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https://subs.emis.de/LIPIcs/frontdoor_e30d.html | License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2009.2333
URN: urn:nbn:de:0030-drops-23334
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2333/
Go to the corresponding LIPIcs Volume Portal
### The Power of Depth 2 Circuits over Algebras
pdf-format:
### Abstract
We study the problem of polynomial identity testing (PIT) for depth
$2$ arithmetic circuits over matrix algebra. We show that identity
testing of depth $3$ ($\Sigma \Pi \Sigma$) arithmetic circuits over a
field $\F$ is polynomial time equivalent to identity testing of depth
$2$ ($\Pi \Sigma$) arithmetic circuits over
$\mathsf{U}_2(\mathbb{F})$, the algebra of upper-triangular $2\times 2$ matrices with entries from $\F$. Such a connection is a bit
surprising since we also show that, as computational models, $\Pi \Sigma$ circuits over $\mathsf{U}_2(\mathbb{F})$ are strictly weaker'
than $\Sigma \Pi \Sigma$ circuits over $\mathbb{F}$. The equivalence
further implies that PIT of $\Sigma \Pi \Sigma$ circuits reduces to PIT
of width-$2$ commutative \emph{Algebraic Branching
Programs}(ABP). Further, we give a deterministic polynomial time
identity testing algorithm for a $\Pi \Sigma$ circuit of size $s$ over
commutative algebras of dimension $O(\log s/\log\log s)$ over
$\F$. Over commutative algebras of dimension $\poly(s)$, we show that
identity testing of $\Pi \Sigma$ circuits is at least as hard as that
of $\Sigma \Pi \Sigma$ circuits over $\mathbb{F}$.
### BibTeX - Entry
@InProceedings{saha_et_al:LIPIcs:2009:2333,
author = {Chandan Saha and Ramprasad Saptharishi and Nitin Saxena},
title = {{The Power of Depth 2 Circuits over Algebras}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {371--382},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Ravi Kannan and K. Narayan Kumar},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/2333},
URN = {urn:nbn:de:0030-drops-23334},
doi = {10.4230/LIPIcs.FSTTCS.2009.2333},
annote = {Keywords: Polynomial identity testing, depth 3 circuits, matrix algebras, local rings}
}
`
Keywords: Polynomial identity testing, depth 3 circuits, matrix algebras, local rings Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science Issue Date: 2009 Date of publication: 14.12.2009
DROPS-Home | Fulltext Search | Imprint | Privacy | 2022-05-22T13:27:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5305808186531067, "perplexity": 6667.571149792477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662545548.56/warc/CC-MAIN-20220522125835-20220522155835-00515.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2018.12.007 | • •
R&D补贴、寻租与全要素生产率提升
• 出版日期:2018-12-25 发布日期:2018-12-28
R&D Subsidy, Rent-seeking and Up-grading of Total Factor Productivity
Jiao Cuihong & Chen Yufen
• Online:2018-12-25 Published:2018-12-28
Abstract: R&D subsidy may remedy the market dysfunction caused by externality on one aspect, is easy to induce the action of rent-seeking to reduce the efficiency of subsidy. There is no agreement reached on whether the R&D subsidy can promote the escalation of total factor productivity (TFP) or not. This paper constructs a two-stage dynamic game model to relate to a R&D subsidy mechanism from the perspective of interaction between the government and enterprises. It is found that when the intensity of R&D subsidy is higher than certain threshold, it might be easy to seduce the enterprise to emit a false signal in the option of innovation ploys, which reduces the efficiency of government R&D handouts. Furthermore, tests are done on the heterogeneous impacts of various intensities of R&D subsidy on TFP by means of Chinese provincial panel data, and probing for the route of rent-seeking effecting R&D subsidy and TFP. The empirical results show that R&D subsidy in general has a negative effect on TFP, the more the intensity of subsidy, the more the negative effect. The rent-seeking is an important channel for high level R&D subsidy to curb TFP escalation. Therefore, in the process of carrying out innovative policies, the subsidy levels to various innovative enterprises need to be adjusted from time to time to prevent the rent-seeking induced by long-term intensive subsidy. It is essential to ensure the enterprises to obtain what they really need and the TFP to escalate. | 2022-11-28T14:30:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21319587528705597, "perplexity": 4165.874085864218}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710533.96/warc/CC-MAIN-20221128135348-20221128165348-00871.warc.gz"} |
https://apo.ansto.gov.au/dspace/handle/10238/8128?mode=full | Please use this identifier to cite or link to this item: https://apo.ansto.gov.au/dspace/handle/10238/8128
DC FieldValueLanguage
dc.contributor.authorWang, Z-
dc.contributor.authorGarbe, U-
dc.contributor.authorLi, HJ-
dc.contributor.authorWang, Y-
dc.contributor.authorStuder, AJ-
dc.contributor.authorSun, G-
dc.contributor.authorHarrison, RP-
dc.contributor.authorLiao, X-
dc.contributor.authorVicente Alvarez, MA-
dc.contributor.authorSantisteban, JR-
dc.contributor.authorKong, C-
dc.date.accessioned2016-12-07T00:09:20Z-
dc.date.available2016-12-07T00:09:20Z-
dc.date.issued2014-01-01-
dc.identifier.citationWang, Z., Garbe, U., Li, H., Wang, Y., Studer, A. J., Sun, G., Harrison, R. P., Liao, X., Vicente Alvarez, M. A., Santisteban, J. R., & Kong, C. (2014). Microstructure and texture analysis of [delta]-hydride precipitation in Zircaloy-4 materials by electron microscopy and neutron diffraction. Journal of Applied Crystallography, 47(1), 303-315. doi:10.1107/S1600576713031956en_AU
dc.identifier.govdoc7675-
dc.identifier.urihttp://dx.doi.org/10.1107/S1600576713031956en_AU
dc.identifier.urihttp://apo.ansto.gov.au/dspace/handle/10238/8128-
dc.description.abstractThis work presents a detailed microstructure and texture study of various hydrided Zircaloy-4 materials by neutron diffraction and microscopy. The results show that the precipitated [delta]-ZrH1.66 generally follows the [delta](111)//[alpha](0001) and [delta][1{\overline 1}0]//[alpha][11{\overline 2}0] orientation relationship with the [alpha]-Zr matrix. The [delta]-hydride displays a weak texture that is determined by the texture of the [alpha]-Zr matrix, and this dependence essentially originates from the observed orientation correlation between [alpha]-Zr and [delta]-hydride. Neutron diffraction line profile analysis and high-resolution transmission electron microscopy observations reveal a significant number of dislocations present in the [delta]-hydride, with an estimated average density one order of magnitude higher than that in the [alpha]-Zr matrix, which contributes to the accommodation of the substantial misfit strains associated with hydride precipitation in the [alpha]-Zr matrix. The present observations provide an insight into the behaviour of [delta]-hydride precipitation in zirconium alloys and may help with understanding the induced embrittling effect of hydrides.© 2014, International Union of Crystallography.en_AU
dc.language.isoenen_AU
dc.publisherInternational Union of Crystallographyen_AU
dc.subjectMicrostructureen_AU
dc.subjectZircaloyen_AU
dc.subjectNeutron diffractionen_AU
dc.subjectMicrostructureen_AU
dc.subjectElectron sourcesen_AU
dc.subjectZirconium alloysen_AU
dc.titleMicrostructure and texture analysis of [delta]-hydride precipitation in Zircaloy-4 materials by electron microscopy and neutron diffractionen_AU
dc.typeJournal Articleen_AU
dc.date.statistics2016-12-07-
Appears in Collections:Journal Articles
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https://indico.bnl.gov/event/11469/ | High Energy / Nuclear Theory / RIKEN seminars
# Discovering Lepton Flavour Universality Violating New Physics [HET theory seminar]
## by Andreas Crivellin (CERN)
US/Eastern
https://bnl.zoomgov.com/j/1616949369?pwd=dXJzMnlDS0ZPWDJvM0Zyb2ppbjc0UT09
#### https://bnl.zoomgov.com/j/1616949369?pwd=dXJzMnlDS0ZPWDJvM0Zyb2ppbjc0UT09
Description
While the LHC has not discovered any new particles directly yet, hints for the violation of lepton flavour universality (satisfied within the SM) accumulated in recent years. In particular, deviations from the SM predictions were observed in semi-leptonic B decays (b->sll and b->ctau), in the anomalous magnetic moment of the muon (g-2), in leptonic tau decays and di-electron searches. Furthermore, also the deficit in first row CKM unitarity, known as the Cabibbo Angle Anomaly, can be interpreted as a sign of lepton flavour universality violation. In this talk I review the status of these anomalies and give an overview of the possible interpretations in terms of new physics models. | 2023-02-06T07:19:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9260581731796265, "perplexity": 2567.811487295079}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500304.90/warc/CC-MAIN-20230206051215-20230206081215-00292.warc.gz"} |
https://www.gfdl.noaa.gov/blog_held/69-a-modest-proposal-regarding-tcr/?shared=email&msg=fail | # 69. A modest proposal regarding TCR
Posted on May 23rd, 2016 in Isaac Held's Blog
The radative forcing (left) and global mean temperature response (right) using a simple GCM emulator, for the historical CO2 forcing (red) and for the linearly increasing forcing consistent with the simulations used to define the transient climate response (blue), for 3 different ramp-up time scales, the 70 year time scale (solid blue) corresponding to the standard definition.
The terminology surrounding climate sensitivity can be confusing. People talk about equilibrium sensitivity, Charney sensitivity, Earth system sensitivity, effective sensitivity, transient climate response (TCR), etc, making it a challenge to communicate with the public, and sometimes even with ourselves, on this important issue. I am going to focus on the TCR here (yet again). The TCR of a model is determined by what appears to be a rather arbitrary calculation Starting with the climate in equilibrium, increase CO2 at 1% per year until doubling (about 70 years). The global mean warming of the near surface air temperature at the time of doubling is the TCR. In a realistic model with internal variability, you need to do this multiple times and then average to knock down the noise so as to isolate the forced response if you are trying to be precise. If limited to one or two realizations, you average over years 60-80 or use some kind of low-pass filter to help isolate the forced response. Sometimes the TCR is explicitly defined as the warming averaged over years 60-80. Although I have written several posts emphasizing the importance of the TCR in this series, I would like to argue for a de-emphasis of the TCR in favor of another quantity (admittedly very closely related – hence the modesty of this proposal.)
If you talk to someone about the TCR you have to explain why this idealized 1%/yr scenario is of interest. From my perspective, the importance of the TCR stems from its close relationship to the warming from the mid-19th century to the present that can be attributed to the CO2 increase. There is a growing literature on estimating TCR from observations, using the instrumental temperature record over this time frame. But these studies are not direct estimates of TCR; they are estimates of the warming attributable to the CO2 increase which are then converted to TCR by assuming that the warming is proportional to the CO2 radiative forcing. If forcing due to a doubling of CO2 is $\mathcal{F}_{2X}$ and the forcing due to the observed increase in CO2 over the period T = (T1 T2) is $\mathcal {F}$(T) then
TCR = WACO2(T)/ $\xi$
Here I have defined WACO2(T) as the global mean Warming Attributable to CO2 over the time interval T and I have set $\xi = \mathcal{F}(T)/\mathcal{F}_{2X}$. For the rest of this post, I’ll just assume that T = (1850, 2010). For this period, $\xi$ is about 0.45.
The past warming attributable to CO2 is itself important as a constraint on models used to project this warming into the future. Whether your model is a simple extrapolation or an energy balance model or a full GCM that simulates climate by simulating weather, you obviously want the model you are using to be consistent with the past warming.
Estimating WACO2(T) from observations over the past century or so is far from straightforward, due primarily to the uncertainty in the cooling due to anthropogenic aerosols, but also due to the presence of other forcing agents, including other well mixed greenhouse gases, as well as internal variability, But what’s the point of converting someone’s estimate of the range of values of WACO2 consistent with observations into the corresponding range of TCR values? The point is simply that the latter has become a standard for the comparison of GCM responses, so the range of TCR estimates from models is readily available. But this does not seem like a very good reason to try to communicate the importance of the TCR value rather than the more obviously relevant WACO2(T).
How good is the proportionality assumption TCR =$\xi$ WACO2(T)? And if it is good, why? For concreteness I’ll use a very simple three time-scale fit to the response of a particular GCM to an instantaneous doubling of CO2. The model is GFDL’s CM3 and the fit is described in Winton et al 2013. The response takes the form
$T(t) = \sum\limits_{i=1}^{3}\alpha_i[1-\exp(-t/\tau_i)]$
with $[\alpha_1, \alpha_2, \alpha_3]$ = [1.5, 1.3, 1.8]K and $[\tau_1, \tau_2, \tau_3]$ = [3, 60, 1000] years. I have rounded off the time scales a bit. Since this model is linear you can scale this response to that for an infinitesimal increase and then add up the responses to the forcing over time for any CO2(t). (See the discussion of the response to volcanic forcing in post #50,)
I carried it along for these calculations,, but the very long millennial time scale present in the GCM has negligible effect on WACO2 or TCR , so this is really a two-time scale model for our purposes. And you may have noticed that this is a a rather sensitive model. But keep in mind that it is linear, so if you multiply all of the $\alpha$‘s by the same factor you change the amplitude of all responses, including WACO2 and TCR, by this same factor.
[In the calculations to follow, I’m assuming that the radiative forcing due to CO2 is exactly logarithmic in CO2 concentration, so 1% increase/yr is a linear increase in radiative forcing.]
The red line in the figure on the left above shows the CO2 radiative forcing from 1850 to 2010 from GISS. The solid blue line shows the linear increase in forcing over 70 years that ends up at the same value of forcing at 2010 as the red line. This is the forcing due to a 1%/year increase multiplied by $\xi$ — or, equivalently, it is the forcing due to a $\xi$%/yr increase for 70 years. Also shown with the blue dashed lines are the linear forcing trajectories that reach the same point in 2010 but increasing the 70 year interval to 90 years or decreasing it to 50. The 70 year linear increase at $\xi$%/yr is evidently a pretty good fit after 1960. It’s not relevant whether a 1%/yr increase is larger than the increase in CO2 forcing since we are assuming linearity and normalizing the TCR anyway. The key is that a linear fit to the recent period of rapid increase in CO2 forcing requires roughly 70 years starting from zero.
The figure on the right shows the responses of the three-time scale model to these forcing trajectories. The standard (70yr) TCR after normalization underestimates the WACO2 (the red curve) by about 3%, which is basically negligible given the the uncertainties in TCR that we are concerned about. My eyeball estimate of the error, given the forcing that is missed by this linear approximation before 1950, keeping in mind the 60 year intermediate e-folding time in this model, would have been a bit more than this, so I have checked this result a couple of times — which does not guarantee that I did not make a mistake, of course, (It seems that the error made by missing the response to the increases in CO2 in the first half of the 20th century is canceled in part by the fact that the linear fit in the more recent period is not perfect.) Even if you make the sub-optimal choices of 50 or 90 years for the ramp-up, the errors are only of the order of 10%.
So the approximation WACO2 = $\xi$TCR looks good, at least for this particular response function. If you want to modify the model to create a larger difference, you will have to decrease the relative importance of the fast response that occurs on time scales shorter than the time scales of the CO2 evolution itself and put more weight on the longer time scales. Using discrete response times is not the only way of emulating a GCM’s response function. Diffusive models have a long history in this regard. But as long as the fast response is as large a part of the response to centennial-scale forcing as it is in GCMs (see Geoffroy et al 2013) you won’t get very much of a discrepancy.
We could de-emphasize the 1% year simulation in favor of just simulating the response to the historical CO2 increase. This simulation is performed routinely by some groups, but for the CMIP projects, including the upcoming CMIP6, it is the response to the historical evolution of all of the well-mixed greenhouse gases (WMGGs) that is typically requested, without breaking out the CO2 contribution. This raises another issue — the validity of assuming that you can get the response to CO2 from the response to the full set of WMGGs by simply normalizing by the ratio of the radiative forcings. Given questions about how best to define radiative forcing (a good topic for another post), this adds an unnecessary layer if you is are primarily interested in a model’s response to CO2.
Rather than focusing on TCR itself, especially when discussing this topic outside of scientific circles, we should think of it as just a standard way of estimating WACO2 for a model, a technique that could be improved if desired. Perhaps what we need is a good acronym for the warming attributable to CO2. WACO2 seems less that ideal.
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]
## 1 thought on “69. A modest proposal regarding TCR”
1. This is perfectly laid out. The lesser alternative is probably to have something called an effective TCR, where the modifier implies that CO2 effectively pulls in the other GHG’s along with the baseline impact of just CO2.
It’s frustrating to read blogs such as And Then There’s Physics, where every post is the same confusing message of presenting the dry definition for TCR without the necessary context. One clear post is all that is required. Thanks. | 2021-06-17T22:57:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8010335564613342, "perplexity": 916.1548237281677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487634576.73/warc/CC-MAIN-20210617222646-20210618012646-00272.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Aaumann.robert-john | ## Aumann, Robert John
Compute Distance To:
Author ID: aumann.robert-john Published as: Aumann, Robert J.; Aumann, R. J.; Aumann, Robert; Aumann, Robert John Homepage: http://www.ma.huji.ac.il/~raumann/ External Links: MGP · Wikidata · dblp · GND · IdRef Awards: Nobel Memorial Prize in Economic Sciences (2005)
Documents Indexed: 86 Publications since 1956, including 3 Books 3 Contributions as Editor · 4 Further Contributions Biographic References: 10 Publications Co-Authors: 22 Co-Authors with 35 Joint Publications 510 Co-Co-Authors
all top 5
### Co-Authors
55 single-authored 8 Hart, Sergiu 4 Kurz, Mordecai 4 Maschler, Michael Bahir 3 Drèze, Jacques H. 3 Peleg, Bezalel 2 Brandenburger, Adam 2 Neyman, Abraham 2 Perry, Motty 2 Rosenthal, Robert W. 2 Shapley, Lloyd S. 1 Anscombe, Francis John 1 Arieli, Itai 1 Arrow, Kenneth Joseph 1 Gardner, Roy J. 1 Green, Jerry R. 1 Harsanyi, John Charles 1 Hart, Oliver D. 1 Honkapohja, Seppo 1 Katznelson, Yitzhak 1 King, Mervyn A. 1 Laffont, Jean-Jacques 1 Mas-Colell, Andreu 1 Myerson, Roger Bruce 1 Perles, Micha A. 1 Rabinowitz, P. 1 Radner, Roy 1 Rothblum, Uriel George 1 Selten, Reinhard 1 Serrano, Roberto 1 Sorin, Sylvain 1 Taylor, John Brian 1 Weiss, Benjamin 1 Whitehead, George William
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### Serials
13 Econometrica 8 Games and Economic Behavior 6 International Journal of Game Theory 5 Journal of Economic Theory 3 Journal of Mathematical Economics 3 Annals of Mathematics Studies 3 Handbooks in Economics 2 Israel Journal of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Bulletin of the American Mathematical Society 1 Mathematics of Computation 1 The Annals of Statistics 1 Illinois Journal of Mathematics 1 International Economic Review 1 Mathematics of Operations Research 1 Pacific Journal of Mathematics 1 The Review of Economic Studies 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Economic Theory 1 Annals of Mathematics. Second Series 1 Journal of the Society for Industrial & Applied Mathematics 1 Management Science. Ser. B, Application Series 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Annals of Mathematical Statistics 1 Journal of Political Economy
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### Fields
68 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Measure and integration (28-XX) 4 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 Mathematical logic and foundations (03-XX) 2 Statistics (62-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Convex and discrete geometry (52-XX)
### Citations contained in zbMATH Open
75 Publications have been cited 5,350 times in 4,032 Documents Cited by Year
Integrals of set-valued functions. Zbl 0163.06301
Aumann, R. J.
1965
A definition of subjective probability. Zbl 0114.07204
Anscombe, F. J.; Aumann, R. J.
1963
Markets with a continuum of traders. Zbl 0137.39003
Aumann, R. J.
1964
A general theory of equilibrium selection in games. With a foreword by Robert Aumann. Zbl 0693.90098
Harsanyi, John C.; Selten, Reinhard
1988
Agreeing to disagree. Zbl 0379.62003
Aumann, Robert J.
1976
Subjectivity and correlation in randomized strategies. Zbl 0297.90106
Aumann, Robert J.
1974
Game theoretic analysis of a bankruptcy problem from the Talmud. Zbl 0578.90100
Aumann, Robert J.; Maschler, Michael
1985
Values of non-atomic games. Zbl 0311.90084
Aumann, R. J.; Shapley, L. S.
1974
Correlated equilibrium as an expression of Bayesian rationality. Zbl 0633.90094
Aumann, Robert J.
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Cooperative games with coalition structures. Zbl 0313.90074
Aumann, R. J.; Dreze, J. H.
1974
Acceptable points in general cooperative $$n$$-person games. Zbl 0085.13005
Aumann, Robert J.
1959
Utility theory without the completeness axiom. Zbl 0121.15202
Aumann, R. J.
1962
Epistemic conditions for Nash equilibrium. Zbl 0841.90125
1995
Existence of competitive equilibria in markets with a continuum of traders. Zbl 0142.17201
Aumann, R. J.
1966
The bargaining set for cooperative games. Zbl 0132.14003
Aumann, Robert J.; Maschler, Michael
1964
Repeated games with incomplete information. With the collaboration of Richard E. Stearns. Zbl 0972.91501
Aumann, Robert J.; Maschler, Michael B.
1995
Backward induction and common knowledge of rationality. Zbl 0833.90132
Aumann, Robert J.
1995
The core of a cooperative game without side payments. Zbl 0099.36602
Aumann, Robert J.
1961
Interactive epistemology. I: Knowledge. Zbl 0961.91040
Aumann, Robert J.
1999
Von Neumann-Morgenstern solutions to cooperative games without side payments. Zbl 0096.14706
Aumann, R. J.; Peleg, B.
1960
Mixed and behavior strategies in infinite extensive games. Zbl 0173.47803
Aumann, R. J.
1964
Cooperation and bounded recall. Zbl 0727.90103
Aumann, Robert J.; Sorin, Sylvain
1989
An axiomatization of the non-transferable utility value. Zbl 0583.90110
Aumann, Robert J.
1985
Long cheap talk. Zbl 1154.91304
Aumann, Robert J.; Hart, Sergiu
2003
Values of markets with a continuum of traders. Zbl 0325.90082
Aumann, Robert J.
1975
A variational problem arising in economics. Zbl 0137.39201
Aumann, R. J.; Perles, M.
1965
Long-term competition – a game-theoretic analysis. Zbl 0841.90138
Aumann, Robert J.; Shapley, Lloyd S.
1994
An economic index of riskiness. Zbl 1341.91040
Aumann, Robert J.; Serrano, Roberto
2008
Interactive epistemology. II: Probability. Zbl 0961.91039
Aumann, Robert J.
1999
Measurable utility and the measurable choice theorem. Zbl 0221.90003
Aumann, Robert J.
1969
Bi-convexity and bi-martingales. Zbl 0607.52001
Aumann, Robert J.; Hart, Sergiu
1986
Survey of repeated games. Zbl 0493.90094
Aumann, Robert J.
1981
Endogenous formation of links between players and of coalitions: an application of the Shapley value. Zbl 0712.90098
Aumann, Robert J.; Myerson, Roger B.
1989
Some thoughts on the minimax principle. Zbl 0225.90062
Aumann, R. J.; Maschler, M.
1972
Power and taxes. Zbl 0367.90016
Aumann, Robert J.; Kurz, Mordecai
1977
The absent-minded driver. Zbl 0885.90001
Aumann, Robert J.; Hart, Sergiu; Perry, Motty
1997
A note on Gale’s example. Zbl 0285.90007
Aumann, R. J.; Peleg, B.
1974
Rationality and bounded rationality. Zbl 0904.90188
Aumann, Robert J.
1997
On the centipede game. Zbl 0911.90354
Aumann, Robert J.
1998
Handbook of game theory with economic applications. Vol. 1. Zbl 0874.00032
1992
Approximate purification of mixed strategies. Zbl 0532.90101
Aumann, R. J.; Katznelson, Y.; Radner, R.; Rosenthal, R. W.; Weiss, B.
1983
Utility theory without the completeness axiom. A correction. Zbl 0133.13004
Aumann, R. J.
1964
Borel structures for function spaces. Zbl 0101.28401
Aumann, R. J.
1961
Acceptable points in general cooperative $$n$$-person games. Zbl 1054.91502
Aumann, Robert J.
1999
Common priors: a reply to Gul. Zbl 1073.91514
Aumann, Robert J.
1998
Almost strictly competitive games. Zbl 0111.33405
Aumann, R. J.
1961
Acceptable points in games of perfect information. Zbl 0093.33004
Aumann, Robert J.
1960
On the non-transferable utility value: A comment on the Roth-Shafer examples. Zbl 0592.90103
Aumann, Robert J.
1985
Values of markets with satiation or fixed prices. Zbl 0627.90012
Aumann, Robert J.; Drèze, Jacques H.
1986
Power and taxes in a multi-commodity economy. Zbl 0363.90017
Aumann, R. J.; Kurz, M.
1977
An elementary proof that integration preserves uppersemicontinuity. Zbl 0352.28003
Aumann, Robert J.
1976
Asphericity of alternating knots. Zbl 0078.16403
Aumann, Robert J.
1956
Nash equilibria are not self-enforcing. Zbl 0709.90104
Aumann, Robert J.
1990
A method for computing the kernel of $$n$$-person games. Zbl 0133.43104
Aumann, R. J.; Peleg, B.; Rabinowitz, P.
1965
Handbook of game theory with economic applications. Vol. 2. Zbl 0899.90166
1994
The St. Petersburg paradox: A discussion of some recent comments. Zbl 0364.90149
Aumann, Robert J.
1977
The forgetful passenger. Zbl 0885.90002
Aumann, Robert J.; Hart, Sergiu; Perry, Motty
1997
Homotopy theory. Compiled by Robert J. Aumann. Zbl 0053.43402
1953
Handbook of game theory with economic applications. Vol. 3. Zbl 0993.90001
2002
The logic of backward induction. Zbl 1330.91038
Arieli, Itai; Aumann, Robert J.
2015
Mixed and behavior strategies in infinite extensive games. Zbl 0189.20302
Aumann, R. J.
1967
Some non-superadditive games, and their Shapley values, in the talmud. Zbl 1211.91026
Aumann, Robert J.
2010
Spaces of measurable transformations. Zbl 0099.04301
Aumann, Robert J.
1960
Power and public goods. Zbl 0617.90003
Aumann, R. J.; Kurz, M.; Neyman, A.
1987
Economic applications of the Shapley value. Zbl 0862.90056
Aumann, Robert J.
1994
On the rate of convergence of the core. Zbl 0428.90006
Aumann, Robert J.
1979
Voting for public goods. Zbl 0521.90012
Aumann, R. J.; Kurz, M.; Neyman, A.
1983
Epistemic conditions for Nash equilibrium. Zbl 1384.03098
2016
Markets with a continuum of traders. Zbl 0323.90008
Aumann, R. J.
1974
Existence of competitive equilibria in markets with a continuum of traders. Zbl 0324.90009
Aumann, R. J.
1974
Orderable set functions and continuity. III: Orderability and absolute continuity. Zbl 0347.28005
Aumann, Robert J.; Rothblum, Uriel G.
1977
On choosing a function at random. Zbl 0135.18704
Aumann, R. J.
1963
Game engineering. Zbl 1329.91026
Aumann, Robert J.
2008
The Shapley value. Zbl 0862.90138
Aumann, Robert J.
1994
Core and value for a public-goods economy: An example. Zbl 0377.90107
Aumann, R. J.; Gardner, R. J.; Rosenthal, R. W.
1977
Epistemic conditions for Nash equilibrium. Zbl 1384.03098
2016
The logic of backward induction. Zbl 1330.91038
Arieli, Itai; Aumann, Robert J.
2015
Some non-superadditive games, and their Shapley values, in the talmud. Zbl 1211.91026
Aumann, Robert J.
2010
An economic index of riskiness. Zbl 1341.91040
Aumann, Robert J.; Serrano, Roberto
2008
Game engineering. Zbl 1329.91026
Aumann, Robert J.
2008
Long cheap talk. Zbl 1154.91304
Aumann, Robert J.; Hart, Sergiu
2003
Handbook of game theory with economic applications. Vol. 3. Zbl 0993.90001
2002
Interactive epistemology. I: Knowledge. Zbl 0961.91040
Aumann, Robert J.
1999
Interactive epistemology. II: Probability. Zbl 0961.91039
Aumann, Robert J.
1999
Acceptable points in general cooperative $$n$$-person games. Zbl 1054.91502
Aumann, Robert J.
1999
On the centipede game. Zbl 0911.90354
Aumann, Robert J.
1998
Common priors: a reply to Gul. Zbl 1073.91514
Aumann, Robert J.
1998
The absent-minded driver. Zbl 0885.90001
Aumann, Robert J.; Hart, Sergiu; Perry, Motty
1997
Rationality and bounded rationality. Zbl 0904.90188
Aumann, Robert J.
1997
The forgetful passenger. Zbl 0885.90002
Aumann, Robert J.; Hart, Sergiu; Perry, Motty
1997
Epistemic conditions for Nash equilibrium. Zbl 0841.90125
1995
Repeated games with incomplete information. With the collaboration of Richard E. Stearns. Zbl 0972.91501
Aumann, Robert J.; Maschler, Michael B.
1995
Backward induction and common knowledge of rationality. Zbl 0833.90132
Aumann, Robert J.
1995
Long-term competition – a game-theoretic analysis. Zbl 0841.90138
Aumann, Robert J.; Shapley, Lloyd S.
1994
Handbook of game theory with economic applications. Vol. 2. Zbl 0899.90166
1994
Economic applications of the Shapley value. Zbl 0862.90056
Aumann, Robert J.
1994
The Shapley value. Zbl 0862.90138
Aumann, Robert J.
1994
Handbook of game theory with economic applications. Vol. 1. Zbl 0874.00032
1992
Nash equilibria are not self-enforcing. Zbl 0709.90104
Aumann, Robert J.
1990
Cooperation and bounded recall. Zbl 0727.90103
Aumann, Robert J.; Sorin, Sylvain
1989
Endogenous formation of links between players and of coalitions: an application of the Shapley value. Zbl 0712.90098
Aumann, Robert J.; Myerson, Roger B.
1989
A general theory of equilibrium selection in games. With a foreword by Robert Aumann. Zbl 0693.90098
Harsanyi, John C.; Selten, Reinhard
1988
Correlated equilibrium as an expression of Bayesian rationality. Zbl 0633.90094
Aumann, Robert J.
1987
Power and public goods. Zbl 0617.90003
Aumann, R. J.; Kurz, M.; Neyman, A.
1987
Bi-convexity and bi-martingales. Zbl 0607.52001
Aumann, Robert J.; Hart, Sergiu
1986
Values of markets with satiation or fixed prices. Zbl 0627.90012
Aumann, Robert J.; Drèze, Jacques H.
1986
Game theoretic analysis of a bankruptcy problem from the Talmud. Zbl 0578.90100
Aumann, Robert J.; Maschler, Michael
1985
An axiomatization of the non-transferable utility value. Zbl 0583.90110
Aumann, Robert J.
1985
On the non-transferable utility value: A comment on the Roth-Shafer examples. Zbl 0592.90103
Aumann, Robert J.
1985
Approximate purification of mixed strategies. Zbl 0532.90101
Aumann, R. J.; Katznelson, Y.; Radner, R.; Rosenthal, R. W.; Weiss, B.
1983
Voting for public goods. Zbl 0521.90012
Aumann, R. J.; Kurz, M.; Neyman, A.
1983
Survey of repeated games. Zbl 0493.90094
Aumann, Robert J.
1981
On the rate of convergence of the core. Zbl 0428.90006
Aumann, Robert J.
1979
Power and taxes. Zbl 0367.90016
Aumann, Robert J.; Kurz, Mordecai
1977
Power and taxes in a multi-commodity economy. Zbl 0363.90017
Aumann, R. J.; Kurz, M.
1977
The St. Petersburg paradox: A discussion of some recent comments. Zbl 0364.90149
Aumann, Robert J.
1977
Orderable set functions and continuity. III: Orderability and absolute continuity. Zbl 0347.28005
Aumann, Robert J.; Rothblum, Uriel G.
1977
Core and value for a public-goods economy: An example. Zbl 0377.90107
Aumann, R. J.; Gardner, R. J.; Rosenthal, R. W.
1977
Agreeing to disagree. Zbl 0379.62003
Aumann, Robert J.
1976
An elementary proof that integration preserves uppersemicontinuity. Zbl 0352.28003
Aumann, Robert J.
1976
Values of markets with a continuum of traders. Zbl 0325.90082
Aumann, Robert J.
1975
Subjectivity and correlation in randomized strategies. Zbl 0297.90106
Aumann, Robert J.
1974
Values of non-atomic games. Zbl 0311.90084
Aumann, R. J.; Shapley, L. S.
1974
Cooperative games with coalition structures. Zbl 0313.90074
Aumann, R. J.; Dreze, J. H.
1974
A note on Gale’s example. Zbl 0285.90007
Aumann, R. J.; Peleg, B.
1974
Markets with a continuum of traders. Zbl 0323.90008
Aumann, R. J.
1974
Existence of competitive equilibria in markets with a continuum of traders. Zbl 0324.90009
Aumann, R. J.
1974
Some thoughts on the minimax principle. Zbl 0225.90062
Aumann, R. J.; Maschler, M.
1972
Measurable utility and the measurable choice theorem. Zbl 0221.90003
Aumann, Robert J.
1969
Mixed and behavior strategies in infinite extensive games. Zbl 0189.20302
Aumann, R. J.
1967
Existence of competitive equilibria in markets with a continuum of traders. Zbl 0142.17201
Aumann, R. J.
1966
Integrals of set-valued functions. Zbl 0163.06301
Aumann, R. J.
1965
A variational problem arising in economics. Zbl 0137.39201
Aumann, R. J.; Perles, M.
1965
A method for computing the kernel of $$n$$-person games. Zbl 0133.43104
Aumann, R. J.; Peleg, B.; Rabinowitz, P.
1965
Markets with a continuum of traders. Zbl 0137.39003
Aumann, R. J.
1964
The bargaining set for cooperative games. Zbl 0132.14003
Aumann, Robert J.; Maschler, Michael
1964
Mixed and behavior strategies in infinite extensive games. Zbl 0173.47803
Aumann, R. J.
1964
Utility theory without the completeness axiom. A correction. Zbl 0133.13004
Aumann, R. J.
1964
A definition of subjective probability. Zbl 0114.07204
Anscombe, F. J.; Aumann, R. J.
1963
On choosing a function at random. Zbl 0135.18704
Aumann, R. J.
1963
Utility theory without the completeness axiom. Zbl 0121.15202
Aumann, R. J.
1962
The core of a cooperative game without side payments. Zbl 0099.36602
Aumann, Robert J.
1961
Borel structures for function spaces. Zbl 0101.28401
Aumann, R. J.
1961
Almost strictly competitive games. Zbl 0111.33405
Aumann, R. J.
1961
Von Neumann-Morgenstern solutions to cooperative games without side payments. Zbl 0096.14706
Aumann, R. J.; Peleg, B.
1960
Acceptable points in games of perfect information. Zbl 0093.33004
Aumann, Robert J.
1960
Spaces of measurable transformations. Zbl 0099.04301
Aumann, Robert J.
1960
Acceptable points in general cooperative $$n$$-person games. Zbl 0085.13005
Aumann, Robert J.
1959
Asphericity of alternating knots. Zbl 0078.16403
Aumann, Robert J.
1956
Homotopy theory. Compiled by Robert J. Aumann. Zbl 0053.43402
1953
all top 5
### Cited by 3,564 Authors
33 Fishburn, Peter Clingerman 33 Halpern, Joseph Yehuda 29 Borm, Peter E. M. 26 Lehrer, Ehud 25 Shitovitz, Benyamin 24 Karni, Edi 24 Marinacci, Massimo 23 Tijs, Stef H. 22 Thomson, William 22 Yannelis, Nicholas Constantine 21 Gil, María Angeles 21 Peleg, Bezalel 21 Samet, Dov 20 Aumann, Robert John 19 Khan, Mohammed Ali 19 Papageorgiou, Nikolaos S. 18 Einy, Ezra 18 Li, Shoumei 18 Perea, Andrés 18 Wooders, Myrna Holtz 17 López-Díaz, Miguel 17 Moreno-Ternero, Juan D. 17 Wakker, Peter Paul 16 Forges, Françoise 16 Hart, Sergiu 16 Maccheroni, Fabio 16 Neyman, Abraham 16 Sun, Yeneng 15 Chun, Youngsub 15 Gilboa, Itzhak 15 Xu, Huifu 14 LaValle, Irving H. 13 Herings, P. Jean-Jacques 13 Kaneko, Mamoru 13 Mas-Colell, Andreu 13 Moulin, Hervé C. 13 Serrano, Roberto 13 Solan, Eilon 13 Tsakas, Elias 13 Zhang, Deli 12 Casajus, André 12 Grabisch, Michel 12 Moreno-García, Emma 12 Ramos-Guajardo, Ana Belén 12 Schmeidler, David 12 Weber, Shlomo 12 Winter, Eyal 12 Wu, Hsien-Chung 11 Béal, Sylvain 11 Epstein, Leah 11 Flåm, Sjur Didrik 11 Ghosal, Sayantan 11 Guo, Caimei 11 Le Breton, Michel 11 Lubiano, María Asunción 11 Luo, Xiao 11 Monderer, Dov 11 Owen, Guillermo 11 Tomala, Tristan 11 Van den Brink, René 10 Albizuri, M. Josune 10 Alonso-Meijide, José María 10 Artstein, Zvi 10 Colubi, Ana 10 Fiestras-Janeiro, María Gloria 10 Grant, Simon 10 Hendrickx, Ruud 10 Kalai, Ehud 10 Maschler, Michael Bahir 10 Mongin, Philippe 10 Noguchi, Mitsunori 10 Sudhölter, Peter 10 Zimper, Alexander 9 Balder, Erik J. 9 Brandenburger, Adam 9 Cerreia-Vioglio, Simone 9 Chambers, Christopher P. 9 Codognato, Giulio 9 Gossner, Olivier 9 Hervés-Beloso, Carlos 9 Hougaard, Jens Leth 9 Jiménez-Losada, Andrés 9 Montrucchio, Luigi 9 Ostroy, Joseph M. 9 Peters, Hans J. M. 9 Podczeck, Konrad 9 Ralescu, Dan A. 9 Renault, Jérôme 9 Safra, Zvi 9 Samuelson, Larry 9 Sánchez-Soriano, Joaquín 9 Van der Laan, Gerard 9 Vidal-Puga, Juan J. 9 Zhang, Qiang 8 Bach, Christian W. 8 Battigalli, Pierpaolo 8 Bergantiños, Gustavo 8 Bonanno, Giacomo 8 Butnariu, Dan 8 Driessen, Theo S. H. ...and 3,464 more Authors
all top 5
### Cited in 366 Serials
410 Games and Economic Behavior 400 Journal of Economic Theory 353 Journal of Mathematical Economics 255 International Journal of Game Theory 188 Mathematical Social Sciences 154 Theory and Decision 152 Economic Theory 122 Fuzzy Sets and Systems 93 Journal of Mathematical Analysis and Applications 81 European Journal of Operational Research 81 International Game Theory Review 73 Social Choice and Welfare 70 Economics Letters 44 Annals of Operations Research 41 Games 40 Synthese 36 Journal of Optimization Theory and Applications 29 Information Sciences 29 Journal of Mathematical Psychology 29 Top 28 Artificial Intelligence 28 International Journal of Approximate Reasoning 26 Dynamic Games and Applications 22 Journal of Risk and Uncertainty 21 Applied Mathematics and Computation 21 Operations Research Letters 21 Mathematical Methods of Operations Research 20 Studia Logica 18 Israel Journal of Mathematics 18 Journal of Economic Dynamics & Control 18 Mathematical Programming. Series A. Series B 17 Insurance Mathematics & Economics 15 Journal of Philosophical Logic 15 Review of Economic Design 15 Journal of Dynamics and Games 14 Theoretical Computer Science 14 Transactions of the American Mathematical Society 13 Discrete Applied Mathematics 12 Journal of Econometrics 12 Mathematics of Operations Research 12 Optimization 11 Kybernetika 11 Cybernetics and Systems Analysis 10 Operations Research 10 SIAM Journal on Control and Optimization 10 Information and Computation 10 Automation and Remote Control 10 CEJOR. Central European Journal of Operations Research 10 Set-Valued and Variational Analysis 9 Journal of Multivariate Analysis 9 Stochastic Analysis and Applications 9 Journal of Logic, Language and Information 9 Theory of Computing Systems 9 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8 Automatica 8 Statistics & Probability Letters 8 Journal of Economics 8 Journal of Systems Science and Complexity 8 Mathematics and Financial Economics 8 Matematicheskaya Teoriya Igr i eë Prilozheniya 8 Theoretical Economics 7 Journal of Differential Equations 7 The Journal of Mathematical Sociology 7 Finance and Stochastics 7 Journal of Combinatorial Optimization 7 Decisions in Economics and Finance 7 Nonlinear Oscillations 6 Computers & Mathematics with Applications 6 Mathematical Notes 6 The Annals of Probability 6 Journal of Soviet Mathematics 6 Proceedings of the American Mathematical Society 6 Siberian Mathematical Journal 6 Trabajos de Estadistica y de Investigacion Operativa 6 Journal of Mathematical Sciences (New York) 5 Archive for Rational Mechanics and Analysis 5 Bulletin of the Australian Mathematical Society 5 Ukrainian Mathematical Journal 5 Journal of Approximation Theory 5 Journal of Functional Analysis 5 Numerical Functional Analysis and Optimization 5 Results in Mathematics 5 Zeitschrift für Nationalökonomie 5 OR Spektrum 5 Computers & Operations Research 5 Applied Mathematics Letters 5 Test 5 Mathematical Finance 5 Soft Computing 5 Quantitative Finance 5 Bulletin of the American Mathematical Society 5 Journal of Fixed Point Theory and Applications 5 The Review of Symbolic Logic 5 Journal of Theoretical Biology 4 International Journal of General Systems 4 Journal of Statistical Physics 4 Physica A 4 Applied Mathematics and Optimization 4 International Economic Review 4 Journal of Computational and Applied Mathematics ...and 266 more Serials
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### Cited in 50 Fields
3,239 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 260 Operations research, mathematical programming (90-XX) 257 Mathematical logic and foundations (03-XX) 254 Measure and integration (28-XX) 204 Probability theory and stochastic processes (60-XX) 183 Computer science (68-XX) 150 Statistics (62-XX) 120 Calculus of variations and optimal control; optimization (49-XX) 76 Systems theory; control (93-XX) 75 Real functions (26-XX) 68 Functional analysis (46-XX) 60 Ordinary differential equations (34-XX) 57 General topology (54-XX) 38 Operator theory (47-XX) 32 Convex and discrete geometry (52-XX) 31 Numerical analysis (65-XX) 25 Combinatorics (05-XX) 23 Order, lattices, ordered algebraic structures (06-XX) 21 Quantum theory (81-XX) 19 History and biography (01-XX) 19 Information and communication theory, circuits (94-XX) 18 General and overarching topics; collections (00-XX) 18 Partial differential equations (35-XX) 17 Difference and functional equations (39-XX) 16 Biology and other natural sciences (92-XX) 11 Manifolds and cell complexes (57-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Integral equations (45-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Approximations and expansions (41-XX) 8 Mechanics of deformable solids (74-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Category theory; homological algebra (18-XX) 4 Geophysics (86-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 Integral transforms, operational calculus (44-XX) 2 Algebraic topology (55-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Mathematics education (97-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-05-17T13:48:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6284684538841248, "perplexity": 7968.674487955801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00121.warc.gz"} |
https://par.nsf.gov/biblio/10388035-construction-large-diameter-reflective-half-wave-plate-modulator-millimeter-wave-applications | This content will become publicly available on August 31, 2023
Construction of a large diameter reflective half-wave plate modulator for millimeter wave applications
Polarization modulation is a powerful technique to increase the stability of measurements by enabling the distinction of a polarized signal from dominant slow system drifts and unpolarized foregrounds. Furthermore, when placed as close to the sky as possible, modulation can reduce systematic errors from instrument polarization. In this work, we introduce the design and preliminary drive system laboratory performance of a new 60 cm diameter reflective half-wave plate (RHWP) polarization modulator. The wave plate consists of a wire array situated in front of a flat mirror. Using 50 μm diameter wires with 175 μm spacing, the wave plate will be suitable for operation in the millimeter wavelength range with flatness of the wires and parallelism to the mirror held to a small fraction of a wavelength. The presented design targets the 77-108 GHz range. Modulation is performed by a rotation of the wave plate with a custom rotary drive utilizing an actively controlled servo motor.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Editors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10388035
Journal Name:
Proceedings Volume 12190, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI
Volume:
12190
Page Range or eLocation-ID:
121901N
Continuum polarization over the UV-to-microwave range is due to dichroic extinction (or emission) by asymmetric, aligned dust grains. Scattering can also be an important source of polarization, especially at short wavelengths. Because of both grain alignment and scattering physics, the wavelength dependence of the polarization, generally, traces the size of the aligned grains. Similarly because of the differing wavelength dependencies of dichroic extinction and scattering polarization, the two can generally be reliably separated. Ultraviolet (UV) polarimetry therefore provides a unique probe of the smallest dust grains (diameter$< 0.09~\upmu \text{m}$$<0.09\phantom{\rule{0ex}{0ex}}\text{μm}$), their mineralogy and interaction with the environment. However, the current observational status of interstellar UV polarization is very poor with less than 30 lines of sight probed. With the modern, quantitative and well-tested, theory of interstellar grain alignment now available, we have the opportunity to advance the understanding of the interstellar medium (ISM) by executing a systematic study of the UV polarization in the ISM of the Milky Way and near-by galaxies. The Polstar mission will provide the sensitivity and observing time needed to carry out such a program (probing hundreds of stars in the Milky Way and dozens of stars in the LMC/SMC), addressing questions of dust composition asmore » | 2023-03-22T12:05:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43097251653671265, "perplexity": 2267.1979748095996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00563.warc.gz"} |
https://www.lessonplanet.com/teachers/epsilon-delta-limit-definition-2 | # Epsilon Delta Limit Definition 2
By using the Epsilon Delta definition of limits, Sal shows listeners how to prove an example limit problem. Specifically, given any epsilon distance away from L, the limit of f(x), he finds a delta that is within delta of the x value where then f(x) is within epsilon of the limit L.
Concepts
Resource Details
11th - Higher Ed
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BY-NC-SA: 3.0 | 2019-01-17T04:41:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.992548406124115, "perplexity": 4096.77409431028}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658702.9/warc/CC-MAIN-20190117041621-20190117063621-00411.warc.gz"} |
https://par.nsf.gov/biblio/10345660-measurement-sixth-order-cumulant-net-proton-multiplicity-distributions-au+au-collisions-snn-rhic | This content will become publicly available on December 1, 2022
Measurement of the Sixth-Order Cumulant of Net-Proton Multiplicity Distributions in $Au+Au$ Collisions at $sNN=27$ , 54.4, and 200 GeV at RHIC
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10345660
Journal Name:
Physical Review Letters
Volume:
127
Issue:
26
ISSN:
0031-9007 | 2022-09-29T17:51:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 26, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6906838417053223, "perplexity": 14865.55038415195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00019.warc.gz"} |
https://bison.inl.gov/Documentation/getting_started/running_bison.aspx | Running Bison
Bison uses GitLab for code management and distribution. Detailed instructions for checking out (also know as cloning), building and contributing to the code can be found in the Bison Workshop slides located in the Bison repository (bison/docs/workshop) or under the Getting Started section.
Running an Example Problem
When first starting out with Bison, we recommend starting with an example problem similar to the problem that you are trying to solve. Multiple examples can be found in the directories bison/examples/ and bison/assessment/. Additionally, step-by-step instructions for the common fuel rod geometries are given in the Examples & Tutorials section.
We recommend running the example problems to see how the code works. Explore the Bison code functionality by modifying input parameters to see how the run time, results and convergence behavior change. To demonstrate running Bison, consider the 2D-axisymmetric example problems. Do the following in your terminal:
cd ~/bison/examples/tensor_mechanics/2D-RZ_rodlet_10pellets
../../bison-opt -i 2Dtm_discrete_finiteStrain_action.i ## for serial processing
It is also possible to use multiple processors to run a Bison simulation.
mpiexec -n <procs> ../../bison-opt -i 2Dtm_discrete_finiteStrain_action.i ## where <procs> is the number of processors
Required Input and Mesh Files
Two input files are required as input when running Bison: an text input file and a mesh file.
The text input file commonly has "i" as its extension and contains a description of the variables, equations, boundary conditions, and material models associated with an analysis. The structure of the text input file is the main focus of our discussion here.
The mesh file is an ExodusII file (Schoof and Yarberry, 1996). (Athough MOOSE supports several mesh file formats, the ExodusII format is the one used in Bison.) This file commonly has "e" as its file extension. The mesh file may be generated using CUBIT (Sandia National Laboratories, 2008) or another meshing tool. A further option is a meshing script bundled with Bison; this script, dependent on CUBIT and suitable for LWR fuel rod meshes, is discussed in the section on the Meshing Script.
Before running any problem, the power function, axial profile, mesh, and any functions needed for boundary conditions need to be generated.
Typically, a PiecewiseLinear function is used together with an external data file to specify a complex power history. This file has time and power specified in columns or rows, with the first row (or column) being the time (seconds) and the second row (or column) being power (W/m). The axial power profile, if present, is also input as a PiecewiseBilinearFile. Inclusion of these power function and axial profile files are shown in the 2D axisymmetric ten pellet example problem file:
[Functions]
# Define functions to control power and boundary conditions
[./power_history]
type = PiecewiseLinear # reads and interpolates an input file containing rod average linear power vs time
data_file = powerhistory.csv
scale_factor = 1
[../]
[./axial_peaking_factors] # reads and interpolates an input file containing the axial power profile vs time
type = PiecewiseBilinear
data_file = peakingfactors.csv
scale_factor = 1
axis = 1 # (0,1,2) => (x,y,z)
[../]
[./pressure_ramp] # reads and interpolates input data defining amplitude curve for fill gas pressure
type = PiecewiseLinear
x = '-200 0'
y = '0 1'
[../]
[./q]
type = CompositeFunction
functions = 'power_history axial_peaking_factors'
[../]
[]
(examples/tensor_mechanics/2D-RZ_rodlet_10pellets/2Dtm_discrete_finiteStrain_action.i)
Bison can read comma-separate value (csv) files with either Windows or UNIX-style line terminations. In some versions of Excel, you may need to select a Windows or MS-DOS csv option to avoid generating it with the old-style Mac line terminations. If a csv file is generated in Microsoft Excel on the Mac, you should not output it as a Macintosh formatted csv file, because the file will be generated with the line terminations used by Mac OS versions that predate the current UNIX-based Mac OS versions.
As an example of a PiecewiseBilinearFile, we'll look at the axial power profile used in this example Bison problem. The axial peaking factors are input as a table within the CSV file, with the top row being the axial location from the bottom of the rod and the left column as time.
2.24e-3,8.18e-3,1.41e-2,2.01e-2,2.6e-2,3.19e-2,3.79e-2,4.38e-2,4.97e-2,5.57e-2,0.06162,6.76e-2,7.35e-2,7.94e-2,8.54e-2,9.13e-2,9.72e-2,1.03e-1,1.09e-1,1.15e-1,1.21e-1
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
1,5.37e-1,8.68e-1,1.01,1.06,1.06,1.06,1.05,1.06,1.07,1.07,1.08,1.07,1.07,1.06,1.06,1.06,1.06,1.05,1.01,8.68e-1,5.37e-1
1.5e8,5.37e-1,8.68e-1,1.01,1.06,1.06,1.06,1.05,1.06,1.07,1.07,1.08,1.07,1.07,1.06,1.06,1.06,1.06,1.05,1.01,8.68e-1,5.37e-1
(examples/tensor_mechanics/2D-RZ_rodlet_10pellets/peakingfactors.csv)
Note that the top most row in this CSV file has one fewer entry than the remaining rows: this difference is the result of the first column indicating the time at which each row expriences the given peaking factor.
Connecting the Mesh and Input Files
If using a separately built mesh file, include the name of the mesh file in the input file
[Mesh]
# Import mesh file
file = fine10_rz.e
patch_update_strategy = auto
patch_size = 10 # For contact algorithm
partitioner = centroid
centroid_partitioner_direction = y
[]
(examples/tensor_mechanics/2D-RZ_rodlet_10pellets/2Dtm_discrete_finiteStrain_action.i)
The mesh can either be generated with the mesh script, or if you do not have CUBIT, you can generate a simple 2D-RZ axisymmetric mesh with smeared solid fuel pellets (single fuel column) with the SmearedPelletMesh in Bison. To generate a smeared mesh similar to the geometry used in the example problem we have been working with, use the mesh block:
[Mesh]
type = SmearedPelletMesh
patch_size = 10
patch_update_strategy = auto
partitioner = centroid
centroid_partitioner_direction = y
dim = 2
pellet_quantity = 10
pellet_height = 0.01186
pellet_mesh_density = coarse
[]
(examples/tensor_mechanics/2D-RZ_rodlet_10pellets/SmearedCracking_tm.i)
Post Processing
Viewing and analyzing the results of a Bison simulation is a key component of successfully running a Bison simulation. Bison typically writes solution data to an ExodusII file. Data may also be written in other formats: a simple comma separated file giving global data being the most common.
Paraview Visual Post Processings
Several options exist for viewing ExodusII results files. These include commercial as well as open-source tools. One good choice is Paraview, which is open-source.
Paraview is available on a variety of platforms. It is capable of displaying node and element data in several ways. It will also produce line plots of global data or data from a particular node or element. A complete description of Paraview is not possible here, but a quick overview of using Paraview with Bison results is available in the Bison workshop material.
Peacock Graphical User Interface
It is worth noting that a graphical user interface (GUI) exists for all MOOSE-based applications. This GUI is named Peacock. Information about Peacock and how to set it up for use may be found on the MOOSE wiki page.
Peacock may be used to generate a text input file. It is also capable of submitting the analysis, and it provides basic post processing capabilities.
Although this discussion has focused only on 2D axisymmetric (2D-RZ) geometries, Bison simulations can also be run on 3D meshes and 1D meshes. The 3D geometry simulations are useful for examining the effect of localized defects on the fuel performance, while the 1D simulations use simplifying symmetry assumptions to produce faster running simulations. The Mesh Script is used to generate both 2D-RZ and 3D meshes.
1D Spherically Symmetric TRISO Mesh
The mesh class designed to create 1D spherically symmetric TRISO meshes accounts for the multiple layers in a pellet. The TRISO1DMesh documentation page includes more details on using the mesh.
Layered 1D (1.5D) Fuel Rod Mesh
The Layered 1D geometry (also known as 1.5D) in Bison is used to generate fast simulation results when is it not important to account for localized effects in the analysis. Read more about how the Layered 1D simulations in Bison are set up in our upcoming tutorials. The Layered1DMesh documentation page gives more details about the Layered 1D mesh generation.
The Layered 1D input files are constructed with the same tensor mechanics materials as the 2D-RZ simulation we previously ran. The main differences in the input files of these two types of the simulations are in the Mesh block and the calculation of the out of plane strain calculation.
To generate a Layered 1D smeared mesh similar to the geometry used in the 2D-RZ example problem we have been working with, use the mesh block:
[Mesh]
type = Layered1DMesh
patch_update_strategy = auto
partitioner = centroid
centroid_partitioner_direction = y
slices_per_block = 10
[] | 2021-01-21T16:00:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.271279901266098, "perplexity": 2852.825307810946}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703524858.74/warc/CC-MAIN-20210121132407-20210121162407-00534.warc.gz"} |
https://www.usgs.gov/center-news/new-report-details-july-21-fissure-eruption-hazards | # New report details July 21 fissure eruption hazards
Release Date:
For the past six weeks, lava erupting from a fissure east of Puu Oo has been flowing on the surface through an open channel and feeding a series of aa flows.
Closeup of the lower end of the full channel. Note the built up walls perching the channel lava, the spillover feeding a flow advancing along the northeast margin of previous flows, and the seeps feeding a flow advancing along the southern margin of previous flows.
(Public domain.)
The incandescence reflected on clouds from these flows and the fires they have ignited when advancing through nearby forest have caught the eyes of many Puna residents and visitors after dark. Understandably, the flows have also caused concern.
Throughout the entire six weeks, as the Hawaiian Volcano Observatory has been doing since 1912, we have been closely monitoring this eruption and assessing what some future outcomes of the current activity might be. We record a short daily update summary available at (808) 967-8862 and post a detailed daily updates on our website, along with almost-live webcam images. We update our maps and photos 2-3 times per week. Hawaii County Fire personnel are flying over the flows each day to assess the fire danger. On this basis, our assessment is that there is currently no direct threat from lava flows. Here's why:
The current eruptive activity has been somewhat repetitious over the last few weeks. Lava is fed into a channel. The channel feeds an aa lava flow that advances 5-6 km (3-4 miles) from the vent, and then stalls. The channel backs up, overflows, and starts a new aa lava flow that advances along the north side of the previous one. As of August 30, we have seen this happen at least six times. The flows have not progressed farther downslope in the last few weeks, but keep spreading out in the same area.
The map of the lava flows looks something like your forearm with fingers together laid palm down flat on a table. If the vent is halfway between your elbow and wrist (ignore your arm above that point), the channel is the rest of the forearm to the wrist, the end of the channel that overflows is the back of your hand, and the aa lava flows are your fingers.
An aa flow is usually supplied by an open channel. The surface of moving lava in the channel is not completely crusted over and so loses a great amount of heat into the air. Data so far indicate that the temperature of lava in a channel can drop at least 6-7 degrees C. per km (17-20 degrees F. per mile). That's more than 10 times the temperature loss per km (mile) for flow through an open channel than through a lava tube. The greater temperature loss in channels promotes the formation of microscopic crystals in the lava, making it stickier. This is something like thickening gravy with flour.
Ultimately, an aa flow loses so much fluidity that it can't move forward any more. The core of the flow is molten and is just too sticky to advance, so the flow front stops or stalls. When this happens, the channel is blocked, and it starts to overflow its levees or banks.
What would it take to get aa lava flows to advance farther before stalling? Based on studies of such conditions, volcanologists have found that the length of aa flows is directly related to supply rate. It would take an increase in the eruption rate to get the currently forming aa flows to advance more than the 5-6 km (3-4 miles) limit currently observed.
Through most of the 1983-2007 eruption of Puu Oo and Kupaianaha, the long-term average eruption rate has been about 300,000 cubic meters per day (55,000 gal/min). Our estimate of the current eruption rate is somewhere between that and one million cubic meters per day (180,000 gal/min).
Longer aa flows can be produced if the eruption rate increases substantially. For example, the Mauna Loa 1984 eruption produced lava at an average rate of about 25 million cubic meters per day (4.8 million gal/min) and fed an aa flow that was nearly 25 km (16 miles) long. Eruption rates like this are very unlikely for Kīlauea, based on previous eruptions.
There is another way that lava flows can advance farther. If the open channel crusts over and forms a lava tube, the lava moving through it will be much better insulated and able to retain its ability to flow farther, even at the current eruption rates. This has been the eruption mode throughout most of the ongoing Puu Oo eruption that successfully delivered lava to the coastline for many years.
HVO has just published these ideas and supporting information in a report available online. The report reiterates that there is currently no direct threat from lava flows, and also provides some details about future possibilities. Even with no current threat, it is important for members of the public to stay informed about this eruption and the hazards it poses.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
Kīlauea summit and the July 21 fissures continue to deflate. Seismic tremor levels continue to be low. Earthquakes were located beneath Halemaumau crater and the south flank area. The summit monitoring network recorded the third pressure variation, known as a DI or deflation-inflation tilt event in the last two weeks. The pressure variation shows up at Puu Oo between 1-2 hours later, demonstrating the excellent hydraulic connection between the two locations.
Fissure D of the July 21 fissure eruption remains active. The lava enters an open lava channel that transitions into an aa flow moving toward the northeast. Because aa lava flows cool relatively quickly, each flow has been able to reach only 3 - 4 miles from the fissure before stagnating. Lava then piles up behind the stalled flow and is forced to jump out of the channel to make a new aa flow. This process has repeated several times in the past month. For about the last week and a half, when the flow has stalled, the lava has ponded up to form an elongate, perched channel with pahoehoe overflows. This ponding is taking place along the channel from about a half-mile to a mile northeast of the fissure. After a day or two of ponding, the lava has been breaching the lower wall of the perched channel and gushing out to feed new aa flows. The channel then plugs back up again and a new perched channel begins to form.
There has now been a total of six aa flows that have advanced toward the northeast, each robbing the supply from the previous flow. There have also been a few smaller flows that quickly stagnated and did not capture the flow. The currently active aa flow, as of Thursday, August 30, is advancing east across the top of aa flows a few weeks old. This flow still has about a mile to go to reach the stagnant tips of the aa flows from early August. Because of the aa flow-length limitation imposed by cooling, it is likely that the current flow will stagnate in the next day or two and that a new flow will break out from the perched channel closer to the fissure.
Despite the heavy steam and fume, occasional glimpses of incandescence are still seen at night in the Puu Oo crater on the Puu Oo Webcam. As has been seen in years past, Puu Oo could be acting as temporary storage for lava that passes beneath the cone on its way to the erupting fissure. There have also been a number of collapses in the Puu Oo crater in the past few weeks. If you look at the Puu Oo Webcam, you will see mud plastered onto the Webcam window from one of these collapses.
Vent areas are hazardous. Access to the eruption site, in the Puu Kahaualea Natural Area Reserve, is closed (http://www.state.hi.us/dlnr/chair/pio/HtmlNR/07-N076.htm).
Two earthquakes beneath Hawaii Island were reported felt within the past week. A magnitude-2.1 earthquake occurred at 4:53 a.m. H.s.t. on Thursday, August 23, and was located 3 km (2 miles) southeast of Keanae, Maui, at a depth of 16 km (10 miles). A magnitude-2.5 earthquake occurred at 6:35 p.m. on the same day and was located 13 km (8 miles) northeast of Pahala at a depth of 34 km (21 miles).
Mauna Loa is not erupting. Two earthquakes were located beneath the summit; both were short-period quakes. Extension between locations spanning the summit, indicating inflation, continues at steady, slow rates, which have slowed further since May 2007. | 2020-01-20T08:55:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3903651833534241, "perplexity": 1825.0887686560886}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250598217.23/warc/CC-MAIN-20200120081337-20200120105337-00214.warc.gz"} |
https://lammps.sandia.gov/doc/fix_propel_self.html | # fix propel/self command
## Syntax
fix ID group-ID propel/self mode magnitude keyword values ...
• ID, group-ID are documented in fix command
• propel/self = style name of this fix command
• mode = velocity or quat
• magnitude = magnitude of the active force
• one or more keyword/value pairs may be appended to args
• keyword = types
types values = one or more atom types
## Examples
fix active_group all propel/self velocity 1.0
fix constant_velocity all viscous 1.0
fix active_group all propel/self quat 1.0
fix active all propel/self quat 1.0 types 1 2 4
## Description
Adds a force of a constant magnitude to each atom in the group. The nature in which the force is added depends on the mode.
For mode = velocity, the active force acts along the velocity vector of each atom. This can be interpreted as a velocity-dependent friction, such as proposed by (Erdmann).
For mode = quat the force is applied along the axis obtained by rotating the x-axis along the atom’s quaternion. In other words, the force is along the x-axis in the atom’s body frame. This mode requires all atoms in the group to have a quaternion, so atom_style should either be ellipsoid or body. In combination with Langevin thermostat for translation and rotation in the overdamped regime, the quaternion mode corresponds to the active Brownian particle model introduced by (Henkes), (Bialke) and (Fily).
By default, this fix is applied to all atoms in the group. You can override this behavior by specifying the atom types the fix should work on through the types keyword.
Restart, fix_modify, output, run start/stop, minimize info: | 2020-08-03T09:16:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6298258900642395, "perplexity": 3783.4254831965136}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735792.85/warc/CC-MAIN-20200803083123-20200803113123-00326.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-what-if-1984-flow-mauna-loa-hadnt-stopped | Volcano Watch - What if the 1984 flow from Mauna Loa hadn't stopped?
Release Date:
Several recent "Volcano Watch" columns have dealt with Mauna Loa and the implications of renewed inflation of its summit. For better or worse, this one will be no different except that it will be a "What if," rather than a "What is," topic. What if the lava flow produced in the most recent eruption of Mauna Loa had continued to Hilo? Where would the flow have gone?
At the time, many thought that the flow was heading for Waiakea Uka, but it was actually on a path that would have taken it into the upper Kaumana area. How do we know this? Lava, like water, flows downhill, so that we can use a digital elevation model of the Big Island to calculate fairly precise downhill paths. Of course, our computed paths are only as good as the digital elevation model, which is just a computer version of the familiar USGS contour maps.
One check on the accuracy of these computed paths is to compare them with the actual path of the 1984 flow. A quick computation shows that the computed path was pretty good and would have successfully predicted 65 percent of the actual flow path. The maximum difference between the computed and actual path was 750 meters (2,500 feet). The lowest third of the flow was predicted with nearly 100 percent accuracy.
In 1984, the lava flow stopped 8.5 km (5.3 miles) short of Country Club Road off Kaumana Drive. If the flow had continued, it would have touched the south end of Country Club Road and continued across Wilder Avenue at about the intersection with the new Pu'ainako extension. Depending on how wide the flow was, it might have already blocked Kaumana Drive. From there, the flow would have progressed along Mele Manu Street, and through the south side of the upper section of the Sunrise Estates subdivision, thence down the Mohouli extension to its intersection with Komohana Avenue.
Not waiting for the light to change, the 1984 flow would have crossed Komohana and taken a course that was slightly toward Hamakua from Mohouli Street, advancing along Ho'opuni Way, Hale Nani, and Hualalai Street before finally entering the ocean somewhere between Pauahi Street and the Mo'oheau Bandstand.
While we're imagining this fictitious flow going through Hilo, let's think about its effects. The obvious ones are that Hilo would be split, with no vehicular access across the flow, roughly at Mohouli and Hualalai Streets. If Kaumana was also blocked above 'Akolea Road, then the only escape from north Hilo would be towards Hamakua. Citizens living above Country Club Road would be cut off from either part of Hilo. These barriers to travel would also complicate fighting the inevitable fires that would be set along the flow's path.
A flow entering Hilo Bay would pose additional threats. First, the ocean-lava interaction would produce a steam cloud laden with acid droplets and glass particles that would largely be blown back onto the flow and surrounding areas during normal trade winds. This would not disrupt air travel into and out of Hilo airport unless winds shifted or the entry location changed. The second major effect would be that the flow could quickly build a delta inside the shallow Hilo Bay that would extend out to the breakwater and effectively close off our commercial port.
How likely is it that a lava flow will really reach Hilo Bay? Not likely. Of the six Mauna Loa flows that came toward Hilo in the last 150 years, only one crossed what is now Komohana Street. The 1881 lava flow stopped 2 km (1.2 miles) short of entering Hilo Bay. Based on mapping and the examination of older deposits encountered in a deep research drill hole near the airport, Mauna Loa flows have neared the bay on average every 3,500 to 5,000 years. The last time was 1,200 years ago, when the Pana'ewa flow, which underlies the airport and most of Keaukaha, was emplaced.
Volcano Activity Update
Eruptive activity of Kilauea Volcano continued unabated at the Puu Oo vent during the past week. A narrow flow worked its way along the eastern margin of the Mother's Day flow from Paliuli to the coast. The flow stagnated shortly after entering the ocean east of Highcastle. Lava continues to enter the ocean from the Wilipea and West Highcastle lava deltas. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The steam clouds are highly acidic and laced with glass particles. The National Park Service has erected a rope barricade to delineate the edge of the restricted area. Do not venture beyond this rope boundary and onto the lava deltas and benches.
One earthquake was reported felt in the week ending on October 31. Residents of Waimea and Pa`auilo felt an earthquake at 7:38 a.m. on October 30. The magnitude-2.2 earthquake was located 4 km (2.4 mi) east of Waimea at a depth of 18.9 km (11.3 mi).
Mauna Loa is not erupting. The summit region continues to inflate. The earthquake activity is low with only 8 earthquakes located in the summit area during the last seven days. | 2020-02-25T07:32:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25795233249664307, "perplexity": 3968.2640462398977}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146033.50/warc/CC-MAIN-20200225045438-20200225075438-00113.warc.gz"} |
https://pos.sissa.it/301/712/ | Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Gamma-Ray Astronomy. GA-galactic
Decadal VERITAS Observation of LS I +61 ${}^{\circ}$303: Detection of TeV emission around the entire orbit
P. Kar* on behalf of the VERITAS Collaboration
*corresponding author
Full text: pdf
Pre-published on: August 16, 2017
Published on: August 03, 2018
Abstract
The TeV binary system \lsi has a compact object in an eccentric orbit around a Be star about 2 kpc from Earth. \lsi exhibits modulated gamma-ray emission around its 26.5 days orbit, mostly detectable at TeV energies around its apastron passage, with maximum flux during the $\phi = 0.55-0.65$ phase range. Multiple flaring episodes with nightly flux variability at TeV energies have been observed since its detection in 2006. At one time significant TeV emission was also detected in late 2010 from the source close to its periastron passage at superior conjunction. The TeV spectrum is well fitted by a power law with small variations of spectral index of $\sim2.6$ over the years. GeV, X-ray, and radio emission have been detected along the entire orbit, enabling detailed study of the modulation pattern and its super-orbital period, such comprehensive study of the \lsi orbit in the TeV regime has not been presented before. VERITAS has observed \lsi for over a decade now, accruing 200+ hours of data during different parts of its orbit. In this work, we have analyzed all available data for \lsi since September 2007 in individual phase bins of width $\Delta \phi = 0.1$ and performed a spectral analysis for two different parts of the orbit. TeV emission is now detected in 9 out of 10 phase bins, around the entire orbit for the first time in VERITAS data. Hint of spectral variation might also be present between different parts of the orbit. The implication of these results is discussed in the context of determining the nature of the unknown compact object (neutron star or microquasar) and a discussion of the absorption mechanisms in the system.
DOI: https://doi.org/10.22323/1.301.0712
How to cite
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-12-02T01:06:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7398703694343567, "perplexity": 2569.656828914043}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141685797.79/warc/CC-MAIN-20201201231155-20201202021155-00313.warc.gz"} |
https://pos.sissa.it/292/113/ | Volume 292 - Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2016) - Workshop on Geometry and Physics, Ringberg Castle, 20-25 November 2016, invited contributions
$SL(2)\times\mathbb{R}^+$ Exceptional Field Theory: An Action for F-Theory
F. Rudolph
Full text: pdf
Pre-published on: October 04, 2017
Published on: October 05, 2017
Abstract
Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is presented. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to Type IIB supergravity and F-theory. Thus $SL(2)\times\mathbb{R}^+$ Exceptional Field Theory contains both F-theory and M-theory in a single 12-dimensional formalism.
DOI: https://doi.org/10.22323/1.292.0113
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.
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-07-01T08:42:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31750181317329407, "perplexity": 2305.5231835300237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103922377.50/warc/CC-MAIN-20220701064920-20220701094920-00119.warc.gz"} |
https://csrc.nist.gov/Events/1998/assuring-crypto-security-development-validation | # Assuring Cryptographic Security: Development, Validation, and Use of FIPS 140-1 Compliant Products
Federal agencies and departments are required to comply with FIPS 140-1, Security Requirements for Cryptographic Modules. This involves the acquisition of validated cryptographic modules (which may be incorporated in a product/application) for protecting sensitive but unclassified data. Cryptographic modules are used to provide security services such as confidentiality, integrity, and authentication. FIPS 140-1 provides users with 1) a specification of security features that are required at each security level, 2) flexibility in choosing security requirements and environments, and 3) a guide to ensuring the modules in corporate necessary security features. Accredited laboratories perform conformance testing of FIPS 140-1 modules under the Cryptographic Module Validation (CMV) Program, which is a joint effort between NIST and CSE.
##### Topics
Highlights of the workshop include an overview of federal cryptography, a FIPS 140-1 Tutorial, and guidance on implementing FIPS 140-1. Detailed information on how to use the standard, its impact on Federal Agencies and industry, and how agencies can impact the program will also be provided. In addition, vendors will be provide with information on how to obtain validation for their modules. Panel discussions are planned with Federal Agencies currently implementing FIPS 140-1, vendors with available validated modules, the Cryptographic Module Testing Laboratories that perform validation testing, the banking community, and an overview of prudent practices. The workshop will conclude by looking to the future with discussions of possible enhancements to the standard and other related issues.
#### Event Details
Starts: May 11, 1998 - 09:00 AM EST
Ends: May 12, 1998 - 04:00 PM EST
Format: In-person Type: Conference
Attendance Type: Open to public
Audience Type: Industry,Government
NIST: Communications Security Establishment of the Government of Canada
#### Location
Gaithersburg Hilton
Gaithersburg, MD
#### Related Topics
Security and Privacy: cryptography, testing & validation
Technologies: hardware, software & firmware
Created January 11, 2018, Updated June 22, 2020 | 2021-01-24T10:12:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19042913615703583, "perplexity": 6141.3455114741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703547475.44/warc/CC-MAIN-20210124075754-20210124105754-00269.warc.gz"} |
https://interlingua.fandom.com/wiki/Mean | 9 807 Pages
## EnglishModificar
Most common English words: human « kept « business « #383: mean » manner » following » fell
### PronunciationModificar
• enPR: mēn, IPA: /miːn/, SAMPA: /mi:n/
• Audio (US) noicon (file)
Rhymes: -iːn
### Etymology 1Modificar
From Old English mænan (to mean, to allude to). Confer Dutch menen, German meinen. Cognate with mind and German Minne (love).
#### VerbModificar
Infinitive to Mean Third person singular means Simple past meant Past participle meant Present participle meaning
to Mean (third-person singular simple present means, present participle meaning, simple past and past participle )
1. (transitive) To convey, signify, or indicate.
What does this hieroglyph mean?
The sky is red this morning—does that mean we're in for a storm?
2. (transitive) To want or intend to convey.
I'm afraid I don't understand what you mean.
Say what you mean and mean what you say.
3. (transitive) To intend; to plan on doing.
I didn't mean to knock your tooth out.
I mean to go to Baddeck this summer.
I meant to take the car in for a smog check, but it slipped my mind.
4. (transitive) To have conviction in what one says.
Does she really mean what she said to him last night?
Say what you mean and mean what you say.
5. (transitive) To have intentions of a some kind.
Don't be angry; she meant well.
Someone's coming up. He means business.
6. (transitive) To result in; to bring about.
One faltering step means certain death.
##### TranslationsModificar
The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.
#### NounModificar
Singular Mean PluralMeans
Mean (plural Means)
1. (obsolete, in singular) An intermediate step or intermediate steps.
##### QuotationsModificar
For examples of the usage of this term see the citations page.
### Etymology 2Modificar
Middle English mene, imene "common" from Old English ġemǣne "common". Confer Dutch gemeen, German gemein, Gothic gamains. Cognate with Latin communis.
Positive Mean
1. Causing or intending to cause intentional harm; bearing ill will towards another; cruel; malicious.
Watch out for her, she's mean. I said good morning to her, and she punched me in the nose.
2. Miserly; stingy.
He's so mean. I've never seen him spend so much as five pounds on presents for his children.
3. Selfish; acting without consideration of others; unkind.
It was mean to steal the girl's piggy bank, but he just had to get uptown and he had no cash of his own.
4. Powerful; fierce; harsh; damaging.
It must have been a mean typhoon that levelled this town.
5. Accomplished with great skill; deft; hard to compete with.
Your mother can roll a mean cigarette.
He hits a mean backhand.
6. Low in quality; inferior.
##### TranslationsModificar
The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.
### Etymology 3Modificar
From Middle English meene, from Old French meien (French moyen), Late Latin medianus (that is in the middle, middle), from medius (middle). Cognate with mid.
Mean (not comparable)
Positive Mean Superlativenone (absolute)
1. Having the mean (see noun below) as its value.
#### NounModificar
Wikipedia has an article on:
Wikipedia
Singular Mean PluralMeans
Mean (plural Means)
1. Patrono:Statistics The average, the arithmetic mean.
2. Loosely, an intermediate value or range of values; a mid-value; a vague average.
• 1997, John Llewelyn Davies, David J. Vaughan, Republic, translation of original by Plato, page 263:
Then will not this constitution be a kind of mean between aristocracy and oligarchy?</span>
• 1996, Harris Rackham, The Nicomachean Ethics, translation of original by Aristotle, page 118:
as a mean, it implies certain extremes between which it lies, namely the more and the less</span>
• 1875, William Smith and Samuel Cheetham, editors, A Dictionary of Christian Antiquities, Little, Brown and Company, volume 1, page 10, s.v. Accentus Ecclesiasticus,
It presents a sort of mean between speech and song, continually inclining towards the latter, never altogether leaving its hold on the former; it is speech, though always attuned speech, in passages of average interest and importance; it is song, though always distinct and articulate song, in passages demanding more fervid utterance.
3. (mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.
• 1997, Angus Deaton, The Analysis of Household Surveys: A Microeconometric Approach to Development Policy,[1] World Bank Publications, ISBN 9780801852541, page 51:
Note that (1.41) is simply the probability-weighted mean without any explicit allowance for the stratification; each observation is weighted by its inflation factor and the total divided by the total of the inflation factors for the survey.
• 2002, Clifford A. Pickover, The Mathematics of Oz: Mental Gymnastics from Beyond the Edge,[2] Cambridge University Press, ISBN 9780521016780, page 246:
Luckily, even though the arithmetic mean is unusable, both the harmonic and geometric means settle to precise values as the amount of data increases.
• 2003, P. S. Bullen, Handbook of Means and Their Inequalities,[3] Springer, ISBN 978-1-4020-1522-9, page 251:
The generalized power means include power means, certain Gini means, in particular the counter-harmonic means.
4. (mathematics) Either of the two numbers in the middle of a conventionally presented proportion, as 2 and 3 in 1:2=3:6.
• 1825, John Farrar, translator, An Elementary Treatise on Arithmetic by Silvestre François Lacroix, third edition, page 102,
...if four numbers be in proportion, the product of the first and last, or of the two extremes, is equal to the product of the second and third, or of the two means.
• 1999, Dawn B. Sova, How to Solve Word Problems in Geometry, McGraw-Hill, ISBN 007134652X, page 85,
Using the means-extremes property of proportions, you know that the product of the extremes equals the product of the means. The ratio t/4 = 5/2 can be rewritten as t:4 = 5:2, in which the extremes are t and 2, and the means are 4 and 5.
• 2007, Carolyn C. Wheater, Homework Helpers: Geometry, Career Press, ISBN 1564147215, page 99,
In $\frac{18}{27}=\frac23$, the product of the means is $2\cdot27$, and the product of the extremes is $18\cdot3$. Both products are 54.
## ManxModificar
### EtymologyModificar
From Patrono:Sga[[Category:gv:Patrono:Sga derivations|Mean]] [[medón#Patrono:Sga|medón]] (middle, centre) < Latin mediānus.
### NounModificar
Mean m. [[Category:Patrono:Gv nouns|Mean]]
1. centre, middle
2. interior
• [[tar#Patrono:Gv|Tar]] [[stiagh#Patrono:Gv|stiagh]] ayns mean y killagh.
• Come into the body of the church.
3. average
• Trogmayd mean.
• We will strike an average.
## SpanishModificar
### VerbModificar
Mean (infinitive mear)
1. Second-person plural (ustedes) present indicative form of .
2. Third-person plural (ellos, ellas, also used with ustedes?) present indicative form of .
Community content is available under CC-BY-SA unless otherwise noted. | 2020-02-27T18:34:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6106230616569519, "perplexity": 10891.683526126704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146744.74/warc/CC-MAIN-20200227160355-20200227190355-00535.warc.gz"} |
https://www.nist.gov/property-fieldsection/competitive-manufacturing-and-construction-clean-energy-economy-346-million | # Competitive Manufacturing and Construction in a Clean-Energy Economy (+$34.6 million) ## Challenges image: Shutterstock, copyright Christian Lagerek image: Shutterstock, copyright Aaron Kohr By themselves, the nation's manufacturers would rank among the world's 10 largest economies, thanks, in large part, to the sector's nearly 12 million employees, one of the most productive manufacturing workforces ever. But U.S. industry faces relentless competition that has trimmed the nation's share of global manufacturing output from 25 percent in 2000 to about 20 percent today. Our more than 335,000 manufacturing plants must respond quickly and effectively to an ever-changing mix of requirements, risks, and opportunities, from new regulations to rising energy costs to emerging technologies and markets. Though the situation is highly dynamic, one analysis projects that China will overtake the United States as the world's leading manufacturer before 2020.1 Revitalizing the nation's manufacturing industries and helping to ensure that they will continue to be engines of innovation and job creation in the future is essential to building a clean energy economy that can help raise the standard of living for all Americans.2 The U.S. construction industry, another major component of the U.S. economy, also confronts significant challenges and important opportunities. There are almost 900,000 construction-related firms in the United States. Although only 1 percent employs more than 100 people, the construction industry accounts for about 5 percent of the nation's gross domestic product. As important, buildings account for 40 percent of U.S. energy consumption and 72 percent of electricity use, and they generate 39 percent of the nation's greenhouse gas emissions. Right now, according to a recently issued report from the National Research Council, "available technology integrated into a holistic building design could save up to 50 percent of the energy the building would otherwise use, while lowering lifetime cost."3 However, reaching these targets with already-implementable technologies is not guaranteed. Funding this initiative—which aims to achieve net-zero energy buildings that, on balance, consume no energy from non-renewable sources and leave no environmental footprint—will help make the goal more attainable through new measurement science that speeds development and introduction of innovative building technologies. ## Proposed NIST Programs This set of initiatives includes four distinct areas that support the President's efforts to revitalize American manufacturing4 and encourage innovation that helps put in place a clean-energy economy.5 • Green Manufacturing and Construction (+$10 million)
• Develop an information infrastructure, based on open standards, to communicate critical sustainability information efficiently among suppliers, customers, and regulators.
• Identify and disseminate best-practice methods, processes, and assessment tools for sustainable manufacturing in key industrial sectors;
• Establish energy-performance standards for new and existing buildings to achieve national goals for the design and construction of net-zero energy, high-performance green buildings.
• Enable the development and usage of sustainable materials, components, and systems in buildings.
• Develop and disseminate measurement tools for evaluating and improving indoor air quality.
• Leverage the Manufacturing Extension Partnership network, to promote the adoption of best practice methods and technologies for reducing energy consumption in manufacturing and in buildings.
• Innovations for 21st Century U.S. Manufacturing (+$10 million) • Develop new measurement methods and performance-based standards to improve additive manufacturing systems and other rapid prototyping systems for quick turn-around, small-batch production of complex, customized products. • Provide the measurement tools and capabilities necessary to develop and apply robotic technologies that are "smarter," more flexible, and better able to operate safely and effectively in less structured environments, to facilitate mass customization in manufacturing processes. • Develop, validate, and disseminate new scalable techniques and processes to safely and efficiently generate, handle, and assemble nanostructured materials and devices. • Collaborate with industry on development of methods and tools to monitor top-down and bottom-up nanomanufacturing processes in real time. • Expand the Hollings Manufacturing Extension Partnership (+$4.64 million, FY 2011 total is $129.7 million) program to expedite and facilitate adoption of technological innovations by smaller U.S. manufacturers, especially clean technologies and processes that improve manufacturers' competitive position. • Expand the Technology Innovation Program (+$10 million, FY 2011 total is \$79.9 million) to motivate and expedite R&D for the development of advanced, disruptive technologies that enable, for example, accelerated development of next-generation, high-performance processes and materials and in areas such as nanomanufacturing.
## Expected Impacts
Benefits and impacts expected to result from the proposed initiatives and programmatic increases include:
• U.S. manufacturers adopt a widely accepted set of sustainability metrics and achieve a leadership position in the development, design, and application or production of competitive, environmentally sustainable processes and products.
• New and improved industry-consensus standards and building-performance codes are adopted and implemented, yielding significant reductions in the energy use and environmental impact of buildings.
• State-of-the-art contributions toward improving the competitiveness and sustainability of the U.S. manufacturing sector.
• Improvement in the competitive position of U.S. manufacturers because of reduced environmental costs and development of new environmentally focused products.
• U.S. manufacturers increase their competitive capability to produce high-value-added, knowledge-intensive products and respond to new market opportunities.
1 IHS Global Insight, "Revised Forecast Advances Date of China Becoming the Preeminent Global Manufacturer," Aug. 12, 2008.
2 Executive Office of the President, A Framework for Revitalizing American Manufacturing, Dec. 2009.
3 The National Academies, Real Prospects for Energy Efficiency in the United States, Report in Brief, The National Academy of Sciences, 2009.
4 Executive Office of the President, A Framework for Revitalizing American Manufacturing, Dec. 2009.
5 Executive Office of the President, A Strategy for American Innovation: Driving Towards Sustainable Growth and Quality Jobs, Sept. 2009.
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Created February 02, 2010, Updated October 05, 2010 | 2016-09-29T12:09:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23200704157352448, "perplexity": 10931.447638606285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661795.48/warc/CC-MAIN-20160924173741-00269-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://www.anl.gov/event/electron-hydrodynamics-and-thermal-transport-in-graphenebased-materials | # Argonne National Laboratory
Seminar | Materials Science Division
# Electron Hydrodynamics and Thermal Transport in Graphene-Based Materials
MSD Seminar
Abstract: Electric and thermal transport in electronic systems has long been described in terms of a single-particle picture, which emphasizes the role of collisions between electrons and impurities or phonons, with electron-electron interactions playing a secondary role.
It is only in the past two decades that advances in the fabrication of ultra-clean samples have refocused the interest on collective hydrodynamic transport — a transport régime which is controlled by the nearly conserved quantities: number, momentum, and energy, and by electron-electron interactions.
In this talk, I review some of the recent theoretical and experimental progress in our understanding of electronic hydrodynamics in graphene-based materials. I focus on thermal transport and its relation to electric transport, epitomized by the Wiedemann-Franz law, which, in its conventional form, predicts a universal ratio between electric and thermal resistivities. Significant deviations from this prediction are found in single- and double-layer graphene, both in the doped case, where the Wiedemann-Franz ratio is reduced, and in the undoped case, where it is greatly enhanced. In the latter case, an interesting scenario emerges, in which a small amount of disorder helps to expose an underlying singularity of the transport coefficients: vanishing thermal resistivity, finite electric resistivity, and diverging Wiedemann-Franz ratio and Seebeck coefficient. | 2020-06-05T16:47:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8353456854820251, "perplexity": 1820.4082414687293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348502097.77/warc/CC-MAIN-20200605143036-20200605173036-00012.warc.gz"} |
https://lammps.sandia.gov/doc/improper_cossq.html | # improper_style cossq/omp command
## Syntax
improper_style cossq
## Examples
improper_style cossq
improper_coeff 1 4.0 0.0
## Description
The cossq improper style uses the potential
where x is the improper angle, x0 is its equilibrium value, and K is a prefactor.
If the 4 atoms in an improper quadruplet (listed in the data file read by the read_data command) are ordered I,J,K,L then X is the angle between the plane of I,J,K and the plane of J,K,L. Alternatively, you can think of atoms J,K,L as being in a plane, and atom I above the plane, and X as a measure of how far out-of-plane I is with respect to the other 3 atoms.
Note that defining 4 atoms to interact in this way, does not mean that bonds necessarily exist between I-J, J-K, or K-L, as they would in a linear dihedral. Normally, the bonds I-J, I-K, I-L would exist for an improper to be defined between the 4 atoms.
The following coefficients must be defined for each improper type via the improper_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:
• K (energy)
• X0 (degrees)
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed in Section 5 of the manual. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Making LAMMPS section for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See Section 5 of the manual for more instructions on how to use the accelerated styles effectively.
## Restrictions
This improper style can only be used if LAMMPS was built with the USER-MISC package. See the Making LAMMPS section for more info on packages. | 2018-07-17T19:06:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5641544461250305, "perplexity": 2688.0533778128297}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589892.87/warc/CC-MAIN-20180717183929-20180717203929-00539.warc.gz"} |
https://pvx.fandom.com/wiki/Archive_talk:A/N_Deadly_Virulence?diff=1132358&oldid=643905 | ## FANDOM
2,129 Pages
bring yer own bild — SkaKid 16:48, 25 April 2008 (EDT) hehe Buildsmaker 15:21, 29 July 2008 (EDT)
Actually, no! This character is part of a real team build for my Guild. It even kills Dark Alley smurfs:
Super fun. Zuranthium 17:11, 25 April 2008 (EDT)
obaby — SkaKid 17:12, 25 April 2008 (EDT)
Also that better not be an ineptitood mesmer with Fragility tacked on. — SkaKid 19:21, 25 April 2008 (EDT)
It's a Sig Illusions Mesmer. I'll post that one in a bit. Zuranthium 18:29, 26 April 2008 (EDT)
Isn't it like, Shell Shock, Immolate, Steam? — SkaKid 18:42, 26 April 2008 (EDT)
## Team Edit
Wouldn't this be better as a team build with the assa and mesmar? Klumpeet 06:49, 26 April 2008 (EDT)
As stated in description "This can also kill on its own" so no. ɟoʇuɐʌʎʞɔıɹ 07:32, 26 April 2008 (EDT)
Signet of Deadly Corruption must follow a dual attack, so you do have to be within melee range at some point to use twisting fangs. moush$2+2=4$ 15:12, 27 April 2008 (EDT)
True, the wording on that should be cleaned up. The point is that you don't need always need to be in melee range. Can just Shadow Walk into Twisting, teleport right back out with Dash, and keep doing ranged damage. Zuranthium 20:10, 27 April 2008 (EDT)
should this build possibly have a variant mention on removing all points from death magic when playing with a fragility mesmer? -Youngnastyman 08:19, 27 May 2008 (EDT)
## Haha Edit
This is Great cause its meta, even tho people have made this build millions of times b4 (There's even one in my sandbox). Everyone said SoDC sux, too slow, but put it on gank and works perfectly, its meta! I rofl at PvXwiki, they can only see a build when a top guild uses it. -_-' --Relyk 18:33, 27 April 2008 (EDT)
The Assassin build in your sandbox with Signet of Deadly Corruption is bad. This one is not. Zuranthium 19:32, 27 April 2008 (EDT)
DAii is a top 200 (sinsplit) guild. Not a top guild. — SkaKid 19:44, 27 April 2008 (EDT)
Hey, we'll get top 50. If we ever start doing ATs. >_< Zuranthium 19:54, 27 April 2008 (EDT)
=p — SkaKid 20:24, 27 April 2008 (EDT)
And if we get a full dedicated team, lol. WTB monk buddy. Zuranthium 02:29, 28 April 2008 (EDT)
;o — SkaKid 02:31, 28 April 2008 (EDT)
We didn't have a good Ele or HB Monk last night and that specific match was extra terrible because our split Mes couldn't move the first couple minutes of the match, so the split was all confused and of course since it was Druids Isle we basically got stuck in the base. Hopefully next time we can have a real match. ^_^ . Gj on your wins though, didn't know you were in that guild??? Zuranthium 17:15, 28 April 2008 (EDT)
Or actually nm, you're posting about the first match of the night that we lost, not the second one. That first one was better, we boosted and killed most of the NPCs I think, but then wiped cause of the two bad guests (zomg, we sooo would have wiped the opposing main team at one point as well if the Water Ele had bothered to do his job). Zuranthium 17:25, 28 April 2008 (EDT)
I'm just poking fun, I'm bad =P Also I'm in the epic TOOMZ DIVISION — SkaKid 17:41, 28 April 2008 (EDT)
Oh, tombs. Lol. Zuranthium 12:33, 29 April 2008 (EDT)
How can this build be AB without self heal? I tried, and it's terrible. The preceding unsigned comment was added by 98.221.149.216 (contribs) 22:50, 25 May 2008.
I heard playing with a team is good. Also, sign your comments. Zuranthium 04:33, 27 May 2008 (EDT)
Do you need someone to hold your hand? Replace Shadow Walk with Sadist's Signet. It's recharge is too long for AB's 12v12vNPC format anyways. P A R A S I T I C 00:41, 17 June 2008 (EDT)
That would be really dumb. Zuranthium 14:07, 23 June 2008 (EDT)
You make it sound like Shadow Walk is required for you to pull the combo off. — Rapta (talk|contribs) 22:05, 23 June 2008 (EDT)
Shadow Walk allows you to jump into a group of people/NPCs, get the Twisting Fangs off, and then jump out. Sadist's Signet isn't very useful. It's not always healing when you need it and you're going to die anyway if you try to stand there and tank. Zuranthium 23:38, 24 June 2008 (EDT)
Shadow Walk nerf...yikes. Zuranthium 00:23, 11 July 2008 (EDT)
Yea, it made it so you can't jump in and out as easily. Have to tele in at daggers if you don't wanna wait for the recharge. moush 19:01, 16 July 2008 (EDT)
It's actually probably not a big deal for this character, they will be crippled a lot of the time when you tele in and still won't be able to kite from the Twisting Fangs very well, but that little delay can make a difference. Zuranthium 18:07, 22 July 2008 (EDT)
## Tbh-...- Edit
im gonna disagree with the people, spike is actually very slow. damage is high but it gets outhealed quickly cause the spike takes 6 seconds to do not counting aftercast delay also with the nerf to shadow walk twisting fangs can be hard to time. Qoute: Jebus..
I do totally Agree tbh where is the element of suprise here? Idk how many Virulence SoDC builds which been unfavored, cant see this as a big wooah either.. Virulence is a kinda crap Elite.. To trigger the max from SoDC you allready have Cripple, Bleed and DW.. Altough using this whit Fragility ganker may be very good but theres so many better combos out there if your thinking team.. No Selfheal :( Makes this a sad ganker altough Dash - Shadow Walk can be used its stilled quite nerfed whit 1sec Disable then u again loose even moar suprise oO One Mtouch from the Ranger or if u face a Mrunner is gonnna screw this over.. Also:
3x 33dmg, Twisting Fangs, SoDC , SotS wont kill thou the degen is quite nice anyone whit selfheal will survive...
Effective' Not enuff killing power, easy countered by Condition removal.. No kd or disabling of any kind makes this easy to counter.. 6sec chain and no disabling oO. Easy to catch altough nice whit Armor Ingoring but its not enuff :/
Universality No selfheal, thou u have Dash Shadow Walk the 1sec Disabling is kinda boring, altough if u face a say a CC runner your quite fine (if u dont die first) but then they just send back a RC and puff ur out.. Failes in main team if pushed back all the time (they can just send back a ranger to counter this..) And to be real effiencent you need the SoI which then again lower uni since you need help to kill someone whit selfheal.. Altough can kill NPCS but whit no selfheal it can take some time :/ OR a interrupt for troll :/
Innovation Not the a new project whit Virulence + SoDC all got unfavored.. Altough this is one of the better builds, they cant just kill someone whit 660hp and some armor from shield..
Even thou DAI(some guild) uses it and wins doesnt make it insta win :/ at VoD and flagstand theire pretty useless :/ (RC spikke) Massive 17:05, 23 July 2008 (EDT)
See my comment in vote box. Zuranthium 00:14, 25 July 2008 (EDT)
Just wondering, i dont have accsess to GW but can anyone check the damage of this?.. Tbh this doesnt bring anything to a team.. Mostly the opposite team can camp out the match then lets see how this Sin build and 1x Frontline will handle that oO , 1 rc/draw and NEEXT plz.. Also i will gladly see the damage what this character can do ALONE.. As i see this now its a Single Build. I might consider raising the vote if you put it in a team, bceause alone it looks pretty awfull..Massive 18:27, 25 July 2008 (EDT)
Yeah, it's a single build. So what? You have to consider builds in the correct setting. Zuranthium 16:13, 28 July 2008 (EDT)
As you said in your vote "this will outdamage the opposite to heal upp oO" 6 seconds, Thats 3x Sooth Memories? = 300hp and i doubt it does 960 if does then i vote 5-5-5..Massive 18:29, 25 July 2008 (EDT)
Deep Wound reduces healing. The two gankers do 1000+ damage together over the course of the "spike" and that's pre-Vod and doesn't even take Backfire or the perma -10 degen into consideration. Zuranthium 16:13, 28 July 2008 (EDT)
Demolishes a lot of the standard split counters. Shadow Walk nerf is a little annoying but this will still work as a ganker against many builds.Zuranthium You say here its a Ganker so plz put another description or stop staying its a sinsplit bceause gank and split is pretty diffrent..Massive 10:12, 26 July 2008 (EDT)
Lol....Zuranthium 16:13, 28 July 2008 (EDT)
nerf sucks. Any suggestions/replacements? --*Wah Wah Wah!* 07:55, 25 July 2008 (EDT)
Dancing daggers isn't an attack. So why would you replace it. Lord of all tyria 07:58, 25 July 2008 (EDT)
Mostly just plain old aftercast. Also, in usage it says "Use Shadow Walk to teleport to a foe (often for a sudden Twisting Fangs). Try to "anchor" yourself in the best spot possible." Can't do that when your attacks are disabled for 1 second and you have an aftercast. --*Wah Wah Wah!* 08:00, 25 July 2008 (EDT)
There is no aftercast on shadow-walk. All the other non-elite shadowsteps have aftercast now iirc, so this is the best one. Lord of all tyria 08:02, 25 July 2008 (EDT)
Just change usage slightly if you want the chain to go off one second faster, DD->Shadow Walk->Mantis Touch->Twisting Fangs. It's mostly for NPCs anyway, so usage barely matters. - isery (TALK) 08:07, 25 July 2008 (EDT)
I changed it so you Shadowstep then hit them with Mantis Touch. Combined with the aftercast, TF will recharge by the time you use it. Anyway, for ganking NPC's, it really doesn't matter. It's just slightly more efficient now. --*Wah Wah Wah!* 08:12, 25 July 2008 (EDT)
## Variant Edit
Haven't actually tested it in practice yet, but could Twisting Fangs not be replaced by Trampling Ox, then Signet of Toxic Shock by Impale? Tiny amount of damage sacrificed, but it adds a kd on top of that. 157.193.2.8 10:17, 26 July 2008 (EDT)
Build is slow as it is, adding impale gives an extra second of reaction time for enemy monks. Not viable imho Amorality 10:07, 28 July 2008 (EDT)
It would be the same timing... Frosty No U! 10:08, 28 July 2008 (EDT)
dumbass --> Amorality 10:18, 28 July 2008 (EDT)
## forgetting one thing Edit
You guys who are saying it sucks are forgetting all the conditions that the person is suffering AS youre doing spike damage to them. bleeding=3 pips=6 health lost per second. disease=4 pips=8 more health per second lost, totaling 14 health loss per second.poison=4 pips=8 more health, totaling 22 health lost per second. And they are also weakened and DW'd. add all that on to the spike damage and you have yourself a pretty decent pressure build that can warp out at any time thanks to shadow walk and dash70.110.178.100 14:11, 28 July 2008 (EDT)Xodus I
Meh, forgot that max degen is -10 pips, aka 20 health lost per second. Still nice though70.110.178.100 14:13, 28 July 2008 (EDT)Xodus I
More "meh" than "nice". The spike doesn't deal a lot of damage, even with the degen. Virulence will be on for, like 4 secs of the spike. Totals 80 raw focking domage which is RC bait. --Srs Beans 16:20, 28 July 2008 (EDT)
Virulence lasts for 7 seconds, totaling 140 dmg
rc=metaCloseImpactToo Muh Bruh 11:23, 30 July 2008 (EDT)
If they send the RC back to defend against your gank, you=win. - isery (TALK) 11:30, 30 July 2008 (EDT)
You will wipe the RC too. Pretty much none of the RC's atm have mending touch / dismiss with them, so they can't remove their own conditions(and die easy). Nor do they have good self heals(spamming rof isn't really that great). —ǘŋƐxɩsƫ 07:01, 4 August 2008 (EDT)
thats why im trying to say its not that good :/ i personally dont like it at all, but my vote gets removed all the time, even thou my Comment is valide + + oO , reminds me of the GoR sin..-.-Massive 05:18, 1 August 2008 (EDT)
Wtf? Massive I'm saying that if they are sending their RC back to defend against your gank they then lose all their prot and condition removal at the stand and you will roll them there. Sending an RC back to defend against this build is about the dumbest thing you can do. It's pretty poor at the stand, but most assassins are. - isery (TALK) 05:26, 1 August 2008 (EDT)
^-- 10:32, 1 August 2008 (EDT)
Yes but omg.. You guys just said its a split :@!!! so say this splits whit - Mesmer, Monk, Sin.. You bring 2ppl back runner and Rc = 6ppl at stand when opposite have 5.. Thats what im talking about :) Also i faced this tbh was kinda funny... The Sin started to gank first we sent the Ranger (crippshot), he took him down easilly Mtouch ftw! Then he brought a Runner and Mesmer..Btw we played on Frozen, this was knida Secnario ... The Ranger started to Gank middle way.. The RC and Runner protected Base.. We also locked em outside so the Dancing Daggers was kinda oO.. The Ranger started to gank, they didnt respond bceause the Flagger didnt notice so he kinda wiped half their, then they went back and Turtled out.. And we crushed em whit like 15npcs us and they had only chamber left :/ - Was quite funny :D - Altough we where lucky bceause our standteam had a quite defensive twist :).. A Pblock, Snare, Hammer and Evis.. Hammer just linebacked the Single Warrior. ELe kept him snared. Pblocker interrupt prettymuch what was needed at the time, altough he could actually just fall back and give the Domi Mesmer a cry whit Pblock.. We only had one kill when the Mesmer Shattered Holy Veil. used Diversion, Backfire and SHame at the same but didnt really matter.. All in all i think it phails sorry ..Massive 08:25, 5 August 2008 (EDT)
I stopped when I saw the RC was protecting the base. Frosty No U! 08:31, 5 August 2008 (EDT)
## Tag PVP for RA should be removed Edit
Why? because the build has not res signet, and I think that res signet or res hability is mandatory for RA Sinchan Pro(163.244.62.121 09:16, 4 August 2008 (EDT)).
Everything works in RA. --*Wah Wah Wah!* 09:20, 4 August 2008 (EDT)
I had a 5 wins streak with a team of 2 rangers, Essence Spiker (E/W) and a Wammo with RoF, Healing Breeze and Charge. It's not that hard to win RA --Srs Beans 09:25, 4 August 2008 (EDT)
It kills slow...--72.189.85.47 15:38, 4 August 2008 (EDT)
Not if you have "a mesmer using fragility" with you...which the build tells you will help. This build isn't designed to "kill fast" it makes even tough targets squishy, so your team can rape. Karate Jesus 15:52, 4 August 2008 (EDT)
Anyway, speed isn't a factor vs. NPC's, and people are too stupid to catch a spike in RA. --*Wah Wah Wah!* 08:43, 5 August 2008 (EDT)
People are too stupid to spike in RA. 122.104.165.13 04:41, 9 August 2008 (EDT)
people are stupid in RA period.- Jak123X 19:12, 20 October 2008 (EDT)
people are stupid.
Sazzles needs a huggles. 01:57, 17 November 2008 (EST)
## Archive?Edit
No one uses this anymore. Zyke 01:57, 29 October 2008 (EDT)
I love when people use this build against my team when I am monking. 1 mend ailment and my teamate gets full health : P
...? Whoever uses mend condition?152.226.7.213 01:58, 17 November 2008 (EST)
Community content is available under CC-BY-NC-SA 2.5 unless otherwise noted. | 2020-05-31T04:14:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4996626675128937, "perplexity": 9683.329474912949}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347410745.37/warc/CC-MAIN-20200531023023-20200531053023-00545.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Amolev.alexander-i | # zbMATH — the first resource for mathematics
## Molev, Alexander I.
Compute Distance To:
Author ID: molev.alexander-i Published as: Molev, A.; Molev, A. I.; Molev, Alexander; Molev, Alexander I. External Links: MGP · Wikidata
Documents Indexed: 90 Publications since 1983, including 2 Books
all top 5
#### Co-Authors
38 single-authored 12 Ragoucy, Eric 5 Futorny, Vyacheslav M. 5 Jing, Naihuan 5 Kirillov, Alexandre Aleksandrovich 4 Isaev, Alexei P. 3 Liu, Ming 3 Mukhin, Evgeny 3 Nazarov, Maxim Leonidovich 3 Ol’shanskiĭ, Grigoriĭ Iosifovich 3 Ovsienko, Sergei A. 2 Billig, Yuly 2 Hopkins, Mark J. 2 Kontsevich, Maxim Lvovich 2 Kožić, Slaven 2 Ogievetsky, Oleg V. 2 Zhang, Ruibin 1 Arakawa, Tomoyuki 1 Arnaudon, Daniel 1 Borodin, Alexei 1 Bufetov, Aleksandr Igorevich 1 Bufetov, Alekseĭ Igor’evich 1 Chervov, Alexander Viktorovich 1 Davydov, Alekseĭ Aleksandrovich 1 Frappat, Luc 1 Gorin, V. E. 1 Gow, Lucy 1 Iorgov, Nikolai 1 Ismagilov, Rais Sal’manovich 1 Khoroshkin, Sergey M. 1 Matsumoto, Takuya 1 Molchanov, Vladimir Fedorovich 1 Neretin, Yuriĭ Aleksandrovich 1 Nessonov, Nikolai I. 1 Okun’kov, Andreĭ Yur’evich 1 Os’kin, A. F. 1 Petrov, Leonid 1 Retakh, Vladimir Solomonovich 1 Rozhkovskaya, N. A. 1 Rozhkovskaya, Natasha 1 Sagan, Bruce Eli 1 Sorba, Paul 1 Suh, Uhi Rinn 1 Tolstoĭ, Valeriĭ Nikolaevich 1 Tsalenko, L. M. 1 Vershik, Anatoliĭ Moiseevich 1 Yakimova, Oksana S. 1 Yang, Fan
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#### Serials
9 Letters in Mathematical Physics 6 Journal of Algebra 5 Communications in Mathematical Physics 5 Journal of Mathematical Physics 4 Russian Mathematical Surveys 3 Reviews in Mathematical Physics 3 Advances in Mathematics 3 IMRN. International Mathematics Research Notices 3 Selecta Mathematica. New Series 2 Discrete Mathematics 2 Functional Analysis and its Applications 2 Selecta Mathematica Sovietica 2 Journal of Physics A: Mathematical and General 2 Representation Theory 2 Moscow Mathematical Journal 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Mathematical Surveys and Monographs 2 Journal of Physics A: Mathematical and Theoretical 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 The Australian Mathematical Society Gazette 1 Duke Mathematical Journal 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Inventiones Mathematicae 1 Matematicheskiĭ Sbornik. Novaya Seriya 1 Mathematische Annalen 1 Transactions of the American Mathematical Society 1 Bulgarian Journal of Physics 1 Mathematics of the USSR, Sbornik 1 Journal of Algebraic Combinatorics 1 St. Petersburg Mathematical Journal 1 The Electronic Journal of Combinatorics 1 Advances in Theoretical and Mathematical Physics 1 Annales Henri Poincaré 1 Czechoslovak Journal of Physics 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series
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#### Fields
82 Nonassociative rings and algebras (17-XX) 28 Quantum theory (81-XX) 15 Associative rings and algebras (16-XX) 14 Combinatorics (05-XX) 11 Group theory and generalizations (20-XX) 4 Topological groups, Lie groups (22-XX) 2 Algebraic geometry (14-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Category theory; homological algebra (18-XX) 1 Partial differential equations (35-XX) 1 Global analysis, analysis on manifolds (58-XX)
#### Citations contained in zbMATH
75 Publications have been cited 840 times in 466 Documents Cited by Year
Yangians and classical Lie algebras. Zbl 1141.17001
Molev, Alexander
2007
Yangians and classical Lie algebras. Zbl 0876.17014
Molev, A.; Nazarov, M.; Ol’shanskij, G.
1996
Gelfand-Tsetlin bases for classical Lie algebras. Zbl 1211.17009
Molev, A. I.
2006
A Littlewood-Richardson rule for factorial Schur functions. Zbl 0972.05053
Molev, Alexander I.; Sagan, Bruce E.
1999
Finite-dimensional irreducible representations of twisted Yangians. Zbl 0944.17008
Molev, A. I.
1998
Coideal subalgebras in quantum affine algebras. Zbl 1129.17302
Molev, A. I.; Ragoucy, E.; Sorba, P.
2003
A new fusion procedure for the Brauer algebra and evaluation homomorphisms. Zbl 1276.20006
Isaev, A. P.; Molev, A. I.; Ogievetsky, O. V.
2012
Yangians and their applications. Zbl 1086.17008
Molev, A. I.
2003
The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite $$W$$-algebras. Zbl 1268.17012
Futorny, Vyacheslav; Molev, Alexander; Ovsienko, Serge
2010
On the $$R$$-matrix realization of Yangians and their representations. Zbl 1227.17008
Arnaudon, Daniel; Molev, Alexander; Ragoucy, Eric
2006
On higher-order Sugawara operators. Zbl 1225.17031
Chervov, A. V.; Molev, A. I.
2009
Representations of reflection algebras. Zbl 1039.17016
Molev, A. I.; Ragoucy, E.
2002
Capelli identities for classical Lie algebras. Zbl 0989.17006
Molev, Alexander; Nazarov, Maxim
1999
Feigin-Frenkel center in types $$B$$, $$C$$ and $$D$$. Zbl 1266.17016
Molev, A. I.
2013
Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus. Zbl 1144.17019
Billig, Yuly; Molev, Alexander; Zhang, Ruibin
2008
A basis for representations of symplectic Lie algebras. Zbl 0931.17005
Molev, A. I.
1999
Explicit generators in rectangular affine $$\mathcal {W}$$-algebras of type $$A$$. Zbl 1415.17027
Arakawa, Tomoyuki; Molev, Alexander
2017
Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras. Zbl 0861.17009
Molev, Alexander
1995
Gelfand-Tsetlin basis for representations of Yangians. Zbl 0787.17014
Molev, A. I.
1994
Isomorphism between the $$R$$-matrix and Drinfeld presentations of Yangian in types $$B$$, $$C$$ and $$D$$. Zbl 06921832
Jing, Naihuan; Liu, Ming; Molev, Alexander
2018
Factorial supersymmetric Schur functions and super Capelli identities. Zbl 0955.05112
Molev, Alexander
1998
The MacMahon master theorem for right quantum superalgebras and higher Sugawara operators for $$\widehat{\mathfrak{gl}}_{m|n}$$. Zbl 1342.17016
Molev, A. I.; Ragoucy, E.
2014
Irreducibility criterion for tensor products of Yangian evaluation modules. Zbl 1035.17025
Molev, A. I.
2002
Idempotents for Birman-Murakami-Wenzl algebras and reflection equation. Zbl 1343.17010
Isaev, A. P.; Molev, A. I.; Ogievetsky, O. V.
2014
Representations of twisted $$q$$-Yangians. Zbl 1206.81060
Gow, Lucy; Molev, Alexander
2010
Comultiplication rules for the double Schur functions and Cauchy identities. Zbl 1182.05128
Molev, A. I.
2009
On the fusion procedure for the symmetric group. Zbl 1167.20305
Molev, A. I.
2008
Symmetries and invariants of twisted quantum algebras and associated Poisson algebras. Zbl 1190.17009
Molev, A. I.; Ragoucy, E.
2008
Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras. Zbl 0988.17005
Molev, A. I.
2000
Fusion procedure for the Brauer algebra. Zbl 1219.81147
Isaev, A. P.; Molev, A. I.
2011
On the idempotents of Hecke algebras. Zbl 1167.20303
Isaev, A. P.; Molev, A. I.; Os’kin, A. F.
2008
Centralizer construction for twisted Yangians. Zbl 1026.17021
Molev, Alexander; Olshanski, Grigori
2000
Noncommutative symmetric functions and Laplace operators for classical Lie algebras. Zbl 0843.17003
Molev, Alexander
1995
Algebras of intermediate growth. Zbl 0705.17013
Kirillov, A. A.; Kontsevich, M. L.; Molev, A. I.
1990
Sugawara operators for classical Lie algebras. Zbl 1395.17001
Molev, Alexander
2018
Classical $$\mathcal W$$-algebras in types $$A$$, $$B$$, $$C$$, $$D$$ and $$G$$. Zbl 1321.17020
Molev, A. I.; Ragoucy, E.
2015
A $$q$$-analogue of the centralizer construction and skew representations of the quantum affine algebra. Zbl 1138.81028
Hopkins, Mark J.; Molev, Alexander I.
2006
Skew representations of twisted Yangians. Zbl 1143.17005
Molev, A. I.
2006
Harish-Chandra modules for Yangians. Zbl 1190.17006
Futorny, Vyacheslav; Molev, Alexander; Ovsienko, Serge
2005
On irreducibility of tensor products of evaluation modules for the quantum affine algebra. Zbl 1050.17012
Molev, A. I.; Tolstoy, V. N.; Zhang, R. B.
2004
Representations of twisted Yangians. Zbl 0774.17021
Molev, A. I.
1992
Center of the quantum affine vertex algebra in type $$A$$. Zbl 1432.17014
Jing, Naihuan; Kožić, Slaven; Molev, Alexander; Yang, Fan
2018
Eigenvalues of Bethe vectors in the Gaudin model. Zbl 1382.81100
Molev, A. I.; Mukhin, E. E.
2017
Higher Sugawara operators for the quantum affine algebras of type $$A$$. Zbl 1395.17049
Frappat, Luc; Jing, Naihuan; Molev, Alexander; Ragoucy, Eric
2016
Yangian characters and classical $$\mathcal W$$-algebras. Zbl 1329.17025
Molev, A. I.; Mukhin, E. E.
2014
Littlewood-Richardson polynomials. Zbl 1169.05050
Molev, A. I.
2009
Representations of the twisted quantized enveloping algebra of type $$C_n$$. Zbl 1141.17014
Molev, Alexander
2006
Quantisation and nilpotent limits of Mishchenko-Fomenko subalgebras. Zbl 07121930
Molev, Alexander; Yakimova, Oksana
2019
Gelfand-Tsetlin bases for representations of finite $$W$$-algebras and shifted Yangians. Zbl 1202.81093
Futorny, V.; Molev, A.; Ovsienko, S.
2008
Yangians and transvector algebras. Zbl 1035.17024
Molev, A. I.
2002
Segal-Sugawara vectors for the Lie algebra of type $$G_2$$. Zbl 1338.17023
Molev, A. I.; Ragoucy, E.; Rozhkovskaya, N.
2016
Quantization of the shift of argument subalgebras in type $$A$$. Zbl 1376.17017
Futorny, Vyacheslav; Molev, Alexander
2015
Quasideterminants and Casimir elements for the general linear Lie superalgebra. Zbl 1079.17006
2004
Yangians and Laplace operators for classical Lie algebras. Zbl 1049.17502
Molev, Alexander
1995
Invariants of the vacuum module associated with the Lie superalgebra $$\mathfrak{gl}(1| 1)$$. Zbl 1325.81095
Molev, A. I.; Mukhin, E. E.
2015
Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Zbl 0990.20005
Molev, A. I.; Olshanski, G. I.
2001
A weight basis for representations of even orthogonal Lie algebras. Zbl 1008.17003
Molev, Alexander I.
2000
Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra. Zbl 0895.05006
Molev, Alexander I.
1998
Unitarizability of some Enright-Varadarajan $${\mathfrak u}(p,q)$$-modules. Zbl 0759.22020
Molev, A. I.
1991
Isomorphism between the $$R$$-matrix and Drinfeld presentations of quantum affine algebra: type $$C$$. Zbl 1439.81062
Jing, Naihuan; Liu, Ming; Molev, Alexander
2020
Representations of centrally extended Lie superalgebra $$\mathfrak{psl}(2|2)$$. Zbl 1304.82015
Matsumoto, Takuya; Molev, Alexander
2014
Characteristic maps for the Brauer algebra. Zbl 1279.20058
Molev, A. I.; Rozhkovskaya, N.
2013
The Gel’fand-Tsetlin basis for irreducible unitarizable representations of u(p,q) with a highest weight. Zbl 0705.17007
Molev, A. I.
1989
Representations of the symmetric group in the free Lie (super-)algebra and in the space of harmonic polynomials. Zbl 0608.20009
Molev, A. I.; Tsalenko, L. M.
1986
Algebras of intermediate growth. Zbl 0684.17008
Kirillov, A. A.; Kontsevich, M. L.; Molev, A. I.
1983
Center at the critical level for centralizers in type $$A$$. Zbl 07268488
Molev, A. I.
2021
Isomorphism between the $$R$$-matrix and Drinfeld presentations of quantum affine algebra: types $$B$$ and $$D$$. Zbl 07209356
Jing, Naihuan; Liu, Ming; Molev, Alexander
2020
Center of the quantum affine vertex algebra associated with trigonometric $$R$$-matrix. Zbl 1428.17018
Kožić, Slaven; Molev, Alexander
2017
Casimir elements from the Brauer-Schur-Weyl duality. Zbl 1355.17008
Iorgov, N.; Molev, A. I.; Ragoucy, E.
2013
Combinatorial bases for covariant representations of the Lie superalgebra $${\mathfrak{gl}}_{m|n}$$. Zbl 1288.17007
Molev, A. I.
2011
Verma modules for Yangians. Zbl 1124.17004
Billig, Y.; Futorny, V.; Molev, A.
2006
The 8th problem: Littlewood-Richardson problem for Schubert polynomials. Zbl 1066.05147
Molev, Alexander
2004
On Gelfand-Tsetlin bases for representations of classical Lie algebras. Zbl 0993.17007
Molev, A. I.
2000
Gelfand-Zetlin basis for irreducible unitarizable representations of $$\mathfrak u(p,q)$$ with highest weight. Zbl 0685.17003
Molev, A. I.
1989
Proof of the Kirillov-Kontsevich formula. Zbl 0543.17009
Molev, A. I.
1984
Center at the critical level for centralizers in type $$A$$. Zbl 07268488
Molev, A. I.
2021
Isomorphism between the $$R$$-matrix and Drinfeld presentations of quantum affine algebra: type $$C$$. Zbl 1439.81062
Jing, Naihuan; Liu, Ming; Molev, Alexander
2020
Isomorphism between the $$R$$-matrix and Drinfeld presentations of quantum affine algebra: types $$B$$ and $$D$$. Zbl 07209356
Jing, Naihuan; Liu, Ming; Molev, Alexander
2020
Quantisation and nilpotent limits of Mishchenko-Fomenko subalgebras. Zbl 07121930
Molev, Alexander; Yakimova, Oksana
2019
Isomorphism between the $$R$$-matrix and Drinfeld presentations of Yangian in types $$B$$, $$C$$ and $$D$$. Zbl 06921832
Jing, Naihuan; Liu, Ming; Molev, Alexander
2018
Sugawara operators for classical Lie algebras. Zbl 1395.17001
Molev, Alexander
2018
Center of the quantum affine vertex algebra in type $$A$$. Zbl 1432.17014
Jing, Naihuan; Kožić, Slaven; Molev, Alexander; Yang, Fan
2018
Explicit generators in rectangular affine $$\mathcal {W}$$-algebras of type $$A$$. Zbl 1415.17027
Arakawa, Tomoyuki; Molev, Alexander
2017
Eigenvalues of Bethe vectors in the Gaudin model. Zbl 1382.81100
Molev, A. I.; Mukhin, E. E.
2017
Center of the quantum affine vertex algebra associated with trigonometric $$R$$-matrix. Zbl 1428.17018
Kožić, Slaven; Molev, Alexander
2017
Higher Sugawara operators for the quantum affine algebras of type $$A$$. Zbl 1395.17049
Frappat, Luc; Jing, Naihuan; Molev, Alexander; Ragoucy, Eric
2016
Segal-Sugawara vectors for the Lie algebra of type $$G_2$$. Zbl 1338.17023
Molev, A. I.; Ragoucy, E.; Rozhkovskaya, N.
2016
Classical $$\mathcal W$$-algebras in types $$A$$, $$B$$, $$C$$, $$D$$ and $$G$$. Zbl 1321.17020
Molev, A. I.; Ragoucy, E.
2015
Quantization of the shift of argument subalgebras in type $$A$$. Zbl 1376.17017
Futorny, Vyacheslav; Molev, Alexander
2015
Invariants of the vacuum module associated with the Lie superalgebra $$\mathfrak{gl}(1| 1)$$. Zbl 1325.81095
Molev, A. I.; Mukhin, E. E.
2015
The MacMahon master theorem for right quantum superalgebras and higher Sugawara operators for $$\widehat{\mathfrak{gl}}_{m|n}$$. Zbl 1342.17016
Molev, A. I.; Ragoucy, E.
2014
Idempotents for Birman-Murakami-Wenzl algebras and reflection equation. Zbl 1343.17010
Isaev, A. P.; Molev, A. I.; Ogievetsky, O. V.
2014
Yangian characters and classical $$\mathcal W$$-algebras. Zbl 1329.17025
Molev, A. I.; Mukhin, E. E.
2014
Representations of centrally extended Lie superalgebra $$\mathfrak{psl}(2|2)$$. Zbl 1304.82015
Matsumoto, Takuya; Molev, Alexander
2014
Feigin-Frenkel center in types $$B$$, $$C$$ and $$D$$. Zbl 1266.17016
Molev, A. I.
2013
Characteristic maps for the Brauer algebra. Zbl 1279.20058
Molev, A. I.; Rozhkovskaya, N.
2013
Casimir elements from the Brauer-Schur-Weyl duality. Zbl 1355.17008
Iorgov, N.; Molev, A. I.; Ragoucy, E.
2013
A new fusion procedure for the Brauer algebra and evaluation homomorphisms. Zbl 1276.20006
Isaev, A. P.; Molev, A. I.; Ogievetsky, O. V.
2012
Fusion procedure for the Brauer algebra. Zbl 1219.81147
Isaev, A. P.; Molev, A. I.
2011
Combinatorial bases for covariant representations of the Lie superalgebra $${\mathfrak{gl}}_{m|n}$$. Zbl 1288.17007
Molev, A. I.
2011
The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite $$W$$-algebras. Zbl 1268.17012
Futorny, Vyacheslav; Molev, Alexander; Ovsienko, Serge
2010
Representations of twisted $$q$$-Yangians. Zbl 1206.81060
Gow, Lucy; Molev, Alexander
2010
On higher-order Sugawara operators. Zbl 1225.17031
Chervov, A. V.; Molev, A. I.
2009
Comultiplication rules for the double Schur functions and Cauchy identities. Zbl 1182.05128
Molev, A. I.
2009
Littlewood-Richardson polynomials. Zbl 1169.05050
Molev, A. I.
2009
Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus. Zbl 1144.17019
Billig, Yuly; Molev, Alexander; Zhang, Ruibin
2008
On the fusion procedure for the symmetric group. Zbl 1167.20305
Molev, A. I.
2008
Symmetries and invariants of twisted quantum algebras and associated Poisson algebras. Zbl 1190.17009
Molev, A. I.; Ragoucy, E.
2008
On the idempotents of Hecke algebras. Zbl 1167.20303
Isaev, A. P.; Molev, A. I.; Os’kin, A. F.
2008
Gelfand-Tsetlin bases for representations of finite $$W$$-algebras and shifted Yangians. Zbl 1202.81093
Futorny, V.; Molev, A.; Ovsienko, S.
2008
Yangians and classical Lie algebras. Zbl 1141.17001
Molev, Alexander
2007
Gelfand-Tsetlin bases for classical Lie algebras. Zbl 1211.17009
Molev, A. I.
2006
On the $$R$$-matrix realization of Yangians and their representations. Zbl 1227.17008
Arnaudon, Daniel; Molev, Alexander; Ragoucy, Eric
2006
A $$q$$-analogue of the centralizer construction and skew representations of the quantum affine algebra. Zbl 1138.81028
Hopkins, Mark J.; Molev, Alexander I.
2006
Skew representations of twisted Yangians. Zbl 1143.17005
Molev, A. I.
2006
Representations of the twisted quantized enveloping algebra of type $$C_n$$. Zbl 1141.17014
Molev, Alexander
2006
Verma modules for Yangians. Zbl 1124.17004
Billig, Y.; Futorny, V.; Molev, A.
2006
Harish-Chandra modules for Yangians. Zbl 1190.17006
Futorny, Vyacheslav; Molev, Alexander; Ovsienko, Serge
2005
On irreducibility of tensor products of evaluation modules for the quantum affine algebra. Zbl 1050.17012
Molev, A. I.; Tolstoy, V. N.; Zhang, R. B.
2004
Quasideterminants and Casimir elements for the general linear Lie superalgebra. Zbl 1079.17006
2004
The 8th problem: Littlewood-Richardson problem for Schubert polynomials. Zbl 1066.05147
Molev, Alexander
2004
Coideal subalgebras in quantum affine algebras. Zbl 1129.17302
Molev, A. I.; Ragoucy, E.; Sorba, P.
2003
Yangians and their applications. Zbl 1086.17008
Molev, A. I.
2003
Representations of reflection algebras. Zbl 1039.17016
Molev, A. I.; Ragoucy, E.
2002
Irreducibility criterion for tensor products of Yangian evaluation modules. Zbl 1035.17025
Molev, A. I.
2002
Yangians and transvector algebras. Zbl 1035.17024
Molev, A. I.
2002
Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Zbl 0990.20005
Molev, A. I.; Olshanski, G. I.
2001
Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras. Zbl 0988.17005
Molev, A. I.
2000
Centralizer construction for twisted Yangians. Zbl 1026.17021
Molev, Alexander; Olshanski, Grigori
2000
A weight basis for representations of even orthogonal Lie algebras. Zbl 1008.17003
Molev, Alexander I.
2000
On Gelfand-Tsetlin bases for representations of classical Lie algebras. Zbl 0993.17007
Molev, A. I.
2000
A Littlewood-Richardson rule for factorial Schur functions. Zbl 0972.05053
Molev, Alexander I.; Sagan, Bruce E.
1999
Capelli identities for classical Lie algebras. Zbl 0989.17006
Molev, Alexander; Nazarov, Maxim
1999
A basis for representations of symplectic Lie algebras. Zbl 0931.17005
Molev, A. I.
1999
Finite-dimensional irreducible representations of twisted Yangians. Zbl 0944.17008
Molev, A. I.
1998
Factorial supersymmetric Schur functions and super Capelli identities. Zbl 0955.05112
Molev, Alexander
1998
Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra. Zbl 0895.05006
Molev, Alexander I.
1998
Yangians and classical Lie algebras. Zbl 0876.17014
Molev, A.; Nazarov, M.; Ol’shanskij, G.
1996
Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras. Zbl 0861.17009
Molev, Alexander
1995
Noncommutative symmetric functions and Laplace operators for classical Lie algebras. Zbl 0843.17003
Molev, Alexander
1995
Yangians and Laplace operators for classical Lie algebras. Zbl 1049.17502
Molev, Alexander
1995
Gelfand-Tsetlin basis for representations of Yangians. Zbl 0787.17014
Molev, A. I.
1994
Representations of twisted Yangians. Zbl 0774.17021
Molev, A. I.
1992
Unitarizability of some Enright-Varadarajan $${\mathfrak u}(p,q)$$-modules. Zbl 0759.22020
Molev, A. I.
1991
Algebras of intermediate growth. Zbl 0705.17013
Kirillov, A. A.; Kontsevich, M. L.; Molev, A. I.
1990
The Gel’fand-Tsetlin basis for irreducible unitarizable representations of u(p,q) with a highest weight. Zbl 0705.17007
Molev, A. I.
1989
Gelfand-Zetlin basis for irreducible unitarizable representations of $$\mathfrak u(p,q)$$ with highest weight. Zbl 0685.17003
Molev, A. I.
1989
Representations of the symmetric group in the free Lie (super-)algebra and in the space of harmonic polynomials. Zbl 0608.20009
Molev, A. I.; Tsalenko, L. M.
1986
Proof of the Kirillov-Kontsevich formula. Zbl 0543.17009
Molev, A. I.
1984
Algebras of intermediate growth. Zbl 0684.17008
Kirillov, A. A.; Kontsevich, M. L.; Molev, A. I.
1983
all top 5
#### Cited by 449 Authors
40 Molev, Alexander I. 27 Ragoucy, Eric 23 Futorny, Vyacheslav M. 16 Regelskis, Vidas 14 Jing, Naihuan 11 Crampé, Nicolas 10 Mukhin, Evgeny 10 Nazarov, Maxim Leonidovich 10 Rybnikov, Leonid Grigor’evich 10 Zhao, Kaiming 9 Frappat, Luc 9 Guay, Nicolas 8 Liu, Ming 8 Ramirez, Luis Enrique 7 Belliard, Samuel 7 De Sole, Alberto 7 Doikou, Anastasia 7 Finkelberg, Michael Vladlenovich 7 Khoroshkin, Sergey M. 7 Lávička, Roman 7 Mudrov, Andrey I. 7 Slavnov, Nikita A. 7 Varchenko, Alexander Nikolaevich 6 Frassek, Rouven 6 Itoh, Minoru 6 Kac, Victor G. 6 Liu, Genqiang 6 Ovsienko, Sergei A. 6 Stukopin, Vladimir Alekseevich 6 Tarasov, Vitaly Olegovich 6 Valeri, Daniele 6 Wendlandt, Curtis 6 Zhang, Ruibin 5 Arnaudon, Daniel 5 Baseilhac, Pascal 5 Brackx, Fred F. 5 Eelbode, David 5 Feĭgin, Boris L’vovich 5 Kirschner, Roland 5 MacKay, Niall J. 5 Ol’shanskiĭ, Grigoriĭ Iosifovich 5 Pak, Igor 5 Pakuliak, Stanislav Z. 5 Peng, Yung-Ning 5 Schwarz, João Fernando 5 Staudacher, Matthias 4 Arakawa, Tomoyuki 4 Avan, Jean 4 Chekhov, Leonid O. 4 Derkachov, Sergey É 4 Guo, Xiangqian 4 Hartwig, Jonas T. 4 Ikeda, Takeshi 4 Isaev, Alexei P. 4 Kim, Sangjib 4 Kožić, Slaven 4 Lu, Kang 4 Madan, Dilip B. 4 Mazzocco, Marta 4 Mihalcea, Leonardo Constantin 4 Morales, Alejandro H. 4 Naruse, Hiroshi 4 Panova, Greta 4 Poulain D’Andecy, Loïc 4 Raeymaekers, Tim 4 Soucek, Vladimir 4 Tsymbaliuk, Aleksander 4 Vicedo, Benoît 4 Yong, Alexander 4 Young, Charles A. S. 3 Artamonov, Dmitry V. 3 Billig, Yuly 3 Brown, Jonathan S. 3 Brundan, Jonathan 3 Chervov, Alexander Viktorovich 3 Chicherin, Dmitry 3 Conley, Charles H. 3 Creutzig, Thomas 3 De Schepper, Hennie 3 Donnelly, Robert G. 3 Falqui, Gregorio 3 Golubeva, Valentina Alekseevna 3 Grantcharov, Dimitar 3 Gurevich, Dmitrii 3 Liashyk, Andrii 3 łukowski, Tomasz 3 Meneghelli, Carlo 3 Neretin, Yuriĭ Aleksandrovich 3 Ogievetsky, Oleg V. 3 Procházka, Tomáš 3 Rimányi, Richárd 3 Rubtsov, Vladimir Nikolaevich 3 Sahi, Siddhartha 3 Saponov, Pavel A. 3 Sepanski, Mark R. 3 Serganova, Vera V. 3 Tang, Xiaomin 3 Tomasini, Guillaume 3 Torrielli, Alessandro 3 Tsuboi, Zengo ...and 349 more Authors
all top 5
#### Cited in 111 Serials
42 Advances in Mathematics 38 Journal of Algebra 32 Journal of Mathematical Physics 28 Letters in Mathematical Physics 26 Communications in Mathematical Physics 23 Nuclear Physics. B 19 Journal of High Energy Physics 13 Theoretical and Mathematical Physics 12 Selecta Mathematica. New Series 11 Transactions of the American Mathematical Society 9 Journal of Geometry and Physics 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Journal of Algebraic Combinatorics 6 Communications in Algebra 6 Mathematische Zeitschrift 6 Transformation Groups 6 Algebras and Representation Theory 5 Representation Theory 5 Journal of Statistical Mechanics: Theory and Experiment 4 Reviews in Mathematical Physics 4 Functional Analysis and its Applications 4 Journal of Combinatorial Theory. Series A 4 Advances in Applied Mathematics 4 Journal of Mathematical Sciences (New York) 4 Journal of the European Mathematical Society (JEMS) 4 Journal of Algebra and its Applications 4 Journal of Physics A: Mathematical and Theoretical 4 São Paulo Journal of Mathematical Sciences 3 International Journal of Modern Physics A 3 Israel Journal of Mathematics 3 Journal of Pure and Applied Algebra 3 Proceedings of the American Mathematical Society 3 Czechoslovak Journal of Physics 3 Annals of Finance 3 Arnold Mathematical Journal 3 Algebraic Combinatorics 2 Discrete Mathematics 2 Mathematical Methods in the Applied Sciences 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Annales de l’Institut Fourier 2 Compositio Mathematica 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Mathematische Annalen 2 International Journal of Mathematics 2 Linear Algebra and its Applications 2 St. Petersburg Mathematical Journal 2 Séminaire Lotharingien de Combinatoire 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Journal of the Australian Mathematical Society 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Complex Analysis and Operator Theory 2 Science China. Mathematics 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Theory of Probability and its Applications 1 Beiträge zur Algebra und Geometrie 1 Acta Mathematica Vietnamica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Glasgow Mathematical Journal 1 Inventiones Mathematicae 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Monatshefte für Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 SIAM Journal on Computing 1 Transactions of the Moscow Mathematical Society 1 Topology and its Applications 1 European Journal of Combinatorics 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Journal of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 Forum Mathematicum 1 International Journal of Algebra and Computation 1 Geometric and Functional Analysis. GAFA 1 Bulletin of the American Mathematical Society. New Series 1 Computational Complexity 1 Algebra Colloquium 1 Advances in Applied Clifford Algebras 1 The Electronic Journal of Combinatorics 1 Sbornik: Mathematics 1 Izvestiya: Mathematics 1 Documenta Mathematica 1 Finance and Stochastics 1 Mathematical Physics, Analysis and Geometry 1 Mathematical Methods of Operations Research 1 Communications in Contemporary Mathematics 1 Lobachevskii Journal of Mathematics 1 Annales Henri Poincaré 1 Foundations of Computational Mathematics 1 Quantum Information Processing ...and 11 more Serials
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#### Cited in 40 Fields
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The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-03-07T00:16:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5523687601089478, "perplexity": 6539.774429736393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178375529.62/warc/CC-MAIN-20210306223236-20210307013236-00527.warc.gz"} |
http://physics.nist.gov/Pubs/Methane/chap162.html | ## Methane Symmetry Operations
#### 16.2 Coupling of vibrational and rotational basis functions
Let us now apply (eq. 59) to two examples. First consider the coupling of vibrational and rotational angular momenta already discussed in Section 14. The functions | k J m⟩ are eigenfunctions of the operators J2, J, and the functions | L ⟩ are eigenfunctions of the operators s2, sz , with s = 3 or 4. Furthermore, these two sets of eigenfunctions transform, as given in (eq. 33) and (eq. 48), according to the irreducible representations D(J) and D(L) of the continuous three-dimensional rotation group (or according to Dg(J) and Du(L), for L = 1, of the continuous three-dimensional rotation-reflection group).
We wish to construct eigenfunctions of the operators J2, s2, R2 ≡ (J + s)2 and R. According to (eq. 59) we have
(eq. 60)
Eigenfunctions on the left with fixed J, m, , and R transform according to the irreducible representation D(R) of the continuous three-dimensional rotation group when both rotational and vibrational variables are subjected to "point-group-type" rotations.
Two interesting points arise here. First, the quantum number R represents an approximation to the purely rotational angular momentum, since R is the difference between the total angular momentum and 1/ζs times the vibrational angular momentum.
The second point is something of an anomaly. The quantum number determines the amount of vibrational angular momentum and the transformation properties of the vibrational wave functions. On the other hand, the quantum number J determines the amount of total (vibration-rotation) angular momentum and the transformation properties of the rotational wave functions, while the quantum number R gives an approximation to the amount of rotational angular momentum and determines the transformation properties of the total (vibration-rotation) wave functions.
Since the eigenfunctions | J m R kR ⟩ with = 1 transform according to the representation Du(R) of the continuous three-dimensional rotation-reflection group, Table 14 immediately gives the Td symmetry species which can occur for given values of J, = 1 and R. The three groupings of υ3 = 1 symmetry species in Figure 5 correspond to Td species for Du(R) with R = 7, 6, 5.
#### 16.3 Coupling of nuclear spin basis functions
Consider now the introduction of nuclear spin. We can couple the laboratory-fixed projections mI of the nuclear spin functions | ΓI mI ⟩ with the laboratory-fixed projections m of the rovibrational functions | J m R kR ⟩ to obtain eigenfunctions of the operators F2 ≡ (J + I)2 and FZ. Since the laboratory-fixed components of both J and I commute with the ordinary [29] sign of i, atomic coupling formalism can be used immediately. We obtain
(eq. 61)
Furthermore, since the coupling in (eq. 61) involves projections along a laboratory-fixed axis, the continuous three-dimensional rotation-reflection group is the appropriate symmetry group to consider, and no reduction of D(F) into species of the group Td is to be performed. Also, the coupling in (eq. 61) is not a recoupling in the usual sense; summation is over an as yet unused projection m of one of the already coupled angular momenta J, a situation which does not arise in atomic problems.
There remain some considerations associated with the point group Td which have yet to be taken into account. From an examination of transformation properties under point-group rotations and under laboratory-fixed rotations, it can be shown that quantum numbers of the functions |k J m⟩ and |Γ I m⟩ are analogous in pairs: J and I determine the magnitude of angular momentum involved; m and mI determine its projection along the laboratory-fixed Z axis as well as transformation properties of the functions under laboratory-fixed rotations; and k and Γ determine transformation properties under point-group rotations. Unfortunately, as can be seen by evaluating the appropriate commutation relations, it is not possible simultaneously to quantize nuclear spin projections along one laboratory-fixed axis and one molecule-fixed axis, as is done for the total angular momentum J. Thus, the pairwise analogy is not quite exact.
In any case, the nuclear spin functions transform as indicated in Table 15 and Table 16 under the Td point-group operations. The rovibrational functions transform as indicated in (eq. 33) and Table 13, with J and k replaced by R and kR, under these same operations. It is necessary to couple the value of kR with the symmetry species of the nuclear spin functions (e.g., Γ = E, E, F2, etc.) to obtain overall wave functions which transform according to irreducible representations of the point group Td and which obey the correct statistics (see Section 9.2).
The coupling of kR with the nuclear spin species is a true recoupling, since kR is itself a quantum number obtained by coupling k and L. This recoupling can be carried out using atomic formalism when the symmetry species of the nuclear spin functions of given total spin I correspond to the reduction of one of the species Dg ,u(j) of the three-dimensional rotation-reflection group into species of Td (e.g., F2 → Du(1), but E Dg ,u(j) for CH4). Such recoupling is probably best carried out in general, however, using irreducible tensor techniques specifically adapted for tetrahedral molecules [63]. Here, of course (as indeed at any point along the way), a reader doing numerical calculations can retreat to the point group D2, where nuclear-spin coupling becomes almost trivial [25]. | 2015-04-19T10:57:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8862485289573669, "perplexity": 965.7659981666266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246638820.85/warc/CC-MAIN-20150417045718-00181-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.federalreserve.gov/Pubs/feds/2007/200722/index.html | Finance and Economics Discussion Series: 2007-22 Screen Reader version
# Bond Risk Premia and Realized Jump Volatility*
Keywords: Unspanned Stochastic Volatility, Expected Excess Bond Returns, Expectations Hypothesis, Countercyclical Risk Premia, Realized Jump Volatility, Bi-Power Variation
Abstract:
We find that adding a measure of market jump volatility risk to a regression of excess bond returns on the term structure of forward rates nearly doubles the R^2 of the regression. Our market jump volatility measure is based on the realized jumps identified from high-frequency stock market returns using the bi-power variation technique. The significant enhancement of bond return predictability is robust to different forecasting horizons, to using non-overlapping returns and to the choice of different window sizes in computing the jump volatility. This market jump volatility factor also crowds out the price-dividend ratio in explaining much of the countercyclical movement in bond risk premia. We argue that this finding provides support for the unspanned stochastic volatility hypothesis according to which the conditional distribution of excess bond returns is affected by state variables that are not in the span of the term structure of yields and forward rates.
JEL Classification Numbers: G12, G14, E43, C22.
# 1 Introduction
The Expectations Hypothesis (EH) is well known to be a miserable failure, with bond risk premia being large and time-varying_ A regression of yield changes on yield spreads produces a negative slope coefficient instead of unity, as would be implied by the Expectations Hypothesis (Campbell and Shiller, 1991), and forward rates can predict future excess bond returns (Fama and Bliss, 1987). Indeed Cochrane and Piazzesi (2005) recently showed that using multiple forward rates to predict bond excess returns generates a very high degree of predictability, with values of around 30-40 percent. Authors have also used the ARCH in mean (ARCH-M) model to relate excess bond returns to the conditional volatility of those excess returns including Engle, Lilien, and Robins (1987). They found that both conditional variance and the term structure variables had explanatory power for excess bond returns.
The ARCH-M model is a useful tool for considering the relationship between volatility and excess bond returns. But in the last few years, much progress has been made in using high-frequency data to obtain realized volatility estimates. Further, if we observe high-frequency data on the price of an asset, and assume that jumps in the price of this asset are both rare and large, then Barndorff-Nielsen and Shephard (2004), Andersen, Bollerslev, and Diebold (2006), and Huang and Tauchen (2005) show how to detect the days on which jumps occur and how to estimate the magnitude of these jumps. These estimates all have the advantage of being model-free--it has to be assumed that asset prices follow a jump diffusion process, but no specific parametric model needs to be estimated. It then seems natural to try to relate realized volatility and the distribution of jumps to bond risk premia (Tauchen and Zhou, 2006).
Ideally, we would like to study the relationship between risk premia for holding a bond over a given holding period and investors' ex-ante forecasts of volatility and the jump density over that same period. Unfortunately these forecasts are not observed. But, we can easily construct backward-looking rolling estimates of realized volatility, jump intensity, jump mean and jump volatility. Then, treating these as proxies for forecasts of realized volatility, jump intensity, jump mean and jump volatility over the holding period, we can ask whether these risk measures are priced. With this motivation, this paper augments some standard regressions for excess bond returns with measures of realized volatility, jump intensity, jump mean and jump volatility constructed from five-minute S&P500 intraday returns. We also consider using realized jump risk measures constructed from five-minute bond returns, although the theoretical motivation for using the S&P500 returns to construct the jump measure seems strongest, because this is the usual proxy for the market returns of investors.
Our key finding is that augmenting regressions of excess bond returns on forward rates with realized stock market jump volatility greatly increases the predictability of excess bond returns, with values nearly doubling from 24-29 percent to 48-52 percent (our sample is shorter than that used by Cochrane and Piazzesi (2005) and yields a somewhat smaller than they obtained). This result is consistent with Tauchen and Zhou (2006), who find that this jump volatility measure can predict the credit spreads better than interest rate factors and volatility factors including option-implied volatility. In contrast, inclusion of other high-frequency jump measures--jump intensity and jump mean--in the equation for predicting excess bond returns raises the by at most a couple of percentage points. And, if we augment the regression of excess bond returns on forward rates with realized volatility (instead of any of these jump risk measures), the coefficient on realized volatility is significantly positive, but the goes up only to 35-40 percent.
We relate this finding to the recent literature on unspanned stochastic volatility (USV). USV is the hypothesis that bond markets are incomplete and that there is at least one state variable that drives innovations in bond derivatives prices but not innovations in bond yields. As pointed out by Collin-Dufresne and Goldstein (2002), if the bond market is complete, then bond yields can be written as an invertible function of the state variables and so the state variables lie in the span of the term structure of yields. On the other hand, under the USV hypothesis, the state variables do not lie in the span of the term structure of yields. Since expected excess bond returns are a function of the state variables, we argue that this gives a direct test of the USV hypothesis. Similar reasoning is used by Almeida, Graveline, and Joslin (2006) and Joslin (2007). If the USV hypothesis is false, then expected excess bond returns should be spanned by the term structure of yields and so in a regression of excess bond returns on term structure variables and any other predictors, the inclusion of enough term structure control variables should always cause the other predictors to become insignificant. On the other hand, if the USV hypothesis is correct, then the other predictors may be significant as long as they are correlated with the unspanned state variable that does not drive innovations in bond yields but affects the conditional mean of bond yields.
Thus, we interpret our finding that jump volatility is a highly significant predictor of excess bond returns even after controlling for the term structure of forward rates as strong evidence for the USV hypothesis. The USV interpretation is also consistent with the earlier ARCH-M evidence that controlling for the term structure does not eliminate the return-risk trade-off effect on government bond market. Recent work by Ludvigson and Ng (2006) finds that some extracted macroeconomic factors have additional forecasting power for expected bond returns in addition to the information in forward rates and by the same token this is also evidence for the USV hypothesis. Jump volatility however produces a larger improvement in predictive power than these macroeconomic factors and as such represents stronger evidence for USV.
We perform a number of robustness checks, including shortening the holding period, changing the size of the rolling window used to construct the jump measures, using only non-overlapping data, and continue to find an important role for market jump risk in forecasting excess bond returns. The information content of jump volatility seems to complement that of forward rates, such that the of the regression on both jump volatility and forward rates is a good bit larger than the from the regression on either variable alone.
Our measure of jump volatility is highly correlated with the price-dividend ratio. We find that in a regression of excess equity returns on jump volatility and the price-dividend ratio, the two predictors are jointly significant but neither is individually significant. In contrast, augmenting our excess bond return forecasting equations with the price-dividend ratio does little to change the significance of jump volatility. In this sense, although both jump volatility and the price-dividend ratio are informative about the cash flow risk, it is the jump volatility that contains more information about discount rate risk.
Standard affine models can explain the violation of the EH only with quite unusual model specifications that may be inconsistent with the second moments of interest rates (Bansal, Tauchen, and Zhou, 2004; Roberds and Whiteman, 1999; Dai and Singleton, 2000). However, much progress has been made recently in constructing models that may explain some of the predictability patterns in excess bond returns. These include models with richer specifications of the market prices of risk or preferences (Dai and Singleton, 2002; Duarte, 2004; Duffee, 2002; Wachter, 2006) and models with regime shifts. For example, Bansal and Zhou (2002), Ang and Bekaert (2002), Evans (2003), and Dai, Singleton, and Yang (2006) use regime-switching models of the term structure to identify the effect of economic expansions and recessions on bond risk premia. Such nonlinear regime-shifts models and the unspanned stochastic volatility hypothesis may be almost observationally equivalent.
The rest of the paper is organized as follows: the next section discusses the jump identification mechanism based on high-frequency intraday data, then Section 3 contains the empirical work on using realized jump volatility to forecast excess bond returns, Section 4 discusses the relationship with the literature on unspanned stochastic volatility in more detail, and Section 5 concludes.
# 2 Econometric Estimation of Jump Volatility Risk
In this section, we discuss our econometric method for constructing market jump risk measures, which may potentially constitute unspanned volatility factors in predicting excess returns above and beyond those obtained from current yields or forward rates.
Assuming that the stock market price follows a jump-diffusion process (, ), this paper takes a direct approach to identify realized jumps based on the seminal work by Barndorff-Nielsen and Shephard (2006,2004). This approach uses high-frequency data to disentangle realized volatility into separate continuous and jump components (see, Andersen, Bollerslev, and Diebold, 2006; Huang and Tauchen, 2005, as well) and hence to detect days on which jumps occur and to estimate the magnitude of these jumps. The methodology for filtering jumps from bi-power variation is by now fairly standard, but we review it briefly, to keep the paper self-contained.
Let denote the time logarithmic price of an asset, which evolves in continuous time as a jump diffusion process:
(1)
where and are the instantaneous drift and diffusion functions that are completely general and may be stochastic (subject to the regularity conditions), is the standard Brownian motion, is a Poisson jump process with intensity , and refers to the corresponding (log) jump size distributed as Normal. Note that the jump intensity, mean and volatility are all allowed to be time-varying in a completely unrestricted way. Time is measured in daily units and the intra-daily returns are defined as follows:
(2)
where refers to the within-day return on day , and is the sampling frequency within each day.
Barndorff-Nielsen and Shephard (2004) propose two general measures for the quadratic variation process--realized variance and realized bi-power variation--which converge uniformly (as or ) to different functionals of the underlying jump-diffusion process,
(3) (4)
Therefore the difference between the realized variance and bi-power variation is zero when there is no jump and strictly positive when there is a jump (asymptotically). This is the basis of the method for identifying jumps.
A variety of specific jump detection techniques are proposed and studied by Barndorff-Nielsen and Shephard (2004), Andersen, Bollerslev, and Diebold (2006), and Huang and Tauchen (2005). Here we adopted the ratio statistics favored by their findings,
(5)
which converges to a standard normal distribution with appropriate scaling
(6)
This test has excellent size and power properties and is quite accurate in detecting jumps as documented in Monte Carlo work (Huang and Tauchen, 2005).1
Following Tauchen and Zhou (2006), we further assume that there is at most one jump per day and that the jump size dominates the return when a jump occurs. These assumptions allow us to filter out the daily realized jumps as
sign (8)
where is the cumulative distribution function of a standard Normal, is the significance level of the -test, and I is the resulting indicator function that is one if and only if there is a jump during that day.
Once the jumps have been identified, we can then estimate the jump intensity, mean and variance as,
with appropriate formulas for the standard error estimates.
These "realized" jump risk measures can greatly facilitate our effort of estimating various risk premia of interest. The reason is that jump parameters are generally very hard to pin down even with both underlying and derivative assets prices, due to the fact that jumps are latent in daily return data and are rare events in financial markets.2. Direct identification of realized jumps and the characterization of time-varying jump risk measures have important implications for interpreting financial market risk premia.
# 3 Predicting Excess Bond Returns
If jump risk were priced, then the risk premium on any asset over a given holding period should be related to the forecast of the jump density over that holding period. In particular, excess returns on longer term bonds over those on shorter maturity bonds should be related to the forecast of the jump density. The methodology that we described in the previous section allows us to identify and estimate jumps and to construct backward-looking rolling estimates of jump mean, jump intensity and jump volatility. These may in turn be good proxies for the forecasts of future jump mean, jump intensity and jump volatility, and they have the important advantage of being completely model-free--no model has to be specified or estimated to construct them. Accordingly, these rolling jump risk measures may be correlated with risk premia, and may be useful for predicting excess bond returns. Investigating this possibility empirically is the focus of the remainder of this section.
## 3.1 Variable Definitions and Empirical Strategy
Our measures of realized volatility, jump mean, jump intensity and jump volatility are based on data on the S&P500 index at the five-minute frequency from January 1986 to December 2005, provided by the Institute of Financial Markets. The data cover the period from 9:30am to 4:00pm New York time each day, for a total of 78 observations per day and can be used to construct continuously compounded returns as the log difference in price index quotes. Using these data and the methods described in the previous section, we constructed the realized volatility at the daily frequency, tested for jumps on each day, and estimated the magnitude of the jumps on those days when jumps were detected. Let denote the dummy that is 1 if and only if a jump is detected on day and recall that denotes the estimated magnitude of the jump on day . For our empirical work, let the -month rolling average realized volatility, jump intensity, jump mean, and jump volatility be defined as, respectively,
where the means and volatilities are calculated only over days where jumps are detected. Realized volatility can be estimated arbitrarily accurately with a fixed span of sufficiently high-frequency data (abstracting from issues of market microstructure noise), whereas this is not true for jump intensity, mean or volatility. For this reason, while we use a relatively short rolling window for estimating realized volatility ( equal to one month), we use much longer rolling windows for measuring jump intensity, jump mean and jump volatility, setting the parameter to 24 months or 12 months. The tradeoff in selecting is, of course, that a shorter window gives a more noisy, but more timely, measure of agents' perceptions of jump risk. Figure 1 shows plots of the 24-month rolling jump intensity, jump mean and jump volatility, respectively. This measure of jump volatility rose during the recession of the early 1990s, and rose more sharply in the most recent recession, but has been drifting down since late 2001.
Tauchen and Zhou (2006) use these realized jump risk measures to forecast corporate bond spreads, and find that the realized jump volatility measure can predict these spreads better than interest rate factors and volatility factors including option-implied volatility. In this paper, we use these realized jump risk measures to forecast excess bond returns. The excess return on holding an -month bond over the return on holding an -month bond for a holding period of months is given by where denotes the annual continuously compounded yield on a -month zero coupon bond and is the log price of this bond. We used end-of-month data on zero-coupon yields and the three-month risk-free rate from the CRSP Fama-Bliss data, and hence constructed these excess returns.
All the regressions for excess bond returns that we consider in this paper are nested within the specification
(9)
where denotes the -year forward rate with a 12-months period and , , and denote the realized volatility and jump measures in rolling windows ending on the last day of month , constructed from high-frequency equity data as defined earlier. Using just the forward rates gives the regression of Cochrane and Piazzesi (2005), except that, following Bansal, Tauchen, and Zhou (2004), we use three forward rates instead of five, to minimize the near-perfect collinearity problem. But we also consider the predictive power of rolling realized volatility and jump risk variables.
Some summary statistics for these variables are given in Table 1. Realized equity volatility is about 11.5 percentage points (expressed in annualized terms) with a standard deviation of about 5 percentage points. The means of our jump intensity, jump mean and jump volatility measures are 13 percent, 0.06 percentage points and 0.50 percentage points, respectively. Turning to the correlation structure, the excess returns and forward rates are highly collinear. Realized volatility and jump volatility are positively correlated with excess returns. Jump volatility has a strong negative correlation with forward rates (-0.67 to -0.63). The correlation between realized volatility and jump volatility is 0.63, which is not surprising since jump volatility is a component of realized volatility. Now we turn to the main empirical finding in this paper.
## 3.2 The Main Result
Table 2 shows coefficient estimates, associated t-statistics and values for several specifications setting (one-year holding period) and (two-year rolling windows in constructing jump risk measures) where the maturity of the longer-term bond is set to 24, 36, 48 and 60 months. Forward rates are included in all specifications in this table. The forward rates show the familiar "tent-shaped" pattern, are often individually significant, and always jointly overwhelmingly significant, with an in the range 24-29 percent, which is considerable, although somewhat lower than reported for a different sample period by Cochrane and Piazzesi (2005). But if we add jump volatility to the regression of excess returns on forward rates, the coefficient on jump volatility is positive and statistically significant for each and the rises to 48-52 percent. All else equal, higher jump volatility is estimated to lead investors to demand higher future excess returns on longer-maturity bonds. Adding realized volatility to the regression of excess returns on forward rates also improves the fit notably (Table 2), and the coefficient on realized volatility is statistically significant, which is to be expected since jump volatility is a component of realized volatility. However, the significance and magnitude of the improvement in is quite a bit weaker. Meanwhile jump mean and jump intensity have no significant predictive power for excess bond returns. This is true for all choices of the maturity of the longer-term bond, .
Table 3 shows the same regressions as Table 2, except omitting the forward rates. If we do not control for the term structure of forward rates, jump volatility remains positively related to future excess returns, but not significantly so. Jump volatility is clearly not the only variable with predictive power for future excess returns, but it seems to add predictive power over and above the term structure of forward rates that is both statistically and economically significant. And, the information content of jump volatility seems to complement that of forward rates, in that the of the regression on both jump volatility and forward rates is larger than the on either of the variables separately. Controlling for jump volatility does not change the coefficients on the forward rates greatly, suggesting that the term structure of forward rates and jump volatility are measuring different components of bond risk premia. This result is completely in line with the hypothesis of unspanned stochastic volatility (see Section 4), in that the jump volatility risk factor is not spanned by the current term structure but can forecast bond excess returns above and beyond those achieved by current forward rates.
The ex-post excess returns on holding long term bonds (Figure 2, top panel) averaged around zero during the expansion during the mid and late 1990s, with positive excess returns at some times being offset by negative excess returns as the Federal Open Market Committee (FOMC) was tightening monetary policy during 1994 and around the time of the 1998 Long-Term Capital Management (LTCM) crisis. On the other hand, the excess returns were large and positive during and immediately after the 1990 and 2001 recessions. The predicted excess returns using only the forward rate term structure (middle panel) shows some of this countercyclical variation, but are positive for nearly all of the 1990s and so, on average, overpredict excess returns during these years, while underpredicting excess returns during and immediately after the most recent recession. However, adding the market jump volatility risk measure (bottom panel), the model correctly predicts an average risk premium around zero during most of the 1990s, including negative excess returns in 1994 and 1998, and it is also more successful in predicting high returns during and immediately after the most recent recession. Jump volatility has declined since the last recession, and this may indeed help explain some of the recent decline in longer maturity yields that was referred to by former Federal Reserve Chairman Greenspan as a "conundrum" (discussed further in Kim and Wright, 2005), although jump volatility in 24-month windows ending at the end of our sample is still not especially low by historical standards.
## 3.3 Robustness Checks
It is well known that severe small-sample size distortions may arise in return prediction regressions with highly persistent regressors and overlapping returns.3 To mitigate this problem, we re-ran our regressions using non-overlapping data. Table 4 shows the results from the same regressions as in Table 2 (i.e. setting and and various values of ), but using only the forward rates of each December, so that the holding periods do not overlap. The results are very similar to those in Table 2, and the jump volatility measure is highly significant, though realized volatility is not. The overall predictability increases from 20-26 percent when using only forward rates to 42-45 percent when jump volatility is included.
Tables 2-4 follow Cochrane and Piazzesi (2005) in considering a one-year holding period (). But, since we have only 18 non-overlapping periods in our sample, giving a quite small effective sample size, it also seems appropriate to consider results with a one-quarter holding period (), for which there are four times as many non-overlapping periods.4 These results are shown in Table 5. The values are lower at this shorter horizon, but jump volatility is again consistently positively and significantly related to future excess bond returns, once we control for the forward rates. Realized volatility is significant at the 5 percent level for two of the four maturities. The other realized jump measures have no significant association with future excess returns.
For the parameter (rolling window size for jump risk measures), we want to pick a value that is large enough not to give noisy estimates, but small enough to give timely measures of agents' perceptions of jump risk. A range of reasonable choices might be from 6 to 24 months, and our results are not very sensitive to varying over this range. For example, Table 6 shows the results with overlapping data at the one-year horizon () and choosing a shorter rolling window for estimating jump statistics . These results are very similar to those in Table 2, in that the total predictability of bond risk premia is nearly doubled with jump volatility included. The slope coefficient for jump volatility remains positive and highly significant.
## 3.4 Realized Volatility and Jump Measures Using Bond Data
We also investigated regressing excess returns on the term structure of forward rates and realized volatility and jump measures as in Table 2, except using 30-year Treasury bond futures to construct the realized volatility and jump measures rather than stock price data. We obtained five-minute data on Treasury bond futures from RC Research using the same sample period as before, to make the results comparable.
The results are shown in Table 7. Neither bond realized volatility nor bond jump volatility is statistically significant as a predictor of bond excess returns and the improvement in from including these variables is very slight. This is consistent with the finding in Andersen and Benzoni (2006) that bond realized volatility is not spanned by the bond yields, although our approach is different in that we are predicting excess bond returns.
The inclusion of bond jump intensity does not help predict bond excess returns either. However, the bond jump mean is significantly negative as a predictor of excess bond returns implying that downward jumps in bond prices are followed by large positive excess returns. Indeed, adding the bond jump mean to the regression of excess bond returns on forward rates can nearly double the . This suggests that the bond jump mean may act as an unspanned stochastic mean factor that cannot be hedged with the current yields but can forecast bond excess returns, which is again consistent with the multi-factor model of incomplete fixed-income market examined by Collin-Dufresne, Goldstein, and Jones (2006a).
## 3.5 Forecasting Excess Stock Returns
The empirical link between the equity risk premium and macro-finance state variables has been well established (see, e.g., Campbell and Shiller, 1988b,a; , ; Fama and French, 1988), but it seems interesting to examine whether the jump variables that help predict excess bond returns might also have some incremental predictive power for excess stock returns. To investigate this, we augmented the usual dividend-yield regression for predicting excess stock returns with our measures of realized volatility and market jump risk. The three-month excess returns on the stock market are given by , where is the return on the S&P500 dividend-inclusive index from the end of month to the end of month and is the three-month risk-free rate from the CRSP Fama-Bliss data at the end of month . The regressions for excess stock returns that we consider are nested within the specification
(10)
where denotes the log price-dividend ratio for month and , , and denote the realized volatility and jump measures in rolling windows ending on the last day of month .
The results are reported in Table 8. Consistent with the existing literature, the price-dividend ratio can predict a small share of return variation (4 percent), and is just statistically significant. On the other hand, none of the high-frequency based risk measures has any detectable predictive power, except for the jump volatility which on its own gives an of 7 percent and is statistically significant. Using both the price-dividend ratio and realized jump volatility as predictors, neither is statistically significant separately (though they are jointly significant), and the remains at about 7 percent, suggesting that the dividend yield and jump volatility contain similar information about cash flow risk. Note that the sign of the slope coefficient on the jump volatility variable is negative, meaning that higher jump volatility is associated with lower equity risk premia. This is puzzling, but many papers have found the relationship between equity risk and return to be unstable and possibly even to have the wrong sign (see, for example Chou, Engle, and Kane, 1992; Bollerslev and Zhou, 2006; Glosten, Jagannathan, and Runkle, 1993; Campbell, 1987; Turner, Startz, and Nelson, 1989; Lettau and Ludvigson, 2003; Breen, Glosten, and Jagannathan, 1989, among others). A re-examination of this puzzle may be fruitful along the line of Guo and Whitelaw (2006).
The price-dividend ratio covaries positively with jump volatility (with a correlation coefficient of 0.67), consistent with the finding that adding the price-dividend ratio to a regression of excess stock returns on jump volatility leaves the about unchanged. This positive correlation can be seen in Figure 3, which shows the time series of both the price-dividend ratio and jump volatility. Both variables appear countercyclical and reflect the aggregate cash flow risk embedded in stock excess returns. Motivated by this, and the fact that some researchers including Fama and French (1989) have found that the dividend yield helps predict excess bond returns as well as excess stock returns, we investigated augmenting the regressions for excess bond returns shown in Table 2 with the stock price-dividend ratio. As seen in Table 9, in these regressions the jump volatility remains statistically significant, while the coefficient on the price-dividend ratio is not significantly different from zero. Thus, although both jump volatility and the price-dividend ratio are informative about the cash flow risk in equity returns, it is the jump volatility that contains more information about the discount rate risk in bond returns.
# 4 Economic Interpretation under Incomplete Markets
In this section, we discuss in more detail the interpretation of regressions of excess bond returns on term structure control variables and other predictors under the incomplete market setting with unspanned stochastic volatility. Under incomplete markets with affine factor dynamics (Collin-Dufresne and Goldstein, 2002), bond yields alone cannot hedge the unspanned volatility risk. However, an important feature of the USV model is that the unspanned risk factor affects the conditional mean and volatility functions of other spanned risk factors (see, Singleton, 2006, pages 322-325). Therefore expected excess bond returns depend not only on the bond yields through the spanned risk factors, but also on the unspanned risk factor. This link provides an explanation for the earlier finding of the ARCH-in-mean effect in bond market (Engle, Lilien, and Robins, 1987), even after controlling for the term structure of yields.
## 4.1 Unspanned Stochastic Volatility
Recent empirical tests find strong evidence for the existence of unspanned stochastic volatility (see, , ; Casassus, Collin-Dufresne, and Goldstein, 2005; Heidari and Wu, 2003; Collin-Dufresne, Goldstein, and Jones, 2006a; Li and Zhao, 2005; Andersen and Benzoni, 2006, among others).5 The regression of options-implied or estimated volatilities on bond yields is a valid test for the existence of USV, subject to the proper controls for specification error and measurement error in extracting these volatility measures. However, an alternative way is to test the USV implication that the unspanned volatility must predict the bond excess returns above and beyond what can be predicted by the current yields or forward rates.
We illustrate the idea with an specification (Dai and Singleton, 2000)--which is a three factor affine model with one square-root volatility factor. Following Collin-Dufresne and Goldstein (2002), all three factor affine models can be rotated such that the state vectors are the spot rate , the drift of spot rate and the variance of spot rate . The risk-neutral factor dynamics is given by
(11)
where is a three-dimensional vector of independent Brownian motions under the risk-neutral measure, is a non-negative lower bound, and is positive definite. Also, the drift and volatility parameters are restricted in the following form
The model is maximal, as defined in Dai and Singleton (2000), in that all the parameters are identifiable regardless of the data availability (, ).
Then under complete markets, all trivariate affine models have bond prices of the following form
(12)
where , , , and are solutions to a system of ordinary differential equations (Duffie and Kan, 1996). However, under incomplete markets, Collin-Dufresne and Goldstein (2002) show that bond prices can be reduced to
(13)
In other words, bond prices do not depend on the unspanned volatility. This condition further restricts the drift and volatility parameter in the model as
and (14)
In particular, the restriction makes the conditional expectation linearly depend on ; and the (1, 2) entry of matrix makes the conditional expectation linearly depend on through recursively. This feature mirrors an important stochastic volatility model in the equity option literature (Heston, 1993), where the unspanned equity volatility also affects the conditional distribution of the state vector.
## 4.2 Predicting Excess Bond Returns
The fact that unspanned stochastic volatility affects the conditional mean of the state vector has important implications for predicting excess bond returns. Letting the market price of risk process be with , we can transform to the objective dynamics
(15)
which governs the time-series evolution of the state vector.6 Aside from some special cases, the instantaneous drift under the physical measure has the same form as under the risk-neutral measure . Hence the conditional means and are also linear functions of stochastic volatility .
Under incomplete markets, with the bond pricing solution given in eq. (13), the expected excess returns for holding an -period bond over the returns on holding a - period bond for a holding period of periods can be written as
(16)
where the conditional means and are linear functions of , which is not in the span of yields. In contrast, under complete markets, the bond pricing solution given in eq. (12) implies that the expected excess bond return can be written as
(17)
and all the terms in eq. (17) are in the span of yields.
Thus, if the bond market is complete, then there should exist no macroeconomic or financial variable that can improve the population forecastability of excess bond returns once we control for the term structure of bond yields. However, if markets are incomplete, then any variable that is correlated with this unspanned volatility factor may add to the predictability of excess bond returns. Of course the challenge is how to find such a proxy for unspanned stochastic volatility. The current methods include implied volatility from fixed-income derivatives markets (e.g., Collin-Dufresne and Goldstein, 2002) and realized volatility from intraday bond prices (Andersen and Benzoni, 2006). Indeed, Almeida, Graveline, and Joslin (2006) and Joslin (2007) find that an unspanned stochastic volatility factor constructed from fixed income options markets is important for predicting bond excess returns. We instead adopt a measure of jump volatility from the equity market, which has an orthogonal innovation relative to the term structure, and find that this also has substantial forecasting power for bond excess returns.
# 5 Conclusion
There is considerable evidence of predictability in excess returns on a range of assets, but it is especially strong for longer maturity bonds, perhaps because their pricing is not complicated by uncertain cash flows. Part of the predictability may owe to time-variation in the distribution of jump risk, but empirical work on this has been hampered until recently by econometricians' difficulties in identifying jumps. Recently studies (Andersen, Bollerslev, and Diebold, 2006; Tauchen and Zhou, 2006; Huang and Tauchen, 2005; Barndorff-Nielsen and Shephard, 2004) have shown how high-frequency data can be used reliably to detect jumps and to estimate their size, under the assumption that jumps are large and rare, and these methods can then easily be used to construct rolling estimates of jump intensity, jump mean and jump volatility.
A simple implication of jump risk being priced is that these measures should have some predictive power for future excess returns. In this paper, we have found evidence that they do. Augmenting a standard regression of excess bond returns on forward rates with realized jump volatility constructed from high-frequency stock price data, we find that the coefficient on jump volatility is both economically and statistically significant. The predictability of bond risk premia can nearly be doubled by including the jump volatility risk measure. Jump volatility also dominates other risk measures constructed from high-frequency data--namely jump intensity, jump mean, and realized volatility. Although both jump volatility and the price-dividend ratio are informative about the cash flow risk in equity returns, it is the jump volatility that contains more information about the discount rate risk in bond returns.
Jump volatility appears countercyclical--peaking around the 1990 and especially the 2001 recessions. In a number of important episodes, predicted excess returns constructed using both jump volatility and the term structure of forward rates track the actual ex-post excess returns more closely than predicted excess returns constructed using forward rates alone, including during the period in 1994 when the FOMC was tightening monetary policy, the 1998 LTCM crisis, and in the most recent recession. A decline in jump volatility may also account for part of the decline in long-term yields since the FOMC began tightening monetary policy in the middle of 2004. Our result is robust to shortening the holding period, changing the size of the rolling window used to construct the jump measures and using only non-overlapping data. The tent-shape pattern of regression coefficients on the forward term structure however exists regardless whether of whether or not we control for jump volatility.
The existing literature has used implied volatility from fixed-income derivatives (e.g., Collin-Dufresne and Goldstein, 2002) and realized volatility from intraday bond prices (Andersen and Benzoni, 2006) to test the unspanned stochastic volatility hypothesis. Our finding that stock market jump volatility has significant forecasting power for excess bond returns above and beyond that obtained from forward rates alone, is also consistent with this hypothesis.
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Table 1: Summary statistics and correlation matrix for excess returns, forward rates, and jump measures
Summary statistics
Mean 0.91 1.63 2.23 2.5 4.94 6.09 6.44 11.57 0.13 0.06 0.5
Std. Dev. 1.42 2.7 3.74 4.58 2.1 1.62 1.42 5.26 0.06 0.07 0.23
Skewness -0.09 -0.16 -0.19 -0.25 -0.16 -0.18 0.18 1.27 0.37 0.2 0.87
Kurtosis 2.17 2.36 2.46 2.58 2.33 2.43 1.92 4.69 1.79 3.09 2.2
Notes: This table summarizes the main variables used in the empirical exercise. The variable definitions are the same as given in Section 3.1: are the excess returns on holding an -month bond over the return on holding an -month bond for a holding period of months; denotes the one-year forward rate ending months; and , , and denote the realized volatility and jump measures in rolling windows ending on the last day of month .
Table 1: Summary statistics and correlation matrix for excess returns, forward rates, and jump measures
Correlation matrix
R1 1 0.98 0.96 0.92 0.22 0.35 0.33 0.12 0.11 -0.1 0.16
R2 1 0.99 0.97 0.17 0.32 0.31 0.14 0.08 -0.13 0.2
R3 1 0.99 0.13 0.31 0.32 0.1 0.1 -0.17 0.19
R4 1 0.1 0.29 0.32 0.08 0.09 -0.2 0.2
R5 1 0.91 0.78 -0.27 0.09 0.41 -0.65
R6 1 0.94 -0.41 0.27 0.19 -0.67
R7 1 -0.48 0.44 -0.02 -0.63
R8 1 -0.37 0.29 0.63
R9 1 -0.44 -0.27
R10 1 -0.26
R11 1
Notes: This table summarizes the main variables used in the empirical exercise. The variable definitions are the same as given in Section 3.1: are the excess returns on holding an -month bond over the return on holding an -month bond for a holding period of months; denotes the one-year forward rate ending months; and , , and denote the realized volatility and jump measures in rolling windows ending on the last day of month .
Table 2: Excess returns on holding an n-month bond for a holding period of one year, n=24 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.37 (-1.00) -0.73 (-2.89) 1.91 -3.7 -0.89 (-1.74) 0.24
-3.97 (-2.81) -0.81 (-4.15) 1.95 -5.04 -0.65 (-1.53) 1.68 (-3.19) 0.35
-1.36 (-1.00) -0.73 (-2.88) 1.93 -3.46 -0.93 (-1.61) 0.52 (-0.1) 0.24
-0.84 (-0.59) -0.64 (-2.29) 1.99 -3.92 -1.09 (-2.09) -3.47 (-0.84) 0.25
-5.82 (-3.80) -0.58 (-2.89) 2.02 -5.67 -0.75 (-1.83) 4.25 (-4.75) 0.48
Notes: This table reports the coefficient estimates in a regression of the excess returns on a -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 2: Excess returns on holding an n-month bond for a holding period of one year, n=36 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-2.78 (-1.16) -1.6 (-3.19) 3.89 -3.71 -1.77 (-1.81) 0.25
-7.98 (-3.19) -1.76 (-4.61) 3.97 -5.02 -1.29 (-1.65) 3.36 (-3.37) 0.38
-2.83 (-1.19) -1.6 (-3.27) 3.81 -3.45 -1.63 (-1.49) -2 (-0.22) 0.26
-1.87 (-0.77) -1.44 (-2.66) 4.03 -3.83 -2.1 (-2.06) -5.96 (-0.78) 0.27
-11.6 (-4.08) -1.31 (-3.74) 4.11 -6.18 -1.48 (-1.99) 8.42 (-4.92) 0.52
Notes: This table reports the coefficient estimates in a regression of the excess returns on a -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 2: Excess returns on holding an n-month bond for a holding period of one year, n=48 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-4.6 (-1.53) -2.43 (-3.71) 5.41 -3.88 -2.19 (-1.70) 0.29
-11.33 (-3.39) -2.63 (-5.26) 5.51 -5.12 -1.58 (-1.52) 4.34 (-3.06) 0.4
-4.7 (-1.57) -2.44 (-3.85) 5.23 -3.57 -1.92 (-1.30) -4.04 (-0.35) 0.29
-3.4 (-1.13) -2.22 (-3.13) 5.59 -3.94 -2.63 (-1.90) -7.87 (-0.76) 0.3
-16.11 (-4.06) -2.05 (-4.46) 5.69 -6.08 -1.82 (-1.79) 10.99 (-4.41) 0.52
Notes: This table reports the coefficient estimates in a regression of the excess returns on a -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 2: Excess returns on holding an n-month bond for a holding period of one year, n=60 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-6.2 (-1.79) -2.96 (-3.71) 6.1 -3.56 -2.14 (-1.38) 0.28
-14 (-3.52) -3.2 (-5.20) 6.22 -4.55 -1.43 (-1.15) 5.03 (-2.77) 0.38
-6.45 (-1.86) -2.98 (-4.01) 5.65 -3.18 -1.45 (-0.80) -10.2 (-0.74) 0.29
-4.84 (-1.46) -2.73 (-3.19) 6.31 -3.58 -2.64 (-1.56) -8.93 (-0.71) 0.29
-19.98 (-4.06) -2.51 (-4.62) 6.43 -5.51 -1.7 (-1.37) 13.16 (-4.07) 0.51
Notes: This table reports the coefficient estimates in a regression of the excess returns on a -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 3: Excess returns on holding an n-month bond for a holding period of one year, n=24 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
0.52 -0.91 0.53 -0.77 0.02
0.56 -0.74 2.62 -0.5 0.01
1.04 -2.37 -2.08 (-0.45) 0.01
0.4 -0.66 1 -0.9 0.03
Notes: As for Table 2, except that the predictors are realized volatility and jump risk measures without controlling for forward rates.
Table 3: Excess returns on holding an n-month bond for a holding period of one year, n=36 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
0.81 -0.74 1.12 -0.85 0.02
1.14 -0.84 3.65 -0.39 0.01
1.94 -2.47 -5.05 (-0.60) 0.02
0.42 -0.36 2.4 -1.14 0.04
Notes: As for Table 2, except that the predictors are realized volatility and jump risk measures without controlling for forward rates.
Table 3: Excess returns on holding an n-month bond for a holding period of one year, n=48 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
1.41 -0.91 1.12 -0.61 0.01
1.35 -0.77 6.53 -0.54 0.01
-2.82 -2.67 -9.45 (-0.85) 0.03
0.65 -0.41 3.13 -1.13 0.04
Notes: As for Table 2, except that the predictors are realized volatility and jump risk measures without controlling for forward rates.
Table 3: Excess returns on holding an n-month bond for a holding period of one year, n=60 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
1.71 -0.91 1.08 -0.47 0.01
1.6 -0.77 6.76 -0.48 0.01
3.36 -2.85 -13.56 (-1.04) 0.04
0.5 -0.26 3.98 -1.24 0.04
Notes: As for Table 2, except that the predictors are realized volatility and jump risk measures without controlling for forward rates.
Table 4: Excess returns on holding an n-month bond for a holding period of one year with non-overlapping data, n=24 (Heteroskedasticity-robust t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.79 (-1.03) -0.65 (-2.29) 1.54 -1.99 -0.55 (-0.79) 0.2
-3.23 (-0.96) -0.72 (-2.72) 1.57 -2.3 -0.42 (-0.62) 1.14 -0.6 0.24
-1.79 (-1.00) -0.65 (-2.13) 1.54 -2.01 -0.54 (-0.68) -0.28 (-0.04) 0.2
-1.61 (-0.73) -0.61 (-1.75) 1.53 -2.04 -0.58 (-0.72) -0.78 (-0.10) 0.2
-5.84 (-2.73) -0.41 (-2.36) 1.52 -2.93 -0.39 (-0.67) 4.23 -3.09 0.42
Notes: As for Table 2, except that only end-of-year observations are used to avoid overlapping holding periods. Standard errors are heteroskedasticity-robust, but make no correction for serial correlation.
Table 4: Excess returns on holding an n-month bond for a holding period of one year with non-overlapping data, n=36 (Heteroskedasticity-robust t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-4.19 (-1.28) -1.46 (-2.43) 3.17 -1.92 -0.98 (-0.69) 0.23
-6.88 (-1.06) -1.59 (-2.81) 3.21 -2.18 -0.75 (-0.53) 2.11 -0.57 0.26
-4.29 (-1.26) -1.52 (-2.52) 3.16 -2.05 -0.83 (-0.53) -4.2 (-0.29) 0.24
-3.59 (-0.85) -1.34 (-1.91) 3.12 -1.97 -1.09 (-0.65) -2.7 (-0.18) 0.23
-12.23 (-2.78) -0.99 (-2.99) 3.11 -3.02 -0.67 (-0.58) 8.39 -3.07 0.45
Notes: As for Table 2, except that only end-of-year observations are used to avoid overlapping holding periods. Standard errors are heteroskedasticity-robust, but make no correction for serial correlation.
Table 4: Excess returns on holding an n-month bond for a holding period of one year with non-overlapping data, n=48 (Heteroskedasticity-robust t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-6.52 (-1.47) -2.16 (-2.65) 4.37 -1.89 -1.13 (-0.56) 0.26
-9.83 (-1.12) -2.34 (-2.96) 4.41 -2.11 -0.83 (-0.42) 2.61 -0.52 0.29
-6.69 (-1.45) -2.28 (-2.81) 4.36 -2.05 -0.86 (-0.39) -7.21 (-0.37) 0.26
-5.51 (-0.97) -1.98 (-2.05) 4.29 -1.94 -1.31 (-0.56) -4.51 (-0.22) 0.26
-17.13 (-2.66) -1.56 (-3.54) 4.29 -2.94 -0.72 (-0.43) 11.07 -2.74 0.45
Notes: As for Table 2, except that only end-of-year observations are used to avoid overlapping holding periods. Standard errors are heteroskedasticity-robust, but make no correction for serial correlation.
Table 4: Excess returns on holding an n-month bond for a holding period of one year with non-overlapping data, n=60 (Heteroskedasticity-robust t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-8.77 (-1.63) -2.51 (-2.40) 4.34 -1.48 -0.44 (-0.17) 0.25
-12.16 (-1.12) -2.68 (-2.62) 4.39 -1.6 -0.14 (-0.05) 2.67 -0.43 0.27
-9.09 (-1.61) -2.72 (-2.77) 4.33 -1.66 0.05 (-0.02) -13.29 (-0.55) 0.26
-7.89 (-1.13) -2.34 (-1.97) 4.27 -1.52 -0.6 (-0.20) -3.93 (-0.16) 0.25
-21.21 (-2.55) -1.79 (-2.99) 4.25 -2.21 0.03 (-0.01) 12.98 -2.44 0.42
Notes: As for Table 2, except that only end-of-year observations are used to avoid overlapping holding periods. Standard errors are heteroskedasticity-robust, but make no correction for serial correlation.
Table 5: Excess returns on holding an n-month bond for a holding period of 3 months, n=24 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-0.62 (-1.34) -0.42 (-2.48) 1.19 -3.16 -0.66 (-2.43) 0.12
-1.37 (-2.65) -0.44 (-2.58) 1.19 -3.19 -0.6 (-2.23) 0.55 (-2.21) 0.15
-0.63 (-1.36) -0.42 (-2.49) 1.23 -3.19 -0.72 (-2.43) 0.88 (-0.43) 0.12
-0.46 (-0.92) -0.39 (-2.14) 1.22 -3.22 -0.73 (-2.53) -1.21 (-0.70) 0.13
-2.29 (-3.21) -0.35 (-1.98) 1.22 -2.93 -0.62 (-2.13) 1.71 (-2.77) 0.2
Notes: This table reports the coefficient estimates in a regression of the excess returns on a n-month bond over those on a 3 month bond, with a holding period of 3 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 2.
Table 5: Excess returns on holding an n-month bond for a holding period of 3 months, n=36 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.02 (-1.47) -0.75 (-2.84) 1.99 -3.38 -1.08 (-2.54) 0.13
-2.15 (-2.62) -0.77 (-2.93) 1.99 -3.4 -0.98 (-2.36) 0.83 (-1.99) 0.15
-1.04 (-1.49) -0.75 (-2.84) 2.05 -3.37 -1.16 (-2.50) 1.28 (-0.41) 0.13
-0.81 (-1.08) -0.71 (-2.49) 2.03 -3.42 -1.17 (-2.59) -1.63 (-0.59) 0.13
-3.47 (-3.11) -0.64 (-2.37) 2.03 -3.13 -1.02 (-2.25) 2.5 (-2.53) 0.19
Notes: This table reports the coefficient estimates in a regression of the excess returns on a n-month bond over those on a 3 month bond, with a holding period of 3 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 2.
Table 5: Excess returns on holding an n-month bond for a holding period of 3 months, n=48 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.44 (-1.60) -0.99 (-2.80) 2.51 -3.19 -1.31 (-2.31) 0.13
-2.72 (-2.44) -1.01 (-2.87) 2.51 -3.21 -1.19 (-2.16) 0.93 (-1.62) 0.14
-1.46 (-1.60) -0.99 (-2.81) 2.57 -3.17 -1.39 (-2.25) 1.32 (-0.32) 0.13
-1.22 (-1.26) -0.95 (-2.49) 2.55 -3.23 -1.4 (-2.35) -1.71 (-0.47) 0.13
-4.44 (-2.99) -0.86 (-2.38) 2.56 -2.97 -1.23 (-2.05) 3.06 (-2.31) 0.18
Notes: This table reports the coefficient estimates in a regression of the excess returns on a n-month bond over those on a 3 month bond, with a holding period of 3 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 2.
Table 5: Excess returns on holding an n-month bond for a holding period of 3 months, n=60 (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.92 (-1.72) -1.08 (-2.42) 2.61 -2.64 -1.25 (-1.76) 0.1
-3.39 (-2.39) -1.11 (-2.49) 2.61 -2.64 -1.12 (-1.61) 1.07 (-1.49) 0.12
-1.93 (-1.71) -1.08 (-2.42) 2.64 -2.57 -1.29 (-1.65) 0.6 (-0.11) 0.1
-1.73 (-1.45) -1.04 (-2.19) 2.65 -2.66 -1.33 (-1.78) -1.46 (-0.31) 0.11
-5.35 (-2.90) -0.93 (-2.06) 2.67 -2.48 -1.16 (-1.54) 3.51 (-2.14) 0.15
Notes: This table reports the coefficient estimates in a regression of the excess returns on a n-month bond over those on a 3 month bond, with a holding period of 3 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 2.
Table 6: Excess returns on holding an n-month bond for a holding period of one year (12 month rolling jump risk estimates), n=24 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.37 (-1.00) -0.73 (-2.89) 1.91 -3.7 -0.89 (-1.74) 0.24
-3.97 (-2.81) -0.81 (-4.15) 1.95 -5.04 -0.65 (-1.53) 1.68 (-3.19) 0.35
-1.36 (-1.01) -0.73 (-2.86) 1.94 -3.39 -0.93 (-1.66) 0.56 (-0.13) 0.24
-1.27 (-0.93) -0.71 (-2.80) 1.95 -3.69 -0.95 (-1.78) -1 (-0.51) 0.24
-5.53 (-3.84) -0.7 (-4.21) 1.96 -5.94 -0.61 (-1.50) 3.72 (-4.69) 0.49
Notes: As for Table 2, except that 12 month rolling windows are used to measure the jump risk measures.
Table 6: Excess returns on holding an n-month bond for a holding period of one year (12 month rolling jump risk estimates), n=36 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-2.78 (-1.16) -1.6 (-3.19) 3.89 -3.71 -1.77 (-1.81) 0.25
-7.98 (-3.19) -1.76 (-4.61) 3.97 -5.02 -1.29 (-1.65) 3.36 (-3.37) 0.38
-2.78 (-1.19) -1.6 (-3.19) 3.88 -3.29 -1.76 (-1.57) -0.19 (-0.03) 0.25
-2.74 (-1.14) -1.59 (-3.18) 3.91 -3.55 -1.79 (-1.71) -0.37 (-0.10) 0.25
-10.65 (-4.03) -1.55 (-5.30) 4 -6.23 -1.23 (-1.65) 7.04 (-4.64) 0.5
Notes: As for Table 2, except that 12 month rolling windows are used to measure the jump risk measures.
Table 6: Excess returns on holding an n-month bond for a holding period of one year (12 month rolling jump risk estimates), n=48 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-4.6 (-1.53) -2.43 (-3.71) 5.41 -3.88 -2.19 (-1.70) 0.29
-11.33 (-3.39) -2.63 (-5.26) 5.51 -5.12 -1.58 (-1.52) 4.34 (-3.06) 0.4
-4.63 (-1.57) -2.43 (-3.72) 5.36 -3.37 -2.12 (-1.38) -1 (-0.10) 0.29
-4.68 (-1.55) -2.44 (-3.76) 5.38 -3.63 -2.15 (-1.53) 0.73 (-0.15) 0.29
-14.61 (-3.93) -2.37 (-6.07) 5.54 -6.03 -1.51 (-1.47) 8.95 (-4.05) 0.49
Notes: As for Table 2, except that 12 month rolling windows are used to measure the jump risk measures.
Table 6: Excess returns on holding an n-month bond for a holding period of one year (12 month rolling jump risk estimates), n=60 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-6.2 (-1.79) -2.96 (-3.71) 6.1 -3.56 -2.14 (-1.38) 0.28
-14 (-3.52) -3.2 (-5.20) 6.22 -4.55 -1.43 (-1.15) 5.03 (-2.77) 0.38
-6.32 (-1.86) -2.96 (-3.78) 5.86 -2.96 -1.8 (-0.94) -4.8 (-0.40) 0.28
-6.48 (-1.85) -3 (-3.85) 6 -3.26 -1.99 (-1.15) 2.59 (-0.43) 0.28
-17.78 (-3.84) -2.89 (-6.10) 6.26 -5.32 -1.35 (-1.08) 10.35 (-3.63) 0.47
Notes: As for Table 2, except that 12 month rolling windows are used to measure the jump risk measures.
Table 7: Excess returns on holding an n-month bond for a holding period of one year (Treasury futures as volatility/jump measures), n=24 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-1.37 ( -1.00) -0.73 ( -2.89) 1.91 -3.7 -0.89 ( -1.74) 0.24
-1.64 ( -1.13) -0.72 ( -2.80) 1.91 -3.82 -0.9 ( -1.78) 0.51 (-0.38) 0.24
-1.86 ( -1.11) -0.68 ( -2.50) 1.73 -2.8 -0.76 ( -1.31) 6.41 (-0.79) 0.25
-2.22 ( -2.13) -0.49 ( -2.05) 1.41 -2.91 -0.45 ( -1.05) -8.9 ( -4.18) 0.48
-0.16 ( -0.08) -0.69 ( -2.97) 1.81 -3.97 -0.82 ( -1.72) -3.08 ( -1.28) 0.26
Notes: This table reports the coefficient estimates in a regression of the excess returns on an -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized Treasury bond futures volatility and a 24 month rolling window of Treasury bond futures jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 7: Excess returns on holding an n-month bond for a holding period of one year (Treasury futures as volatility/jump measures), n=36 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-2.78 ( -1.16) -1.6 ( -3.19) 3.89 -3.71 -1.77 ( -1.81) 0.25
-3.39 ( -1.34) -1.58 ( -3.14) 3.9 -3.84 -1.79 ( -1.86) 1.17 (-0.49) 0.26
-3.37 ( -1.15) -1.54 ( -2.85) 3.68 -3.01 -1.61 ( -1.47) 7.77 (-0.55) 0.26
-4.41 ( -2.53) -1.14 ( -2.62) 2.93 -3.16 -0.92 ( -1.16) -17.2 ( -4.57) 0.51
-0.78 ( -0.21) -1.54 ( -3.40) 3.73 -3.93 -1.65 ( -1.78) -5.08 ( -1.09) 0.27
Notes: This table reports the coefficient estimates in a regression of the excess returns on an -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized Treasury bond futures volatility and a 24 month rolling window of Treasury bond futures jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 7: Excess returns on holding an n-month bond for a holding period of one year (Treasury futures as volatility/jump measures), n=48 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-4.6 ( -1.53) -2.43 ( -3.71) 5.41 -3.88 -2.19 ( -1.70) 0.29
-5.21 ( -1.62) -2.41 ( -3.65) 5.42 -3.98 -2.21 ( -1.73) 1.17 (-0.36) 0.29
-5.46 ( -1.50) -2.35 ( -3.29) 5.09 -3.13 -1.96 ( -1.37) 11.35 (-0.62) 0.29
-6.73 ( -3.06) -1.83 ( -3.25) 4.15 -3.34 -1.09 ( -1.03) -22.41 ( -4.63) 0.51
-2.81 ( -0.58) -2.37 ( -3.89) 5.27 -3.97 -2.09 ( -1.66) -4.55 ( -0.71) 0.29
Notes: This table reports the coefficient estimates in a regression of the excess returns on an -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized Treasury bond futures volatility and a 24 month rolling window of Treasury bond futures jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 7: Excess returns on holding an n-month bond for a holding period of one year (Treasury futures as volatility/jump measures), n=60 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-6.2 ( -1.79) -2.96 ( -3.71) 6.1 -3.56 -2.14 ( -1.38) 0.28
-7.01 ( -1.87) -2.93 ( -3.65) 6.11 -3.66 -2.17 ( -1.41) 1.55 (-0.4) 0.28
-6.93 ( -1.71) -2.89 ( -3.35) 5.83 -2.99 -1.95 ( -1.16) 9.63 (-0.46) 0.28
-8.78 ( -3.58) -2.23 ( -3.34) 4.58 -3.03 -0.81 ( -0.64) -27.11 ( -4.71) 0.5
-5.04 ( -0.86) -2.92 ( -3.80) 6.01 -3.57 -2.08 ( -1.36) -2.96 ( -0.37) 0.28
Notes: This table reports the coefficient estimates in a regression of the excess returns on an -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized Treasury bond futures volatility and a 24 month rolling window of Treasury bond futures jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 8: Excess returns on S&P500 market index over a 3-month bill for a holding period of 3 months (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-0.01 (-0.64) -0.04 (-2.04) 0.04
-0.04 (-1.35) -0.05 (-2.41) 0.03 (-1.01) 0.05
(-0.08) -0.05 (-2.79) -0.12 (-1.13) 0.05
-0.01 (-0.94) -0.04 (-2.18) 0.07 (-0.67) 0.05
0.04 (-1.17) -0.1 (-0.40) -0.07 (-1.44) 0.07
0.02 (-1.46) -0.01 (-0.29)
0.01 (-0.44) 0.06 (-0.46)
0.02 (-1.95) 0.01 (-0.11)
0.06 (-3.32) -0.08 (-2.24) 0.07
Notes: This table reports the coefficient estimates in a regression of three-month excess returns of S&P500 market index, on log price-dividend ratio, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, constructed as described in the text. Observations are at the quarterly frequency (end-of-quarter). Standard errors are heteroskedasticity-robust, but make no correction for serial correlation.
Table 9: Excess returns on holding an n-month bond for a holding period of one year--market jump volatility versus price-dividend ratio, n=24 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-3.16 ( -2.78) -0.74 ( -4.15) 1.56 (-3.59) ( -0.01) 2.26 (-2.51) 0.36
-4.54 ( -3.51) -0.8 ( -4.85) 1.68 (-4.59) -0.07 ( -0.19) 1.2 (-2.25) 1.66 (-1.84) 0.41
-3.36 ( -2.90) -0.74 ( -4.20) 1.73 (-3.8) -0.21 ( -0.47) 5.37 (-1.14) 2.67 (-2.61) 0.38
-2.48 ( -2.07) -0.56 ( -2.85) 1.65 (-4.02) -0.21 ( -0.54) -7.01 ( -1.69) 2.75 (-3.21) 0.41
-5.84 ( -3.97) -0.6 ( -3.06) 1.9 (-5.81) -0.5 ( -1.49) 3.76 (-3.29) 0.66 (-0.77) 0.49
Notes: This table reports the coefficient estimates in a regression of the excess returns on an n-month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, and the log price-dividend ratio, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 9: Excess returns on holding an n-month bond for a holding period of one year--market jump volatility versus price-dividend ratio, n=36 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-6.59 ( -3.29) -1.63 ( -5.06) 3.15 (-3.95) 0.13 (-0.18) 4.83 (-3.01) 0.41
-9.24 ( -4.06) -1.73 ( -5.86) 3.38 (-4.96) ( -0.01) 2.3 (-2.33) 3.67 (-2.34) 0.46
-6.88 ( -3.38) -1.62 ( -5.08) 3.4 (-4.04) -0.17 ( -0.22) 7.86 (-0.97) 5.43 (-2.95) 0.42
-5.29 ( -2.65) -1.29 ( -3.66) 3.32 (-4.47) -0.26 ( -0.41) -13.39 ( -1.79) 5.75 (-3.74) 0.46
-11.64 ( -4.35) -1.37 ( -4.16) 3.79 (-6.48) -0.81 ( -1.44) 7.09 (-3.34) 1.82 (-1.21) 0.54
Notes: This table reports the coefficient estimates in a regression of the excess returns on an n-month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, and the log price-dividend ratio, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 9: Excess returns on holding an n-month bond for a holding period of one year--market jump volatility versus price-dividend ratio, n=48 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-9.97 ( -3.84) -2.47 ( -6.21) 4.36 (-4.25) 0.48 (-0.55) 6.8 (-3.31) 0.44
-13.17 ( -4.32) -2.6 ( -7.02) 4.64 (-5.15) 0.32 (-0.37) 2.78 (-2.04) 5.4 (-2.74) 0.48
-10.33 ( -3.92) -2.46 ( -6.26) 4.64 (-4.3) 0.12 (-0.12) 9.65 (-0.91) 7.54 (-3.15) 0.45
-8.19 ( -3.35) -2 ( -4.57) 4.64 (-4.77) -0.05 ( -0.06) -18.29 ( -1.87) 8.07 (-4.03) 0.5
-16.18 ( -4.38) -2.15 ( -5.16) 4.64 (-6.3) -0.68 ( -0.89) 8.71 (-2.9) 3.1 (-1.59) 0.55
Notes: This table reports the coefficient estimates in a regression of the excess returns on an n-month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, and the log price-dividend ratio, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Table 9: Excess returns on holding an n-month bond for a holding period of one year--market jump volatility versus price-dividend ratio, n=60 , (Newey-West t-statistics in parentheses)
Intercept
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
t-statistic
-13.42 ( -4.45) -3.02 ( -7.02) 4.69 (-3.98) 1.44 (-1.42) 9.13 (-3.82) 0.47
-16.64 ( -4.63) -3.14 ( -7.74) 4.97 (-4.62) 1.28 (-1.25) 2.8 (-1.68) 7.73 (-3.41) 0.5
-13.69 ( -4.51) -3.01 ( -7.01) 4.93 (-3.92) 1.16 (-1) 7.41 (-0.6) 9.7 (-3.46) 0.48
-11.21 ( -4.30) -2.43 ( -5.09) 4.98 (-4.49) 0.78 (-0.86) -22.76 ( -2.03) 10.71 (-4.61) 0.53
-20.1 ( -4.47) -2.67 ( -5.98) 5.54 (-5.55) 0.2 (-0.22) 9.38 (-2.51) 5.16 (-2.24) 0.55
Notes: This table reports the coefficient estimates in a regression of the excess returns on an n-month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, and the log price-dividend ratio, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
Notes: This table reports the coefficient estimates in a regression of the excess returns on an -month bond over those on a 12 month bond, with a holding period of 12 months, on the term structure of forward rates, a one-month rolling window of realized S&P500 volatility and a 24 month rolling window of S&P500 jump mean, jump intensity, and jump volatility, and the log price-dividend ratio, constructed as described in the text. Observations are at the monthly frequency (end-of-month). T-statistics are shown in parentheses and are based on Newey-West standard errors with a lag truncation parameter of 11.
#### Footnotes
* We thank Darrell Duffie, Cam Harvey, Monika Piazzesi, and George Tauchen for helpful discussions. The views presented here are solely those of the authors and do not necessarily represent those of the Federal Reserve Board or its staff. Return to Text
* Division of Monetary Affairs, Federal Reserve Board, Mail Stop 91, Washington DC 20551 USA, E-mail [email protected], Phone 202-452-3605, Fax 202-452-2301. Return to Text
* Division of Research and Statistics, Federal Reserve Board, Mail Stop 91, Washington DC 20551 USA, E-mail [email protected], Phone 202-452-3360, Fax 202-728-5887. Return to Text
1_ Note that is the Tri-Power Quarticity robust to jumps, and as shown by Barndorff-Nielsen and Shephard (2004),
(7) | 2016-10-24T08:49:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8128269910812378, "perplexity": 7427.7336223452385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719547.73/warc/CC-MAIN-20161020183839-00512-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S015XL | #### Long-Lived Particle (LLP) Search at Hadron Collisions
Limits are for cross section times branching ratio.
VALUE (fb) CL% DOCUMENT ID TECN COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
1
2021 AL
ATLS charged LLPs search
2
2021 BA
ATLS LLP from higgs decay search
3
2021 V
LHCB LLP $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}{{\mathit \nu}}$ search
4
2021 AF
CMS LLP search via displaced jets
$<0.07$ 95 5
2021 U
CMS LLP search via displaced jets
6
2021
CMS LLP endcap muon detector searches
7
2020 D
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ LLPs at 13 TeV
8
2020 J
ATLS scalar boson decay to LLPs
9
2020 M
ATLS LLP top squark decay to ${{\mathit \mu}}$
10
2020 P
ATLS LLP dark photon search
11
2020 AL
LHCB ${{\mathit p}}{{\mathit p}}$ dimuon resonance
12
2020
LLP milli-charged particles at LHC
13
2019 AE
ATLS ${{\mathit p}}{{\mathit p}}$ at 13 TeV
14
2019 AK
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Phi}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}_{{d}}}$
15
2019 AM
ATLS DY multi-charged LLP production
16
2019 AO
ATLS LLP via displaced jets
17
2019 AT
ATLS heavy, charged LLPs
18
2019 G
ATLS LLP decay to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$
19
2019 BH
CMS LLP via displaced jets
20
2019 BT
CMS LLP via displaced jets+MET
21
2019 CA
CMS LLP $\rightarrow$ ${{\mathit \gamma}}$ search
22
2019 Q
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}$ + displaced dark quark jet
23
2018 AW
CMS Long-lived particle search
24
2016 AR
LHCB ${{\mathit H}}$ $\rightarrow$ ${{\mathit X}}{{\mathit X}}$ LLPs
25
2016 BW
CMS direct production: HSCPs
$<2000$ 90 26
1986
BDMP $\tau$ = (0.05$-1.){\times }10^{-8}$s
1 AAD 2021AL reports on ATLAS search for long-lived charged particles with 139 fb${}^{-1}$ at 13 TeV. No signal observed. Limits placed in lifetime vs. mass plane: e.g. for ${{\mathit \tau}}$ (LLP) $\sim{}$ 0.1 ns, m(selectron) $>$ 720 GeV.
2 AAD 2021BA search for long-lived particles from ${{\mathit Z}}{{\mathit H}}$ production ( ${{\mathit H}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ ) with 2 displaced vertices in 139 fb${}^{-1}$ of data at 13 TeV. No signal detected. Limits placed in branching fraction vs. lifetime plane.
3 AAIJ 2021V search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ LLP + LLP with LLP $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}{{\mathit \nu}}$ in the lifetime range between 2 and 50 ps at LHCb with 5.4 fb${}^{-1}$ at 13 TeV. No signal observed. Limits placed in LLP cross section vs. mass or lifetime plane for m(LLP) $\sim{}$ 7 to 50 GeV.
4 SIRUNYAN 2021AF search for LLPs at CMS via jets with 2 displaced vertices in 140 fb${}^{-1}$ of data at 13 TeV. No signal observed. Limits placed for RPV SUSY models in which a long-lived neutralino or gluino decays into a multijet final state with top, bottom, and strange quarks.
5 SIRUNYAN 2021U search for long-lived particles (LLPs) via displaced jets at CMS with LHC13 and 132 fb${}^{-1}$. No signal detected. Limits placed on simplified model production of LLP ${{\mathit X}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$ with ${{\mathit \sigma}}$ $<$ 0.07 fb for m(X) $>$ 500 GeV and c${{\mathit \tau}}$ $\sim{}$ 2 to 250 mm.
6 TUMASYAN 2021 search for long-lived particles in CMS muon endcap detector in 137 fb${}^{-1}$ of data at 13 TeV. No signal detected. Limits are placed depending on the branching fraction of Higgs boson to LLP decaying to ${{\mathit d}}{{\mathit d}}$ , ${{\mathit b}}{{\mathit b}}$ , and ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ , depending on proper decay length, and LLP masses.
7 AAD 2020D search for opposite-sign dileptons originating from long-lived particles in ${{\mathit p}}{{\mathit p}}$ collisions at 13 Tev with 32.8 fb${}^{-1}$; limits placed in squark cross section vs. c${{\mathit \tau}}$ plane for RPV SUSY.
8 AAD 2020J search for scalar boson decay to two long-lived particles; no signal; limits placed in BF vs c${{\mathit \tau}}$ plane for various mass hypotheses. This search is also combined with other ATLAS displaced-jet searches.
9 AAD 2020M search for long-lived top-squarks decay to ${{\mathit \mu}}$ and hadrons; no signal; limits placed in cross section vs. mass and mass vs. lifetime planes .
10 AAD 2020P search for long-lived dark photons produced from the decay of a scalar boson, with each dark photon decaying into displaced collimated leptons or light hadrons at 13 TeV with 36 fb${}^{-1}$; no signal; limits placed in ${{\mathit \sigma}}$ $\cdot{}$BF vs. c${{\mathit \tau}}$ and other planes.
11 AAIJ 2020AL search for long-lived ${{\mathit X}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ decays in 5.1 fb${}^{-1}$ of LHCb data at 13 TeV; no signal; limits placed on m(${{\mathit X}}$ ) up to 3 GeV depending on kinetic mixing.
12 BALL 2020 search for long-lived milli-charged particles produced at LHC; limits placed in charge vs. mass plane (Fig. 8).
13 AABOUD 2019AE search for long-lived particles via displaced jets using 10.8 fb${}^{-1}$ or 33.0 fb${}^{-1}$ data (depending on a trigger) at 13 TeV; no signal found and limits set in branching ratio vs. decay length plane.
14 AABOUD 2019AK searches for long-lived particle ${{\mathit Z}_{{d}}}$ via ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Phi}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}_{{d}}}$ at 13 TeV with 36.1 fb${}^{-1}$; no signal found and limits set in ${{\mathit \sigma}}{\times }$BR vs. lifetime plane for simplified model.
15 AABOUD 2019AM search for Drell-Yan (DY) production of long-lived multi-charge particles at 13 TeV with 36.1 fb${}^{-1}$ of data; no signal found and exclude 50 GeV $<$ m(LLMCP) $<$ $980 - 1220$ GeV for electric charge $\vert$q$\vert$ = ($2 - 7$)e.
16 AABOUD 2019AO search for neutral long-lived particles producing displaced jets at 13 TeV with 36.1 fb${}^{-1}$ of data; no signal found and exclude regions of ${{\mathit \sigma}}$ $\cdot{}$BR vs. lifetime plane for various models.
17 AABOUD 2019AT search for heavy, charged long-lived particles at 13 TeV with 36.1 fb${}^{-1}$; no signal found and upper limits set on masses of various hypothetical particles.
18 AABOUD 2019G search for long-lived particle with decay to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ at 13 TeV with 32.9 fb${}^{-1}$; no signal found and limits set in combinations of lifetime, mass and coupling planes for various simplified models.
19 SIRUNYAN 2019BH search for long-lived SUSY particles via displaced jets at 13 TeV with 35.9 fb${}^{-1}$; no signal found and limits placed in mass vs lifetime plane for various hypothetical models.
20 SIRUNYAN 2019BT search for displaced jet(s)+$\not E_T$ at 13 TeV with 137 fb${}^{-1}$; no signal found and limits placed in mass vs lifetime plane for gauge mediated SUSY breaking models.
21 SIRUNYAN 2019CA search for gluino/squark decay to long-lived neutralino, decay to ${{\mathit \gamma}}$ in GMSB; no signal, limits placed in m(${{\mathit \chi}}$ ) vs. lifetime plane for SPS8 GMSB benchmark point .
22 SIRUNYAN 2019Q search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}$ + displaced jet via dark quark with 13 TeV at 16.1 fb${}^{-1}$; no signal found and limits set in mass vs lifetime plane for dark quark/dark pion model.
23 SIRUNYAN 2018AW search for very long lived particles (LLPs) decaying hadronically or to ${{\mathit \mu}}{{\overline{\mathit \mu}}}$ in CMS detector; none seen/limits set on lifetime vs. cross section.
24 AAIJ 2016AR search for long lived particles from ${{\mathit H}}$ $\rightarrow$ ${{\mathit X}}{{\mathit X}}$ with displaced ${{\mathit X}}$ decay vertex using 0.62 fb${}^{-1}$ at 7 TeV; limits set in Fig. 7.
25 KHACHATRYAN 2016BW search for heavy stable charged particles via ToF with 2.5 fb${}^{-1}$ at 13 TeV; require stable m(gluinoball) $>$ 1610 GeV.
26 BADIER 1986 looked for long-lived particles at 300 GeV ${{\mathit \pi}^{-}}$ beam dump. The limit applies for nonstrongly interacting neutral or charged particles with mass $>$2 GeV. The limit applies for particle modes, ${{\mathit \mu}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ X, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{\pm}}$ etc. See their figure 5 for the contours of limits in the mass-$\tau$ plane for each mode.
References:
AAD 2021BA
JHEP 2111 229
AAD 2021AL
PRL 127 051802 Search for Displaced Leptons in $\sqrt{s} = 13$ TeV $pp$ Collisions with the ATLAS Detector
AAIJ 2021V
EPJ C81 261 Search for long-lived particles decaying to $e^\pm \mu^\mp \nu$
SIRUNYAN 2021AF
PR D104 052011
SIRUNYAN 2021U
PR D104 012015 Search for long-lived particles using displaced jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV
TUMASYAN 2021
PRL 127 261804
AAD 2020M
PR D102 032006 Search for long-lived, massive particles in events with a displaced vertex and a muon with large impact parameter in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector
AAD 2020D
PL B801 135114 Search for displaced vertices of oppositely charged leptons from decays of long-lived particles in $pp$ collisions at $\sqrt {s}$ =13 TeV with the ATLAS detector
AAD 2020J
PR D101 052013 Search for long-lived neutral particles produced in $pp$ collisions at $\sqrt{s} = 13$ TeV decaying into displaced hadronic jets in the ATLAS inner detector and muon spectrometer
AAD 2020P
EPJ C80 450 Search for light long-lived neutral particles produced in $pp$ collisions at $\sqrt{s} =$ 13 TeV and decaying into collimated leptons or light hadrons with the ATLAS detector
AAIJ 2020AL
JHEP 2010 156 Searches for low-mass dimuon resonances
BALL 2020
PR D102 032002 Search for millicharged particles in proton-proton collisions at $\sqrt{s} = 13$ TeV
AABOUD 2019AO
PR D99 052005 Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS muon spectrometer
AABOUD 2019AE
EPJ C79 481 Search for long-lived neutral particles in $pp$ collisions at $\sqrt{s}$ = 13 TeV that decay into displaced hadronic jets in the ATLAS calorimeter
AABOUD 2019AT
PR D99 092007 Search for heavy charged long-lived particles in the ATLAS detector in 36.1 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV
AABOUD 2019AM
PR D99 052003 Search for heavy long-lived multicharged particles in proton-proton collisions at $\sqrt{s}$ = 13 TeV using the ATLAS detector
AABOUD 2019AK
PRL 122 151801 Search for the Production of a Long-Lived Neutral Particle Decaying within the ATLAS Hadronic Calorimeter in Association with a $Z$ Boson from $pp$ Collisions at $\sqrt{s} =$ 13 TeV
AABOUD 2019G
PR D99 012001 Search for long-lived particles in final states with displaced dimuon vertices in $pp$ collisions at $\sqrt{s}=$ 13 TeV with the ATLAS detector
SIRUNYAN 2019CA
PR D100 112003 Search for long-lived particles using delayed photons in proton-proton collisions at $\sqrt{s}=$ 13 TeV
SIRUNYAN 2019Q
JHEP 1902 179 Search for new particles decaying to a jet and an emerging jet
SIRUNYAN 2019BH
PR D99 032011 Search for long-lived particles decaying into displaced jets in proton-proton collisions at $\sqrt{s}=$ 13 TeV
SIRUNYAN 2019BT
PL B797 134876 Search for long-lived particles using nonprompt jets and missing transverse momentum with proton-proton collisions at $\sqrt{s} =$ 13 TeV
SIRUNYAN 2018AW
JHEP 1805 127 Search for decays of stopped exotic long-lived particles produced in proton-proton collisions at $\sqrt{s}=$ 13 TeV
AAIJ 2016AR
EPJ C76 664 Search for Higgs-Like Bosons Decaying into Long-Lived Exotic Particles
KHACHATRYAN 2016BW
PR D94 112004 Search for Long-Lived Charged Particles in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
BADIER 1986
ZPHY C31 21 Mass and Lifetime Limits on New Longlived Particles in 300 ${\mathrm {GeV/}}\mathit c$ ${{\mathit \pi}^{-}}$ Interactions | 2023-03-29T23:47:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.921132504940033, "perplexity": 11712.011705909728}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949035.66/warc/CC-MAIN-20230329213541-20230330003541-00362.warc.gz"} |
http://trove.nla.gov.au/work/78103?q&versionId=83442 | # English, Article edition: MAXIMIZING THE PROBABILITY OF A PERFECT HEDGE USING AN IMPERFECTLY CORRELATED INSTRUMENT DAVID HOBSON; JEREMY PENN
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### Edition details
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• MAXIMIZING THE PROBABILITY OF A PERFECT HEDGE USING AN IMPERFECTLY CORRELATED INSTRUMENT
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• DAVID HOBSON
• JEREMY PENN
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Notes
• Let XÏ denote the trading wealth generated using a strategy Ï, and let CT be a contingent claim which is not spanned by the traded assets. Consider the problem of finding the strategy which maximizes the probability of terminal wealth meeting or exceeding the claim value at some fixed time horizon, i.e., of finding $\sup_{\phi} {\mathbb P}^x (X^{\phi}_T \geq C_T)$. This problem is sometimes referred to as the quantile hedging problem.We consider the quantile hedging problem when the traded asset and the contingent claim are correlated geometric Brownian motions. This fits with several important examples. One of the benefits of working with such a concrete model is that although it is incomplete we can still do calculations. In particular, we can consider some detailed issues such as the impact of the timing at which information about CT is revealed.
• Hedging strategies, stochastic control, Brownian motion, policy improvement, timely information
• RePEc:wsi:ijtafx:v:08:y:2005:i:06:p:763-789
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https://vsbattles.fandom.com/wiki/The_Kardashev_Scale | 26,000 Pages
## Explanation
The Kardashev Scale is a measurement created by Russian astrophysicist Nikolai Kardashev, meant to measure the scale of a civilization’s technological advancement, measured through energy output. In theory this could allow astronomers to predict the advancement of an alien civilization the same way as observing the luminosity of stars. Though the Kardashev Scale failed in its original purpose, it became quite popular amongst Science Fiction communities and theoretical scientists.
The original Kardashev Scale possessed 3 categories, these were:
• Type Ⅰ: "Technological level close to the level presently (here referring to 1964) attained on earth, with energy consumption at ≈4×1E19 erg/sec (4 × 1E12 watts)" Guillermo A. Lemarchand stated this as "A level near contemporary terrestrial civilization with an energy capability equivalent to the solar insolation on Earth, between 1E16 and 1E17 watts."
• Type Ⅱ: "A civilization capable of harnessing the energy radiated by its own star (for example, the stage of successful construction of a Dyson sphere), with energy consumption at ≈4×1E33 erg/sec." Lemarchand stated this as "A civilization capable of utilizing and channeling the entire radiation output of its star. The energy utilization would then be comparable to the luminosity of our Sun, about 4 × 1E26 watts."
• Type Ⅲ: "A civilization in possession of energy on the scale of its own galaxy, with energy consumption at ≈4×10E4 erg/sec." Lemarchand stated this as "A civilization with access to the power comparable to the luminosity of the entire Milky Way galaxy, about 4 × 1E37 Watts."
As time passed, the Scale was expanded, with Type 0 Civilizations (Those who have yet to master the Geothermal Energy of their home planet) and Type IV Civilizations (Civilizations that can drain the available power of an entire universe) being added.
Much later, using extrapolation based on the original 3 categories, cosmologist and astrophysicist Carl Sagan suggested a mathematical formula for defining intermediates:
$K = \tfrac{\log_{10}(P)-6}{10}$
Where K is the civilization’s development on the Kardashev Scale and P is the civilization’s entire available power in Watts. For instance, in 2008, the world’s average power consumption was 16 terawatts (1.6 x 1E13 W), with Sagan’s formula that equals (log(1.6*10^(13))-6)/10 = 0.72
The following scale expands beyond the Original three types, and the added two types, to fully encapsulate the most powerful civilizations that can be encountered in science fiction.
However, it should be noted that being higher on the Kardashev Scale does not always dictate greater firepower, as the scale measures only the energy which the civilization uses.
## The Scale
Type 0: 0 – 1E16 watts. A civilization that harnesses a significant portion of the energy of its home planet, but not to its full potential.
• Humanity (Real Life) (Type 0.73)
• Holy Britannian Empire (Code Geass)
Type I: 1E16 – 1E26 watts. A civilization that can harness the entirety of the geothermal energy of Earth.
• The United Federation of Planets (Star Trek)
• The Imperium of Man (Warhammer 40,000) (Borderline Type II)
Type II: 1E26 – 1E36 watts. A civilization that can harness the energy of a star.
• DAoT Humanity, Pre-Fall Aeldari, the T’au Empire and The Necrons (Warhammer 40,000)
• The Old Republic (Star Wars)
• Humanity (Blame!)
Type III: 1E36 – 1E46 watts. A civilization that can harness the energy of a galaxy.
• The Forerunners (Halo)
• The Culture (The Culture)
Type IV: 1E46 – 1E56 watts. A civilization that can harness the energy of a galactic supercluster.
• The Precursors (Halo)
Type V: 1E56 – 1E69 watts. A civilization that can harness all of the energy of its universe.
• Asgard (Marvel Comics)
• Marble Aliens (Men in Black)
• Mazoku / Shinzoku (Slayers)
Type VI: 3.9 x 1E69 watts and above. A civilization that generates more energy than the universe every second.
• The Celestials (Marvel Comics)
• The Q (Star Trek)
Type VII: Immeasurable. Civilizations beyond any known quantification of joules.
• The Time Lords and the Daleks (Doctor Who)
• The Downstreamers (Manifold)
• The Beyonders (Marvel Comics)
## Start a Discussion Discussions about The Kardashev Scale
• #### Kardashev Scale Calculation Error?
5 messages
• The formula seems to be getting the right answer now. We should probably get that page formula tweaked then.
• done
• #### Outstanding Soviet astrophysicist and radio astronomer Nikolai Kardashev dies, 1932-2019
39 messages
• Well guess sure thing that Kardashev Scale something do ask staff make CRT?
• Nice info.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-08-12T20:51:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5695999264717102, "perplexity": 8843.586294645524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738944.95/warc/CC-MAIN-20200812200445-20200812230445-00034.warc.gz"} |
http://dlmf.nist.gov/10.22 | §10.22 Integrals
§10.22(i) Indefinite Integrals
In this subsection and denote cylinder functions(§10.2(ii)) of orders and , respectively, not necessarily distinct.
10.22.1
For the Struve function see §11.2(i).
§10.22(ii) Integrals over Finite Intervals
Throughout this subsection .
¶ Trigonometric Arguments
For see §10.25(ii).
¶ Fractional Integral
When the left-hand side of (10.22.36) is the th repeated integral of (§§1.4(v) and 1.15(vi)).
¶ Orthogonality
If , then
where and are zeros of 10.21(i)), and is Kronecker’s symbol.
Also, if are real constants with and , then
where and are positive zeros of . (Compare (10.22.55)).
§10.22(iv) Integrals over the Interval
10.22.45.
10.22.47.
For see §10.25(ii).
10.22.50.
For the hypergeometric function see §15.2(i).
For and see §10.25(ii).
For the confluent hypergeometric function see §13.2(i).
When ,
10.22.63
¶ Other Double Products
In (10.22.66)–(10.22.70) are positive constants.
For the associated Legendre function see §14.3(ii) with . For and see §10.25(ii).
Equation (10.22.70) also remains valid if the order of the functions on both sides is replaced by , , and the constraint is replaced by .
See also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions.
¶ Triple Products
In (10.22.74) and (10.22.75), are positive constants and
10.22.73
(Thus if are the sides of a triangle, then is the area of the triangle.)
Additional infinite integrals over the product of three Bessel functions (including modified Bessel functions) are given in Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b).
§10.22(v) Hankel Transform
The Hankel transform (or Bessel transform) of a function is defined as
Hankel’s inversion theorem is given by
Sufficient conditions for the validity of (10.22.77) are that when , or that and when ; see Titchmarsh (1986a, Theorem 135, Chapter 8) and Akhiezer (1988, p. 62).
For asymptotic expansions of Hankel transforms see Wong (1976, 1977) and Frenzen and Wong (1985).
For collections of Hankel transforms see Erdélyi et al. (1954b, Chapter 8) and Oberhettinger (1972).
§10.22(vi) Compendia
For collections of integrals of the functions , , , and , including integrals with respect to the order, see Andrews et al. (1999, pp. 216–225), Apelblat (1983, §12), Erdélyi et al. (1953b, §§7.7.1–7.7.7 and 7.14–7.14.2), Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000, §§5.5 and 6.5–6.7), Gröbner and Hofreiter (1950, pp. 196–204), Luke (1962), Magnus et al. (1966, §3.8), Marichev (1983, pp. 191–216), Oberhettinger (1974, §§1.10 and 2.7), Oberhettinger (1990, §§1.13–1.16 and 2.13–2.16), Oberhettinger and Badii (1973, §§1.14 and 2.12), Okui (1974, 1975), Prudnikov et al. (1986b, §§1.8–1.10, 2.12–2.14, 3.2.4–3.2.7, 3.3.2, and 3.4.1), Prudnikov et al. (1992a, §§3.12–3.14), Prudnikov et al. (1992b, §§3.12–3.14), Watson (1944, Chapters 5, 12, 13, and 14), and Wheelon (1968). | 2013-05-19T13:28:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9504998326301575, "perplexity": 6728.554190224675}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697552127/warc/CC-MAIN-20130516094552-00088-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://algebra2014.wikidot.com/theorem-15-8 | Theorem 15.8
Return to Theorems, Glossary, Homework Problems.
Statement:
Let $G=H \times K$ be the direct product of groups $H$ and $K$. Then $\bar{H} = \{(h,e) | h \in H \}$ is a normal subgroup of $G$. Also $G/\bar{H}$ is isomorphic to $K$ in a natural way. Similarly, $G/\bar{K} \simeq H$ in a natural way.
Proof:
Consider the homomorphism $\pi_2 : H \times K \rightarrow K$, where $\pi_2(h,k) = k$. Because $Ker(\pi_2)= \bar{H}$, we see that $\bar{H}$ is a normal subgroup of $H \times K$. Because $\pi_2$ is onto $K$, Theorem 14.11 tells us that $(H \times K)/\bar{H} \simeq K$.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2019-03-23T05:04:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8549549579620361, "perplexity": 132.23157348571542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202723.74/warc/CC-MAIN-20190323040640-20190323062640-00009.warc.gz"} |
http://dlmf.nist.gov/34.15 | # §34.15 Software
In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. Citations in bulleted lists refer to papers for which research software has been made available and can be downloaded via the Web. References to research software that is available in other ways is listed separately.
A more complete list of available software for computing these functions is found in the Software Index.
• Bar-Shalom and Klapisch (1988). Fortran.
• Berrington et al. (1974). Fortran.
• Burke (1970). Fortran.
• Dodds and Wiechers (1972). Fortran.
• Fang and Shriner (1992). Fortran.
• Kaeding (1995). Pascal.
• Lai and Chiu (1992). Fortran.
• Schulten and Gordon (1976). Fortran.
• Shapiro (1970). Fortran.
• Stone and Wood (1980). Fortran.
• Tamura (1970). Fortran.
See also Lai and Chiu (1990) and Srinivasa Rao and Rajeswari (1993, Appendix C, pp. 266–292). | 2014-09-18T17:45:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5643357038497925, "perplexity": 7097.980812811554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657128337.85/warc/CC-MAIN-20140914011208-00107-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2011.2011.1158 | Article Contents
Article Contents
# Determination of motion from orbit in the three-body problem
• We discuss the equal mass three-body motion in which the shape of the orbit is given. The conservation of the center of mass and a constant of motion (the total angular momentum or the total energy) leads to the uniqueness of the equal mass three-body motion in given some sorts of orbits. Although the proof was already published on an article by the present authors in 2009, here we give some complementary explanations. We show that, even in the unequal mass three-body periodic motions in which each of bodies draws its own orbit, the shape of the orbits, conservation of the center of mass and a constant of motion provide some candidates of the motion of three bodies. The reality of the motion should be tested whether the equation of motion is satisfied or not. Even if the three bodies draw unclosed orbits, we can show that similarly.
Mathematics Subject Classification: Primary: 70F07, 70F15; Secondary: 51P05.
Citation:
Open Access Under a Creative Commons license | 2023-04-01T20:31:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.18911418318748474, "perplexity": 377.8848056297778}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950247.65/warc/CC-MAIN-20230401191131-20230401221131-00407.warc.gz"} |
https://par.nsf.gov/biblio/10187157-deep-transfer-learning-star-cluster-classification-application-phangshst-survey | Deep transfer learning for star cluster classification: I. application to the PHANGS–HST survey
ABSTRACT We present the results of a proof-of-concept experiment that demonstrates that deep learning can successfully be used for production-scale classification of compact star clusters detected in Hubble Space Telescope(HST) ultraviolet-optical imaging of nearby spiral galaxies ($D\lesssim 20\, \textrm{Mpc}$) in the Physics at High Angular Resolution in Nearby GalaxieS (PHANGS)–HST survey. Given the relatively small nature of existing, human-labelled star cluster samples, we transfer the knowledge of state-of-the-art neural network models for real-object recognition to classify star clusters candidates into four morphological classes. We perform a series of experiments to determine the dependence of classification performance on neural network architecture (ResNet18 and VGG19-BN), training data sets curated by either a single expert or three astronomers, and the size of the images used for training. We find that the overall classification accuracies are not significantly affected by these choices. The networks are used to classify star cluster candidates in the PHANGS–HST galaxy NGC 1559, which was not included in the training samples. The resulting prediction accuracies are 70 per cent, 40 per cent, 40–50 per cent, and 50–70 per cent for class 1, 2, 3 star clusters, and class 4 non-clusters, respectively. This performance is competitive with consistency achieved in previously published human and automated quantitative classification of star more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10187157
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
493
Issue:
3
Page Range or eLocation-ID:
3178 to 3193
ISSN:
0035-8711
In the hierarchical view of star formation, giant molecular clouds (GMCs) undergo fragmentation to form small-scale structures made up of stars and star clusters. Here we study the connection between young star clusters and cold gas across a range of extragalactic environments by combining the high resolution (1″) PHANGS–ALMA catalogue of GMCs with the star cluster catalogues from PHANGS–HST. The star clusters are spatially matched with the GMCs across a sample of 11 nearby star-forming galaxies with a range of galactic environments (centres, bars, spiral arms, etc.). We find that after 4 − 6 Myr the star clusters are no longer associated with any gas clouds. Additionally, we measure the autocorrelation of the star clusters and GMCs as well as their cross-correlation to quantify the fractal nature of hierarchical star formation. Young (≤10 Myr) star clusters are more strongly autocorrelated on kpc and smaller spatial scales than the $\gt \, 10$ Myr stellar populations, indicating that the hierarchical structure dissolves over time. | 2022-11-27T15:06:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.683921754360199, "perplexity": 1708.563050976252}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00357.warc.gz"} |
https://www.allaboutcircuits.com/worksheets/signal-modulation | # Signal Modulation
## Discrete Semiconductor Devices and Circuits
PDF Version
• #### Question 1
A modern method of electrical power control involves inserting a fast-operating switch in-line with an electrical load, to switch power on and off to it very rapidly over time. Usually, a solid-state device such as a transistor is used:
This circuit has been greatly simplified from that of a real, pulse-control power circuit. Just the transistor is shown (and not the “pulse” circuit which is needed to command it to turn on and off) for simplicity. All you need to be aware of is the fact that the transistor operates like a simple, single-pole single-throw (SPST) switch, except that it is controlled by an electrical current rather than by a mechanical force, and that it is able to switch on and off millions of times per second without wear or fatigue.
If the transistor is pulsed on and off fast enough, power to the light bulb may be varied as smoothly as if controlled by a variable resistor. However, there is very little energy wasted when using a fast-switching transistor to control electrical power, unlike when a variable resistance is used for the same task. This mode of electrical power control is commonly referred to as Pulse-Width Modulation, or PWM.
Explain why PWM power control is much more efficient than controlling load power by using a series resistance.
Reveal answer
• #### Question 2
Explain the difference between AM (Amplitude Modulation) and FM (Frequency Modulation).
Reveal answer
• #### Question 3
A very important concept in electronics is modulation. Explain what “modulation” means, and give one or two examples of it.
Reveal answer
• #### Question 4
A primitive form of communication long ago was the use of smoke signals: interrupting the rising stream of smoke from a fire by waving a blanket over it so that specific sequences of smoke “puffs” could be seen some distance away. Explain how this is an example of modulation, albeit in a non-electronic form.
Reveal answer
• #### Question 5
One of the simplest electronic methods of modulation is amplitude modulation, or AM. Explain how a high-frequency carrier signal would be modulated by a lower-frequency signal such as in the case of the two signals shown here in the time domain:
Reveal answer
• #### Question 6
A circuit often used to amplitude-modulate a carrier signal is a multiplier:
Explain how the instantaneous multiplication of two sine waves results in amplitude modulation. If possible, graph this on a graphing calculator or other computer plotting device.
Reveal answer
• #### Question 7
A common modulation technique employed in radio broadcasting is frequency modulation, or FM. Explain how a high-frequency carrier signal would be modulated by a lower-frequency signal such as in the case of the two signals shown here in the time domain:
Reveal answer
• #### Question 8
At the heart of an FM transmitter is a circuit called a voltage-controlled oscillator, or VCO. Explain what the purpose of a VCO is, and how this directly relates to frequency modulation.
Reveal answer
• #### Question 9
This is a schematic for a very simple VCO:
The oscillator is of the “Colpitts” design. The key to understanding this circuit’s operation is knowing how the varactor diode responds to different amounts of DC bias voltage. Explain how this circuit works, especially how the diode exerts control over the oscillation frequency. Why does the output frequency vary as the control voltage varies? Does the output frequency increase or decrease as the control voltage input receives a more positive voltage?
Note: “RFC” is an acronym standing for Radio-Frequency Choke, an iron-core inductor whose purpose it is to block radio frequency current from passing through.
Reveal answer
• #### Question 10
This is a schematic for a simple VCO:
The oscillator is of the RC “phase shift” design. Explain how this circuit works. Why does the output frequency vary as the control voltage varies? Does the output frequency increase or decrease as the control voltage input receives a more positive voltage?
Hint: the JFETs in this circuit are not functioning as amplifiers!
Reveal answer
• #### Question 11
FM tends to be a far more noise-resistant means of signal modulation than AM. For instance, the “crackling” form of radio interference caused by natural lightning or the “buzzing” noise produced by high-voltage power lines are both easy to hear on an AM radio, but absent on an FM radio. Explain why.
Reveal answer
• #### Question 12
When transmitting audio information (such as music and speech) in the form of radio waves, why bother modulating a high-frequency carrier signal? Why not just connect a powerful audio amplifier straight to an antenna and broadcast the audio frequencies directly?
Reveal answer
• #### Question 13
Predict how the output frequency of this voltage-controlled oscillator (VCO) circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
Capacitor C1 fails open:
Inductor L1 fails open:
Resistor R1 fails open:
Resistor R2 fails open:
Inductor L2 fails partially shorted:
For each of these conditions, explain why the resulting effects will occur. Note: the voltage-dependent capacitance of a varactor diode is given by the following equation:
$$C_j = \frac{C_o}{\sqrt{2V+1}}$$
Where,
CJ = Junction capacitance
Co = Junction capacitance with no applied voltage
V = Applied reverse junction voltage
Reveal answer
• #### Question 14
Determine the duty cycle of this square wave signal:
Reveal answer
• #### Question 15
Determine the duty cycle of this square wave signal:
Reveal answer
• #### Question 16
A resistive DC load receives pulse-width modulated (PWM) power from a controller circuit, and an oscilloscope shows the load voltage waveform as such:
Calculate the duty cycle of this waveform, and also the average power dissipated by the load assuming a load resistance of 1.8 Ω.
Reveal answer
• #### Question 17
A resistive DC load receives pulse-width modulated (PWM) power from a controller circuit, and an oscilloscope shows the load voltage waveform as such:
Calculate the duty cycle of this waveform, and also the average power dissipated by the load assuming a load resistance of 10.3 Ω.
Reveal answer
• #### Question 18
The oscillator circuit in this diagram generates a square wave with an adjustable duty cycle:
A student desires to use this circuit as the basis for a pulse-width modulation (PWM) power controller, to vary the amount of power delivered to a DC load. Since the oscillator circuit is built to produce weak signals and not deliver power directly to a load, the student adds a power MOSFET to switch heavy load currents:
Correlate the duty cycle of the oscillator’s output signal with motor power. In other words, describe how increases and decreases in signal duty cycle affect the amount of power delivered to the electric motor.
Reveal answer
• #### Question 19
Explain why it is important for the final power transistor(s) in a PWM power control circuit to operate at full cutoff and full saturation, and not in the linear (active) mode in between those two extremes. What might happen if the power transistor(s) were to be less than cut-off or less than saturated when carrying load current?
Reveal answer
• #### Question 20
If a pulse-width modulated (PWM) signal is sent to a passive integrator circuit from a circuit capable of both sourcing and sinking current (as is the case with the dual-MOSFET output stage), the output will be a DC voltage (with some ripple):
Determine the relationship between the PWM signal’s duty cycle and the DC voltage output by the integrator. What does this suggest about PWM as a means of communicating information, such as analog data from a measuring device?
Reveal answer
• #### Question 21
Plot what the frequency spectrum would look like for a pure (undistorted) 1 MHz sine wave:
Reveal answer
• #### Question 22
Determine the frequency spectrum for a high-frequency, sine wave “carrier” signal that is amplitude-modulated (AM) by an audio-frequency sine wave signal, as the following block diagram shows:
The spectra for these respective waveforms are shown individually:
Plot the modulated signal spectrum here:
Reveal answer
• #### Question 23
Determine the frequency spectrum for a high-frequency, sine wave “carrier” signal that is amplitude-modulated (AM) by an audio-frequency signal with a spectrum of its own. The spectra for these respective waveforms are shown individually:
Plot the modulated signal spectrum here:
Reveal answer
• #### Question 24
An important measurement of pulse waveforms is duty cycle. Give a precise. mathematical definition for this term.
Also, write an equation solving for pulse width given duty cycle (D) and frequency (f).
Reveal answer
• #### Question 25
Determine the duty cycle of this square wave signal:
Reveal answer
• #### Question 26
Determine the duty cycle of this square wave signal:
Reveal answer
• #### Question 27
How would a permanent-magnet DC motor respond if the switch in this circuit were repeatedly closed and opened at a very high frequency?
Would it rotate at full speed, just the same as if the switch were closed all the time? Would it rotate at all? Explain your answer.
Reveal answer
• #### Question 28
A resistive DC load receives pulse-width modulated (PWM) power from a controller circuit, and an oscilloscope shows the load voltage waveform as such:
Calculate the duty cycle of this waveform, and also the average power dissipated by the load assuming a load resistance of 2.5 Ω.
Reveal answer
• #### Question 29
A resistive DC load receives pulse-width modulated (PWM) power from a controller circuit, and an oscilloscope shows the load voltage waveform as such:
Calculate the duty cycle of this waveform, and also the average power dissipated by the load assuming a load resistance of 40.7 Ω.
Reveal answer
• #### Question 30
How is pulse-width modulation power control similar to the form of control exerted by TRIACs and SCRs in AC power circuits? How does it differ?
Reveal answer
• #### Question 31
Pulse-density modulation (PDM) is closely related to pulse-width modulation (PWM). Describe the similarities and differences in your own words.
Reveal answer
### Related Content
Published under the terms and conditions of the Creative Commons Attribution License
0 Comments | 2022-12-08T23:53:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35151004791259766, "perplexity": 2901.054939123435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711368.1/warc/CC-MAIN-20221208215156-20221209005156-00262.warc.gz"} |
https://gocompetition.energy.gov/challenges/challenge-1/trial-event-1 | # Challenges
## TESTING ENVIRONMENT
The sandbox is a testing environment that allows Entrants to try the submission, evaluation, and scoring process using datasets that may be small for quick turnaround or debugging as well as the actual Trial Event datasets from previous Trials for algorithm development.
Concluded
Challenge 1 solved a security-constrained (AC) optimal power flow (SCOPF) problem. Algorithms were tested on complex, realistic power system models, and Entrants were scored on how well their algorithms perform relative to other Entrants’ algorithms.
Ten teams were awarded $3.4 million. Concluded Challenge 2 expanded upon the SCOPF problem posed in Challenge 1 by adding price-responsive demand, ramp rate constrained generators and loads, fast-start unit commitment, adjustable transformer tap ratios, phase shifting transformers, and switchable shunts. Nine teams were awarded$2.4 million.
Concluded
This Event focuses on finding improved solutions to the security-constrained optimal power flow (SCOPF) problem introduced in Challenge 2. Teams generated solutions on their own with no software or hardware constraints and no time limits. Solution Files were uploaded to PNNL for solution evaluatipon.
This event kicked off on January 3, 2022 and concluded October 31, 2022. This competition rewarded the teams that found the better solutions first as well as teams that found solutions with >1% improvement over Challenge 2 results.
Two teams were awarded \$440,000.
See the C2-MoM Leaderboard for results.
Challenge 3 will focus on multiperiod dynamic markets including advisory models for extreme weather events, day-ahead markets, and the real-time markets with an extended look-ahead. These problems will include active bid-in demand and topology optimization.
Challenge 3 FOA released February 16, 2022.
Challenge 3 Event 1 (no prize money) submission window was January 25-27, 2023. | 2023-03-21T17:34:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3816128969192505, "perplexity": 7379.446988665952}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00096.warc.gz"} |
https://www.itl.nist.gov/div898/handbook/mpc/section6/mpc622.htm | 2. Measurement Process Characterization
2.6. Case studies
2.6.2. Check standard for resistivity measurements
## Analysis and interpretation
Estimates of the repeatability standard deviation and level-2 standard deviation The level-1 standard deviations (with J - 1 = 5 degrees of freedom each) from the database are pooled over the K = 25 days to obtain a reliable estimate of repeatability. This pooled value is
s1 = 0.06139 ohm.cm
with K(J - 1) = 125 degrees of freedom. The level-2 standard deviation is computed from the daily averages to be
s2 = 0.02680 ohm.cm
with K - 1 = 24 degrees of freedom.
Relationship to uncertainty calculations These standard deviations are appropriate for estimating the uncertainty of the average of six measurements on a wafer that is of the same material and construction as the check standard. The computations are explained in the section on sensitivity coefficients for check standard measurements. For other numbers of measurements on the test wafer, the computations are explained in the section on sensitivity coefficients for level-2 designs.
Illustrative table showing computations of repeatability and level-2 standard deviations A tabular presentation of a subset of check standard data (J = 6 repetitions and K = 6 days) illustrates the computations. The pooled repeatability standard deviation with K(J - 1) = 30 degrees of freedom from this limited database is shown in the next to last row of the table. A level-2 standard deviation with K - 1= 5 degrees of freedom is computed from the center averages and is shown in the last row of the table.
Control chart for probe #2362 The control chart for monitoring the precision of probe #2362 is constructed as discussed in the section on control charts for standard deviations. The upper control limit (UCL) for testing for degradation of the probe is computed using the critical value from the F table with numerator degrees of freedom J - 1 = 5 and denominator degrees of freedom K(J - 1) = 125. For a 0.05 significance level,
$$F_{0.05, 5, 125} = 2.29$$
$$UCL = s_1 \sqrt{F_{0.05, 5, 125}} = 0.09238 \,\, \mbox{ohm.cm}$$
Interpretation of control chart for probe #2362 The control chart shows two points exceeding the upper control limit. We expect 5 % of the standard deviations to exceed the UCL for a measurement process that is in-control. Two outliers are not indicative of significant problems with the repeatability for the probe, but the probe should be monitored closely in the future.
Control chart for bias and variability The control limits for monitoring the bias and long-term variability of resistivity with a Shewhart control chart are given by
$$UCL = Average + 2 \cdot s_2 = 97.1234 \,\, \mbox{ohm.cm}$$
$$Centerline = Average = 97.0698 \,\, \mbox{ohm.cm}$$
$$LCL = Average - 2 \cdot s_2 = 97.0162 \,\, \mbox{ohm.cm}$$
Interpretation of control chart for bias The control chart shows that the points scatter randomly about the center line with no serious problems, although one point exceeds the upper control limit and one point exceeds the lower control limit by a small amount. The conclusion is that there is:
• No evidence of bias, change or drift in the measurement process.
• No evidence of long-term lack of control.
Future measurements that exceed the control limits must be evaluated for long-term changes in bias and/or variability. | 2018-08-17T20:45:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8010119199752808, "perplexity": 1062.266977526325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221212910.25/warc/CC-MAIN-20180817202237-20180817222237-00299.warc.gz"} |
http://wikimechanics.org/newtonian-particles-summary | Conservation of Energy and Mass
Baby Collar, Dong people. China, Yunnan province, 20th century 38 x 19 cm. From the collection of Tan Tim Qing, Kunming. Photograph by D Dunlop.
Newtonian particles are dense and heavy. And we regularly assume that they are in dynamic equilibrium with their surroundings. Then as discussed earlier, their enthalpy $H$, is related to their mass $m$, by the approximation
$\left| \, H \, \right| \simeq mc^{2}$
But the mechanical energy $E$ of any material particle is approximately $E \simeq \gamma m c^{2}$ where $\gamma$ is the Lorentz factor. Then
$E \simeq \gamma \, \left| \, H \, \right|$
For particles in slow motion, $\gamma \simeq 1$ so that $E \simeq \, \left| \, H \, \right|$. But the absolute-value signs can usually be ignored because ordinary particles are composed from electrons, neutrons and protons which all have positive enthalpy. So if we exclude anti-particles and processes like annihilation, then we usually have
$H \simeq E \simeq m c^{2}$
Thus the mechanical energy and the enthalpy are almost interchangeable for slow Newtonian particles made of ordinary matter. But enthalpy is conserved for all particles and conditions. So the energy and mass must also be approximately conserved for slow Newtonian particles too. This idea is honoured as an energy conservation law because it is so important in classical mechanics. Moreover, a conservation law for mass is a basic principle in benchtop chemistry. These excellent approximations are used everyday. Together with the routine assumption of dynamic equilibrium they typify Newtonian particles.
Next step: Counting quarks by the bundle.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2020-10-01T15:33:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.569728672504425, "perplexity": 1056.297997027414}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402131777.95/warc/CC-MAIN-20201001143636-20201001173636-00497.warc.gz"} |
http://encyclopedia-magnetica.com/doku.php/ltspice/variable_resistor | # Encyclopedia Magnetica
Encyclopedia of magnetics and electromagnetics.
### Site Tools
ltspice:variable_resistor
# Variable resistor
Stan Zurek, Variable resistor , Encyclopedia-Magnetica.com, {accessed 2019-06-16}
Go to: LTspice.
The Arbitrary Behavioral Current Source in LTspice can be used to simulate time-variable resistor in transient simulations.
### Method 1 (proportional resistance)
The steps are:
1. Connect a voltage source to ground and label its other end for example as “var”. Set the voltage waveform/pulse such that its value in volts corresponds directly to the desired variable resistance in ohms (e.g. “50 V” will correspond to “50 Ω”).
2. In value of the variable resistor enter:
R = V(var)
such that the name “var” represents the node name from step 1.
Variable resistance: green curve shows an example of sinusoidal supply voltage, blue is the resultant current, red is the function by which the load current is scaled, namely V(var). Resistance is directly proportional to the variable voltage.
by S. Zurek, E. Magnetica, CC-BY-3.0
### Method 2 (proportional current)
The steps are:
1. Label the node(s) the variable resistor is going to be connected between.
2. Use “Arbitrary Behavioral Current Source (bi)” and put it between the labelled nodes. If the resistor is connected to ground then only one node needs to be labelled (e.g. “test”).
3. Create a new voltage source connected somewhere to ground, and label its voltage output (e.g. “VAR”). The shape of this voltage source will determine how the resistance changes - this can be set to be a pulse, sine with offset, piece-wise linear (PWL) etc. Set the shape of this voltage source to vary between zero (infinite resistance, zero current) to unity (resistance equal to the value “LOAD”, see next point).
4. Add directive “.param LOAD 100” where “LOAD” represents a variable and “100” is the minimum value of resistance.
5. Edit the function of the Behavioral Current Source to be:
I=V(VAR)*V(test)/LOAD
This will set the current to vary anywhere between zero (if V(VAR)=0 then resistance = infinity), scaled to the real voltage “V(test)” and the value of LOAD (if V(VAR)=1 then resistance = LOAD). If the variable resistor is placed between two labelled nodes then a voltage difference between these nodes needs to be calculated in the equation.
Variable resistance: green curve shows an example of sinusoidal supply voltage, blue is the resultant current, red is the function by which the load current is scaled, namely V(VAR). Resistance is proportional to the inverse of the current.
by S. Zurek, E. Magnetica, CC-BY-3.0
### Method 3 (proportional resistance)
The steps are:
1. Label the node(s) the variable resistor is going to be connected between.
2. Use “Arbitrary Behavioral Current Source (bi)” and put it between the labelled nodes. If the resistor is connected to ground then only one node needs to be labelled (e.g. “test”).
3. Create a new voltage source connected somewhere to ground, and label its voltage output (e.g. “VAR”). The shape of this voltage source will determine how the resistance changes - this can be set to be a pulse, sine with offset, piece-wise linear (PWL) etc. Set the shape of this voltage source to vary between any positive values (zero and negative values are not allowed). For “infinitely high” resistance use very high value, for example “1G” (1 giga) as the amplitude. For “infinitely low” resistance use a very low value, for example “1f” (1 femto).
4. Edit the function of the Behavioral Current Source to be:
I=V(test)/V(VAR)
This will set the resistance to be directly proportional to the V(VAR) voltage. If the variable resistor is placed between two labelled nodes then a voltage difference between these nodes needs to be calculated in the equation.
Variable resistance: green curve shows an example of sinusoidal supply voltage, blue is the resultant current, red is the function by which the load resistance is scaled, namely V(VAR).
by S. Zurek, E. Magnetica, CC-BY-3.0
### Method 4 (operating point)
This method is applicable only in the operating point simulation (.op) not transient (.tran).
The steps are:
.step param Rvar list 1 2 3 4 5 10
where “Rvar” denotes a variable resistance.
2. In the given resistor enter the value of resistance as “{Rvar}” (with curly brackets).
3. Run the simulation in the .op mode (operating point). When plotting currents and voltages, they will be plotted with the Rvar in the horizontal axis of the graphs.
Variable resistance in “.op” mode: green curve shows the supply voltage, blue is the resultant current.
by S. Zurek, E. Magnetica, CC-BY-3.0 | 2019-06-16T15:22:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6393224000930786, "perplexity": 2966.5679371485808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998250.13/warc/CC-MAIN-20190616142725-20190616164725-00258.warc.gz"} |
http://cnls.lanl.gov/~ebn/pubs/rotation/rotation.html | ## Singular Energy Distributions in Driven and Undriven Granular Media
### E. Ben-Naim and A. Zippelius
We study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy $E$ and the ratio $x=\sqrt{E_w/E}$ of rotational energy $E_w$ to total energy. Extremely energetic particles have a unique and well-defined distribution $f(x)$ which has several remarkable features: $x$ is not uniformly distributed as in molecular gases; $f(x)$ is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, $f(x)$ is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior.
source, ps, pdf | 2013-05-21T06:10:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7033344507217407, "perplexity": 642.6732479342797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699730479/warc/CC-MAIN-20130516102210-00060-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://bison.inl.gov/Documentation/source/materials/ComputeInstantaneousThermalExpansionFunctionEigenstrain.aspx | # Compute Instantaneous Thermal Expansion Function Eigenstrain
Computes eigenstrain due to thermal expansion using a function that describes the instantaneous thermal expansion as a function of temperature
## Description
This model computes the eigenstrain tensor resulting from isotropic thermal expansion where the temperature-dependent thermal expansion is defined by a user-supplied function that describes the instantaneous thermal expansion coefficient as a function of temperature, . Using a trapezoidal rule to perform time integration of this function, the current value of the thermal eigenstrain tensor, is computed at a given time as: (1) where denotes quantities at the new step, and denotes quantities at the previous step, is the temperature, is the instantaneous thermal expansion at a given temperature, and is the identity matrix. On the first step, the stress-free temperature is used as the previous step's temperature.
## Example Input File Syntax
[./thermal_expansion_strain1]
type = ComputeMeanThermalExpansionFunctionEigenstrain
block = 1
thermal_expansion_function = cte_func_mean
thermal_expansion_function_reference_temperature = 0.5
stress_free_temperature = 0.0
temperature = temp
eigenstrain_name = eigenstrain
[../]
(moose/modules/tensor_mechanics/test/tests/thermal_expansion_function/thermal_expansion_function_finite_const_alpha_test.i)
The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting is shown below:
[Modules/TensorMechanics/Master]
[./all]
strain = FINITE
incremental = true
eigenstrain_names = eigenstrain
generate_output = 'strain_xx strain_yy strain_zz'
[../]
[]
(moose/modules/tensor_mechanics/test/tests/thermal_expansion_function/thermal_expansion_function_finite_const_alpha_test.i)
## Input Parameters
• stress_free_temperatureReference temperature at which there is no thermal expansion for thermal eigenstrain calculation
C++ Type:std::vector
Description:Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation
• thermal_expansion_functionFunction describing the instantaneous thermal expansion coefficient as a function of temperature
C++ Type:FunctionName
Description:Function describing the instantaneous thermal expansion coefficient as a function of temperature
• eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
### Required Parameters
• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
Default:True
C++ Type:bool
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
• temperatureCoupled temperature
C++ Type:std::vector
Description:Coupled temperature
• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Description:The list of boundary IDs from the mesh where this boundary condition applies
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• 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
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
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
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
Description:Determines whether this object is calculated using an implicit or explicit form
• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
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https://www.ssa.gov/policy/docs/ssb/v82n2/v82n2p1.html | # What Is the Relationship Between Socioeconomic Deprivation and Child Supplemental Security Income Participation?
by
Social Security Bulletin, Vol. 82 No. 2, 2022
This article examines how socioeconomic deprivation relates to child Supplemental Security Income (SSI) participation in local areas. We construct a deprivation index that reflects a range of socioeconomic factors. We find that local areas with higher deprivation generally have higher levels of child SSI participation, but we also see substantial geographic variation. To explore this variation, we assess the demographic and economic factors associated with the deviation between observed child SSI participation and a level of participation predicted by the deprivation index. Local areas in which child SSI participation is substantially lower than the deprivation index predicts might be promising targets for outreach to better inform families about the SSI program. By measuring the deviation between predicted and actual SSI participation at the census tract level, outreach efforts can pinpoint the precise locations where they might plausibly have the greatest effect.
Michael Levere is a visiting assistant professor of economics at Haverford College and a senior researcher at Mathematica. David Wittenburg is a senior fellow at Mathematica. Jeffrey Hemmeter is the Acting Deputy Associate Commissioner for the Office of Research, Demonstration, and Employment Support, Office of Retirement and Disability Policy, Social Security Administration.
Acknowledgments: We are grateful to Manasi Deshpande, Özlen Luznar, Rachel Edmonds, Robert Weathers, Susan Wilschke, and participants at the 2021 Retirement and Disability Research Consortium Annual Meeting for valuable feedback. We also wish to thank Ijun Lai and Addison Larson for their important contributions.
The findings and conclusions presented in the Bulletin are those of the authors and do not necessarily represent the views of the Social Security Administration.
## Introduction
ACS American Community Survey ADI Area Deprivation Index CDR continuing disability review MSA metropolitan statistical area SSA Social Security Administration SSI Supplemental Security Income
Recent reductions in the number of children receiving Supplemental Security Income (SSI) raise questions of how well the program currently reaches those who need it. Administered by the Social Security Administration (SSA), SSI provides cash payments to families that have children with significant disabilities and meet certain income and asset criteria. The number of children participating in SSI peaked in 2013 but has gradually declined since then, for reasons that are not yet fully understood. In addition, child applications for SSI have dropped sharply during the COVID-19 pandemic, resulting in far fewer awards than SSA had projected (SSA 2021b).
SSI participation varies by county and state. Understanding the drivers of these geographic differences could help identify local areas where children and families not currently receiving SSI are likely to benefit from SSI receipt. Factors that may have driven the growth in child SSI participation through 2013 include a tightening of eligibility requirements for other state programs as well as increases in the numbers of children living in low-income families, identification of mental disorders by special education services, frequency of childhood mental disorder diagnoses, and awareness of childhood disability prevalence (Government Accountability Office 2012; Schmidt and Sevak 2017). Additional factors may relate directly to administrative processes in SSA. For example, changes in the frequency of continuing disability reviews (CDRs) likely play an important role in driving patterns of payment receipt among SSI children (Hemmeter and others 2021).
The decline in child SSI participation since 2013 is directly relevant to SSA's responsibility under the Social Security Act to provide outreach to potentially eligible populations.1 The act authorizes SSA to partner with federal, state, private, and nonprofit entities to support outreach efforts. The agency received increased funding beginning in fiscal year 2021 to identify and reach out to potential child SSI applicants in response to the sharp decline in applications during the pandemic (SSA 2021b). In June 2021, SSA designated certain claims officers as Vulnerable Population Liaisons to support and advise over 1,100 external organizations that take in and submit SSI applications on behalf of targeted groups.
Geographic variation, especially at local levels, represents an important consideration for outreach efforts and for understanding SSI program dynamics more broadly. In 2013, per capita child SSI participation was relatively higher in northeastern and southern states, although considerable variation existed within states at the county level (Schmidt and Sevak 2017). The large variation reflects how SSI operates alongside varying local and state systems that serve children with disabilities in different socioeconomic and political environments (Shogren and Wittenburg 2020). Outreach and other initiatives that attempt to influence program participation must take these factors into account to make the most efficient use of available resources. In turn, by targeting outreach to highly localized areas, SSA and its partners can try to address the underlying geographic variations in SSI participation.
One likely driver of child SSI participation is the local area's socioeconomic deprivation, which reflects a variety of factors such as income, education, employment, and housing quality. Our analysis uses a measure that we developed by adapting the methodology used to create the Area Deprivation Index (ADI), a data set used by researchers and policymakers to study health care delivery and inform policy.2 Our measure captures deprivation at the census tract level, allowing us to examine variation in SSI participation within highly localized areas. To qualify for payments under SSI's stringent asset and income limits, families must have sufficiently low resources. Almost half of child SSI recipients come from families with income below the poverty level, and median liquid family assets in 2001 were less than $100 (Rupp and others 2005/2006). Levels of deprivation vary widely across the United States (Kind and others 2014), which may explain the geographic variations in SSI participation. This article examines the extent to which socioeconomic deprivation explains geographic variations in SSI participation among children. We calculate local SSI participation rates at the county and census tract levels. Census tract data can reveal the variations that exist within counties. Our measure of deprivation allows us to rank socioeconomic factors across census tracts. This measure is similar to the ADI measure used in Kind and others (2014), reflecting a given area's general income, education, employment, and housing quality at a precise local level. Using a simple linear regression, we develop a measure of predicted area child SSI participation based on local area deprivation, which we then compare against the area's actual participation. We define this measure as deviation to highlight the difference between predicted and actual SSI participation. We also analyze the characteristics of communities that have lower-than-predicted SSI participation, which might help us understand how various factors contribute to the geographic variation in child SSI participation. Finally, we explore the extent to which areas with higher (or lower) deprivation experienced greater declines in applications after the onset of the COVID-19 pandemic. These findings contribute to an understanding of broader trends in SSI participation, particularly in identifying the areas with the greatest unmet need for SSI, which might be best served by targeted outreach. We find that SSI participation often varies substantially within census tracts, even after controlling for measures of deprivation. As a caveat, deviations represent only one measure of SSI participation and do not fully capture other factors that might influence outcomes, such as systemic disparities in access to resources and opportunities, the availability of related programs, or the economic environment in the local area. Hence, a large deviation only reflects that the area's caseload is above or below the national average for locations with a similar level of deprivation. Even in areas where actual participation exceeds predicted participation, large populations of eligible children might not currently receive SSI. Nonetheless, our quantitative measures provide a way to categorize areas that potentially deviate from these averages, which can be especially useful as an initial step in considering options for targeted outreach. ## Background SSI eligibility for applicants younger than age 18 is determined by disability, income, and asset criteria. To meet the disability criteria, a child must have “a medically determinable physical or mental impairment, which results in marked and severe functional limitations, and which can be expected to result in death or which has lasted or can be expected to last for a continuous period of not less than 12 months” (42 U.S.C. § 1382c[C][i]; emphasis added). To meet the income and asset criteria, a child's own financial resources, as well as any parental resources “deemed” to the child, must be sufficiently low.3 SSA excludes certain resources, such as the primary residential home or one vehicle (as long as it is used for transportation), in the calculation.4 Local field offices handle the application process.5 Recent research suggests that field office closures can affect local SSI participation by increasing the costs of application both for those who need to travel farther to access the office and for those affected by longer wait times (Deshpande and Li 2019). In 2021, the federal maximum SSI payment was$794 per month, and 23 states exercised their option to provide a supplementation payment to children with disabilities.6 On average, among families that include a child SSI recipient, almost half of family income comes from SSI (Davies, Rupp, and Wittenburg 2009). Children who qualify for SSI may qualify for services from other programs as well. For example, most children who receive SSI are automatically enrolled in Medicaid. Because of their limited income, many also qualify for other means-tested supports, such as Supplemental Nutrition Assistance Program (food stamp) benefits (Romig 2017).
SSA periodically reassesses the medical eligibility of SSI recipients during medical CDRs, which often result in benefit cessations. For a child whose impairment is expected to improve, SSA generally conducts a CDR within 6 to 18 months of SSI award; for a child whose impairment is judged “probable” to improve, SSA is supposed to conduct CDRs every 3 years; for a child whose impairment is not expected to improve, SSA is supposed to conduct CDRs at least every 7 years.7 However, the numbers of CDRs SSA conducts varies over time depending on caseload size, administrative priorities, and budgets. SSA also conducts an eligibility redetermination when a recipient reaches age 18, which entails both a review of nonmedical eligibility and a new disability determination using the adult disability criteria.8 At all ages, to remain eligible for payments, recipients must continue to not exceed the asset and income limits (including deemed income and assets from a parent for SSI recipients younger than 18). The number of CDRs SSA conducts has increased substantially since 2015, which might be an important driver of the decrease in SSI participation during this time, as frequent CDRs contribute to shorter durations of payment receipt (Hemmeter and others 2021).
The number of child SSI recipients has fluctuated substantially since 1996 despite no significant changes in the rules for eligibility (Chart 1). Although the statutory definition of eligibility for children has not changed in that time, administrative processes have changed in ways that can influence who becomes and remains eligible for SSI payments, with the most notable example being the large increase in CDRs in recent years. In the first years after the current SSI eligibility rules were implemented as part of larger welfare reforms in 1996, SSI caseloads dipped.9 Caseloads then increased from 2000 through 2013. The possible causes for rising caseloads were discussed in congressional hearings (for example, Wittenburg 2011), which drew particular interest because the increase coincided with contractions in other cash transfer programs such as Temporary Assistance for Needy Families (Schmidt and Sevak 2004, 2017). Since their 2013 peak of 1.3 million, SSI child-recipient caseloads have declined; 1.1 million children received SSI as of December 2020. Caseloads have declined further during the COVID-19 pandemic, with the closure of SSA field offices cited as an important driver (Emanuel 2021). Other factors, such as supplemental unemployment benefits, eviction embargoes, and stimulus payments—which increased income and reduced poverty (Wheaton and others 2021)—might also have contributed to declines in SSI participation.
Show as table
Table equivalent for Chart 1. Number of child SSI recipients, 1996–2020 (in millions)
Year Number
1996 0.955
1997 0.880
1998 0.887
1999 0.847
2000 0.847
2001 0.882
2002 0.915
2003 0.959
2004 0.993
2005 1.036
2006 1.079
2007 1.121
2008 1.154
2009 1.200
2010 1.239
2011 1.277
2012 1.312
2013 1.322
2014 1.300
2015 1.267
2016 1.213
2017 1.183
2018 1.148
2019 1.132
2020 1.109
SOURCE: SSA (2021a, Table 7.A9).
Prior literature highlights substantial geographic variation in caseload growth through 2013. Wittenburg and others (2015) showed that more than half of the growth in caseloads from 1998 to 2013 took place in four states (California, Florida, Pennsylvania, and Texas). The authors also showed that, more generally, SSI participation rates per capita were higher in southern and northeastern states. Schmidt and Sevak (2017) showed that regional and state differences in the number of people living in poverty and the availability of special education services, among other factors, contributed to differential growth in child SSI caseloads. Several studies identified other factors that could affect local caseload trends, such as availability of advocacy networks, proximity and access to SSA field offices, information about SSI that is tied to other programs, and cultural issues (for example, views of disability that vary by region) (Deshpande and Li 2019; Duggan, Kearney, and Rennane 2016; Government Accountability Office 2012).
Understanding the drivers of recent geographic variation in child SSI participation is important to ensure equitable access to the program. SSA has prioritized outreach to vulnerable populations such as children. The agency set aside $96 million in its fiscal year 2022 budget to support outreach efforts designed to acknowledge and address recent program declines associated with the COVID-19 pandemic (SSA 2021b). To better inform outreach efforts, and to understand SSI program dynamics more generally, this article addresses three notable gaps in the existing literature. First, recent geographic variation in child SSI participation is not well understood. Most studies analyze the period of large program growth through 2013, but recent declines in child SSI participation necessitate another look at whether geographic patterns might have changed. Second, most studies focus on larger geographic units such as counties, whereas understanding even narrower geographic areas such as census tracts might enable a deeper understanding of local patterns.10 Finally, quantitative information that could be used to identify promising targets for potential outreach (or to learn how child SSI participation in those areas is correlated with demographic and other characteristics) is not widely available. ### Deprivation We incorporate a measure of local area socioeconomic deprivation into our geographic analysis of child SSI participation rates. Our measure is based on the ADI, which was initially developed by the Health Resources and Services Administration. The ADI, and our deprivation measure, capture information about income, education, housing, and other local characteristics. A research team from the University of Wisconsin updates and maintains a data set on the ADI, which offers a relative ranking of socioeconomic disadvantage at the level of the census block group, a subunit of the census tract. Table 1 shows the correlations of child SSI participation with the full list of our deprivation input variables, which are based on data from the Census Bureau's American Community Survey (ACS). Table 1. Correlation of deprivation input variables for the period 2015–2019 with child SSI participation in 2019 at the county and census tract levels Variable Coefficient ACS question County Census tract Educational attainment, adults aged 25 or older Less than 9 years 0.197 0.250 B15003 High school diploma/equivalent or more -0.390 -0.409 B15003 Employment status, individuals aged 16 or older Employed in white-collar job a -0.377 -0.491 C24010 Unemployed 0.456 0.419 B23025 Housing characteristics Homeowners -0.326 -0.442 B25003 More than one person per room in household 0.019 0.135 B25014 Median monthly mortgage ($) -0.376 -0.395 B25088
Median gross rent ($) -0.403 -0.379 B25064 Median home value ($) -0.376 -0.348 B25077
Income and poverty characteristics
Median family income ($) -0.624 -0.553 B19113 Disparity ratio b 0.658 0.355 B19001 Family poverty rate 0.721 0.600 B17010 Individuals with earnings under 150 percent of federal poverty limit 0.703 0.634 C17002 Households with— Single parent and child(ren) under age 18 0.713 0.569 B11003 No motor vehicle 0.377 0.450 B25044 No telephone 0.288 0.235 B25043 Occupied housing units without complete plumbing 0.318 0.277 B25047 Overall deprivation 0.626 0.634 . . . SOURCE: Authors' calculations using SSA program records and ACS data. NOTES: In a linear regression of child SSI participation, the coefficient is statistically significant at the 1-percent level for all input variables and both area types except "more than one person per room in household" at the county level. . . . = not applicable. a. Management, business, science, and arts occupations. b. Ratio of individuals with income below$15,000 to individuals with income above $75,000. Researchers and policymakers use measures of deprivation such as the ADI to examine health care delivery and inform policy. Not limited to measuring poverty or income alone, socioeconomic deprivation provides a more holistic view of the ways that a local area might be disadvantaged. We use this measure to rank neighborhoods by socioeconomic disadvantage relative to the national average. Research has linked areas with greater deprivation to worse health outcomes, such as higher rates of obesity and hospital readmission (Kind and others 2014; Hu, Kind, and Nerenz 2018). Areas with higher deprivation also have higher rates of infant mortality (Singh and Kogan 2007) and shorter life expectancies at birth (Singh and Siahpush 2006). Socioeconomic deprivation is not the only way to measure local needs, which is a noteworthy consideration when interpreting findings. Kim and Loh (2020) identified eight measures developed by federal agencies or nonprofit research groups that capture different dimensions of local needs, including the ADI.11 All eight measures included poverty rate as one of their input metrics, although some of the measures diverged notably from others in their regional results. The authors also showed that all high-need communities fare worse than other communities on a range of alternative measures, such as greater prevalence of employment in low-wage occupations. Although our ADI-based measure of deprivation captures an essential component of need, Kim and Loh showed that of the eight measures, ADI identified relatively few high-need areas in the West and Midwest. Hence, using this measure of deprivation might lead to characterizations of high-need local areas that differ from those of other measures, a notable caveat when targeting localized outreach efforts. Nevertheless, the families of children with disabilities in areas with high deprivation are likely to have greater need for services or income support such as SSI. Local areas with low child SSI participation relative to the level of participation one might expect based on a deprivation measure could therefore be suitable targets for outreach. ## Data and Methods We used administrative data from the Supplemental Security Record, SSA's main system of records for the SSI program, to measure the number of children receiving SSI payments at the census tract and county levels in 2019. We also measured the number of child SSI applicants at the county level for 2019 and 2020. The administrative data contain the recipient's address, including the county. To assign a census tract, we geocoded the addresses of all child SSI recipients.12 We were able to assign a census tract with geocoding for 95 percent of the records. About 3.5 percent of the records had an unusable address, and 1.5 percent had an address that could not be geocoded for various reasons and thus could not be placed in a particular census tract. We dropped those records from the analysis. Our primary outcome measure is the number of child SSI recipients per 1,000 children in the geographic unit. We gathered data on the population of individuals aged 0–17 from ACS 5-year estimates for the period 2015–2019. These data were available at the census tract and county levels. We also explored the characteristics of child SSI recipients in each local area. Specifically, we measured the percentage distributions of child SSI recipients in each local area by sex, age (0–4, 5–13, 14–17), and primary diagnosis. For the latter, we used the standard list of primary diagnoses presented in the SSI Annual Statistical Report (SSA 2021c). Chart 2 shows the prevalence of child SSI participation in 2019 by county. As previous studies have shown, we find heavier concentrations of children receiving SSI in the southern and northeastern states. We measured deprivation using ACS 5-year estimates for the period 2015–2019. We calculated deprivation at the county and census tract levels by following the process described in Singh (2003).13 Specifically, we gathered data on the components of the ADI.14 We conducted a factor analysis to assign weights to each of the components, then created a raw index measure using those weights. We express the resulting value as a percentile so that the final index indicates the level of deprivation in the local area relative to the rest of the country. Chart 3 shows the geographic variation in relative deprivation across the United States at the county level. Deprivation is relatively high in southern states such as Arkansas, Kentucky, and Louisiana, many of which also have high levels of SSI participation (shown in Chart 2). However, many counties with relatively high deprivation also have lower levels of SSI participation, for example in North Dakota and South Dakota, and some counties combine lower deprivation with higher SSI participation. To better understand the relationship between deprivation and child SSI participation, we developed a regression framework to examine correlations between the two measures. We first estimated a simple linear regression of child SSI participation on deprivation as shown in equation 1: (1) $SSI g =α+β Deprivation g + ε g$ . We weighted this regression by the child population in the geographic unit. Using the coefficient $β$ from the regression, we created a predicted value of child SSI participation based on the local level of deprivation. As discussed above, we conducted separate analyses for census tracts and counties (both designated with the geographic variable $g$). Based on this regression, we then calculated deviation, which captures the gap between actual SSI participation and a prediction based on deprivation. In short, the deviation is the residual from the regression ($εg$). Deviation can be negative or positive. A negative deviation indicates that actual child SSI participation was lower than predicted participation. Conversely, a positive deviation indicates that actual SSI participation was higher than predicted participation. In the maps that follow, we consider a geographic unit to have less-than-predicted participation if deviation in that unit is lower than the 25th percentile of the deviation distribution. Similarly, we consider a geographic unit to have greater-than-predicted participation if deviation in that unit is greater than the 75th percentile of the deviation distribution.15 All metrics, even those presented for specific local areas, are based on the national distribution of deviation. We next explore how characteristics of local areas, listed in Box 1, are associated with larger or smaller deviations to help identify the types of places that would most likely benefit from outreach. These measures capture a range of local and regional characteristics in publicly available data. Our analysis includes information on demographic characteristics, disability prevalence, and other features of the local areas (such as population density, availability of social capital, and presence of Opportunity Zones) that might be correlated with deviations. We regress deviation ($εg$ in equation 1) on the list of measures from Box 1, signified as $Xg$ in equation 2:16 (2) $Deviation g =γ+δ X g + ω g$ . Box 1. Selected sociodemographic characteristics of local areas with which deviations between predicted and observed child SSI participation can be associated Characteristic Description and/or data source Percentage of population that is non-White Based on ACS 2015–2019 5-year estimates. Percentage of population that has a disability Based on ACS 2015–2019 5-year estimates. Region Northeast, South, Midwest, and West, defined at Census Bureau (2021a). Urbanicity Metropolitan, suburban, and rural, based on categories adapted from Economic Research Service (2020). Population density (counties only) Population from ACS 2015–2019 5-year estimates; land area from Census Bureau (2021b). Social capital (counties only) Measures of participation in civic, religious, and sports organizations, defined in Rupasingha, Goetz, and Freshwater (2006). Opportunity Zone (census tracts only) Economically distressed areas nominated by governors and certified by the Secretary of the Treasury. Opportunity Zones are listed at https://www.irs.gov/pub/irs-drop/n-18-48.pdf. SOURCES: Cited above. We estimated multivariate regressions, including all control variables, and weighted the regressions by population size. Because deviation does not have a readily intuitive cardinal interpretation, we present only standardized coefficients and p-values. This enables us to identify measures that have relatively higher and lower correlations with deviation. Because this estimation requires two steps, we bootstrap the entire process to calculate standard errors. Finally, we explore how the COVID-19 pandemic has affected the underlying relationship between deprivation and child SSI participation. Specifically, we assess whether the change in SSI applications from 2019 to 2020 was associated with deprivation and deviation. SSI applications for children declined by 17 percent in 2020 (SSA 2021c, Table 57), with substantial geographic variation in the decline. Because census tract–level data were not available, we focused on counties for this aspect of the analysis. ## Results There is a strong positive relationship between deprivation and child SSI participation (Chart 4), which is expected because SSI serves low-income populations. For each successive decile of deprivation (for example, the 20th percentile relative to the 10th), child SSI participation increases by 3.5 per 1,000, on average. Relative to the 17.3 child recipients per 1,000 child residents in the average census tract, this represents an increase of nearly 20 percent. Table 2 presents the results of this regression at both the county and census tract levels, weighted and not weighted for the area's child population size. Results are statistically significant at both geographic levels, although the magnitude of the relationship is substantially stronger in the census tract analysis.17 The R2 from the simple linear regression in equation 1 (weighted for child population) is 0.392 at the county level and 0.402 at the census tract level. This indicates that although there is a strong correlation between deprivation and SSI receipt, much variation remains in predicting local area SSI participation. Show as table Table equivalent for Chart 4. Relationship between census tract socioeconomic deprivation in the period 2015–2019 and child SSI participation rate in 2019 Deprivation index percentile Child SSI recipients per 1,000 children 5 1.103 10 2.267 15 3.578 20 4.758 25 6.028 30 7.521 35 9.001 40 10.108 45 11.686 50 12.922 55 14.080 60 15.549 65 17.095 70 18.387 75 20.750 80 23.034 85 25.398 90 29.374 95 33.438 100 37.981 SOURCE: Authors' calculations using SSA program records and ACS data. NOTE: Plotted points represent the average participation rate in all census tracts within a given ventile (5th-percentile interval). For example, the point plotted for the 5th percentile represents the average participation rate among all census tracts in the 1st through 5th percentiles of socioeconomic deprivation. Table 2. Results of separate linear regressions on the relationship between child SSI participation and each of two measures of local area socioeconomic conditions in 2019 (weighted and not weighted for child population) Measure County level Census tract level Weighted Not weighted Weighted Not weighted Number of observations 3,130 3,130 71,976 71,976 Regression 1: Deprivation a Coefficient 0.209 0.197 0.349 0.407 Standard error 0.014 0.006 0.002 0.004 R2 0.392 0.331 0.402 0.089 Regression 2: Poverty rate b Coefficient 0.229 0.206 0.335 0.392 Standard error 0.013 0.005 0.002 0.007 R2 0.487 0.378 0.375 0.084 SOURCE: Authors' calculations using SSA program records and ACS data. a. Local area percentile on a deprivation index. The deprivation measure is based on data for the period 2015–2019. b. Percentage of population with family income below 150 percent of the federal poverty level. The percentage is converted to a percentile for consistency with the deprivation measure. The distribution of child SSI recipients by primary diagnosis18 varies depending on the level of deprivation (Chart 5), while distributions by sex and age do not (Table 3). Using descriptive data on the average characteristics of child SSI recipients in each census tract, we find that communities with higher levels of deprivation have a lower percentage of child SSI recipients with autistic disorders as their primary diagnosis.19 This is consistent with evidence that autism diagnosis rates are higher in places with higher socioeconomic status (Thomas and others 2012). By contrast, children in communities with higher deprivation have greater incidence of developmental disorders or other childhood and adolescent disorders as their primary diagnosis.20 The age and sex distributions of child SSI recipients are mostly constant across communities regardless of the level of deprivation. Show as table Table equivalent for Chart 5. Percentage of child SSI recipients with selected primary diagnoses in 2019, by census tract deprivation index for the period 2015–2019 Deprivation index percentile Autistic disorders Developmental disorders Other childhood and adolescent disorders 5 28.38 11.77 11.20 10 27.05 14.18 12.39 15 26.09 13.69 12.76 20 26.05 14.33 12.75 25 24.89 14.21 13.88 30 24.51 15.17 14.52 35 23.50 15.86 14.63 40 23.14 15.76 14.43 45 22.87 15.66 15.33 50 22.59 16.17 15.61 55 21.29 16.62 16.03 60 21.85 16.46 16.20 65 20.70 17.08 16.43 70 20.46 17.05 16.63 75 20.28 17.58 16.50 80 20.07 18.06 16.87 85 18.62 18.52 17.36 90 17.48 19.68 17.93 95 16.72 20.36 18.57 100 15.24 21.17 19.87 SOURCE: Authors' calculations using SSA program records and ACS data. NOTES: For each primary diagnosis, the plotted points represent the average percentage of child SSI recipients with that diagnosis in all census tracts within a given deprivation ventile (5th-percentile interval). For example, the point plotted for the 5th percentile represents the average percentage among all census tracts in the 1st through 5th percentiles of socioeconomic deprivation. Percentages for other primary diagnoses are available on request from the authors. Table 3. Percentage distributions of child SSI recipients in 2019 by age and sex, by local area deprivation index percentile for the period 2015–2019 Deprivation index percentile Age Sex 0–4 5–12 13–17 Female Male 5 15.76 50.17 34.08 31.90 68.10 10 15.22 48.50 36.29 32.55 67.45 15 14.98 48.76 36.27 34.27 65.73 20 15.04 49.98 34.98 33.59 66.41 25 14.80 50.05 35.15 32.81 67.19 30 14.38 50.94 34.69 32.83 67.17 35 14.63 50.14 35.23 32.93 67.07 40 14.45 50.61 34.94 32.73 67.27 45 14.20 50.45 35.35 32.96 67.04 50 14.09 50.55 35.36 32.49 67.51 55 13.95 50.62 35.43 32.28 67.72 60 13.74 50.63 35.63 32.44 67.56 65 13.38 50.71 35.91 32.52 67.48 70 13.76 51.05 35.19 32.40 67.60 75 13.66 50.73 35.61 32.57 67.43 80 13.67 50.98 35.35 32.26 67.74 85 13.30 51.15 35.55 32.41 67.59 90 13.79 51.17 35.04 32.76 67.24 95 13.05 51.30 35.65 32.33 67.67 100 13.11 51.82 35.07 32.44 67.56 SOURCE: Authors' calculations using SSA program records and ACS data. ### Geographic Heterogeneity and Deviation Between Predicted and Actual Child SSI Participation We next examine the geographic dispersion of deviation (Chart 6). We show that most census tracts have deviation values close to zero, although some can be very high (or low). Note that Chart 6 top-codes values at 65, representing the 99th percentile of deviation, to simplify the presentation. Show as table Table equivalent for Chart 6. Percentage distribution of census tracts by deviation between actual child SSI participation and the level of participation predicted by deprivation index in 2019 Deviation value Percent -35 0.03 -30 0.16 -25 0.44 -20 1.86 -15 5.55 -10 11.71 -5 19.81 0 29.08 5 13.34 10 5.91 15 3.44 20 2.26 25 1.55 30 1.09 35 0.80 40 0.62 45 0.44 50 0.33 55 0.28 60 0.20 65 1.09 SOURCE: Authors' calculations using SSA program records and ACS data. NOTES: Deviations are top-coded at 65. Each bar shows the percent of tracts that have deviations in a bucket centered at the number shown. For example, the bucket around 0 shows tracts with deviations between −2.5 and 2.5. Chart 7 shows that child SSI participation in many areas is notably higher—or lower—than predicted. Recall that we define an area to have higher-than-predicted participation if the deviation measure is greater than the 75th percentile, and lower-than-predicted participation if the measure is below the 25th percentile, of the deviation distribution.21 Areas with lower-than-predicted participation are disproportionately located in the Midwest, where about 32 percent of census tracts fall into this category, versus 23 percent in the rest of the country. Outreach might benefit areas with relatively limited SSI participation such as these. Areas with higher-than-predicted participation are disproportionately located in the Northeast and the South; about 35 percent of census tracts in the Northeast and 32 percent in the South fall into this category, versus 16 percent in the rest of the country. The areas with higher-than-predicted participation drove much of the growth in child SSI caseloads from 1996 to 2015 (Wittenburg and others 2015). Within counties, individual census tracts often vary in whether actual participation is higher or lower than predicted. For example, Chart 8 shows the census tracts that make up the metropolitan statistical area (MSA) for Detroit, Michigan. Metro Detroit has about 4.4 million people, making it the 14th largest MSA in the country. In 2019, it ranked 91st of 384 MSAs in per capita personal income (Bureau of Economic Analysis 2020). The Detroit MSA contains a mix of areas in which actual participation is greater than predicted (positive deviation, shown in green) and in which actual participation is less than predicted (negative deviation, in brown). This result prompts a question, which we address below: What factors are associated with local areas having higher or lower deviations? Narrowing in on these highly localized areas can help SSA precisely pinpoint where to target resources; for example, by helping identify specific neighborhoods in which to recruit local partners. More broadly, it can help researchers and policymakers better understand the heterogeneity of SSI participation at local levels, including factors such as the relative prevalence of networking (that is, learning about the program through local relationships) that might influence SSI dynamics and interactions with other programs. ### Correlations with Deviation To understand the factors associated with higher and lower levels of deviation, we next estimate regressions using equation 2. We use measures of deviation as an outcome variable with the control variables that are listed in Box 1. We weight the regression by child population in the local area. These regressions explore the extent to which certain community characteristics predict positive or negative deviation. By identifying patterns common to local areas with a mismatch between deprivation and SSI participation, policymakers could target resources to communities with the characteristics frequently associated with high measures of deviation. Areas that have a larger share of non-White residents have greater positive deviation (Table 4). Conversely, the larger the share of White residents in a local area, the lower the actual child SSI participation relative to predicted participation based on deprivation. In other words, a smaller positive or larger negative magnitude in the measure of deviation is associated with a larger White share of the population. This finding is consistent with evidence showing that Black individuals are about twice as likely to receive SSI payments as White individuals (Musumeci and Orgera 2021). The standardized coefficient for the non-White population variable has a large magnitude for counties and census tracts alike, indicating that among the chosen predictors, this one has a strong relationship with deviation. Table 4. Correlations of selected local area characteristics with deviation in 2019 Characteristic County level Census tract level Standardized coefficient p-value Standardized coefficient p-value Percentage of population that— Is non-White 0.337 0.000 0.105 0.000 Has a disability 0.276 0.000 0.146 0.000 Region Northeast 0.255 0.000 0.159 0.000 South 0.112 0.004 0.069 0.000 Midwest (reference variable omitted) . . . . . . . . . . . . West -0.195 0.000 -0.140 0.000 Urbanicity Metropolitan 0.326 0.000 0.135 0.000 Suburban (reference variable omitted) . . . . . . . . . . . . Rural -0.071 0.000 -0.028 0.000 Population density 0.176 0.049 . . . . . . Social capital 0.246 0.000 . . . . . . Opportunity Zone . . . . . . 0.037 0.000 SOURCE: Authors' calculations using SSA program records, ACS data, and the sources cited in Box 1. NOTES: A positive coefficient indicates that the characteristic is positively associated with deviation. Results are weighted by local area child population. . . . = not applicable. Other factors that prior research has associated with SSI participation are also associated with deviation. For example, deviation increases with the share of the population that has a disability, consistent with the disability criteria for children to receive SSI. There are notable differences in deviation by region, with areas in the Northeast and the South having higher deviation than those in the Midwest and the West. Counties with higher social capital have greater deviation, indicating that places with lower participation in civic, religious, and sports organizations do not participate in SSI to the extent that would otherwise be expected based on the level of deprivation. Metropolitan areas have substantially higher deviation, while rural areas tend to have lower deviation. We also consider an alternative specification in which the outcome is an indicator of negative deviation (that is, actual participation is less than predicted participation) rather than the continuous value of deviation (Table 5). The geographic pattern of results is similar, with counties or census tracts in the Northeast and South less likely than those in the Midwest and West to have lower-than-predicted participation. However, some of the other characteristics exhibit different patterns. For example, census tracts with a higher percentage of the population that is non-White are more likely to have lower-than-predicted participation, while the non-White share of the population is not a significant predictor at the county level. Other characteristics, such as population density, also are no longer significant predictors. Table 5. Correlations of selected local area characteristics with lower-than-predicted child SSI participation in 2019 Characteristic County level Census tract level Standardized coefficient p-value Standardized coefficient p-value Percentage of population that— Is non-White 0.044 0.335 0.135 0.000 Has a disability 0.100 0.012 0.047 0.000 Region Northeast -0.095 0.000 -0.152 0.000 South -0.092 0.002 -0.132 0.000 Midwest (reference variable omitted) . . . . . . . . . . . . West 0.003 0.946 0.028 0.000 Urbanicity Metropolitan -0.323 0.000 -0.205 0.000 Suburban (reference variable omitted) . . . . . . . . . . . . Rural 0.111 0.000 0.037 0.000 Population density -0.017 0.712 . . . . . . Social capital -0.078 0.009 . . . . . . Opportunity Zone . . . . . . 0.030 0.000 SOURCE: Authors' calculations using SSA program records, ACS data, and the sources cited in Box 1. NOTES: Results are weighted by local area child population. . . . = not applicable. ### SSI Applications During the COVID-19 Pandemic We estimate that the number of child SSI applications filed during 2020 fell to 310,688, a decline of 17.5 percent from the 376,557 child SSI applications filed during 2019.22 Counties with higher deprivation had slightly larger declines in child SSI applications in 2020 (Table 6). For each successively higher decile of deprivation, SSI applications declined by an additional 0.5 percentage points, indicating that these changes contributed a very small fraction to the total decline in child SSI applications during 2020. In addition, counties with greater deviation saw larger declines in child SSI applications. Counties that had smaller positive deviation (or larger negative deviation) likely began 2019 with low application levels because actual participation was already less than predicted participation, making application numbers in those areas unlikely to decline. Table 6. Correlations of the county-level decline in child SSI applications from 2019 to 2020 with deprivation and with the deviation between actual and predicted child SSI participation Measure Deprivation Deviation Coefficient -0.053 -0.799 Standard error 0.024 0.073 Number of observations 3,130 SOURCE: Authors' calculations using SSA program records and ACS data. NOTES: Correlation coefficients reflect the regression of the percentage change in SSI applications. Regressions are weighted by county child population. ## Conclusion We find substantial differences in child SSI participation across geographic areas even after controlling for deprivation. These differences existed before the drop in applications associated with the COVID-19 pandemic, yet high-deprivation areas saw somewhat larger declines in application volume during the first year of the pandemic. In response to that drop, SSA increased outreach efforts in at-risk communities and for populations facing barriers to participation (SSA 2021b). The agency established new liaisons and partnerships to facilitate application and released public service announcements focusing on children with disabilities. Our research can support SSA by suggesting a metric with which to target areas for more effective outreach. A deprivation metric succinctly identifies areas with multiple characteristics that are likely to be associated with barriers to participating in SSI (and other programs). As such, deprivation could be more useful than single-measure identifiers such as poverty rate. By identifying specific geographic areas with notably lower-than-expected SSI participation, SSA can effectively pinpoint its outreach efforts. Although the deprivation index is one potential metric, our work highlights several additional local-area factors, such as race, disability prevalence, and social capital, that are correlated with gaps between predicted and actual SSI participation. Other factors beyond the scope of this article that could also inform targeted outreach include aspects of the local program environment such as the availability of services and supports, which vary substantially by region and within counties (National Academies of Sciences, Engineering, and Medicine 2018); SSA field office proximity (Deshpande and Li 2019); and CDR frequencies. Although our deviation metric is a useful starting point for understanding geographic variation in program dynamics, it has limitations. Deviation is measured relative to the average national caseload, so it can only capture whether SSI participation is low relative to all other areas, not whether all who are eligible are participating. Further, deviation may not reveal some of the systemic barriers that can influence outcomes. For example, residential segregation resulting from redlining and other discriminatory practices (Aaronson, Hartley, and Mazumder 2021) might unevenly affect the underlying input measures, which include housing variables, as the extent of such practices varies from location to location. If the measure of deprivation underestimates or overestimates the need for SSI in communities with a larger non-White population because it cannot distinguish the relative effects of such systemic factors, our ability to draw conclusions from the model may be limited.23 Despite these limitations, using the deviation measure provides SSA a useful starting point for identifying potentially underserved populations. Although we focus on areas with high deprivation and low child SSI participation, understanding more about the areas where actual participation exceeds predicted participation is also important. Perhaps through stronger community ties (such as social capital) and greater understanding of available programs, people in such areas take better advantage of services and supports available to them. Yet many people do not take up benefits for which they are eligible (Currie 2006). Although these areas have greater-than-predicted participation relative to the national average, such areas might nevertheless have many children who are eligible for SSI but do not participate and thus might also benefit from outreach efforts. ## Notes 1 For the Social Security Act section requiring SSA outreach to children who are potentially eligible for SSI payments, see https://www.ssa.gov/OP_Home/ssact/title16b/1635.htm. 2 Singh (2003) developed the ADI methodology. The University of Wisconsin maintains and updates the ADI data set. 3 A child can qualify for SSI if her or his own countable resources do not exceed$2,000. Parental resources deemed to the child affect the eligibility threshold; in a 2-parent household, for example, resources can be as high as $5,000 before the child is no longer eligible. 4 For more details on resource limits, see https://www.ssa.gov/ssi/spotlights/spot-resources.htm. 5 Applicants can be assisted in person or by phone. For more details on the child SSI application process, see https://www.ssa.gov/benefits/disability/apply-child.html. 6 The Policy Surveillance Program provides details on state supplementation payments for child SSI recipients at http://lawatlas.org/datasets/supplemental-security-income-for-children-with-disabilities. 7 For SSA's policies on the frequency of CDRs, see https://www.ssa.gov/OP_Home/cfr20/404/404-1590.htm. 8 Unlike those for children, the adult criteria rely on a disability definition that focuses on work (the inability to engage in substantial gainful activity, which in 2021 was defined as monthly earnings above$1,310 for a nonblind individual). In making age-18 redeterminations, SSA uses the same medical, income, and asset criteria it uses in adult application decisions. Among children receiving SSI payments on reaching age 18, 82 percent have a redetermination at that time; the others do not have redeterminations until after age 18, for various reasons (Hemmeter and Bailey 2015).
9 For a history of SSI program changes in (and before) 1996, see Wittenburg and Livermore (2021) and Berkowitz and DeWitt (2013).
10 One example of a study using census tract–level analysis is Chetty, Hendren, and Katz (2016).
11 The other seven measures are (1) the federal statutory definition of Low-Income Community; (2) the Internal Revenue Service designation as a Qualified Opportunity Zone; (3) the Centers for Disease Control and Prevention's Social Vulnerability Index; (4) diversitydatakids.org's Child Opportunity Index; (5) the Robert Graham Center's Social Deprivation Index; (6) the Economic Innovation Group's Distressed Communities Index; and (7) Kim and Loh's adaptation of the “persistent poverty counties” classification used by the Department of Agriculture's Economic Research Service.
12 The United States is composed of about 74,000 census tracts, which are designed to have about 4,000 people each, although their populations range roughly from 2,500 to 8,000.
13 The ADI provided by the University of Wisconsin is only available at the census block group level and captures a relative ranking. Because the ADI is a relative ranking, we could not convert the census block group values to census tract or county values simply by aggregating the narrower units into the broader ones and then computing an average. Rather, we needed the underlying raw score, which we could use to construct a relative percentile at the geographic variable of interest. Even so, there is a strong positive correlation (greater than 0.80) between the percentile computed by averaging the values for an area's component subunits and the percentile calculated from the raw data.
14 Input variables are missing for as many as 5.9 percent of census tracts. In these instances, we imputed the tract-level value using the county-level value (when available), following the same procedure used to create the ADI.
15 The choice of 25th and 75th percentiles is somewhat arbitrary, but the interquartile range provides a reasonable definition of low and high deviation. Alternative thresholds, such as those based on the standard deviation, could also be used.
16 Many of these measures are correlated with both deprivation and SSI participation. However, this regression seeks to correlate each measure with deviation, not directly with either deprivation or actual SSI participation. In other words, a measure that is correlated with both deprivation and SSI participation is not necessarily correlated with the gap between actual SSI participation and a level of SSI participation that is predicted based on deprivation.
17 Table 2 also includes an alternative specification that replaces deprivation with a measure of poverty rate—specifically, the percentage of the local population earning less than 150 percent of the federal poverty limit, converted to a percentile score—which yields remarkably similar results.
18 Children may have more than one diagnosis; however, not all are recorded in SSA's administrative records. Additionally, the primary diagnosis may or may not reflect the condition causing the most significant functional barriers to the child. Whether a given condition is identified as the primary diagnosis may reflect underlying differences in access to medical care or SSA's disability determination process itself.
19 On average, nearly one child SSI recipient in five had a primary diagnosis of autistic disorders. In the highest deprivation areas, fewer than 15 percent had that primary diagnosis, while in the lowest deprivation areas, nearly 30 percent did.
20 On average, about 30 percent of child SSI recipients had a primary diagnosis of either developmental disorders or other childhood and adolescent disorders. In the highest deprivation areas, more than 40 percent had one of these two conditions as a primary diagnosis, while in the lowest deprivation areas, only about 23 percent did.
21 Because Table 2 indicates a similar relationship between our poverty measure and child SSI participation, we constructed an alternative measure of deviation based on the regression on poverty. This alternative deviation is highly correlated with deviation based on the regression on deprivation. The correlation is about 0.95 at the county level and 0.99 at the census tract level. Using a simpler measure would yield nearly identical findings but would not explicitly account for other socioeconomic factors.
22 Our estimates may not match official SSA statistics because of differing estimation methodologies for cases involving individuals with more than one application or applications that are not recorded timely.
23 As another example, health care outcomes are worse for Black patients than for White patients with the same levels of spending, suggesting differential access to care (Obermeyer and others 2019). This leads to bias in comparing measures of spending across racial groups. If similar issues affect the deprivation inputs—and thus SSI participation—our findings may be compromised.
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Wittenburg, David, and Gina Livermore. 2021. “Youth Transition.” In Lessons from SSA Demonstrations for Disability Policy and Future Research, edited by Austin Nichols, Jeffrey Hemmeter, and Debra Goetz Engler (223–260). Rockville, MD: Abt Associates.
Wittenburg, David, John Tambornino, Elizabeth Brown, Gretchen Rowe, Mason DeCamillis, and Gilbert Crouse. 2015. “The Child SSI Program and the Changing Safety Net.” ASPE Research Brief. Washington, DC: Department of Health and Human Services, Office of the Assistant Secretary for Planning and Evaluation. | 2022-06-30T19:42:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21369130909442902, "perplexity": 11372.20180372064}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103877410.46/warc/CC-MAIN-20220630183616-20220630213616-00056.warc.gz"} |
http://gams.cam.nist.gov/10.55 | # §10.55 Continued Fractions
For continued fractions for $\mathop{\mathsf{j}_{n+1}\/}\nolimits\!\left(z\right)/\mathop{\mathsf{j}_{n}\/}% \nolimits\!\left(z\right)$ and $\mathop{{\mathsf{i}^{(1)}_{n+1}}\/}\nolimits\!\left(z\right)/\mathop{{\mathsf{% i}^{(1)}_{n}}\/}\nolimits\!\left(z\right)$ see Cuyt et al. (2008, pp. 350, 353, 362, 363, 367–369). | 2016-09-25T08:48:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 2, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8459334969520569, "perplexity": 1808.5071179358888}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660158.72/warc/CC-MAIN-20160924173740-00163-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://large-numbers.fandom.com/wiki/Bouncing_Factorial?oldid=5216 | ## FANDOM
1,138 Pages
The Bouncing Factorial is a type of factorial that multiplies together the integers from 1 to some number n, then back to 1, then back to (n-1), then to 1, then to (n-2), and so on. It is denoted
$n\Lambda$ .[1]
## Example Edit
For instance, the bouncing factorial of 9 is equal to 1*2*3*4*5*6*7*8*9*8*7*6*5*4*3*2*1*2*3*4*5*6*7*8*7*6*5*4*3*2*1*2*3*4*5*6*7*6*5*4*3*2*1*2*3*4*5*6*5*4*3*2*1*2*3*4*5*4*3*2*1*2*3*4*3*2*1*2*3*2*1*2*1, or 9,278,496,603,801,318,870,491,332,608,000,000,000.
Pictured above is a visualization of the bouncing factorial of 9, where every new multiplication peak has been colored for clarity. The numbers above the peaks refer to their height in units. The x-axis may be thought of as time, and the y-axis as quantity. The bouncing factorial of 9 is equal to the product of the quantities of all those little colored squares.
## Values Edit
The first few values of the function are:
• $$1Λ = 1$$
• $$2Λ = 2$$ (1×2×1)
• $$3Λ = 24$$ (1×2×3×2×1×2×1)
• $$4Λ = 3,456$$ (1×2×3×4×3×2×1×2×3×2×1×2×1)
• $$5Λ = 9,953,280$$ (1×2×3×4×5×4×3×2×1×2×3×4×3×2×1×2×3×2×1×2×1)
• $$6Λ = 859,963,392,000$$ (1×2×3×4×5×6×5×4×3×2×1×...)
• $$7Λ = 3,120,635,156,889,600,000$$ (1×2×3×4×5×6×7×6×5×4×3×2×1×...)
• $$8Λ = 634,153,008,009,974,906,880,000,000$$ (1×2×3×4×5×6×7×8×7×6×5×4×3×2×1×...)
• $$9Λ = 9,278,496,603,801,318,870,491,332,608,000,000,000$$ (1×2×3×4×5×6×7×8×9×8×7×6×5×4×3×2×1×...)
• $$10Λ = 912,218,100,099,725,239,100,847,669,366,019,325,952,000,000,000,000$$ (1×2×3×4×5×6×7×8×9×10×9×8×7×6×5×4×3×2×1×...)
## Formal description Edit
The Bouncing Factorial of n can be formally defined as
$n(\prod_{i=1}^{n-1} i^{2n-2i+1})$ . This formula holds true for all values of n greater than 1. When n equals one, the bouncing factorial is 1. It may also be recursively defined as
$Z_{n+1}={{(n+1)!^2}/(n+1)}*Z_n$ where
$Z_1=1$ .
It can also be calculated as n!×(n-1)!×(n-1)Λ for n > 1.
## Primes Edit
$$3\Lambda -1$$ is prime. As of the time this was written, no other primes have been found of the form $$n\Lambda -1$$ for values of n less than or equal to 10.
## Source Edit
1. Powerful Functions - The Repository Of Large Numbers
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https://phys.libretexts.org/TextBooks_and_TextMaps/College_Physics/Book%3A_Conceptual_Physics_(Crowell)/12%3A_Optics/12.4%3A_Refraction | $$\require{cancel}$$
# 12.4: Refraction
[ "article:topic", "Snell\u2019s law of refraction", "authorname:crowellb", "index of refraction", "Lens-Maker\u2019s Equation" ]
Economists normally consider free markets to be the natural way of judging the monetary value of something, but social scientists also use questionnaires to gauge the relative value of privileges, disadvantages, or possessions that cannot be bought or sold. They ask people to imagine that they could trade one thing for another and ask which they would choose. One interesting result is that the average light-skinned person in the U.S. would rather lose an arm than suffer the racist treatment routinely endured by African-Americans. Even more impressive is the value of sight. Many prospective parents can imagine without too much fear having a deaf child, but would have a far more difficult time coping with raising a blind one.
So great is the value attached to sight that some have imbued it with mystical aspects. Joan of Arc saw visions, and my college has a “vision statement.” Christian fundamentalists who perceive a conflict between evolution and their religion have claimed that the eye is such a perfect device that it could never have arisen through a process as helter-skelter as evolution, or that it could not have evolved because half of an eye would be useless. In fact, the structure of an eye is fundamentally dictated by physics, and it has arisen separately by evolution somewhere between eight and 40 times, depending on which biologist you ask. We humans have a version of the eye that can be traced back to the evolution of a light-sensitive “eye spot” on the head of an ancient invertebrate. A sunken pit then developed so that the eye would only receive light from one direction, allowing the organism to tell where the light was coming from. (Modern flatworms have this type of eye.) The top of the pit then became partially covered, leaving a hole, for even greater directionality (as in the nautilus). At some point the cavity became filled with jelly, and this jelly finally became a lens, resulting in the general type of eye that we share with the bony fishes and other vertebrates. Far from being a perfect device, the vertebrate eye is marred by a serious design flaw due to the lack of planning or intelligent design in evolution: the nerve cells of the retina and the blood vessels that serve them are all in front of the light-sensitive cells, blocking part of the light. Squids and other molluscs, whose eyes evolved on a separate branch of the evolutionary tree, have a more sensible arrangement, with the light-sensitive cells out in front.
### 12.4.1 Refraction
The fundamental physical phenomenon at work in the eye is that when light crosses a boundary between two media (such as air and the eye's jelly), part of its energy is reflected, but part passes into the new medium. In the ray model of light, we describe the original ray as splitting into a reflected ray and a transmitted one (the one that gets through the boundary). Of course the reflected ray goes in a direction that is different from that of the original one, according to the rules of reflection we have already studied. More surprisingly --- and this is the crucial point for making your eye focus light --- the transmitted ray is bent somewhat as well. This bending phenomenon is called refraction. The origin of the word is the same as that of the word “fracture,” i.e., the ray is bent or “broken.” (Keep in mind, however, that light rays are not physical objects that can really be “broken.”) Refraction occurs with all waves, not just light waves.
Figure $$\PageIndex{1}$$: A human eye. Figure $$\PageIndex{2}$$: The anatomy of the eye.
The actual anatomy of the eye, Figure $$\PageIndex{2}$$, is quite complex, but in essence it is very much like every other optical device based on refraction. The rays are bent when they pass through the front surface of the eye, Figure $$\PageIndex{3}$$. Rays that enter farther from the central axis are bent more, with the result that an image is formed on the retina. There is only one slightly novel aspect of the situation. In most human-built optical devices, such as a movie projector, the light is bent as it passes into a lens, bent again as it reemerges, and then reaches a focus beyond the lens. In the eye, however, the “screen” is inside the eye, so the rays are only refracted once, on entering the jelly, and never emerge again.
Figure $$\PageIndex{3}$$: A simplified optical diagram of the eye. Light rays are bent when they cross from the air into the eye. (A little of the incident rays' energy goes into the reflected rays rather than the ones transmitted into the eye.)
A common misconception is that the “lens” of the eye is what does the focusing. All the transparent parts of the eye are made of fairly similar stuff, so the dramatic change in medium is when a ray crosses from the air into the eye (at the outside surface of the cornea). This is where nearly all the refraction takes place. The lens medium differs only slightly in its optical properties from the rest of the eye, so very little refraction occurs as light enters and exits the lens. The lens, whose shape is adjusted by muscles attached to it, is only meant for fine-tuning the focus to form images of near or far objects.
#### Refractive Properties of Media
What are the rules governing refraction? The first thing to observe is that just as with reflection, the new, bent part of the ray lies in the same plane as the normal (perpendicular) and the incident ray, Figure $$\PageIndex{4}$$.
Figure $$\PageIndex{4}$$: The incident, reflected, and transmitted (refracted) rays all lie in a plane that includes the normal (dashed line). Figure $$\PageIndex{5}$$: The angles $$\theta_1$$ and $$\theta_2$$ are related to each other, and also depend on the properties of the two media. Because refraction is time-reversal symmetric, there is no need to label the rays with arrowheads.
If you try shooting a beam of light at the boundary between two substances, say water and air, you'll find that regardless of the angle at which you send in the beam, the part of the beam in the water is always closer to the normal line, Figure $$\PageIndex{5}$$.
It doesn't matter if the ray is entering the water or leaving, so refraction is symmetric with respect to time-reversal, Figure $$\PageIndex{6}$$ .
Figure $$\PageIndex{6}$$: Refraction has time-reversal symmetry. Regardless of whether the light is going into or out of the water, the relationship between the two angles is the same, and the ray is closer to the normal while in the water.
If, instead of water and air, you try another combination of substances, say plastic and gasoline, again you'll find that the ray's angle with respect to the normal is consistently smaller in one and larger in the other. Also, we find that if substance A has rays closer to normal than in B, and B has rays closer to normal than in C, then A has rays closer to normal than C. This means that we can rank-order all materials according to their refractive properties. Isaac Newton did so, including in his list many amusing substances, such as “Danzig vitriol” and “a pseudo-topazius, being a natural, pellucid, brittle, hairy stone, of a yellow color.” Several general rules can be inferred from such a list:
• Vacuum lies at one end of the list. In refraction across the interface between vacuum and any other medium, the other medium has rays closer to the normal.
• Among gases, the ray gets closer to the normal if you increase the density of the gas by pressurizing it more.
• The refractive properties of liquid mixtures and solutions vary in a smooth and systematic manner as the proportions of the mixture are changed.
• Denser substances usually, but not always, have rays closer to the normal.
The second and third rules provide us with a method for measuring the density of an unknown sample of gas, or the concentration of a solution. The latter technique is very commonly used, and the CRC Handbook of Physics and Chemistry, for instance, contains extensive tables of the refractive properties of sugar solutions, cat urine, and so on.
### Snell's Law
The numerical rule governing refraction was discovered by Snell, who must have collected experimental data something like what is shown on this graph and then attempted by trial and error to find the right equation. The equation he came up with was
$\frac{\sin\theta_1}{\sin\theta_2} = \text{constant} .$
The value of the constant would depend on the combination of media used. For instance, any one of the data points in the graph would have sufficed to show that the constant was 1.3 for an air-water interface (taking air to be substance 1 and water to be substance 2).
Figure $$\PageIndex{7}$$: The relationship between the angles in refraction.
Snell further found that if media A and B gave a constant $$K_{AB}$$ and media B and C gave a constant $$K_{BC}$$, then refraction at an interface between A and C would be described by a constant equal to the product, $$K_{AC}=K_{AB}K_{BC}$$. This is exactly what one would expect if the constant depended on the ratio of some number characterizing one medium to the number characteristic of the second medium. This number is called the index of refraction of the medium, written as $$n$$ in equations. Since measuring the angles would only allow him to determine the ratio of the indices of refraction of two media, Snell had to pick some medium and define it as having $$n=1$$. He chose to define vacuum as having $$n=1$$. (The index of refraction of air at normal atmospheric pressure is 1.0003, so for most purposes it is a good approximation to assume that air has $$n=1$$.) He also had to decide which way to define the ratio, and he chose to define it so that media with their rays closer to the normal would have larger indices of refraction. This had the advantage that denser media would typically have higher indices of refraction, and for this reason the index of refraction is also referred to as the optical density. Written in terms of indices of refraction, Snell's equation becomes
$\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} ,$
but rewriting it in the form
$n_1 \sin \theta_1=n_2 \sin \theta_2$
[relationship between angles of rays at the interface between media with indices of refraction $$n_1$$ and $$n_2$$; angles are defined with respect to the normal] makes us less likely to get the 1's and 2's mixed up, so this the way most people remember Snell's law. A few indices of refraction are given in the back of the book.
Exercise $$\PageIndex{1}$$
1. What would the graph look like for two substances with the same index of refraction?
2. Based on the graph, when does refraction at an air-water interface change the direction of a ray most strongly?
Example $$\PageIndex{1}$$: Finding an angle using Snell's law
A submarine shines its searchlight up toward the surface of the water. What is the angle $$\alpha$$ shown in Figure $$\PageIndex{8}$$?
Figure $$\PageIndex{8}$$: Example 10.
Solution
The tricky part is that Snell's law refers to the angles with respect to the normal. Forgetting this is a very common mistake. The beam is at an angle of $$30°$$ with respect to the normal in the water. Let's refer to the air as medium 1 and the water as 2. Solving Snell's law for $$\theta_1$$, we find
$\theta_1 = \sin^{-1}\left(\frac{n_2}{n_1}\sin\theta_2\right) .$
As mentioned above, air has an index of refraction very close to 1, and water's is about 1.3, so we find $$\theta_1=40°$$. The angle $$\alpha$$ is therefore $$50°$$.
What neither Snell nor Newton knew was that there is a very simple interpretation of the index of refraction. This may come as a relief to the reader who is taken aback by the complex reasoning involving proportionalities that led to its definition. Later experiments showed that the index of refraction of a medium was inversely proportional to the speed of light in that medium. Since $$c$$ is defined as the speed of light in vacuum, and $$n=1$$ is defined as the index of refraction of vacuum, we have
$n=\frac{c}{v} .$
[$$n=$$ medium's index of refraction, $$v=$$ speed of light in that medium, $$c=$$ speed of light in a vacuum]
Many textbooks start with this as the definition of the index of refraction, although that approach makes the quantity's name somewhat of a mystery, and leaves students wondering why $$c/v$$ was used rather than $$v/c$$. It should also be noted that measuring angles of refraction is a far more practical method for determining $$n$$ than direct measurement of the speed of light in the substance of interest.
A mechanical model of Snell's law
Why should refraction be related to the speed of light? The mechanical model shown in the figure may help to make this more plausible. Suppose medium 2 is thick, sticky mud, which slows down the car. The car's right wheel hits the mud first, causing the right side of the car to slow down. This will cause the car to turn to the right until is moves far enough forward for the left wheel to cross into the mud. After that, the two sides of the car will once again be moving at the same speed, and the car will go straight.
Figure $$\PageIndex{8}$$: A mechanical model of refraction.
Of course, light isn't a car. Why should a beam of light have anything resembling a “left wheel” and “right wheel?” After all, the mechanical model would predict that a motorcycle would go straight, and a motorcycle seems like a better approximation to a ray of light than a car. The whole thing is just a model, not a description of physical reality.
#### A Derivation of Snell's law
However intuitively appealing the mechanical model may be, light is a wave, and we should be using wave models to describe refraction. In fact Snell's law can be derived quite simply from wave concepts. Figure $$\PageIndex{9}$$ shows the refraction of a water wave. The water in the upper left part of the tank is shallower, so the speed of the waves is slower there, and their wavelengths is shorter. The reflected part of the wave is also very faintly visible.
Figure $$\PageIndex{9}$$: A derivation of Snell's law.
In the close-up view on the right, the dashed lines are normals to the interface. The two marked angles on the right side are both equal to $$\theta_1$$, and the two on the left to $$\theta_2$$.
Trigonometry gives
\begin{align*} \sin \theta_1 &= \lambda_1/h \text{and} \\ \sin \theta_2 &= \lambda_2/h . \end{align*}
Eliminating $$h$$ by dividing the equations, we find
$\frac{\sin\theta_1}{\sin\theta_2}=\frac{\lambda_1}{\lambda_2} .$
The frequencies of the two waves must be equal or else they would get out of step, so by $$v=f\lambda$$ we know that their wavelengths are proportional to their velocities. Combining $$\lambda\propto v$$ with $$v\propto 1/n$$ gives $$\lambda\propto 1/n$$, so we find
$\frac{\sin\theta_1}{\sin\theta_2}=\frac{n_2}{n_1} ,$
which is one form of Snell's law.
Example $$\PageIndex{1}$$: Ocean waves near and far from shore
Ocean waves are formed by winds, typically on the open sea, and the wavefronts are perpendicular to the direction of the wind that formed them. At the beach, however, you have undoubtedly observed that waves tend come in with their wavefronts very nearly (but not exactly) parallel to the shoreline. This is because the speed of water waves in shallow water depends on depth: the shallower the water, the slower the wave. Although the change from the fast-wave region to the slow-wave region is gradual rather than abrupt, there is still refraction, and the wave motion is nearly perpendicular to the normal in the slow region.
#### Color and Refraction
In general, the speed of light in a medium depends both on the medium and on the wavelength of the light. Another way of saying it is that a medium's index of refraction varies with wavelength. This is why a prism can be used to split up a beam of white light into a rainbow. Each wavelength of light is refracted through a different angle.
#### How much light is reflected, and how much is transmitted?
In section 6.2 we developed an equation for the percentage of the wave energy that is transmitted and the percentage reflected at a boundary between media. This was only done in the case of waves in one dimension, however, and rather than discuss the full three dimensional generalization it will be more useful to go into some qualitative observations about what happens. First, reflection happens only at the interface between two media, and two media with the same index of refraction act as if they were a single medium. Thus, at the interface between media with the same index of refraction, there is no reflection, and the ray keeps going straight. Continuing this line of thought, it is not surprising that we observe very little reflection at an interface between media with similar indices of refraction.
The next thing to note is that it is possible to have situations where no possible angle for the refracted ray can satisfy Snell's law. Solving Snell's law for $$\theta_2$$, we find
$\theta_2 = \sin^{-1}\left(\frac{n_1}{n_2}\sin\theta_1\right) ,$
and if $$n_1$$ is greater than $$n_2$$, then there will be large values of $$\theta_1$$ for which the quantity $$(n_1/n_2)\sin\theta$$ is greater than one, meaning that your calculator will flash an error message at you when you try to take the inverse sine. What can happen physically in such a situation? The answer is that all the light is reflected, so there is no refracted ray. This phenomenon is known as total internal reflection, and is used in the fiber-optic cables that nowadays carry almost all long-distance telephone calls.
Figure $$\PageIndex{10}$$: Total internal reflection in a fiber-optic cable.
The electrical signals from your phone travel to a switching center, where they are converted from electricity into light. From there, the light is sent across the country in a thin transparent fiber. The light is aimed straight into the end of the fiber, and as long as the fiber never goes through any turns that are too sharp, the light will always encounter the edge of the fiber at an angle sufficiently oblique to give total internal reflection. If the fiber-optic cable is thick enough, one can see an image at one end of whatever the other end is pointed at.
Figure $$\PageIndex{11}$$: A simplified drawing of a surgical endoscope. The first lens forms a real image at one end of a bundle of optical fibers. The light is transmitted through the bundle, and is finally magnified by the eyepiece.
Alternatively, a bundle of cables can be used, since a single thick cable is too hard to bend. This technique for seeing around corners is useful for making surgery less traumatic. Instead of cutting a person wide open, a surgeon can make a small “keyhole” incision and insert a bundle of fiber-optic cable (known as an endoscope) into the body.
Figure $$\PageIndex{12}$$: Endoscopic images of a duodenal ulcer.
Since rays at sufficiently large angles with respect to the normal may be completely reflected, it is not surprising that the relative amount of reflection changes depending on the angle of incidence, and is greatest for large angles of incidence.
##### Discussion Questions
◊ What index of refraction should a fish have in order to be invisible to other fish?
◊ Does a surgeon using an endoscope need a source of light inside the body cavity? If so, how could this be done without inserting a light bulb through the incision?
◊ A denser sample of a gas has a higher index of refraction than a less dense sample (i.e., a sample under lower pressure), but why would it not make sense for the index of refraction of a gas to be proportional to density?
◊ The earth's atmosphere gets thinner and thinner as you go higher in altitude. If a ray of light comes from a star that is below the zenith, what will happen to it as it comes into the earth's atmosphere?
◊ Does total internal reflection occur when light in a denser medium encounters a less dense medium, or the other way around? Or can it occur in either case?
### 12.4.2 Lenses
Figures n/1 and n/2 show examples of lenses forming images. There is essentially nothing for you to learn about imaging with lenses that is truly new. You already know how to construct and use ray diagrams, and you know about real and virtual images. The concept of the focal length of a lens is the same as for a curved mirror. The equations for locating images and determining magnifications are of the same form. It's really just a question of flexing your mental muscles on a few examples. The following self-checks and discussion questions will get you started.
Figure $$\PageIndex{13}$$: 1. A converging lens forms an image of a candle flame. 2. A diverging lens.
Exercise $$\PageIndex{1}$$
1. In figures Figure $$\PageIndex{13; part 1}$$ and Figure $$\PageIndex{13; part 2}$$, classify the images as real or virtual.
2. Glass has an index of refraction that is greater than that of air. Consider the topmost ray in Figure $$\PageIndex{13; part 1}$$. Explain why the ray makes a slight left turn upon entering the lens, and another left turn when it exits.
3. If the flame in Figure $$\PageIndex{13; part 2}$$ were moved closer to the lens, what would happen to the location of the image?
### Discussion Questions
◊ In figures n/1 and n/2, the front and back surfaces are parallel to each other at the center of the lens. What will happen to a ray that enters near the center, but not necessarily along the axis of the lens? Draw a BIG ray diagram, and show a ray that comes from off axis.
In discussion questions B-F, don't draw ultra-detailed ray diagrams as in A.
◊ Suppose you wanted to change the setup in figure n/1 so that the location of the actual flame in the figure would instead be occupied by an image of a flame. Where would you have to move the candle to achieve this? What about in n/2?
◊ There are three qualitatively different types of image formation that can occur with lenses, of which figures n/1 and n/2 exhaust only two. Figure out what the third possibility is. Which of the three possibilities can result in a magnification greater than one? Cf. problem 10, p. 797.
◊ Classify the examples shown in figure o according to the types of images delineated in discussion question C.
◊ In figures n/1 and n/2, the only rays drawn were those that happened to enter the lenses. Discuss this in relation to figure o.
◊ In the right-hand side of figure o, the image viewed through the lens is in focus, but the side of the rose that sticks out from behind the lens is not. Why?
Figure $$\PageIndex{14}$$: Two images of a rose created by the same lens and recorded with the same camera.
#### The Lensmaker's Equation
Figure $$\PageIndex{15}$$: The radii of curvature appearing in the lensmaker's equation.
The focal length of a spherical mirror is simply $$r/2$$, but we cannot expect the focal length of a lens to be given by pure geometry, since it also depends on the index of refraction of the lens. Suppose we have a lens whose front and back surfaces are both spherical. (This is no great loss of generality, since any surface with a sufficiently shallow curvature can be approximated with a sphere.) Then if the lens is immersed in a medium with an index of refraction of 1, its focal length is given approximately by
$f = \dfrac{1}{(n-1) \left|\dfrac{1}{r_1}\pm\dfrac{1}{r_2}\right|} \label{LM}$
where $$n$$ is the index of refraction and $$r_1$$ and $$r_2$$ are the radii of curvature of the two surfaces of the lens. Equation \ref{LM} is known as the lensmaker's equation. In my opinion it is not particularly worthy of memorization. The positive sign is used when both surfaces are curved outward or both are curved inward; otherwise a negative sign applies. The proof of this equation is left as an exercise to those readers who are sufficiently brave and motivated.
### 12.4.3 Dispersion
For most materials, we observe that the index of refraction depends slightly on wavelength, being highest at the blue end of the visible spectrum and lowest at the red. For example, white light disperses into a rainbow when it passes through a prism, q.
Figure $$\PageIndex{16}$$: Dispersion of white light by a prism. White light is a mixture of all the wavelengths of the visible spectrum. Waves of different wavelengths undergo different amounts of refraction.
Even when the waves involved aren't light waves, and even when refraction isn't of interest, the dependence of wave speed on wavelength is referred to as dispersion. Dispersion inside spherical raindrops is responsible for the creation of rainbows in the sky, and in an optical instrument such as the eye or a camera it is responsible for a type of aberration called chromatic aberration (subsection 12.3.3 and problem 28). As we'll see in subsection 13.3.2, dispersion causes a wave that is not a pure sine wave to have its shape distorted as it travels, and also causes the speed at which energy and information are transported by the wave to be different from what one might expect from a naive calculation. The microscopic reasons for dispersion of light in matter are discussed in optional subsection 12.4.6.
#### The principle of least time for refraction
We have seen previously how the rules governing straight-line motion of light and reflection of light can be derived from the principle of least time. What about refraction? In the figure, it is indeed plausible that the bending of the ray serves to minimize the time required to get from a point A to point B. If the ray followed the unbent path shown with a dashed line, it would have to travel a longer distance in the medium in which its speed is slower. By bending the correct amount, it can reduce the distance it has to cover in the slower medium without going too far out of its way. It is true that Snell's law gives exactly the set of angles that minimizes the time required for light to get from one point to another. The proof of this fact is left as an exercise (problem 38, p. 802).
Figure $$\PageIndex{17}$$: The principle of least time applied to refraction.
#### Microscopic description of refraction
Given that the speed of light is different in different media, we've seen two different explanations (on p. 774 and in subsection 12.4.5 above) of why refraction must occur. What we haven't yet explained is why the speed of light does depend on the medium.
Figure $$\PageIndex{18}$$: Index of refraction of silica glass, redrawn from Kitamura, Pilon, and Jonasz, Applied Optics 46 (2007) 8118, reprinted online at http://www.seas.ucla.edu/~pilon/Publications/AO2007-1.pdf.
A good clue as to what's going on comes from the figure s. The relatively minor variation of the index of refraction within the visible spectrum was misleading. At certain specific frequencies, $$n$$ exhibits wild swings in the positive and negative directions. After each such swing, we reach a new, lower plateau on the graph. These frequencies are resonances. For example, the visible part of the spectrum lies on the left-hand tail of a resonance at about $$2\times10^{15}\ \text{Hz}$$, corresponding to the ultraviolet part of the spectrum. This resonance arises from the vibration of the electrons, which are bound to the nuclei as if by little springs. Because this resonance is narrow, the effect on visible-light frequencies is relatively small, but it is stronger at the blue end of the spectrum than at the red end. Near each resonance, not only does the index of refraction fluctuate wildly, but the glass becomes nearly opaque; this is because the vibration becomes very strong, causing energy to be dissipated as heat. The “staircase” effect is the same one visible in any resonance, e.g., figure k on p. 180: oscillators have a finite response for $$f \ll f_0$$, but the response approaches zero for $$f \gg f_0$$.
So far, we have a qualitative explanation of the frequency-variation of the loosely defined “strength” of the glass's effect on a light wave, but we haven't explained why the effect is observed as a change in speed, or why each resonance is an up-down swing rather than a single positive peak. To understand these effects in more detail, we need to consider the phase response of the oscillator. As shown in the bottom panel of figure j on p. 181, the phase response reverses itself as we pass through a resonance.
Figure $$\PageIndex{19}$$: 1. A wave incident on a sheet of glass excites current in the glass, which produce a secondary wave. 2. The secondary wave superposes with the original wave, as represented in the complex-number representation introduced in subsection 10.5.7.
Suppose that a plane wave is normally incident on the left side of a thin sheet of glass, t/1, at $$f \ll f_0$$. The light wave observed on the right side consists of a superposition of the incident wave consisting of $$\mathbf{E}_0$$ and $$\mathbf{B}_0$$ with a secondary wave $$\mathbf{E}^*$$ and $$\mathbf{B}^*$$ generated by the oscillating charges in the glass. Since the frequency is far below resonance, the response $$q\mathbf{x}$$ of a vibrating charge $$q$$ is in phase with the driving force $$\mathbf{E}_0$$. The current is the derivative of this quantity, and therefore 90 degrees ahead of it in phase. The magnetic field generated by a sheet of current has been analyzed in subsection 11.2.1, and the result, shown in figure e on p. 664, is just what we would expect from the right-hand rule. We find, t/1, that the secondary wave is 90 degrees ahead of the incident one in phase. The incident wave still exists on the right side of the sheet, but it is superposed with the secondary one. Their addition is shown in t/2 using the complex number representation introduced in subsection 10.5.7. The superposition of the two fields lags behind the incident wave, which is the effect we would expect if the wave had traveled more slowly through the glass.
In the case $$f \gg 0$$, the same analysis applies except that the phase of the secondary wave is reversed. The transmitted wave is advanced rather than retarded in phase. This explains the dip observed in figure s after each spike.
All of this is in accord with our understanding of relativity, ch. 7, in which we saw that the universal speed $$c$$ was to be understood fundamentally as a conversion factor between the units used to measure time and space --- not as the speed of light. Since $$c$$ isn't defined as the speed of light, it's of no fundamental importance whether light has a different speed in matter than it does in vacuum. In fact, the picture we've built up here is one in which all of our electromagnetic waves travel at $$c$$; propagation at some other speed is only what appears to happen because of the superposition of the $$(\mathbf{E}_0,\mathbf{B}_0)$$ and $$(\mathbf{E}^*,\mathbf{B}^*)$$ waves, both of which move at $$c$$.
But it is worrisome that at the frequencies where $$n\lt1$$, the speed of the wave is greater than $$c$$. According to special relativity, information is never supposed to be transmitted at speeds greater than $$c$$, since this would produce situations in which a signal could be received before it was transmitted! This difficulty is resolved in subsection 13.3.2, where we show that there are two different velocities that can be defined for a wave in a dispersive medium, the phase velocity and the group velocity. The group velocity is the velocity at which information is transmitted, and it is always less than $$c$$.
### Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license. | 2018-10-18T18:35:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6946278810501099, "perplexity": 398.5520644417459}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511897.56/warc/CC-MAIN-20181018173140-20181018194640-00448.warc.gz"} |
https://indico.fnal.gov/event/20381/timetable/?view=standard_inline_minutes | # New Perspectives 2019
US/Central
One West (Fermi National Accelerator Laboratory)
### One West
#### Fermi National Accelerator Laboratory
Description
New Perspectives is a conference for, and by, early career researchers in the Fermilab community. It provides a forum for graduate students, postdocs, visiting researchers, and all other early career researchers that contribute to the scientific program at Fermilab to present their work to an audience of peers. New Perspectives has a rich history of providing the Fermilab community with a venue for early career researchers to present their work. Oftentimes, the content of these talks wouldn't appear at typical HEP conferences because of its work-in-progress status or because it's part of work that will never be published. However, it is exactly this type of work, frequently performed by the youngest members of our community, that forms the backbone of the research programme at Fermilab. The New Perspectives Organizing Committee is deeply committed to presenting to the community a programme that accurately reflects the breadth and depth of research being done by early career researchers at Fermilab. New Perspectives is organized by the Fermilab Student and Postdoc Association (FSPA) and serves as a preamble to the Fermilab Users Annual Meeting. Please direct any questions, concerns, and comments to [email protected].
Participants
• Abhilash Yallappa Dombara
• Aleena Rafique
• Alessandra Luca
• Alexandra Haslund-Gourley
• Alexandre Sousa
• Amit Bashyal
• Amy Filkins
• Andre Sterenberg Frankenthal
• Andres Alba Hernandez
• Andrew Furmanski
• Andrew Mogan
• Andrew Olivier
• Ankur Agrawal
• Anna Heggestuen
• Anthony Villano
• Anthony Wood
• Anushree Ghosh
• Ashley Back
• Athula Wickremasinghe
• Austin Dick
• Avinay Bhat
• Barbara Yaeggy
• Beatriz Tapia Oregui
• Benjamin Simons
• Bianca Giaccone
• Bin Zhong
• Biswaranjan Behera
• Brandon Cathey
• Brody Oleson
• Carlos Sarasty Segura
• Cathal Sweeney
• Chatura Kuruppu
• Chin Lung Tan
• Christopher Hilgenberg
• Chun-Min Jen
• Claire Laffan
• Claudius Krause
• Colin Fallon
• Cory Rude
• Cristina Mantilla Suarez
• Daniel Mishins
• Daniel Ruterbories
• Dat Tran
• Davi Costa
• David Caratelli
• David Sweigart
• David Tarazona
• David Vanegas Forero
• Davio Cianci
• DEEPIKA JENA
• Derek Sherry
• Diego Lopez Gutierrez
• Diktys Stratakis
• Donnie Munford
• Elizabeth Pater
• Emrah Tiras
• Evan Angelico
• Gabriele Benelli
• Gianantonio Pezzullo
• Gleb Lukicov
• Gonzalo Díaz Bautista
• Grant Nikseresht
• Heather Tanner
• Heather Tanner
• Helenka Casler
• Iker de Icaza Astiz
• Iris Ponce
• Ivan Caro Terrazas
• Ivan Lepetic
• James Griggs
• James Popp
• James Santucci
• Jason Poh
• Jennica LeClerc
• Jessica Esquivel
• Jieun Yoo
• Joshua Hoskins
• Joshua Isaacson
• Karl Warburton
• Kathryn Sutton
• Katrina Miller
• Kenneth Cecire
• Kevin Kelly
• Khandaker Rahman
• Kirsty Duffy
• Krishan Mistry
• Kuntal Mondal
• Kyle Hazelwood
• Lauren Yates
• Louise Suter
• Maria Martinez-Casales
• Marianette Wospakrik
• Mary Anne Cummings
• Matt King
• Maura Spanu
• Meghna Bhattacharya
• Mehreen Sultana
• Michael Revering
• Michael Syphers
• Michael Wallbank
• Michael Whalen
• Mikhail Yurov
• Minjung Kim
• Miranda Elkins
• Monica Nunes
• Nabin Poudyal
• Nora Sherman
• Nora Shipp
• Ohkyung Kwon
• Oleksandr Tomalak
• Osama Mohsen
• Owen Goodwin
• Pawel Guzowski
• Polina Abratenko
• Prudhvi Raj Varma Chintalapati
• Raffaella Donghia
• Ramanpreet Singh
• Reddy pratap Gandrajula
• Rhiannon Jones
• Richard Diurba
• Rob Fine
• Rory Fitzpatrick
• Rui An
• Ryan Staten
• Sabya Sachi Chatterjee
• Samantha Sword-fehlberg
• Samuel Grant
• Sandeep Kaur
• Sans Basnet
• Saptaparna Bhattacharya
• Savannah King
• Sebastian Sanchez
• Sidney Mau
• Simone Marcocci
• Sophie Berkman
• Sophie Middleton
• Steven Calvez
• Tanvi Wamorkar
• Teresa Lackey
• Tiffany Price
• Tom Brooks
• Vassili Papavassiliou
• Vincent Basque
• Wanwei Wu
• Xuan Chen
• Yaqian Wang
• Yiding Yu
• Yifan Chen
• Yu-Dai Tsai
• Yujing Sun
• Monday, June 10
• 9:00 AM 10:40 AM
Monday Morning I
Convener: Dr Brenna Flaugher (Fermilab)
• 9:00 AM
Welcome 10m
Speakers: Andrew Furmanski, Andrew Furmanski
• 9:10 AM
DES in 10 Minutes 15m
The Dark Energy Survey (DES) is a deep, wide-area optical imaging survey in the southern hemisphere. The unprecedented photometry from DES has allowed for exciting science results on topics ranging from cosmology to our Galaxy. I will discuss details of the survey -- which completed its 5.5-year observations in January 2019 -- and highlight some recent science results from the collaboration.
Speaker: Nora Shipp (University of Chicago, Fermilab)
• 9:25 AM
Searching for the lowest luminosity companions of the Milky Way 15m
The Milky Way satellites are among the least luminous and most dark matter-dominated galaxies in the known universe. I present on a search for low-luminosity dwarf galaxy companions of the Milky Way in three years of data from the Dark Energy Survey (DES) and the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS PS1). Together, these two surveys cover roughly three-quarters of the sky with deep multi-band optical imaging. I will describe a search algorithm, SimpleBinner, for detecting satellite galaxy candidates by their individually resolved stars. I apply this algorithm consistently to the actual survey data and simulated satellites in order to characterize our search sensitivity. In this talk, I will present on the performance of SimpleBinner on DES and PS1 data and discuss the ongoing search for new ultra-faint stellar systems in DES, PS1. I will also note our recent discovery of a faint halo star cluster in the Blanco Imaging of the Southern Sky (BLISS) Survey using DECam. Finally, using these results, I comment on constraints of dark matter models.
Speaker: Sidney Mau (University of Chicago)
• 9:40 AM
Strong Lensing Science from Current and Future Astronomical Surveys 15m
Strong gravitational lenses are cosmic magnifying glasses that can be used as a probe of cosmic phenomena, like dark energy and dark matter. However, strong lensing systems are rare and complex, which means they are both hard to find and analyze. We present two important results in strong lensing science: 1) new deep learning techniques for finding and measuring strong lenses; and 2) dark energy forecasts for future surveys that will find hundreds of thousands of lensing systems. Current surveys, like DES, are predicted to discover thousands of galaxy-scale strong lenses, while future surveys, like LSST will increase that number by 1-2 orders of magnitude. The large number of strong lenses discoverable in future surveys will make strong lensing a highly competitive and complementary cosmic probe, but only if they can be analyzed on realistic time-scales. We demonstrate a novel deep learning regression analysis which can infer strong lensing observables from ground-based imaging for thousands of lenses to within 10-15% of their true values in a fraction of the time conventional modeling techniques take. We then use these uncertainties to inform how well we can constrain cosmology with galaxy-scale lenses in the DES and LSST era, demonstrating the statistical power of this probe in relation with other conventional probes of cosmology.
Speaker: Jason Poh (University of Chicago)
• 9:55 AM
Development of a new imager testing projector using a micromirror array 15m
Charge Coupled Devices and MKIDs are pixelated imaging sensors used for astronomy. FNAL in involved in the development of instruments using these sensors. I will describe the development of a novel micro-mirror array projector for the characterization of these imaging sensors. The CCD require tight control of the light intensity and the exposure time, and the micromirror array allow to also control the illumination pattern at the level of 100 um. I will describe the design of a 3D printed dark box with an automated shutter, and a focusing system to house the projector. The final device will allow new ways for the characterization of the scientific imagers.
Speaker: Brody Oleson
• 10:10 AM
Machine learning dark matter halo formation 15m
Dark matter halos are the fundamental building blocks of cosmic large-scale structure. Improving our theoretical understanding of their structure, evolution and formation is an essential step towards understanding how galaxies form, which in turn will allow us to fully exploit the large amount of data from future galaxy surveys. I will present a machine learning approach which aims to provide new physical insights into the physics driving halo formation. We train a machine learning algorithm to learn cosmological structure formation directly from N-body simulation. The algorithm infers the relationship between the initial conditions and the final dark matter halos, based on inputs describing different properties of the local environment surrounding the dark matter particles in the initial conditions. I will demonstrate that one can infer which aspects of the early-Universe density field impact the formation of the final dark matter halos by evaluating the predictive performance of the algorithm when provided with different types of information.
Speaker: Ms Luisa Lucie-Smith (University College London)
• 10:25 AM
Improving the spatial resolution of the ATLAS IBL silicon pixel detectors 15m
This project was realized primarily to test and improve the spatial tracking resolution of the ANL (Argonne National Laboratory) telescope consisting of the ATLAS IBL silicon pixel sensors and FE-I4 chips by making use of the test beam at Fermilab. In this paper, we will discuss the overall performance of the modules and how it can be improved. We will also discuss efforts made to improve the spatial resolution of the modules. In addition, we will also talk about successful attempts to simulate the spatial resolution of the modules using Allpix$^2$.
Speaker: Spoorthi Nagasamudram
• 10:40 AM 11:00 AM
Coffee break
• 11:00 AM 12:15 PM
Monday Morning II
Convener: Mark Lancaster
• 11:00 AM
Plasma processing for LCLS-II 1.3GHz SRF cavities 15m
This study is focused on the development of an in-situ plasma cleaning procedure for 1.3GHz 9-cell TESLA shaped SRF cavities. The goal of this technique is to reduce field emission through the removal of adsorbed hydrocarbons that lower the work function of the cavity surface. In this work I present the first results of plasma processing applied to LCLS-II cavities focusing on plasma ignition and studies of quality factor vs accelerating field measured before and after plasma processing.
Speaker: Bianca Giaccone
• 11:15 AM
Simulation of Resonant Extraction at Fermilab's Delivery Ring 15m
The Muon Campus at Fermilab presently houses two experiments that aim to find discrepancies (if any) in the Standard Model. The Delivery Ring is a 500m circumference storage ring which is used to deliver protons to muon experiments Muon g-2 and Mu2e. Although these experiments are based on the same particle, they require different intensities because of their detector constraints. For the Mu2e case, resonant extraction is the method used for introducing small perturbations in the transverse magnetic field of the ring in order to provide controlled extraction of protons depending upon the required particle rates at the target. Work presented here will be an analysis and simulation of resonant extraction at the Delivery Ring using the beam parameters of Mu2e to study various factors that contribute to its successful use, including meeting intensity requirements while keeping beam losses to a minimum.
Speaker: Mr Prudhvi Raj Varma Chintalapati (Chintalapati)
• 11:30 AM
Design and analysis of a halo-measurement diagnostics 15m
A large dynamical-range diagnostics (LDRD) design at Jefferson Lab will be used at the FAST-IOTA injector to measure the transverse distribution of halo associated with a high-charge electron beam. One important aspect of this work is to explore the halo distribution when the beam has significant angular momentum (i.e. is magnetized). The beam distribution is measured by recording radiation produced as the beam impinges a YAG:Ce screen. The optical radiation is split with a fraction directed to a charged-couple device (CCD) camera. The other part of the radiation is reflected by a digital micromirror device (DMD) that masks the core of the beam distribution. Combining the images recorded by the two cameras provides a measurement of the transverse distribution with over a large dynamical range. The design and analysis of the optical system will be discussed including optical simulation using SRW and the result of a mockup experiment to test the performances of the system will be presented.
Speaker: Mr Christopher Marshall (Northern Illinois University)
• 11:45 AM
High Luminosity Spin-Polarized Target for the SpinQuest Experiment 15m
The SpinQuest collaboration will measure the sea quark Sivers asymmetry using Drell-Yan production from the 120 GeV proton beam of the Fermilab Main Injector incident on transversely polarized proton and deuteron targets. Measuring a nonzero Sivers asymmetry would provide strong evidence for nonzero orbital angular momentum of sea quarks. The use of both polarized hydrogen and deuterium targets will provide an independent extraction of the $\overline{u}$ and $\overline{d}$ contributions in the range of $0.1 < x < 0.5$. In order to provide high figure-of-merit measurements of the sea quark Sivers functions, high luminosity, transversely polarized targets are required. The polarized target system constructed by UVA-LANL consists of a 5T, split-coil, superconducting magnet and uses a 140 GHz microwave source to provide highly polarized protons and deuterons via dynamic nuclear polarization (DNP). The expected average target polarization for SpinQuest is 80\% and 32\% for the hydrogen and deuterium targets, respectively. A brief overview of the SpinQuest experiment and a survey of the high luminosity polarized target will be presented.
Speaker: Joshua Hoskins
• 12:00 PM
E1039/SpinQuest Polarized Drell-Yan Experiment at Fermilab 15m
E1039/SpinQuest is the first transversally-polarized Drell-Yan experiment at Fermilab. SpinQuest data-taking is anticipated to begin this coming fall 2019. In SpinQuest, a transversely-polarized NH3 or ND3 target is employed with the unpolarized 120-GeV extracted proton beam from Fermilab Main Injector to obtain various measurements of transverse single spin asymmetries in J/psi, psi’, lambda, di-muon (Drell-Yan) productions without the need to account for final-state fragmentation effects. These measurements shed light on virtual-quark and gluon Sivers functions, and are sensitive to the contribution of virtual quark orbital angular momentum to the nucleon spin, as well as multi-gluon correlation dynamics, respectively. During the entire beam-off/-on commissioning periods, my primary focus is to bring up our multi-wire proportional chambers, along with tightly related chamber readout electronics and data acquisition system to our final-state detections, ready for the data-taking late this year. E1039 comprises three stations of multi-wire proportional chambers plus one station of proportional tubes. The former is in use of track reconstruction and the determination of track kinematics, while the later is specifically designed for the final-state muon identification. During the no-beam commissioning, we re-organized the chamber gas supply system, inspect/repair chamber wires at Lab 6, set up stand-alone chamber readout electronics test bench at NM4/KTeV experimental hall and turn on high voltages to evaluation the performance of chambers from all stations.
Speaker: Dr Chun-Min Jen (Los Alamos National Lab)
• 12:15 PM 1:45 PM
Lunch: Careers panel discussion
Conveners: Andrew Furmanski, Andrew Furmanski, Ms Barbara Yaeggy (Universidad Tecnica Federico Santa Maria), Dr Deepika Jena (FERMILAB), Karl Warburton (Iowa State University), Michael Wallbank (University of Cincinnati)
• 1:45 PM 3:45 PM
Monday Afternoon I
Convener: Dr Michael Kirby (FNAL)
• 1:45 PM
Neutrino Theory in 10 Minutes 15m
I will discuss the current state of neutrino theory work, specifically focusing on how we interface with interpretations of current experiments and predictions for upcoming experiments. I will discuss ideas that Fermilab theorists are currently exploring regarding the experimental neutrino program at Fermilab, from the SBN experiments to DUNE.
Speaker: Kevin Kelly
• 2:00 PM
MicroBooNE in 10 Minutes 15m
MicroBooNE is one of three liquid argon time projection chambers (LArTPCs) making up the Short-Baseline Neutrino Program at FNAL. Located on the Booster Neutrino Beamline, MicroBooNE has been collecting data since October 2015 to determine the source of the low-energy electromagnetic event excess previously reported by MiniBooNE and LSND. In addition to its signature analysis, MicroBooNE is employed in studying various forms of neutrino interactions in liquid argon, measuring low-energy neutrino cross sections, and developing technological advancements for future LArTPC experiments such as DUNE. This talk will summarize the current status of MicroBooNE’s physics program, highlight exciting new results, and provide an outlook of future experimental efforts.
Speaker: Ms Katrina Miller (University of Chicago)
• 2:15 PM
Progress towards the extraction of exclusive ν μ - 40 Ar cross sections with a single proton using the MicroBooNE LArTPC detector 15m
Next generation neutrino oscillation experiments aim towards high-precision extraction of oscillation parameters, which in turn requires an unprecedented understanding of neutrino-nucleus interactions. Neutrino processes producing a charged lepton and a single intact nucleon in the final state can offer an important window into the dynamics of neutrino interactions with direct importance for accelerator–based oscillation measurements. MicroBooNE is the first liquid argon time projection chamber (LArTPC) commissioned as part of the Short Baseline Neutrino (SBN) program at Fermilab and its excellent particle reconstruction capabilities allow detailed study of neutrino interactions. This poster will present the latest progress towards the first measurement of the total and differential cross–sections for exclusive ν μ - 40 Ar interactions with a single proton final state using data from the MicroBooNE LArTPC detector.
• 2:30 PM
Towards the measurement of the charged-current electron-neutrino inclusive cross-section on argon in MicroBooNE using the NuMI beam. 15m
The MicroBooNE experiment is an 87 t active mass Liquid Argon Time Projection Chamber (LArTPC) located on the Booster Neutrino Beam (BNB) at Fermilab, Chicago. The primary physics goals of this experiment are to investigate the excess of low energy electron-like events observed by MiniBooNE, perform precise measurements of neutrino on argon cross sections, and provide research and development for future liquid argon experiments such as SBN and DUNE. MicroBooNE also receives a significant neutrino flux from the highly off-axis NuMI beam. This flux can be utilised due to its high electron neutrino component (5%) to perform independent cross section measurements. This talk will cover the current status of the flux integrated inclusive charged-current electron-neutrino cross section measurement on argon performed using data from the NuMI beam collected during MicroBooNE’s first run period.
Speaker: Mr Krishan Mistry (The University of Manchester)
• 2:45 PM
Chimera Events in the MicroBooNE Experiment 15m
MicroBooNE is a short baseline neutrino oscillation experiment based at Fermilab that employs a Liquid Argon Time Projection Chamber (LArTPC) to investigate the excess of low energy events observed by MiniBooNE, study neutrino-argon cross-sections, and perform detector R&D for future LArTPC experiments. The MicroBooNE detector lies along the Booster Neutrino Beamline, which produces neutrinos with energies ranging from tens of MeV to 2 GeV. To study systematic uncertainties in MicroBooNE, the performance of algorithms used must be tested against event samples with known properties. Testing purely on Monte Carlo is limited by how well we understand the discrepancies between simulation and data. An alternative is to test against samples of "chimera" events, which consist of separate single-particle components from data that are combined to create neutrino-like events. This presentation will cover the ability and performance of finding and isolating tracks that match a target neutrino topology to create chimera events in MicroBooNE.
Speaker: Polina Abratenko
• 3:00 PM
SBND in 10 minutes 15m
The Short-Baseline Near Detector (SBND) will be a 112 ton liquid argon time projection chamber devoted to researching neutrino oscillations. Located 110 m downstream from the Booster Neutrino Beam (BNB) target, SBND will be the near detector of the three-detector Short Baseline Neutrino (SBN) program at Fermilab. The SBN program will probe neutrino oscillations at the $\sim \! 1 \textrm{eV}^2$ scale, addressing tensions pointing to the possible existence of sterile neutrinos. SBND will see the un-oscillated content of the BNB and as such its role is to constraint uncertainties in the oscillation analysis. Due to its size and proximity to the neutrino beam source, SBND will have a rich cross-section measurement program where just a few months of data will yield a record number of $\nu\!-\!\textrm{Ar}$ interactions. It is also a testbed for R&D of new technology for DUNE. I will summarize the physics program of SBND and the current status of its construction.
Speaker: Iker de Icaza Astiz (University of Sussex)
• 3:15 PM
Overview of the Cold Electronics of SBND 15m
The Short-Baseline Near Detector (SBND) will be one of three liquid argon neutrino detectors sitting in the Booster Neutrino Beam (BNB) at Fermilab as part of the Short-Baseline Neutrino (SBN) Program. SBND is a 112-ton active mass liquid argon time projection chamber (LArTPC) to be located only 110 m from the BNB neutrino source. An important aspect of LArTPC detector design is that the readout and digitization electronics are placed in the liquid argon, directly on the anode planes, because digitizing the signal locally reduces both signal noise and impurities in the liquid argon by reducing the distance that analog signals must be transported and the number of cables and cryostat penetrations that are required to transport signals out of the detector. SBND's "cold electronics" consist of custom ASICs for signal amplification and shaping, commercial ADCs for digitization, and commercial FPGAs for data handling. I will present the SBND front-end electronics system design, show results of system and component performance tests, and describe the status of SBND front-end electronics production and installation.
Speaker: Ryan Lazur
• 3:30 PM
A Preliminary $\nu_{\mu}$ CC 0$\pi$ Event Selection in SBND 15m
SBND is a Liquid Argon Time Projection Chamber (LArTPC) experiment and the near detector in the Short Baseline Neutrino (SBN) program at Fermilab. With a 110 m baseline and a 112 tonne active mass, the detector will observe ~5,000,000 charged current muon neutrino ($\nu_{\mu}$ CC) interactions at energies of <$E_{\nu}$> $\sim$ 650 MeV in its 6.6 $\times 10^{20}$ POT (3 year) exposure. SBND will constrain the systematics on the event rate for sterile neutrino searches in the SBN program and have a rich program of neutrino cross-section measurements. The most abundant topology in SBND, pionless charged current muon neutrino ($\nu_{\mu}$ CC 0$\pi$), is a key channel for oscillation searches due to its simple final-state: a single muon, possibly several nucleons and no meson. However, the well-understood charged current quasielastic (CC QE) interaction on free nuclei is not sufficient to correctly model the $\nu_{\mu}$ CC 0$\pi$ final state in nuclear target experiments. This talk will demonstrate a preliminary $\nu_{\mu}$ CC 0$\pi$ selection using automated reconstruction in SBND, in an effort to fully understand its properties in a LArTPC for the purpose of making cross-section and oscillation measurements.
Speaker: Rhiannon Jones
• 3:45 PM 4:15 PM
Coffee break
• 4:15 PM 6:15 PM
Monday Afternoon II
Convener: Dr Stephen Brice (FNAL)
• 4:15 PM
Cosmogenic Background Suppression at the SBN Far Detector (ICARUS) with the Cosmic Ray Tagging System 15m
As the SBN far-detector, the ICARUS T600, a set of liquid argon time-projection chambers (TPC), will operate at shallow depth and therefore be exposed to the full surface flux of cosmic rays. This poses a problematic background to the neutrino oscillation search, especially photons produced by muons passing in close proximity to, but not through, the active volume. A direct way to reject this background is to surround the cryostat with a detector capable of tagging incident cosmic muons with high efficiency (95%), the cosmic ray tagging system (CRT). I will present my work on a method of separating background muons from neutrino interactions in the fiducial volume by a time-of-flight measurement between the CRT and the signal from scintillation light in the TPC.
Speaker: Mr Christopher Hilgenberg (Colorado State University)
• 4:30 PM
LArIAT in 10 minutes 15m
Liquid Argon Time Projection Chambers (LArTPCs) are currently being used extensively for neutrino physics due to their excellent capabilities in performing particle identification, and precise 3D and calorimetric energy reconstruction. The Liquid Argon In A Test Beam (LArIAT) experiment was located at the Test Beam Facility where it was exposed to a known charged particle beam. The capability of understanding and knowing the charged particle beam is a crucial aspect of LArIAT that allows it to improve on LArTPCs advantages to perform state of the art analyses. This made LArIAT an excellent test-bed to perform cross-section measurements with different charged particles as well as performing R&D studies for future large LArTPCs such as the Short-Baseline Near Detector (SBND) and the Deep Underground Neutrino Experiment (DUNE). This talk will give an overview of the LArIAT detector as well as provide a highlight of recent results from on-going analyses.
Speaker: Vincent Basque (University of Manchester)
• 4:45 PM
Elastic neutrino-electron scattering within the effective field theory approach 15m
Elastic neutrino-electron scattering provides an important tool for normalizing neutrino flux in modern experiments. This process is subject to large radiative corrections. We determine the Fermi effective theory performing the one-loop matching to the Standard model at the electroweak scale with subsequent running down to GeV scale. Based on this theory, we analytically evaluate virtual corrections and distributions with one radiated photon beyond the electron energy spectrum. We discuss the relevance of radiative corrections depending on conditions of modern accelerator-based neutrino experiments.
Speaker: Oleksandr Tomalak
• 5:00 PM
MINERvA in 10 minutes 15m
Based in the NuMI beamline at Fermi National Laboratory, the on-axis MINERvA experiment is focused on reaching precision measurements of neutrino and antineutrino interactions in diverse nuclei materials for energies up to 50 GeV. The results support the current and future oscillation experiments as well as to provide information about the structure of nuclei. A look at the latest results from the MINERvA experiment and those who will come will be presented.
Speaker: Ms Barbara Yaeggy (Universidad Tecnica Federico Sta. Maria)
• 5:15 PM
ANNIE in 10 minutes: multiplicities, cross sections, and models (oh my!) 15m
The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a gadolinium-doped water Cherenkov detector located in the Fermilab Booster Neutrino Beam line. Many long-baseline neutrino measurements rely on efficient reconstruction of charged-current quasi-elastic (CCQE) neutrino interactions, whose final-state particles include only the recoiling nucleus, a proton, and an outgoing lepton. One known indicator of an event's inelasticity is the presence of final-state neutrons, which are often challenging to detect. Understanding the expected number of neutrons following CCQE-like inelastic events is pivotal for identifying and rejecting such events from CCQE datasets. ANNIE is sensitive to final-state neutrons and will measure the neutron multiplicity of neutrino charged-current interactions. This neutron multiplicity measurement can also help constrain and refine models for atmospheric neutrino interactions, a dominant background in proton decay searches and supernova neutrino detection. Throughout operation, ANNIE will also measure the total muon neutrino charged-current cross section and perform exclusive cross-section measurements, with an emphasis on the CC0pi cross section. This talk will provide an overview of the ANNIE physics goals and event reconstruction chain that will be used to complete these measurements.
Speaker: Teal Pershing
• 5:30 PM
ANNIE: Phase II Detector Design and Construction 15m
The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a gadolinium-loaded water Cherenkov detector located on the Booster Neutrino Beam at Fermilab. The experiment seeks to better understand neutrino-nucleus interactions by studying the number of final state neutrons produced in charged current interactions. It will be the first experiment testing Large Area Picosecond Photodetectors (LAPPDs), and the first application of gadolinium-loaded water in a neutrino beam. The ANNIE detector is currently undergoing an upgrade for its main physics measurement and a rigorous detector R&D work is ongoing alongside. This presentation will give an overview of the detector R&D studies and detector design and construction of the ANNIE Phase II.
Speaker: Dr Emrah Tiras (Iowa State University)
• 5:45 PM
SuperCDMS in 10 Minutes 15m
The Super Cryogenic Dark Matter Search (SuperCDMS) is at the low-threshold frontier. Our detector technology can detect nuclear recoils at the eV-scale energies necessary for generation-two low-mass dark matter searches. The SNOLAB installation, which will be commissioned in the next two years, will produce world-class limits on the presence of low-mass (between 0.5 and 10\,GeV/c$^2$) dark matter. In this brief presentation I will discuss the detection mechanisms; SNOLAB running and backgrounds; and new mechanisms of dark matter interactions that these astonishingly sensitive detectors are beginning to probe.
Speaker: Dr Anthony Villano (University of Colorado Denver)
• 6:00 PM
FerMINI: Fermilab Search for Minicharged Particles 15m
We propose a low-cost and movable setup to probe minicharged particles (or milli-charged particles) using high-intensity proton fixed-target facilities. This proposal, FerMINI, consists of a milliQan-type detector, requiring multi-coincident (nominally, triple-coincident) scintillation signatures within a small time window, located downstream of the proton target of a neutrino experiment. During the collisions of a large number of protons on the target, intense minicharged particle beams may be produced via meson photo-decays and Drell-Yan production. We take advantage of the high statistics, shielding, and potential neutrino-detector-related background reduction to search for minicharged particles in two potential sites: the MINOS near detector hall and the proposed DUNE near detector hall, both at Fermilab. We also explore several alternative designs, including the modifications of the nominal detector to increase signal yield, and combining this detector technology with existing and planned neutrino detectors to better search for minicharged particles. The CERN SPS beam and associated experimental structure also provide a similar alternative. FerMINI can achieve unprecedented sensitivity for minicharged particles in the MeV to few GeV regime with fractional charge ε=Qχ/e between 10−4 (potentially saturating the detector limitation) and 10−1. This talk is mainly based on arxiv:1812.03998 If time allowed, I will also talk about new physics cases studied in arXiv:1806.03310, arXiv:1812.08768, arXiv:1803.03262, and arXiv:1706.00424
Speaker: Dr Yu-Dai Tsai (Fermilab)
• 6:30 PM 10:30 PM
Barbeque!
Conveners: Andrew Furmanski, Andrew Furmanski, Ms Barbara Yaeggy (Universidad Tecnica Federico Santa Maria), Dr Deepika Jena (FERMILAB), Karl Warburton (Iowa State University), Michael Wallbank (University of Cincinnati)
• Tuesday, June 11
• 9:00 AM 10:30 AM
Tuesday Morning I
Convener: Dr Mandy Rominsky (Fermilab)
• 9:00 AM
CMS in 10 minutes 15m
The LHC is the worlds highest energy proton-proton collider with a center-of-mass energy of 13 TeV. The world's largest machine is currently running at twice its designed luminosity and represents forefront of the energy frontier. The CMS detector is a multipurpose detector that features a 4 Tesla magnet and over a 100 million active channels taking data every 25 ns. It, along with its sister experiment ATLAS, is measuring the precise properties of the recently discovered Higgs boson, and leading the search for new and exciting physics: such as supersymmetry, dark matter, and extra dimensions. In this talk we give a quick overview of the detector and the methodology for physics searches and measurements.
Speaker: Cristina Ana Mantilla Suarez (Johns Hopkins University)
• 9:15 AM
Perturbative QCD in 10 Minutes 15m
A brief overview of perturbative QCD and its role in precision measurements at the LHC. There will be a focus on efforts that are being done here at Fermilab. Here at Fermilab, the QCD group focuses on three distinct topics. Therefore, the talk will focus on the importance of improving precision for measurements at the LHC, through the use of higher order corrections, analytic resummation, and parton showers. Additionally, there will be some brief overview of parton distribution functions. The talk will show the current comparison between theory and data at the LHC, and the work that is required to help drive the theoretical uncertainty down in order to improve the systematic uncertainties of the LHC. This comparison will include comparison to total cross sections and differential distributions. In addition, I will address the difficulties and importance of the $W$ mass measurement and the top mass measurement. Finally, I will discuss the importance of improving our understanding of perturbative QCD in order to reduce the background uncertainty in BSM physics searches at the LHC.
Speaker: Joshua Isaacson
• 9:30 AM
Lattice QCD in 10 Minutes 15m
In this talk I summarize the current status of the field in lattice QCD. My goal will be to provide an accessible overview. I will emphasize work done at Fermilab and work affecting Fermilab experiments.
Speaker: William Jay
• 9:45 AM
Scintillator Tiles for the High Granularity Calorimeter of the CMS Detector at the HL-LHC 15m
The CMS Phase II upgrade, High Granularity Calorimeter (HGCal) will have fine transverse and longitudinal segmentation to allow for superior particle identification and pileup rejection in the high radiation and large event pileup environment of the endcap region. A significant portion of the hadronic portion of the HGCal will be instrumented with scintillator tiles directly coupled to Silicon Photomultiplers. We report on the proposed design and R&D associated with tile fabrication, characterization and assembly for this detector.
Speaker: Ramanpreet Singh
• 10:00 AM
Layout and performance of GE1/1 chambers for the CMS muon spectrometer upgrade 15m
The CMS Muon group has proposed the use of Gas Electron Multiplier (GEM) technology to maintain an efficient and reliable operation during the High Luminosity phase of the LHC (HL-LHC). This is particularly important to study many physics processes with muons in the final state. The CMS GEM chambers will cover eta region 1.6 to 2.2 of the endcap. We report on the GE1/1 layout and their performance studies estimated during the R&D and beam tests at CERN. We also provide the current status of GE1/1 project and future GEM upgrade plans.
Speaker: Mr Aashaq Shah (University of Delhi)
• 10:15 AM
Reconstructing proton-proton collision positions at the Large Hadron Collider with a D-Wave quantum computer 15m
Clustering of charged particle tracks along the beam axis is the first step in reconstructing the positions of proton-proton (p-p) collisions at Large Hadron Collider (LHC) experiments. In this talk, we formulate this problem for a 2048 qubit D-Wave quantum computer that works by quantum annealing. We show the performance of the quantum annealer on artificial events generated from p-p collision and track distributions measured by the Compact Muon Solenoid experiment at the LHC. The quantum clustering algorithm is found to be limited by the connectivity of the qubits and the overall efficiency of the algorithm in addressing event topologies with more than 5 collisions. We identify three obstacles to reaching current LHC event complexities and outline research directions we are embarking on to overcome each.
Speakers: Andrew Wildridge, Mr Sachin Vaidya (Purdue University), Souvik Das
• 10:30 AM 11:00 AM
Coffee break
• 11:00 AM 12:45 PM
Tuesday Morning II
Convener: Dr Thomas Junk (Fermilab)
• 11:00 AM
Searching for Dark Matter with Semi-Visible Jets at CMS 15m
Most theories that predict dark matter production at colliders rely on weakly coupled dark matter and the existence of WIMPs, or weakly interacting massive particles; however, there can be dark matter signatures in colliders that emerge from strongly coupled dark matter. These signatures are varied, ranging from emerging jets to Stealth Dark Matter. Another possible signature is semi-visible jets. These occur if the dark sector is comprised of a strong-like structure with dark hadrons made up of dark quarks. Once produced, a heavy dark quark would then hadronize into stable dark "pions", which leave the detector as dark matter, and unstable dark hadrons that shower and appear as SM hadronic showers. Since the true jet is made up of visible SM quarks and missing transverse energy closely aligned with the shower, the jet is called semi-visible. This presentation will discuss a Hidden Valley theory that results in such a signature, as well as a work-in-progress analysis by members of the CMS Collaboration trying to find this signature.
Speaker: Colin Fallon
• 11:15 AM
Search for Supersymmetry at CMS in Events with Large Jet Multiplicity and Low Missing Transverse Momentum at sqrt(s)=13 TeV 15m
In traditional searches for physics beyond the standard model, a requirement of high missing transverse momentum (MET) is often used. However, without any signs of significant deviations from the standard model expectations, we decided to relax this requirement for the search reported in this talk. Many new physics models, including versions of supersymmetry (SUSY) characterized by R-parity violation, compressed mass spectra, long decay chains, or with additional hidden sectors predict the production of events with low MET, many jets, and top quarks. The results of a general search for new physics featuring two top quarks and six additional light flavor jets are reported. The search is performed using events with at least seven jets and exactly one electron or muon. No requirement on MET is imposed. With the use of a neural-network-based signal-to-background discriminator, a background estimation was achieved where more traditional techniques was not an option. The study is based on a sample of proton-proton collisions at sqrt(s) = 13 TeV corresponding to 77.4 fb-1 of integrated luminosity collected with the CMS detector at the LHC in 2016 and 2017. Results of the search are interpreted for pair production of scalar top quarks in the frameworks of stealth SUSY and SUSY with R-parity violation.
• 11:30 AM
Search for dark photons with CMS and fixed-target experiments 15m
Searches for dark matter in the past two decades have largely focused on Weakly Interacting Massive Particles (WIMPs). But what if instead of just one type of dark matter particle, there exists a richer dark sector hidden from ordinary view? This opens up a whole new paradigm for dark matter searches, allowing us to focus not only on the coupling between dark matter and the Standard Model, but also on the interactions between dark sector constituents themselves. In this talk, I describe two complementary approaches to this new kind of dark matter program: (1) PADME, a fixed-target, missing-mass experiment seeking evidence for the dark photon, a hypothetical mediator of a new U(1) gauge symmetry in the dark sector; and (2) a search for inelastic dark matter (iDM) with a unique signature in the CMS detector, using dark photons as DM-SM mediators. The complementarity of these two methods is explored, both in terms of accessible parameter space and experimental challenges.
Speaker: Andre Sterenberg Frankenthal (Cornell University)
• 11:45 AM
DUNE in 10 Minutes 15m
A brief talk on the updates and technical details of DUNE in a concentrated format.
Speaker: Richard Diurba
• 12:00 PM
Cold Electronics Readout System for the ProtoDUNE-SP LAr-TPC 15m
The Deep Underground Neutrino Experiment (DUNE) is an international long-baseline neutrino experiment. DUNE will consist of an intense neutrino beam produced at Fermi National Accelerator Laboratory in Batavia, Illinois. The far detector will comprise of four Liquid Argon Time Projection Chambers (LArTPC) holding in total around 40 ktons of fiducial mass and will be placed at the Sanford Underground Research Laboratory in South Dakota at 1300 kilometres downstream of the source. The availability of two variants of the LArTPC technology, Single- and Dual-Phase, for the DUNE far detector, has led to an extensive prototype program development at the European Research Center (CERN) Neutrino Platform facility. The Single Phase (SP) TPC readout electronics are referred to as the “Cold Electronics (CE)” because they will operate in LAr, to minimize channel capacitance and noise by keeping the length of the connection between the anode wires and its corresponding electronics input to an absolute minimum. I will summarize the CE system and present preliminary results from cold electronics after the ProtoDUNE-SP beam run in late 2018.
Speaker: Mrs Maura Spanu (BNL)
• 12:15 PM
Michel electron reconstruction in ProtoDUNE 15m
The Deep Underground Neutrino Experiment (DUNE) is a leading-edge experiment for neutrino science and proton decay studies. The single-phase liquid argon prototype detector at CERN is a crucial milestone for the DUNE that will inform the construction and operation of the far detector modules. In this talk, I will present the current status of reconstructing Michel electrons from cosmic-ray muons in the ProtoDUNE detector. These Michel electrons are distributed uniformly inside the detector and serve as a natural and powerful sample to study the detector’s response for low-energy (tens of MeV) interactions as a function of position. We have developed a selection tool to identify such Michel electrons which could benefit any LArTPC experiment generically.
Speaker: Dr Aleena Rafique (Argonne National Laboratory)
• 12:30 PM
Overcoming Neutrino Interaction Mis-modeling with DUNE-PRISM 15m
The expected precision of current long-baseline neutrino oscillation experiments (T2K, NO$\nu$A) will be limited by uncertainties in neutrino interaction models in addition to sample statistics. The interaction uncertainties will also play a significant role in next-generation experiments (DUNE, Hyper-K), which aim to collect much larger samples of oscillated neutrinos. Without significant advancements in neutrino-nucleus interaction modeling, traditional analyses will be susceptible to biased oscillation measurements. The DUNE-PRISM (Precision Reaction Independent Spectrum Measurement) technique offers a complementary approach to the oscillation analysis methods used by T2K, NO$\nu$A, and MINOS. DUNE-PRISM uses direct extrapolation of near detector data to infer oscillation probabilities with significantly less dependence on the validity of neutrino interaction models. This is achieved by combining multiple near detector measurements, each taken with the detector at a different off beam axis position, in order to sample a variety of neutrino energy spectra. This talk will introduce DUNE-PRISM and show how the oscillation parameters extracted using this technique are robust to unknown interaction modeling errors.
Speaker: Dr Luke Pickering (Michigan State University)
• 12:45 PM 2:00 PM
Lunch
• 2:00 PM 4:05 PM
Tuesday Afternoon I
• 2:00 PM
FSPA report 10m
Speaker: Dr Deepika Jena (FERMILAB)
• 2:10 PM
UEC report 10m
Speaker: Dr Gavin S. Davies (Indiana University)
• 2:20 PM
NOvA in 10 minutes 15m
The long-baseline neutrino oscillation experiment named NOvA is comprised of two detectors utilizing liquid scintillator tracking calorimeters. Both are positioned 14 mrad off-axis with respect to the NuMI beam with the near detector being at Fermilab. The far detector, at 14 kton, can be found approximately 810 km away in Ash River, Minnesota. The main physics goals of NOvA include, but are not limited to, the measurement of muon neutrino disappearance and electron neutrino appearance. This measurement will help resolve the mass hierarchy problem as well as put constraints on θ23, the large mixing angle and its octant, and the CP violating phase. The goal of this talk is to give a general description of the NOvA experiment and present the progress made on these physics goals thus far.
Speaker: Miranda Elkins (Iowa State University)
• 2:35 PM
NuMi Beam Muon Monitor Simulation for Neutrio Beam Quality Improvement 15m
Muon monitors are a very important diagnostic tool for the NOvA experiment at Fermilab. With the MINOS experiment decommissioned, MM are the only detectors to indicate and help mitigate the issues with the NuMI beam. The goal of our study is to maintain the quality of the MM signal and to establish the neutrino beam profile and MM signal correlations. This study could also inform the LBNF decision on the beam diagnostic tools. We report here on the progress of beam scan data analysis (beam position, spot size, and magnetic horn current scan) and comparison with the simulation outcomes.
Speaker: Yiding Yu
• 2:50 PM
Neutrino Event Classification with Deep Learning in NOvA 15m
Deep learning has aided the NOvA experiment in selection of NuMI beam neutrino events. Low statistics makes enhancements in signal efficiency especially critical to the success of the NOvA analysis. Use of convolutional neural networks (CNNs) for event and particle identification has led to significant gains in signal efficiency for neutrino event selection while also reducing the complexity of the reconstruction chain. Convolutional Visual Network (CVN) was introduced in 2016 as the class of methods and CNN architectures used for solving image recognition tasks in NOvA. Initial adoption of CNNs increased effective exposure by 30%, while optimizing training sample composition led to a 14% improvement in efficiency. Despite these advances, numerous avenues remain that show potential to increase signal efficiency. Recent efforts to improve the performance of CVN are summarized in this talk. Among these efforts, residual learning has shown the most promise for enhancing the purity and efficiency of neutrino event selection in the NOvA far detector. Large-scale hyperparameter optimization of existing CVN models is another tool for improving classifier performance despite presenting new computational challenges. Models are trained and evaluated using Monte Carlo samples of the NOvA Far Detector and results and insight from experiments with residual learning and hyperparameter optimization are shown.
Speaker: Grant Nikseresht
• 3:05 PM
NOvA's far detector predictions and understanding key systematic uncertainties. 15m
NOvA continues as one of the leading long-baseline neutrino experiments, thanks to Fermilab's powerful 700 kW NuMI beam, which provides NOvA with a beam of predominantly muon neutrinos or antineutrinos. NOvA studies neutrino oscillations using two detectors, both constructed from plastic extrusions filled with liquid scintillator, placed 810 km apart and both slightly off-axis from the beam center. A key part of NOvA's approach is that we sample the NuMI beam with a near detector close to the target. This allows us to build an accurate far detector prediction and, since the detectors are functionally identical, largely cancel key flux and cross-section systematic uncertainties. The three-flavour long-baseline search probes undetermined physics parameters that describe neutrino mixing matrix, such as the mass hierarchy, CP violation in the lepton sector and the octant of $\theta_{23}$. Although statistical uncertainties dominate in our current results, understanding key sources of systematic uncertainty and their correlations is crucial in a joint fit to selected $\nu_{\mu}$ disappearance and $\nu_e$ appearance events, in both neutrino and antineutrino beam modes. In this talk, I will describe how we build up an accurate prediction at the far detector, using near detector data, and how we seek to understand key sources of systematic uncertainty by studying systematically shifted far detector predictions.
Speaker: Dr Ashley Back (Iowa State University)
• 3:20 PM
NOvA’s approaches on estimation of wrong sign contamination 15m
NOvA is a long-baseline neutrino experiment with two functionally identical liquid scintillator detectors 809 km apart, off-axis from the NuMI beam. The main goal of this experiment is to determine the mass hierarchy and precise measurement of several neutrino oscillation parameters. To measure these parameters precisely we need to have a correct estimate of the neutrino and antineutrino composition in our beam. There are two modes of beam operation, Forward Horn Current (FHC) which is mostly neutrinos and Reverse Horn Current (RHC) which is mostly antineutrinos. The RHC beam has comparatively higher contamination from neutrinos. In NOvA we use several techniques to identify neutrinos and antineutrinos and employ various data-driven methods to estimate this contamination. A summary of our approaches to determine wrong sign contamination in RHC will be presented.
Speaker: Mr abhilash dombara (syracuse university)
• 3:35 PM
Cross section model tuning and multiplicity studies in NOvA 15m
NOvA is a long baseline neutrino experiment based at Fermilab that studies neutrino oscillation parameters via electron neutrino appearance and muon neutrino disappearance. The oscillation measurements compare the Far Detector data to an oscillated prediction which accounts for the Near Detector (ND) data and our understanding of neutrino interactions and cross-sections by using GENIE simulation. By tuning the cross section model to better represent neutrino scattering data from NOvA’s ND and other experiments, we can extract oscillation parameters with a more accurate representation of cross section uncertainties. This tuning process is performed in the ND, before the oscillations occur. The effectiveness of the tuning will be discussed through studies of subsets of different multiplicities in the final state. Potential improvements to the cross section tune used for NOvA’s 2018 joint neutrino and antineutrino analysis will also be discussed.
Speaker: Maria Martinez-Casales
• 3:50 PM
The NOvA Test Beam Program 15m
NOvA is a two-detector long-baseline neutrino oscillation experiment which aims to make a determination of the neutrino mass hierarchy, the octant of ${\theta}_{23}$, and measure possible CP violation. The NOvA Test Beam program consists of a scaled-down NOvA detector placed in a beamline capable of delivering 0.3 - 2.0 GeV/c protons, electrons, pions, and kaons. The beamline detectors provide us with particle identification and momentum measurements so we can study our detector technology with known inputs. Studying these particles will provide us a more detailed understanding of our calibration, detector response, and energy scale, which are some of the largest sources of systematic uncertainty in NOvA analyses. We will also collect a selection of single-particle data events for training particle identification algorithms. In this talk, I will present the current status of the NOvA Test Beam program and discuss plans for data taking and analysis.
Speaker: Teresa Lackey
• 4:05 PM 4:30 PM
Coffee break
• 4:30 PM 5:50 PM
Tuesday Afternoon II
Convener: Mary Convery (Fermilab)
• 4:30 PM
BSM theory in 10 minutes 15m
Despite that the Standard Model has been put through many stringent tests, it still can not be the full picture of particle physics. In this short talk, we give an overview of the motivations to go beyond the Standard Model and discuss a few plausible scenarios in its extension.
Speaker: Yang Gao
• 4:45 PM
Muon g-2 in 10 minutes 15m
The Muon $g-2$ Experiment (E989) is measuring the magnetic anomaly, $a_\mu$, of the muon to 140 parts per billion (ppb) to resolve the outstanding discrepancy between the value predicted by the Standard Model and the best measurement to date. The magnetic anomaly receives contributions from loops of any particle type in the muon-photon vertex, so a discrepancy between theory and experiment is a strong indication of physics beyond the Standard Model. Determining $a_\mu$ involves storing muons in a well-known and highly uniform magnetic field and measuring their anomalous precession frequency, $\omega_a$---the rate at which their spins rotate relative to their momenta. Segmented electromagnetic calorimeters measure the hit times and energies of decay positrons to probe $\omega_a$. NMR probes measure and track the $1.45\,\text{T}$ magnetic field in terms of the Larmor precession frequency of a free proton, $\omega_p$. Pulsed magnetic kickers allow proper injection onto the $7.1\,\text{m}$ radius storage orbit, and pulsed electrostatic quadrupoles provide vertical focusing of the muon beam. Following explanation of the motivation and experimental technique of Muon $g-2$, some snippets of the data taken in $\text{Run}~1$ and $\text{Run}~2$ will be shown.
Speaker: Jason Hempstead (University of Washington)
• 5:00 PM
Pileup Systematic Studies in the Fermilab Muon g-2 Experiment 15m
The Muon g-2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon, $a_{\mu}$, to a precision of $140$ ppb, a four-fold increase in precision over the previous experiment at Brookhaven National Laboratory (BNL). The value of $a_{\mu}$ from BNL currently differs from the Standard Model prediction by $\sim 3.5$ standard deviations or higher, suggesting the potential for new physics and therefore, motivating a new experiment. The Fermilab experiment follows the measurement principles of the BNL experiment, injecting a beam of positive muons into a storage ring, which focuses the beam with a combination of magnetic and electric fields. The muon anomaly relies on the measurement of the spin precession frequency $\omega_a$ about the muon momentum. This presentation will focus on one of the most important sources of systematics to the $\omega_a$ analysis: pileup effects. Pileup refers to the overlap of decays in the detector that originate from separate muon decays, too close to each other in time and space to be resolved into individual pulses. A complete description of how pileup events are identified will be presented along with a discussion of how the correction to a traditional $\omega_a$ analysis is formulated and applied
Speaker: Ms Meghna Bhattacharya (University of Mississippi)
• 5:15 PM
Mu2e in 10 minutes 15m
The discovery of neutrino oscillation manifests the violation of lepton number conservation. It further indicates Charged Lepton Flavor Violation (CLFV) is not explicitly forbidden in the Standard Model (SM), although it is dynamically suppressed which remain unobserved. Many well-motivated physics models predict rates for CLFV processes that are within a few orders of magnitude of the current experimental bounds, such as the MSSM with right-handed neutrinos, SUSY with R-parity violation as well as models with leptoquarks, new gauge bosons, large extra-dimensions, and a non-minimal Higgs sector. The Mu2e experiment at Fermilab will be 10,000 times more sensitive than previous experiments looking for muon-to-electron conversion with a single-event sensitivity of a few 10-17 for the ratio of μ− N → e− N conversions to conventional muon capture. Mu2e experiment has real discovery potential over a wide range of New Physics models and may prove to be a powerful discriminant among models.
Speaker: Yujing Sun
• 5:30 PM
Design and status of the Mu2e crystal calorimeter 15m
The Mu2e experiment at Fermilab will search for the charged-lepton flavour violating neutrino-less conversion of a negative muon into an electron in the field of an aluminum nucleus. The Mu2e detector is composed of a tracker and an electromagnetic calorimeter and an external veto for cosmic rays. The calorimeter plays an important role in providing excellent particle identification capabilities, a fast online trigger filter while aiding the track reconstruction capabilities. The calorimeter requirements are to provide a large acceptance for ~100 MeV electrons and reach: 1) a time resolution better than 0.5 ns @ 100 MeV; 2) an energy resolution O(10%) @ 100 MeV; 3) a position resolution of 1 cm. The calorimeter consists of two disks, each one made of 674 pure CsI crystals readout by two large area 2x3 array of UV-extended SiPMs of 6x6 mm^2 dimensions. A large scale prototype has also been constructed and tested at the beam test facility in Frascati. It consists of 51 pre-production crystals readout by a Mu2e SiPM.
Speaker: Dr Raffaella Donghia (LNF-INFN)
• 5:45 PM
Closing 5m
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https://www.usgs.gov/center-news/volcano-watch-nyirangongo-could-it-happen-here | # Volcano Watch — Nyirangongo -- Could it happen here?
Release Date:
At dawn on January 17, 2002, the residents of Goma, a city of 500,000 along the eastern border of the Republic of Congo, awoke to glowing red skies and falling ash. A large eruption of Mount Nyiragongo was underway, the first since 1977.
Over the next 48 hours, lava flows exiting from three different fissures spilled over the countryside, destroying 14 villages and eventually entering Goma itself. At its widest, the flow that cut into Goma was more than 60 meters (200 feet) across.
The heat of the lava ignited buildings along the periphery of the flow and, within hours, fires were spreading throughout the city. Early reports suggest that nearly half of the buildings in Goma were either damaged or destroyed. By January 19, the eruptive activity was largely over, but large earthquakes are continuing to this day, and new fissures have opened on the outskirts of Goma. In the aftermath, more than 40 people were burned to ashes and hundreds of thousands found themselves homeless.
The 1977 eruption of Nyiragongo bears many similarities to this current eruption. It, too, began suddenly and with little warning, involved major crater floor collapse, and culminated in voluminous and fast moving lava flows. Unlike the recent eruption, however, the lava flows did not reach Goma. Because of the extremely high speeds of the 1977 lava flows, estimated by some observers to peak at 100 km/hr (62 mph) on Nyiragongo's steep upper slopes, the death toll from the 1977 eruption was staggering. Some reports put the number killed in the thousands. Exact numbers will never be known. The fast-moving flows swept through rural villages in the middle of the night, catching the villagers unaware and, in most cases, asleep.
Residents of Hawaii, no strangers to volcanic activity and the destruction it often brings, may still wonder if such rapid and sudden catastrophes could strike here. Though we can never be certain about the future, the short answer to this question is still probably "no." There are two main reasons why Hawaii residents need not fear a Nyiragongo-like cataclysm. First, the nature of Hawaii's volcanoes, though similar to Nyiragongo in some ways, has several important differences. Second, hundreds of instruments operated by many scientists keep a careful watch over the local volcanoes. Taken together, these two factors virtually assure that Hawaiians need not fear sudden lava flows entering populated areas without warning.
The chemical composition of the Nyiragongo lava is unusual, almost unique. Nyiragongo lava contains very little silica. This makes it highly fluid and capable of flowing at very great speeds. Hawaiian lava also contains only modest amounts of silica, but still enough to limit flow velocity to about walking speed in most cases. Only when lava moves down very steep slopes can it move very fast, and then only when the effusion rate is high. But, most slopes on Hawaiian volcanoes are gradual, in contrast to Nyiragongo, which has built a steep and dramatic cone. Moreover, Nyiragongo is prone to radial fissures that can open suddenly on its lower slopes.
Until the recent eruption (and prior to the 1977 eruption) an active lava lake sat within Nyiragongo's crater. The danger here is easy to see: a large reservoir of very fluid lava perched above a populated area and contained only by a potentially leaky cone. Conditions like these exist nowhere in Hawaii, and if they ever do occur, scientists at HVO would begin vigilant monitoring that would not end until the dangerous conditions abated.
The greatest volcanic dangers facing Hawaii residents are on the populated west slopes of Hualalai, the southwest slopes of Mauna Loa, and along Kīlauea's east rift zone in lower Puna. Eruptions at Hualalai's summit or Mauna Loa's southwest rift zone could send lava flows into populated regions within hours and, for Kīlauea's east rift zone, within minutes. Still, this lava would not be moving at great speed, and seismic monitoring, combined with GPS and tiltmeter observations, would almost certainly have anticipated an imminent eruption. Thanks to the relatively benign nature of most Hawaiian volcanism and to the efforts of HVO, the primary victim of Hawaiian lava flows will remain property rather than people.
### Volcano Activity Update
Eruptive activity of Kīlauea Volcano continued unabated at the Puu Oo vent during the past week. The two shields built over the main tube system above Pulama pali are still topped with active lava ponds. Overflows from the ponds feed short, multidirectional flows radial to the shields. No molten lava was observed descending Pulama pali or flowing in the coastal flats during an overflight on January 31. Heavy rainfall earlier in the week obscured most visual observations of flow activity. The ocean entry at Kamoamoa stopped some time after the morning of January 29 when it was last seen active. Lava is not entering the ocean anywhere along the coastline.
There were no earthquakes reported felt during the week ending on January 31. | 2020-08-13T18:13:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2166636437177658, "perplexity": 6457.108740794652}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739048.46/warc/CC-MAIN-20200813161908-20200813191908-00376.warc.gz"} |
https://par.nsf.gov/biblio/10345609-search-light-higgs-boson-single-photon-decays-using-tagging-method | This content will become publicly available on February 1, 2023
Search for a Light Higgs Boson in Single-Photon Decays of $ϒ(1S)$ Using $ϒ(2S)→π+π−ϒ(1S)$ Tagging Method
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10345609
Journal Name:
Physical Review Letters
Volume:
128
Issue:
8
ISSN:
0031-9007 | 2022-10-06T18:23:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44255560636520386, "perplexity": 14600.97017582369}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337853.66/warc/CC-MAIN-20221006155805-20221006185805-00065.warc.gz"} |
https://www.khanacademy.org/computing/computer-programming/programming-natural-simulations/programming-forces/a/gravitational-attraction | # Gravitational attraction
Probably the most famous force of all is gravity. We humans on earth think of gravity as an apple hitting Isaac Newton on the head. Gravity means that stuff falls down. But this is only our experience of gravity. In truth, just as the earth pulls the apple towards it due to a gravitational force, the apple pulls the earth as well. The thing is, the earth is just so massive that it overwhelms all the gravity interactions of every other object on the planet. Every object with mass exerts a gravitational force on every other object. And there is a formula for calculating the strengths of these forces, as depicted in the diagram below:
Let’s examine this formula a bit more closely.
• F refers to the gravitational force, the vector we ultimately want to compute and pass into our applyForce() function.
• G is the universal gravitational constant, which in our world equals 6.67428 x 10^-11 meters cubed per kilogram per second squared. This is a pretty important number if your name is Isaac Newton or Albert Einstein. It’s not an important number if you are a ProcessingJS programmer. Again, it’s a constant that we can use to make the forces in our world weaker or stronger. Just making it equal to one and ignoring it isn’t such a terrible choice either.
• m_1 and m_2 are the masses of objects 1 and 2. As we saw with Newton’s second law (\vec{F} = M\vec{A}), mass is also something we could choose to ignore. After all, shapes drawn on the screen don’t actually have a physical mass. However, if we keep these values, we can create more interesting simulations in which “bigger” objects exert a stronger gravitational force than smaller ones.
• \hat{r} refers to the unit vector pointing from object 1 to object 2. As we’ll see in a moment, we can compute this direction vector by subtracting the location of one object from the other.
• r^2 refers to the distance between the two objects squared. Let’s take a moment to think about this a bit more. With everything on the top of the formula—G, m_1, m_2—the bigger its value, the stronger the force. Big mass, big force. Big G, big force. Now, when we divide by something, we have the opposite. The strength of the force is inversely proportional to the distance squared. The farther away an object is, the weaker the force; the closer, the stronger.
Hopefully by now the formula makes some sense to us. We’ve looked at a diagram and dissected the individual components of the formula. Now it’s time to figure out how we translate the math into ProcessingJS code. Let’s make the following assumptions.
We have two objects, and:
1. Each object has a PVector location: location1 and location2.
2. Each object has a numeric mass: mass1 and mass2.
3. There is a numeric variable G for the universal gravitational constant.
Given these assumptions, we want to compute a PVector force, the force of gravity. We’ll do it in two parts. First, we’ll compute the direction of the force \hat{r} in the formula above. Second, we’ll calculate the strength of the force according to the masses and distance.
Remember when we figured out how to have an object accelerate towards the mouse? We're going to use the same logic here.
A vector is the difference between two points. To make a vector that pointed from the circle to the mouse, we simply subtracted one point from another:
var dir = PVector.sub(mouse, location);
In our case, the direction of the attraction force that object 1 exerts on object 2 is equal to:
var dir = PVector.sub(location1, location2);
Don’t forget that since we want a unit vector, a vector that tells us about direction only, we’ll need to normalize the vector after subtracting the locations:
dir.normalize();
OK, we’ve got the direction of the force. Now we just need to compute the magnitude and scale the vector accordingly.
var m = (G * mass1 * mass2) / (distance * distance);
dir.mult(m);
The only problem is that we don’t know the distance. G, mass1, and mass2 were all givens, but we’ll need to actually compute distance before the above code will work. Didn’t we just make a vector that points all the way from one location to another? Wouldn’t the length of that vector be the distance between two objects?
Well, if we add just one line of code and grab the magnitude of that vector before normalizing it, then we’ll have the distance.
// The vector that points from one object to another
var force = PVector.sub(location1, location2);
// The length (magnitude) of that vector is the distance between the two objects.
var distance = force.mag();
// Use the formula for gravity to compute the strength of the force.
var strength = (G * mass1 * mass2) / (distance * distance);
// Normalize and scale the force vector to the appropriate magnitude.
force.normalize();
force.mult(strength);
Note that I also renamed the PVector “dir” as “force.” After all, when we’re finished with the calculations, the PVector we started with ends up being the actual force vector we wanted all along.
Now that we’ve worked out the math and the code for calculating an attractive force (emulating gravity), we need to turn our attention to applying this technique in the context of an actual ProcessingJS program. Earlier in this section, we created a simple Mover object—an object with PVector’s location, velocity, and acceleration as well as an applyForce(). Let’s take this exact class and put it in a program with:
• A single Mover object.
• A single Attractor object (a new object type that will have a fixed location).
The Mover object will experience a gravitational pull towards the Attractor object, as illustrated in the diagram.
We can start by making the new Attractor object very simple—giving it a location and a mass, along with a method to display itself (tying mass to size).
var Attractor = function() {
this.position = new PVector(width/2, height/2);
this.mass = 20;
this.G = 1;
this.dragOffset = new PVector(0, 0);
this.dragging = false;
this.rollover = false;
};
// Method to display
Attractor.prototype.display = function() {
ellipseMode(CENTER);
strokeWeight(4);
stroke(0);
fill(175, 175, 175, 200);
ellipse(this.position.x, this.position.y, this.mass*2, this.mass*2);
};
After defining that, we can create an instance of the Attractor object type.
var mover = new Mover();
var attractor = new Attractor();
draw = function() {
background(50, 50, 50);
attractor.display();
mover.update();
mover.display();
};
This is a good structure: a main program with a Mover and an Attractor object. The last piece of the puzzle is how to get one object to attract the other. How do we get these two objects to talk to each other?
There are a number of ways we could do this, architecturally. Here are just a few possibilities.
1. A function that receives both an Attractor and a Mover: attraction(a, m);
2. A method in the Attractor object that receives a Mover: a.attract(m);
3. A method in the Mover object that receives an Attractor: mover.attractedTo(a);
4. A method in the Attractor object that receives a Mover and returns a PVector, which is the attraction force. That attraction force is then passed into the Mover's applyForce() method. var f = a.calculateAttraction(m); mover.applyForce(f);
It’s good to look at a range of options for making objects talk to each other, and you could probably make arguments for each of the above possibilities. Let's start by discarding the first one, since an object-oriented approach is really a much better choice over an arbitrary function not tied to either the Mover or Attractor objects. Whether you pick option 2 or option 3 is the difference between saying “The attractor attracts the mover” or “The mover is attracted to the attractor.” Number 4 seems the most appropriate, at least in terms of where we are in this course. After all, we spent a lot of time working out the applyForce() method, and I think our examples will be clearer if we continue with the same methodology.
In other words, where we once had:
var f = new PVector(0.1, 0); // Made up force
mover.applyForce(f);
We will now have:
var f = a.calculateAttraction(m); // Attraction force between two objects
mover.applyForce(f);
And so our draw() function can now be written as:
draw = function() {
background(50, 50, 50);
// Calculate attraction force and apply it
var f = a.calculateAttraction(m);
mover.applyForce(f);
attractor.display();
mover.update();
mover.display();
};
We’re almost there. Since we decided to put the calculateAttraction() method inside of the Attractor object type, we’ll need to actually write that function. The function needs to receive a Mover object and return a PVector. And what goes inside that function? All of that nice math we worked out for gravitational attraction!
Attractor.prototype.calculateAttraction = function(mover) {
// What's the force's direction?
var force = PVector.sub(this.position, mover.position);
var distance = force.mag();
force.normalize();
// What's the force's magnitude?
var strength = (this.G * this.mass * mover.mass) / (distance * distance);
force.mult(strength);
// Return the force so it can be applied!
return force;
};
And we’re done. Sort of. Almost. There’s one small kink we need to work out. Let’s look at the above code again. See that symbol for divide, the slash? Whenever we have one of these, we need to ask ourselves the question: What would happen if the distance happened to be a really, really small number or (even worse!) zero??! Well, we know we can’t divide a number by 0, and if we were to divide a number by something like 0.0001, that is the equivalent of multiplying that number by 10,000! Yes, this is the real-world formula for the strength of gravity, but we don’t live in the real world. We live in the ProcessingJS world. And in the ProcessingJS world, the mover could end up being very, very close to the attractor and the force could become so strong the mover would just fly way off the screen. And so with this formula, it’s good for us to be practical and constrain the range of what distance can actually be. Maybe, no matter where the Mover actually is, we should never consider it less than 5 pixels or more than 25 pixels away from the attractor.
distance = constrain(distance, 5, 25);
For the same reason that we need to constrain the minimum distance, it’s useful for us to do the same with the maximum. After all, if the mover were to be, say, 500 pixels from the attractor (not unreasonable), we’d be dividing the force by 250,000. That force might end up being so weak that it’s almost as if we’re not applying it at all.
Now, it’s really up to you to decide what behaviors you want. But in the case of, “I want reasonable-looking attraction that is never absurdly weak or strong,” then constraining the distance is a good technique.
Let's put it all together now in one program. The Mover object type hasn't changed at all, but now our program includes an Attractor object, and code that ties them together. We've also added code to the program to control the attractor with a mouse, so that it's easier to observe the effects.
And we could, of course, expand this example using an array to include many Mover objects, just as we did with friction and drag. The main change that we've made to the program is to adjust our Mover object to accept mass, x, and y (as we've done in the past), initialize an array of randomly placed Movers, and loop over that array to calculate the attraction force on each of them, each time:
var movers = [];
var attractor = new Attractor();
for (var i = 0; i < 10; i++) {
movers[i] = new Mover(random(0.1, 2), random(width), random(height));
}
draw = function() {
background(50, 50, 50);
attractor.display();
for (var i = 0; i < movers.length; i++) {
var force = attractor.calculateAttraction(movers[i]);
movers[i].applyForce(force);
movers[i].update();
movers[i].display();
}
};
This "Natural Simulations" course is a derivative of "The Nature of Code" by Daniel Shiffman, used under a Creative Commons Attribution-NonCommercial 3.0 Unported License. | 2016-10-25T01:29:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5642051696777344, "perplexity": 844.4164111585108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719843.44/warc/CC-MAIN-20161020183839-00558-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.pnnl.gov/news-media/pnnls-self-healing-cement-could-transform-geothermal-industry | May 3, 2019
Web Feature
## PNNL’s Self-Healing Cement Could Transform Geothermal Industry
Research shows 87 percent reduction in cement fractures
PNNL chemist Carlos Fernandez and a team of researchers have developed a self-healing cement that could transform the geothermal energy industry
Andrea Starr | Pacific Northwest National Laboratory
A self-healing cement developed by PNNL can outperform conventional concrete, offering a potentially pollution-preventing technology for the growing geothermal industry.
This game-changing combination uses a flexible ingredient, a polymer, to repair fractured surfaces and fill cracks, minimizing mechanical failure risks and offering a sustainable energy source.
Chemist Carlos Fernandez and his team, in collaboration with Simerjeet Gill of Brookhaven National Laboratory, detail the polymer’s healing properties and how it can improve the mechanical performance of cement in their paper, Insights into the physical and chemical properties of a cement-polymer composite developed for geothermal wellbore applications in Cement and Concrete Composites.
Funding for the research was provided by the Department of Energy’s Geothermal Technologies Office.
## Polymers under pressure
Cement used in geothermal wells is known to crack under pressure and in high-temperature environments associated with drilling for geothermal energy. The objective of the team’s study was to see how its self-healing cement would hold up when tested against conventional cement in these extreme heat conditions. Through a variety of tests, performed at PNNL and BNL’s National Synchrotron Light Source II, the team found that the self-healing cement technology could eliminate the need to remove, repair and replace cracked cement wells.
PNNL researchers tested their self-healing cement’s strength and reactions to mechanical stress and conducted analyses of surface area, chemical composition, and surface topography. The tests confirmed that the self-healing cement is a significant alternative to conventional cement because it is flexible and autonomously heals cracks.
The flexibility is attributed to chemically “soft” or flexible bonding between the atoms in the polymer and cement. This soft bonding allows large deformations that can be contained within the cement without breaking the bonds. This was predicted through computational modeling done by PNNL’s Vanda Glezakou. The polymer adds 60 to 70 percent more elasticity to the cement when it is added, reducing fractures in the cement, Fernandez reports in the paper.
On their own, polymers are large, chain-like molecules that work to hold substances together and are naturally found in the human body. When added to cement, polymers add flexibility to brittle material and keep cracks from spreading quickly. The polymer detaches, migrates to the crack, and attaches back to fill the crack. There was an 87 percent reduction in crack size when the polymer was added to the concrete.
## Cementing the future
Cement is the second largest consumable in the world behind water. Thus, finding a way to make cement even more effective could be a game changer not only for the geothermal industry, but the construction industry overall.
“The idea in a few years would be to extend it to everything,” Fernandez said. “The sky’s the limit.”
The cement industry earns more than $37 billion annually. However, cracking cement averages$12 billion a year to repair infrastructure alone. The polymer-cement combination could amount to \$3.4 billion a year in savings for infrastructure like dams, nuclear waste facilities and skyscrapers, Fernandez predicts. This could mean fewer road closures and maintenance repairs that clog roads and create inconveniences for daily commutes.
Like an LED light fixture, the polymer-cement could create long-term savings. Conventional cement is 5 cents per pound. The estimated cost for the polymer-cement is 30 to 35 cents per pound. However, it could potentially extend the life of concrete-based structures by 30 to 50 years, Fernandez said.
For the oil industry, specifically, where high temperatures are a constant, removing and replacing cracked concrete is a time consuming, costly venture, Fernandez said. Replacing conventional cement with self-healing cement can amount to millions of dollars in savings.
The self-healing cement also could be used at nuclear waste facilities and hydropower dams where cracks in the structures and mechanical failure could result in flooding or contamination. Costly annual and biannual inspections and repairs could decrease in number, Fernandez said. The flexible nature of the self-healing cement also allows it to withstand greater mechanical stress from natural disasters and extreme weather conditions such as earthquake tremors or high winds.
## A concrete alternative for the environment
Self-healing cement could resolve major concerns about the sealing of wellbores for oil, gas, and geothermal heat production. Leaks in wellbores cause contamination and limit the ability to provide clean energy alternatives. These leaks contaminate aquifers and surface waters.
Other self-healing polymer-cement blends developed for the oil and gas industry often have poor mechanical properties and cannot withstand the high-temperature environments found in geothermal wells.
“The development of a self-healing polymer-cement combination which is functional in geothermal environments could represent a game-changing technology towards the growth of the geothermal energy industry,” the team reported in the paper.
There are large geothermal energy reserves across the country and around the world that are not in use because wellbore cement fails in high temperature conditions and in chemically corrosive environments. Geothermal energy is thermal energy that the Earth generates and stores. With improvements like self-healing cement, geothermal energy has the potential to be an applicable, sustainable energy source. The self-healing cement can deliver significant energy with minimal carbon release to the atmosphere.
Additionally, tens of thousands of tons of conventional cement ends up in landfills, Fernandez said. With the extension of more than 30 years of additional usage of the composite, less cement would go to landfills.
Work by PNNL researchers was performed at EMSL, the Environmental Molecular Sciences Laboratory, a DOE Office of Science user facility located at PNNL, and at Brookhaven National Laboratory in Upton, NY.
Published: May 3, 2019
### PNNL Research Team
Carlos A. Fernandez
Kenton A. Rod
Manh-Thuong Nguyen
Tamás Varga | 2019-05-20T14:24:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5918555855751038, "perplexity": 5748.516251704095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256040.41/warc/CC-MAIN-20190520142005-20190520164005-00000.warc.gz"} |
https://dlmf.nist.gov/4.13 | §4.13 Lambert $W$-Function
The Lambert $W$-function $W\left(z\right)$ is the solution of the equation
4.13.1 $W{\mathrm{e}}^{W}=z.$ ⓘ Defines: $W\left(\NVar{z}\right)$: Lambert $W$-function Symbols: $\mathrm{e}$: base of natural logarithm and $z$: complex variable Referenced by: §4.13 Permalink: http://dlmf.nist.gov/4.13.E1 Encodings: TeX, pMML, png See also: Annotations for §4.13 and Ch.4
On the $z$-interval $[0,\infty)$ there is one real solution, and it is nonnegative and increasing. On the $z$-interval $(-{\mathrm{e}}^{-1},0)$ there are two real solutions, one increasing and the other decreasing. We call the increasing solution for which $W\left(z\right)\geq W\left(-{\mathrm{e}}^{-1}\right)=-1$ the principal branch and denote it by $W_{0}\left(z\right)$. See Figure 4.13.1.
The decreasing solution can be identified as $W_{\pm 1}\left(x\mp 0\mathrm{i}\right)$. Other solutions of (4.13.1) are other branches of $W\left(z\right)$. They are denoted by $W_{k}\left(z\right)$, $k\in\mathbb{Z}$, and have the property
4.13.1_1 $W_{k}\left(z\right)={\rm ln}_{k}(z)-\ln\left({\rm ln}_{k}(z)\right)+o\left(1% \right),$ $\left|z\right|\to\infty$, ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $o\left(\NVar{x}\right)$: order less than, $\ln\NVar{z}$: principal branch of logarithm function, $k$: integer and $z$: complex variable Notes: See Corless et al. (1996, §4). Permalink: http://dlmf.nist.gov/4.13.E1_1 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
where ${\rm ln}_{k}(z)=\ln\left(z\right)+2\pi\mathrm{i}k$. $W_{0}\left(z\right)$ is a single-valued analytic function on $\mathbb{C}\setminus(-\infty,-{\mathrm{e}}^{-1}]$, real-valued when $z>-{\mathrm{e}}^{-1}$, and has a square root branch point at $z=-{\mathrm{e}}^{-1}$. See (4.13.6) and (4.13.9_1). The other branches $W_{k}\left(z\right)$ are single-valued analytic functions on $\mathbb{C}\setminus(-\infty,0]$, have a logarithmic branch point at $z=0$, and, in the case $k=\pm 1$, have a square root branch point at $z=-{\mathrm{e}}^{-1}\mp 0\mathrm{i}$ respectively. See Figure 4.13.2.
Alternative notations are $\operatorname{Wp}\left(x\right)$ for $W_{0}\left(x\right)$, $\operatorname{Wm}\left(x\right)$ for $W_{-1}\left(x+0\mathrm{i}\right)$, both previously used in this section, the Wright $\omega$-function $\omega\left(z\right)=W\left({\mathrm{e}}^{z}\right)$, which is single-valued, satisfies
4.13.1_2 $\omega\left(z\right)+\ln\left(\omega\left(z\right)\right)=z,$ ⓘ Symbols: $\omega\left(\NVar{z}\right)$: Wright $\omega$-function, $\ln\NVar{z}$: principal branch of logarithm function and $z$: complex variable Referenced by: (4.13.3), §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E1_2 Encodings: TeX, pMML, png Rearrangement (effective with 1.1.7): This equation, which was originally (4.13.3), was moved here, and the symbol for $\omega$ was originally $U$. See also: Annotations for §4.13 and Ch.4
and has several advantages over the Lambert $W$-function (see Lawrence et al. (2012)), and the tree $T$-function $T\left(z\right)=-W\left(-z\right)$, which is a solution of
4.13.1_3 $T{\mathrm{e}}^{-T}=z.$ ⓘ Symbols: $T\left(\NVar{z}\right)$: Tree $T$-function, $\mathrm{e}$: base of natural logarithm and $z$: complex variable Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E1_3 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
Properties include:
4.13.2 $\displaystyle W_{0}\left(-{\mathrm{e}}^{-1}\right)$ $\displaystyle=W_{\pm 1}\left(-{\mathrm{e}}^{-1}\mp 0\mathrm{i}\right)=-1,$ $\displaystyle W_{0}\left(0\right)$ $\displaystyle=0,$ $\displaystyle W_{0}\left(\mathrm{e}\right)$ $\displaystyle=1.$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\mathrm{e}$: base of natural logarithm and $\mathrm{i}$: imaginary unit Permalink: http://dlmf.nist.gov/4.13.E2 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png See also: Annotations for §4.13 and Ch.4
4.13.3 Moved to (4.13.1_2). ⓘ Referenced by: (4.13.1_2) Permalink: http://dlmf.nist.gov/4.13.E3 See also: Annotations for §4.13 and Ch.4
4.13.3_1 $W_{0}\left(x{\mathrm{e}}^{x}\right)=\begin{cases}x,&-1\leq x,\\ \text{(no simpler form)},&x<-1.\end{cases}$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\mathrm{e}$: base of natural logarithm and $x$: real variable Proof sketch: Take $x=W_{0}\left(t\right)>-1$, with $t>-{\mathrm{e}}^{-1}$. Then $W_{0}\left(x{\mathrm{e}}^{x}\right)=W_{0}\left(W_{0}\left(t\right){\mathrm{e}}% ^{W_{0}\left(t\right)}\right)=W_{0}\left(t\right)=x$. Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E3_1 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.3_2 $W_{\pm 1}\left(x{\mathrm{e}}^{x}\mp 0\mathrm{i}\right)=\begin{cases}\text{(no % simpler form)},&-1\leq x,\\ x,&x<-1.\end{cases}$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit and $x$: real variable Proof sketch: Take $x=W_{1}\left(t-0\mathrm{i}\right)<-1$, with $-{\mathrm{e}}^{-1}. Then $W_{1}\left(x{\mathrm{e}}^{x}-0\mathrm{i}\right)=W_{1}\left(W_{1}\left(t-0% \mathrm{i}\right){\mathrm{e}}^{W_{1}\left(t-0\mathrm{i}\right)}-0\mathrm{i}% \right)=W_{1}\left(t-0\mathrm{i}\right)=x$. Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E3_2 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.4 $\frac{\mathrm{d}W}{\mathrm{d}z}=\frac{{\mathrm{e}}^{-W}}{1+W}=\frac{W}{z(1+W)}.$
4.13.4_1 $\frac{{\mathrm{d}}^{n}W}{{\mathrm{d}z}^{n}}=\frac{{\mathrm{e}}^{-nW}p_{n-1}(W)% }{\left(1+W\right)^{2n-1}},$ $n=1,2,3,\dots$, ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$: derivative, $\mathrm{e}$: base of natural logarithm, $n$: integer and $z$: complex variable Notes: See Corless et al. (1997, formula (7)). Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E4_1 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
in which the $p_{n}(x)$ are polynomials of degree $n$ with
4.13.4_2 $\displaystyle p_{0}(x)$ $\displaystyle=1,$ $\displaystyle p_{n}(x)$ $\displaystyle=(1+x)p_{n-1}^{\prime}(x)+(1-n(x+3))p_{n-1}(x),$ $n=1,2,3,\dots$. ⓘ Symbols: $n$: integer and $x$: real variable Notes: See Corless et al. (1997, formula (8)). Permalink: http://dlmf.nist.gov/4.13.E4_2 Encodings: TeX, TeX, pMML, pMML, png, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
Explicit representations for the $p_{n}(x)$ are given in Kalugin and Jeffrey (2011).
4.13.5 $W_{0}\left(z\right)=\sum_{n=1}^{\infty}\frac{\left(-n\right)^{n-1}}{n!}z^{n},$ $|z|<{\mathrm{e}}^{-1}$.
4.13.5_1 $\left(\frac{W_{0}\left(z\right)}{z}\right)^{a}={\mathrm{e}}^{-aW_{0}\left(z% \right)}=\sum_{n=0}^{\infty}\frac{a\left(n+a\right)^{n-1}}{n!}\left(-z\right)^% {n},$ $|z|<{\mathrm{e}}^{-1}$, $a\in\mathbb{C}$. ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\mathbb{C}$: complex plane, $\in$: element of, $\mathrm{e}$: base of natural logarithm, $!$: factorial (as in $n!$), $n$: integer, $a$: real or complex constant and $z$: complex variable Notes: See Corless et al. (1996, formula (2.36)). Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E5_1 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.5_2 $\frac{1}{1+W_{0}\left(-z\right)}=\sum_{n=0}^{\infty}\frac{n^{n}}{n!}z^{n},$ $|z|<{\mathrm{e}}^{-1}$. ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\mathrm{e}$: base of natural logarithm, $!$: factorial (as in $n!$), $n$: integer and $z$: complex variable Notes: See Corless et al. (1997, formula (14)). Referenced by: §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E5_2 Encodings: TeX, pMML, png See also: Annotations for §4.13 and Ch.4
4.13.6 $W\left(-{\mathrm{e}}^{-1-(t^{2}/2)}\right)=\sum_{n=0}^{\infty}(-1)^{n-1}c_{n}t% ^{n},$ $|t|<2\sqrt{\pi}$,
where $t\geq 0$ for $W_{0}$, $t\leq 0$ for $W_{\pm 1}$ on the relevant branch cuts,
4.13.7 $c_{0}=1,\quad c_{1}=1,\quad c_{2}=\tfrac{1}{3},\quad c_{3}=\tfrac{1}{36},\quad c% _{4}=-\tfrac{1}{270},$ ⓘ Symbols: $c_{i}$: coefficients Permalink: http://dlmf.nist.gov/4.13.E7 Encodings: TeX, pMML, png See also: Annotations for §4.13 and Ch.4
4.13.8 $c_{n}=\frac{c_{n-1}}{n+1}-\tfrac{1}{2}\sum_{k=2}^{n-1}c_{k}c_{n+1-k},$ $n=2,3,4,\dots$, ⓘ Symbols: $k$: integer, $n$: integer and $c_{i}$: coefficients Permalink: http://dlmf.nist.gov/4.13.E8 Encodings: TeX, pMML, png See also: Annotations for §4.13 and Ch.4
and
4.13.9 $1\cdot 3\cdot 5\cdots(2n+1)c_{2n+1}=g_{n},$ ⓘ Symbols: $n$: integer, $c_{i}$: coefficients and $g_{n}$: Unknown defined in GA Permalink: http://dlmf.nist.gov/4.13.E9 Encodings: TeX, pMML, png See also: Annotations for §4.13 and Ch.4
where $g_{n}$ is defined in §5.11(i). See Jeffrey and Murdoch (2017) for an explicit representation for the $c_{n}$ in terms of associated Stirling numbers.
4.13.9_1 $W_{0}\left(z\right)=\sum_{n=0}^{\infty}d_{n}\left(\mathrm{e}z+1\right)^{\ifrac% {n}{2}},$ $\left|\mathrm{e}z+1\right|<1$, $\left|\operatorname{ph}\left(z+{\mathrm{e}}^{-1}\right)\right|<\pi$, ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\pi$: the ratio of the circumference of a circle to its diameter, $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$: derivative, $\mathrm{e}$: base of natural logarithm, $\operatorname{ph}$: phase, $n$: integer and $z$: complex variable Proof sketch: Substitute (4.13.9_1) into $z(1+W)\frac{\mathrm{d}W}{\mathrm{d}z}=W$. Referenced by: (4.13.9_1), §4.13, §4.13, Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E9_1 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
where
4.13.9_2 $\displaystyle d_{0}$ $\displaystyle=-1,\quad d_{1}=\sqrt{2},\quad d_{2}=-\tfrac{2}{3},\quad d_{3}=% \tfrac{11}{36}\sqrt{2},\quad d_{4}=-\tfrac{43}{135},$ $\displaystyle(n+2)d_{1}d_{n+1}$ $\displaystyle=-2d_{n}+\frac{n}{2}\sum_{k=1}^{n-1}d_{k}d_{n-k}-\frac{n+2}{2}% \sum_{k=1}^{n-1}d_{k+1}d_{n-k+1},$ $n=1,2,3,\dots$. ⓘ Symbols: $k$: integer and $n$: integer Permalink: http://dlmf.nist.gov/4.13.E9_2 Encodings: TeX, TeX, pMML, pMML, png, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
For the definition of Stirling cycle numbers of the first kind $\genfrac{[}{]}{0.0pt}{}{n}{k}$ see (26.13.3). As $\left|z\right|\to\infty$
4.13.10 $W_{k}\left(z\right)\sim\xi_{k}-\ln\xi_{k}+\sum_{n=1}^{\infty}\frac{(-1)^{n}}{% \xi_{k}^{n}}\sum_{m=1}^{n}\genfrac{[}{]}{0.0pt}{}{n}{n-m+1}\frac{\left(-\ln\xi% _{k}\right)^{m}}{m!},$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{k}}$: Stirling cycle number of the first kind, $\sim$: Poincaré asymptotic expansion, $!$: factorial (as in $n!$), $\ln\NVar{z}$: principal branch of logarithm function, $k$: integer, $m$: integer, $n$: integer and $z$: complex variable Notes: See Corless et al. (1996, p. 350) and Jeffrey et al. (1995, Theorem 2). Referenced by: §4.13, §4.13, §4.45(iii), Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E10 Encodings: TeX, pMML, png Addition (effective with 1.1.7): Originally we gave only the first three terms of the infinite series. See also: Annotations for §4.13 and Ch.4
where $\xi_{k}=\ln\left(z\right)+2\pi\mathrm{i}k$. For large enough $\left|z\right|$ the series on the right-hand side of (4.13.10) is absolutely convergent to its left-hand side. In the case of $k=0$ and real $z$ the series converges for $z\geq\mathrm{e}$. As $x\to 0-$
4.13.11 $W_{\pm 1}\left(x\mp 0\mathrm{i}\right)\sim-\eta-\ln\eta+\sum_{n=1}^{\infty}% \frac{1}{\eta^{n}}\sum_{m=1}^{n}\genfrac{[}{]}{0.0pt}{}{n}{n-m+1}\frac{\left(-% \ln\eta\right)^{m}}{m!},$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{k}}$: Stirling cycle number of the first kind, $\sim$: Poincaré asymptotic expansion, $!$: factorial (as in $n!$), $\mathrm{i}$: imaginary unit, $\ln\NVar{z}$: principal branch of logarithm function, $m$: integer, $n$: integer, $x$: real variable and $\eta$ Notes: See Corless et al. (1996, p. 350). Referenced by: §4.13, Erratum (V1.1.2) for Equation (4.13.11), Erratum (V1.1.7) for Expansion Permalink: http://dlmf.nist.gov/4.13.E11 Encodings: TeX, pMML, png Addition (effective with 1.1.7): Originally we gave only the first three terms of the infinite series. See also: Annotations for §4.13 and Ch.4
where $\eta=\ln\left(-1/x\right)$. For these results and other asymptotic expansions see Corless et al. (1997).
For integrals of $W\left(z\right)$ use the substitution $w=W\left(z\right)$, $z=w{\mathrm{e}}^{w}$ and $\,\mathrm{d}z=(w+1){\mathrm{e}}^{w}\,\mathrm{d}w$. Examples are
4.13.12 $\int W\left(z\right)\,\mathrm{d}z=\frac{z}{W\left(z\right)}+zW\left(z\right)-z,$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\,\mathrm{d}\NVar{x}$: differential, $\int$: integral and $z$: complex variable Permalink: http://dlmf.nist.gov/4.13.E12 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.13 $\int\frac{W\left(z\right)}{z}\,\mathrm{d}z=\tfrac{1}{2}W\left(z\right)^{2}+W% \left(z\right),$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\,\mathrm{d}\NVar{x}$: differential, $\int$: integral and $z$: complex variable Permalink: http://dlmf.nist.gov/4.13.E13 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.14 $2\int\sin\left(W\left(z\right)\right)\,\mathrm{d}z=z\left(1+\frac{1}{W\left(z% \right)}\right)\sin\left(W\left(z\right)\right)-z\cos\left(W\left(z\right)% \right).$ ⓘ Symbols: $W\left(\NVar{z}\right)$: Lambert $W$-function, $\cos\NVar{z}$: cosine function, $\,\mathrm{d}\NVar{x}$: differential, $\int$: integral, $\sin\NVar{z}$: sine function and $z$: complex variable Permalink: http://dlmf.nist.gov/4.13.E14 Encodings: TeX, pMML, png Addition (effective with 1.1.7): This equation was added. See also: Annotations for §4.13 and Ch.4
4.13.15 $W_{0}\left(z\right)=\frac{z}{\pi}\int_{0}^{\pi}\frac{\left(1-t\cot t\right)^{2% }+t^{2}}{z+t{\mathrm{e}}^{-t\cot t}\csc t}\,\mathrm{d}t.$
4.13.16 $W_{0}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}\ln\left(1+z\frac{\sin t}{t}{% \mathrm{e}}^{t\cot t}\right)\,\mathrm{d}t.$ ⓘ
For these and other integral representations of the Lambert $W$-function see Kheyfits (2004), Kalugin et al. (2012) and Mező (2020).
For the foregoing results and further information see Borwein and Corless (1999), Corless et al. (1996), de Bruijn (1961, pp. 25–28), Olver (1997b, pp. 12–13), and Siewert and Burniston (1973).
For a generalization of the Lambert $W$-function connected to the three-body problem see Scott et al. (2006), Scott et al. (2013) and Scott et al. (2014). | 2023-02-08T12:48:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 309, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9629656672477722, "perplexity": 8725.019158602321}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500813.58/warc/CC-MAIN-20230208123621-20230208153621-00386.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Abliss.gilbert-ames | # zbMATH — the first resource for mathematics
## Bliss, Gilbert Ames
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Author ID: bliss.gilbert-ames Published as: Bliss, G. A.; Bliss, Gilbert Ames; Bliss, Gilbert A.; Bliss, Gibert A.; Bliss, Gilbert; Bliss, G. External Links: Celebratio Mathematica · MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 99 Publications since 1902, including 13 Books 2 Further Contributions Biographic References: 2 Publications
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#### Co-Authors
81 single-authored 6 Hestenes, Magnus Rudolph 6 Schoenberg, Isaac Jacob 3 Mason, Max 2 Schwank, Friedrich 1 Abbott, James C. 1 Coral, Max 1 Davis, Martin David 1 Davis, Philip J. 1 Evans, Griffith Conrad 1 Hale-La Salle 1 Hardy, Godfrey Harold 1 Hefner, Ralph Aubrie 1 Henkin, Leon Albert 1 Hersh, Reuben 1 Hu, Kuen-sen 1 Jackson, Dunham 1 Kasner, Edward 1 Lanczos, Cornelius 1 Lax, Peter David 1 Levinson, Norman 1 Mac Lane, Leslie Saunders 1 McShane, Edward James 1 Olds, C. D. 1 Pixley, Henry Howes 1 Porter, Thomas Isaac 1 Powell, James Ellis 1 Raab, Albert William 1 Sanger, Ralph Grafton 1 Trèves, François 1 Underhill, A. S. 1 Whyburn, Gordon Thomas 1 Zalcman, Lawrence Allen
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#### Serials
35 Bulletin of the American Mathematical Society 22 Transactions of the American Mathematical Society 8 Annals of Mathematics. Second Series 7 American Mathematical Monthly 5 American Journal of Mathematics 4 Colloquium Publications. American Mathematical Society 2 Proceedings of the National Academy of Sciences of the United States of America 2 The Carus Mathematical Monographs 1 Mathematische Annalen 1 Journal of the London Mathematical Society 1 Science
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#### Fields
13 Calculus of variations and optimal control; optimization (49-XX) 3 History and biography (01-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX)
#### Citations contained in zbMATH Open
70 Publications have been cited 537 times in 424 Documents Cited by Year
Lectures on the calculus of variations. Zbl 0063.00459
Bliss, Gibert A.
1946
An integral inequality. JFM 56.0434.02
Bliss, G. A.
1930
A boundary value problem for a system of ordinary linear differential equations of the first order. JFM 52.0453.13
Bliss, G. A.
1926
Algebraic functions. Zbl 0008.21004
Bliss, Gilbert Ames
1933
The problem of Lagrange in the calculus of variations. JFM 56.0435.01
Bliss, G. A.
1930
Algebraic functions. Zbl 0141.05002
Bliss, G. A.
1966
Lectures on the calculus of variations. Zbl 0036.34401
Bliss, Gilbert A.
1947
Calculus of variations. JFM 51.0372.01
Bliss, G. A.
1925
The problem of Bolza in the calculus of variations. Zbl 0004.15502
Bliss, Gilbert Ames
1932
Sufficient conditions for a problem of Mayer in the calculus of variations. Zbl 0006.25903
Bliss, G. A.; Hestenes, M. R.
1933
Definitely self-adjoint boundary value problems. Zbl 0020.03204
Bliss, Gilbert A.
1938
The problem of Mayer with variable end points. JFM 46.0758.04
Bliss, G. A.
1918
Definitely self-adjoint boundary value problems. JFM 64.0438.02
Bliss, G. A.
1938
Mathematics for exterior ballistics. Zbl 0063.00457
Bliss, Gilbert Ames
1944
A generalization of the notion of angle. JFM 37.0490.01
Bliss, G. A.
1906
On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations. Zbl 0003.25702
Bliss, G. A.; Schoenberg, I. J.
1931
The calculus of variations for multiple integrals. Zbl 0063.00455
Bliss, G. A.
1942
Jacobi’s condition for problems of the calculus of variations in parametric form. JFM 46.0758.03
Bliss, G. A.
1916
The Princeton Colloquium 1909. Part I: Fundamental existence theorems. JFM 44.0365.01
Bliss, G. A.
1913
A boundary value problem in the calculus of variations. JFM 52.0509.02
Bliss, G. A.
1926
Algebraic functions. JFM 59.0384.03
Bliss, G. A.
1933
The reduction of singularities of plane curves by birational transformation. JFM 49.0264.01
Bliss, G. A.
1923
The properties of curves in space which minimize a definite integral. JFM 39.0441.01
Mason, M.; Bliss, Gilbert Ames
1908
An existence theorem for a differential equation of the second order, with an application to the calculus of variations. JFM 35.0340.01
Bliss, G. A.
1904
The geodesic lines on the anchor ring. JFM 33.0670.02
Bliss, G. A.
1902
Integrals of Lebesgue. JFM 46.0383.01
Bliss, G. A.
1918
The Weierstraß $$E$$-Funktion for problems of the calculus of variations in space. JFM 45.0604.03
Bliss, G. A.
1914
A note on the problem of Lagrange in the calculus of variations. JFM 45.0605.01
Bliss, G. A.
1916
Abnormality in the calculus of variations. JFM 61.0556.12
Bliss, G. A.
1935
Eliakim Hastings Moore. JFM 59.0038.02
Bliss, G. A.
1933
Algebraic functions and their divisors. JFM 50.0699.03
Bliss, G. A.
1924
Differential equations containing arbitrary functions. - Functions of lines in ballistics. JFM 47.0382.02
Bliss, G. A.
1920
Sufficient condition for a minimum with respect to one-sided variations. JFM 35.0370.02
Bliss, G. A.
1904
Generalizations of geodesic curvature and a theorem of Gauss concerning geodesic triangles. JFM 45.0859.02
Bliss, G. A.
1915
A new proof of the existence theorem for implicit functions. JFM 43.0483.04
Bliss, G. A.
1912
A generalization of Weierstraß’ preparation theorem for a power series in several variables. JFM 43.0504.02
Bliss, G. A.
1912
The problem of Bolza in the calculus of variations . JFM 58.0535.02
Bliss, G. A.
1932
On the derivation of necessary conditions for the problem of Bolza. Zbl 0006.25902
Bliss, G. A.; Schoenberg, I. J.
1932
The evolution of problems of the calculus of variations. Zbl 0015.35702
Bliss, G. A.
1936
Normality and abnormality in the calculus of variations. Zbl 0019.12303
Bliss, G. A.
1938
A problem in the calculus of variations in which the integrand is discontinuous. JFM 37.0402.01
Bliss, G. A.; Mason, M.
1906
The exterior and interior of a plane curve. JFM 35.0506.01
Bliss, G. A.
1904
Jacobi’s criterion when both end-points are variable. JFM 34.0402.01
Bliss, G. A.
1904
The Chauvenet papers. A collection of prize-winning expository papers in mathematics. Vols. I and II. Zbl 0384.01013
1978
Calculus of variations. 6th impression. Zbl 0317.49001
Bliss, Gilbert Ames
1971
A note on symmetric matrices. JFM 45.0262.05
Bliss, G. A.
1914
A substitute for Duhamel’s theorem. JFM 45.0452.02
Bliss, G. A.
1914
A note on functions of lines. JFM 45.0550.01
Bliss, G. A.
1915
The minimum of a definite integral for unilateral variations in space. JFM 45.0605.03
Bliss, G. A.; Underhill, A. S.
1914
Herbert Ellsworth Slaught teacher and friend. JFM 64.0023.14
Bliss, G. A.
1938
Normality and abnormality in the calculus of variations. JFM 64.0510.01
Bliss, G. A.
1938
Mathematical interpretation of geometrical and physical phenomena. JFM 59.0060.01
Bliss, G. A.
1932
On the derivation of necessary conditions for the problem of Bolza . JFM 58.0535.01
Bliss, G. A.; Schoenberg, I. J.
1932
Ernest Julius Wilczynski . JFM 58.0995.07
Bliss, G. A.
1932
On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations. JFM 57.0528.01
Bliss, G. A.; Schoenberg, I. J.
1931
The transformation of Clebsch in the calculus of variations. JFM 54.0532.03
Bliss, G. A.
1928
Contributions that have been made by pure science to the advancement of engineering and industry. {G. A. Bliss.} Mathematics. JFM 52.0036.11
Bliss, G. A.
1927
Birational transformations simplifying singularities of algebraic curves. JFM 50.0266.02
Bliss, G. A.
1924
Solutions of differential equations as functions of the constants of integration. JFM 47.0399.03
Bliss, G. A.
1918
Some recent developments in the calculus of variations. JFM 47.0471.04
Bliss, G. A.
1920
The calculus of variations and the quantum theory. Zbl 0004.15601
Bliss, G. A.
1932
Contributions to the calculus of variations 1931-1932. Zbl 0006.40401
1933
A new proof of Weierstrass’s theorem concerning the factorization of a power series. JFM 41.0286.03
Bliss, G. A.
1910
Fields of extremals in space. JFM 41.0437.01
Bliss, G. A.; Mason, M.
1910
On the inverse problem of the calculus of variations. JFM 39.0445.01
Bliss, G. A.
1908
A new form of the simplest problem of the calculus of variations. JFM 38.0408.01
Bliss, G. A.
1907
The construction of a field of extremals about a given point. JFM 38.0408.02
Bliss, G. A.
1907
A proof of the fundamental theorem of analysis situs. JFM 37.0495.02
Bliss, G. A.
1906
The solutions of differential equations of the first order as functions of their initial values. JFM 36.0389.01
Bliss, G. A.
1905
The second variation of a definite integral when one end-point is variable. JFM 33.0385.01
Bliss, G. A.
1902
The Chauvenet papers. A collection of prize-winning expository papers in mathematics. Vols. I and II. Zbl 0384.01013
1978
Calculus of variations. 6th impression. Zbl 0317.49001
Bliss, Gilbert Ames
1971
Algebraic functions. Zbl 0141.05002
Bliss, G. A.
1966
Lectures on the calculus of variations. Zbl 0036.34401
Bliss, Gilbert A.
1947
Lectures on the calculus of variations. Zbl 0063.00459
Bliss, Gibert A.
1946
Mathematics for exterior ballistics. Zbl 0063.00457
Bliss, Gilbert Ames
1944
The calculus of variations for multiple integrals. Zbl 0063.00455
Bliss, G. A.
1942
Definitely self-adjoint boundary value problems. Zbl 0020.03204
Bliss, Gilbert A.
1938
Definitely self-adjoint boundary value problems. JFM 64.0438.02
Bliss, G. A.
1938
Normality and abnormality in the calculus of variations. Zbl 0019.12303
Bliss, G. A.
1938
Herbert Ellsworth Slaught teacher and friend. JFM 64.0023.14
Bliss, G. A.
1938
Normality and abnormality in the calculus of variations. JFM 64.0510.01
Bliss, G. A.
1938
The evolution of problems of the calculus of variations. Zbl 0015.35702
Bliss, G. A.
1936
Abnormality in the calculus of variations. JFM 61.0556.12
Bliss, G. A.
1935
Algebraic functions. Zbl 0008.21004
Bliss, Gilbert Ames
1933
Sufficient conditions for a problem of Mayer in the calculus of variations. Zbl 0006.25903
Bliss, G. A.; Hestenes, M. R.
1933
Algebraic functions. JFM 59.0384.03
Bliss, G. A.
1933
Eliakim Hastings Moore. JFM 59.0038.02
Bliss, G. A.
1933
Contributions to the calculus of variations 1931-1932. Zbl 0006.40401
1933
The problem of Bolza in the calculus of variations. Zbl 0004.15502
Bliss, Gilbert Ames
1932
The problem of Bolza in the calculus of variations . JFM 58.0535.02
Bliss, G. A.
1932
On the derivation of necessary conditions for the problem of Bolza. Zbl 0006.25902
Bliss, G. A.; Schoenberg, I. J.
1932
Mathematical interpretation of geometrical and physical phenomena. JFM 59.0060.01
Bliss, G. A.
1932
On the derivation of necessary conditions for the problem of Bolza . JFM 58.0535.01
Bliss, G. A.; Schoenberg, I. J.
1932
Ernest Julius Wilczynski . JFM 58.0995.07
Bliss, G. A.
1932
The calculus of variations and the quantum theory. Zbl 0004.15601
Bliss, G. A.
1932
On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations. Zbl 0003.25702
Bliss, G. A.; Schoenberg, I. J.
1931
On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations. JFM 57.0528.01
Bliss, G. A.; Schoenberg, I. J.
1931
An integral inequality. JFM 56.0434.02
Bliss, G. A.
1930
The problem of Lagrange in the calculus of variations. JFM 56.0435.01
Bliss, G. A.
1930
The transformation of Clebsch in the calculus of variations. JFM 54.0532.03
Bliss, G. A.
1928
Contributions that have been made by pure science to the advancement of engineering and industry. {G. A. Bliss.} Mathematics. JFM 52.0036.11
Bliss, G. A.
1927
A boundary value problem for a system of ordinary linear differential equations of the first order. JFM 52.0453.13
Bliss, G. A.
1926
A boundary value problem in the calculus of variations. JFM 52.0509.02
Bliss, G. A.
1926
Calculus of variations. JFM 51.0372.01
Bliss, G. A.
1925
Algebraic functions and their divisors. JFM 50.0699.03
Bliss, G. A.
1924
Birational transformations simplifying singularities of algebraic curves. JFM 50.0266.02
Bliss, G. A.
1924
The reduction of singularities of plane curves by birational transformation. JFM 49.0264.01
Bliss, G. A.
1923
Differential equations containing arbitrary functions. - Functions of lines in ballistics. JFM 47.0382.02
Bliss, G. A.
1920
Some recent developments in the calculus of variations. JFM 47.0471.04
Bliss, G. A.
1920
The problem of Mayer with variable end points. JFM 46.0758.04
Bliss, G. A.
1918
Integrals of Lebesgue. JFM 46.0383.01
Bliss, G. A.
1918
Solutions of differential equations as functions of the constants of integration. JFM 47.0399.03
Bliss, G. A.
1918
Jacobi’s condition for problems of the calculus of variations in parametric form. JFM 46.0758.03
Bliss, G. A.
1916
A note on the problem of Lagrange in the calculus of variations. JFM 45.0605.01
Bliss, G. A.
1916
Generalizations of geodesic curvature and a theorem of Gauss concerning geodesic triangles. JFM 45.0859.02
Bliss, G. A.
1915
A note on functions of lines. JFM 45.0550.01
Bliss, G. A.
1915
The Weierstraß $$E$$-Funktion for problems of the calculus of variations in space. JFM 45.0604.03
Bliss, G. A.
1914
A note on symmetric matrices. JFM 45.0262.05
Bliss, G. A.
1914
A substitute for Duhamel’s theorem. JFM 45.0452.02
Bliss, G. A.
1914
The minimum of a definite integral for unilateral variations in space. JFM 45.0605.03
Bliss, G. A.; Underhill, A. S.
1914
The Princeton Colloquium 1909. Part I: Fundamental existence theorems. JFM 44.0365.01
Bliss, G. A.
1913
A new proof of the existence theorem for implicit functions. JFM 43.0483.04
Bliss, G. A.
1912
A generalization of Weierstraß’ preparation theorem for a power series in several variables. JFM 43.0504.02
Bliss, G. A.
1912
A new proof of Weierstrass’s theorem concerning the factorization of a power series. JFM 41.0286.03
Bliss, G. A.
1910
Fields of extremals in space. JFM 41.0437.01
Bliss, G. A.; Mason, M.
1910
The properties of curves in space which minimize a definite integral. JFM 39.0441.01
Mason, M.; Bliss, Gilbert Ames
1908
On the inverse problem of the calculus of variations. JFM 39.0445.01
Bliss, G. A.
1908
A new form of the simplest problem of the calculus of variations. JFM 38.0408.01
Bliss, G. A.
1907
The construction of a field of extremals about a given point. JFM 38.0408.02
Bliss, G. A.
1907
A generalization of the notion of angle. JFM 37.0490.01
Bliss, G. A.
1906
A problem in the calculus of variations in which the integrand is discontinuous. JFM 37.0402.01
Bliss, G. A.; Mason, M.
1906
A proof of the fundamental theorem of analysis situs. JFM 37.0495.02
Bliss, G. A.
1906
The solutions of differential equations of the first order as functions of their initial values. JFM 36.0389.01
Bliss, G. A.
1905
An existence theorem for a differential equation of the second order, with an application to the calculus of variations. JFM 35.0340.01
Bliss, G. A.
1904
Sufficient condition for a minimum with respect to one-sided variations. JFM 35.0370.02
Bliss, G. A.
1904
The exterior and interior of a plane curve. JFM 35.0506.01
Bliss, G. A.
1904
Jacobi’s criterion when both end-points are variable. JFM 34.0402.01
Bliss, G. A.
1904
The geodesic lines on the anchor ring. JFM 33.0670.02
Bliss, G. A.
1902
The second variation of a definite integral when one end-point is variable. JFM 33.0385.01
Bliss, G. A.
1902
all top 5
#### Cited by 505 Authors
14 Reid, William T. 12 Miele, Angelo 9 Hestenes, Magnus Rudolph 7 Postlethwaite, Ian 5 Arutyunov, Aram Vladimirovic 4 Berkovitz, Leonard David 4 Bliss, Gilbert Ames 4 Bonnard, Bernard 4 Krall, Allan M. 4 Morse, Marston 4 Pagani, Enrico M. 4 Saker, Samir H. 3 Ahlbrandt, Calvin D. 3 Avakov, Evgeniĭ Rachievich 3 Bruno, Danilo 3 Clarke, Francis H. 3 Hölder, Ernst 3 Krym, Victor R. 3 Luria, Gianvittorio 3 MacFarlane, Alistair George James 3 Massa, Enrico 3 Nazarov, Alexander I. 3 Osuna-Gómez, Rafaela 3 Schiavoni, Nicola 3 Vincent, Thomas L. 2 Arana-Jiménez, Manuel 2 Balestro, Vitor 2 Blot, Joël 2 Brown, Richard Clark 2 Carvalho, Francisco Das Chagas 2 Cheng, Sui Sun 2 Chyba, Monique 2 Curtiss, John Hamilton 2 Da Silva Fernandes, Sandro 2 Damoulakis, J. N. 2 Day, Martin V. 2 Dmitruk, Andrei V. 2 Evtushenko, Yuriĭ Gavrilovich 2 Fusco, Nicola 2 Gift, Stephan J. G. 2 Gluchoff, Alan D. 2 Goh, Bean San 2 Grässer, H. S. P. 2 Graves, Lawrence Murray 2 Greenspan, Donald 2 He, Qianjun 2 Hernández-Jiménez, Beatriz 2 Hinton, Don Barker 2 Horváth, Ákos G. 2 Hussain, Amjad 2 Jacobson, David Harris 2 Kosa, Andras 2 Kushner, Harold J. 2 Leighton, Walter jun. 2 Levy, Alejandro V. 2 Lieb, Elliott H. 2 Locatelli, Arturo 2 Magaril-Il’yaev, Gregoriĭ Geogrievich 2 Magenes, Enrico 2 Maggi, Francesco 2 Martini, Horst 2 Mereau, P. M. 2 Montgomery, Richard 2 Nitsche, Johannes Carl Christian 2 Osękowski, Adam 2 Osman, Mahmoud M. 2 Poteaux, Adrien 2 Powers, William F. 2 Rojas-Medar, Marko Antonio 2 Ruiz-Garzón, Gabriel 2 Rund, Hanno 2 Rybowicz, Marc 2 Sánchez, Justino 2 Schäfke, Friedrich-Wilhelm 2 Schmitendorf, William E. 2 Sinnamon, Gord 2 Spijker, Marc N. 2 Takemura, Kazuo 2 Talenti, Giorgio G. 2 Tapley, Byron D. 2 Tietze, J. L. 2 Tikhomirov, Vladimir Mikhaĭlovich 2 Tonelli, Leonida 2 Trélat, Emmanuel 2 Tret’yakov, Alexey A. 2 Tsyganov, Andreĭ Vladimirovich 2 Vergara, Vicente 2 Vinter, Richard B. 2 von Schwarz, Josefa 2 Walsh, Peter Gareth 2 Watanabe, Kohtaro 2 Well, Klaus H. 2 Yan, Dunyan 2 Zeidan, Vera Michel 1 Abohela, I. 1 Abramovich, Shoshana 1 Agarwal, Ravi P. 1 Aggarwal, A. K. 1 Agrachev, Andreĭ Aleksandrovich 1 Agrawal, Om Prakash ...and 405 more Authors
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#### Cited in 165 Serials
40 Journal of Optimization Theory and Applications 36 Transactions of the American Mathematical Society 24 Journal of Mathematical Analysis and Applications 16 International Journal of Control 14 Mathematische Annalen 10 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Journal of Differential Equations 8 Archive for Rational Mechanics and Analysis 8 Bulletin of the American Mathematical Society 7 Historia Mathematica 6 Mathematics of Computation 6 Journal of Functional Analysis 6 Proceedings of the American Mathematical Society 5 Journal of the Franklin Institute 5 Applied Mathematics and Optimization 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Aequationes Mathematicae 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 International Journal of Control, I. Series 3 Archive for History of Exact Sciences 3 International Journal of Engineering Science 3 Mathematical Notes 3 Acta Mathematica 3 Advances in Mathematics 3 Archiv der Mathematik 3 Rendiconti del Seminario Matematico della Università di Padova 3 Bulletin of the American Mathematical Society. New Series 3 Mathematical Programming. Series A. Series B 3 Journal of Dynamical and Control Systems 3 International Journal of Geometric Methods in Modern Physics 3 Rendiconti del Circolo Matematico di Palermo 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 Applicable Analysis 2 Computers & Mathematics with Applications 2 Journal of Applied Mathematics and Mechanics 2 Journal of Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Journal of Geometry and Physics 2 Automatica 2 Compositio Mathematica 2 Inventiones Mathematicae 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Rendiconti del Seminario Matemàtico e Fisico di Milano 2 Ergodic Theory and Dynamical Systems 2 Physica D 2 Differential Geometry and its Applications 2 The Journal of Geometric Analysis 2 Journal of Global Optimization 2 Annals of Physics 2 Linear Algebra and its Applications 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Vestnik St. Petersburg University. Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Journal of Mathematical Sciences (New York) 2 Computational and Applied Mathematics 2 Journal of Inequalities and Applications 2 Mathematical Inequalities & Applications 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Differential Equations 2 Naval Research Logistics Quarterly 2 Proceedings of the Steklov Institute of Mathematics 2 Frontiers of Mathematics in China 2 Science China. Mathematics 2 Journal of Function Spaces 1 International Journal of Modern Physics A 1 Centaurus 1 Communications in Algebra 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Houston Journal of Mathematics 1 International Journal for Numerical Methods in Fluids 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Physica A 1 Reports on Mathematical Physics 1 Russian Mathematical Surveys 1 Studia Mathematica 1 Ukrainian Mathematical Journal 1 Wave Motion 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Bulletin of Mathematical Biology 1 Mathematics Magazine 1 Annales Polonici Mathematici 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Computation 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Mathematical Psychology 1 Mathematika 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the Japan Academy. Series A 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Semigroup Forum ...and 65 more Serials
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#### Cited in 47 Fields
120 Calculus of variations and optimal control; optimization (49-XX) 45 Ordinary differential equations (34-XX) 44 Systems theory; control (93-XX) 42 Real functions (26-XX) 31 Partial differential equations (35-XX) 30 Differential geometry (53-XX) 27 Functional analysis (46-XX) 24 Numerical analysis (65-XX) 23 Operations research, mathematical programming (90-XX) 22 Global analysis, analysis on manifolds (58-XX) 21 Operator theory (47-XX) 21 Mechanics of particles and systems (70-XX) 17 History and biography (01-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Mechanics of deformable solids (74-XX) 10 Algebraic geometry (14-XX) 9 Computer science (68-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Convex and discrete geometry (52-XX) 7 Field theory and polynomials (12-XX) 7 Functions of a complex variable (30-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Difference and functional equations (39-XX) 5 Measure and integration (28-XX) 5 Fluid mechanics (76-XX) 4 Approximations and expansions (41-XX) 4 Geometry (51-XX) 4 Probability theory and stochastic processes (60-XX) 3 Number theory (11-XX) 3 Potential theory (31-XX) 3 Special functions (33-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Biology and other natural sciences (92-XX) 2 Commutative algebra (13-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX)
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https://us.edugain.com/questions/In-the-figure-it-is-given-that-AC-BC-angle-4-2-space-angle-1-and-angle-3-2-space-angle-2-Prove-that-triangle-ADC-cong-triangle-B | ### In the figure, it is given that $AC = BC, \angle 4 = 2 \space \angle 1$ and $\angle 3 = 2 \space \angle 2$. Prove that $\triangle ADC \cong \triangle BEC.$ C A B E D 1 2 4 3
Answer:
Step by Step Explanation:
1. We are given that $AC = BC, \angle 4 = 2 \space \angle 1$ and $\angle 3 = 2 \space \angle 2.$
2. We need to find a triangle congruent to $\triangle ADC.$
3. In $\triangle ABC$, we have \begin{aligned} &AC = BC &&\text{[Given]} \\ \implies &\angle CAB = \angle CBA && \text{[Angles opposite to equal sides are equal]} &&\ldots (1) \end{aligned} Also, \begin{aligned} &\angle 4 = \angle 3 && \text{[Vertically opposite angles]} \\ \implies &2 \space \angle 1 = 2 \space \angle 2 && \text{[As } \angle 4 = 2 \space \angle 1 \text{ and } \angle 3 = 2 \space \angle 2] \\ \implies &\angle 1 = \angle 2 && \ldots (2) \end{aligned} Subtracting equation (2) from equation (1), we have \begin{aligned} &\angle CAB - \angle 1 = \angle CBA - \angle 2 \\ \implies &\angle CAD = \angle CBE && \ldots (3) \end{aligned}
4. In $\triangle ADC$ and $\triangle BEC$, we have \begin{aligned} &\angle ACB = \angle ACB &&\text{[Common]} \\ &AC = BC &&\text{[Given]} \\ &\angle CAD = \angle CBE &&\text{[From equation (3)]} \\ \therefore {\space} &\triangle ACD \cong \triangle BCE &&\text{[By ASA criterion]} \end{aligned}
5. Thus, $\bf { \triangle ACD \cong \triangle BCE}$.
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https://par.nsf.gov/biblio/10265906-sami-galaxy-survey-reconciling-strong-emission-line-metallicity-diagnostics-using-metallicity-gradients | The SAMI Galaxy Survey: reconciling strong emission line metallicity diagnostics using metallicity gradients
ABSTRACT We measure the gas-phase metallicity gradients of 248 galaxies selected from Data Release 2 of the SAMI Galaxy Survey. We demonstrate that there are large systematic discrepancies between the metallicity gradients derived using common strong emission line metallicity diagnostics. We determine which pairs of diagnostics have Spearman’s rank coefficients greater than 0.6 and provide linear conversions to allow the accurate comparison of metallicity gradients derived using different strong emission line diagnostics. For galaxies within the mass range 8.5 < log (M/M⊙) < 11.0, we find discrepancies of up to 0.11 dex/Re between seven popular diagnostics in the metallicity gradient–mass relation. We find a suggestion of a break in the metallicity gradient–mass relation, where the slope shifts from negative to positive, occurs between 9.5 < log (M/M⊙) < 10.5 for the seven chosen diagnostics. Applying our conversions to the metallicity gradient–mass relation, we reduce the maximum dispersion from 0.11 dex/Re to 0.02 dex/Re. These conversions provide the most accurate method of converting metallicity gradients when key emission lines are unavailable. We find that diagnostics that share common sets of emission line ratios agree best, and that diagnostics calibrated through the electron temperature provide more consistent results compared to those calibrated through photoionization models.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10265906
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
502
Issue:
3
Page Range or eLocation-ID:
3357 to 3373
ISSN:
0035-8711
1. ABSTRACT We analyse the rest-optical emission-line ratios of z ∼ 1.5 galaxies drawn from the Multi-Object Spectrometer for Infra-Red Exploration Deep Evolution Field (MOSDEF) survey. Using composite spectra, we investigate the mass–metallicity relation (MZR) at z ∼ 1.5 and measure its evolution to z = 0. When using gas-phase metallicities based on the N2 line ratio, we find that the MZR evolution from z ∼ 1.5 to z = 0 depends on stellar mass, evolving by $\Delta \rm log(\rm O/H) \sim 0.25$ dex at M*< $10^{9.75}\, \mathrm{M}_{\odot }$ down to $\Delta \rm log(\rm O/H) \sim 0.05$ at M* ≳ $10^{10.5}\, \mathrm{M}_{\odot }$. In contrast, the O3N2-based MZR shows a constant offset of $\Delta \rm log(\rm O/H) \sim 0.30$ across all masses, consistent with previous MOSDEF results based on independent metallicity indicators, and suggesting that O3N2 provides a more robust metallicity calibration for our z ∼ 1.5 sample. We investigated the secondary dependence of the MZR on star formation rate (SFR) by measuring correlated scatter about the mean M*-specific SFR and M*−$\log (\rm O3N2)$ relations. We find an anticorrelation between $\log (\rm O/H)$ and sSFR offsets, indicating the presence of a M*−SFR−Z relation, though with limited significance. Additionally, we find that our z ∼ 1.5more »
We compare the oxygen abundance (O/H) of the narrow-line regions (NLRs) of Seyfert 2 AGNs obtained through strong-line methods and from direct measurements of the electron temperature (Te-method). The aim of this study is to explore the effects of the use of distinct methods on the range of metallicity and on the mass–metallicity relation of active galactic nuclei (AGNs) at low redshifts (z ≲ 0.4). We used the Sloan Digital Sky Survey (SDSS) and NASA/IPAC Extragalactic Database (NED) to selected optical (3000 < λ(Å) < 7000) emission line intensities of 463 confirmed Seyfert 2 AGNs. The oxygen abundances of the NLRs were estimated using the theoretical Storchi-Bergmann et al. calibrations, the semi-empirical N2O2 calibration, the Bayesian H ii-Chi-mistry code and the Te-method. We found that the oxygen abundance estimations via the strong-line methods differ from each other up to ∼0.8 dex, with the largest discrepancies in the low-metallicity regime ($\rm 12+\log (O/H) \: \lesssim \: 8.5$). We confirmed that the Te-method underestimates the oxygen abundance in NLRs, producing unreal subsolar values. We did not find any correlation between the stellar mass of the host galaxies and the metallicity of their AGNs. This result is independent of the method used to estimate Z.
We present a chemodynamical study of the Grus I ultra-faint dwarf galaxy (UFD) from medium-resolution (R∼ 11,000) Magellan/IMACS spectra of its individual member stars. We identify eight confirmed members of Grus I, based on their low metallicities and coherent radial velocities, and four candidate members for which only velocities are derived. In contrast to previous work, we find that Grus I has a very low mean metallicity of 〈[Fe/H]〉 = −2.62 ± 0.11 dex, making it one of the most metal-poor UFDs. Grus I has a systemic radial velocity of −143.5 ± 1.2 km s−1and a velocity dispersion of$σrv=2.5−0.8+1.3$km s−1, which results in a dynamical mass of$M1/2(rh)=8−4+12×105$Mand a mass-to-light ratio ofM/LV=$440−250+650$M/L. Under the assumption of dynamical equilibrium, our analysis confirms that Grus I is a dark-matter-dominated UFD (M/L> 80M/L). However, we do not resolve a metallicity dispersion (σ[Fe/H]< 0.44 dex). Our results indicate that Grus I is a fairly typical UFD with parameters that agree with mass–metallicity and metallicity-luminosity trends for faint galaxies. This agreement suggests that Grus I has not lost an especially significant amount of mass from tidal encounters with the Milky Way, in linemore »
4. ABSTRACT We present an analysis of spatially resolved gas-phase metallicity relations in five dwarf galaxies ($\rm \mathit{M}_{halo} \approx 10^{11}\, {\rm M}_\odot$, $\rm \mathit{M}_\star \approx 10^{8.8}{-}10^{9.6}\, {\rm M}_\odot$) from the FIRE-2 (Feedback in Realistic Environments) cosmological zoom-in simulation suite, which include an explicit model for sub-grid turbulent mixing of metals in gas, near z ≈ 0, over a period of 1.4 Gyr, and compare our findings with observations. While these dwarf galaxies represent a diverse sample, we find that all simulated galaxies match the observed mass–metallicity (MZR) and mass–metallicity gradient (MZGR) relations. We note that in all five galaxies, the metallicities are effectively identical between phases of the interstellar medium (ISM), with 95 ${{\ \rm per\ cent}}$ of the gas being within ±0.1 dex between the cold and dense gas (T < 500 K and nH > 1 cm−3), ionized gas (near the H αT ≈ 104 K ridge-line), and nebular regions (ionized gas where the 10 Myr-averaged star formation rate is non-zero). We find that most of the scatter in relative metallicity between cold dense gas and ionized gas/nebular regions can be attributed to either local starburst events or metal-poor inflows. We also note the presence of a major merger in one of our galaxies,more » | 2023-03-26T00:00:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.616546094417572, "perplexity": 3859.2733487738274}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00380.warc.gz"} |
https://par.nsf.gov/biblio/10330260-close-puffy-neptune-hidden-friends-enigma-toi | This content will become publicly available on May 16, 2023
A Close-in Puffy Neptune with Hidden Friends: The Enigma of TOI 620
Abstract We present the validation of a transiting low-density exoplanet orbiting the M2.5 dwarf TOI 620 discovered by the NASA Transiting Exoplanet Survey Satellite (TESS) mission. We utilize photometric data from both TESS and ground-based follow-up observations to validate the ephemerides of the 5.09 day transiting signal and vet false-positive scenarios. High-contrast imaging data are used to resolve the stellar host and exclude stellar companions at separations ≳0.″2. We obtain follow-up spectroscopy and corresponding precise radial velocities (RVs) with multiple precision radial velocity (PRV) spectrographs to confirm the planetary nature of the transiting exoplanet. We calculate a 5 σ upper limit of M P < 7.1 M ⊕ and ρ P < 0.74 g cm −3 , and we identify a nontransiting 17.7 day candidate. We also find evidence for a substellar (1–20 M J ) companion with a projected separation ≲20 au from a combined analysis of Gaia, adaptive optics imaging, and RVs. With the discovery of this outer companion, we carry out a detailed exploration of the possibilities that TOI 620 b might instead be a circum-secondary planet or a pair of eclipsing binary stars orbiting the host in a hierarchical triple system. We find, under scrutiny, that more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10330260
Journal Name:
The Astronomical Journal
Volume:
163
Issue:
6
Page Range or eLocation-ID:
269
ISSN:
0004-6256
5. ABSTRACT We report on the discovery and validation of TOI 813 b (TIC 55525572 b), a transiting exoplanet identified by citizen scientists in data from NASA’s Transiting Exoplanet Survey Satellite (TESS) and the first planet discovered by the Planet Hunters TESS project. The host star is a bright (V = 10.3 mag) subgiant ($R_\star =1.94\, R_\odot$, $M_\star =1.32\, M_\odot$). It was observed almost continuously by TESS during its first year of operations, during which time four individual transit events were detected. The candidate passed all the standard light curve-based vetting checks, and ground-based follow-up spectroscopy and speckle imaging enabled us to place an uppermore » | 2022-09-30T00:28:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.723724365234375, "perplexity": 6685.644716218077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335396.92/warc/CC-MAIN-20220929225326-20220930015326-00584.warc.gz"} |
http://cepa.fnal.gov/psm/simulation/mcgen/lund/pythia_manual/pythia6.3/pythia6301/node63.html | Next: Resonance Production Up: Process Generation Previous: Equivalent photon flux in Contents
## Kinematics and Cross Section for a Two-body Process
In this section we begin the description of kinematics selection and cross-section calculation. The example is for the case of a process, with final-state masses assumed to be vanishing. Later on we will expand to finite fixed masses, and to resonances.
Consider two incoming beam particles in their c.m. frame, each with energy . The total squared c.m. energy is then . The two partons that enter the hard interaction do not carry the total beam momentum, but only fractions and , respectively, i.e. they have four-momenta
(67)
There is no reason to put the incoming partons on the mass shell, i.e. to have time-like incoming four-vectors, since partons inside a particle are always virtual and thus space-like. These space-like virtualities are introduced as part of the initial-state parton-shower description, see section , but do not affect the formalism of this section, wherefore massless incoming partons is a sensible ansatz. The one example where it would be appropriate to put a parton on the mass shell is for an incoming lepton beam, but even here the massless kinematics description is adequate as long as the c.m. energy is correctly calculated with masses.
The squared invariant mass of the two partons is defined as
(68)
Instead of and , it is often customary to use and either or :
(69) (70) (71)
In addition to and , two additional variables are needed to describe the kinematics of a scattering . One corresponds to the azimuthal angle of the scattering plane around the beam axis. This angle is always isotropically distributed for unpolarized incoming beam particles, and so need not be considered further. The other variable can be picked as , the polar angle of parton 3 in the c.m. frame of the hard scattering. The conventional choice is to use the variable
(72)
with defined as above. In the following, we will make use of both and . It is also customary to define ,
(73)
but is not an independent variable since
(74)
If the two outgoing particles have masses and , respectively, then the four-momenta in the c.m. frame of the hard interaction are given by
(75)
where
(76)
Then and are modified to
(77)
with
(78)
The cross section for the process may be written as
(79)
The choice of scale is ambiguous, and several alternatives are available in the program. For massless outgoing particles the default is the squared transverse momentum
(80)
which is modified to
(81)
when masses are introduced in the final state. The mass term is selected such that, for , the expression reduces to the squared transverse mass, . For cases with spacelike virtual incoming photons, of virtuality , a further generalization to
(82)
is offered.
The expresses the differential cross section for a scattering, as a function of the kinematical quantities , and . It is in this function that the physics of a given process resides.
The performance of a machine is measured in terms of its luminosity , which is directly proportional to the number of particles in each bunch and to the bunch crossing frequency, and inversely proportional to the area of the bunches at the collision point. For a process with a as given by eq. (), the differential event rate is given by , and the number of events collected over a given period of time
(83)
The program does not calculate the number of events, but only the integrated cross sections.
Next: Resonance Production Up: Process Generation Previous: Equivalent photon flux in Contents
Stephen Mrenna 2005-07-11 | 2013-06-20T01:32:37 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8073171377182007, "perplexity": 806.0980083090826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368710006573/warc/CC-MAIN-20130516131326-00016-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://googology.wikia.org/wiki/Transcendental_number | 11,052 Pages
Not to be confused with Transcendental integer.
A transcendental number is a number which is not an algebraic number[1]. This means that an $$r \in \mathbb{R}$$ is a transcendental number if there exists no non-zero polynomial $$f(x)$$ with coefficients in $$\mathbb{Q}$$ such that $$f(r) = 0$$.
The notion is obviously extended to other systems of numbers such as $$\mathbb{C}$$. One of various theorems called Liouville's theorem gives a useful criterion to determine whether a given complex number is a transcendental number or not. An analogous result for $$\mathbb{Q}_p$$ is also known, while it has less usability.
Common mistakes
The notion of a transcendental number is sometimes misunderstood. For example, the description "it cannot be solved by any polynomial" is wrong, as the transcendental number $$\pi$$ is the solution of the first-degree polynomial equation $$x-\pi=0$$ and the zero-degree polynomial equation $$0 = 0$$. In other words, $$\pi$$ is a root of $$x-\pi$$ and $$0$$.
In googology
There are several transcendental numbers relating to googology:
Community content is available under CC-BY-SA unless otherwise noted. | 2021-06-22T15:00:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9055926203727722, "perplexity": 194.23880203825124}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488517820.68/warc/CC-MAIN-20210622124548-20210622154548-00597.warc.gz"} |
https://repo.scoap3.org/record/20983 | # Classical BRST Charge and Observables in Reducible Gauge Theories
Bratchikov, Andrei V. (Kuban State Technological University, Krasnodar 350072, Russia)
08 August 2017
Abstract: We study the construction of the classical Becchi--Rouet--Stora--Tyutin (BRST) charge and observables for arbitrary reducible gauge theory. Using a special coordinate system in the extended phase space, we obtain an explicit expression for the Koszul--Tate differential and show that the BRST charge can be found by a simple iterative method. We also give a formula for the classical BRST observables.
Published in: Acta Physica Polonica B 48 (2017) 1335-1348
Published by: Jagiellonian University
DOI: 10.5506/APhysPolB.48.1335
arXiv: 1203.1937
License: CC-BY-4.0
Fulltext:
PDF PDF (PDFA) | 2019-04-26T07:49:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8546345233917236, "perplexity": 2460.795520439916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578762045.99/warc/CC-MAIN-20190426073513-20190426095513-00352.warc.gz"} |
https://www.bts.dot.gov/archive/publications/national_transportation_statistics/2000/4-30a | Find the latest Coronavirus-related transportation statistics on the BTS Covid-19 landing page
# Table 4-30a. Federal Exhaust Emission Certification Standards for Newly Manufactured Gasoline- and Diesel-Powered Light Duty Trucks (Category LDT1) (Grams per mile)
Engine type and pollutant Prior to controlg 1968-1969 1970-1971 1972 1973-1974 1975 1976-1978 1979-1981 1982-1983 1984 1985-1986 1987 1988-1993 Tier 1k
1994
Tier 1k
1995-2003
Interim Tier 2k
2004-2006
Tier 2k
2007+
Gasoline
HC (total) 11 i 2.2 3.4 3.4 2.0 2.0 1.7 1.7 0.80 0.80 0.80 0.80 j j j j
NMHC h j j j j j j j j j j j j 0.25(0.31) 0.25(0.31) j j
NMOG h j j j j j j j j j j j j j j 0.125(0.156) 0.100(0.125)
CO 80 i 23 39 39 20 20 18 18 10 10 10 10 3.4(4.2) 3.4(4.2) 3.4(4.2) 3.4(4.2)
Cold-temp. COd e j j j j j j j j j j j j 10(j) 10(j) 10(j) 10(j)
NOx 4 j j j 3.0 3.1 3.1 2.3 2.3 2.3 2.3 2.3 1.2 0.4(0.6) 0.4(0.6) 0.4(0.6) 0.14(0.20)
Particulates h j j j j j j j j j j j j j 0.08(0.10) 0.08 (0.08) 0.02(0.02)
Formaldehyde h j j j j j j j j j j j j j j 0.015(0.018) 0.015(0.018)
Diesel
HC (total) 11 j j j j j 2.0 1.7 1.7 0.80 0.80 0.80 0.80 j (0.80) j (0.80) j j
NMHC h j j j j j j j j j j j j 0.25(0.31) 0.25(0.31) j j
NMOG h j j j j j j j j j j j j j j j (0.156) 0.100(0.125)
CO 80 j j j j j 20 18 18 10 10 10 10 3.4(4.2) 3.4(4.2) j (4.2) 3.4(4.2)
NOx 4 j j j j j 3.1 2.3 2.3 2.3 2.3 2.3 1.2 1.0(1.25) 1.0(1.25) j (0.6) 0.14(0.20)
Particulates h j j j j j j j 0.60 0.60 0.60 0.26 0.26 0.26 0.08(0.10) j (0.10) 0.02(0.02)
Formaldehyde h j j j j j j j j j j j j j j j (0.018) 0.015(0.018)
LDT1 weight criterae GVWR up through 6,000 pounds GVWR up through 6,000 pounds GVWR up through 6,000 pounds GVWR up through 6,000 pounds GVWR up through 6,000 pounds GVWR up through 6,000 pounds GVWR up through 8,500 pounds GVWR up through 8,500 pounds GVWR up through 8,500 pounds GVWR up through
8,500
pounds
GVWR up through
8,500
pounds
GVWR up through 6,000 lbs; LVW up through 3,750 pounds GVWR up through 6,000 lbs; LVW up through 3,750 pounds GVWR up through 6,000 lbs; LVW up through 3,750 pounds GVWR up through 6,000 lbs; LVW up through 3,750
pounds
GVWR up through 6,000 lbs; LVW up through 3,750
pounds
Test procedure b 7-mode 7-mode CVS-72 CVS-72 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75 CVS-75
Useful life (intermediate) c,f j j j j j j j j j j j j 5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000
miles
5 years/
50,000
miles
(full) 5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
5 years/
50,000 miles
11 years/
120,000 miles
11 years/
120,000 miles
11 years/
120,000 miles
10 years/
100,000 miles
10 years/
100,000 miles
10 years/
100,000
miles
10 years/
120,000
miles
KEY: CO=carbon monoxide; GVWR=gross vehicle weight rating; HC=hydrocarbons; LVW=loaded vehicle weight; NMHC=nonmethane hydrocarbons; NMOG= nonmethane organic gases; NOx=nitrogen oxides.
aLight-duty truck categories LDT1-LDT4 were not created until 1994. From 1968 to 1978, all trucks with a GVWR up to 6,000 pounds were classified as light-duty trucks and were required to meet the same standards. As of 1979, the maximum weight was raised to 8,500 pounds GVWR. During 1988-93, light duty trucks were divided into two subcategories that coincide with the current LDT1-LDT4 categories. The standards for LDT2, LDT3, and LDT4 are shown in tables 4-30b through 4-30d.
bThe test procedure for measuring exhaust emissions has changed several times over the course of vehicle emissions regulation. The 7-mode procedure was used through model year 1971 and was replaced by the CVS-72 procedure beginning in model year 1972. The CVS-75 procedure became the test procedure as of model year 1975. While it may appear that total HC and CO standards were relaxed in 1972-74, these standards were actually more stringent due to the more stringent nature of the CVS-72 test procedure. Additional standards for CO and composite standards for NMHC and NOx tested over the new Supplemental Federal Test Procedure will be phased-in beginning with model year 2000. These standards are not shown in this table.
cEmissions standards had to be met for a useful life of 5 years/50,000 miles through model year 1983, and a full useful life of 11 years/120,000 miles was defined for 1985-93 (several useful life options were available for 1984). Beginning in model year 1994, emissions standards were established for an intermediate useful life of 5 years/50,000 miles as well as a full useful life (full useful life standards are shown in parentheses). HC standards, however, were established only for full useful life. Tier 1 exhaust standards, except particulates standards, were phased-in during 1994-96 at a rate of 40%, 80%, and 100%, respectively. PM standards were phased-in at a rate of 40%, 80%, and 100% during 1995-97.
dThe cold CO emissions standard is measured at 20 degrees F (rather than 75 degrees F) and is applicable for a 5-year/50,000-mile useful life.
eGVWR is the maximum design loaded weight. LVW is the curb weight (nominal vehicle weight) plus 300 pounds.
f Manufacturers can opt to certify vehicles for a full useful life of 15 years/150,000 miles and either have (1) intermediate useful life standards waived or (2) receive additional NOx credits.
gThe "Prior to controls" column reports emissions estimates of a typical newly manufactured car in the years before exhaust emissions certification standard were implemented.
h No estimate available.
iIn 1968-69, exhaust emissions standards were issued in parts per million rather than grams per mile and are, therefore, incompatible with this table.
j No standard has been set.
kThe term "tier" refers to a level of standards for specific years. Interim Tier 2 refers to an intermediate level of standards that move manufacturers toward compliance with Tier 2 standards. Interim Tier 2 and Tier 2 standards are established as "bins." Each bin is a set of standards for NOx, CO, NMOG, formaldehyde, and particulates (HC and NMHC standards are dropped for Tier 2 and Interim Tier 2). Manufacturers may certify any given vehicle family to any of the bins available for that vehicle class as long as the resultingsales-weighted corporate average NOx standard is met for the full useful life. The Tier 2 corporate average NOx standard is 0.07 grams/mile. Interim corporate-based average NOx standards are based on vehicle type. The interim corporate sales-weighted average for LDT1 vehicles is 0.3 grams/mile. Tier 2 standards will be phased in at a rate of 25% in 2004, 50% in 2005, 75% in 2006, and 100% in 2007. During this period, all LDT1 vehicles not meeting the Tier 2 standards must meet Interim Tier 2 standards.
SOURCES:
40 CFR 86, Subpart A (July 1, 1998). U.S. Environmental Protection Agency, Office of Air and Radiation, personal communication, April 1999, and Federal Register, Vol. 65, No. 28, pp. 6851-6870.
Updated: Saturday, May 20, 2017 | 2020-09-20T01:26:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8890297412872314, "perplexity": 5639.81050752694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400193087.0/warc/CC-MAIN-20200920000137-20200920030137-00127.warc.gz"} |
https://par.nsf.gov/biblio/10121526-bridging-capacity-gap-between-interactive-one-way-communication | Bridging the Capacity Gap Between Interactive and One-Way Communication
We study the communication rate of coding schemes for interactive communication that transform any two-party interactive protocol into a protocol that is robust to noise. Recently, Haeupler [11] showed that if an ∊ > 0 fraction of transmissions are corrupted, adversarially or randomly, then it is possible to achieve a communication rate of Furthermore, Haeupler conjectured that this rate is optimal for general input protocols. This stands in contrast to the classical setting of one-way communication in which error-correcting codes are known to achieve an optimal communication rate of 1 In this work, we show that the quadratically smaller rate loss of the one-way setting can also be achieved in interactive coding schemes for a very natural class of input protocols. We introduce the notion of average message length, or the average number of bits a party sends before receiving a reply, as a natural parameter for measuring the level of interactivity in a protocol. Moreover, we show that any protocol with average message length ℓ = Ω(poly(1/∊)) can be simulated by a protocol with optimal communication rate 1 - Θ(Η(∊)) over an oblivious adversarial channel with error fraction e. Furthermore, under the additional assumption of access to public shared randomness, the more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10121526
Journal Name:
ACM-SIAM Symposium on Discrete Algorithms
Page Range or eLocation-ID:
2123 to 2142
Recent new constructions of rate-1 OT [Döttling, Garg, Ishai, Malavolta, Mour, and Ostrovsky, CRYPTO 2019] have brought this primitive under the spotlight and the techniques have led to new feasibility results for private-information retrieval, and homomorphic encryption for branching programs. The receiver communication of this construction consists of a quadratic (in the sender's input size) number of group elements for a single instance of rate-1 OT. Recently [Garg, Hajiabadi, Ostrovsky, TCC 2020] improved the receiver communication to a linear number of group elements for a single string-OT. However, most applications of rate-1 OT require executing it multiple times, resulting in large communication costs for the receiver. In this work, we introduce a new technique for amortizing the cost of multiple rate-1 OTs. Specifically, based on standard pairing assumptions, we obtain a two-message rate-1 OT protocol for which the amortized cost per string-OT is asymptotically reduced to only four group elements. Our results lead to significant communication improvements in PSI and PIR, special cases of SFE for branching programs. - PIR: We obtain a rate-1 PIR scheme with client communication cost of $O(\lambda\cdot\log N)$ group elements for security parameter $\lambda$ and database size $N$. Notably, after a one-time setup (or onemore » | 2023-03-28T11:43:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5085135698318481, "perplexity": 1165.4990125738045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00294.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S044PHI | # AVERAGE PARTICLE MULTIPLICITIES IN HADRONIC ${{\boldsymbol Z}}$ DECAY
Summed over particle and antiparticle, when appropriate.
# $\langle{}\boldsymbol N_{{{\boldsymbol \phi}}}\rangle{}$ INSPIRE search
VALUE DOCUMENT ID TECN COMMENT
$\bf{ 0.098 \pm0.006}$ OUR AVERAGE Error includes scale factor of 2.0.
$0.105$ $\pm0.008$
1999 E
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
$0.091$ $\pm0.002$ $\pm0.003$
1998 Q
OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
$0.104$ $\pm0.003$ $\pm0.007$
1996 U
DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
$0.122$ $\pm0.004$ $\pm0.008$
1996 H
ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV
$\langle{}\mathit N_{{{\mathit \phi}}}\rangle{}$
References:
ABE 1999E
PR D59 052001 Production of ${{\mathit \pi}^{+}}$, ${{\mathit K}^{+}}$, ${{\mathit K}^{0}}$, ${{\mathit K}^{*0}}$, ${{\mathit \phi}}$, ${{\mathit p}}$ and ${{\mathit \Lambda}^{0}}$ in Hadronic ${{\mathit Z}}$ Decays
ACKERSTAFF 1998Q
EPJ C4 19 Production of ${{\mathit f}_{{0}}{(980)}}$, ${{\mathit f}_{{2}}{(1270)}}$ and ${{\mathit \phi}{(1020)}}$ in Hadronic ${{\mathit Z}^{0}}$ Decay
ABREU 1996U
ZPHY C73 61 Measurement of Inclusive ${{\mathit K}^{*}{(892)}^{0}}$, ${{\mathit \phi}{(1020)}}$ and ${{\mathit K}_{{2}}^{*}{(1430)}^{0}}$ Production in Hadronic ${{\mathit Z}}$ Decays
BUSKULIC 1996H
ZPHY C69 379 Inclusive Production of Neutral Vector Mesons in Hadronic ${{\mathit Z}}$ Decays | 2019-01-18T15:39:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9892417788505554, "perplexity": 12768.302225842279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660175.18/warc/CC-MAIN-20190118151716-20190118173716-00510.warc.gz"} |
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# Atomic Spectroscopy - Atomic Lifetimes
## Share
The radiative lifetime τk of an atomic level k is related to the sum of transition probabilities to all levels i lower in energy than k:
$$\tau_k=\left(\sum_i \, A_{ki}\right)^{-1}\quad.$$
(27)
The branching ratio of a particular transition, say to state i ′, is defined as
$$A_{ki\prime} \Big/ \sum_i \, A_{ki} = A_{ki\prime} \, \tau_k\quad.$$
(28)
If only one branch (i ′) exists (or if all other branches may be neglected), one obtains Aki ′ τk = 1, and
$$\tau_k=1/A_{ki\prime} \tau_k\quad.$$
(29)
Precision lifetime measurement techniques are discussed in Atomic, Molecular, & Optical Physics Handbook, Chaps. 17 and 18, ed. by G.W.F. Drake (AIP, Woodbury, NY, 1996).
### Transitions in Hydrogenic (One-Electron) Species
The nonrelativistic energy of a hydrogenic transition [Eqs. (1), (10)] is
$$(\Delta E)_Z=(E_k-E_i)_Z=R_M\, hc\,Z^2(1/n_i^2-1/n_k^2)\quad.$$
(30)
Hydrogenic Z scaling. The spectroscopic quantities for a hydrogenic ion of nuclear charge Z are related to the equivalent quantities in hydrogen (Z = 1) as follows (neglecting small differences in the values of RM):
$$(\Delta E)_Z=Z^2(\Delta E)_{\rm H}\quad,$$
(31)
$$(\lambda_{\rm vac})_Z=Z^2(\lambda_{\rm vac})_{\rm H}\quad,$$
(32)
$$S_Z=Z^{-2}\, S_{\rm H}\quad,$$
(33)
$$f_Z=f_{\rm H}\quad,$$
(34)
$$A_Z=Z^4 A_{\rm H}\quad,$$
(35)
For large values of Z, roughly Z > 20, relativistic corrections become noticeable and must be taken into account.
f-value trends. f values for high series members (large n′ values) of hydrogenic ions decrease according to
$$f(n,l\rightarrow n^\prime, l\pm1)\, \alpha(n^\prime)^{-3}\quad.$$
(36)
Data for some lines of the main spectral series of hydrogen are given in the table below.
Some transitions of the main spectral series of hydrogen
Transition Customary name a λ b (Å) gi c gk Aki (108 s-1)
1-2 (Lα ) 1 215. 67 2 8 4.699
1-3 (Lβ ) 1 025. 73 2 18 5.575(-1) d
1-4 (Lγ ) 972. 537 2 32 1.278(-1)
1-5 (Lδ ) 949. 743 2 50 4.125(-2)
1-6 (Lε ) 937. 80 2 72 1.644(-2)
2-3 (Hα ) 6 562. 80 8 18 4.410(-1)
2-4 (Hβ ) 4 861. 32 8 32 8.419(-2)
2-5 (Hγ ) 4 340. 46 8 50 2.530(-2)
2-6 (Hδ ) 4 101. 73 8 72 9.732(-3)
2-7 (Hε ) 3 970. 07 8 98 4.389(-3)
3-4 (Pα ) 18 751. 0 18 32 8.986(-2)
3-5 (Pβ ) 12 818. 1 18 50 2.201(-2)
3-6 (Pγ ) 10 938. 1 18 72 7.783(-3)
3-7 (Pδ ) 10 049. 4 18 98 3.358(-3)
3-8 (Pε ) 9 545. 97 18 128 1.651(-3)
a Lα is often called Lyman α, Hα = Balmer α, Pα = Paschen α, etc. b Wavelengths below 2000 Å are in vacuum; values above 2000 Å are in air. c For transitions in hydrogen, gi(k) = 2(ni(k))2, where ni(k), is the principal quantum number of the lower (upper) electron shell. d The number in parentheses indicates the power of 10 by which the value has to be multiplied.
### Systematic Trends and Regularities in Atoms and Ions with Two or More Electrons
Nonrelativistic atomic quantities for a given state or transition in an isoelectronic sequence may be expressed as power series expansions in Z -1:
Z -2E = E0 + E1Z -1 + E2Z -2 + ... ,
(37)
Z 2S = S0 + S1Z -1 + S2Z -2 + ... ,
(38)
f = f0 + f1Z -1 + f2Z -2 + ... ,
(39)
where E0, f0, and S0 are hydrogenic quantities. For transitions in which n does not change (ni = nk), f0 = 0, since states i and k are degenerate.
For equivalent transitions of homologous atoms, f values vary gradually. Transitions to be compared in the case of the "alkalis" are [34]
$$\begin{eqnarray*} (nl-n^\prime l^\prime)_{\rm Li}&\rightarrow& \left[ (n+1)l-(n^\prime+1) l^\prime \right]_{\rm Na}\\ &\rightarrow& \left[ (n+2)l-(n^\prime+2) l^\prime \right]_{\rm Cu}~\rightarrow~\ldots \quad . \end{eqnarray*}$$
(Eq)
Complex atomic structures, as well as cases involving strong cancellation in the integrand of the transition integral, generally do not adhere to this regular behavior.
## Contacts
Created October 3, 2016, Updated December 23, 2019 | 2020-08-03T15:15:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5624599456787109, "perplexity": 2965.7440515439603}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735812.88/warc/CC-MAIN-20200803140840-20200803170840-00053.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/19%3A_Electric_Potential_and_Electric_Field/19.5%3A_Capacitors_and_Dielectrics | Skip to main content
$$\require{cancel}$$
# 19.5: Capacitors and Dielectrics
A capacitor is a device used to store electric charge. Capacitors have applications ranging from filtering static out of radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another, but not touching, such as those in Figure $$\PageIndex{1}$$. (Most of the time an insulator is used between the two plates to provide separation—see the discussion on dielectrics below.)
Figure $$\PageIndex{1}$$: Both capacitors shown here were initially uncharged before being connected to a battery. They now have separated charges of $$+Q$$ and $$-Q$$ on their two halves. (a) A parallel plate capacitor. (b) A rolled capacitor with an insulating material between its two conducting sheets.
Definition: CAPACITOR
A capacitor is a device used to store electric charge.
When battery terminals are connected to an initially uncharged capacitor, equal amounts of positive and negative charge, $$+Q$$ and $$-Q$$, are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge $$Q$$ in this circumstance. The amount of charge $$Q$$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
A system composed of two identical, parallel conducting plates separated by a distance, as in Figure $$\PageIndex{2}$$, is called a parallel plate capacitor. It is easy to see the relationship between the voltage and the stored charge for a parallel plate capacitor, as shown in Figure $$\PageIndex{2}$$. Each electric field line starts on an individual positive charge and ends on a negative one, so that there will be more field lines if there is more charge. (Drawing a single field line per charge is a convenience, only. We can draw many field lines for each charge, but the total number is proportional to the number of charges.) The electric field strength is, thus, directly proportional to $$Q$$.
Figure $$\PageIndex{2}$$: Electric field lines in this parallel plate capacitor, as always, start on positive charges and end on negative charges. Since the electric field strength is proportional to the density of field lines, it is also proportional to the amount of charge on the capacitor.
The field is proportional to the charge:
$E\propto Q,$
where the symbol $$\propto$$ means “proportional to.” From the discussion in Electric Potential in a Uniform Electric Field, we know that the voltage across parallel plates is $$V=Ed$$. Thus,
$V\propto E.$
It follows, then, that $$V \propto Q$$, and conversely,
$Q\propto V.$
This is true in general: The greater the voltage applied to any capacitor, the greater the charge stored in it.
Different capacitors will store different amounts of charge for the same applied voltage, depending on their physical characteristics. We define their capacitance $$C$$ to be such that the charge $$Q$$ stored in a capacitor is proportional to $$C$$. The charge stored in a capacitor is given by
$Q=CV.$
This equation expresses the two major factors affecting the amount of charge stored. Those factors are the physical characteristics of the capacitor, $$C$$, and the voltage, $$V$$. Rearranging the equation, we define the capacitance $$C$$ of a capacitor.
Definition: CAPACITANCE
Capacitance $$C$$ is the amount of charge stored per volt, or
$C=\dfrac{Q}{V}.$
The unit of capacitance is the farad (F), named for Michael Faraday (1791–1867), an English scientist who contributed to the fields of electromagnetism and electrochemistry. Since capacitance is charge per unit voltage, we see that a farad is a coulomb per volt, or
$1\: \mathrm{F}=\dfrac{1\: \mathrm{C}}{1\: \mathrm{V}}.$
A 1-farad capacitor would be able to store 1 coulomb (a very large amount of charge) with the application of only 1 volt. One farad is, thus, a very large capacitance. Typical capacitors range from fractions of a picofarad $$(1\: \mathrm{pF}=10^{-12}\mathrm{F})$$ to millifarads $$(1\: \mathrm{mF}=10^{-3}\mathrm{F})$$.
Figure $$\PageIndex{3}$$ shows some common capacitors. Capacitors are primarily made of ceramic, glass, or plastic, depending upon purpose and size. Insulating materials, called dielectrics, are commonly used in their construction, as discussed below.
Figure $$\PageIndex{3}$$: Some typical capacitors. Size and value of capacitance are not necessarily related. (credit: Windell Oskay)
## Parallel Plate Capacitor
The parallel plate capacitor shown in Figure $$\PageIndex{4}$$ has two identical conducting plates, each having a surface area $$A$$, separated by a distance $$d$$ (with no material between the plates). When a voltage $$V$$ is applied to the capacitor, it stores a charge $$Q$$, as shown. We can see how its capacitance depends on $$A$$ and $$d$$ by considering the characteristics of the Coulomb force. We know that like charges repel, unlike charges attract, and the force between charges decreases with distance. So it seems quite reasonable that the bigger the plates are, the more charge they can store—because the charges can spread out more. Thus $$C$$ should be greater for larger $$A$$. Similarly, the closer the plates are together, the greater the attraction of the opposite charges on them. So $$C$$ should be greater for smaller $$d$$.
Figure $$\PageIndex{4}$$: Parallel plate capacitor with plates separated by a distance $$d$$. Each plate has an area $$A$$.
It can be shown that for a parallel plate capacitor there are only two factors ($$A$$ and $$d$$) that affect its capacitance $$C$$. The capacitance of a parallel plate capacitor in equation form can be defined:
Definition: CAPACITANCE OF A PARALLEL PLATE CAPACITOR
The capacitance of a parallel plate capacitor in equation form is given by
$C=\varepsilon _{0} \dfrac{A}{d}.$
$$A$$ is the area of one plate in square meters, and $$d$$ is the distance between the plates in meters. The constant $$\varepsilon _{0}$$ is the permittivity of free space; its numerical value in SI units is $$\varepsilon _{0}=8.85\times 10^{-12} \mathrm{F/m}$$. The units of F/m are equivalent to $$\mathrm{C^{2}/N\cdot m^{2}}$$. The small numerical value of $$\varepsilon _{0}$$ is related to the large size of the farad. A parallel plate capacitor must have a large area to have a capacitance approaching a farad. (Note that the above equation is valid when the parallel plates are separated by air or free space. When another material is placed between the plates, the equation is modified, as discussed below.)
Example $$\PageIndex{1}$$: Capacitance and Charge Stored in a Parallel Plate Capacitor
1. What is the capacitance of a parallel plate capacitor with metal plates, each of area $$1.00 \mathrm{m^{2}}$$, separated by 1.00 mm?
2. What charge is stored in this capacitor if a voltage of $$3.00\times 10^{3} \mathrm{V}$$ is applied to it?
Strategy
Finding the capacitance $$C$$ is a straightforward application of the equation $$C=\varepsilon _{0} A/d$$. Once $$C$$ is found, the charge stored can be found using the equation $$Q=CV$$.
Solution for (a)
Entering the given values into the equation for the capacitance of a parallel plate capacitor yields
\begin{align*} C&=\varepsilon \dfrac{A}{d} \\[4pt] &=(8.85\times 10^{-12} \mathrm{\dfrac{F}{m}}) \dfrac{1.00 \mathrm{m^{2}}}{1.00\times 10^{-3} \mathrm{m}} \\[4pt] &=8.85\times 10^{-9} \mathrm{F} =8.85 \mathrm{nF}. \end{align*}
Discussion for (a)
This small value for the capacitance indicates how difficult it is to make a device with a large capacitance. Special techniques help, such as using very large area thin foils placed close together.
Solution for (b)
The charge stored in any capacitor is given by the equation $$Q=CV$$. Entering the known values into this equation gives
\begin{align*} Q &=CV\\[5pt] &=(8.85 \times 10^{-9}\mathrm{F})(3.00\times 10^{3}\mathrm{V}) \\[5pt] &=26.6 \mathrm{ \mu C}. \end{align*}
Discussion for (b)
This charge is only slightly greater than those found in typical static electricity. Since air breaks down at about $$3.00\times 10^{6} \mathrm{V/m}$$, more charge cannot be stored on this capacitor by increasing the voltage.
Membrane Potential
Another interesting biological example dealing with electric potential is found in the cell’s plasma membrane. The membrane sets a cell off from its surroundings and also allows ions to selectively pass in and out of the cell. There is a potential difference across the membrane of about $$-70 \mathrm{mV}$$. This is due to the mainly negatively charged ions in the cell and the predominance of positively charged sodium ($$\mathrm{Na}^{+}$$) ions outside. Things change when a nerve cell is stimulated. $$\mathrm{Na}^{+}$$ ions are allowed to pass through the membrane into the cell, producing a positive membrane potential—the nerve signal. The cell membrane is about 7 to 10 nm thick. An approximate value of the electric field across it is given by
\begin{align*} E&=\dfrac{V}{d} \\[5pt] &=\dfrac{-70\times 10^{-3}\mathrm{V}}{8\times 10^{-9} \mathrm{m}} \\[5pt] &= -9\times 10^{6} \mathrm{V/m}. \end{align*}
This electric field is enough to cause a breakdown in air.
## Dielectric
The previous example highlights the difficulty of storing a large amount of charge in capacitors. If $$d$$ is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since $$E=V/d$$). An important solution to this difficulty is to put an insulating material, called a dielectric, between the plates of a capacitor and allow $$d$$ to be as small as possible. Not only does the smaller $$d$$ make the capacitance greater, but many insulators can withstand greater electric fields than air before breaking down.
There is another benefit to using a dielectric in a capacitor. Depending on the material used, the capacitance is greater than that given by the equation $$C=\varepsilon \dfrac{A}{d}$$ by a factor $$\kappa$$, called the dielectric constant. A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$C=\kappa \varepsilon _{0} \dfrac{A}{d} (\mathrm{parallel\: plate\: capacitor\: with\: dielectric}).$
Values of the dielectric constant $$\kappa$$ for various materials are given in Table $$\PageIndex{1}$$. Note that $$\kappa$$ for vacuum is exactly 1, and so the above equation is valid in that case, too. If a dielectric is used, perhaps by placing Teflon between the plates of the capacitor in Example $$\PageIndex{1}$$, then the capacitance is greater by the factor $$\kappa$$, which for Teflon is 2.1.
TAKE-HOME EXPERIMENT: BUILDING A CAPACITOR
How large a capacitor can you make using a chewing gum wrapper? The plates will be the aluminum foil, and the separation (dielectric) in between will be the paper.
Table $$\PageIndex{1}$$: Dielectric Constants and Dielectric Strengths for Various Materials at 20ºC
MaterialDielectric constant ($$\mathbf{\kappa}$$)Dielectric Strength ($$\mathbf{\mathrm{V/m}}$$)
Vacuum$$1.00000$$$$-$$
Air$$1.00059$$$$3\times 10^{6}$$
Bakelite$$4.9$$$$24\times 10^{6}$$
Fused quartz$$3.78$$$$8\times 10^{6}$$
Neoprene rubber$$6.7$$$$12\times 10^{6}$$
Nylon$$3.4$$$$14\times 10^{6}$$
Paper$$3.7$$$$16\times 10^{6}$$
Polystyrene$$2.56$$$$24\times 10^{6}$$
Pyrex glass$$5.6$$$$14\times 10^{6}$$
Silicon oil$$2.5$$$$15\times 10^{6}$$
Strontium titanate$$233$$$$8\times 10^{6}$$
Teflon$$2.1$$$$60\times 10^{6}$$
Water$$80$$$$-$$
Note also that the dielectric constant for air is very close to 1, so that air-filled capacitors act much like those with vacuum between their plates except that the air can become conductive if the electric field strength becomes too great. (Recall that $$E=V/d$$ for a parallel plate capacitor.) Also shown in Table $$\PageIndex{1}$$ are maximum electric field strengths in V/m, called dielectric strengths, for several materials. These are the fields above which the material begins to break down and conduct. The dielectric strength imposes a limit on the voltage that can be applied for a given plate separation. For instance, in Example, the separation is 1.00 mm, and so the voltage limit for air is
\begin{align*} V&=E\cdot V \\[4pt] &=(3\times 10^{6} \mathrm{V/m})(1.00\times 10^{-3}\mathrm{m}) \\[4pt] &=3000\mathrm{V}. \end{align*}
However, the limit for a 1.00 mm separation filled with Teflon is 60,000 V, since the dielectric strength of Teflon is $$60\times 10^{6} \mathrm{V/m}$$ V/m. So the same capacitor filled with Teflon has a greater capacitance and can be subjected to a much greater voltage. Using the capacitance we calculated in the above example for the air-filled parallel plate capacitor, we find that the Teflon-filled capacitor can store a maximum charge of
\begin{align*} Q&=CV \\[4pt] &=\kappa C_{air}V \\[4pt] &=(2.1)(8.85\mathrm{nF})(6.0\times 10^{4} \mathrm{V}) \\[4pt] &=1.1 \mathrm{mC}. \end{align*}
This is 42 times the charge of the same air-filled capacitor.
DIELECTRIC STRENGTH
The maximum electric field strength above which an insulating material begins to break down and conduct is called its dielectric strength.
Microscopically, how does a dielectric increase capacitance? Polarization of the insulator is responsible. The more easily it is polarized, the greater its dielectric constant $$\kappa$$. Water, for example, is a polar molecule because one end of the molecule has a slight positive charge and the other end has a slight negative charge. The polarity of water causes it to have a relatively large dielectric constant of 80. The effect of polarization can be best explained in terms of the characteristics of the Coulomb force. Figure $$\PageIndex{5}$$ shows the separation of charge schematically in the molecules of a dielectric material placed between the charged plates of a capacitor. The Coulomb force between the closest ends of the molecules and the charge on the plates is attractive and very strong, since they are very close together. This attracts more charge onto the plates than if the space were empty and the opposite charges were a distance $$d$$ away.
Figure $$\PageIndex{5}$$: (a) The molecules in the insulating material between the plates of a capacitor are polarized by the charged plates. This produces a layer of opposite charge on the surface of the dielectric that attracts more charge onto the plate, increasing its capacitance. (b) The dielectric reduces the electric field strength inside the capacitor, resulting in a smaller voltage between the plates for the same charge. The capacitor stores the same charge for a smaller voltage, implying that it has a larger capacitance because of the dielectric.
Another way to understand how a dielectric increases capacitance is to consider its effect on the electric field inside the capacitor. Figure $$\PageIndex{5}$$(b) shows the electric field lines with a dielectric in place. Since the field lines end on charges in the dielectric, there are fewer of them going from one side of the capacitor to the other. So the electric field strength is less than if there were a vacuum between the plates, even though the same charge is on the plates. The voltage between the plates is $$V=Ed$$, so it too is reduced by the dielectric. Thus there is a smaller voltage $$V$$ for the same charge $$Q$$; since $$C=Q/V$$, the capacitance $$C$$ is greater.
The dielectric constant is generally defined to be $$\kappa =E_{0}/E$$, or the ratio of the electric field in a vacuum to that in the dielectric material, and is intimately related to the polarizability of the material.
THINGS GREAT AND SMALL: The Submicroscopic Origin of Polarization
Polarization is a separation of charge within an atom or molecule. As has been noted, the planetary model of the atom pictures it as having a positive nucleus orbited by negative electrons, analogous to the planets orbiting the Sun. Although this model is not completely accurate, it is very helpful in explaining a vast range of phenomena and will be refined elsewhere, such as in the Chapter on Atomic Physics. The submicroscopic origin of polarization can be modeled as shown in Figure $$\PageIndex{6}$$.
Figure $$\PageIndex{6}$$: Artist’s conception of a polarized atom. The orbits of electrons around the nucleus are shifted slightly by the external charges (shown exaggerated). The resulting separation of charge within the atom means that it is polarized. Note that the unlike charge is now closer to the external charges, causing the polarization.
We will find in Atomic Physics that the orbits of electrons are more properly viewed as electron clouds with the density of the cloud related to the probability of finding an electron in that location (as opposed to the definite locations and paths of planets in their orbits around the Sun). This cloud is shifted by the Coulomb force so that the atom on average has a separation of charge. Although the atom remains neutral, it can now be the source of a Coulomb force, since a charge brought near the atom will be closer to one type of charge than the other.
Some molecules, such as those of water, have an inherent separation of charge and are thus called polar molecules.Figure $$\PageIndex{7}$$ illustrates the separation of charge in a water molecule, which has two hydrogen atoms and one oxygen atom ($$\mathrm{H_{2}O}$$). The water molecule is not symmetric—the hydrogen atoms are repelled to one side, giving the molecule a boomerang shape. The electrons in a water molecule are more concentrated around the more highly charged oxygen nucleus than around the hydrogen nuclei. This makes the oxygen end of the molecule slightly negative and leaves the hydrogen ends slightly positive. The inherent separation of charge in polar molecules makes it easier to align them with external fields and charges. Polar molecules therefore exhibit greater polarization effects and have greater dielectric constants. Those who study chemistry will find that the polar nature of water has many effects. For example, water molecules gather ions much more effectively because they have an electric field and a separation of charge to attract charges of both signs. Also, as brought out in the previous chapter, polar water provides a shield or screening of the electric fields in the highly charged molecules of interest in biological systems.
Figure $$\PageIndex{7}$$: Artist’s conception of a water molecule. There is an inherent separation of charge, and so water is a polar molecule. Electrons in the molecule are attracted to the oxygen nucleus and leave an excess of positive charge near the two hydrogen nuclei. (Note that the schematic on the right is a rough illustration of the distribution of electrons in the water molecule. It does not show the actual numbers of protons and electrons involved in the structure.)
PHET EXPLORATIONS: CAPACITOR LAB
Explore how a capacitor works! Change the size of the plates and add a dielectric to see the effect on capacitance. Change the voltage and see charges built up on the plates. Observe the electric field in the capacitor. Measure the voltage and the electric field.
Figure $$\PageIndex{8}$$: Capacitor Lab
# Summary
• A capacitor is a device used to store charge.
• The amount of charge $$Q$$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
• The capacitance $$C$$ is the amount of charge stored per volt, or $$C=\dfrac{Q}{V}.$$
• The capacitance of a parallel plate capacitor is $$C=\varepsilon _{0} \dfrac{A}{d}$$, when the plates are separated by air or free space. $$\varepsilon _{0}$$ is called the permittivity of free space.
• A parallel plate capacitor with a dielectric between its plates has a capacitance given by $$C=\kappa \varepsilon _{0} \dfrac{A}{d},$$ where $$\kappa$$ is the dielectric constant of the material.
• The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.
# Glossary
capacitor
a device that stores electric charge
capacitance
amount of charge stored per unit volt
dielectric
an insulating material
dielectric strength
the maximum electric field above which an insulating material begins to break down and conduct
parallel plate capacitor
two identical conducting plates separated by a distance
polar molecule
a molecule with inherent separation of charge
# Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-11-12T19:11:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7637929916381836, "perplexity": 446.72483985245435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665726.39/warc/CC-MAIN-20191112175604-20191112203604-00210.warc.gz"} |
https://indico.fnal.gov/event/19348/contributions/187323/ | # Neutrino 2020
June 22, 2020 to July 2, 2020
US/Central timezone
## Neutrino oscillations in a magnetic field and CP violation: The three-flavor case
Not scheduled
10m
Poster
### Speaker
Artem Popov (Moscow State University)
### Description
We develop an approach to neutrino oscillations in a magnetic field and extend it to the case of three neutrino generations. The theoretical framework suitable for computation of the Dirac neutrino spin, flavour and spin-flavour oscillations probabilities in a magnetic field is given. The closed analytic expressions for the probabilities of oscillations are obtained accounting for the normal and inverted hierarchies and the possible effect of CP violation. In particular, it is shown that the probabilities of conversions without neutrino flavor change (νLe→νLe and νLe→νRe) do not exhibit the dependence on the CP phase, while other neutrino conversions are affected by the CP phase. In general, the neutrino oscillation probabilities exhibit quite a complicated interplay of oscillations on the magnetic μνB and vacuum frequencies. The obtained are of interest to neutrino oscillations in extreme astrophysical environments such as magnetars and supernovas, as well as neutrino propagation in interstellar magnetic fields.
### Mini-abstract
Three-flavor neutrino oscillations in a magnetic field are derived and exhibit complicated effects.
### Primary author
Artem Popov (Moscow State University)
### Co-authors
Alexander Studenikin (Department of Theoretical Physics, Moscow State University) Alexey Lichkunov (Moscow State University) | 2022-11-28T08:15:10 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.84682297706604, "perplexity": 2104.7080163482665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710488.2/warc/CC-MAIN-20221128070816-20221128100816-00614.warc.gz"} |
http://popflock.com/learn?s=Rabin_automaton | Rabin Automaton
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Rabin Automaton
In automata theory, a branch of theoretical computer science, an ?-automaton (or stream automaton) is a variation of finite automata that runs on infinite, rather than finite, strings as input. Since ?-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states.
?-automata are useful for specifying behavior of systems that are not expected to terminate, such as hardware, operating systems and control systems. For such systems, one may want to specify a property such as "for every request, an acknowledge eventually follows", or its negation "there is a request that is not followed by an acknowledge". The former is a property of infinite words: one cannot say of a finite sequence that it satisfies this property.
Classes of ?-automata include the Büchi automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ?-automata differ only in terms of acceptance condition. They all recognize precisely the regular ?-languages except for the deterministic Büchi automata, which is strictly weaker than all the others. Although all these types of automata recognize the same set of ?-languages, they nonetheless differ in succinctness of representation for a given ?-language.
## Deterministic ?-automata
Formally, a deterministic ?-automaton is a tuple A = (Q,?,?,Q0,Acc) that consists of the following components:
• Q is a finite set. The elements of Q are called the states of A.
• ? is a finite set called the alphabet of A.
• ?: Q × ? -> Q is a function, called the transition function of A.
• Q0 is an element of Q, called the initial state.
• Acc is the acceptance condition, formally a subset of Q?.
An input for A is an infinite string over the alphabet ?, i.e. it is an infinite sequence ? = (a1,a2,a3,...). The run of A on such an input is an infinite sequence ? = (r0,r1,r2,...) of states, defined as follows:
• r0 = q0.
• r1 = ?(r0,a1).
• r2 = ?(r1,a2).
...
• rn = ?(rn-1,an).
The main purpose of an ?-automaton is to define a subset of the set of all inputs: The set of accepted inputs. Whereas in the case of an ordinary finite automaton every run ends with a state rn and the input is accepted if and only if rn is an accepting state, the definition of the set of accepted inputs is more complicated for ?-automata. Here we must look at the entire run ?. The input is accepted if the corresponding run is in Acc. The set of accepted input ?-words is called the recognized ?-language by the automaton, which is denoted as L(A).
The definition of Acc as a subset of Q? is purely formal and not suitable for practice because normally such sets are infinite. The difference between various types of ?-automata (Büchi, Rabin etc.) consists in how they encode certain subsets Acc of Q? as finite sets, and therefore in which such subsets they can encode.
## Nondeterministic ?-automata
Formally, a nondeterministic ?-automaton is a tuple A = (Q,?,?,Q0,Acc) that consists of the following components:
• Q is a finite set. The elements of Q are called the states of A.
• ? is a finite set called the alphabet of A.
• ? is a subset of Q × ? × Q and is called the transition relation of A.
• Q0 is a subset of Q, called the initial set of states.
• Acc is the acceptance condition, a subset of Q?.
Unlike a deterministic ?-automaton, which has a transition function ?, the non-deterministic version has a transition relation ?. Note that ? can be regarded as a function : Q × ? -> P(Q) from Q × ? to the power set P(Q). Thus, given a state qn and a symbol an, the next state qn+1 is not necessarily determined uniquely, rather there is a set of possible next states.
A run of A on the input ? = (a1,a2,a3,...) is any infinite sequence ? = (r0,r1,r2,...) of states that satisfies the following conditions:
• r0 is an element of Q0.
• r1 is an element of ?(r0,a1).
• r2 is an element of ?(r1,a2).
...
• rn is an element of ?(rn-1,an).
A nondeterministic ?-automaton may admit many different runs on any given input, or none at all. The input is accepted if at least one of the possible runs is accepting. Whether a run is accepting depends only on Acc, as for deterministic ?-automata. Every deterministic ?-automaton can be regarded as a nondeterministic ?-automaton by taking ? to be the graph of ?. The definitions of runs and acceptance for deterministic ?-automata are then special cases of the nondeterministic cases.
## Acceptance conditions
Acceptance conditions may be infinite sets of ?-words. However, people mostly study acceptance conditions that are finitely representable. The following lists a variety of popular acceptance conditions.
Before discussing the list, let's make the following observation. In the case of infinitely running systems, one is often interested in whether certain behavior is repeated infinitely often. For example, if a network card receives infinitely many ping requests, then it may fail to respond to some of the requests but should respond to an infinite subset of received ping requests. This motivates the following definition: For any run ?, let Inf(?) be the set of states that occur infinitely often in ?. This notion of certain states being visited infinitely often will be helpful in defining the following acceptance conditions.
• A Büchi automaton is an ?-automaton A that uses the following acceptance condition, for some subset F of Q:
Büchi condition
A accepts exactly those runs ? for which Inf(?) ? F is not empty, i.e. there is an accepting state that occurs infinitely often in ?.
Since F is finite, this is equivalent to the condition that ?n is accepting for infinitely many natural numbers n.
• A Rabin automaton is an ?-automaton A that uses the following acceptance condition, for some set ? of pairs (Bi,Gi) of sets of states:
Rabin condition
A accepts exactly those runs ? for which there exists a pair (Bi,Gi) in ? such that Bi ? Inf(?) is empty and Gi ? Inf(?) is not empty.
• A Streett automaton is an ?-automaton A that uses the following acceptance condition, for some set ? of pairs (Bi,Gi) of sets of states:
Streett condition
A accepts exactly those runs ? such that for all pairs (Bi,Gi) in ?, Bi ? Inf(?) is empty or Gi ? Inf(?) is not empty.
The Streett condition is the negation of the Rabin condition. Therefore a deterministic Streett automaton accepts exactly the complement of the language accepted by the deterministic Rabin automaton consisting of the same data.
• A parity automaton is an automaton A whose set of states is Q = {0,1,2,...,k} for some natural number k, and that has the following acceptance condition:
Parity condition
A accepts ? if and only if the smallest number in Inf(?) is even.
• A Muller automaton is an ?-automaton A that uses the following acceptance condition, for a subset F of P(Q) (the power set of Q):
Muller condition
A accepts exactly those runs ? for which Inf(?) is an element of F.
Every Büchi automaton can be regarded as a Muller automaton. It suffices to replace F by F' consisting of all subsets of Q that contain at least one element of F. Similarly every Rabin, Streett or parity automaton can also be regarded as a Muller automaton.
## Example
A non-deterministic Büchi automaton that recognizes (0?1)*0?
The following ?-language L over the alphabet ? = {0,1}, which can be recognized by a nondeterministic Büchi automaton: L consists of all ?-words in ?? in which 1 occurs only finitely many times. A non-deterministic Büchi automaton recognizing L needs only two states q0 (the initial state) and q1. ? consists of the triples (q0,0,q0), (q0,1,q0), (q0,0,q1) and (q1,0,q1). F = {q1}. For any input ? in which 1 occurs only finitely many times, there is a run that stays in state q0 as long as there are 1s to read, and goes to state q1 afterwards. This run is successful. If there are infinitely many 1s, then there is only one possible run: the one that always stays in state q0. (Once the machine has left q0 and reached q1, it cannot return. If another 1 is read, there is no successor state.)
Notice that above language cannot be recognized by a deterministic Büchi automaton, which is strictly less expressive than its non-deterministic counterpart.
## Expressive power of ?-automata
An ?-language over a finite alphabet ? is a set of ?-words over ?, i.e. it is a subset of ??. An ?-language over ? is said to be recognized by an ?-automaton A (with the same alphabet) if it is the set of all ?-words accepted by A. The expressive power of a class of ?-automata is measured by the class of all ?-languages that can be recognized by some automaton in the class.
The nondeterministic Büchi, parity, Rabin, Streett, and Muller automata, respectively, all recognize exactly the same class of ?-languages.[1] These are known as the ?-Kleene closure of the regular languages or as the regular ?-languages. Using different proofs it can also be shown that the deterministic parity, Rabin, Streett, and Muller automata all recognize the regular ?-languages. It follows from this that the class of regular ?-languages is closed under complementation. However, the example above shows that the class of deterministic Büchi automata is strictly weaker.
## Conversion between ?-automata
Because nondeterministic Muller, Rabin, Streett, parity, and Büchi automata are equally expressive, they can be translated to each other. Let us use the following abbreviation ${\displaystyle \{N,D\}\times \{M,R,S,P,B\}}$: for example, NB stands for nondeterministic Büchi ?-automaton, while DP stands for deterministic parity ?-automaton. Then the following holds.
• Clearly, any deterministic automaton can be viewed as a nondeterministic one.
• ${\displaystyle NB\rightarrow NR/NS/NP}$ with no blow-up in the state space.
• ${\displaystyle NR\rightarrow NB}$ with a polynomial blow-up in the state space, i.e., the number of states in the resulting NB is ${\displaystyle 2nm+1}$, where ${\displaystyle n}$ is the number of states in the NB and ${\displaystyle m}$ is the number of Rabin acceptance pairs (see, for example, [2]).
• ${\displaystyle NS/NM/NP\rightarrow NB}$ with exponential blow-up in the state space.
• ${\displaystyle NB\rightarrow DR/DP}$ with exponential blow-up in the state space. This determinization result uses Safra's construction.
A comprehensive overview of translations can be found on the referenced web source. [3]
## Further reading
• Farwer, Berndt (2002), "?-Automata", in Grädel, Erich; Thomas, Wolfgang; Wilke, Thomas (eds.), Automata, Logics, and Infinite Games, Lecture Notes in Computer Science, Springer, pp. 3-21, ISBN 978-3-540-00388-5.
• Perrin, Dominique; Pin, Jean-Éric (2004), Infinite Words: Automata, Semigroups, Logic and Games, Elsevier, ISBN 978-0-12-532111-2
• Thomas, Wolfgang (1990), "Automata on infinite objects", in van Leeuwen, Jan (ed.), Handbook of Theoretical Computer Science, vol. B, MIT Press, pp. 133-191, ISBN 978-0-262-22039-2
• Bakhadyr Khoussainov; Anil Nerode (6 December 2012). Automata Theory and its Applications. Springer Science & Business Media. ISBN 978-1-4612-0171-7.
## References
1. ^ Safra, S. (1988), "On the complexity of ?-automata", Proceedings of the 29th Annual Symposium on Foundations of Computer Science (FOCS '88), Washington, DC, USA: IEEE Computer Society, pp. 319-327, doi:10.1109/SFCS.1988.21948.
2. ^ Esparza, Javier (2017), Automata Theory: An Algorithmic Approach (PDF)
3. ^ Boker, Udi (18 April 2018). "Word-Automata Translations". Udi Boker's webpage. Retrieved 2019.
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0. | 2020-10-24T06:46:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8043638467788696, "perplexity": 1176.8457162474333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882102.31/warc/CC-MAIN-20201024051926-20201024081926-00361.warc.gz"} |
https://www.nist.gov/property-fieldsection/sustainable-energy-sources-and-nanomaterials-5-million-advanced-solar | # Sustainable Energy Sources and Nanomaterials (+$5 million for Advanced Solar Technologies; +$4 million for Nanomaterial Environmental Health and Safety)
## Challenge
Sustainability—meeting today's needs without sacrificing tomorrow's—is the watchword of the 21st century. NIST's 2011 budget request promotes a sustainable U.S. economy through initiatives for research on green manufacturing and construction, advanced solar technologies, and factors determining the environmental, health, and safety (EHS) risks of nanomaterials.
Sunlight offers an inexhaustible energy source; however, its widespread adoption is limited by the relatively high cost and low efficiency of conventional photovoltaic cells that convert solar energy into electricity. A mismatch exists between the full range of "colors" or wavelengths of light energy emitted by the sun, and those that can be efficiently absorbed by current photovoltaic technologies. New nanotechnology-based photovoltaic materials—so called third-generation solar technologies—may greatly enhance the absorption properties of photocells through multi-layer structures optimized to absorb light at specific wavelengths spanning the full spectrum of the sun's output. However, the new materials lack the durability needed for commercial applications and developers need measurement tools to systematically optimize the electricity-generating properties of the devices.
Beyond solar cells, nanomaterials promise to solve a whole host of technology problems from better medications to less flammable plastics, and the value of nano-enabled products is expected to hit \$2.6 trillion by 2014. However, nanomaterials and products that contain them pose unknown risks throughout all stages of their lifecycles to people and the environment. This uncertainty threatens to erode public trust in the safety of nanotechnology products broadly and to stifle innovation and commercialization of nanotechnology products. U.S. regulatory agencies and industry need measurement tools—standards, protocols, and models—to link measured properties of nanomaterials such as size and shape with hazardous effects such as toxicity, and properly assess and manage EHS risks.
The National Nanotechnology Initiative identifies NIST as the lead agency for developing instrumentation, metrology, and analytical methods for advancing nano-EHS knowledge, and other major stakeholders recognize NIST as the lead organization for providing nano-EHS measurement methods and standards.
## Proposed NIST Program
Funding provided through these initiatives will allow NIST to partner with industry and other government agencies to:
• design measurement platforms and methods that rapidly find defects or quantify other properties important to the reliability, lifetime, and failure modes of nanomaterial-based photovoltaic cells;
• develop and disseminate measurement techniques that link the efficiency of third-generation photovoltaic materials with specific nanoscale properties;
• develop and release standards and methods to accurately measure and models to predict transformations—changes in properties—of common nanomaterial-containing products in relevant environments such as water, soil, sediments, and biological materials;
• produce quantitative data and standards to assess the transport and movement of nanomaterials within and between various environments through both laboratory investigations and computer modeling; and
• design standard assays to identify the critical properties of nanomaterials that produce toxicological responses in ecosystems and humans.
## Expected Impacts
Technical results produced through this funding are expected to:
• help manufacturers improve efficiency, quality, and durability, while lowering the cost, of third-generation photovoltaics;
• allow industry and U.S. regulatory agencies to accurately assess and manage the risks posed by key nanomaterials and products containing them throughout a full product lifecycle, thus enabling appropriate regulation of their use to minimize harm to people and the environment; and
• provide consumers with accurate information on EHS risks associated with specific products containing nanomaterials.
Back to FY 2011 Budget in Brief>>
Created February 02, 2010, Updated October 05, 2010 | 2016-10-28T21:42:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23793749511241913, "perplexity": 6878.593667237137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988725475.41/warc/CC-MAIN-20161020183845-00086-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10293464 | Robust Estimation of Covariance Matrices: Adversarial Contamination and Beyond
Abstract: We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when d is large compared to n but the covariance matrix $\Sigma$ of interest has (exactly or approximately) low rank. We assume that the given sample is (a) $\epsilon$-adversarially corrupted, meaning that $\epsilon$ fraction of the observations could have been replaced by arbitrary vectors, or that (b) the sample is i.i.d. but the underlying distribution is heavy-tailed, meaning that the norm of Y possesses only 4 finite moments. We propose an estimator that is adaptive to the potential low-rank structure of the covariance matrix as well as to the proportion of contaminated data, and admits tight deviation guarantees despite rather weak assumptions on the underlying distribution. Finally, we discuss the algorithms that allow to approximate the proposed estimator in a numerically efficient way.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10293464
Journal Name:
Technical report
ISSN:
0109-1344
1. This paper studies M-estimators with gradient-Lipschitz loss function regularized with convex penalty in linear models with Gaussian design matrix and arbitrary noise distribution. A practical example is the robust M-estimator constructed with the Huber loss and the Elastic-Net penalty and the noise distribution has heavy-tails. Our main contributions are three-fold. (i) We provide general formulae for the derivatives of regularized M-estimators $\hat\beta(y,X)$ where differentiation is taken with respect to both X and y; this reveals a simple differentiability structure shared by all convex regularized M-estimators. (ii) Using these derivatives, we characterize the distribution of the residuals in the intermediate high-dimensional regime where dimension and sample size are of the same order. (iii) Motivated by the distribution of the residuals, we propose a novel adaptive criterion to select tuning parameters of regularized M-estimators. The criterion approximates the out-of-sample error up to an additive constant independent of the estimator, so that minimizing the criterion provides a proxy for minimizing the out-of-sample error. The proposed adaptive criterion does not require the knowledge of the noise distribution or of the covariance of the design. Simulated data confirms the theoretical findings, regarding both the distribution of the residuals and the success of the criterion asmore »
4. The matrix completion problem seeks to recover a $d\times d$ ground truth matrix of low rank $r\ll d$ from observations of its individual elements. Real-world matrix completion is often a huge-scale optimization problem, with $d$ so large that even the simplest full-dimension vector operations with $O(d)$ time complexity become prohibitively expensive. Stochastic gradient descent (SGD) is one of the few algorithms capable of solving matrix completion on a huge scale, and can also naturally handle streaming data over an evolving ground truth. Unfortunately, SGD experiences a dramatic slow-down when the underlying ground truth is ill-conditioned; it requires at least $O(\kappa\log(1/\epsilon))$ iterations to get $\epsilon$-close to ground truth matrix with condition number $\kappa$. In this paper, we propose a preconditioned version of SGD that preserves all the favorable practical qualities of SGD for huge-scale online optimization while also making it agnostic to $\kappa$. For a symmetric ground truth and the Root Mean Square Error (RMSE) loss, we prove that the preconditioned SGD converges to $\epsilon$-accuracy in $O(\log(1/\epsilon))$ iterations, with a rapid linear convergence rate as if the ground truth were perfectly conditioned with $\kappa=1$. In our numerical experiments, we observe a similar acceleration for ill-conditioned matrix completion under the 1-bit cross-entropymore » | 2023-02-03T01:34:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7580140829086304, "perplexity": 363.756545378786}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500041.2/warc/CC-MAIN-20230202232251-20230203022251-00338.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?node=B042&home=sumtabB | ${{\mathit \Lambda}}$ BARYONS($\mathit S$ = $-1$, $\mathit I$ = 0) ${{\mathit \Lambda}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$ INSPIRE search
#### ${{\boldsymbol \Lambda}{(2350)}}$
$I(J^P)$ = $0(9/2^{+})$
DAUM 1968 favors $\mathit J{}^{P} = 7/2{}^{-}$ or ${}^{}9/2{}^{+}$. BRICMAN 1970 favors ${}^{}9/2{}^{+}$. LASINSKI 1971 suggests three states in this region using a Pomeron + resonances model. There are now also three formation experiments from the College de France-Saclay group, DEBELLEFON 1977 , BACCARI 1977 , and DEBELLEFON 1978 , which find ${}^{}9/2{}^{+}$ in energy-dependent partial-wave analyses of ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit \pi}}$ , ${{\mathit \Lambda}}{{\mathit \omega}}$ , and ${{\mathit N}}{{\overline{\mathit K}}}$ .
${{\mathit \Lambda}{(2350)}}$ MASS $2340\text{ to }2370\text{ }(\approx2350)$ MeV
${{\mathit \Lambda}{(2350)}}$ WIDTH $100\text{ to }250\text{ }(\approx150)$ MeV
$\Gamma_{1}$ ${{\mathit N}}{{\overline{\mathit K}}}$ $\sim{}12\%$ 915
$\Gamma_{2}$ ${{\mathit \Sigma}}{{\mathit \pi}}$ $\sim{}10\%$ 867
$\Gamma_{3}$ ${{\mathit \Lambda}}{{\mathit \omega}}$ 686
FOOTNOTES | 2022-01-18T19:07:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7699683308601379, "perplexity": 2786.0092086430377}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00546.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Ajackson.john-david | # zbMATH — the first resource for mathematics
## Jackson, John David
Compute Distance To:
Author ID: jackson.john-david Published as: Jackson, J. D.; Jackson, J. David; Jackson, John; Jackson, John D.; Jackson, John David Homepage: http://www-theory.lbl.gov/jdj/ External Links: Wikidata · GND
Documents Indexed: 26 Publications since 1949, including 7 Books Biographic References: 1 Publication
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#### Co-Authors
7 single-authored 1 Ault, Richard W. 1 Blatt, John M. 1 Burmeister, Edwin 1 Okun, Lev B. 1 Ross, Stephen A. 1 Saba, Richard P.
#### Serials
1 International Journal of Modern Physics A 1 Reviews of Modern Physics 1 Journal of Urban Economics 1 American Journal of Physics 1 Physical Review, II. Series
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#### Fields
4 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)
#### Citations contained in zbMATH
17 Publications have been cited 1,628 times in 1,356 Documents Cited by Year
Classical electrodynamics. Zbl 0114.42903
Jackson, J. D.
1963
Classical electrodynamics. 2nd ed. Zbl 0997.78500
Jackson, John David
1975
Classical electrodynamics. 3rd ed. Zbl 0920.00012
Jackson, John David
1999
On the interpretation of neutron-proton scattering data by the Schwinger variational method. Zbl 0033.32702
Blatt, John M.; Jackson, J. David
1949
Historical roots of gauge invariance. Zbl 1205.81017
Jackson, J. D.; Okun, L. B.
2001
A study of turbulence under conditions of transient flow in a pipe. Zbl 0948.76516
He, S.; Jackson, J. D.
2000
An experimental study of pulsating turbulent flow in a pipe. Zbl 1156.76319
He, S.; Jackson, J. D.
2009
Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection. Zbl 1137.80004
Kim, W. S.; He, S.; Jackson, J. D.
2008
A study of squeezing flow. Zbl 0124.19703
Jackson, J. D.
1962
On the use of the complete interaction Hamiltonian in atomic rearrangement collisions. Zbl 0077.23205
Jackson, J. D.
1957
Polarization effects following beta decay. Zbl 0079.21004
Frauenfelder, H.; Jackson, J. D.; Wyld, H. W. jun.
1958
Mathematics for quantum mechanics. An introductory survey of operators, eigenvalues, and linear vector spaces. Unabridged republication of the 1962 edition. Zbl 1118.47001
Jackson, John David
2006
On the equivalence of different treatments of two-body final-state interactions. Zbl 0118.44903
Jackson, J. D.
1962
Mathematics for quantum mechanics. An introductory survey of operators, eigenvalues, and linear vector spaces. Zbl 0115.43902
Jackson, John David
1962
Criticism of “Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics” by Chubykalo and Vlaev. Zbl 1015.78009
Jackson, J. D.
2002
Osborne Reynolds: Scientist, engineer and pioneer. Zbl 0861.01033
Jackson, J. D.
1995
Note on relativistic coulomb wave functions. Zbl 0083.44304
Jackson, J. D.; Treiman, S. B.; Wyld, H. W. jun.
1958
An experimental study of pulsating turbulent flow in a pipe. Zbl 1156.76319
He, S.; Jackson, J. D.
2009
Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection. Zbl 1137.80004
Kim, W. S.; He, S.; Jackson, J. D.
2008
Mathematics for quantum mechanics. An introductory survey of operators, eigenvalues, and linear vector spaces. Unabridged republication of the 1962 edition. Zbl 1118.47001
Jackson, John David
2006
Criticism of “Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics” by Chubykalo and Vlaev. Zbl 1015.78009
Jackson, J. D.
2002
Historical roots of gauge invariance. Zbl 1205.81017
Jackson, J. D.; Okun, L. B.
2001
A study of turbulence under conditions of transient flow in a pipe. Zbl 0948.76516
He, S.; Jackson, J. D.
2000
Classical electrodynamics. 3rd ed. Zbl 0920.00012
Jackson, John David
1999
Osborne Reynolds: Scientist, engineer and pioneer. Zbl 0861.01033
Jackson, J. D.
1995
Classical electrodynamics. 2nd ed. Zbl 0997.78500
Jackson, John David
1975
Classical electrodynamics. Zbl 0114.42903
Jackson, J. D.
1963
A study of squeezing flow. Zbl 0124.19703
Jackson, J. D.
1962
On the equivalence of different treatments of two-body final-state interactions. Zbl 0118.44903
Jackson, J. D.
1962
Mathematics for quantum mechanics. An introductory survey of operators, eigenvalues, and linear vector spaces. Zbl 0115.43902
Jackson, John David
1962
Polarization effects following beta decay. Zbl 0079.21004
Frauenfelder, H.; Jackson, J. D.; Wyld, H. W. jun.
1958
Note on relativistic coulomb wave functions. Zbl 0083.44304
Jackson, J. D.; Treiman, S. B.; Wyld, H. W. jun.
1958
On the use of the complete interaction Hamiltonian in atomic rearrangement collisions. Zbl 0077.23205
Jackson, J. D.
1957
On the interpretation of neutron-proton scattering data by the Schwinger variational method. Zbl 0033.32702
Blatt, John M.; Jackson, J. David
1949
all top 5
#### Cited by 2,396 Authors
14 Greengard, Leslie F. 9 Zohdi, Tarek I. 7 Figotin, Alexander 7 He, Shuisheng 7 Kholmetskii, Alexander L. 7 Papageorgiou, Demetrios T. 6 Babin, Anatoli V. 6 Horwitz, Lawrence Paul 6 Lazar, Markus 6 Mostafazadeh, Ali 6 Müller, Wolfgang H. 6 Peralta-Salas, Daniel 6 Pitts, J. Brian 6 Reich, Felix A. 6 Singleton, Douglas A. 6 Vanden-Broeck, Jean-Marc 5 Chacón, Luis 5 de Lange, O. L. 5 D’Eath, Peter D. 5 Farley, A. N. St J. 5 Kopeikin, Sergei M. 5 Lin, Shihyuin 5 Missevitch, Oleg V. 5 Raab, R. E. 5 Seddighi, Mehdi 5 Vardy, Alan E. 5 Yarman, Tolga 4 Aluru, Narayana R. 4 Amirat, Youcef Aït 4 Arora, Kasturi L. 4 Blyth, Mark G. 4 Cai, Wei 4 De Nittis, Giuseppe 4 Deng, Shaozhong 4 Ellis, George Francis Rayner 4 Feshbach, Herman 4 Friedberg, Richard M. 4 Frisch, Mathias 4 Gascón, Francisco G. 4 Grandison, Scott 4 Hansen, Thorkild B. 4 Hehl, Friedrich W. 4 Heras, José A. 4 Lambiase, Gaetano 4 Lein, Max 4 Liu, Liping 4 Manassah, Jamal T. 4 Rubinow, Sol I. 4 Schöps, Sebastian 3 Aharonovich, Igal 3 Amooshahi, Majid 3 Ariyaratne, C. 3 Athanasiadis, Christodoulos E. 3 Banks, Harvey Thomas 3 Barnett, Alex H. 3 Bethe, Hans Albrecht 3 Bičák, Jiří 3 Cheng, Hongwei 3 Cohen, Leon W. 3 Davidson, Mark P. 3 De Luca, Jayme 3 Dragnev, Peter D. 3 Eggers, Jens G. 3 Eriksen, Erik 3 Esposito, Giampiero 3 Exl, Lukas 3 França, Humberto M. 3 Furtado, Claudio 3 Gao, Hao 3 Gimbutas, Zydrunas 3 Gogberashvili, Merab 3 Gratus, Jonathan 3 Grøn, Øyvind Geelmuyden 3 Grote, Marcus J. 3 Hsiang, Jen-Tsung 3 Itin, Yakov 3 Ivezić, Tomislav 3 James, Richard D. 3 Jiang, Shidong 3 Jung, Young-Dae 3 Kansu, Mustafa Emre 3 Knoll, Dana A. 3 Kushch, Volodymyr I. 3 Lawley, Sean D. 3 Lee, Dashin 3 Lee, June-Yub 3 Mavraganis, A. G. 3 Milton, Graeme Walter 3 Munz, Claus-Dieter 3 Nguyen, Hoai-Minh 3 O’Neil, Michael 3 Pérez-Aparicio, José L. 3 Petropoulos, Peter G. 3 Pietsch, Wolfgang 3 Power, Henry 3 Rapetti, Francesca 3 Salpeter, Edwin E. 3 Sanchez, Clemente Cobos 3 Saravanan, Moorthi 3 Sarisaman, Mustafa ...and 2,296 more Authors
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#### Cited in 208 Serials
128 Journal of Computational Physics 85 Physics Letters. A 80 Annals of Physics 55 Physical Review, II. Series 52 Journal of Mathematical Physics 41 General Relativity and Gravitation 37 International Journal of Theoretical Physics 32 Foundations of Physics 27 Computer Physics Communications 26 Wave Motion 23 International Journal of Modern Physics A 22 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 21 Computer Methods in Applied Mechanics and Engineering 21 Physics Letters. B 21 Engineering Analysis with Boundary Elements 19 International Journal of Engineering Science 18 Nuclear Physics. B 18 Physica D 17 Modern Physics Letters A 17 Journal of Mathematical Analysis and Applications 16 Physics Reports 15 Journal of Fluid Mechanics 14 International Journal of Modern Physics D 13 Astrophysics and Space Science 13 Journal of the Mechanics and Physics of Solids 13 Reports on Mathematical Physics 12 Journal of Statistical Physics 12 Journal of Computational and Applied Mathematics 11 International Journal of Modern Physics B 11 Applied Mathematics and Computation 11 Journal of Modern Optics 10 Journal of Engineering Mathematics 10 Physics of Fluids 9 Applied Numerical Mathematics 9 Journal of High Energy Physics 9 International Journal of Geometric Methods in Modern Physics 8 European Journal of Physics 8 Continuum Mechanics and Thermodynamics 8 Communications in Nonlinear Science and Numerical Simulation 7 Mathematical Biosciences 7 Physics of Fluids 7 Mathematical and Computer Modelling 7 Applied Mathematical Modelling 6 Modern Physics Letters B 6 Archive for Rational Mechanics and Analysis 6 Computers and Fluids 6 Communications in Mathematical Physics 6 Applied Mathematics Letters 6 Journal of Scientific Computing 6 European Journal of Mechanics. B. Fluids 6 Il Nuovo Cimento, X. Series 5 Acta Mechanica 5 Computers & Mathematics with Applications 5 International Journal of Heat and Mass Transfer 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 International Journal for Numerical Methods in Engineering 5 Mathematics and Computers in Simulation 5 Neural Computation 5 European Journal of Mechanics. A. Solids 5 International Journal of Quantum Information 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Mathematics of Computation 4 Journal of Geometry and Physics 4 Journal of Differential Equations 4 Numerische Mathematik 4 COMPEL 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Linear Algebra and its Applications 4 Journal of Nonlinear Science 4 SIAM Journal on Scientific Computing 4 Advances in Applied Clifford Algebras 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Nonlinear Analysis. Real World Applications 4 Advances in High Energy Physics 3 Letters in Mathematical Physics 3 Physica A 3 Reviews of Modern Physics 3 SIAM Journal on Numerical Analysis 3 Communications in Partial Differential Equations 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 SIAM Journal on Applied Mathematics 3 Archive of Applied Mechanics 3 Mathematics and Mechanics of Solids 3 Multiscale Modeling & Simulation 3 Foundations of Physics Letters 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Advances in Mathematical Physics 3 Journal of Theoretical Biology 2 Archive for History of Exact Sciences 2 Biological Cybernetics 2 International Journal of Solids and Structures 2 Mathematical Methods in the Applied Sciences 2 Theoretical and Mathematical Physics 2 Transport Theory and Statistical Physics 2 BIT 2 Information Sciences 2 Mechanics Research Communications 2 Quarterly of Applied Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 SIAM Journal on Control and Optimization ...and 108 more Serials
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#### Cited in 54 Fields
502 Optics, electromagnetic theory (78-XX) 297 Quantum theory (81-XX) 239 Partial differential equations (35-XX) 221 Fluid mechanics (76-XX) 205 Relativity and gravitational theory (83-XX) 186 Numerical analysis (65-XX) 110 Statistical mechanics, structure of matter (82-XX) 98 Mechanics of deformable solids (74-XX) 72 Mechanics of particles and systems (70-XX) 53 Biology and other natural sciences (92-XX) 38 Astronomy and astrophysics (85-XX) 35 Differential geometry (53-XX) 28 Classical thermodynamics, heat transfer (80-XX) 27 Ordinary differential equations (34-XX) 22 Dynamical systems and ergodic theory (37-XX) 20 General and overarching topics; collections (00-XX) 19 Probability theory and stochastic processes (60-XX) 18 Special functions (33-XX) 16 Global analysis, analysis on manifolds (58-XX) 14 History and biography (01-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 13 Potential theory (31-XX) 13 Integral equations (45-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 13 Information and communication theory, circuits (94-XX) 12 Operator theory (47-XX) 10 Approximations and expansions (41-XX) 10 Computer science (68-XX) 8 Integral transforms, operational calculus (44-XX) 8 Systems theory; control (93-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Geophysics (86-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Mathematical logic and foundations (03-XX) 5 Number theory (11-XX) 5 Functions of a complex variable (30-XX) 5 Functional analysis (46-XX) 5 Operations research, mathematical programming (90-XX) 4 Real functions (26-XX) 4 Statistics (62-XX) 3 Algebraic geometry (14-XX) 3 Group theory and generalizations (20-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Abstract harmonic analysis (43-XX) 3 Mathematics education (97-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Measure and integration (28-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-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. | 2021-02-26T04:58:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3781365752220154, "perplexity": 6190.810932949326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178356140.5/warc/CC-MAIN-20210226030728-20210226060728-00429.warc.gz"} |
http://www.legisquebec.gouv.qc.ca/en/showversion/cs/E-20.001?code=se:118_40&pointInTime=20201126 | E-20.001 - Act respecting the exercise of certain municipal powers in certain urban agglomerations
118.40. Section 115.1 is amended
(1) by replacing subparagraph 1 of the first paragraph by the following subparagraph:
(1) is required under section 118.29;”;
(2) by replacing the third paragraph by the following paragraph:
The possibility that an overpayment of an aliquot share referred to in section 118.27 be used to reduce an aliquot share determined for the following fiscal year is one way of managing the resolutory effects of a refusal.”.
2007, c. 33, s. 9. | 2021-03-08T06:13:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9195433855056763, "perplexity": 5961.399947539583}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381989.92/warc/CC-MAIN-20210308052217-20210308082217-00208.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?node=S053&home=sumtabB | CHARMED BARYONS($\boldsymbol C$ = $+1$) ${{\mathit \Lambda}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit d}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit d}}{{\mathit c}}$ , ${{\mathit \Sigma}_{{c}}^{0}}$ = ${{\mathit d}}{{\mathit d}}{{\mathit c}}$ ,${{\mathit \Xi}_{{c}}^{+}}$ = ${{\mathit u}}{{\mathit s}}{{\mathit c}}$ , ${{\mathit \Xi}_{{c}}^{0}}$ = ${{\mathit d}}{{\mathit s}}{{\mathit c}}$ , ${{\mathit \Omega}_{{c}}^{0}}$ = ${{\mathit s}}{{\mathit s}}{{\mathit c}}$ INSPIRE search
# ${{\boldsymbol \Omega}_{{c}}{(2770)}^{0}}$ $I(J^P)$ = $0(3/2^{+})$
The natural assignment is that this goes with the ${{\mathit \Sigma}_{{c}}{(2520)}}$ and ${{\mathit \Xi}_{{c}}{(2645)}}$ to complete the lowest mass $\mathit J{}^{P}$ = ${}^{}3/2{}^{+}$ SU(3) sextet, part of the SU(4) 20-plet that includes the ${{\mathit \Delta}{(1232)}}$. But $\mathit J$ and ${}^{P}$ have not been measured.
${{\mathit \Omega}_{{c}}{(2770)}^{0}}$ MASS $2765.9 \pm2.0$ MeV (S = 1.2)
${{\mathit \Omega}_{{c}}{(2770)}^{0}}–{{\mathit \Omega}_{{c}}^{0}}$ MASS DIFFERENCE $70.7 {}^{+0.8}_{-0.9}$ MeV
The ${{\mathit \Omega}_{{c}}{(2770)}^{0}}-{{\mathit \Omega}_{{c}}^{0}}$ mass difference is too small for any strong decay to occur. | 2021-02-28T20:10:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7090216875076294, "perplexity": 256.372659788767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361723.15/warc/CC-MAIN-20210228175250-20210228205250-00451.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S018DM&home=sumtabB | # (${\boldsymbol m}_{{{\boldsymbol \Lambda}}}–{\boldsymbol m}_{{{\overline{\boldsymbol \Lambda}}}}$) $/$ ${\boldsymbol m}_{{{\boldsymbol \Lambda}}}$ INSPIRE search
A test of $\mathit CPT$ invariance.
VALUE ($10^{-5}$) EVTS DOCUMENT ID TECN COMMENT
$\bf{ -0.1 \pm1.1}$ OUR AVERAGE Error includes scale factor of 1.6.
$+1.3$ $\pm1.2$ 31k 1
1996
NA32 ${{\mathit \pi}^{-}}{}^{}\mathrm {Cu}$, 230 GeV
$-1.08$ $\pm0.90$
1994
SPEC ${{\mathit p}}{{\mathit p}}$ $27.5$ ${\mathrm {GeV/}}\mathit c$
$4.5$ $\pm5.4$
1966
HBC 6.9 ${\mathrm {GeV/}}\mathit c$ ${{\overline{\mathit p}}}{{\mathit p}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-26$ $\pm13$
1967
HBC 2.4 ${\mathrm {GeV/}}\mathit c$ ${{\overline{\mathit p}}}{{\mathit p}}$
1 RYBICKI 1996 is an analysis of old ACCMOR (NA32) data.
Conservation Laws:
$\mathit CPT$ INVARIANCE
References:
RYBICKI 1996
APP B27 2155 Measurement of ${{\mathit \Lambda}}{{\overline{\mathit \Lambda}}}$ Mass Difference
HARTOUNI 1994
PRL 72 1322 Precise Measurement of the ${{\mathit \Lambda}^{0}}$ and ${{\overline{\mathit \Lambda}}^{0}}$ Masses and a Test of $\mathit CPT$ Invariance
PL 25B 152 Reactions ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\overline{\mathit \Lambda}}}{{\mathit \Lambda}}$ at 2.5 ${\mathrm {GeV/}}\mathit c$
PR 152 1171 Hyperon and Antihyperon Production in ${{\overline{\mathit p}}}{{\mathit p}}$ Collisions at 7 ${\mathrm {GeV/}}\mathit c$ | 2021-03-03T09:32:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7836846709251404, "perplexity": 11896.064775680861}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178366477.52/warc/CC-MAIN-20210303073439-20210303103439-00126.warc.gz"} |
https://par.nsf.gov/biblio/10311659-dynamics-signature-based-anomaly-detection | This content will become publicly available on November 15, 2022
Dynamics signature based anomaly detection
Identifying anomalies, especially weak anomalies in constantly changing targets, is more difficult than in stable targets. In this article, we borrow the dynamics metrics and propose the concept of dynamics signature (DS) in multi-dimensional feature space to efficiently distinguish the abnormal event from the normal behaviors of a variable star. The corresponding dynamics criterion is proposed to check whether a star's current state is an anomaly. Based on the proposed concept of DS, we develop a highly optimized DS algorithm that can automatically detect anomalies from millions of stars' high cadence sky survey data in real-time. Microlensing, which is a typical anomaly in astronomical observation, is used to evaluate the proposed DS algorithm. Two datasets, parameterized sinusoidal dataset containing 262,440 light curves and real variable stars based dataset containing 462,996 light curves are used to evaluate the practical performance of the proposed DS algorithm. Experimental results show that our DS algorithm is highly accurate, sensitive to detecting weak microlensing events at very early stages, and fast enough to process 176,000 stars in less than 1 s on a commodity computer.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10311659
Journal Name:
Software: Practice and Experience
ISSN:
0038-0644
4. ABSTRACT We explore the synergy between photometric and spectroscopic surveys by searching for periodic variable stars among the targets observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) using photometry from the All-Sky Automated Survey for Supernovae (ASAS-SN). We identified 1924 periodic variables among more than $258\, 000$ APOGEE targets; 465 are new discoveries. We homogeneously classified 430 eclipsing and ellipsoidal binaries, 139 classical pulsators (Cepheids, RR Lyrae, and δ Scuti), 719 long-period variables (pulsating red giants), and 636 rotational variables. The search was performed using both visual inspection and machine learning techniques. The light curves were also modelled with the damped random walk stochastic process. We find that the median [Fe/H] of variable objects is lower by 0.3 dex than that of the overall APOGEE sample. Eclipsing binaries and ellipsoidal variables are shifted to a lower median [Fe/H] by 0.2 dex. Eclipsing binaries and rotational variables exhibit significantly broader spectral lines than the rest of the sample. We make ASAS-SN light curves for all the APOGEE stars publicly available and provide parameters for the variable objects. | 2022-10-04T23:13:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2833751440048218, "perplexity": 2607.8148048444923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00173.warc.gz"} |
http://dlmf.nist.gov/28.29 | # §28.29 Definitions and Basic Properties
## §28.29(i) Hill’s Equation
A generalization of Mathieu’s equation (28.2.1) is Hill’s equation
with
28.29.2
and
is either a continuous and real-valued function for or an analytic function of in a doubly-infinite open strip that contains the real axis. is the minimum period of .
## §28.29(ii) Floquet’s Theorem and the Characteristic Exponent
Let be a real or complex constant satisfying (without loss of generality)
28.29.6
throughout this section. Then (28.29.1) has a nontrivial solution with the pseudoperiodic property
iff is an eigenvalue of the matrix
Equivalently,
This is the characteristic equation of (28.29.1), and is an entire function of . Given together with the condition (28.29.6), the solutions of (28.29.9) are the characteristic exponents of (28.29.1). A solution satisfying (28.29.7) is called a Floquet solution with respect to (or Floquet solution). It has the form
28.29.10
where the function is -periodic.
If is a solution of (28.29.9), then , comprise a fundamental pair of solutions of Hill’s equation.
If or 1, then (28.29.1) has a nontrivial solution which is periodic with period (when ) or (when ). Let be a solution linearly independent of . Then
where is a constant. The case is equivalent to
The solutions of period or are exceptional in the following sense. If (28.29.1) has a periodic solution with minimum period , , then all solutions are periodic with period .
Furthermore, for each solution of (28.29.1)
A nontrivial solution is either a Floquet solution with respect to , or is a Floquet solution with respect to .
In the symmetric case , is an even solution and is an odd solution; compare §28.2(ii). (28.29.9) reduces to
The cases and split into four subcases as in (28.2.21) and (28.2.22). The -periodic or -antiperiodic solutions are multiples of , respectively.
For details and proofs see Magnus and Winkler (1966, §1.3).
## §28.29(iii) Discriminant and Eigenvalues in the Real Case
is assumed to be real-valued throughout this subsection.
The function
is called the discriminant of (28.29.1). It is an entire function of . Its order of growth for is exactly ; see Magnus and Winkler (1966, Chapter II, pp. 19–28).
For a given , the characteristic equation has infinitely many roots . Conversely, for a given , the value of is needed for the computation of . For this purpose the discriminant can be expressed as an infinite determinant involving the Fourier coefficients of ; see Magnus and Winkler (1966, §2.3, pp. 28–36).
To every equation (28.29.1), there belong two increasing infinite sequences of real eigenvalues:
28.29.16
28.29.17
In consequence, (28.29.1) has a solution of period iff , and a solution of period iff . Both and as , and interlace according to the inequalities
28.29.18
Assume that the second derivative of in (28.29.1) exists and is continuous. Then with
we have for
28.29.20
28.29.21
If has continuous derivatives, then as | 2013-05-20T16:21:11 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9626051783561707, "perplexity": 1200.532543116778}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699068791/warc/CC-MAIN-20130516101108-00044-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://repo.scoap3.org/record/30211 | Exotic $bc\overline{q}\overline{q}$ four-quark states
Caramés, T. F. (Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, 37008 Salamanca, Spain) ; Vijande, J. (Unidad Mixta de Investigación en Radiofísica e Instrumentación Nuclear en Medicina (IRIMED), Instituto de Investigación Sanitaria La Fe (IIS-La Fe)-Universitat de Valencia (UV) and IFIC (UV-CSIC), 46100 Valencia, Spain) ; Valcarce, A. (Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, 37008 Salamanca, Spain)
11 January 2019
Abstract: We carry out a systematic study of exotic $Q{Q}^{\prime }\overline{q}\overline{q}$ four-quark states containing distinguishable heavy flavors, $b$ and $c$. Different generic constituent models are explored in an attempt to extract general conclusions. The results are robust, predicting the same sets of quantum numbers as the best candidates to lodge bound states independently of the model used, the isoscalar ${J}^{P}={0}^{+}$ and ${J}^{P}={1}^{+}$ states. The first state would be strong and electromagnetic-interaction stable, while the second would decay electromagnetically to $\overline{B}D\gamma$. Isovector states are found to be unbound, preventing the existence of charged partners. The interest on exotic heavy-light tetraquarks with nonidentical heavy flavors comes reinforced by the recent estimation of the production rate of the isoscalar $bc\overline{u}\overline{d}$ ${J}^{P}={1}^{+}$ state, 2 orders of magnitude larger than that of the $bb\overline{u}\overline{d}$ analogous state.
Published in: Physical Review D 99 (2019)
Published by: APS
DOI: 10.1103/PhysRevD.99.014006
arXiv: 1812.08991
License: CC-BY-4.0
Fulltext:
XML PDF | 2019-01-17T19:09:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4071284830570221, "perplexity": 8641.926905240834}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659063.33/warc/CC-MAIN-20190117184304-20190117210304-00287.warc.gz"} |
https://seikai.fandom.com/wiki/Planar_Space | ## FANDOM
157 Pages
Planar Space is a term referring to a universe through which ships travel from star system to star system. It is the current means for interstellar travel for the Humankind Empire of Abh and the Four Nations Alliance to control and travel the Milkyway Galaxy.
## Normal SpaceEdit
Normal Space is a term referring to four dimensional space-time with Einsteinian Relativity. For centuries, travel trough normal space has been a dangerous, tedious, and long term adventure for humans.
## Plane SpaceEdit
Plane Space is a term referring to an alternate universe with two spatial dimensions and one time dimension. It has different laws of physics than normal space. It connects vast distances in Normal Space with far less space and time traveled. Natural access to Plane Space is possible through Sords or Gates. Matter that enters a Sord from Normal Space is transformed into Space-Time particles without an artificial space-time field to protect them (Supflasath). Traveling ships need a space-time generator to create the necessary artificial space-time field/bubble encasing the ship to protect it. Space-Time particles that exit a Sord from Plane Space are released as visible energy. The stream of matter or space time particles is determine by the vacuum pressure within Normal Space. A Sord that is close to a star will be under the solar pressure of the star and receive more matter from the solar wind. Sords that are near the galactic center receive the high pressure of young stars and the galactic pressure waves leading to a constant stream from those Sords. These 'volcano' Sords are known as Kiigaf. Because of the high streams of these Sords the galactic center are near impossible to navigate. The streams of space-time particle act as a fluid in plane space and create friction to traveling ships. Therefore, these streams are displayed as density gradients which make Sords look like hills or valleys just like high or low pressure zones on a weather map. The gradients also indicate the direction of flow. A ship traveling through plane space 'displaces' or disturbs the space-time particle sea which send out mass waves (Sesuwas) detectable by sensors. Mass waves travel indefinitely through Plane Space. The frequencies and wavelengths of mass waves are fixed in Plane Space; they overlapped and created unavoidable interference. Sending Space-Time particle is the only effective means of communication. However, transmission speed is slow and has very limited range. For distance communication, communication boats or ships are necessary.
The common measurement for distances is the Imperial nautical mile Cédlairh and the Imperial knot Dirgh. One Cédlairh is defined as the distance a space-time bubble with a mass of 100 tons travels in perfect motion in one second of plane-space time. One Dirgh is the velocity at which it is possible to travel one Cédlairh in one hour of plane-space time.
A Pelia can travel six thousand Cédlairh in about five hours. A slow supply vessel (Isath) could cover that distance in about seventy hours.
## HistoryEdit
The theoretical work for plane space was first published by Nadia Hudini (ナディア・フーディニ) for a mathematical lecture. Through trade during the Wandering Age, the Abh gained access to the Hudini theory. Bibo Suryumune, a specialized scientist in stellar evolution, became aware of the theory, and discovered the possibility of plane-space navigation, including the research. After a long period of research and experimentation, the Abh were finally able to create an artificial space-time field generator which allowed travel through plane space. Independently, human people from Midgrat (now Dakufo) in the Suumei system developed their own plane space technology shortly before the Abh. The Midgratians happily sold their technology for a price to various human colonies.
## Yuanon particleEdit
After a long time of sending ships into space, a research vessel named the Oort Cloud [1]discovered a mysterious particle approximately three-tenths of a lightyear from the sun. It was only about a thousand times the mass of a proton, but radiated nearly five hundred megawatts of energy. It was hypothized as a "white hole" or "null space" or "hyperspace." Scientists named them Yuanons. Then for a long time these rare and precious particles were used as the heart of interstellar ships to explore distant system ad colonized them. It was only later that they were discovered to be the state of a "closed Sord" (Sord Loeza). The yuanon particle is a low energy state of a Sord.
## Space-Time particleEdit
A space-time particle is the state of matter within plane-space. As plane-space does not support the third dimension, all matter entering plane-space is reduced to this state. Technically it is not a particle. (It does have a mass, though.) When it leaves plane space and come into normal space, it is transformed to a four-dimensional space-time particles about the size of an electron.
Space-time particle roam plane-space from a high density area to a lower density area. In practice this means from a spewing geyser Sord to a sinkhole Sord.
A stream or current of space-time particle causes resistance to ships moving in reverse direction, while imparting some relative velocity in the other direction.
## SordEdit
A Sord is the second form of the yuanon particle. It is also called an "open Sord" (Sord Gulark). As a Sord allow ships to transit into plane-space it also referred as a gate. It has the appearance of a phosphorescent, and spherical singularity space with a size of one SeDagh(1000 km) in diameter. Left alone a Sord can loose enough energy to become a closed Sord within twelve years.
A transit through a Sord is dangerous in that the difference of dimensions causes ships to appear at a random position around the Sord on the other side. As the sole access point to plane-space or normal space a Sord is a military asset of high value. As communication and sensors are limited a transit can be a dangerous task for military ships.
### Sord RingsEdit
There are approximately thirty billion Sords all existed in the Milky Way Galaxy (Elukufa). However, their position in normal space do not to the plane-space sides of the Sord.
In normal space, the Sord are scattered in a ripple-like formation: a central cluster surrounded by numerous rings (Speish) that increased in size away from the center. The gap between the central cluster and the first ring (Speish Kasna) was slightly smaller than the gap between the first and second ring (Speish Mata). Gaps and rings alternated, making up the basic structure of the Milky Way Sord Group (Sordlash Elukufar).
The number of gates in each ring was the same, so the Sord are farther apart in the outer rings than they are in the inner rings.
Most of the Sord that humanity used existed in the relatively crowded Central Territory (Sorl Bandak), which form seven of the rings. Many of these Sord led to central plane-space locations, enabling explorers to exit plane-space through different Sord and come out in completely different ripples of the Milky Way galaxy.
From the eighth to the eleventh ring, the Sords were scattered far from each other, such that they are regarded as Unexplored Territory (Sorl Geiraza).
Of the eight Imperial Kingdom, seven lay in the central territory. Only Sord Ilysr led to the outer reaches, where Sord were harder to come by.
The Abh viewed their single-frontier Sord as an opportunity, using it to take control of the twelfth ring (Speish Lomata) and establish military bases to prevent others from using Speish Lomata's Sord.
The Ilysr Kingdom was also known as "Arms of the Abh" as it surrounds the Milky Way Sord Group.
At the outer edge of the twelfth ring there was an anomalistic cluster of Sord which, it was widely believed, led to an entirely different galaxy. As long as the Empire had Ilysr Kingdom, no other nations could access those gates, and so only the Empire would be able to reach the other galaxy.
## Space-Time GeneratorEdit
A space-time generator is essential for a ship to travel and survive within plane space. A space-time generator creates a three dimensional space-time bubble around the ship which protects as well as serves as a means of propulsion and communication.
Space-time generator technology is currently the only known technology for faster than light interstellar travel. There are two distinct lines of technology:
• Abh
• Sumei
The technology revolutionized interstellar travel for humans for the past thousand years. Until then humans traveled for a long time in generation ships through normal space under Einstein relativity. The space-time generator technology is still one of the most guarded secrets of their owners and operators.
## Space-Time BubbleEdit
A space-time bubble is the artificial three-dimensional space created by a space-time generator. It is a safe haven for ships.
As the space-time bubble is fixed due to the generator within the ship so is the space it represents. Non-moving objects within the bubble will not change their relative position to the ship.
As mass is a direct transdimensional property it plays an important role for a space-time bubble. The bubble's "size" in plane-space is fixed by the mass within the bubble. This affects the resistance and velocity within plane-space.
The space-time bubble is always in constant rotation. If its axis of rotation was perpendicular to the floor, then it would remain stationary, but if the bubble rotated around an axis parallel to the floor, then it would roll. A rolling bubble was called Noktaf, and a stationary bubble was called Skobrotaf.
Any adjustments to travel speed had to come from adjusting the angle of the axis of rotation. Similarly changing direction can be achieved by turning the ship.
When two space-time bubble meet in order to occupy the same space, this is called merging. When two or more ships gather in one and the same bubble, only one ship is needed to maintain the bubble. This allows a group of ships to save fuel. The merging causes a visible illuminating effect. Due to the nature of plane-space ships emerge at random altitude when merging.
When ships within a group generate their own bubble and disperse, the separation is simply called separating. The mode by which ships travel by themselves is termed as moving in single bubbles.
By emitting space-time particles a space-time bubble can serve as a means of limited communication within plane-space.
## Plane Space AnalyzedEdit
### FactsEdit
• Fact 1
“ To an outside observer, a Flasath looked like a single rotating particle. Noktaf and Skobrotaf described the direction of a Flasath's revolution. Every Sazoirl needed to know that in order to enroll. Jinto remembered learning that a Flasath in Fath was like a ball spinning on the floor. If its axis of rotation was perpendicular to the floor, then it would remain stationary, but if the ball rotated around an axis parallel to the floor, then it would roll. A rolling ball was Noktaf, and a stationary ball was Skobrotaf. Now, the Flasath's rotational speed was constant, so any adjustments to travel speed had to come from adjusting the angle of the axis of rotation. ”
• Fact 2
“ "One hundred twenty confirmed Flasath, with a total mass of about ninety Zesabo. That's comparable to four Jadbyr." There were a number of Sord, winding black coils, lurking in the vicinity of the ship, which appeared as a blinking blue dot. Due to their constant energy emissions, Sord and solar winds repelled each other. This, in conjunction with the gate's relatively small mass in normal space, meant that they were generally located on the outskirts of star systems. However, Sord on the other side of the event horizon took in more energy than they gave off. In these cases, for the majority of Sord, the energy flowed from Fath to Dath. The Abh name for these special eruptive Sord was Kiigaf. Kiigaf were like volcanoes that continuously spewed space-time particles (Supflasath) from Plane Space into Dath. When they went from Plane Space to normal space, Supflasath were reduced to four-dimensional space-time particles about the size of an electron. Flasath absorbed Supflasath, reacted with them, and then ejected a much greater quantity of Supflasath. The byproduct of these reactions was an enormous amount of energy, which was the fuel that propelled the first Yuanon-powered ships. Flasath also emitted mass waves (Sesuwas) that could be detected from very far away. The unidentified objects on the Gosroth's radar were undeniably Flasath. Unfortunately, the laws of physics prohibited that kind of communication in Fath. The frequencies and wavelengths of Sesuwas were fixed in Plane Space. Consequently, they overlapped and created unavoidable interference. Sadly, sending Supflasath was the only effective means of communication between Flasath. However, this space-time bubble's (Drosh Flacteder) transmission speed was unbearably slow and only worked over very short distances. The maximum speed of a Flasath was proportional to its mass. Technological efficiency improvements were not effective, so a Flasath could only be as fast as it was light. Thus, battleships and transport ships were slower than patrol ships. Assault ships, however, were a different story. It was disarmingly clear the group of Flasath that separated intended to seize the Gosroth. Lafiel and Jinto didn't know of the Gosroth's defeat. Even if Sesuwas communications could travel that far, the Pelia's crude instruments wouldn't be able to receive the mass waves. On top of that, there was a Sord in the way. ”
• Fact 4
“ Space-time particles (Supflasath) continually flowed outward from the central, high-density area of Sordlash Elukufar. Eventually, these Supflasath collided with those erupting from the space-time volcanoes (Kiigaf) near Sord Sufagnaum in Speish Lomata. It would be difficult for Labule Flasath to enter that high-activity area, especially if they had to dodge mines. Thus, that area was this battle's high ground. Naturally, there was a large number of enemy Flasath congregating there, in the ideal position to defend Sord Sufagnaum. ”
• Fact 5
“ The Abh were relieved; Iliish Kingdom and its Sord were a mere six thousand Gedolel from Loebhynu Suf agnaum. A Pelia could rip through six thousand Gedolel in about five hours. Even something as slow as an Isath could cover that distance in about seventy hours. ”
• Fact 6
“ "Guessing from the mass here, we're dealing with three half fleets. Not much at all." Trife smiled; he'd expected much more opposition than that. ”
• Fact 7
“ Naturally, Plane Space, which is governed by different laws of physics than normal space, requires a different system of measurements. In Plane Space, the common measurement is the Imperial nautical mile (Kedlairl) and the Imperial knot (Digrl). One Kedlairl is defined as "the distance a space-time with a mass of one Seboh (100 tons) in perfect motion travels in one second of Flasath time." The Digrl is "the speed at which it is possible to travel one Kedlairl in one hour of Flasath time." ”
• Fact 8
“ Some of the enemy Hoksath were coerced into reluctant Gor Putarloth. When the time-space bubbles fused, the mines exploded, throwing out large quantities of time-space particles (Supflasath). Plane Space (Fath) rippled like the surface of a pond, as large waves of Supflasath spread outward in rings, shaking nearby Flasath. ”
• Fact 9
“ At that time, one Flasath held the whole half fleet. In sequence, the battleships separated from the main time-space bubble, in their own individual Flasath. Accelerating one point seven three times faster than the rest of the fleet, they fell into a vertical formation. ”
• Fact 0
### AnalysisEdit
Despite all the facts given we don't know anything about how to derive to speed or the size of the space-time bubbles. It appears things were developed over time and novel books, hence, the facts are not quite consistent. It also appears Morioka isn't well versed in math or physics, hence, the facts are also messed up. There is a possibility of faulty Tokyopop translation, not to mention that it's abridged, but these facts mostly agree with fan translations.
#### CommunicationEdit
Fact 2 says mass waves travel very far. Fan translation actually say there's no limit to distance. Practical communication distance is limited by the quality of the transmission. As the waves interact with other waves, the longer the distance the more broken up is the original wave e.g. noise. Therefore, communication distance is further in less sord active or calm areas. Fact 2 & Fact 8 states raging battle cause chaos with Supflasath, hence, communication with Supflasath between Flasath becomes less effective.
#### Speed of shipsEdit
Fact 1 & Fact 2 support each other by saying mass is the deciding factor in a ship's speed, and that it's proportional. We don't know whether it's linear or exponential or inverted proportional.
Fact 4 says that Supflasath are the resistance acting factor.
Fact 7 established the measurement system.
Fact 5 is supposed to tell the reader two things.
• a rough distance measure of a part of the galaxy in plane space
• a comparision of ships and speeds
However, it's an utterly mess if both point of views are combined.
• The Pelia Lafiel and Jinto used needed two days (Keishu to Febdash) to traverse what appears to be 20 degrees of circumference on the 12th Sord ring. Yet it says what appears to be 80 degrees of circumference is 6000 Kedlairl/Gedolel(K) and can be traversed in 5 hours.
Here, it seems there a mess of distance and time. It is reasonable to believe it would take a day for every 10 degrees of cicumferance otherwise a Pelia could travel around the galaxy in just 22.5 hours. The speeds given would become false.
It's also reasonable to believe a Pelia does insdeed travel 6000 Kedlairl in 5 hours. Fact 5 & Fact 7 Here a mine would be comparable to a missile (3600K/h) while a Pelia would equal a fighter jet (1200K/h). However, the distance given for Sugfugnoff and Ilysr Sord would be false.
• If speed and mass are linear proportional then supposedly a mine is 100 tons, a Pelia 300 tons, and a transport ship is 4200 tons.
No matter how this is viewed it can't right. A Pelia by best estimate is around 100 tons, perhaps a bit on the light side, but 300 tons e.g. comparable to the space shuttle is off. Likewise a transport with just 4200 tons is utterly worthless compared to the expanditure and investment. It also means a million tons ship is so slow it takes forever to get anywhere. There would be no difference to travel in normal space.
• If speed and mass are inversed exponential proportional then supposedly a mine is 100 tons, a Pelia 900 tons, and a transport 2469600 tons. This looks more reasonable, but the Pelia is still way off.
• Fact 9 supports an inverted exponential proportional function. Jadbayr Usem Futune consists of 45 patrol ships and like-massed transports.
$speed-factor= (mass2/mass1)^b=1/(v2/v1).$
solving $(1/45)^b=1.73$ gives $b = (\log(1.73) / \log(1/45)) = -0.14399002012462608463430663139281$
solving for the Pelia $(x/100)^b=1/3$ gives $x = \sqrt[b]{(100^b)/3} = 205859.8$ tons.
#### Size of space-time bubbleEdit
Fact 1 says the rotation is constant, hence, size doesn't matter either for speed. It may matter regarding resistance as in Fact 4.
The space-time bubble is a spatial field, and like any field its strength wanes/decreases with distance. Like any kind of energy field its strength-gradient is inverse to distance following the inverse square law. We don't know how quickly the energy dissipates over a certain distance, though. Yet, the bubbles are said to have a wall while they are shown to have gradient lines in the animation. It can be surmised there's a threshold strength beyond which a bubble becomes reality.
As far as energy to power it is concerned, we can surmised that it follows the power law, meaning the difference is cubed. A two unit radius sized bubble would require 8 times the energy of a one unit radius sized bubble. Size matters! Therefore, to conserve fuel a fleet or group of ships often bunch together to use a single bubble from a single ship. Needless to say, the disadvantage is decreased speed. If speed and mass are inverted exponential proportional this is very advantageous.
## ReferencesEdit
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https://www.zbmath.org/authors/?q=ai%3Amakowsky.johann-andreas | # zbMATH — the first resource for mathematics
## Makowsky, Johann-Andreas
Compute Distance To:
Author ID: makowsky.johann-andreas Published as: Makowski, J.; Makowsky, J.; Makowsky, J. A.; Makowsky, Janos A.; Makowsky, Johann; Makowsky, Johann A.; Makowsky, Johann Andreas; Makowsky, Johann-Andreas External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 150 Publications since 1972, including 5 Books
all top 5
#### Co-Authors
35 single-authored 16 Kotek, Tomer 11 Ravve, Elena V. 6 Rotics, Udi 5 Dahlhaus, Elias 5 Fischer, Eldar 5 Godlin, Benny 5 Labai, Nadia 4 Courcelle, Bruno 4 Kaminsky, Michael 4 Pnueli, Yachin B. 4 Shelah, Saharon 3 Averbouch, Ilia 3 Averbouch, Ilya 3 Mahr, Bernd 3 Mariño, J. P. 3 Meer, Klaus 3 Tiomkin, Michael 2 Bläser, Markus 2 Cohen, Ariel 2 Dell, Holger 2 Grohe, Martin 2 Marcja, Annalisa 2 Niwiński, Damian 2 Rakita, Vsevolod 2 Tittmann, Peter 2 Zilber, Boris I. 1 Adámek, Jiří 1 Baaz, Matthias 1 Bargury, Y. 1 Blanchard, Nicolas K. 1 Calò, A. 1 Durand, Arnaud 1 Engeler, Erwin 1 Francez, Nissim 1 Glikson, Alexander 1 Goodall, Andrew J. 1 Grégoire, Jean-Charles 1 Grumberg, Orna 1 Hermann, Martin 1 Hungerbuhler, Norbert 1 Hyland, J. Martin E. 1 Israeli, Amos 1 Itai, Alon 1 Johnstone, Peter T. 1 Jones, Neil D. 1 Katz, Emilia 1 Lotz, Martin 1 Madanlal, M. S. 1 Markowitz, Victor M. 1 Mohanty, Sri Gopal 1 More, Malika 1 Noble, Steven Derek 1 Rangan, Chandrasekharan Pandu 1 Razborov, Aleksandr Aleksandrovich 1 Rinaldi, Simone 1 Rosický, Jiří 1 Rotics, Nimrod 1 Sagiv, S. 1 Sain, Ildikó 1 Sharell, Abraham 1 Stavi, Jonathan 1 Tiomkin, M. L. 1 Tulipani, Sauro 1 Vardi, Moshe Y. 1 Venkatesan, G. 1 Zamansky, Anna 1 Zhang, Runxuan 1 Ziegler, Martin
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#### Serials
5 European Journal of Combinatorics 4 Theoretical Computer Science 4 Annals of Pure and Applied Logic 3 Archiv für Mathematische Logik und Grundlagenforschung 3 Discrete Applied Mathematics 3 Journal of Computer and System Sciences 3 The Journal of Symbolic Logic 3 Advances in Applied Mathematics 3 Information and Computation 3 Journal of Logic and Computation 3 Theory of Computing Systems 2 Fundamenta Mathematicae 2 The Journal of Logic Programming 2 Annals of Mathematics and Artificial Intelligence 2 Fundamenta Informaticae 1 Acta Informatica 1 Annals of Mathematical Logic 1 Information and Control 1 Notre Dame Journal of Formal Logic 1 Rendiconti del Seminario Matematico della Università di Padova 1 Transactions of the American Mathematical Society 1 Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 1 Data & Knowledge Engineering 1 MSCS. Mathematical Structures in Computer Science 1 International Journal of Foundations of Computer Science 1 Elemente der Mathematik 1 The Australasian Journal of Combinatorics 1 Formal Methods in System Design 1 Journal of Logic, Language and Information 1 The Bulletin of Symbolic Logic 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Contemporary Mathematics 1 Lecture Notes in Computer Science 1 Lecture Notes in Logic 1 Logical Methods in Computer Science 1 Moscow Journal of Combinatorics and Number Theory
all top 5
#### Fields
82 Computer science (68-XX) 74 Mathematical logic and foundations (03-XX) 49 Combinatorics (05-XX) 7 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Number theory (11-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH
109 Publications have been cited 977 times in 635 Documents Cited by Year
Linear time solvable optimization problems on graphs of bounded clique-width. Zbl 1009.68102
Courcelle, B.; Makowsky, J. A.; Rotics, U.
2000
On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Zbl 0972.05023
Courcelle, B.; Makowsky, J. A.; Rotics, U.
2001
Algorithmic uses of the Feferman-Vaught theorem. Zbl 1099.03009
Makowsky, J. A.
2004
On the clique-width of graph with few $$P_{4}$$’s. Zbl 1320.05096
Makowsky, J. A.; Rotics, U.
1999
Counting truth assignments of formulas of bounded tree-width or clique-width. Zbl 1131.68093
Fischer, E.; Makowsky, J. A.; Ravve, E. V.
2008
Unification as a complexity measure for logic programming. Zbl 0641.68143
Itai, A.; Makowsky, J. A.
1987
$$\Delta$$-logics and generalized quantifiers. Zbl 0346.02007
Makowsky, J. A.; Shelah, Saharon; Stavi, Jonathan
1976
From a zoo to a zoology: Towards a general theory of graph polynomials. Zbl 1162.68502
Makowsky, J. A.
2008
A proof rule for fair termination of guarded commands. Zbl 0577.68022
Grumberg, Orna; Francez, Nissim; Makowsky, Johann A.
1985
An extension of the bivariate chromatic polynomial. Zbl 1198.05099
Averbouch, Ilia; Godlin, Benny; Makowsky, J. A.
2010
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width. Zbl 1084.05505
Makowsky, J. A.
2005
Restrictions of minimum spanner problems. Zbl 0890.68106
Venkatesan, G.; Rotics, U.; Madanlal, M. S.; Makowsky, J. A.; Pandu Rangan, C.
1997
Why Horn formulas matter in computer science: initial structures and generic examples. Zbl 0619.68029
Makowsky, J. A.
1987
On the location of roots of graph polynomials. Zbl 1300.05136
Makowsky, Johann A.; Ravve, Elena V.; Blanchard, Nicolas K.
2014
The enumeration of vertex induced subgraphs with respect to the number of components. Zbl 1229.05124
Tittmann, P.; Averbouch, I.; Makowsky, J. A.
2011
Fusion in relational structures and the verification of monadic second-order properties. Zbl 1005.68105
Courcelle, B.; Makowsky, J. A.
2002
Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width. Zbl 0988.05087
Makowsky, J. A.
2001
The theorems of Beth and Craig in abstract model theory. I: The abstract setting. Zbl 0428.03032
Makowsky, J. A.; Shelah, S.
1979
Arity and alternation in second-order logic. Zbl 0854.03006
Makowsky, J. A.; Pnueli, Y. B.
1996
Linear time solvable optimization problems on graphs of bounded clique width. Zbl 0929.90084
Courcelle, B.; Makowsky, J. A.; Rotics, U.
1998
Some model theory for monotone quantifiers. Zbl 0365.02042
Makowsky, J. A.; Tulipani, S.
1977
On some conjectures connected with complete sentences. Zbl 0285.02042
Makowsky, J. A.
1974
Buckling equations for elastic shells with rotational degrees of freedom undergoing finite strain deformation. Zbl 0706.73044
Makowski, J.; Stumpf, H.
1990
On large strain deformations of shells. Zbl 0602.73035
Stumpf, H.; Makowski, J.
1987
Positive results in abstract model theory: a theory of compact logics. Zbl 0544.03013
Makowsky, J. A.; Shelah, S.
1983
A most general edge elimination polynomial. Zbl 1202.05063
Averbouch, Ilia; Godlin, Benny; Makowsky, Johann A.
2008
Farrell polynomials on graphs of bounded tree width. Zbl 1023.68070
Makowsky, J. A.; Mariño, J. P.
2003
Vopěnka’s principle and compact logics. Zbl 0623.03041
Makowsky, J. A.
1985
Characterizing specification languages which admit initial semantics. Zbl 0536.68011
Mahr, B.; Makowsky, J. A.
1984
The theorems of Beth and Craig in abstract model theory. II. Compact logics. Zbl 0472.03028
Makowsky, J. A.; Shelah, S.
1981
Fifty years of the spectrum problem: survey and new results. Zbl 1309.03014
Durand, Arnaud; Jones, Neil D.; Makowsky, Johann A.; More, Malika
2012
On counting generalized colorings. Zbl 1253.05071
Kotek, Tomer; Makowsky, Johann A.; Zilber, Boris
2011
Computing graph polynomials on graphs of bounded clique-width. Zbl 1167.05335
Makowsky, J. A.; Rotics, Udi; Averbouch, Ilya; Godlin, Benny
2006
The parametrized complexity of knot polynomials. Zbl 1093.68043
Makowsky, J. A.; Mariño, J. P.
2003
Why Horn formulas matter in computer science: initial structures and generic examples. Zbl 0563.68013
Makowsky, J. A.
1985
On counting generalized colorings. Zbl 1157.05024
Kotek, T.; Makowsky, J. A.; Zilber, B.
2008
On the algebraic complexity of some families of coloured Tutte polynomials. Zbl 1041.05042
Lotz, Martin; Makowsky, Johann A.
2004
Extensions for open default theories via the domain closure assumption. Zbl 0901.68188
Kaminski, Michael; Makowsky, Johann A.; Tiomkin, Michael
1998
Decidability of finite probabilistic propositional dynamic logics. Zbl 0732.03022
Tiomkin, M.; Makowsky, J. A.
1991
On the expressive power of data dependencies. Zbl 0617.68085
Makowsky, Johann A.; Vardi, Moshe Y.
1986
Propositional dynamic logic with local assignments. Zbl 0574.03011
Tiomkin, M. L.; Makowsky, J. A.
1985
Application of logic to combinatorial sequences and their recurrence relations. Zbl 1282.03019
Fischer, Eldar; Kotek, Tomer; Makowsky, Johann A.
2011
Evaluations of graph polynomials. Zbl 1202.05065
Godlin, Benny; Kotek, Tomer; Makowsky, Johann A.
2008
Linear recurrence relations for graph polynomials. Zbl 1134.05099
Fischer, Eldar; Makowsky, Johann A.
2008
The Specker-Blatter theorem revisited. Zbl 1276.03034
Fischer, E.; Makowsky, J. A.
2003
The Ehrenfeucht-Fraïssé games for transitive closure. Zbl 0978.03525
Calò, A.; Makowsky, J. A.
1992
The expressive power of transitive closure and 2-way multihead automata. Zbl 0783.03018
Bargury, Y.; Makowsky, J.
1992
Finite strains and rotations in shells. Zbl 0615.73042
Makowski, J.; Stumpf, H.
1986
Model theoretic issues in theoretical computer science. I: Relational data bases and abstract data types. Zbl 0553.68028
Makowsky, J. A.
1984
Connection matrices and the definability of graph parameters. Zbl 1345.03054
Kotek, Tomer; Makowsky, Johann A.
2014
A computational framework for the study of partition functions and graph polynomials. Zbl 1364.03055
Kotek, T.; Makowsky, J. A.; Ravve, E. V.
2013
Tree-width and the monadic quantifier hierarchy. Zbl 1044.68130
Makowsky, J. A.; Mariño, J. P.
2003
On the complexity of combinatorial and metafinite generating functions of graph properties of the computational model of Blum, Shub and Smale. Zbl 0973.68524
Makowsky, J. A.; Meer, K.
2000
Incremental model checking for decomposable structures. Zbl 1193.68164
Makowsky, J. A.; Ravve, E. V.
1995
Oracles and quantifiers. Zbl 0953.03049
Makowsky, J. A.; Pnueli, Y. B.
1994
The choice of programming primitives for SETL-like programming languages. Zbl 0587.68005
Dahlhaus, E.; Makowsky, J. A.
1986
Characterizing specification languages which admit initial semantics. Zbl 0522.68026
Mahr, B.; Makowsky, J. A.
1983
Topological model theory with an interior operator: Consistency properties and back-and-forth arguments. Zbl 0472.03027
Makowsky, J. A.; Ziegler, M.
1981
On sequences of polynomials arising from graph invariants. Zbl 1371.05135
Kotek, T.; Makowsky, J. A.; Ravve, E. V.
2018
Graph polynomials: from recursive definitions to subset expansion formulas. Zbl 1239.05095
Godlin, B.; Katz, E.; Makowsky, J. A.
2012
Complexity of the Bollobás-Riordan polynomial. Exceptional points and uniform reductions. Zbl 1143.05023
Bläser, Markus; Dell, Holger; Makowsky, Johann A.
2008
From a zoo to a zoology: Descriptive complexity for graph polynomials. Zbl 1145.68432
Makowsky, J. A.
2006
On spectra of sentences of monadic second order logic with counting. Zbl 1070.03018
Fischer, E.; Makowsky, J. A.
2004
NCE graph grammars and clique-width. Zbl 1255.68088
Glikson, Alexander; Makowsky, Johann A.
2003
Polynomials of bounded tree-width. Zbl 1018.65063
Makowsky, Janos A.; Meer, Klaus
2002
Dependency preserving refinements and the fundamental problem of database design. Zbl 0893.68049
Makowsky, J. A.; Ravve, E. V.
1998
Computable quantifiers and logics over finite structures. Zbl 0905.03018
Makowsky, Johann A.; Pnueli, Yachin B.
1995
On the “symmetry” of tangent operators in nonlinear mechanics. Zbl 0839.70013
Makowski, J.; Stumpf, H.
1995
Weak second order characterizations of various program verification systems. Zbl 0678.68008
Makowsky, J. A.; Sain, I.
1989
Quantifying over countable sets: Positive vs stationary logic. Zbl 0469.03021
Makowsky, J. A.
1978
Completeness theorems for modal model theory with the MontagueChang semantics. I. Zbl 0362.02043
Makowsky, J. A.; Marcja, A.
1977
On the complexity of generalized chromatic polynomials. Zbl 1378.05059
Goodall, A.; Hermann, M.; Kotek, T.; Makowsky, J. A.; Noble, S. D.
2018
Finiteness conditions for graph algebras over tropical semirings. Zbl 1393.05180
2014
Recurrence relations for graph polynomials on bi-iterative families of graphs. Zbl 1300.05135
Kotek, Tomer; Makowsky, Johann A.
2014
Indistinguishability by default. Zbl 1219.68148
Cohen, Ariel; Kaminski, Michael; Makowsky, Johann A.
2005
Finitary sketches. Zbl 0885.18001
Adámek, Jiří; Johnstone, P. T.; Makowsky, J. A.; Rosický, Jiří
1997
Invariant definability. (Extended abstract). Zbl 0881.03022
Makowsky, J. A.
1997
Arity vs. alternation in second order logic. Zbl 0946.03041
Makowsky, J. A.; Pnueli, Y. B.
1994
Mechanics of irregular shell structures. Zbl 0837.73041
Makowski, J.; Stumpf, H.
1994
Finite axisymmetric deformation of shells of revolution with application to flexural buckling of circular plates. Zbl 0712.73031
Makowski, J.; Stumpf, H.
1989
Computable directory queries. Zbl 0604.68109
Dahlhaus, E.; Makowsky, J. A.
1986
On the derivation and comparative analysis of large rotation shell theories. Zbl 0576.73055
Nolte, L.-P.; Makowski, J.; Stumpf, H.
1986
Characterizing data base dependencies. Zbl 0515.68068
Makowsky, J. A.
1981
Measuring the expressive power of dynamic logics: An application of abstract model theory. Zbl 0465.68012
Makowsky, J. A.
1980
Securable quantifiers, k-unions and admissible sets. Zbl 0311.02023
Makowsky, Johann Andreas
1975
On weakly distinguishing graph polynomials. Zbl 1411.05131
Makowsky, Johann A.; Rakita, Vsevolod
2019
Semantic equivalence of graph polynomials definable in second order logic. Zbl 06625893
Makowsky, Johann A.; Ravve, Elena V.
2016
Hankel matrices: from words to graphs (extended abstract). Zbl 1451.68207
2015
Connection matrices and the definability of graph parameters. Zbl 1252.03085
Kotek, Tomer; Makowsky, Johann A.
2012
A representation theorem for holonomic sequences based on counting lattice paths. Zbl 1245.68151
Kotek, Tomer; Makowsky, Johann A.
2012
The universal edge elimination polynomial and the dichromatic polynomial. Zbl 1274.05231
Averbouch, I.; Kotek, T.; Makowsky, J. A.; Ravve, E.
2011
Definability of combinatorial functions and their linear recurrence relations. Zbl 1287.05008
Kotek, Tomer; Makowsky, Johann A.
2010
Complexity of the Bollobás-Riordan polynomial. Exceptional points and uniform reductions. Zbl 1206.68137
Bläser, Markus; Dell, Holger; Makowsky, Johann A.
2010
From Hilbert’s program to a logic tool box. Zbl 1167.00011
Makowsky, J. A.
2008
Notions of sameness by default and their application to anaphora, vagueness, and uncertain reasoning. Zbl 1188.68275
Cohen, Ariel; Kaminski, Michael; Makowsky, Johann A.
2008
Encounters with A. Mostowski. Zbl 1147.01326
Makowsky, J. A.
2008
Polynomials of bounded tree width (extended abstract). Zbl 0972.05035
Makowsky, J. A.; Meer, K.
2000
Invariant definability and P/poly. Zbl 0934.03053
Makowsky, J. A.
1999
Strain localization in stress-resultant theory of shells. Zbl 0971.74052
Makowski, J.; Stumpf, H.
1998
The impact of model theory on theoretical computer science. Zbl 0854.03040
Makowsky, J. A.
1994
On weakly distinguishing graph polynomials. Zbl 1411.05131
Makowsky, Johann A.; Rakita, Vsevolod
2019
On sequences of polynomials arising from graph invariants. Zbl 1371.05135
Kotek, T.; Makowsky, J. A.; Ravve, E. V.
2018
On the complexity of generalized chromatic polynomials. Zbl 1378.05059
Goodall, A.; Hermann, M.; Kotek, T.; Makowsky, J. A.; Noble, S. D.
2018
Semantic equivalence of graph polynomials definable in second order logic. Zbl 06625893
Makowsky, Johann A.; Ravve, Elena V.
2016
Hankel matrices: from words to graphs (extended abstract). Zbl 1451.68207
2015
On the location of roots of graph polynomials. Zbl 1300.05136
Makowsky, Johann A.; Ravve, Elena V.; Blanchard, Nicolas K.
2014
Connection matrices and the definability of graph parameters. Zbl 1345.03054
Kotek, Tomer; Makowsky, Johann A.
2014
Finiteness conditions for graph algebras over tropical semirings. Zbl 1393.05180
2014
Recurrence relations for graph polynomials on bi-iterative families of graphs. Zbl 1300.05135
Kotek, Tomer; Makowsky, Johann A.
2014
A computational framework for the study of partition functions and graph polynomials. Zbl 1364.03055
Kotek, T.; Makowsky, J. A.; Ravve, E. V.
2013
Fifty years of the spectrum problem: survey and new results. Zbl 1309.03014
Durand, Arnaud; Jones, Neil D.; Makowsky, Johann A.; More, Malika
2012
Graph polynomials: from recursive definitions to subset expansion formulas. Zbl 1239.05095
Godlin, B.; Katz, E.; Makowsky, J. A.
2012
Connection matrices and the definability of graph parameters. Zbl 1252.03085
Kotek, Tomer; Makowsky, Johann A.
2012
A representation theorem for holonomic sequences based on counting lattice paths. Zbl 1245.68151
Kotek, Tomer; Makowsky, Johann A.
2012
The enumeration of vertex induced subgraphs with respect to the number of components. Zbl 1229.05124
Tittmann, P.; Averbouch, I.; Makowsky, J. A.
2011
On counting generalized colorings. Zbl 1253.05071
Kotek, Tomer; Makowsky, Johann A.; Zilber, Boris
2011
Application of logic to combinatorial sequences and their recurrence relations. Zbl 1282.03019
Fischer, Eldar; Kotek, Tomer; Makowsky, Johann A.
2011
The universal edge elimination polynomial and the dichromatic polynomial. Zbl 1274.05231
Averbouch, I.; Kotek, T.; Makowsky, J. A.; Ravve, E.
2011
An extension of the bivariate chromatic polynomial. Zbl 1198.05099
Averbouch, Ilia; Godlin, Benny; Makowsky, J. A.
2010
Definability of combinatorial functions and their linear recurrence relations. Zbl 1287.05008
Kotek, Tomer; Makowsky, Johann A.
2010
Complexity of the Bollobás-Riordan polynomial. Exceptional points and uniform reductions. Zbl 1206.68137
Bläser, Markus; Dell, Holger; Makowsky, Johann A.
2010
Counting truth assignments of formulas of bounded tree-width or clique-width. Zbl 1131.68093
Fischer, E.; Makowsky, J. A.; Ravve, E. V.
2008
From a zoo to a zoology: Towards a general theory of graph polynomials. Zbl 1162.68502
Makowsky, J. A.
2008
A most general edge elimination polynomial. Zbl 1202.05063
Averbouch, Ilia; Godlin, Benny; Makowsky, Johann A.
2008
On counting generalized colorings. Zbl 1157.05024
Kotek, T.; Makowsky, J. A.; Zilber, B.
2008
Evaluations of graph polynomials. Zbl 1202.05065
Godlin, Benny; Kotek, Tomer; Makowsky, Johann A.
2008
Linear recurrence relations for graph polynomials. Zbl 1134.05099
Fischer, Eldar; Makowsky, Johann A.
2008
Complexity of the Bollobás-Riordan polynomial. Exceptional points and uniform reductions. Zbl 1143.05023
Bläser, Markus; Dell, Holger; Makowsky, Johann A.
2008
From Hilbert’s program to a logic tool box. Zbl 1167.00011
Makowsky, J. A.
2008
Notions of sameness by default and their application to anaphora, vagueness, and uncertain reasoning. Zbl 1188.68275
Cohen, Ariel; Kaminski, Michael; Makowsky, Johann A.
2008
Encounters with A. Mostowski. Zbl 1147.01326
Makowsky, J. A.
2008
Computing graph polynomials on graphs of bounded clique-width. Zbl 1167.05335
Makowsky, J. A.; Rotics, Udi; Averbouch, Ilya; Godlin, Benny
2006
From a zoo to a zoology: Descriptive complexity for graph polynomials. Zbl 1145.68432
Makowsky, J. A.
2006
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width. Zbl 1084.05505
Makowsky, J. A.
2005
Indistinguishability by default. Zbl 1219.68148
Cohen, Ariel; Kaminski, Michael; Makowsky, Johann A.
2005
Algorithmic uses of the Feferman-Vaught theorem. Zbl 1099.03009
Makowsky, J. A.
2004
On the algebraic complexity of some families of coloured Tutte polynomials. Zbl 1041.05042
Lotz, Martin; Makowsky, Johann A.
2004
On spectra of sentences of monadic second order logic with counting. Zbl 1070.03018
Fischer, E.; Makowsky, J. A.
2004
Farrell polynomials on graphs of bounded tree width. Zbl 1023.68070
Makowsky, J. A.; Mariño, J. P.
2003
The parametrized complexity of knot polynomials. Zbl 1093.68043
Makowsky, J. A.; Mariño, J. P.
2003
The Specker-Blatter theorem revisited. Zbl 1276.03034
Fischer, E.; Makowsky, J. A.
2003
Tree-width and the monadic quantifier hierarchy. Zbl 1044.68130
Makowsky, J. A.; Mariño, J. P.
2003
NCE graph grammars and clique-width. Zbl 1255.68088
Glikson, Alexander; Makowsky, Johann A.
2003
Fusion in relational structures and the verification of monadic second-order properties. Zbl 1005.68105
Courcelle, B.; Makowsky, J. A.
2002
Polynomials of bounded tree-width. Zbl 1018.65063
Makowsky, Janos A.; Meer, Klaus
2002
On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Zbl 0972.05023
Courcelle, B.; Makowsky, J. A.; Rotics, U.
2001
Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width. Zbl 0988.05087
Makowsky, J. A.
2001
Linear time solvable optimization problems on graphs of bounded clique-width. Zbl 1009.68102
Courcelle, B.; Makowsky, J. A.; Rotics, U.
2000
On the complexity of combinatorial and metafinite generating functions of graph properties of the computational model of Blum, Shub and Smale. Zbl 0973.68524
Makowsky, J. A.; Meer, K.
2000
Polynomials of bounded tree width (extended abstract). Zbl 0972.05035
Makowsky, J. A.; Meer, K.
2000
On the clique-width of graph with few $$P_{4}$$’s. Zbl 1320.05096
Makowsky, J. A.; Rotics, U.
1999
Invariant definability and P/poly. Zbl 0934.03053
Makowsky, J. A.
1999
Linear time solvable optimization problems on graphs of bounded clique width. Zbl 0929.90084
Courcelle, B.; Makowsky, J. A.; Rotics, U.
1998
Extensions for open default theories via the domain closure assumption. Zbl 0901.68188
Kaminski, Michael; Makowsky, Johann A.; Tiomkin, Michael
1998
Dependency preserving refinements and the fundamental problem of database design. Zbl 0893.68049
Makowsky, J. A.; Ravve, E. V.
1998
Strain localization in stress-resultant theory of shells. Zbl 0971.74052
Makowski, J.; Stumpf, H.
1998
Restrictions of minimum spanner problems. Zbl 0890.68106
Venkatesan, G.; Rotics, U.; Madanlal, M. S.; Makowsky, J. A.; Pandu Rangan, C.
1997
Finitary sketches. Zbl 0885.18001
Adámek, Jiří; Johnstone, P. T.; Makowsky, J. A.; Rosický, Jiří
1997
Invariant definability. (Extended abstract). Zbl 0881.03022
Makowsky, J. A.
1997
Arity and alternation in second-order logic. Zbl 0854.03006
Makowsky, J. A.; Pnueli, Y. B.
1996
Incremental model checking for decomposable structures. Zbl 1193.68164
Makowsky, J. A.; Ravve, E. V.
1995
Computable quantifiers and logics over finite structures. Zbl 0905.03018
Makowsky, Johann A.; Pnueli, Yachin B.
1995
On the “symmetry” of tangent operators in nonlinear mechanics. Zbl 0839.70013
Makowski, J.; Stumpf, H.
1995
Oracles and quantifiers. Zbl 0953.03049
Makowsky, J. A.; Pnueli, Y. B.
1994
Arity vs. alternation in second order logic. Zbl 0946.03041
Makowsky, J. A.; Pnueli, Y. B.
1994
Mechanics of irregular shell structures. Zbl 0837.73041
Makowski, J.; Stumpf, H.
1994
The impact of model theory on theoretical computer science. Zbl 0854.03040
Makowsky, J. A.
1994
The Ehrenfeucht-Fraïssé games for transitive closure. Zbl 0978.03525
Calò, A.; Makowsky, J. A.
1992
The expressive power of transitive closure and 2-way multihead automata. Zbl 0783.03018
Bargury, Y.; Makowsky, J.
1992
Query languages for hierarchic databases. Zbl 0765.68029
Dahlhaus, E.; Makowsky, J. A.
1992
Decidability of finite probabilistic propositional dynamic logics. Zbl 0732.03022
Tiomkin, M.; Makowsky, J. A.
1991
Buckling equations for elastic shells with rotational degrees of freedom undergoing finite strain deformation. Zbl 0706.73044
Makowski, J.; Stumpf, H.
1990
Weak second order characterizations of various program verification systems. Zbl 0678.68008
Makowsky, J. A.; Sain, I.
1989
Finite axisymmetric deformation of shells of revolution with application to flexural buckling of circular plates. Zbl 0712.73031
Makowski, J.; Stumpf, H.
1989
A simple buckling problem within the shell theory of rubber-like materials. Zbl 0711.73104
Makowski, J.; Stumpf, H.
1988
Gandy’s principles for mechanisms as a model of parallel computation. Zbl 0676.68018
Dahlhaus, Elias; Makowsky, Johann A.
1988
Mental images and the architecture of concepts. Zbl 0661.68028
Makowsky, Johann A.
1988
Unification as a complexity measure for logic programming. Zbl 0641.68143
Itai, A.; Makowsky, J. A.
1987
Why Horn formulas matter in computer science: initial structures and generic examples. Zbl 0619.68029
Makowsky, J. A.
1987
On large strain deformations of shells. Zbl 0602.73035
Stumpf, H.; Makowski, J.
1987
Simple equations in terms of displacements for finite axisymmetric deflections of shells of revolution. Zbl 0605.73034
Makowski, J.; Nolte, L.-P.
1987
On the expressive power of data dependencies. Zbl 0617.68085
Makowsky, Johann A.; Vardi, Moshe Y.
1986
Finite strains and rotations in shells. Zbl 0615.73042
Makowski, J.; Stumpf, H.
1986
The choice of programming primitives for SETL-like programming languages. Zbl 0587.68005
Dahlhaus, E.; Makowsky, J. A.
1986
Computable directory queries. Zbl 0604.68109
Dahlhaus, E.; Makowsky, J. A.
1986
On the derivation and comparative analysis of large rotation shell theories. Zbl 0576.73055
Nolte, L.-P.; Makowski, J.; Stumpf, H.
1986
A proof rule for fair termination of guarded commands. Zbl 0577.68022
Grumberg, Orna; Francez, Nissim; Makowsky, Johann A.
1985
Vopěnka’s principle and compact logics. Zbl 0623.03041
Makowsky, J. A.
1985
Why Horn formulas matter in computer science: initial structures and generic examples. Zbl 0563.68013
Makowsky, J. A.
1985
Propositional dynamic logic with local assignments. Zbl 0574.03011
Tiomkin, M. L.; Makowsky, J. A.
1985
Finite in-plane deformations of flexible rods insight into nonlinear shell problems. Zbl 0583.73038
Makowski, J.; Nolte, L.-P.; Stumpf, H.
1985
Characterizing specification languages which admit initial semantics. Zbl 0536.68011
Mahr, B.; Makowsky, J. A.
1984
Model theoretic issues in theoretical computer science. I: Relational data bases and abstract data types. Zbl 0553.68028
Makowsky, J. A.
1984
Positive results in abstract model theory: a theory of compact logics. Zbl 0544.03013
Makowsky, J. A.; Shelah, S.
1983
Characterizing specification languages which admit initial semantics. Zbl 0522.68026
Mahr, B.; Makowsky, J. A.
1983
An axiomatic approach to semantics of specification languages. Zbl 0493.68023
Mahr, B.; Makowsky, J. A.
1982
The theorems of Beth and Craig in abstract model theory. II. Compact logics. Zbl 0472.03028
Makowsky, J. A.; Shelah, S.
1981
Topological model theory with an interior operator: Consistency properties and back-and-forth arguments. Zbl 0472.03027
Makowsky, J. A.; Ziegler, M.
1981
Characterizing data base dependencies. Zbl 0515.68068
Makowsky, J. A.
1981
Measuring the expressive power of dynamic logics: An application of abstract model theory. Zbl 0465.68012
Makowsky, J. A.
1980
...and 9 more Documents
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#### Cited by 773 Authors
47 Makowsky, Johann-Andreas 28 Lozin, Vadim Vladislavovich 27 Courcelle, Bruno 21 Brandstädt, Andreas 16 Ganian, Robert 16 Paulusma, Daniël 16 Szeider, Stefan 15 Dabrowski, Konrad Kazimierz 13 Gurski, Frank 13 Milanič, Martin 11 Kotek, Tomer 11 Lampis, Michael 10 Hliněný, Petr 10 Meister, Daniel 10 Mosca, Raffaele 9 Rotics, Udi 8 Golovach, Petr A. 8 Kanté, Mamadou Moustapha 8 Ravve, Elena V. 8 Rossmanith, Peter 8 Zamaraev, Victor A. 7 Malyshev, Dmitry S. 7 Oum, Sang-Il 7 Väänänen, Jouko Antero 6 Belmonte, Rémy 6 Kneis, Joachim 6 Korpelainen, Nicholas 6 Kwon, Ojoung 6 Langer, Alexander 6 Müller, Haiko 6 Nešetřil, Jaroslav 6 Otachi, Yota 6 Papadopoulos, Charis 6 Rautenbach, Dieter 6 Shelah, Saharon 6 Vatshelle, Martin 6 Wanke, Egon 5 Boros, Endre 5 Goodall, Andrew J. 5 Heggernes, Pinar 5 Huang, Shenwei 5 Kučera, Petr 5 Meer, Klaus 5 Monnot, Jérôme 5 Obdržálek, Jan 5 Rao, Michaël 5 Ries, Bernard 5 Sikdar, Somnath 5 Torres, Pablo Daniel 5 Vardi, Moshe Y. 4 Argiroffo, Gabriela R. 4 Bazgan, Cristina 4 Bodlaender, Hans L. 4 Broersma, Hajo J. 4 Čepek, Ondřej 4 Das, Bireswar 4 Eiben, Eduard 4 Enduri, Murali Krishna 4 Eremeyev, Victor A. 4 Kopczyński, Eryk 4 Hoàng-Oanh Le 4 Leoni, Valeria Alejandra 4 Liedloff, Mathieu 4 Maffray, Frédéric 4 Makowski, Jerzy 4 Marques-Silva, João P. 4 Mencía, Carlos 4 Ordyniak, Sebastian 4 Paschos, Vangelis Th. 4 Pietraszkiewicz, Wojciech 4 Reddy, I. Vinod 4 Stumpf, Helmut 4 Telle, Jan Arne 3 Beck, Matthias 3 Blanchet-Sadri, Francine 3 Bläser, Markus 3 Blumensath, Achim 3 Brown, Jason Ira 3 Bui-Xuan, Binh-Minh 3 Cicalese, Ferdinando 3 Dell, Holger 3 Dragan, Feodor F. 3 Fagin, Ronald 3 Fernau, Henning 3 Fischer, Eldar 3 Fomin, Fedor V. 3 Francez, Nissim 3 Garijo, Delia 3 Gaspers, Serge 3 Godlin, Benny 3 Hodges, Wilfrid 3 Kaminsky, Michael 3 Katsikarelis, Ioannis 3 Katz, Shmuel 3 Koiran, Pascal 3 Kolaitis, Phokion G. 3 Kratsch, Dieter 3 Krynicki, Michał Marian 3 Lê Văn Băng 3 Libkin, Leonid O. ...and 673 more Authors
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#### Cited in 108 Serials
88 Discrete Applied Mathematics 77 Theoretical Computer Science 23 Journal of Computer and System Sciences 20 Algorithmica 17 Information Processing Letters 17 Annals of Pure and Applied Logic 15 Discrete Mathematics 15 The Journal of Symbolic Logic 14 European Journal of Combinatorics 14 Information and Computation 11 Theory of Computing Systems 9 Artificial Intelligence 9 Journal of Combinatorial Theory. Series B 9 Annals of Mathematics and Artificial Intelligence 8 Graphs and Combinatorics 7 Studia Logica 7 Archive for Mathematical Logic 6 Archiv für Mathematische Logik und Grundlagenforschung 6 Computer Methods in Applied Mechanics and Engineering 6 SIAM Journal on Discrete Mathematics 6 ACM Transactions on Computational Logic 6 Journal of Applied Logic 5 Journal of Graph Theory 5 International Journal of Foundations of Computer Science 5 Journal of Combinatorial Optimization 5 Journal of Discrete Algorithms 4 Applied Mathematics and Computation 4 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 4 Distributed Computing 4 Mathematical Logic Quarterly (MLQ) 4 The Bulletin of Symbolic Logic 4 Logical Methods in Computer Science 4 Computer Science Review 3 Israel Journal of Mathematics 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Algebra Universalis 3 Synthese 3 Advances in Applied Mathematics 3 International Journal of Computer Mathematics 3 Linear Algebra and its Applications 3 Combinatorics, Probability and Computing 3 Discrete Optimization 2 Acta Informatica 2 Ingenieur-Archiv 2 International Journal of Engineering Science 2 International Journal of Solids and Structures 2 International Journal for Numerical Methods in Engineering 2 Journal of Combinatorial Theory. Series A 2 SIAM Journal on Computing 2 Formal Aspects of Computing 2 European Journal of Operational Research 2 The Australasian Journal of Combinatorics 2 Computational Complexity 2 Logica Universalis 2 Optimization Letters 1 Acta Mechanica 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Journal of Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Advances in Mathematics 1 Algebra and Logic 1 Fuzzy Sets and Systems 1 Information Sciences 1 Mathematische Zeitschrift 1 Meccanica 1 Networks 1 Notre Dame Journal of Formal Logic 1 Rendiconti del Seminario Matematico della Università di Padova 1 Topology and its Applications 1 Cybernetics 1 Mathematical Social Sciences 1 Order 1 Optimization 1 Journal of Symbolic Computation 1 Computational Mechanics 1 International Journal of Approximate Reasoning 1 Annals of Operations Research 1 Computational Geometry 1 Discrete Mathematics and Applications 1 Elemente der Mathematik 1 Journal of Elasticity 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Archive of Applied Mechanics 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Formal Methods in System Design 1 Journal of Logic, Language and Information 1 Applied Categorical Structures 1 Journal of Applied Non-Classical Logics 1 Selecta Mathematica. New Series 1 Discussiones Mathematicae. Graph Theory 1 International Transactions in Operational Research 1 Journal of Heuristics 1 Mathematics and Mechanics of Solids 1 Mathematical Methods of Operations Research 1 Geometry & Topology 1 Journal of Graph Algorithms and Applications 1 Annals of Combinatorics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS ...and 8 more Serials
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#### Cited in 36 Fields
341 Computer science (68-XX) 307 Combinatorics (05-XX) 204 Mathematical logic and foundations (03-XX) 26 Mechanics of deformable solids (74-XX) 21 Operations research, mathematical programming (90-XX) 14 Order, lattices, ordered algebraic structures (06-XX) 8 History and biography (01-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Category theory; homological algebra (18-XX) 6 Convex and discrete geometry (52-XX) 6 Manifolds and cell complexes (57-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Probability theory and stochastic processes (60-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General algebraic systems (08-XX) 3 Number theory (11-XX) 3 Commutative algebra (13-XX) 3 General topology (54-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 2 Mathematics education (97-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-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. | 2021-03-07T21:59:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7071294188499451, "perplexity": 9583.104229367076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178378872.82/warc/CC-MAIN-20210307200746-20210307230746-00336.warc.gz"} |
http://algebra2014.wikidot.com/onto | Onto
Return to Glossary.
Formal Definition
A function $\phi:X \rightarrow Y$ is onto (or surjective) if $\forall y \in Y, \exists x \in X$ such that $f(x)=y$.
Informal Definition
A function is onto if every element of its codomain has some element of the function's domain that maps to it.
Example(s)
Say we have a function $\phi:X \rightarrow Y$ where $\phi(x) = 5x$. In order to show $\phi$ is onto, we must show $\exists x \in X$ such that $\phi(x) = y$. Let $x=(1/5) y$. Then, $\phi(x)=5[(1/5) y]=y$. Therefore, $\phi$ is onto. $\blacksquare$
Non-example(s)
Say we have a function $\phi:\mathbb{Z} \rightarrow \mathbb{R}$ where $\phi(x) = x$ ($x \in \mathbb{Z}$ and $y \in \mathbb{R}$). Let $y = 1.5$. Since the domain of $\phi$ is only the integers, it is obvious that $\nexists x$ such that $\phi(x) = 1.5 = y$. $\blacksquare$
Additional Comments
Add any other comments you have about the term here
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https://zbmath.org/authors/?q=ai%3Agiansiracusa.noah | ## Giansiracusa, Noah
Compute Distance To:
Author ID: giansiracusa.noah Published as: Giansiracusa, Noah Homepage: https://www.noahgian.com/ External Links: MGP · Wikidata · Google Scholar · Twitter · dblp
Documents Indexed: 19 Publications since 2009 Reviewing Activity: 40 Reviews Co-Authors: 22 Co-Authors with 16 Joint Publications 364 Co-Co-Authors
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### Co-Authors
2 single-authored 2 Giansiracusa, Jeffrey 2 Moon, Han-Bom 2 Ricciardi, Cameron 1 Ballinger, Brandon 1 Blekherman, Grigoriy 1 Bolognesi, Michele 1 Caminata, Alessio 1 Cohn, Henry Lee 1 Crowley, Colin 1 David, Jensen 1 Doran, Brent 1 Gallardo, Patricio 1 Gibney, Angela 1 Gillam, William Danny 1 Kelly, Elizabeth 1 Lazar, Nicole A. 1 Manaker, Jacob 1 Moon, Chul-Woo 1 Mundinger, Joshua 1 Schaffler, Luca 1 Schürmann, Achill 1 Simpson, Matthew J.
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### Serials
4 Advances in Mathematics 2 IMRN. International Mathematics Research Notices 1 American Mathematical Monthly 1 Archiv der Mathematik 1 Duke Mathematical Journal 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Mathematical Social Sciences 1 Experimental Mathematics 1 Journal of Algebraic Geometry 1 Turkish Journal of Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Computational and Graphical Statistics
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### Fields
15 Algebraic geometry (14-XX) 4 Combinatorics (05-XX) 4 Convex and discrete geometry (52-XX) 3 Field theory and polynomials (12-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Geometry (51-XX) 1 Computer science (68-XX)
### Citations contained in zbMATH Open
14 Publications have been cited 128 times in 109 Documents Cited by Year
Equations of tropical varieties. Zbl 1409.14100
Giansiracusa, Jeffrey; Giansiracusa, Noah
2016
Experimental study of energy-minimizing point configurations on spheres. Zbl 1185.68771
Ballinger, Brandon; Blekherman, Grigoriy; Cohn, Henry; Giansiracusa, Noah; Kelly, Elizabeth; Schürmann, Achill
2009
Conformal blocks and rational normal curves. Zbl 1279.14029
Giansiracusa, Noah
2013
The cone of type $$A$$, level 1, conformal blocks divisors. Zbl 1316.14051
Giansiracusa, Noah; Gibney, Angela
2012
On Kapranov’s description of $$\overline{M}_{0,n}$$ as a Chow quotient. Zbl 1306.14010
Giansiracusa, Noah; Gillam, William Danny
2014
GIT compactifications of $$M_{0,n}$$ and flips. Zbl 1345.14034
Giansiracusa, Noah; Jensen, David; Moon, Han-Bom
2013
A Grassmann algebra for matroids. Zbl 1384.05063
Giansiracusa, Jeffrey; Giansiracusa, Noah
2018
A simplicial approach to effective divisors in $$\overline{M}_{0,n}$$. Zbl 1405.14020
Doran, Brent; Giansiracusa, Noah; David, Jensen
2017
Factorization of point configurations, cyclic covers, and conformal blocks. Zbl 1329.14060
Bolognesi, Michele; Giansiracusa, Noah
2015
The dual complex of $${\overline{M}_{0,n}}$$ via phylogenetics. Zbl 1342.14056
Giansiracusa, Noah
2016
GIT compactifications of $$\mathcal M_{0,n}$$ from conics. Zbl 1256.14047
Giansiracusa, Noah; Simpson, Matthew
2011
Persistence terrace for topological inference of point cloud data. Zbl 07498934
Moon, Chul; Giansiracusa, Noah; Lazar, Nicole A.
2018
Modular interpretation of a non-reductive Chow quotient. Zbl 1433.14003
Gallardo, Patricio; Giansiracusa, Noah
2018
A module-theoretic approach to matroids. Zbl 1430.14114
Crowley, Colin; Giansiracusa, Noah; Mundinger, Joshua
2020
A module-theoretic approach to matroids. Zbl 1430.14114
Crowley, Colin; Giansiracusa, Noah; Mundinger, Joshua
2020
A Grassmann algebra for matroids. Zbl 1384.05063
Giansiracusa, Jeffrey; Giansiracusa, Noah
2018
Persistence terrace for topological inference of point cloud data. Zbl 07498934
Moon, Chul; Giansiracusa, Noah; Lazar, Nicole A.
2018
Modular interpretation of a non-reductive Chow quotient. Zbl 1433.14003
Gallardo, Patricio; Giansiracusa, Noah
2018
A simplicial approach to effective divisors in $$\overline{M}_{0,n}$$. Zbl 1405.14020
Doran, Brent; Giansiracusa, Noah; David, Jensen
2017
Equations of tropical varieties. Zbl 1409.14100
Giansiracusa, Jeffrey; Giansiracusa, Noah
2016
The dual complex of $${\overline{M}_{0,n}}$$ via phylogenetics. Zbl 1342.14056
Giansiracusa, Noah
2016
Factorization of point configurations, cyclic covers, and conformal blocks. Zbl 1329.14060
Bolognesi, Michele; Giansiracusa, Noah
2015
On Kapranov’s description of $$\overline{M}_{0,n}$$ as a Chow quotient. Zbl 1306.14010
Giansiracusa, Noah; Gillam, William Danny
2014
Conformal blocks and rational normal curves. Zbl 1279.14029
Giansiracusa, Noah
2013
GIT compactifications of $$M_{0,n}$$ and flips. Zbl 1345.14034
Giansiracusa, Noah; Jensen, David; Moon, Han-Bom
2013
The cone of type $$A$$, level 1, conformal blocks divisors. Zbl 1316.14051
Giansiracusa, Noah; Gibney, Angela
2012
GIT compactifications of $$\mathcal M_{0,n}$$ from conics. Zbl 1256.14047
Giansiracusa, Noah; Simpson, Matthew
2011
Experimental study of energy-minimizing point configurations on spheres. Zbl 1185.68771
Ballinger, Brandon; Blekherman, Grigoriy; Cohn, Henry; Giansiracusa, Noah; Kelly, Elizabeth; Schürmann, Achill
2009
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### Cited by 153 Authors
8 Giansiracusa, Noah 8 Jun, Jaiung 7 Moon, Han-Bom 5 Gibney, Angela 5 Rowen, Louis Halle 4 Bannai, Eiichi 4 Lorscheid, Oliver 4 Nam, Tran Giang 4 Rincón, Felipe 3 Ascher, Kenneth 3 Bannai, Etsuko 3 Belkale, Prakash 3 Boĭvalenkov, Pet”r Georgiev 3 Dragnev, Peter D. 3 Gallardo, Patricio 3 Hardin, Douglas P. 3 Maclagan, Diane 3 Saff, Edward Barry 3 Schaffler, Luca 3 Stoyanova, Maya M. 3 Swinarski, David 2 Bejleri, Dori 2 Brauchart, Johann S. 2 Cohn, Henry Lee 2 Di Nola, Antonio 2 Dutour-Sikiric, Mathieu 2 Hampe, Simon 2 Hirao, Masatake 2 Kazanova, Anna 2 Lenzi, Giacomo 2 Macpherson, Andrew W. 2 Mincheva, Kalina 2 Mixon, Dustin G. 2 Mukhopadhyay, Swarnava 2 Ranganathan, Dhruv 2 Sawa, Masanori 2 Schürmann, Achill 2 Szczesny, Matthew 2 Tolliver, Jeffrey 2 Ulirsch, Martin 2 Zumbrägel, Jens 1 Abdukhalikov, Kanat S. 1 Alexeev, Valery A. 1 Anderson, Laura 1 Anderson, Nicholas B. 1 Bachoc, François 1 Bernoff, Andrew J. 1 Bertram, Aaron 1 Birtea, Petre 1 Blume, Mark 1 Boulier, François 1 Bowler, Nathan 1 Caminata, Alessio 1 Castravet, Ana-Maria 1 Cavalieri, Renzo 1 Chan, Melody 1 Clader, Emily 1 Comănescu, Dan 1 Connes, Alain 1 Consani, Caterina 1 Crowley, Colin 1 Dick, Josef 1 Easton, Robert W. 1 Eberhardt, Jens Niklas 1 Ehler, Martin 1 Elkies, Noam David 1 Eppolito, Chris 1 Falkensteiner, Sebastian 1 Feng, Renjie 1 Feng, Tao 1 Ferreira da Rosa, Rodrigo 1 Fickus, Matthew C. 1 Foster, Tyler 1 Freedman, Sam 1 Fritzen, Felix 1 Fulger, Mihai 1 Garay López, Cristhian 1 Gatto, Letterio 1 Ge, Gennian 1 Giansiracusa, Jeffrey 1 Gillam, William Danny 1 Gonzalez, Jose Luis 1 Grabner, Peter J. 1 Gräf, Manuel 1 Gunther, Elijah 1 Güzel, Ismail 1 Haiech, Mercedes 1 Hille, Lutz 1 Hlavinka, Joseph 1 Hobson, Natalie L. F. 1 Hu, Sihuang 1 Inchiostro, Giovanni 1 Ito, Kanami 1 Izhakian, Zur 1 Jasper, John 1 Johnson, Marianne 1 Joó, Dániel 1 Joswig, Michael 1 Kambites, Mark 1 Kannan, Siddarth ...and 53 more Authors
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### Cited in 59 Serials
14 Advances in Mathematics 6 Journal of Algebra 6 Manuscripta Mathematica 4 Journal of Pure and Applied Algebra 4 Mathematische Zeitschrift 4 Journal of Algebraic Combinatorics 3 Proceedings of the American Mathematical Society 3 Constructive Approximation 2 Journal of Combinatorial Theory. Series A 2 Mathematische Annalen 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Transactions of the American Mathematical Society 2 European Journal of Combinatorics 2 Graphs and Combinatorics 2 Journal of Algebraic Geometry 2 Advances in Computational Mathematics 2 Transformation Groups 2 European Journal of Mathematics 1 Communications in Algebra 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Journal of Combinatorial Theory. Series B 1 Journal of Optimization Theory and Applications 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Topology and its Applications 1 Chinese Annals of Mathematics. Series B 1 Journal of Symbolic Computation 1 Journal of Complexity 1 Discrete & Computational Geometry 1 Journal of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 Forum Mathematicum 1 Designs, Codes and Cryptography 1 Computational Statistics 1 SIAM Journal on Applied Mathematics 1 International Journal of Robust and Nonlinear Control 1 SIAM Journal on Optimization 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal de Théorie des Nombres de Bordeaux 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Engineering Analysis with Boundary Elements 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Advances in Geometry 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 Algebra & Number Theory 1 Forum of Mathematics, Sigma 1 Proceedings of the American Mathematical Society. Series B 1 SIAM Journal on Applied Algebra and Geometry 1 Algebraic Combinatorics 1 Portugaliae Mathematica
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### Cited in 36 Fields
68 Algebraic geometry (14-XX) 28 Combinatorics (05-XX) 21 Associative rings and algebras (16-XX) 18 Convex and discrete geometry (52-XX) 14 Field theory and polynomials (12-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 8 Numerical analysis (65-XX) 7 Category theory; homological algebra (18-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Information and communication theory, circuits (94-XX) 5 Group theory and generalizations (20-XX) 4 Number theory (11-XX) 4 Commutative algebra (13-XX) 4 Quantum theory (81-XX) 3 General algebraic systems (08-XX) 3 $$K$$-theory (19-XX) 3 Potential theory (31-XX) 3 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Nonassociative rings and algebras (17-XX) 2 Partial differential equations (35-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-11-28T01:34:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2430073320865631, "perplexity": 12996.074347877824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710462.59/warc/CC-MAIN-20221128002256-20221128032256-00546.warc.gz"} |
https://lammps.sandia.gov/doc/compute_meso_t_atom.html | # compute meso/t/atom command
## Syntax
compute ID group-ID meso/t/atom
• ID, group-ID are documented in compute command
• meso/t/atom = style name of this compute command
## Examples
compute 1 all meso/t/atom
## Description
Define a computation that calculates the per-atom internal temperature for each atom in a group.
The internal temperature is the ratio of internal energy over the heat capacity associated with the internal degrees of freedom of a mesoscopic particles, e.g. a Smooth-Particle Hydrodynamics particle.
T_int = E_int / C_V, int
See this PDF guide to using SPH in LAMMPS.
The value of the internal energy will be 0.0 for atoms not in the specified compute group.
Output info:
This compute calculates a per-atom vector, which can be accessed by any command that uses per-atom values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.
The per-atom vector values will be in temperature units.
## Restrictions
This compute is part of the USER-SPH package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. | 2018-10-21T10:57:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5260801315307617, "perplexity": 5040.99288611153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583513844.48/warc/CC-MAIN-20181021094247-20181021115747-00270.warc.gz"} |
http://indico.vecc.gov.in/conferenceDisplay.py/closeMenu%3FcurrentURL=http%253A%252F%252Findico.vecc.gov.in%252Findico%252FcontributionDisplay.py%253FcontribId%253D163%2526confId%253D1&confId=1.html | # ICPAQGP-2010
5-10 December 2010
6th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP 2010)
Home > Timetable > Contribution details
$J/\Psi$ suppression: Medium modified heavy quark potential and equation of state
Content: We have proposed an equation of state of strongly coupled quark-gluon plasma in the framework of strongly coupled electromagnetic plasma with appropriate modifications to take account of color and flavor degrees of freedom and QCD running coupling constant. To do so we have derived the expression for plasma paramter, $\Gamma$ (defined as the ratio of average potential energy to average kinetic energy) incorporating the nonpertubative effects, present at and/or beyond $T_c$ to explain the nonideal behavior of QGP. Our results on thermodynamic observables {\em viz.} pressure, energy density, speed of sound etc. nicely fit the results of lattice equation of state with gluon, massless and as well {\em massive} flavored plasma. Motivated by this excellent agreement with lattice equation of state we apply our model to estimate the $J/\psi$ suppression in an expanding dissipative strongly interacting QGP produced in relativistic heavy-ion collisions and reproduce the experimental results on $J/\Psi$ suppression.
Id: 163
Place:
Room: Main Auditorium
Starting date:
--not yet scheduled--
Duration: 00'
Primary Authors: Dr. BINOY, Binoy (Indian Institute of Technology Roorkee)
Co-Authors: Mr. AGOTIYA, Vineet (Deptt. of Physics, IIT Roorkee)
Presenters: Dr. BINOY, Binoy | 2021-09-25T21:58:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5770413279533386, "perplexity": 3160.1859529805233}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00150.warc.gz"} |
https://www.ctcms.nist.gov/potentials/iprPy/calculation/relax_static/calc.html | # calc_relax_static.py
## Calculation script functions
main(*args)
Main function called when script is executed directly.
process_input(input_dict, UUID=None, build=True)
Processes str input parameters, assigns default values if needed, and generates new, more complex terms as used by the calculation.
Parameters
• input_dict (dict) – Dictionary containing the calculation input parameters with string values. The allowed keys depends on the calculation style.
• UUID (str, optional) – Unique identifier to use for the calculation instance. If not given and a ‘UUID’ key is not in input_dict, then a random UUID4 hash tag will be assigned.
• build (bool, optional) – Indicates if all complex terms are to be built. A value of False allows for default values to be assigned even if some inputs required by the calculation are incomplete. (Default is True.)
relax_static(lammps_command, system, potential, mpi_command=None, p_xx=0.0, p_yy=0.0, p_zz=0.0, p_xy=0.0, p_xz=0.0, p_yz=0.0, dispmult=0.0, etol=0.0, ftol=0.0, maxiter=10000, maxeval=100000, dmax=0.01, maxcycles=100, ctol=1e-10)
Repeatedly runs the ELASTIC example distributed with LAMMPS until box dimensions converge within a tolerance.
Parameters
• lammps_command (str) – Command for running LAMMPS.
• system (atomman.System) – The system to perform the calculation on.
• potential (atomman.lammps.Potential) – The LAMMPS implemented potential to use.
• mpi_command (str, optional) – The MPI command for running LAMMPS in parallel. If not given, LAMMPS will run serially.
• p_xx (float, optional) – The value to relax the x tensile pressure component to (default is 0.0).
• p_yy (float, optional) – The value to relax the y tensile pressure component to (default is 0.0).
• p_zz (float, optional) – The value to relax the z tensile pressure component to (default is 0.0).
• p_xy (float, optional) – The value to relax the xy shear pressure component to (default is 0.0).
• p_xz (float, optional) – The value to relax the xz shear pressure component to (default is 0.0).
• p_yz (float, optional) – The value to relax the yz shear pressure component to (default is 0.0).
• dispmult (float, optional) – Multiplier for applying a random displacement to all atomic positions prior to relaxing. Default value is 0.0.
• etol (float, optional) – The energy tolerance for the structure minimization. This value is unitless. (Default is 0.0).
• ftol (float, optional) – The force tolerance for the structure minimization. This value is in units of force. (Default is 0.0).
• maxiter (int, optional) – The maximum number of minimization iterations to use (default is 10000).
• maxeval (int, optional) – The maximum number of minimization evaluations to use (default is 100000).
• dmax (float, optional) – The maximum distance in length units that any atom is allowed to relax in any direction during a single minimization iteration (default is 0.01 Angstroms).
• pressure_unit (str, optional) – The unit of pressure to calculate the elastic constants in (default is ‘GPa’).
• maxcycles (int, optional) – The maximum number of times the minimization algorithm is called. Default value is 100.
• ctol (float, optional) – The relative tolerance used to determine if the lattice constants have converged (default is 1e-10).
Returns
Dictionary of results consisting of keys:
• ’relaxed_system’ (float) - The relaxed system.
• ’E_coh’ (float) - The cohesive energy of the relaxed system.
• ’measured_pxx’ (float) - The measured x tensile pressure of the relaxed system.
• ’measured_pyy’ (float) - The measured y tensile pressure of the relaxed system.
• ’measured_pzz’ (float) - The measured z tensile pressure of the relaxed system.
• ’measured_pxy’ (float) - The measured xy shear pressure of the relaxed system.
• ’measured_pxz’ (float) - The measured xz shear pressure of the relaxed system.
• ’measured_pyz’ (float) - The measured yz shear pressure of the relaxed system.
Return type
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https://www.zbmath.org/authors/?q=ai%3Aqi.liqun | ## Qi, Liqun
Compute Distance To:
Author ID: qi.liqun Published as: Qi, Liqun; Qi, L.; Qi, Li-qun; Qi, L. Q.; Qi, Liquin; Qi, Li-Qun; Qi, Li Qun; Qi, LiQun Homepage: http://www.polyu.edu.hk/ama/staff/new/QiLQ.htm External Links: MGP · Wikidata · Google Scholar · ResearchGate · dblp · GND
Documents Indexed: 365 Publications since 1979, including 3 Books 14 Contributions as Editor Co-Authors: 173 Co-Authors with 342 Joint Publications 6,189 Co-Co-Authors
all top 5
### Co-Authors
35 single-authored 31 Ling, Chen 22 Zhou, Guanglu 21 Sun, Defeng 19 Hu, ShengLong 17 Chen, Yannan 17 Huang, Zheng-Hai 17 Zhang, Xinzhen 16 Wei, Yimin 15 Song, Yisheng 13 Li, Guoyin 13 Tong, Xiaojiao 12 Qi, Houduo 11 Chen, Xiaojun 11 Wang, Yiju 11 Wei, Zengxin 11 Wu, Soon-Yi 10 Chen, Haibin 10 Sun, Wenyu 10 Xu, Yi 9 Birge, John R. 9 Jiang, Houyuan 9 Li, Donghui 9 Luo, ZiYan 9 Yin, Hongxia 8 Che, Maolin 8 Yang, Yufei 7 Ding, Weiyang 7 Fukushima, Masao 7 Yu, Gaohang 7 Zhang, Liping 6 Han, Deren 6 He, Hongjin 6 Shao, Jiayu 6 Teo, Kok Lay 6 Wang, Qun 6 Xu, Changqing 5 Chen, Zhongming 5 Liao, Li-Zhi 5 Liu, Jinjie 5 Wu, Ed Xuekui 5 Xu, Yanwei 5 Yang, Qingzhi 4 Caccetta, Louis 4 Dontchev, Asen L. 4 Ni, Qin 4 Sun, Jie 4 Womersley, Robert S. 4 Wu, Felix F. 4 Yan, Hong 4 Ye, Yinyu 4 Yuan, Xiying 4 Zhang, Jianzhong 4 Zou, Wennan 3 Chang, Jingya 3 Chen, Zhibing 3 Miao, Yun 3 Ng, Michael Kwok-Po 3 Ni, Guyan 3 Ouyang, Chen 3 Polak, Elijah (Lucien) 3 Xie, Jinshan 3 Yang, Xiaoqi 3 Yang, Yuning 2 Balas, Egon 2 Chang, Kung-Ching 2 Chen, Jinhai 2 Chi, Zongtao 2 Dai, Hui-Hui 2 Gwan, Geena 2 Kelley, Carl T. 2 Li, Yaotang 2 Mifflin, Robert 2 Mo, Jiangtao 2 Nashed, Zuhair 2 Pang, Jong-Shi 2 Tseng, Paul 2 Zhang, Guofeng 2 Zhang, Tan 1 Alqahtani, Mohammed 1 Bai, Minru 1 Bai, Zhengjian 1 Bakshi, Mayank 1 Bohnet-Waldraff, Fabian 1 Bomze, Immanuel M. 1 Braun, Daniel 1 Bu, Changjiang 1 Burke, James V. 1 Chan, Cheong-ki K. 1 Chen, Chiyu 1 Chen, Xin 1 Chu, Moody T. 1 Cui, Chunfeng 1 Du, Ding-Zhu 1 Du, Shouqiang 1 Facchinei, Francisco 1 Fang, Shu-Cherng 1 Friedland, Shmuel 1 Giraud, Olivier 1 Gu, Guangze 1 Gu, Lejia ...and 73 more Co-Authors
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### Serials
29 Journal of Optimization Theory and Applications 21 Linear Algebra and its Applications 20 Journal of Global Optimization 19 SIAM Journal on Optimization 19 Computational Optimization and Applications 15 Mathematical Programming. Series A. Series B 15 Numerical Linear Algebra with Applications 14 Journal of Computational and Applied Mathematics 13 Frontiers of Mathematics in China 11 SIAM Journal on Matrix Analysis and Applications 11 Communications in Mathematical Sciences 9 Applied Mathematics and Computation 8 Mathematics of Operations Research 8 Journal of Industrial and Management Optimization 7 Journal of Mathematical Analysis and Applications 7 Pacific Journal of Optimization 6 Linear and Multilinear Algebra 6 Optimization Methods & Software 5 Numerical Functional Analysis and Optimization 5 SIAM Journal on Numerical Analysis 5 Journal of Scientific Computing 5 Journal of Combinatorial Optimization 4 Mathematics of Computation 4 Annals of Operations Research 4 Optimization Letters 4 Science China. Mathematics 3 Discrete Applied Mathematics 3 Numerische Mathematik 3 SIAM Journal on Control and Optimization 3 Numerical Mathematics 3 Operations Research Letters 3 Optimization 3 Journal of Symbolic Computation 3 Journal of the Operations Research Society of China 2 Applied Mathematics and Optimization 2 IEEE Transactions on Automatic Control 2 Mathematical Programming Study 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Asia-Pacific Journal of Operational Research 2 Applied Mathematics Letters 2 SIAM Journal on Scientific Computing 2 Journal of Convex Analysis 2 Applied Optimization 2 SIAM Journal on Imaging Sciences 2 Numerical Mathematics: Theory, Methods and Applications 2 Journal of Suzhou University of Science and Technology. Natural Science Edition 2 Numerical Algebra, Control and Optimization 2 Nonlinear Analysis. Theory, Methods & Applications 2 Minimax Theory and its Applications 1 International Journal of Theoretical Physics 1 Journal of Mathematical Physics 1 Physics Letters. A 1 BIT 1 Computing 1 Management Science 1 Journal of Computational Mathematics 1 Constructive Approximation 1 Journal of Tsinghua University. Science and Technology 1 Signal Processing 1 IEEE Transactions on Signal Processing 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Journal of Elasticity 1 The Australasian Journal of Combinatorics 1 Journal of Mathematical Imaging and Vision 1 Numerical Mathematics 1 Mathematics and Mechanics of Solids 1 Journal of Inequalities and Applications 1 Optimization and Engineering 1 Analysis and Applications (Singapore) 1 International Journal of Numerical Analysis and Modeling 1 Advances in Mechanics and Mathematics 1 Advanced Modeling and Optimization 1 Journal of Physics A: Mathematical and Theoretical 1 Inverse Problems and Imaging 1 Communications in Mathematical Research 1 Scientia Sinica. Mathematica 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Annals of Applied Mathematics 1 Other Titles in Applied Mathematics 1 Communications on Applied Mathematics and Computation
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### Fields
212 Operations research, mathematical programming (90-XX) 150 Numerical analysis (65-XX) 137 Linear and multilinear algebra; matrix theory (15-XX) 50 Calculus of variations and optimal control; optimization (49-XX) 28 Combinatorics (05-XX) 15 General and overarching topics; collections (00-XX) 12 Differential geometry (53-XX) 9 Operator theory (47-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Real functions (26-XX) 8 Quantum theory (81-XX) 7 Approximations and expansions (41-XX) 6 Mechanics of deformable solids (74-XX) 5 Algebraic geometry (14-XX) 5 Probability theory and stochastic processes (60-XX) 5 Computer science (68-XX) 5 Information and communication theory, circuits (94-XX) 4 Functional analysis (46-XX) 4 Convex and discrete geometry (52-XX) 4 Biology and other natural sciences (92-XX) 3 Commutative algebra (13-XX) 3 Ordinary differential equations (34-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Statistics (62-XX) 2 Optics, electromagnetic theory (78-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX)
### Citations contained in zbMATH Open
330 Publications have been cited 8,862 times in 2,985 Documents Cited by Year
A nonsmooth version of Newton’s method. Zbl 0780.90090
Qi, Liqun; Sun, Jie
1993
Eigenvalues of a real supersymmetric tensor. Zbl 1125.15014
Qi, Liqun
2005
Convergence analysis of some algorithms for solving nonsmooth equations. Zbl 0776.65037
Qi, Liqun
1993
A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Zbl 0989.90124
Qi, Liqun; Sun, Defeng; Zhou, Guanglu
2000
Finding the largest eigenvalue of a nonnegative tensor. Zbl 1197.65036
Ng, Michael; Qi, Liqun; Zhou, Guanglu
2010
Nonsmooth equations: Motivation and algorithms. Zbl 0784.90082
Pang, Jong-Shi; Qi, Liqun
1993
Tensor analysis. Spectral theory and special tensors. Zbl 1370.15001
Qi, Liqun; Luo, Ziyan
2017
$$M$$-tensors and some applications. Zbl 1307.15034
Zhang, Liping; Qi, Liqun; Zhou, Guanglu
2014
$$M$$-tensors and nonsingular $$M$$-tensors. Zbl 1283.15074
Ding, Weiyang; Qi, Liqun; Wei, Yimin
2013
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities. Zbl 0894.90143
Chen, X.; Qi, L.; Sun, D.
1998
Symmetric nonnegative tensors and copositive tensors. Zbl 1281.15025
Qi, Liqun
2013
A smoothing method for mathematical programs with equilibrium constraints. Zbl 0959.65079
Facchinei, Francisco; Jiang, Houyuan; Qi, Liqun
1999
Eigenvalues and invariants of tensors. Zbl 1113.15020
Qi, Liqun
2007
Smoothing methods and semismooth methods for nondifferentiable operator equations. Zbl 0979.65046
Chen, Xiaojun; Nashed, Zuhair; Qi, Liqun
2000
On the constant positive linear dependence condition and its application to SQP methods. Zbl 0999.90037
Qi, Liqun; Wei, Zengxin
2000
An eigenvalue method for testing positive definiteness of a multivariate form. Zbl 1367.93565
Ni, Qin; Qi, Liqun; Wang, Fei
2008
Properties of some classes of structured tensors. Zbl 1390.15085
Song, Yisheng; Qi, Liqun
2015
Z-eigenvalue methods for a global polynomial optimization problem. Zbl 1169.90022
Qi, Liqun; Wang, Fei; Wang, Yiju
2009
Higher order positive semidefinite diffusion tensor imaging. Zbl 1197.92032
Qi, Liqun; Yu, Gaohang; Wu, Ed X.
2010
$$H^{+}$$-eigenvalues of Laplacian and signless Laplacian tensors. Zbl 1305.05134
Qi, Liqun
2014
On determinants and eigenvalue theory of tensors. Zbl 1259.15038
Hu, Shenglong; Huang, Zheng-Hai; Ling, Chen; Qi, Liqun
2013
Positive-definite tensors to nonlinear complementarity problems. Zbl 1334.90174
Che, Maolin; Qi, Liqun; Wei, Yimin
2016
A new nonsmooth equations approach to nonlinear complementarity problems. Zbl 0872.90097
Jiang, Houyuan; Qi, Liqun
1997
The sparsest solutions to $$Z$$-tensor complementarity problems. Zbl 1394.90540
Luo, Ziyan; Qi, Liqun; Xiu, Naihua
2017
New quasi-Newton methods for unconstrained optimization problems. Zbl 1100.65054
Wei, Zengxin; Li, Guoyin; Qi, Liqun
2006
Algebraic connectivity of an even uniform hypergraph. Zbl 1261.05072
Hu, Shenglong; Qi, Liqun
2012
Tensor complementarity problem and semi-positive tensors. Zbl 1349.90803
Song, Yisheng; Qi, Liqun
2016
Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues. Zbl 1282.05171
Hu, Shenglong; Qi, Liqun; Shao, Jia-Yu
2013
On NCP-functions. Zbl 1040.90544
Sun, Defeng; Qi, Liqun
1999
Formulating an $$n$$-person noncooperative game as a tensor complementarity problem. Zbl 1393.90120
Huang, Zheng-Hai; Qi, Liqun
2017
D-eigenvalues of diffusion kurtosis tensors. Zbl 1176.65046
Qi, Liqun; Wang, Yiju; Wu, Ed X.
2008
A practical method for computing the largest $$M$$-eigenvalue of a fourth-order partially symmetric tensor. Zbl 1224.65101
Wang, Yiju; Qi, Liqun; Zhang, Xinzhen
2009
A survey on the spectral theory of nonnegative tensors. Zbl 1313.15015
Chang, Kungching; Qi, Liqun; Zhang, Tan
2013
The $$Z$$-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory. Zbl 1313.65081
Li, Guoyin; Qi, Liqun; Yu, Gaohang
2013
Inexact Newton methods for solving nonsmooth equations. Zbl 0833.65045
Martínez, José Mario; Qi, Liqun
1995
Numerical multilinear algebra and its applications. Zbl 1134.65033
Qi, Liqun; Sun, Wenyu; Wang, Yiju
2007
Biquadratic optimization over unit spheres and semidefinite programming relaxations. Zbl 1221.90074
Ling, Chen; Nie, Jiawang; Qi, Liqun; Ye, Yinyu
2009
Tensor eigenvalues and their applications. Zbl 1398.15001
Qi, Liqun; Chen, Haibin; Chen, Yannan
2018
An even order symmetric $$B$$ tensor is positive definite. Zbl 1295.15017
Qi, Liqun; Song, Yisheng
2014
The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Zbl 1288.05157
Hu, Shenglong; Qi, Liqun
2014
The extremal spectral radii of $$k$$-uniform supertrees. Zbl 1378.90084
Li, Honghai; Shao, Jia-Yu; Qi, Liqun
2016
Sub-quadratic convergence of a smoothing Newton algorithm for the $$P_0$$- and monotone LCP. Zbl 1168.90646
Huang, Zheng-Hai; Qi, Liqun; Sun, Defeng
2004
A globally and superlinearly convergent algorithm for nonsmooth convex minimization. Zbl 0868.90109
Fukushima, Masao; Qi, Liqun
1996
Superlinearly convergent approximate Newton methods for LC$$^ 1$$ optimization problems. Zbl 0820.90102
Qi, Liqun
1994
Improving the convergence of non-interior point algorithms for nonlinear complementarity problems. Zbl 0947.90117
Qi, Liqun; Sun, Defeng
2000
Strictly nonnegative tensors and nonnegative tensor partition. Zbl 1312.15035
Hu, Shenglong; Huang, Zhenghai; Qi, Liqun
2014
Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines. Zbl 1121.14050
Qi, Liqun
2006
Spectral properties of positively homogeneous operators induced by higher order tensors. Zbl 1355.15009
Song, Yisheng; Qi, Liqun
2013
The largest Laplacian and signless Laplacian $$H$$-eigenvalues of a uniform hypergraph. Zbl 1305.05129
Hu, Shenglong; Qi, Liqun; Xie, Jinshan
2015
Smoothing functions and smoothing Newton method for complementarity and variational inequality problems. Zbl 1032.49017
Qi, L.; Sun, D.
2002
Properties of tensor complementarity problem and some classes of structured tensors. Zbl 1399.15036
Song, Yisheng; Qi, Liqun
2017
The best rank-1 approximation of a symmetric tensor and related spherical optimization problems. Zbl 1269.15026
Zhang, Xinzhen; Ling, Chen; Qi, Liqun
2012
Column sufficient tensors and tensor complementarity problems. Zbl 1418.90253
Chen, Haibin; Qi, Liqun; Song, Yisheng
2018
Conditions for strong ellipticity and M-eigenvalues. Zbl 1233.74004
Qi, Liqun; Dai, Hui-Hui; Han, Deren
2009
Semismooth Karush-Kuhn-Tucker equations and convergence analysis of Newton and quasi-Newton methods for solving these equations. Zbl 0881.65054
Qi, Liqun; Jiang, Houyuan
1997
Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor. Zbl 1274.65129
Zhang, Liping; Qi, Liqun
2012
Nonnegative tensor factorization, completely positive tensors, and a hierarchical elimination algorithm. Zbl 1317.65114
Qi, Liqun; Xu, Changqing; Xu, Yi
2014
Conditions for strong ellipticity of anisotropic elastic materials. Zbl 1252.74006
Han, Deren; Dai, H. H.; Qi, Liqun
2009
The degree of the E-characteristic polynomial of an even order tensor. Zbl 1154.15304
Ni, Guyan; Qi, Liqun; Wang, Fei; Wang, Yiju
2007
Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors. Zbl 1371.15023
Chen, Haibin; Qi, Liqun
2015
A globally convergent successive approximation method for severely nonsmooth equations. Zbl 0833.90109
Qi, Liqun; Chen, Xiaojun
1995
A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization. Zbl 0999.90038
Qi, Hou-Duo; Qi, Liqun
2000
Multivariate polynomial minimization and its application in signal processing. Zbl 1023.90064
Qi, Liqun; Teo, Kok Lay
2003
A globally convergent Newton method for convex $$SC^ 1$$ minimization problems. Zbl 0831.90095
Pang, J. S.; Qi, L.
1995
A parameterized Newton method and a quasi-Newton method for nonsmooth equations. Zbl 0821.65029
Chen, Xiaojun; Qi, Liqun
1994
Active-set projected trust-region algorithm for box-constrained nonsmooth equations. Zbl 1140.65331
Qi, L.; Tong, X. J.; Li, D. H.
2004
Hankel tensors: associated Hankel matrices and Vandermonde decomposition. Zbl 1331.15020
Qi, Liqun
2015
A trust region method for solving generalized complementarity problems. Zbl 0911.90324
Jiang, Houyuan; Fukushima, Masao; Qi, Liqun; Sun, Defeng
1998
A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems. Zbl 1079.90094
Sun, Jie; Sun, Defeng; Qi, Liqun
2004
Singular values of a real rectangular tensor. Zbl 1201.15003
Chang, Kungching; Qi, Liqun; Zhou, Guanglu
2010
On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions. Zbl 1069.65055
Tong, X. J.; Qi, L.
2004
Necessary and sufficient conditions for copositive tensors. Zbl 1311.15026
Song, Yisheng; Qi, Liqun
2015
Descent directions of quasi-Newton methods for symmetric nonlinear equations. Zbl 1047.65032
Gu, Guang-Ze; Li, Dong-Hui; Qi, Liqun; Zhou, Shu-Zi
2002
Strictly semi-positive tensors and the boundedness of tensor complementarity problems. Zbl 1454.90098
Song, Yisheng; Qi, Liqun
2017
A smoothing Newton method for semi-infinite programming. Zbl 1066.90131
Li, Dong-Hui; Qi, Liqun; Tam, Judy; Wu, Soon-Yi
2004
Infinite and finite dimensional Hilbert tensors. Zbl 1292.15027
Song, Yisheng; Qi, Liqun
2014
Semismooth Newton methods for solving semi-infinite programming problems. Zbl 1033.90137
Qi, Liqun; Wu, Soon-Yi; Zhou, Guanglu
2003
A survey of some nonsmooth equations and smoothing Newton methods. Zbl 0957.65042
Qi, L.; Sun, D.
1999
Secant methods for semismooth equations. Zbl 0914.65051
Potra, Florian A.; Qi, Liqun; Sun, Defeng
1998
New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems. Zbl 1106.65055
Wei, Zengxin; Li, Guoyin; Qi, Liqun
2006
The best rank-one approximation ratio of a tensor space. Zbl 1228.15010
Qi, Liqun
2011
On the cone eigenvalue complementarity problem for higher-order tensors. Zbl 1339.15008
Ling, Chen; He, Hongjin; Qi, Liqun
2016
Regular uniform hypergraphs, $$s$$-cycles, $$s$$-paths and their largest Laplacian H-eigenvalues. Zbl 1282.05174
Qi, Liqun; Shao, Jia-Yu; Wang, Qun
2014
A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map. Zbl 1342.90150
Ni, Qin; Qi, Liqun
2015
Global convergence of the Polak-Ribière-Polyak conjugate gradient method with an Armijo-type inexact line search for nonconvex unconstrained optimization problems. Zbl 1198.65091
Wei, Zeng Xin; Li, Guo Yin; Qi, Li Qun
2008
Comments on: “Explicit criterion for the positive definiteness of a general quartic form” by W. H. Ku. Zbl 1365.13048
Wang, Fei; Qi, Liqun
2005
Copositivity detection of tensors: theory and algorithm. Zbl 1377.65060
Chen, Haibin; Huang, Zheng-Hai; Qi, Liqun
2017
Computing block-angular Karmarkar projections with applications to stochastic programming. Zbl 0664.90051
Birge, John R.; Qi, Liqun
1988
Some simple estimates for singular values of a matrix. Zbl 0525.15009
Qi, Liqun
1984
$$\mathrm{P}$$-tensors, $$\mathrm{P}_0$$-tensors, and their applications. Zbl 1396.15020
Ding, Weiyang; Luo, Ziyan; Qi, Liqun
2018
Copositive tensor detection and its applications in physics and hypergraphs. Zbl 1383.65061
Chen, Haibin; Huang, Zheng-Hai; Qi, Liqun
2018
Tensor complementarity problems. I: Basic theory. Zbl 1434.90203
Huang, Zheng-Hai; Qi, Liqun
2019
On the minimum norm solution of linear programs. Zbl 1043.90046
Kanzow, C.; Qi, H.; Qi, L.
2003
The Laplacian of a uniform hypergraph. Zbl 1309.05120
Hu, Shenglong; Qi, Liqun
2015
A fast algorithm for the spectral radii of weakly reducible nonnegative tensors. Zbl 06861606
Zhou, Guanglu; Wang, Gang; Qi, Liqun; Alqahtani, Mohammed
2018
A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test. Zbl 1438.65060
Chen, Haibin; Chen, Yannan; Li, Guoyin; Qi, Liqun
2018
A trust region algorithm for minimization of locally Lipschitzian functions. Zbl 0821.90108
Qi, Liqun; Sun, Jie
1994
Tensor complementarity problems. II: Solution methods. Zbl 1429.90082
Qi, Liqun; Huang, Zheng-Hai
2019
A feasible sequential linear equation method for inequality constrained optimization. Zbl 1101.90394
Yang, Yu-Fei; Li, Dong-Hui; Qi, Liqun
2003
Differentiability and semismoothness properties of integral functions and their applications. Zbl 1079.90143
Qi, Liqun; Shapiro, Alexander; Ling, Chen
2005
Spectral norm and nuclear norm of a third order tensor. Zbl 07475159
Qi, Liqun; Hu, Shenglong; Xu, Yanwei
2022
T-Jordan canonical form and T-Drazin inverse based on the T-product. Zbl 1476.15045
Miao, Yun; Qi, Liqun; Wei, Yimin
2021
Triple decomposition and tensor recovery of third order tensors. Zbl 1467.15020
Qi, Liqun; Chen, Yannan; Bakshi, Mayank; Zhang, Xinzhen
2021
Analytical expressions of copositivity for fourth-order symmetric tensors. Zbl 07421751
Song, Yisheng; Qi, Liqun
2021
Generalized tensor function via the tensor singular value decomposition based on the T-product. Zbl 1437.15034
Miao, Yun; Qi, Liqun; Wei, Yimin
2020
Modified gradient dynamic approach to the tensor complementarity problem. Zbl 1432.37105
Wang, Xuezhong; Che, Maolin; Qi, Liqun; Wei, Yimin
2020
Further study on tensor absolute value equations. Zbl 1469.15017
Ling, Chen; Yan, Weijie; He, Hongjin; Qi, Liqun
2020
Elasticity $$\mathcal{M}$$-tensors and the strong ellipticity condition. Zbl 1433.74028
Ding, Weiyang; Liu, Jinjie; Qi, Liqun; Yan, Hong
2020
Expected residual minimization method for monotone stochastic tensor complementarity problem. Zbl 1466.90113
Ming, Zhenyu; Zhang, Liping; Qi, Liqun
2020
M-eigenvalues of the Riemann curvature tensor of conformally flat manifolds. Zbl 1474.53192
Miao, Yun; Qi, Liqun; Yiminwei
2020
The generalized order tensor complementarity problems. Zbl 1463.90221
Che, Maolin; Qi, Liqun; Wei, Yimin
2020
Stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. Zbl 1454.60117
Huang, Zheng-Hai; Qi, Liqun
2020
Tensor complementarity problems. I: Basic theory. Zbl 1434.90203
Huang, Zheng-Hai; Qi, Liqun
2019
Tensor complementarity problems. II: Solution methods. Zbl 1429.90082
Qi, Liqun; Huang, Zheng-Hai
2019
Tensor complementarity problems. III: Applications. Zbl 1433.90169
Huang, Zheng-Hai; Qi, Liqun
2019
Stochastic $$R_0$$ tensors to stochastic tensor complementarity problems. Zbl 1417.90108
Che, Maolin; Qi, Liqun; Wei, Yimin
2019
Test of copositive tensors. Zbl 1463.65141
Li, Li; Zhang, Xinzhen; Huang, Zheng-Hai; Qi, Liqun
2019
Birkhoff-von Neumann theorem and decomposition for doubly stochastic tensors. Zbl 1425.65065
Chen, Haibin; Qi, Liqun; Caccetta, Louis; Zhou, Guanglu
2019
Nonnegative tensors revisited: plane stochastic tensors. Zbl 1412.15010
Che, Maolin; Bu, Changjiang; Qi, Liqun; Wei, Yimin
2019
Two irreducible functional bases of isotropic invariants of a fourth-order three-dimensional symmetric and traceless tensor. Zbl 07273355
Chen, Zhongming; Chen, Yannan; Qi, Liqun; Zou, Wennan
2019
Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor. Zbl 1411.15020
Chen, Yannan; Hu, Shenglong; Qi, Liqun; Zou, Wennan
2019
Tensor eigenvalues and their applications. Zbl 1398.15001
Qi, Liqun; Chen, Haibin; Chen, Yannan
2018
Column sufficient tensors and tensor complementarity problems. Zbl 1418.90253
Chen, Haibin; Qi, Liqun; Song, Yisheng
2018
$$\mathrm{P}$$-tensors, $$\mathrm{P}_0$$-tensors, and their applications. Zbl 1396.15020
Ding, Weiyang; Luo, Ziyan; Qi, Liqun
2018
Copositive tensor detection and its applications in physics and hypergraphs. Zbl 1383.65061
Chen, Haibin; Huang, Zheng-Hai; Qi, Liqun
2018
A fast algorithm for the spectral radii of weakly reducible nonnegative tensors. Zbl 06861606
Zhou, Guanglu; Wang, Gang; Qi, Liqun; Alqahtani, Mohammed
2018
A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test. Zbl 1438.65060
Chen, Haibin; Chen, Yannan; Li, Guoyin; Qi, Liqun
2018
Tensor absolute value equations. Zbl 1401.15024
Du, Shouqiang; Zhang, Liping; Chen, Chiyu; Qi, Liqun
2018
Global uniqueness and solvability of tensor variational inequalities. Zbl 1409.90207
Wang, Yong; Huang, Zheng-Hai; Qi, Liqun
2018
A globally and quadratically convergent algorithm for solving multilinear systems with $$\mathcal {M}$$-tensors. Zbl 1397.65047
He, Hongjin; Ling, Chen; Qi, Liqun; Zhou, Guanglu
2018
Positive definiteness of paired symmetric tensors and elasticity tensors. Zbl 1392.74015
Huang, Zheng-Hai; Qi, Liqun
2018
Octupolar tensors for liquid crystals. Zbl 1383.82065
Chen, Yannan; Qi, Liqun; Virga, Epifanio G.
2018
Spectral radii of two kinds of uniform hypergraphs. Zbl 1427.05136
Kang, Liying; Liu, Lele; Qi, Liqun; Yuan, Xiying
2018
An irreducible function basis of isotropic invariants of a third order three-dimensional symmetric tensor. Zbl 1467.74009
Chen, Zhongming; Liu, Jinjie; Qi, Liqun; Zheng, Quanshui; Zou, Wennan
2018
How entangled can a multi-party system possibly be? Zbl 1428.81030
Qi, Liqun; Zhang, Guofeng; Ni, Guyan
2018
Computing the $$p$$-spectral radii of uniform hypergraphs with applications. Zbl 1386.05103
Chang, Jingya; Ding, Weiyang; Qi, Liqun; Yan, Hong
2018
$$M$$-eigenvalues of the Riemann curvature tensor. Zbl 1417.83012
Qi, Liqun; Wei, Yimin; Xiang, Hua
2018
Some properties and applications of odd-colorable $$r$$-hypergraphs. Zbl 1377.05133
Yuan, Xiying; Qi, Liqun; Shao, Jiayu; Ouyang, Chen
2018
A quadratic penalty method for hypergraph matching. Zbl 1393.90093
Cui, Chunfeng; Li, Qingna; Qi, Liqun; Yan, Hong
2018
Isotropic polynomial invariants of Hall tensor. Zbl 1416.15020
Liu, Jinjie; Ding, Weiyang; Qi, Liqun; Zou, Wennan
2018
A note on the multidimensional moment problem. Zbl 1405.44007
Qi, Liqun
2018
Tensor analysis. Spectral theory and special tensors. Zbl 1370.15001
Qi, Liqun; Luo, Ziyan
2017
The sparsest solutions to $$Z$$-tensor complementarity problems. Zbl 1394.90540
Luo, Ziyan; Qi, Liqun; Xiu, Naihua
2017
Formulating an $$n$$-person noncooperative game as a tensor complementarity problem. Zbl 1393.90120
Huang, Zheng-Hai; Qi, Liqun
2017
Properties of tensor complementarity problem and some classes of structured tensors. Zbl 1399.15036
Song, Yisheng; Qi, Liqun
2017
Strictly semi-positive tensors and the boundedness of tensor complementarity problems. Zbl 1454.90098
Song, Yisheng; Qi, Liqun
2017
Copositivity detection of tensors: theory and algorithm. Zbl 1377.65060
Chen, Haibin; Huang, Zheng-Hai; Qi, Liqun
2017
Programmable criteria for strong $$\mathcal {H}$$-tensors. Zbl 1357.65048
Li, Yaotang; Liu, Qilong; Qi, Liqun
2017
The first few unicyclic and bicyclic hypergraphs with largest spectral radii. Zbl 1365.15024
Ouyang, Chen; Qi, Liqun; Yuan, Xiying
2017
The Fiedler vector of a Laplacian tensor for hypergraph partitioning. Zbl 1375.05184
Chen, Yannan; Qi, Liqun; Zhang, Xiaoyan
2017
Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms. Zbl 1360.65121
Ding, Weiyang; Qi, Liqun; Wei, Yimin
2017
The adjacency and signless Laplacian spectra of cored hypergraphs and power hypergraphs. Zbl 1368.05099
Yue, Jun-Jie; Zhang, Li-Ping; Lu, Mei; Qi, Li-Qun
2017
Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems. Zbl 1371.15010
Che, Maolin; Li, Guoyin; Qi, Liqun; Wei, Yimin
2017
Improved approximation results on standard quartic polynomial optimization. Zbl 1410.90167
Ling, Chen; He, Hongjin; Qi, Liqun
2017
New classes of positive semi-definite Hankel tensors. Zbl 1409.15008
Wang, Qun; Li, Guoyin; Qi, Liqun; Xu, Yi
2017
Iterative algorithms for computing US- and U-eigenpairs of complex tensors. Zbl 1357.65042
Che, Maolin; Qi, Liqun; Wei, Yimin
2017
Infinite-dimensional Hilbert tensors on spaces of analytic functions. Zbl 1390.30058
Song, Yisheng; Qi, Liqun
2017
Tensor and hypergraph. Zbl 1391.00053
2017
Positive-definite tensors to nonlinear complementarity problems. Zbl 1334.90174
Che, Maolin; Qi, Liqun; Wei, Yimin
2016
Tensor complementarity problem and semi-positive tensors. Zbl 1349.90803
Song, Yisheng; Qi, Liqun
2016
The extremal spectral radii of $$k$$-uniform supertrees. Zbl 1378.90084
Li, Honghai; Shao, Jia-Yu; Qi, Liqun
2016
On the cone eigenvalue complementarity problem for higher-order tensors. Zbl 1339.15008
Ling, Chen; He, Hongjin; Qi, Liqun
2016
Eigenvalue analysis of constrained minimization problem for homogeneous polynomial. Zbl 1341.15009
Song, Yisheng; Qi, Liqun
2016
Computing extreme eigenvalues of large scale Hankel tensors. Zbl 1377.65046
Chen, Yannan; Qi, Liqun; Wang, Qun
2016
Circulant tensors with applications to spectral hypergraph theory and stochastic process. Zbl 1364.15017
Chen, Zhongming; Qi, Liqun
2016
Completely positive tensors: properties, easily checkable subclasses, and tractable relaxations. Zbl 1349.15026
Luo, Ziyan; Qi, Liqun
2016
The proof of a conjecture on largest Laplacian and signless Laplacian H-eigenvalues of uniform hypergraphs. Zbl 1330.15025
Yuan, Xiying; Qi, Liqun; Shao, Jiayu
2016
SOS tensor decomposition: theory and applications. Zbl 1351.90148
Chen, Haibin; Li, Guoyin; Qi, Liqun
2016
A semismooth Newton method for tensor eigenvalue complementarity problem. Zbl 1377.90096
Chen, Zhongming; Qi, Liqun
2016
Higher-degree eigenvalue complementarity problems for tensors. Zbl 1338.15027
Ling, Chen; He, Hongjin; Qi, Liqun
2016
A tensor analogy of Yuan’s theorem of the alternative and polynomial optimization with sign structure. Zbl 1338.90317
Hu, Shenglong; Li, Guoyin; Qi, Liqun
2016
Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors. Zbl 1334.15025
Chen, Yannan; Qi, Liqun; Wang, Qun
2016
Comon’s conjecture, rank decomposition, and symmetric rank decomposition of symmetric tensors. Zbl 1349.15004
Zhang, Xinzhen; Huang, Zheng-Hai; Qi, Liqun
2016
Further results on Cauchy tensors and Hankel tensors. Zbl 1410.15048
Chen, Haibin; Li, Guoyin; Qi, Liqun
2016
Spectral directed hypergraph theory via tensors. Zbl 1335.05125
Xie, Jinshan; Qi, Liqun
2016
Perturbation bounds of tensor eigenvalue and singular value problems with even order. Zbl 1344.15007
Che, Maolin; Qi, Liqun; Wei, Yimin
2016
Computing eigenvalues of large scale sparse tensors arising from a hypergraph. Zbl 1350.05109
Chang, Jingya; Chen, Yannan; Qi, Liqun
2016
A necessary and sufficient condition for existence of a positive Perron vector. Zbl 1355.15019
Hu, Shenglong; Qi, Liqun
2016
Positive semi-definiteness of generalized anti-circulant tensors. Zbl 1353.15026
Li, Guoyin; Qi, Liqun; Wang, Qun
2016
Spectral properties of odd-bipartite $$Z$$-tensors and their absolute tensors. Zbl 1360.90237
Chen, Haibin; Qi, Liqun
2016
$$\{0,1\}$$ completely positive tensors and multi-hypergraphs. Zbl 1354.05099
Xu, Changqing; Luo, Ziyan; Qi, Liqun; Chen, Zhibing
2016
Linear algebra and multilinear algebra. Zbl 1360.00134
2016
Properties of some classes of structured tensors. Zbl 1390.15085
Song, Yisheng; Qi, Liqun
2015
The largest Laplacian and signless Laplacian $$H$$-eigenvalues of a uniform hypergraph. Zbl 1305.05129
Hu, Shenglong; Qi, Liqun; Xie, Jinshan
2015
Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors. Zbl 1371.15023
Chen, Haibin; Qi, Liqun
2015
Hankel tensors: associated Hankel matrices and Vandermonde decomposition. Zbl 1331.15020
Qi, Liqun
2015
Necessary and sufficient conditions for copositive tensors. Zbl 1311.15026
Song, Yisheng; Qi, Liqun
2015
A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map. Zbl 1342.90150
Ni, Qin; Qi, Liqun
2015
The Laplacian of a uniform hypergraph. Zbl 1309.05120
Hu, Shenglong; Qi, Liqun
2015
Fast Hankel tensor-vector product and its application to exponential data fitting. Zbl 1349.65070
Ding, Weiyang; Qi, Liqun; Wei, Yimin
2015
Some new trace formulas of tensors with applications in spectral hypergraph theory. Zbl 1310.15042
Shao, Jia-Yu; Qi, Liqun; Hu, Shenglong
2015
$$MB$$-tensors and $$MB_0$$-tensors. Zbl 1325.15022
Li, Chaoqian; Qi, Liqun; Li, Yaotang
2015
Linear operators and positive semidefiniteness of symmetric tensor spaces. Zbl 1308.15025
Luo, ZiYan; Qi, LiQun; Ye, YinYu
2015
On solving a class of linear semi-infinite programming by SDP method. Zbl 1311.90160
Xu, Yi; Sun, Wenyu; Qi, Liqun
2015
The clique and coclique numbers’ bounds based on the H-eigenvalues of uniform hypergraphs. Zbl 1329.05221
Xie, Jinshan; Qi, Liqun
2015
Three dimensional strongly symmetric circulant tensors. Zbl 1321.15043
Qi, Liqun; Wang, Qun; Chen, Yannan
2015
$$M$$-tensors and some applications. Zbl 1307.15034
Zhang, Liping; Qi, Liqun; Zhou, Guanglu
2014
$$H^{+}$$-eigenvalues of Laplacian and signless Laplacian tensors. Zbl 1305.05134
Qi, Liqun
2014
An even order symmetric $$B$$ tensor is positive definite. Zbl 1295.15017
Qi, Liqun; Song, Yisheng
2014
The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Zbl 1288.05157
Hu, Shenglong; Qi, Liqun
2014
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### Cited by 2,851 Authors
207 Qi, Liqun 59 Huang, Zheng-Hai 49 Ma, Changfeng 46 Wang, Yiju 45 Wei, Yimin 42 Kanzow, Christian 36 Chen, Jein-Shan 35 Hu, ShengLong 34 Martínez, José Mario 34 Zhang, Liwei 33 Wei, Zengxin 33 Yuan, Gonglin 31 Li, Chaoqian 30 Bu, Changjiang 30 Sun, Defeng 29 Li, Yaotang 29 Ling, Chen 28 Jian, Jinbao 27 Zhou, Guanglu 26 Chen, Haibin 26 Chen, Xiaojun 26 Sun, Jie 25 Zhang, Liping 22 Fukushima, Masao 22 Tang, Jingyong 22 Zhang, Xinzhen 21 Andreani, Roberto 21 Li, Wen 20 Chen, Yannan 20 Du, Shouqiang 20 Liu, Sanyang 20 Song, Yisheng 20 Wu, Soon-Yi 19 He, Jun 19 Li, Donghui 19 Pu, Dingguo 19 Zhou, Jinchuan 18 Gao, Yan 18 Sun, Wenyu 18 Xiu, Naihua 18 Zhao, Jianxing 17 Pan, Shaohua 16 Fang, Liang 16 Kang, Liying 16 Toh, Kim Chuan 16 Tong, Xiaojiao 16 Zhang, Jianzhong 15 Che, Maolin 15 Fan, Yizheng 15 Haeser, Gabriel 15 Li, Guoyin 15 Yang, Qingzhi 14 Birgin, Ernesto G. 14 Chiou, Suh-Wen 14 He, Hongjin 14 Liu, Hongwei 14 Liu, Yanmin 14 Ng, Michael Kwok-Po 14 Ou, Yigui 14 Pang, Jong-Shi 14 Yang, Xiaoqi 13 Dong, Li 13 Li, Zhening 13 Liao, Li-Zhi 13 Ni, Qin 13 Nie, Jiawang 13 Qi, Houduo 13 Sang, Caili 13 Shen, Chungen 13 Vong, Seakweng 13 Wang, Qingwen 13 Zhou, Jiang 12 Che, Haitao 12 Ding, Weiyang 12 Fan, Jinyan 12 Ferreira, Orizon Pereira 12 Shao, Jiayu 12 Śmietański, Marek J. 12 Wan, Zhong 12 Wang, Ligong 12 Yang, Yuning 12 Yuan, Xiying 12 Zhang, Shuzhong 11 Chang, An 11 Han, Deren 11 Lin, Guihua 11 Shan, Erfang 11 Sheng, Zhou 11 Stechlinski, Peter G. 11 Sun, Zhe 11 Tang, Jia 11 Tawhid, Mohamed Aly 11 Wang, Changyu 11 Xu, Yi 11 Zheng, Bing 11 Zhu, Detong 11 Zhu, Zhibin 10 Babaie-Kafaki, Saman 10 Barton, Paul I. 10 Cui, Lubin ...and 2,751 more Authors
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### Cited in 301 Serials
199 Journal of Optimization Theory and Applications 163 Applied Mathematics and Computation 161 Computational Optimization and Applications 157 Journal of Computational and Applied Mathematics 142 Linear Algebra and its Applications 117 Mathematical Programming. Series A. Series B 85 Journal of Global Optimization 73 Optimization Methods & Software 63 Optimization 59 Linear and Multilinear Algebra 59 Frontiers of Mathematics in China 57 Computational and Applied Mathematics 57 Journal of Inequalities and Applications 57 Journal of Industrial and Management Optimization 55 SIAM Journal on Optimization 53 Numerical Algorithms 43 Journal of Applied Mathematics and Computing 42 Mathematical Problems in Engineering 42 Optimization Letters 41 Computers & Mathematics with Applications 41 Numerical Functional Analysis and Optimization 37 International Journal of Computer Mathematics 33 European Journal of Operational Research 32 Journal of Mathematical Analysis and Applications 31 Numerical Linear Algebra with Applications 29 Applied Numerical Mathematics 29 SIAM Journal on Matrix Analysis and Applications 26 Abstract and Applied Analysis 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 Mathematical Methods of Operations Research 20 Annals of Operations Research 18 Calcolo 18 Asia-Pacific Journal of Operational Research 18 Journal of Scientific Computing 17 Journal of Applied Mathematics 17 Journal of the Operations Research Society of China 16 Operations Research Letters 16 Applied Mathematics Letters 16 SIAM Journal on Scientific Computing 16 Journal of Combinatorial Optimization 16 Science China. Mathematics 14 Applied Mathematical Modelling 14 Set-Valued and Variational Analysis 14 Numerical Algebra, Control and Optimization 13 Computer Methods in Applied Mechanics and Engineering 13 Acta Mathematicae Applicatae Sinica. English Series 13 Open Mathematics 12 Mathematics of Computation 12 Numerische Mathematik 12 Applications of Mathematics 11 Discrete Applied Mathematics 11 Automatica 11 Top 11 Nonlinear Analysis. Real World Applications 11 Journal of Systems Science and Complexity 10 Computing 10 Applied Mathematics. Series B (English Edition) 10 Acta Mathematica Sinica. English Series 9 Discrete Mathematics 9 Applied Mathematics and Optimization 9 Information Sciences 8 International Journal for Numerical Methods in Engineering 8 Bulletin of the Iranian Mathematical Society 8 Computers & Operations Research 8 Japan Journal of Industrial and Applied Mathematics 7 BIT 7 Mathematics of Operations Research 7 Journal of Symbolic Computation 7 The Electronic Journal of Combinatorics 7 Optimization and Engineering 7 SIAM Journal on Imaging Sciences 6 Journal of Computational Physics 6 Acta Applicandae Mathematicae 6 Mathematical and Computer Modelling 6 Journal of Elasticity 6 The ANZIAM Journal 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Mathematical Programming Computation 6 Nonlinear Analysis. Theory, Methods & Applications 5 Mathematics and Computers in Simulation 5 SIAM Journal on Control and Optimization 5 SIAM Journal on Numerical Analysis 5 Journal of Mathematical Sciences (New York) 5 Journal of Convex Analysis 5 ELA. The Electronic Journal of Linear Algebra 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Positivity 5 Structural and Multidisciplinary Optimization 5 4OR 5 Discrete Optimization 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 SIAM Journal on Applied Algebra and Geometry 5 Communications on Applied Mathematics and Computation 4 Journal of the Franklin Institute 4 Mathematical Methods in the Applied Sciences 4 Applied Mathematics and Mechanics. (English Edition) 4 Computational Mechanics 4 Vietnam Journal of Mathematics 4 Taiwanese Journal of Mathematics 4 Soft Computing ...and 201 more Serials
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### Cited in 51 Fields
1,810 Operations research, mathematical programming (90-XX) 1,280 Numerical analysis (65-XX) 736 Linear and multilinear algebra; matrix theory (15-XX) 446 Calculus of variations and optimal control; optimization (49-XX) 188 Combinatorics (05-XX) 97 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 92 Mechanics of deformable solids (74-XX) 89 Operator theory (47-XX) 83 Computer science (68-XX) 55 Partial differential equations (35-XX) 45 Systems theory; control (93-XX) 42 Probability theory and stochastic processes (60-XX) 41 Algebraic geometry (14-XX) 40 Statistics (62-XX) 38 Information and communication theory, circuits (94-XX) 31 Real functions (26-XX) 27 Fluid mechanics (76-XX) 26 Ordinary differential equations (34-XX) 24 Differential geometry (53-XX) 23 Quantum theory (81-XX) 20 Convex and discrete geometry (52-XX) 15 Commutative algebra (13-XX) 15 Biology and other natural sciences (92-XX) 12 Dynamical systems and ergodic theory (37-XX) 11 Functional analysis (46-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of particles and systems (70-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Approximations and expansions (41-XX) 6 Field theory and polynomials (12-XX) 5 General and overarching topics; collections (00-XX) 5 Number theory (11-XX) 5 Integral transforms, operational calculus (44-XX) 5 General topology (54-XX) 4 Functions of a complex variable (30-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Nonassociative rings and algebras (17-XX) 3 Integral equations (45-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-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. | 2022-05-16T14:40:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6826561689376831, "perplexity": 10437.748883356879}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510138.6/warc/CC-MAIN-20220516140911-20220516170911-00224.warc.gz"} |
https://prevention.cancer.gov/research-groups/biometry/measurement-error-impact/software-measurement-error/single-nutrient-density-or | # Single nutrient density or ratio of two components (the denominator must be regularly-consumed)
## Macros
• NLMIXED UNIVARIATE
• NLMIXED BIVARIATE
• PREDICT_INTAKE_DENSITY
## Procedure
First, call the NLMIXED_UNIVARIATE macro twice (once for each variable) to get starting estimates for subsequent NLMIXED_BIVARIATE calls
Because replication methods (bootstrap or BRR) are used to estimate standard errors of calculated statistics, the following tasks must be performed repeatedly – once for the original data set (or using the base sampling weight variable) to obtain point estimates and again for each resampled data set (or using each of the bootstrap/BRR weight variables in turn):
1. Use the NLMIXED_BIVARIATE macro to fit the measurement error model and store parameter estimates, then
2. Use the parameter estimates as input to the PREDICT_INTAKE_DENSITY macro to compute the conditional expectation of the ratio of usual intakes of each individual given their FFQ response, then
3. Fit an appropriate health outcome-exposure model, using the conditional expectations as the dietary exposures
After calculating desired statistics for all data sets/sampling weights, use the appropriate bootstrap/BRR algorithms to estimate standard errors for the coefficients in the health outcome–exposure model by taking the square root of the (adjusted, if BRR) variance across replicates.
## Notes
• The conditional expectations produced by PREDICT_INTAKE_DENSITY are not true intakes for a particular individual. The computations involve averaging over an assumed (i.e., not observable) distribution of individual effects. Two individuals may have very different true usual intakes, yet report the same on FFQ. Their corresponding output from the PREDICT_INTAKE_DENSITY macro would be the same. Thus, categorizing the two individuals based on their PREDICT_INTAKE_DENSITY output would be subject to potentially extreme misclassification. However, under the assumptions required of the regression calibration method, using the output from PREDICT_INTAKE_DENSITY yields a measurement-error-corrected estimate of the regression slopes in a health outcome-exposure model.
• Using resampling methods to calculate standard errors of the coefficients for exposures in the health outcome-exposure model properly accounts for variability in all stages of the estimation.
• PREDICT_INTAKE_DENSITY can estimate conditional expectations of (Box-Cox) transformed ratios of usual intakes, if the health outcome-exposure model is nonlinear in the exposure. Second-degree and higher polynomial terms of exposure can be obtained by repeated calls to the PREDICT_INTAKE_DENSITY macro and some algebra.
## Example Code
This application is similar to the following application: Estimation of the association between a dietary intake and a health outcome; FFQ is the main instrument; Two regularly-consumed or one regularly-consumed and one episodically-consumed foods or nutrients. The crucial difference is that only one call to PREDICT_INTAKE_DENSITY is required for a model with a single ratio as in this application. | 2022-08-19T19:33:46 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8230050206184387, "perplexity": 2824.951895286516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573760.75/warc/CC-MAIN-20220819191655-20220819221655-00798.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Alu.jiang-hua | # zbMATH — the first resource for mathematics
## Lu, Jiang-Hua
Compute Distance To:
Author ID: lu.jiang-hua Published as: Lu, J.; Lu, Jiang-Hua; Lü, Jianghua Homepage: http://hkumath.hku.hk/~jhlu/ External Links: MGP · Wikidata · ResearchGate
Documents Indexed: 50 Publications since 1987, including 2 Books
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#### Co-Authors
11 single-authored 6 Evens, Sam 6 Weinstein, Alan David 3 Mouquin, Victor 3 Yakimov, Milen T. 3 Yan, Min 3 Zhu, Yongchang 2 Dito, Giuseppe 2 Foth, Philip A. 2 Jin, Chengzhi 2 Maeda, Yoshiaki 1 Chan, Kei Yuen 1 Dazord, Pierre 1 Ginzburg, Viktor L’vovich 1 He, Xuhua 1 Ji, Lizhen 1 Mi, Yipeng 1 Ratiu, Tudor Stefan 1 Sondaz, Daniel 1 To, Simon Kai-Ming 1 Yu, Shizhuo
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#### Serials
4 Communications in Mathematical Physics 4 IMRN. International Mathematics Research Notices 4 Transformation Groups 3 Duke Mathematical Journal 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Comptes Rendus de l’Académie des Sciences. Série I 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Journal of Algebra 1 Journal of Differential Geometry 1 Mathematische Zeitschrift 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 International Journal of Mathematics 1 Indagationes Mathematicae. New Series 1 Selecta Mathematica. New Series 1 Moscow Mathematical Journal 1 Journal of Jilin University. Science Edition 1 Journal of Software 1 Contemporary Mathematics 1 Travaux Mathématiques
all top 5
#### Fields
21 Differential geometry (53-XX) 14 Topological groups, Lie groups (22-XX) 11 Nonassociative rings and algebras (17-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Group theory and generalizations (20-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Associative rings and algebras (16-XX) 4 Algebraic geometry (14-XX) 2 General and overarching topics; collections (00-XX) 2 Category theory; homological algebra (18-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX)
#### Citations contained in zbMATH
42 Publications have been cited 698 times in 542 Documents Cited by Year
Poisson Lie groups, dressing transformations, and Bruhat decompositions. Zbl 0673.58018
Lu, Jiang-Hua; Weinstein, Alan
1990
Transverse measures, the modular class and a cohomology pairing for Lie algebroids. Zbl 0968.58014
Evens, Sam; Lu, Jiang-Hua; Weinstein, Alan
1999
Hopf algebroids and quantum groupoids. Zbl 0884.17010
Lu, Jiang-Hua
1996
On the set-theoretical Yang-Baxter equation. Zbl 0960.16043
Lu, Jiang-Hua; Yan, Min; Zhu, Yong-Chang
2000
Momentum mappings and reduction of Poisson actions. Zbl 0735.58004
Lu, Jiang-Hua
1991
Poisson homogeneous spaces and Lie algebroids associated to Poisson actions. Zbl 0889.58036
Lu, Jiang-Hua
1997
On the Drinfeld double and the Heisenberg double of a Hopf algebra. Zbl 0815.16020
Lu, Jiang-Hua
1994
Groupoïdes symplectiques doubles des groupes de Lie-Poisson. (Symplectic double groupoids of Poisson Lie groups). Zbl 0701.58025
Lu, Jiang-Hua; Weinstein, Alan
1989
On the variety of Lagrangian subalgebras. II. Zbl 1162.17020
Evens, Sam; Lu, Jiang-Hua
2006
Poisson cohomology of Morita-equivalent Poisson manifolds. Zbl 0783.58026
Ginzburg, Viktor L.; Lu, Jiang-Hua
1992
On the variety of Lagrangian subalgebras. I. Zbl 1098.17006
Evens, Sam; Lu, Jiang-Hua
2001
Poisson geometry of the Grothendieck resolution of a complex semisimple group. Zbl 1148.53061
Evens, Sam; Lu, Jiang-Hua
2007
On the nonlinear convexity theorem of Kostant. Zbl 0785.22019
Lu, Jiang-Hua; Ratiu, Tudor
1991
Group orbits and regular partitions of Poisson manifolds. Zbl 1153.53059
Lu, Jiang-Hua; Yakimov, Milen
2008
Moment maps at the quantum level. Zbl 0801.17019
Lu, Jiang-Hua
1993
Classical dynamical $$r$$-matrices and homogeneous Poisson structures on $$G/H$$ and $$K/T$$. Zbl 1008.53064
Lu, Jiang-Hua
2000
Poisson harmonic forms, Kostant harmonic forms, and the $$S^1$$-equivariant cohomology of $$K/T$$. Zbl 0914.22009
Evens, Sam; Lu, Jiang-Hua
1999
Coordinates on Schubert cells, Kostant’s harmonic forms, and the Bruhat Poisson structure on $$G/B$$. Zbl 0938.22012
Lu, Jiang-Hua
1999
On intersections of conjugacy classes and Bruhat cells. Zbl 1207.20042
Chan, Kei Yuen; Lu, Jiang-Hua; To, Simon Kai-Ming
2010
Partitions of the wonderful group compactification. Zbl 1144.20028
Lu, Jiang-Hua; Yakimov, Milen
2007
Quasi-triangular structures on Hopf algebras with positive bases. Zbl 0978.16034
Lu, Jiang-Hua; Yan, Min; Zhu, Yongchang
2000
Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures. Zbl 1176.74051
Benabbou, A.; Borouchaki, H.; Laug, P.; Lu, J.
2009
A Poisson structure on compact symmetric spaces. Zbl 1067.53062
Foth, Philip A.; Lu, Jiang-Hua
2004
On Hopf algebras with positive bases. Zbl 0991.16032
Lu, Jiang-Hua; Yan, Min; Zhu, Yongchang
2001
On a dimension formula for spherical twisted conjugacy classes in semisimple algebraic groups. Zbl 1246.20040
Lu, Jiang-Hua
2011
On a class of double cosets in reductive algebraic groups. Zbl 1066.22019
Lu, Jiang-Hua; Yakimov, Milen
2005
Load share and finite element stress analysis for double circular-arc helical gears. Zbl 0835.73064
Lu, J.; Litvin, F. L.; Chen, J. S.
1995
Double Bruhat cells and symplectic groupoids. Zbl 1416.22013
Lu, Jiang-Hua; Mouquin, Victor
2018
Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Zbl 1391.90064
Hu, C.; Lu, J.; Liu, X.; Zhang, G.
2018
On the $$T$$-leaves of some Poisson structures related to products of flag varieties. Zbl 1356.53084
Lu, Jiang-Hua; Mouquin, Victor
2017
A note on Poisson homogeneous spaces. Zbl 1155.53050
Lu, Jiang-Hua
2008
Poisson structures on complex flag manifolds associated with real forms. Zbl 1083.53032
Foth, Philip; Lu, Jiang-Hua
2006
Thompson’s conjecture for real semisimple Lie groups. Zbl 1084.22010
Evens, Sam; Lu, Jiang-Hua
2005
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
Computerized design and generation of double circular-arc helical gears with low transmission errors. Zbl 0865.70002
Litvin, F. L.; Lu, J.
1995
Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras. Zbl 1405.53113
Lu, Jiang-Hua; Mouquin, Victor
2017
On intersections of certain partitions of a group compactification. Zbl 1253.20049
He, Xuhua; Lu, Jiang-Hua
2011
Generalized Bruhat cells and completeness of Hamiltonian flows of Kogan-Zelevinsky integrable systems. Zbl 07065404
Lu, Jiang-Hua; Mi, Yipeng
2018
Large eddy simulation of flow and mass exchange in an embayment with or without vegetation. Zbl 07162925
Lu, J.; Dai, H. C.
2016
On the $$T$$-leaves and the ranks of a Poisson structure on twisted conjugacy classes. Zbl 1298.53084
Lu, Jiang-Hua
2014
Poisson geometry in mathematics and physics. Proceedings of the international conference, Tokyo, Japan, June 5–9, 2006. Zbl 1131.53002
Dito, Giuseppe (ed.); Lu, Jiang-Hua (ed.); Maeda, Yoshiaki (ed.); Weinstein, Alan (ed.)
2008
Affinoïdes de Poisson. (Affinoid Poisson structures). Zbl 0728.58013
Dazord, Pierre; Lu, Jiang-Hua; Sondaz, Daniel; Weinstein, Alan
1991
Double Bruhat cells and symplectic groupoids. Zbl 1416.22013
Lu, Jiang-Hua; Mouquin, Victor
2018
Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Zbl 1391.90064
Hu, C.; Lu, J.; Liu, X.; Zhang, G.
2018
Generalized Bruhat cells and completeness of Hamiltonian flows of Kogan-Zelevinsky integrable systems. Zbl 07065404
Lu, Jiang-Hua; Mi, Yipeng
2018
On the $$T$$-leaves of some Poisson structures related to products of flag varieties. Zbl 1356.53084
Lu, Jiang-Hua; Mouquin, Victor
2017
Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras. Zbl 1405.53113
Lu, Jiang-Hua; Mouquin, Victor
2017
Large eddy simulation of flow and mass exchange in an embayment with or without vegetation. Zbl 07162925
Lu, J.; Dai, H. C.
2016
On the $$T$$-leaves and the ranks of a Poisson structure on twisted conjugacy classes. Zbl 1298.53084
Lu, Jiang-Hua
2014
On a dimension formula for spherical twisted conjugacy classes in semisimple algebraic groups. Zbl 1246.20040
Lu, Jiang-Hua
2011
On intersections of certain partitions of a group compactification. Zbl 1253.20049
He, Xuhua; Lu, Jiang-Hua
2011
On intersections of conjugacy classes and Bruhat cells. Zbl 1207.20042
Chan, Kei Yuen; Lu, Jiang-Hua; To, Simon Kai-Ming
2010
Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures. Zbl 1176.74051
Benabbou, A.; Borouchaki, H.; Laug, P.; Lu, J.
2009
Group orbits and regular partitions of Poisson manifolds. Zbl 1153.53059
Lu, Jiang-Hua; Yakimov, Milen
2008
A note on Poisson homogeneous spaces. Zbl 1155.53050
Lu, Jiang-Hua
2008
Poisson geometry in mathematics and physics. Proceedings of the international conference, Tokyo, Japan, June 5–9, 2006. Zbl 1131.53002
Dito, Giuseppe (ed.); Lu, Jiang-Hua (ed.); Maeda, Yoshiaki (ed.); Weinstein, Alan (ed.)
2008
Poisson geometry of the Grothendieck resolution of a complex semisimple group. Zbl 1148.53061
Evens, Sam; Lu, Jiang-Hua
2007
Partitions of the wonderful group compactification. Zbl 1144.20028
Lu, Jiang-Hua; Yakimov, Milen
2007
On the variety of Lagrangian subalgebras. II. Zbl 1162.17020
Evens, Sam; Lu, Jiang-Hua
2006
Poisson structures on complex flag manifolds associated with real forms. Zbl 1083.53032
Foth, Philip; Lu, Jiang-Hua
2006
On a class of double cosets in reductive algebraic groups. Zbl 1066.22019
Lu, Jiang-Hua; Yakimov, Milen
2005
Thompson’s conjecture for real semisimple Lie groups. Zbl 1084.22010
Evens, Sam; Lu, Jiang-Hua
2005
A Poisson structure on compact symmetric spaces. Zbl 1067.53062
Foth, Philip A.; Lu, Jiang-Hua
2004
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
On the variety of Lagrangian subalgebras. I. Zbl 1098.17006
Evens, Sam; Lu, Jiang-Hua
2001
On Hopf algebras with positive bases. Zbl 0991.16032
Lu, Jiang-Hua; Yan, Min; Zhu, Yongchang
2001
On the set-theoretical Yang-Baxter equation. Zbl 0960.16043
Lu, Jiang-Hua; Yan, Min; Zhu, Yong-Chang
2000
Classical dynamical $$r$$-matrices and homogeneous Poisson structures on $$G/H$$ and $$K/T$$. Zbl 1008.53064
Lu, Jiang-Hua
2000
Quasi-triangular structures on Hopf algebras with positive bases. Zbl 0978.16034
Lu, Jiang-Hua; Yan, Min; Zhu, Yongchang
2000
Transverse measures, the modular class and a cohomology pairing for Lie algebroids. Zbl 0968.58014
Evens, Sam; Lu, Jiang-Hua; Weinstein, Alan
1999
Poisson harmonic forms, Kostant harmonic forms, and the $$S^1$$-equivariant cohomology of $$K/T$$. Zbl 0914.22009
Evens, Sam; Lu, Jiang-Hua
1999
Coordinates on Schubert cells, Kostant’s harmonic forms, and the Bruhat Poisson structure on $$G/B$$. Zbl 0938.22012
Lu, Jiang-Hua
1999
Poisson homogeneous spaces and Lie algebroids associated to Poisson actions. Zbl 0889.58036
Lu, Jiang-Hua
1997
Hopf algebroids and quantum groupoids. Zbl 0884.17010
Lu, Jiang-Hua
1996
Load share and finite element stress analysis for double circular-arc helical gears. Zbl 0835.73064
Lu, J.; Litvin, F. L.; Chen, J. S.
1995
Computerized design and generation of double circular-arc helical gears with low transmission errors. Zbl 0865.70002
Litvin, F. L.; Lu, J.
1995
On the Drinfeld double and the Heisenberg double of a Hopf algebra. Zbl 0815.16020
Lu, Jiang-Hua
1994
Moment maps at the quantum level. Zbl 0801.17019
Lu, Jiang-Hua
1993
Poisson cohomology of Morita-equivalent Poisson manifolds. Zbl 0783.58026
Ginzburg, Viktor L.; Lu, Jiang-Hua
1992
Momentum mappings and reduction of Poisson actions. Zbl 0735.58004
Lu, Jiang-Hua
1991
On the nonlinear convexity theorem of Kostant. Zbl 0785.22019
Lu, Jiang-Hua; Ratiu, Tudor
1991
Affinoïdes de Poisson. (Affinoid Poisson structures). Zbl 0728.58013
Dazord, Pierre; Lu, Jiang-Hua; Sondaz, Daniel; Weinstein, Alan
1991
Poisson Lie groups, dressing transformations, and Bruhat decompositions. Zbl 0673.58018
Lu, Jiang-Hua; Weinstein, Alan
1990
Groupoïdes symplectiques doubles des groupes de Lie-Poisson. (Symplectic double groupoids of Poisson Lie groups). Zbl 0701.58025
Lu, Jiang-Hua; Weinstein, Alan
1989
all top 5
#### Cited by 564 Authors
18 Lu, Jiang-Hua 15 Rump, Wolfgang 15 Xu, Ping 10 Böhm, Gabriella 9 Weinstein, Alan David 8 Fernandes, Rui Loja 8 Gateva-Ivanova, Tatiana 8 Majid, Shahn 8 Stiénon, Mathieu 8 Vendramin, Leandro 7 Foth, Philip A. 7 Kadison, Lars 7 Mackenzie, Kirill Charles Howard 7 Meljanac, Stjepan 7 Militaru, Gigel 6 Brzeziński, Tomasz 6 Mehta, Rajan Amit 6 Mrčun, Janez 6 Rubtsov, Vladimir Nikolaevich 6 Yakimov, Milen T. 5 Agore, Ana-Loredana 5 Bonechi, Francesco 5 Bruzzo, Ugo 5 Bursztyn, Henrique 5 Catino, Francesco 5 Colazzo, Ilaria 5 Crainic, Marius 5 Grabowski, Janusz 5 He, Xuhua 5 Jespers, Eric 5 Kosmann-Schwarzbach, Yvette 5 Lebed, Victoria 5 Liu, Zhangju 5 Stefanelli, Paola 5 Szlachányi, Kornél 5 Tang, Xiang 5 Wang, Shuanhong 4 Alekseev, Anton Yu. 4 Andruskiewitsch, Nicolás 4 Boucetta, Mohamed 4 Caseiro, Raquel 4 Cedó, Ferran 4 Chen, Zhuo 4 Ciccoli, Nicola 4 Donin, Joseph 4 Esen, Oğul 4 Esposito, Chiara 4 Etingof, Pavel Il’ich 4 Evens, Sam 4 Fehér, László Gy. 4 Fehér, László M. 4 Jotz, Madeleine 4 Kahng, Byung-Jay 4 Marrero, Juan Carlos 4 Panaite, Florin 4 Sheu, Albert Jeu-Liang 4 Smoktunowicz, Agata 4 Timmermann, Thomas 4 Zabzine, Maxim 4 Zakrzewski, Stanisław 3 Bachiller, David 3 Boalch, Philip P. 3 Cahen, Michel 3 Chemla, Sophie 3 Das, Apurba 3 Drummond, Thiago 3 Ginzburg, Viktor L’vovich 3 Goodearl, Kenneth R. 3 Gualtieri, Marco 3 Gurevich, Dmitrii 3 Gutt, Simone 3 Hodges, Timothy J. 3 Jurčo, Branislav 3 Kubarski, Jan 3 Laugwitz, Robert 3 Laurent-Gengoux, Camille 3 Malkin, Anton Z. 3 Masuoka, Akira 3 Meinrenken, Eckhard 3 Miranda, Eva 3 Montani, H. 3 Mouquin, Victor 3 Mudrov, Andrey I. 3 Pachol, Anna 3 Pickrell, Doug 3 Ratiu, Tudor Stefan 3 Semikhatov, Alexei M. 3 Shibukawa, Youichi 3 Šťovíček, Pavel 3 Štrajn, Rina 3 Sütlü, Serkan 3 Tarlini, Marco 3 Van Daele, Alfons 3 van Oystaeyen, Freddy 3 Xu, Xiaomeng 3 Zambon, Marco 2 Acri, Emiliano F. 2 Andrada, Adrián 2 Ardizzoni, Alessandro 2 Balcerzak, Bogdan ...and 464 more Authors
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#### Cited in 124 Serials
44 Communications in Mathematical Physics 43 Journal of Algebra 39 Advances in Mathematics 37 Journal of Geometry and Physics 21 Communications in Algebra 21 Letters in Mathematical Physics 16 Journal of Pure and Applied Algebra 13 Transactions of the American Mathematical Society 13 Transformation Groups 11 Journal of Mathematical Physics 10 Duke Mathematical Journal 9 International Journal of Mathematics 9 Indagationes Mathematicae. New Series 8 Annales de l’Institut Fourier 8 Differential Geometry and its Applications 7 Israel Journal of Mathematics 7 Mathematische Annalen 7 Proceedings of the American Mathematical Society 7 Journal of Noncommutative Geometry 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Algebra and its Applications 5 Nuclear Physics. B 5 Applied Categorical Structures 4 Reports on Mathematical Physics 4 Theoretical and Mathematical Physics 4 International Journal of Mathematics and Mathematical Sciences 4 Journal of Functional Analysis 4 Pacific Journal of Mathematics 4 Topology and its Applications 4 Algebras and Representation Theory 4 Mechanism and Machine Theory 4 Journal of High Energy Physics 4 International Journal of Geometric Methods in Modern Physics 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 International Journal of Modern Physics A 3 Computer Methods in Applied Mechanics and Engineering 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Zeitschrift 3 Journal of the American Mathematical Society 3 Forum Mathematicum 3 Linear Algebra and its Applications 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 3 Journal of Lie Theory 3 Representation Theory 3 Bulletin of the Brazilian Mathematical Society. New Series 2 Physics Letters. B 2 Monatshefte für Mathematik 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Tohoku Mathematical Journal. Second Series 2 Science in China. Series A 2 International Journal of Algebra and Computation 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Journal of Knot Theory and its Ramifications 2 Selecta Mathematica. New Series 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Annales Henri Poincaré 2 Journal of Nonlinear Mathematical Physics 2 Algebraic & Geometric Topology 2 Central European Journal of Mathematics 2 Mediterranean Journal of Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of Homotopy and Related Structures 1 Modern Physics Letters A 1 Computers & Mathematics with Applications 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Archiv der Mathematik 1 Compositio Mathematica 1 Czechoslovak Mathematical Journal 1 Functional Analysis and its Applications 1 International Journal for Numerical Methods in Engineering 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Manuscripta Mathematica 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Semigroup Forum 1 Tokyo Journal of Mathematics 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 $$K$$-Theory 1 Computers & Operations Research 1 Mathematical and Computer Modelling 1 Geometric and Functional Analysis. GAFA 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Bulletin of the American Mathematical Society. New Series ...and 24 more Serials
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#### Cited in 42 Fields
204 Differential geometry (53-XX) 196 Associative rings and algebras (16-XX) 184 Nonassociative rings and algebras (17-XX) 107 Quantum theory (81-XX) 93 Global analysis, analysis on manifolds (58-XX) 84 Topological groups, Lie groups (22-XX) 58 Group theory and generalizations (20-XX) 50 Dynamical systems and ergodic theory (37-XX) 40 Algebraic geometry (14-XX) 39 Category theory; homological algebra (18-XX) 38 Functional analysis (46-XX) 26 Manifolds and cell complexes (57-XX) 21 Mechanics of particles and systems (70-XX) 17 Several complex variables and analytic spaces (32-XX) 13 Algebraic topology (55-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 7 Commutative algebra (13-XX) 7 Relativity and gravitational theory (83-XX) 6 Combinatorics (05-XX) 6 $$K$$-theory (19-XX) 6 Ordinary differential equations (34-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Partial differential equations (35-XX) 5 Geometry (51-XX) 5 Numerical analysis (65-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Special functions (33-XX) 4 Convex and discrete geometry (52-XX) 3 General algebraic systems (08-XX) 2 Mathematical logic and foundations (03-XX) 2 Field theory and polynomials (12-XX) 2 Operator theory (47-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Sequences, series, summability (40-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-03-02T11:27:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48465999960899353, "perplexity": 6201.995868054261}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00061.warc.gz"} |
https://pdglive.lbl.gov/ParticleGroup.action?init=0&node=BXXX030 | ${{\mathit \Xi}}$ BARYONS ($\mathit S$ = $-2$, $\mathit I$ = 1/2)
${{\mathit \Xi}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit s}}$ ${\mathit {\mathit s}}$, ${{\mathit \Xi}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$ ${\mathit {\mathit s}}$
Radiative Hyperon Decays ${{\mathit \Xi}}$ Resonances | 2022-08-16T17:21:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9961498379707336, "perplexity": 1553.9043523644086}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572408.31/warc/CC-MAIN-20220816151008-20220816181008-00035.warc.gz"} |
https://indico.fnal.gov/event/19348/contributions/186340/ | Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
# Neutrino 2020
June 22, 2020 to July 2, 2020
US/Central timezone
## From oscillation dip to oscillation valley in atmospheric neutrino experiments
Not scheduled
10m
Poster
### Speaker
Mr Anil Kumar (Insitute of Physics, Bhubaneswar. Homi Bhabha National Institute, Mumbai)
### Description
Atmospheric neutrino experiments can show the “oscillation dip” feature in data, due to their sensitivity over a large $L/E$ range. In experiments that can distinguish between neutrinos and antineutrinos, like INO, oscillation dips can be observed in both these channels separately. We present a data-driven approach -- that uses the asymmetry in the up and down events, binned in the reconstructed $L/E$ of muons – to demonstrate the dip, thereby confirming the oscillation hypothesis. We further propose, for the first time, the identification of an “oscillation valley” in the ($E_{\mu} - \cos\theta_{\mu}$) plane, feasible for detectors like INO having excellent muon energy and direction resolutions. We illustrate how this two-dimensional valley offers a clear visual representation and test of the $L/E$ dependence, the alignment of the valley quantifying the atmospheric mass-squared difference.
### Mini-abstract
Reconstructing oscillation dip and two-dimensional valley using up-down asymmetry of muons at INO
Experiment/Collaboration India-based Neutrino Observatory (INO)
### Primary author
Mr Anil Kumar (Insitute of Physics, Bhubaneswar. Homi Bhabha National Institute, Mumbai)
### Co-authors
Amina Khatun (Comenius University, Bratislava, Slovakia) Mr Sanjib Kumar Agarwalla (Institute of Physics, Bhubaneswar, Homi Bhabha National Institute, and International Centre for Theoretical Physics) Prof. Amol Dighe (Tata Institute of Fundamental Research, Mumbai)
### Presentation Materials
Poster-ID-573-Anil-Kumar.pdf Video-ID-573-Anil-Kumar.mp4 | 2021-11-27T17:00:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23990799486637115, "perplexity": 11009.571121021836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00122.warc.gz"} |
https://par.nsf.gov/biblio/10130297-observation-electroweak-wz-boson-pair-production-association-two-jets-pp-collisions-tev-atlas-detector | Observation of electroweak W±Z boson pair production in association with two jets in pp collisions at $s=13$ TeV with the ATLAS detector | 2022-09-29T18:21:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995070695877075, "perplexity": 1722.7049822937872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00331.warc.gz"} |
https://par.nsf.gov/biblio/10364848-evidence-liquidliquid-phase-transition-_2-_2-from-path-integral-molecular-dynamics-simulations | Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations
Abstract
We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$${}_{2}$O and D$$_2$$${}_{2}$O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$$\rho \left(T\right)$, isothermal compressibility$$\kappa _T(T)$$${\kappa }_{T}\left(T\right)$, and self-diffusion coefficientsD(T) of H$$_2$$${}_{2}$O and D$$_2$$${}_{2}$O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$${C}_{P}\left(T\right)$obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$${}_{2}$O and D$$_2$$${}_{2}$O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$${}_{2}$O and D$$_2$$${}_{2}$O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$${}_{2}$O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$${P}_{c}=167±9$ MPa,$$T_c = 159 \pm 6$$${T}_{c}=159±6$ K, and$$\rho _c = 1.02 \pm 0.01$$${\rho }_{c}=1.02±0.01$ g/cm$$^3$$${}^{3}$. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$${}_{2}$O is estimated to be$$P_c = 176 \pm 4$$${P}_{c}=176±4$ MPa,$$T_c = 177 \pm 2$$${T}_{c}=177±2$ K, and$$\rho _c = 1.13 \pm 0.01$$${\rho }_{c}=1.13±0.01$ g/cm$$^3$$${}^{3}$. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects more »
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10364848
Journal Name:
Scientific Reports
Volume:
12
Issue:
1
ISSN:
2045-2322
Publisher:
Nature Publishing Group
National Science Foundation
##### More Like this
1. Abstract
Initially, vanadium dioxide seems to be an ideal first-order phase transition case study due to its deceptively simple structure and composition, but upon closer inspection there are nuances to the driving mechanism of the metal-insulator transition (MIT) that are still unexplained. In this study, a local structure analysis across a bulk powder tungsten-substitution series is utilized to tease out the nuances of this first-order phase transition. A comparison of the average structure to the local structure using synchrotron x-ray diffraction and total scattering pair-distribution function methods, respectively, is discussed as well as comparison to bright field transmission electron microscopy imaging through a similar temperature-series as the local structure characterization. Extended x-ray absorption fine structure fitting of thin film data across the substitution-series is also presented and compared to bulk. Machine learning technique, non-negative matrix factorization, is applied to analyze the total scattering data. The bulk MIT is probed through magnetic susceptibility as well as differential scanning calorimetry. The findings indicate the local transition temperature ($$T_c$$${T}_{c}$) is less than the average$$T_c$$${T}_{c}$supporting the Peierls-Mott MIT mechanism, and demonstrate that in bulk powder and thin-films, increasing tungsten-substitution instigates local V-oxidation through the phase pathway VO$$_2\, \rightarrow$$${}_{2}\phantom{\rule{0ex}{0ex}}\to$V$$_6$$${}_{6}$O$$_{13} \, \rightarrow$$${}_{13}\phantom{\rule{0ex}{0ex}}\to$V$$_2$$${}_{2}$O$$_5$$${}_{5}$.
2. Abstract
We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$for$$\kappa '$$${\kappa }^{\prime }$in (4, 8) that is drawn on an independent$$\gamma$$$\gamma$-LQG surface for$$\gamma ^2=16/\kappa '$$${\gamma }^{2}=16/{\kappa }^{\prime }$. The results are similar in flavor to the ones from our companion paper dealing with$$\hbox {CLE}_{\kappa }$$${\text{CLE}}_{\kappa }$for$$\kappa$$$\kappa$in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$independently into two colors with respective probabilitiespand$$1-p$$$1-p$. This description was complete up to one missing parameter$$\rho$$$\rho$. The results of the present paper about CLE on LQG allow us to determine its value in terms ofpand$$\kappa '$$${\kappa }^{\prime }$. It shows in particular that$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$and$$\hbox {CLE}_{16/\kappa '}$$${\text{CLE}}_{16/{\kappa }^{\prime }}$are related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {FK}_q$$${\text{FK}}_{q}$percolation and theq-state Potts model (which makes sense evenmore »
3. Abstract
We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu$$$B\to {D}^{\ast }\ell \nu$at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$${N}_{f}=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$$a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$$|{V}_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$$\left({V}_{\mathrm{cb}}\right)=\left(38.40±0.{68}_{\text{th}}±0.{34}_{\text{exp}}±0.{18}_{\text{EM}}\right)×{10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$${\chi }^{2}\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is inmore »
4. Abstract
We provide moment bounds for expressions of the type$$(X^{(1)} \otimes \cdots \otimes X^{(d)})^T A (X^{(1)} \otimes \cdots \otimes X^{(d)})$$${\left({X}^{\left(1\right)}\otimes \cdots \otimes {X}^{\left(d\right)}\right)}^{T}A\left({X}^{\left(1\right)}\otimes \cdots \otimes {X}^{\left(d\right)}\right)$where$$\otimes$$$\otimes$denotes the Kronecker product and$$X^{(1)}, \ldots , X^{(d)}$$${X}^{\left(1\right)},\dots ,{X}^{\left(d\right)}$are random vectors with independent, mean 0, variance 1, subgaussian entries. The bounds are tight up to constants depending ondfor the case of Gaussian random vectors. Our proof also provides a decoupling inequality for expressions of this type. Using these bounds, we obtain new, improved concentration inequalities for expressions of the form$$\Vert B (X^{(1)} \otimes \cdots \otimes X^{(d)})\Vert _2$$$‖B\left({X}^{\left(1\right)}\otimes \cdots \otimes {X}^{\left(d\right)}\right){‖}_{2}$.
5. Abstract
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_{i}{x}_{i}$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:
#SAT algorithms fornk-size$\mathcal { C}$$C$-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
#SAT algorithms for$2^{n^{{\varepsilon }}}$${2}^{{n}^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$${2}^{n-{n}^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.
Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJACC0THRcircuits of polynomialmore » | 2023-01-30T17:29:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 81, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5549270510673523, "perplexity": 3358.9917214168695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499826.71/warc/CC-MAIN-20230130165437-20230130195437-00683.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aschelter.william-f | # zbMATH — the first resource for mathematics
## Schelter, William F.
Compute Distance To:
Author ID: schelter.william-f Published as: Schelter, William; Schelter, William F.; Schelter, W.; Schelter, W. F. External Links: MGP · Wikidata
Documents Indexed: 26 Publications since 1971
all top 5
#### Co-Authors
14 single-authored 6 Artin, Michael 2 Chou, Shangching 2 Tate, John Torrence jun. 1 Handelman, David E. 1 Lawrence, John W. 1 Paré, Robert 1 Roberts, Paul C. 1 Small, Lance W. 1 Yang, Jingen
all top 5
#### Serials
8 Journal of Algebra 2 Advances in Mathematics 2 Archiv der Mathematik 2 Journal of the London Mathematical Society. Second Series 1 Communications on Pure and Applied Mathematics 1 Houston Journal of Mathematics 1 American Journal of Mathematics 1 Canadian Journal of Mathematics 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Algorithmica 1 Journal of Automated Reasoning 1 Bulletin of the American Mathematical Society
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#### Fields
24 Associative rings and algebras (16-XX) 4 Algebraic geometry (14-XX) 3 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Computer science (68-XX) 1 Group theory and generalizations (20-XX) 1 Geometry (51-XX)
#### Citations contained in zbMATH Open
25 Publications have been cited 513 times in 453 Documents Cited by Year
Graded algebras of global dimension 3. Zbl 0633.16001
Artin, Michael; Schelter, William F.
1987
Quantum deformations of $$\text{GL}_ n$$. Zbl 0753.17015
Artin, Michael; Schelter, William; Tate, John
1991
Integral extensions of rings satisfying a polynomial identity. Zbl 0341.16009
Schelter, William
1976
Non-commutative affine P. I. rings are catenary. Zbl 0375.16015
Schelter, William
1978
Finite extensions are integral. Zbl 0404.16011
Pare, Robert; Schelter, William
1978
Integral ring homomorphisms. Zbl 0461.16014
Artin, M.; Schelter, W.
1981
Proving geometry theorems with rewrite rules. Zbl 0642.68162
Chou, Shang-Ching; Schelter, William F.
1986
Smooth algebras. Zbl 0604.16015
Schelter, William F.
1986
On a question concerning generic matrices over the integers. Zbl 0577.16009
Schelter, William F.
1985
Two-sided rings of quotients. Zbl 0269.16001
Schelter, William
1973
On the Krull-Akizuki theorem. Zbl 0331.16017
Schelter, William
1976
Some pathological rings of quotients. Zbl 0344.16002
Schelter, William; Small, Lance W.
1976
Skew group rings. Zbl 0389.16004
Handelman, David; Lawrence, John; Schelter, William
1978
A version of Zariski’s main theorem for polynomial identity rings. Zbl 0406.16011
Artin, M.; Schelter, W.
1979
The centers of 3-dimensional Sklyanin algebras. Zbl 0823.17019
Artin, Michael; Schelter, William; Tate, John
1994
Essential extensions and intersection theorems. Zbl 0331.16016
Schelter, W.
1975
Azumaya algebras and Artin’s theorem. Zbl 0353.16008
Schelter, W.
1977
Flat modules and torsion theories. Zbl 0262.16023
Schelter, William; Roberts, Paul
1972
Affine PI rings are catenary. Zbl 0372.16011
Schelter, W.
1977
An algorithm for constructing Gröbner bases from characteristic sets and its application to geometry. Zbl 0703.13023
Chou, Shang-Ching; Schelter, William F.; Yang, Jin-Gen
1990
Products of torsion theories. Zbl 0244.16001
Schelter, William
1971
Intersection theorems for some noncommutative noetherian rings. Zbl 0328.16028
Schelter, William
1976
Topological rings of quotients. Zbl 0259.16019
Schelter, William
1974
On two-sided modules which are left projective. Zbl 0468.16019
Artin, M.; Schelter, W.
1981
Affine rings satisfying a polynomial identity. Zbl 0504.16010
Schelter, William F.
1982
The centers of 3-dimensional Sklyanin algebras. Zbl 0823.17019
Artin, Michael; Schelter, William; Tate, John
1994
Quantum deformations of $$\text{GL}_ n$$. Zbl 0753.17015
Artin, Michael; Schelter, William; Tate, John
1991
An algorithm for constructing Gröbner bases from characteristic sets and its application to geometry. Zbl 0703.13023
Chou, Shang-Ching; Schelter, William F.; Yang, Jin-Gen
1990
Graded algebras of global dimension 3. Zbl 0633.16001
Artin, Michael; Schelter, William F.
1987
Proving geometry theorems with rewrite rules. Zbl 0642.68162
Chou, Shang-Ching; Schelter, William F.
1986
Smooth algebras. Zbl 0604.16015
Schelter, William F.
1986
On a question concerning generic matrices over the integers. Zbl 0577.16009
Schelter, William F.
1985
Affine rings satisfying a polynomial identity. Zbl 0504.16010
Schelter, William F.
1982
Integral ring homomorphisms. Zbl 0461.16014
Artin, M.; Schelter, W.
1981
On two-sided modules which are left projective. Zbl 0468.16019
Artin, M.; Schelter, W.
1981
A version of Zariski’s main theorem for polynomial identity rings. Zbl 0406.16011
Artin, M.; Schelter, W.
1979
Non-commutative affine P. I. rings are catenary. Zbl 0375.16015
Schelter, William
1978
Finite extensions are integral. Zbl 0404.16011
Pare, Robert; Schelter, William
1978
Skew group rings. Zbl 0389.16004
Handelman, David; Lawrence, John; Schelter, William
1978
Azumaya algebras and Artin’s theorem. Zbl 0353.16008
Schelter, W.
1977
Affine PI rings are catenary. Zbl 0372.16011
Schelter, W.
1977
Integral extensions of rings satisfying a polynomial identity. Zbl 0341.16009
Schelter, William
1976
On the Krull-Akizuki theorem. Zbl 0331.16017
Schelter, William
1976
Some pathological rings of quotients. Zbl 0344.16002
Schelter, William; Small, Lance W.
1976
Intersection theorems for some noncommutative noetherian rings. Zbl 0328.16028
Schelter, William
1976
Essential extensions and intersection theorems. Zbl 0331.16016
Schelter, W.
1975
Topological rings of quotients. Zbl 0259.16019
Schelter, William
1974
Two-sided rings of quotients. Zbl 0269.16001
Schelter, William
1973
Flat modules and torsion theories. Zbl 0262.16023
Schelter, William; Roberts, Paul
1972
Products of torsion theories. Zbl 0244.16001
Schelter, William
1971
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#### Cited by 389 Authors
23 Zhang, James J. 13 Braun, Amiram 13 Van den Bergh, Michel 11 Schelter, William F. 11 Smith, S. Paul 10 Kirkman, Ellen E. 10 Lu, Jiafeng 10 Vancliff, Michaela 9 Berger, Roland 9 Stafford, J. Toby 8 Gateva-Ivanova, Tatiana 8 Goodearl, Kenneth R. 8 Le Bruyn, Lieven 7 Cassidy, Thomas 7 van Oystaeyen, Freddy 6 Chou, Shangching 6 Letzter, Edward S. 6 Lu, Di-Ming 6 Rogalski, Daniel 6 Shelton, Brad 6 Small, Lance W. 6 Wu, Quanshui S. 5 Dubois-Violette, Michel 5 Iyudu, Natalia K. 5 Jing, Naihuan 5 Kuzmanovich, James J. 5 Lomp, Christian 5 Mori, Izuru 5 Stephenson, Darin R. 5 Ueyama, Kenta 5 Vonessen, Nikolaus 5 Walton, Chelsea 4 Artin, Michael 4 Bichon, Julien 4 Bocklandt, Raf 4 Carvalho, Paula A. A. B. 4 De Laet, Kevin 4 Gao, Xiaoshan 4 Lenagan, Thomas H. 4 Levasseur, Thierry 4 Mao, XueFeng 4 Marconnet, Nicolas 4 Montgomery, Susan 4 Musson, Ian M. 4 Park, Jae Keol 4 Reyes, Manuel L. 4 Rump, Wolfgang 4 Shen, Yuan 4 Yakimov, Milen T. 3 Andruskiewitsch, Nicolás 3 Chirvăsitu, Alexandru 3 De Naeghel, Koen 3 Gaddis, Jason 3 Goetz, Pete 3 He, Jiwei 3 Hu, Naihong 3 Iyama, Osamu 3 Kaygun, Atabey 3 Le Meur, Patrick 3 Lorenz, Martin 3 Passman, Donald Steven 3 Regev, Amitai 3 Sierra, Susan J. 3 Tagne Pelap, Serge Roméo 3 Towber, Jacob 3 Van Rompay, Kristel 3 Vaš, Lia 3 Wang, Xingting 3 Westreich, Sara 3 Zhang, Jian 3 Zhang, Yinhuo 3 Zhu, Can 2 Angiono, Iván Ezequiel 2 Armendariz, Efraim P. 2 Beidar, Konstantin Igorevich 2 Bell, Allen D. 2 Brown, Kenneth Alexander 2 Brzeziński, Tomasz 2 Cameron, Peter Jephson 2 Cauchon, Gerard 2 Chen, Jianmin 2 Chen, Pei-Sen 2 Chin, William 2 Cohen, Miriam 2 Cuntz, Joachim 2 Davies, Andrew 2 Drensky, Vesselin 2 Faith, Carl C. 2 García, Gastón Andrés 2 Ginzburg, Victor 2 Gómez Torrecillas, José 2 Hajarnavis, Charudatta R. 2 Jakobsen, Hans Plesner 2 Jespers, Eric 2 Johnson, Garrett 2 Jøndrup, Søren 2 Kanda, Ryo 2 Kapur, Deepak 2 Kharchenko, Vladislav K. 2 Kriegk, Benoit ...and 289 more Authors
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#### Cited in 80 Serials
111 Journal of Algebra 58 Communications in Algebra 32 Journal of Pure and Applied Algebra 20 Proceedings of the American Mathematical Society 20 Transactions of the American Mathematical Society 20 Algebras and Representation Theory 17 Advances in Mathematics 13 Israel Journal of Mathematics 10 Journal of Noncommutative Geometry 9 Mathematische Zeitschrift 7 Glasgow Mathematical Journal 5 Journal of Automated Reasoning 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Science China. Mathematics 4 Artificial Intelligence 4 Communications in Mathematical Physics 4 Mathematical Notes 4 Journal of Symbolic Computation 4 $$K$$-Theory 4 Journal of Algebra and its Applications 3 Indian Journal of Pure & Applied Mathematics 3 Letters in Mathematical Physics 3 Journal of Geometry and Physics 3 Inventiones Mathematicae 3 Journal für die Reine und Angewandte Mathematik 3 Journal of Soviet Mathematics 3 Journal of Mathematical Sciences (New York) 3 Selecta Mathematica. New Series 3 Annals of Mathematics and Artificial Intelligence 3 Frontiers of Mathematics in China 2 Journal of Mathematical Physics 2 Archiv der Mathematik 2 Compositio Mathematica 2 Duke Mathematical Journal 2 Pacific Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Advances in Applied Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Transformation Groups 2 Acta Mathematica Sinica. English Series 2 Bulletin of the American Mathematical Society 1 Bulletin of the Australian Mathematical Society 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nuclear Physics. B 1 Rocky Mountain Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Functional Analysis and its Applications 1 Journal of the Mathematical Society of Japan 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Nagoya Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Ricerche di Matematica 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Computer Aided Geometric Design 1 Journal of Computer Science and Technology 1 Algorithmica 1 Journal of the American Mathematical Society 1 Science in China. Series A 1 Computational Geometry 1 IMRN. International Mathematics Research Notices 1 Linear Algebra and its Applications 1 Russian Mathematics 1 Advances in Applied Clifford Algebras 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Systems Science and Complexity 1 Central European Journal of Mathematics 1 International Journal of Geometric Methods in Modern Physics 1 International Electronic Journal of Algebra (IEJA) 1 Journal of $$K$$-Theory 1 São Paulo Journal of Mathematical Sciences 1 Kyoto Journal of Mathematics 1 Forum of Mathematics, Sigma 1 Proceedings of the American Mathematical Society. Series B 1 Higher Structures
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#### Cited in 29 Fields
396 Associative rings and algebras (16-XX) 92 Nonassociative rings and algebras (17-XX) 84 Algebraic geometry (14-XX) 32 Category theory; homological algebra (18-XX) 30 Commutative algebra (13-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 20 Group theory and generalizations (20-XX) 17 Computer science (68-XX) 15 Functional analysis (46-XX) 13 Quantum theory (81-XX) 9 Number theory (11-XX) 7 Combinatorics (05-XX) 7 Geometry (51-XX) 7 Differential geometry (53-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Mathematical logic and foundations (03-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 $$K$$-theory (19-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-09-17T01:28:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2702122926712036, "perplexity": 6920.9563540349845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00064.warc.gz"} |
https://mooseframework.inl.gov/syntax/InterfaceKernels/index.html | # InterfaceKernels System
Interface kernels are meant to assist in coupling different physics across sub-domains. The most straightforward example is the case in which one wants to set the flux of a specie A in subdomain 0 equal to the flux of a specie B in subdomain 1 at the boundary between subdomains 0 and 1. In mathematical terms, we might be interested in establishing the condition:
(1)
where is the diffusion coefficient of specie in subdomain , and is the concentration of specie in subdomain . An example of this condition is shown in the MOOSE test directory; see files below:
coupled_value_coupled_flux.i
InterfaceDiffusion.C
InterfaceDiffusion.h
Interface kernels can be used to provide any general flux condition at an interface, and even more generally can be used to impose any interfacial condition that requires access to values of different variables and gradients of different variables on either side of an interface. In an input file, the user will specify at a minimum the following parameters:
• type: The type of interface kernel to be used
• variable: This is the "master" variable. Note that the master variable must exist on the same subdomain as the sideset specified in the boundary parameter. The existence of a "master" and "slave" or "neighbor" variable ensures that the interface kernel residual and jacobian functions get called the correct number of times. variable could be from our example above.
• neighbor_var: The "slave" variable. This could be from our example above.
• boundary: The interfacial boundary between the subdomains. Note that this must be a sideset and again must exist on the same subdomain as the master variable. The fact that this boundary is a sideset allows access to variable gradients.
For additional information about the interface kernel system, don't hesitate to email the moose list at [email protected]. | 2019-02-22T14:53:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3967391848564148, "perplexity": 986.6777888735157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247518425.87/warc/CC-MAIN-20190222135147-20190222161147-00564.warc.gz"} |
https://indico.bnl.gov/event/10646/ | High Energy / Nuclear Theory / RIKEN seminars
# [NT/RIKEN seminar] Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x
## by Ian Balitsky (JLab/ODU)
US/Eastern
https://bluejeans.com/456036356
#### https://bluejeans.com/456036356
Description
The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $s\gg Q^2\gg q_\perp^2$ with ${1\over Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^\perp$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics. | 2023-02-07T20:56:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.978628396987915, "perplexity": 9048.976577930009}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00258.warc.gz"} |
https://math.libretexts.org/TextMaps/Calculus/Book%3A_Calculus_(Apex)/8%3A_Sequences_and_Series/8.3%3A_Integral_and_Comparison_Tests |
# 8.3: Integral and Comparison Tests
• Page ID
4201
•
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Knowing whether or not a series converges is very important, especially when we discusses Power Series. Theorems 60 and 61 give criteria for when Geometric and $$p$$-series converge, and Theorem 63 gives a quick test to determine if a series diverges. There are many important series whose convergence cannot be determined by these theorems, though, so we introduce a set of tests that allow us to handle a broad range of series. We start with the Integral Test.
#### Integral Test
We stated in Section 8.1 that a sequence $$\{a_n\}$$ is a function $$a(n)$$ whose domain is $$\mathbb{N}$$, the set of natural numbers. If we can extend $$a(n)$$ to $$\mathbb{R}$$, the real numbers, and it is both positive and decreasing on $$[1,\infty)$$, then the convergence of $$\sum\limits_{n=1}^\infty a_n$$ is the same as $$\int\limits_1^\infty a(x)dx$$.
theorem $$\PageIndex{1}$$: integral test
Let a sequence $$\{a_n\}$$ be defined by $$a_n=a(n)$$, where $$a(n)$$ is continuous, positive and decreasing on $$[1,\infty)$$. Then $$\sum\limits_{n=1}^\infty a_n$$ converges, if, and only if, $$\int\limits_1^\infty a(x) dx$$ converges.
We can demonstrate the truth of the Integral Test with two simple graphs. In Figure $$\PageIndex{1a}$$, the height of each rectangle is $$a(n)=a_n$$ for $$n=1,2,\ldots$$, and clearly the rectangles enclose more area than the area under $$y=a(x)$$. Therefore we can conclude that
$\int\limits_1^\infty a(x) dx < \sum\limits_{n=1}^\infty a_n.\label{eq:integral_testa}$
Figure $$\PageIndex{1}$$:
Illustrating the truth of the Integral Test.
In Figure $$\PageIndex{1b}$$, we draw rectangles under $$y=a(x)$$ with the Right-Hand rule, starting with $$n=2$$. This time, the area of the rectangles is less than the area under $$y=a(x)$$, so $$\sum\limits_{n=2}^\infty a_n < \int\limits_1^\infty a(x) dx$$. Note how this summation starts with $$n=2$$; adding $$a_1$$ to both sides lets us rewrite the summation starting with $$n=1$$:
$\sum\limits_{n=1}^\infty a_n < a_1 +\int\limits_1^\infty a(x) dx.\label{eq:integral_testb}$
Combining Equations \ref{eq:integral_testa} and \ref{eq:integral_testb}, we have
$\sum\limits_{n=1}^\infty a_n< a_1 +\int\limits_1^\infty a(x) dx < a_1 + \sum\limits_{n=1}^\infty a_n.\label{eq:integral_testc}$
Theorem $$\PageIndex{1}$$
From Equation \ref{eq:integral_testc} we can make the following two statements:
1. If $$\sum\limits_{n=1}^\infty a_n$$ diverges, so does $$\int\limits_1^\infty a(x) dx$$ (because $$\sum\limits_{n=1}^\infty a_n < a_1 +\int\limits_1^\infty a(x) dx)$$
2. If $$\sum\limits_{n=1}^\infty a_n$$ converges, so does $$\int\limits_1^\infty a(x) dx$$ (because $$\int\limits_1^\infty a(x) dx < \sum\limits_{n=1}^\infty a_n.)$$
Therefore the series and integral either both converge or both diverge.
Theorem$$\PageIndex{1}$$ allows us to extend this theorem to series where $$a(n)$$ is positive and decreasing on $$[b,\infty)$$ for some $$b>1$$.
Example $$\PageIndex{1}$$: Using the Integral Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac{\ln n}{n^2}$$. (The terms of the sequence $$\{a_n\} = \{\ln n/n^2\}$$ and the n$$^{\text{th}}$$ partial sums are given in Figure $$\PageIndex{2}$$).
SOLUTION
Figure $$\PageIndex{2}$$ implies that $$a(n) = (\ln n)/n^2$$ is positive and decreasing on $$[2,\infty)$$. We can determine this analytically, too. We know $$a(n)$$ is positive as both $$\ln n$$ and $$n^2$$ are positive on $$[2,\infty)$$. To determine that $$a(n)$$ is decreasing, consider $$a^\prime(n) = (1-2\ln n)/n^3$$, which is negative for $$n\geq 2$$. Since $$a^\prime(n)$$ is negative, $$a(n)$$ is decreasing.
Figure $$\PageIndex{2}$$:
Plotting the sequence and series in Example $$\PageIndex{1}$$.
Applying the Integral Test, we test the convergence of $$\int\limits_1^\infty \dfrac{\ln x}{x^2} dx$$. Integrating this improper integral requires the use of Integration by Parts, with $$u = \ln x$$ and $$dv = 1/x^2 dx$$.
\begin{align*}\int\limits_1^\infty \dfrac{\ln x}{x^2} dx &=\lim\limits_{b\to\infty} \int\limits_1^b \dfrac{\ln x}{x^2} dx\\ &=\lim\limits_{b\to\infty} -\dfrac1x\ln x\Big|_1^b + \int\limits_1^b\dfrac1{x^2} dx \\ &=\lim\limits_{b\to\infty} -\dfrac1x\ln x -\dfrac 1x\Big|_1^b\\ &=\lim\limits_{b\to\infty}1-\dfrac1b-\dfrac{\ln b}{b}.\quad \text{Apply L'H$$\hat o$$pital's Rule:}\\ &= 1. \end{align*}
Since $$\int\limits_1^\infty \dfrac{\ln x}{x^2} dx$$ converges, so does $$\sum\limits_{n=1}^\infty \dfrac{\ln n}{n^2}$$.
Theorem 61 was given without justification, stating that the general $$p$$-series $$\sum\limits_{n=1}^\infty \dfrac 1{(an+b)^p}$$ converges if, and only if, $$p>1$$. In the following example, we prove this to be true by applying the Integral Test.
Example $$\PageIndex{2}$$: Using the Integral Test to establish Theorem 61
Use the Integral Test to prove that $$\sum\limits_{n=1}^\infty \dfrac1{(an+b)^p}$$ converges if, and only if, $$p>1$$.
SOLUTION
Consider the integral $$\int\limits_1^\infty \dfrac1{(ax+b)^p} dx$$; assuming $$p\neq 1$$,
\begin{align*} \int\limits_1^\infty \dfrac1{(ax+b)^p} dx &=\lim\limits_{c\to\infty} \int\limits_1^c \dfrac1{(ax+b)^p} dx \\ &=\lim\limits_{c\to\infty} \dfrac{1}{a(1-p)}(ax+b)^{1-p}\Big|_1^c\\ &=\lim\limits_{c\to\infty} \dfrac{1}{a(1-p)}\big((ac+b)^{1-p}-(a+b)^{1-p}\big). \end{align*}
This limit converges if, and only if, $$p>1$$. It is easy to show that the integral also diverges in the case of $$p=1$$. (This result is similar to the work preceding Key Idea 21.)
Therefore $$\sum\limits_{n=1}^\infty \dfrac 1{(an+b)^p}$$ converges if, and only if, $$p>1$$.
We consider two more convergence tests in this section, both comparison tests. That is, we determine the convergence of one series by comparing it to another series with known convergence.
#### Direct Comparison Test
theorem $$\PageIndex{1}$$: direct comparison test
Let $$\{a_n\}$$ and $$\{b_n\}$$ be positive sequences where $$a_n\leq b_n$$ for all $$n\geq N$$, for some $$N\geq 1$$.
1. If $$\sum\limits_{n=1}^\infty b_n$$ converges, then $$\sum\limits_{n=1}^\infty a_n$$ converges.
2. If $$\sum\limits_{n=1}^\infty a_n$$ diverges, then $$\sum\limits_{n=1}^\infty b_n$$ diverges.
Note: A sequence $$\{a_n\}$$ is a positive sequence if $$a_n>0$$ for all $$n$$.
Because of Theorem 64, any theorem that relies on a positive sequence still holds true when $$a_n>0$$ for all but a finite number of values of $$n$$.
Example $$\PageIndex{3}$$: Applying the Direct Comparison Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac1{3^n+n^2}$$.
SOLUTION
This series is neither a geometric or $$p$$-series, but seems related. We predict it will converge, so we look for a series with larger terms that converges. (Note too that the Integral Test seems difficult to apply here.)
Since $$3^n < 3^n+n^2$$, $$\dfrac1{3^n}> \dfrac1{3^n+n^2}$$ for all $$n\geq1$$. The series $$\sum\limits_{n=1}^\infty \dfrac{1}{3^n}$$ is a convergent geometric series; by Theorem 66, $$\sum\limits_{n=1}^\infty \dfrac1{3^n+n^2}$$ converges.
Example $$\PageIndex{4}$$: Applying the Direct Comparison Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac{1}{n-\ln n}$$.
SOLUTION
We know the Harmonic Series $$\sum\limits_{n=1}^\infty \dfrac1n$$ diverges, and it seems that the given series is closely related to it, hence we predict it will diverge.
Since $$n\geq n-\ln n$$ for all $$n\geq 1$$, $$\dfrac1n \leq \dfrac1{n-\ln n}$$ for all $$n\geq 1$$.
The Harmonic Series diverges, so we conclude that $$\sum\limits_{n=1}^\infty \dfrac{1}{n-\ln n}$$ diverges as well.
The concept of direct comparison is powerful and often relatively easy to apply. Practice helps one develop the necessary intuition to quickly pick a proper series with which to compare. However, it is easy to construct a series for which it is difficult to apply the Direct Comparison Test.
Consider $$\sum\limits_{n=1}^\infty \dfrac1{n+\ln n}$$. It is very similar to the divergent series given in Example 8.3.5. We suspect that it also diverges, as $$\dfrac 1n \approx \dfrac1{n+\ln n}$$ for large $$n$$. However, the inequality that we naturally want to use "goes the wrong way'': since $$n\leq n+\ln n$$ for all $$n\geq 1$$, $$\dfrac1n \geq \dfrac{1}{n+\ln n}$$ for all $$n\geq 1$$. The given series has terms less than the terms of a divergent series, and we cannot conclude anything from this.
Fortunately, we can apply another test to the given series to determine its convergence.
#### Large Limit Comparison Test
Theorem 67: limit comparison test
Let $$\{a_n\}$$ and $$\{b_n\}$$ be positive sequences.
1. If $$\lim_{n\to\infty} \dfrac{a_n}{b_n} = L$$, where $$L$$ is a positive real number, then $$\sum\limits_{n=1}^\infty a_n$$ and $$\sum\limits_{n=1}^\infty b_n$$ either both converge or both diverge.
2. If $$\lim_{n\to\infty} \dfrac{a_n}{b_n} = 0$$, then if $$\sum\limits_{n=1}^\infty b_n$$ converges, then so does $$\sum\limits_{n=1}^\infty a_n$$.
3. If $$\lim_{n\to\infty} \dfrac{a_n}{b_n} = \infty$$, then if $$\sum\limits_{n=1}^\infty b_n$$ diverges, then so does $$\sum\limits_{n=1}^\infty a_n$$.
Theorem 67 is most useful when the convergence of the series from $$\{b_n\}$$ is known and we are trying to determine the convergence of the series from $$\{a_n\}$$.
We use the Limit Comparison Test in the next example to examine the series $$\sum\limits_{n=1}^\infty \dfrac1{n+\ln n}$$ which motivated this new test.
Example $$\PageIndex{5}$$: Applying the Limit Comparison Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac1{n+\ln n}$$ using the Limit Comparison Test.
SOLUTION
We compare the terms of $$\sum\limits_{n=1}^\infty \dfrac1{n+\ln n}$$ to the terms of the Harmonic Sequence $$\sum\limits_{n=1}^\infty \dfrac1{n}$$:
\begin{align*} \lim_{n\to\infty}\dfrac{1/(n+\ln n)}{1/n} &=\lim\limits_{n\to\infty} \dfrac{n}{n+\ln n} \\ &= 1\quad \text{(after applying L'H$$\hat o$$pital's Rule)}. \end{align*}
Since the Harmonic Series diverges, we conclude that $$\sum\limits_{n=1}^\infty \dfrac1{n+\ln n}$$ diverges as well.
Example $$\PageIndex{6}$$: Applying the Limit Comparison Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac1{3^n-n^2}$$
SOLUTION
This series is similar to the one in Example 8.3.3, but now we are considering "$$3^n-n^2$$'' instead of "$$3^n+n^2$$.'' This difference makes applying the Direct Comparison Test difficult.
Instead, we use the Limit Comparison Test and compare with the series $$\sum\limits_{n=1}^\infty \dfrac1{3^n}$$:
\begin{align*} \lim_{n\to\infty}\dfrac{1/(3^n-n^2)}{1/3^n} &=\lim\limits_{n\to\infty}\dfrac{3^n}{3^n-n^2} \\ &= 1 \quad \text{(after applying L'H$$\hat o$$pital's Rule twice)}. \end{align*}
We know $$\sum\limits_{n=1}^\infty \dfrac1{3^n}$$ is a convergent geometric series, hence $$\sum\limits_{n=1}^\infty \dfrac1{3^n-n^2}$$ converges as well.
As mentioned before, practice helps one develop the intuition to quickly choose a series with which to compare. A general rule of thumb is to pick a series based on the dominant term in the expression of $$\{a_n\}$$. It is also helpful to note that factorials dominate exponentials, which dominate algebraic functions (e.g., polynomials), which dominate logarithms. In the previous example, the dominant term of $$\dfrac{1}{3^n-n^2}$$ was $$3^n$$, so we compared the series to $$\sum\limits_{n=1}^\infty \dfrac1{3^n}$$. It is hard to apply the Limit Comparison Test to series containing factorials, though, as we have not learned how to apply L'H$$\hat o$$pital's Rule to $$n!$$.
Example $$\PageIndex{7}$$: Applying the Limit Comparison Test
Determine the convergence of $$\sum\limits_{n=1}^\infty \dfrac{\sqrt{n}+3}{n^2-n+1}$$.
SOLUTION
We naively attempt to apply the rule of thumb given above and note that the dominant term in the expression of the series is $$1/n^2$$. Knowing that $$\sum\limits_{n=1}^\infty \dfrac1{n^2}$$ converges, we attempt to apply the Limit Comparison Test:
\begin{align*} \lim_{n\to\infty}\dfrac{(\sqrt{n}+3)/(n^2-n+1)}{1/n^2} &=\lim\limits_{n\to\infty}\dfrac{n^2(\sqrt n+3)}{n^2-n+1}\\ &= \infty \quad \text{(Apply L'H$$\hat o$$pital's Rule)}. \end{align*}
Theorem 67 part (3) only applies when $$\sum\limits_{n=1}^\infty b_n$$ diverges; in our case, it converges. Ultimately, our test has not revealed anything about the convergence of our series.
The problem is that we chose a poor series with which to compare. Since the numerator and denominator of the terms of the series are both algebraic functions, we should have compared our series to the dominant term of the numerator divided by the dominant term of the denominator.
The dominant term of the numerator is $$n^{1/2}$$ and the dominant term of the denominator is $$n^2$$. Thus we should compare the terms of the given series to $$n^{1/2}/n^2 = 1/n^{3/2}$$:
\begin{align*} \lim_{n\to\infty}\dfrac{(\sqrt{n}+3)/(n^2-n+1)}{1/n^{3/2}} &=\lim\limits_{n\to \infty} \dfrac{n^{3/2}(\sqrt n+3)}{n^2-n+1} \\ &= 1\quad \text{(Apply L'H$$\hat o$$pital's Rule)}. \end{align*}
Since the $$p$$-series $$\sum\limits_{n=1}^\infty \dfrac1{n^{3/2}}$$ converges, we conclude that $$\sum\limits_{n=1}^\infty \dfrac{\sqrt{n}+3}{n^2-n+1}$$ converges as well.
We mentioned earlier that the Integral Test did not work well with series containing factorial terms. The next section introduces the Ratio Test, which does handle such series well. We also introduce the Root Test, which is good for series where each term is raised to a power.
### Contributors
• Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/ | 2018-09-23T01:32:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9928606748580933, "perplexity": 334.1752304722175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158766.65/warc/CC-MAIN-20180923000827-20180923021227-00363.warc.gz"} |
https://mooseframework.inl.gov/source/mesh/RinglebMesh.html | # RinglebMesh
## Overview
This mesh can be applied to a Ringleb problem. This problem tests the spatial accuracy of high-order methods. The flow is transonic and smooth. The geometry is also smooth, and high-order curved boundary representation appears to be critical.
## Governing Equations
The governing equations are the 2D Euler equations with .
## Geometry
Let be a streamline parameter, i.e., on each streamline. The two stream lines for the two wall boundaries are for the inner wall, and for the outer wall. Let be the velocity magnitude. For each fixed , , the variable varies between and . For each , define the speed of sound , density , pressure , and a quantity denoted by by:
For each pair , set:
## Mesh Overlook
For example, let's consider the following input file:
[Mesh]
type = RinglebMesh
kmin = 0.7
num_k_pts = 9
num_q_pts = 20
kmax = 1.2
n_extra_q_pts = 2
gamma = 1.4
triangles = true
[]
The corresponding mesh looks like this:
## Input Parameters
• num_k_ptsHow many points in the range k=(kmin, kmax).
C++ Type:int
Options:
Description:How many points in the range k=(kmin, kmax).
• kminValue of k on the outer wall.
C++ Type:double
Options:
Description:Value of k on the outer wall.
• num_q_ptsHow many points to discretize the range q = (0.5, k) into.
C++ Type:int
Options:
Description:How many points to discretize the range q = (0.5, k) into.
• n_extra_q_ptsHow many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.
C++ Type:int
Options:
Description:How many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.
• kmaxValue of k on the inner wall.
C++ Type:double
Options:
Description:Value of k on the inner wall.
• gammaGamma parameter
C++ Type:double
Options:
Description:Gamma parameter
### Required Parameters
• outer_wall_bid4The boundary id to use for the outer wall
Default:4
C++ Type:short
Options:
Description:The boundary id to use for the outer wall
• outflow_bid3The boundary id to use for the outflow
Default:3
C++ Type:short
Options:
Description:The boundary id to use for the outflow
• allow_renumberingTrueIf allow_renumbering=false, node and element numbers are kept fixed until deletion
Default:True
C++ Type:bool
Options:
Description:If allow_renumbering=false, node and element numbers are kept fixed until deletion
• ghosting_patch_sizeThe number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.
C++ Type:unsigned int
Options:
Description:The number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.
• inner_wall_bid2The boundary id to use for the inner wall
Default:2
C++ Type:short
Options:
Description:The boundary id to use for the inner wall
• inflow_bid1The boundary id to use for the inflow
Default:1
C++ Type:short
Options:
Description:The boundary id to use for the inflow
• max_leaf_size10The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.
Default:10
C++ Type:unsigned int
Options:
Description:The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.
• trianglesFalseIf true, all the quadrilateral elements will be split into triangles
Default:False
C++ Type:bool
Options:
Description:If true, all the quadrilateral elements will be split into triangles
• parallel_typeDEFAULTDEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh
Default:DEFAULT
C++ Type:MooseEnum
Options:DEFAULT REPLICATED DISTRIBUTED
Description:DEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh
### Optional Parameters
• dim1This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!
Default:1
C++ Type:MooseEnum
Options:1 2 3
Description:This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!
• nemesisFalseIf nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.
Default:False
C++ Type:bool
Options:
Description:If nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.
• patch_update_strategyneverHow often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all slave nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all slave nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of slave nodes for which penetration is not detected. If there can be substantial relative motion between the master and slave surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.
Default:never
C++ Type:MooseEnum
Options:never always auto iteration
Description:How often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all slave nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all slave nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of slave nodes for which penetration is not detected. If there can be substantial relative motion between the master and slave surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.
• 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.
• construct_node_list_from_side_listTrueWhether or not to generate nodesets from the sidesets (usually a good idea).
Default:True
C++ Type:bool
Options:
Description:Whether or not to generate nodesets from the sidesets (usually a good idea).
• patch_size40The number of nodes to consider in the NearestNode neighborhood.
Default:40
C++ Type:unsigned int
Options:
Description:The number of nodes to consider in the NearestNode neighborhood.
• partitionerdefaultSpecifies a mesh partitioner to use when splitting the mesh for a parallel computation.
Default:default
C++ Type:MooseEnum
Options:default metis parmetis linear centroid hilbert_sfc morton_sfc
Description:Specifies a mesh partitioner to use when splitting the mesh for a parallel computation.
• centroid_partitioner_directionSpecifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial
C++ Type:MooseEnum
Options:x y z radial
Description:Specifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial | 2019-04-23T12:53:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4957534074783325, "perplexity": 5116.884511203146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578602767.67/warc/CC-MAIN-20190423114901-20190423140901-00120.warc.gz"} |
https://par.nsf.gov/biblio/10324343-unsupervised-machine-learning-reveals-slab-hydration-variations-from-deep-earthquake-distributions-beneath-northwest-pacific | This content will become publicly available on December 1, 2023
Unsupervised machine learning reveals slab hydration variations from deep earthquake distributions beneath the northwest Pacific
Abstract Although transformational faulting in the rim of the metastable olivine wedge is hypothesized as a triggering mechanism of deep-focus earthquakes, there is no direct evidence of such rim. Variations of the b value – slope of the Gutenberg-Richter distribution – have been used to decipher triggering and rupture mechanisms of deep earthquakes. However, detection limits prevent full understanding of these mechanisms. Using the Japan Meteorological Agency catalog, we estimate b values of deep earthquakes in the northwestern Pacific Plate, clustered in four regions with unsupervised machine learning. The b -value analysis of Honshu and Izu deep seismicity reveals a kink at magnitude 3.7–3.8, where the b value abruptly changes from 1.4–1.7 to 0.6–0.7. The anomalously high b values for small earthquakes highlight enhanced transformational faulting, likely catalyzed by deep hydrous defects coinciding with the unstable rim of the metastable olivine wedge, the thickness of which we estimate at $$\sim$$ ~ 1 km.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10324343
Journal Name:
Communications Earth & Environment
Volume:
3
Issue:
1
ISSN:
2662-4435 | 2022-08-14T22:46:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6064515113830566, "perplexity": 8676.35260746587}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572077.62/warc/CC-MAIN-20220814204141-20220814234141-00197.warc.gz"} |
https://par.nsf.gov/biblio/10108095-askap-detection-periodic-elliptically-polarized-radio-pulses-from-uv-ceti | ASKAP detection of periodic and elliptically polarized radio pulses from UV Ceti
ABSTRACT Active M dwarfs are known to produce bursty radio emission, and multiwavelength studies have shown that solar-like magnetic activity occurs in these stars. However, coherent bursts from active M dwarfs have often been difficult to interpret in the solar activity paradigm. We present Australian Square Array Pathfinder (ASKAP) observations of UV Ceti at a central frequency of 888 MHz. We detect several periodic, coherent pulses occurring over a time-scale consistent with the rotational period of UV Ceti. The properties of the pulsed emission show that they originate from the electron cyclotron maser instability, in a cavity at least 7 orders of magnitude less dense than the mean coronal density at the estimated source altitude. These results confirm that auroral activity can occur in active M dwarfs, suggesting that these stars mark the beginning of the transition from solar-like to auroral magnetospheric behaviour. These results demonstrate the capabilities of ASKAP for detecting polarized, coherent bursts from active stars and other systems.
Authors:
; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10108095
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
488
Issue:
1
Page Range or eLocation-ID:
559 to 571
ISSN:
0035-8711
4. Abstract We discuss observational strategies to detect prompt bursts associated with gravitational wave (GW) events using the Australian Square Kilometre Array Pathfinder (ASKAP). Many theoretical models of binary neutron stars mergers predict that bright, prompt radio emission would accompany the merger. The detection of such prompt emission would greatly improve our knowledge of the physical conditions, environment, and location of the merger. However, searches for prompt emission are complicated by the relatively poor localisation for GW events, with the 90% credible region reaching hundreds or even thousands of square degrees. Operating in fly’s eye mode, the ASKAP field of view can reach $\sim1\,000$ deg $^2$ at $\sim$ $888\,{\rm MHz}$ . This potentially allows observers to cover most of the 90% credible region quickly enough to detect prompt emission. We use skymaps for GW170817 and GW190814 from LIGO/Virgo’s third observing run to simulate the probability of detecting prompt emission for GW events in the upcoming fourth observing run. With only alerts released after merger, we find it difficult to slew the telescope sufficiently quickly as to capture any prompt emission. However, with the addition of alerts released before merger by negative-latency pipelines, we find that it should be possible to searchmore » | 2022-10-05T19:44:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5594491362571716, "perplexity": 2760.859740499776}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337663.75/warc/CC-MAIN-20221005172112-20221005202112-00422.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M012W0&home=MXXX005 | #### ${{\boldsymbol K}}{{\overline{\boldsymbol K}}}$ AND ${{\boldsymbol \eta}}{{\boldsymbol \pi}}$ MODES
VALUE (MeV)
$\bf{ 107 \pm5}$ OUR ESTIMATE
$\bf{ 110.4 \pm1.7}$ OUR AVERAGE | 2021-09-28T06:27:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9253605604171753, "perplexity": 11865.19873491585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060538.11/warc/CC-MAIN-20210928062408-20210928092408-00288.warc.gz"} |
https://www.federalreserve.gov/econres/notes/feds-notes/are-there-competitive-concerns-in-middle-market-lending-20200810.htm | August 10, 2020
### Are There Competitive Concerns in “Middle Market” Lending?
David Benson and Ken Onishi1
This note analyzes competition and concentration in "middle market" lending using loan level data obtained from large bank holding companies' Y14 reports to the Federal Reserve. The middle market segment is typically considered to be credit for firms larger than small businesses but too small for large-scale commercial lending or syndicated credit. Lender choice and the supply of credit to large and small firms has been studied extensively by academics and policy makers. Yet, much less is known about mid-sized firms' access to capital. Addressing this gap, we study market structure, the geography of borrower-lender proximity, and the persistence of lending relationships from loans supplied to medium-sized businesses in the Y14 data.
Three contributions highlight this work. First, we document patterns in market shares and concentration for an industry which has not received much attention in the literature. Second, we assess what the appropriate geographic market definition is, providing guidance for economic policy and future study of the middle market. Finally, we document middle market borrower inertia in the Y14, providing to our knowledge the first evidence on the extent of lender switching costs for medium-sized businesses.
The economic importance of middle market lending motivates addressing this gap in understanding. Our data contain $549 Billion in credit facilities extended to mid-sized firms, firms with annual revenue between$10 million to $250 million, in the fourth quarter of 2018. Over the same period, middle market credit utilization was relatively high, totaling$355 Billion or about two-thirds of the aggregate credit line.2
Understanding middle market borrowers' access to capital is also important for economic policy. Credit market structure and lender substitutability for mid-sized firms could impact their access to short term lending facilities during a financial crisis, for example. During the COVID19 pandemic, Congress and the Federal Reserve created the Main Street Lending Program to ensure medium-sized businesses had access to needed liquidity.
Additionally, an important open question for antitrust regulators is whether proposed bank mergers should receive more scrutiny for competitive effects on middle market lending. Mergers increase lenders' market power, and hence could increase medium-sized firms' costs of capital. Antitrust authorities routinely scrutinize proposed mergers for their competitive effects on small business lending (Federal Reserve Board, 2020; Department of Justice, 2000), and apparently do not usually scrutinize mergers for competitive effects on large-business lending. Neither the literature nor antitrust regulators have systematic measures of middle market concentration by which to assess a proposed merger's competitive effects, nor is there a consensus geographic market definition to begin such an assessment.
Since there is no consensus geographic market definition, we study market structure at local, regional, and national levels. By examining telescoping geographic market definitions, we are able to provide best and worst case assessments of middle market competition. For each of these market definitions, we describe market concentration using the Herfindahl-Hirschman Index (HHI), the sum of squared market shares within a geographic market. Note that market concentration measured using the Y14 data may overstate or understate actual concentration, since the data do not contain lending activity of non-bank lenders and banks who are not Y14 reporters. In general, we believe that our HHI measure overstates actual market concentration, because non-bank lenders are known to be a significant substitute to traditional banks in the middle market (Chernenko, Erel, and Robert, 2019). We also measure market size, for example documenting the aggregate credit line, and describe the number of middle market borrowers and the number of lenders operating a bank branch in the local market.
We find that at small geographic regions, measured by Federal Reserve banking markets ("Fed markets"), middle market concentration is generally high. There are several monopoly Fed markets, and several markets with neither a middle market borrower or lender. However, at larger geographic regions, measured by states, we find overall low HHIs. No states are monopoly markets, and most states have more than six lenders. Likewise, national market concentration is low. Therefore, whether there are competitive concerns in middle market lending depends on the geographic scope of borrowers' substitution to alternative lenders.
We use a formal test to discern whether a national market, larger regional markets as proxied by states, or smaller local Fed markets are a more appropriate geographic scope for the middle market. The Hypothetical Monopolist test is a common tool used in antitrust practice for this purpose. Our adaptation incorporates the geography of lender substitution observed in the data in order to infer the smallest profit margin necessary and sufficient for a candidate market definition to be profitably controlled by a hypothetical monopolist. The test's economic intuition is that middle market borrowers' willingness to substitute to out-of-market lenders is a key determinant of the profitability of any hypothetical price increase. Our Hypothetical Monopolist test minimal passible margins (MPM) provide a theoretically appropriate metric to gauge the sensibility of narrow versus broader market geographies.
We find that the minimal passible margins for Fed markets are too large to be sensible. In fact, many MPMs are infinite. This suggests that Fed markets are too narrow to appropriately assess competition in the middle market. In comparison, threshold margins for state-based markets are very reasonable. State market MPMs are similar to large banks' return on average assets measured using Call Reports. These results do not necessarily indicate that states are accurate market definitions, but do confirm that middle market geography is broader than Fed markets and have a regional character.
The formal market definition test is necessary because borrowers' proximity to their lenders only provides mixed evidence for the geographic scope of the middle market. The branch location data suggest that medium-sized businesses indeed have a preference for lender proximity. While many mid-sized firms choose an in-market lender, a significant faction are also willing to choose out-of-state or more distant lenders. Furthermore, results from loan-level linear regressions suggest that the borrowing firm's scale, the size of the loan, and expected utilization of the credit line are all negatively correlated with lender proximity.
Therefore, the baseline evidence from borrower-lender proximity does not endorse narrow geographic markets over broader regional markets, or vice versa, and therefore does not confirm or rule out competitive concerns in middle market lending. However, the Hypothetical Monopolist test results do suggest that state-based HHIs more appropriately measure competition for middle market lending. Since state HHIs are generally low, the results paint a picture of relatively healthy competition.
Lenders can obtain market power by means other than market concentration. For example, returns to relationship lending and other information or search frictions can create switching costs. Borrowers with switching costs are less likely to change lenders in response to an interest rate hike or a degradation of quality. We therefore conclude our study with an analysis of borrower inertia. We find that a significant fraction of borrowers switch lenders at the end of their loan term, and that borrowers who switch lenders have similar geographic substitution patterns as were measured using the market cross-sectional data. These results do not suggest that middle market firms have significant switching costs. Instead, middle market firms have substitution patterns which likely facilitates competition among lenders.
Taken together, our findings thus suggest that there are unlikely to be competitive concerns in the provision of middle market financial services. As a matter of economic policy, capital markets for mid-sized firms are likely regional: larger than the borrower's immediate local area but smaller than a national market. Since medium-sized businesses' characteristics and lender choice alternatives vary from region to region, we suggest that monetary authorities account for potential regional variation in the middle market's need for intervention, in particular during a financial crisis. Since state level market concentration is moderate, at most, we also conclude that antitrust authorities should reserve scrutiny to very large bank merger proposals which significantly increase regional market concentration. Such mergers might impact mid-sized firms' access to and costs of capital.
Data & Market Definitions
The Federal Reserve's Y14 quarterly report contains the universe of commercial and industrial (C&I) loans supplied to firms with more than $1 million in sales by stress-tested banks (bank holding companies with more than$100 Billion in assets). In 2018, the largest 30 banking holding companies that operate in the United States filed Y14 reports. Most of our analysis focuses on loans reported in the fourth quarter of 2018. The data include the lender's identity, the loan's committed amount of credit, utilization of this credit line, the duration of the contract, and several characteristics of the borrowing firm including office location and annual sales. In the analysis, we only use C&I loan data that report positive annual sales of borrowers. Lender branch locations data are obtained from the FDIC's June 2018 Summary of Deposits report.
There is no consensus market definition for middle market lending. Antitrust markets have two characteristics, products and geography. The first component involves identifying what types of customers and products should be the focus of the analysis, in this case identifying "middle market" borrowers and loans. The second component involves identifying where consumers' choice alternatives are located, in this case identifying how far away are lenders to which medium-sized businesses are willing to substitute. For a product market definition, we focus on loans made to firms with $10M-$250M in annual sales. This conservative definition is guided by the distribution of firm sizes and loan sizes in the Y14 data, as evidenced later in Figure 1, and is also informed by various by industry and academic publications (Brevoort and Hannan, 2006; Tannenwald, 1994; Elliehausen and Wolken, 1990; Kwast, Starr-McCluer, and Wolken, 1997).3 We use three proxy definitions for the geographic component of the market: Fed banking markets, states, and a national market.
Fed markets are a natural starting point for geographic boundaries of middle market lending. Fed markets are somewhat limited in geographic scope, defined as local economic areas within which representative consumers and small businesses travel for retail banking services. Fed markets often align with MSAs in the vicinity of large urban areas, and often align with counties or collections of smaller municipalities in rural and micropolitan areas.
Fed markets are the starting point antitrust authorities use to measure the competitive effects of bank mergers. Studies suggest that small business lending is a highly local geographic market (FDIC, 2018; Anenberg et al, 2018), potentially smaller even than Fed markets. It is plausible, then, that medium-sized businesses search for lenders in their immediate local area as well. However, due to their size, middle market firms might also have incentives to search more broadly than Fed markets for a credit supplier. Medium-sized businesses have larger balance sheets, a lower external finance premium, and often a wider scope of activity than small businesses. This suggests larger regional geographic markets or perhaps a national market may be more appropriate for middle market lending. We use states as a proxy definition for regional geographic markets.
Market Structure Results
Our market structure analysis begins with the loan-level data. We present the loan-level summary statistics and national aggregates in Table 1.
##### Table 1: Loan-level Summary Statistics for the Middle Market
Mean St. Dev. 10% 25% Median 75% 90%
Committed Credit ($M) 7.1 12.9 1.1 1.6 3 7.1 17 Utilized Credit ($M) 4.6 9.3 0 0.4 1.7 4.6 11.9
Borrower Sales ($M) 70.1 59.9 14.6 23.5 47.6 100.7 165.9 Aggregates: N Loans 77,070; HHI 737; Committed Credit$549 (B); Utilized Credit $355 (B) In the fourth quarter of 2018, Y14 filers reported 77,070 outstanding loans to firms with$10M-$250M in annual sales. The average annual sales of middle market borrowers was about$70M, and the firm size standard deviation was about $60M. Committed credit to the middle market totaled$549B, and 65 percent or $355B of total credit was utilized. The average credit line was$7M and the standard deviation of committed credit was $13M. However, most middle market loans are more modest compared to the average. The median credit limit was only$3M, and the 75th-percentile credit limit was equal to the mean credit limit. The bulk of credit utilization was similarly modest. While average credit utilization was $4.6M, over 10 percent of loans were unutilized and median utilization was$1.7M.
Calculating market concentration using loan-level credit lines provides a national HHI of 737. The national HHI is well below the 1800 threshold that antitrust authorities commonly consider for merger scrutiny (Federal Reserve Board, 2020). In the best case, the middle market is large, economically important, and unconcentrated and fairly competitive.
Is the best case robust to measuring market structure at finer geographic partitions? Table 2 contains summary statistics for Fed markets and states, conditional on the market having at least one borrower and at least one lender.
##### Table 2: Market Structure Summary Statistics for Fed Markets and States
Mean St. Dev. 10% 25% Median 75% 90%
Fed Markets
HHI 5,214 3,075 1,713 2,617 4,499 8,108 10,000
Banks 5.2 5.1 1 2 3 7 12
Borrowers 44.1 216.7 1 2 5 18 62
Market Size ($M) 483 2446 5 13 48 188 643 State Markets HHI 1456 465 886 1051 1421 1759 2033 Banks 21.2 5.5 13 17 22 26 28 Borrowers 979 1,167 122 197 592 1,270 2,781 Market Size ($M) 10,766 12,835 1,208 2,173 6,329 13,413 28,783
Notes: Calculations based on 1,132 Fed markets and 51 states + DC having at least one middle market borrower. Market size is measured by committed credit, denominated in millions. HHI is the Herfindahl-Hirschman Index, the sum of squared market shares by geographic market.
There are 1,398 Federal Reserve banking markets in 2018, but at least one middle market borrower exists in only 1,132 Fed markets in the Y14 data. We also find that at local geographic markets, middle market concentration is generally high. Roughly 22 percent of Fed markets are monopolies, and the median market only has 3 lenders. Over 75 percent of Fed markets are highly concentrated, defined as an HHI greater than 2500. Consequently, the mean HHI is also high at 5214. Only 132 of the 1,132 Fed markets have HHIs below 1800, the benchmark HHI at which antitrust authorities commonly apply more scrutiny to merger proposals. Thus, if local geographic markets are appropriate for the middle market, the data raise competitive concerns.
The lower panel of Figure 1 illustrates a strong negative relationship between lender proximity and loan size. The fraction of loans originated by in-market banks decreases sharply as loan size increases until credit lines exceed 50M. This suggests that medium-sized businesses tend to search for lenders more frequently outside their geographic area as loan size increases. This can be rationalized by an external funding premium that is increasing in credit demand, since the opportunity costs of high interest rates or fees increase with the size of the loan. This is also consistent with the view that markets for small business lending are local while the market for large-scale loans is national. The statistics above show the relationship between firm size and loan size and a middle market borrower's choice of geographically close banks. We naturally expect that firm size is correlated with loan size and, therefore, their raw correlations in the data do not allow us to separately quantify their relationships with lender proximity. To more formally assess borrowers' choice of lenders conditional on other variables, we estimate the following equation using Ordinary Least Squares (OSL). Here, we identify firm size, loan size, expected utilization of the credit line, and market size as the primary determinants of the geographic scope of demand. Formally, we estimate: \begin{align} {Local}_{ijt} &= \beta_1 Log({FirmSize})_{it} + \beta_2 Log({TotalCreditLine})_{ijt} + \beta_3 \frac{{UtilizedAmount}_{ijt}}{{TotalCreditLine}_{ijt}} \\\ &+ \beta_4 Log({FedMarketSize})_{ijt} + \beta_5 Log({StateMarketSize})_{ijt} + \varepsilon_{ijt}\end{align}, Where $i$ is an index for the borrowing firm, $j$ is an index for the loan, ${Local}_{ijt}$ is an indicator variable which equals 1 if the loan is originated by an in-market bank, $\varepsilon_{ijt}$ is an error term, and $\beta$s are the parameter to be estimated. Table 4 presents the OLS estimation results, reporting coefficients for firm size, loan size, and credit utilization. The first row measures ${Local}_{ijt}$ at the Fed market level, and the second row measures ${Local}_{ijt}$ at the state level. Surprisingly, we find that the results are not sensitive to including controls for market size. The market size variables have positive and statistically significant relationships with lender proximity, as well. ##### Table 4: Lender Proximity Regression Results ${Local}_{ijt}$ Log(Firm Size) Log(Loan Size) Utilization Fraction Fed Market Lender -0.024 -0.056 -0.078 (0.002) (0.001) (0.003) State Market Lender -0.008 -0.055 -0.056 (0.002) (0.001) (0.003) Notes: Both regressions have 77,070 observations (loans) and unreported market size control variables. Standard errors are reported in parentheses; all coefficients are statistically different from 0 at 0.1 % significance level. The adjusted R-squared statistics for in-Fed-market lender and in-State lender models are 0.119 and 0.049, respectively. The results in Table 4 show, at both the Fed market-level and state-level, that there is negative and statistically significant relationship between choosing an in-market bank and the borrower's scale and loan size. The regression results are consistent with an external funding premium that is increasing in credit demand and increasing in firm scale. The regression results also suggest that the scale relationship is driven by borrower substitution to regional lenders, while most of the loan size relationship is driven by broader regional or national substitution. The latter finding is to be expected, given the lower panel of Figure 1. Both the firm size and loan size relationships are significant even after controlling for the other variables. However, in terms of magnitude, the results suggest that loan size and expected utilization of the credit line are the primary determinants of the geographic scope of demand. Lender proximity has a negative and statistically significant relationship with the utilized credit fraction, defined as the utilized credit amount divided by the total credit line of the loan. The role of scale in the regression estimates confirms our expectation from the upper panel of Figure 1. The results presented in Table 4 and Figure 1 are consistent with the hypothesis that firms with larger sales, searching for larger loans, and with higher expected utilization of the loan are more likely to search for lenders in larger geographic scope. This provides heuristic guidance in favor of larger geographic market definitions for loans to medium-sized businesses, especially for borrowers seeking larger loans and expecting more credit utilization. However, most firms still choose an in-market lender. Therefore, the baseline evidence on lender proximity does not endorse broader regional markets over narrow geographic markets, or vice versa, and therefore does not confirm or rule out competitive concerns in middle market lending. Which Geographic Market Definition? To formally assess the appropriateness of geographic market definitions for middle market lending, we employ a Hypothetical Monopolist test.4 This test is commonly used by antitrust authorities to establish market definitions for merger proposals. Can a hypothetical monopolist who controls all lenders within the candidate geographic market definition raise an interest rate without losing so many borrowers that such a price increase, a Small but Significant and Nontransitory Increase in Price (SSNIP), would be unprofitable? If the data suggest the SSNIP is unprofitable, then the candidate market is too narrowly defined. How can the profitability of a SSNIP be measured? The tradeoff between the SSNIP $x$ and lost demand $L$ depends on the hypothetical monopolist's profit margin $m=\frac{p-c}{p}$. In percentage changes, the monopolist breaks even imposing a SSNIP if $(m+x)(1-L) = m$. Solving this break even condition provides a formula for “critical loss” $L=\frac{x}{x+m}$. If data are available for the “critical loss” version of the hypothetical monopolist test, one compares actual lost demand $\hat{L}$ due to the SSNIP with critical loss, and if $\hat{L} \le L(m,x)$ then a hypothetical monopolist has incentives to impose the SSNIP and the candidate market definition passes the test. If, instead, one finds that actual loss is greater than critical loss, $\hat{L} \gt L(m,x)$, then the candidate geographic market is too narrow. Therefore, three numbers are needed to measure the profitability of the SSNIP: $(m,x,\hat{L})$. Actual lost demand due to the SSNIP is counterfactual. Therefore, the market definition test requires estimating loss $\hat{L}$. Because the hypothetical monopolist recaptures medium-sized businesses that switch to alternative lenders inside the market definition, only diversion to lenders outside the candidate market count toward loss. Thus, a close approximation to loss is given by the elasticity of demand $\epsilon$ times the percentage change in price $x$ times the probability $D_0$ that displaced consumers do not switch to some other lender inside the market, formally $\hat{L} = \epsilon x D_0$. Because pre-SSNIP must be profit maximizing, the margin and demand elasticity are inversely related, $m = 1/\epsilon$, which simplifies the loss formula to $\hat{L} = x \ D_0/m$. Comparing estimated loss to critical loss, the hypothetical monopolist test for a candidate geographic market definition is $$\hat{L} \le L(m,x) \text{ if and only if } D_0 \le \frac{m}{x+m}$$ For the diversion ratio to lenders outside the market, $D_0$, we use a common estimator that is based on lender choice probabilities, $\hat{D}_0 = \frac{s_0}{1-s}$. The aggregate share of out-of-market lenders is $s_0$, and the market share of the lender subjected to the SNNIP is $s$. Both of these values can be read off the data given a candidate geographic market definition. Diversion is proportional to observed choice probabilities, as we assume, if borrower preferences for one lender over another depend only on ranking those two alternatives relative to each other.5 Lacking data on lender profit margins $m$, the last ingredient needed to test the market definition is also counterfactual. To proceed, we compute the smallest margin necessary and sufficient for the candidate geographic market definition to pass the hypothetical monopolist test given values for $D_0$ and $x$. The margin threshold is an instrument to gauge whether the candidate market is too narrowly defined. A bank's return on assets, though an accounting metric and not a measure of economic profit, is useful to compare to our SSNIP test margins. Banks in the U.S. with more than15B is assets had an average return on assets of about 1.4 percent (FRED, 2020) over our sample window.
Rearranging the SSNIP test criterion characterizes the general lower bound or threshold margin: $M \ge x \ D_0/(1-D_0)$. Plugging in our estimate for $\hat{D}_0$, margins must be at least
$$m^{\ast} = x\frac{s_0}{1-s-s_0}$$
for all in-market lenders in order for a candidate geographic market definition to pass the hypothetical monopolist test. Since $m^{\ast}$ is increasing in the share $s$ of the lender affected by the SSNIP, the candidate market definition's minimal passable margin (MPM) is
$$MPM = x \frac{s_0}{1-s_0}$$
We conduct the test, estimating MPM and $m^{\ast}$, assuming a five percent SSNIP. The MPM is a more lenient criterion, only depends on the out-of-market lender share, and only varies across markets. Since $m^{\ast}$ depends on each in-market lender's market share, every market has a distribution of threshold margins. We therefore take the mean of $m^{\ast}$ market-by-market and report the between-market variation in SSNIP threshold margins for comparison to the MPM. The results are summarized in Table 5.
##### Table 5: SSNIP Test Margin Summary Statistics for Fed Markets and States
Mean St. Dev. 10% 25% Median 75% 90%
Fed market’s MPM 13.00% 29.60% 0.60% 2.30% 11.40% Inf Inf
Fed market’s average m* 20.80% 57.70% 1.80% 6.00% Inf Inf Inf
State’s MPM 2.90% 2.50% 0.80% 1.40% 2.00% 3.90% 5.60%
State’s average m* 5.00% 8.80% 0.90% 1.60% 2.30% 4.40% 9.60%
We begin by examining the narrower candidate market definition. The results strongly suggest that Fed markets are too narrow to assess competition in middle market lending. For most Fed banking markets, the threshold margins are too large to be sensible; over half of Fed markets require infinite margins to pass the test. The more lenient MPM measure is kinder to Fed market definitions, but still requires infinite margins from over 25 percent of markets.
Due to these infinite margins, the between-market mean and variance is undefined if geographic markets are Fed markets. Thus in Table 5 we report infinity-censored moments for Fed markets. The censored average margins are 12-13 percent, which we believe is high but still reasonable. These censored averages are driven primarily by MSA Fed markets. Smaller MSA markets have very large test margins, which generates large standard deviations that are approximately twice the scale of the mean. Fed markets defined around large MSAs have sensible results. However, large MSA Fed markets have wider geographic scope than typical Fed markets, and so are closer to a regional market definition and already include more close substitutes than a typical Fed market.
Next we incorporate the next closest substitutes into an expanded candidate market definition, widening the geographic scope of the market to a larger regional area as proxied by states. The state-level results suggests that wider geographic scope is indeed more appropriate for assessing competition in middle market lending. No states have infinite MPM or average threshold margins $m^{\ast}$. Therefore, the moments in Table 5 are not censored for state markets. The mean MPM across states is 2.9 percent, and the mean of the stricter SSNIP threshold $m^{\ast}$ is 5.5 percent. Nearly all state-based geographic markets have MPMs less than 6 percent. Compared to the Fed market results, between-state variation in SSNIP margins is also closer to the scale of the mean and more symmetrically distributed.
The hypothetical monopolist test results strongly favor larger regional market definitions over Fed banking market definitions for assessing competition in the middle market. However, the results do not necessarily imply that states are themselves the correct market definition. States are only a proxy for regional markets, and there are other possible regional geographic partitions which have not been subjected to the test and compared to our state-level results. However, we believe alternative geographic regions would produce an overall similar distribution of market concentration as the state-based partition. Hence, were we to hone in on a more accurate regional geographic market definition, our conclusion that middle market lending is relatively unconcentrated is unlikely to change.
Borrower Inertia
In the previous sections, we investigate how geographic proximity affects a borrower's lender choice. In this section, we further investigate borrower's choice from the perspective of the frequency of a borrower's lender-switching behavior. Table 6 presents basic statistics on the number of lenders that each borrower has a relationship with. We report the borrower’s total number of lenders, total number of in-state lenders, and the percentage of borrowers who changed lenders between Q4 2017 and Q4 2018.
##### Table 6: Borrower’s Lender Relationships and Switching Behavior
Number of Lenders Number of In-State Lenders Switched Lenders
Mean 1.06 0.9 4.55%
Standard Deviation 0.37 0.44
Notes: Calculations based on 49,707 loans observed in both Q4 2017 and Q4 2018.
On average, each borrower only has a credit line from one lender, and most of these lenders are in-state banks. The third column of Table 6 shows that 4.55 percent of middle market firms either switched banks (bank-to-bank substitution), formed a new credit line (outside-to-inside substitution), or destroyed a credit line (inside-to-outside substitution). We observe similar switching rates in prior years. Since the median loan term is seven years for middle market firms, the data imply that middle market firms do in fact search for and switch lenders frequently. About 1/7 = 14 percent of all loans reach maturity each year. A back-of-the-envelope calculation from an overall switching probability of 4.55 percent thus indicates that about 32 percent of borrowers switch lenders at maturity.
This within-borrower analysis suggests that switching costs and other forms of inertia do not encumber middle market firms. In light of the market cross-sectional analysis of competition, farther regional banks are likely close substitutes for geographically near banks for medium-sized businesses who switch lenders. Taken together, this evidence suggests that bank mergers with small effects on regional market structure are unlikely to harm mid-sized firms' access to and costs of capital.
Conclusion
Our findings from the Y14 data suggest that there are unlikely to be competitive concerns in the provision of middle market financial services. Lender choice data support broader geographic market definitions than those suited for analysis of small business credit and consumer deposits. For narrower geographic markets, the profit margins implied by formal hypothetical monopolist tests are implausibly large, a strong indicator such market definitions should be expanded in the case of middle market loans. Broader geographic markets seem to be especially appropriate for larger firms and larger loans, with loan size and expected credit utilization being the key determinants of the geographic scope of lender substitution. Regional market concentration is moderate, at most. Competition appears especially healthy for larger firms and larger loans, who act on their incentives to search more broadly for lenders. Evidence on borrower inertia complements these findings, suggesting that medium-sized businesses' substitution patterns foster rather than impede lender competition.
Our findings support scrutiny of proposed bank mergers that affect concentration at the regional level, since these mergers might impact middle market firms' access to capital markets. Antitrust authorities can likely forgo scrutiny of smaller mergers that only impact market structure locally. Nonetheless, economic policy makers should be mindful of the middle market's regional character, as it could shape a policy's impact on mid-sized firms' access to capital and costs of credit.
Bibliography
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1. All authors: Federal Reserve Board of Governors, 20th & C St NW, Washington, DC 20551, David.A.Ben[email protected], and [email protected] The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the staff, by the Board of Governors or the Federal Reserve Banks. Return to text
2. These figures, while sizable, establish a lower bound on the economic importance of the middle market, because Y14 reports were only filed by the 30 largest bank holding companies in 2018. Return to text
3. Alternative characterizations of the middle market might focus on loan sizes instead of on firm scale, on assets instead of sales to measure scale, or on a more restricted core range of sales. Instead of adopting such restrictions a priori, we prefer to subsume them and consider narrower notions of the middle market as a robustness exercise. Return to text
4. Antitrust authorities "employ the hypothetical monopolist test to evaluate whether groups of products in candidate markets are sufficiently broad to constitute relevant antitrust markets. … Specifically, the test requires that a hypothetical profit-maximizing firm, not subject to price regulation, that was the only present and future seller of those products ("hypothetical monopolist") likely would impose at least a small but significant and non-transitory increase in price ("SSNIP") on at least one product in the market, including at least one product sold by one of the merging firms. … The hypothetical monopolist test ensures that markets are not defined too narrowly, but it does not lead to a single relevant market. The Agencies may evaluate a merger in any relevant market satisfying the test, guided by the overarching principle that the purpose of defining the market and measuring market shares is to illuminate the evaluation of competitive effects. Because the relative competitive significance of more distant substitutes is apt to be overstated by their share of sales, when the Agencies rely on market shares and concentration, they usually do so in the smallest relevant market satisfying the hypothetical monopolist test. … The hypothetical monopolist's incentive to raise prices depends both on the extent to which customers would likely substitute away from the products in the candidate market in response to such a price increase and on the profit margins earned on those products." (U.S. Department of Justice - Federal Trade Commission Horizontal Merger Guidelines, 2010, Sections 4.1.1 & 4.1.3.) Return to text
5. Formally, we assume that mid-sized firms’ preferences for lenders satisfy the Independence of Irrelevant Alternatives (IIA) property. To illustrate IIA, suppose a borrower prefers lender $A$ to lender $B$. If the borrower then contemplates a third lender, $C$, the IIA property requires that alternative $B$ is not chosen. That is, the borrower may or may not prefer $C$ to $A$, but the ranking of $A$ relative to $B$ is independent of $C$. The SSNIP $x_i$ causes some borrowers to switch or divert from lender $i$. The IIA assumption implies that diversion $d_{ik}$ from lender $i$ to lender $k$ is equal to the probability that $k$ is preferred given that $i$ is not chosen, formally expressed $d_{ik} = s_k / (1-s_i)$. Total diversion to out-of-market lenders is thus $D_0 = s_0 / (1-s_i)$. Return to text | 2022-07-03T16:02:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42852792143821716, "perplexity": 4600.761445643046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104244535.68/warc/CC-MAIN-20220703134535-20220703164535-00577.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M147M1&home=MXXX005 | # ${{\boldsymbol \pi}}{{\boldsymbol \pi}}$ MODE INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$1400$ $\pm40$ 1
2009 L
BABR ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$
$1470$ ${}^{+6}_{-7}$ ${}^{+72}_{-255}$ 2
2008 A
BELL 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$1259$ $\pm55$ 2.6k
2007
CLEO ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$
$1309$ $\pm1$ $\pm15$ 3
2007 A
RVUE 0.0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$
$1449$ $\pm13$ 4.3k 4
2006
BELL ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1350$ $\pm50$
2005
BES2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1265$ $\pm30$ ${}^{+20}_{-35}$
2005 Q
BES2 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$
$1434$ $\pm18$ $\pm9$ 848
2001 A
E791 ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$
$1308$ $\pm10$
1999 B
OMEG 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}_{{s}}}{{\mathit p}_{{f}}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1315$ $\pm50$
1999
GAM4 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$1315$ $\pm30$
1998
GAM4 100 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit n}}$
$1280$ $\pm55$
1998
OBLX $0.05 - 0.405$ ${{\overline{\mathit n}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1186$ 5, 6
1995
RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit \eta}}{{\mathit \pi}}$
$1472$ $\pm12$
1991
OMEG 300 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit p}}{{\mathit p}}{{\mathit K}}{{\overline{\mathit K}}}$
$1275$ $\pm20$
1990
SFM 62 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1420$ $\pm20$
1986
SPEC 63 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1256$
1977
RVUE ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ channel
1 Breit-Wigner mass.
2 Breit-Wigner mass. May also be the ${{\mathit f}_{{0}}{(1500)}}$.
3 Reanalysis of ABELE 1996C data.
4 Also observed by GARMASH 2007 in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays. Supersedes GARMASH 2005 .
5 Uses data from BEIER 1972B, OCHS 1973 , HYAMS 1973 , GRAYER 1974 , ROSSELET 1977 , CASON 1983 , ASTON 1988 , and ARMSTRONG 1991B. Coupled channel analysis with flavor symmetry and all light two-pseudoscalars systems.
6 Also observed by ASNER 2000 in ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ decays
References:
AUBERT 2009L
PR D79 072006 Dalitz Plot Analysis of ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$ Decays
UEHARA 2008A
PR D78 052004 High-Statistics Measurement of Neutral-Pion Pair Production in Two-Photon Collisions
BONVICINI 2007
PR D76 012001 Dalitz Plot Analysis of the ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ Decay
BUGG 2007A
JP G34 151 The Mass of the $\sigma$ Pole
GARMASH 2006
PRL 96 251803 Evidence for Large Direct $\mathit CP$ Violation in ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \rho}{(770)}^{0}}{{\mathit K}^{\pm}}$ from Analysis of Three-Body Charmless ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\pm}}$ Decays
ABLIKIM 2005
PL B607 243 Resonances in ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \phi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$
ABLIKIM 2005Q
PR D72 092002 Partial Wave Analysis of ${{\mathit \chi}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$
AITALA 2001A
PRL 86 765 Study of the ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ Decay Measurement of ${{\mathit f}_{{0}}}$ Masses and Widths
BARBERIS 1999B
PL B453 316 A Partial Wave Analysis of the Centrally Produced ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ System in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$
BELLAZZINI 1999
PL B467 296 A Partial Wave Analysis of the Centrally Produced ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$
ALDE 1998
EPJ A3 361 Study of the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System with the GAMS-4000 Spectrometer at 100 ${\mathrm {GeV/}}\mathit c$
BERTIN 1998
PR D57 55 Study of the ${{\mathit f}_{{0}}{(1500)}}/{{\mathit f}_{{2}}{(1565)}}$ Production in the Exclusive Annihilation ${{\overline{\mathit n}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ in Flight
TORNQVIST 1995
ZPHY C68 647 Understanding the Scalar Meson ${\mathit {\mathit q}}{\mathit {\overline{\mathit q}}}$ Nonet
ARMSTRONG 1991
ZPHY C51 351 Study of the Centrally Produced ${{\mathit \pi}}{{\mathit \pi}}$ and ${{\mathit K}}{{\overline{\mathit K}}}$ Systems at 85 and 300 ${\mathrm {GeV/}}\mathit c$
BREAKSTONE 1990
ZPHY C48 569 The Reaction pomeron pomeron $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and an Unusual Production Mechanism for the ${{\mathit f}_{{2}}{(1270)}}$
AKESSON 1986
NP B264 154 A Search for Glueballs and a Study of Double Pomeron Exchange at the CERN Intersecting Storage Rings
FROGGATT 1977
NP B129 89 Phase Shift Analysis of ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Scattering between 1.0 and 1.8 GeV Based on Fixed Momentum Transfer Analyticity. 2. | 2021-03-02T21:08:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8154770731925964, "perplexity": 4987.5088715406755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00242.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S004DT | # ${\boldsymbol \tau}_{{{\boldsymbol \mu}^{+}}}/{\boldsymbol \tau}_{{{\boldsymbol \mu}^{-}}}$ MEAN LIFE RATIO INSPIRE search
A test of $\mathit CPT$ invariance.
VALUE DOCUMENT ID TECN COMMENT
$1.000024$ $\pm0.000078$
1984
CNTR
• • • We do not use the following data for averages, fits, limits, etc. • • •
$1.0008$ $\pm0.0010$
1979
CNTR Storage ring
$1.000$ $\pm0.001$
1963
CNTR Mean life ${{\mathit \mu}^{+}}$/ ${{\mathit \mu}^{-}}$
References:
BARDIN 1984
PL 137B 135 A New Measurement of the Positive Muon Lifetime
BAILEY 1979
NP B150 1 Final Report on the CERN Muon Storage Ring Including the Anomalous Magnetic Moment and the Electric Dipole Moment of the Muon, and a Direct Test of Relativistic Time Dilation
MEYER 1963
PR 132 2693 Precision Lifetime Measurements on Positive and Negative Muons | 2021-03-02T20:36:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7619079947471619, "perplexity": 5493.9242547371205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00038.warc.gz"} |
https://atlaswww.hep.anl.gov/hepsim/doc/doku.php?id=hepsim:dev_tags | # Submitting tags
As a HepSim user, you can submit your detector description and the simulation/reconstruction chain to HepSim using “tag” files.
All detector simulations in HepSim are created using the concept of tags, which are small (<5 MB) files that include necessary information to convert truth-level files to final reconstructed events. All tags can be found in this page. In many cases we call them “reconstruction” tags, but, generally, they include Geant4 simulation and reconstruction steps.
A reconstruction tag is associated with the file with the name rfull[XXX].tgz, where [XXX] is a number. Fast simulations have tags with the name rfast[XXX].tgz.
The tag files are used for:
• archiving the detector geometry
• creating the web page with the detector description
• archiving calibration files etc.
• defining the used software
• defining the tag name to be used for downloading events
• defining the workflow of the simulation-reconstruction steps
• creating the necessary files for event visualization using Jas4pp (only for slic/lcsim complied software)
• feeding the HPC and grid jobs for simulation and reconstruction (for dockers & singularity images).
Reconstruction tags have unique names. There can be several reconstruction tags corresponding to a single detector, since simulation and reconstruction can be done using different software. They are small files that are sourced by reconstruction software on grid or HPC. A file rfull[XXX].tgz has everything you need to create LCIO/ROOT files with reconstructed events.
# Structure of tags
In most cases, the directory inside rfull[XXX].tgz has this structure (for a detector called “sifcch7”):
A_RUN # main script to process events (free form)
TEST # script for testing (optional)
source.sh # setup script (optional)
..... # other required files if needed
sifcch7 # the directory with detector geometry (always required!)
- compact.xml # main detector geometry file (always required, but can be a dummy)
- other.xml ... # some other XML files with detector components -> optional
- sifcch7.heprep # some converted files, if needed -> optional file
- sifcch7.lcdd # file for event displays -> optional file
- sifcch7.pandora # file for Pandora -> optional file
- sifcch7.json # geometry JSON file -> optional file
- sifcch7.root # geometry file (use to make 3D display) -> optional file
- sifcch7.html # HTML description -> required file
- view1.png # main image to view the detector (440x480 px, Y-Z) -> required for HepSim page
- view2.png # 2nd image to view the detector (440x480 px, X-Y) -> optional file
- some config files
To see what is inside, download “rful009.tgz” from http://atlaswww.hep.anl.gov/hepsim/taginfo.php?id=rfull009.
Such files include the detector geometry. In addition to the detector geometry, the tag files include the settings needed for creation of events. Generally, the form of this file is free, as long as it includes sufficient information to create reconstructed events. In many cases, the tag file has several scripts : A_RUN (to make a complete reconstruction chain) and TEST (to test on a few events). The software to run these scripts should be fully specified, and it is up to the author to make sure that one can use such files to run over events on a dedicated computing resource.
Note that the simulation and reconstruction software should not be put inside rfull[XXX].tgz files. This file size limit of 5 MB is important to keep a low network bandwidth when the tag files are sourced by reconstruction software on each node on HPC or grid, which are assumed to contain the needed software used in combination with rfull[XXX].tgz files.
You should create the reconstruction tag if:
• detector geometry was changed. In this case, use a different detector name inside rfull[XXX].tgz
• detector geometry is the same, but configuration files and setup scripts were changed.
HepSim provides a mechanism for uploading rfull[XXX].tgz files. After upload, HepSim automatically extracts the detector from rfull[XXX].tgz and builds an information detector page. Then you will see two entries:
As mentioned before, we leave the authors with the liberty to design the rfull[XXX].tgz files. The only strict requirement is that they should have the directory with the detector description, a PNG image and the HTML description, since such populate the information page with the detector in HepSim. The simulation and reconstruction scripts can include all the required workflow to work together with the installed software (git, makefiles, wget commands etc).
A tag file should have a directory with the detector name, and the compact.xml file inside this directory. This structure helps automatically extract the detector for inclusion in HepSim. Please add compact.xml even if it is a dummy file not used for detector description.
After a tag file is uploaded, HepSim performs the following operations with this file:
• Moves the file to the standard location, so it can be used as a source on computing nodes
• Extracts the detector, and makes a zip file for download
• Builds a web page with the detector information (uses included HTML, view1.png, compact.xml and other available files)
• For the SiD derived software, prepares a zip file with detector description for Jas4pp to view the detector inside the Wired4 display
# How to submit detector tags
First, request the account HepSim login page. Then, go to HepSim and look at the yellow menu “Admin info” and then “Tag manager”. Use the submit panel to upload the tag file. HepSim does some basic checks that your tag file has the required structure, and updates the tag description and the detector page.
Sergei Chekanov 2017/08/12 21:58 | 2022-09-28T23:29:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40987738966941833, "perplexity": 6348.15798284112}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00530.warc.gz"} |
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