Concurrent reading and writing. Zbl 0361.68091
Lamport, Leslie
1977
The ”Hoare logic” of concurrent programs. Zbl 0416.68032
Lamport, Leslie
1980
Disk Paxos. Zbl 0987.68667
Gafni, Eli; Lamport, Leslie
2000
Distributed computing: Models and methods. Zbl 0900.68089
Lamport, Leslie; Lynch, Nancy
1990
A new approach to proving the correctness of multiprocess programs. Zbl 0463.68022
Lamport, Leslie
1979
How to write a proof. Zbl 1041.00501
Lamport, Leslie
1993
LaTeX: a document preparation system. (Das LaTeX-Handbuch.) Zbl 0852.68115
Lamport, Leslie
1995
The PlusCal algorithm language. Zbl 1250.68284
Lamport, Leslie
2009
How to write a 21$$^{\text{st}}$$ century proof. Zbl 1271.03082
Lamport, Leslie
2012
An assertional correctness proof of a distributed algorithm. Zbl 0514.68014
Lamport, Leslie
1982
A theorem on atomicity in distributed algorithms. Zbl 0699.68044
Lamport, Leslie
1990
On-the-fly garbage collection: An exercise in cooperation. Zbl 0347.68019
Dijkstra, Edsger W.; Lamport, Leslie; Martin, A. J.; Scholten, C. S.; Steffens, E. F. M.
1976
LA$$\TeX$$: a document preparation system. User’s guide and reference manual. 2nd ed. Zbl 0824.68121
Lamport, Leslie
1994
Real-time model checking is really simple. Zbl 1159.68328
Lamport, Leslie
2005
Lower bounds for asynchronous consensus. Zbl 1018.68728
Lamport, Leslie
2003
Byzantizing Paxos by refinement. Zbl 1350.68281
Lamport, Leslie
2011
Processes are in the eye of the beholder. Zbl 0901.68126
Lamport, Leslie
1997
Buridan’s principle. Zbl 1447.81009
Lamport, Leslie
2012
The specification and proof of correctness of interactive programs. Zbl 0404.68017
Lamport, Leslie
1979
On the proof of correctness of a calendar program. Zbl 0412.68014
Lamport, Leslie
1979
The Byzantine generals problem. Zbl 1448.68139
Lamport, Leslie; Shostak, Robert; Pease, Marshall
2019
The part-time parliament. Zbl 1455.68033
Lamport, Leslie
2019
Comment on Bell’s quadratic quotient method for hash code searching. Zbl 0199.52104
Lamport, L.
1970
Lower bounds for asynchronous consensus. Zbl 1266.68119
Lamport, Leslie
2006
Checking cache-coherence protocols with TLA$$^+$$. Zbl 1021.68052
Joshi, Rajeev; Lamport, Leslie; Matthews, John; Tasiran, Serdar; Tuttle, Mark; Yu, Yuan
2003
The mailbox problem. (Extended abstract). Zbl 1161.68325
Aguilera, Marcos K.; Gafni, Eli; Lamport, Leslie
2008
The mailbox problem. Zbl 1231.68063
Aguilera, Marcos K.; Gafni, Eli; Lamport, Leslie
2010
The synchronization of independent processes. Zbl 0332.68024
Lamport, Leslie
1976
the hyperplane method for an array computer. Zbl 0302.68044
Lamport, Leslie
1975
Critique of the Lake Arrowhead three. Zbl 0748.68015
Lamport, Leslie
1992
Open systems in TLA. Zbl 1374.68315
1994
An axiomatic semantics of concurrent programming languages. Zbl 0582.68006
Lamport, Leslie
1985
The mutual exclusion problem. I: A theory of interprocess communication. Zbl 1448.68135
Lamport, Leslie
2019
An extension of a theorem of Hamada on the Cauchy problem with singular data. Zbl 0269.35002
Lamport, Leslie
1973
Implementing dataflow with threads. Zbl 1267.68037
Lamport, Leslie
2008
TLA$$^{ + }$$ proofs. Zbl 1372.68168
Cousineau, Denis; Doligez, Damien; Lamport, Leslie; Merz, Stephan; Ricketts, Daniel; Vanzetto, Hernán
2012
Formal specification of a web services protocol. Zbl 1271.68090
Johnson, James E.; Langworthy, David E.; Lamport, Leslie; Vogt, Friedrich H.
2004
Checking a multithreaded algorithm with $$^{+}$$CAL. Zbl 1155.68564
Lamport, Leslie
2007
Concurrency. The works of Leslie Lamport. Zbl 1434.68029
2019
The Byzantine generals problem. Zbl 1448.68139
Lamport, Leslie; Shostak, Robert; Pease, Marshall
2019
The part-time parliament. Zbl 1455.68033
Lamport, Leslie
2019
The mutual exclusion problem. I: A theory of interprocess communication. Zbl 1448.68135
Lamport, Leslie
2019
Concurrency. The works of Leslie Lamport. Zbl 1434.68029
2019
How to write a 21$$^{\text{st}}$$ century proof. Zbl 1271.03082
Lamport, Leslie
2012
Buridan’s principle. Zbl 1447.81009
Lamport, Leslie
2012
TLA$$^{ + }$$ proofs. Zbl 1372.68168
Cousineau, Denis; Doligez, Damien; Lamport, Leslie; Merz, Stephan; Ricketts, Daniel; Vanzetto, Hernán
2012
Byzantizing Paxos by refinement. Zbl 1350.68281
Lamport, Leslie
2011
The mailbox problem. Zbl 1231.68063
Aguilera, Marcos K.; Gafni, Eli; Lamport, Leslie
2010
The PlusCal algorithm language. Zbl 1250.68284
Lamport, Leslie
2009
The mailbox problem. (Extended abstract). Zbl 1161.68325
Aguilera, Marcos K.; Gafni, Eli; Lamport, Leslie
2008
Implementing dataflow with threads. Zbl 1267.68037
Lamport, Leslie
2008
Checking a multithreaded algorithm with $$^{+}$$CAL. Zbl 1155.68564
Lamport, Leslie
2007
Fast Paxos. Zbl 1266.68218
Lamport, Leslie
2006
Lower bounds for asynchronous consensus. Zbl 1266.68119
Lamport, Leslie
2006
Real-time model checking is really simple. Zbl 1159.68328
Lamport, Leslie
2005
Formal specification of a web services protocol. Zbl 1271.68090
Johnson, James E.; Langworthy, David E.; Lamport, Leslie; Vogt, Friedrich H.
2004
Lower bounds for asynchronous consensus. Zbl 1018.68728
Lamport, Leslie
2003
Checking cache-coherence protocols with TLA$$^+$$. Zbl 1021.68052
Joshi, Rajeev; Lamport, Leslie; Matthews, John; Tasiran, Serdar; Tuttle, Mark; Yu, Yuan
2003
Disk Paxos. Zbl 0987.68667
Gafni, Eli; Lamport, Leslie
2000
Specifying concurrent systems with TLA$$^+$$. Zbl 0959.68080
Lamport, Leslie
1999
Processes are in the eye of the beholder. Zbl 0901.68126
Lamport, Leslie
1997
How to write a proof. Zbl 0877.00005
Lamport, Leslie
1995
LaTeX: a document preparation system. (Das LaTeX-Handbuch.) Zbl 0852.68115
Lamport, Leslie
1995
LA$$\TeX$$: a document preparation system. User’s guide and reference manual. 2nd ed. Zbl 0824.68121
Lamport, Leslie
1994
Open systems in TLA. Zbl 1374.68315
1994
How to write a proof. Zbl 1041.00501
Lamport, Leslie
1993
Critique of the Lake Arrowhead three. Zbl 0748.68015
Lamport, Leslie
1992
The existence of refinement mappings. Zbl 0728.68083
1991
Distributed computing: Models and methods. Zbl 0900.68089
Lamport, Leslie; Lynch, Nancy
1990
A theorem on atomicity in distributed algorithms. Zbl 0699.68044
Lamport, Leslie
1990
On interprocess communication. I: Basic formalism. Zbl 0598.68022
Lamport, Leslie
1986
On interprocess communication. II: Algorithms. Zbl 0598.68023
Lamport, Leslie
1986
The mutual exclusion problem. II: Statement and solutions. Zbl 0627.68018
Lamport, Leslie
1986
The mutual exclusion problem. I: A theory of interprocess communication. Zbl 0627.68017
Lamport, Leslie
1986
Synchronizing clocks in the presence of faults. Zbl 0629.68025
Lamport, Leslie; Melliar-Smith, P. M.
1985
An axiomatic semantics of concurrent programming languages. Zbl 0582.68006
Lamport, Leslie
1985
The ”Hoare logic” of CSP, and all that. Zbl 0536.68017
Lamport, Leslie; Schneider, Fred B.
1984
Specifying concurrent program modules. Zbl 0516.68010
Lamport, Leslie
1983
The weak Byzantine Generals Problem. Zbl 0627.68026
Lamport, L.
1983
The Byzantine generals problem. Zbl 0483.68021
Lamport, Leslie; Shostak, Robert; Pease, Marshall
1982
Proving liveness properties of concurrent programs. Zbl 0483.68013
Owicki, Susan; Lamport, Leslie
1982
An assertional correctness proof of a distributed algorithm. Zbl 0514.68014
Lamport, Leslie
1982
Reaching agreement in the presence of faults. Zbl 0434.68031
Pease, M.; Shostak, R.; Lamport, L.
1980
The ”Hoare logic” of concurrent programs. Zbl 0416.68032
Lamport, Leslie
1980
How to make a microprocessor computer that correctly executes multiprocess programs. Zbl 0419.68045
Lamport, Leslie
1979
A new approach to proving the correctness of multiprocess programs. Zbl 0463.68022
Lamport, Leslie
1979
The specification and proof of correctness of interactive programs. Zbl 0404.68017
Lamport, Leslie
1979
On the proof of correctness of a calendar program. Zbl 0412.68014
Lamport, Leslie
1979
Time, clocks, and the ordering of events in a distributed system. Zbl 0378.68027
Lamport, Leslie
1978
On-the-fly garbage collection: An exercise in cooperation. Zbl 0386.68024
Dijkstra, Edsger W.; Lamport, Leslie; Martin, A. J.; Scholten, C. S.; Steffens, E. F. M.
1978
Proving the correctness of multiprocess programs. Zbl 0349.68006
Lamport, Leslie
1977
Concurrent reading and writing. Zbl 0361.68091
Lamport, Leslie
1977
On-the-fly garbage collection: An exercise in cooperation. Zbl 0347.68019
Dijkstra, Edsger W.; Lamport, Leslie; Martin, A. J.; Scholten, C. S.; Steffens, E. F. M.
1976
The synchronization of independent processes. Zbl 0332.68024
Lamport, Leslie
1976
the hyperplane method for an array computer. Zbl 0302.68044
Lamport, Leslie
1975
A new solution of Dijkstra’s concurrent programming problem. Zbl 0281.68004
Lamport, Leslie
1974
The parallel execution of DO loops. Zbl 0273.68012
Lamport, Leslie
1974
An extension of a theorem of Hamada on the Cauchy problem with singular data. Zbl 0269.35002
Lamport, Leslie
1973
Comment on Bell’s quadratic quotient method for hash code searching. Zbl 0199.52104
Lamport, L.
1970
all top 5
### Cited by 1,822 Authors
44 Raynal, Michel 22 Hesselink, Wim H. 19 Guerraoui, Rachid 18 Taubenfeld, Gadi 15 Moses, Yoram 14 Lynch, Nancy Ann 13 Lamport, Leslie 12 Dolev, Shlomi 12 Mostefaoui, Achour 11 Baldoni, Roberto 11 Gafni, Eli M. 11 Schmid, Ulrich 10 Fauconnier, Hugues 10 Halpern, Joseph Yehuda 10 Herlihy, Maurice P. 10 Peled, Doron A. 9 Garay, Juan A. 9 Garg, Vijay K. 9 Welch, Jennifer Lundelius 8 Anderson, James H. 8 Delporte-Gallet, Carole 8 Gilbert, Seth 8 Kshemkalyani, Ajay D. 8 Pnueli, Amir 8 Rajsbaum, Sergio 8 Schwarzmann, Alexander A. 8 Widder, Josef 7 Abraham, Uri 7 Aspnes, James 7 Cohen, Ran 7 Dolev, Danny 7 Hadzilacos, Vassos 7 Hélary, Jean-Michel 7 Janicki, Ryszard 7 Malkhi, Dahlia 7 Merritt, Michael J. 7 Mittal, Neeraj 7 Neiger, Gil 7 Schiper, André 7 Toueg, Sam 6 Abadi, Martín 6 Alistarh, Dan 6 Bouajjani, Ahmed 6 Charron-Bost, Bernadette 6 Chockler, Gregory V. 6 Katz, Shmuel 6 Konnov, Igor V. 6 Koutny, Maciej 6 Lenzen, Christoph 6 Spirakis, Paul G. 6 Tixeuil, Sébastien 6 van Glabbeek, Robert Jan 6 Vardi, Moshe Ya’akov 5 Aravind, Alex A. 5 Censor-Hillel, Keren 5 Coan, Brian A. 5 Dubois, Swan 5 Függer, Matthias 5 Godard, Emmanuel 5 Golab, Wojciech 5 Henzinger, Thomas A. 5 Imbs, Damien 5 Israeli, Amos 5 Keidar, Idit 5 Kulkarni, Sandeep S. 5 Meisels, Amnon 5 Misra, Jayadev 5 Potop-Butucaru, Maria Gradinariu 5 Schiller, Elad Michael 5 Shavit, Nir N. 5 Travers, Corentin 5 Tsigas, Philippas 5 Tuttle, Mark R. 5 Veith, Helmut 5 Vidyasankar, Krishnamurthy 5 Wehrheim, Heike 5 Zikas, Vassilis 5 Zivan, Roie 4 Abdulla, Parosh Aziz 4 Afek, Yehuda 4 Attiya, Hagit 4 Back, Ralph-Johan 4 Bazzi, Rida A. 4 Biely, Martin 4 Bjørner, Dines 4 Dwork, Cynthia 4 Enea, Constantin 4 Fiadeiro, José Luiz 4 Francez, Nissim 4 Higham, Lisa 4 Jard, Claude 4 Jiménez, Ernesto 4 Joseph, Mathai 4 Korman, Amos 4 Kupferman, Orna 4 Kuznetsov, Petr 4 Li, Xiaozhou 4 Liu, Zhiming 4 Lobanov, A. V. 4 Maibaum, Thomas Stephen Edward ...and 1,722 more Authors
all top 5
### Cited in 135 Serials
173 Distributed Computing 170 Theoretical Computer Science 91 Information Processing Letters 55 Formal Aspects of Computing 47 Information and Computation 36 Acta Informatica 27 Journal of Computer and System Sciences 23 Journal of Parallel and Distributed Computing 22 Formal Methods in System Design 19 International Journal of Parallel Programming 12 Journal of Automated Reasoning 11 Journal of Logical and Algebraic Methods in Programming 10 Journal of Cryptology 10 Parallel Algorithms and Applications 10 Theory of Computing Systems 9 Algorithmica 9 International Journal of Computer Mathematics 8 Artificial Intelligence 8 Automatica 8 International Journal of Foundations of Computer Science 8 Logical Methods in Computer Science 7 Computing 7 Science of Computer Programming 6 Mathematical Systems Theory 6 Cybernetics 6 Real-Time Systems 6 RAIRO. Informatique Théorique et Applications 6 Annals of Mathematics and Artificial Intelligence 6 The Journal of Logic and Algebraic Programming 6 International Journal of Parallel, Emergent and Distributed Systems 5 Journal of Computer Science and Technology 5 MSCS. Mathematical Structures in Computer Science 5 Automation and Remote Control 5 Cybernetics and Systems Analysis 5 Concurrency and Computation: Practice & Experience 5 Sādhanā 4 International Journal of Theoretical Physics 4 Information Sciences 4 Journal of Functional Programming 4 Constraints 4 Journal of the ACM 4 Computer Languages, Systems & Structures 4 Frontiers of Computer Science 4 Computer Science Review 3 Discrete Applied Mathematics 3 SIAM Journal on Control and Optimization 3 Annals of Pure and Applied Logic 3 Journal of Symbolic Computation 3 Games and Economic Behavior 3 Mathematical Problems in Engineering 3 Journal of Applied Logic 3 Algorithms 2 Computer Physics Communications 2 International Journal of Control 2 BIT 2 Journal of Soviet Mathematics 2 SIAM Journal on Computing 2 Order 2 Neural Computation 2 Discrete Event Dynamic Systems 2 The Journal of Supercomputing 2 European Journal of Operational Research 2 Journal of Applied Non-Classical Logics 2 European Journal of Control 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 New Journal of Physics 2 Fundamenta Informaticae 2 Lobachevskii Journal of Mathematics 2 ACM Transactions on Computational Logic 2 The Review of Symbolic Logic 1 ACM Computing Surveys 1 Astrophysics and Space Science 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 General Relativity and Gravitation 1 International Journal of Systems Science 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Physics 1 Mathematische Semesterberichte 1 Nonlinearity 1 The Mathematical Intelligencer 1 Applied Mathematics and Computation 1 Biometrical Journal 1 Journal of Combinatorial Theory. Series B 1 Journal of Computational and Applied Mathematics 1 Journal of Economic Theory 1 Journal of Mathematical Psychology 1 Journal of Philosophical Logic 1 The Journal of Symbolic Logic 1 Mathematische Annalen 1 Software. Practice & Experience 1 Synthese 1 Moscow University Computational Mathematics and Cybernetics 1 Advances in Applied Mathematics 1 History and Philosophy of Logic 1 Acta Applicandae Mathematicae 1 International Journal of Production Research 1 Parallel Computing 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Acta Mathematicae Applicatae Sinica. English Series ...and 35 more Serials
all top 5
### Cited in 34 Fields
1,090 Computer science (68-XX) 103 Mathematical logic and foundations (03-XX) 67 Information and communication theory, circuits (94-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 26 Systems theory; control (93-XX) 23 Combinatorics (05-XX) 18 Operations research, mathematical programming (90-XX) 11 Numerical analysis (65-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 9 Quantum theory (81-XX) 7 Biology and other natural sciences (92-XX) 6 General and overarching topics; collections (00-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 4 Category theory; homological algebra (18-XX) 3 Partial differential equations (35-XX) 3 General topology (54-XX) 3 Relativity and gravitational theory (83-XX) 3 Mathematics education (97-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-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.
| 2022-05-16T04:41:04 |
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|
https://www.legisquebec.gouv.qc.ca/en/version/cr/B-1,%20r.%2016%20?code=se:9&history=20211128
|
### B-1, r. 16 - Regulation respecting the standards for equivalence of diplomas and training of the Barreau du Québec
9. In appraising whether a candidate’s training is equivalent, the committee shall take into account the following factors in particular:
(1) the nature and duration of the candidate’s experience;
(2) the fact that the candidate holds one or more diplomas awarded in Québec or elsewhere;
(3) the nature and content of the courses taken;
(4) the training sessions completed; and
(5) the total number of years of schooling.
O.C. 670-96, s. 9.
| 2022-07-02T01:35:57 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=S022MMD
|
#### (${\boldsymbol \mu}_{{{\boldsymbol \Xi}^{-}}}$ + ${\boldsymbol \mu}_{{{\overline{\boldsymbol \Xi}}^{+}}}$) $/$ $\vert {\boldsymbol \mu}_{{{\boldsymbol \Xi}^{-}}}\vert$
A test of $\mathit CPT$ invariance. We calculate this from the ${{\mathit \Xi}^{-}}$ and ${{\overline{\mathit \Xi}}^{+}}$ magnetic moments above.
VALUE
$\bf{ +0.01 \pm0.05}$ OUR EVALUATION
Conservation Laws:
$\mathit CPT$ INVARIANCE
| 2021-10-18T17:25:10 |
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|
https://discourse.mc-stan.org/t/submission-of-case-study-golf-putting/10868
|
# Submission of case study, Golf Putting
I’d like to submit a case study, Golf Putting. I’ve placed it all at http://www.stat.columbia.edu/~gelman/temp/
Author: Andrew Gelman
Keywords: sports, workflow
R Package Dependencies: rstan
3 Likes
I’ve updated the case study and put it at the same web-location as above.
I’m not quite sure what to do next. On the Stan Case studies page, it says: “To contribute a case study, please contact us through the Stan Forums…” I didn’t see any place on Stan Forums specifically for contributing case studies, hence these posts on the General page.
1 Like
Maybe @breckbaldwin can put it on the web page?
I guess it would be good for us to have more specific directions of where to submit case studies, at least if we want to encourage more submissions.
But then we’ll also need someone to manage the case studies page. It’s kind of like being a journal editor. We’ll need a volunteer or group of volunteers to do this!
I do not have the statistical/Stan chops to function as the case studies editor. Any volunteers?
Breck
I’ll take a look. I’m also looking at Imad’s.
Hi, just to let you know, I updated the case study once again; current version is at http://www.stat.columbia.edu/~gelman/temp/
1 Like
I may be commenting on an older one. I just saw that it was updated when I went to report.
Very cool case study. Definitely think we should add it.
The classical standard deviations here are standard deviations for the maximum likelihood estimator, right?
In the model, can you say y[j] is the number of successes observed in n[j] trials at distance x[j]?
You could mention that Stan vectorizes. I don’t know how much help you want to give the reader.
I don’t like that printing with comment = ‘##’, but that’s presumably the default.
You need something like options(“width” = 120) in order to avoid that wrapping in the figure. When it renders you’ll be able to scroll over. You could also drop the lp__ by including an argument: pars = c(“a”, “b”).
It’s hard to see the difference between light lines and dark lines. I’d plot the draws, then make sure to plot the other one in a different color over it if you can.
After the description, I espected a comparison involving the angle, not just the bare expression 2 * Phi(...) - 1.
You’re assuming a lot of trig here that might be helpful to work out. But one thing that you should do is discuss that you’re measuring angle from straight in radians, right, so it’ll be 0 +/- error? And it’s the absolute value of that which needs to be below the threshold.
Oops, looks like you’re talking about degrees in the next plot.
The formula for p[j] doesn’t make sense as j never shows up in it. I think it needs x[j] instead of just x.
Is there a way to put the degrees above the line without the sigma = ? They look odd cut in half by the lines.
I don’t like saying Stan sweeps over values consistent with the posterior—can you just say Stan samples from the posterior? Or that it sweeps over values consistent with the prior (improper) and data, i.e., values drawn from the posterior? Or is there a subtle point you’re trying to make here?
Stray a in “σa” after “in preparation to estimating”
You can combine declaration and definition and should wherever possible:
vector[J] p = 2 * Phi(asin((R - r) ./ x) / sigma) - 1;
...
real sigma_degrees = sigma * 180 / pi();
Plus, we recommend spaces between all operators and unfolding as much as possible to remove parens—it really helps with readability in text.
R never ceases to amaze me with its c and list shenanigans.
For efficiency, asin((R - r) ./ x) should be defined as trasnformed data. You might just make a note of it if you don’t want to clutter the program with a new block and constant.
You don’t need parens in (a / b) / c—it’s equal to a / b / c because / (like * and + and -) is left associative.
Can you come up with a better name than golf.stan and golf1.stan? How about golf_logit, and golf_angle and golf_angle_distance?
Won’t logistic regression be better at those long puts as it falls off faster?
Starting with this section, it’s getting confusing how you’re mixing computer notation (* for multiplication) and LaTeX (italic variables), as in the definition of u in the second paragraph of “A new model”). Also, some space before that sigma_distance would help—the rendering of LaTeX by MathJax is rough. Fractions might make it more readable aas they’d let you drop a layer of parens.
Same comment about declare and define in the program. And adding spaces between operators. In Stan, we can line up on next line as in most math typesetting.
There’s a dangling “Here’s the new Stan program:” after you included it a paragraph earlier.
Did you coin the folk theorem usage? If so, it’s odd for you to refer to it as “so-called”!
Same comment about width as earlier.
There’s a dangling $in third bullet point of “new parameter estimates are:” There’s a dangline paragraph start “Compared to the” Is that the same new data as before that didn’t match the old data? Did you fit the new model with the old data? If so, it looks like it fits the new data better even being fit to the old data. Not impossible, but if that’s what’s going on, you should say so in order for everyone else not to wonder what’s up. One of the other problems in your model is no priors on the sigma. Given that they get close to 0, that can be problematic. Rather than using to_vector, you could define the data variables as vectors and then just use ./. If you are going to apply to_vector to constants, you should do it once in the transformed data block so as not to have to construct new vectors and do the division every single evaluation. Rather than “.*”, you can just use backtick and it’ll render as computer code. That’s how you should be handling inline code anyway in markdown. This general point about having too much data at one point is important in a lot of models, I think. It seems like we should just be able to throw more data at a problem, but if it doesn’t have the right leverage or whatever you call it, it doesn’t help and can cause you to mess up other estimates. I guess it depends on what the goal is here—get the most new predictions right or try to get a sense of accuracy versus distance. Anyway, good grist for the philosophy mill here when it comes to the “we only care about predictions” philosophy. You need open source licenses if we’re going to publish them and a link to a repository where people can find the source. We can put the latter in example-models if you don’t already have it in your own organization. I recommend these: • Code © 2019, Trustees of Columbia University in New York, licensed under BSD-3. • Text © 2019, Andrew Gelman, licensed under CC-BY-NC 4.0. We also generally ask people to run from a clean start and report sessionInfo() so that people will be able to see which versions of R packages (like rstan) you used to generate the output. So that’s just a single block with sessionInfo() called and reported. No citations? Was that note about distance on a personal correspondence? P.S. Here’s how I’d write that final model for efficiency, though I probably wouldn’t combine all those priors into a one-liner—I just thought it’d amuse you until we get the parameters { real<lower = 0> sigma_, sigma_b, sigma_c; ... model { sigma_a, sigma_b, sigma_c ~ foo(theta) notation into production. thing into production. Anyway, here it is: data { int<lower = 0> J; vector<lower = 0>[J] n; vector<lower = 0>[J] x; vector<lower = 0>[J] y; real<lower = 0> r; real<lower = 0> R; real<lower = 0> overshot; real<lower = 0> distance_tolerance; } transformed data { vector[J] x_p_overshot = x + overshot; vector[J] asins = asin((R - r) ./ x); } parameters { real<lower = 0> sigma_theta; real<lower = 0> sigma_distance; real<lower = 0> sigma_y; } model { vector[J] p_angle = 2 * Phi(asins / sigma_theta) - 1; vector[J] denom = x_p_overshot * sigma_distance; vector[J] p_distance = Phi((distance_tolerance - overshot) ./ denom) - Phi(-overshot ./ denom); vector[J] p = p_angle .* p_distance; y ./ n ~ normal(p, sqrt(p .* (1 - p) ./ n + sigma_y^2)); { sigma_theta, sigma_distance, sigma_y } ~ normal(0, 1); } generated quantities { real sigma_degrees = sigma_theta * 180 / pi(); } 4 Likes Thanks for the detailed peer review! I posted an update here: http://www.stat.columbia.edu/~gelman/temp/ In addition to addressing your comments, I’ve made a bunch more changes throughout. I’ve interspersed some comments/questions below. Andrew Bob_Carpenter September 16 I don’t like that printing with comment = ‘##’, but that’s presumably the default. I agree. I find that ## thing ugly too. It’s what happens when I use the command print_file() in R. Is there a better way to do this? I looked at your case study of the predator-prey model, and it had Stan code fragments directly quoted. But I had the impression that for Markdown it was better to directly print the model (that way we know that all the Stan code is runnable, there are no synching problems with what’s in the .Rmd file and what’s in the .stan files. Is there a way to print R output in Markdown without the ## things? You need something like options(“width” = 120) in order to avoid that wrapping in the figure. I’m assuming this will be fixed in our new default rstan output that we’ve been talking about, as currently I think our default display is too long. I’ll have to confer with Aki, Ben, and Jonah when Aki’s visiting next month. In the meantime, I’ve changed the display options for now to keep things clean. You don’t need parens in (a / b) / c—it’s equal to a / b / c because / (like * and + and -) is left associative. That I know but I like to be unambiguous in such settings! Won’t logistic regression be better at those long puts as it falls off faster? Only by luck! Once we’ve fit the geometry-based model, I’ll just go with that, and I’m not really interested in the logistic model anymore. SIs that the same new data as before that didn’t match the old data? Did you fit the new model with the old data? If so, it looks like it fits the new data better even being fit to the old data. Not impossible, but if that’s what’s going on, you should say so in order for everyone else not to wonder what’s up. I don’t understand your question. We have two datasets. First we fit golf_logistic and golf_angle to the small dataset, then we fit golf_angle to the second dataset and see a problem, then we fit golf_angle_2,3 to the second dataset and get a good fit, then we fit golf_angle_4 to the second dataset but we don’t display the fit, we just discuss it. Anyway, I added a section at the end to clarify this point. This general point about having too much data at one point is important in a lot of models, I think. It seems like we should just be able to throw more data at a problem, but if it doesn’t have the right leverage or whatever you call it, it doesn’t help and can cause you to mess up other estimates. I guess it depends on what the goal is here—get the most new predictions right or try to get a sense of accuracy versus distance. Anyway, good grist for the philosophy mill here when it comes to the “we only care about predictions” philosophy. You perhaps won’t be surprised to hear that I think the resolution of this particular issue is to think of this a problem of poststratification. It’s fine to have the goal of optimizing average predictive accuracy, but then the question is, what average are you interested in? An average over the data will put most of the weight on those very short putts where the n’s are largest. An equally weighted average from 0 to 80 feet is another story. You need open source licenses if we’re going to publish them and a link to a repository where people can find the source. We can put the latter in example-models if you don’t already have it in your own organization. Yes, please do. I will also put this example in the Workflow book but it’s ok to have it in two places, I guess. I recommend these: • Code © 2019, Trustees of Columbia University in New York, licensed under BSD-3. • Text © 2019, Andrew Gelman, licensed under CC-BY-NC 4.0. I followed the example of what Sophia et al. did here: https://mc-stan.org/users/documentation/case-studies/dyadic_irt_model.html P.S. Here’s how I’d write that final model for efficiency, though I probably wouldn’t combine all those priors into a one-liner—I just thought it’d amuse you until we get the parameters { real<lower = 0> sigma_, sigma_b, sigma_c; ... model { sigma_a, sigma_b, sigma_c ~ foo(theta) notation into production. What we really need is combining the declaration with the distribution as here: real<lower=0> sigma_a ~ foo(theta); thing into production. Anyway, here it is: data { int<lower = 0> J; vector<lower = 0>[J] n; vector<lower = 0>[J] x; vector<lower = 0>[J] y; I agree that changing y and n to vectors simplifies the code. But it seems confusing to me to switch the data types just because we’re changing the model. I’d rather be explicit about what we’re doing to the data to make the approximate model. The right thing to do, I think, would be to fit the binomial model with an error term that’s a smooth function of x. That’s a lot of work, hence I fudged it with independent errors (as noted at the end of the case study). But to add independent errors to the binomial model is a pain in the ass, because (a) we’re now introducing a new latent variable for each parameter, and (b) we’d have to bring back the logit, or something like it, to keep the probabilities bounded between 0 and 1. That’s a lot of complexity in the model and code, and lots of splainin to do, so I thought the better choice for expository purposes would be to just use the normal approximation. P.S. I added one more thing to the case study. Updated version (dated 19 Sep 2019) is again here: http://www.stat.columbia.edu/~gelman/temp/ 1 Like I’m no longer in charge of the web site or case studies, so you’ll need to figure out who this is to get it posted. print_file <- function(file) { cat(paste(readLines(file), "\n", sep=""), sep="") } But then you need to control the knitr options. I’ve been using something like this for the Tufte format output: knitr::opts_chunk$set(
include = TRUE,
cache = TRUE,
collapse = TRUE,
echo = FALSE,
message = FALSE,
tidy = FALSE,
warning = FALSE,
comment = " ",
dev = "png",
dev.args = list(bg = '#FFFFF8'),
dpi = 300,
fig.align = "center",
fig.width = 7,
fig.asp = 0.618,
fig.show = "hold",
out.width = "90%"
)
You’ll see comment = " ", whic indents all the R output two lines. I’ve also used comment = "| ", which creates what look more like a vertical bar like an HTML quote.
Just writing text out, like in the user’s guide, is dangerous because it might not work or match what’s actually run. On the other hand, just printing the whole model out is unwieldy when it gets big or there are a few minor modifications. I’ve sometimes dumped all the code out as an appendix.
You could also control the quantiles printed. But until RStan changes, you need something that works for the tutorial as writtten.
Associativity and precedence are unambiguous! That’s why we can write a + b * c and not have it be ambiguous—we know * binds more tightly. Similarly, when we write a * b * c, we know it’ll be interpreted as (a * b) * c. This can matter. If a = 10^300 and b = 10^300 and c = 10^-300, then a * (b * c) will produce the mathematically correct answer whereas (a * b) * c will overflow double precision.
Fair enough. You’re not going to get a bunch of empirically minded ML researchers reading this.
This is why I get confused in these papers. I missed the switch in training data from the golf_angle to golf_angle_2,3.
But how do we do that? Do we reweight the training data or separate into a bunch of little models?
That’s insufficient. I should contact Sophia, but I’m tired of playing license police.
License notices need to indicate who owns the copyright. Like me, Columbia owns the copyright to all your code (but they’ve given us a perpetual right to release under open source), whereas you own the copyright to all your text. Also, the licensing is different for text and code. In the past, we’ve wanted the text to be open-sourced, too. Did you explicitly not want to do that? This should also be up to whoever’s in charge of the web site.
:-) That’s a discussion for a different thread.
Hi, thanks. It looks like we’ll be having a case studies director soon so I guess that new person will be able to handle my submission. I don’t think we need all the case studies in anything like a uniform format. All that’s really necessary is that they’re all in markdown, that they all run and that someone has looked each one over so we don’t have anything really horrible showing up.
Also we have someone translating some of the case studies from R to Python so I hope that will be appearing soon.
Some of them are in the form of Jupyter notebooks and we’d probably take one in the form of shell scripts running CmdStan if someone wanted to submit one.
We can post it whenever you’re ready—we don’t need to wait to pay someone else to do it. I just didn’t put it up because (a) I thought you were still revising it because I’m still seeing pull requestions, and (b) I was hoping someone else could do it. But it really only takes me 10 minutes or so to do these if the HTML and licensing is in order.
Put comment = NA into the R chunk header.
The case study is now up:
https://mc-stan.org/users/documentation/case-studies/golf.html
Thanks, all, for the help.
5 Likes
@andrewgelman: I would very much like to maintain a web policy where we do not distribute anything we do not have a license to distribute. As is, there is no license allowing us to distribute the text of your case study.
I’m not in charge of the web, so I’m not going to rip it out for non-compliance, but I would very much appreciate it if you updated this to include a license for the text. I don’t care what that license is as long as it allows us to distribute your case study.
I believe @breckbaldwin is still nominally in charge of our web site.
1 Like
@andrewgelman quite popular choice for the text license seems to be
licensed under CC-BY-NC 4.0
`
(allows derivative work but with BY = need to keep your name, NC = non-commercial)
Thanks. My case study currently says, “All code in this document is licensed via the BSD 3-clause license.”
I can replace it by “licensed under CC-BY-NC 4.0”.
Not replace, but add. You need separate license for code and text. So you would have
| 2019-11-18T16:54:45 |
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|
https://pos.sissa.it/396/148/
|
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Machine learning Hadron Spectral Functions in Lattice QCD
C. ShiYang*, H. Ding, F.Y. Liu, G. Papp and C.B. Yang
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
Hadron spectral functions carry all the information of hadrons and are encoded in the Euclidean two-point correlation functions. The extraction of hadron spectral functions from the correlator is a typical ill-posed inverse problem and infinite number of solutions to this problem exists. We propose a novel neural network (sVAE) based on the Variation Auto-Encoder (VAE) and Bayesian theorem. Inspired by the maximum entropy method (MEM) we construct the loss function of the neural work such that it includes a Shannon-Jaynes entropy term and a likelihood term. The sVAE is then trained to provide the most probable spectral functions.
For the training samples of spectral function we used general spectral functions produced from the Gaussian Mixture Model. After the training is done we performed the mock data tests with input spectral functions consisting 1) only a free continuum, 2) only a resonance peak, 3) a resonance peak plus a free continuum and 4) a NRQCD motivated spectral function. From the mock data test we find that the sVAE in most cases is comparable to the maximum entropy method in the quality of reconstructing spectral functions and even outperforms the MEM in the case where the spectral function has sharp peaks with insufficient number of data points in the correlator. By applying to temporal correlation functions of charmonium in the pseudoscalar channel obtained in the quenched lattice QCD at 0.75 $T_c$ on $128^3\times96$ lattices and $1.5$ $T_c$ on $128^3\times48$ lattices, we find that the resonance peak of $\eta_c$ extracted from both the sVAE and MEM has a substantial dependence on the number of points in the temporal direction ($N_\tau$) adopted in the lattice simulation and $N_\tau$ larger than 48 is needed to resolve the fate of $\eta_c$ at 1.5 $T_c$.
DOI: https://doi.org/10.22323/1.396.0148
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2022-06-28T06:44:15 |
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|
http://gams.cam.nist.gov/23.7
|
# §23.7 Quarter Periods
23.7.1 $\displaystyle\wp\left(\tfrac{1}{2}\omega_{1}\right)$ $\displaystyle=e_{1}+\sqrt{(e_{1}-e_{3})(e_{1}-e_{2})}=e_{1}+\omega_{1}^{-2}(K% \left(k\right))^{2}k^{\prime},$ 23.7.2 $\displaystyle\wp\left(\tfrac{1}{2}\omega_{2}\right)$ $\displaystyle=e_{2}-i\sqrt{(e_{1}-e_{2})(e_{2}-e_{3})}=e_{2}-i\omega_{1}^{-2}(% K\left(k\right))^{2}kk^{\prime},$ 23.7.3 $\displaystyle\wp\left(\tfrac{1}{2}\omega_{3}\right)$ $\displaystyle=e_{3}-\sqrt{(e_{1}-e_{3})(e_{2}-e_{3})}=e_{3}-\omega_{1}^{-2}(K% \left(k\right))^{2}k,$
where $k,k^{\prime}$ and the square roots are real and positive when the lattice is rectangular; otherwise they are determined by continuity from the rectangular case.
| 2017-09-21T03:24:49 |
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|
http://www.federalreserve.gov/pubs/ifdp/2006/853/revision/ifdp853r.htm
|
# Inference in Long-Horizon Regressions
NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.
Abstract:
I develop new results for long-horizon predictive regressions with overlapping observations. I show that rather than using auto-correlation robust standard errors, the standard t-statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data; this is asymptotically an exact correction and not an approximate result. Further, when the regressors are persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and it is shown how similar corrections and test procedures as those proposed for the short-run case can also be implemented in the long-run. New results for the power properties of long-horizon tests are also developed. The theoretical results are illustrated with an application to long-run stock-return predictability, where it is shown that once correctly sized tests are used, the evidence of predictability is generally much stronger at short rather than long horizons.
Keywords: Predictive regressions, long-horizon regressions, stock return predictability
JEL classification: C22, G1
# 1 Introduction
Predictive regressions are used frequently in empirical finance and economics. The underlying economic motivation is often the test of a rational expectations model, which implies that the innovations to the dependent variable should be orthogonal to all past information; i.e., the dependent variable should not be predictable using any lagged regressors. Although this orthogonality condition should hold at any time horizon, it is popular to test for predictability by regressing sums of future values of the dependent variable onto the current value of the regressor. A leading example is the question of stock return predictability, where regressions with 5 or 10 year returns are often used (e.g. Campbell and Shiller, 1988, and Fama and French, 1988). While stock return predictability will also serve as the motivating example in this paper, the results derived are applicable to a much wider range of empirical questions.1
The main inferential issue in long-horizon regressions has been the uncertainty regarding the proper calculation of standard errors. Since overlapping observations are typically used, the regression residuals will exhibit strong serial correlation; standard errors failing to account for this fact will lead to biased inference. Typically, auto-correlation robust estimation of the standard errors (e.g. Newey and West, 1987) is therefore used. However, these robust estimators tend to perform poorly in finite samples since the serial correlation induced in the error terms by overlapping data is often very strong.2
The main contribution of this paper is the development of new asymptotic results for long-run regressions with overlapping observations. Using a framework where the predictors are highly persistent variables, as in Stambaugh (1999) and Campbell and Yogo (2006), I show how to obtain asymptotically correct test-statistics, with good small sample properties, for the null hypothesis of no predictability.3 Rather than using robust standard errors, I find that the standard statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data. This is not an approximation, but rather an exact asymptotic result. Further, when the regressor is persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and similar corrections and test procedures as those proposed by Campbell and Yogo (2006) for the short-run case should also be used in the long-run; again, the resulting test statistics should be scaled due to the overlap.4 Thus, these results lead to simple and more efficient inference in long-run regressions by obviating the need for robust standard error estimation methods and controlling for the endogeneity and persistence of the regressor.
The results in this paper are derived under the assumption that the forecasting horizon increases with the sample size, but at a slower pace. Most previous work, e.g. Richardson and Stock (1989) and Valkanov (2003), rely on the assumption that the forecasting horizon grows at the same pace as the sample size so that the forecasting horizon remains a fraction of the sample size asymptotically. In some related work, Moon et al. (2004) consider both asymptotic approaches and find that although the asymptotic distributions are seemingly quite different under the two assumptions, they both tend to provide good approximations for the finite sample properties. Indeed, Valkanov (2003), who studies a similar econometric model to the one analyzed in this paper, derives a similar scaling result to the one found here. Asymptotic results are, of course, only useful to the extent that they provide us with relevant information regarding the finite sample properties of an econometric procedure. As shown in Monte Carlo simulations, both the asymptotic results derived under the assumptions in this paper and those derived under the assumptions in Valkanov's paper provide good approximations of finite sample behavior.
In relation to Valkanov's study, the current paper makes two important contributions. First, I show that with exogenous regressors the scaled standard statistic will be normally distributed and standard inference can thus be performed. Second, when the regressors are endogenous, the inferential methods can be suitably modified to correct for the biasing endogeneity effects; this can be seen as an analogue of the inferential procedures developed by Campbell and Yogo (2006) for short-run, one-period horizon, regressions. Importantly, the modified test-statistic in the endogenous case is again normally distributed. In contrast, Valkanov's test statistics have highly non-standard distributions, both for exogenous and endogenous regressors, which require simulation of the critical values for each specific case.
Monte Carlo simulations show that the asymptotic normal distribution of the test statistics derived in this paper provides a good approximation in finite samples, resulting in rejection rates that are very close to the nominal size of the test under the null hypothesis. This is also true when the overlap in the data is large. This shows that although the asymptotic results are derived under an assumption that the forecasting horizon is small compared to the sample size, the normal distribution of the scaled test statistics is not very sensitive to this restriction. In fact, the tests tend to become somewhat conservative and under reject, rather than over reject, as the forecasting horizon becomes large.
Since the size properties of both the tests proposed here and those of Valkanov (2003) are good, it becomes interesting to compare the power properties. Using Monte Carlo simulations, it is evident that for exogenous regressors the power properties of the test proposed here are quite similar to that of Valkanov, although there are typically some slight power advantages to the current procedure. When the regressors are endogenous, however, the test procedure derived here is often much more powerful than the test proposed by Valkanov. This stems partly from the fact that the test here explicitly takes into account, and controls for, the biasing effects of the endogenous regressors, whereas Valkanov's test only adjusts the critical values of the test statistic. Part of the power gains are also achieved by using a Bonferroni method, as in Campbell and Yogo (2006), to control for the unknown persistence in the regressors, whereas Valkanov relies on a sup-bound method, which is typically less efficient; Campbell and Yogo (2006) find the same result in the one-period case when they compare their method to the sup-bound method proposed by Lewellen (2004).
In fact, the power simulations, and additional asymptotic results, reveal three interesting facts about the properties of long-run predictive tests. First, the power of long-run tests increases only with the sample size relative to the forecasting horizon. Keeping this ratio fixed as the sample size increases does not lead to any power gains for the larger sample size. This result also suggests that for a given sample size, the power of a test will generally decrease as the forecasting horizon increases; additional simulations also support this conjecture and find that in general the one-period test will be the most powerful test. Second, when the regressors are endogenous, tests that are based on the standard long-run OLS estimator will result in power curves that are sometimes decreasing in the magnitude of the slope coefficient. That is, as the model drifts further away from the null hypothesis, the power may decrease. This is true both for Valkanov's test, but also if one uses, for instance, Newey-West standard errors in a normal statistic. The test proposed here for the case of endogenous regressors does not suffer from this problem. The third finding is related to the second one, and shows that although the power of the long-horizon tests increases with the magnitude of the slope coefficient for alternatives close to the null hypothesis, there are no gains in power as the slope coefficient grows large. That is, the power curve is asymptotically horizontal when viewed as a function of the slope coefficient. Both the second and third findings arise from the fact that when forecasting over multiple horizons, there is uncertainty not just regarding the future path of the outcome variable (e.g. future excess stock returns), but also about the future path of the forecasting variable over these multiple horizons. These results therefore add a further note of caution to attempts at forecasting at very long-horizons relative to the sample size: even though correctly sized tests are available, the power properties of the test can be very poor. The sometimes decreasing power curves for endogenous regressors also makes the case stronger for using test of the type proposed here, which attempts to correct for the bias and inefficiency induced in the estimation procedure by the endogeneity, and not just correct the critical values.
The theoretical results in the paper are illustrated with an application to stock-return predictability. I use a U.S. data set with excess returns on the S&P 500, as well as the value weighted CRSP index as dependent variables. The dividend price ratio, the smoothed earnings price ratio suggested by Campbell and Shiller (1988), the short interest rate and the yield spread are used as predictor variables. In addition, I also analyze an international data set with nine additional countries with monthly data spanning at least fifty years for each country. The predictor variables in the international data include the dividend-price ratio and measures of both the short interest rate and the term spread.
The evidence of predictability using the dividend- and earnings-price ratios is overall fairly weak, both in the U.S. and the international data, once the endogeneity and persistence in the regressors have been controlled for. The empirical results are more favorable of predictability when using either of the interest rate variables as predictors. This is particularly true in the U.S. data, but also to some extent in other countries. Contrary to some popular beliefs, however, the case for predictability does not increase with the forecast horizon. In fact, the near opposite is true, with generally declining statistics as the forecasting horizon increases (similar results are also found by Torous et al., 2004, and Ang and Bekaert, 2007). Given the fairly weak evidence of predictability at the short horizon, these results are consistent with a loss of power as the forecasting horizon increases, which is in line with the theoretical results derived in this paper.
The rest of the paper is organized as follows. Section 2 sets up the model and derives the theoretical results and Section 3 discusses the practical implementation of the methods in the paper. Section 4 describes the Monte-Carlo simulations that illustrate the finite sample properties of the methods and Section 5 provides further discussion and analysis of the power properties of long-horizon tests under an alternative of predictability. The empirical application is given in Section 6 and Section 7 concludes. Technical proofs are found in the Appendix.
# 2 Long-run estimation
## 2.1 Model and assumptions
Although the results derived in this paper are of general applicability, it is helpful to discuss the model and derivations in light of the specific question of stock return predictability. Thus, let the dependent variable be denoted , which would typically represent excess stock returns when analyzing return predictability, and the corresponding regressor, .5 The behavior of and are assumed to satisfy,
(1) (2)
where , and is the sample size. The error processes are assumed to satisfy the following conditions.
Assumption 1 ; Let and be the filtration generated by . Then
1.
2.
3. , , and .
The model described by equations (1) and (2) and Assumption 1 captures the essential features of a predictive regression with a nearly persistent regressor. It states the usual martingale difference assumption for the error terms and allows the innovations to be conditionally heteroskedastic, as long as they are covariance stationary. The error terms and are also often highly correlated; the regressor will be referred to as endogenous whenever this correlation, which will be labelled , is non-zero.
The auto-regressive root of the regressor is parameterized as being local-to-unity, which captures the near unit-root, or highly persistent, behavior of many predictor variables, but is less restrictive than a pure unit-root assumption. The near unit-root construction, where the autoregressive root drifts closer to unity as the sample size increases, is used as a tool to enable an asymptotic analysis where the persistence in the data remains large relative to the sample size, also as the sample size increases to infinity. That is, if is treated as fixed and strictly less than unity, then as the sample size grows, the process will behave as a strictly stationary process asymptotically, and the standard first order asymptotic results will not provide a good guide to the actual small sample properties of the model. For , the usual unit-root asymptotics apply to the model, but this is clearly a restrictive assumption for most potential predictor variables. Instead, by letting , the effects from the high persistence in the regressor will appear also in the asymptotic results, but without imposing the strict assumption of a unit root. Cavanagh et al. (1995), Lanne (2002), Valkanov (2003), Torous et al. (2004), and Campbell and Yogo (2006) all use similar models, with a near unit-root construct, to analyze the predictability of stock returns.
The greatest problem in dealing with regressors that are near unit-root processes is the nuisance parameter ; is generally unknown and not consistently estimable.6 It is nevertheless useful to first derive inferential methods under the assumption that is known, and then use the arguments of Cavanagh et al. (1995) to construct feasible tests. The remainder of this section derives and outlines the inferential methods used for estimating and performing tests on in equation (1), treating as known. Section 3 discusses how the methods of Cavanagh et al. (1995), and Campbell and Yogo (2006), can be used to construct feasible tests with unknown.
## 2.2 The fitted regression
In long-run regressions, the focus of interest is the fitted regression,
(3)
where , and long-run future returns are regressed onto a one period predictor.
Let the OLS estimator of in equation (3), using overlapping observations, be denoted by . A long-standing issue is the calculation of correct standard errors for . Since overlapping observations are used to form the estimates, the residuals will exhibit serial correlation; standard errors failing to account for this fact will lead to biased inference. The common solution to this problem has been to calculate auto-correlation robust standard errors, using methods described by Hansen and Hodrick (1980) and Newey and West (1987). However, these robust estimators tend to have rather poor finite sample properties.
In this section, I derive the asymptotic properties of under the assumption that the forecasting horizon grows with the sample size but at a slower pace. The results complement those of Valkanov (2003), who treats the case where the forecasting horizon grows at the same rate as the sample size. Simulation results in Valkanov (2003) and later on in this paper show that both asymptotic approaches provide limiting distributions that are good proxies for the finite sample behavior of the long-run estimators. The asymptotic results derived here also provide additional understanding of the properties of the long-run estimators. In particular, the results here show the strong connection between the limiting distributions of the short- and long-run estimators. This finding has important implications for the construction of more efficient estimators and test-statistics that control for the endogeneity and persistence in the regressors. Unlike Valkanov (2003), the procedures in this paper avoid the need for simulation methods; the proposed test-statistics have limiting normal distributions, although in the case of endogenous regressors with unknown persistence, Bonferroni type methods need to be used to construct feasible tests.
## 2.3 The limiting distribution of the long-run OLS estimator
The following theorem states the asymptotic distribution of the long-run OLS estimator of equation (3), and provides the key building block for the rest of the analysis. The result is derived under the null hypothesis of no predictability, in which case the one period data generating process is simply , and the long-run coefficient will also be equal to zero.
Theorem 1 Suppose the data is generated by equations (1) and (2), and that Assumption 1 holds. Under the null hypothesis of no predictability such that , as , with ,
(4)
where denotes a two dimensional Brownian motion with variance-covariance matrix , , and .
Theorem 1 shows that under the null of no predictability, the limiting distribution of is identical to that of the standard short-run, one-period, OLS estimator in equation (1), which is easily shown to converge to this distribution at a rate (Cavanagh et al., 1995), although needs to be standardized by . This additional standardization follows since the estimated parameter is of an order times larger than the original short-run parameter , as discussed at length in Boudoukh et al. (2005).
The convergence rate of for the long-run estimator also confirms the conjecture made by Nelson and Kim (1993), regarding the size of the bias in a long-run regression with endogenous regressors. They conjecture, based on simulation results, that the size of the bias is consistent with Stambaugh's (1999) approximation of the one-period bias, if one takes the total number of non-overlapping observations as the relevant sample size. In the near unit-root framework analyzed here, the Stambaugh bias is revealed in the non-standard asymptotic distribution of , which has a non-zero mean whenever the correlation between and differs from zero. Thus, since the rate of convergence is , the size of the bias in a given finite sample will be proportional to the number of non-overlapping observations.
The equality between the long-run asymptotic distribution under the null hypothesis, shown in Theorem 1, and that of the short-run OLS estimator may seem puzzling. The intuition behind this result stems from the persistent nature of the regressors. In a (near) unit-root process, the long-run movements dominate the behavior of the process. Therefore, regardless of whether one focuses on the long-run behavior, as is done in a long-horizon regression, or includes both the short-run and long-run information as is done in a standard one-period OLS estimation, the asymptotic result is the same since, asymptotically, the long-run movements are all that matter.7
The limiting distribution of is non-standard and a function of the local-to-unity parameter . Since is not known, and not consistently estimable, the exact limiting distribution is therefore not known in practice, which makes valid inference difficult. Cavanagh et al. (1995) suggest putting bounds on in some manner, and find the most conservative value of the limiting distribution for some value of within these bounds. Campbell and Yogo (2006) suggest first modifying the estimator or, ultimately, the resulting test-statistic, in an optimal manner for a known value of , which results in more powerful tests. Again using a bounds procedure, the most conservative value of the modified test-statistic can be chosen for a value of within these bounds. I will pursue a long-run analogue of this latter approach here since it leads to more efficient tests and because the relevant limiting distribution is standard normal, which greatly simplifies practical inference. Before deriving the modified estimator and test statistic, however, it is instructive to consider the special case of exogenous regressors where no modifications are needed.
## 2.4 The special case of exogenous regressors
Suppose the regressor is exogenous in the sense that is uncorrelated with and thus . In this case, the limiting processes and are orthogonal to each other and the limiting distribution in (4) simplifies. In particular, it follows that
(5)
where denotes a mixed normal distribution. That is, is asymptotically distributed as a normal distribution with a random variance. Thus, conditional on this variance, is asymptotically normally distributed. The practical implication of this result is that regular test statistics will have standard distributions. In fact, the following convenient result for the standard statistic now follows easily.
Corollary 1 Let denote the standard statistic corresponding to . That is,
(6)
where are the estimated residuals. Then, under Assumption 1 and the null hypothesis of , as , such that ,
(7)
Thus, by standardizing the statistic for by the square root of the forecasting horizon, the effects of the overlap in the data are controlled for and a standard normal distribution is obtained. Although the mechanics behind this result are spelled out in the proof in the Appendix, it is useful to outline the intuition. Note that the result in (5) implies that
(8)
for some consistent estimator , since . Now, as discussed in the Appendix, a consistent estimator of is given by where the extra division by is required given the overlapping nature of the residuals. The result now follows immediately from the definition of above.
## 2.5 Endogeneity corrections
As discussed above, the long-run OLS estimator suffers from the same endogeneity problems as the short-run estimator; that is, when the regressors are endogenous, the limiting distribution is non-standard and a function of the unknown parameter . To address this issue, I consider a version of the augmented regression of Phillips (1991a), together with the Bonferroni methods of Campbell and Yogo (2006). For now, I assume that , or equivalently , is known and derive an estimator and test statistic under this assumption.
Note that, for a given , the innovations can be obtained from . Consider first the one-period regression. Once the innovations are obtained, an implementation of the augmented regression equation of Phillips (1991a), which he proposed for the pure unit-root case, is now possible:
(9)
Here and (Phillips, 1991a), and denote the variance of as . The idea behind (9) is that by including the innovations as a regressor, the part of that is correlated with is removed from the regression residuals, which are now denoted to emphasize this fact. The regressor therefore behaves as if it were exogenous. It follows that under Assumption 1, the OLS estimator of in equation (9) will have an asymptotic mixed normal distribution, with the same implications as discussed above in the case of exogenous regressors.
As discussed in Hjalmarsson (2007), there is a close relationship between inference based on the augmented regression equation (9) and the inferential procedures proposed by Campbell and Yogo (2006). To see this, suppose first that the covariance matrix for the innovation process, , is known, and hence also and . The test for in (9) is then asymptotically equivalent to
(10)
which is, in fact, identical to Campbell and Yogo's statistic. In practice, is not known, but will be consistently estimated by OLS estimation of (9) and is estimated as the sample variance of the residuals. Campbell and Yogo derive their statistic as the optimal test in a Gaussian framework. The optimality of the test in the augmented regression equation thus follows from their analysis, but also directly from the analysis of Phillips (1991a). He shows that OLS estimation of (9) is identical to Gaussian full information maximum likelihood of the system described by equations (1) and (2), which thus immediately leads to the optimality result.
In the current context, the augmented regression equation is attractive since it can easily be generalized to the long-horizon case. Thus, consider the augmented long-run regression equation
(11)
where . The idea is the same as in the one-period case, only now the corresponding long-run innovations are included as an additional regressor. Let be the OLS estimator of in equation (11), using overlapping observations. The following result now holds.
Theorem 2 Suppose the data is generated by equations (1) and (2), and that Assumption 1 holds. Under the null hypothesis that , as , such that ,
(12)
The only difference from the result for the exogenous regressor case is the variance , which reflects the fact that the variation in that is correlated with has been removed. As in the exogenous case, given the asymptotically mixed normal distributions of , standard test procedures can now be applied to test the null of no predictability. In particular, the scaled statistic corresponding to will be normally distributed, as shown in the following corollary.
Corollary 2 Let denote the standard statistic corresponding to . That is,
(13)
where are the estimated residuals, , and . Then, under Assumption 1 and the null-hypothesis of , as , such that ,
(14)
Thus, for a given , inference becomes trivial also in the case with endogenous regressors since the scaled statistic corresponding to the estimate of from the augmented regression equation (11) is normally distributed. In practice, is typically unknown and the next section outlines methods for implementing a feasible test.
# 3 Feasible methods
To implement the methods for endogenous regressors described in the previous section, knowledge of the parameter (or equivalently, for a given sample size, ) is required. Since is typically unknown and not estimable in general, the bounds procedures of Cavanagh et al. (1995) and Campbell and Yogo (2006) can be used to obtain feasible tests.
Although is not estimable, a confidence interval for can be obtained, as described by Stock (1991). By evaluating the estimator and corresponding test-statistic for each value of in that confidence interval, a range of possible estimates and values of the test-statistic are obtained. A conservative test can then be formed by choosing the most conservative value of the test statistic, given the alternative hypothesis. If the confidence interval for has a coverage rate of and the nominal size of the test is percent, then by Bonferroni's inequality, the final conservative test will have a size no greater than percent.
Thus, suppose that one wants to test versus . The first step is to obtain a confidence interval for , with confidence level , which is denoted . For all values of , and the corresponding are calculated, where the estimator and test statistic are written as functions of to emphasize the fact that a different value is obtained for each . Let be the minimum value of that is obtained for and be the maximum value. A conservative test of the null hypothesis of no predictability, against a positive alternative, is then given by evaluating against the critical values of a standard normal distribution; the null is rejected if , where denotes the quantile of the standard normal distribution. The resulting test of the null hypothesis will have a size no greater than . An analogous procedure can be used to test against a negative alternative.8
Unlike in the short-run methods in Campbell and Yogo (2006), there is no guarantee that and will be the endpoints of the confidence interval for , although for most values of they typically are; in fact, it is easy to show that asymptotically the minimum and maximum will always be at the endpoints, but this does not hold in finite samples for . The test-statistic should thus be evaluated for all values in in order to find and ; for , the same result as in Campbell and Yogo (2006) holds and the extreme values of the test statistic will always be obtained at the endpoints.
In general, Bonferroni's inequality will be strict and the overall size of the test just outlined will be less than . A test with a pre-specified size can be achieved by fixing and adjusting . That is, by shrinking the size of the confidence interval for , a test of a desired size can be achieved. Such procedures are discussed at length in Campbell and Yogo (2006) and I rely on their results here. That is, since, for all values of , the asymptotic properties of the estimators and corresponding test-statistics derived here are identical to those in Campbell and Yogo, it is reasonable to test if their adjustments to the confidence level of the interval for also work in the long-run case considered here. Since the Campbell and Yogo methods are frequently used in one-period regressions, this allows the use of very similar procedures in long-run regressions. As discussed below in conjunction with the Monte Carlo results, using the Campbell and Yogo adjustments in the long-run case appear to work well, although there is a tendency to under reject when the forecasting horizon is large relative to the sample size. The power properties of the test still remain good, however. Thus, there may be some scope for improving the procedure by size adjusting the confidence interval for differently for different combinations of and , but at the expense of much simplicity. Since the potential gains do not appear large, I do not pursue that here, although it would be relatively easy to implement on a case by case basis in applied work.
Campbell and Yogo fix at ten percent, so that the nominal size of the tests evaluated for each is equal to ten percent. They also set the desired size of the overall Bonferroni test, which they label , to ten percent. Since the degree of endogeneity, and hence the size of the biasing effects, is a function of the correlation between the innovations and , they then search for each value of , for values of , such that the overall size of the test will be no greater than .9
The practical implementation of the methods in this paper can be summarized as follows:
(i)
Using OLS estimation for each equation, obtain the estimated residuals from equations (1) and (2). Calculate the correlation from these residuals.
(ii)
Calculate the DF-GLS unit-root test statistic of Elliot et al. (1996), and obtain and from Tables 2-11 in Campbell and Yogo (2005) corresponding to the estimated value of .
(iii)
For a grid of values , calculate and and find , and .
(iv)
If the alternative hypothesis is , compare to the percent critical values of the standard normal distribution (i.e. and if the alternative hypothesis is , compare to the five percent critical values of the standard normal distribution.
The above procedure results in a one-sided test at the five percent level, or alternatively a two-sided test at the ten percent level. Note that, although the analysis in Section 2.5 proposes an improved point estimator, , for a given , in practice it is merely used as a device to deliver an improved and feasible test statistic. That is, since is not known in practice, the scope for improving upon the standard (long-run) OLS estimator is limited, even though improved test statistics are obtained.
The estimate of and the confidence interval for can be made more robust by allowing the regressors to follow an autoregressive process with lags , rather than an process. That is, an process can be estimated for the regressor, and the DF-GLS statistic can be calculated using lags. Since the outcome of and can be quite sensitive to the choice of , when is large in absolute terms, it can be important to pin down the confidence interval as well as possible. Although the augmented regression equation is only formally justified for the case, the outcome of and will in general be much more sensitive to the choice of than the effects of a, typically small, serially correlated component for higher order lags in the regressor. Thus, the main benefits from allowing for a richer auto-correlation structure in the regressor come from the proper calculation of ; the effects of using the augmented regression equation rather than a method that explicitly controls for higher order auto-correlations should be small on the other hand. In practice, as evidenced in Campbell and Yogo (2006), the difference between results based on an and an assumption seems to be fairly small. However, in order to keep the analysis as robust as possible, the empirical results in Section 6 are obtained using the specification; the implementation follows the methods described in Campbell and Yogo (2005), using the Bayesian information criterion (BIC) to choose the appropriate lag length.
# 4 Monte Carlo results
All of the above asymptotic results are derived under the assumption that the forecasting horizon grows with the sample size, but at a slower rate. Valkanov (2003) also studies long-run regressions with near-integrated regressors, but derives his asymptotic results under the assumption that as . That is, he assumes that the forecasting horizon grows at the same pace as the sample size. Under such conditions, the asymptotic results are, at least at first glance, quite different from those derived in this paper. There is, of course, no right or wrong way to perform the asymptotic analysis; what matters in the end is how well the asymptotic distributions capture the actual finite sample properties of the test statistics. To this end, Monte Carlo simulations are therefore conducted. Since Valkanov's methods are known to have good size properties, I merely present power results for his tests.
## 4.1 Size properties
I start with analyzing the size properties of the scaled statistics proposed earlier in the paper. Equations (1) and (2) are simulated, with and drawn from an bivariate normal distribution with mean zero, unit variance and correlations and . The intercept is set to zero and the local-to-unity parameter is set to either 0 or . The sample size is either equal to or . Since the size of the tests are evaluated, the slope coefficient is set to zero, which implies that as well. All results are based on repetitions.
Three different test statistics are considered: the scaled statistic corresponding to the long-run OLS estimate , the scaled Bonferroni statistic described above , and the scaled infeasible statistic corresponding to the infeasible estimate for a known value of . In practice, of course, the infeasible test is not feasible but in the Monte Carlo simulations the parameter is known, and the test based on the infeasible estimate thus provides a benchmark. All tests are evaluated against a positive one-sided alternative at the five percent level; i.e. the null is rejected if the scaled test statistic exceeds .
The results are shown in Table 1. The first set of columns shows the rejection rates for the scaled OLS statistic under the null hypothesis of no predictability. When the regressors are exogenous, such that , this test statistic should be asymptotically normally distributed. The normal distribution appears to work well in finite samples, with rejection rates close to the nominal five percent size. For and for large relative to , the size drops and the test becomes somewhat conservative; this is primarily true for forecasting horizons that span more than percent of the sample size. Overall, however, the scaling by of the standard test appears to work well in practice for exogenous regressors. As is expected from the asymptotic analysis previously, the scaled OLS test tends to over reject for endogenous regressors with , which highlights that the biasing effects of endogenous regressors are a great problem also in long-horizon regressions.
The next set of columns shows the results for the scaled Bonferroni test. The rejection rates for all are now typically close to, or below, five percent, indicating that the proposed correction in the augmented regressions equation (9) works well in finite samples. Only for and is there a slight tendency to over reject when is small, but the average rejection rates are still well within the acceptable range; Campbell and Yogo (2006) find similar rejection rates in their one-period test, for . Again, as in the OLS case, there is a tendency to under reject for large relative to the sample size . Since the Bonferroni test is formed based on the shrunk confidence intervals for with the confidence levels provided in Table 2 of Campbell and Yogo (2006), this could perhaps be somewhat remedied by adjusting these confidence levels for large .10 However, as seen in the power simulations below, the Bonferroni test is not dramatically less powerful than the infeasible test, and there seems to be little need for complicating the procedure by requiring different tables for the confidence level for , for different combinations of and .
Finally, the last set of columns in Table 1 shows the rejection rates for the scaled infeasible test , resulting from the infeasible estimate , which uses knowledge of the true value of . As in the case of the Bonferroni test, the rejection rates are all close to the nominal five percent level, although there is still a tendency to under reject when is large.
In summary, the above simulations confirm the main conclusions from the formal asymptotic analysis: (i) when the regressor is exogenous, the standard statistic scaled by the square root of the forecasting horizon will be normally distributed, and (ii) when the regressor is endogenous, the scaled statistic corresponding to the augmented regression equation will be normally distributed. The simulations also show that these scaled tests tend to be somewhat conservative when is large relative to ; this observation is further discussed in the context of the power properties of the tests, analyzed below.
The size simulations were also performed under the assumption that the innovation processes were drawn from distributions with five degrees of freedom, to proxy for the fat tails that are observed in returns data. The results were very similar to those presented here and are available upon request.
## 4.2 Power properties
Since the test procedures proposed in this paper appear to have good size properties and, if anything, under reject rather than over reject the null, the second important consideration is their power to reject the null when the alternative is in fact true. The same simulation design as above is used, with the data generated by equations (1) and (2). In order to assess the power of the tests, however, the slope coefficient in equation (1) now varies between 0 and . For simplicity, I only consider the cases of and .
In addition to the three scaled statistics considered in the size simulations - i.e. the scaled OLS test, the scaled Bonferroni test, and the scaled infeasible test - I now also study two additional test-statistics based on Valkanov (2003). Valkanov derives his asymptotic results under the assumption that as , and shows that under this assumption, will have a well defined distribution. That is, he proposes to scale the standard OLS statistic by the square root of the sample size, rather than by the square root of the forecasting horizon, as suggested in this paper. The scaled statistic in Valkanov's analysis is not normally distributed. It's asymptotic distribution is a function of the parameters (the degree of overlap), the local-to-unity parameter , and the degree of endogeneity ; critical values must be obtained by simulation for a given combination of these three parameters.11 Since the critical values are a function of , Valkanov's scaled test is generally infeasible since this parameter is unknown. He therefore proposes a so-called sup-bound test, where the test is evaluated at some bound for , outside of which it is assumed that will not lie. Ruling out explosive processes, he suggests using in the sup-bound test, which results in a conservative one-sided test against for .12 In the results below, I report the power curves for both the infeasible test and the sup-bound test; for , they are identical. To avoid confusion, I will continue to refer to the tests proposed in this paper as scaled tests, whereas I will refer to the tests suggested by Valkanov explicitly as Valkanov's infeasible and sup-bound tests. Following Valkanov's exposition, I focus on the case of , but given the apparently conservative nature of the tests proposed here for large , I also consider some results for .
Figure 1 shows the power curves for the scaled OLS test proposed in this paper and the two tests suggested by Valkanov, for , and . For , the power curves are virtually identical, whereas for , Valkanov's infeasible test has some power advantages. The scaled OLS test is, however, marginally more powerful than Valkanov's sup-bound test for . Overall, for the case of exogenous regressors, there appears to be no loss of power from using the simple scaled and normally distributed test suggested here.
Figure 2 shows the results for endogenous regressors with , and . Since the scaled test based on the OLS estimator is known to be biased in this case, I only show the results for the scaled Bonferroni test and the scaled infeasible test based on the augmented regression, along with Valkanov's two tests. The results are qualitatively similar to those for exogenous regressors with . For , the power curves for the three tests are nearly identical, although the scaled infeasible test proposed in this paper tends to slightly dominate Valkanov's infeasible test. For , the scaled infeasible test is still the most powerful, and Valkanov's infeasible test is somewhat more powerful than the scaled Bonferroni test. The least powerful test is Valkanov's (feasible) sup-bound test. Note that one would expect the scaled infeasible test proposed here to be more powerful than Valkanov's infeasible test, since the test proposed here attempts to correct the bias in the estimation procedure and not just adjust the critical values of the test; this comparison is thus the analogue of the comparison between the infeasible (short-run) test proposed by Campbell and Yogo and the infeasible test proposed by Cavanagh et al. (1995). Finally, it is noteworthy that the power of Valkanov's sup-bound test appears to decrease for large values of when . A similar pattern is also hinted at for Valkanov's test with . These patterns become clearer as the forecasting horizon increases and will be analyzed at length below.
Given that the scaled Bonferroni test, in particular, seemed to be under sized for large values of relative to , it is interesting to see if this also translates into poor power properties. Figure 3 shows the results for , , and . Two observations are immediately obvious from studying the plots. First, the scaled Bonferroni test is reasonably powerful when compared to the infeasible scaled test, and very powerful compared to Valkanov's sup-bound test. Second, the declining pattern in the power curves for Valkanov's two tests that were hinted at in Figure 2 are now evident; as becomes larger, the power of these two tests decline. This result is of course perplexing, since Valkanov's tests were explicitly derived under the assumption that is large relative to the sample size . In the following section, additional analytical results are derived that will shed some light on these findings. However, before turning to the formal analysis, results shown in Figure 4 provide further confirmation of the results in Figure 3, as well as highlight some additional findings.
Figure 4 confirms and elaborates on the findings in Figure 3. The right hand graph shows the power curves for , , and . Using confirms that the previous findings were not just a small sample artefact. The same pattern as in Figure 3 emerges for Valkanov's two tests: after an initial increase in power as becomes larger, the power starts to decrease. Further results for larger values of , which are not shown, indicate that the power curves do not converge to zero as grows large; rather, they seem to level out after the initial decrease. Furthermore, the power curves for the scaled Bonferroni test and the scaled infeasible test do not seem to converge to one as increases, although they do not decrease either, and stabilize at a much higher level than the power curves for Valkanov's tests. In addition, the power curve for the scaled OLS test is also shown. This test is biased for but provides an interesting comparison to the power curves of Valkanov's test. As is seen, the scaled OLS test behaves in a very similar manner to Valkanov's infeasible test. It is thus apparent that the difference in behavior between the Bonferroni test and Valkanov's tests stems primarily from the endogeneity correction and not the manner in which they are scaled. Finally, the right hand graph in Figure 4 also shows that the patterns established for the power curves of the tests proposed both in this paper and in Valkanov (2003) are not a result of scaling the test statistic by either the sample size or the forecasting horizon. As shown, if one uses Newey-West standard errors to calculate the (non scaled) statistic from the long-run OLS regression, a similar pattern emerges; note that the test based on Newey-West standard errors will be biased both for the well established reason that the standard errors do not properly control for the overlap in the data, but also because the statistic from the long-run OLS regression does not control for the endogeneity in the regressors. The Newey-West standard errors were calculated using lags.
It is worth pointing out that Valkanov (2003) also performs a Monte Carlo experiment of the power properties of his proposed test-statistics, without finding the sometimes decreasing patterns in the power curves reported here. However, Valkanov (2003) only considers the case with , and , for values of between 0 and . As seen in Figurehere, the power curves of all the tests are strictly increasing in for these parameter values.
The left hand graph in Figure 4 further illustrates the above observations for the scaled OLS statistic in the case of . Here, with , and , the power of the scaled OLS statistic and Valkanov's (infeasible) test statistic are almost identical and again seem to converge to some fixed level less than one. The results also suggest that the decrease in power seen for Valkanov's test in the previous plots does not occur when the regressors are exogenous. The statistic based on Newey-West standard errors is also shown to exhibit the same pattern; here, the bias in this test resulting from the overlap in the data alone is evident, with a rejection rate around 20 percent under the null.
To sum up, the simulations show that both the scaled OLS test and the scaled Bonferroni test have good (local) power properties when compared to the tests proposed by Valkanov (2003). This is especially true for the Bonferroni test used with endogenous regressors, which tends to dominate Valkanov's sup test for all values of , and also dominates Valkanov's infeasible test for large values of .
However, all of the tests discussed here, including the standard test based on Newey-West standard errors, seem to behave in a non-standard way as the value of the slope coefficient drift further away from the null hypothesis: rather than converging to one as grows large, the power of the tests seem to converge to some value less than unity. In the next section, I provide an analytical explanation of these findings and discuss its implications.
# 5 Long-run inference under the alternative of predictability
## 5.1 Asymptotic power properties of long-run tests
The simulation evidence in the previous section raises questions about the properties of long-run tests under the alternative of predictability. In particular, the power of the tests does not seem to converge to one as the slope coefficient increases and, in addition, the power curves appear to sometimes decrease as the slope coefficient drifts away from the null hypothesis. In this section, I therefore derive some analytical results for the power properties of long-run tests. I first start by considering a fixed alternative, which provides the answer to why the power does not converge to unity when the slope coefficient increases. In the following sub-section, I consider the power against a local alternative, which helps explain the hump shaped pattern in the power curves. These analytical results also reveal some interesting features about the consistency of long-run tests. I focus on the standard (scaled) OLS statistic, since the behavior of the statistic is similar to the former with exogenous regressors.
The following theorem provides the asymptotic results for the distribution of the statistic under a fixed alternative of predictability. Results are given both for the asymptotics considered so far in this paper, i.e. , as well as the type of asymptotics considered by Valkanov (2003).
Theorem 3 Suppose the data is generated by equations (1) and (2), and that Assumption 1 holds. Under the alternative hypothesis that :
(i) As , such that ,
and thus (15)
(ii) As , such that ,
(16)
where .
The asymptotic results in Theorem 3 help shed light on the general patterns seen in the figures above. Part (i) of the theorem, which provides the limiting distribution of the scaled test analyzed in this paper, shows that the power of this test will increase with the relative size of the sample to the forecasting horizon; thus, as long as the ratio between and is fixed, there are no asymptotic power gains. The power is also independent of the value of the slope coefficient , as long as it is different from zero. This explains the leveling out of the power curves as grows large, and their failure to converge to one for large values of . The intuition behind the independence of in the limiting distribution is best understood by explicitly writing out the equation for the long-run returns under the alternative of predictability. That is, since the true model is given by equations (1) and (2), the long-run regression equation is a fitted regression, rather than the data generating process. As shown in the proof of Theorem 3 in the Appendix, under the alternative of predictability, the long-run returns actually satisfy the following relationship when ignoring the constant, derived from equations (1) and (2):
(17)
There are now, in effect, two error terms, the usual plus the additional term , which stems from the fact that at time there is uncertainty regarding the path of for . That is, since the true model is given by equations (1) and (2), there is uncertainty regarding both the future realizations of the returns, as well as of the predictor variable, when forming period ahead forecasts. Since the first error term is of an order of magnitude larger than , it will dominate the asymptotic behavior of the least squares estimator of . As seen in the proof, the multiplication of this error term by ultimately explains why a larger will also lead to a larger error term, cancelling out any power gains that might otherwise have occurred as drifts further away from zero.
Part (ii) of the theorem states that Valkanov's scaled statistic converges to a well defined limiting distribution that is independent of and , although it is a function of . Thus, under the assumptions on and maintained by Valkanov, the statistic scaled by does not diverge and hence the power of the test does not converge to one. Of course, for a fixed , the same heuristic result follows from part (i), since as long as does not change, there are no power gains. Thus, although some caution is required when comparing the results in parts (i) and (ii) of the theorem, since they are derived under different assumptions, they lead to the same heuristic result. Indeed, for a fixed , it follows that and that the results for the scaled tests in this paper should be similar to those of Valkanov's tests.
The main message of Theorem 3 is thus that the only way to achieve power gains in long-run regressions is by increasing the sample size relative to the forecasting horizon; as long as this ratio is fixed, there are no asymptotic power gains as the sample size increases. The results in Theorem 3 also provide some intuition to a somewhat counter intuitive result in Valkanov (2003). As shown there, under the assumption that asymptotically, the estimator of the long-run coefficient is not consistent; however, a scaled version of the statistic has a well defined distribution. That is, even though the coefficient is not estimated consistently, valid tests can still be performed. Theorem 3 shows the limitation of this result: like the estimator, the test is not consistent since there are no asymptotic power gains for a fixed .
Part (i) of Theorem 3 also suggests that for a fixed sample size, more powerful tests of predictability are achieved by setting the forecasting horizon as small as possible. That is, in general, one might expect power to be decreasing with the forecasting horizon. This is merely a heuristic argument, since the result in part (i) of Theorem 3 is an asymptotic result based on the assumption that . Nevertheless, it is interesting to briefly compare the finite sample power properties between tests at different horizons. The simulation results in the previous section already support the conjecture that power is decreasing with the horizon, in finite samples, as evidenced by the rather poor power properties for the really long horizons studied in Figures 3 and 4. The simulations in Figure 5 make these results even clearer. The simulation setup is the same as before, with and . The left hand graph shows the power curves for the scaled OLS test, when , for three different forecasting horizons, and . It is evident that as increases, the power uniformly decreases. The right hand graph shows the case of , and illustrates the power curves for the scaled Bonferroni test, for and . Again, there is a clear ranking of the power curves from short to long horizon. Qualitatively identical results, which are not shown, are obtained for , and for .
Overall, the results here are thus supportive of the notion that tests of predictability generally lose power as the forecasting horizon increases. This is in line with what one might expect based on classical statistical and econometric theory. In the case of exogenous regressors, the OLS estimates of the single period regression in equation (1) are identical to the full information maximum likelihood estimates and in the endogenous regressor case, OLS estimation of the one-period augmented regression equation (9) is likewise efficient. Standard analysis of power against a sequence of local alternatives then implies that a one-period Wald test (or, equivalently, a test) is asymptotically optimal (Engle, 1984). Campbell (2001) makes this point, but also finds that some alternative ways of comparing asymptotic power across horizons suggest that there may be power gains from using longer horizons; however, he finds little support for this in his Monte Carlo simulations.
## 5.2 Local asymptotic power
The asymptotic power properties in the previous section were derived under the assumption of a fixed alternative . As seen in the power curves in the figures above, it is clear that for small values of , the power of the long-run tests is a function of . And, in particular, there appears to be regions of the parameter space where the power of the tests are decreasing in the magnitude of the slope coefficient. These facts are not reflected in the results in Theorem 3, however, and the power properties in these regions of the parameter space are therefore likely better analyzed with a local alternative for , as is common in the literature on evaluating the power of statistical tests. The following theorem provides a guide to the local power properties of the scaled OLS test proposed in this paper.
Theorem 4 Suppose the data is generated by equations (1) and (2), and that Assumption 1 holds. Under the local alternative of ,
(18)
where ' denotes an approximate distributional equivalence.
This theorem heuristically shows the approximate distribution of the scaled OLS statistic for alternatives that are close to the null hypothesis, in the sense that the slope coefficient shrinks towards zero with the forecasting horizon. For small to moderate values of , it is evident that the statistic, and hence the power of the test, will depend on the value of . For large , and small relative to , it follows that
(19)
which is independent of and identical to the result under the fixed alternative. For , the distribution under the null hypothesis is recovered. In fact, it is useful to separate the numerator of the statistic as follows:
(20)
Here the first term is the pure drift part, which will dominate asymptotically provided that , the second term is the usual variance term under the null hypothesis, and the third term reflects the uncertainty regarding the future path of the regressor in a long-run regression, as discussed above in conjunction with the representation in equation (17). Obviously, the pure drift term is increasing in , and the second term does not change with . The third term is on average decreasing in , since the outcomes of the random variable tend to be negative. That is, by effectively omitting the term in equation (17), a downward bias is induced in the estimator and the subsequent statistic because the relevant asymptotic covariance' measure between and is negative. However, these terms are all linear in the coefficient , and can therefore not explain the non-monotonicity in the power curves that were found in the Monte Carlo simulations. Instead, the answer must be in the denominator.
For large , the denominator is increasing in but, in the case of , there is a range of for which the denominator is decreasing in ; this explains the hump-shaped pattern in the power curves that was documented in the Monte Carlo study. To form an intuition behind these results, consider again the representation of the long-run regression in equation (17). Under the assumption that , the usual error term and the additional term will both be of the same order of magnitude. When calculating the variance of the fitted residual, which enters into the denominator of the statistic, the variance of both of these terms as well as their covariance will thus enter. The covariance , when it is negative, will induce the non-monotonicity in the statistic as a function of . Initially, as the slope coefficient drifts away from zero, the first term will dominate and the power of the test is increasing in , since the variance of is independent of . In a middle stage, the covariance term becomes important as well and the statistic decreases with the slope coefficient. Finally, as grows large, the last term dominates and will exactly cancel out the dependence on in the numerator and denominator.
Figure 6 shows the average power curves that result from direct simulations of the limiting random variables in equation (18). As in the previous simulations, the variances and are both set equal to one. I let so that the results correspond to the finite sample power curves shown in Figures 3 and 4, where the forecasting horizon is equal to 20 percent of the sample size. The local-to-unity parameter is set equal to zero and repetitions are used.
The left hand graph in Figure 6 shows the case of exogenous regressors . The local power curve is weakly increasing and looks very similar to the finite sample results seen in Figure 4. For endogenous regressors with , shown in the right hand graph in Figure 6, the same hump shaped pattern as in Figures 3 and 4 is evident; the biased nature of the OLS test with endogenous regressors is also clearly evident with a rejection rate around 40 percent under the null. The power curves based directly on the asymptotic results in Theorem 4 thus seem to correspond well to the finite sample ones.
## 5.3 Practical implications
The results in this section help shed more light on the properties of long-run tests under the alternative of predictability. The main lesson is that the power of long-horizon tests only grows with the size of the sample relative to the forecasting horizon; keeping fixed as increases does not result in any power gains. The practical implications and recommendations must therefore be that inference on forecasts at very long horizons will be imprecise, and caution should be used in extending the forecasting horizon as larger samples become available. The results here also show that the asymptotic device used in this paper, where , provides an important benchmark comparison to the commonly used framework with , since the test statistics are only consistent under the former assumption. The theoretical results here also help explain the puzzling non-monotonicity in the power curves for long-run regressors, a finding which adds an additional note of caution to the use of long forecasting horizons. Note that the turning point of the power curve is not outside the relevant parameter region. As seen in Figure 3, for , the power is already declining for ; the results in Campbell and Yogo (2006) show that in annual data, which the 100 observations in each simulated sample used to generate Figure 3 might represent, the estimates of are between and for the dividend and earnings-price ratios. This also provides a strong case for the test based on the long-run augmented regression equation suggested in this paper, since it does not suffer from non-monotone power.
The results here also suggest that the power of predictive tests may be decreasing with the forecasting horizon, which would seem to imply that using one period tests is the best approach. The simulation results are supportive of this conjecture and the empirical results presented in the next section can also be interpreted as favorable of this view. However, the power comparisons across different forecasting horizons conducted in this paper are all informal and heuristic; a more thorough analysis, which is outside the scope of the current study, is required before any definitive statements can be made. Finally, one should recall one important caveat. The power results are all derived under the assumption that the true model is the one given by equations (1) and (2). This is a standard assumption used by, for instance, Nelson and Kim (1993) and Campbell (2001), but clearly other potential data generating processes that might lead to different results are possible. The results under the model analyzed here, however, can be considered a point of reference against which to compare other specifications.
# 6 Long-run stock return predictability
To illustrate the theoretical results derived in this paper, I revisit the question of stock return predictability. There have been many conflicting results regarding the existence of a predictable component in stock returns. However, recent work by Lewellen (2004) and Campbell and Yogo (2006), which rely on both more robust as well as more efficient methods of inference than previous research, do find evidence that stock returns are predictable to some degree. In this section, I extend their empirical analysis to the long-horizon case. Since the scaled long-run Bonferroni test, which controls for the endogeneity and persistence in the regressors, is effectively a long-run version of the methods developed in Campbell and Yogo (2006), the empirical results presented here provide a direct comparison with previous work. In the first part of the empirical analysis, I therefore analyze the same data as those used by Campbell and Yogo. I then consider the evidence in an international data set from nine additional countries. The section ends with a discussion of the results.
## 6.1 The data
### 6.1.1 The U.S. data
The data on U.S. stock returns and predictor variables are the same as those used by Campbell and Yogo (2006).13The returns data consist of the monthly and annual excess returns on the CRSP NYSE/AMEX value-weighted index over the period 1926-2002, as well as annual returns on the S&P 500 index over the period 1880-2002. The excess returns are calculated as the stock returns over the risk free rate, measured by the return on the one-month T-bill for the monthly data, and by the return on the three-month T-bill rolled over quarterly for the annual data. The predictor variables are the dividend-price ratio , the smoothed earnings-price ratio suggested by Campbell and Shiller (1988), the 3-month T-bill rate , and the long-short yield spread , which is defined as the difference between Moody's seasoned Aaa corporate bond yield and the one month T-bill rate. The dividend-price ratio is calculated as dividends over the past year divided by the current price and the (smoothed) earnings-price ratio as the average earnings of the past 10 years divided by the current price. Since earnings are not available for the CRSP data, the corresponding S&P 500 earnings are used. All regressions are run using log-transformed variables with the log excess returns as the dependent variable. The regressions involving the short-rate and the yield-spread as predictors are estimated over the period 1952-2002, since prior to this time period the interest rate was pegged by the Federal Reserve. The regressions with the CRSP data, using the dividend- and earnings-price ratios as predictors, are also analyzed over this period as a comparison to the full sample results.
### 6.1.2 The international data
The international data used in this paper come from Global Financial Data. Total returns, including direct returns from dividends, on market-wide indices in nine countries with at least 50 years of data were obtained, as well as the corresponding dividend-price ratios. Earnings data were typically only available over much shorter time periods and long-run regressions with the earnings-price ratio as a predictor are therefore not included in the international analysis. In addition, for each country, measures of the short and long interest rates were obtained, from which measures of the term spread were constructed. The variable definitions follow the usual conventions in the literature. The dividend-price ratio is defined as the sum of dividends during the past year, divided by the current price. The measure of the short interest rate comes from the interest rate series constructed by Global Financial Data and uses rates on 3-month T-bills when available or, otherwise, private discount rates or interbank rates. The long rate is measured by the yield on long-term government bonds. When available, a 10 year bond is used; otherwise, I use that with the closest maturity to 10 years. The term spread is defined as the log difference between the long and the short rate. Excess stock returns are defined as the return on stocks, in the local currency, over the local short rate, which provides the international analogue of the typical forecasting regressions estimated for U.S. data.
The predictor variables used in the international sample are therefore the dividend-price ratio , the short interest rate and the term spread , where the latter two are meant to capture similar features of stock return predictability as the corresponding interest rate variables in the U.S. sample, even though they are not defined in an identical manner.
The countries in the data are: Australia, Belgium, Canada, France, Germany, Italy, Japan, Sweden, and the U.K. The end date for each series is March 2004, although the starting date varies between the countries. The longest series is for Australia, which dates back to 1882, and the shortest for Germany, which goes back to 1953. All returns and interest rate data are on a monthly frequency. For a few of the older observations, the dividend-price ratios are given on an annual basis; these are transformed to monthly data by filling in the monthly dividends over the year with the previous year's values.14
All regressions are run using log-transformed variables with the log excess returns over the domestic short rate as the dependent variable. Following the convention used in the U.S. data, the data used in all interest rate regressions are restricted to start in 1952 or after.15 Again, as a comparison, the predictive regression with the dividend price ratios are also run over this restricted sample period; in the international data, this is particularly useful, since the starting points of the series vary from country to country and imposing a common starting date allows for easier cross-country comparison.
## 6.2 Characteristics of the predictor variables
The two key data characteristics that define the properties of the regression estimators analyzed in this paper are the near persistence and endogeneity of the regressors. For the U.S. data, Table 2 shows confidence intervals for the autoregressive root , and the analogue intervals for the local-to-unity parameter , calculated by inverting the DF-GLS unit-root test, as well as estimates of the correlation between the innovations to returns and the innovations to the regressors . The results are shown both for the full sample period, as well as for the post 1952 sample. As is evident, there is a large negative correlation between the innovations to the returns and the valuation-ratios. The short interest rate is nearly exogenous, however. The yield spread is also almost exogenous in the monthly data, although it exhibits a somewhat larger correlation in the annual data. Standard OLS inference might thus be expected to work fairly well when using the short rate or the yield spread as predictor variables. In addition, all variables, except perhaps the annual yield spread, show signs of having autoregressive roots that are close to unity.
The corresponding results for the international data are given in Table 3, where the sample period available for each country is also given. Overall, the international predictor variables are similar to the corresponding U.S. ones. The dividend-price ratio is highly persistent in all countries, and the null hypothesis of a unit root can typically not be rejected based on the DF-GLS test statistic. Furthermore, the dividend-price ratio is generally fairly endogenous, in the sense that the estimates of , the correlation between the innovations to the returns and the predictor process, are large in absolute value. Compared to the U.S. data, however, the estimates of for the dividend-price ratio are generally somewhat smaller in absolute value, typically ranging from to , whereas in the U.S. data absolute values above are common. The short interest rate and the term spread also behave similar to the U.S. counterparts. They are mostly exogenous but still highly persistent.
Both the U.S. and the international data thus seem to fit well the assumptions under which the results in this paper are derived. In addition, at least for the valuation ratios, there is a strong case for using test statistics that take into account the bias induced by the endogeneity and persistence in the regressors. For the interest rate variables, OLS inference should be fairly accurate.
## 6.3 Long-run regression results for the U.S. data
The results from the long-run regressions are presented graphically as plots of the scaled statistics against the forecasting horizon . Although the results in previous sections suggest that using very long forecasting horizons are generally not advisable, I will show results for forecasting horizons out to 20 years in the annual data and 10 years in the monthly data, to illustrate the properties of the test statistics across most potential forecasting horizons that may be used in applied work.
In each plot, the values of the scaled OLS statistics along with the scaled Bonferroni statistics are plotted against the forecasting horizon; as a point of reference, the five percent significance level in a one sided test is also shown, i.e. a flat line equal to . The Bonferroni test statistic is calculated in the same manner as described in Section 3. Given the asymptotic results developed previously, the scaled Bonferroni statistic will be approximately normally distributed for all predictor variables, whereas for the scaled OLS test, the normal approximation will only be satisfied for exogenous variables and might thus be expected to work well with the interest rate variables. In addition to the scaled Bonferroni test statistic, I also show the value of the scaled statistic evaluated for (i.e. ). The maximum of this test statistic and the Bonferroni test statistic can be seen as the value of the Bonferroni test when explosive roots are ruled out a priori.16 This additional statistic is not shown for the interest rate variables where the Bonferroni and OLS statistics are already very close to each other.17
The first set of results are displayed in Figure 7, which shows the scaled OLS and Bonferroni statistics from the regressions with the dividend- and earnings-price ratios in the annual full sample U.S. data. As is to be expected, the results for the one period forecasting horizon are qualitatively identical to those in Campbell and Yogo (2006). Thus, at the shorter horizons, there is some mixed evidence of predictability, with the null rejected for both the S&P 500 and the CRSP returns when using the earnings-price ratio, but only for the CRSP returns when using the dividend-price ratio. It is interesting to note that although the Bonferroni test is more robust than the OLS test, the numerical outcome of the Bonferroni test need not always be smaller than the biased OLS statistic. In addition, in Figure 7, the statistics based on Newey-West standard errors are also shown, calculated using lags. Comparing the plots of these against the properly scaled statistics, it is apparent that Newey-West errors can fail substantially in controlling the size of long-horizon test. They also illustrate why long-run predictability is often thought to be stronger than short-run predictability. Given the well known biases in the Newey-West statistics, in the subsequent figures they are not shown in order to keep the graphs more easily readable.
Similar results to those in Figure 7 are also found in Figure 8, which shows the results for monthly CRSP returns, both for the full sample from 1926 and in the post 1952 sample, using the dividend- and earnings-price ratios as predictors. Again, there is mixed evidence of predictability. The results in Figure 8 also illustrates that ruling out explosive processes, i.e. restricting to be less than or equal to one, can have a substantial impact on the results. In the sub sample from 1952-2002, the evidence in favour of predictability is substantially greater when ruling out explosive processes. This great sensitivity stems from the extreme endogeneity of the dividend- and earnings-price ratios in the U.S. data, with absolute values of upwards of .
From the perspective of the theoretical analysis in the current paper, the results in Figures 7 and 8 illustrate two key findings. First, and contrary to many popular beliefs, the evidence of predictability does not typically become stronger at longer forecasting horizons. There are some exceptions, such as the results for the dividend-price ratio in the full CRSP sample in Figure 8, but overall there is little tendency for the results to look stronger at longer horizons. If anything, there is a tendency for the properly scaled statistics to become smaller as the horizon increases, which would be consistent with a loss of power. Second, these results show that it is important to control for the biasing effect of persistent and endogenous regressors also in long-horizon regressions, as seen from the often large difference between the OLS and the Bonferroni test statistics.
Figure 9 shows the results for the short rate and the yield spread, both for the annual and the monthly data. As expected, the OLS and Bonferroni results are now very close to each other, reflecting the nearly exogenous nature of the interest rate variables. For the short rate, the one-sided alternative is now a negative coefficient. In order to achieve easy comparison with the rest of the results in general, and the yield-spread in particular, the negative of the test statistics are plotted for the short rate. As seen, there is evidence of predictability at very short horizons, which disappears very fast as the horizon increases. In fact, the evidence is already gone in the annual data at the one-period horizon. A similar result is found for the yield spread, where the expected coefficient under the alternative of predictability is again positive.
The one-period, or short-run, empirical findings for the U.S. data are qualitatively identical to those of Campbell and Yogo (2006). The bottom line is that there is fairly robust evidence of predictability in U.S. data in the short run when using the two interest rate variables as predictors, whereas the evidence for the valuation ratios is more mixed. The results from the regressions with the dividend- and earnings-price ratios are made more difficult to interpret given the large endogeneity of the regressors. As is seen, for instance, restricting the autoregressive root to be less than or equal to unity can change the results rather dramatically, a point which is discussed in detail in Campbell and Yogo (2006); these results thus illustrate well the power gains that can be made with additional knowledge regarding the true autoregressive root in the process. Although restricting the regressor to be a non-explosive process seems like a fairly sensible restriction in most cases, it should also be stressed that imposing a non-explosive condition on the dividend-price ratio, for instance, is not necessarily completely innocuous. Lettau and Van Nieuwerburgh (2007) show that there is evidence of structural breaks in the valuation ratios in U.S. data and that if one takes into account these breaks, the predictive ability of these ratios improves. A structural break process is inherently non-stationary and is indeed very hard to distinguish from a highly persistent process of the kinds analyzed in this paper, especially if one allows for explosive roots. Some caution is therefore required in ruling out explosive processes, a point also made by Campbell and Yogo (2006).
## 6.4 Long-run regression results for the international data
The results for the international data are shown in Figures 10-13. The results for the dividend-price ratio are shown in Figure 10 for the full sample and in Figure 11 for the post 1952 sample. Given the somewhat mixed and overall fairly weak results in the U.S. data, the international results are close to what one might expect. There is some weak evidence of predictability in the full sample for Canada, as well as for Japan. In both the Canadian and Japanese cases, however, these results are no longer significant in the post 1952 sample, which is particularly striking for Japan since the full sample only stretches back to 1949. The results for both Canada and Japan are also sensitive to the exclusion of explosive roots. The only country for which there is consistently strong evidence is the U.K. Again, there is little evidence of stronger predictability in the long-run. The only significant result in this direction is for the full Canadian sample where there is no predictability at the first few horizons; the results are far from striking, however.
The results for the interest rate variables, shown in Figures 12 and 13, are somewhat more favorable of predictability. For the short-rate, shown in Figure 12, where again the alternative hypothesis is a negative coefficient and the negative of the test statistic is plotted, significance is found at short horizons in Canada and Germany, and close to significance in Australia, France, and Italy. The corrections for endogeneity have little effect, and the OLS and Bonferroni results are very close to each other. The only exception is at long horizons for Japan where there is some discrepancy, although not enough to change any conclusions if one were to rely on the OLS analysis.
For the term spread, shown in Figure 13, the results look similar but somewhat stronger, with significant short-run coefficients found for Canada, France, Germany, and Italy, and for a few horizons for Australia. Again, with the exception of Australia, the evidence of predictability disappears very fast as the horizon increases.
The results from the international data support the U.S. conclusions to some extent. The evidence in favour of predictability using the dividend-price ratio in international data is overall weak, with the only solid evidence coming from the U.K. data. The evidence from Canada and Japan is weaker and more sensitive to the sampling period. Although the scaled Bonferroni statistic is generally much smaller than the scaled OLS statistic in the international data as well, the evidence based on the OLS results themselves is not that supportive of a predictive relationship either. Thus, although some power gains would still be had from a more precise knowledge of the autoregressive root in the data, the international results may be somewhat less susceptible to this critique than the U.S. results. The international results for the interest rate variables are again similar to those of the U.S. data, but do not fully support any generic statements about the predictive ability of these variables. However, there is some commonality across the country results for these variables. This is particularly true for Australia, Canada, France, Germany, and Italy, where the significant results are found.
## 6.5 Discussion of the empirical findings
The empirical findings can broadly be summed up as follows: (i) The evidence of predictability using the valuation ratios is overall fairly weak, both in the U.S. and the international data. (ii) The predictive ability of the interest rate variables appears fairly robust in the U.S. data and extends to some degree to the international data. (iii) With few exceptions, all evidence of predictability is found for the shortest horizons and any evidence that does exist tends to disappear as the forecasting horizon increases; this is particularly true for the interest rate variables where the test statistics are often almost monotonically declining in value with the forecasting horizons.
Points (i) and (ii) are discussed at some length in Campbell and Yogo (2006) and Ang and Bekaert (2007), although the international sample used by the latter is somewhat smaller than the one used here. Instead, I will focus on the third point regarding the long-run results. Contrary to many popular beliefs, the results here show that evidence of predictability in the long-run is not stronger than in the short-run. In fact, in most cases the opposite appears true.
If the data are generated by the standard model in equations (1) and (2), predictability in the short-run also implies predictability in the long-run. However, the analytical results in this paper also show that tests lose power as the horizon increases, which could explain the findings presented here. That is, even if the results from the one-period regressions are correct, and there is predictability in some cases, there is no guarantee that this predictability will be evident at longer horizons, given a decrease in the power to detect it. In practice, the evidence of predictability is weak also at short horizons, and it should therefore not be surprising that the null of no predictability cannot be rejected for longer horizons.18 The empirical results are thus consistent with the model in equations (1) and (2), under which the analytical results were derived. Consistent empirical findings of long-run, but not short-run, predictability, on the other hand, would suggest that equations (1) and (2) are not adequate tools for modelling return predictability.
Torous et al. (2004) and Ang and Bekaert (2007) also find that the evidence of predictability tends to be strongest at shorter horizons, although they do not suggest the possibility that this may be due to a lack of power in long horizon tests. Boudoukh et al. (2005) explicitly question the prevailing view of long-horizon predictability and reach similar conclusions to those presented here, although their focus is on the joint properties of the regression estimators across different horizons. Taken together, there is thus mounting evidence against the previously prevailing view that stock return predictability is more apparent in the long-run than in the short-run.
# 7 Conclusion
I derive several new results for long-horizon regressions that use overlapping observations when the regressors are endogenous and highly persistent. I show how to properly correct for the overlap in the data in a simple manner that obviates the need for auto-correlation robust standard error methods in these regressions. Further, when the regressors are persistent and endogenous, I show how to correct the long-run OLS estimators and test procedures in a manner similar to that proposed by Campbell and Yogo (2006) for the short-run case.
The analysis also highlights the boundaries of long-horizon regressions. Analytical results, supported by Monte Carlo simulations, show that there are no power gains to long-run tests as long as the ratio between the forecasting horizon and the sample size is fixed. Thus, increasing the forecasting horizon as more data becomes available is not a good strategy.
An empirical application to stock-return predictability illustrates these results and shows that, in line with the theoretical results of this paper, the evidence for predictability is typically weaker as the forecasting horizon gets longer, reflecting at least to some extent the loss of power in long-run tests.
# A Proofs
For ease of notation the case with no intercept is treated. The results generalize immediately to regressions with fitted intercepts by replacing all variables by their demeaned versions. Unless otherwise noted, all limits as are under the condition that .
Proof of Theorem 1. Under the null hypothesis,
By standard arguments, as , such that , since for any , (Phillips, 1987 and 1988). Therefore,
Proof of Theorem 2. Let be the vector of observations, and define and analogously . Also, let . The OLS estimator of in (11) is now given by Under the null hypothesis, and thus First,
Let and denote . By some algebraic manipulations,
Now, observe that and . is thus an identical estimator to , but uses observations shifted steps. Letting ' denote distributional equivalence, it follows that,
and as , by the results in Andrews (1991), since . Similarly, as , and by the same arguments used in the previous proof, Thus,
Finally, as , using the above results, since it follows that,
Proof of Corollary 1 . Observe that under the null hypothesis, as ,
where the asymptotic limit follows by same argument as in the previous proof.
Proof of Corollary 2. This follows in an identical manner, since, as ,
Proof of Theorem 3. (i) Consider first the case when as . Under the alternative of predictability, by summing up on both sides in equation (1), it follows that
where , since . Using the results in Hjalmarsson (2008), it follows easily that, as , with , , and thus . Using the expression above, Clearly, is the dominant term. Now, using the fact that ,
where the first equality follows from the local-to-unity nature of , and the second equality from the martingale difference assumption on . The scaled statistic, for , thus satisfies
(ii) Consider next the case when as . By summing up on both sides in equation (1), , and the fitted regression is . It follows that,
Now, when as , it follows that and thus,
Similarly, and by the CMT,
It follows that The fitted residuals satisfy and
The scaled statistic of Valkanov (2003), for testing the null hypothesis of , therefore satisfy, as , with ,
Proof of Theorem 4. Using the results in Hjalmarsson (2008) again, it follows that for , where , and thus . As before,
and, Now, consider
By previous results, and . Further, by similar arguments as before,
since as . Thus, and
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Table 1.1a - Long-Run OLS t-Test: T = 100, c = 0
Finite sample sizes for the scaled long-run OLS t-test, the scaled Bonferroni test and the scaled infeasible test. The first column gives the forecasting horizon q, and the top row below the labels gives the value of the parameter , the correlation between the innovation processes. The remaining entires show, for each combination of q and , the average rejection rates under the null hypothesis of no predictability for the corresponding test. The results are based on the Monte Carlo simulation described in the main text and the average rejection rates are calculated over 10,000 repetitions. Results for the sample sizes T equal to 100 and 500 and for local-to-unity parameters c equal to 0 and -10 are shown; for T=100, these values correspond to autoregressive roots =1 and =0.9, respectively, and for T=500, they correspond to =1 and =0.98.
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
1
0.0580.1020.1880.2950.3850.419
50.0520.1100.1860.3030.3990.434
100.0480.1020.1850.3060.4210.458
150.0480.1010.1710.2940.405.0451
200.0430.0880.1660.2890.3920.435
250.0400.0820.1540.2610.3650.403
Table 1.1b - Long-Run OLS t-Test: T = 500, c = 0
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0510.0990.1760.2980.3810.415
250.0510.1000.1790.3050.4070.438
500.0530.1080.1810.3010.4100.458
750.0510.0990.1770.2870.3980.450
1000.0450.0920.1610.2800.3820.436
1250.0390.0800.1460.2580.3630.406
Table 1.1c - Long-Run OLS t-Test: T = 100, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0520.0710.0970.1230.1370.143
50.0440.0580.0830.1020.1170.130
100.0330.0450.0630.0820.0980.108
150.0220.0360.0480.0670.0820.089
200.0180.0270.0390.0560.0640.069
250.0110.0190.0280.0390.0460.048
Table 1.1d - Long-Run OLS t-Test: T = 500, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0500.0690.0910.1220.1360.140
250.0380.0590.0780.1060.1230.128
500.0330.0450.0700.0870.1040.104
750.0240.0360.0540.0760.0860.091
1000.0180.0290.0400.0570.0640.071
1250.0100.0200.0310.0380.0510.053
1.2a - Bonferroni Test: T = 100, c = 0
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
1
0.0440.0450.0420.0460.0530.068
50.0430.0460.0420.0430.0530.057
100.0410.0480.0460.0420.0440.048
150.0420.0470.0440.0350.0320.034
200.0410.0420.0430.0310.0250.023
250.0330.0360.0340.0250.0160.013
1.2b - Bonferroni Test: T = 500, c = 0
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0450.0430.0340.0340.0400.043
250.0430.0420.0360.0290.0340.041
500.0450.0420.0390.0330.0280.035
750.0420.0450.0360.0300.0240.022
1000.0360.0390.0350.0230.0170.018
1250.0320.0290.0250.0170.0140.012
1.2c - Bonferroni Test: T = 100, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0440.040.0320.0340.0430.051
50.0300.0330.0260.0250.0340.037
100.0270.0240.0210.0160.0170.020
150.0210.0220.0170.0110.0090.011
200.0170.0140.0120.0070.0060.007
250.0130.0110.0090.0050.0050.003
1.2d - Bonferroni Test: T = 500, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0470.0330.0270.0230.0330.039
250.0330.0310.0230.0200.0210.027
500.0220.0300.0220.0140.0140.016
750.0240.0230.0160.0100.0090.008
1000.0180.0180.0150.0080.0050.006
1250.0150.0150.010.0050.0040.003
1.3a Infeasible Test (using true value of c): T = 100, c = 0
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
1
0.0530.0560.0510.0570.0570.052
50.0540.0650.0610.0570.0470.041
100.0650.0630.0640.0600.0500.043
150.0660.0660.0640.0600.0490.041
200.0640.0630.0600.0590.0480.044
250.0600.0590.0610.0530.0460.040
1.3b Infeasible Test (using true value of c): T = 500, c = 0
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0500.0540.0520.0480.0510.048
250.0590.0580.0640.0490.0470.039
500.0670.0660.0630.0550.0480.037
750.0640.0670.0680.0580.0500.036
1000.0670.0620.0670.0590.0470.036
1250.0580.0550.0560.0540.0440.042
1.3c Infeasible Test (using true value of c): T = 100, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0540.0530.0540.0530.0570.059
50.0490.0470.0470.0490.0460.050
100.0440.0430.0440.0460.0410.038
150.0410.0370.0400.0400.0340.031
200.0350.0350.0300.0310.0280.029
250.0260.0290.0280.0290.0250.023
1.3d Infeasible Test (using true value of c): T = 500, c = -10
q=0.00=-0.25=-0.50=-0.75=-0.90=-0.95
10.0490.0560.0520.0520.0530.055
250.0460.0490.0430.0480.0440.041
500.0440.0450.0440.0430.0380.039
750.0390.0400.0390.0410.0380.030
1000.0340.0350.0340.0310.0290.027
1250.0290.0250.0280.0260.0220.022
Table 2
Characteristics of the predictor variables in the U.S. data. This table reports the key time-series characteristics of the dividend-price ratio , the earnings-price ratio , the short interest rate , and the yield spread . The S&P 500 variables are on an annual frequency, whereas results for both the annual and monthly CRSP data are reported. All series end in . The first two columns indicate the data set and predictor variable being used. The following three columns show the sampling frequency, the start date of the sample period, and the number of observations in that sample. The column labeled DF-GLS gives the value of the DF-GLS unit-root test statistic, and the column labeled gives the estimated correlations between the innovations to the predictor variables and the innovations to the corresponding excess returns. The last two columns give the 95% confidence intervals for the autoregressive root and the corresponding local-to-unity parameter , obtained by inverting the DF-GLS unit-root test statistic.
SeriesVariableSample Freq.Sample BeginsObs.DF-GLS CI for CI for
S&P 500 Annual
S&P 500 Annual
CRSP Annual
CRSP Annual
CSRP Monthly
CRSP Monthly
CRSP Monthly
CRSP Monthly
CSRP Annual
CRSP Annual
CSRP Monthly
CRSP Monthly
Table 3
Characteristics of the predictor variables in the international data. This table reports the key time-series characteristics of the dividend-price ratio , the short interest rate , and the term spread . All data are on a monthly frequency, and all series end in 2004. The first two columns indicate the country and predictor variable being used, and the next two columns show the start date of the sample period and the number of observations in that sample. The column labeled DF-GLS gives the value of the DF-GLS unit-root test statistic, and the column labeled gives the estimated correlations between the innovations to the predictor variables and the innovations to the corresponding excess returns. The last two columns give the 95% confidence intervals for the autoregressive root and the corresponding local-to-unity parameter , obtained by inverting the DF-GLS unit-root test statistic.
CountryVariableSample BeginsObs.DF-GLS CI for CI for
Australia
Belgium
France
Germany
Italy
Japan
Sweden
UK
Australia
Belgium
France
Germany
Italy
Japan
Sweden
UK
Australia
Belgium
France
Germany
Italy
Japan
Sweden
UK
Australia
Belgium
France
Germany
Italy
Japan
Sweden
UK
Figure 1
Power curves for exogenous regressors with , , and The graphs show the average rejection rates for a one-sided percent test of the null hypothesis of against a positive alternative. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left-hand graph gives the results for the case of , and the right-hand graph gives the results for . The results for the scaled OLS test derived in this paper are given by the solid lines, the results for Valkanov's infeasible test are given by the long dashed lines, and the results for Valkanov's feasible sup-bound test are given by the short dashed lines. The results are based on the Monte Carlo simulations described in the main text, and the power is calculated as the average rejection rates over 10,000 repetitions.
Figure 2
Power curves for endogenous regressors with , , and The graphs show the average rejection rates for a one-sided percent test of the null hypothesis of against a positive alternative. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left-hand graph gives the results for the case of , and the right-hand graph gives the results for . The results for the scaled Bonferroni test are given by the solid lines, the results for the scaled infeasible test from the augmented regression equation, which uses knowledge of the true value of , are given by the dotted line, the results for Valkanov's infeasible test are given by the long dashed lines, and the results for Valkanov's feasible sup-bound test are given by the short dashed lines. The results are based on the Monte Carlo simulations described in the main text, and the power is calculated as the average rejection rates over 10,000 repetitions.
Figure 3
Power curves for endogenous regressors with , , and The graphs show the average rejection rates for a one-sided percent test of the null hypothesis of against a positive alternative. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left-hand graph gives the results for the case of , and the right-hand graph gives the results for . The results for the scaled Bonferroni test are given by the solid lines, the results for the scaled infeasible test from the augmented regression equation, which uses knowledge of the true value of , are given by the dotted line, the results for Valkanov's infeasible test are given by the long dashed lines, and the results for Valkanov's feasible sup-bound test are given by the short dashed lines. The results are based on the Monte Carlo simulations described in the main text, and the power is calculated as the average rejection rates over 10,000 repetitions.
Figure 4
Power curves for , and . The graphs show the average rejection rates for a one-sided percent test of the null hypothesis of against a positive alternative. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left hand graph gives the results for the case of exogenous regressors with and . The results for the scaled OLS test are given by the solid lines, the results for Valkanov's infeasible test, which coincides with Valkanov's sup-bound test for , are given by the long dashed lines, and the results for the (non-scaled) test using Newey-West standard errors are given by the dotted and dashed line. The right hand graph gives the results for the case of endogenous regressors with and . The results for the scaled Bonferroni test are given by the solid lines, the results for the scaled infeasible test from the augmented regression equation, which uses knowledge of the true value of , are given by the dotted line, the results for Valkanov's infeasible test are given by the long dashed lines, the results for Valkanov's feasible sup-bound test are given by the short dashed lines, the results for the (non-scaled) test using Newey-West standard errors are given by the dotted and dashed line, and the results for the scaled OLS test are given by the finely dotted line. The results are based on the Monte Carlo simulations described in the main text, and the power is calculated as the average rejection rates over 10,000 repetitions.
Figure 5
Comparison of power across horizons for and . The graphs show the average rejection rates for a one-sided percent test of the null hypothesis of against a positive alternative. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left hand graph gives the results for the case of exogenous regressors with . The results for the one period OLS test are given by the solid line (), and the results for the scaled OLS tests for and are given by the the short dashed line and the dotted line, respectively. The right hand graph gives the results for the case of endogenous regressors with . The results for the one period () Bonferroni test are given by the solid line, and the results for the scaled Bonferroni tests for and are given by the the short dashed line and the dotted line, respectively. The results are based on the Monte Carlo simulations described in the main text, and the power is calculated as the average rejection rates over 10,000 repetitions.
Figure 6
Local power curves for and . The graphs show the average power curves for a one-sided percent test of the null hypothesis against a positive local alternative, based on the distribution of the scaled OLS statistic derived in Theorem 4. The axis shows the true value of the parameter , and the axis indicates the average rejection rate. The left-hand graph gives the results for exogenous regressors with , and the right-hand graph gives the results for endogeneous regressors with . The results are obtained from direct simulation of the limiting random variables in equation (18), and the power is calculated as the average rejection rate over 10,000 repetitions.
Figure 7
Empirical results for the annual U.S. data with valuation ratios as predictors. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The left-hand graphs give the results for the dividend price ratio , and the right-hand graphs give the results for the earnings-price ratio . Results for the S&P 500 data are shown in the top graphs and results for the CRSP data in the bottom graphs. The results for the scaled OLS test are given by the short dashed lines, the results for the scaled Bonferroni test are given by the dotted lines, the results for the scaled test from the augmented regression equation under the assumption of are given by the long dashed lines, and the results for the (non-scaled) test using Newey-West standard errors are given by the dotted and dashed line. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 8
Empirical results for the monthly U.S. data with valuation ratios as predictors. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The left-hand graphs give the results for the dividend price ratio , and the right-hand graphs give the results for the earnings-price ratio . Results for the full CRSP sample from 1926-2002 are shown in the top graphs and results for the restricted CRSP sample from 1952-2002 in the bottom graphs. The results for the scaled OLS test are given by the short dashed lines, the results for the scaled Bonferroni test are given by the dotted lines, and the results for the scaled test from the augmented regression equation under the assumption of are given by the long dashed lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 9
Empirical results for the U.S. data with interest rate variables as predictors. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The left-hand graphs give the results for the short interest rate , and the right-hand graphs give the results for the yield spread . Results for the annual data are shown in the top graphs and results for the monthly data in the bottom graphs. The results for the scaled OLS test are given by the short dashed lines and the results for the scaled Bonferroni test are given by the dotted lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 10
Empirical results for the international data with the dividend-price ratio as predictor, using the full sample for each country. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The title of each graph indicates the country and sample period to which the results correspond. The results for the scaled OLS test are given by the short dashed lines, the results for the scaled Bonferroni test are given by the dotted lines, and the results for the scaled test from the augmented regression equation under the assumption of are given by the long dashed lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 11
Empirical results for the international data with the dividend-price ratio as predictor, using data after 1952. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The title of each graph indicates the country and sample period to which the results correspond. The results for the scaled OLS test are given by the short dashed lines, the results for the scaled Bonferroni test are given by the dotted lines, and the results for the scaled test from the augmented regression equation under the assumption of are given by the long dashed lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 12
Empirical results for the international data with the short interest rate as predictor. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The title of each graph indicates the country and sample period to which the results correspond. The results for the scaled OLS test are given by the short dashed lines and the results for the scaled Bonferroni test are given by the dotted lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
Figure 13
Empirical results for the international data with the term spread as predictor. The graphs show the outcomes of the long-run test statistics as functions of the forecasting horizon. The axis shows the forecasting horizon , and the axis shows the value of the test statistic. The title of each graph indicates the country and sample period to which the results correspond. The results for the scaled OLS test are given by the short dashed lines and the results for the scaled Bonferroni test are given by the dotted lines. The flat solid line shows the 5% significance level, equal to 1.645 based on the normal distribution, for the one sided test.
# Footnotes
* I have greatly benefitted from advice by Peter Phillips and Robert Shiller. Other helpful comments have also been provided by Don Andrews, John Campbell, Dobrislav Dobrev, Ray Fair, Jon Faust, Lennart Hjalmarsson, Randi Hjalmarsson, Yuichi Kitamura, Taisuke Otsu, as well as participants in the econometrics seminar and workshop at Yale University, the international finance seminar at the Federal Reserve Board, the finance seminar at Göteborg University, the World meeting of the Econometric Society in London, 2005, and the Copenhagen Conference on Stock Return Predictability, 2007. Excellent research assistance has been provided by Benjamin Chiquoine. Tel.: +1-202-452-2426; fax: +1-202-263-4850; email: [email protected]. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Return to text
1. Other applications of long-horizon regressions include tests of exchange rate predictability (Mark, 1995, Berkowitz and Giorgianni, 2001, and Rossi 2005), the Fisher effect (Mishkin, 1990, 1992, and Boudoukh and Richardson, 1993), and the neutrality of money (Fisher and Seater, 1993). Return to text
2. Ang and Bekaert (2007) suggest using Hodrick (1992) auto-correlation robust standard errors, which they argue have good finite sample properties. However, these rely on the regressors being covariance stationary, which is a restrictive assumption for most forecasting variables as evidenced by the results in the empirical analysis in this paper. Return to text
3. There is now a large literature on regressions with overlapping observations. Additional references to those mentioned previously include Hansen and Hodrick (1980), Richardson and Stock (1989), Richardson and Smith (1991), Nelson and Kim (1993), Goetzman and Jorion (1993), Campbell (2001), Daniel (2001), Mark and Sul (2004), Moon et al. (2004), Torous et al. (2004), Boudoukh et al. (2005), and Rapach and Wohar (2005). The study by Valkanov (2003) is the most closely related to this paper and is discussed in more detail below. Studies on (short-run) predictive regressions in the context of persistent regressors include Mankiw and Shapiro (1986), Cavanagh et al. (1995), Stambaugh (1999), Lewellen (2004), Campbell and Yogo (2006), Janson and Moreira (2006), and Polk et al. (2006). Return to text
4. A predictive regressor is generally referred to as endogenous if the innovations to the returns are contemporaneously correlated with the innovations to the regressor. When the regressor is strictly stationary, such endogeneity has no impact on the properties of the estimator, but when the regressor is persistent in some manner, the properties of the estimator will be affected (e.g. Stambaugh, 1999). Nelson and Kim (1993) may be the first to raise the biasing problems of endogenous regressors in the long-horizon case. Return to text
5. The asymptotic results presented in Section 2 all generalize immediately to the case of multiple regressors. However, the Bonferroni methods described in Section 3 are currently only developed for the case of a single regressor. Return to text
6. That is, can be estimated consistently, but not with enough precision to identify Return to text
7. A similar point is made by Phillips (1991b) and Corbae et al. (2002) in regards to frequency domain estimation with persistent variables. They show that the asympototic distribution of the narrow band least squares estimator, which only uses frequencies close to zero and thus captures the long-run relationship in the data, is identical to the asymptotic distribution of the full frequency estimator (which is identical to standard OLS). Return to text
8. An alternative approach is to invert the test-statistics and form conservative confidence intervals instead. This approach will deliver qualitatively identical results, in terms of whether the null hypothesis is rejected or not. However, the distribution of the long-run estimator under the alternative hypothesis is not the same as under the null hypothesis (see the proofs of Theorems 3 and 4 in the Appendix), in which case the confidence intervals are only valid under the null hypothesis. Presenting confidence intervals based on the distribution under the null hypothesis may therefore be misleading. Return to text
9. In practice, the confidence levels of the lower and upper bounds in the shrunk confidence interval are not symmetrical, and Campbell and Yogo (2006) find separate confidence levels and that correspond to the lower and upper bounds. Return to text
10. Table 2 in Campbell and Yogo (2006) gives the confidence levels for the confidence interval for that is used in the Bonferroni test, for a given . Tables 2-11 in Campbell and Yogo (2005) give the actual confidence intervals for , for a given and value of the DF-GLS unit-root test statistic. That is, for a given value of and the DF-GLS statistic, Tables 2-11 in Campbell and Yogo (2005) present the confidence intervals for with confidence levels corresponding to those in Table 2 in Campbell and Yogo (2006). Return to text
11. Valkanov (2003) provides critical values for , for different combinations of and , and I use these values when applicable. In the power simulations below where , I simulate critical values in the same manner as in the original paper, with , and using repetitions. Return to text
12. Lewellen (2004) suggests a similar procedure in one-period (short-run) regressions. Return to text
| 2016-02-06T03:06:33 |
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|
https://par.nsf.gov/biblio/10307589-imaging-topology-hofstadter-ribbons
|
Abstract
Physical systems with non-trivial topological order find direct applications in metrology (Klitzinget al1980Phys.Rev. Lett.45494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math.1183–204; Kitaev 2003Ann. Phys.3032–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev.B235632–33). At magnetic fields beyond the reach of current condensed matter experiment, around$104$T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al1982Phys. Rev. Lett.49405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003New J. Phys.556; Miyakeet al2013Phys. Rev. Lett.111185302; Aidelsburgeret al2013Phys. Rev. Lett.111185301; Celiet al2014Phys. Rev. Lett.112043001; Stuhlet al2015Science3491514; Manciniet al2015Science3491510; Anet al2017Sci. Adv.3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of$5%$, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.
Authors:
; ; ; ; ;
Publication Date:
NSF-PAR ID:
10307589
Journal Name:
New Journal of Physics
Volume:
21
Issue:
5
Page Range or eLocation-ID:
Article No. 053021
ISSN:
1367-2630
Publisher:
IOP Publishing
National Science Foundation
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The stratospheric influence on summertime high surface ozone ($O3$) events is examined using a twenty-year simulation from the Whole Atmosphere Community Climate Model. We find that$O3$transported from the stratosphere makes a significant contribution to the surface$O3$variability where background surface$O3$exceeds the 95thpercentile, especially over western U.S. Maximum covariance analysis is applied to$O3$anomalies paired with stratospheric$O3$tracer anomalies to identify the stratospheric intrusion and the underlying dynamical mechanism. The first leading mode corresponds to deep stratospheric intrusions inmore »
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Chiral and helical Majorana fermions are two archetypal edge excitations in two-dimensional topological superconductors. They emerge from systems of different Altland–Zirnbauer symmetries and characterized by$Z$and$Z2$topological invariants respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate in a single system without symmetry breaking. Here, we explore the peculiar behaviors of Majorana edge modes in topological superconductors with an additional ‘mirror’ symmetry which changes the bulk topological invariant to$Z⊕Z$type. A theoretical toy model describing the proximity structure of a Chern insulator andmore »
| 2022-06-27T23:59:02 |
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|
https://dlmf.nist.gov/4.4
|
# §4.4 Special Values and Limits
## §4.4(i) Logarithms
4.4.1 $\displaystyle\ln 1$ $\displaystyle=0,$ ⓘ Symbols: $\ln\NVar{z}$: principal branch of logarithm function A&S Ref: 4.1.12 Permalink: http://dlmf.nist.gov/4.4.E1 Encodings: TeX, pMML, png See also: Annotations for §4.4(i), §4.4 and Ch.4 4.4.2 $\displaystyle\ln\left(-1\pm\mathrm{i}0\right)$ $\displaystyle=\pm\pi\mathrm{i},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{i}$: imaginary unit and $\ln\NVar{z}$: principal branch of logarithm function A&S Ref: 4.1.14 (modified) Permalink: http://dlmf.nist.gov/4.4.E2 Encodings: TeX, pMML, png See also: Annotations for §4.4(i), §4.4 and Ch.4 4.4.3 $\displaystyle\ln\left(\pm\mathrm{i}\right)$ $\displaystyle=\pm\tfrac{1}{2}\pi\mathrm{i}.$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{i}$: imaginary unit and $\ln\NVar{z}$: principal branch of logarithm function A&S Ref: 4.1.15 Permalink: http://dlmf.nist.gov/4.4.E3 Encodings: TeX, pMML, png See also: Annotations for §4.4(i), §4.4 and Ch.4
## §4.4(ii) Powers
4.4.4 $\displaystyle e^{0}$ $\displaystyle=1,$ ⓘ Symbols: $\mathrm{e}$: base of natural logarithm A&S Ref: 4.2.23 Permalink: http://dlmf.nist.gov/4.4.E4 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.5 $\displaystyle e^{\pm\pi\mathrm{i}}$ $\displaystyle=-1,$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit A&S Ref: 4.2.26 Permalink: http://dlmf.nist.gov/4.4.E5 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.6 $\displaystyle e^{\pm\pi\mathrm{i}/2}$ $\displaystyle=\pm\mathrm{i},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit A&S Ref: 4.2.27 Permalink: http://dlmf.nist.gov/4.4.E6 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.7 $\displaystyle e^{2\pi k\mathrm{i}}$ $\displaystyle=1,$ $k\in\mathbb{Z}$, 4.4.8 $\displaystyle e^{\pm\pi\mathrm{i}/3}$ $\displaystyle=\frac{1}{2}\pm\mathrm{i}\frac{\sqrt{3}}{2},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.4.E8 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.9 $\displaystyle e^{\pm 2\pi\mathrm{i}/3}$ $\displaystyle=-\frac{1}{2}\pm\mathrm{i}\frac{\sqrt{3}}{2},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.4.E9 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.10 $\displaystyle e^{\pm\pi\mathrm{i}/4}$ $\displaystyle=\frac{1}{\sqrt{2}}\pm\mathrm{i}\frac{1}{\sqrt{2}},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.4.E10 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.11 $\displaystyle e^{\pm 3\pi\mathrm{i}/4}$ $\displaystyle=-\frac{1}{\sqrt{2}}\pm\mathrm{i}\frac{1}{\sqrt{2}},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.4.E11 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4 4.4.12 $\displaystyle{\mathrm{i}}^{\pm\mathrm{i}}$ $\displaystyle=e^{\mp\pi/2}.$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.4.E12 Encodings: TeX, pMML, png See also: Annotations for §4.4(ii), §4.4 and Ch.4
## §4.4(iii) Limits
4.4.13 $\lim_{x\to\infty}x^{-a}\ln x=0,$ $\Re a>0$, ⓘ Symbols: $\ln\NVar{z}$: principal branch of logarithm function, $\Re$: real part, $a$: real or complex constant and $x$: real variable A&S Ref: 4.1.30 Permalink: http://dlmf.nist.gov/4.4.E13 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
4.4.14 $\lim_{x\to 0}x^{a}\ln x=0,$ $\Re a>0$, ⓘ Symbols: $\ln\NVar{z}$: principal branch of logarithm function, $\Re$: real part, $a$: real or complex constant and $x$: real variable A&S Ref: 4.1.31 Permalink: http://dlmf.nist.gov/4.4.E14 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
4.4.15 $\lim_{x\to\infty}x^{a}e^{-x}=0,$ ⓘ Symbols: $\mathrm{e}$: base of natural logarithm, $a$: real or complex constant and $x$: real variable Permalink: http://dlmf.nist.gov/4.4.E15 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
4.4.16 $\lim_{z\to\infty}z^{a}e^{-z}=0,$ $|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta$ ($<\tfrac{1}{2}\pi$),
where $a$ ($\in\mathbb{C}$) and $\delta$ ($\in(0,\tfrac{1}{2}\pi]$) are constants.
4.4.17 $\lim_{n\to\infty}\left(1+\frac{z}{n}\right)^{n}=e^{z},$ $z=$ constant. ⓘ Symbols: $\mathrm{e}$: base of natural logarithm, $n$: integer and $z$: complex variable A&S Ref: 4.2.21 Permalink: http://dlmf.nist.gov/4.4.E17 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
4.4.18 $\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=e.$ ⓘ Symbols: $\mathrm{e}$: base of natural logarithm and $n$: integer A&S Ref: 4.1.17 Permalink: http://dlmf.nist.gov/4.4.E18 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
4.4.19 $\lim_{n\to\infty}\left(\left(\sum^{n}_{k=1}\frac{1}{k}\right)-\ln n\right)=% \gamma=0.57721\ 56649\ 01532\ 86060\dots,$ ⓘ Symbols: $\gamma$: Euler’s constant, $\ln\NVar{z}$: principal branch of logarithm function, $k$: integer and $n$: integer A&S Ref: 4.1.32 (with 10D value) Notes: For more digits see OEIS Sequence A001620; see also Sloane (2003). Permalink: http://dlmf.nist.gov/4.4.E19 Encodings: TeX, pMML, png See also: Annotations for §4.4(iii), §4.4 and Ch.4
where $\gamma$ is Euler’s constant; see (5.2.3).
| 2022-10-04T06:49:17 |
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https://pdglive.lbl.gov/DataBlock.action?node=S026M-&home=sumtabB
|
${{\mathit \Sigma}_{{b}}^{-}}$ MASS
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 5815.64 \pm0.27}$ OUR AVERAGE
$5815.64$ $\pm0.14$ $\pm0.24$ 1
2019 A
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$5815.5$ ${}^{+0.6}_{-0.5}$ $\pm1.7$ 2
2012 F
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$5815.2$ $\pm1.0$ $\pm1.7$ 3
2007 K
CDF Repl. by AALTONEN 2012F
1 Measured using fully reconstructed ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \Lambda}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays.
2 Measured using fully reconstructed ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \Lambda}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays.
3 Observed four ${{\mathit \Lambda}_{{b}}^{0}}{{\mathit \pi}^{\pm}}$ resonances in the fully reconstructed decay mode ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{-}}$ , where ${{\mathit \Lambda}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ .
References:
AAIJ 2019A
PRL 122 012001 Observation of two resonances in the $\Lambda_b^0 \pi^\pm$ systems and precise measurement of $\Sigma_b^\pm$ and $\Sigma_b^{*\pm}$ properties
AALTONEN 2012F
PR D85 092011 Measurement of the Masses and Widths of the Bottom Baryons ${{\mathit \Sigma}_{{b}}^{\pm}}$ and ${{\mathit \Sigma}_{{b}}^{*\pm}}$
AALTONEN 2007K
PRL 99 202001 Observation of the Heavy Baryons ${{\mathit \Sigma}_{{b}}}$ and ${{\mathit \Sigma}_{{b}}^{*}}$
| 2023-02-01T22:02:48 |
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|
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/58dd3cf7472d4a03227bf9e3
|
### Integration By Trigonometric Substitution:
There are several techniques of integration. One of the methods is the method of substitution. In this video, we will learn about integral of tan X, cot X, sec X and cosec X.
| 2019-11-15T07:18:34 |
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