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https://www.nist.gov/publications/optical-microwave-frequency-comparison-fractional-uncertainty-10-15 | An official website of the United States government
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# Optical-to-microwave frequency comparison with fractional uncertainty of 10-15
Published
### Author(s)
Jason Stalnaker, Scott A. Diddams, Tara M. Fortier, K Kim, Leo W. Hollberg, James C. Bergquist, Wayne M. Itano, Marie Delaney, Luca Lorini, Windell Oskay, Thomas P. Heavner, Steven R. Jefferts, Filippo Levi, Thomas E. Parker, Jon H. Shirley
### Abstract
We report the technical aspects of the optical-to-microwave comparison for our recent measurements of the optical frequency of the mercury single-ion frequency standard in terms of the SI second as realized by the NIST-F1 cesium fountain clock. Over the course of six years, these measurements have resulted in a determination of the mercury single-ion frequency with a fractional uncertainty less than $7 \times 10^{-16}$ making it the most accurately measured optical frequency to date. In this paper, we focus on the details of the comparison techniques used in the experiment and discuss the uncertainties associated with the optical-to-microwave synthesis based on a femtosecond laser frequency comb. We also present our most recent results in the context of the previous measurements of the mercury single-ion frequency and arrive at a final determination of the mercury single ion optical frequency: $f({\rm Hg}^+) = 1 \, 064 \, 721 \, 609 \, 899 \, 145.30(69) \: {\rm Hz}$.
Citation
Applied Physics B
### Keywords
cesium frequency standard, femtosecond frequency comb, mercury ion clock, optical clock, optical frequency measurement, optical-to-microwave conversion
## Citation
Stalnaker, J. , Diddams, S. , Fortier, T. , Kim, K. , Hollberg, L. , Bergquist, J. , Itano, W. , Delaney, M. , Lorini, L. , Oskay, W. , Heavner, T. , Jefferts, S. , Levi, F. , Parker, T. and Shirley, J. (2007), Optical-to-microwave frequency comparison with fractional uncertainty of 10<sup>-15</sup>, Applied Physics B, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50555 (Accessed May 11, 2021)
Created October 1, 2007, Updated November 29, 2016 | 2021-05-12T02:49:40 | {"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": 0.40306493639945984, "perplexity": 10984.093313753321}, "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-2021-21/segments/1620243991693.14/warc/CC-MAIN-20210512004850-20210512034850-00389.warc.gz"} |
http://dlmf.nist.gov/15.15 | # §15.15 Sums
15.15.1 $\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop c};\frac{1}{z}\right)=\left(1-% \frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\mathop{% \mathbf{F}\/}\nolimits\!\left({-s,b\atop c};\frac{1}{z_{0}}\right)\left(1-% \frac{z}{z_{0}}\right)^{-s}.$
Here $z_{0}$ (${\neq 0}$) is an arbitrary complex constant and the expansion converges when $|z-z_{0}|>\max(|z_{0}|,|z_{0}-1|)$. For further information see Bühring (1987a) and Kalla (1992).
For compendia of finite sums and infinite series involving hypergeometric functions see Prudnikov et al. (1990, §§5.3 and 6.7) and Hansen (1975). | 2014-09-02T16:55:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 12, "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": 0.9949465990066528, "perplexity": 1932.413530433446}, "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-2014-35/segments/1409535922089.6/warc/CC-MAIN-20140901014522-00059-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Stochastic_process.html | # Stochastic process
Stock market fluctuations have been modeled by stochastic processes.
A stochastic (/stˈkæstɪk/) process (or random process) is a probability model used to describe phenomena that evolve over time or space.[1][2] More specifically, in probability theory, a stochastic process is a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation.[3] This is the probabilistic counterpart to a deterministic process (or deterministic system). Instead of describing a process which can only evolve in one way (as in the case, for example, of solutions of an ordinary differential equation), in a stochastic, or random process, there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely many) directions in which the process may evolve. In many stochastic processes, the movement to the next state or position depends on only the current state, and is independent from prior states or values the process has taken.
In the simple case of discrete time, as opposed to continuous time, a stochastic process is a sequence of random variables. (For example, see Markov chain, also known as discrete-time Markov chain.) The random variables corresponding to various times may be completely different, the only requirement being that these different random quantities all take values in the same space (the codomain of the function). One approach may be to model these random variables as random functions of one or several deterministic arguments (in most cases, the time parameter). Although the random values of a stochastic process at different times may be independent random variables, in most commonly considered situations they exhibit complicated statistical dependence.
Familiar examples of stochastic processes include stock market and exchange rate fluctuations; signals such as speech; audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks.
A generalization, the random field, is defined by letting the variables be parametrized by members of a topological space instead of time. Examples of random fields include static images, random terrain (landscapes), wind waves and composition variations of a heterogeneous material.
## Formal definition and basic properties
### Definition
Given a probability space and a measurable space , an S-valued stochastic process is a collection of S-valued random variables on , indexed by a totally ordered set T ("time"). That is, a stochastic process X is a collection
where each is an S-valued random variable on . The space S is then called the state space of the process.
### Finite-dimensional distributions
Let X be an S-valued stochastic process. For every finite sequence , the k-tuple is a random variable taking values in . The distribution of this random variable is a probability measure on . This is called a finite-dimensional distribution of X.
Under suitable topological restrictions, a suitably "consistent" collection of finite-dimensional distributions can be used to define a stochastic process (see Kolmogorov extension in the "Construction" section).
## History of stochastic processes
Stochastic processes were first studied rigorously in the late 19th century to aid in understanding financial markets and Brownian motion. The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by Louis Bachelier in 1900 in his PhD thesis "The theory of speculation", in which he presented a stochastic analysis of the stock and option markets. Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. Their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1908.
An excerpt from Einstein's paper describes the fundamentals of a stochastic model:
"It must clearly be assumed that each individual particle executes a motion which is independent of the motions of all other particles; it will also be considered that the movements of one and the same particle in different time intervals are independent processes, as long as these time intervals are not chosen too small.
We introduce a time interval into consideration, which is very small compared to the observable time intervals, but nevertheless so large that in two successive time intervals , the motions executed by the particle can be thought of as events which are independent of each other".
[4]
## Construction
In the ordinary axiomatization of probability theory by means of measure theory, the problem is to construct a sigma-algebra of measurable subsets of the space of all functions, and then put a finite measure on it. For this purpose one traditionally uses a method called Kolmogorov extension.[5]
### Kolmogorov extension
The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables . Now, from this n-dimensional probability distribution we can deduce an (n 1)-dimensional marginal probability distribution for . Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement. Such a condition only holds, for example, if the stochastic process is a Wiener process (in which case the marginals are all gaussian distributions of the exponential class) but not in general for all stochastic processes. When this condition is expressed in terms of probability densities, the result is called the Chapman–Kolmogorov equation.
The Kolmogorov extension theorem guarantees the existence of a stochastic process with a given family of finite-dimensional probability distributions satisfying the Chapman–Kolmogorov compatibility condition.
### Separability, or what the Kolmogorov extension does not provide
Recall that in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.
The Kolmogorov extension starts by declaring to be measurable all sets of functions where finitely many coordinates are restricted to lie in measurable subsets of . In other words, if a yes/no question about f can be answered by looking at the values of at most finitely many coordinates, then it has a probabilistic answer.
In measure theory, if we have a countably infinite collection of measurable sets, then the union and intersection of all of them is a measurable set. For our purposes, this means that yes/no questions that depend on countably many coordinates have a probabilistic answer.
The good news is that the Kolmogorov extension makes it possible to construct stochastic processes with fairly arbitrary finite-dimensional distributions. Also, every question that one could ask about a sequence has a probabilistic answer when asked of a random sequence. The bad news is that certain questions about functions on a continuous domain don't have a probabilistic answer. One might hope that the questions that depend on uncountably many values of a function be of little interest, but the really bad news is that virtually all concepts of calculus are of this sort. For example:
all require knowledge of uncountably many values of the function.
One solution to this problem is to require that the stochastic process be separable. In other words, that there be some countable set of coordinates whose values determine the whole random function f.
The Kolmogorov continuity theorem guarantees that processes that satisfy certain constraints on the moments of their increments have continuous modifications and are therefore separable.
## Filtrations
Given a probability space , a filtration is a weakly increasing collection of sigma-algebras on , , indexed by some totally ordered set , and bounded above by , i.e. for s,t with s < t,
.
A stochastic process on the same time set is said to be adapted to the filtration if, for every t , is -measurable.[6]
### Natural filtration
Given a stochastic process , the natural filtration for (or induced by) this process is the filtration where is generated by all values of up to time s = t, i.e. .
A stochastic process is always adapted to its natural filtration.
## Classification
Stochastic processes can be classified according to the cardinality of its index set (usually interpreted as time) and state space.
### Discrete time and discrete state space
If both and belong to , the set of natural numbers, then we have models which lead to Markov chains. For example:
(a) If means the bit (0 or 1) in position of a sequence of transmitted bits, then can be modelled as a Markov chain with two states. This leads to the error-correcting Viterbi algorithm in data transmission.
(b) If represents the combined genotype of a breeding couple in the th generation in an inbreeding model, it can be shown that the proportion of heterozygous individuals in the population approaches zero as goes to ∞.[7]
### Continuous time and continuous state space
The paradigm of continuous stochastic process is that of the Wiener process. In its original form the problem was concerned with a particle floating on a liquid surface, receiving "kicks" from the molecules of the liquid. The particle is then viewed as being subject to a random force which, since the molecules are very small and very close together, is treated as being continuous and since the particle is constrained to the surface of the liquid by surface tension, is at each point in time a vector parallel to the surface. Thus, the random force is described by a two-component stochastic process; two real-valued random variables are associated to each point in the index set, time, (note that since the liquid is viewed as being homogeneous the force is independent of the spatial coordinates) with the domain of the two random variables being R, giving the x and y components of the force. A treatment of Brownian motion generally also includes the effect of viscosity, resulting in an equation of motion known as the Langevin equation.[8]
### Discrete time and continuous state space
If the index set of the process is N (the natural numbers), and the range is R (the real numbers), there are some natural questions to ask about the sample sequences of a process {Xi}iN, where a sample sequence is {Xi(ω)}iN.
1. What is the probability that each sample sequence is bounded?
2. What is the probability that each sample sequence is monotonic?
3. What is the probability that each sample sequence has a limit as the index approaches ∞?
4. What is the probability that the series obtained from a sample sequence from converges?
5. What is the probability distribution of the sum?
Main applications of discrete time continuous state stochastic models include Markov chain Monte Carlo (MCMC) and the analysis of Time Series.
### Continuous time and discrete state space
Similarly, if the index space I is a finite or infinite interval, we can ask about the sample paths {Xt(ω)}t I
1. What is the probability that it is bounded/integrable...?
2. What is the probability that it has a limit at ∞
3. What is the probability distribution of the integral?
## References
1. Dodge, Yadolah (2006). The Oxford Dictionary of Statistical Terms. Oxford, England: Oxford University Press. p. 335. ISBN 9780199206131.
2. Lindsey, J. K. (2004). Statistical Analysis of Stochastic Processes in Time. Cambridge, England: Cambridge University Press. p. 3. ISBN 9780521837415.
3. Lawler, G. (2006). Introduction to Stochastic processes (2 ed.). CRC Press. p. 1. A stochastic process is a random process evolving with time. More precisely, a stochastic process is a collection of random variables indexed by time.
4. Einstein, Albert (1926). "Investigations on the Theory of the Brownian Movement" (PDF).
5. Karlin, Samuel & Taylor, Howard M. (1998). An Introduction to Stochastic Modeling, Academic Press. ISBN 0-12-684887-4.
6. Durrett, Rick (2010). Probability: Theory and Examples (Fourth ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-76539-8.
7. Allen, Linda J. S., An Introduction to Stochastic Processes with Applications to Biology, 2nd Edition, Chapman and Hall, 2010, ISBN 1-4398-1882-7
8. Gardiner, C. Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences, 3rd ed., Springer, 2004, ISBN 3540208828
## Further reading
This article is issued from Wikipedia - version of the 11/18/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files. | 2022-05-22T04:16:36 | {"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": 0.8267233967781067, "perplexity": 354.73213633103563}, "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-2022-21/segments/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00440.warc.gz"} |
https://www.abs.gov.au/methodologies/work-related-injuries-methodology/2017-18 | Latest release
# Work-related injuries methodology
Reference period
2017-18 financial year
Released
30/10/2018
Next release Unknown
First release
## Explanatory notes
### Introduction
The statistics presented in this publication were compiled from data collected in the Multipurpose Household Survey (MPHS) conducted throughout Australia in the 2017–18 financial year as a supplement to the monthly Labour Force Survey (LFS). The MPHS was designed to provide statistics annually for a small number of labour, social and economic topics. The topics collected in 2017–18 were:
• Work-Related Injuries
• Participation in Sport and Physical Recreation
• Attendance at Selected Cultural Venues and Events
• Patient Experience
• Crime Victimisation.
For all topics, information on labour force characteristics, education, income and other demographics are also available.
The publication Labour Force, Australia (cat. no. 6202.0) contains information about survey design, scope, coverage and population benchmarks relevant to the monthly LFS, which also applies to the MPHS. It also contains definitions of demographic and labour force characteristics, and information about interviewing relevant to both the monthly LFS and MPHS.
### Concepts sources and methods
The conceptual framework used in Australia's LFS aligns closely with the standards and guidelines set out in Resolutions of the International Conference of Labour Statisticians. Descriptions of the underlying concepts and structure of Australia's labour force statistics, and the sources and methods used in compiling these estimates, are presented in Labour Statistics: Concepts, Sources and Methods (cat. no. 6102.0.55.001).
### Collection methodology
ABS interviewers conducted personal interviews by either telephone or at selected dwellings during the 2017–18 financial year. Each month a sample of dwellings were selected for the MPHS from the responding households in the LFS. In these dwellings, after the LFS had been fully completed for each person in the household, a usual resident aged 15 years and over was selected at random and asked the additional MPHS questions in a personal interview. Information for this survey was collected using Computer Assisted Interviewing (CAI), and responses are recorded directly onto an electronic questionnaire in a notebook computer.
### Scope
The scope of the LFS is restricted to people aged 15 years and over and excludes the following:
• members of the permanent defence forces;
• certain diplomatic personnel of overseas governments, customarily excluded from census and estimated population estimates;
• overseas residents in Australia; and
• members of non-Australian defence forces (and their dependants).
In addition the 2017–18 MPHS excluded the following:
• people living in Aboriginal and Torres Strait Islander communities in very remote parts of Australia; and
• people living in non-private dwellings such as hotels, university residences, students at boarding schools, patients in hospitals, inmates of prisons and residents of other institutions (e.g. retirement homes, homes for people with disabilities).
### Coverage
In the LFS, coverage rules are applied which aim to ensure that each person is associated with only one dwelling and hence has only one chance of selection in the survey. See Labour Force, Australia (cat. no. 6202.0) for more details.
### Sample size
The initial sample for the MPHS 2017–18 consisted of approximately 26,000 private dwellings. Of the private dwellings that remained in the survey after sample loss (e.g. households with LFS non-response, no residents in scope for the LFS, vacant or derelict dwellings and dwellings under construction), approximately 71% were fully responding to the MPHS. The number of completed interviews obtained from these private dwelling households (after taking into account the scope, coverage and subsampling exclusions) was 28,200 for the Work Related Injuries topic.
### Estimation methods
Weighting is the process of adjusting results from a sample survey to infer results for the total in scope population. To do this, a 'weight' is allocated to each sample unit. For the data in this publication the sample unit is a person. The weight is a value which indicates how many population units are represented by the sample unit. The first step in calculating weights for each unit is to assign an initial weight, which is the inverse of the probability of being selected in the survey. The initial weights are then calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks'. Weights are calibrated against population benchmarks to ensure that the survey estimates conform to the independently estimated distribution of the population rather than the distribution within the sample itself.
The statistics presented in this publication have been benchmarked to the Estimated Resident Population for December 2017, independently produced according to the scope of the survey. This ensures that the survey estimates conform to person benchmarks by state, part of state, age and sex. The statistics have been further benchmarked to labour force survey estimates averaged over the 12 month MPHS reference period. This ensures that survey estimates are also consistent with the estimated in-scope population by state, part of state, sex, age and labour force status.
LFS estimates are revised every five years to take into account the outcome of the 5-yearly rebasing of the Estimated Resident Population following the latest Census. LFS supplementary survey and MPHS estimates are not revised in this way. Small differences will therefore exist between the civilian population aged 15 years and over reflected in the Labour Force Survey's revised estimates and corresponding estimates from other household surveys.
### Reliability of the estimates
Estimates in this publication are subject to sampling and non-sampling errors:
• Sampling error is the difference between the published estimate and the value that would have been produced if all dwellings had been included in the survey. For more information see the Technical Note.
• Non-sampling errors are inaccuracies that occur because of imperfections in reporting by respondents and interviewers, and errors made in coding and processing data. These inaccuracies may occur in any enumeration, whether it be a full count or a sample. Every effort is made to reduce the non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and effective processing procedures.
### Classifications used
Country of birth data are classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0).
Occupation data are classified according to the ANZSCO – Australian and New Zealand Standard Classification of Occupations, 2013, Version 1.2 (cat. no. 1220.0).
Industry data are classified according to the Australian and New Zealand Standard Industrial Classification (ANZSIC), 2006 (Revision 2.0) (cat. no. 1292.0).
Educational attainment data are classified according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0).
Work-related injuries data are classified according to Safe Work Australia's Type of Occurrence Classifications System (TOOCS). See Appendix for more information.
### Comparability with monthly LFS statistics
Due to differences in the scope and sample size of the MPHS and that of the LFS, the estimation procedure may lead to some variations between labour force estimates from this survey and those from the LFS.
### Data quality
Proxy interviews were conducted for persons aged 15-17 years, if an adult member of the household did not grant permission to allow the 15-17 year old respondent to personally respond to the interview. If permission was not granted, the adult member of the household would respond to the interview on behalf of the 15-17 year old. For some questions which called for personal opinions, such as self-assessed health, responses from proxy interviews were not collected.
### Previous surveys
The Work-related injuries topic was last conducted in the 2013-14 financial year. Results were published in Work-Related Injuries, Australia (cat. no. 6324.0).
### Changes in this issue
No changes were made to Work-related injuries topic in 2017 - 2018.
For a more detailed list of available data items and their categories – Work-related injuries 2017–18 Data Items List, is available in a spreadsheet, on the Topic page under the Data downloads section.
### Next survey
The ABS is planning to collect the Work-related injuries topic again during the 2021–22 financial year.
### Acknowledgement
ABS publications draw extensively on information provided freely by individuals, businesses, governments and other organisations. Their continued co-operation is very much appreciated: without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act 1905.
### Products and services
An electronic version of the tables released in this publication are available on the ABS website in spreadsheets attached to this publication. The spreadsheets present the tables and the relative standard errors (RSEs) for each publication table.
### Related publications
ABS publications which may also be of interest include:
The following may also be of interest:
Current publications and other products released by the ABS are available from the Statistics Page on the ABS website. The ABS also issues a daily Release Advice on the website which details products to be released in the week ahead.
## Appendix - work-related injury or illness classifications
### Show all
Work-related injuries data are classified according to the Type of Occurrence Classifications System (TOOCS) which was developed by SafeWork Australia for coding workers' compensation claims.
The work-related injury or illness classification used in this survey was based on the TOOCS nature of injury codes. The classification of how work-related injury or illness occurred was based on the TOOCS mechanism of injury codes.
#### Fracture
Breaking of a bone, cartilage, etc.
#### Chronic joint or muscle condition
Arthritis
Disorders of the joints
Disorders of the spinal vertebrae and inervertebral discs
Disorders of muscle, tendons and other soft tissues (e.g. Occupational Overuse Syndrome and Repetitive Strain Injury if this is the only description given)
Acquired musculoskeletal deformities (e.g. flat feet, mallet finger, hammer toe)
#### Sprain/strain
Sprains and strains of joints and adjacent muscles
Acute trauma sprains and strains
Sprains and strains of cartilage
Dislocations
#### Cut/open wound
Open wound not involving traumatic amputation (e.g. broken tooth, cuts, punctures, dog bites, tearing away of fingernail, serious wounds containing glass, metal or other foreign body)
#### Crushing injury/internal organ damage
Internal injury of chest, abdomen and pelvis
Injury with intact skin surface and crushing injury (e.g. bruises, haematomas)
#### Superficial injury - covers minor injuries such as:
Needle stick puncture
Abrasions, grazes, friction burns or blisters
Scratch injury from a foreign body in eye
Splinter or other foreign body in places other than eye
#### Stress or other mental condition
Stress
Anxiety
Depression
Nervous breakdown
Effects of witnessing traumatic events
Effects of involvement in a hold-up
Victim of harassment
Hyperventilation (hysterical, psychogenic)
Hysterical symptoms
Phobias
Obsessional and compulsive symptoms
Short term shock
#### Amputation
Traumatic amputation including loss of eyeball
#### Burns
Electrical burns, chemical burns, cold burns, hot burns, friction burns, combination burn or burns not elsewhere classified
#### Other
Responses that could not be included into one of the categories above such as asthma, cancer, concussion or heart attack
#### Lifting, pushing, pulling, bending
Muscular stress while lifting, carrying or putting down objects
Single or multiple events
Lifting or carrying resulting in stress fractures
Muscular stress while handling objects
Single or multiple events
Pushing or pulling objects
Throwing or pressing objects
Stress fractures from handling objects
Continually shovelling
Climbing ladders causing upper and lower limb injuries
Muscular stress with no objects being handled
Bending down, reaching, turning and twisting movements where no objects are being handled
Stress fractures without objects being handled (e.g. from running)
Continually twisting neck with no object being handled
Occupational overuse and repetitive movement occurrences
#### Prolonged standing, working in cramped or unchanging positions
Working in cramped or unchanging positions
Prolonged standing causing varicose veins
#### Vehicle accident
Any accident or incident on a private road, farm, mine site or footpath involving a vehicle where the most serious injury is sustained as a result of that accident or injury
A vehicle catching on fire after the accident
Any accident or incident in a factory, mine or car park involving a fall from a moving vehicle
#### Hitting, being hit or cut by object or vehicle
Hitting stationary objects or moving objects (e.g. cutting oneself while using a knife or other tool)
Rubbing and chafing from wearing footwear or clothes, using tools or handling objects
Being hit by falling objects
Being bitten by an animal
Being bitten by a snake
Being trapped by moving machinery or equipment or between stationary and moving objects
Exposure to mechanical vibration (e.g. from chain saws)
Being assaulted by a person or persons
#### Fall on same level
All slips, trips, stumbles, steps and jumps, even if a fall does not follow
Falls of short distances such as off a curb or into a gutter
Falls up stairs
Fall with no further description
#### Fall from a height
A fall from ground level to below ground level
Landing awkwardly after a jump from a height
Falling off an animal
A fall down stairs etc.
#### Exposure to mental stress
Exposure to a traumatic event
Exposure to workplace or occupational violence (e.g. victim of assault or threatened assault by a person or persons, being a victim of or witnessing hold-ups etc.)
Being a victim of sexual, racial, or other verbal harassment
Work pressure (e.g. mental stress arising from work responsibilities, conflict with peers, performance counselling)
Attempted suicide
Other mental stress factors
#### Long term exposure to sound
Long term exposure to workshop or factory noise, sharp sudden sounds, or low frequency (subsonic pressure) sounds
#### Contact with a chemical or substance
Single contact with chemical or substance
Immediate allergic reactions to a substance
Splash with acid
Caustic or corrosive substances in the eyes
Contact dermatitis
Swallowing chemical substances
Exposure to smoke from a bush fire, chemical fire etc.
Long term contact with chemicals or substances
Acquired allergic reactions
Slow poisoning, as with lead or other heavy metals
Long term inhalation of dust or fibres, as with asbestos fibres
Exposure to cigarette smoke
Insect and spider bites and stings
Contact with poisonous parts of plant or marine life (e.g. blue ringed octopus, bluebottles, stone fish etc.)
Other and unspecified contact with chemical or substance
#### Other
Those responses that could not be included into one of the categories above such as contact with hot food/drink/beverages, exposure to extreme weather, jumping on objects, struck by lightning or sunburn
## Technical note - data quality
### Show all
#### Reliability of the estimates
The estimates in this publication are based on information obtained from a sample survey. Any data collection may encounter factors, known as non-sampling error, which can impact on the reliability of the resulting statistics. In addition, the reliability of estimates based on sample surveys are also subject to sampling variability. That is, the estimates may differ from those that would have been produced had all persons in the population been included in the survey.
#### Non-sampling error
Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers and errors in coding and processing data. Every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing.
#### Sampling error
Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if the total population (as defined by the scope of the survey) had been included in the survey. One measure of the sampling error is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of persons was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
$$R S E \%=\left(\frac{S E}{estimate}\right) \times 100$$
RSEs for count estimates have been calculated using the Jackknife method of variance estimation. This involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the obtained sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the count estimate.
The Excel spreadsheets in the Data downloads section on the Key findings page contain all the tables produced for this release and the calculated RSEs for each of the estimates.
Only estimates (numbers or percentages) with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. However, estimates with larger RSEs have been included. Estimates with an RSE in the range 25% to 50% should be used with caution while estimates with RSEs greater than 50% are considered too unreliable for general use. All cells in the Excel spreadsheets with RSEs greater than 25% contain a comment indicating the size of the RSE. These cells can be identified by a red indicator in the corner of the cell. The comment appears when the mouse pointer hovers over the cell.
Another measure is the Margin of Error (MOE), which shows the largest possible difference that could be between the estimate due to sampling error and what would have been produced had all persons been included in the survey with a given level of confidence. It is useful for understanding and comparing the accuracy of proportion estimates.
Where provided, MOEs for estimates are calculated at the 95% confidence level. At this level, there are 19 chances in 20 that the estimate will differ from the population value by less than the provided MOE. The 95% MOE is obtained by multiplying the SE by 1.96.
$$M O E=S E \times 1.96$$
#### Calculation of standard error
Standard errors can be calculated using the estimates (counts or percentages) and the corresponding RSEs. See What is a Standard Error and Relative Standard Error, Reliability of estimates for Labour Force data for more details.
#### Proportions and percentages
Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y:
$$R S E\left(\frac{x}{y}\right) \approx \sqrt{[R S E(x)]^{2}-[R S E(y)]^{2}}$$
#### Differences
The difference between two survey estimates (counts or percentages) can also be calculated from published estimates. Such an estimate is also subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
$$S E(x-y) \approx \sqrt{[S E(x)]^{2}+[S E(y)]^{2}}$$
While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.
#### Significance testing
A statistical significance test for a comparison between estimates can be performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The SE of the difference between two corresponding estimates (x and y) can be calculated using the formula shown above in the Differences section. This SE is then used to calculate the following test statistic:
$$\left(\frac{x-y}{S E(x-y)}\right)$$
If the value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations with respect to that characteristic.
## Glossary
### Show all
#### Applied for workers' compensation
To have formally applied for workers' compensation by completing an application for compensation.
#### Contributing family workers
People who work without pay, in an economic enterprise operated by a relative.
#### Current job
A job that a person was working in during the reference week which had lasted or was likely to last for a period of two weeks or more.
#### Current main job
The job that a person was working in during the reference week in which most hours were usually worked.
#### Current other job
Refers to a current job other than the current main job.
#### Days or shifts absent from work
Includes all work hours spent on medical consultation, hospitalisation and rest due to the injury or illness. The days or shifts absent do not have to be consecutive.
#### Duration of current main job
Length of time worked in current main job.
#### Duration of employment in job where most recent work-related injury or illness occurred
Length of time worked in job where most recent work-related injury or illness occurred.
#### Level of highest educational attainment
Level of highest educational attainment identifies the highest achievement a person has attained in any area of study. It is not a measurement of the relative importance of different fields of study but a ranking of qualifications and other educational attainments regardless of the particular area of study or the type of institution in which the study was undertaken. It is categorised according to the Australian Standard Classification of Education, 2001 (cat. no. 1272.0) Level of education classification.
#### Employed
People aged 15 years and over who, during the reference week:
• worked for one hour or more for pay, profit, commission or payment in kind, in a job or business or on a farm (comprising employees, employers and own account workers); or
• worked for one hour or more without pay in a family business or on a farm (i.e. contributing family workers); or
• were employees who had a job but were not at work and were:
• away from work for less than four weeks up to the end of the reference week; or
• away from work for more than four weeks up to the end of the reference week and received pay for some or all of the four week period to the end of the reference week; or
• away from work as a standard work or shift arrangement; or
• on strike or locked out; or
• on workers' compensation and expected to return to their job; or
• were employers or own account workers who had a job, business or farm, but were not at work.
#### Employees
People who work for a public or private employer and receive remuneration in wages, salary, on a commission basis (with or without a retainer), tips, piece rates, or payment in kind. From August 2014, the Work Related Injuries (WRI) Survey definition of employees differs from the definition used in surveys prior to July 2014 including, the Labour Force Survey, other household surveys.
#### Employees with paid leave entitlements
Employees who were entitled to either paid sick leave or paid holiday leave (or both).
#### Employees without paid leave entitlements
Employees who were not entitled to, or did not know whether they were entitled to, paid sick and paid holiday leave.
#### Employers
People who operate their own unincorporated economic enterprise or engage independently in a profession or trade, and hire one or more employees.
#### Financial assistance
Monetary assistance received from any party to cover medical expenses or income loss, incurred due to their work-related injury or illness.
#### Fixed term contract
See 'Worked on a fixed-term contract'.
#### Full-time workers
Employed persons who usually worked 35 hours or more a week (in all jobs) and others who, although usually working less than 35 hours a week, worked 35 hours or more during the reference week.
#### Incorporated enterprise
An enterprise which is registered as a separate legal entity to its members or owners (also known as a limited liability company).
#### Industry
In this publication, industry relates to a group of businesses or organisations that perform similar sets of activities in terms of the production of goods or services. Industry is classified according to Australian and New Zealand Standard Industrial Classification (ANZSIC), 2006 (Revision 2.0) (cat. no. 1292.0).
#### Injury or illness sustained
See 'Work-related injury or illness'.
#### Last 12 months
The 12 months up to and including the survey reference week.
#### Main job
The job in which most hours are usually worked.
#### Multiple jobholder
People who worked in more than one job or business during the survey reference week, excluding those who only worked in more than one job because they had changed jobs during the reference week.
#### Non-school qualification
Non-school qualifications are awarded for educational attainments other than those of pre-primary, primary or secondary education. They include qualifications at the Postgraduate Degree Level, Master Degree Level, Graduate Diploma and Graduate Certificate Level, Bachelor Degree Level, Advanced Diploma and Diploma level, and Certificates I, II, III and IV levels. Non-school qualifications may be attained concurrently with school qualifications.
#### Not employed
People who are either unemployed or not in the labour force.
#### Not in the labour force
People who are not in the categories 'employed' or 'unemployed' as defined.
#### Occupation
In this publication, occupation relates to a collection of jobs that are sufficiently similar in their main tasks to be grouped together for the purposes of classification. Occupation is classified according to ANZSCO - Australian and New Zealand Standard Classification of Occupations, 2013, Version 1.2 (cat. no. 1220.0).
#### Owner managers of incorporated enterprises (OMIEs)
Persons who work in their own incorporated enterprise, that is, a business entity which is registered as a separate legal entity to its members or owners (may also be known as a limited liability company).
An owner manager of an incorporated enterprise may or may not hire one or more employees in addition to themselves and/or other owners of that business. See Status in employment for more information.
#### Owner managers of unincorporated enterprises (OMUEs)
A person who operates his or her own unincorporated enterprise or engages independently in a profession or trade.
An owner manager of an unincorporated enterprise may or may not hire one or more employees in addition to themselves and/or other owners of that business. See Status in employment for more information.
#### Paid leave entitlements
The entitlement of employees (excluding owner managers or incorporated enterprises) to either paid holiday leave or paid sick leave (or both) in their job. People employed in their own business or who were contributing family workers were not asked about their leave entitlements.
#### Previous job
The last job in which employment ceased during the last 12 months.
#### Reference week
The week preceding the week in which the interview was conducted.
#### Shift arrangements
A system of working whereby the daily hours of operation at the place of employment are split into at least two set work periods (shifts), for different groups of workers.
#### Shift work
Worked under shift arrangements.
#### Status of employment
Status of employment is determined by an employed person's position in relation to their job, and is usually in respect to a person's main job if they hold more than one job.
Employed persons are classified according to the reported relationship between the person and the enterprise for which they work, together with the legal status of the enterprise where this can be established. The groups include:
• Employees
• Owner manager of incorporated enterprise (OMIEs) with employees;
• Owner manager of incorporated enterprise (OMIEs) without employees;
• Owner manager of unincorporated enterprise (OMUEs) with employees;
• Owner manager of unincorporated enterprise (OMUEs) without employees; and
• Contributing family workers.
#### Unemployed
Persons who were not employed during the reference week, and:
• had actively looked for full-time or part-time work at any time in the four weeks up to the end of the reference week and;
• were available for work in the reference week; or
• were waiting to start a new job within four weeks from the end of the reference week and could have started in the reference week if the job had been available then.
#### Usual hours worked
The hours usually worked per week by an employed person.
#### Unincorporated enterprise
A business entity in which the owner and the business are legally inseparable, so that the owner is liable for any business debts that are incurred.
#### Worked at some time in the last 12 months
People who worked in a job which lasted for two weeks or more, in the last 12 months, regardless of whether they worked full-time or part-time.
#### Worked full-time
People who usually worked 35 hours or more per week in the job in which the work-related injury or illness occurred.
#### Worked part-time
People who usually worked less than 35 hours or more per week in the job in which the work-related injury or illness occurred.
#### Workers' compensation
Workers' compensation includes:
• payments by an insurer or other liable party for costs related to a work-related injury or illness:
• medical payments, incapacity payments (income maintenance and salary top-up), rehabilitation payments, travel payments and legal payments; and
• any 'settlement' or 'judgement of claim'.
#### Work-related injury or illness
Any injury or illness or disease which first occurred in the last 12 months, where a person suffers either physically or mentally from a condition that has arisen out of, or in the course of, employment.
The injury or illness was considered to be in scope if the respondent first became aware of it in the last 12 months, even though the cause of the injury or illness may have occurred outside the 12 month reference period. Included are injuries or illnesses that occurred while commuting to and from work, outside the place of work but while on work duty, or during work breaks.
Information was collected about the respondent's most recent work-related injury or illness if there was more than one work-related injury or illness in the reference period.
#### Works on a contract basis
Owner managers who were engaged by an organisation to provide a particular service or undertake a particular task at an agreed price or rate, and generally for a specified period.
#### Worked on a fixed-term contract
Employees (excluding owner managers of incorporated enterprises) with a contract of employment which specifies that the employment will be terminated on a particular date or on completion of a specific task.
## Quality declaration
### Institutional environment
For information on the institutional environment of the Australian Bureau of Statistics (ABS), including the legislative obligations of the ABS, financing and governance arrangements, and mechanisms for scrutiny of ABS operations, please see ABS Institutional Environment.
### Relevance
Relevance relates to the degree to which statistical information meets the needs of users. It involves client liaison, program review, priority setting and assuring that the statistics produced together with the underlying concepts conform with international statistical standards. The ABS regularly reviews its statistical programs to ensure that they remain relevant to user needs. For the work-related injuries topic, this happens primarily through the Labour Statistics Advisory Group and in consultation with key clients.
The concepts, definitions and classifications used in the work-related injuries topic help to ensure its relevance to clients. Work-related injuries data are classified according to the Type of Occurrence Classification System which is maintained by Safe Work Australia for coding workers' compensation claims. This includes a classification for the injury or illness itself, and a classification for how the injury or illness occurred. Other classifications, concepts and definitions used in this publication are consistent with those used in Labour Force, Australia (cat. no. 6202.0).
Data on work-related injuries were collected as part of the 2017-18 Multipurpose Household Survey (MPHS). The MPHS is a supplement to the monthly Labour Force Survey (LFS) and is designed to collect annual statistics on a small number of self-contained topics. The scope of the LFS is restricted to people aged 15 years and over and excludes members of the permanent defence forces; certain diplomatic personnel of overseas governments usually excluded from census and estimated resident populations; overseas residents in Australia; and members of non-Australian defence forces (and their dependants). The 2017-18 MPHS excluded people living in remote Aboriginal and Torres Strait Islander communities and people living in non-private dwellings such as hotels, university residences, students at boarding schools, patients in hospitals, inmates of prisons and residents of other institutions (e.g. retirement homes, homes for persons with disabilities).
### Timeliness
The timeliness of statistical information refers to the delay between the reference period to which the information pertains and the date on which the information is made available. Work-Related Injuries, Australia (cat. no. 6324.0) is published approximately 5 months after the end of the enumeration period.
### Accuracy
For sample surveys, accuracy describes how close a statistical estimate is likely to be to its true value. The accuracy of statistical estimates in sample surveys can be impacted by two types of error: non-sampling error and sampling error.
Non-sampling error arises from inaccuracies in collecting, recording and processing the data. Non-sampling error may also arise because information cannot be obtained from all persons selected in the survey. Every effort has been made to minimise non-sampling error for work-related injuries by designing effective questionnaires, providing appropriate training for interviewers, and undertaking good data processing procedures.
Sampling error occurs because a sample of the population of interest is surveyed, rather than the entire population. One measure of the likely difference resulting from not including all dwellings in the survey is given by the standard error (SE). There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included in the survey, and about 19 chances in 20 that the difference will be less than two SEs. Measures of the relative standard errors (RSE) of the estimates for this survey are included with this release.
Only estimates (numbers and proportions) with RSEs less than 25% are considered sufficiently reliable for most purposes. Estimates with RSEs between 25% to 50% are annotated to indicate they are subject to high sample variability and should be used with caution. In addition, estimates with RSEs greater than 50% are annotated to indicate they are considered too unreliable for general use.
### Coherence
Coherence of statistical data includes coherence between different data items pertaining to the same point in time, coherence between the same data item for different points in time, and coherence between various jurisdictions.
Data on occupational injuries and illnesses are also compiled by SafeWork Australia using information supplied by Commonwealth, state and territory work cover authorities. Like the ABS work-related injuries data, this information is also disseminated using the Type of Occurrence Classification System. However, the population covered by the ABS estimates differs from SafeWork Australia's as it includes injuries sustained by all categories of employed workers; injuries that have been claimed under workers' compensation; and injuries that have not been claimed under workers' compensation.
Information in Work-Related Injuries, Australia (cat. no. 6324.0) uses the same standards, definitions and classifications that are used in Labour Force, Australia (cat. no. 6202.0), however estimates are not directly comparable due to differences in the scope and sample of the MPHS and the LFS.
International recommendations on the concepts associated with work-related hazards and risks are made by the International Conferences of Labour Statisticians (ICLS). While the terminology used in the ABS work-related injuries topic differs from that used in the international standards, the underlying definitions are broadly consistent. More information, refer to Occupational Injuries and Diseases, Labour Statistics: Concepts, Sources and Methods (cat. no. 6102.0.55.001).
### Interpretability
To aid in the interpretation of the data, detailed explanatory notes, technical notes and definitions are provided with the publication.
### Accessiblity
For the 2017–18 release, tables and associated RSEs are available in spreadsheet form on the ABS website.
For further information about ABS data available on request, contact the National Information and Referral Centre on 1300 135 070 or via email to [email protected]. | 2021-05-11T05:32:00 | {"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": 0.226315438747406, "perplexity": 4155.298129491731}, "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-2021-21/segments/1620243991641.5/warc/CC-MAIN-20210511025739-20210511055739-00228.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Akochubei.anatoly-n | # zbMATH — the first resource for mathematics
## Kochubeĭ, Anatoliĭ Naumovych
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Author ID: kochubei.anatoly-n Published as: Kochubei, A. N.; Kochubei, Anatolii N.; Kochubei, Anatoly; Kochubei, Anatoly N.; Kochubej, A. N.; Kochubej, Anatolij N.; Kochubeĭ, A. N. Homepage: https://www.imath.kiev.ua/people/profile.php?pid=32 External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 147 Publications since 1971, including 7 Books Reviewing Activity: 2,025 Reviews Biographic References: 1 Publication
all top 5
#### Co-Authors
116 single-authored 7 Gorbachuk, Myroslav L’vovych 6 Kondrat’yev, Yuriĭ Grygorovych 5 Berezans’kyĭ, Yuriĭ Makarovych 4 Eĭdel’man, Samuïl Davydovych 4 Gorbachuk, Valentyna Ivanivna 3 Adamyan, Vadym Movsesovych 3 Antonyuk, Oleksandra Viktorivna 3 Khrennikov, Andreĭ Yur’evich 3 Sait-Ametov, Mustafa R. 2 da Silva, José Luís 2 Gohberg, Israel 2 Khruslov, Eugene Yakovlevich 2 Langer, Heinz 2 Luchko, Yuri 2 Popov, Gennadiĭ Yakovlevich 1 Anashin, Vladimir Sergeevich 1 Boĭchuk, Oleksandr Andriĭovych 1 Dragovich, Branko 1 Gerasimenko, Viktor Ivanovich 1 Gubreev, Gennadiĭ Mykhaĭlovych 1 Hutlyans’kyi, V. Ya. 1 Ivasyshen, Stepan Dmytrovych 1 Kaneko, Hiroshi 1 Korolyuk, Volodymyr Semenovych 1 Kozyrev, Sergeĭ Vladimirovich 1 Kushnir, Roman M. 1 Lukovsky, Ivan Oleksandrovych 1 Makarov, Volodymyr Leonidovich 1 Malamud, Mark M. 1 Marchenko, V. O. 1 Mykhajlets’, V. A. 1 Nikitin, A. H. 1 Nizhnik, Leonid Pavlovich 1 Parasyuk, Igor O. 1 Pastur, Leonid Andreevich 1 Perestyuk, Mykola Oleksiĭovych 1 Piskarëv, S. I. 1 Portenko, Mykola Ivanovych 1 Rofe-Beketov, Fedor Semenovich 1 Ronto, M. I. 1 Rybak, M. A. 1 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Samoĭlenko, Yuriĭ Stefanovych 1 Sharkovskiĭ, Oleksandr Mykolaiovych 1 Shklyar, Alexander Ya. 1 Soskin, Daniel S. 1 Tkachenko, Victor Ivanovich 1 Trofimchuk, Sergei I. 1 Volovich, Igor’ Vasil’evich
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#### Serials
12 Ukrainian Mathematical Journal 9 Ukraïns’kyĭ Matematychnyĭ Zhurnal 8 Differential Equations 7 Methods of Functional Analysis and Topology 5 Differentsial’nye Uravneniya 4 Siberian Mathematical Journal 4 Soviet Mathematics. Doklady 3 Mathematical Notes 3 Mathematics of the USSR. Izvestiya 3 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 3 Potential Analysis 3 Doklady Mathematics 3 Fractional Calculus & Applied Analysis 3 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 3 Operator Theory: Advances and Applications 2 Applicable Analysis 2 Journal of Mathematical Analysis and Applications 2 Journal of Mathematical Physics 2 Theoretical and Mathematical Physics 2 Functional Analysis and its Applications 2 Journal of Number Theory 2 Pacific Journal of Mathematics 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 2 Russian Academy of Sciences. Izvestiya. Mathematics 2 Algebras and Representation Theory 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 2 Handbook of Fractional Calculus with Applications 1 Letters in Mathematical Physics 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Theory of Probability and its Applications 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Integral Equations and Operator Theory 1 Journal of Algebra 1 Journal of Differential Equations 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Tohoku Mathematical Journal. Second Series 1 Advances in Applied Mathematics 1 Soviet Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Journal of Theoretical Probability 1 Izvestiya Akademii Nauk Armyanskoi SSR. Matematika 1 Journal of Physics A: Mathematical and General 1 Expositiones Mathematicae 1 Teoriya Funktsiĭ, Funktsional’nyĭ Analiz i ikh Prilozheniya 1 Funktsional’nyĭ Analiz 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Finite Fields and their Applications 1 Izvestiya: Mathematics 1 The Journal of Fourier Analysis and Applications 1 European Mathematical Society Newsletter 1 Analysis (München) 1 Stochastics and Dynamics 1 International Journal of Number Theory 1 Cambridge Tracts in Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Pure and Applied Mathematics, Marcel Dekker 1 Translations. Series 2. American Mathematical Society 1 Journal of Physics A: Mathematical and Theoretical 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Kinetic and Related Models 1 Journal of Pseudo-Differential Operators and Applications
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#### Fields
59 Operator theory (47-XX) 51 Partial differential equations (35-XX) 43 Ordinary differential equations (34-XX) 33 Number theory (11-XX) 24 Functional analysis (46-XX) 21 Probability theory and stochastic processes (60-XX) 17 Real functions (26-XX) 10 Quantum theory (81-XX) 9 Field theory and polynomials (12-XX) 7 Functions of a complex variable (30-XX) 6 General and overarching topics; collections (00-XX) 6 Associative rings and algebras (16-XX) 6 Special functions (33-XX) 5 Abstract harmonic analysis (43-XX) 4 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Measure and integration (28-XX) 3 Fluid mechanics (76-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX)
#### Citations contained in zbMATH
75 Publications have been cited 1,011 times in 707 Documents Cited by Year
Cauchy problem for fractional diffusion equations. Zbl 1068.35037
Eidelman, Samuil D.; Kochubei, Anatoly N.
2004
Distributed order calculus and equations of ultraslow diffusion. Zbl 1149.26014
Kochubei, Anatoly N.
2008
Pseudo-differential equations and stochastics over non-Archimedean fields. Zbl 0984.11063
Kochubei, Anatoly N.
2001
Fractional-order diffusion. Zbl 0729.35064
Kochubei, A. N.
1990
Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Zbl 1062.35003
Eidelman, Samuil D.; Ivasyshen, Stepan D.; Kochubei, Anatoly N.
2004
General fractional calculus, evolution equations, and renewal processes. Zbl 1250.26006
Kochubei, Anatoly N.
2011
A Cauchy problem for evolution equations of fractional order. Zbl 0696.34047
Kochubej, A. N.
1989
Cauchy problem for evolution equations of a fractional order. Zbl 1129.35427
Kochubei, A. N.; Èidelman, S. D.
2004
Extensions of symmetric operators and symmetric binary relations. Zbl 0322.47006
Kochubej, A. N.
1975
Fractional-parabolic systems. Zbl 1259.35218
Kochubei, Anatoly N.
2012
A non-Archimedean wave equation. Zbl 1190.35235
Kochubei, Anatoly N.
2008
Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes. Zbl 0682.35113
Kochubej, A. N.
1989
Cauchy problem for fractional diffusion-wave equations with variable coefficients. Zbl 1297.35274
Kochubei, Anatoly N.
2014
Extension theory for symmetric operators and boundary value problems for differential equations. Zbl 0706.47001
Gorbachuk, V. I.; Gorbachuk, M. L.; Kochubej, A. N.
1989
Asymptotic properties of solutions of the fractional diffusion-wave equation. Zbl 1323.35197
Kochubei, Anatoly N.
2014
Distributed order derivatives and relaxation patterns. Zbl 1191.34005
Kochubei, Anatoly N.
2009
Fundamental solutions of pseudodifferential equations connected with $$p$$-adic quadratic forms. Zbl 0934.35218
Kochubei, A. N.
1998
Stochastic integrals and stochastic differential equations over the field of $$p$$-adic numbers. Zbl 0874.60047
Kochubei, Anatoly N.
1997
$$p$$-adic analogue of the porous medium equation. Zbl 1401.35165
Khrennikov, Andrei Yu.; Kochubei, Anatoly N.
2018
Interaction measures on the space of distributions over the field of $$p$$-adic numbers. Zbl 1053.81067
Kochubei, Anatoly N.; Sait-Ametov, Mustafa R.
2003
One-dimensional point interactions. Zbl 0703.34086
Kochubej, A. N.
1989
Elliptic operators with boundary conditions on a subset of measure zero. Zbl 0506.35029
Kochubej, A. N.
1982
Weak solutions of stochastic differential equations over the field of $$p$$-adic numbers. Zbl 1136.60039
Kaneko, Hiroshi; Kochubei, Anatoly N.
2007
Limit theorems for sums of $$p$$-adic random variables. Zbl 0954.60001
Kochubei, Anatoly N.
1998
A Schrödinger-type equation over the field of $$p$$-adic numbers. Zbl 0780.35088
Kochubei, Anatolii N.
1993
Hausdorff measure for a stable-like process over an infinite extension of a local field. Zbl 1018.60038
Kochubei, Anatoly N.
2002
Harmonic oscillator in characteristic $$p$$. Zbl 1036.11520
Kochubei, Anatoly N.
1998
$$p$$-adic commutation relations. Zbl 0905.46051
Kochubei, Anatoly N.
1996
Distributed-order calculus: An operator-theoretic interpretation. Zbl 1164.26009
Kochubei, A. N.
2008
Differential equations for $${\mathbb F}_q$$-linear functions. Zbl 1010.11066
Kochubei, Anatoly N.
2000
Diffusion of fractional order. Zbl 0712.35049
Kochubej, A. N.
1990
Fractional-hyperbolic systems. Zbl 1312.35183
Kochubei, Anatoly
2013
Analysis in positive characteristic. Zbl 1171.12005
Kochubei, Anatoly N.
2009
On $$p$$-adic Green’s functions. Zbl 0843.35147
Kochubei, A. N.
1993
Parabolic equations on a p-adic number field. Zbl 0765.35002
Kochubej, A. N.
1991
Schrödinger-type operator over $$p$$-adic number field. Zbl 0809.47060
Kochubej, A. N.
1991
On characteristic functions of symmetric operators and their extensions. Zbl 0444.47023
Kochubej, A. N.
1980
Analysis and probability over infinite extensions of a local field. Zbl 1023.60501
Kochubei, Anatoly N.
1999
$$\mathbb{F}_q$$-linear calculus over function fields. Zbl 1029.11019
Kochubei, Anatoly N.
1999
Additive and multiplicative fractional differentiations over the field of $$p$$-adic numbers. Zbl 0882.26015
Kochubei, Anatoly N.
1997
One-dimensional point interactions. Zbl 0693.34018
Kochubej, A. N.
1989
Fractional kinetic hierarchies and intermittency. Zbl 1359.82014
Kochubei, Anatoly N.; Kondratiev, Yuri
2017
Radial solutions of non-Archimedean pseudodifferential equations. Zbl 1396.35070
Kochubei, Anatoly N.
2014
On some classes of non-Archimedean operator algebras. Zbl 1335.47047
Kochubei, Anatoly N.
2013
Differential equations for $$\mathbb F_q$$-linear functions. II: Regular singularity. Zbl 1081.11075
Kochubei, Anatoly N.
2003
Symmetric operators and nonclassical spectral problems. Zbl 0454.47023
Kochubej, A. N.
1979
Multidimensional nonlinear pseudo-differential evolution equation with $$p$$-adic spatial variables. Zbl 07193644
Antoniouk, Alexandra V.; Khrennikov, Andrei Yu.; Kochubei, Anatoly N.
2020
Linear and nonlinear heat equations on a $$p$$-adic ball. Zbl 1439.35537
Kochubei, A. N.
2018
On the compactness and the uniform continuity of a resolvent family for a fractional differential equation. Zbl 1313.34001
Antonyuk, O. V.; Kochubei, A. N.; Piskarev, S. I.
2014
Fractional differential equations: $$\alpha$$-entire solutions, regular and irregular singularities. Zbl 1178.26007
Kochubei, Anatoly N.
2009
Umbral calculus in positive characteristic. Zbl 1062.05020
Kochubei, Anatoly N.
2005
Equations of one-dimensional fractal diffusion. Zbl 1037.35117
Kochubeĭ, A. N.; Èĭdel’man, S. D.
2003
Heat equation in a $$p$$-adic ball. Zbl 0926.60091
Kochubej, Anatolij N.
1996
Parabolic equations over the field of $$p$$-adic numbers. Zbl 0778.35001
Kochubej, A. N.
1991
On extensions of a positive-definite symmetric operator. Zbl 0555.47029
Kochubej, A. N.
1984
On best approximation in normed modules. Zbl 0262.41035
Kochubej, A. N.
1973
Dissipative extensions of differential operators in a space of vector- functions. Zbl 0261.47026
Gorbachuk, M. L.; Kochubej, A. N.; Rybak, M. A.
1972
Basic theory. Zbl 1410.26003
Kochubei, Anatoly (ed.); Luchko, Yuri (ed.)
2019
Fractional approximation of solutions of evolution equations. Zbl 1338.34109
Kochubei, Anatoly N.; Kondratiev, Yuri G.
2016
Non-Archimedean group algebras with Baer reductions. Zbl 1320.47074
Kochubei, Anatoly N.
2014
Non-Archimedean normal operators. Zbl 1309.47089
Kochubei, Anatoly N.
2010
$$p$$-adic spherical coordinates and their applications. Zbl 1187.60039
Kochubei, A. N.
2009
On a $$p$$-adic wave equation. Zbl 1191.47090
Kochubei, Anatoly N.
2009
Dwork-Carlitz exponential and overconvergence for additive functions in positive characteristic. Zbl 1160.11033
Kochubei, Anatoly N.
2008
Evolution equations and functions of hypergeometric type over fields of positive characteristics. Zbl 1197.12004
Kochubei, Anatoly N.
2007
Hypergeometric functions and Carlitz differential equations over function fields. Zbl 1211.12008
Kochubei, Anatoly N.
2007
Construction of interaction measures on the space of distributions over the field of $$p$$-adic numbers. Zbl 1098.81060
Kochubei, A. N.; Sait-Ametov, M. R.
2004
The differentiation operator on subsets of the field of $$p$$-adic numbers. Zbl 0784.47057
Kochubej, A. N.
1992
Self-adjoint extensions of a Schrödinger operator with singular potential. Zbl 0737.34061
Kochubej, A. N.
1991
Self-adjoint extensions of Schrödinger operators with singular potentials. Zbl 0725.47006
Kochubei, A. N.
1990
Stabilization of solutions of dissipative hyperbolic equations with almost-periodic coefficients. Zbl 0697.35082
Kochubej, A. N.
1987
Stabilization of solutions of dissipative hyperbolic equations. Zbl 0625.35051
Kochubej, A. N.
1986
On extensions of a positive definite symmetric operator. Zbl 0454.47022
Kochubej, A. N.
1979
The extensions of a nondensely defined symmetric operator. Zbl 0409.47014
Kochubej, A. N.
1977
On extensions of a nondensely defined symmetric operator. Zbl 0362.47008
Kochubej, A. N.
1977
Multidimensional nonlinear pseudo-differential evolution equation with $$p$$-adic spatial variables. Zbl 07193644
Antoniouk, Alexandra V.; Khrennikov, Andrei Yu.; Kochubei, Anatoly N.
2020
Basic theory. Zbl 1410.26003
Kochubei, Anatoly (ed.); Luchko, Yuri (ed.)
2019
$$p$$-adic analogue of the porous medium equation. Zbl 1401.35165
Khrennikov, Andrei Yu.; Kochubei, Anatoly N.
2018
Linear and nonlinear heat equations on a $$p$$-adic ball. Zbl 1439.35537
Kochubei, A. N.
2018
Fractional kinetic hierarchies and intermittency. Zbl 1359.82014
Kochubei, Anatoly N.; Kondratiev, Yuri
2017
Fractional approximation of solutions of evolution equations. Zbl 1338.34109
Kochubei, Anatoly N.; Kondratiev, Yuri G.
2016
Cauchy problem for fractional diffusion-wave equations with variable coefficients. Zbl 1297.35274
Kochubei, Anatoly N.
2014
Asymptotic properties of solutions of the fractional diffusion-wave equation. Zbl 1323.35197
Kochubei, Anatoly N.
2014
Radial solutions of non-Archimedean pseudodifferential equations. Zbl 1396.35070
Kochubei, Anatoly N.
2014
On the compactness and the uniform continuity of a resolvent family for a fractional differential equation. Zbl 1313.34001
Antonyuk, O. V.; Kochubei, A. N.; Piskarev, S. I.
2014
Non-Archimedean group algebras with Baer reductions. Zbl 1320.47074
Kochubei, Anatoly N.
2014
Fractional-hyperbolic systems. Zbl 1312.35183
Kochubei, Anatoly
2013
On some classes of non-Archimedean operator algebras. Zbl 1335.47047
Kochubei, Anatoly N.
2013
Fractional-parabolic systems. Zbl 1259.35218
Kochubei, Anatoly N.
2012
General fractional calculus, evolution equations, and renewal processes. Zbl 1250.26006
Kochubei, Anatoly N.
2011
Non-Archimedean normal operators. Zbl 1309.47089
Kochubei, Anatoly N.
2010
Distributed order derivatives and relaxation patterns. Zbl 1191.34005
Kochubei, Anatoly N.
2009
Analysis in positive characteristic. Zbl 1171.12005
Kochubei, Anatoly N.
2009
Fractional differential equations: $$\alpha$$-entire solutions, regular and irregular singularities. Zbl 1178.26007
Kochubei, Anatoly N.
2009
$$p$$-adic spherical coordinates and their applications. Zbl 1187.60039
Kochubei, A. N.
2009
On a $$p$$-adic wave equation. Zbl 1191.47090
Kochubei, Anatoly N.
2009
Distributed order calculus and equations of ultraslow diffusion. Zbl 1149.26014
Kochubei, Anatoly N.
2008
A non-Archimedean wave equation. Zbl 1190.35235
Kochubei, Anatoly N.
2008
Distributed-order calculus: An operator-theoretic interpretation. Zbl 1164.26009
Kochubei, A. N.
2008
Dwork-Carlitz exponential and overconvergence for additive functions in positive characteristic. Zbl 1160.11033
Kochubei, Anatoly N.
2008
Weak solutions of stochastic differential equations over the field of $$p$$-adic numbers. Zbl 1136.60039
Kaneko, Hiroshi; Kochubei, Anatoly N.
2007
Evolution equations and functions of hypergeometric type over fields of positive characteristics. Zbl 1197.12004
Kochubei, Anatoly N.
2007
Hypergeometric functions and Carlitz differential equations over function fields. Zbl 1211.12008
Kochubei, Anatoly N.
2007
Umbral calculus in positive characteristic. Zbl 1062.05020
Kochubei, Anatoly N.
2005
Cauchy problem for fractional diffusion equations. Zbl 1068.35037
Eidelman, Samuil D.; Kochubei, Anatoly N.
2004
Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Zbl 1062.35003
Eidelman, Samuil D.; Ivasyshen, Stepan D.; Kochubei, Anatoly N.
2004
Cauchy problem for evolution equations of a fractional order. Zbl 1129.35427
Kochubei, A. N.; Èidelman, S. D.
2004
Construction of interaction measures on the space of distributions over the field of $$p$$-adic numbers. Zbl 1098.81060
Kochubei, A. N.; Sait-Ametov, M. R.
2004
Interaction measures on the space of distributions over the field of $$p$$-adic numbers. Zbl 1053.81067
Kochubei, Anatoly N.; Sait-Ametov, Mustafa R.
2003
Differential equations for $$\mathbb F_q$$-linear functions. II: Regular singularity. Zbl 1081.11075
Kochubei, Anatoly N.
2003
Equations of one-dimensional fractal diffusion. Zbl 1037.35117
Kochubeĭ, A. N.; Èĭdel’man, S. D.
2003
Hausdorff measure for a stable-like process over an infinite extension of a local field. Zbl 1018.60038
Kochubei, Anatoly N.
2002
Pseudo-differential equations and stochastics over non-Archimedean fields. Zbl 0984.11063
Kochubei, Anatoly N.
2001
Differential equations for $${\mathbb F}_q$$-linear functions. Zbl 1010.11066
Kochubei, Anatoly N.
2000
Analysis and probability over infinite extensions of a local field. Zbl 1023.60501
Kochubei, Anatoly N.
1999
$$\mathbb{F}_q$$-linear calculus over function fields. Zbl 1029.11019
Kochubei, Anatoly N.
1999
Fundamental solutions of pseudodifferential equations connected with $$p$$-adic quadratic forms. Zbl 0934.35218
Kochubei, A. N.
1998
Limit theorems for sums of $$p$$-adic random variables. Zbl 0954.60001
Kochubei, Anatoly N.
1998
Harmonic oscillator in characteristic $$p$$. Zbl 1036.11520
Kochubei, Anatoly N.
1998
Stochastic integrals and stochastic differential equations over the field of $$p$$-adic numbers. Zbl 0874.60047
Kochubei, Anatoly N.
1997
Additive and multiplicative fractional differentiations over the field of $$p$$-adic numbers. Zbl 0882.26015
Kochubei, Anatoly N.
1997
$$p$$-adic commutation relations. Zbl 0905.46051
Kochubei, Anatoly N.
1996
Heat equation in a $$p$$-adic ball. Zbl 0926.60091
Kochubej, Anatolij N.
1996
A Schrödinger-type equation over the field of $$p$$-adic numbers. Zbl 0780.35088
Kochubei, Anatolii N.
1993
On $$p$$-adic Green’s functions. Zbl 0843.35147
Kochubei, A. N.
1993
The differentiation operator on subsets of the field of $$p$$-adic numbers. Zbl 0784.47057
Kochubej, A. N.
1992
Parabolic equations on a p-adic number field. Zbl 0765.35002
Kochubej, A. N.
1991
Schrödinger-type operator over $$p$$-adic number field. Zbl 0809.47060
Kochubej, A. N.
1991
Parabolic equations over the field of $$p$$-adic numbers. Zbl 0778.35001
Kochubej, A. N.
1991
Self-adjoint extensions of a Schrödinger operator with singular potential. Zbl 0737.34061
Kochubej, A. N.
1991
Fractional-order diffusion. Zbl 0729.35064
Kochubei, A. N.
1990
Diffusion of fractional order. Zbl 0712.35049
Kochubej, A. N.
1990
Self-adjoint extensions of Schrödinger operators with singular potentials. Zbl 0725.47006
Kochubei, A. N.
1990
A Cauchy problem for evolution equations of fractional order. Zbl 0696.34047
Kochubej, A. N.
1989
Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes. Zbl 0682.35113
Kochubej, A. N.
1989
Extension theory for symmetric operators and boundary value problems for differential equations. Zbl 0706.47001
Gorbachuk, V. I.; Gorbachuk, M. L.; Kochubej, A. N.
1989
One-dimensional point interactions. Zbl 0703.34086
Kochubej, A. N.
1989
One-dimensional point interactions. Zbl 0693.34018
Kochubej, A. N.
1989
Stabilization of solutions of dissipative hyperbolic equations with almost-periodic coefficients. Zbl 0697.35082
Kochubej, A. N.
1987
Stabilization of solutions of dissipative hyperbolic equations. Zbl 0625.35051
Kochubej, A. N.
1986
On extensions of a positive-definite symmetric operator. Zbl 0555.47029
Kochubej, A. N.
1984
Elliptic operators with boundary conditions on a subset of measure zero. Zbl 0506.35029
Kochubej, A. N.
1982
On characteristic functions of symmetric operators and their extensions. Zbl 0444.47023
Kochubej, A. N.
1980
Symmetric operators and nonclassical spectral problems. Zbl 0454.47023
Kochubej, A. N.
1979
On extensions of a positive definite symmetric operator. Zbl 0454.47022
Kochubej, A. N.
1979
The extensions of a nondensely defined symmetric operator. Zbl 0409.47014
Kochubej, A. N.
1977
On extensions of a nondensely defined symmetric operator. Zbl 0362.47008
Kochubej, A. N.
1977
Extensions of symmetric operators and symmetric binary relations. Zbl 0322.47006
Kochubej, A. N.
1975
On best approximation in normed modules. Zbl 0262.41035
Kochubej, A. N.
1973
Dissipative extensions of differential operators in a space of vector- functions. Zbl 0261.47026
Gorbachuk, M. L.; Kochubej, A. N.; Rybak, M. A.
1972
all top 5
#### Cited by 765 Authors
30 Kochubeĭ, Anatoliĭ Naumovych 25 Khrennikov, Andreĭ Yur’evich 24 Zúñiga-Galindo, Wilson A. 14 Cuevas, Claudio 12 Albeverio, Sergio A. 12 Lopushans’ka, Galyna Petrovna 12 Luchko, Yuri 12 Shelkovich, Vladimir M. 11 Kozyrev, Sergeĭ Vladimirovich 11 Mainardi, Francesco 11 Nane, Erkan 10 Yamamoto, Masahiro 9 Lopushans’kyi, Andriy Olegovich 9 Malamud, Mark M. 9 Peng, Jigen 9 Zacher, Rico 8 Kaneko, Hiroshi 8 Meerschaert, Mark M. 7 Allahverdiev, Bilender Paşaoğlu 7 Bazhlekova, Emilia G. 7 Chen, Pengyu 7 D’Ovidio, Mirko 7 Li, Yongxiang 7 Lizama, Carlos 7 Protsakh, Nataliya P. 6 Chen, Zhen-Qing 6 Kemppainen, Jukka T. 6 Kolokoltsov, Vassili N. 6 Krasnoshchok, Mykola Valeriĭovych 6 Leonenko, Nikolai N. 6 Sandev, Trifce 6 Vasylyeva, Nataliya V. 6 Wang, Rongnian 5 Agarwal, Ravi P. 5 Ahmad, Bashir 5 Behrndt, Jussi 5 Beshtokov, Murat Khamidbievich 5 Bikulov, Al’bert Khakimovich 5 Fu, Zunwei 5 Gao, Jinghuai 5 Gorenflo, Rudolf 5 Kirane, Mokhtar 5 Li, Kexue 5 Li, Zhiyuan 5 Mamchuev, Murat Osmanovich 5 Mukhamedov, Farruh Maksutovich 5 Osypchuk, Mykhailo M. 5 Povstenko, Yuriy Z. 5 Toaldo, Bruno 5 Vergara, Vicente 5 Wu, Qingyan 5 Zhou, Zhi 4 Anh, Vo V. 4 Atanackovic, Teodor M. 4 Bendikov, Alexander D. 4 Casas-Sánchez, Oscar Francisco 4 Chacón-Cortes, Leonardo Fabio 4 Chechkin, Aleksei V. 4 de Andrade, Bruno 4 Estala-Arias, Samuel 4 Feng, Binhua 4 Galeano-Peñaloza, Jeanneth 4 Ivasyshen, Stepan Dmytrovych 4 Jin, Bangti 4 Kim, Panki 4 Li, Yaning 4 Liu, Fawang 4 Luchko, Yurii F. 4 Mei, Zhandong 4 Mijena, Jebessa B. 4 Murugesu, R. 4 Oleschko, Klaudia 4 Piskarëv, S. I. 4 Torresblanca-Badillo, Anselmo 4 Umarov, Sabir R. 4 Wu, Bo 4 Zhang, Quanguo 4 Zhang, Shuqin 4 Zhang, Zufeng 4 Zhou, Yong 3 Abbaszadeh, Mostafa 3 Al-Refai, Mohammed 3 Al-saedi, Ahmed Eid Salem 3 Ansari, Alireza 3 Băleanu, Dumitru I. 3 Bazzaev, Aleksandr Kazbekovich 3 Cao, Junfei 3 Cygan, Wojciech 3 Derkach, Vladimir Alexandrovich 3 Digernes, Trond 3 Dos Santos, José Paulo Carvalho 3 Fëdorov, Vladimir Evgen’evich 3 Gao, Guanghua 3 Garrappa, Roberto 3 Gesztesy, Fritz 3 Geyler, Vladimir A. 3 Giusti, Andrea 3 Grubb, Gerd 3 Gu, Haibo 3 Jia, Junxiong ...and 665 more Authors
all top 5
#### Cited in 195 Serials
44 Fractional Calculus & Applied Analysis 33 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 30 Journal of Mathematical Analysis and Applications 21 Ukrainian Mathematical Journal 20 Computers & Mathematics with Applications 18 Journal of Mathematical Sciences (New York) 16 Journal of Differential Equations 14 Applied Mathematics and Computation 14 Stochastic Processes and their Applications 13 Journal of Functional Analysis 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 12 Abstract and Applied Analysis 11 Advances in Difference Equations 11 Carpathian Mathematical Publications 10 Journal of Computational and Applied Mathematics 10 The Journal of Fourier Analysis and Applications 9 Journal of Mathematical Physics 9 Differential Equations 9 Proceedings of the Steklov Institute of Mathematics 8 Mathematical Methods in the Applied Sciences 8 Doklady Mathematics 7 Chaos, Solitons and Fractals 7 Applied Mathematics Letters 7 Potential Analysis 7 Integral Transforms and Special Functions 6 Nonlinear Dynamics 6 Communications in Nonlinear Science and Numerical Simulation 6 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 6 Journal of Pseudo-Differential Operators and Applications 5 Applicable Analysis 5 Theoretical and Mathematical Physics 5 Integral Equations and Operator Theory 5 Proceedings of the American Mathematical Society 5 Siberian Mathematical Journal 5 Journal of Evolution Equations 5 Fractional Differential Calculus 4 Mathematical Notes 4 Functional Analysis and its Applications 4 Journal of Number Theory 4 Mathematische Nachrichten 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Tohoku Mathematical Journal. Second Series 4 Statistics & Probability Letters 4 Numerical Algorithms 4 Computational and Applied Mathematics 4 Stochastics and Dynamics 4 Ufimskiĭ Matematicheskiĭ Zhurnal 4 Evolution Equations and Control Theory 4 Mathematics 4 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki 3 Reports on Mathematical Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Reviews in Mathematical Physics 3 Advances in Mathematics 3 The Annals of Probability 3 Mathematische Annalen 3 Applied Numerical Mathematics 3 Journal of Theoretical Probability 3 Computational Mathematics and Mathematical Physics 3 Applied Mathematical Modelling 3 Applied and Computational Harmonic Analysis 3 Electronic Journal of Differential Equations (EJDE) 3 Discrete and Continuous Dynamical Systems 3 Matematychni Metody ta Fizyko-Mekhanichni Polya 3 Matematychni Studiï 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Nonlinear Analysis. Real World Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Communications on Pure and Applied Analysis 3 Journal of Applied Mathematics and Computing 3 Mediterranean Journal of Mathematics 2 Communications in Mathematical Physics 2 International Journal of Theoretical Physics 2 Inverse Problems 2 Nonlinearity 2 Nuclear Physics. B 2 Mathematics of Computation 2 Journal of Pure and Applied Algebra 2 Mathematische Zeitschrift 2 Meccanica 2 Numerical Functional Analysis and Optimization 2 Rendiconti del Seminario Matematico della Università di Padova 2 Results in Mathematics 2 Transactions of the Moscow Mathematical Society 2 Acta Applicandae Mathematicae 2 Probability Theory and Related Fields 2 Journal of Scientific Computing 2 Forum Mathematicum 2 Journal of Integral Equations and Applications 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Expositiones Mathematicae 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Indagationes Mathematicae. New Series 2 Theory of Probability and Mathematical Statistics 2 Journal of Inverse and Ill-Posed Problems 2 Mathematical Problems in Engineering 2 Algebras and Representation Theory 2 Matematicheskie Trudy 2 Journal of Applied Mathematics ...and 95 more Serials
all top 5
#### Cited in 52 Fields
381 Partial differential equations (35-XX) 181 Operator theory (47-XX) 147 Probability theory and stochastic processes (60-XX) 131 Ordinary differential equations (34-XX) 117 Real functions (26-XX) 64 Number theory (11-XX) 62 Numerical analysis (65-XX) 55 Integral equations (45-XX) 45 Quantum theory (81-XX) 44 Functional analysis (46-XX) 36 Harmonic analysis on Euclidean spaces (42-XX) 35 Special functions (33-XX) 23 Statistical mechanics, structure of matter (82-XX) 18 Systems theory; control (93-XX) 16 Integral transforms, operational calculus (44-XX) 14 Dynamical systems and ergodic theory (37-XX) 13 Abstract harmonic analysis (43-XX) 13 Fluid mechanics (76-XX) 9 Field theory and polynomials (12-XX) 9 Mechanics of deformable solids (74-XX) 9 Biology and other natural sciences (92-XX) 8 Potential theory (31-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Associative rings and algebras (16-XX) 7 Measure and integration (28-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Functions of a complex variable (30-XX) 6 Difference and functional equations (39-XX) 5 Combinatorics (05-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Relativity and gravitational theory (83-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Commutative algebra (13-XX) 4 Group theory and generalizations (20-XX) 4 Topological groups, Lie groups (22-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Approximations and expansions (41-XX) 2 Statistics (62-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX)
#### Wikidata Timeline
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https://www.federalreserve.gov/monetarypolicy/principles-for-the-conduct-of-monetary-policy.htm | ### Principles for the Conduct of Monetary Policy
Three key principles of good monetary policy
Over the past decades, policymakers and academic economists have formulated several key principles for the conduct of monetary policy; these principles are based on historical experience with a range of monetary policy frameworks.1
One principle is that monetary policy should be well understood and systematic. The objectives of monetary policy should be stated clearly and communicated to the public. The Congress has directed the Federal Reserve to use monetary policy to promote both maximum employment and price stability; those are the objectives of U.S. monetary policy. Fed policymakers' understanding of that statutory mandate is summarized in Monetary Policy: What Are Its Goals? How Does It Work? To be systematic, policymakers should respond consistently and predictably to changes in economic conditions and the economic outlook; policymakers also should clearly explain their policy strategy and actions to the public, and they should follow through on past policy announcements and communications unless circumstances change in ways that warrant adjusting past plans. Following this principle helps households and firms make economic decisions and plan for the future; it also promotes economic stability by avoiding policy surprises.
A second principle is that the central bank should provide monetary policy stimulus when economic activity is below the level associated with full resource utilization and inflation is below its stated goal. Conversely, the central bank should implement restrictive monetary policy when the economy is overheated and inflation is above its stated goal. In some circumstances, the central bank should follow this principle in a preemptive manner. For example, economic developments such as a large, unanticipated change in financial conditions might not immediately alter inflation and employment but would do so in the future and thus might call for a prompt, forward-looking policy response. Conveying how monetary policy would respond to irregular future events is not easy, but the overarching principle remains the same: Policymakers should strive to communicate how these events may affect the future evolution of inflation and employment and set monetary policy accordingly.
A third principle is that the central bank should raise the policy interest rate, over time, by more than one-for-one in response to a persistent increase in inflation and lower the policy rate more than one-for-one in response to a persistent decrease in inflation. For example, if the inflation rate rises from 2 percent to 3 percent and the increase is not caused by temporary factors, the central bank should raise the policy rate by more than one percentage point. Such an adjustment to the policy rate translates into an increase in the real policy rate--that is, the level of the policy rate adjusted for inflation--when inflation rises and a decrease in the real policy rate when inflation slows. As the real policy rate rises, it feeds through to other real interest rates that determine how expensive it is for households and businesses to borrow money to finance consumption or investment spending, adjusted for inflation. Raising real interest rates tends to reduce growth of economic activity, and firms tend to increase prices less rapidly when they see slower growth in their sales. As a result, inflation is kept in check. A symmetric logic applies to the central bank's response to persistent decreases in inflation.
In the academic research literature, a standard way to codify these principles is to assume that policymakers set the policy rate according to an equation or policy rule that relates the policy rate to a small set of economic variables. One such rule is the Taylor rule.
The Taylor rule
In an article published in 1993, John Taylor showed how U.S. monetary policy from 1987 through 1992 could be approximated fairly well by a simple equation that linked the level of the federal funds rate--the policy interest rate of the Federal Reserve--to three variables. The first variable is the neutral value of the policy interest rate in the longer run (adjusted for inflation). The second is the deviation of current inflation from the Federal Open Market Committee's (FOMC) objective. And the third is the percentage difference of gross domestic product (GDP) from its potential level--the level of output associated with the full utilization of resources.2 Taylor's simple equation takes the following general form:
$$FFR_t = r_t^{LR} + \pi_t + 0.5(\pi_t - \pi^*) + 0.5(y_t - y_t^P),$$
where $FFR_t$ is the federal funds rate in quarter $t$, $r_t^{LR}$ is the neutral federal funds rate in the longer run (adjusted for inflation), $\pi_t$ is the four-quarter inflation rate, $\pi^*$ is the central bank's objective for inflation, and $y_t - y_t^P$ measures the percentage difference of GDP from its potential level.3 Taylor set the value of $r_t^{LR}$ at a constant level of 2 percent and assumed the Fed's inflation objective, $\pi^*$, was 2 percent. If inflation is running at 2 percent and GDP is equal to its potential level, then Taylor's formula prescribes setting the federal funds rate at 4 percent. If inflation moves above 2 percent, the equation increases the federal funds rate by 1.5 times the increase in inflation. If GDP exceeds its potential level, then the equation increases the federal funds rate by 0.5 times the percentage difference of GDP from its potential level.
This so-called Taylor rule reflects the three key principles of monetary policy discussed previously. First, the equation makes the policy interest rate predictable if the neutral real federal funds rate in the longer run, the actual and target inflation rates, the level of real GDP, and its potential level are known. Second, it prescribes an increase in the policy rate when inflation rises or resource utilization rises--and a decrease when inflation falls or resource utilization falls--consistent with the Federal Reserve's dual mandate to foster maximum sustainable employment and price stability. Third, the equation prescribes that the federal funds rate be adjusted by more than one-for-one when inflation rises or falls--this feature is sometimes called the Taylor principle.
In subsequent work, Taylor (1999) argued that the equation he proposed in 1993 performed well in the context of economic models when it was used to simulate monetary policy in such models.4 Taylor showed that, in simulations of the models he considered, monetary policy that adhered to his rule tended to do reasonably well in stabilizing inflation rates close to 2 percent and unemployment rates close to the maximum rates that were sustainable over the longer run in those models.
While Taylor's equation performs well in a set of economic models, these models omit features of the actual economy that are relevant for monetary policy.5 Unfortunately, it is often only with the benefit of hindsight that the importance of simplifications and omissions in economic models is fully appreciated. For example, before the Global Financial Crisis that began in 2007, most existing economic models of the United States and other countries did not accurately reflect how much problems in the financial sector could affect the rest of the economy. This oversight became apparent during the Global Financial Crisis. In his 1993 article, Taylor pointed out that "operating monetary policy by mechanically following a policy rule . . . is not practical," in part because there would be episodes in which "monetary policy will need to be adjusted to deal with special factors."6 Over the period since Taylor wrote those words, the Global Financial Crisis would seem to be the most prominent example of such an episode.
In practice, policymakers exercise judgment in determining the appropriate level for the policy rate while taking into account data from a wide variety of sources, not just the current values of inflation and unemployment. For example, movements in measures of financial conditions, financial innovation, expectations about inflation and output, changes in the composition of the labor market, and economic developments abroad can all affect future values of inflation and unemployment. As a result, policymakers need to adjust the federal funds rate in response to incoming data so as to achieve the central bank's objectives; policy rules that narrowly focus on one or two economic variables are likely to miss or lag behind important developments in the economy.
In addition, the FOMC has made decisions about aspects of monetary policy other than just the policy interest rate. Over the past decade, policymakers have changed the size and composition of the Federal Reserve's balance sheet, issued forward guidance on the likely path for the federal funds rate in the future, and announced likely changes in balance sheet policy before making those changes. The Taylor rule is silent on how to take such decisions, in part because the simple economic models in which rules are commonly studied usually ignore the effect of such decisions on inflation and economic activity.
While the Taylor rule is among the best-known formulations of a relationship between the short-term policy rate and other economic variables, a wide range of alternative formulations have been proposed. Specifying a particular rule requires making a number of decisions: Should the policy rate be specified in terms of the level of the policy interest rate or its change from the previous period? Should the policy rate respond to the rate of inflation or the price level? Should it respond to quarter-over-quarter or year-over-year inflation or even to a forecast of future inflation? Should it respond to the resource utilization gap, the unemployment gap, or both--or even to other measures such as credit growth or asset prices? Finally, how strongly and how fast should the policy rate respond to changes in each of these items? For alternatives to the Taylor rule and answers to some of these questions, see Policy Rules and How Policymakers Use Them.
1. For a discussion of that historical experience, see Historical Approaches to Monetary Policy. Return to text
2. See John B. Taylor (1993), "Discretion versus Policy Rules in Practice," Carnegie-Rochester Conference Series on Public Policy, vol. 39 (December), pp. 195-214. Return to text
3. The Taylor rule can be written in terms of the gap between the actual level of the unemployment rate and the level of the unemployment rate that corresponds to full employment. An empirical relationship known as Okun's law indicates that a 1 percentage point increase in GDP relative to its potential level will result in a decline of the unemployment rate of 0.5 percent. The Taylor rule and Okun's law can be combined to yield $$R_t = r_t^{LR} + \pi_t + 0.5(\pi_t - \pi^*) + (u^{LR} - u_t),$$
here $u_t$ is the unemployment rate and $u^{LR}$ is the longer-term average level of the unemployment rate. This formulation is more directly related to the Fed's statutory mandate of promoting maximum employment and price stability. See Janet L. Yellen (2017), "The Economic Outlook and the Conduct of Monetary Policy," speech delivered at the Stanford Institute for Economic Policy Research, Stanford, Calif., January 19. Return to text
4. John B. Taylor (1999), "A Historical Analysis of Monetary Policy Rules," in John B. Taylor, ed., Monetary Policy Rules (Chicago: University of Chicago Press), pp. 319-41. Return to text
5. An economic model makes simplifying assumptions about the way that the economy operates and offers mathematical equations that link business and household decisions to the macroeconomy. One example of such a model is the FRB/US model of the U.S. economy--one of several models that the Federal Reserve Board staff consults for forecasting and the analysis of macroeconomic issues, including both monetary and fiscal policies. For more information on FRB/US, see Flint Brayton, Thomas Laubach, and David Reifschneider (2014), "The FRB/US Model: A Tool for Macroeconomic Policy Analysis," FEDS Notes (Washington: Board of Governors of the Federal Reserve System, April 3). Return to text
6. See Taylor, "Discretion versus Policy Rules in Practice," in endnote 2, pp. 208 and 197. Return to text | 2023-01-31T07:59:49 | {"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": 0.3445524573326111, "perplexity": 1756.695555853395}, "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/1674764499845.10/warc/CC-MAIN-20230131055533-20230131085533-00167.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/mbe.2015.12.393 | Article Contents
Article Contents
# A hybrid model for traffic flow and crowd dynamics with random individual properties
• Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.
Mathematics Subject Classification: Primary: 35L40, 35L65, 90B20, 35R60.
Citation:
• [1] P. Amorim, R. M. Colombo and A. Teixeira, On the numerical integration of scalar conservation laws, preprint, 2013. [2] A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938 (electronic).doi: 10.1137/S0036139997332099. [3] N. Bellomo and C. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models, Math. Models Methods Appl. Sci., 18 (2008), 1317-1345.doi: 10.1142/S0218202508003054. [4] N. Bellomo and C. Dogbé, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Review, 53 (2011), 409-463.doi: 10.1137/090746677. [5] R. M. Colombo, M. Garavello and M. Lécureux-Mercier, A class of non-local models for pedestrian traffic, Mathematical Models and Methods in the Applied Sciences, 22 (2012), 1150023, 34 p.doi: 10.1142/S0218202511500230. [6] R. M. Colombo and N. Pogodaev, Confinement strategies in a model for the interaction between individuals and a continuum, SIAM J. Appl. Dyn. Syst., 11 (2012), 741-770.doi: 10.1137/110854321. [7] M. Crandall and A. Majda, The method of fractional steps for conservation laws, Numer. Math., 34 (1980), 285-314.doi: 10.1007/BF01396704. [8] E. Cristiani, B. Piccoli and A. Tosin, Multiscale modeling of granular flows with application to crowd dynamics, Multiscale Model. Simul., 9 (2011), 155-182.doi: 10.1137/100797515. [9] C. F. Daganzo, Requiem for second-order fluid approximations to traffic flow, Transp. Res. B, 29 (1995), 277-286.doi: 10.1016/0191-2615(95)00007-Z. [10] G. Dal Maso, P. G. Lefloch and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. (9), 74 (1995), 483-548. [11] D. Helbing, Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models, The European Physical Journal B, 69 (2009), 539-548.doi: 10.1140/epjb/e2009-00192-5. [12] D. Helbing and A. F. Johansson, On the controversy around Daganzo's requiem for and Aw-Rascle's resurrection of second-order traffic flow models, Modelling and Optimisation of Flows on Networks, (2013), 271-302.doi: 10.1007/978-3-642-32160-3_4. [13] R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36 (2002), 507-535.doi: 10.1016/S0191-2615(01)00015-7. [14] S. N. Kružhkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), 228-255. [15] M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317-345.doi: 10.1098/rspa.1955.0089. [16] S. Mishra and C. Schwab, Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data, Math. Comp., 81 (2012), 1979-2018.doi: 10.1090/S0025-5718-2012-02574-9. [17] P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.doi: 10.1287/opre.4.1.42. [18] M. Sabry Hassouna and A. A. Farag, Multistencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29 (2007), 1563-1574.doi: 10.1109/TPAMI.2007.1154. [19] Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S.-i. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam, New Journal of Physics, 10 (2008), 033001.doi: 10.1088/1367-2630/10/3/033001. [20] S.-i. Tadaki, M. Kikuchi, F. Minoru, A. Nakayama, K. Nishinari, A. Shibata, Y. Sugiyama, T. Yosida and S. Yukawa, Phase transition in traffic jam experiment on a circuit, New Journal of Physics, 15 (2013), 103034.doi: 10.1088/1367-2630/15/10/103034.
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https://zbmath.org/authors/?q=ai%3Ashigekawa.ichiro | # zbMATH — the first resource for mathematics
## Shigekawa, Ichiro
Compute Distance To:
Author ID: shigekawa.ichiro Published as: Shigekawa, I.; Shigekawa, Ichiro; Shigekawa, Ichirō External Links: Wikidata · GND
Documents Indexed: 53 Publications since 1978, including 3 Books
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#### Co-Authors
32 single-authored 5 Taniguchi, Setsuo 3 Kazumi, Tetsuya 2 Aida, Shigeki 2 Fukushima, Masatoshi 2 Ueki, Naomasa 1 Elworthy, K. David 1 Ikeda, Nobuyuki 1 Kotani, Shinichi 1 Kusuoka, Seiichiro Kusuoka 1 Kusuoka, Shigeo 1 Manabe, Shojiro 1 Masuda, Takao 1 Matsumoto, Hiroyuki 1 Miyokawa, Tomohiro 1 Watanabe, Shinzo 1 Yoshida, Nobuo 1 Yun, Yong Sik
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#### Serials
7 Journal of Functional Analysis 5 Osaka Journal of Mathematics 4 Journal of Mathematics of Kyoto University 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Probability Theory and Related Fields 2 Sūgaku 2 Kyoto Journal of Mathematics 1 Journal of the Mathematical Society of Japan 1 Mathematical Journal of Okayama University 1 Proceedings of the Japan Academy. Series A 1 Acta Applicandae Mathematicae 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Far East Journal of Mathematical Sciences 1 Translations of Mathematical Monographs 1 Frontiers of Mathematics in China 1 RIMS Kôkyûroku Bessatsu 1 Communications on Stochastic Analysis
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#### Fields
43 Probability theory and stochastic processes (60-XX) 19 Global analysis, analysis on manifolds (58-XX) 14 Operator theory (47-XX) 6 Functional analysis (46-XX) 5 Partial differential equations (35-XX) 5 Differential geometry (53-XX) 4 Potential theory (31-XX) 2 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistical mechanics, structure of matter (82-XX)
#### Citations contained in zbMATH Open
43 Publications have been cited 437 times in 357 Documents Cited by Year
Derivatives of Wiener functionals and absolute continuity of induced measures. Zbl 0476.28008
Shigekawa, Ichiro
1980
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold. Zbl 0629.58023
Shigekawa, Ichiro
1987
De Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. Zbl 0611.58006
Shigekawa, Ichiro
1986
Stochastic analysis. Translated from the Japanese by Ichiro Shigekawa. Zbl 1064.60003
Shigekawa, Ichiro
2004
Spectral properties of Schrödinger operators with magnetic fields for a spin $${1 \over{} 2}$$ particle. Zbl 0742.47002
Shigekawa, Ichiro
1991
Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator. Zbl 0777.60047
Shigekawa, Ichiro
1992
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
Transformations of the Brownian motion on a Riemannian symmetric space. Zbl 0518.60087
Shigekawa, Ichiro
1984
Sobolev spaces of Banach-valued functions associated with a Markov process. Zbl 0801.60044
Shigekawa, Ichiro
1994
Existence of invariant measures of diffusions on an abstract Wiener space. Zbl 0636.60080
Shigekawa, Ichiro
1987
On stochastic horizontal lifts. Zbl 0487.60056
Shigekawa, Ichiro
1982
Measures of finite $$(r,p)$$-energy and potentials on a separable metric space. Zbl 0769.60069
Kazumi, Tetsuya; Shigekawa, Ichiro
1992
Itô-Wiener expansions of holomorphic functions on the complex Wiener space. Zbl 0727.60053
Shigekawa, Ichiro
1991
$$L^ p$$ contraction semigroups for vector valued functions. Zbl 0886.47024
Shigekawa, Ichiro
1997
Absolute continuity of probability laws of Wiener functionals. Zbl 0422.60032
Shigekawa, Ichiro
1978
A Kähler metric on a based loop group and a covariant differentiation. Zbl 0867.53029
Shigekawa, Ichiro; Taniguchi, Setsuo
1996
On a quasi everywhere existence of the local time of the 1-dimensional Brownian motion. Zbl 0551.60076
Shigekawa, Ichiro
1984
Vanishing theorem of the Hodge-Kodaira operator for differential forms on a convex domain of the Wiener space. Zbl 1077.58022
Shigekawa, Ichiro
2003
Semigroup domination on a Riemannian manifold with boundary. Zbl 0992.60081
Shigekawa, Ichiro
2000
An example of regular $$(r,p)$$-capacity and essential self-adjointness of a diffusion operator in infinite dimensions. Zbl 0855.31005
Shigekawa, Ichiro
1995
Littlewood-Paley-Stein inequality for a symmetric diffusion. Zbl 0764.60060
Shigekawa, Ichiro; Yoshida, Nobuo
1992
The Meyer inequality for the Ornstein-Uhlenbeck operator in $$L^1$$ and probabilistic proof of Stein’s $$L^p$$ multiplier theorem. Zbl 1010.60051
Shigekawa, Ichiro
1997
Differential calculus on a submanifold of an abstract Wiener space. II: Weitzenböck formula. Zbl 0836.60064
Kazumi, Tetsuya; Shigekawa, Ichiro
1995
A quasihomeomorphism on the Wiener space. Zbl 0821.60059
Shigekawa, Ichiro
1995
The Malliavin calculus and long time asymptotics of certain Wiener integrals. Zbl 0573.60055
Ikeda, Nobuyuki; Shigekawa, Ichiro; Taniguchi, Setsuo
1985
Transformations of the Brownian motion on the Lie group. Zbl 0563.58035
Shigekawa, Ichiro
1984
Defective intertwining property and generator domain. Zbl 1113.47028
Shigekawa, Ichiro
2006
On equivalence of $$L^{p}$$-norms related to Schrödinger type operators on Riemannian manifolds. Zbl 1094.53034
Miyokawa, Tomohiro; Shigekawa, Ichiro
2006
Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary. Zbl 1016.58022
Shigekawa, Ichiro
2002
Differential calculus on a submanifold of an abstract Wiener space. I: Covariant derivative. Zbl 0829.46031
Kazumi, T.; Shigekawa, I.
1994
Dirichlet forms on separable metric spaces. Zbl 0818.60068
Shigekawa, Ichiro; Taniguchi, Setsuo
1992
Limit theorems for stochastic flows of diffeomorphisms of jump type. Zbl 0548.60035
Matsumoto, Hiroyuki; Shigekawa, I.
1985
Exponential convergence of Markovian semigroups and their spectra on $$L^p$$-spaces. Zbl 1306.60107
Kusuoka, Seiichiro; Shigekawa, Ichiro
2014
Non-symmetric diffusions on a Riemannian manifold. Zbl 1200.58024
Shigekawa, Ichiro
2010
Orlicz norm equivalence for the Ornstein-Uhlenbeck operator. Zbl 1063.60083
Shigekawa, Ichiro
2004
A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary. Zbl 0704.58056
Shigekawa, Ichiro; Ueki, Naomasa; Watanabe, Shinzo
1989
A stochastic approach to the Riemann-Roch theorem. Zbl 0709.58036
Shigekawa, Ichiro; Ueki, Naomasa
1988
Dual ultracontractivity and its applications. Zbl 1322.47040
Shigekawa, Ichiro
2014
Schrödinger operators on the Wiener space. Zbl 1328.60157
Shigekawa, Ichiro
2007
$$L^p$$ multiplier theorem for the Hodge-Kodaira operator. Zbl 1080.58024
Shigekawa, Ichiro
2005
The domain of a generator and the intertwining property. Zbl 0972.60080
Shigekawa, Ichiro
2000
A comparison theorem for eigenvalues of the covariant Laplacian. Zbl 0716.58030
Manabe, Shojiro; Shigekawa, Ichiro
1990
Exponential convergence of Markovian semigroups and their spectra on $$L^p$$-spaces. Zbl 1306.60107
Kusuoka, Seiichiro; Shigekawa, Ichiro
2014
Dual ultracontractivity and its applications. Zbl 1322.47040
Shigekawa, Ichiro
2014
Non-symmetric diffusions on a Riemannian manifold. Zbl 1200.58024
Shigekawa, Ichiro
2010
Schrödinger operators on the Wiener space. Zbl 1328.60157
Shigekawa, Ichiro
2007
Defective intertwining property and generator domain. Zbl 1113.47028
Shigekawa, Ichiro
2006
On equivalence of $$L^{p}$$-norms related to Schrödinger type operators on Riemannian manifolds. Zbl 1094.53034
Miyokawa, Tomohiro; Shigekawa, Ichiro
2006
$$L^p$$ multiplier theorem for the Hodge-Kodaira operator. Zbl 1080.58024
Shigekawa, Ichiro
2005
Stochastic analysis. Translated from the Japanese by Ichiro Shigekawa. Zbl 1064.60003
Shigekawa, Ichiro
2004
Orlicz norm equivalence for the Ornstein-Uhlenbeck operator. Zbl 1063.60083
Shigekawa, Ichiro
2004
Vanishing theorem of the Hodge-Kodaira operator for differential forms on a convex domain of the Wiener space. Zbl 1077.58022
Shigekawa, Ichiro
2003
Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary. Zbl 1016.58022
Shigekawa, Ichiro
2002
Semigroup domination on a Riemannian manifold with boundary. Zbl 0992.60081
Shigekawa, Ichiro
2000
The domain of a generator and the intertwining property. Zbl 0972.60080
Shigekawa, Ichiro
2000
$$L^ p$$ contraction semigroups for vector valued functions. Zbl 0886.47024
Shigekawa, Ichiro
1997
The Meyer inequality for the Ornstein-Uhlenbeck operator in $$L^1$$ and probabilistic proof of Stein’s $$L^p$$ multiplier theorem. Zbl 1010.60051
Shigekawa, Ichiro
1997
A Kähler metric on a based loop group and a covariant differentiation. Zbl 0867.53029
Shigekawa, Ichiro; Taniguchi, Setsuo
1996
An example of regular $$(r,p)$$-capacity and essential self-adjointness of a diffusion operator in infinite dimensions. Zbl 0855.31005
Shigekawa, Ichiro
1995
Differential calculus on a submanifold of an abstract Wiener space. II: Weitzenböck formula. Zbl 0836.60064
Kazumi, Tetsuya; Shigekawa, Ichiro
1995
A quasihomeomorphism on the Wiener space. Zbl 0821.60059
Shigekawa, Ichiro
1995
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
Sobolev spaces of Banach-valued functions associated with a Markov process. Zbl 0801.60044
Shigekawa, Ichiro
1994
Differential calculus on a submanifold of an abstract Wiener space. I: Covariant derivative. Zbl 0829.46031
Kazumi, T.; Shigekawa, I.
1994
Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator. Zbl 0777.60047
Shigekawa, Ichiro
1992
Measures of finite $$(r,p)$$-energy and potentials on a separable metric space. Zbl 0769.60069
Kazumi, Tetsuya; Shigekawa, Ichiro
1992
Littlewood-Paley-Stein inequality for a symmetric diffusion. Zbl 0764.60060
Shigekawa, Ichiro; Yoshida, Nobuo
1992
Dirichlet forms on separable metric spaces. Zbl 0818.60068
Shigekawa, Ichiro; Taniguchi, Setsuo
1992
Spectral properties of Schrödinger operators with magnetic fields for a spin $${1 \over{} 2}$$ particle. Zbl 0742.47002
Shigekawa, Ichiro
1991
Itô-Wiener expansions of holomorphic functions on the complex Wiener space. Zbl 0727.60053
Shigekawa, Ichiro
1991
A comparison theorem for eigenvalues of the covariant Laplacian. Zbl 0716.58030
Manabe, Shojiro; Shigekawa, Ichiro
1990
A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary. Zbl 0704.58056
Shigekawa, Ichiro; Ueki, Naomasa; Watanabe, Shinzo
1989
A stochastic approach to the Riemann-Roch theorem. Zbl 0709.58036
Shigekawa, Ichiro; Ueki, Naomasa
1988
Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold. Zbl 0629.58023
Shigekawa, Ichiro
1987
Existence of invariant measures of diffusions on an abstract Wiener space. Zbl 0636.60080
Shigekawa, Ichiro
1987
De Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. Zbl 0611.58006
Shigekawa, Ichiro
1986
The Malliavin calculus and long time asymptotics of certain Wiener integrals. Zbl 0573.60055
Ikeda, Nobuyuki; Shigekawa, Ichiro; Taniguchi, Setsuo
1985
Limit theorems for stochastic flows of diffeomorphisms of jump type. Zbl 0548.60035
Matsumoto, Hiroyuki; Shigekawa, I.
1985
Transformations of the Brownian motion on a Riemannian symmetric space. Zbl 0518.60087
Shigekawa, Ichiro
1984
On a quasi everywhere existence of the local time of the 1-dimensional Brownian motion. Zbl 0551.60076
Shigekawa, Ichiro
1984
Transformations of the Brownian motion on the Lie group. Zbl 0563.58035
Shigekawa, Ichiro
1984
On stochastic horizontal lifts. Zbl 0487.60056
Shigekawa, Ichiro
1982
Derivatives of Wiener functionals and absolute continuity of induced measures. Zbl 0476.28008
Shigekawa, Ichiro
1980
Absolute continuity of probability laws of Wiener functionals. Zbl 0422.60032
Shigekawa, Ichiro
1978
all top 5
#### Cited by 348 Authors
12 Léandre, Rémi 12 Röckner, Michael 11 Wang, Feng-Yu 10 Bogachev, Vladimir Igorevich 9 Albeverio, Sergio A. 9 Cruzeiro, Ana-Bela 9 Nualart, David 9 Shigekawa, Ichiro 7 Aida, Shigeki 6 Driver, Bruce K. 6 Ghanmi, Allal 6 Gordina, Maria 6 Intissar, Ahmed 6 Li, Xue-Mei 6 Ren, Jiagang 5 Bobkov, Sergey Germanovich 5 Elworthy, K. David 5 Haslinger, Friedrich 5 Ismail, Mourad El-Houssieny 5 Li, Xiang-Dong 5 Malliavin, Paul 5 Nourdin, Ivan 5 Tudor, Ciprian A. 5 Zakai, Moshe 5 Zhang, Xicheng 4 Goldys, Beniamin 4 Ledoux, Michel 4 Ogurisu, Osamu 4 Sanz-Solé, Marta 4 Taniguchi, Setsuo 3 Arai, Asao 3 Cattiaux, Patrick 3 Colbois, Bruno 3 Da Prato, Giuseppe 3 Fang, Shizan 3 Fukushima, Masatoshi 3 Götze, Friedrich W. 3 Hino, Masanori 3 Inahama, Yuzuru 3 Kosov, Egor D. 3 Kusuoka, Seiichiro Kusuoka 3 Maas, Jan 3 Nikitin, E. V. 3 Peccati, Giovanni 3 Pontier, Monique 3 Privault, Nicolas 3 Russo, Francesco 3 Savo, Alessandro 3 Thalmaier, Anton 3 van Neerven, Jan M. A. M. 3 Wang, Fengyu 3 Wang, Jian 3 Zhang, Tusheng S. 2 Airault, Hélène 2 Bakry, Dominique 2 Baudoin, Fabrice 2 Bismut, Jean-Michel 2 Breton, Jean-Christophe 2 Brzeźniak, Zdzisław 2 Cass, Thomas Richard 2 Chojnowska-Michalik, Anna 2 Cianchi, Andrea 2 Daletskii, Alexei 2 Darling, Richard W. R. 2 de la Pradelle, Arnaud 2 Deck, Thomas 2 Feyel, Denis 2 Friz, Peter Karl 2 Funaki, Tadahisa 2 Grong, Erlend 2 Gross, Leonard 2 Guillin, Arnaud 2 Güneysu, Batu 2 He, Kai 2 Helffer, Bernard 2 Hinz, Michael 2 Hirsch, Francis 2 Houdré, Christian 2 Imkeller, Peter 2 Intissar, Abdelkader 2 Iwatsuka, Akira 2 Kawabi, Hiroshi 2 Kondrat’yev, Yuriĭ Grygorovych 2 Kusuoka, Shigeo 2 Liu, Yong 2 Liu, Yuan 2 Long, Hongwei 2 Lunardi, Alessandra 2 Luo, Dejun 2 Lytvynov, Eugene W. 2 Mao, Yonghua 2 Maslowski, Bohdan 2 Mayer-Wolf, Eduardo 2 Melcher, Tai 2 Olivera, Christian 2 Ouyang, Cheng 2 Pallara, Diego 2 Pick, Luboš 2 Qian, Zhongmin M. 2 Raikov, Georgi D. ...and 248 more Authors
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#### Cited in 101 Serials
83 Journal of Functional Analysis 20 Potential Analysis 18 Probability Theory and Related Fields 15 The Annals of Probability 13 Journal of Mathematical Analysis and Applications 13 Stochastic Processes and their Applications 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 9 Journal of Mathematical Physics 7 Transactions of the American Mathematical Society 6 Journal of Geometry and Physics 6 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 6 Statistics & Probability Letters 5 Reviews in Mathematical Physics 5 Kyoto Journal of Mathematics 4 Stochastics 4 Mathematische Nachrichten 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Bulletin des Sciences Mathématiques 3 Letters in Mathematical Physics 3 Advances in Mathematics 3 Journal of the Mathematical Society of Japan 3 Mathematische Annalen 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Stochastic Analysis and Applications 3 Revista Matemática Iberoamericana 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Journal of Mathematical Sciences (New York) 3 Integral Transforms and Special Functions 3 Bernoulli 3 Acta Mathematica Sinica. English Series 2 Israel Journal of Mathematics 2 Journal of Statistical Physics 2 Mathematical Notes 2 Annales de l’Institut Fourier 2 Duke Mathematical Journal 2 Mathematische Zeitschrift 2 Proceedings of the Japan Academy. Series A 2 Results in Mathematics 2 Journal of Theoretical Probability 2 Communications in Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Doklady Mathematics 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Russian Mathematical Surveys 1 Theory of Probability and its Applications 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Polonici Mathematici 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Publications Mathématiques 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of Multivariate Analysis 1 Kodai Mathematical Journal 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Probabilités et Applications 1 Science in China. Series A 1 Japan Journal of Industrial and Applied Mathematics 1 Differential Geometry and its Applications 1 Expositiones Mathematicae 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Stochastics and Stochastics Reports 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Calculus of Variations and Partial Differential Equations 1 Applied and Computational Harmonic Analysis 1 Kyushu Journal of Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Positivity 1 Annals of Mathematics. Second Series 1 Communications in Contemporary Mathematics 1 Annales Henri Poincaré 1 Brazilian Journal of Probability and Statistics 1 Journal of Nonlinear Mathematical Physics 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Mediterranean Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal of the Korean Statistical Society 1 Complex Analysis and Operator Theory 1 Electronic Journal of Statistics 1 Discrete and Continuous Dynamical Systems. Series S ...and 1 more Serials
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#### Cited in 37 Fields
235 Probability theory and stochastic processes (60-XX) 98 Global analysis, analysis on manifolds (58-XX) 70 Operator theory (47-XX) 68 Partial differential equations (35-XX) 50 Functional analysis (46-XX) 42 Quantum theory (81-XX) 30 Potential theory (31-XX) 24 Differential geometry (53-XX) 22 Measure and integration (28-XX) 15 Real functions (26-XX) 13 Topological groups, Lie groups (22-XX) 13 Special functions (33-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Dynamical systems and ergodic theory (37-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 7 Statistical mechanics, structure of matter (82-XX) 4 Number theory (11-XX) 4 Ordinary differential equations (34-XX) 4 Difference and functional equations (39-XX) 4 Abstract harmonic analysis (43-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Functions of a complex variable (30-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Combinatorics (05-XX) 2 Nonassociative rings and algebras (17-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Numerical analysis (65-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-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. | 2021-06-22T17:50:59 | {"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": 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": 0.5046452283859253, "perplexity": 3871.8313670972652}, "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-2021-25/segments/1623488519183.85/warc/CC-MAIN-20210622155328-20210622185328-00084.warc.gz"} |
https://nbviewer.org/github/barbagroup/jupyter-tutorial/blob/master/3--Jupyter%20like%20a%20pro.ipynb | # Jupyter like a pro¶
In this third notebook of the tutorial "The World of Jupyter", we want to leave you with pro tips for using Jupyter in your future work.
## Importing libraries¶
First, a word on importing libraries. Previously, we used the following command to load all the functions in the NumPy library:
import numpy
Once you execute that command in a code cell, you call any NumPy function by prepending the library name, e.g., numpy.linspace(), numpy.ones(), numpy.zeros(), numpy.empty(), numpy.copy(), and so on (explore the documentation for these very useful functions!).
But, you will find a lot of sample code online that uses a different syntax for importing. They will do:
import numpy as np
All this does is create an alias for numpy with the shorter string np, so you then would call a NumPy function like this: np.linspace(). This is just an alternative way of doing it, for lazy people that find it too long to type numpy and want to save 3 characters each time. For the not-lazy, typing numpy is more readable and beautiful. We like it better like this:
In [1]:
import numpy
When you make a plot using Matplotlib, you have many options to make your plots beautiful and publication-ready. Here are some of our favorite tricks.
First, let's load the pyplot module—and remember, %matplotlib notebook gets our plots inside the notebook (instead of a pop-up).
Our first trick is rcparams: we use it to customize the appearance of the plots. Here, we set the default font to a serif type of size 14 pt and make the size of the font for the axes labels 18 pt. Honestly, the default font is too small.
In [2]:
from matplotlib import pyplot
%matplotlib notebook
pyplot.rcParams['font.family'] = 'serif'
pyplot.rcParams['font.size'] = 14
pyplot.rcParams['axes.labelsize'] = 18
The following example is from a tutorial by Dr. Justin Bois, a lecturer in Biology and Biological Engineering at Caltech, for his class in Data Analysis in the Biological Sciences (2015). He has given us permission to use it.
In [3]:
# Get an array of 100 evenly spaced points from 0 to 2*pi
x = numpy.linspace(0.0, 2.0 * numpy.pi, 100)
# Make a pointwise function of x with exp(sin(x))
y = numpy.exp(numpy.sin(x))
Here, we added comments in the Python code with the # mark. Comments are often useful not only for others who read the code, but as a "note to self" for the future you!
Let's see how the plot looks with the new font settings we gave Matplotlib, and make the plot more friendly by adding axis labels. This is always a good idea!
In [4]:
pyplot.figure()
pyplot.plot(x, y, color='k', linestyle='-')
pyplot.xlabel('$x$')
pyplot.ylabel('$\mathrm{e}^{\sin(x)}$')
pyplot.xlim(0.0, 2.0 * numpy.pi);
Did you see how Matplotlib understands LaTeX mathematics? That is beautiful. The function pyplot.xlim() specifies the limits of the x-axis (you can also manually specify the y-axis, if the defaults are not good for you).
Continuing with the tutorial example by Justin Bois, let's have some mathematical fun and numerically compute the derivative of this function, using finite differences. We need to apply the following mathematical formula on all the discrete points of the x array:
$$\frac{\mathrm{d}y(x_i)}{\mathrm{d}x} \approx \frac{y(x_{i+1}) - y(x_i)}{x_{i+1} - x_i}.$$
By the way, did you notice how we can typeset beautiful mathematics within a markdown cell? The Jupyter notebook is happy typesetting mathematics using LaTeX syntax.
Since this notebook is "Jupyter like a pro," we will define a custom Python function to compute the forward difference. It is good form to define custon functions to make your code modular and reusable.
In [5]:
def forward_diff(y, x):
"""Compute derivative by forward differencing."""
# Use numpy.empty to make an empty array to put our derivatives in
deriv = numpy.empty(y.size - 1)
# Use a for-loop to go through each point and compute the derivative.
for i in range(deriv.size):
deriv[i] = (y[i+1] - y[i]) / (x[i+1] - x[i])
# Return the derivative (a NumPy array)
return deriv
# Call the function to perform finite differencing
deriv = forward_diff(y, x)
Notice how we define a function with the def statement, followed by our custom name for the fuction, the function arguments in parenthesis, and ending the statement with a colon. The contents of the function are indicated by the indentation (four spaces, in this case), and the return statement indicates what the function returns to the code that called it (in this case, the contents of the variable deriv). Right after the function definition (in between triple quotes) is the docstring, a short text documenting what the function does. It is good form to always write docstrings for your functions!
In our custom forward_diff() function, we used numpy.empty() to create an empty array of length y.size-1, that is, one less than the length of the array y. Then, we start a for-loop that iterates over values of i using the range() function of Python. This is a very useful function that you should think about for a little bit. What it does is create a list of integers. If you give it just one argument, it's a "stop" argument: range(stop) creates a list of integers from 0 to stop-1, i.e., the list has stop numbers in it because it always starts at zero. But you can also give it a "start" and "step" argument.
Experiment with this, if you need to. It's important that you internalize the way range() works. Go ahead and create a new code cell, and try things like:
for i in range(5):
print(i)
changing the arguments of range(). (Note how we end the for statement with a colon.) Now think for a bit: how many numbers does the list have in the case of our custom function forward_diff()?
Now, we will make a plot of the numerical derivative of $\exp(\sin(x))$. We can also compare with the analytical derivative:
$$\frac{\mathrm{d}y}{\mathrm{d}x} = \mathrm{e}^{\sin x}\,\cos x = y \cos x,$$
In [6]:
deriv_exact = y * numpy.cos(x) # analytical derivative
pyplot.figure()
pyplot.plot((x[1:] + x[:-1]) / 2.0, deriv,
label='numerical',
marker='.', color='gray',
linestyle='None', markersize=10)
pyplot.plot(x, deriv_exact,
label='analytical',
color='k', linestyle='-') # analytical derivative in black line
pyplot.xlabel('$x$')
pyplot.ylabel('$\mathrm{d}y/\mathrm{d}x$')
pyplot.xlim(0.0, 2.0 * numpy.pi)
pyplot.legend(loc='upper center', numpoints=1);
Stop for a bit and look at the first pyplot.plot() call above. The square brackets normally are how you access a particular element of an array via its index: x[0] is the first element of x, and x[i+1] is the i-th element. What's very cool is that you can also use negative indices: they indicate counting backwards from the end of the array, so x[-1] is the last element of x.
A neat trick of arrays is called slicing: picking elements using the colon notation. Its general form is x[start:stop:step]. Note that, like the range() function, the stop index is exclusive, i.e., x[stop] is not included in the result.
For example, this code will give the odd numbers from 1 to 7:
x = numpy.array( [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] )
x[1:-1:2]
Try it! Remember, Python arrays are indexed from 0, so x[1] is the second element. The end-point in the slice above is index -1, that's the last array element (not included in the result), and we're stepping by 2, i.e., every other element. If the step is not given, it defaults to 1. If start is not given, it defaults to the first array element, and if stop is not given, it defaults to the last element. Try several variations on the slice, until you're comfortable with it.
## There's a built-in for that¶
Here's another pro tip: whenever you find yourself writing a custom function for something that seems that a lot of people might use, find out first if there's a built-in for that. In this case, NumPy does indeed have a built-in for taking the numerical derivative by differencing! Check it out. We also use the function numpy.allclose() to check if the two results are close.
In [7]:
numpy_deriv = numpy.diff(y) / numpy.diff(x)
print('Are the two results close? {}'.format(numpy.allclose(numpy_deriv, deriv)))
Are the two results close? True
Not only is the code much more compact and easy to read with the built-in NumPy function for the numerical derivative ... it is also much faster:
In [8]:
%timeit numpy_deriv = numpy.diff(y) / numpy.diff(x)
%timeit deriv = forward_diff(y, x)
100000 loops, best of 3: 13.4 µs per loop
10000 loops, best of 3: 75.2 µs per loop
NumPy functions will always be faster than equivalent code you write yourself because at the heart they use pre-compiled code and highly optimized numerical libraries, like BLAS and LAPACK.
## Do math like a pro¶
Do you want to compute the integral of $y(x) = \mathrm{e}^{\sin x}$? Of course you do. We find the analytical integral using the integral formulas for modified Bessel functions:
$$\int_0^{2\pi}\mathrm{d} x\, \mathrm{e}^{\sin x} = 2\pi \,I_0(1),$$
where $I_0$ is the modified Bessel function of the first kind. But if you don't have your special-functions handbook handy, we can find the integral with Python. We just need the right modules from the SciPy library. SciPy has a module of special functions, including Bessel functions, called scipy.special. Let's get that loaded, then use it to compute the exact integral:
In [9]:
import scipy.special
exact_integral = 2.0 * numpy.pi * scipy.special.iv(0, 1.0)
print('Exact integral: {}'.format(exact_integral))
Exact integral: 7.95492652101
Or instead, we may want to compute the integral numerically, via the trapezoid rule. The integral is over one period of a periodic function, so only the constant term of its Fourier series will contribute (the periodic terms integrate to zero). The constant Fourier term is the mean of the function over the interval, and the integral is the area of a rectangle: $2\pi \langle y(x)\rangle_x$. Sampling $y$ at $n$ evenly spaced points over the interval of length $2\pi$, we have:
\begin{align} \int_0^{2\pi}\mathrm{d} x\, y(x) \approx \frac{2\pi}{n}\sum_{i=0}^{n} y(x_i), \end{align}
NumPy gives as a mean method to quickly get the sum:
In [10]:
approx_integral = 2.0 * numpy.pi * y[:-1].mean()
print('Approximate integral: {}'.format(approx_integral))
print('Error: {}'.format(exact_integral - approx_integral))
Approximate integral: 7.95492652101
Error: 0.0
In [11]:
approx_integral = 2.0 * numpy.pi * numpy.mean(y[:-1])
print('Approximate integral: {}'.format(approx_integral))
print('Error: {}'.format(exact_integral - approx_integral))
Approximate integral: 7.95492652101
Error: 0.0
The syntax y.mean() applies the mean() NumPy method to the array y. Here, we apply the method to a slice of y that does not include the last element (see discussion of slicing above). We could have also done numpy.mean(y[:-1]) (the function equivalent of the method mean() applied to an array); they give equivalent results and which one you choose is a matter of style.
## Beautiful interactive plots with Bokeh¶
Matplotlib will be your workhorse for creating plots in notebooks. But it's not the only game in town! A recent new player is Bokeh, a visualization library to make amazing interactive plots and share them online. It can also handle very large data sets with excellent performance.
If you installed Anaconda in your system, you will probably already have Bokeh. You can check if it's there by running the conda list command. If you installed Miniconda, you will need to install it with conda install bokeh.
After installing Bokeh, we have many modules available: bokeh.plotting gives you the ability to create interactive figures with zoom, pan, resize, save, and other tools.
In [12]:
from bokeh import plotting as bplotting
Bokeh integrates with Jupyter notebooks by calling the output function, as follows:
In [13]:
bplotting.output_notebook()
In [14]:
# create a new Bokeh plot with axis labels, name it "bop"
bop = bplotting.figure(x_axis_label='x', y_axis_label='dy/dx')
# add a title, change the font
bop.title = "Derivative of exp(sin(x))"
bop.title_text_font = "palatino"
# add a line with legend and line thickness to "bop"
bop.line(x, deriv_exact, legend="analytical", line_width=2)
# add circle markers with legend, specify color
bop.circle((x[1:] + x[:-1]) / 2.0, deriv, legend="numerical", fill_color="gray", size=8, line_color=None)
bop.grid.grid_line_alpha=0.3
bplotting.show(bop);
Note—As of June 2016 (v.0.11.1), Bokeh does not support LaTeX on axis labels. This is an issue they are working on, so stay tuned!
Look at the neat tools on the Bokeh figure: you can zoom in to any portion to explore the data, you can drag the plot area around, resize and finally save the figure to a file. You also have many beautiful styling options!
# Optional next step: get interactive with Lorenz¶
We found two really cool ways for you to get interactive with the Lorenz equations! Try out the interactive blog post by Tim Head on Exploring the Lorenz equations (January 2016), and learn about IPython widgets. Or, check out the Lorentz example on Bokeh plots. Better yet, try them both.
(c) 2016 Lorena A. Barba. Free to use under Creative Commons Attribution CC-BY 4.0 License. This notebook was written for the tutorial "The world of Jupyter" at the Huazhong University of Science and Technology (HUST), Wuhan, China.
Example from Justin Bois (c) 2015 also under a CC-BY 4.0 License. | 2022-10-02T19:43:36 | {"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": 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": 1, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.36572226881980896, "perplexity": 1827.3429948739474}, "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/1664030337339.70/warc/CC-MAIN-20221002181356-20221002211356-00333.warc.gz"} |
https://par.nsf.gov/biblio/10391768-target-selection-validation-desi-luminous-red-galaxies | Target Selection and Validation of DESI Luminous Red Galaxies
Abstract
The Dark Energy Spectroscopic Instrument (DESI) is carrying out a five-year survey that aims to measure the redshifts of tens of millions of galaxies and quasars, including 8 million luminous red galaxies (LRGs) in the redshift range 0.4 <z≲ 1.0. Here we present the selection of the DESI LRG sample and assess its spectroscopic performance using data from Survey Validation (SV) and the first two months of the Main Survey. The DESI LRG sample, selected usingg,r,z, andW1 photometry from the DESI Legacy Imaging Surveys, is highly robust against imaging systematics. The sample has a target density of 605 deg−2and a comoving number density of 5 × 10−4h3Mpc−3in 0.4 <z< 0.8; this is a significantly higher density than previous LRG surveys (such as SDSS, BOSS, and eBOSS) while also extending toz∼ 1. After applying a bright star veto mask developed for the sample, 98.9% of the observed LRG targets yield confident redshifts (with a catastrophic failure rate of 0.2% in the confident redshifts), and only 0.5% of the LRG targets are stellar contamination. The LRG redshift efficiency varies with source brightness and effective exposure time, and we present a simple model that accurately characterizes this dependence. In the appendices, we more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10391768
Journal Name:
The Astronomical Journal
Volume:
165
Issue:
2
Page Range or eLocation-ID:
Article No. 58
ISSN:
0004-6256
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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1. Abstract
We present the characteristics of 2 mm selected sources from the largest Atacama Large Millimeter/submillimeter Array (ALMA) blank-field contiguous survey conducted to date, the Mapping Obscuration to Reionization with ALMA (MORA) survey covering 184 arcmin2at 2 mm. Twelve of 13 detections above 5σare attributed to emission from galaxies, 11 of which are dominated by cold dust emission. These sources have a median redshift of$〈z2mm〉=3.6−0.3+0.4$primarily based on optical/near-infrared photometric redshifts with some spectroscopic redshifts, with 77% ± 11% of sources atz> 3 and 38% ± 12% of sources atz> 4. This implies that 2 mm selection is an efficient method for identifying the highest-redshift dusty star-forming galaxies (DSFGs). Lower-redshift DSFGs (z< 3) are far more numerous than those atz> 3 yet are likely to drop out at 2 mm. MORA shows that DSFGs with star formation rates in excess of 300Myr−1and a relative rarity of ∼10−5Mpc−3contribute ∼30% to the integrated star formation rate density at 3 <z< 6. The volume density of 2 mm selected DSFGs is consistent with predictions from some cosmological simulations and is similar to the volume density of their hypothesized descendants: massive, quiescent galaxies atz> 2. Analysis of MORA sources’more »
2. Abstract
A key component of the Dark Energy Spectroscopic Instrument (DESI) survey validation (SV) is a detailed visual inspection (VI) of the optical spectroscopic data to quantify key survey metrics. In this paper we present results from VI of the quasar survey using deep coadded SV spectra. We show that the majority (≈70%) of the main-survey targets are spectroscopically confirmed as quasars, with ≈16% galaxies, ≈6% stars, and ≈8% low-quality spectra lacking reliable features. A nonnegligible fraction of the quasars are misidentified by the standard spectroscopic pipeline, but we show that the majority can be recovered using post-pipeline “afterburner” quasar-identification approaches. We combine these “afterburners” with our standard pipeline to create a modified pipeline to increase the overall quasar yield. At the depth of the main DESI survey, both pipelines achieve a good-redshift purity (reliable redshifts measured within 3000 km s−1) of ≈99%; however, the modified pipeline recovers ≈94% of the visually inspected quasars, as compared to ≈86% from the standard pipeline. We demonstrate that both pipelines achieve a median redshift precision and accuracy of ≈100 km s−1and ≈70 km s−1, respectively. We constructed composite spectra to investigate why some quasars are missed by the standard pipeline and find thatmore »
3. Abstract
Far-ultraviolet (FUV; ∼1200–2000 Å) spectra are fundamental to our understanding of star-forming galaxies, providing a unique window on massive stellar populations, chemical evolution, feedback processes, and reionization. The launch of the James Webb Space Telescope will soon usher in a new era, pushing the UV spectroscopic frontier to higher redshifts than ever before; however, its success hinges on a comprehensive understanding of the massive star populations and gas conditions that power the observed UV spectral features. This requires a level of detail that is only possible with a combination of ample wavelength coverage, signal-to-noise, spectral-resolution, and sample diversity that has not yet been achieved by any FUV spectral database. We present the Cosmic Origins Spectrograph Legacy Spectroscopic Survey (CLASSY) treasury and its first high-level science product, the CLASSY atlas. CLASSY builds on the Hubble Space Telescope (HST) archive to construct the first high-quality (S/N1500 Å≳ 5/resel), high-resolution (R∼ 15,000) FUV spectral database of 45 nearby (0.002 <z< 0.182) star-forming galaxies. The CLASSY atlas, available to the public via the CLASSY website, is the result of optimally extracting and coadding 170 archival+new spectra from 312 orbits of HST observations. The CLASSY sample covers a broad range of properties including stellarmore »
4. Abstract
We present environmental analyses for 13 KPNO International Spectroscopic Survey Green Pea (GP) galaxies. These galaxies were discovered via their strong [Oiii] emission in the redshift range 0.29 <z< 0.42, and they are undergoing a major burst of star formation. A primary goal of this study is to understand what role the environment plays in driving the current star formation activity. By studying the environments around these extreme star-forming galaxies, we can learn more about what triggers their star formation processes and how they fit into the narrative of galaxy evolution. Using the Hydra multifiber spectrograph on the WIYN 3.5 m telescope, we mapped out the galaxy distribution around each of the GPs (out to ∼15 Mpc at the redshifts of the targets). Using three density analysis methodologies chosen for their compatibility with the geometry of our redshift survey, we categorized the galaxian densities of the GPs into different density regimes. We find that the GPs in our sample tend to be located in low-density environments. We find no correlation between the density and the SFRs seen in the GPs. We conclude that the environments the GPs are found in are likely not the driving factor behind their extrememore »
5. Abstract
We present a search for extreme emission line galaxies (EELGs) atz< 1 in the COSMOS and North Ecliptic Pole (NEP) fields with imaging from Subaru/Hyper Suprime-Cam (HSC) and a combination of new and existing spectroscopy. We select EELGs on the basis of substantial excess flux in thezbroad band, which is sensitive to Hαat 0.3 ≲z≲ 0.42 and [Oiii]λ5007 at 0.7 ≲z≲ 0.86. We identify 10,470 galaxies withzexcesses in the COSMOS data set and 91,385 in the NEP field. We cross-reference the COSMOS EELG sample with the zCOSMOS and DEIMOS 10k spectral catalogs, finding 1395 spectroscopic matches. We made an additional 71 (46 unique) spectroscopic measurements withY< 23 using the HYDRA multiobject spectrograph on the WIYN 3.5 m telescope, and 204 spectroscopic measurements from the DEIMOS spectrograph on the Keck II telescope, providing a total of 1441/10,470 spectroscopic redshifts for the EELG sample in COSMOS (∼14%). We confirm that 1418 (∼98%) are Hαor [Oiii]λ5007 emitters in the above stated redshift ranges. We also identify 240 redshifted Hαand [Oiii]λ5007 emitters in the NEP using spectra taken with WIYN/HYDRA and Keck/DEIMOS. Using broadband-selection techniques in thegricolor space, we distinguish between Hαand [Oiii]λ5007 emitters with 98.6% accuracy. We test our EELG selection bymore » | 2023-03-31T09:47:36 | {"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": 0.5901031494140625, "perplexity": 6244.69113276436}, "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/1679296949598.87/warc/CC-MAIN-20230331082653-20230331112653-00679.warc.gz"} |
https://par.nsf.gov/biblio/10149423-cosmic-explorer-contribution-gravitational-wave-astronomy-beyond-ligo | Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO
This white paper describes the research and development needed over the next decade to realize "Cosmic Explorer," the U.S. node of a future third-generation detector network that will be capable of observing and characterizing compact gravitational-wave sources to cosmological redshifts.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10149423
Journal Name:
2019 BAAS 51(7) 035 / arXiv:1907.04833 | 2023-03-26T19:52:31 | {"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": 0.8524843454360962, "perplexity": 14173.653910694025}, "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/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00064.warc.gz"} |
http://trilinos.sandia.gov/packages/docs/r6.0/packages/nox/doc/html/classNOX_1_1StatusTest_1_1NormF.html | # NOX::StatusTest::NormF Class Reference
Various convergence tests based on the norm of the residual. More...
#include <NOX_StatusTest_NormF.H>
Inheritance diagram for NOX::StatusTest::NormF:
[legend]
Collaboration diagram for NOX::StatusTest::NormF:
[legend]
List of all members.
## Public Types
enum ScaleType { Unscaled, Scaled }
Type that determines whether to scale the norm by the problem size. More...
enum ToleranceType { Relative, Absolute }
Type that determines whether the norm is absolute or relative to the intial guess. More...
## Public Member Functions
NormF (double tolerance, NOX::Abstract::Vector::NormType ntype, ScaleType stype=Scaled)
Constructor for absolute norm.
NormF (double tolerance, ScaleType stype=Scaled)
Constructor for absolute norm.
NormF (NOX::Abstract::Group &initialGuess, double tolerance, NOX::Abstract::Vector::NormType ntype, ScaleType stype=Scaled)
Constructor with initial guess (for relative norms).
NormF (NOX::Abstract::Group &initialGuess, double tolerance, ScaleType stype=Scaled)
Constructor with initial guess (for relative norms).
virtual ~NormF ()
Destructor.
virtual NOX::StatusTest::StatusType checkStatus (const NOX::Solver::Generic &problem)
Test the stopping criterion
virtual NOX::StatusTest::StatusType checkStatusEfficiently (const NOX::Solver::Generic &problem, NOX::StatusTest::CheckType checkType)
Test the stopping criterion efficiently
virtual NOX::StatusTest::StatusType getStatus () const
Return the result of the most recent checkStatus call.
virtual ostream & print (ostream &stream, int indent=0) const
Output formatted description of stopping test to output stream.
virtual double getNormF () const
Returns the value of the F-norm computed in the last call to checkStatus.
virtual double getTrueTolerance () const
Returns the true tolerance.
virtual double getSpecifiedTolerance () const
Returns the specified tolerance set in the constructor.
virtual double getInitialTolerance () const
Returns the initial tolerance.
## Detailed Description
Various convergence tests based on the norm of the residual.
Use the constructor to define the test based on the type of scaling (see ScaleType) and the type of Tolerance (see Tolerance).
If checkStatus is called with the type set to NOX::StatusTest::None, then the status is set to NOX::StatusTest::Unevaluated and returned. (Also #normF is set to 0.0.)
If checkStatus is called on a problem where the solution group does not have F evaluated (i.e., problem.getSolutionGroup().isF() is false), then the status is set to NOX::StatusTest::Unconverged and returned. (Also #normF is set to -1.0.)
Finally, we return NOX::StatusTest::Converged if , and NOX::StatusTest::Unconverged otherwise. Here represents the norm of and represents the tolerance, as described below.
Let denote an optional scale factor defined as
• if sType in the constructor is NOX::NormF::Scaled, and
Then is defined as follows:
• If nType in the constructor is Abstract::Vector::TWO, then
• If nType in the constructor is Abstract::Vector::ONE, then
• If nType in the constructor is Abstract::Vector::INF, then
We set as follows, based on the value of tolerance in the constructor.
• If an initial guess is provided, we use a relative tolerance defined by
Here is the (as defined above) associated with the initial guess.
• Otherwise, we use an absolute tolerance defined by
## Member Enumeration Documentation
Type that determines whether to scale the norm by the problem size.
Enumeration values:
Unscaled No norm scaling. Scaled Scale the norm by the length of the vector.
Type that determines whether the norm is absolute or relative to the intial guess.
Enumeration values:
Relative Relative to starting guess. Absolute Absolute.
## Constructor & Destructor Documentation
NOX::StatusTest::NormF::NormF ( double tolerance, NOX::Abstract::Vector::NormType ntype, ScaleType stype = Scaled )
Constructor for absolute norm. This constructor defaults to the Absolute tolerance type.
NOX::StatusTest::NormF::NormF ( double tolerance, ScaleType stype = Scaled )
Constructor for absolute norm. This constructor defaults to the Absolute ToleranceType and TWO NormType.
NOX::StatusTest::NormF::NormF ( NOX::Abstract::Group & initialGuess, double tolerance, NOX::Abstract::Vector::NormType ntype, ScaleType stype = Scaled )
Constructor with initial guess (for relative norms). This constructor defaults to the Relative tolerance type.
NOX::StatusTest::NormF::NormF ( NOX::Abstract::Group & initialGuess, double tolerance, ScaleType stype = Scaled )
Constructor with initial guess (for relative norms). This constructor defaults to the Relative ToleranceType and TWO NormType.
## Member Function Documentation
NOX::StatusTest::StatusType NOX::StatusTest::NormF::checkStatusEfficiently ( const NOX::Solver::Generic & problem, NOX::StatusTest::CheckType checkType ) [virtual]
Test the stopping criterion efficiently The test can (and should, if possible) be skipped if checkType is NOX::StatusType::None. If the test is skipped, then the status should be set to NOX::StatusTest::Unevaluated. Reimplemented from NOX::StatusTest::Generic.
The documentation for this class was generated from the following files:
• NOX_StatusTest_NormF.H
• NOX_StatusTest_NormF.C
Generated on Thu Sep 18 12:40:52 2008 for NOX by 1.3.9.1 | 2014-07-29T10:51:35 | {"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": 0.6732480525970459, "perplexity": 13160.045411584373}, "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-2014-23/segments/1406510267075.55/warc/CC-MAIN-20140728011747-00471-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.hadar-simulator.org/assets/notebook/Get%20Started/ | Except where otherwise noted, this content is Copyright (c) 2020, RTE and licensed under a CC-BY-4.0 license.
## Hadar is a adequacy python library for deterministic and stochastic computation¶
Each kind of network has a needs of adequacy. On one side, some network nodes need to consume items such as watt, litter, package. And other side, some network nodes produce items. Applying adequacy on network, is tring to find the best available exchanges to avoid any lack at the best cost.
For example, a electric grid can have some nodes wich produce too more power and some nodes wich produce not enough power.
In this case, at t=0, A produce 10 more and B need 10 more. Then nodes are well balanced. And at t=2, B produce 10 more and A need 10 more.
For this example, perform adequacy will done ten quantities exachanges from A to B, then zero and at the end 10 quantities from B to A.
Hadar compute adequacy from simple to complex network. For example, to compute above network, just few line need::
Firstly, install hadar : pip install hadar
In [1]:
import hadar as hd
In [2]:
study = hd.Study(horizon=3)\
.network()\
.node('a')\
.consumption(cost=10 ** 6, quantity=[20, 20, 20], name='load')\
.production(cost=10, quantity=[30, 20, 10], name='prod')\
.node('b')\
.consumption(cost=10 ** 6, quantity=[20, 20, 20], name='load')\
.production(cost=10, quantity=[10, 20, 30], name='prod')\
.link(src='a', dest='b', quantity=[10, 10, 10], cost=2)\
.link(src='b', dest='a', quantity=[10, 10, 10], cost=2)\
.build()
In [3]:
optimizer = hd.LPOptimizer()
res = optimizer.solve(study)
Then you can analyze by yourself result or use hadar aggragator and plotting
In [4]:
plot = hd.HTMLPlotting(agg=hd.ResultAnalyzer(study, res),
node_coord={'a': [2.33, 48.86], 'b': [4.38, 50.83]})
In [5]:
plot.network().node('a').stack() | 2021-06-24T23:00:53 | {"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": 0.6265987157821655, "perplexity": 8455.354916702443}, "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-2021-25/segments/1623488559139.95/warc/CC-MAIN-20210624202437-20210624232437-00048.warc.gz"} |
https://indico.fnal.gov/contributionListDisplay.py?confId=2658 | # XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010)
from June 28, 2010 to July 2, 2010 (US/Central)
Fermilab
US/Central timezone
Home > Contribution List
Displaying 92 contributions out of 92
Type: Invited Session: Hadronic cross sections
Using the Froissart bound as a unifying theme, I will show that the experimental data for hadronic crosssections, from nucleon-nucleon, pion-proton, gamma-p and gamma*-p, are all consistent with a high energy behavior saturating the Froissart bound, all rising with energy as log^2(s). Using analyticity constraints that tie in very accurate low-energy total cross section measurements for pp ... More
Presented by Prof. Martin BLOCK on 29 Jun 2010 at 1:20 PM
Type: Poster Session: Poster Session I
Track: Extensive air shower experiments
<p>A recommencement of CR researches with a unique X-Ray emulsion chamber (XREC) located at a high-altitude experimental site at the Pamirs (4360 m a.s.l.) in the framework of the Pamir-Chacaltaya International Scientific Research Center, recently established by the Governments of the Russian Federation and Tajikistan (2008), opens up a possibility for deep upgrading of the experimental setup and ... More
Presented by Dr. Alexander BORISOV on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
For a long time the three main components of extensive air showers have been measured at the Yakutsk array: the whole charged component, muons with e_{th} \ge 1 GeV and Cherenkov light. Using these data we reconstruct energy of primary cosmic particle (with quasi-colorimetric method), estimate the depth of shower maximum (by the shape of charged particles lateral distribution and a pulse shape ... More
Presented by Dr. Stanislav KNURENKO on 1 Jul 2010 at 12:05 PM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
We present preliminary results from the most recent data on the absolute yield of fluorescence photons in atmospheric gases by the AIRFLY collaboration. Currently, the uncertainty in the yield forms the dominant contribution to the systematic uncertainty in the Pierre Auger Observatory's energy spectrum, and are at the level of 10%. Data were taken in 2009 and 2010 at the test beam facility, ... More
Presented by Dr. Frederick KUEHN on 1 Jul 2010 at 1:50 PM
Type: Invited Session: Introductory presentations
Track: Accelerator data
I shall present selected examples of accelerator data, mainly from hadron colliders, that are relevant for understanding cosmic ray showers. I focus on the forward region, x(Feynman) > 0.05, where high energy data are scarce, since the emphasis in collider physics became high-pT phenomena. I discuss whether that situation can be improved.
Presented by Dr. Michael ALBROW on 28 Jun 2010 at 9:00 AM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
Abstract: The Telescope Array experiment is the largest cosmic ray experiment in the northern hemisphere. It consists of a surface detector (SD) of 507 scintillation counters and three fluorescence stations overlooking the SD. We develop new techniques for estimating cosmic ray energies and calculating the aperture for TA SD which utilize an accurate CORSIKA Monte Carlo (MC) simulation of natural ... More
Presented by Mr. Dmitri IVANOV on 1 Jul 2010 at 11:50 AM
Type: Contributed Session: Emulsion chambers
Track: Emulsion chambers
Analysis on a especial event with a main characteristics of Centauro type events, i.e. mean transverse momentum of hadrons in an order of 1 GeV/c will be presented. In spite of this event (Centauro V) doesn’t show the aspect of pioneer event (Centauro I), that is the upper part of the detector has more particles than the lower part, the event Centauro V shows other common characteristics of Cent ... More
Presented by Dr. EDISON HIROYUKI SHIBUYA on 1 Jul 2010 at 3:15 PM
Type: Contributed Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
It has been suggested that events such as supernovae, gamma ray bursts (GRBs) and motion of the Sun perpendicular to the galactic plane may expose the Earth to an enhanced flux of high energy Cosmic Rays (HECRs). The electromagnetic component of the resulting air showers leads to an increase in ionization and dissociation in the atmosphere which results in a series of chemical reactions. These re ... More
Presented by Mr. Dimitra ATRI on 29 Jun 2010 at 12:05 PM
Type: Invited Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
Direct measurements of cosmic rays with satellite or balloon-borne detectors are used for understanding cosmic ray origin, acceleration and propagation, exploring the supernova acceleration limit, and searching for exotic sources such as dark matter. Their energy reach is currently limited to ~10^15 eV by the detector size and exposure time, but incident particles are identified element-by-element ... More
Presented by Prof. Eun-Suk SEO on 29 Jun 2010 at 9:40 AM
Type: Invited Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
Using high-performance superconducting or permanent magnets coupled with precision detector systems, magnetic-rigidity spectrometers have the unique ability to completely identify incident particles by charge, charge-sign, mass, and energy. Magnetic spectrometers are central to measurements of cosmic antiparticles and the spectra of light isotopes and elements. Positron and antiproton spectra meas ... More
Presented by Dr. John MITCHELL on 29 Jun 2010 at 8:50 AM
Type: Contributed Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
We are planning to observe cosmic gamma-ray in the energy range 10MeV to 100GeV by balloon-borne gamma-ray telescope with nuclear emulsion. Nuclear emulsion is a precise tracker. By detecting starting point of electron pair, gamma-ray direction can be determined precisely (1.4mrad@1-2GeV). This is much better than Fermi Gamma-ray Space Telescope launched June 2008. Now we are developing the gamma- ... More
Presented by Dr. Satoru TAKAHASHI on 29 Jun 2010 at 11:20 AM
Type: Contributed Session: Extensive air shower experiments
Track: Extensive air shower experiments
We review the different definitions of the age parameter used in the lateral and longitudinal electron distributions. In order to remove ambiguities in the interpretation of the experimental data, we have compared simulations with CORSIKA carried simultaneously with the options NKG and EGS. The effect of the positron annihilation cross section missing in the NKG approach is pointed out for small ... More
Presented by Prof. Jean-Noël CAPDEVIELLE on 1 Jul 2010 at 9:15 AM
Type: Poster Session: Poster Session I
Track: Experiments above the Ankle
Progress in the study of high energy cosmic ray physics is limited by low flux. In order to collect substantial statistics above $10^{19}$~eV, the two largest ground arrays currently in operation cover 800~$\mbox{km}^2$ (Telescope Array, Utah) and 3000~$\mbox{km}^2$ (Auger Observatory, Argentina). The logistics and cost of an order-of-magnitude increase in ground array aperture is prohibitive. In ... More
Presented by Mr. Isaac MYERS on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
CASTOR, a very forward (5.2<η<6.6) Čerenkov-light, tungsten/quartz calorimeter was installed and commissioned at CMS (LHC) in 2009. The calorimeter, with 16-fold φ-segmentation, 14-fold z-segmentation (224 channels) and 10λ(int), has been obtaining data since November 2009. The physics to be addressed with CASTOR include forward energy flow in pp, AA and pA, critical for the screening of EAS M ... More
Presented by Prof. Edwin NORBECK on 28 Jun 2010 at 5:00 PM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
Present results of the LHC (up to 26 PeV in the Lab. system) are a very small lever arm for the extrapolation of models up to 100 EeV. However, the measurements of CMS exhibit a central pseudo rapidity density larger than the prediction of the different models. Introducing on this basis new guidelines, with larger multiplicities in the models inserted in thesimulation, we examine the consequences ... More
Presented by Prof. Jean-Noël CAPDEVIELLE on 30 Jun 2010 at 9:15 AM
Type: Poster Session: Poster Session I
Track: Anisotropy
Extragalactic diffuse background radiation blocks the propagation of TeV γ-ray over large distances (z>0.1) by producing electron-positron pairs. As a result, primary spectrum of gamma-source is changed, depending on spectrum of background light. So, a hard spectra of Active Galactic Nuclei with high red shifts of 0.03 – 1.8 allow to determine an absorption by Extragalactic Background Light and ... More
Presented by Dr. Vera Yurievna SINITSYNA on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Extensive air shower experiments
Track: Extensive air shower experiments
IceTop air shower array, as the surface component of the IceCube Neutrino Observatory at the South Pole, is now 92% complete and taking data with 73 stations. The detector will study the mass composition of primary cosmic rays from the knee up to about 1 EeV. In this talk the performance of IceTop, and the preliminary results in the energy range of 1 PeV to 80 PeV will be reported.
Presented by Dr. Serap TILAV on 30 Jun 2010 at 12:05 PM
Type: Invited Session: Anisotropy
Track: Anisotropy
A review will be given of what is known, and surmised about magnetic fields in space, from our Milky Way to the distant Universe well beyond the GZK horizon. Various analysis methods are described. These include Faraday rotation (RM) measures of extragalactic radio sources, Faraday probes of the cosmic background radiation, and the recent detection of faint diffuse synchrotron radiation in extra ... More
Presented by Prof. Philipp KRONBERG on 2 Jul 2010 at 9:05 AM
Type: Poster Session: Poster Session I
Track: Emulsion chambers
The Ne spectra for EAS and EAS with gamma-families are analyzed (Experiment "Hadron"-Tien-Shan).Presence thin structure (peaks) in EAS spectrum with gamma-families and necessity of simultaneous approximation of two spectra (EAS and EAS+γ) essentially the same mass composition limits possible models of nucleus individual spectra. The elementary variant of model when spectra of all five nuclear gro ... More
Presented by Prof. Sergey SHAULOV on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Extensive air shower experiments
Track: Extensive air shower experiments
The Tibet hybrid air shower experiment is composed by an air-shower core detector array and the air-shower array (and a large muon detector from October, 2010), that has been operated at Yangbajing (4300 m above sea level) in Tibet, China, since 1996. This multi-detector system is used for the search for high energy celestial gamma-ray and cosmic ray sources, and for the study of the chemical co ... More
Presented by Prof. Yuqian MA on 30 Jun 2010 at 10:05 AM
Type: Invited Session: Introductory presentations
Track: Introductory presentations
Important new results in four areas of particle astrophysics are on the agenda of this conference: atmospheric leptons; direct measurements of composition and spectrum to 100 TeV; air shower measurements from the knee to the ankle; and the upper end of the cosmic-ray spectrum. Each of these topics has a long history, with the techniques and the basic questions being established early on. What is ... More
Presented by Prof. Thomas GAISSER on 28 Jun 2010 at 9:50 AM
Type: Invited Session: Summary lectures
Track: Summary lectures
Presented by Prof. Paul SOMMERS on 2 Jul 2010 at 1:30 PM
Type: Poster Session: Poster Session I
Track: Extensive air shower experiments
The history of ultra-high energy cosmic ray observation is now approaching 50 years. However, until quite recently, the full simulation of an extensive air shower was computationally impossible due to the vast quantity of daughter particles involved. However, with the advent of modern cluster computing, simulations that once would have taken years to complete can be done in a matter of hours or ev ... More
Presented by Dr. Benjamin STOKES on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Experiments above the Ankle
Track: Experiments above the Ankle
Final results from the HiRes experiment on the spectrum, composition and anisotropy of ultra-high energy cosmic rays will be presented. Stereo and monocular data analysis will be described. The HiRes experiment has observed the Greisen-Zatsepin-Kuzmin cutoff. This analysis and evidence for a light composition of cosmic rays to the highest energies will be presented. Recent results on anisotropy re ... More
Presented by Prof. Pierre SOKOLSKY on 1 Jul 2010 at 9:30 AM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
The Large Hadron Collider (LHC) at CERN (Geneva, Switzerland) has successfully started operation in 2009. Collisions of protons at energies of 7 TeV are being provided to the experiments, the highest center-of-mass energy ever achieved in accelerators. The ALICE experiment at the LHC is designed for the investigation of heavy-ion collisions, but it is also well suited for studies of pp collisions. ... More
Presented by Dr. Henner BUESCHING on 29 Jun 2010 at 8:30 AM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
First pp collisions at sqrt(s) = 0.9 and 7 TeV have been recorded by the LHCb detector using a minimum bias trigger. These data are very valuable to commission the detector and trigger algorithms, but will also be used to perform a number of interesting minimum bias physics measurements, in the forward region covered by the LHCb detector (polar angles between 15 and 300 mrad), amongst which measur ... More
Presented by Mr. Christian LINN on 28 Jun 2010 at 5:15 PM
Type: Poster Session: Poster Session I
Track: Muons
By using the integral methods in the muon propagation through water, we calculate the range fluctuation of high and ultra high energy muons. Many authors divide all radiative processes into two part, namely, the continuous part and stochastic part in their Monte Carlo simulation in order to consider the fluctuation in the both range and energies of the muons, while we treat all radiative processes ... More
Presented by Dr. Nobusuke TAKAHASHI on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Anisotropy
Track: Anisotropy
The quest for sources of ultrahigh energy cosmic rays has long been associated with the search of their secondary gamma ray signatures. While propagating, the former indeed produce very high energy photons through the interactions with particles of the intergalactic medium, or by synchrotron emission in the presence of substantial magnetic fields. We examine the prospects for the detectability ... More
Presented by Dr. Kumiko KOTERA on 2 Jul 2010 at 11:15 AM
Type: Invited Session: Emulsion chambers
Track: Emulsion chambers
The Chacaltaya hybrid experiment together with emulsion chamber and EAS-array can detect air-showers by the air-shower array, the accompanied atmospheric families (a bundle of high energy electrons and gamma-rays) by emulsion chambers and hadrons by burst detectors just under the emulsion chambers. We study overall characteristics of the experimental data, gamma-families and hadron burs ... More
Presented by Dr. Masanobu TAMADA on 1 Jul 2010 at 2:40 PM
Type: Invited Session: Experiments above the Ankle
Track: Experiments above the Ankle
Presented by Prof. Pierre SOKOLSKY
Type: Poster Session: Poster Session I
High-energy neutrinos, arising from decays of mesons that were produced through the cosmic rays collisions with air nuclei, form unavoidable background noise in the astrophysical neutrino detection problem. The atmospheric neutrino flux above 1 PeV should be supposedly dominated by the contribution of charmed particle decays. These (prompt) neutrinos originated from decays of massive shortlived ... More
Presented by Prof. Sergei SINEGOVSKY on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Anisotropy
Track: Anisotropy
Non-trivial toplogical properties of string world sheets with three boundaries can give rise to superpotentials which preserve supersymmetry but violate R-symmetry by two units. This results in four point functions which permit s-wave annihilation of two neutralinos into gauge bosons. If the topological partition function is such as to allow saturation of the WMAP dark matter density for low stri ... More
Presented by Prof. Luis ANCHORDOQUI on 2 Jul 2010 at 9:50 AM
Type: Poster Session: Poster Session I
Track: Emulsion chambers
Analysis of various data accumulated in X-ray emulsion chamber experiments, especially, data on gamma–hadron families with unusual characteristics (Centauros, aligned events etc.), requires a comprehensive computer code to simulate propagation of electromagnetic and various-type hadron particles through a sandwich-like medium of emulsion chambers as well as measuring procedures employed for emul ... More
Presented by Dr. Alexander BORISOV on 29 Jun 2010 at 4:30 PM
Type: Poster Session: Poster Session I
Track: Balloon and satellite experiments
New-type coordinate detector is considered which is based on special-purpose integrated circuit designed for detection of charged particles, local amplification and direct transmission of signal into computer. It is shown that such detectors make it possible to achieve a higher coordinate determination accuracy and processing speed as well as to bring down their cost as compared with modern detect ... More
Presented by Prof. Rauf MUKHAMEDSHIN on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
LHCf (Large Hadron Collider forward) is a dedicated experiment to measure the neutral particles emitted around zero degree of LHC interactions. Energy and Pt spectra of photons, pi-zero and neutral hadrons at such forward region are crucial to qualify the existing interaction models and to improve them for cosmic-ray physics. From the end of 2009, LHCf has successfully taken data at LHC col ... More
Presented by Dr. Takashi SAKO on 28 Jun 2010 at 4:30 PM
Type: Invited Session: Muons
Track: Muons
When high energy cosmic rays interact in the stratosphere, mesons are produced in the primary hadronic interactions. The MINOS experiment detects cosmic ray produced muons using two magnetized detectors at underground depths of 220 and 2080 mwe. The muon charge ratio and the variation of muon intensity with atmospheric temperature are used to obtain information on meson production by the primary ... More
Presented by Prof. Philip SCHREINER on 2 Jul 2010 at 12:00 PM
Type: Invited Session: Experiments above the Ankle
Track: Experiments above the Ankle
The Telescope Array (TA) experiment, located in the west desert of Utah, USA, observes ultra-high energy cosmic rays (UHECRs) with energies above 10^18.5 eV. TA employs a surface detector (SD) array and 3 batteries of fluorescence detectors (FDs) to measure extensive air showers. The direction and the energy of incoming cosmic rays are measured by both detectors, and the results can be cross check ... More
Presented by Prof. Masaki FUKUSHIMA on 1 Jul 2010 at 11:10 AM
Type: Invited Session: Muons
Track: Muons
The L3+C is a unique tool in detecting cosmic muons and measuring their momenta in the range of 15-3000 GeV/c. About 1.2 x 10<sup>10</sup> cosmic muon events have been collected during its running period in 1999-2000. With these high quality data many results on cosmic rays and gamma rays have been obtained, for example, the measurement of the atmospheric muon spectrum and the muon charge r ... More
Presented by Prof. Yuqian MA on 2 Jul 2010 at 11:30 AM
Type: Invited Session: Muons
Track: Muons
A measurement is presented of the ratio of positive to negative muon fluxes from cosmic-ray interactions in the atmosphere, using data collected by the CMS detector at ground level and in the underground experimental cavern. Muons were detected in the momentum range from 3 GeV/c to 1 TeV/c. For muon momenta below 100 GeV/c the flux ratio is measured to be a constant 1.2766 ± 0.0032 (stat) ± ... More
Presented by Dr. Gavin HESKETH on 2 Jul 2010 at 11:45 AM
Type: Invited Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
After introducing the general structure of event generators used for simulating cosmic ray interactions we describe the underlying philosophy of the Monte Carlo models EPOS, QGSJET, SIBYLL, and DPMJET. Some of the important assumptions of the models are reviewed in detail and the prediction obtained with the models are discussed. The reliability of the predictions is one of the key questions for w ... More
Presented by Dr. Ralph ENGEL on 29 Jun 2010 at 2:25 PM
Type: Poster Session: Poster Session I
Track: Extensive air shower experiments
Three-level (3340, 1750 and 850 m a.s.l) ATHLET (Almaty Three Level Experimental Technique) complex is built up for investigations in fields of cosmic ray (CR) physics, astrophysics and gamma-ray astronomy of superhigh energies. The ATHLET’s highest part has to include a) 1-km2-area ADRON-M facility with a “dense” location of detectors to detect electromagnetic, hadron, muon, neutron and rad ... More
Presented by Prof. Rauf MUKHAMEDSHIN FOR ATHLET COLLABORATION on 29 Jun 2010 at 4:30 PM
Type: Poster Session: Poster Session I
Track: Emulsion chambers
We present our observations on the various features from the 855 interactions of 14.6 A GeV 28Si in nuclear emulsion. Multiplicity distribution, mean multiplicities, multiplicity correlations of black, grey, shower and helium fragments are studied in this investigation. A comparative study of the results obtained from the interactions at 14.6 A GeV with o ... More
Presented by Mr. Ashwini KUMAR on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
Since 2006, EPOS hadronic interaction model is being used for very high energy cosmic ray analysis. Designed for minimum bias particle physics and used to have a precise description of SPS and RHIC heavy ion collisions, EPOS brought more detailed description of hadronic interactions in air shower development. Thanks to this model it was possible to understand why there was less muons in air shower ... More
Presented by Dr. Tanguy PIEROG on 30 Jun 2010 at 8:30 AM
Type: Poster Session: Poster Session I
Track: Muons
We present results of caslculations of transverse and longitudinal cross sections of photoabsorption on the nucleon target, in a broad region of very small Bjorken x values and not very large photon virtualities, using the two-component model developed by authors in their previous works. The model is based on the generalized vector dominance concept and color dipole approaches. The detailed compar ... More
Presented by Prof. Edgar BUGAEV on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Emulsion chambers
Track: Emulsion chambers
Capability of high coordinate-resolution techniques to study features of hadron-nuclear interactions at superhigh-energies are considered by the example of X-ray emulsion chamber (XREC) techniques. Main results accumulated by this way are discussed. Sensitivity of this approach to hadron-nuclear interaction features is analyzed. Predictions for future LHC experiments are formulated. Some proposals ... More
Presented by Prof. Rauf MUKHAMEDSHIN on 1 Jul 2010 at 2:05 PM
Type: Poster Session: Poster Session I
Track: Balloon and satellite experiments
The positron fraction observed by PAMELA and other experiments up to ~100 GeV is analyzed in terms of models of cosmic-ray propagation. It is shown that generically we expect the positron fraction to reach ~0.6 at energies of several TeV, and its energy dependence bears an intimate but subtle connection with that of the boron to carbon ratio in cosmic rays. The observed positron fraction can be fi ... More
Presented by Mr. Benjamin BURCH on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
Based on the cosmic rays acceleration in the young supernova remnant like environment, electron and positron pair production through the interactions between high energy cosmic rays and radiation background photons is studied. It is found that both the electron/positron excesses and the knee structure of the cosmic ray spectra can be explained with one set of the source parameters.
Presented by Prof. Yuqian MA on 29 Jun 2010 at 11:50 AM
Type: Poster Session: Poster Session I
Track: Anisotropy
Active galactic nuclei (AGNs) appear to be the most plausible source of ultra-high energy cosmic rays (UHECRs), yet there is currently no conclusive evidence for this hypothesis. Correlation between the arrival directions of some UHECRs and the positions of nearby AGNs has been reported for a sample of 27 UHECRs detected by the Pierre Auger Observatory (PAO 2007), although analyses of larger samp ... More
Presented by Ms. Laura WATSON on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Summary lectures
Track: Summary lectures
Presented by Prof. Francis HALZEN on 2 Jul 2010 at 2:50 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
Calculations of fluxes of atmospheric neutrinos and muons from extensive air showers suffer from our lack of knowledge of hadronic production processes. We are dependent of particle production models which suffer from systematics from both model dependent assumptions as well as the data used to tune them. We will present recent published data from NA49, and NA61 experiments as well as present ana ... More
Presented by Dr. Rajendran RAJA on 28 Jun 2010 at 12:00 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
Recent ultra high-energy cosmic ray data hints an increase of heavier nuclei in the composition of the cosmic ray flux, accentuating the importance of more precise nuclear physics input. In this talk recent results from relativistic heavy ion and other nuclear experiments will be summarized and the possible impact of these results on understanding cosmic ray interactions will be discussed.
Presented by Prof. Baha BALANTEKIN on 28 Jun 2010 at 1:30 PM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
We describe the rapidity density distribution and the transverse momentum (p_{t}) distribution in multiple particle production, assuming a simple mechanism. It is an assumed mechanism that the newly produced particles are emitted isotropically from several emitting centers which are distributed on the rapidity axis in CMS. The energy distribution of the emitted particles is an exponential type i ... More
Presented by Dr. AKINORI OHSAWA on 30 Jun 2010 at 9:45 AM
Type: Poster Session: Poster Session I
Track: Accelerator data
In our previous presentation we showed how well the rapidity density distributions and the transverse momentum (p_{T}) distributions at sqrt{s}=22.4, 546 and 1800 GeV are described by our phenomenological formulation. Based on the energy dependence of the values of the parameters, which are obtained by fitting the calculated distributions to those of the experiments, we examine how the present f ... More
Presented by Dr. AKINORI OHSAWA on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Muons
Track: Muons
In the first part of the talk the interesting new results of L3, MINOS and CMS collaborations are briefly discussed from theoretical point of view: an observational evidence of the rise in the muon charge ratio (L3 and MINOS data) at muon energies around 1 TeV and detailed studies of electromagnetic interactions of high energy muons (in a momentum range up to 1 TeV/c) in the medium of CMS detector ... More
Presented by Prof. Edgar BUGAEV on 2 Jul 2010 at 12:15 PM
Type: Poster Session: Poster Session I
Track: Accelerator data
An important approach to studying high-energy cosmic rays is the investigation of the properties of extensive air showers; however, the lateral distribution of particles in simulations of such showers strongly depends on the applied model of low-energy hadronic interactions. It has been shown that many constraints to be applied to these models can be obtained by studying identified-particle spectr ... More
Presented by Dr. Marek SZUBA on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Emulsion chambers
Track: Emulsion chambers
A detailed study of X-Ray emulsion chamber response with ECSim 2.1 computer package adopted from GEANT 3.21 code and suited for imitation of measuring procedures, employed in the Pamir experiment makes it possible to determine more accurately the proton fraction in the primary cosmic ray (PCR) flux at energies around the “knee” E_0=1-100 PeV. In particular, it is shown that the proton fraction ... More
Presented by Dr. Alexander BORISOV on 2 Jul 2010 at 8:50 AM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
The status of CMS concerning the 2009 run and the first data recorded at 7 TeV in 2010 will be reported. After a summary of the LHC and detector performance, including some example of interesting events, the talk will focus to the first results obtained. In particular, emphasis will be given to low-pT QCD physics including charged hadron spectra, the measurement of Bose-Einstein correlations (BEC) ... More
Presented by Dr. Ambra GRESELE on 28 Jun 2010 at 3:00 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
We present relevant results from CDF and D0, including diffractive and elastic scattering, and other inclusive measurements.
Presented by Dr. Mary CONVERY on 28 Jun 2010 at 2:00 PM
Type: Invited Session: Introductory presentations
Track: Introductory presentations
The study of high energy cosmic rays requires a good understanding of the properties of hadronic interactions. Information on the strong interactions can be obtained in experimental studies at accelerators, however the modeling of cosmic rays showers requires an extrapolation of the observations made at accelators with some guidance from theoretical ideas. This talk will review s ... More
Presented by Dr. Paolo LIPARI on 28 Jun 2010 at 11:10 AM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
Only by measurement of extensive air showers it is possible to explore the nature of cosmic ray particles at the highest energies. Most properties can only be obtained from the interpretation of air shower data and are thus depending on predictions of hadronic interaction models at ultra-high energies. We discuss different scenarios of model extrapolations from accelerator data to air showe ... More
Presented by Dr. Ralf ULRICH on 30 Jun 2010 at 9:00 AM
Type: Invited Session: Extensive air shower experiments
Track: Extensive air shower experiments
Status of the GAMMA experiment is presented. The all-particle energy spectrum of the primary cosmic rays at energies 1 – 300 PeV has been obtained on the basis of the GAMMA experimental improved data. The irregularities of the energy spectrum above the knee are discussed in comparison with other experiments. An upper limit of Galactic diffuse gamma ray flux measured with the GAMMA experiment at ... More
Presented by Dr. Romen MARTIROSOV on 30 Jun 2010 at 11:35 AM
Type: Invited Session: Experiments above the Ankle
Track: Experiments above the Ankle
The Pierre Auger Observatory in the southern site of Mendoza, Argentina is the largest cosmic ray detector ever built. Since its completion in 2008, the Observatory is steadily taking data with 3000 km**2 of active detection area, accumulating an unprecedented statistics of high quality events. Results are presented on the energy spectrum of cosmic rays from 10**18 eV to the highest energy, on ... More
Presented by Prof. Paolo PRIVITERA on 1 Jul 2010 at 10:35 AM
Type: Poster Session: Poster Session I
Track: Extensive air shower experiments
The arrival directions of ultrahigh energy extensive air showers (EAS) by Yakutsk, AGASA and P. Auger data are considered. For the first time, the arrival directions of extensive air showers of ultrahigh energy, registered by Yakutsk EAS array more carefully are considered. It is found that the arrival directions of EAS Yakutsk data are correlated with pulsars from side Input of Loca ... More
Presented by Dr. Aleksei A. MIKHAILOV on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
KASCADE-Grande is a large detector array for the measurement of cosmic ray air showers in the primary energy range of 100 TeV to 1 EeV. Due to the multi-detector concept of the experimental set-up, various observables of the electromagnetic, the muonic and for lower primary energies also the hadronic particle component are measured for individual air showers. The experimental data are compared to ... More
Presented by Dr. Donghwa KANG on 30 Jun 2010 at 8:45 AM
Type: Contributed Session: Sensitivity of Monte Carlo models to data
Track: Monte Carlo models
The cosmic ray interaction event generator Sibyll is widely used in extensive air shower simulations for cosmic ray and neutrino experiments. Charm particle production has been added to the Monte Carlo with a phenomenological, non-perturbative model that properly accounts for charm production in the forward direction. As prompt decays of charm can become a significant background for neutrino detec ... More
Presented by Dr. Eun-Joo AHN on 30 Jun 2010 at 9:30 AM
Type: Poster Session: Poster Session I
Track: Balloon and satellite experiments
In the present study, we inspecte a refined sample of 117 bursts from SGR1900+14 observed with RXTE, PCA. We use 10 spectral-models, and the best fitting spectral-models has been found statistically to be the thermal bremsstrahlung and the power-law. Data are analyzed more by model-independent techniques. The global color-color diagrams are obtained with no distinguishable patterns as other objec ... More
Presented by Mr. Mohammed Hasan SOLEIMAN YUSSEF on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
Since the startup of the LHC in December 2009, the ATLAS detector has been accumulating data from collisions at center of mass energies of 900 GeV and 7 TeV. Although the integrated luminosity is still low, it is increasing at an accelerated pace. The data have already made it possible to commission and calibrate the various subdetectors, understand their performance in detail and refine the trigg ... More
Presented by Prof. Georges AZUELOS on 28 Jun 2010 at 2:30 PM
Type: Invited Session: Recent relevant accelerator data and results
Track: Accelerator data
Totem is exploring the forward region at pseudorapidity larger than 3.1; its main goal is the measurement of the total and elastic cross-section at 14 TeV and the study of diffractive physics in the forward region. The experiment is now built and almost completely commissioned; data taking started in December 2009. TOTEM aims at measuring the total cross section beyond 1 TeV/c with the ... More
Presented by Dr. Emilio RADICIONI on 28 Jun 2010 at 4:00 PM
Type: Invited Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
The Alpha Magnetic Spectrometer (AMS) is a major particle physics experiment on the International Space Station (ISS). AMS is a general purpose particle physics spectrometer using the technologies commonly employed at CERN and Fermilab and upgraded for space applications. The properties of the AMS detector are that it will provide a coordinate resolution of 10 microns, a timing resolution of 150 ... More
Presented by Prof. Samuel C.C. TING, Prof. Andrei KOUNINE on 29 Jun 2010 at 11:00 AM
Type: Poster Session: Poster Session I
Track: Accelerator data
Analysis has been done for the emitted particles in (12C, 16O, 22Ne, 28Si) + Emulsion interactions at (4.1-4.5) A GeV/c. The multiplicity of the emitted particles; as a function of the mass-number of the interacting projectiles nuclei; has been calculated. The multiplicity distribution and the average-values of the emitted particles (the experimental-values) are compared with that calculated val ... More
Presented by Prof. Sayed SALEH on 29 Jun 2010 at 4:30 PM
Type: Poster Session: Poster Session I
Track: Balloon and satellite experiments
Mathematical model of experimental conditions on research for primary cosmic radiation (PCR) on the lunar surface and circumlunar orbit is considered. The fundamental possibility of detection of PCR particles is shown by the use of simultaneous detection of three components produced by cascades in the lunar regolith (secondary neutrons, gamma-ray and radio emission) measured by detectors placed on ... More
Presented by Prof. Rauf MUKHAMEDSHIN on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Extensive air shower experiments
Track: Extensive air shower experiments
The Muon Tracking Detector (MTD) in KASCADE-Grande experiment measures with high accuracy muon directions in EAS (Emu>800MeV). In addition, shower directions are determined by the surface detectors with high precision. These two conditions allow to study shower longitudinal development by means of quantities like muon production heights and muon pseudorapidities and lateral distributions of m ... More
Presented by Dr. Paul DOLL on 1 Jul 2010 at 9:00 AM
Type: Invited Session: Welcome
Presented by LOCAL ORGANIZING COMMITTEE on 28 Jun 2010 at 8:45 AM
Type: Poster Session: Poster Session I
Track: Anisotropy
Galaxy clusters have been consider as sources of TeV gamma-rays emitted by high-energy protons and electrons accelerated by large scale structure formation shocks, galactic winds, or active galactic nuclei. The Perseus cluster of galaxies is one of the best studied clusters due to its proximity and its brightness. Galaxy NGC 1275 is the central dominant galaxy of the Perseus Cluster of Galaxies an ... More
Presented by Prof. Vera Georgievna SINITSYNA on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Anisotropy
Track: Anisotropy
Using the Milagro data from 2000 to 2007 containing more than 95 billion events (the largest such data set in existence), we performed a harmonic analysis of the large-scale cosmic-ray anisotropy. We observe an anisotropy with a magnitude around 0.1% for cosmic rays with a median energy of 6 TeV. The dominant feature is a deficit region of depth 0.25% in the direction of the Galactic North Pole ce ... More
Presented by Dr. Jordan GOODMAN on 2 Jul 2010 at 10:30 AM
Type: Invited Session: Colloquium
Track: Summary lectures
Even though cosmic rays have been observed for almost a century, they remain enigmatic messengers from distant regions in space, and many questions about their origin and acceleration are still open. Details of the composition and of the energy spectra of the individual components are required to find answers, but are increasingly difficult to obtain with increasing particle energies. We will revi ... More
Presented by Prof. Dietrich MüLLER on 30 Jun 2010 at 4:00 PM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
We present a new data on Cherenkov light observations obtained during 1994-2009 period, after a modernization of the Yakutsk EAS array. A complex analysis of x_{max} and its fluctuations \sigma(x_{max}) was performed in a wide energy range. With the new data, accord- ing to QGSJet II model, an estimation was made of cosmic rays mass composition for E_0 \sim 10^{17} - 3 \times 10^{19} eV. The ... More
Presented by Dr. Stanislav KNURENKO on 1 Jul 2010 at 1:20 PM
Type: Contributed Session: Balloon and Satellite Experiments
Track: Balloon and satellite experiments
The JEM-EUSO mission explores the origin of the extreme energy comic-rays (EECRs) above 10^20 eV and challenges to the limit of the basic physics, through the observations, of their arrival directions and energies. It is designed to observe more than 1,000 events of EECRs above 7x10^19 eV in its five-year operation with an exposure larger than 1 million km^2 /sr/year. The super-wide-field (60 degr ... More
Presented by Dr. James H. ADAMS, JR. on 29 Jun 2010 at 11:35 AM
Type: Invited Session: Extensive air shower experiments
Track: Extensive air shower experiments
The study of the cosmic ray energy spectrum in the interval 10^16 eV - 10^18 eV results of particular importance for several reasons, one of them is the possible existence of a second knee, other one is the possible presence of a galactic-extragalactic transition in the cosmic ray flux and another one is the prediction from some astrophysical models of a knee ... More
Presented by Dr. Juan Carlos ARTEAGA-VELáZQUEZ on 1 Jul 2010 at 8:30 AM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
Recent measurements suggest free electrons created in ultra-high energy cosmic ray extensive air showers (EAS) can interact with neutral air molecules producing Bremsstrahlung radiation in the microwave regime. The microwave radiation produced is expected to scale with the number of free electrons in the shower, which itself is a function of the energy of the primary particle and atmospheric dept ... More
Presented by Mr. Christopher WILLIAMS on 1 Jul 2010 at 1:35 PM
Type: Poster Session: Poster Session I
Track: Experiments above the Ankle
The Telescope Array's Middle Drum fluorescence detector was constructed using refurbished telescopes from the High Resolution Fly's Eye (HiRes) experiment. As such, there is a direct comparison between these two experiments' fluorescence energy spectra. A progress report will be presented based on over 2 years of collected data by the Middle Drum site of Telescope Array.
Presented by Mr. Douglas RODRIGUEZ on 29 Jun 2010 at 4:30 PM
Type: Contributed Session: Experiments above the Ankle
Track: Experiments above the Ankle
The Telescope Array (TA) experiment is the largest cosmic ray detector in the northern hemisphere. It also operates the largest scintillation counter array in the world. Together with the three fluorescence detectors (FDs), it is optimized to study cosmic rays as independent detectors and in hybrid mode at energies above the ankle structure. The TA low energy extension will add two additio ... More
Presented by Prof. Charles JUI on 1 Jul 2010 at 11:35 AM
Type: Poster Session: Poster Session I
Track: Muons
The WILLI detector, built in IFIN-HH Bucharest, in collaboration with KIT Karlsruhe, is a rotatable modular detector for measuring charge ratio for cosmic muons with energy < 1 GeV. It is under construction a mini-array for measuring the muon charge ratio in Extensive Air Showers. The EAS simulations have been performed with CORSIKA code. The values of the muon flux, calculated with semi-analyti ... More
Presented by Dr. Iliana BRANCUS on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Extensive air shower experiments
Track: Extensive air shower experiments
The GRAPES-3 experiment is a high density array of 400 plastic scintillator detectors and a large (560 sq.m.) area muon detector located at Ooty at an altitude of 2200 m above sea level. The primary objective of this experiment is to study the high energy processes occurring in the universe through a systematic study of composition of primary cosmic rays below and above the `knee', compact sources ... More
Presented by Prof. Sunil GUPTA on 30 Jun 2010 at 11:05 AM
Type: Contributed Session: Hadronic cross sections
The proton-air inelastic cross section measurement at sqrt(s) ~2 TeV from the EAS-TOP Extensive Air Shower experiment is reported. The technique exploits cosmic ray proton primaries, in the energy region \$E_0 = 1.5- 2.5 x 10^15 eV, studying the absorption length of their cascades when detected at maximum development. Primary energies are selected through the EAS muon number, and proton originate ... More
Presented by Dr. Gian Carlo TRINCHERO on 29 Jun 2010 at 2:10 PM
Type: Invited Session: Summary lectures
Track: Summary lectures
Presented by Prof. Angela OLINTO on 2 Jul 2010 at 2:10 PM
Type: Poster Session: Poster Session I
Track: Muons
I present the prototype Threshold Cerenkov Detector with Radial Segmentation; as a part of the detector development and implementation research. The detector has three concentric cylinders, each with a different dielectric medium, and four scintillators that triggers cosmic particles with a time of fly of 5 ns. The radiator is designed to produce more photons as the particles travels into the TCDR ... More
Presented by Dr. Ely LEON on 29 Jun 2010 at 4:30 PM
Type: Poster Session: Poster Session I
Track: Emulsion chambers
The emission of projectile fragments alpha has been studied in 84Kr interactions with nuclei of the nuclear emulsion detector composition at relativistic energy below 2 GeV per nucleon. The angular distribution of projectile fragments alpha in terms of transverse momentum could not be explained by a straight and clean-cut collision geometry hypothesis of Participant – Spectator (PS) Model. There ... More
Presented by Dr. Venktesh SINGH on 29 Jun 2010 at 4:30 PM
Type: Poster Session: Poster Session I
Track: Muons
We calculate high and ultra-high energy upward-going muon neutrino propagation through the Earth and the induced muon energy distribution near the one cubic kilometer detector using the Monte Carlo simulation, according to neutral current interaction. The primary neutrino energies on the surface of the Earth are 1PeV, 1EeV, and 1ZeV. The mean free paths of ultra-high energy neutrino events gen ... More
Presented by Dr. Nobusuke TAKAHASHI on 29 Jun 2010 at 4:30 PM
Type: Invited Session: Welcome
Presented by Dr. Young-Kee KIM on 28 Jun 2010 at 8:50 AM
Type: Invited Session: Joint Experimental-Theoretical Physics Seminar
Track: Summary lectures
Xmax, the depth of maximum number of charged particles in the atmosphere during the longitudinal development of an air shower, is a valuable parameter to understand the nature of cosmic rays. The behaviour of Xmax is closely related to the composition of the primary particle. Hadronic interaction models, which are tuned with accelerator data, are required to understand the composition. Hence past, ... More
Presented by Dr. Eun-Joo AHN, Dr. Ralph ENGEL on 2 Jul 2010 at 4:00 PM
Type: Contributed Session: Emulsion chambers
Track: Emulsion chambers
During last tens years many unusual results which are very difficult to explain in frames of existing theories and models were obtained in cosmic ray investigations. But it is possible to explain all these results if to suppose that some new state of matter with effective mass about TeV and with large orbital momentum appears. This new state of matter can be, for example, quark-gluon plasma, some ... More
Presented by Prof. Anatoly PETRUKHIN on 2 Jul 2010 at 8:30 AM | 2016-09-30T13:34:08 | {"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": 0.5424575209617615, "perplexity": 4711.44422976945}, "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-2016-40/segments/1474738662197.73/warc/CC-MAIN-20160924173742-00193-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://imr.sandia.gov/papers/abstracts/Si811.html | # On Tetrahedralisations of Reduced Chazelle Polyhedra with Interior Steiner Points
The non-convex polyhedron constructed by Chazelle, known as the {\it Chazelle polyhedron}~\cite{Chazelle1984}, establishes a quadratic lower bound on the minimum number of convex pieces for the 3d polyhedron partitioning problem. In this paper, we study the problem of tetrahedralising the Chazelle polyhedron without modifying its exterior boundary. It is motivated by a crucial step in tetrahedral mesh generation in which a set of arbitrary constraints (edges or faces) need to be entirely preserved. The goal of this study is to gain more knowledge about the family of 3d indecomposable polyhedra, and to tetrahedralise them efficiently. The requirement of only using interior Steiner points for the Chazelle polyhedron is extremely challenging. We first cut off the volume of the Chazelle polyhedron by removing the regions that are tetrahedralisable. This leads to a 3d non-convex polyhedron whose vertices are all in the two slightly shifted saddle surfaces which are used to construct the Chazelle polyhedron. We call it the {\it reduced Chazelle polyhedron}. It is an indecomposable polyhedron. We then give a set of $(N+1)^2$ interior Steiner points that ensures the existence of a tetrahedralisation of the reduced Chazelle polyhedron with $4(N+1)$ vertices. Our proof uses a natural correspondence that any sequence of edge flips converting one triangulation of a convex polygon into another gives a tetrahedralization of a 3d polyhedron which have the two triangulations as its boundary. Finally, we exhibit a larger family of reduced Chazelle polyhedra. Our placement of interior Steiner points also applies to tetrahedralise polyhedra in this family. | 2018-07-22T22:02:17 | {"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": 0.586788535118103, "perplexity": 641.0511986346012}, "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-2018-30/segments/1531676594018.55/warc/CC-MAIN-20180722213610-20180722233610-00122.warc.gz"} |
https://finalfantasy.fandom.com/wiki/Twister_(ability) | ## FANDOM
36,590 Pages
Call forth a tornado to damage the surrounding area.
Final Fantasy Tactics description
Twister (ツイスター, Tsuisutā?), also known as Tornado, is a recurring enemy attack in the Final Fantasy series. It usually does Wind-elemental damage to all enemies.
## AppearancesEdit
### Final Fantasy IXEdit
Causes Wind damage to all enemies.
—Description
Twister deals random Wind-elemental damage and is used by Deathguise, both versions of Tiamat, Silver Dragon, and Nova Dragon. It can be learned as a Blue Magic spell for Quina by eating a Red Dragon, Abadon, or the crystal version of Tiamat fought in the Crystal World. It costs 22 MP to use. It can't be reflected and works with Return Magic.
Twister uses the following formula to calculate damage:
$55 * \text{Rand}(1 .. [(Lv + Mag) - 1])$
Twister ignores the target's magic defense.
### Final Fantasy XIII-2Edit
Tornado is the Feral Link of Pleuston and Clione. It deals magic damage to the target and surrounding foes and launches them into the air.
### Final Fantasy XIVEdit
Twister is used during phase 4 of the battle against Twintania, the superboss at the end of Turn 5 of the Binding Coil of Bahamut. The spell places small green tornados at the feet of several randomly-chosen players, which instantly kill any player who touches them. This mechanic requires all players to move as soon as Twintania begins casting the spell, since the twisters are placed where the player was standing at the beginning of the cast.
Whipping whirlwind. Reduces HP by half in an area.
—Description
Twister is an ability used by Lilith. It halves the HP of enemies in an area, essentially making it an area version of Demi. It can be learned by Blue Mages, and costs 20 MP.
#### Final Fantasy Tactics A2: Grimoire of the RiftEdit
Twister is an enemy ability exclusive to the Lamia genus.
### Pictlogica Final FantasyEdit
This article or section is a stub about an ability in Pictlogica Final Fantasy. You can help the Final Fantasy Wiki by expanding it.
This article or section is a stub about an ability in Final Fantasy Airborne Brigade. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Record KeeperEdit
This article or section is a stub about an ability in Final Fantasy Record Keeper. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Brave ExviusEdit
This article or section is a stub about an ability in Final Fantasy Brave Exvius. You can help the Final Fantasy Wiki by expanding it.
## GalleryEdit
This gallery is incomplete and requires Final Fantasy XIII-2 added. You can help the Final Fantasy Wiki by uploading images.
## EtymologyEdit
Twister is another name for a tornado. A tornado is a violently rotating column of air that is in contact with both the surface of the earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud.
Community content is available under CC-BY-SA unless otherwise noted. | 2019-08-22T03:43:00 | {"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": 0.3632664680480957, "perplexity": 6613.6090141595405}, "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-2019-35/segments/1566027316718.64/warc/CC-MAIN-20190822022401-20190822044401-00476.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aheyde.christopher-charles | # zbMATH — the first resource for mathematics
## Heyde, Christopher Charles
Compute Distance To:
Author ID: heyde.christopher-charles Published as: Heyde, C.; Heyde, C. C.; Heyde, Chris; Heyde, Chris C.; Heyde, Christopher C.; Heyde, Christopher Charles External Links: MGP · Wikidata
Documents Indexed: 167 Publications since 1963, including 9 Books Biographic References: 4 Publications
all top 5
#### Co-Authors
98 single-authored 7 Seneta, Eugene 5 Anh, Vo V. 4 Gay, Roger 4 Hall, Peter Gavin 4 Lin, Yanxia 3 Leslie, Julian R. 3 Liu, Shuangzhe 3 Wong, Bernard 2 Basawa, Ishwar V. 2 Brown, Bruce M. 2 Dai, Wangchen 2 Gao, Jiti 2 Leonenko, Nikolai N. 2 Morton, Richard 2 Thavaneswaran, Aerambamoorthy 2 Tieng, Quang Minh 1 Accardi, Luigi 1 Au, K. 1 Becker, Niels G. 1 Chen, Kejing 1 Cohen, Joel E. 1 Dai, Wei 1 Daley, Daryl John 1 Ewens, Warren J. 1 Feigin, Paul David 1 Godambe, Vidyadhar P. 1 Hannan, Edward James 1 Johnstone, Iain M. 1 Kou, Shing-Gang 1 Kou, Steven 1 Kulkarni, Pandu M. 1 Morton, Rebecca B. 1 Najock, D. 1 Nakata, Taisuke 1 Pakes, Anthony G. 1 Peng, Xianhua 1 Prokhorov, Yuriĭ Vasil’evich 1 Pyke, Ronald 1 Rachev, Svetlozar T. 1 Rohatgi, Vijay K. 1 Schuh, Hans-Jürgen 1 Scott, David John 1 Sly, Allan 1 Taylor, Robert Lee 1 Wang, Dingcheng 1 Westcott, Mark 1 Williams, Emlyn R. 1 Wong, Wing-Keung 1 Yang, Yuecheng
all top 5
#### Serials
28 Journal of Applied Probability 11 Stochastic Processes and their Applications 10 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 8 Annals of Mathematical Statistics 7 The Annals of Probability 7 Journal of Statistical Planning and Inference 5 Biometrika 5 Journal of the Royal Statistical Society. Series B 4 Journal of Mathematical Biology 4 Sankhyā. Series A. Methods and Techniques 3 Advances in Applied Probability 3 Bulletin of the Australian Mathematical Society 3 The Australian Journal of Statistics 3 The Mathematical Scientist 3 Journal of the Australian Mathematical Society 3 Lecture Notes in Statistics 2 Journal of Statistical Physics 2 International Statistical Review 2 Operations Research 2 Proceedings of the American Mathematical Society 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Theoretical Population Biology 2 Journal of Time Series Analysis 2 Journal of Applied Mathematics and Stochastic Analysis 2 Statistical Papers 2 Proceedings of the Cambridge Philosophical Society 1 Mathematical Biosciences 1 Annals of the Institute of Statistical Mathematics 1 The Annals of Statistics 1 The Australian Mathematical Society Gazette 1 Canadian Journal of Mathematics 1 Journal of the Korean Mathematical Society 1 Mathematics of Operations Research 1 Statistics & Probability Letters 1 Operations Research Letters 1 Statistical Science 1 Mathematical and Computer Modelling 1 Communications in Statistics. Theory and Methods 1 Mathematical Methods of Operations Research 1 Australian & New Zealand Journal of Statistics 1 Stochastics 1 Bulletin of the International Statistical Institute 1 Institute of Mathematical Statistics Lecture Notes - Monograph Series 1 Journal of Statistical Theory and Practice 1 Springer Series in Statistics
all top 5
#### Fields
91 Probability theory and stochastic processes (60-XX) 72 Statistics (62-XX) 13 Biology and other natural sciences (92-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 History and biography (01-XX) 6 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 2 Numerical analysis (65-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH
140 Publications have been cited 3,401 times in 2,755 Documents Cited by Year
Martingale limit theory and its application. Zbl 0462.60045
Hall, P.; Heyde, C. C.
1980
Quasi-likelihood and its application. A general approach to optimal parameter estimation. Zbl 0879.62076
Heyde, Christopher C.
1997
Quasi-likelihood and optimal estimation. Zbl 0671.62007
Godambe, V. P.; Heyde, C. C.
1987
A supplement to the strong law of large numbers. Zbl 0305.60008
Heyde, C. C.
1975
Itô’s formula with respect to fractional Brownian motion and its application. Zbl 0867.60029
Dai, W.; Heyde, C. C.
1996
Student processes. Zbl 1081.60035
Heyde, C. C.; Leonenko, N. N.
2005
Estimation theory for growth and immigration rates in a multiplicative process. Zbl 0243.60047
Heyde, C. C.; Seneta, E.
1972
On limit theorems for quadratic functions of discrete time series. Zbl 0254.62057
Hannan, E. J.; Heyde, C. C.
1972
On the departure from normality of a certain class of martingales. Zbl 0225.60026
Heyde, C. C.; Brown, B. M.
1970
On large deviation probabilities in the case of attraction to a non- normal stable law. Zbl 0182.22903
Heyde, C. C.
1968
External risk measures and Basel accords. Zbl 1297.91089
Kou, Steven; Peng, Xianhua; Heyde, Chris C.
2013
Extension of a result of Seneta for the super-crtical Galton-Watson process. Zbl 0195.19201
Heyde, C. C.
1970
On large deviation problems for sums of random variables which are not attracted to the normal law. Zbl 0189.51704
Heyde, C. C.
1967
Avoiding the likelihood. Zbl 0905.62014
Heyde, C. C.
1997
Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Zbl 0771.60021
Heyde, C. C.; Gay, R.
1993
Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments. Zbl 0259.60021
Heyde, C. C.; Scott, D. J.
1973
A contribution to the theory of large deviations for sums of independent random variables. Zbl 0158.17001
Heyde, C. C.
1967
Dynamic models of long-memory processes driven by Lévy noise. Zbl 1016.60039
Anh, V. V.; Heyde, C. C.; Leonenko, N. N.
2002
Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims. Zbl 1162.60014
Heyde, C. C.; Wang, Dingcheng
2009
A risky asset model strong dependence through fractal activity time. Zbl 1102.62345
Heyde, C. C.
1999
On a property of the lognormal distribution. Zbl 0114.33802
Heyde, C. C.
1963
On the martingale property of stochastic exponentials. Zbl 1066.60064
Wong, Bernard; Heyde, C. C.
2004
On defining long-range dependence. Zbl 0912.60050
Heyde, C. C.; Yang, Y.
1997
On the central limit theorem for stationary processes. Zbl 0297.60014
Heyde, C. C.
1974
On central limit and iterated logarithm supplements to the martingale convergence theorem. Zbl 0385.60033
Heyde, C. C.
1977
A pair of complementary theorems on convergence rates in the law of large numbers. Zbl 0147.16905
Heyde, C. C.; Rohatgi, V. K.
1967
On the number of terminal vertices in certain random trees with an application to stemma construction in philology. Zbl 0487.60012
Najock, D.; Heyde, C. C.
1982
On the central limit theorem and iterated logarithm law for stationary processes. Zbl 0287.60035
Heyde, C. C.
1975
On the influence of moments on the rate of convergence to the normal distribution. Zbl 0149.14001
Heyde, C. C.
1967
Prediction via estimating functions. Zbl 0929.62096
Thavaneswaran, A.; Heyde, C. C.
1999
On combining quasi-likelihood estimating functions. Zbl 0636.62086
Heyde, C. C.
1987
On asymptotic posterior normality for stochastic processes. Zbl 0408.62073
Heyde, C. C.; Johnstone, I. M.
1979
Asymptotic properties of maximum likelihood estimators for stochastic processes. Zbl 0388.62079
Basawa, I. V.; Feigin, P. D.; Heyde, C. C.
1976
An invariance principle and some convergence rate results for branching processes. Zbl 0212.49505
Heyde, C. C.; Brown, B. M.
1971
Some central limit analogues for super-critical Galton-Watson processes. Zbl 0222.60054
Heyde, C. C.
1971
On the controversy over tailweight of distributions. Zbl 1075.62039
Heyde, C. C.; Kou, S. G.
2004
Parameter estimation of stochastic process with long-range dependence and intermittency. Zbl 0979.62071
Gao, Jiti; Anh, Vo; Heyde, Chris; Tieng, Quang
2001
Characterization of the normal law by the symmetry of a certain conditional distribution. Zbl 0209.50702
Heyde, C. C.
1970
Remarks on efficiency in estimation for branching processes. Zbl 0297.62069
Heyde, C. C.
1975
Notes on ’Estimation theory for growth and immigration rates in a multiplicative process’. Zbl 0294.60063
Heyde, C. C.; Seneta, E.
1974
On the maximum of sums of random variables and the supremum functional for stable processes. Zbl 0192.55003
Heyde, C. C.
1969
A note concerning behaviour of iterated logarithm type. Zbl 0185.46901
Heyde, C. C.
1969
Asymptotics and criticality for a correlated Bernoulli process. Zbl 1088.60013
Heyde, C. C.
2004
Some properties of metrics in a study on convergence to normality. Zbl 0169.20902
Heyde, C. C.
1969
Some renewal theorems with application to a first passage problem. Zbl 0143.19102
Heyde, C. C.
1966
On changes of measure in stochastic volatility models. Zbl 1147.60321
Wong, Bernard; Heyde, C. C.
2006
Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency. Zbl 1059.60024
Gao, Jiti; Anh, Vo; Heyde, Chris
2002
On estimating the variance of the offspring distribution in a simple branching process. Zbl 0305.60044
Heyde, C. C.
1974
Analogues of classical limit theorems for the supercritical Galton-Watson process with immigration. Zbl 0224.60042
Heyde, C. C.; Seneta, E.
1971
On asymptotic quasi-likelihood estimation. Zbl 0684.62067
Heyde, C. C.; Gay, R.
1989
Confidence intervals for demographic projections based on products of random matrices. Zbl 0584.92015
Heyde, C. C.; Cohen, Joel E.
1985
Asymptotic renewal results for a natural generalization of classical renewal theory. Zbl 0166.14003
Heyde, C. C.
1967
On modes of long-range dependence. Zbl 1016.60040
Heyde, C. C.
2002
Some remarks on the moment problem. I. Zbl 0112.10005
Heyde, C. C.
1963
Empirical realities for a minimal description risky asset model. The need for fractal features. Zbl 0999.91070
Heyde, Christopher C.; Liu, Shuangzhe
2001
Stochastic models for fractal processes. Zbl 0954.62099
Anh, V. V.; Heyde, C. C.; Tieng, Q.
1999
On the robustness to small trends of estimation based on the smoothed periodogram. Zbl 0845.62059
Heyde, C. C.; Dai, W.
1996
Fixed sample and asymptotic optimality for classes of estimating functions. Zbl 0684.62066
Heyde, C. C.
1988
Rates of convergence in the martingale central limit theorem. Zbl 0459.60042
Hall, Peter; Heyde, C. C.
1981
On an optimal asymptotic property of the maximum likelihood estimator of a parameter from a stochastic process. Zbl 0387.62068
Heyde, C. C.
1978
On moment measures of departure from the normal and exponential laws. Zbl 0341.60013
Heyde, C. C.; Leslie, J. R.
1976
A nonuniform bound on convergence to normality. Zbl 0323.60021
Heyde, C. C.
1975
On the converse to the iterated logarithm law. Zbl 0159.47303
Heyde, C. C.
1968
Scaling issues for risky asset modelling. Zbl 1166.91016
Heyde, Chris C.
2009
On estimation in conditional heteroskedastic time series models under non-normal distributions. Zbl 1148.62076
Liu, Shuangzhe; Heyde, Chris C.
2008
Nonstandard limit theorem for infinite variance functionals. Zbl 1144.60030
Sly, Allan; Heyde, Chris
2008
Statisticians of the centuries. Zbl 1016.01025
Heyde, C. C. (ed.); Seneta, E. (ed.)
2001
A quasi-likelihood approach to the REML estimating equations. Zbl 0805.62056
Heyde, C. C.
1994
On a class of random field models which allows long range dependence. Zbl 0711.62086
Gay, R.; Heyde, C. C.
1990
The genetic balance between random sampling and random population size. Zbl 0305.92009
Heyde, C. C.; Seneta, E.
1975
Some almost sure convergence theorems for branching processes. Zbl 0212.19703
Heyde, C. C.
1971
Two probability theorems and their application to some first passage problems. Zbl 0124.08501
Heyde, C. C.
1964
Multiple roots in general estimating equations. Zbl 0921.62022
Heyde, C. C.; Morton, R.
1998
On spaces of estimating functions. Zbl 0921.62023
Lin, Y.-X.; Heyde, C. C.
1997
Optimal robust estimation for discrete time stochastic processes. Zbl 0655.62092
Kulkarni, P. M.; Heyde, C. C.
1987
Invariance principles in statistics. Zbl 0473.62043
Heyde, C. C.
1981
Uniform bounding of probability generating functions and the evolution of reproduction rates in birds. Zbl 0385.60070
Heyde, C. C.; Schuh, H.-J.
1978
Quasi-likelihood and generalizing the EM algorithm. Zbl 0853.62021
Heyde, C. C.; Morton, R.
1996
On quasi-likelihood methods and estimation for branching processes and heteroscedastic regression models. Zbl 0781.62135
Heyde, C. C.; Lin, Y.-X.
1992
On martingale limit theory and strong convergence results for stochastic approximation procedures. Zbl 0298.62022
Heyde, C. C.
1974
An iterated logarithm result for martingales and its application in estimation theory for autoregressive processes. Zbl 0258.60039
Heyde, C. C.
1973
A rate of convergence result for the super-critical Galton-Watson process. Zbl 0198.22501
Heyde, C. C.
1970
Special issue on Long-range dependence. Queensland Univ. of Technology, Brisbane, Australia, January 28–30, 1997. Zbl 0929.00050
Anh, V. V. (ed.); Heyde, C. C. (ed.)
1999
New developments in inference for temporal stochastic processes. Zbl 0752.62062
Heyde, C. C.
1992
On assessing the potential severity of an outbreak of a rare infectious disease: A Bayesian approach. Zbl 0426.92020
Heyde, C. C.
1979
On a unified approach to the law of the iterated logarithm for martingales. Zbl 0368.60059
Hall, P. G.; Heyde, C. C.
1976
On the influence of moments on approximations by portion of a Chebyshev series in central limit convergence. Zbl 0215.25502
Heyde, C. C.; Leslie, J. R.
1972
Improved classical limit analogues for Galton-Watson processes with or without immigration. Zbl 0219.60070
Heyde, C. C.; Leslie, J. R.
1971
A limit theorem for random walks with drift. Zbl 0152.16602
Heyde, C. C.
1967
Optimal estimating functions and Wedderburn’s quasi-likelihood. Zbl 0791.62026
Lin, Yan-Xia; Heyde, C. C.
1993
On the asymptotic behavior of random walks on an anisotropic lattice. Zbl 0511.60066
Heyde, C. C.
1982
Optimal estimation of the criticality parameter of a supercritical branching process having random environments. Zbl 0483.60082
Pakes, Anthony G.; Heyde, C. C.
1982
On the growth of the maximum queue length in a stable queue. Zbl 0218.60096
Heyde, C. C.
1971
Variations on a renewal theorem of Smith. Zbl 0233.60073
Heyde, C. C.
1968
Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models. Zbl 1234.62121
Liu, Shuangzhe; Heyde, Chris C.; Wong, Wing-Keung
2011
Some results on inference for stationary processes and queueing systems. Zbl 0786.62088
Heyde, C. C.
1992
On the asymptotic equivalence of $$L_ p$$ metrics for convergence to normality. Zbl 0535.60029
Heyde, C. C.; Nakata, T.
1984
On the survival of a gene represented in a founder population. Zbl 0461.92008
Heyde, C. C.
1981
A log log improvement to the Riemann hypothesis for the Hawkins random sieve. Zbl 0414.60032
Heyde, C. C.
1978
The effect of selection on genetic balance when the population size is varying. Zbl 0355.92016
Heyde, C. C.
1977
External risk measures and Basel accords. Zbl 1297.91089
Kou, Steven; Peng, Xianhua; Heyde, Chris C.
2013
Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models. Zbl 1234.62121
Liu, Shuangzhe; Heyde, Chris C.; Wong, Wing-Keung
2011
Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims. Zbl 1162.60014
Heyde, C. C.; Wang, Dingcheng
2009
Scaling issues for risky asset modelling. Zbl 1166.91016
Heyde, Chris C.
2009
On estimation in conditional heteroskedastic time series models under non-normal distributions. Zbl 1148.62076
Liu, Shuangzhe; Heyde, Chris C.
2008
Nonstandard limit theorem for infinite variance functionals. Zbl 1144.60030
Sly, Allan; Heyde, Chris
2008
On changes of measure in stochastic volatility models. Zbl 1147.60321
Wong, Bernard; Heyde, C. C.
2006
Student processes. Zbl 1081.60035
Heyde, C. C.; Leonenko, N. N.
2005
On the martingale property of stochastic exponentials. Zbl 1066.60064
Wong, Bernard; Heyde, C. C.
2004
On the controversy over tailweight of distributions. Zbl 1075.62039
Heyde, C. C.; Kou, S. G.
2004
Asymptotics and criticality for a correlated Bernoulli process. Zbl 1088.60013
Heyde, C. C.
2004
Dynamic models of long-memory processes driven by Lévy noise. Zbl 1016.60039
Anh, V. V.; Heyde, C. C.; Leonenko, N. N.
2002
Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency. Zbl 1059.60024
Gao, Jiti; Anh, Vo; Heyde, Chris
2002
On modes of long-range dependence. Zbl 1016.60040
Heyde, C. C.
2002
Parameter estimation of stochastic process with long-range dependence and intermittency. Zbl 0979.62071
Gao, Jiti; Anh, Vo; Heyde, Chris; Tieng, Quang
2001
Empirical realities for a minimal description risky asset model. The need for fractal features. Zbl 0999.91070
Heyde, Christopher C.; Liu, Shuangzhe
2001
Statisticians of the centuries. Zbl 1016.01025
Heyde, C. C. (ed.); Seneta, E. (ed.)
2001
A note on filtering for long memory processes. Zbl 1003.62078
Thavaneswaran, A.; Heyde, C. C.
2001
A risky asset model strong dependence through fractal activity time. Zbl 1102.62345
Heyde, C. C.
1999
Prediction via estimating functions. Zbl 0929.62096
Thavaneswaran, A.; Heyde, C. C.
1999
Stochastic models for fractal processes. Zbl 0954.62099
Anh, V. V.; Heyde, C. C.; Tieng, Q.
1999
Special issue on Long-range dependence. Queensland Univ. of Technology, Brisbane, Australia, January 28–30, 1997. Zbl 0929.00050
Anh, V. V. (ed.); Heyde, C. C. (ed.)
1999
Multiple roots in general estimating equations. Zbl 0921.62022
Heyde, C. C.; Morton, R.
1998
Probability towards 2000. Symposium, Columbia Univ., New York, NY, USA, October 2–6, 1995. Zbl 1041.00508
Accardi, L. (ed.); Heyde, C. C. (ed.)
1998
Quasi-likelihood and its application. A general approach to optimal parameter estimation. Zbl 0879.62076
Heyde, Christopher C.
1997
Avoiding the likelihood. Zbl 0905.62014
Heyde, C. C.
1997
On defining long-range dependence. Zbl 0912.60050
Heyde, C. C.; Yang, Y.
1997
On spaces of estimating functions. Zbl 0921.62023
Lin, Y.-X.; Heyde, C. C.
1997
Itô’s formula with respect to fractional Brownian motion and its application. Zbl 0867.60029
Dai, W.; Heyde, C. C.
1996
On the robustness to small trends of estimation based on the smoothed periodogram. Zbl 0845.62059
Heyde, C. C.; Dai, W.
1996
Quasi-likelihood and generalizing the EM algorithm. Zbl 0853.62021
Heyde, C. C.; Morton, R.
1996
On the use of quasi-likelihood for estimation in hidden Markov random fields. Zbl 0848.62052
Heyde, C. C.
1996
A conversation with Joe Gani. Zbl 0955.01545
Heyde, Chris
1995
On the robustness of limit theorems. Zbl 0882.60019
Heyde, C. C.; Dai, W.
1995
On asymptotic optimality of estimating functions. Zbl 0848.62015
Chen, K.; Heyde, C. C.
1995
A quasi-likelihood approach to the REML estimating equations. Zbl 0805.62056
Heyde, C. C.
1994
A quasi-likelihood approach to estimating parameters in diffusion-type processes. Zbl 0804.60067
Heyde, C. C.
1994
Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Zbl 0771.60021
Heyde, C. C.; Gay, R.
1993
Optimal estimating functions and Wedderburn’s quasi-likelihood. Zbl 0791.62026
Lin, Yan-Xia; Heyde, C. C.
1993
Asymptotics for two-dimensional anisotropic random walks. Zbl 0783.60068
Heyde, C. C.
1993
On constrained quasi-likelihood estimation. Zbl 0795.62018
Heyde, C. C.; Morton, R.
1993
On quasi-likelihood methods and estimation for branching processes and heteroscedastic regression models. Zbl 0781.62135
Heyde, C. C.; Lin, Y.-X.
1992
New developments in inference for temporal stochastic processes. Zbl 0752.62062
Heyde, C. C.
1992
Some results on inference for stationary processes and queueing systems. Zbl 0786.62088
Heyde, C. C.
1992
Thoughts on the modelling and identification of random processes and fields subject to possible long-range dependence. Zbl 0761.62128
Heyde, C. C.; Gay, Roger
1992
On best asymptotic confidence intervals for parameters of stochastic processes. Zbl 0745.62027
Heyde, C. C.
1992
Approximate confidence zones in an estimating function context. Zbl 0755.62035
Heyde, C. C.; Lin, Y.-X.
1991
On a class of random field models which allows long range dependence. Zbl 0711.62086
Gay, R.; Heyde, C. C.
1990
On asymptotic quasi-likelihood estimation. Zbl 0684.62067
Heyde, C. C.; Gay, R.
1989
On efficiency for quasi-likelihood and composite quasi-likelihood methods. Zbl 0729.62552
Heyde, C. C.
1989
Fixed sample and asymptotic optimality for classes of estimating functions. Zbl 0684.62066
Heyde, C. C.
1988
Quasi-likelihood and optimal estimation. Zbl 0671.62007
Godambe, V. P.; Heyde, C. C.
1987
On combining quasi-likelihood estimating functions. Zbl 0636.62086
Heyde, C. C.
1987
Optimal robust estimation for discrete time stochastic processes. Zbl 0655.62092
Kulkarni, P. M.; Heyde, C. C.
1987
Confidence intervals for demographic projections based on products of random matrices. Zbl 0584.92015
Heyde, C. C.; Cohen, Joel E.
1985
On inference for demographic projection of small populations. Zbl 1375.91209
Heyde, C. C.
1985
An asymptotic representation for products of random matrices. Zbl 0576.60025
Heyde, C. C.
1985
On the asymptotic equivalence of $$L_ p$$ metrics for convergence to normality. Zbl 0535.60029
Heyde, C. C.; Nakata, T.
1984
On limit theorems for gene survival. Zbl 0567.92007
Heyde, C. C.
1984
An alternative approach to asymptotic results on genetic composition when the population size is varying. Zbl 0531.92014
Heyde, C. C.
1983
On the number of terminal vertices in certain random trees with an application to stemma construction in philology. Zbl 0487.60012
Najock, D.; Heyde, C. C.
1982
On the asymptotic behavior of random walks on an anisotropic lattice. Zbl 0511.60066
Heyde, C. C.
1982
Optimal estimation of the criticality parameter of a supercritical branching process having random environments. Zbl 0483.60082
Pakes, Anthony G.; Heyde, C. C.
1982
The asymptotic behavior of a random walk on a dual-medium lattice. Zbl 0512.60063
Heyde, C. C.; Westcott, M.; Williams, E. R.
1982
The effect of differential reproductive rates on the survival of a gene represented in a founder population. Zbl 0489.92012
Heyde, C. C.
1982
Further results on the survival of a gene represented in a founder population. Zbl 0493.92015
Daley, D. J.; Hall, Peter; Heyde, C. C.
1982
Rates of convergence in the martingale central limit theorem. Zbl 0459.60042
Hall, Peter; Heyde, C. C.
1981
Invariance principles in statistics. Zbl 0473.62043
Heyde, C. C.
1981
On the survival of a gene represented in a founder population. Zbl 0461.92008
Heyde, C. C.
1981
On Fibonacci (or lagged Bienayme-Galton-Watson) branching processes. Zbl 0478.60087
Heyde, C. C.
1981
Martingale limit theory and its application. Zbl 0462.60045
Hall, P.; Heyde, C. C.
1980
On a probabilistic analogue of the Fibonacci sequence. Zbl 0443.60043
Heyde, C. C.
1980
On asymptotic posterior normality for stochastic processes. Zbl 0408.62073
Heyde, C. C.; Johnstone, I. M.
1979
On assessing the potential severity of an outbreak of a rare infectious disease: A Bayesian approach. Zbl 0426.92020
Heyde, C. C.
1979
On an optimal asymptotic property of the maximum likelihood estimator of a parameter from a stochastic process. Zbl 0387.62068
Heyde, C. C.
1978
Uniform bounding of probability generating functions and the evolution of reproduction rates in birds. Zbl 0385.60070
Heyde, C. C.; Schuh, H.-J.
1978
A log log improvement to the Riemann hypothesis for the Hawkins random sieve. Zbl 0414.60032
Heyde, C. C.
1978
On central limit and iterated logarithm supplements to the martingale convergence theorem. Zbl 0385.60033
Heyde, C. C.
1977
The effect of selection on genetic balance when the population size is varying. Zbl 0355.92016
Heyde, C. C.
1977
An optimal property of maximum likelihood with application to branching process estimation. Zbl 0515.62082
Heyde, C. C.
1977
Asymptotic properties of maximum likelihood estimators for stochastic processes. Zbl 0388.62079
Basawa, I. V.; Feigin, P. D.; Heyde, C. C.
1976
On moment measures of departure from the normal and exponential laws. Zbl 0341.60013
Heyde, C. C.; Leslie, J. R.
1976
On a unified approach to the law of the iterated logarithm for martingales. Zbl 0368.60059
Hall, P. G.; Heyde, C. C.
1976
On asymptotic behavior for the Hawkins random sieve. Zbl 0336.60030
Heyde, C. C.
1976
A supplement to the strong law of large numbers. Zbl 0305.60008
Heyde, C. C.
1975
On the central limit theorem and iterated logarithm law for stationary processes. Zbl 0287.60035
Heyde, C. C.
1975
Remarks on efficiency in estimation for branching processes. Zbl 0297.62069
Heyde, C. C.
1975
A nonuniform bound on convergence to normality. Zbl 0323.60021
Heyde, C. C.
1975
The genetic balance between random sampling and random population size. Zbl 0305.92009
Heyde, C. C.; Seneta, E.
1975
On the central limit theorem for stationary processes. Zbl 0297.60014
Heyde, C. C.
1974
Notes on ’Estimation theory for growth and immigration rates in a multiplicative process’. Zbl 0294.60063
Heyde, C. C.; Seneta, E.
1974
On estimating the variance of the offspring distribution in a simple branching process. Zbl 0305.60044
Heyde, C. C.
1974
On martingale limit theory and strong convergence results for stochastic approximation procedures. Zbl 0298.62022
Heyde, C. C.
1974
An iterated logarithm result for autocorrelations of a stationary linear process. Zbl 0283.62084
Heyde, C. C.
1974
Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments. Zbl 0259.60021
Heyde, C. C.; Scott, D. J.
1973
An iterated logarithm result for martingales and its application in estimation theory for autoregressive processes. Zbl 0258.60039
Heyde, C. C.
1973
On the uniform metric in the context of convergence to normality. Zbl 0256.60010
Heyde, C. C.
1973
Revisits for transient random walk. Zbl 0256.60042
Heyde, C. C.
1973
Estimation theory for growth and immigration rates in a multiplicative process. Zbl 0243.60047
Heyde, C. C.; Seneta, E.
1972
On limit theorems for quadratic functions of discrete time series. Zbl 0254.62057
Hannan, E. J.; Heyde, C. C.
1972
...and 40 more Documents
all top 5
#### Cited by 2,999 Authors
47 Heyde, Christopher Charles 44 Leonenko, Nikolai N. 41 Liang, Hanying 33 Hall, Peter Gavin 26 Zhang, Li-Xin 23 Basawa, Ishwar V. 22 Horváth, Lajos 22 Thavaneswaran, Aerambamoorthy 21 Peligrad, Magda 20 Wang, Dehui 19 Hu, Shuhe 18 Merlevède, Florence 18 Phillips, Peter Charles Bonest 18 Volný, Dalibor 17 Mahmoud, Hosam M. 16 Gao, Jiti 16 Seneta, Eugene 15 Anh, Vo V. 15 Dedecker, Jérôme 14 Hu, Feifang 14 Hwang, Sun Young 13 Berkes, István 13 Fort, Gersende 13 Masry, Elias 13 Mykland, Per Aslak 13 Rosalsky, Andrew 13 Yang, Wenzhi 12 Bai, Zhi-Dong 12 Crimaldi, Irene 12 Fu, Ke’ang 12 Koul, Hira Lal 12 Lin, Yanxia 12 Wang, Xuejun 11 Cai, Zongwu 11 Fan, Guoliang 11 Fel’dman, Gennadiĭ Mikhaĭlovich 11 Park, Joon Y. 11 Peng, Liang 11 Wang, Dingcheng 11 Wu, Wei Biao 10 Gut, Allan 10 Laib, Naâmane 10 Li, Deli 10 Lin, Lu 10 Ruiz-Medina, María Dolores 10 Sorensen, Michael 10 Surgailis, Donatas 10 Wang, Qiying 9 Chan, Ngai Hang 9 de Uña-Álvarez, Jacobo 9 Doukhan, Paul 9 Fan, Xiequan 9 Ling, Shiqing 9 Ma, Chunsheng 9 Maller, Ross Arthur 9 Nielsen, Morten Ørregaard 9 Pagès, Gilles 9 Pakes, Anthony G. 9 Qi, Yongcheng 9 Tjøstheim, Dag B. 8 Lin, Jinguan 8 Lin, Zhengyan 8 Liu, Quansheng 8 Mokkadem, Abdelkader 8 Moulines, Eric 8 Rahimov, Ibrahim 8 Sakhno, Lyudmyla Mykhaĭlivna 8 Sunklodas, Jonas Kazys 8 Wang, Yougan 8 Yang, Kai 8 Yin, Gang George 8 Zhang, Lan 7 Appadoo, S. S. 7 Atchadé, Yves F. 7 Comte, Fabienne 7 Fokianos, Konstantinos 7 Glynn, Peter W. 7 Iksanov, Aleksander M. 7 Kifer, Yuri 7 Kokoszka, Piotr S. 7 Lee, Sangyeol 7 Linton, Oliver Bruce 7 Liu, Shuangzhe 7 Mukherjee, Kanchan 7 Nualart, David 7 Pelletier, Mariane 7 Pratelli, Luca 7 Robinson, Peter Michael 7 Rosenberger, William F. 7 Shao, Qi-Man 7 Sikorskii, Alla 7 Sriram, T. N. 7 Su, Chun 7 Woodroofe, Michael Barrett 7 Zang, Qingpei 7 Zhao, Zhiwen 6 Alsmeyer, Gerold 6 Angulo, José Miguel 6 Beran, Jan 6 Bercu, Bernard ...and 2,899 more Authors
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#### Cited in 307 Serials
196 Stochastic Processes and their Applications 187 Statistics & Probability Letters 147 Journal of Econometrics 140 Journal of Statistical Planning and Inference 102 Journal of Multivariate Analysis 81 The Annals of Statistics 79 Communications in Statistics. Theory and Methods 59 Journal of Applied Probability 55 Journal of Time Series Analysis 51 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 49 Bernoulli 47 The Annals of Probability 47 Econometric Theory 45 Probability Theory and Related Fields 45 The Annals of Applied Probability 41 Journal of Theoretical Probability 39 Lithuanian Mathematical Journal 35 Advances in Applied Probability 32 Journal of Mathematical Analysis and Applications 32 Statistics 29 Computational Statistics and Data Analysis 28 Stochastic Analysis and Applications 25 The Canadian Journal of Statistics 25 Annals of the Institute of Statistical Mathematics 25 Journal of Nonparametric Statistics 22 Acta Mathematicae Applicatae Sinica. English Series 20 Electronic Journal of Statistics 19 Journal of Statistical Physics 19 Statistical Papers 19 Acta Mathematica Sinica. English Series 17 Scandinavian Journal of Statistics 17 Journal of the Korean Statistical Society 16 Test 16 Statistical Inference for Stochastic Processes 15 Stochastics and Dynamics 14 Journal of Mathematical Biology 14 Journal of Computational and Applied Mathematics 14 Econometric Reviews 14 Journal of Inequalities and Applications 14 Quantitative Finance 14 Science China. Mathematics 13 Biometrics 13 Mathematical Methods of Statistics 12 Journal of Soviet Mathematics 12 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 12 Methodology and Computing in Applied Probability 11 Communications in Mathematical Physics 11 Mathematical Biosciences 11 Metrika 11 Science in China. Series A 11 Journal of Statistical Computation and Simulation 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Bulletin of the Australian Mathematical Society 10 Transactions of the American Mathematical Society 10 Acta Applicandae Mathematicae 10 Communications in Statistics. Simulation and Computation 9 Theory of Probability and its Applications 9 Automatica 9 Theoretical Population Biology 9 Mathematical and Computer Modelling 9 Economics Letters 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Statistical Methodology 8 Journal of Mathematical Physics 8 Insurance Mathematics & Economics 8 Acta Mathematica Hungarica 8 European Journal of Operational Research 8 Abstract and Applied Analysis 7 Computers & Mathematics with Applications 7 Mathematics and Computers in Simulation 7 Proceedings of the American Mathematical Society 7 Sequential Analysis 7 Queueing Systems 7 Annals of Operations Research 7 Journal of Mathematical Sciences (New York) 7 The Annals of Applied Statistics 6 Stochastics 6 Applied Mathematics and Computation 6 Journal of the American Statistical Association 6 Monatshefte für Mathematik 6 Systems & Control Letters 6 Operations Research Letters 6 Journal of Economic Dynamics & Control 6 Theory of Probability and Mathematical Statistics 6 Mathematical Problems in Engineering 6 Finance and Stochastics 6 Mathematical Finance 6 The Econometrics Journal 6 Brazilian Journal of Probability and Statistics 6 Journal of Systems Science and Complexity 6 Stochastic Models 5 Acta Mathematica Academiae Scientiarum Hungaricae 5 Mathematical Notes 5 Rocky Mountain Journal of Mathematics 5 Siberian Mathematical Journal 5 Computational Statistics 5 Applied Mathematics. Series B (English Edition) 5 International Journal of Theoretical and Applied Finance 5 Statistical Methods and Applications 5 Stochastics ...and 207 more Serials
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#### Cited in 48 Fields
1,594 Statistics (62-XX) 1,555 Probability theory and stochastic processes (60-XX) 248 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 216 Numerical analysis (65-XX) 63 Biology and other natural sciences (92-XX) 57 Systems theory; control (93-XX) 53 Operations research, mathematical programming (90-XX) 50 Dynamical systems and ergodic theory (37-XX) 46 Combinatorics (05-XX) 45 Statistical mechanics, structure of matter (82-XX) 30 Partial differential equations (35-XX) 25 Computer science (68-XX) 23 Measure and integration (28-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 17 Functional analysis (46-XX) 14 Integral transforms, operational calculus (44-XX) 13 History and biography (01-XX) 12 Information and communication theory, circuits (94-XX) 11 Number theory (11-XX) 10 Ordinary differential equations (34-XX) 8 Real functions (26-XX) 7 Operator theory (47-XX) 7 Fluid mechanics (76-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 6 Quantum theory (81-XX) 5 Approximations and expansions (41-XX) 5 Integral equations (45-XX) 5 Geophysics (86-XX) 4 Topological groups, Lie groups (22-XX) 4 Difference and functional equations (39-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Mathematical logic and foundations (03-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-04-11T15:06:34 | {"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": 0.5148235559463501, "perplexity": 4908.508638839929}, "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-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00605.warc.gz"} |
https://math.wikia.org/wiki/Characteristic_polynomial | ## FANDOM
1,168 Pages
The characteristic polynomial of a matrix A is the polynomial satisfies the equation
$|\lambda I_n - A| = 0$
The roots of this function will be the eigenvalues of the matrix.
## Example
Given the matrix
$A = \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix}$
The characteristic polynomial will be
$\begin{vmatrix} \lambda I - \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix} \end{vmatrix} = \begin{vmatrix} \lambda \begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix} - \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix} \end{vmatrix} = 0$
$\begin{vmatrix} \lambda - 3 & 0 \\1 & \lambda + 1 \end{vmatrix} = (\lambda - 3) (\lambda + 1) - (0)(1) = (\lambda - 3) (\lambda + 1) = 0$
The eigenvalues of A will be -1 and 3.
Community content is available under CC-BY-SA unless otherwise noted. | 2019-12-12T02:39:09 | {"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": 0.8521149158477783, "perplexity": 801.0209247039181}, "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-2019-51/segments/1575540536855.78/warc/CC-MAIN-20191212023648-20191212051648-00519.warc.gz"} |
https://par.nsf.gov/biblio/10159380-relative-alignment-between-dense-molecular-cores-ambient-magnetic-field-synergy-numerical-models-observations | Relative alignment between dense molecular cores and ambient magnetic field: the synergy of numerical models and observations
ABSTRACT The role played by magnetic field during star formation is an important topic in astrophysics. We investigate the correlation between the orientation of star-forming cores (as defined by the core major axes) and ambient magnetic field directions in (i) a 3D magnetohydrodynamic simulation, (ii) synthetic observations generated from the simulation at different viewing angles, and (iii) observations of nearby molecular clouds. We find that the results on relative alignment between cores and background magnetic field in synthetic observations slightly disagree with those measured in fully 3D simulation data, which is partly because cores identified in projected 2D maps tend to coexist within filamentary structures, while 3D cores are generally more rounded. In addition, we examine the progression of magnetic field from pc to core scale in the simulation, which is consistent with the anisotropic core formation model that gas preferably flows along the magnetic field towards dense cores. When comparing the observed cores identified from the Green Bank Ammonia Survey and Planck polarization-inferred magnetic field orientations, we find that the relative core–field alignment has a regional dependence among different clouds. More specifically, we find that dense cores in the Taurus molecular cloud tend to align perpendicular to the background more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10159380
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
494
Issue:
2
Page Range or eLocation-ID:
1971 to 1987
ISSN:
0035-8711
5. ABSTRACT We investigate the time evolution of dense cores identified in molecular cloud simulations using dendrograms, which are a common tool to identify hierarchical structure in simulations and observations of star formation. We develop an algorithm to link dendrogram structures through time using the three-dimensional density field from magnetohydrodynamical simulations, thus creating histories for all dense cores in the domain. We find that the population-wide distributions of core properties are relatively invariant in time, and quantities like the core mass function match with observations. Despite this consistency, an individual core may undergo large (>40 per cent), stochastic variations due to the redefinition of the dendrogram structure between time-steps. This variation occurs independent of environment and stellar content. We identify a population of short-lived (<200 kyr) overdensities masquerading as dense cores that may comprise $\sim\!20$ per cent of any time snapshot. Finally, we note the importance of considering the full history of cores when interpreting the origin of the initial mass function; we find that, especially for systems containing multiple stars, the core mass defined by a dendrogram leaf in a snapshot is typically less than the final system stellar mass. This work reinforces that there is no time-stable density contour that defines a star-formingmore » | 2022-12-03T23:35:04 | {"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": 0.6814545392990112, "perplexity": 1621.902106827627}, "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/1669446710941.43/warc/CC-MAIN-20221203212026-20221204002026-00177.warc.gz"} |
https://toontownrewritten.fandom.com/wiki/Cog_Health_Guide | ## FANDOM
2,359 Pages
Guide
A guide is a helpful resource created by users on the wiki that covers a specific topic in detail and help readers gain a better understanding of the topic.
Cogs have a certain number of health points (HP) depending on their level. Cog levels range from level 1 to level 12. Level 1 Cogs have the lowest health points, while level 12 Cogs have the highest health points.
The chart below shows how much HP each Cog level has and what gag can destroy it at once.
## Health by Cog levels
Level Health Points One-hit knock gags
1 6
Cupcake (6 damage)
Flower Pot (10 damage)
Glass of Water (6 damage)
2 12
Banana Peel (12 damage)
Sandbag (18 damage)
3 20 Rake (20 damage)
4 30 Hose (30 damage)
Anvil (30 damage)
Marbles (35 damage)
5 42 Big Weight (45 damage)
Organic Whole Cream Pie (44 Damage)
Quicksand (50 damage)
6 56 Safe (60 damage)
Trap Door (70 damage)
7 72 Organic Trap Door (77 damage)
Storm Cloud (80 damage)
8 90 Opera Singer (90 damage)
Birthday Cake (100 damage)
9 110 Organic Birthday Cake (110 damage)
Organic Geyser (115 damage)
10 132 Organic Wedding Cake (132 damage)
11 156 Grand Piano (170 damage)
TNT (180 damage)
12 200 Organic Railroad (214 damage)
## Formulas
The formula for a Cog's health is the following:
$f(x) = x^{2} + 3x + 2$
Or, in a simplified way:
$f(x) = (x + 1) \times (x + 2)$
Where x is the Cog's level, and f(x) is a function that returns the health value of cogs. For instance, for Level 4 Cogs, who have a health of 30, the formula works in the following way:
$f(4) = (4 + 1) \times (4 + 2)$
$f(4) = (5) \times (6)$
$f(4) = 30$
This formula applies to every Cog level except level 12, which has 200 health points.
In order to get the cog level from a given HP, rather than getting the HP from the level, the HP formula's quadratic formula can be used (where n is the HP):
$x_{1,2} = \frac{-3 \pm \sqrt{9 - 4 * (2 - n)}}{2}$
So, for instance, in order to find which cog has 156 HP, the equation will be solved in the following way:
$x_{1,2} = \frac{-3 \pm \sqrt{9 - 4 * (2 - 156)}}{2}$
$x_{1,2} = \frac{-3 \pm \sqrt{9 - 4 * - 154}}{2}$
$x_{1,2} = \frac{-3 \pm \sqrt{9 + 616}}{2}$
$x_{1,2} = \frac{-3 \pm \sqrt{625}}{2}$
$x_{1,2} = \frac{-3 \pm 25}{2}$
$x_{1} = \frac{-3 - 25}{2} , x_{2} = \frac{-3 + 25}{2}$
$x_{1} = \frac{-28}{2} , x_{2} = \frac{22}{2}$
$x_{1} = -14 , x_{2} = 11$
Since the original equation- f(x)- is a function of a parabola, and since none are the solutions are the function's minimum value, there are two answers for the equation: -14 ,which is not a real Cog level; and 11, which does exist.
Although this formula works for all Toontown Cog levels, when going beyond regular Cog levels, this formula starts to be inapplicable in practice because of complex numbers. For any 'n' value less than -0.25, this equation introduces complex numbers, which still work in theory but not in practice.
## Trivia
• Level 12 Cogs have 200 health points, instead of the expected value from the formula- 182. This is essentially a 10% boost, rounded down. According to the formula, a Cog with 200 health should be about level 12.65 (or about -15.65, though negative values are not compatible with cog levels).
• According to the formula, the Director of Ambush Marketing would have 2,652 health, given that the Director of Ambush Marketing is level 50.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-01-24T06:04:01 | {"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": 0.4471304416656494, "perplexity": 4944.76259802447}, "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/1579250615407.46/warc/CC-MAIN-20200124040939-20200124065939-00437.warc.gz"} |
https://runescape.fandom.com/wiki/Template:Item/doc | ## FANDOM
44,132 Pages
For help editing, using, or reading this template, see Template:Infobox Item/FAQ
This is a documentation subpage for Template:Item.It contains usage information, categories, and other content that is not part of the original template page.
Template:Item invokes Module:Item using Lua.
## Parameters
### name
The name of the item as it appears in game, exactly.
### aka
Alternative name of the item. Avoid duplicate and derivative alternates.
### image
The inventory icon of the item.
### release
Release date of the item as when it became technically available; e.g. the release date of Treasure Hunter items are the date the promo begins, even though they entered the game config earlier.
Format:
|update = [[D MMMM]] [[YYYY]]
### update
Name of the update post associated with the item's release. Do not include Update: prefix or square brackets.
Format:
|update = PAGENAME
### removal
Date when the item was removed from the game. Only applicable for deleted content; i.e. items that are discontinued but still exist should not use this parameter.
Format:
|removal = [[D MMMM]] [[YYYY]]
### removalupdate
Name of the update post associated with the item's removal. Do not include Update: prefix or square brackets.
Format:
|removalupdate = PAGENAME
### members
Whether or not this item is members only.
### quest
If the item is strictly a quest item, link the quest it is from.
Whether or not the item can be traded with other players.
Accepted values (case insensitive):
### bankable
Whether or not this item may be banked. This parameter will be hidden unless it is set to no, and should be omitted if unused.
### stacksinbank
Whether or not this item will stack with itself when inside the bank. This parameter will be hidden unless it is set to no, and should be omitted if unused.
### lendable
Whether or not this item can be lent to other players via the Item Lending system. This parameter will be hidden unless it is set to yes, and should be omitted if unused.
### equipable
Whether or not this item can be equipped.
### stackable
Whether or not this item will stack in the inventory.
### disassembly
Whether or not this item may be disassembled.
Accepted values (case insensitive):
• yes (will create a link to the {{Disassemble}} template at #DisassemblyT)
• no
• restricted (item can only be obtained in a disassembly-free area)
• n/a (item no longer exists or is otherwise impossible to obtain)
### noteable
Whether or not the item may be turned into a bank note. This parameter will be hidden unless it is set to yes, and should be omitted if unused.
### edible
Whether or not the item may be ingested, either as an edible item or a potable beverage. This parameter will be hidden unless it is set to yes, and should be omitted if unused.
### value
The internal value of the item. This parameter only accepts numbers.
### convert
The amount of coins received for converting the item when won on Treasure Hunter or the discontinued Squeal of Fortune.
### alchable
Whether or not the item may be alched (Low Level Alchemy / High Level Alchemy). This parameter will serve no function unless it is set to no, and should be omitted if unused. The default behaviour of items is alchability is true.
Accepted values (case insensitive):
• no
### alchmultiplier
An override for the alchemy multiplier that defines the relationship between value and high alchemy, such that for $M$ multiplier:
$highalch = \lfloor M \times value \rfloor$
Low alchemy is always assumed to be two-thirds of the high alchemy value.
The alchmultiplier parameter only accepts numbers and will default to 0.6. It should generally be unused and omitted.
### destroy
The destruction behaviour of the item or its corresponding message. Items that are dropped should pass the value Drop. Items that are destroyed should pass the text of the confirmation dialogue that is prompted when the "destroy" option is chosen.
### kept
Whether or not the item is kept on death.
Accepted values (case insensitive):
• reclaimable (items that are reclaimable from Death's office)
• never (items always lost on death)
• always (items always kept on death, unless inside the wilderness)
• alwaysinclwild (items always kept on death, including when inside the wilderness)
• dropped (items that are dropped to the floor on death; generally minigame or boss fight items)
• safe (items that can only exist inside safe death areas, and are thus always kept)
### ikod
Override for the item's value with Death. This is the first number listed in the item tooltip in the items kept on death interface.
Module priority in choosing value:
• ikod
• gemw (Grand Exchange value)
• value
### reclaim
Override for the item's reclaim value with Death. This parameter only accepts number values, and should be omitted if unused. The default behaviour is that which is described in the comments of the keptondeatharg function (search "Death formula").
### sacrifice
Override for the item's sacrifice value with Death. This parameter only accepts number values, and should be omitted if unused. The default behaviour is multiplying the reclaim by four (4).
### exchange
Whether or not this item is tradeable on the Grand Exchange. This parameter may be omitted; however, its existence in the code may help lead other editors.
Accepted values (case insensitive):
• gemw (note that "yes" will not serve the same function)
• no (do not add to untradeable items; only applies for tradeable items not in the Grand Exchange. See: Category:Non-GE items for more.)
### gemwname
Use this parameter if the item's name value is different from the location of its Exchange page on the wiki.
### weight
The weight of the item in kilograms (kg). This parameter only accepts numbers; the "kg" should be omitted when written in the source code.
Note that weights in RuneScape have a precision of up to 3 places, or 1 gram (1 g).
### tooltip
Custom tooltips that the item has. Multiple values are supported, separated by a comma. Each value can be one of the following presets, or custom text:
• passive - If the tooltip displays the item's passive effect (shown as Item bonus)
• set - If the tooltip displays the set bonus of an item set the item is part of
• time - If the tooltip displays the item's time remaining
• degrade - If the tooltip displays the degradation level (shown as Item Charge or Charges remaining)
• items - If the tooltip displays an item and the number consumed (ex. Attuned ectoplasmator)
• urn - If the tooltip displays the percentage filled level (for urns)
### examine
The examine text of the item as it appears in game exactly.
### id
The item's internal ID in the game config. Every item has a single ID, though multiple versions of an item may be listed in a single infobox.
### rscid
The item's internal ID in the game config for RuneScape Classic. This parameter should only exist on the few items that were exclusive to RuneScape Classic; it should not appear on any newly created articles.
## Deprecated parameters
### high
Defines the high alchemy value of an item, overriding all other calculations. This parameter should be omitted in favour of either the general formula, or the alchmultiplier parameter unless absolutely necessary.
Same as above.
### store
The price at which an item is sold by stores. This parameter should be deleted in favour of a dynamic listing with {{Store locations list}}. This parameter will no longer display any value.
### seller
Deleted along with the store parameter. This parameter will not display, nor will it add any tracking categories.
### currency
Deleted along with the store parameter. This parameter will not display, nor will it add any tracking categories.
## Defining multiple items at once
Infobox Item supports the ability to display multiple items with a single template. Additional items will be stored quietly and displayed when prompted by user input. Proper display of the switchfobox version requires the reader to have JavaScript enabled.
Additional items are defined with the respective version# parameter. The value passed to this parameter will also define its label to the reader. The module will look for the highest version in an unbroken sequence; i.e. the module begins its search at version1 and will count up until version# does not exist.
When a version is defined, other parameters may be defined for it by using param#, where # is the number of the version. If undefined, param# will default to the value of the unqualified param.
## Blank infobox
{{Infobox Item
|name =
|image =
|release =
|update =
|members =
|quest =
|equipable =
|stackable =
|disassembly =
|noteable =
|value =
|destroy =
|kept =
|exchange =
|tooltip =
|examine =
|weight =
|id =
}}
{{Infobox Item
|name = <!-- The ingame name of the item -->
|image = <!-- [[File:ItemName.png]] -->
|release = <!-- [[D MMMM]] [[YYYY]], e.g. [[1 January]] [[2016]] -->
|update = <!--PAGENAME, of the update without the Update: prefix -->
|members = <!-- yes/no -->
|quest = <!-- [[Quest name]] -->
|equipable = <!-- yes/no -->
|stackable = <!-- yes/no -->
|disassembly = <!-- yes/no/restricted or N/A -->
|value = <!-- value of the item -->
|destroy = <!-- Either no, or the destroy message of the item -->
|kept = <!-- reclaimable/never/always/alwaysinclwild/dropped/safe -->
|examine = <!-- examine text -->
|weight = <!-- weight of the item in kg -->
|id = <!-- the internal game id of the item. -->
<!-- Properties that can be omitted if not applicable -->
|removal = <!-- [[D MMMM]] [[YYYY]], e.g. [[1 January]] [[2016]] -->
|removalupdate = <!--PAGENAME, of the update without the Update: prefix -->
|noteable = <!-- yes if noteable, otherwise empty -->
|exchange = <!-- gemw if on the grand exchange, otherwise omitted -->
|lendable = <!-- yes if lendable -->
|edible = <!-- yes if edible -->
|alchable = <!-- no if not alchable, yes by default -->
|ikod = <!-- amount of gp, only if needed -->
|reclaim = <!-- amount of gp, only if needed -->
|sacrifice = <!-- amount of gp, only if needed -->
|rscid = <!-- id of the item in runescape classic -->
|stacksinbank = <!-- Does the item stack in the bank? Yes by default. -->
|bankable = <!-- can the item be banked? Yes by default -->
|convert = <!-- value obtaine when converting. (Treasure Hunter/Squeel of fortune) -->
|alchmultiplier = <!-- High alch multiplier. Always 0.6 except for some rare exceptions -->
|aka = <!-- Commonly recognised alternative names -->
|tooltip = <!-- if the item has any custom tooltips -->
}}
Community content is available under CC-BY-SA unless otherwise noted. | 2020-03-29T03:49:32 | {"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": 0.22604210674762726, "perplexity": 8484.02802858902}, "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-2020-16/segments/1585370493684.2/warc/CC-MAIN-20200329015008-20200329045008-00184.warc.gz"} |
http://dergipark.gov.tr/atnaa/issue/39947/481339 | Yıl 2018, Cilt 2, Sayı 4, Sayfalar 224 - 237 2018-12-24
| | | |
## Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory
##### 11 31
The focus of the current paper is to prove nonexistence results for the Cauchy
problem of a wave equation with fractional damping and non linear memory.
Our method of proof is based on suitable choices of the test
functions in the weak formulation of the sought solutions.
Damped wave equation, Fujita’s exponent, fractional derivative
• [1] V. Barbu, Partial Differential Equations and Boundry Value Problems. Science + Business media, B. V. Springer. Vol. 441.
• [2] A.A. Kilbas, H.M. Sarisvatana, J.J. Trujillo, Theory and applications of fractional Differential Equations, North-Holland mathematics studies. 204, ELSEVIER 2006.
• [3] H. Fujita, On the Blowing up of solutions of the problem for ut = ∆u+u1+α, Faculty of science, University of Tokyo. 13 (1966) 109-124.
• [4] T. Cazenave, F. Dickstein, F. D. Weissler, An equation whose Fujita critical exponent is not given by scaling, Nonlinear anal. 68 (2008) 862-874.
• [5] A. Fino, Critical exponent for damped wave equations with nonlinear memory, Hal Arch. Ouv. Id: 00473941v2 (2010).
• [6] M. Berbiche, A. Hakem, Finite time blow-up of solutions for damped wave Equation with non linear Memory, Comm. Math. Analysis. (14)(1)(2013) 72-84.
• [7] S. Selberg, Lecture Notes, Math. 632 PDE, http//www.math.ntnu.no/ sselberg, (2001).
• [8] I. Podlubny, Fractional Differetial Equations, Mathematics in science and engineering. Vol 198, University of Kosice,Slovak republic.
• [9] G. Todorova, B. Yardanov, Critical exponent for a non linear wave equation with damping, Journal of Differential equations. 174 (2001) 464-489.
• [10] Qi S. Zhang, A Blow up result for a nonlinear wave equation with damping, C.R. Acad. Sciences, Paris. (2001).
• [11] S. Katayama, Md A. Sheikh, S. Tarama, The Cauchy and mixed problems for semilinear wave equations with damping terms, Math. Japonica. 50 (3) (2000) 459-566.
• [12] S. I. Pohozaev, A. Tesei, Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Cl. Sci. Fis. Math. Natur. Rend. Lincei. 9 Math. App. 11 N◦2 (2000) 99-109.
• [13] E. Mitidieri, S.I. Pohozaev, Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on RN,J. Evol. Equations. (1) (2001) 189-220.
• [14] E. Mitidieri, S.I. Pohozaev, A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov. Inst. Math. 234 (2001) 1-383.
• [15] S.G. Samko, A.A. Kilbas, O. I. Marichev, Fractional Integrals and derivatives, Theory and application, Gordon andBreach Publishers. (1987).
• [16] J.L. Lions, W.A. Strauss, Some nonlinear evolution equations, Bull. Soc. Math. France. 93(1965) 43-96.
• [17] Yuta Wakasugi, On the diffusive structure for the damped wave equation with variable coefficients, doctoral thesis, Graduate school of science, Osaka University. (2014).
• [18] P. Souplet, Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory, Z. angew. Math. Phys. 55(2004) 28-31.
• [19] M.E. Taylor, Partial differential equations III in nonlinear equations, Springer, New York. (1966)
Birincil Dil en Matematik December 2018 Articles Yazar: Tayep Hadj Kaddour (Sorumlu Yazar)Ülke: Algeria Yazar: Ali HakemÜlke: Turkey
Bibtex @araştırma makalesi { atnaa481339, journal = {Advances in the Theory of Nonlinear Analysis and its Application}, issn = {}, eissn = {2587-2648}, address = {Erdal KARAPINAR}, year = {2018}, volume = {2}, pages = {224 - 237}, doi = {10.31197/atnaa.481339}, title = {Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory}, key = {cite}, author = {Hadj Kaddour, Tayep and Hakem, Ali} } APA Hadj Kaddour, T , Hakem, A . (2018). Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory. Advances in the Theory of Nonlinear Analysis and its Application, 2 (4), 224-237. DOI: 10.31197/atnaa.481339 MLA Hadj Kaddour, T , Hakem, A . "Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 224-237 Chicago Hadj Kaddour, T , Hakem, A . "Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 224-237 RIS TY - JOUR T1 - Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory AU - Tayep Hadj Kaddour , Ali Hakem Y1 - 2018 PY - 2018 N1 - doi: 10.31197/atnaa.481339 DO - 10.31197/atnaa.481339 T2 - Advances in the Theory of Nonlinear Analysis and its Application JF - Journal JO - JOR SP - 224 EP - 237 VL - 2 IS - 4 SN - -2587-2648 M3 - doi: 10.31197/atnaa.481339 UR - http://dx.doi.org/10.31197/atnaa.481339 Y2 - 2018 ER - EndNote %0 Advances in the Theory of Nonlinear Analysis and its Application Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory %A Tayep Hadj Kaddour , Ali Hakem %T Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory %D 2018 %J Advances in the Theory of Nonlinear Analysis and its Application %P -2587-2648 %V 2 %N 4 %R doi: 10.31197/atnaa.481339 %U 10.31197/atnaa.481339 ISNAD Hadj Kaddour, Tayep , Hakem, Ali . "Sufficient conditions of non global solution for fractional damped wave equations with non-linear memory". Advances in the Theory of Nonlinear Analysis and its Application 2 / 4 (Aralık 2018): 224-237. http://dx.doi.org/10.31197/atnaa.481339 | 2019-02-20T07:05:36 | {"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": 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": 0.2827410399913788, "perplexity": 6211.98774265536}, "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/1550247494485.54/warc/CC-MAIN-20190220065052-20190220091052-00350.warc.gz"} |
https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Sturm-Zhang-1.html | ## Symmetric primal-dual path following algorithms for semidefinite programming
### Jos Sturm and Shuzhong Zhang
In this paper a symmetric primal-dual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newton search directions for primal-dual path-following algorithms for semidefinite programming. In particular, we generalize: (1) the short step path following algorithm, (2) the predictor-corrector algorithm and (3) the largest step algorithm to semidefinite programming. It is shown that these algorithms require at most ${\cal O}(\sqrt{n}\mid \log \epsilon \mid )$ main iterations for computing an $\epsilon$-optimal solution. The symmetric primal-dual transformation discussed in this paper can be interpreted as a specialization of the scaling-point concept introduced by Nesterov and Todd \cite{NT95} for self-scaled conic problems. The difference is that we explicitly use the usual $v$-space notion and the proofs look very similar to the linear programming case.
Report 9554/A, Econometric Institute, Erasmus University, Rotterdam. | 2021-09-19T17:40:06 | {"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": 0.8766968846321106, "perplexity": 1266.2674998749096}, "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/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00494.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aeckhaus.wiktor | # zbMATH — the first resource for mathematics
## Eckhaus, Wiktor
Compute Distance To:
Author ID: eckhaus.wiktor Published as: Eckhaus, W.; Eckhaus, Wiktor External Links: MGP · Wikidata · GND
Documents Indexed: 53 Publications since 1961, including 9 Books Biographic References: 1 Publication
all top 5
#### Co-Authors
22 single-authored 7 van Harten, Aart 6 Doelman, Arjen 4 Garbey, Marc 3 Brauner, Claude-Michel 3 Calogero, Francesco A. 3 de Jager, Eduard M. 3 Kaper, Tasso J. 3 Peradzyński, Zbigniew 2 Kuske, Rachel A. 1 Besseling, J. F. 1 Cook, L. Pamela 1 DiPrima, Richard C. 1 Duistermaat, Johannes Jisse 1 Iooss, Gérard 1 Moet, Henry Johan Karel 1 Penning, H. P. 1 Schielen, Ralph 1 Schuur, Peter Cornelis 1 Segel, Lee Aaron 1 Trad, A. T. 1 van der Wel, F. V. 1 Verhulst, Ferdinand
all top 5
#### Serials
4 SIAM Journal on Applied Mathematics 4 North-Holland Mathematics Studies 3 Inverse Problems 3 Physica D 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 2 Journal of Fluid Mechanics 1 Archives of Mechanics 1 Archive for Rational Mechanics and Analysis 1 International Journal of Non-Linear Mechanics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Verslag van de Gewone Vergadering van de Afdeling Natuurkunde 1 Studies in Applied Mathematics 1 European Journal of Mechanics. B. Fluids 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Techniques 1 Nieuw Archief voor Wiskunde. Derde Serie 1 Journal of Nonlinear Science 1 Journal of the Aerospace Sciences 1 Journal de Mécanique 1 Epsilon Uitgaven 1 Lecture Notes in Mathematics
all top 5
#### Fields
30 Partial differential equations (35-XX) 20 Ordinary differential equations (34-XX) 13 Fluid mechanics (76-XX) 4 General and overarching topics; collections (00-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Mechanics of particles and systems (70-XX) 3 Biology and other natural sciences (92-XX) 2 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX)
#### Citations contained in zbMATH Open
37 Publications have been cited 802 times in 676 Documents Cited by Year
Studies in non-linear stability theory. Zbl 0125.33101
Eckhaus, W.
1965
Asymptotic analysis of singular perturbations. Zbl 0421.34057
Eckhaus, Wiktor
1979
Relaxation oscillations including a standard chase on French ducks. Zbl 0509.34037
Eckhaus, Wiktor
1983
Matched asymptotic expansions and singular perturbations. Zbl 0255.34002
Eckhaus, Wiktor
1973
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
Calogero, Francesco; Eckhaus, Wiktor
1987
Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Zbl 0151.15101
Eckhaus, W.; de Jager, E. M.
1966
Boundary layers in linear elliptic singular perturbation problems. Zbl 0234.35009
Eckhaus, Wiktor
1972
Non-linear wave-number interaction in near-critical two-dimensional flows. Zbl 0229.76039
Diprima, R. C.; Eckhaus, W.; Segel, L. A.
1971
The inverse scattering transformation and the theory of solitons. An introduction. Zbl 0463.35001
Eckhaus, Wiktor; van Harten, Aart
1981
Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058
Doelman, Arjen; Eckhaus, Wiktor
1991
Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2000
Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2001
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations. Zbl 0677.76046
Eckhaus, Wiktor; Iooss, Gérard
1989
The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions. Zbl 0518.35074
Eckhaus, W.; Schuur, P.
1983
The Ginzburg-Landau manifold is an attractor. Zbl 0797.35070
Eckhaus, W.
1993
Nonlinear evolution equations, rescalings, model PDEs and their integrability. II. Zbl 0702.35210
Calogero, Francesco; Eckhaus, Wiktor
1988
Resonance in a boundary value problem of singular perturbation type. Zbl 0264.34070
Cook, L. Pamela; Eckhaus, W.
1973
Singular perturbations of homoclinic orbits in $${\mathbb{R}{}}^ 4$$. Zbl 0760.34048
Eckhaus, Wiktor
1992
New approach to the asymptotic theory of nonlinear oscillations and wave- propagation. Zbl 0296.34038
Eckhaus, Wiktor
1975
Fundamental concepts of matching. Zbl 0806.35015
Eckhaus, Wiktor
1994
Formal approximations and singular perturbations. Zbl 0384.35007
Eckhaus, Wiktor
1977
Theory of flame-front stability. Zbl 0098.41801
Eckhaus, Wiktor
1961
Asymptotic analysis on large timescales for singular perturbations of hyperbolic type. Zbl 0703.65054
Eckhaus, W.; Garbey, M.
1990
The long-time behaviour for perturbed wave-equations and related problems. Zbl 0629.35085
Eckhaus, Wiktor
1986
A singularly perturbed free boundary problem describing a laser sustained plasma. Zbl 0566.35060
Eckhaus, Wiktor; Van Harten, Aart; Peradzynski, Zbigniew
1985
Theory and applications of singular perturbations. Proceedings of a Conference Held in Oberwolfach, August 16-22, 1981. Zbl 0478.00011
Eckhaus, W. (ed.); de Jager, E. M. (ed.)
1982
Matching principles and composite expansions. Zbl 0374.35007
Eckhaus, Wiktor
1977
Two-body problem with slowly decreasing mass. Zbl 0217.54503
Verhulst, F.; Eckhaus, W.
1970
On water waves at Froude number slightly higher than one and Bond number less than 1/3. Zbl 0764.76008
Eckhaus, Wiktor
1992
Necessary conditions for integrability of nonlinear PDEs. Zbl 0645.35089
Calogero, Francesco; Eckhaus, Wiktor
1987
Asymptotic solutions in free boundary problems of singularly perturbed elliptic variational inequalities. Zbl 0395.35004
Eckhaus, W.; Moet, H. J. K.
1978
Pattern formation in systems with slowly varying geometry. Zbl 0870.35051
Eckhaus, Wiktor; Kuske, Rachel
1997
Analysis of ordinary differential equations. Zbl 1342.34002
Duistermaat, Johannes Jisse; Eckhaus, Wiktor
1995
The theory of ducks. Zbl 0785.34038
Eckhaus, W.
1993
Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation. Zbl 0654.76116
Eckhaus, W.; Van Harten, A.; Peradzyński, Z.
1987
On some basic concepts in the analysis of singular perturbations. Zbl 0492.34047
Eckhaus, Wiktor
1980
Sur l’influence de l’epaisseur dans le problème de diffraction de Sommerfeld. Zbl 0151.43101
1966
Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2001
Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2000
Pattern formation in systems with slowly varying geometry. Zbl 0870.35051
Eckhaus, Wiktor; Kuske, Rachel
1997
Analysis of ordinary differential equations. Zbl 1342.34002
Duistermaat, Johannes Jisse; Eckhaus, Wiktor
1995
Fundamental concepts of matching. Zbl 0806.35015
Eckhaus, Wiktor
1994
The Ginzburg-Landau manifold is an attractor. Zbl 0797.35070
Eckhaus, W.
1993
The theory of ducks. Zbl 0785.34038
Eckhaus, W.
1993
Singular perturbations of homoclinic orbits in $${\mathbb{R}{}}^ 4$$. Zbl 0760.34048
Eckhaus, Wiktor
1992
On water waves at Froude number slightly higher than one and Bond number less than 1/3. Zbl 0764.76008
Eckhaus, Wiktor
1992
Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058
Doelman, Arjen; Eckhaus, Wiktor
1991
Asymptotic analysis on large timescales for singular perturbations of hyperbolic type. Zbl 0703.65054
Eckhaus, W.; Garbey, M.
1990
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations. Zbl 0677.76046
Eckhaus, Wiktor; Iooss, Gérard
1989
Nonlinear evolution equations, rescalings, model PDEs and their integrability. II. Zbl 0702.35210
Calogero, Francesco; Eckhaus, Wiktor
1988
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
Calogero, Francesco; Eckhaus, Wiktor
1987
Necessary conditions for integrability of nonlinear PDEs. Zbl 0645.35089
Calogero, Francesco; Eckhaus, Wiktor
1987
Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation. Zbl 0654.76116
Eckhaus, W.; Van Harten, A.; Peradzyński, Z.
1987
The long-time behaviour for perturbed wave-equations and related problems. Zbl 0629.35085
Eckhaus, Wiktor
1986
A singularly perturbed free boundary problem describing a laser sustained plasma. Zbl 0566.35060
Eckhaus, Wiktor; Van Harten, Aart; Peradzynski, Zbigniew
1985
Relaxation oscillations including a standard chase on French ducks. Zbl 0509.34037
Eckhaus, Wiktor
1983
The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions. Zbl 0518.35074
Eckhaus, W.; Schuur, P.
1983
Theory and applications of singular perturbations. Proceedings of a Conference Held in Oberwolfach, August 16-22, 1981. Zbl 0478.00011
Eckhaus, W. (ed.); de Jager, E. M. (ed.)
1982
The inverse scattering transformation and the theory of solitons. An introduction. Zbl 0463.35001
Eckhaus, Wiktor; van Harten, Aart
1981
On some basic concepts in the analysis of singular perturbations. Zbl 0492.34047
Eckhaus, Wiktor
1980
Asymptotic analysis of singular perturbations. Zbl 0421.34057
Eckhaus, Wiktor
1979
Asymptotic solutions in free boundary problems of singularly perturbed elliptic variational inequalities. Zbl 0395.35004
Eckhaus, W.; Moet, H. J. K.
1978
Formal approximations and singular perturbations. Zbl 0384.35007
Eckhaus, Wiktor
1977
Matching principles and composite expansions. Zbl 0374.35007
Eckhaus, Wiktor
1977
New approach to the asymptotic theory of nonlinear oscillations and wave- propagation. Zbl 0296.34038
Eckhaus, Wiktor
1975
Matched asymptotic expansions and singular perturbations. Zbl 0255.34002
Eckhaus, Wiktor
1973
Resonance in a boundary value problem of singular perturbation type. Zbl 0264.34070
Cook, L. Pamela; Eckhaus, W.
1973
Boundary layers in linear elliptic singular perturbation problems. Zbl 0234.35009
Eckhaus, Wiktor
1972
Non-linear wave-number interaction in near-critical two-dimensional flows. Zbl 0229.76039
Diprima, R. C.; Eckhaus, W.; Segel, L. A.
1971
Two-body problem with slowly decreasing mass. Zbl 0217.54503
Verhulst, F.; Eckhaus, W.
1970
Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Zbl 0151.15101
Eckhaus, W.; de Jager, E. M.
1966
Sur l’influence de l’epaisseur dans le problème de diffraction de Sommerfeld. Zbl 0151.43101
1966
Studies in non-linear stability theory. Zbl 0125.33101
Eckhaus, W.
1965
Theory of flame-front stability. Zbl 0098.41801
Eckhaus, Wiktor
1961
all top 5
#### Cited by 906 Authors
19 Doelman, Arjen 18 Schneider, Guido 17 Temam, Roger Meyer 16 Jung, Changyeol 15 Kadalbajoo, Mohan K. 9 Kaper, Tasso J. 9 Maccari, Attilio 8 Howes, Fred A. 8 Reddy, Yanala Narsimha 7 Desroches, Mathieu 7 Krupa, Martin 7 Mancas, Stefan C. 7 Shen, Huichuan 7 Szmolyan, Peter 7 Ward, Michael J. 6 Eckhaus, Wiktor 6 Knobloch, Edgar 6 Kolokolnikov, Theodore 6 Kramer, Lorenz 6 Malomed, Boris A. 6 Martel, Yvan 6 Merle, Frank 6 van Harten, Aart 6 Wei, Juncheng 5 Bridges, Thomas J. 5 Calogero, Francesco A. 5 Hong, Youngjoon 5 Nunez, Manuel A. 5 Wechselberger, Martin 4 De Maesschalck, Peter 4 Fruchard, Augustin 4 Gie, Gung-Min 4 Hamouda, Makram 4 Han, Maoan 4 Kuske, Rachel A. 4 Levi, Decio 4 Mielke, Alexander 4 Patidar, Kailash C. 4 Rademacher, Jens Diederich Michael 4 Roychoudhury, Satrajit 4 Verhulst, Ferdinand 4 Zumbrun, Kevin R. 3 Banasiak, Jacek 3 Bastiaansen, Robbin 3 Bodenschatz, Eberhard 3 Choudhury, Sumitra Roy 3 de Groen, Pieter P. N. 3 de Mottoni, Piero 3 Duan, Jinqiao 3 Düll, Wolf-Patrick 3 Duyckaerts, Thomas 3 Grasman, Johan 3 Imaikin, Valery 3 Kapitula, Todd M. 3 Kaushik, Aditya 3 Kenig, Carlos Eduardo 3 Komech, Alexander Ilich 3 Kühn, Christian 3 Lin, Ming-Che 3 Lin, Xiaobiao 3 Matkowsky, Bernard J. 3 Nishiura, Yasumasa 3 Qiu, Deqin 3 Rotstein, Horacio G. 3 Rottschäfer, Vivi 3 Sanchez-Palencia, Enrique 3 Schäfke, Reinhard 3 Sengupta, Tapan K. 3 Tordeux, Sébastien 3 Tursunov, Dilmurat Abdillazhanovich 3 Tzou, J. C. 3 Wang, Xiaoming 3 Zimmermann, Dominik 2 Ai, Shangbing 2 Algaba, Antonio 2 Aranson, Igor S. 2 Arora, Puneet 2 Barker, Blake 2 Bendali, Abderrahmane 2 Berg, Lothar 2 Besjes, J. G. 2 Bobisud, Larry E. 2 Bockelman, Brian 2 Braaksma, Barteld 2 Brauner, Claude-Michel 2 Budd, Christopher John 2 Burke, John L. 2 Carter, Paul M. 2 Chen, Cha’o-Kuang 2 Cheng, Wenguang 2 Chiffaudel, Arnaud 2 Chirilus-Bruckner, Martina 2 Chung, Kwok-Wai 2 Clavin, Paul 2 Cong, Hongzi 2 Côte, Raphaël 2 Coulaud, Olivier 2 Daripa, Prabir K. 2 Dash, Ranjan K. 2 Daviaud, François ...and 806 more Authors
all top 5
#### Cited in 176 Serials
76 Physica D 30 Journal of Mathematical Physics 28 Journal of Differential Equations 26 Journal of Mathematical Analysis and Applications 18 Applied Mathematics and Computation 17 Journal of Nonlinear Science 15 Chaos 11 Archive for Rational Mechanics and Analysis 11 Computers & Mathematics with Applications 11 Journal of Fluid Mechanics 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Studies in Applied Mathematics 11 Applied Mathematics and Mechanics. (English Edition) 11 Applied Mathematics Letters 9 Mathematical Methods in the Applied Sciences 9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Communications in Mathematical Physics 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Communications in Partial Differential Equations 8 Journal of Dynamics and Differential Equations 7 Chaos, Solitons and Fractals 7 Nonlinear Analysis. Theory, Methods & Applications 6 Journal of Engineering Mathematics 6 Journal of Mathematical Biology 6 Physics Letters. A 6 Journal of Computational and Applied Mathematics 6 Transactions of the American Mathematical Society 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Nonlinear Dynamics 5 International Journal of Engineering Science 5 Mathematics and Computers in Simulation 5 RAIRO. Modélisation Mathématique et Analyse Numérique 5 Mathematical and Computer Modelling 5 Celestial Mechanics 5 Discrete and Continuous Dynamical Systems 5 SIAM Journal on Applied Dynamical Systems 4 Applicable Analysis 4 Computer Methods in Applied Mechanics and Engineering 4 Fluid Dynamics 4 Journal of Computational Physics 4 Journal of Statistical Physics 4 Physica A 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Acta Applicandae Mathematicae 4 Numerical Methods for Partial Differential Equations 4 European Journal of Applied Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Nonlinear Mathematical Physics 4 Nonlinear Analysis. Real World Applications 3 Computers and Fluids 3 Journal of Applied Mathematics and Mechanics 3 Mathematical Biosciences 3 Nonlinearity 3 Physics of Fluids 3 Theoretical and Mathematical Physics 3 Wave Motion 3 Mathematics of Computation 3 Theoretical and Computational Fluid Dynamics 3 Automatica 3 Journal of Optimization Theory and Applications 3 Numerische Mathematik 3 Applied Numerical Mathematics 3 Journal of Scientific Computing 3 Japan Journal of Industrial and Applied Mathematics 3 International Journal of Computer Mathematics 3 SIAM Journal on Mathematical Analysis 3 Dynamical Systems 2 International Journal of Modern Physics B 2 Communications on Pure and Applied Mathematics 2 Journal d’Analyse Mathématique 2 Rocky Mountain Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Meccanica 2 Numerical Functional Analysis and Optimization 2 Chinese Annals of Mathematics. Series B 2 Communications in Applied Numerical Methods 2 Applications of Mathematics 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Geometric and Functional Analysis. GAFA 2 Applied Mathematical Modelling 2 SIAM Journal on Applied Mathematics 2 Physics of Fluids 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 European Journal of Mechanics. B. Fluids 2 Lobachevskii Journal of Mathematics 2 Analysis and Applications (Singapore) 2 Séminaire Laurent Schwartz. EDP et Applications 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Biological Cybernetics 1 International Journal of Solids and Structures 1 Israel Journal of Mathematics 1 Physics Reports 1 Reviews of Modern Physics 1 Russian Mathematical Surveys ...and 76 more Serials
all top 5
#### Cited in 36 Fields
377 Partial differential equations (35-XX) 157 Ordinary differential equations (34-XX) 152 Fluid mechanics (76-XX) 126 Dynamical systems and ergodic theory (37-XX) 85 Numerical analysis (65-XX) 59 Biology and other natural sciences (92-XX) 31 Mechanics of deformable solids (74-XX) 21 Mechanics of particles and systems (70-XX) 20 Classical thermodynamics, heat transfer (80-XX) 18 Optics, electromagnetic theory (78-XX) 18 Statistical mechanics, structure of matter (82-XX) 12 Quantum theory (81-XX) 11 Systems theory; control (93-XX) 10 Approximations and expansions (41-XX) 10 Probability theory and stochastic processes (60-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Geophysics (86-XX) 7 Operator theory (47-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Difference and functional equations (39-XX) 3 Nonassociative rings and algebras (17-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-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. | 2021-05-17T20:14:38 | {"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": 0.3045766055583954, "perplexity": 7262.181505475807}, "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-2021-21/segments/1620243992440.69/warc/CC-MAIN-20210517180757-20210517210757-00296.warc.gz"} |
https://par.nsf.gov/biblio/10361526-abacushod-highly-efficient-extended-multitracer-hod-framework-its-application-boss-eboss-data | AbacusHOD : a highly efficient extended multitracer HOD framework and its application to BOSS and eBOSS data
ABSTRACT
We introduce the AbacusHOD model and present two applications of AbacusHOD and the AbacusSummit simulations to observations. AbacusHOD is a Halo Occupation Distribution (HOD) framework written in Python that is particle-based, multitracer, highly generalized, and highly efficient. It is designed specifically with multitracer/cosmology analyses for next-generation large-scale structure surveys in mind, and takes advantage of the volume and precision offered by the new state-of-the-art AbacusSummit cosmological simulations. The model is also highly customizable and should be broadly applicable to any upcoming surveys and a diverse range of cosmological analyses. In this paper, we demonstrate the capabilities of the AbacusHOD framework through two example applications. The first example demonstrates the high efficiency and the large HOD extension feature set through an analysis of full-shape redshift-space clustering of BOSS galaxies at intermediate to small scales ($\lt 30\, h^{-1}$ Mpc), assessing the necessity of introducing secondary galaxy biases (assembly bias). We find strong evidence for using halo environment instead of concentration to trace secondary galaxy bias, a result which also leads to a moderate reduction in the ‘lensing is low’ tension. The second example demonstrates the multitracer capabilities of the AbacusHOD package through an analysis of the extended Baryon Oscillation Spectroscopic Survey cross-correlation more »
Authors:
; ; ; ;
Publication Date:
NSF-PAR ID:
10361526
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
510
Issue:
3
Page Range or eLocation-ID:
p. 3301-3320
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. ABSTRACT
We employ the hydrodynamical simulation illustrisTNG to inform the galaxy–halo connection of the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples of the Dark Energy Spectroscopic Instrument (DESI) survey at redshift z ∼ 0.8. Specifically, we model the galaxy colours of illustrisTNG and apply sliding DESI colour–magnitude cuts, matching the DESI target densities. We study the halo occupation distribution (HOD) model of the selected samples by matching them to their corresponding dark matter haloes in the illustrisTNG dark matter run. We find the HOD of both the LRG and ELG samples to be consistent with their respective baseline models, but also we find important deviations from common assumptions about the satellite distribution, velocity bias, and galaxy secondary biases. We identify strong evidence for concentration-based and environment-based occupational variance in both samples, an effect known as ‘galaxy assembly bias’. The central and satellite galaxies have distinct dependencies on secondary halo properties, showing that centrals and satellites have distinct evolutionary trajectories and should be modelled separately. These results serve to inform the necessary complexities in modelling galaxy–halo connection for DESI analyses and also prepare for building high-fidelity mock galaxies. Finally, we present a shuffling-based clustering analysis that reveals amore »
2. ABSTRACT
Tracking the formation and evolution of dark matter haloes is a critical aspect of any analysis of cosmological N-body simulations. In particular, the mass assembly of a halo and its progenitors, encapsulated in the form of its merger tree, serves as a fundamental input for constructing semi-analytic models of galaxy formation and, more generally, for building mock catalogues that emulate galaxy surveys. We present an algorithm for constructing halo merger trees from abacussummit, the largest suite of cosmological N-body simulations performed to date consisting of nearly 60 trillion particles, and which has been designed to meet the Cosmological Simulation Requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. Our method tracks the cores of haloes to determine associations between objects across multiple time slices, yielding lists of halo progenitors and descendants for the several tens of billions of haloes identified across the entire suite. We present an application of these merger trees as a means to enhance the fidelity of abacussummit halo catalogues by flagging and ‘merging’ haloes deemed to exhibit non-monotonic past merger histories. We show that this cleaning technique identifies portions of the halo population that have been deblended due to choices made by the halo finder,more »
3. ABSTRACT Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the mock-X analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-y and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS, and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias b ≈ 0.13 with cluster mass, independent of hydrodynamical method, or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to b = 0.3 for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased lowmore »
4. ABSTRACT Galaxy–galaxy lensing is a powerful probe of the connection between galaxies and their host dark matter haloes, which is important both for galaxy evolution and cosmology. We extend the measurement and modelling of the galaxy–galaxy lensing signal in the recent Dark Energy Survey Year 3 cosmology analysis to the highly non-linear scales (∼100 kpc). This extension enables us to study the galaxy–halo connection via a Halo Occupation Distribution (HOD) framework for the two lens samples used in the cosmology analysis: a luminous red galaxy sample (redmagic) and a magnitude-limited galaxy sample (maglim). We find that redmagic (maglim) galaxies typically live in dark matter haloes of mass log10(Mh/M⊙) ≈ 13.7 which is roughly constant over redshift (13.3−13.5 depending on redshift). We constrain these masses to ${\sim}15{{\ \rm per\ cent}}$, approximately 1.5 times improvement over the previous work. We also constrain the linear galaxy bias more than five times better than what is inferred by the cosmological scales only. We find the satellite fraction for redmagic (maglim) to be ∼0.1−0.2 (0.1−0.3) with no clear trend in redshift. Our constraints on these halo properties are broadly consistent with other available estimates from previous work, large-scale constraints, and simulations. The framework built in this paper willmore »
5. ABSTRACT
We describe our non-linear emulation (i.e. interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with N-body simulations of non-linear structure formation, designed to accurately predict the projected clustering and galaxy–galaxy lensing signals from luminous red galaxies in the redshift range 0.16 < z < 0.36 on comoving scales 0.6 < rp < 30 $h^{-1} \, \text{Mpc}$. The interpolation accuracy is ≲ 1–2 per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter S8 = (σ8/0.8228)(Ωm/0.3107)0.6 from mock measurements produced via subhalo abundance matching (SHAM)-based light-cones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and galaxy-shear cross-correlation measurements made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over wCDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of S8 = 0.847 ± 0.037, in 3.5σ tension with the Planck cosmological results of 1.00 ± 0.02. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy. | 2023-03-31T02:44:49 | {"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": 0.4404052197933197, "perplexity": 3282.5456934954236}, "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/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00428.warc.gz"} |
https://www.federalreserve.gov/econres/notes/feds-notes/the-international-role-of-the-u-s-dollar-20211006.htm | October 06, 2021
### The International Role of the U.S. Dollar
For most of the last century, the preeminent role of the U.S. dollar in the global economy has been supported by the size and strength of the U.S. economy, its stability and openness to trade and capital flows, and strong property rights and the rule of law. As a result, the depth and liquidity of U.S. financial markets is unmatched, and there is a large supply of extremely safe dollar-denominated assets. This note reviews the use of the dollar in international reserves, as a currency anchor, and in transactions.2 By most measures the dollar is the dominant currency and plays an outsized international role relative to the U.S. share of global GDP (see Figure 1). That said, this dominance should not be taken for granted and the note ends with a discussion of possible challenges to the dollar's status.
#### There is widespread confidence in the U.S. dollar as a store of value
A key function of a currency is as a store of value which can be saved and retrieved in the future without a significant loss of purchasing power. One measure of confidence in a currency as a store of value is its usage in official foreign exchange reserves. As shown in Figure 2, the dollar comprised 60 percent of globally disclosed official foreign reserves in 2021. This share has declined from 71 percent of reserves in 2000, but still far surpassed all other currencies including the euro (21 percent), Japanese yen (6 percent), British pound (5 percent), and the Chinese renminbi (2 percent). Moreover, the decline in the U.S. dollar share has been taken up by a wide range of other currencies, rather than by a single other currency. Thus, while countries have diversified their reserve holdings somewhat over the past two decades, the dollar remains by far the dominant reserve currency.
##### Figure 4. Foreign holdings of U.S. dollar banknotes
Additionally, many foreign countries leverage the effectiveness of the U.S. dollar as a store of value by limiting the movements of their currencies with respect to the U.S. dollar – in other words, using it as an anchor currency. As Ilzetzki, Reinhart, and Rogoff (2020) highlight, the dollar's usage as an anchor currency has increased over the past two decades. They estimate that 50 percent of world GDP in 2015 was produced in countries whose currency is anchored to the U.S. dollar (not counting the United States itself).3 In contrast, the share of world GDP anchored to the euro was only 5 percent (not counting the euro area itself). Moreover, since the end of the Ilzetzki et al. sample in 2015, this anchoring has changed little. One exception might be the re-anchoring of the the Chinese renminbi from the U.S. dollar to a basket of currencies. However, the U.S. dollar and currencies anchored to the U.S. dollar comprise over 50 percent of this basket. So in practice, the Chinese renminbi remained effectively anchored to the U.S. dollar according to the Ilzetzki et al. definition, because in 90 percent of months between January 2016 and April 2021 the renminbi moved less than 2 percent against the U.S. dollar.4
#### The U.S. dollar is dominant in international transactions and financial markets
The international role of a currency can also be measured by its usage as a medium of exchange. The dominance of the dollar internationally has been highlighted in several recent studies of the currency composition of global trade and international financial transactions. The U.S. dollar is overwhelmingly the world's most frequently used currency in global trade. An estimate of the U.S. dollar share of global trade invoices is shown in Figure 5. Over the period 1999-2019, the dollar accounted for 96 percent of trade invoicing in the Americas, 74 percent in the Asia-Pacific region, and 79 percent in the rest of the world. The only exception is Europe, where the euro is dominant.
##### Figure 5. Share of export invoicing
In part because of its dominant role as a medium of exchange, the U.S. dollar is also the dominant currency in international banking. As shown in Figure 6, about 60 percent of international and foreign currency liabilities (primarily deposits) and claims (primarily loans) are denominated in U.S. dollars. This share has remained relatively stable since 2000 and is well above that for the euro (about 20 percent).
##### Figure 6. Share of international and foreign currency banking claims and liabilities
With dollar financing in particularly high demand during times of crisis, foreign financial institutions may face difficulties in obtaining dollar funding. In response, the Federal Reserve has introduced two programs to ease crisis-induced strains in international dollar funding markets, thus mitigating the effects of strains on the supply of credit to domestic and foreign firms and households. To ensure that dollar financing remained available during the 2008-2009 financial crisis, the Federal Reserve introduced temporary swap lines with several foreign central banks, a subset of which were made permanent in 2013.5 During the COVID-19 crisis in March 2020, the Federal Reserve increased the frequency of operations for the standing swap lines and introduced temporary swap lines with additional counterparties.6 The Federal Reserve also introduced a repo facility available to Foreign and International Monetary Authorities (FIMA) with accounts at the Federal Reserve Bank of New York, which was made permanent in 2021.7 Both the swap lines and FIMA repo facility have enhanced the standing of the dollar as the dominant global currency, as approved users know that in a crisis they have access to a stable source of dollar funding. The swap lines were extensively used during the 2008-2009 financial crisis and the 2020 COVID-19 crisis, reaching outstanding totals of $585 billion and$450 billion, respectively (see Figure 7a). Although other central banks have also established swap lines, non-dollar-denomindated swap lines offered by the European Central Bank and other central banks saw little usage (see Figure 7b). This fact highlights how crucial dollar funding is in the operations of many internationally active banks.
##### Figure 7. Central bank swap lines
Issuance of foreign currency debt—debt issued by firms in a currency other than that of their home country — is also dominated by the U.S. dollar. The percentage of foreign currency debt denominated in U.S. dollars has remained around 60 percent since 2010, as seen in Figure 8. This puts the dollar well ahead of the euro, whose share is 23 percent.
##### Figure 8. Share of foreign currency debt issuance
The many sources of demand for U.S. dollars are also reflected in the high U.S. dollar share of foreign exchange (FX) transactions. The most recent Triennial Central Bank Survey for 2019 from the Bank for International Settlements indicated that the U.S. dollar was bought or sold in about 88 percent of global FX transactions in April 2019. This share has remained stable over the past 20 years (Figure 9). In contrast, the euro was bought or sold in 32 percent of FX transactions, a decline from its peak of 39 percent in 2010.8
#### Overall, U.S. dollar dominance has remained stable over the past 20 years
A review of the use of the dollar globally over the last two decades suggests a dominant and relatively stable role. To illustrate this stability, we construct an aggregate index of international currency usage. This index is computed as the weighted average of five measures of currency usage for which time series data are available: Official currency reserves, FX transaction volume, foreign currency debt instruments outstanding, cross-border deposits, and cross-border loans. We display this index of international currency usage in Figure 10. The dollar index level has remained stable at a value of about 75 since the Global Financial Crisis in 2008, well ahead of all other currencies. The euro has the next-highest value at about 25, and its value has remained fairly stable as well. While international usage of the Chinese renminbi has increased over the past 20 years, it has only reached an index level of about 3, remaining even behind the Japanese yen and British pound, which are at about 8 and 7, respectively.
#### Diminution of the U.S. dollar's status seems unlikely in the near term
Near-term challenges to the U.S. dollar's dominance appear limited. In modern history there has been only one instance of a predominant currency switching—the replacement of the British pound by the dollar. The dollar rose to prominence after the financial crisis associated with World War I, then solidified its international role after the Bretton Woods Agreement in 1944 (Tooze 2021, Eichengreen and Flandreau 2008, Carter 2020).9
However, over a longer horizon there is more risk of a challenge to the dollar's international status, and some recent developments have the potential to boost the international usage of other currencies.
Increased European integration is one possible source of challenge, as the European Union (EU) is a large economy with fairly deep financial markets, generally free trade, and robust and stable institions. During the COVID-19 crisis, the EU made plans to issue an unprecedented amount of jointly backed debt. If fiscal integration progresses and a large, liquid market for EU bonds develops, the euro could become more attractive as a reserve currency. This integration could potentially be accelerated by enhancements to the EU's sovereign debt market infrastructure and introducing a digital euro. Additionally, the euro's prominent role in corporate and sovereign green finance could bolster its international status if these continue to grow. However, even with more fiscal integration, remaining political separation will continue to cause policy uncertainty.
Another source of challenges to the U.S. dollar's dominance could be the continued rapid growth of China. Chinese GDP already exceeds U.S. GDP on a purchasing power parity basis (IMF World Economic Outlook, July 2021) and is projected to exceed U.S. GDP in nominal terms in the 2030s.10 It is also by far the world's largest exporter, though it lags the United States by value of imports (IMF Direction of Trade Statistics, 2021-Q2). There are significant roadblocks to more widespread use of the Chinese renminbi. Importantly, the renminbi is not freely exchangeable, the Chinese capital account is not open, and investor confidence in Chinese institutions, including the rule of law, is relatively low (Wincuinas 2019). These factors all make the Chinese renmimbi—in whatever form—relatively unattractive for international investors.
A shifting payments landscape could also pose a challenge to the U.S. dollar's dominance. For example, the rapid growth of digital currencies, both private sector and official, could reduce reliance on the U.S. dollar. Changing consumer and investor preferences, combined with the possibility of new products, could shift the balance of perceived costs and benefits enough at the margin to overcome some of the inertia that helps to maintain the dollar's leading role. That said, it is unlikely that technology alone could alter the landscape enough to completely offset the long-standing reasons the dollar has been dominant.
In sum, absent any large-scale political or economic changes which damage the value of the U.S. dollar as a store of value or medium of exchange and simultaneously bolster the attractiveness of dollar alternatives, the dollar will likely remain the world's dominant international currency for the foreseeable future.
#### References
Bank for International Settlements. BIS Data Bank.
Boz, E., C. Casas, G. Georgiadis, G. Gopinath, H. Le Mezo, A. Mehl, and T. Nguyen (2020). "Patterns in Invoicing Currency in Global Trade." IMF Working Paper No. 20-126.
Carter, Z. (2020). The Price of Peace: Money, Democracy, and the Life of John Maynard Keynes. Random House.
Committee on the Global Financial System (CGFS), (2020). "U.S. dollar funding: an international perspective." BIS CGFS Papers No 65.
Dealogic, DCM Manager, http://www.dealogic.com/en/fixedincome.htm.
The Economist (2020). "Dollar dominance is as secure as American leadership." https://www.economist.com/finance-and-economics/2020/08/06/dollar-dominance-is-as-secure-as-american-global-leadership. Accessed August 18, 2021.
Eichengreen, B. and M. Flandreau (2008). "The Rise and Fall of the Dollar, or When Did the Dollar Replace Sterling as the Leading International Currency?" NBER Working Papers No. 14154.
Judson, R. (2017). "The Death of Cash? Not So Fast: Demand for U.S. Currency at Home and Abroad, 1990-2016." International Cash Conference 2017.
Refinitiv, Thomson ONE Investment Banking with Deals module and SDC Platinum, http://www.thomsonone.com/.
Tooze, A. (2021). "The Rise and Fall and Rise (and Fall) of the U.S. Financial Empire." Foreign Policy https://foreignpolicy.com/2021/01/15/rise-fall-united-states-financial-empire-dollar-global-currency Accessed August 13, 2021.
Wincuinas, J. (2019). "The China position: Gauging institutional investor confidence." Economist Intelligence Unit. https://eiuperspectives.economist.com/financial-services/china-position-gauging-institutional-investor-confidence Accessed August 18, 2021.
1. We thank John Caramichael for excellent research assistance. Return to text
2. For a detailed discussion of the dollar's use in international financial markets see Committee on the Global Financial System (2020). Return to text
3. Their definition of anchored currencies includes currencies explicitly pegged to the dollar as well as currencies that move less than 2 percent against the dollar in over 90 percent of months. Return to text
4. Even excluding China, about 30 percent of world GDP (excluding the United States) is anchored to the U.S. dollar, significantly more than for any other currency. Return to text
5. Since 2013, the following six central banks have had permanent bilateral swap arrangements with each other: the Bank of Canada, the Bank of England, the Bank of Japan, the European Central Bank, the Federal Reserve, and the Swiss National Bank. Return to text
7. The FIMA repo facility allows approved foreign central banks and other foreign monetary authorities to temporarily raise dollars by selling U.S. Treasuries to the Federal Reserve's System Open Market Account and agreeing to buy them back at the maturity of the repurchase agreement. Thus, it provides an alternative temporary source of U.S. dollars for FIMA account holders of Treasury securities other than sales of the securities in the open market. Additional information about the facility can be found at https://www.federalreserve.gov/monetarypolicy/fima-repo-facility.htm. Return to text
8. Because one currency is purchased and another currency is sold in FX transactions, each trade is counted twice, so the sum of the FX transactions measure is 200 percent. Return to text
9. U.S. GDP may have eclipsed British GDP as early as the late 1800s, but the dollar did not completely solidify its dominance until after the Bretton Woods Agreement in 1944 (Eichengreen and Flandreau (2008)). Return to text
10. Bloomberg's base case forecast predicts that Chinese GDP will exceed U.S. GDP in nominal terms in 2033 (https://www.bloomberg.com/news/features/2021-07-05/when-will-china-s-economy-beat-the-u-s-to-become-no-1-why-it-may-never-happen?srnd=premium&sref=c1gYoH2n). Return to text | 2021-10-16T00:22:04 | {"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": 0.2086300551891327, "perplexity": 3449.007572955971}, "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-2021-43/segments/1634323583087.95/warc/CC-MAIN-20211015222918-20211016012918-00628.warc.gz"} |
http://dlmf.nist.gov/2.7 | # §2.7 Differential Equations
## §2.7(i) Regular Singularities: Fuchs–Frobenius Theory
An ordinary point of the differential equation
is one at which the coefficients and are analytic. All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients.
Other points are singularities of the differential equation. If both and are analytic at , then is a regular singularity (or singularity of the first kind). All other singularities are classified as irregular.
In a punctured neighborhood of a regular singularity
with at least one of the coefficients , , nonzero. Let , denote the indices or exponents, that is, the roots of the indicial equation
Provided that is not zero or an integer, equation (2.7.1) has independent solutions , , such that
with , and
when .
If , then (2.7.4) applies only in the case . But there is an independent solution
The coefficients and constant are again determined by equating coefficients in the differential equation, beginning with when , or with when .
The radii of convergence of the series (2.7.4), (2.7.6) are not less than the distance of the next nearest singularity of the differential equation from .
To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing in (2.7.1) with ; see Olver (1997b, pp. 153–154). For corresponding definitions, together with examples, for linear differential equations of arbitrary order see §§16.8(i)16.8(ii).
## §2.7(ii) Irregular Singularities of Rank 1
If the singularities of and at are no worse than poles, then has rank , where is the least integer such that and are analytic at . Thus a regular singularity has rank 0. The most common type of irregular singularity for special functions has rank 1 and is located at infinity. Then
these series converging in an annulus , with at least one of , , nonzero.
Formal solutions are
where , are the roots of the characteristic equation
2.7.9
, and
when . The construction fails iff , that is, when : this case is treated below.
For large ,
where and are constants, and the th remainder terms in the sums are and , respectively (Olver (1994a)). Hence unless the series (2.7.8) terminate (in which case the corresponding is zero) they diverge. However, there are unique and linearly independent solutions , , such that
as in the sectors
2.7.15,
2.7.16,
being an arbitrary small positive constant.
Although the expansions (2.7.14) apply only in the sectors (2.7.15) and (2.7.16), each solution can be continued analytically into any other sector. Typical connection formulas are
in which , are constants, the so-called Stokes multipliers. In combination with (2.7.14) these formulas yield asymptotic expansions for in , and in . Furthermore,
Note that the coefficients in the expansions (2.7.12), (2.7.13) for the “late” coefficients, that is, , with large, are the “early” coefficients , with small. This phenomenon is an example of resurgence, a classification due to Écalle (1981a, b). See §2.11(v) for other examples.
The exceptional case is handled by Fabry’s transformation:
The transformed differential equation either has a regular singularity at , or its characteristic equation has unequal roots.
For error bounds for (2.7.14) see Olver (1997b, Chapter 7). For the calculation of Stokes multipliers see Olde Daalhuis and Olver (1995b). For extensions to singularities of higher rank see Olver and Stenger (1965). For extensions to higher-order differential equations see Stenger (1966a, b), Olver (1997a, 1999), and Olde Daalhuis and Olver (1998).
## §2.7(iii) Liouville–Green (WKBJ) Approximation
For irregular singularities of nonclassifiable rank, a powerful tool for finding the asymptotic behavior of solutions, complete with error bounds, is as follows:
### ¶ Liouville–Green Approximation Theorem
In a finite or infinite interval let be real, positive, and twice-continuously differentiable, and be continuous. Then in the differential equation
has twice-continuously differentiable solutions
such that
provided that . Here is the error-control function
and denotes the variational operator (§2.3(i)). Thus
Assuming also , we have
Suppose in addition is unbounded as and . Then there are solutions , , such that
The solutions with the properties (2.7.26), (2.7.27) are unique, but not those with the properties (2.7.28), (2.7.29). In fact, since
2.7.30,
is a recessive (or subdominant) solution as , and is a dominant solution as . Similarly for and as .
### ¶ Example
We cannot take and because would diverge as . Instead set , . By approximating
we arrive at
as , being recessive and dominant.
For other examples, and also the corresponding results when is negative, see Olver (1997b, Chapter 6), Olver (1980a), Taylor (1978, 1982), and Smith (1986). The first of these references includes extensions to complex variables and reversions for zeros.
## §2.7(iv) Numerically Satisfactory Solutions
One pair of independent solutions of the equation
is , . Another is , . In theory either pair may be used to construct any other solution
2.7.36
or
2.7.37
where are constants. From the numerical standpoint, however, the pair and has the drawback that severe numerical cancellation can occur with certain combinations of and , for example if and are equal, or nearly equal, and , or , is large and negative. This kind of cancellation cannot take place with and , and for this reason, and following Miller (1950), we call and a numerically satisfactory pair of solutions.
The solutions and are respectively recessive and dominant as , and vice versa as . This is characteristic of numerically satisfactory pairs. In a neighborhood, or sectorial neighborhood of a singularity, one member has to be recessive. In consequence, if a differential equation has more than one singularity in the extended plane, then usually more than two standard solutions need to be chosen in order to have numerically satisfactory representations everywhere.
In oscillatory intervals, and again following Miller (1950), we call a pair of solutions numerically satisfactory if asymptotically they have the same amplitude and are out of phase. | 2013-12-13T20:48:10 | {"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": 0.9345535039901733, "perplexity": 1284.259001854083}, "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-2013-48/segments/1386164992771/warc/CC-MAIN-20131204134952-00076-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/Sensitivity/TSSetRHSHessianProduct.html | petsc-master 2019-07-21
Report Typos and Errors
TSSetRHSHessianProduct
Sets the function that computes the vecotr-Hessian-vector product. The Hessian is the second-order derivative of G (RHSFunction) w.r.t. the state variable.
Synopsis
#include "petscts.h"
PetscErrorCode TSSetRHSHessianProduct(TS ts,Vec *rhshp1,PetscErrorCode (*rhshessianproductfunc1)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
Vec *rhshp2,PetscErrorCode (*rhshessianproductfunc2)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
Vec *rhshp3,PetscErrorCode (*rhshessianproductfunc3)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
Vec *rhshp4,PetscErrorCode (*rhshessianproductfunc4)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
void *ctx)
Logically Collective on TS
Calling sequence of ihessianproductfunc
rhshessianproductfunc (TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx);
ts - TS context obtained from TSCreate() rhshp1 - an array of vectors storing the result of vector-Hessian-vector product for G_UU hessianproductfunc1 - vector-Hessian-vector product function for G_UU rhshp2 - an array of vectors storing the result of vector-Hessian-vector product for G_UP hessianproductfunc2 - vector-Hessian-vector product function for G_UP rhshp3 - an array of vectors storing the result of vector-Hessian-vector product for G_PU hessianproductfunc3 - vector-Hessian-vector product function for G_PU rhshp4 - an array of vectors storing the result of vector-Hessian-vector product for G_PP hessianproductfunc4 - vector-Hessian-vector product function for G_PP
t - current timestep U - input vector (current ODE solution) Vl - an array of input vectors to be left-multiplied with the Hessian Vr - input vector to be right-multiplied with the Hessian VHV - an array of output vectors for vector-Hessian-vector product ctx - [optional] user-defined function context
Notes
The first Hessian function and the working array are required. As an example to implement the callback functions, the second callback function calculates the vector-Hessian-vector product $Vl_n^T*G_UP*Vr where the vector Vl_n (n-th element in the array Vl) and Vr are of size N and M respectively, and the Hessian G_UP is of size N x N x M. Each entry of G_UP corresponds to the derivative$ G_UP[i][j][k] = \frac{\partial^2 G[i]}{\partial U[j] \partial P[k]}. The result of the vector-Hessian-vector product for Vl_n needs to be stored in vector VHV_n with j-th entry being \$ VHV_n[j] = \sum_i \sum_k {Vl_n[i] * G_UP[i][j][k] * Vr[k]} If the cost function is a scalar, there will be only one vector in Vl and VHV.
intermediate
Location
src/ts/interface/sensitivity/tssen.c
Examples
src/ts/examples/tutorials/ex20opt_p.c.html
src/ts/examples/tutorials/ex20opt_ic.c.html
Index of all Sensitivity routines | 2019-07-23T03:54:50 | {"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": 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": 0.4133838415145874, "perplexity": 14349.457873302948}, "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-2019-30/segments/1563195528687.63/warc/CC-MAIN-20190723022935-20190723044935-00068.warc.gz"} |
http://dlmf.nist.gov/4.2 | §4.2 Definitions
§4.2(i) The Logarithm
The general logarithm function is defined by
4.2.1,
where the integration path does not intersect the origin. This is a multivalued function of with branch point at .
The principal value, or principal branch, is defined by
4.2.2
where the path does not intersect ; see Figure 4.2.1. is a single-valued analytic function on and real-valued when ranges over the positive real numbers.
Figure 4.2.1: -plane: Branch cut for and .
The real and imaginary parts of are given by
4.2.3.
For see §1.9(i).
The only zero of is at .
Most texts extend the definition of the principal value to include the branch cut
4.2.4,
by replacing (4.2.3) with
With this definition the general logarithm is given by
where is the excess of the number of times the path in (4.2.1) crosses the negative real axis in the positive sense over the number of times in the negative sense.
In the DLMF we allow a further extension by regarding the cut as representing two sets of points, one set corresponding to the “upper side” and denoted by , the other set corresponding to the “lower side” and denoted by . Again see Figure 4.2.1. Then
with either upper signs or lower signs taken throughout. Consequently is two-valued on the cut, and discontinuous across the cut. We regard this as the closed definition of the principal value.
In contrast to (4.2.5) the closed definition is symmetric. As a consequence, it has the advantage of extending regions of validity of properties of principal values. For example, with the definition (4.2.5) the identity (4.8.7) is valid only when , but with the closed definition the identity (4.8.7) is valid when . For another example see (4.2.37).
In the DLMF it is usually clear from the context which definition of principal value is being used. However, in the absence of any indication to the contrary it is assumed that the definition is the closed one. For other examples in this chapter see §§4.23, 4.24, 4.37, and 4.38.
§4.2(ii) Logarithms to a General Base
Natural logarithms have as base the unique positive number
4.2.11
such that
Equivalently,
Thus
4.2.17
4.2.18
is also called the Napierian or hyperbolic logarithm. is the common or Briggs logarithm.
§4.2(iii) The Exponential Function
4.2.19
The function is an entire function of , with no real or complex zeros. It has period :
Also,
4.2.22
The general value of the phase is given by
If then
§4.2(iv) Powers
¶ Powers with General Bases
The general power of is defined by
In particular, , and if , then
4.2.27
In all other cases, is a multivalued function with branch point at . The principal value is
This is an analytic function of on , and is two-valued and discontinuous on the cut shown in Figure 4.2.1, unless .
where for the principal value of , and is unrestricted in the general case. When is real
Unless indicated otherwise, it is assumed throughout the DLMF that a power assumes its principal value. With this convention,
but the general value of is
For
If has its general value, with , and if , then
4.2.35
This result is also valid when has its principal value, provided that the branch of satisfies
Another example of a principal value is provided by
4.2.37
Again, without the closed definition the and signs would have to be replaced by and , respectively. | 2013-05-21T19:50:02 | {"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": 0.9456864595413208, "perplexity": 729.2842310713427}, "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-2013-20/segments/1368700477029/warc/CC-MAIN-20130516103437-00093-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://psychology.wikia.com/wiki/Correlated_equilibrium | # Correlated equilibrium
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Correlated equilibrium
A solution concept in game theory
Relationships
Superset of: Nash equilibrium
Significance
Proposed by: Robert Aumann
Example: Chicken
In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann (1974). The idea is that a strategy profile is chosen at random according to some distribution. If no player would want to deviate from the recommended strategy (assuming the others don't deviate), the distribution is called a correlated equilibrium.
## An exampleEdit
D C 0, 0 7, 2 2, 7 6, 6
Consider the game of chicken (pictured to the right). In this game two individuals are challenging each other to a contest where each can either dare or chicken out. If one is going to Dare, it is better for the other to chicken out. But if one is going to chicken out it is better for the other to Dare. This leads to an interesting situation where each wants to dare, but only if the other might chicken out.
In this game, there are three Nash equilibria. The two pure strategy Nash equilibria are (D, C) and (C, D). There is also a mixed strategy equilibrium where each player Dares with probability 1/3.
Now consider a third party (or some natural event) that draws one of three cards labeled: (C, C), (D, C), and (C, D). After drawing the card the third party informs the players of the strategy assigned to them on the card (but not the strategy assigned to their opponent). Suppose a player is assigned D, he would not want to deviate supposing the other player played their assigned strategy since he will get 7 (the highest payoff possible). Suppose a player is assigned C. Then the other player will play C with probability 1/2 and D with probability 1/2. The expected utility of Daring is 0(1/2) + 7(1/2) = 3.5 and the expected utility of chickening out is 2(1/2) + 6(1/2) = 4. So, the player would prefer to Chicken out.
Since neither player has an incentive to deviate, this is a correlated equilibrium. Interestingly, the expected payoff for this equilibrium is 7(1/3) + 2(1/3) + 6(1/3) = 5 which is higher than the expected payoff of the mixed strategy Nash equilibrium.
## Formal definitionEdit
A probability distribution, $p(\cdot)$ is a correlated equilibrium if for all strategies $s_i$ such that $p(s_i) > 0$ and every alternative strategy $s_{i}'$
$\sum_{s_{-i} \in S_{-i}} p(s_{-i}|s_i)u_i(s_i, s_{-i}) \geq \sum_{s_{-i} \in S_{-i}} p(s_{-i}|s_{i})u_i(s_{i}', s_{-i})$
where $u_i(\cdot)$ is i's utility function and $S_{-i}$ is the set of all possible strategies that i's opponents might take.
## ReferencesEdit
• Aumann, Robert (1974) Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1:67-96.
• Fudenberg, Drew and Jean Tirole (1991) Game Theory, MIT Press, 1991, ISBN 0-262-06141-4
• Tardos, Eva (2004) Class notes from Algorithmic game theory (note an important typo) [1]
This page uses Creative Commons Licensed content from Wikipedia (view authors). | 2017-03-25T13:52:11 | {"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": 0, "mathjax_asciimath": 0, "img_math": 7, "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": 0.8226127028465271, "perplexity": 852.048167015054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2017-13/segments/1490218188926.39/warc/CC-MAIN-20170322212948-00466-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://dlmf.nist.gov/22.20 | §22.20 Methods of Computation
§22.20(i) Via Theta Functions
A powerful way of computing the twelve Jacobian elliptic functions for real or complex values of both the argument $z$ and the modulus $k$ is to use the definitions in terms of theta functions given in §22.2, obtaining the theta functions via methods described in §20.14.
§22.20(ii) Arithmetic-Geometric Mean
Given real or complex numbers $a_{0},b_{0}$, with $b_{0}/a_{0}$ not real and negative, define
22.20.1 $\displaystyle a_{n}$ $\displaystyle=\tfrac{1}{2}\left(a_{n-1}+b_{n-1}\right),$ $\displaystyle b_{n}$ $\displaystyle=\left(a_{n-1}b_{n-1}\right)^{1/2},$ $\displaystyle c_{n}$ $\displaystyle=\tfrac{1}{2}\left(a_{n-1}-b_{n-1}\right),$ ⓘ Symbols: $a_{n}$: numbers, $b_{n}$: numbers, $c_{n}$: numbers and $n$: positive Referenced by: §22.20(ii), §22.20(iv), §22.20(iv), §22.20(ii) Permalink: http://dlmf.nist.gov/22.20.E1 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png See also: Annotations for §22.20(ii), §22.20 and Ch.22
for $n\geq 1$, where the square root is chosen so that $\operatorname{ph}b_{n}=\tfrac{1}{2}(\operatorname{ph}a_{n-1}+\operatorname{ph}% b_{n-1})$, where $\operatorname{ph}a_{n-1}$ and $\operatorname{ph}b_{n-1}$ are chosen so that their difference is numerically less than $\pi$. Then as $n\to\infty$ sequences $\{a_{n}\}$, $\{b_{n}\}$ converge to a common limit $M=M(a_{0},b_{0})$, the arithmetic-geometric mean of $a_{0},b_{0}$. And since
22.20.2 $\max\left(\left|a_{n}-M\right|,\left|b_{n}-M\right|,\left|c_{n}\right|\right)% \leq\text{(const.)}\times 2^{-2^{n}},$ ⓘ Symbols: $a_{n}$: numbers, $b_{n}$: numbers, $c_{n}$: numbers, $n$: positive and $M(a_{0},b_{0})$: limit Permalink: http://dlmf.nist.gov/22.20.E2 Encodings: TeX, pMML, png See also: Annotations for §22.20(ii), §22.20 and Ch.22
convergence is very rapid.
For $x$ real and $k\in(0,1)$, use (22.20.1) with $a_{0}=1$, $b_{0}=k^{\prime}\in(0,1)$, $c_{0}=k$, and continue until $c_{N}$ is zero to the required accuracy. Next, compute $\phi_{N},\phi_{N-1},\dots,\phi_{0}$, where
22.20.3 $\phi_{N}=2^{N}a_{N}x,$ ⓘ Symbols: $x$: real, $a_{n}$: numbers and $\phi_{N}$: approximations Referenced by: §22.20(ii) Permalink: http://dlmf.nist.gov/22.20.E3 Encodings: TeX, pMML, png See also: Annotations for §22.20(ii), §22.20 and Ch.22
22.20.4 $\phi_{n-1}=\frac{1}{2}\left(\phi_{n}+\operatorname{arcsin}\left(\frac{c_{n}}{a% _{n}}\sin\phi_{n}\right)\right),$
and the inverse sine has its principal value (§4.23(ii)). Then
22.20.5 $\displaystyle\operatorname{sn}\left(x,k\right)$ $\displaystyle=\sin\phi_{0},$ $\displaystyle\operatorname{cn}\left(x,k\right)$ $\displaystyle=\cos\phi_{0},$ $\displaystyle\operatorname{dn}\left(x,k\right)$ $\displaystyle=\frac{\cos\phi_{0}}{\cos\left(\phi_{1}-\phi_{0}\right)},$ ⓘ Symbols: $\operatorname{cn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function, $\operatorname{dn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function, $\operatorname{sn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function, $K\left(\NVar{k}\right)$: Legendre’s complete elliptic integral of the first kind, $\cos\NVar{z}$: cosine function, $\sin\NVar{z}$: sine function, $x$: real, $k$: modulus and $\phi_{N}$: approximations Referenced by: (22.20.5), §22.20(ii), 3rd item Permalink: http://dlmf.nist.gov/22.20.E5 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png Note (effective with 1.0.10): A note was added after (22.20.5) to deal with cases when computation of $\operatorname{dn}\left(x,k\right)$ with (22.20.5) becomes numerically unstable near $x=K$. Suggested 2014-10-20 by Hartmut Henkel See also: Annotations for §22.20(ii), §22.20 and Ch.22
and the subsidiary functions can be found using (22.2.10). This formula for $\operatorname{dn}$ becomes unstable near $x=K$. If only the value of $\operatorname{dn}\left(x,k\right)$ at $x=K$ is required then the exact value is in the table 22.5.1. If both $k$ and $x$ are real then $\operatorname{dn}$ is strictly positive and $\operatorname{dn}\left(x,k\right)=\sqrt{1-k^{2}{\operatorname{sn}^{2}}\left(x,% k\right)}$ which follows from (22.6.1). If either $k$ or $x$ is complex then (22.2.6) gives the definition of $\operatorname{dn}\left(x,k\right)$ as a quotient of theta functions.
Example
To compute $\operatorname{sn}$, $\operatorname{cn}$, $\operatorname{dn}$ to 10D when $x=0.8$, $k=0.65$.
Four iterations of (22.20.1) lead to $c_{4}=\Sci{6.5}{-12}$. From (22.20.3) and (22.20.4) we obtain $\phi_{1}=1.40213\;91827$ and $\phi_{0}=0.76850\;92170$. Then from (22.20.5), $\operatorname{sn}\left(0.8,0.65\right)=0.69506\;42165$, $\operatorname{cn}\left(0.8,0.65\right)=0.71894\;76580$, $\operatorname{dn}\left(0.8,0.65\right)=0.89212\;34349$.
§22.20(iii) Landen Transformations
By application of the transformations given in §§22.7(i) and 22.7(ii), $k$ or $k^{\prime}$ can always be made sufficently small to enable the approximations given in §22.10(ii) to be applied. The rate of convergence is similar to that for the arithmetic-geometric mean.
Example
To compute $\operatorname{dn}\left(x,k\right)$ to 6D for $x=0.2$, $k^{2}=0.19$, $k^{\prime}=0.9$.
From (22.7.1), $k_{1}=\tfrac{1}{19}$ and $x/(1+k_{1})=0.19$. From the first two terms in (22.10.6) we find $\operatorname{dn}\left(0.19,\tfrac{1}{19}\right)=0.999951$. Then by using (22.7.4) we have $\operatorname{dn}\left(0.2,\sqrt{0.19}\right)=0.996253$.
If needed, the corresponding values of $\operatorname{sn}$ and $\operatorname{cn}$ can be found subsequently by applying (22.10.4) and (22.7.2), followed by (22.10.5) and (22.7.3).
§22.20(iv) Lattice Calculations
If either $\tau$ or $q=e^{i\pi\tau}$ is given, then we use $k={\theta_{2}^{2}}\left(0,q\right)/{\theta_{3}^{2}}\left(0,q\right)$, $k^{\prime}={\theta_{4}^{2}}\left(0,q\right)/{\theta_{3}^{2}}\left(0,q\right)$, $K=\frac{1}{2}\pi{\theta_{3}^{2}}\left(0,q\right)$, and $K^{\prime}=-i\tau K$, obtaining the values of the theta functions as in §20.14.
If $k,k^{\prime}$ are given with $k^{2}+{k^{\prime}}^{2}=1$ and $\Im k^{\prime}/\Im k<0$, then $K,K^{\prime}$ can be found from
22.20.6 $\displaystyle K$ $\displaystyle=\frac{\pi}{2M(1,k^{\prime})},$ $\displaystyle K^{\prime}$ $\displaystyle=\frac{\pi}{2M(1,k)},$
using the arithmetic-geometric mean.
Example 1
If $k=k^{\prime}=1/\sqrt{2}$, then three iterations of (22.20.1) give $M=0.84721\;30848$, and from (22.20.6) $K=\pi/(2M)=1.85407\;46773$ — in agreement with the value of $\left(\Gamma\left(\tfrac{1}{4}\right)\right)^{2}/\left(4\sqrt{\pi}\right)$; compare (23.17.3) and (23.22.2).
Example 2
If $k^{\prime}=1-i$, then four iterations of (22.20.1) give $K=1.23969\;74481+i0.56499\;30988$.
§22.20(v) Inverse Functions
See Wachspress (2000).
§22.20(vi) Related Functions
$\operatorname{am}\left(x,k\right)$ can be computed from its definition (22.16.1) or from its Fourier series (22.16.9). Alternatively, Sala (1989) shows how to apply the arithmetic-geometric mean to compute $\operatorname{am}\left(x,k\right)$.
Jacobi’s epsilon function can be computed from its representation (22.16.30) in terms of theta functions and complete elliptic integrals; compare §20.14. Jacobi’s zeta function can then be found by use of (22.16.32).
§22.20(vii) Further References
For additional information on methods of computation for the Jacobi and related functions, see the introductory sections in the following books: Lawden (1989), Curtis (1964b), Milne-Thomson (1950), and Spenceley and Spenceley (1947). | 2018-09-20T23:05:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 128, "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": 0.9451159238815308, "perplexity": 1887.37522892582}, "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-2018-39/segments/1537267156622.36/warc/CC-MAIN-20180920214659-20180920235059-00150.warc.gz"} |
https://bison.inl.gov/Documentation/source/materials/tensor_mechanics/ChromiumPlasticityUpdate.aspx | # Chromium Isotropic Plasticity Update
Calculates the plastic strain as a function of strain rate for pure chromium. Note: This material must be run in conjunction with ComputeMultipleInelasticStress.
## Description
ChromiumPlasticityUpdate calculates the plastic strain for chromium cladding materials as a function of temperature. This material must be run in conjunction with ComputeMultipleInelasticStress. The material model inherits from IsotropicPlasticityStressUpdate and sets the yield_stress_function internally based upon temperature. Then irradiation hardening is incorporated as a function of fast neutron fluence that increases the yield stress. The yield stress as a function of temperature is given by Wagih et al. (2018): (1) where is the yield stress (MPa) and is the temperature (K). Irradiation hardening is then included via: (2)
## Example Input Syntax
[./chromium_plasticity]
type = ChromiumPlasticityUpdate
block = '1 2 3 4'
temperature = temp
fast_neutron_fluence = fast_neutron_fluence
yield_stress = 1e-6 # is ignored
hardening_constant = 0.0
[../]
ChromiumPlasticityUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:
[./stress]
type = ComputeMultipleInelasticStress
tangent_operator = elastic
inelastic_models = 'chromium_plasticity'
block = '1 2 3 4'
[../]
## Input Parameters
• fast_neutron_fluenceThe coupled fast neutron flux variable.
C++ Type:std::vector
Description:The coupled fast neutron flux variable.
• hardening_functionTrue stress as a function of plastic strain
C++ Type:FunctionName
Description:True stress as a function of plastic strain
• max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Description:The maximum inelastic strain increment allowed in a time step
• temperatureCoupled Temperature
C++ Type:std::vector
Description:Coupled Temperature
• base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
• max_its30Maximum number of Newton iterations
Default:30
C++ Type:unsigned int
Description:Maximum number of Newton iterations
• yield_stress0The point at which plastic strain begins accumulating
Default:0
C++ Type:double
Description:The point at which plastic strain begins accumulating
• acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
• relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Description:Relative convergence tolerance for Newton iteration
• absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Description:Absolute convergence tolerance for Newton iteration
• 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
• hardening_constant0Hardening slope
Default:0
C++ Type:double
Description:Hardening slope
• yield_stress_functionYield stress as a function of temperature
C++ Type:FunctionName
Description:Yield stress as a function of temperature
• 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
• effective_inelastic_strain_nameeffective_plastic_strainName of the material property that stores the effective inelastic strain
Default:effective_plastic_strain
C++ Type:std::string
Description:Name of the material property that stores the effective inelastic strain
• 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
• internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Description:When to output internal Newton solve information
• internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.
Default:False
C++ Type:bool
Description:Set true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.
### Debug Parameters
• 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
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
### Outputs Parameters
• yield_stress_scale_factor1Scale factor to be applied to yield stress. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Description:Scale factor to be applied to yield stress. Used for calibration and sensitivity studies | 2020-12-04T04:52:09 | {"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": 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": 0.30116191506385803, "perplexity": 5155.939470871544}, "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-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00476.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?node=Q004&home= | QUARKS
#### ${\mathit {\mathit c}}$
$I(J^P)$ = $0(1/2^{+})$
Charge = ${2\over 3}$ $\mathit e$ Charm = $+$1
${\mathit {\mathit c}}$-QUARK MASS $1.27 \pm0.02$ GeV
${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ MASS RATIO $11.76 {}^{+0.05}_{-0.10}$
${\mathit m}_{{{\mathit b}}}/{\mathit m}_{{{\mathit c}}}$ MASS RATIO $4.58 \pm0.01$
${\mathit m}_{{{\mathit b}}}−{\mathit m}_{{{\mathit c}}}$ QUARK MASS DIFFERENCE $3.45 \pm0.05$ GeV
FOOTNOTES | 2023-04-01T00:42:05 | {"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": 0.9340371489524841, "perplexity": 4402.642066750164}, "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-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00125.warc.gz"} |
https://bea.gov/scb/account_articles/national/0492trip/maintext.htm | # Economic Theory and BEA's Alternative Quantity and Price Indexes
## By Jack E. Triplett
In this issue, BEA is introducing new, alternative price and quantity indexes for the major components of the national income and product accounts (see "Alternative Measures of Change in Real Output and Prices" on page 32). This article describes the index number theory underlying these alternative indexes and discusses the interpretation of them.
### Index number theory
Economic theory has long been used to specify the construction of price and quantity index numbers. The modern treatment originated in an article published in the 1920's by the Russian mathematician and economist A.A. Konüs./1/ Konüs analyzed the measurement of consumer prices, the theory of which he named the "true index of the cost of living." Cost-of-living index theory was developed independently by English-language economists in the early 1930's. The theory was summarized by Ragnar Frisch in 1936 in a famous review article on index numbers./2/
The theory of the cost-of-living index applies directly to the measurement of consumption prices, such as the price index for the personal consumption expenditures (PCE) component of gross domestic product (GDP). This article will summarize the theory of the cost-of-living index, which is the best known and best developed part of the economic theory of index numbers; with suitable changes in language and notation and in some conditions and assumptions, the principles can be extended to investment goods as well.
Cost-of-living index number theory proceeds from the proposition that a consumption price index should measure the change in the cost of maintaining a fixed, or constant, standard of living. If the price index holds the standard of living constant, then any increase in per capita consumption expenditures that exceeds the increase in the price index can be interpreted as an increase in the standard of living. Conversely, if per capita consumption expenditures rise more slowly than the price index, the standard of living, or real per capita consumption, is falling. Real consumption, either per capita or in the aggregate, can be expressed as a quantity index, which is the counterpart of the consumption price index.
Thus, from the standard-of-living orientation, the price index measures the changing cost of a constant standard of living, and the quantity index measures increases or decreases in the standard of living. The same interpretation may also be given to conventional fixed-weighted indexes, such as the base-weighted indexes that traditionally have been employed in measuring real GDP. In the fixed-weighted PCE price index, one holds constant the collection of goods and services actually consumed in 1987, which is a way of holding constant the living standard that existed in 1987.
Cost-of-living index theory stresses, however, that consumers can reach the same standard of living in more than one way. Consumers may substitute between commodities that serve similar general purposes (for example, chicken or fish for beef) or even dissimilar ones (a new car for a vacation). Substitution implies that differing collections of goods and services may still represent equivalent standards of living.
Moreover, nationwide data indicate that consumers systematically substitute away from those goods and services whose prices rise the most rapidly and toward those goods and services whose prices rise less rapidly or decline. Commodities whose prices grow most rapidly show, on average, the slowest growth in consumption; commodities whose prices grow more slowly (or decline) show, on average, the most rapid growth in consumption. The same patterns also apply to many nonconsumption goods, such as investment or capital goods; for example, the prices of computer equipment have declined at an extremely rapid rate over the past several decades, while the proportion of investment expenditures accounted for by computer equipment has increased dramatically.
Economic theory suggests that a consumption price index that truly tracks the cost of living should be based on the costs of collections of commodities that represent equivalent living standards and that this index should not, therefore, hold quantities fixed as consumers shift their expenditures. For example, when chicken is substituted for beef, one should look at meat consumption as a whole, rather than at fixed quantities of different kinds of meats, and perhaps one should even look at food consumption as a whole, rather than at fixed quantities of meat, vegetables, and so forth.
Economic theory also suggests that when consumers do substitute toward commodities whose prices rise less rapidly or decline, the cost of maintaining an equivalent standard of living rises less rapidly than the cost of the fixed basket of commodities that were consumed in a previous period, such as 1987. For example, when used to measure consumption prices between 1987 and 1992, a fixed basket of the commodities consumed in 1987 gives too much weight to the prices that rise rapidly over the timespan and too little weight to the prices that fall; as a result, using the 1987 fixed basket overstates the 1987–92 cost-of-living change. Conversely, because consumers substitute, a fixed basket of the commodities consumed in 1992 gives too much weight to the prices that have fallen over the timespan and too little to the prices that have risen; as a result, the 1992 fixed basket understates the 1987–92 cost-of-living change.
The difference between a fixed-weighted price index and a price index that accounts for substitution is often termed the "substitution bias" in fixed-weighted indexes.
### Development of superlative indexes
The theoretical cost-of-living index was for many years regarded as purely an abstraction, an idea that could not be implemented in actual price index calculations. To compute a constant standard of living, one would have to know how much consumers substitute among commodities in response to relative price changes. In other words, one would have to be able to separate changes in consumption spending that raise (or lower) the standard of living from changes in spending that merely represent alternative ways of achieving the same living standard. Even with econometric methods, which have been applied to the problem,/3/ the research task is enormous, and the research results still leave a range of uncertainties.
In 1976, W. Erwin Diewert published an article that suggested a relatively simple way to approximate the theoretical cost-of-living index./4/ Abandoning the attempt to find a formula for the "exact" cost-of-living index, Diewert showed that a class of index numbers, which he named "superlative index numbers," would give good approximations to the "exact" formula. Some of these superlative index formulas turn out to be relatively simple to compute and use.
One of the most attractive of these superlative index numbers is the Fisher Ideal index, proposed by Irving Fisher in 1922. The Fisher Ideal index is simply the geometric mean of the fixed-weighted Paasche and Laspeyres indexes, the formulas for which have long been the primary ones used in constructing indexes for the U.S. national accounts./5/
Another superlative index is the Tornqvist index, developed in the 1930's at the Bank of Finland. This index is a logarithmically defined index that employs an average of the weights for the two periods being considered./6/
Diewert showed that the Fisher Ideal index and the Tornqvist index are theoretically better measures of the cost of living than the traditional fixed-weighted Paasche or Laspeyres indexes. The superlative indexes accommodate substitution in consumer spending while holding living standards constant, something the Paasche and Laspeyres indexes do not do. From the view of theory, the Fisher Ideal formula and the Tornqvist formula are equally good; therefore, one can choose between the two on pragmatic grounds.
The Fisher Ideal formula is somewhat easier to compute than the Tornqvist formula; modern computers make this only a marginal advantage. The Fisher Ideal index is also somewhat easier to interpret; a user can examine its component Laspeyres and Paasche indexes to gain a mechanical understanding of movements in the index, and such calculations assist in the analysis of price and quantity movements.
Finally, a major advantage of the Fisher Ideal formula is that it has a "dual" property that is not shared by the Tornqvist formula. A Fisher Ideal price index implies a Fisher Ideal quantity index, and the converse: That is, the product of a Fisher Ideal price index between two periods and a Fisher Ideal quantity index between the same two periods is equal to the total change in value (change in current-dollar expenditures) between those periods. In contrast, a Tornqvist price index multiplied by a Tornqvist quantity index does not equal the change in value between the two periods. In fact, the quantity index that corresponds to a Tornqvist price index does not have an explicit, algebraic formula (and likewise, the price index corresponding to a Tornqvist quantity index has no explicit formula).
### Constructing time series with superlative indexes
Though economic theory indicates preferred index number formulas for making two-period comparisons, it gives less guidance on forming time series of index numbers covering three or more periods.
Consider the following table of annual price indexes that can be computed covering the years 1987–90:
Terminal year Initial year 1987 1988 1989 1990 1987 I87,87 1988 I87,88 I88,88 1989 I87,89 I88,89 I89,89 1990 I87,90 I88,90 I89,90 I90,90
Each entry in the table designates a superlative index (the Fisher Ideal, in these examples) that measures price change between 2 years with different quantity weights. For example, $I_87,88_$ is a Fisher Ideal index number computed as the geometric mean of two indexes measuring price change between 1987 and 1988; the first uses weights from 1987 and the second, weights from 1988. Similarly, $I_87,90_$ measures price change between 1987 and 1990 using a Fisher Ideal formula that is the geometric mean of one index having 1987 weights and a second having 1990 weights.
Starting with the index for 1987 ($I_87,87_$, which is, of course, equal to 1), there are two ways to measure price change between 1987 and 1990. One way is to use the "direct" index calculation procedure—that is, to go straight down the column labeled 1987 to compute the direct index number between 1987 and the year that is designated. The index $I_87,88_$, for example, uses weights for 1987 and 1988; the index $I_87,89_$ uses weights for 1987 and 1989 (ignoring 1988), and the index $I_87,90_$ uses weights for 1987 and 1990. In this time series of index numbers, each entry measures price change from the base year of 1987 directly to the designated year, without considering either prices or quantities of intervening years. A statistical table would then record the results of the computations indicated in the column headed "1987" in the table.
The disadvantage of the direct index procedure is that some relevant index calculations are not in the 1987 column. Suppose one wants to know the price change between 1988 and 1989. For most purposes, it is reasonable to specify that the weights for such a price index should be taken from 1988 and 1989 (that is, the index $I_88,89_$ from the second column of the table). This index is not, of course, present in the 1987 column. For some purposes, therefore, the direct index procedure does not give the "best," or most relevant, measure of period-to-period price change.
The second way to obtain price measures between 1987 and 1990 is to use the "chain" index calculation procedure. In terms of the table, the chain index uses the calculations that are indicated by the boldfaced diagonal; that is, starting with the $I_87,88_$ index value, this value is multiplied by the indexes in the boldfaced diagonal, so that the chain index (1987–90) = $I_87,87_ × I_87,88_ × I_88,89_ × I_89,90_.$ With the chain index procedure, the price index for every adjacent pair of years has weights from exactly those 2 years.
The disadvantage of the chain index procedure is that for price comparisons over a whole period, such as 1987–90, the chain index incorporates all the intervening shifting weights. Thus, if one wants to know the change in the cost of a constant standard of living between 1987 and 1990, the answer is given by the direct index $I_87,90_$, which has weights only from 1987 and 1990.
It may be difficult to decide which calculation procedure to use. Neither one is best for all purposes. For some purposes, one wants a measure of the total change between 1987 and 1990; this will generally be given by the direct index between 1987 and 1990. However, for other purposes, one wants the best measure for, say, 1989–90, which is obtained from one of the links in the chain index. Because there are different uses for price measures—and also for quantity measures—it is generally advantageous for users to have access both to chain indexes, which are preferable for year-to-year or quarter-to-quarter comparisons, and to some form of direct index, which is preferable for longer term comparisons (1982 to 1987, or 1987 to 1990). To provide measures for different purposes, the new BEA alternative price and quantity measures include both a chain-type index (the annual weighted index) and a form of direct index (the benchmark-years-weighted index), both of which are based on the Fisher Ideal index number formula.
One qualification needs to be stated. For very long intervals, the assumptions necessary to produce direct indexes become insupportable. Suppose, for example, one wished to compare the change in a fixed standard of living between 1930 and 1990. Such a question becomes conceptually problematic because over an interval of 60 years, too many changes have occurred in the economy, in the way people live, and in tastes and customs. It might be reasonable to assume that economic conditions are sufficiently constant over, say, 5 years, so that a meaningful cost-of-living index can be computed. Computing one over 10 years poses perhaps a few more problems (for example,
new goods are introduced or tastes change), but the calculations may still be useful because the assumptions necessary to make such calculations are not sufficiently implausible as to render the interpretation of the numbers meaningless. The problematical parts become increasingly of concern as the interval lengthens to 15, 20, or 25 years. As one pushes these comparisons back further in time, any economic measurement becomes increasingly uncertain. Measuring the cost of a constant standard living over an interval as long as 500 years or more (which has been tried in some studies in economic history) involves a very large range of uncertainty that cannot be eliminated by any refinements in the formula used for calculating the price index.
The new BEA alternative price and quantity indexes provide direct indexes (in the form of the benchmark-years-weighted indexes) that cover the intervals between benchmarks, usually 5 years. Indexes for longer intervals (10 or 15 years or more) are produced by chaining these benchmark-years-weighted indexes together. Using this procedure does not necessarily imply that chain indexes are preferred for long-term comparisons. Rather, it recognizes that time series of index numbers will always require compromise, and the compromise adopted seems a useful one. The benchmark-years-weighted index procedure could readily be adapted to provide direct indexes covering longer intervals (for example, 1977–87, which encompasses two benchmark intervals), and such indexes might be of interest for some purposes.
1. A.A. Konüs, "The Problem of the True Index of the Cost of Living," Econometrica 7 (January 1939): 10–29.
2. Ragnar Frisch, "Annual Survey of General Economic Theory: The Problem of Index Numbers," Econometrica 4 (January 1936): 1–38.
3. The major studies are by Steven D. Braithwait, "The Substitution Bias of the Laspeyres Price Index: An Analysis Using Estimated Cost-of-Living Indexes," American Economic Review 70 (March 1980): 64–77; and Marilyn E. Manser and Richard J. McDonald, "An Analysis of Substitution Bias in Measuring Inflation, 1959–85," Econometrica 56 (July 1988): 909–930.
4. W. Erwin Diewert, "Exact and Superlative Index Numbers," Journal of Econometrics 46 (May 1976): 115–45.
5. Fisher Ideal quantity index = $\left\{∑ P_1_Q_2_∑ P_1_Q_1_\right\} × \left\{\sum P_2_Q_2_\sum P_2_Q_1_\right\}.$
6. Logarithm of Tornqvist quantity index = $∑ &ln; \left\{Q_2_Q_1_\right\} \left\{12\right\} \left( \left\{P_1_Q_1_∑ P_1_Q_1_\right\} + \left\{P_2_Q_2_∑ P_2_Q_2_\right\}\right).$ | 2017-04-28T21:58:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "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": 0.6951643228530884, "perplexity": 1326.2311637959663}, "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-2017-17/segments/1492917123097.48/warc/CC-MAIN-20170423031203-00113-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GDR3/Gaia_archive/chap_datamodel/sec_dm_performance_verification/ssec_dm_synthetic_photometry_gspc.html | # 20.14.8 synthetic_photometry_gspc
Gaia Synthetic Photometry Catalogue (GSPC)
This is a catalogue of synthetic photometry generated from the Gaia BP/RP mean spectra in Data Release 3 and standardised using wide and reliable sets of external standard stars.
Only sources that have BP/RP mean spectra in Gaia DR3 can be included in this catalogue. Individual magnitudes and fluxes are included only if $F/\sigma_{F}>30$ in that passband, where $F$ and $\sigma_{F}$ are the flux and its uncertainty.
Synthetic photometry is provided in a selection of photometric systems.
Further details on the generation and composition of the catalogue are available in Gaia Collaboration et al. (2022h).
Columns description:
source_id : Unique source identifier (unique within a particular Data Release) (long)
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).
c_star : BP/RP excess factor corrected for the expected colour dependency (float)
BP/RP excess factor corrected for the expected colour dependency as prescribed in Riello et al. (2021).
u_jkc_flux : U flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the U band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
u_jkc_flux_error : Error on the U flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the U band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
u_jkc_mag : U magnitude in the Johnson-Kron-Cousins system (float, Magnitude[mag])
Magnitude in the U band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
u_jkc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
b_jkc_flux : B flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the B band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
b_jkc_flux_error : Error on the B flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the B band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
b_jkc_mag : B magnitude in the Johnson-Kron-Cousins system (float, Magnitude[mag])
Magnitude in the B band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
b_jkc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
v_jkc_flux : V flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the V band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
v_jkc_flux_error : Error on the V flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the V band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
v_jkc_mag : V magnitude in the Johnson-Kron-Cousins system (float, Magnitude[mag])
Magnitude in the V band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
v_jkc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
r_jkc_flux : R flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the R band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
r_jkc_flux_error : Error on the R flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the R band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
r_jkc_mag : R magnitude in the Johnson-Kron-Cousins system (float, Magnitude[mag])
Magnitude in the R band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
r_jkc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
i_jkc_flux : I flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the I band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
i_jkc_flux_error : Error on the I flux in the Johnson-Kron-Cousins system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the I band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
i_jkc_mag : I magnitude in the Johnson-Kron-Cousins system (float, Magnitude[mag])
Magnitude in the I band of the standardised Johnson-Kron-Cousins photometric system as derived from the BP/RP spectra.
i_jkc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
u_sdss_flux : u flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the u band of the standardised SDSS photometric system as derived from the BP/RP spectra.
u_sdss_flux_error : Error on the u flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the u band of the standardised SDSS photometric system as derived from the BP/RP spectra.
u_sdss_mag : u magnitude in the SDSS system (float, Magnitude[mag])
Magnitude in the u band of the standardised SDSS photometric system as derived from the BP/RP spectra.
u_sdss_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
g_sdss_flux : g flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the g band of the standardised SDSS photometric system as derived from the BP/RP spectra.
g_sdss_flux_error : Error on the g flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the g band of the standardised SDSS photometric system as derived from the BP/RP spectra.
g_sdss_mag : g magnitude in the SDSS system (float, Magnitude[mag])
Magnitude in the g band of the standardised SDSS photometric system as derived from the BP/RP spectra.
g_sdss_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
r_sdss_flux : r flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the r band of the standardised SDSS photometric system as derived from the BP/RP spectra.
r_sdss_flux_error : Error on the r flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the r band of the standardised SDSS photometric system as derived from the BP/RP spectra.
r_sdss_mag : r magnitude in the SDSS system (float, Magnitude[mag])
Magnitude in the r band of the standardised SDSS photometric system as derived from the BP/RP spectra.
r_sdss_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
i_sdss_flux : i flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the i band of the standardised SDSS photometric system as derived from the BP/RP spectra.
i_sdss_flux_error : Error on the i flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the i band of the standardised SDSS photometric system as derived from the BP/RP spectra.
i_sdss_mag : i magnitude in the SDSS system (float, Magnitude[mag])
Magnitude in the i band of the standardised SDSS photometric system as derived from the BP/RP spectra.
i_sdss_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
z_sdss_flux : z flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the z band of the standardised SDSS photometric system as derived from the BP/RP spectra.
z_sdss_flux_error : Error on the z flux in the SDSS system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the z band of the standardised SDSS photometric system as derived from the BP/RP spectra.
z_sdss_mag : z magnitude in the SDSS system (float, Magnitude[mag])
Magnitude in the z band of the standardised SDSS photometric system as derived from the BP/RP spectra.
z_sdss_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
y_ps1_flux : y flux in the Pan-STARRS1 system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the y band of the standardised Pan-STARRS1 photometric system as derived from the BP/RP spectra.
y_ps1_flux_error : Error on the y flux in the Pan-STARRS1 system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the y band of the standardised Pan-STARRS1 photometric system as derived from the BP/RP spectra.
y_ps1_mag : y magnitude in the Pan-STARRS1 system (float, Magnitude[mag])
Magnitude in the y band of the standardised Pan-STARRS1 photometric system as derived from the BP/RP spectra.
y_ps1_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
f606w_acswfc_flux : F606W flux in the HST ACS/WFC system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the F606W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f606w_acswfc_flux_error : Error on the F606W flux in the HST ACS/WFC system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the F606W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f606w_acswfc_mag : F606W magnitude in the HST ACS/WFC system (float, Magnitude[mag])
Magnitude in the F606W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f606w_acswfc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system.
f814w_acswfc_flux : F814W flux in the HST ACS/WFC system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Flux in the F814W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f814w_acswfc_flux_error : Error on the F814W flux in the HST ACS/WFC system (float, Flux[W m${}^{-2}$ nm${}^{-1}$])
Error on the flux in the F814W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f814w_acswfc_mag : F814W magnitude in the HST ACS/WFC system (float, Magnitude[mag])
Magnitude in the F814W band of the standardised HST ACS/WFC photometric system as derived from the BP/RP spectra.
f814w_acswfc_flag : Flag indicating if G mag and BP-RP color of the source lie in the validated range (byte)
Flag indicating if G mag and BP-RP color of the source lie in the validated range for this band and photometric system. | 2022-08-08T04:47:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 55, "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": 0.5790683031082153, "perplexity": 6625.319971733593}, "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/1659882570765.6/warc/CC-MAIN-20220808031623-20220808061623-00170.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aetingof.pavel-i | ## Etingof, Pavel Il’ich
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Author ID: etingof.pavel-i Published as: Etingof, Pavel; Etingof, Pavel I.; Etingof, P.; Etingof, P. I.; Ehtingof, P. I. more...less Homepage: http://www-math.mit.edu/~etingof/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Documents Indexed: 227 Publications since 1987, including 9 Books 7 Contributions as Editor · 4 Further Contributions Co-Authors: 134 Co-Authors with 198 Joint Publications 3,190 Co-Co-Authors
all top 5
### Co-Authors
35 single-authored 31 Gelaki, Shlomo 12 Ostrik, Victor Valentinovich 11 Ginzburg, Victor 10 Nikshych, Dmitri 10 Rains, Eric M. 10 Schedler, Travis 10 Schiffmann, Olivier G. 9 Kazhdan, David A. 9 Varchenko, Alexander Nikolaevich 9 Walton, Chelsea 8 Enriquez, Benjamin 8 Entov, Vladimir M. 8 Kirillov, Alexander A. jun. 6 Ma, Xiaoguang 6 Oblomkov, Alexei A. 4 Berest, Yuri Yu. 4 Cuadra, Juan 4 Retakh, Vladimir Solomonovich 3 Andruskiewitsch, Nicolás 3 Braverman, Alexander 3 Chalykh, Oleg A. 3 Frenkel, Igor B. 3 Gan, Wee Liang 3 Khovanov, Mikhail G. 3 Soloviev, Alexandre A. 2 Abughazalah, Nabilah Hani 2 Bezrukavnikov, Roman 2 Calaque, Damien 2 Dobrovolska, Galyna 2 Eu, Ching-Hwa 2 Finkelberg, Michael Vladlenovich 2 Gel’fand, Israil’ Moiseevich 2 Gerovitch, Slava 2 Griffeth, Stephen 2 Guralnick, Robert Michael 2 Kleinbock, Dmitry Ya. 2 Latour, Frédéric 2 Loktev, Sergey A. 2 Losev, Ivan V. 2 Marshall, Ian 2 Moura, Adriano A. 2 Rybnikov, Leonid Grigor’evich 2 Savage, Alistair 2 Stryker, Douglas 2 Styrkas, Konstantin 1 Adler, Vsevolod Eduardovich 1 Aizenbud, Inna Entova 1 Aljadeff, Eli 1 Bartholdi, Laurent 1 Benson, David John 1 Bhupatiraju, Surya 1 Brookner, Aaron 1 Brundan, Jonathan 1 Bukhshtaber, Viktor Matveevich 1 Chmutova, Tatyana 1 Corwin, David 1 Coulembier, Kevin 1 Crawley-Boevey, William 1 Davydov, Alekseĭ Aleksandrovich 1 Deligne, Pierre René 1 Ding, Jintai 1 Dolgushev, Vasily A. 1 Dubrovin, Boris Anatol’evich 1 Duncan, John F. R. 1 Feigin, Misha V. 1 Felder, Giovanni 1 Felder, J. 1 Ferapontov, Evgeny Vladimirovich 1 Freed, Daniel Stuart 1 Frenkel, Edward V. 1 Freund, Rebecca 1 Gaitsgory, Dennis 1 Galindo Martínez, César Neyit 1 Geer, Nathan 1 Golberg, Oleg 1 Gong, Sherry 1 Gorsky, Eugene 1 Goswami, Debashish 1 Grinevich, Pëtr Georgievich 1 Gusein-Zade, Sabir M. 1 Harman, Nate 1 Henriques, André G. 1 Hensel, Sebastian Wolfgang 1 Ilyashenko, Yulij Sergeevich 1 Ip, Ivan Chi-Ho 1 Jeffrey, Lisa Claire 1 Jordan, David Andrew 1 Kamnitzer, Joel 1 Kapranov, Mikhail M. 1 Khesin, Boris A. 1 Khovanova, Tanya 1 Kinser, Ryan 1 Klejnbok, D. Ya. 1 Klyuev, Daniil 1 Krichever, Igor’ Moiseevich 1 Krylov, Vasily 1 Kuszmaul, William 1 Lando, Sergei K. 1 Li, Jason Jingshi 1 Libine, Matvei ...and 38 more Co-Authors
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### Serials
24 IMRN. International Mathematics Research Notices 22 Mathematical Research Letters 19 Journal of Algebra 15 Advances in Mathematics 9 Communications in Mathematical Physics 9 Duke Mathematical Journal 8 Transformation Groups 8 Moscow Mathematical Journal 6 Selecta Mathematica. New Series 6 Representation Theory 5 European Journal of Applied Mathematics 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Journal für die Reine und Angewandte Mathematik 4 Geometric and Functional Analysis. GAFA 3 Communications in Algebra 3 Letters in Mathematical Physics 3 Compositio Mathematica 3 The Asian Journal of Mathematics 3 Algebras and Representation Theory 2 Fluid Dynamics 2 Journal of Mathematical Physics 2 Journal of Pure and Applied Algebra 2 Michigan Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Notices of the American Mathematical Society 2 Electronic Research Announcements of the American Mathematical Society 2 Annals of Mathematics. Second Series 2 Journal of Algebra and its Applications 2 Contemporary Mathematics 2 Mathematical Surveys and Monographs 2 Algebra & Number Theory 2 Quantum Topology 1 Computers & Mathematics with Applications 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Russian Mathematical Surveys 1 American Journal of Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Journal of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 L’Enseignement Mathématique. 2e Série 1 Soviet Physics. Doklady 1 Experimental Mathematics 1 Applied Categorical Structures 1 Journal of the European Mathematical Society (JEMS) 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oberwolfach Reports 1 Pure and Applied Mathematics Quarterly 1 Oxford Lecture Series in Mathematics and its Applications 1 Progress in Mathematics 1 University Lecture Series 1 Student Mathematical Library 1 Journal of Noncommutative Geometry 1 Arnold Mathematical Journal 1 Zurich Lectures in Advanced Mathematics
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### Fields
109 Nonassociative rings and algebras (17-XX) 108 Associative rings and algebras (16-XX) 50 Group theory and generalizations (20-XX) 49 Quantum theory (81-XX) 46 Category theory; homological algebra (18-XX) 31 Algebraic geometry (14-XX) 15 Several complex variables and analytic spaces (32-XX) 15 Differential geometry (53-XX) 13 Special functions (33-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Fluid mechanics (76-XX) 11 Commutative algebra (13-XX) 10 Combinatorics (05-XX) 10 Partial differential equations (35-XX) 9 Difference and functional equations (39-XX) 7 General and overarching topics; collections (00-XX) 6 Topological groups, Lie groups (22-XX) 5 Functions of a complex variable (30-XX) 5 Manifolds and cell complexes (57-XX) 4 Number theory (11-XX) 4 $$K$$-theory (19-XX) 3 History and biography (01-XX) 3 Potential theory (31-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Field theory and polynomials (12-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Abstract harmonic analysis (43-XX) 2 Algebraic topology (55-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Mathematical logic and foundations (03-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)
### Citations contained in zbMATH Open
206 Publications have been cited 4,338 times in 2,622 Documents Cited by Year
On fusion categories. Zbl 1125.16025
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
2005
Tensor categories. Zbl 1365.18001
Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor
2015
Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism. Zbl 1061.16032
Etingof, Pavel; Ginzburg, Victor
2002
Set-theoretical solutions to the quantum Yang-Baxter equation. Zbl 0969.81030
Etingof, Pavel; Schedler, Travis; Soloviev, Alexandre
1999
Finite tensor categories. Zbl 1077.18005
Etingof, Pavel; Ostrik, Viktor
2004
Fusion categories and homotopy theory. Zbl 1214.18007
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
2010
Quantization of Lie bialgebras. I. Zbl 0863.17008
Etingof, Pavel; Kazhdan, David
1996
Weakly group-theoretical and solvable fusion categories. Zbl 1210.18009
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2011
Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1998
Noncommutative geometry and quiver algebras. Zbl 1111.53066
Crawley-Boevey, William; Etingof, Pavel; Ginzburg, Victor
2007
Finite-dimensional representations of rational Cherednik algebras. Zbl 1063.20003
Berest, Yuri; Etingof, Pavel; Ginzburg, Victor
2003
Quantization of Lie bialgebras. V: Quantum vertex operator algebras. Zbl 0948.17008
Etingof, Pavel; Kazhdan, David
2000
Some properties of finite-dimensional semisimple Hopf algebras. Zbl 0907.16016
Etingof, Pavel; Gelaki, Shlomo
1998
Calogero-Moser systems and representation theory. Zbl 1331.53002
Etingof, Pavel
2007
Parabolic induction and restriction functors for rational Cherednik algebras. Zbl 1226.20002
Bezrukavnikov, Roman; Etingof, Pavel
2009
Noncommutative del Pezzo surfaces and Calabi-Yau algebras. Zbl 1204.14004
Etingof, Pavel; Ginzburg, Victor
2010
Quantization of Lie bialgebras. II, III. Zbl 0915.17009
Etingof, Pavel; Kazhdan, David
1998
Cherednik algebras and differential operators on quasi-invariants. Zbl 1067.16047
Berest, Yuri; Etingof, Pavel; Ginzburg, Victor
2003
On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic. Zbl 0918.16027
Etingof, Pavel; Gelaki, Shlomo
1998
On rack cohomology. Zbl 1054.16028
Etingof, P.; Graña, M.
2003
Universal KZB equations: the elliptic case. Zbl 1241.32011
Calaque, Damien; Enriquez, Benjamin; Etingof, Pavel
2009
Whittaker functions on quantum groups and $$q$$-deformed Toda operators. Zbl 1157.33327
Etingof, Pavel
1999
Instanton counting via affine Lie algebras. II: From Whittaker vectors to the Seiberg-Witten prepotential. Zbl 1177.14036
Braverman, A.; Etingof, P.
2006
Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Zbl 0915.17018
Etingof, Pavel; Varchenko, Alexander
1998
The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points. Zbl 1206.14051
Etingof, Pavel; Henriques, André; Kamnitzer, Joel; Rains, Eric M.
2010
Quantum fields and strings: a course for mathematicians. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Zbl 0984.00503
1999
Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups. Zbl 0957.17019
Etingof, Pavel; Varchenko, Alexander
1998
Factorization of differential operators, quasideterminants, and nonabelian Toda field equations. Zbl 0959.37054
Etingof, Pavel; Gelfand, Israel; Retakh, Vladimir
1997
Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with a prime number of elements. Zbl 1018.17007
Etingof, Pavel; Soloviev, Alexander; Guralnick, Robert
2001
Lectures on quantum groups. 2nd ed. Zbl 1106.17015
Etingof, Pavel; Schiffmann, Olivier
2002
Why the boundary of a round drop becomes a curve of order four. Zbl 0768.76073
Varchenko, A. N.; Etingof, P. I.
1992
Triangular Hopf algebras with the Chevalley property. Zbl 1016.16029
Andruskiewitsch, Nicolás; Etingof, Pavel; Gelaki, Shlomo
2001
Semisimple Hopf actions on commutative domains. Zbl 1297.16029
Etingof, Pavel; Walton, Chelsea
2014
An analogue of Radford’s $$S^4$$ formula for finite tensor categories. Zbl 1079.16024
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
2004
Lectures on quantum groups. Zbl 1105.17300
Etingof, Pavel; Schiffmann, Olivier
1998
Macdonald’s polynomials and representations of quantum groups. Zbl 0833.17007
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
The classification of triangular semisimple and cosemisimple Hopf algebras over an algebraically closed field. Zbl 0957.16029
Etingof, Pavel; Gelaki, Shlomo
2000
Dynamical quantum groups at roots of 1. Zbl 1023.17007
Etingof, Pavel; Nikshych, Dmitri
2001
Lectures on the dynamical Yang-Baxter equations. Zbl 1036.17013
Etingof, Pavel; Schiffmann, Olivier
2001
Exchange dynamical quantum groups. Zbl 0943.17010
Etingof, P.; Varchenko, A.
1999
Spherical functions on affine Lie groups. Zbl 0848.43010
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1995
Dynamical Weyl groups and applications. Zbl 1033.17010
Etingof, P.; Varchenko, A.
2002
Cherednik algebras and Hilbert schemes in characteristic $$p$$. With an appendix by Pavel Etingof. Zbl 1130.14005
Bezrukavnikov, Roman; Finkelberg, Michael; Ginzburg, Victor
2006
Finite dimensional quasi-Hopf algebras with radical of codimension 2. Zbl 1080.16041
Etingof, Pavel; Gelaki, Shlomo
2004
Representations of rational Cherednik algebras with minimal support and torus knots. Zbl 1321.16020
Etingof, Pavel; Gorsky, Eugene; Losev, Ivan
2015
Bubble contraction in Hele-Shaw cells. Zbl 0743.76020
Entov, V. M.; Etingof, P. I.
1991
On the exponent of finite-dimensional Hopf algebras. Zbl 0954.16028
Etingof, Pavel; Gelaki, Shlomo
1999
Classification of fusion categories of dimension $$pq$$. Zbl 1063.18005
Etingof, Pavel; Gelaki, Shlomo; Ostrik, Viktor
2004
On twisting of finite-dimensional Hopf algebras. Zbl 1053.16026
Aljadeff, Eli; Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri
2002
Unitary representations of rational Cherednik algebras. (With an appendix by Stephen Griffeth). Zbl 1237.20005
Etingof, Pavel; Stoica, Emanuel
2009
Explicit quantization of dynamical $$r$$-matrices for finite dimensional semisimple Lie algebras. Zbl 0957.17011
Etingof, Pavel; Schedler, Travis; Schiffmann, Olivier
2000
Nonabelian integrable systems, quasideterminants, and Marchenko lemma. Zbl 0948.37055
Etingof, Pavel; Gelfand, Israel; Retakh, Vladimir
1998
Semisimple Hopf algebras of dimension $$pq$$ are trivial. Zbl 0919.16028
Etingof, Pavel; Gelaki, Shlomo
1998
Braid group representations from twisted quantum doubles of finite groups. Zbl 1207.16038
Etingof, Pavel; Rowell, Eric; Witherspoon, Sarah
2008
Isocategorical groups. Zbl 0988.20003
Etingof, Pavel; Gelaki, Shlomo
2001
On families of triangular Hopf algebras. Zbl 0998.16028
Etingof, Pavel; Gelaki, Shlomo
2002
Representations of affine Lie algebras, parabolic differential equations, and Lamé functions. Zbl 0811.17026
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
Geometric crystals and set-theoretical solutions to the quantum Yang-Baxter equation. Zbl 1020.17008
Etingof, Pavel
2003
Quantum integrable systems and differential Galois theory. Zbl 0901.58021
Braverman, A.; Etingof, P.; Gaitsgory, D.
1997
Groups and Lie algebras corresponding to the Yang-Baxter equations. Zbl 1169.17004
Bartholdi, Laurent; Enriquez, Benjamin; Etingof, Pavel; Rains, Eric
2006
A method of construction of finite-dimensional triangular semisimple Hopf algebras. Zbl 0935.16029
Etingof, Pavel; Gelaki, Shlomo
1998
Central extensions of current groups in two dimensions. Zbl 0822.22014
Etingof, Pavel I.; Frenkel, Igor B.
1994
Quantization of classical dynamical $$r$$-matrices with nonabelian base. Zbl 1063.17013
Enriquez, Benjamin; Etingof, Pavel
2005
Traces of intertwiners for quantum groups and difference equations. I. Zbl 1004.17006
Etingof, Pavel; Varchenko, Alexander
2000
Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces. Zbl 1118.14003
Etingof, Pavel; Oblomkov, Alexei; Rains, Eric
2007
Poisson traces and $$D$$-modules on Poisson varieties. With an appendix by Ivan Losev. Zbl 1223.17023
Etingof, Pavel; Schedler, Travis
2010
Module categories over representations of $$\text{SL}_q(2)$$ and graphs. Zbl 1053.17010
Etingof, Pavel; Ostrik, Viktor
2004
On some representations of the rational Cherednik algebra. Zbl 1070.20005
Chmutova, Tatyana; Etingof, Pavel
2003
The classification of finite-dimensional triangular Hopf algebras over an algebraically closed field of characteristic 0. Zbl 1062.16043
Etingof, Pavel; Gelaki, Shlomo
2003
A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups. Zbl 1230.33011
Etingof, Pavel
2010
Introduction to representation theory. With historical interludes by Slava Gerovitch. Zbl 1242.20001
Etingof, Pavel; Golberg, Oleg; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex; Vaintrob, Dmitry; Yudovina, Elena
2011
Continuous Hecke algebras. Zbl 1115.20005
Etingof, Pavel; Gan, Wee Liang; Ginzburg, Victor
2005
Algebraic integrability of Macdonald operators and representations of quantum groups. Zbl 0918.17011
Etingof, Pavel; Styrkas, Konstantin
1998
Pointed Hopf actions on fields. I. Zbl 1338.16035
Etingof, Pavel; Walton, Chelsea
2015
On $$m$$-quasi-invariants of a Coxeter group. Zbl 1028.81027
Etingof, Pavel; Ginzburg, Victor
2002
Noncommutative complete intersections and matrix integrals. Zbl 1151.14006
Etingof, Pavel; Ginzburg, Victor
2007
On universal Lie nilpotent associative algebras. Zbl 1236.16021
Etingof, Pavel; Kim, John; Ma, Xiaoguang
2009
Radically graded finite-dimensional quasi-Hopf algebras. Zbl 1084.16030
Etingof, Pavel; Gelaki, Shlomo
2005
Lectures on tensor categories. Zbl 1160.18004
Calaque, Damien; Etingof, Pavel
2008
Quantization of geometric classical $$r$$-matrices. Zbl 0999.17025
Etingof, Pavel; Soloviev, Alexandre
1999
Quantization of Alekseev-Meinrenken dynamical $$r$$-matrices. Zbl 1039.17013
Enriquez, Benjamin; Etingof, Pavel
2003
Morita equivalence of Cherednik algebras. Zbl 1067.16046
Berest, Yuri; Etingof, Pavel; Ginzburg, Victor
2004
Quantization of Lie bialgebras. VI: Quantization of generalized Kac-Moody algebras. Zbl 1191.17004
Etingof, Pavel; Kazhdan, David
2008
On Hopf algebras of dimension $$pq$$. Zbl 1068.16054
Etingof, Pavel; Gelaki, Shlomo
2004
When is the Fourier transform of an elementary function elementary? Zbl 1037.11080
Etingof, Pavel; Kazhdan, David; Polishchuk, Alexander
2002
Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups. Zbl 1171.16007
Etingof, Pavel; Rains, Eric
2006
Representation theory in complex rank. II. Zbl 1403.20055
Etingof, Pavel
2016
The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems. Zbl 1071.17012
Etingof, Pavel; Latour, Frédéric
2005
On the quasi-exponent of finite-dimensional Hopf algebras. Zbl 1012.16038
Etingof, Pavel; Gelaki, Shlomo
2002
On Vafa’s theorem for tensor categories. Zbl 1035.18004
Etingof, Pavel
2002
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products. Zbl 1188.16010
Etingof, Pavel; Gan, Wee Liang; Ginzburg, Victor; Oblomkov, Alexei
2007
Koszulity and the Hilbert series of preprojective algebras. Zbl 1138.16006
Etingof, Pavel; Eu, Ching-Hwa
2007
Quantization, orbifold cohomology, and Cherednik algebras. Zbl 1137.16014
Etingof, Pavel; Oblomkov, Alexei
2006
Quantum integrable systems and representations of Lie algebras. Zbl 0861.17002
Etingof, Pavel I.
1995
Representation theory in complex rank. I. Zbl 1336.20011
Etingof, Pavel
2014
On the invertibility of quantization functors. Zbl 1152.17005
Enriquez, Benjamin; Etingof, Pavel
2005
New deformations of group algebras of Coxeter groups. Zbl 1099.20019
Etingof, Pavel; Rains, Eric
2005
Finite dimensional representations of symplectic reflection algebras associated to wreath products. Zbl 1153.16011
Etingof, Pavel; Montarani, Silvia
2005
Hochschild cohomology of quantized symplectic orbifolds and the Chen-Ruan cohomology. Zbl 1088.53061
Dolgushev, Vasiliy; Etingof, Pavel
2005
Comparison of Poisson structures and Poisson-Lie dynamical $$r$$-matrices. Zbl 1092.53057
Enriquez, Benjamin; Etingof, Pavel; Marshall, Ian
2005
An analytic version of the Langlands correspondence for complex curves. Zbl 1475.14021
Etingof, Pavel; Frenkel, Edward; Kazhdan, David
2021
On the Frobenius functor for symmetric tensor categories in positive characteristic. Zbl 1478.18019
Etingof, Pavel; Ostrik, Victor
2021
Finite symmetric tensor categories with the Chevalley property in characteristic $$2$$. Zbl 1470.17009
Etingof, Pavel; Gelaki, Shlomo
2021
Short star-products for filtered quantizations. I. Zbl 1480.81078
Etingof, Pavel; Stryker, Douglas
2020
Semisimplification of the category of tilting modules for $$GL_n$$. Zbl 07281385
Brundan, Jonathan; Entova-Aizenbud, Inna; Etingof, Pavel; Ostrik, Victor
2020
Invariant Hopf 2-cocycles for affine algebraic groups. Zbl 1480.20113
Etingof, Pavel; Gelaki, Shlomo
2020
Cyclotomic double affine Hecke algebras. Zbl 07346523
Braverman, Alexander; Etingof, Pavel; Finkelberg, Michael
2020
Contingency tables with variable margins (with an appendix by Pavel Etingof). Zbl 1454.05012
Kapranov, Mikhail; Schechtman, Vadim
2020
Symmetric tensor categories in characteristic 2. Zbl 1430.18013
Benson, Dave; Etingof, Pavel
2019
$$p$$-adic dimensions in symmetric tensor categories in characteristic $$p$$. Zbl 1390.18016
Etingof, Pavel; Harman, Nate; Ostrik, Victor
2018
Autoequivalences of tensor categories attached to quantum groups at roots of 1. Zbl 1451.18034
Davydov, Alexei; Etingof, Pavel; Nikshych, Dmitri
2018
Koszul duality and the PBW theorem in symmetric tensor categories in positive characteristic. Zbl 1440.18030
Etingof, Pavel
2018
Reflection fusion categories. Zbl 1442.18039
Etingof, Pavel; Galindo, César
2018
On faithfulness of the lifting for Hopf algebras and fusion categories. Zbl 1440.16034
Etingof, Pavel
2018
A Tannakian interpretation of the elliptic infinitesimal braid Lie algebras. Zbl 1423.14063
Enriquez, Benjamin; Etingof, Pavel
2018
Exact sequences of tensor categories with respect to a module category. Zbl 1367.18002
Etingof, Pavel; Gelaki, Shlomo
2017
Cherednik and Hecke algebras of varieties with a finite group action. Zbl 1474.20005
Etingof, Pavel
2017
Proof of the Broué-Malle-Rouquier conjecture in characteristic zero (after I. Losev and I. Marin-G. Pfeiffer). Zbl 1386.20003
Etingof, Pavel
2017
Computations in symmetric fusion categories in characteristic $$p$$. Zbl 1405.18011
Etingof, Pavel; Ostrik, Victor; Venkatesh, Siddharth
2017
Finite dimensional Hopf actions on deformation quantizations. Zbl 1388.16033
Etingof, Pavel; Walton, Chelsea
2017
Finite dimensional Hopf actions on central division algebras. Zbl 1405.16040
Cuadra, Juan; Etingof, Pavel
2017
Hopf coactions on commutative algebras generated by a quadratically independent comodule. Zbl 1395.16037
Etingof, Pavel; Goswami, Debashish; Mandal, Arnab; Walton, Chelsea
2017
Semisimple and $$G$$-equivariant simple algebras over operads. Zbl 1386.18035
Etingof, Pavel
2017
Representation theory in complex rank. II. Zbl 1403.20055
Etingof, Pavel
2016
Pointed Hopf actions on fields. II. Zbl 1356.16026
Etingof, Pavel; Walton, Chelsea
2016
Finite dimensional Hopf actions on algebraic quantizations. Zbl 1355.16030
Etingof, Pavel; Walton, Chelsea
2016
Co-invariants of Lie algebras of vector fields on algebraic varieties. Zbl 1397.17027
Etingof, Pavel; Schedler, Travis
2016
On Cohen-Macaulayness of algebras generated by generalized power sums. With an appendix by Misha Feigin. Zbl 1357.13016
Etingof, Pavel; Rains, Eric
2016
On Cohen-Macaulayness of $$S_n$$-invariant subspace arrangements. Zbl 1404.14063
Brookner, Aaron; Corwin, David; Etingof, Pavel; Sam, Steven V.
2016
Finite dimensional Hopf actions on Weyl algebras. Zbl 1356.16025
Cuadra, Juan; Etingof, Pavel; Walton, Chelsea
2016
On properties of the lower central series of associative algebras. Zbl 1378.16031
Abughazalah, Nabilah; Etingof, Pavel
2016
Tensor categories. Zbl 1365.18001
Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor
2015
Representations of rational Cherednik algebras with minimal support and torus knots. Zbl 1321.16020
Etingof, Pavel; Gorsky, Eugene; Losev, Ivan
2015
Pointed Hopf actions on fields. I. Zbl 1338.16035
Etingof, Pavel; Walton, Chelsea
2015
Semisimple Hopf actions on Weyl algebras. Zbl 1369.16026
Cuadra, Juan; Etingof, Pavel; Walton, Chelsea
2015
Galois bimodules and integrality of PI comodule algebras over invariants. Zbl 1329.16028
Etingof, Pavel
2015
On two finiteness conditions for Hopf algebras with nonzero integral. Zbl 1333.16031
Andruskiewitsch, Nicolás; Cuadra, Juan; Etingof, Pavel
2015
Semisimple Hopf actions on commutative domains. Zbl 1297.16029
Etingof, Pavel; Walton, Chelsea
2014
Representation theory in complex rank. I. Zbl 1336.20011
Etingof, Pavel
2014
Poisson traces for symmetric powers of symplectic varieties. Zbl 1331.17019
Etingof, Pavel; Schedler, Travis
2014
Exploring noncommutative algebras via deformation theory. Zbl 1328.16013
Etingof, Pavel
2014
Invariants of Hamiltonian flow on locally complete intersections. Zbl 1320.14034
Etingof, Pavel; Schedler, Travis
2014
Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions. Zbl 1282.33028
Chalykh, Oleg; Etingof, Pavel
2013
On some properties of quantum doubles of finite groups. Zbl 1318.16035
Etingof, Pavel
2013
Symplectic reflection algebras and affine Lie algebras. Zbl 1293.17030
Etingof, Pavel
2012
Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups. (With an appendix by Stephen Griffeth). Zbl 1238.20008
Etingof, Pavel
2012
Lower central series of a free associative algebra over the integers and finite fields. Zbl 1320.16012
Bhupatiraju, Surya; Etingof, Pavel; Jordan, David; Kuszmaul, William; Li, Jason
2012
Computational approaches to Poisson traces associated to finite subgroups of $$\text{Sp}_{2n}(\mathbb C)$$. Zbl 1246.53111
Etingof, Pavel; Gong, Sherry; Pacchiano, Aldo; Ren, Qingchun; Schedler, Travis
2012
Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities. Zbl 1244.53092
Etingof, Pavel; Schedler, Travis
2012
Descent and forms of tensor categories. Zbl 1246.18003
Etingof, Pavel; Gelaki, Shlomo
2012
Weakly group-theoretical and solvable fusion categories. Zbl 1210.18009
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2011
Introduction to representation theory. With historical interludes by Slava Gerovitch. Zbl 1242.20001
Etingof, Pavel; Golberg, Oleg; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex; Vaintrob, Dmitry; Yudovina, Elena
2011
On elliptic Calogero-Moser systems for complex crystallographic reflection groups. Zbl 1243.14036
Etingof, Pavel; Felder, Giovanni; Ma, Xiaoguang; Veselov, Alexander
2011
On the breakup of air bubbles in a Hele-Shaw cell. Zbl 1429.76046
Entov, Vladimir; Etingof, Pavel
2011
On algebraically integrable differential operators on an elliptic curve. Zbl 1247.37045
Etingof, Pavel; Rains, Eric
2011
Fusion categories and homotopy theory. Zbl 1214.18007
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
2010
Noncommutative del Pezzo surfaces and Calabi-Yau algebras. Zbl 1204.14004
Etingof, Pavel; Ginzburg, Victor
2010
The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points. Zbl 1206.14051
Etingof, Pavel; Henriques, André; Kamnitzer, Joel; Rains, Eric M.
2010
Poisson traces and $$D$$-modules on Poisson varieties. With an appendix by Ivan Losev. Zbl 1223.17023
Etingof, Pavel; Schedler, Travis
2010
A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups. Zbl 1230.33011
Etingof, Pavel
2010
Root extensions and factorization in affine domains. Zbl 1198.13018
Etingof, P.; Malcolmson, P.; Okoh, F.
2010
Traces on finite $$\mathcal{W}$$-algebras. Zbl 1253.17007
Etingof, Pavel; Schedler, Travis
2010
Parabolic induction and restriction functors for rational Cherednik algebras. Zbl 1226.20002
Bezrukavnikov, Roman; Etingof, Pavel
2009
Universal KZB equations: the elliptic case. Zbl 1241.32011
Calaque, Damien; Enriquez, Benjamin; Etingof, Pavel
2009
Unitary representations of rational Cherednik algebras. (With an appendix by Stephen Griffeth). Zbl 1237.20005
Etingof, Pavel; Stoica, Emanuel
2009
On universal Lie nilpotent associative algebras. Zbl 1236.16021
Etingof, Pavel; Kim, John; Ma, Xiaoguang
2009
A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type $$BC_n$$. Zbl 1171.20004
Etingof, Pavel; Freund, Rebecca; Ma, Xiaoguang
2009
The small quantum group as a quantum double. Zbl 1267.17010
Etingof, Pavel; Gelaki, Shlomo
2009
Braid group representations from twisted quantum doubles of finite groups. Zbl 1207.16038
Etingof, Pavel; Rowell, Eric; Witherspoon, Sarah
2008
Lectures on tensor categories. Zbl 1160.18004
Calaque, Damien; Etingof, Pavel
2008
Quantization of Lie bialgebras. VI: Quantization of generalized Kac-Moody algebras. Zbl 1191.17004
Etingof, Pavel; Kazhdan, David
2008
Quasisymmetric and unipotent tensor categories. Zbl 1168.18003
Etingof, Pavel; Gelaki, Shlomo
2008
An upper bound for the lower central series quotients of a free associative algebra. Zbl 1146.16011
Dobrovolska, Galyna; Etingof, Pavel
2008
An algebraic extension of the MacMahon master theorem. Zbl 1191.05018
Etingof, Pavel; Pak, Igor
2008
On the lower central series of an associative algebra (with an appendix by Pavel Etingof). Zbl 1153.16023
Dobrovolska, Galyna; Kim, John; Ma, Xiaoguang
2008
New deformations of group algebras of Coxeter groups. II. Zbl 1148.20027
Etingof, Pavel; Rains, Eric
2008
A Lie-theoretic construction of spherical symplectic reflection algebras. Zbl 1186.17006
Etingof, P.; Loktev, S.; Oblomkov, A.; Rybnikov, L.
2008
On elliptic Dunkl operators. Zbl 1184.43011
Etingof, Pavel; Ma, Xiaoguang
2008
Noncommutative geometry and quiver algebras. Zbl 1111.53066
Crawley-Boevey, William; Etingof, Pavel; Ginzburg, Victor
2007
Calogero-Moser systems and representation theory. Zbl 1331.53002
Etingof, Pavel
2007
Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces. Zbl 1118.14003
Etingof, Pavel; Oblomkov, Alexei; Rains, Eric
2007
Noncommutative complete intersections and matrix integrals. Zbl 1151.14006
Etingof, Pavel; Ginzburg, Victor
2007
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products. Zbl 1188.16010
Etingof, Pavel; Gan, Wee Liang; Ginzburg, Victor; Oblomkov, Alexei
2007
Koszulity and the Hilbert series of preprojective algebras. Zbl 1138.16006
Etingof, Pavel; Eu, Ching-Hwa
2007
Hochschild and cyclic homology of preprojective algebras of ADE quivers. Zbl 1138.16004
Etingof, Pavel; Eu, Ching-Hwa
2007
Quantization of some Poisson-Lie dynamical $$r$$-matrices and Poisson homogeneous spaces. Zbl 1197.17008
Enriques, Benjamin; Etingof, Pavel; Marshall, Ian
2007
On a generalized two-fluid Hele-Shaw flow. Zbl 1132.76019
Entov, V. M.; Etingof, P.
2007
Density of eigenvalues of random normal matrices with an arbitrary potential, and of generalized normal matrices. Zbl 1139.15014
Etingof, Pavel; Ma, Xiaoguang
2007
Monodromy of trigonometric KZ equations. Zbl 1161.32005
Etingof, Pavel; Geer, Nathan
2007
On central extensions of preprojective algebras. Zbl 1181.16013
Etingof, Pavel; Latour, Frédéric; Rains, Eric
2007
Instanton counting via affine Lie algebras. II: From Whittaker vectors to the Seiberg-Witten prepotential. Zbl 1177.14036
Braverman, A.; Etingof, P.
2006
Cherednik algebras and Hilbert schemes in characteristic $$p$$. With an appendix by Pavel Etingof. Zbl 1130.14005
Bezrukavnikov, Roman; Finkelberg, Michael; Ginzburg, Victor
2006
Groups and Lie algebras corresponding to the Yang-Baxter equations. Zbl 1169.17004
Bartholdi, Laurent; Enriquez, Benjamin; Etingof, Pavel; Rains, Eric
2006
Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups. Zbl 1171.16007
Etingof, Pavel; Rains, Eric
2006
Quantization, orbifold cohomology, and Cherednik algebras. Zbl 1137.16014
Etingof, Pavel; Oblomkov, Alexei
2006
Liftings of graded quasi-Hopf algebras with radical of prime codimension. Zbl 1091.16022
Etingof, Pavel; Gelaki, Shlomo
2006
Generalized double affine Hecke algebras of higher rank. Zbl 1130.20006
Etingof, Pavel; Gan, Wee Liang; Oblomkov, Alexei
2006
Casimirs of the Goldman Lie algebra of a closed surface. Zbl 1151.17310
Etingof, Pavel
2006
On fusion categories. Zbl 1125.16025
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
2005
Quantization of classical dynamical $$r$$-matrices with nonabelian base. Zbl 1063.17013
Enriquez, Benjamin; Etingof, Pavel
2005
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### Cited by 2,222 Authors
93 Etingof, Pavel Il’ich 34 Rump, Wolfgang 29 Jespers, Eric 26 Rowell, Eric C. 24 Natale, Sonia 24 Schweigert, Christoph 23 Runkel, Ingo 22 Fehér, László Gy. 22 Mudrov, Andrey I. 21 Cedó, Ferran 21 Li, Haisheng 21 Nikshych, Dmitri 21 Okniński, Jan 20 Gelaki, Shlomo 20 Varchenko, Alexander Nikolaevich 20 Wang, Zhenghan 19 Galindo Martínez, César Neyit 19 Losev, Ivan V. 19 Ng, Siu-Hung 19 Schedler, Travis 18 Andruskiewitsch, Nicolás 18 Dong, Jingcheng 18 Fuchs, Jürgen 17 Bellamy, Gwyn 17 Burciu, Sebastian M. 17 Vendramin, Leandro 17 Witherspoon, Sarah J. 16 Ginzburg, Victor 16 Zhang, Yinhuo 15 Catino, Francesco 15 Kong, Liang 15 Walton, Chelsea 14 Ostrik, Victor Valentinovich 14 Shimizu, Kenichi 14 Snyder, Noah 13 Huang, Hua-Lin 13 Liu, Gongxiang 13 Morrison, Scott 13 Plavnik, Julia Yael 13 Stolin, Alexander 12 Angiono, Iván Ezequiel 12 Enriquez, Benjamin 12 Gateva-Ivanova, Tatiana 12 Kožić, Slaven 11 Creutzig, Thomas 11 Finkelberg, Michael Vladlenovich 11 Griffeth, Stephen 11 Jordan, David Andrew 11 Stefanelli, Paola 11 Zhang, James J. 10 Bai, Chengming 10 Bichon, Julien 10 Chalykh, Oleg A. 10 Davydov, Alekseĭ Aleksandrovich 10 Gaiffi, Giovanni 10 Kadison, Lars 10 Kirkman, Ellen E. 10 Oblomkov, Alexei A. 10 Rains, Eric M. 10 Stokman, Jasper V. 10 van Oystaeyen, Freddy 9 Bonatto, Marco 9 Bulacu, Daniel 9 Cherednik, Ivan V. 9 Jones, Corey 9 Kirillov, Alexander A. jun. 9 Mombelli, Martín 9 Negron, Cris 9 Neshveyev, Sergey V. 9 Przytycki, Józef H. 9 Schauenburg, Peter 9 Shepler, Anne V. 9 Sun, Jiancai 8 Bachiller, David 8 Beattie, Margaret 8 Bruillard, Paul 8 Chirvăsitu, Alexandru 8 Cohen, Miriam 8 Cox, Ben Lewis 8 De Commer, Kenny 8 Dong, Chongying 8 Feigin, Misha V. 8 Gainutdinov, Azat M. 8 Geer, Nathan 8 Halbout, Gilles 8 Karolinsky, Eugene 8 Khare, Apoorva 8 Li, Libin 8 Ma, Xiaoguang 8 Pusztai, Béla Gábor 8 Razumov, Alexander V. 8 Schaumann, Gregor 8 Schlotterer, Oliver 8 Smoktunowicz, Agata 8 Tarasov, Vitaly Olegovich 8 Tikaradze, Akaki 8 Vasserot, Eric 8 Veselov, Alexander Petrovich 8 Westreich, Sara 8 Ye, Yu ...and 2,122 more Authors
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327 Journal of Algebra 193 Advances in Mathematics 169 Communications in Mathematical Physics 107 Journal of Pure and Applied Algebra 92 Communications in Algebra 76 Letters in Mathematical Physics 76 Selecta Mathematica. New Series 72 Journal of Mathematical Physics 70 Journal of High Energy Physics 68 Algebras and Representation Theory 56 Transactions of the American Mathematical Society 43 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 37 Nuclear Physics. B 37 Journal of Geometry and Physics 36 Proceedings of the American Mathematical Society 36 Journal of Algebra and its Applications 34 Mathematische Zeitschrift 34 Transformation Groups 29 Journal of Knot Theory and its Ramifications 28 Theoretical and Mathematical Physics 26 Duke Mathematical Journal 25 Journal of Noncommutative Geometry 24 Compositio Mathematica 23 International Journal of Mathematics 22 Representation Theory 19 Applied Categorical Structures 19 Communications in Contemporary Mathematics 15 Israel Journal of Mathematics 14 Inventiones Mathematicae 14 Journal of Nonlinear Mathematical Physics 13 Journal of the American Mathematical Society 13 Bulletin of the American Mathematical Society. New Series 13 Journal of Algebraic Combinatorics 12 Forum Mathematicum 12 Annales Henri Poincaré 11 Glasgow Mathematical Journal 11 Journal für die Reine und Angewandte Mathematik 11 Mathematische Annalen 11 International Journal of Algebra and Computation 11 Algebraic & Geometric Topology 11 Quantum Topology 10 Annales de l’Institut Fourier 10 Journal of Combinatorial Theory. Series A 10 Journal of Functional Analysis 10 Algebra Colloquium 10 Theory and Applications of Categories 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 9 Frontiers of Mathematics in China 8 Journal of Mathematical Analysis and Applications 8 Proceedings of the Edinburgh Mathematical Society. Series II 8 Topology and its Applications 7 Reviews in Mathematical Physics 7 Monatshefte für Mathematik 7 European Journal of Applied Mathematics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Arnold Mathematical Journal 6 Manuscripta Mathematica 6 Memoirs of the American Mathematical Society 6 Advances in Applied Mathematics 6 Physica D 6 Journal of Mathematical Sciences (New York) 6 Computational Methods and Function Theory 5 Bulletin of the London Mathematical Society 5 Osaka Journal of Mathematics 5 IMRN. International Mathematics Research Notices 5 Indagationes Mathematicae. New Series 5 Journal of Lie Theory 5 Documenta Mathematica 5 Geometry & Topology 5 Journal of the European Mathematical Society (JEMS) 5 Central European Journal of Mathematics 5 Journal of Physics A: Mathematical and Theoretical 5 Algebra & Number Theory 5 Japanese Journal of Mathematics. 3rd Series 5 São Paulo Journal of Mathematical Sciences 5 Forum of Mathematics, Sigma 4 International Journal of Modern Physics A 4 Journal of Statistical Physics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Physics Letters. A 4 Mathematics of Computation 4 Acta Mathematica 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Archiv der Mathematik 4 Pacific Journal of Mathematics 4 Acta Applicandae Mathematicae 4 Experimental Mathematics 4 Annales Mathématiques Blaise Pascal 4 Séminaire Lotharingien de Combinatoire 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Acta Mathematica Sinica. English Series 4 Journal of the Institute of Mathematics of Jussieu 4 Science China. Mathematics 4 Kyoto Journal of Mathematics 4 Analysis and Mathematical Physics 4 Bulletin of Mathematical Sciences 3 Modern Physics Letters A 3 Russian Mathematical Surveys 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Algebra Universalis ...and 181 more Serials
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1,092 Associative rings and algebras (16-XX) 823 Nonassociative rings and algebras (17-XX) 609 Quantum theory (81-XX) 538 Category theory; homological algebra (18-XX) 531 Group theory and generalizations (20-XX) 302 Algebraic geometry (14-XX) 200 Differential geometry (53-XX) 184 Manifolds and cell complexes (57-XX) 152 Dynamical systems and ergodic theory (37-XX) 149 Combinatorics (05-XX) 122 Functional analysis (46-XX) 105 Special functions (33-XX) 92 Partial differential equations (35-XX) 85 Global analysis, analysis on manifolds (58-XX) 83 Topological groups, Lie groups (22-XX) 78 Commutative algebra (13-XX) 59 Algebraic topology (55-XX) 58 $$K$$-theory (19-XX) 54 Number theory (11-XX) 54 Several complex variables and analytic spaces (32-XX) 54 Statistical mechanics, structure of matter (82-XX) 47 Relativity and gravitational theory (83-XX) 41 Fluid mechanics (76-XX) 33 Functions of a complex variable (30-XX) 32 Ordinary differential equations (34-XX) 32 Difference and functional equations (39-XX) 31 Linear and multilinear algebra; matrix theory (15-XX) 29 Mechanics of particles and systems (70-XX) 26 Order, lattices, ordered algebraic structures (06-XX) 21 Potential theory (31-XX) 20 Field theory and polynomials (12-XX) 17 General algebraic systems (08-XX) 16 Operator theory (47-XX) 14 Convex and discrete geometry (52-XX) 13 Abstract harmonic analysis (43-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Geometry (51-XX) 11 Probability theory and stochastic processes (60-XX) 9 Mathematical logic and foundations (03-XX) 9 Computer science (68-XX) 6 General and overarching topics; collections (00-XX) 6 Numerical analysis (65-XX) 5 Real functions (26-XX) 4 Approximations and expansions (41-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Measure and integration (28-XX) 3 Integral transforms, operational calculus (44-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Biology and other natural sciences (92-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Sequences, series, summability (40-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Operations research, mathematical programming (90-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-08-14T21:39:07 | {"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": 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": 0.47413700819015503, "perplexity": 7850.494965235068}, "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-2022-33/segments/1659882572077.62/warc/CC-MAIN-20220814204141-20220814234141-00356.warc.gz"} |
https://www.federalreserve.gov/econres/notes/ifdp-notes/how-vulnerable-are-eme-corporates-20180619.htm | June 19, 2018
### How vulnerable are EME corporates?
Daniel O. Beltran and Christopher G. Collins1
1. Introduction
Nonfinancial corporate debt in emerging market economies (EME) has tripled since the global financial crisis (GFC), reaching a peak of \$25 trillion (110 percent of GDP) in 2016:Q1 (Figure 1). The sharp increase in corporate debt has raised concerns about the risks this debt poses to emerging markets and the global economy.
In a previous note, we assessed vulnerabilities in the EME corporate sector using firm-level data from financial statements through 2016:Q3, and found these vulnerabilities to be moderate. At the time, only a few countries exhibited significant levels of risky corporate debt as a share of total debt. However, the amount of risky debt had reached its highest level since the GFC, even without any crises, and appeared quite sensitive to earnings, interest rate, and to a lesser extent, exchange rate shocks.
##### Figure 2: Global Debt at Risk and Corporate Defaults
This note provides an update on the health of EME corporates and examines the extent to which they are vulnerable to risks, including those that might be associated with monetary policy normalization in advanced economies. Overall, the health of the EME corporate sector has improved since 2016, as the firming of global growth has boosted EME corporate earnings, which has enhanced their capacity to service debt. Furthermore, levels of EME corporate debt as a share of GDP have stabilized, and an orderly deleveraging process is underway in many economies. Average borrowing costs remain low as most EME central banks are still easing monetary policy, and EME corporate bond spreads are well below their long-run averages. As a result, the amount of debt at risk, as a share of total debt, has moved down near the bottom of its range over the past decade.
At the same time, several advanced economy central banks have been tightening monetary policy, and others are expected to follow suit. Given the likelihood that policy normalization will proceed gradually and predictably, and with solid prospects for global economic growth, policy normalization should prove manageable for EME corporates.2 There is some risk, however, that rising global interest rates could lead to higher debt burdens, weaker currencies, capital outflows, and lower earnings. Such adverse developments could weigh on EME corporates, especially those with dollar-denominated debt, triggering loan losses, bond defaults, and broader financial stress. To assess these concerns, we stress test the EME corporate sector by imposing shocks to firms' borrowing costs, earnings, and the exchange rate.
1. Debt at risk
We assess the riskiness of the corporate debt stock by analyzing balance sheet and income statement data from Capital IQ for a sample of roughly 12,000 public and private firms in 15 emerging market economies. We compute the share of risky debt as the debt of firms with interest coverage ratio (ICR)—the ratio of earnings to interest expense— less than 2, divided by the total debt of firms in our sample.3 Our estimated shares of risky debt appear to be closely associated with corporate distress events; global debt at risk is highly correlated with the issuer-weighted global corporate default rate from the rating agency Moody's (Figure 2).
As shown in Figure 3, we estimate that 23 percent of the EME corporate debt stock is at risk. For comparison, we estimate the share of risky debt to be about 8 percent both in the United States and the euro area. This share has declined notably since 2016 for most EMEs in our sample. While somewhat high in some economies, such as Argentina, and having increased significantly in others, such as India, Turkey, and Thailand, the share of risky debt is below the level seen in East Asia on the eve of the Asian financial crisis for all of the economies in our sample.
##### Figure 3: Emerging Market Nonfinancial Corporate Debt at Risk, 2017:Q3
The overall decline in the share of risky debt owes to the increase in ICRs since mid-2016 (Figure 4). Taking a closer look at the drivers of this improvement, we decompose ICR into its components: return on assets, financial leverage, and average borrowing cost.
$ICR = \frac{Earnings}{Interest Expense} = \frac{Earnings}{Assets}*\frac{Debt}{Interest Expense} = \frac{Return on Assets}{Financial Leverage*Average Borrowing Cost}$
Equation 1 tells us that, all else equal, firms that are more profitable, are less leveraged, or have lower borrowing costs will have higher ICRs, indicating a greater capacity to service debt. The improvement in ICRs (and reduction in the share of risky debt) is mostly attributed to an increase in return on assets, and a decrease in financial leverage (Figures 5 and 6). As shown in Figure 7, average borrowing costs have been trending down in China since 2016, and have been mostly flat for the other EMEs.
##### Figure 7: Average Borrowing Cost
Even if a high share of corporate debt is at risk in a particular country, it may pose limited systemic risk if corporate debt is itself a small share of GDP. Conversely, systemic risk may be greater if corporate debt outstanding is large relative to GDP, even with a smaller share of debt at risk. To provide an estimate of the systemic importance of the risky corporate debt, we scale risky debt for each economy by GDP. This can help gauge the potential costs to governments of rescuing these companies or their lenders if the debt were to turn bad.4
##### Figure 8: Emerging Market Nonfinancial Corporate Debt at Risk
When scaled by GDP, risky debt in China exceeds 40 percent of GDP, a level just below that of the East Asian economies before the Asian financial crisis. The amount of risky debt relative to GDP is also notable in India, Turkey, and Brazil. For the other EMEs (including Argentina), the amount of risky debt seems manageable at less than 10 percent of GDP.
1. Stress-testing the EME corporate sector
How vulnerable are EME NFCs to an increase in borrowing costs, perhaps related to monetary policy tightening in the advanced economies? To gauge these effects, we use firm-level data and stress each firm's financials by increasing the average borrowing cost 1 percentage point (the effects of which are shown by the red portion of the bars in Figure 9).5 Except for China, where debt at risk is estimated to rise 20 percentage points of GDP, this increase in borrowing costs by itself would not be problematic. But higher global interest rates might be accompanied by broader financial stress and slower EME growth. To model these effects, we consider two additional shocks: reducing earnings 20 percent and imposing a 20 percent exchange rate devaluation on the amount of debt that is denominated in foreign currency (the gray portion of the bars).6
Taken together, the three shocks double the share of overall EME risky debt in GDP to around the level observed for the East Asian economies before the Asian financial crisis. The increase mostly reflects China. Still, even outside of China, the shocks more than double the amount of risky debt in many EMEs. Despite this, even with all three shocks, debt at risk remains low as a share of GDP in many economies, because current ICRs are sufficiently high (Figure 10). If normalization of monetary policy in the advanced economies results only in higher borrowing costs for EME corporates, this problem appears to be manageable. However, if that rise in interest rates is accompanied by broader financial stress, which in turn results in depressed earnings and weaker currencies, the effects will be more adverse. Such developments could pose a threat to financial stability if they spill over to banks and create an adverse feedback loop that the authorities have trouble containing.
##### Figure 10: Emerging Market Nonfinancial Corporate Interest Coverage Ratios, 2017:Q3
References
Ayala, D., M. Nedeljkovic, and C. Saborowski (2015): "What Slice of the Pie? The Corporate Bond Market Boom in Emerging Economies," IMF Working Paper 148, International Monetary Fund.
Beltran, Daniel, Keshav Garud, and Aaron Rosenblum (2017). "Emerging Market Nonfinancial Corporate Debt: How Concerned Should We Be?," IFDP Notes. Washington: Board of Governors of the Federal Reserve System, June 2017.
Pomerleano, M. (1998): "Corporate Finance Lessons from the East Asian Crisis," Discussion Paper 155, The World Bank Group.
1. Federal Reserve Board of Governors, Division of International Finance. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. We thank Shaghil Ahmed, Carol Bertaut, Christopher Erceg, Steven Kamin, and Beth Anne Wilson for helpful comments. Return to text
2. See speech by Federal Reserve Chairman Jerome H. Powell "Monetary Policy Influences on Global Financial Conditions and International Capital Flows," May 8, 2018. Return to text
3. Throughout, earnings refers to earnings before interest, taxes, depreciation, and amortization, or EBITDA. For example, just before the Asian financial crisis, firms in Korea, Thailand, and Indonesia had an average ICR of 2; see Michael Pomerleano (1998) "Corporate Finance Lessons from the East Asian Crisis," Viewpoint: Public Policy for the Private Sector Note 155 (Washington: World Bank, October), https://openknowledge.worldbank.org/handle/10986/11531. Return to text
4. Because our sample does not include all the firms in an economy, we need to scale up our estimate of risky debt to approximate its likely total size. We use BIS data on credit to the nonfinancial private sector (total debt) as a share of GDP as the scale factor. Implicit in this scaling is the assumption that the share of risky debt of the firms in our sample is the same as that of the entire corporate sector in each economy. Return to text
5. Although on the face of it this shock does not seem too large, it is applied to the average interest rate on the entire existing debt, not just on new debt. Given that the average interest rate for EME firms is about 4¾ percent, a 1 percentage point rise increases the interest expense about one-fifth. Return to text
6. Because firm-level data on the currency composition of assets and liabilities are scarce, we compute the effect of this shock on the level of debt at risk by using aggregate foreign currency shares of debt provided by Ayala et al. (2015). That is, we assume that each firm within an economy holds the same share of foreign currency debt, equal to the aggregate share. Return to text | 2023-01-31T23:52:14 | {"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": 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": 0.21438944339752197, "perplexity": 4756.8324836876645}, "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/1674764499891.42/warc/CC-MAIN-20230131222253-20230201012253-00451.warc.gz"} |
https://pos.sissa.it/397/240/ | Volume 397 - The Ninth Annual Conference on Large Hadron Collider Physics (LHCP2021) - Poster Session
$\rm{\Lambda^{+}_{c}}$ production cross section in pp and p--Pb collisions down to $p_{\rm T}$ = 0 at $\sqrt{s_{\rm NN}}$ = 5.02 TeV measured with ALICE
A.S. Kalteyer* on behalf of the ALICE collaboration
Full text: pdf
Pre-published on: October 20, 2021
Published on: November 17, 2021
Abstract
The open heavy-flavour hadron measurements in proton--proton and proton--lead collisions give insight into the charm production and hadronization mechanisms. In this contribution, the latest measurements of the production cross section of prompt $\Lambda^+_{\rm c}$ and its charge conjugate performed with the ALICE detector at midrapidity in pp, and the new measurement of $\Lambda_\mathrm{c}^+ \to \mathrm{p} \mathrm{K}_\mathrm{S}^0$ performed down to $p_{\rm T}=0$ in p--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV are presented. We also present the first ALICE measurement of the baryon-to-meson ratio $\Lambda^+_{\rm c}/{\rm D^0}$ and the $\Lambda^+_{\rm c}$ nuclear modification factor $R_{\rm pPb}$ down to $p_{\rm T}$ = 0 in p--Pb collisions. The $\Lambda^+_{\rm c}/{\rm D^0}$ ratio at midrapidity at the LHC is significantly higher than the one in ${\rm e^+e^-}$ collisions, suggesting that the fragmentation of charm is not universal across different collision systems. The results are compared with theoretical calculations.
DOI: https://doi.org/10.22323/1.397.0240
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2021-12-08T06:22:36 | {"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": 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": 0.5505568385124207, "perplexity": 2322.488983983484}, "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-2021-49/segments/1637964363445.41/warc/CC-MAIN-20211208053135-20211208083135-00502.warc.gz"} |
http://adriann.github.io/linear_optimization/polyhedra.html | In the previous section we saw how the feasible region of a linear program is constructed as the intersection of a number of halfplanes, one for each constraint. Using this insight we developed a graphical approach for solving 2D LPs. Together with Fourier-Motzkin elimination as a means for reducing the dimensionality of an LP, this gave us a general method for solving linear programs.
Unfortunately Fourier-Motzkin produces a rather large number of constraints, so it is unsuited for solving problems with many variables.
In this section I will talk more about the properties of the feasible region. With more knowledge about the feasible region, we’ll eventually be able to understand a very popular method for solving linear programs, the Simplex Method.
Let us start by introducing some notation and some terms.
Already in the last part we started writing the variables $x_1,\ldots, x_n$ as a column vector $\vec x$ and the constants $a_{ij}$ as a row vector $\vec a_i$. We did the same with the cost function, writing the weights for each variable as a row vector $\vec c$. This way we could use the dot product instead of writing sums explicitly.
$\vec a_i \cdot \vec x = a_{i1}x_1+\ldots+a_{in}x_n$
The constraints can be written using a matrix vector product. We write the $a_{ji}$ in a matrix $A$ like so
A=\left(\begin{aligned} a_{11} & a_{12} & \ldots & a_{1n}\\ a_{21} & \ldots \\ \vdots & \\ a_{m1} & \ldots & & a_{mn} \end{aligned}\right)
Note that the rows of $A$ are simply the vectors $\vec a_i$.
Now we can write the constraints simply as $Ax\le b$, where $b$ is a column vector of the $b_j$. Summarizing we get the general form of a linear program:
\begin{aligned} \text{minimize:}& \vec c \cdot \vec x \\ \text{subject to:} & A \cdot \vec x \le \vec b\end{aligned}
Note that it really doesn’t matter whether we use $\le$ or $\ge$. Just multiplying by $-1$ switches a constraint around without changing it.
Def A polyhedron is a set in $\text{R}^n$ whose members obey a set of linear inequalities
$\{x\in \text{R}^n | Ax \geq b\} \qquad A\in \text{R}^{m\times n},\ b\in \text{R}^m$
If the region is bounded (i.e. it has a finite volume) it can also be called polytope. We say $n$ is the dimensionality of the polyhedron.
I already used the word halfspace without giving a formal definition. Let us remedy this.
Def Let $a,x\in \text{R}^n$, $a\neq 0$.
1. $\{x|ax=b\}$ is a hyperplane (a line in 2D)
2. $\{x|ax\geq b\}$ is a halfspace (halfplane in 2D)
With this definition we can say that a polyhedron is an intersection of a bunch of halfspaces.
Corners of Polyhedra
A corner of a $n$-dimensional polyhedron is, intuitively, a point where $n$ edges meet. I will give a bunch of different definitions and them prove them to be equal.
The simplest definition uses a line. A corner of a polyhedron is a point $p$ in the polyhedron where we can find a line that touches the polyhedron only at $p$.
Def Let $P$ be a polyhedron. A vector $x\in P$ is a vertex of P if $\exists \vec c\in \text{R}^n$ s.t. $cx < cy$ for all $y\in P, y \neq x$; that is, $x$ is the minimal point for some cost vector $c$ (the unique optimal solution for some LP with the feasible set P). See figure [Fig:vertex]
Corners are interesting for optimization because the converse is also kind of true, at least for bounded polyhedra. For any cost vector $c$, we can find a vertex $x$ of the (bounded) polyhedron such that $cx \le cy$ for all points $y$ in the polyhedron. There is no strict inequality here because the line defined by $c$ might be parallel to one of the edges of the polyhedron. If the polyhedron is not bounded, there are some $c$ such that for any point $y$ there is a point $y'$ such that $cy' < cy$, that is, the optimal value for this cost vector is unbounded. These are of course the cost vectors that define a line that doesn’t leave the polyhedron.
However, we need some more definitions and theorems before we can prove the above statement.
Def An extreme point of a polyhedron P is a vector $x\in P$ s.t. $x$ is not a convex combination of any two distinct vectors $y,z\in P$ different from $x$.
Convex combinations of two points $x,y$ are all points $z$ for which the equation $\lambda x + (1-\lambda) y = z$ has a solution for $\lambda$ in $[0,1]$. Geometrically, the points $z$ lie on a line between $x$ and $y$. You can also take the convex combinations of more than two points. The principle is the same though, you add all the points, scaling each one with a non-negative scaling factor $\lambda_i$. The combination is convex if the $\lambda_i$ sum to 1.
Example: In 2D we can always select the two adjacent corners of a point $x$ on the edge of $P$ if and only if $x$ is not a corner. Then $x$ will be on the line between the two corners.
Def Let $P$ be a polyhedron that is defined by some linear inequalities $a_i$: $P=\{x|a_ix\geq b_i\}$. We’ll say that the $i$-th constraint is active at a point $x$ if we have equality: $a_ix = b_i$
The constraints define the edges of polyhedron. If a point is on an edge that constraint is active. Intuitively the point must be a corner if it lies on the intersection of $n$ edges.
Def Let $P\in \text{R}^n$ be a polyhedron in standard form and let $x^{*}\in \text{R}^n$. The vector $x^{*}$ is a basic solution if at $x^*$ all equality constraints are active and there are $n$ active constraints that are linearly independent. See solution $A$ in figure [Fig:bsfVSbs] for an example of a basic solution. If a basic solution is also feasible, we call it a basic feasible solution (b.f.s.). See the point $B$ in figure [Fig:bsfVSbs] for an example of a basic feasible solution.
A polyhedron with fever than $n$ constraints never has a basic solution.
Now we want to prove that the three definitions are all equivalent to each other.
Theorem Let $P$ be a polyhedron and $x\in P$. The following statements are equivalent
1. $x$ is a vertex
2. $x$ is an extreme point
3. $x$ is a basic feasible solution
Proof
We show 1.) $\Rightarrow$ 2.) $\Rightarrow$ 3.) $\Rightarrow$ 1.).
• $x$ is a vertex $\Rightarrow$ $x$ is an extreme point: Proof by contraposition.
Assume the existence of $y,z \in P$ both different from $x$ such that $x$ is a linear combination of $y$ and $z$, i.e. $x= \lambda y + (1-\lambda )z$. Since $x$ is a linear combination of two vectors, it’s not an extreme point. We show that it is also not a vertex.
From the definition of vertex we know that some cost vector $c$ should exist such that $c x < c w$, for all $w\in P$, that is $x$ is optimal w.r.t. $c$. Together with the assumption $x= \lambda y + (1-\lambda )z$ this leads to a contradiction.
\begin{aligned} cx &= \lambda cy +(1-\lambda)cz\\ &> \lambda cx + (1-\lambda)cx = cx && \text{since }cx< cy, cx< cz\\\end{aligned}
• extreme point $\Rightarrow$ bsf. Proof by contraposition.
Suppose $x$ is not a basic feasible solution. Then $x$ is either not feasible, or not a basic solution. If it’s not feasible, then it can’t be an extreme point. Hence we can assume $x\in P$ and it’s not a basic solution.
Let $B$ be a matrix of active constraints at $x$ and $C$ the matrix of the inactive constraints such that $Bx=d$, $Cx>f$. Since $x$ is not a bfs the matrix $B$ doesn’t have full rank and hence its kernel is nonempty. So we can find some vector in the kernel:
$\exists \delta \in \text{R}^n, \delta \neq 0:\ B\delta =0$
With $\delta$ we define two vectors:
$y=x-\epsilon \delta \quad z = x+\epsilon \delta$
Note that $x=(z+y)/2$. That means that $x$ is not an extreme point if $z,y \in P$, because $x$ is a convex combination of the two. Consider
$Bz = B(x+\epsilon \delta) = Bx + \epsilon B\delta = Bx$
Since $B\delta = 0$ the active constraints are still active. For the inactive constraints we have some slack before we leave the polyhedron. If we choose $\epsilon$ small enough we’re still within. It suffices to choose $\epsilon$ such that
$\forall i: \epsilon |c_i z| < c_i x - f_i\qquad \vec c_i\in C,\ f_i \in \vec f$
That is, we make epsilon small enough such that we don’t violate the tightest of the constraints in $C$.
Hence $z$ (and analogous $y$) are still in the polyhedron and $x$ is not an extreme point.
• bfs $\Rightarrow$ vertex: Suppose $x$ is a bfs. We construct a cost vector for which $b$ is the unique optimal solution.
Let $B$ be the matrix of active constraints s.t. $Bx=b$. Let $c$ be the sum of the $n$ rows of $B$. We know the objective value for $x$ w.r.t. $c$. It’s $c x = \sum b_i$.
Because $B$ has rank $n$, $x$ is the unique solution to $Bx=b$. For all $y\in P$ that are different from $x$, $By > b$, hence $x$ is the optimal point for the cost vector $c$. Therefore $x$ is a vertex.
The shape of polyhedra
So far we’ve shown that the extreme points of a polyhedron, i.e. its corners, are also vertices, that is, optimal solutions for some cost vector. However, we want to be able to say that for every cost vector we can find an optimal solution that is also an extreme point.
In this section we’ll learn that polyhedra are so called convex sets and, for bounded polyhedra, every point inside the set can be expressed as a linear combination of the extreme points. Recall that a vector $x$ is a linear combinations of some vectors $y_1,\ldots, y_n$ if you can find constants $\lambda_1,\ldots, \lambda_n$ such that $x=\sum_i \lambda_i y_i$, or in vector notation $x=\lambda \cdot y$.
Def A subset $S\subseteq R^n$ is called convex if for any to points $x,y\in S$ the line connecting $x$ and $y$ is also in $S$. That is
$\forall \lambda \in [0,1], \forall x,y\in S: \lambda x + (1-\lambda)y \in S$
Theorem Polyhedra are convex sets.
Proof This follows directly from the definition. Recall that we defined a polyhedron as the set of points
$\{x\in \text{R}^n | Ax \geq b\}$
for some matrix A. Since matrix multiplication is linear we have for some $y_1,y_2$ from $P$ that
$A\cdot (\lambda y_1 + (1-\lambda) y_2) \ge \lambda b + (1-\lambda) b = b$
Note that the notion of convex combination can be extended to sets of more than two points trivially. It is a simple exercise to show that this doesn’t change what it means to be a convex set. I will just use it.
Def The convex hull of a set of vectors $X=x_1,\ldots, x_n$ is the set
$\text{CH}(X)=\bigcup_{\sum \lambda_i=1} \left\{\sum_{i=1}^n \lambda_i x_i\right\}$
That is, the convex hull is the union of all convex combinations that can be formed from the vectors in $X$.
Intuitively the convex hull is the set you get by spanning a tight rubber band around the vectors of $X$.
We come to the central result of this section. The next theorem shows that the extreme points of a polyhedron span the whole polyhedron. This is what allows us to only look at the extreme points when looking for an optimal solution to a LP.
Theorem Let $P$ be a non-empty bounded polyhedron and let $E$ be the set of extreme points of $P$. Then $P = \text{CH}(E)$
Proof We show both directions. First we show $\text{CH}(E) \subseteq P$. This direction is particularly easy. We already showed that polyhedra are convex sets, hence any convex combination of points from $P$ still lies in $P$.
Now we show the other direction $P \subseteq \text{CH}(E)$. To do so we show that an arbitrary point $x\in P$ can be expressed as a convex combination of extreme points. The proof of this is very similar to the proof we gave above that extreme points are basic feasible solutions.
Consider $Ax \ge b$. We rearrange the rows of $A$, $x$, and $b$ such that the first $k$ inequalities are tight. We can decompose $A$ into two matrices $B$ and $C$ such that $A=B+C$ by taking $B$ as the first $k$ rows of $A$ (and fill it with 0) and $C$ as the last $n-k$ rows of $A$ (and fill with 0 from the top).
If the rank of $B$ is $n$, then $x$ is a basic feasible solution (i.e. an extreme point by the theorem above) and we’re done. Otherwise we can find some vector $y$ in the kernel of $B$, i.e. $By=0$. Since the equalities defined by $C$ are not tight, we can move $x$ by some $\epsilon_1$ in the $y$ direction without leaving the polyhedron. We chose $\epsilon_1$ such that at least one constraint of $C$ becomes tight for $x=x+\epsilon_1 y$. There also has to be an $\epsilon_2$ that takes us to a boundary in the opposite direction. Let $x_2=x-\epsilon_2 y$.
As in the previous proof $x$ can be expressed as a convex combination of $x_1$ and $x_2$. If $x_1$ and $x_2$ are extreme points, we’re done. Otherwise we can repeat the same process for $x_1$ and $x_2$, only this time the rank of $B$ is one greater than before. Eventually we will reach full rank and hence a set of extreme points that can express $x$ as a convex combination.
Now that we know that every point in the polyhedron can be expressed as a convex combination of extreme points, we can use this fact to show that for every const vector $c$ we can find an optimal point that is also an extreme point.
Corollary Let $P$ be a non-empty bounded polyhedron. Then the LP $\text{min } cx$ such that $x\in P$ has an optimal solution that is an extreme point.
Proof Let $x^*$ be an optimal solution and let $v=cx$ be the optimal objective value. By the previous theorem we can write $x^*$ as a convex combination of extreme points
$x^* = \sum \lambda_i y_i.$
We want to show that there is a $y_i$ such that $c y_i= c x^*$. We already know that $v=cx^*$ is minimal, so we know that $cy_i\geq v$ for all $i$. Since the $\lambda_i$ must sum to 1, we can conclude that for at least one $y_i$ we actually have $cy_i=v$. Otherwise can can quickly derive the following contradiction:
$v=c x^* = c\sum \lambda_i y_i > c\sum \lambda_i x^* = \sum \lambda_i cx^* = v\sum \lambda_i = v$
Now we have all ingredients for an algorithm. We have shown that for every cost vector there is an extreme point that is an optimal solution. Therefore we can find the optimal solution to a LP by enumerating extreme points. We also know that extreme points are basic feasible solutions, that is, points where the matrix of active constraints has full rank. That is, once we found one basic feasible solution we can move to another one by manipulating a matrix – throwing out one active constraint and replacing it by a different one. This is the basic strategy of the Simplex method, that we’ll discuss in the next section.
(The next section is coming when I get around to writing it.)
Click here to go back to the index
CC-BY-SA Adrian Neumann (PGP Key A0A8BC98) | 2018-01-23T05:53:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 239, "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": 0.9404870271682739, "perplexity": 111.52628089851524}, "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-2018-05/segments/1516084891750.87/warc/CC-MAIN-20180123052242-20180123072242-00781.warc.gz"} |
https://wlresources.dpi.wi.gov/authoring/1776-careers-that-use-math-in-a-foundry/view | # Careers that Use Math in a Foundry
ACP Lesson Plan
Overview / Description:
This lesson will be an introduction to the many areas where math is utilized in an iron foundry.
Learning goals/objectives:
After completing this activity, students should be able to . . .
• Explain why math is important
• Name a variety of jobs that use math with in a foundry
• Provide examples of the types of math used with a job at a foundry
Content Standards:
Wisconsin Standards for Mathematics
Number and Operations: Fractions
Apply and extend previous understandings of multiplication and division.
CCSS.Math.Content.5.NF.B.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Materials:
Foundry Jobs Powerpoint -
Word Problems-Foundry Jobs assessment
Learning Activities:
Assessment
Formative Assessment - Small group answer sheet - teacher will solicit answers from students to check for understanding.
Summative Assessment - Word Problems - Foundry Jobs assessment linked above
Wrap-Up:
• Review what a foundry is and what jobs it provides. Explain current salaries that people in a foundry may make.
• Students could discuss other career areas and how math is significant for those careers as well.
Extension Activity (for intervention or enrichment):
• Tour a foundry
• Have speakers in the classroom from the foundry (Foundry in a box presentation)
• Have each student or pair/group of students create their own word problem using the information found in the Powerpoint | 2022-05-29T08:33:08 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.408850759267807, "perplexity": 5001.084135674091}, "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/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00572.warc.gz"} |
https://verse-and-dimensions.fandom.com/wiki/Dimension | ## FANDOM
1,123 Pages
A dimension is a degree of freedom in which position can vary. Each degree of freedom can be indexed by a single variable, which means that the dimensionality of a space is the number of coordinates needed to specify a point in that space. For example, a solid cube requires an x, y and z coordinate to define a position within, so it is three-dimensional.
In many physical theories, dimensions can either be spatial, temporal, or compact. Spatial dimensions are typical dimensions, allowing for free movement in all directions. Temporal dimensions correspond to time, and only allow changes to propagate in one direction. Compact dimensions are small, finite and periodic, meaning that they do not have a clear extent macroscopically but alter the behavior of microscopic phenomena.
In mathematics, other notions of the word "dimension" can be considered and serve as useful for studying more complicated objects such as fractals. One of these notions is Hausdorff dimensionality. The Hausdorff dimension of a metric space $X$ is the infimum of the set of all $d \in [0, \infty)$ such that the $d$-dimensional Hausdorff measure of $X$ is 0.
## See Also
Dimensionality Negative One Zero One Two Three Four Five Six Seven Eight Nine Ten ... Aleph null
Hyperbolic space
$\mathbb H^{n}$
Hyperbolic plane
$\mathbb H^{2}$
Hyperbolic realm
$\mathbb H^{3}$
Hyperbolic flune
$\mathbb H^{4}$
Hyperbolic pentrealm
$\mathbb H^{5}$
Hyperbolic hexealm
$\mathbb H^{6}$
Hyperbolic heptealm
$\mathbb H^{7}$
Hyperbolic octealm
$\mathbb H^{8}$
Hyperbolic ennealm
$\mathbb H^{9}$
Hyperbolic decealm
$\mathbb H^{10}$
... Hyperbolic omegealm
$\mathbb H^{\aleph_0}$
Euclidean space
$\mathbb R^{n}$
Null polytope
$\emptyset$
Point
$\mathbb R^{0}$
Euclidean line
$\mathbb R^{1}$
Euclidean plane
$\mathbb R^{2}$
Euclidean realm
$\mathbb R^{3}$
Euclidean flune
$\mathbb R^{4}$
Euclidean pentrealm
$\mathbb R^{5}$
Euclidean hexealm
$\mathbb R^{6}$
Euclidean heptealm
$\mathbb R^{7}$
Euclidean octealm
$\mathbb R^{8}$
Euclidean ennealm
$\mathbb R^{9}$
Euclidean decealm
$\mathbb R^{10}$
... Euclidean omegealm
$\mathbb R^{\aleph_0}$
Hypersphere
$\mathbb S^{n}$
Point pair
$\mathbb S^{0}$
Circle
$\mathbb S^{1}$
Sphere
$\mathbb S^{2}$
Glome
$\mathbb S^{3}$
Tetrasphere
$\mathbb S^{4}$
Pentasphere
$\mathbb S^{5}$
Hexasphere
$\mathbb S^{6}$
Heptasphere
$\mathbb S^{7}$
Octasphere
$\mathbb S^{8}$
Enneasphere
$\mathbb S^{9}$
Dekasphere
$\mathbb S^{10}$
... Omegasphere
$\mathbb S^{\aleph_0}$
Community content is available under CC-BY-SA unless otherwise noted. | 2020-10-28T05:51:15 | {"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": 0.8614867925643921, "perplexity": 1391.9821756794154}, "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-2020-45/segments/1603107896778.71/warc/CC-MAIN-20201028044037-20201028074037-00289.warc.gz"} |
https://mfix.netl.doe.gov/doc/nodeworks/19.1.1/developers/nodewidget_examples.html | # NodeWidget Examples¶
Nodeworks can be used in other applications, like MFiX. To use nodeworks in other applications, the NodeWidget can be used like other Qt widgets. The following examples show how to use the NodeWidget in a GUI application.
## basicapp¶
The basicapp example shows how to use the NodeWidget.
examples/basicapp.py
## tabbedapp¶
The tabbedapp shows how to create an application with tabs that can open an individual NodeWidget.
examples/tabbedapp.py
examples/threads.py | 2019-09-21T10:57:10 | {"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": 0.5563228726387024, "perplexity": 4032.743459173346}, "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-2019-39/segments/1568514574409.16/warc/CC-MAIN-20190921104758-20190921130758-00416.warc.gz"} |
https://www.ecb.europa.eu/pub/financial-stability/macroprudential-bulletin/html/ecb.mpbu201810_01.el.html | Επιλογές αναζήτησης
Η ΕΚΤ Ενημέρωση Επεξηγήσεις Έρευνα & Εκδόσεις Στατιστικές Νομισματική πολιτική Το ευρώ Πληρωμές & Αγορές Θέσεις εργασίας
Προτάσεις
Εμφάνιση κατά
Δεν διατίθεται στα ελληνικά.
# The implications of removing repo assets from the leverage ratio
Prepared by Jan Philipp Fritsche, Michael Grill and Claudia Lambert
This article summarises the key findings from a counterfactual exercise where the effect of removing repo assets from the leverage ratio on banks’ default probabilities is considered. The findings suggest that granting such an exemption may have adverse effects on the stability of the financial system, even when measures are introduced to compensate for the decline in capital required by the leverage ratio framework. Increases in probabilities of default are mainly seen for larger banks which are more active in the repo market. Moreover, it is observed that the predictive power of the model improves when repo assets are included. Overall, the analysis in this article does not support a more lenient treatment of repo assets in the leverage ratio framework, e.g. by exempting them or allowing for more netting with repo liabilities or against high-quality government bonds.
## 1 Introduction
In the context of evaluating the impact of post-crisis regulatory reforms, concerns have been raised that the leverage ratio (LR) has had a negative impact on the functioning of repurchase agreement (repo) markets. To address these concerns, some stakeholders have suggested providing for a more lenient treatment of repo assets in the LR framework, e.g. by exempting them or allowing for more netting with repo liabilities or against high-quality government bonds. However, such a change in treatment could lead to the re-emergence of risks related to the build-up of excessive leverage and over-reliance on short-term wholesale funding in financial markets related to securities financing transactions and the re-use of collateral.[1]
This article intends to inform this debate by assessing the implications of such a regulatory change by considering two counterfactual exercises. Building on the framework developed in Acosta, Grill and Lang (2017)[2], first of all, the impact of exempting repo transactions from the LR framework on banks’ default probabilities is estimated. More specifically, in the counterfactual analysis it is assumed that banks will lower their capital by the amount that they had been required to hold against their repo asset before the change in treatment. At the same time, it is assumed that all banks will need to increase their LRs uniformly to compensate for this drop in capital required in the whole banking system.[3] Second, in a complementary exercise, it is analysed whether the change in regulatory treatment affects the predictive power of the LR for bank default.[4]
## 2 The impact of bank default probabilities
To assess the impact of banks’ leverage on their distress probabilities, following Acosta, Grill and Lang (2017) in a first exercise a panel logit model with time and country fixed effects is estimated for a sample of 500 European banks. On the basis of this model, bank default probabilities are predicted.
$P r ( d i , t + 1 = 1 L R i , t =$
In the above equation, $( . )$ is the cumulative distribution function of the logistic distribution. The left-hand-side variable is the binary distress indicator for bank 𝑖 in year 𝑡 + 1; 𝑋𝑖,𝑡 and 𝑌𝑗,𝑡 are vectors of bank-specific and country-specific control variables (such as capital over risk-weighted assets, non-performing loans over total assets, pre-tax return over assets, loans over total assets, GDP, the unemployment rate, etc.); and $τ t$ and are time and country fixed effects respectively. $L R$ is the leverage ratio measured as observed capital levels over total assets, i.e. over
The dataset for the empirical analysis consists of a large unbalanced panel of 500 EU banks for the period 2005-14. For the analysis, data from multiple sources are used: (1) bank-specific variables from SNL and Bankscope; (2) country-level macroeconomic variables from the ECB Statistical Data Warehouse; and (3) a unique collection of bank distress events that covers bankruptcies, defaults, liquidations, State aid cases and distressed mergers.[5]
In a second exercise, a two-step counterfactual analysis is conducted. In a scenario under which repo assets are exempted from the LR, first of all, banks’ new level of capital and total assets ( are re-estimated. More specifically, it is assumed that banks will lower their capital by exactly the amount they had been required to hold against their repo asset before the change in treatment. In other words, it is assumed that an exemption of repo assets would incentivise banks to reduce capital ( ) to a new level ( such that banks’ LRs are kept constant, i.e.:
It is also assumed that an exemption is likely to be accompanied by some form of compensatory measure to keep the overall level of capital in the banking sector constant. As a consequence, an exemption of repo assets in the LR treatment will be accompanied by a simultaneous increase in the minimum LR requirement to ensure that the total amount of capital in the system stays constant.[6] More specifically, it is assumed that this is achieved by a uniform increase in capital across all banks following the exemption of repo assets. Hence, to maintain a constant level of capital across the 500 banks in the sample, the average capital per bank has to increase by 6.8%.[7] In a second step, using these new levels of capital the individual bank default probabilities are re-estimated and then compared with the ones that were obtained without the policy change. The model in Equation (1) is re-estimated but now includes the new leverage ratio ( $L R i , t n e w )$ and the new distress probabilities.
$P r ( d i , t + 1 = 1 L R i , t n e w =$
$( 2 )$
Comparing the default probabilities in the two states (with and without a change in the treatment of repos in the LR framework) suggests that the asset-weighted median bank default probability increases by 7%. The asset-weighted median bank default probability is specified as the median default probability of all banks in the sample ordered by assets and not by magnitude of default probability.[8] The 7% increase is a significant one, which suggests that the exemption of repo assets from the LR may have adverse effects on the stability of the financial system, even when measures are introduced to compensate for the decline in capital required by the LR framework.
When focusing on the ten banks with the largest repo position in absolute terms, it is observed that for this set of banks the median default probability increases by 91%. Given the systemic relevance of these banks, an exemption of repo assets may be considered particularly harmful from a financial stability perspective. The effect is greater for these banks, because the repo assets are very asymmetrically distributed across the banks: while most banks only hold negligible amounts of repo assets, the set of large banks report a considerable part of the repo assets in the sample.
To get an idea of the economic magnitude of these changes, the 7% increase for all banks and the 91% increase for the ten largest banks are compared with changes in the median default probability for the year 2009. More specifically, the results are compared with the 2009 numbers since annual defaults in the sample peaked in 2009. Compared with pre-crisis averages[9], asset-weighted default probabilities increased by 250% in 2009. This implies that a change in default probabilities of 91% for big banks (following the exclusion of repo assets) represents more than one-third of the observed changes in median default probabilities between the pre-crisis period and the peak of systemic uncertainty in the post-crisis period.
In addition, the effect of exempting central bank reserves is also considered. An exemption of both balances with central banks and repo assets would lead to a decrease in total capital of 9% which is offset by uniformly increasing the amount of capital to compensate for this decrease. The results show that the median total asset-weighted default probability increases by 16%. Hence, considering the combination of exemptions of central bank reserves and repo assets more than doubles the effects observed for the repo exemption as some banks (in particular larger ones) significantly benefit from both changes in regulatory treatment.
Chart 1 shows that the amplification effect is driven by a non-linear relationship between the LR and the default probability. When the LR decreases to a level of 3% from higher levels, the graph illustrates that the default probability changes proportionally more than for a change of the LR from 6% to 5%. The change in the regulatory treatment for both central bank reserves and repo assets pushes the banks’ original leverage ratios further to the left as they can significantly reduce their capital and may increase the probability of distress substantially. It is noteworthy that this effect particularly holds for some larger banks that had low LRs to begin with and that benefit most from the exemptions.
## 3 Implications for the predictive power of the leverage ratio
In a second analysis, it is assessed whether the change in regulatory treatment affects the predictive power of the LR for bank default. Using the framework developed in Acosta, Grill and Lang (2017), the goodness of fit of the model for alternative measures of the LR is examined. More specifically, the ability of diverse measures to explain variation in probabilities of default and the in-sample fit are compared.
Assessing the pseudo R², a measure of the quality of the different models, in Table 1 it can be observed that the model using the LR without repo is slightly less suited to fitting the data (second row).[10] The model in the bottom row of Table 1 separately accounts for repo assets/total assets. This highlights that repo assets are an important factor to assess the default risk of a given bank regardless of whether they are included indirectly through the LR or separately as an extra indicator. If we include repo assets/total assets separately, this even increases the model’s in-sample performance slightly.
Assessing the out-of-sample predictive power of the model using ROC curves, it can be observed that model performance is very similar for both specifications. ROC curves are a standard tool to evaluate and compare predictive models. Accuracy is measured by the area under the ROC curve, where broadly speaking an area of 1 represents a perfect test. For the analysis, the areas under the ROC curves are 0.913 for the model with an LR including repo positions and 0.912 for the model excluding repo positions. Overall, while the results are not very strong, we find that excluding repo assets slightly decreases the fit of the model.
## 4 Conclusion
Overall, the findings suggest that the exemption of repo assets (and central bank reserves) from the LR may have adverse effects on the stability of the financial system, even when measures are introduced to compensate for the decline in capital required by the LR framework. Against the background of a pronounced increase of median default probabilities for large systemically relevant banks, an exemption of repo assets could considerably weaken the LR for some banks and may have adverse effects from a financial stability perspective.
The analysis therefore does not support a more lenient treatment of repo assets in the LR framework, e.g. by exempting them or allowing for more netting with repo liabilities or against high-quality government bonds. As the analysis does not consider the potential negative consequences of increased repo activity following the exemption of repo assets from the LR exposure measure, the estimate of a potential increase in default probability should be seen as a lower bound.
The results in this article complement previous findings[11] of an overall functioning repo market in the euro area, showing that regulatory reforms have not had a material unintended effect on the amount of euro area banks’ outstanding repo transactions. It should be borne in mind that the analysis in this article does not consider the negative consequences of increased repo activity following an exemption of repo assets from the LR exposure measure, including a potential further increase in default probability.
## References
Acosta Smith, J., Grill, M. and Lang, J.H. (2017), “The leverage ratio, risk-taking and bank stability”, Working Paper Series, No 2079, European Central Bank, June.
Aikman, D., Galesic, M., Gigerenzer, G., Kapadia, S., Katsikopoulos, K., Kothiyal, A., Murphy, E. and Neumann, T. (2014), “Taking uncertainty seriously: simplicity versus complexity in financial regulation”, Bank of England Financial Stability Paper No 28, May.
Betz, F., Oprica, S., Peltonen, T.A. and Sarlin, P. (2014), “Predicting distress in European banks”, Journal of Banking & Finance, Vol. 45.
Financial Stability Board (2017), “Re-hypothecation and collateral re-use: Potential financial stability issues, market evolution and regulatory approaches”, January.
Grill, M., Jakovicka, J., Lambert, C., Nicoloso, P., Steininger, L. and Wedow, M. (2017), “Recent developments in euro area repo markets, regulatory reforms and their impact on repo market functioning”, Financial Stability Review, European Central Bank, November.
Schularick, M. and Taylor, A.M. (2012), “Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870-2008”, American Economic Review, Vol. 102(2), April.
1. The FSB Re-hypothecation and Re-use Expert Group also highlighted the LR as the main brake put in place after the crisis to address these concerns. See Financial Stability Board (2017), “Re-hypothecation and collateral re-use: Potential financial stability issues, market evolution and regulatory approaches”, January.
2. Acosta Smith, J., Grill, M. and Lang, J.H. (2017), “The leverage ratio, risk-taking and bank stability”, Working Paper Series, No 2079, ECB, June.
3. This could, for example, be achieved by uniformly increasing the minimum LR requirement as the Bank of England has done in the case of the exemption of central bank reserves. It should be noted that such a uniform increase may disproportionally affect banks not involved in repo business and may therefore cause additional costs.
4. It is important to note that the leverage ratio is a better predictor of bank default than the risk-based ratio; see, for example, Betz, F., Oprica, S., Peltonen, T.A. and Sarlin, P. (2014), “Predicting distress in European banks”, Journal of Banking & Finance, Vol. 45, and Aikman, D., Galesic, M., Gigerenzer, G., Kapadia, S., Katsikopoulos, K., Kothiyal, A., Murphy, E. and Neumann, T. (2014), “Taking uncertainty seriously: simplicity versus complexity in financial regulation”, Bank of England Financial Stability Paper No 28, May. In addition, Schularick, M. and Taylor, A.M. (2012), “Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870-2008”, American Economic Review, Vol. 102(2), April, highlight that excessive leverage contributes to financial instability.
5. Bank distress events are taken from Acosta, Grill and Lang (2017).
6. This could, for example, be achieved by uniformly increasing the minimum LR requirement as the Bank of England has done in the case of the exemption of central bank reserves.
7. This increase in capital translates into a change in the LR from 5.9 to 6.3 for the median bank.
8. This measure (instead of median default probability) is considered for two reasons. First, it is a more systemic measure since it gives more weight to banks with more assets. Second, larger banks tend to have larger shares of repo in terms of total assets and therefore benefit more from the reduction of capital required and are relatively less affected by the compensating increase in capital requirements. Calculating the median default probability would not show the increase above, since it would not account for the asymmetric holdings of repo assets per bank.
9. This is the average of the years 2005, 2006 and 2007 in the sample.
10. It should be noted that the leverage ratio also enters the model at lower levels of significance.
11. Grill, M., Jakovicka, J., Lambert, C., Nicoloso, P., Steininger, L. and Wedow, M. (2017), “Recent developments in euro area repo markets, regulatory reforms and their impact on repo market functioning”, Financial Stability Review, ECB, November. | 2021-10-25T19:37:56 | {"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": 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": 0.4395669996738434, "perplexity": 2960.4438732344897}, "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-2021-43/segments/1634323587767.18/warc/CC-MAIN-20211025185311-20211025215311-00145.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Apokhozhaev.stanislav-i | ## Pokhozhaev, Stanislav I.
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Author ID: pokhozhaev.stanislav-i Published as: Pokhozhaev, S. I.; Pohozaev, S. I.; Pohozaev, Stanislav I.; Pohozaev, Stanislav; Pohozhaev, S. I.; Pokhozaev, S. I.; Pokhozhaev, Stanislav I.; Pokhozhaev, Stanislav; Pohožaev, Stanislav; Pohozaev, A. I.; Pohožaev, S. I.; Pokhozhaev, S.; Pohozaev, S. Further Spellings: Похожаев Станислав Иванович Homepage: http://www.mi-ras.ru/~pokhozhaev/ External Links: MGP · Wikidata · Math-Net.Ru · IdRef
Documents Indexed: 162 Publications since 1960, including 6 Books 1 Contribution as Editor Biographic References: 4 Publications Co-Authors: 68 Co-Authors with 62 Joint Publications 2,852 Co-Co-Authors
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### Fields
139 Partial differential equations (35-XX) 8 Operator theory (47-XX) 7 Fluid mechanics (76-XX) 6 History and biography (01-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Global analysis, analysis on manifolds (58-XX) 3 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Classical thermodynamics, heat transfer (80-XX)
### Citations contained in zbMATH Open
113 Publications have been cited 2,077 times in 1,478 Documents Cited by Year
Eigenfunctions of the equation $$\Delta u+\lambda f(u) = 0$$. Zbl 0141.30202
Pokhozhaev, S. I.
1965
A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. Transl. from the Russian. Zbl 1074.35500
Mitidieri, E.; Pohozaev, S. I.
2001
Positive solutions for the $$p$$-Laplacian: Application of the fibrering method. Zbl 0880.35045
Drábek, Pavel; Pohozaev, Stanislav I.
1997
A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. (Apriornye otsenki i otsutstvie reshenij nelinejnykh uravnenij i neravenstv v chastnykh proizvodnykh.) Zbl 0987.35002
Mitidieri, E.; Pokhozhaev, S. I.
2001
Nonexistence results and estimates for some nonlinear elliptic problems. Zbl 1018.35040
Bidaut-Véron, Marie-Francoise; Pohozaev, Stanislav
2001
On a class of quasilinear hyperbolic equations. Zbl 0328.35060
Pohozaev, S. I.
1976
The absence of global positive solutions of quasilinear elliptic inequalities. Zbl 0976.35100
Mitidieri, E.; Pokhozhaev, S. I.
1998
Entire solutions of semilinear elliptic equations. Zbl 0882.35003
Kuzin, I.; Pohozaev, S.
1997
Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $$\mathbb{R}^n$$. Zbl 0988.35095
Mitidieri, Enzo; Pohozaev, Stanislav I.
2001
Existence and blow up for higher-order semilinear parabolic equations: majorizing order-preserving operators. Zbl 1082.35079
Galaktionov, V. A.; Pohozaev, S. I.
2002
Nonexistence of positive solutions for quasilinear elliptic problems in $$\mathbb R^N$$. Zbl 1056.35507
Mitidieri, E.; Pokhozhaev, S. I.
1999
Blow-up and critical exponents for nonlinear hyperbolic equations. Zbl 1012.35058
Galaktionov, V. A.; Pohozaev, S. I.
2003
The essentially nonlinear capacities induced by differential operators. Zbl 0963.35056
Pokhozhaev, S. I.
1997
Towards a unified approach to nonexistence of solutions for a class of differential inequalities. Zbl 1115.35157
Mitidieri, Enzo; Pohozaev, Stanislav I.
2004
Global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1122.35040
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
2004
Third-order nonlinear dispersive equations: shocks, rarefaction, and blowup waves. Zbl 1177.76183
Galaktionov, V. A.; Pokhozhaev, S. I.
2008
Blow-up results for nonlinear hyperbolic inequalities. Zbl 0965.35197
Pohozaev, Stanislav; Véron, Laurent
2000
The Dirichlet problem for the equation $$\Delta u=u^2$$. Zbl 0097.08503
Pokhozhaev, S. I.
1960
On the necessary conditions of global existence to a quasilinear inequality in the half-space. Zbl 0943.35110
Egorov, Yuri V.; Galaktionov, Victor A.; Kondratiev, Vladimir A.; Pohozaev, Stanislav I.
2000
Solvability of nonlinear equations with odd operators. Zbl 0165.49502
Pokhozhaev, S. I.
1967
Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group. Zbl 0964.35046
Pohozaev, Stanislav; Véron, Laurent
2000
Nonexistence of local solutions to semilinear partial differential inequalities. Zbl 1064.35220
Pohozaev, Stanislav I.; Tesei, Alberto
2004
Some Liouville theorems for quasilinear elliptic inequalities. Zbl 1387.35207
Caristi, G.; Mitidieri, E.; Pokhozhaev, S. I.
2009
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations. Zbl 1176.35094
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2009
On the method of fibering a solution of nonlinear boundary value problems. Zbl 0734.35036
Pokhozhaev, S. I.
1990
On equations of the form (Delta u) = f(x,u,Du). Zbl 0483.35033
Pokhozhaev, S. I.
1982
Blow-up of nonnegative solutions to quasilinear parabolic inequalities. Zbl 1007.35003
Pohozaev, Stanislav I.; Tesei, Alberto
2000
Nonexistence of weak solutions for some degenerate and singular hyperbolic problems on $$\mathbb{R}_+^{n+1}$$. Zbl 1032.35138
Mitidieri, E.; Pohozaev, S. I.
2001
Critical nonlinearities in partial differential equations. Zbl 1205.35024
Pohozaev, Stanislav I.
2009
Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators. Zbl 1109.35015
Galaktionov, V. A.; Pohozaev, S. I.
2006
Nonexistence of positive solutions for a system of quasilinear elliptic equations and inequalities in $${\mathbb{R}}^N$$. Zbl 0969.35052
Mitidieri, E.; Pokhozhaev, S. I.
1999
The fibering method in nonlinear variational problems. Zbl 0901.35018
Pohozaev, A. I.
1997
On equations of the form $$\Delta u=f(x,u,Du)$$. Zbl 0457.35032
Pokhozhaev, S. I.
1980
Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations. Zbl 1320.35002
Galaktionov, Victor A.; Mitidieri, Enzo L.; Pohozaev, Stanislav I.
2015
On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1020.35029
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
2002
Representation formulae and inequalities for solutions of a class of second order partial differential equations. Zbl 1081.35014
D’Ambrosio, Lorenzo; Mitidieri, Enzo; Pohozaev, Stanislav I.
2006
Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition. Zbl 1374.35176
Kirane, Mokhtar; Nabana, Eric; Pohozaev, Stanislav I.
2004
Nonlinear variational problems via the fibering method. Zbl 1184.35001
Pohozaev, Stanislav I.
2008
On the solvability of quasilinear elliptic equations of arbitrary order. Zbl 0491.35020
Pokhozhaev, S. I.
1982
Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II. Zbl 1244.35019
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2011
On the nonexistence of global solutions of some initial-boundary value problems for the Korteweg-de Vries equation. Zbl 1232.35147
Pokhozhaev, S. I.
2011
Existence and nonexistence of solutions of nonlinear Dirichlet problems with first order terms. Zbl 0976.35025
Moschini, Luisa; Pohozaev, Stanislav I.; Tesei, Alberto
2000
On an approach to nonlinear equations. Zbl 0456.47053
Pokhozhaev, S. I.
1979
On the global fibering method in nonlinear variational problems. Zbl 0940.35092
Pohozaev, S. I.
1997
The absence of solutions of elliptic systems with dynamic boundary conditions. Zbl 1290.35119
Kirane, M.; Nabana, E.; Pokhozhaev, S. I.
2002
On blow-up of solutions of the Kuramoto-Sivashinsky equation. Zbl 1161.35491
Pokhozhaev, S. I.
2008
The fibering method and its applications to nonlinear boundary value problem. Zbl 0964.58016
Pohožaev, S. I.
1999
Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range: second-order diffusion. Zbl 1298.35020
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
2014
Multiple positive solutions of some quasilinear Neumann problems. Zbl 1063.35065
Pohozaev, Stanislav I.; Véron, Laurent
2000
Some generalizations of the Bernstein theorem. Zbl 1274.35120
Mitidieri, E.; Pokhozhaev, S. I.
2002
On similarity solutions and blow-up spectra for a semilinear wave equation. Zbl 1039.35066
Galaktionov, V. A.; Pohozaev, S. I.
2003
On the eigenfunctions of quasilinear elliptic problems. Zbl 0217.13203
Pokhozhaev, S. I.
1971
Concerning an equation in the theory of combustion. Zbl 1233.35050
Pokhozhaev, S. I.
2010
Blow-up of smooth solutions of the Korteweg-de Vries equation. Zbl 1246.35182
Pohozaev, Stanislav I.
2012
Lifespan estimates for solutions of some evolution inequalities. Zbl 1184.35075
Mitidieri, E.; Pokhozhaev, S. I.
2009
Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation. Zbl 1152.35101
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2008
On the nonexistence of global solutions of the Cauchy problem for the Korteweg-de Vries equation. Zbl 1309.35115
Pokhozhaev, S. I.
2012
Critical exponents for the absence of solutions for systems of quasilinear parabolic inequalities. Zbl 0994.35026
Pokhozhaev, S. I.; Tesei, A.
2001
Liouville theorems for some classes of nonlinear nonlocal problems. Zbl 1123.35087
Mitidieri, E.; Pokhozhaev, S. I.
2005
Nonexistence of global solutions of nonlinear evolution equations. Zbl 1277.35076
Pokhozhaev, S. I.
2013
On the absence of global solutions of the Korteweg-de Vries equation. Zbl 1276.35134
Pohozaev, S. I.
2013
Variational approach to complicated similarity solutions of higher order nonlinear evolution partial differential equations. Zbl 1179.35074
Galaktionov, Victor; Mitidieri, Enzo; Pokhozhaev, Stanislav
2009
On the singular solutions of the Korteweg-de Vries equation. Zbl 1231.35211
Pokhozhaev, S. I.
2010
Existence of positive solutions to some nonlinear Neumann problems. Zbl 0968.35049
Pokhozhaev, S. I.; Tesej, A.
1998
Multidimensional scalar conservation laws. Zbl 1049.35130
Pokhozhaev, S. I.
2003
A general approach to the theory of nonexistence of global solutions to nonlinear partial differential equations and inequalities. Zbl 1125.35348
Pokhozhaev, S. I.
2002
Instantaneous blow-up of solutions to a class of hyperbolic inequalities. Zbl 1024.35081
Pohozaev, Stanislav I.; Tesei, Alberto
2002
The Kirchhoff quasilinear hyperbolic equation. Zbl 0584.35073
Pokhozhaev, S. I.
1985
On stationary solutions of the Vlasov-Poisson equations. Zbl 1204.35163
Pokhozhaev, S. I.
2010
On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain. Zbl 1004.35091
Mustonen, Vesa; Pohožaev, Stanislav
1998
On nonlinear operators having weakly closed range, and quasilinear elliptic equations. Zbl 0201.46501
Pokhozhaev, S. I.
1969
Local estimates and Liouville theorems for a class of quasilinear inequalities. Zbl 1159.35342
Caristi, Gabriella; Mitidieri, Enzo; Pohozaev, Stanislav I.
2008
Weighted identities for solutions of generalized Korteweg-de Vries equations. Zbl 1231.35212
Pokhozhaev, S. I.
2011
Fujita-type theorems for quasilinear parabolic inequalities with nonlinear gradient. Zbl 1146.35382
Mitidieri, E.; Pokhozhaev, S. I.
2002
On the solvability of quasilinear elliptic equations of arbitrary order. Zbl 0511.35014
Pokhozhaev, S. I.
1983
Capacity induced by a nonlinear operator and applications. Zbl 1157.35305
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
2008
On the nonexistence of global solutions of the Hamilton-Jacobi equation. Zbl 1194.35103
Pohozaev, S. I.
2008
On a class of initial-boundary value problems for equations of Korteweg-de Vries type. Zbl 1246.35183
Pokhozhaev, S. I.
2012
Existence and nonexistence of solutions of nonlinear Neumann problems. Zbl 0944.35030
Pohozaev, Stanislav I.; Tesei, Alberto
1999
Normal solubility of nonlinear equations in convex uniform Banach spaces. Zbl 0191.14803
Pohozaev, S. I.
1969
On a constructive method of the calculus of variations. Zbl 0717.58012
Pokhozhaev, S. I.
1988
On elliptic problems in $$\mathbb{R}{}^ N$$ with a supercritical exponent of nonlinearity. Zbl 0746.35015
Pokhozhaev, S. I.
1991
On a class of singular solutions to the Korteweg-de Vries equation. Zbl 1217.35165
Pohozaev, S. I.
2010
On a class of nonlinear Dirichlet problems with first order terms. Zbl 1098.35555
Moschini, L.; Tesei, A.; Pohozaev, S. I.
2001
Riemann quasi-invariants. Zbl 1232.35095
Pokhozhaev, S. I.
2011
On the dependence of the critical exponent of the nonlinear heat equation on the initial function. Zbl 1227.35054
Pokhozhaev, S. I.
2011
On entire solutions of semilinear elliptic equations. Zbl 0821.35046
Pokhozhaev, S.
1992
On the reaction-diffusion electrolysis nonlinear elliptic equations. Zbl 0912.35063
Pokhozhaev, S. I.
1998
On a priori estimates and gradient catastrophes of smooth solutions to hyperbolic systems of conservation laws. Zbl 1077.35093
Pokhozhaev, S. I.
2003
The general blowup for nonlinear PDE’s. Zbl 1064.35219
Pohozaev, Stanislav
2003
Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data. Zbl 1178.35336
Pokhozhaev, S. I.
2009
Convergence in gradient systems with branching of equilibria. Zbl 1229.35078
Galaktionov, V. A.; Pohozaev, S. I.; Shishkov, A. E.
2007
On the asymptotics of entire radial solutions of quasilinear elliptic equations. Zbl 0793.35031
Pokhozhaev, S. I.
1991
On Maslov equations. Zbl 0852.45014
Pokhozhaev, S. I.
1995
Vladimir Alexandrovich Kondratiev. July 2, 1935–March 11, 2010. Zbl 1277.01013
Agranovich, M. S.; Astashova, I. V.; Bagirov, L. A.; Vlasov, V. V.; Zhikov, V. V.; Ilyashenko, Yu. S.; Kozlov, V. V.; Kon’kov, A. A; Pokhozhaev, S. I.; Radkevich, E. V.; Rozov, N. Kh.; Sergeev, I. N.; Skubachevskii, A. L.; Chechkin, G. A.; Shamaev, A. S.; Shaposhnikova, T. A.
2013
Blowup for nonlinear initial-boundary value problems. Zbl 1327.35163
Galaktionov, V. A.; Pohozaev, S. I.
2007
The set of critical values of a functional. Zbl 0174.46103
Pokhozhaev, S. I.
1969
Normal solvability of nonlinear equations. Zbl 0181.42803
Pohozaev, S. I.
1969
On the blow-up of solutions to nonlinear initial-boundary value problems. Zbl 1233.35071
Pohozaev, S. I.
2008
On weakly nonlinear hyperbolic systems. Zbl 0223.35064
Pohozhaev, S. I.
1970
Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations. Zbl 1320.35002
Galaktionov, Victor A.; Mitidieri, Enzo L.; Pohozaev, Stanislav I.
2015
Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range: second-order diffusion. Zbl 1298.35020
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
2014
Nonexistence of global solutions of nonlinear evolution equations. Zbl 1277.35076
Pokhozhaev, S. I.
2013
On the absence of global solutions of the Korteweg-de Vries equation. Zbl 1276.35134
Pohozaev, S. I.
2013
Vladimir Alexandrovich Kondratiev. July 2, 1935–March 11, 2010. Zbl 1277.01013
Agranovich, M. S.; Astashova, I. V.; Bagirov, L. A.; Vlasov, V. V.; Zhikov, V. V.; Ilyashenko, Yu. S.; Kozlov, V. V.; Kon’kov, A. A; Pokhozhaev, S. I.; Radkevich, E. V.; Rozov, N. Kh.; Sergeev, I. N.; Skubachevskii, A. L.; Chechkin, G. A.; Shamaev, A. S.; Shaposhnikova, T. A.
2013
Critical nonlinearities in partial differential equations. Zbl 1320.35099
Pokhozhaev, S. I.
2013
Blow-up of smooth solutions of the Korteweg-de Vries equation. Zbl 1246.35182
Pohozaev, Stanislav I.
2012
On the nonexistence of global solutions of the Cauchy problem for the Korteweg-de Vries equation. Zbl 1309.35115
Pokhozhaev, S. I.
2012
On a class of initial-boundary value problems for equations of Korteweg-de Vries type. Zbl 1246.35183
Pokhozhaev, S. I.
2012
Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II. Zbl 1244.35019
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2011
On the nonexistence of global solutions of some initial-boundary value problems for the Korteweg-de Vries equation. Zbl 1232.35147
Pokhozhaev, S. I.
2011
Weighted identities for solutions of generalized Korteweg-de Vries equations. Zbl 1231.35212
Pokhozhaev, S. I.
2011
Riemann quasi-invariants. Zbl 1232.35095
Pokhozhaev, S. I.
2011
On the dependence of the critical exponent of the nonlinear heat equation on the initial function. Zbl 1227.35054
Pokhozhaev, S. I.
2011
On the existence and nonexistence of solutions of some quasilinear hyperbolic equations. Zbl 1243.35126
Pokhozhaev, S. I.
2011
Concerning an equation in the theory of combustion. Zbl 1233.35050
Pokhozhaev, S. I.
2010
On the singular solutions of the Korteweg-de Vries equation. Zbl 1231.35211
Pokhozhaev, S. I.
2010
On stationary solutions of the Vlasov-Poisson equations. Zbl 1204.35163
Pokhozhaev, S. I.
2010
On a class of singular solutions to the Korteweg-de Vries equation. Zbl 1217.35165
Pohozaev, S. I.
2010
Blow-up of sign-changing solutions to quasilinear parabolic equations. Zbl 1202.35039
Pohozaev, S. I.
2010
Some Liouville theorems for quasilinear elliptic inequalities. Zbl 1387.35207
Caristi, G.; Mitidieri, E.; Pokhozhaev, S. I.
2009
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations. Zbl 1176.35094
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2009
Critical nonlinearities in partial differential equations. Zbl 1205.35024
Pohozaev, Stanislav I.
2009
Lifespan estimates for solutions of some evolution inequalities. Zbl 1184.35075
Mitidieri, E.; Pokhozhaev, S. I.
2009
Variational approach to complicated similarity solutions of higher order nonlinear evolution partial differential equations. Zbl 1179.35074
Galaktionov, Victor; Mitidieri, Enzo; Pokhozhaev, Stanislav
2009
Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data. Zbl 1178.35336
Pokhozhaev, S. I.
2009
Third-order nonlinear dispersive equations: shocks, rarefaction, and blowup waves. Zbl 1177.76183
Galaktionov, V. A.; Pokhozhaev, S. I.
2008
Nonlinear variational problems via the fibering method. Zbl 1184.35001
Pohozaev, Stanislav I.
2008
On blow-up of solutions of the Kuramoto-Sivashinsky equation. Zbl 1161.35491
Pokhozhaev, S. I.
2008
Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation. Zbl 1152.35101
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
2008
Local estimates and Liouville theorems for a class of quasilinear inequalities. Zbl 1159.35342
Caristi, Gabriella; Mitidieri, Enzo; Pohozaev, Stanislav I.
2008
Capacity induced by a nonlinear operator and applications. Zbl 1157.35305
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
2008
On the nonexistence of global solutions of the Hamilton-Jacobi equation. Zbl 1194.35103
Pohozaev, S. I.
2008
On the blow-up of solutions to nonlinear initial-boundary value problems. Zbl 1233.35071
Pohozaev, S. I.
2008
Convergence in gradient systems with branching of equilibria. Zbl 1229.35078
Galaktionov, V. A.; Pohozaev, S. I.; Shishkov, A. E.
2007
Blowup for nonlinear initial-boundary value problems. Zbl 1327.35163
Galaktionov, V. A.; Pohozaev, S. I.
2007
Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators. Zbl 1109.35015
Galaktionov, V. A.; Pohozaev, S. I.
2006
Representation formulae and inequalities for solutions of a class of second order partial differential equations. Zbl 1081.35014
D’Ambrosio, Lorenzo; Mitidieri, Enzo; Pohozaev, Stanislav I.
2006
Liouville theorems for some classes of nonlinear nonlocal problems. Zbl 1123.35087
Mitidieri, E.; Pokhozhaev, S. I.
2005
Towards a unified approach to nonexistence of solutions for a class of differential inequalities. Zbl 1115.35157
Mitidieri, Enzo; Pohozaev, Stanislav I.
2004
Global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1122.35040
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
2004
Nonexistence of local solutions to semilinear partial differential inequalities. Zbl 1064.35220
Pohozaev, Stanislav I.; Tesei, Alberto
2004
Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition. Zbl 1374.35176
Kirane, Mokhtar; Nabana, Eric; Pohozaev, Stanislav I.
2004
Blow-up and critical exponents for nonlinear hyperbolic equations. Zbl 1012.35058
Galaktionov, V. A.; Pohozaev, S. I.
2003
On similarity solutions and blow-up spectra for a semilinear wave equation. Zbl 1039.35066
Galaktionov, V. A.; Pohozaev, S. I.
2003
Multidimensional scalar conservation laws. Zbl 1049.35130
Pokhozhaev, S. I.
2003
On a priori estimates and gradient catastrophes of smooth solutions to hyperbolic systems of conservation laws. Zbl 1077.35093
Pokhozhaev, S. I.
2003
The general blowup for nonlinear PDE’s. Zbl 1064.35219
Pohozaev, Stanislav
2003
Existence and blow up for higher-order semilinear parabolic equations: majorizing order-preserving operators. Zbl 1082.35079
Galaktionov, V. A.; Pohozaev, S. I.
2002
On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1020.35029
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
2002
The absence of solutions of elliptic systems with dynamic boundary conditions. Zbl 1290.35119
Kirane, M.; Nabana, E.; Pokhozhaev, S. I.
2002
Some generalizations of the Bernstein theorem. Zbl 1274.35120
Mitidieri, E.; Pokhozhaev, S. I.
2002
A general approach to the theory of nonexistence of global solutions to nonlinear partial differential equations and inequalities. Zbl 1125.35348
Pokhozhaev, S. I.
2002
Instantaneous blow-up of solutions to a class of hyperbolic inequalities. Zbl 1024.35081
Pohozaev, Stanislav I.; Tesei, Alberto
2002
Fujita-type theorems for quasilinear parabolic inequalities with nonlinear gradient. Zbl 1146.35382
Mitidieri, E.; Pokhozhaev, S. I.
2002
A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. Transl. from the Russian. Zbl 1074.35500
Mitidieri, E.; Pohozaev, S. I.
2001
A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. (Apriornye otsenki i otsutstvie reshenij nelinejnykh uravnenij i neravenstv v chastnykh proizvodnykh.) Zbl 0987.35002
Mitidieri, E.; Pokhozhaev, S. I.
2001
Nonexistence results and estimates for some nonlinear elliptic problems. Zbl 1018.35040
Bidaut-Véron, Marie-Francoise; Pohozaev, Stanislav
2001
Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $$\mathbb{R}^n$$. Zbl 0988.35095
Mitidieri, Enzo; Pohozaev, Stanislav I.
2001
Nonexistence of weak solutions for some degenerate and singular hyperbolic problems on $$\mathbb{R}_+^{n+1}$$. Zbl 1032.35138
Mitidieri, E.; Pohozaev, S. I.
2001
Critical exponents for the absence of solutions for systems of quasilinear parabolic inequalities. Zbl 0994.35026
Pokhozhaev, S. I.; Tesei, A.
2001
On a class of nonlinear Dirichlet problems with first order terms. Zbl 1098.35555
Moschini, L.; Tesei, A.; Pohozaev, S. I.
2001
Blow-up results for nonlinear hyperbolic inequalities. Zbl 0965.35197
Pohozaev, Stanislav; Véron, Laurent
2000
On the necessary conditions of global existence to a quasilinear inequality in the half-space. Zbl 0943.35110
Egorov, Yuri V.; Galaktionov, Victor A.; Kondratiev, Vladimir A.; Pohozaev, Stanislav I.
2000
Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group. Zbl 0964.35046
Pohozaev, Stanislav; Véron, Laurent
2000
Blow-up of nonnegative solutions to quasilinear parabolic inequalities. Zbl 1007.35003
Pohozaev, Stanislav I.; Tesei, Alberto
2000
Existence and nonexistence of solutions of nonlinear Dirichlet problems with first order terms. Zbl 0976.35025
Moschini, Luisa; Pohozaev, Stanislav I.; Tesei, Alberto
2000
Multiple positive solutions of some quasilinear Neumann problems. Zbl 1063.35065
Pohozaev, Stanislav I.; Véron, Laurent
2000
Nonexistence of positive solutions for quasilinear elliptic problems in $$\mathbb R^N$$. Zbl 1056.35507
Mitidieri, E.; Pokhozhaev, S. I.
1999
Nonexistence of positive solutions for a system of quasilinear elliptic equations and inequalities in $${\mathbb{R}}^N$$. Zbl 0969.35052
Mitidieri, E.; Pokhozhaev, S. I.
1999
The fibering method and its applications to nonlinear boundary value problem. Zbl 0964.58016
Pohožaev, S. I.
1999
Existence and nonexistence of solutions of nonlinear Neumann problems. Zbl 0944.35030
Pohozaev, Stanislav I.; Tesei, Alberto
1999
The Cauchy problem for the extended Fisher-Kolmogorov equation. Zbl 0937.35083
Peletier, L. A.; Pokhozhaev, S. I.
1999
The existence and nonexistence of periodic solutions to certain nonlinear hyperbolic equations. Zbl 0990.35015
Pokhozhaev, S. I.
1999
The absence of global positive solutions of quasilinear elliptic inequalities. Zbl 0976.35100
Mitidieri, E.; Pokhozhaev, S. I.
1998
Existence of positive solutions to some nonlinear Neumann problems. Zbl 0968.35049
Pokhozhaev, S. I.; Tesej, A.
1998
On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain. Zbl 1004.35091
Mustonen, Vesa; Pohožaev, Stanislav
1998
On the reaction-diffusion electrolysis nonlinear elliptic equations. Zbl 0912.35063
Pokhozhaev, S. I.
1998
On the existence and nonexistence of periodic solutions to some nonlinear hyperbolic equations. Zbl 0972.35073
Pokhozhaev, S. I.
1998
Positive solutions for the $$p$$-Laplacian: Application of the fibrering method. Zbl 0880.35045
Drábek, Pavel; Pohozaev, Stanislav I.
1997
Entire solutions of semilinear elliptic equations. Zbl 0882.35003
Kuzin, I.; Pohozaev, S.
1997
The essentially nonlinear capacities induced by differential operators. Zbl 0963.35056
Pokhozhaev, S. I.
1997
The fibering method in nonlinear variational problems. Zbl 0901.35018
Pohozaev, A. I.
1997
On the global fibering method in nonlinear variational problems. Zbl 0940.35092
Pohozaev, S. I.
1997
On Maslov equations. Zbl 0852.45014
Pokhozhaev, S. I.
1995
A nonlinear elliptic problem of H. Amann. Zbl 0827.35038
Pokhozhaev, S. I.
1994
On entire radial solutions of quasilinear elliptic equations. Zbl 0865.35046
Pokhozhaev, S. I.
1993
On entire solutions of semilinear elliptic equations. Zbl 0821.35046
Pokhozhaev, S.
1992
On entire radial solutions of some quasilinear elliptic equations. Zbl 0797.35041
Pokhozhaev, S. I.
1992
On elliptic problems in $$\mathbb{R}{}^ N$$ with a supercritical exponent of nonlinearity. Zbl 0746.35015
Pokhozhaev, S. I.
1991
On the asymptotics of entire radial solutions of quasilinear elliptic equations. Zbl 0793.35031
Pokhozhaev, S. I.
1991
On entire solutions of a class of quasilinear elliptic equations. Zbl 0782.35012
Pokhozhaev, S. I.
1991
On the method of fibering a solution of nonlinear boundary value problems. Zbl 0734.35036
Pokhozhaev, S. I.
1990
On a constructive method of the calculus of variations. Zbl 0717.58012
Pokhozhaev, S. I.
1988
The Kirchhoff quasilinear hyperbolic equation. Zbl 0584.35073
Pokhozhaev, S. I.
1985
On the solvability of quasilinear elliptic equations of arbitrary order. Zbl 0511.35014
Pokhozhaev, S. I.
1983
A priori bounds of solutions of quasilinear elliptic equations of arbitrary order. Zbl 0523.35049
Pokhozhaev, S. I.
1983
On equations of the form (Delta u) = f(x,u,Du). Zbl 0483.35033
Pokhozhaev, S. I.
1982
On the solvability of quasilinear elliptic equations of arbitrary order. Zbl 0491.35020
Pokhozhaev, S. I.
1982
On quasilinear elliptic equations of high order. Zbl 0456.35035
Pokhozhaev, S. I.
1981
...and 13 more Documents
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### Cited by 1,344 Authors
42 Korpusov, Maksim Olegovich 33 Galaktionov, Victor Aleksandrovich 32 Pokhozhaev, Stanislav I. 30 Kirane, Mokhtar 28 Samet, Bessem 25 Jleli, Mohamed Boussairi 23 Mitidieri, Enzo Luigi 22 Galakhov, Evgeniĭ Igorevich 22 Wu, Tsungfang 18 D’Ambrosio, Lorenzo 16 Salieva, Olga Alekseevna 15 Dzhokhadze, Otar Mikhajlovich 15 Kharibegashvili, S. S. 14 Chen, Caisheng 14 Farina, Alberto 14 Filippucci, Roberta 14 Kon’kov, Andrej A. 13 Il’yasov, Yavdat Shavkatovich 12 Álvarez-Caudevilla, Pablo 12 Nguyen Thanh Long 12 Passaseo, Donato 11 Al-saedi, Ahmed Eid Salem 11 Punzo, Fabio 11 Sun, Yuhua 11 Véron, Laurent 11 Wei, Juncheng 11 Yang, Zuodong 10 Ahmad, Bashir 10 Fino, Ahmad Z. 10 Gazzola, Filippo 10 Yushkov, Egor Vladislavovich 9 Alves, Claudianor Oliveira 9 Musso, Monica 9 Panin, Aleksandr Anatol’evich 9 Pistoia, Angela 9 Quaas, Alexander 9 Yuldashev, Tursun Kamaldinovich 8 Aliev, Akbar B. 8 Bidaut-Veron, Marie-Françoise 8 Ghergu, Marius 8 Ishige, Kazuhiro 8 Kawakami, Tatsuki 8 Miyagaki, Olimpio Hiroshi 8 Muravnik, Andreĭ Borisovich 8 Saoudi, Kamel 8 Souplet, Philippe 8 Sreenadh, Konijeti 8 Ubilla, Pedro 7 Chen, Wenjing 7 García-Melián, Jorge 7 Molle, Riccardo 7 Skrzypczak, Leszek 7 Sun, Juntao 7 Tatar, Nasser-eddine 7 Tesei, Alberto 7 Xiu, Zonghu 6 Astashova, Irina Viktorovna 6 D’Abbicco, Marcello 6 Dancer, Edward Norman 6 Del Pino, Manuel A. 6 El Hamidi, Abdallah 6 Ferrero, Alberto 6 Franca, Matteo 6 Grossi, Massimo 6 Grunau, Hans-Christoph 6 Harrabi, Abdellaziz 6 Klimov, Vladimir Stepanovich 6 Le Thi Phuong Ngoc 6 Levashova, Natalia T. 6 Monticelli, Dario Daniele 6 Pacella, Filomena 6 Pucci, Patrizia 6 Sciunzi, Berardino 6 Serrin, James 6 Yin, Jingxue 5 An, Tianqing 5 Antontsev, Stanislav Nikolaevich 5 Bozhkov, Yuri Dimitrov 5 Carvalho, Marcos L. M. 5 Clapp, Mónica 5 Cowan, Craig 5 Da Silva, Edcarlos Domingos 5 Dai, Wei 5 Do Ó, João M. Bezerra 5 Evans, Jonathan David 5 Felmer, Patricio L. 5 Feng, Zhaosheng 5 Goulart, Claudiney 5 Goyal, Sarika 5 Gutlyanskiĭ, Vladimir Ya. 5 Hsu, TsingSan 5 Kajikiya, Ryuji 5 Laptev, Gennady G. 5 Le Xuan Truong 5 Li, Xiaohong 5 Lions, Pierre-Louis 5 Lorca, Sebastian Antonio 5 Nefedov, Nikolaĭ Nikolaevich 5 Okabe, Shinya 5 Phan, Quoc Hung ...and 1,244 more Authors
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### Cited in 235 Serials
137 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 117 Journal of Differential Equations 113 Journal of Mathematical Analysis and Applications 46 Mathematical Notes 46 Differential Equations 40 Nonlinear Analysis. Theory, Methods & Applications 36 Calculus of Variations and Partial Differential Equations 32 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 31 Journal of Mathematical Sciences (New York) 30 Journal of Functional Analysis 28 Communications on Pure and Applied Analysis 25 Computers & Mathematics with Applications 23 Discrete and Continuous Dynamical Systems 22 Applied Mathematics Letters 19 Theoretical and Mathematical Physics 19 Advances in Nonlinear Analysis 18 Boundary Value Problems 16 Journal of Mathematical Physics 16 NoDEA. Nonlinear Differential Equations and Applications 16 Proceedings of the Steklov Institute of Mathematics 14 Archive for Rational Mechanics and Analysis 14 Applied Mathematics and Computation 14 Communications in Contemporary Mathematics 14 Nonlinear Analysis. Real World Applications 14 Complex Variables and Elliptic Equations 13 Applicable Analysis 13 Annali di Matematica Pura ed Applicata. Serie Quarta 13 Transactions of the American Mathematical Society 13 Advanced Nonlinear Studies 12 Mathematical Methods in the Applied Sciences 12 Computational Mathematics and Mathematical Physics 11 Mathematische Annalen 11 Proceedings of the American Mathematical Society 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 10 Communications in Partial Differential Equations 10 Mediterranean Journal of Mathematics 9 Manuscripta Mathematica 9 Acta Applicandae Mathematicae 9 Izvestiya: Mathematics 9 Abstract and Applied Analysis 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Journal of Evolution Equations 8 Journal of Function Spaces 7 Communications in Mathematical Physics 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 7 Siberian Mathematical Journal 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Doklady Mathematics 7 Milan Journal of Mathematics 6 Duke Mathematical Journal 6 Monatshefte für Mathematik 6 Electronic Journal of Differential Equations (EJDE) 6 Discrete and Continuous Dynamical Systems. Series S 5 Nonlinearity 5 Proceedings of the Japan Academy. Series A 5 Journal of Dynamics and Differential Equations 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Topological Methods in Nonlinear Analysis 5 Analysis and Mathematical Physics 4 Journal d’Analyse Mathématique 4 Advances in Mathematics 4 Quarterly of Applied Mathematics 4 Studies in Applied Mathematics 4 Physica D 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Potential Analysis 4 Boletín de la Sociedad Matemática Mexicana. Third Series 4 Journal of Inequalities and Applications 4 Fractional Calculus & Applied Analysis 4 Lobachevskii Journal of Mathematics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Advances in Difference Equations 4 Science China. Mathematics 4 Eurasian Mathematical Journal 3 Rocky Mountain Journal of Mathematics 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of Computational and Applied Mathematics 3 Journal of Soviet Mathematics 3 Mathematische Nachrichten 3 Numerische Mathematik 3 Forum Mathematicum 3 Russian Mathematics 3 Bulletin des Sciences Mathématiques 3 The Journal of Fourier Analysis and Applications 3 Revista Matemática Complutense 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Nonlinear Mathematical Physics 3 Discrete and Continuous Dynamical Systems. Series B 3 International Journal of Differential Equations 3 Ufimskiĭ Matematicheskiĭ Zhurnal 3 Arabian Journal of Mathematics 3 Journal of Elliptic and Parabolic Equations 3 SN Partial Differential Equations and Applications 2 Journal of Engineering Mathematics 2 Lithuanian Mathematical Journal 2 Mathematics of Computation 2 Functional Analysis and its Applications 2 Mathematische Zeitschrift 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 Zeitschrift für Analysis und ihre Anwendungen ...and 135 more Serials
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### Cited in 38 Fields
1,363 Partial differential equations (35-XX) 85 Ordinary differential equations (34-XX) 79 Operator theory (47-XX) 70 Global analysis, analysis on manifolds (58-XX) 42 Functional analysis (46-XX) 35 Real functions (26-XX) 33 Fluid mechanics (76-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 32 Numerical analysis (65-XX) 32 Mechanics of deformable solids (74-XX) 27 Integral equations (45-XX) 20 Potential theory (31-XX) 17 Differential geometry (53-XX) 16 Quantum theory (81-XX) 15 Statistical mechanics, structure of matter (82-XX) 14 Dynamical systems and ergodic theory (37-XX) 7 Biology and other natural sciences (92-XX) 6 Topological groups, Lie groups (22-XX) 6 Measure and integration (28-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 History and biography (01-XX) 5 Systems theory; control (93-XX) 4 Functions of a complex variable (30-XX) 4 Algebraic topology (55-XX) 4 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 3 Abstract harmonic analysis (43-XX) 3 Mechanics of particles and systems (70-XX) 3 Astronomy and astrophysics (85-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX)
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https://par.nsf.gov/biblio/10125578-galaxy-morphological-classification-deep-wide-surveys-via-unsupervised-machine-learning | Galaxy morphological classification in deep-wide surveys via unsupervised machine learning
ABSTRACT
Galaxy morphology is a fundamental quantity, which is essential not only for the full spectrum of galaxy-evolution studies, but also for a plethora of science in observational cosmology (e.g. as a prior for photometric-redshift measurements and as contextual data for transient light-curve classifications). While a rich literature exists on morphological-classification techniques, the unprecedented data volumes, coupled, in some cases, with the short cadences of forthcoming ‘Big-Data’ surveys (e.g. from the LSST), present novel challenges for this field. Large data volumes make such data sets intractable for visual inspection (even via massively distributed platforms like Galaxy Zoo), while short cadences make it difficult to employ techniques like supervised machine learning, since it may be impractical to repeatedly produce training sets on short time-scales. Unsupervised machine learning, which does not require training sets, is ideally suited to the morphological analysis of new and forthcoming surveys. Here, we employ an algorithm that performs clustering of graph representations, in order to group image patches with similar visual properties and objects constructed from those patches, like galaxies. We implement the algorithm on the Hyper-Suprime-Cam Subaru-Strategic-Program Ultra-Deep survey, to autonomously reduce the galaxy population to a small number (160) of ‘morphological clusters’, populated by galaxies more »
Authors:
; ; ; ;
Publication Date:
NSF-PAR ID:
10125578
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
491
Issue:
1
Page Range or eLocation-ID:
p. 1408-1426
ISSN:
0035-8711
Publisher:
Oxford University Press
4. ABSTRACT We explore unsupervised machine learning for galaxy morphology analyses using a combination of feature extraction with a vector-quantized variational autoencoder (VQ-VAE) and hierarchical clustering (HC). We propose a new methodology that includes: (1) consideration of the clustering performance simultaneously when learning features from images; (2) allowing for various distance thresholds within the HC algorithm; (3) using the galaxy orientation to determine the number of clusters. This set-up provides 27 clusters created with this unsupervised learning that we show are well separated based on galaxy shape and structure (e.g. Sérsic index, concentration, asymmetry, Gini coefficient). These resulting clusters also correlate well with physical properties such as the colour–magnitude diagram, and span the range of scaling relations such as mass versus size amongst the different machine-defined clusters. When we merge these multiple clusters into two large preliminary clusters to provide a binary classification, an accuracy of $\sim 87{{\ \rm per\ cent}}$ is reached using an imbalanced data set, matching real galaxy distributions, which includes 22.7 per cent early-type galaxies and 77.3 per cent late-type galaxies. Comparing the given clusters with classic Hubble types (ellipticals, lenticulars, early spirals, late spirals, and irregulars), we show that there is an intrinsic vagueness in visual classification systems, in particularmore » | 2022-11-27T20:00:27 | {"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": 0.4736880362033844, "perplexity": 3235.7231187179764}, "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/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00634.warc.gz"} |
https://linkeddata.tern.org.au/viewer/tern/id/http://linked.data.gov.au/def/tern-cv/6e1e3b67aeba1c21123d2009b1237319016a12340818f42a3550370c0f34d587 | # gross primary productivity of biomass expressed as carbon
URI: http://linked.data.gov.au/def/tern-cv/6e1e3b67aeba1c21123d2009b1237319016a12340818f42a3550370c0f34d587
Also known as gross_primary_productivity_of_biomass_expressed_as_carbon
Date created: 2013-11-28
Date modified: 2022-06-10
Parameter Type
##### Definition
"Production of carbon" means the production of biomass expressed as the mass of carbon which it contains. Gross primary production is the rate of synthesis of biomass from inorganic precursors by autotrophs ("producers"), for example, photosynthesis in plants or phytoplankton. The producers also respire some of this biomass and the difference is "net_primary_production". "Productivity" means production per unit area. The phrase "expressed_as" is used in the construction A_expressed_as_B, where B is a chemical constituent of A. It means that the quantity indicated by the standard name is calculated solely with respect to the B contained in A, neglecting all other chemical constituents of A.
##### source
http://vocab.nerc.ac.uk/collection/P07/current/
##### notation
gross_primary_productivity_of_biomass_expressed_as_carbon
##### note
This concept was harvested from the controlled vocabulary at http://vocab.nerc.ac.uk/collection/P07/current/ on 2022-06-10. Information was pulled as-is for the following properties: dcterms:created, skos:definition, skos:exactMatch, skos:related and skos:notation. The URI of the concept is generated using SHA256 on the CF standard name (in the skos:notation) and concatenated with the TERN controlled vocabularies' base URI (http://linked.data.gov.au/def/tern-cv/).
##### related
http://vocab.nerc.ac.uk/collection/P06/current/KSP2/
TERN is supported by the Australian Government through the National Collaborative Research Infrastructure Strategy, NCRIS. | 2022-08-15T21:52:34 | {"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": 0.5417250394821167, "perplexity": 7236.229447796725}, "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/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00397.warc.gz"} |
https://pos.sissa.it/358/435/ | Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
The status and performance of Cosmic Ray Air Fluorescence Fresnel lens Telescope (CRAFFT) for the next generation UHECR observatory
Y. Tameda*, T. Tomida, D. Ikeda, K. Yamazaki, M. Yamamoto, H. Iwakura, Y. Nakamura and Y. Kaino
Full text: pdf
Pre-published on: July 22, 2019
Published on: July 02, 2021
Abstract
The next generation ultra-high energy cosmic ray (UHECR) observatory should be expanded due to the very small flux. In order to realize a huge UHECR observatory, cost reduction of detectors is one of the useful strategy. Then we are developing a Cosmic Ray Air Fluorescence Fresnel lens Telescope (CRAFFT) which is a very simple structure fluorescence detector. CRAFFT detector consists of mainly a $1.4 {\rm m^2}$ Fresnel lens, an UV transmitting filter, an 8 inch photomultiplier tube, an FADC board, and power supply system. We tested CRAFFT detector performance at Telescope Array (TA) site, and succeeded to detect UHECR air showers synchronized with TA Fluorescence Detectors. CRAFFT detector will be deployed as a huge ground array with ∼ 20 km spacing without the enough infrastructure such as in desert. Therefore, CRAFFT detectors can stand alone. We are developing automatic observation and protecting detector system. Additionally, we are studying our detector performance by detector simulation to estimate trigger efficiency, establish a reconstruction procedure, and optimize our detector configuration. In this presentation, we will report the result of the test operation of automatic observation and protecting detector system for CRAFFT detector, and the detector performance and optimization.
DOI: https://doi.org/10.22323/1.358.0435
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-06-26T05:16:56 | {"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": 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": 0.22659805417060852, "perplexity": 4503.453079567807}, "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-2022-27/segments/1656103037089.4/warc/CC-MAIN-20220626040948-20220626070948-00041.warc.gz"} |
https://caps.gov.harvard.edu/faqs | # FAQs
### What is MAPS? How did it start?
MAPS is a new program, started by CAPS in 2010, as a way to help undergraduates learn the process of doing original research before getting to the senior-thesis-writing stage. We at CAPS have for several years heard juniors and seniors talking about wanting to write a senior thesis, but feeling like they didn’t have enough experience, or didn’t know where to begin. This often meant that, when they applied for research funding, they didn’t get the grants they needed. The awards available to undergraduates for thesis research and writing demand a thoughtful and well-considered research question. But if you’ve never done original research, it’s hard to know how to formulate a good question. We at CAPS conceived of the MAPS program as a way to help give undergraduates some experience and training in question-development and original research before they get to the thesis-writing stage.
### How did I get selected to be invited to join MAPS?
MAPS undergraduates are nominated by someone who has been in a position to observe their work, either as a professor or TF or director of undergraduate study (DUG) in their program or department. If you have not been nominated, but would like to be, ask a professor, TF, or DUG to nominate you to the MAPS coordinator, Katie Derzon ([email protected]).
### Who is nominated to join MAPS?
MAPS is not just for the top one or two students in each cohort. Rather, we conceive of MAPS as useful and appropriate for bright, thoughtful undergraduates who are intellectually curious and interested in doing original research – but who, for whatever reason, may not know where to begin or have the resources and confidence to undertake original research on their own.
### How much work is involved? How long will it take?
MAPS is a program designed to help undergraduates develop skills in original research. Any research project will involve some nontrivial amount of time and effort. However, MAPS is not a class or a thesis, and will not take as much time as either of those. It’s also fairly self-directed, so the time and work involved can expand or contract, according to what you are willing to put into it. In large part, the time and work involved depend on the scope of your research question and design. If you don’t have much time but still want to do MAPS, you can work with your mentor to design a project that won’t overburden you but will still give you the chance to explore doing some original research. MAPS mentors can help you design a flexible research program for yourself.
### What’s in it for me?
MAPS is a program designed to help you learn the process of original research *before* you get to your senior year. We at CAPS have found that most undergrads don’t get much chance to engage in their own research until their senior thesis, usually. We want to help you prepare better in your early college years by giving you access to a grad student mentor who can help you figure out what it means to formulate a good research question, design a research methodology, perhaps collect data, and produce a final product of some sort, like a paper or short report. The experience you get will increase your abilities and confidence about doing original research in the future, for a class, or for a senior thesis, or in graduate school (it is great, when applying to graduate school, to be able to show some evidence of research of your own, like this).
### What can I expect?
Once you are nominated and accepted into the program, you will be contacted by the MAPS Coordinator (Katie Derzon, [email protected]), who will interview you briefly about some potential research topics you might like to explore. Based on these topics, Katie will match you with a graduate student mentor. You will then sit down with this mentor to meet, make sure the match is a good one, and then hash out a research question for your project. The graduate student mentor will be able to help you transform a general topic you have in mind into a good research question. Then you two should figure out how to answer your question (what method to use, what kinds of data to collect, what readings you’ll need to do). In many ways, this process will be like a mini-class, but you get to set the pace and the topic. By the end of the project, you will be asked to submit to the MAPS Coordinator a description of your research and its result, in some form (can be a paper you write, or a short report, or an article you might want to get published somewhere). Your mentor and the MAPS Coordinator can help as you prepare your final report, as well.
### How do I nominate a student to be invited to join MAPS? Who should be nominated?
CAPS is looking for especially attentive and curious Harvard undergraduates in fields relating to American politics. This could include Government, Economics, Sociology, Social Studies, Women’s and Gender Studies, African and African American Studies, Ethnic Studies, Psychology, History, perhaps History of Science also – we’re actually fairly flexible, as long as the student’s project relates in some way to American politics or society. To nominate a student, please send their name to MAPS Coordinator Katie Derzon ([email protected]), with just a quick line about why you think they would do well in this program. Thank you for your nomination(s)! | 2018-07-22T14:21:52 | {"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": 0.17924608290195465, "perplexity": 1066.5194024123007}, "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-2018-30/segments/1531676593302.74/warc/CC-MAIN-20180722135607-20180722155607-00011.warc.gz"} |
http://www.csm.ornl.gov/workshops/SciDAC2005/poster-abs/sugiyama.html | ## Plasmas beyond MHD: Two-fluids and symmetry breaking
### L E Sugiyama, W Park, H R Strauss, G Fu, J Breslau, J Chen, S. Klasky
Extended MHD effects are important in the nonlinear behavior of magnetically confined plasmas, even at the simplest level represented by the self-consistent diamagnetic ($\mathbf{B} \times \nabla p$) drifts. Allowing the electrons and ions to move independently, even as fluids, breaks certain geometrical symmetries preserved by the MHD equations that can be important for toroidal fusion burning plasmas. These symmetries are also broken by certain experimental designs and high temperature plasma conditions. Results are shown from the two-fluid and hybrid particle/fluid models in the M3D MPP code, part of the SciDAC CEMM (Center for Extended Magnetohydrodynamic Modeling) project. | 2015-09-04T01:31:16 | {"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": 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": 0.6296601891517639, "perplexity": 7413.223871481885}, "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-2015-35/segments/1440645330816.69/warc/CC-MAIN-20150827031530-00240-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://indico.fnal.gov/event/15949/contributions/34722/ | Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
36th Annual International Symposium on Lattice Field Theory
22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone
Contribution to the anomalous magnetic moment of the muon from the disconnected hadronic vacuum polarization with four-flavors of highly-improved staggered quarks.
Jul 24, 2018, 6:45 PM
2h
Lincoln (Kellogg Hotel and Conference Center)
Lincoln
Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Poster
Speaker
Mr Shuhei Yamamoto (The University of Utah)
Description
We describe a computation of the contribution to the anomalous magnetic moment of the muon from the disconnected part of the hadronic vacuum polarization. We use the highly-improved staggered quark (HISQ) formulation for the current density with gauge configurations generated with four flavors of HISQ sea quarks. The computation is performed by stochastic estimation of the current density using the truncated solver method combined with deflation of low-modes. The parameters are tuned to minimize the computational cost for a given target uncertainty in the current-current correlation function. The calculation presented here is carried out on a single gauge-field ensemble of size $32^3 \times 48$ with an approximate lattice spacing of 0.15 fm and with physical sea-quark masses. We describe the methodology and the analysis procedure.
Primary author
Mr Shuhei Yamamoto (The University of Utah)
Co-authors
Prof. Aida El-Khadra (University of Illinois at Urbana-Champaign) Dr Alejandro Vaquero (University of Utah) Carleton DeTar (University of Utah) Dr Craig McNeile (University of Plymouth) Dr Ruth Van de Water (Fermilab)
Slides | 2021-10-27T02:43:42 | {"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": 0.49023377895355225, "perplexity": 4296.745055126018}, "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-2021-43/segments/1634323588053.38/warc/CC-MAIN-20211027022823-20211027052823-00275.warc.gz"} |
http://malditobarbudo.xyz/blog/r/starting-bars-and-histograms-at-zero-in-ggplot2/ | Image credit: MalditoBarbudo (CC-BY 4.0)
# Starting bars and histograms at zero in ggplot2
When creating histograms or barplots in ggplot2 we found that the data is placed at some distance from the x axis, which means the y axis starts below zero:
This is because, internally, ggplot2 is expanding x and y axes by a multiplicative or additive constant1. This makes sense in almost all plots, except for the bar and histogram ones, as we see above.
## Workaround
To avoid this behaviour, we have to modify the y scale indicating the expand value as well as the limits value:
As you can see, here we add the following layer to the gpplot call:
scale_y_continuous(expand = c(0,0),
limits = c(0,30)) +
This way we avoid the y axis expand, but we need to set (harcode) the y max limit to allow for a space above the data (the y max value depends on the count range, so you have to take a look at the plot first).
• You have to provide a hardcoded limit value, so you have to generate the plot one time and modify the code to generate the final version. So no automatization here, in case you need it.
• It does not play well with free y faceted plots.
### Barplots
For barplots is the same:
## Summary
As you can see, default plot adds a gap at both ends, up and down. Setting expand to zero removes both gaps, no ideal. Finally setting expand to zero and setting the optimal y max limit does the trick.
## Bits of code
Code for the summary cowplot:
## Sources
1. See the expand parameter in ?scale_y_continuous for details
2. It seems an asymmetrical expand argument is on its way | 2022-05-27T19:22:14 | {"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": 0.695410966873169, "perplexity": 1674.2064568805347}, "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/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00579.warc.gz"} |
https://www.bnl.gov/event.php?q=12159 | # HET Lunch Discussions
## "B-decay Anomalies in a Composite Leptoquark Model"
#### Presented by Christopher Murphy, BNL
Friday, February 17, 2017, 12:15 pm — Building 510, Room 2-160
The collection of a few anomalies in semileptonic $B$-decays, especially in $b \to c \tau \bar{\nu}$ invites us to speculate about the emergence of some striking new phenomena, perhaps interpretable in terms of a weakly broken $U(2)^n$ flavor symmetry and of leptoquark mediators. Here we aim at a partial UV completion of this interpretation by generalizing the minimal composite Higgs model to include a composite vector leptoquark as well.
Reference: arXiv:1611.04930 w/ R. Barbieri and F. Senia
Hosted by: Christoph Lehner
12159 | INT/EXT | Events Calendar | 2021-06-18T03:10:56 | {"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": 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": 0.37099942564964294, "perplexity": 3879.787113361812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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/1623487634616.65/warc/CC-MAIN-20210618013013-20210618043013-00247.warc.gz"} |
https://mooseframework.inl.gov/source/materials/HeatConductionMaterial.html | # HeatConductionMaterial
General-purpose material model for heat conduction
## Description
HeatConductionMaterial is a general-purpose material model for heat conduction. It sets the thermal conductivity and specific heat at integration points.
## Input Parameters
• specific_heat_temperature_functionSpecific heat as a function of temperature.
C++ Type:FunctionName
Options:
Description:Specific heat as a function of temperature.
• 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
Options:
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.
• tempCoupled Temperature
C++ Type:std::vector
Options:
Description:Coupled Temperature
• thermal_conductivityThe thermal conductivity value
C++ Type:double
Options:
Description:The thermal conductivity value
• specific_heatThe specific heat value
C++ Type:double
Options:
Description:The specific heat value
• thermal_conductivity_temperature_functionThermal conductivity as a function of temperature.
C++ Type:FunctionName
Options:
Description:Thermal conductivity as a function of temperature.
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Options:
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
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
### Outputs Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
• 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
Options:NONE ELEMENT SUBDOMAIN
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 | 2019-04-23T12:18:17 | {"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": 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": 0.23397418856620789, "perplexity": 6019.077569213479}, "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-2019-18/segments/1555578602767.67/warc/CC-MAIN-20190423114901-20190423140901-00494.warc.gz"} |
https://andrewferguson.net/category/tech/ | ## I Bought a 3D Printer
Guys! I bought a 3D printer! It hasn’t even arrived yet, but I already feel like I should have done this ages ago! I ended up going with the
Wanhao i3 v2.1 Duplicator. It’s an upgraded version of the v2.0, which is effectively the same model that MonoPrice rebrands and sells as the Maker Select 3D Printer v2.
All around it seems to hit the sweet spot between price and capability. For me, the big selling points are:
• Sufficient large build envelope: 200 mm x 200 mm x 180 mm
• Sufficient build resolution: 0.1 mm, but can go down to 0.05 mm!
• Multiple-material filament capabilities
• Good community support
• Easy to make your improvements/repairs
I had to pay a bit of a premium since I’m in the UK, but I think it will be worth it. Printer arrives tomorrow, and I hope to have a report out soon thereafter.
## You Can’t Always Get What You Want
Jeffrey Goldberg at Agilebits, who make 1Password, has a great primer on why law enforcement back doors are bad for security architecture. The entire article is worth a read, presents a solid yet easily understood technical discussion — but I think it really can be distilled down to this:
From blog.agilebits.com:
Just because something would be useful for law enforcement doesn’t mean that they should have it. There is no doubt that law enforcement would be able to catch more criminals if they weren’t bound by various rules. If they could search any place or anybody any time they wished (instead of being bound by various rules about when they can), they would clearly be able to solve and prevent more crimes. That is just one of many examples of where we deny to law enforcement tools that would obviously be useful to them.
Quite simply, non-tyrannical societies don’t give every power to law enforcement that law enforcement would find useful. Instead we make choices based on a whole complex array of factors. Obviously the value of some power is one factor that plays a role in such a decision, and so it is important to hear from law enforcement about what they would find useful. But that isn’t where the conversation ends, it is where it begins.
Whenever that conversation does takes place, it is essential that all the participants understand the nature of the technology: There are some things that we simply can’t do without deeply undermining the security of the systems that we all rely on to keep us safe.
## Конструктор: Engineer of the People
This is one of those niche games that probably only applies to enginerds1, but if you — like me — are one of those people be prepared to lose yourself in this game as you deposit silicon and metal to make real life circuits.
Конструктор is Russian for designer or contractor.
1. and those who like to dabble in such realms
Is @Comcast throttling iOS 8 downloads? Direct through Comcast: 600 KB/s. Proxy through Linode server (over Comcast): 7 MB/s
```find ~/Downloads -type f -maxdepth 1 -mtime +7 -exec rm {} \;
find ~/Downloads -type d -maxdepth 1 -mtime +7 -exec rm -r {} \;
```
Here’s the gist: https://gist.github.com/fergbrain/8ddda2108dbc497e9f6b
I use Cronnix to manage and edit cron jobs on my Mac.
## Calendar Invitation Email Gone Awry
Here’s some more details on calendar email issue I noted late Monday.
Just after 10pm on Monday, I attempted to migrate my calendar from Google Calendar to Fastmail Calendar1.
I did this by exporting my existing calendar from Google (per https://support.google.com/calendar/answer/37111?hl=en) and then re-importing it back into Fastmail using Apple’s Calendar App. During this re-importing process, it appears that the Fastmail system regenerated the event requests and emailed all the participants of the events; although I initially suspected Apple’s Calendar app.
My wife, who was sitting next to me, was the first to let me know something was awry when she received over 400 emails from me.
After aborting last nights attempt, I tried again to import the data again Tuesday morning by using FastMail’s “Subscribe to a public calendar” feature (https://www.fastmail.fm/help/calendar/publiccalendar.html), which should not have resulted in emails being sent but still did.
In total, 109 people were affected by this issue and up to 2904 emails were sent (1452 from each incident).
The good news (if there is such a thing) is that 45% of those affected only received a single email (well, two emails), and 78% of those affected received less than 10 emails (20 emails across both incidents).
Unfortunately, emails were also sent to people even when I was not the original organizer of the event. This accounted for over half the emails that were sent.
I have opened a ticket with Fastmail (Calendar import emailing participants (Ticket Id: 479473)). Fastmail has been prompt and the issue is, in theory, resolved. However, in the future I plan on scrubbing the calendar file of email address to prevent this issue from occurring again.
For those curious, here’s how I extracted2 the number of those affected from the ICS file:
`grep -Eiorh 'mailto:([[:alnum:]_.-]+@[[:alnum:]_.-]+?\.[[:alpha:].]{2,6})' "\$@" basic.ics | sort | uniq -c | sort -r`
Mea Culpa.
1. there’s a larger story about why, but that’s not important at the moment
2. based on mosg’s answer on http://stackoverflow.com/questions/2898463/using-grep-to-find-all-emails/2898907#2898907
## If you got one ((or maybe a bazzilion)) calendar r…
If you got a calendar Invitation from me1, I am so sorry. I’m switching servers, did an export -> import, and Calendar decided to be helpful and email everyone. Face palm.
1. or maybe a bazzilion invites
## VMWare and USB 3
It took me a while to figure out why my external Seagate harddrive wasn’t working on Windows 7 and VMware Fusion 5. As it turns out, VMware Fusion 5 does not support USB 3.0 with Windows 71.
What is not intuitive — and frankly doesn’t make sense — is that VMware Fusion 5 will not automatically revert to USB 2.0 to attempt to support it.
The solution to this is to run your USB 3.0 capable device through a USB 2.0 hub, such as an Apple Keyboard with Numeric Keypad.
1. you need Windows 8, per their features list “Microsoft Windows 8 required for USB 3 support”
## Why You’re Doing Passwords Wrong
If you use passwords, there’s a good chance you’re doing them wrong and exposing yourself to unnecessary risk.
My intent is provide some basic information on how you can do passwords better1, suitable for grandma to use (no offense grandma), because there’s no reason that you can’t do passwords better.
In the beginning, the internet was a benevolent place. If I said I was fergbrain, everyone knew I was fergbrain. I didn’t need to prove I was fergbrain. Of course, that didn’t last long and so passwords were created to validate that I was, in fact, fergbrain.
Passwords are one of three ways in which someone can authenticate who they are:
2. Token: something you have that can’t be duplicated (such as an RSA token or YubiKey)
3. Biometric: something you are (such as a fingerprint or other biometric marker unique to you)
Back In The Day™, passwords were the de facto method of authentication because they were the easiest to implement and in many ways still are.
At the time, token-based methods were just on the verge of development with many of the technologies (such as public-key encryption) not even possible until the mid 1970’s. And once suitable encryption was more completely developed2, it could not be legally deployed outside of the United States until 1996 (President Clinton signed Executive Order 13026).
Finally, biometric authentication was an expensive pipe dream3.
The point being: passwords where the method of choice; and as we know, it is quite difficult to change the path of something once it gets moving.
Having just one password is easy enough, especially if you use it often enough. But how many places do you need to use a password? Email, social media, work, banking, games, utilities…the list goes on.
It would be pretty hard to remember all those different passwords. So we do the only thing we believe is reasonable: we use the same password. Or maybe a couple of different passwords: one for bank stuff, another for social media, maybe a third one for email.
## Why Passwords Can Be a Problem
Bad guys know that most people use the same username, email address, and password for multiple services. This creates a massive incentive for bad guys to try and get that information. If the bad guys can extract your information from one web site, it’s likely they can use your hacked data to get into your account at other web sites.
For bad guys, the most bang for the buck comes from attacking systems that store lots of usernames and passwords. And this is how things have gone. Over just the last two years Kickstarter, Adobe, LinkedIn, eHarmony, Zappos.com, last.fm, LivingSocial, and Yahoo have all been hacked and had passwords compromised. And those are just the big companies.
In my opinion, most people know they have bad passwords, but don’t know what to do about it. It’s likely your IT person at work4 keeps telling you to make “more complex” passwords, but what does that mean? Does it even help? What are we to do about this? Can we do anything to keep ourselves safer?
# How to do Passwords Better
There is no single best way to do passwords. The best way for any particular person is a compromise between security, cost, and ease of use.
There are several parts to doing passwords better:
If one web site is hacked, that should not compromise your data at another web site. Web sites generally identify you by your username (or email address) and password. You could have a different username for every single web site you use, but that would probably be more confusing (and could possible lead to personality disorder). Besides, having to explain to your friends why you go by TrogdorTheMagnificent on one site but TrogdorTheBold on another side would get tiring pretty quick.
### General Rule of Thumb
Passwords should be unique for each web site or service.
Why: If a unique passwords is compromised (e.g. someone hacked the site), the compromised password cannot be used to gain access to additional resources (i.e. other web sites)
1. For the 1st character in your password, give yourself 4 points.
2. For 2nd through 8th character in your password, give yourself 2 points for each character.
3. For the 9th through 20th character in your password, give yourself 1.5 points.
4. If you password has upper case, lower case, and numbers (or special characters), give yourself an additional 6 points.
5. If your password does not contain any words from the dictionary, give yourself an additional 6 points.
• If you score 44 points or more, you have a good password!
• If you score between 21 and 44 points, your password sucks.
• If you score 20 points or less, your password really sucks.
If my password was, for example, Ferguson86Gmail, I would only have 34.5 points:
• F: 4 points
• erguson: 2 points each, 14 points
• 86gmail: 1.5 points each, 10.5 points
• I have uppercase, lowercase, and a number: 6 points
• “Ferguson” and “gmail” are both considered dictionary words, so I get no extra points
Instead choosing Ferguson86Gmail as my password, what if my password was Dywpac27Najunst? The password is still 15 characters long, it still has two capital letters, and it still has two numbers. However, since it’s randomly generated it would score 89.3 — over twice as many points as the password I choose.
What’s going on here?
When you make up your own password, such as Ferguson86Gmail, you’re not choosing it at random and thus your password will not have a uniform random distribution of information5.
Passwords chosen by users probably roughly reflect the patterns and character frequency distributions of ordinary English text, and are chosen by users so that they can remember them. Experience teaches us that many users, left to choose their own passwords will choose passwords that are easily guessed and even fairly short dictionaries of a few thousand commonly chosen passwords, when they are compared to actual user chosen passwords, succeed in “cracking” a large share of those passwords.6
The “goodness” of a password is measured by randomness, which is usually referred to as bits of entropy (which I cleverly disguised as “points” in the above test) the reality of the situation is that humans suck at picking their own passwords.
### More Entropy!
If more entropy leads to better passwords, let’s look at what leads to more bits of entropy in a password. The number of bits of entropy, H, in a randomly generated password (versus a password you picked) of length, L, is:
$H=log_{2}N^{L}$
Where N is the number of characters possible. If you use only lowercase letters, N is 26. If you use lower and uppercase, N is 52. Adding numbers increases NÂ to 62.
For example:
• `mougiasw` is an eight-character all lowercase password that has $log_{2}26^{8}=37.6$ bits of entropy.
• `gLAviAco` is an eight-character lowercase and uppercase password that has $log_{2}52^{8}=45.6$ bits of entropy
• `Pr96Regu` is an eight-character lowercase, uppercase, and numeric password that has $log_{2}62^{8}=47.6$ bits of entropy.
• `vubachukus` is a ten-character all lowercase password that has $log_{2}26^{10}=47.0$ bits of entropy.
• `neprajubrawa` is a twelve-character all lowercase password that has $log_{2}26^{12}=56.4$ bits of entropy.
For every additional character, you add $log_{2}N$ bits of entropy. And unlike expanding the character set (e.g. using uppercase letters and/or numbers and/or special characters), you get more bits of entropy for every additional character you extend your password by…not just the first one.
The good news is that for randomly generated passwords, increasing the length by one character increases the difficulty to guess it by a factor of 32. The bad news is that for user selected passwords, every additional character added to make a password longer only quadruples the difficulty (adds roughly 2 bits of entropy which, based on NIST Special Publication 800-63 Rev 1 for the first 12 characters of a password).
More bits of entropy is better and I usually like to have at least 44 bits of entropy in my passwords. More is better.
Having to break out a calculator to determine the entropy of your passwords is not easy, and passwords should be easy. So let’s make it easy:
### General Rule of Thumb<
Longer passwords (at least ten characters long) are better than more complex passwords.
Why: Adding complexity only provides a minimal and one time benefit. Adding length provides benefit for each character added and is likely to be easier to remember.
The inevitable reality of doing passwords better is that you need a way to keep track of them. There simply is no way a person can keep track of all the different passwords for all the different sites.
This leaves us with two other options:
From www.schneier.com:
Simply, people can no longer remember passwords good enough to reliably defend against dictionary attacks, and are much more secure if they choose a password too complicated to remember and then write it down. We’re all good at securing small pieces of paper. I recommend that people write their passwords down on a small piece of paper, and keep it with their other valuable small pieces of paper: in their wallet.
Bruce Schneier, 2005
Writing down passwords can be appropriate because the most common attack vector is online (i.e. someone you’ve never even heard of trying to hack into your account from half-a-world away) with the following caveat: you make them more unique and more entropic.
By writing down passwords, you can increase their entropy (i.e. making them harder to guess) since you don’t have to memorize them. And since you don’t have to memorize them, you are more likely to create a better password. Additionally, if you write your passwords down, you don’t have to remember which password goes with which account so you can have a different password for each account: this also increases password uniqueness.
It would be reasonable to obfuscate your password list — instead of just writing them down in plaintext — so that if someone were to riffle through your wallet, they wouldn’t immediately recognize it as a password list or know exactly which passwords go with which accounts.
Instead of keeping them on a piece of paper, you could use a program to encrypt your passwords for you. There are a variety of ways to safely encrypt and store your passwords on your computer. I have been using 1Password for several years now and have been very impressed with their products7.
KeePass is another password manager I’ve used, however it does not have good support for OSX. There are other systems one could use, including Password Safe YubiKey.
I tend to be leery of web-based systems, such as LastPass and Passpack for two reasons:
1. Having lots of sensitive data stored in a known location on the internet is ripe for an attack.
2. The defense against such an attack is predicated on the notion that the company has implemented their encryption solution correctly!
### General Rule of Thumb
Why: It’s better to have unique and more entropic passwords than it is to never write down your password.
1. Arguably, there is no one right way to do passwords
2. it’s one thing to prove the mathematics of something, it’s a whole other thing to release a suitable product
3. and still sort of is
5. this is, in part, how predictive typing technologies such as SWYPE work
6. as well as their technechal discusions on topics such as threats to confidentiality versus threats to availability
## The Day We Fight Back
Six months ago, primarily in light of the issues concerning the NSA’s use of what I believe to be unconstitutional searches I started the process of moving my email system (which is also the email system my family and extended family uses) away from Google Apps.
Last week, I completed the technical transition to the new mail system provided by FastMail.
Today, the fight continues. I called both my Senators, as well as my Representative…yes, I called them. On the phone.
I talked to a live human being and I told them what I thought:
I’d like my Senator / Representative to support and co-sponsor H.R. 3361 / S. 1599, the USA Freedom Act. I would also like my Senator / Representative to oppose S. 1631, the so-called FISA Improvements Act. Moreover, I’d like like my Senator / Representative to work to prevent the NSA from undermining encryption standards.
If you visit AFDN today, you will see a small large banner that will help you contact your Senators and Representative to do the same.
“I Do Not Consent to the Search of this Device / EFF.org” image used under Creative Commons License from EFF | 2018-03-23T20:37:01 | {"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": 7, "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": 0.284793883562088, "perplexity": 1915.3945716894234}, "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-2018-13/segments/1521257648594.80/warc/CC-MAIN-20180323200519-20180323220519-00602.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S067AER | Events (observed/expected) from accelerator ${{\boldsymbol \nu}_{{\mu}}}$ experiments. INSPIRE search
Some neutrino oscillation experiments compare the flux in two or more detectors. This is usually quoted as the ratio of the event rate in the far detector to the expected rate based on an extrapolation from the near detector in the absence of oscillations.
VALUE DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$1.01$ $\pm0.10$ 1
2014 B
T2K ${{\mathit \nu}_{{e}}}$ rate in T2K near detect.
$0.71$ $\pm0.08$ 2
2006 A
K2K K2K to Super-K
$0.64$ $\pm0.05$ 3
2006
MINS All charged current events
$0.71$ ${}^{+0.08}_{-0.09}$ 4
2005
K2K KEK to Super-K
$0.70$ ${}^{+0.10}_{-0.11}$ 5
2003
K2K KEK to Super-K
1 The rate of ${{\mathit \nu}_{{e}}}$ from ${{\mathit \mu}}$ decay was measured to be $0.68$ $\pm0.30$ compared to the predicted flux. From ${{\mathit K}}$ decay $1.10$ $\pm0.14$ compared to the predicted flux.
2 Based on the observation of 112 events when $158.1$ ${}^{+9.2}_{-8.6}$ were expected without oscillations. Including not only the number of events but also the shape of the energy distribution, the evidence for oscillation is at the level of about 4.3 $\sigma$. Supersedes ALIU 2005 .
3 This ratio is based on the observation of 215 events compared to an expectation of $336$ $\pm14$ without oscillations. See also ADAMSON 2008 .
4 This ratio is based on the observation of 107 events at the far detector 250 km away from KEK, and an expectation of $151$ ${}^{+12}_{-10}$.
5 This ratio is based on the observation of 56 events with an expectation of $80.1$ ${}^{+6.2}_{-5.4}$.
References:
ABE 2014B
PR D89 092003 Measurement of the Intrinsic Electron Neutrino Component in the T2K Neutrino Beam with the ND280 Detector
AHN 2006A
PR D74 072003 Measurement of Neutrino Oscillation by the K2K Experiment
MICHAEL 2006
PRL 97 191801 Observation of Muon Neutrino Disappearance with the MINOS Detectors in the NuMI Neutrino Beam
ALIU 2005
PRL 94 081802 Evidence for Muon Neutrino Oscillation in an Accelerator-Based Experiment
AHN 2003
PRL 90 041801 Indications of Neutrino Oscillation in a 250 km Long Baseline Experiment | 2020-02-24T12:48:25 | {"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": 0.8894662857055664, "perplexity": 2207.6780658992247}, "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-2020-10/segments/1581875145941.55/warc/CC-MAIN-20200224102135-20200224132135-00266.warc.gz"} |
https://zbmath.org/authors/brenier.yann | ## Brenier, Yann
Compute Distance To:
Author ID: brenier.yann Published as: Brenier, Yann; Brenier, Y. External Links: MGP · Wikidata · IdRef · theses.fr
Documents Indexed: 110 Publications since 1981, including 2 Books Co-Authors: 38 Co-Authors with 39 Joint Publications 1,523 Co-Co-Authors
all top 5
### Co-Authors
71 single-authored 7 Benamou, Jean-David 4 Puel, Marjolaine 3 Corrias, Lucilla 2 Ambrosio, Luigi 2 Cottet, Georges-Henri 2 Duan, Xianglong 2 Gangbo, Wilfrid 2 Grenier, Emmanuel 2 Guittet, Kevin 2 Loeper, Grégoire 2 Mauser, Norbert Julius 2 Natalini, Roberto 2 Osher, Stanley Joel 1 Baradat, Aymeric 1 Berthelin, Florent 1 Bertrand, Pierre 1 Besse, Nicolas 1 Bolley, François 1 Bouchut, François 1 Buttazzo, Giuseppe 1 Caffarelli, Luis Ángel 1 Cortes, Julien 1 Cullen, Mike 1 De Lellis, Camillo 1 Jaffré, Jérôme 1 Kenyon, Richard W. 1 Kontsevich, Maxim Lvovich 1 Levy, Doron 1 Otto, Felix 1 Ripoll, J. F. 1 Roesch, Michel 1 Salsa, Sandro 1 Savaré, Giuseppe 1 Seis, Christian 1 Székelyhidi, László jun. 1 Villani, Cédric 1 Vorotnikov, Dmitry A. 1 Westdickenberg, Michael 1 Yong, Wen-An
all top 5
### Serials
7 Comptes Rendus de l’Académie des Sciences. Série I 6 SIAM Journal on Numerical Analysis 5 Archive for Rational Mechanics and Analysis 4 Communications in Mathematical Physics 3 Calculus of Variations and Partial Differential Equations 3 Séminaire Équations aux Dérivées Partielles 3 Communications in Mathematical Sciences 2 Communications on Pure and Applied Mathematics 2 Physica D 2 SIAM Journal on Mathematical Analysis 2 Journal of Nonlinear Science 2 Methods and Applications of Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Mathematical Physics 1 Nonlinearity 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Monatshefte für Mathematik 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of the American Mathematical Society 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Journal of Convex Analysis 1 Bulletin des Sciences Mathématiques 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Mathematical Fluid Mechanics 1 Journal of Hyperbolic Differential Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Lecture Notes in Mathematics 1 SMF Journée Annuelle 1 Kinetic and Related Models 1 Confluentes Mathematici 1 Annales Mathématiques du Québec 1 Séminaire Laurent Schwartz. EDP et Applications 1 Tunisian Journal of Mathematics
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### Fields
80 Partial differential equations (35-XX) 53 Fluid mechanics (76-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 18 Statistical mechanics, structure of matter (82-XX) 15 Numerical analysis (65-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Optics, electromagnetic theory (78-XX) 5 Geophysics (86-XX) 4 Real functions (26-XX) 4 Measure and integration (28-XX) 4 Quantum theory (81-XX) 4 Relativity and gravitational theory (83-XX) 3 Functional analysis (46-XX) 3 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematical logic and foundations (03-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX)
### Citations contained in zbMATH Open
81 Publications have been cited 2,515 times in 1,814 Documents Cited by Year
Polar factorization and monotone rearrangement of vector-valued functions. Zbl 0738.46011
Brenier, Yann
1991
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Zbl 0968.76069
Benamou, Jean-David; Brenier, Yann
2000
Sticky particles and scalar conservation laws. Zbl 0924.35080
Brenier, Yann; Grenier, Emmanuel
1998
Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Zbl 0970.35110
Brenier, Y.
2000
Décomposition polaire et réarrangement monotone des champs de vecteurs. (Polar decomposition and increasing rearrangement of vector fields). Zbl 0652.26017
Brenier, Yann
1987
Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations. Zbl 1085.35097
Brenier, Y.
2005
Weak-strong uniqueness for measure-valued solutions. Zbl 1219.35182
Brenier, Yann; De Lellis, Camillo; Székelyhidi, László jun.
2011
The least action principle and the related concept of generalized flows for incompressible perfect fluids. Zbl 0697.76030
Brenier, Yann
1989
Averaged multivalued solutions for scalar conservation laws. Zbl 0565.65054
Brenier, Yann
1984
Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028
Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric
2003
Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Zbl 0910.35098
Brenier, Yann
1999
Extended Monge-Kantorovich theory. Zbl 1064.49036
Brenier, Yann
2003
A kinetic formulation for multi-branch entropy solutions of scalar conservation laws. Zbl 0893.35068
Brenier, Y.; Corrias, L.
1998
Homogeneous hydrostatic flows with convex velocity profiles. Zbl 0984.35131
Brenier, Yann
1999
Weak existence for the semigeostrophic equations formulated as a coupled Monge–Ampère/transport problem. Zbl 0915.35024
Benamou, J.-D.; Brenier, Y.
1998
Upstream differencing for multiphase flow in reservoir simulation. Zbl 0735.76071
Brenier, Yann; Jaffré, Jérôme
1991
Hydrodynamic structure of the augmented Born-Infeld equations. Zbl 1055.78003
Brenier, Yann
2004
Résolution d’équations d’évolution quasilinéaires en dimension N d’espace à l’aide d’équations linéaires en dimension $$N+1$$. Zbl 0549.35055
Brenier, Yann
1983
The dual least action problem for an ideal, incompressible fluid. Zbl 0797.76006
Brenier, Y.
1993
Sticky particle dynamics with interactions. Zbl 1282.35236
Brenier, Y.; Gangbo, W.; Savaré, G.; Westdickenberg, M.
2013
A hierarchy of models for two-phase flows. Zbl 0998.76088
Bouchut, F.; Brenier, Y.; Cortes, Julien; Ripoll, J.-F.
2000
On a relaxation approximation of the incompressible Navier-Stokes equations. Zbl 1080.35064
Brenier, Yann; Natalini, Roberto; Puel, Marjolaine
2004
Remarks on the derivation of the hydrostatic Euler equations. Zbl 1040.35068
Brenier, Yann
2003
Incompressible Euler and e-MHD as scaling limits of the Vlasov/Maxwell system. Zbl 1089.35048
Brenier, Yann; Mauser, Norbert; Puel, Marjolaine
2003
Contractive metrics for scalar conservation laws. Zbl 1071.35081
Bolley, François; Brenier, Yann; Loeper, Grégoire
2005
The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation. Zbl 1058.76586
Benamou, J.-D.; Brenier, Y.; Guittet, K.
2002
Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations. Zbl 1177.49064
Brenier, Yann
2009
Generalized solutions and hydrostatic approximation of the Euler equations. Zbl 1143.76386
Brenier, Yann
2008
A homogenized model for vortex sheets. Zbl 0962.35140
Brenier, Yann
1997
Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes. (A fast algorithm for the computation of the discrete Legendre-Fenchel transform). Zbl 0667.65006
Brenier, Yann
1989
$$L^{2}$$ formulation of multidimensional scalar conservation laws. Zbl 1180.35346
Brenier, Yann
2009
The discrete one-sided Lipschitz condition for convex scalar conversation laws. Zbl 0637.65090
Brenier, Yann; Osher, Stanley
1988
A numerical method for the optimal time-continuous mass transport problem and related problems. Zbl 0916.65068
Benamou, Jean-David; Brenier, Yann
1999
Derivation of particle, string, and membrane motions from the born-infeld electromagnetism. Zbl 1110.78004
Brenier, Yann; Yong, Wen-An
2005
Singular limit of the Vlasov-Poisson system in the quasi-neutral regime: The time independent case. (Limite singulière du système de Vlasov-Poisson dans le régime de quasi neutralité: Le cas indépendant du temps.) Zbl 0803.35110
Brenier, Yann; Grenier, Emmanuel
1994
Mixed $$L^2$$-Wasserstein optimal mapping between prescribed density functions. Zbl 1010.49029
Benamou, J. D.; Brenier, Y.
2001
The multi-water-bag equations for collisionless kinetic modeling. Zbl 1185.35292
Besse, Nicolas; Berthelin, Florent; Brenier, Yann; Bertrand, Pierre
2009
Upper bounds on coarsening rates in demixing binary viscous liquids. Zbl 1226.82045
Brenier, Yann; Otto, Felix; Seis, Christian
2011
Topology-preserving diffusion of divergence-free vector fields and magnetic relaxation. Zbl 1294.35077
Brenier, Yann
2014
Some geometric PDEs related to hydrodynamics and electrodynamics. Zbl 1136.37355
Brenier, Yann
2002
A geometric approximation to the Euler equations: the Vlasov-Monge-Ampère system. Zbl 1075.35046
Brenier, Y.; Loeper, G.
2004
Derivation of the Euler equations from a caricature of Coulomb interaction. Zbl 1025.82012
Brenier, Yann
2000
Une application de la symetrisation de Steiner aux équations hyperboliques: la méthode de transport et ecroulement. Zbl 0459.35006
Brenier, Yann
1981
$$L^p$$ approximation of maps by diffeomorphisms. Zbl 1055.26008
Brenier, Yann; Gangbo, Wilfrid
2003
Numerical analysis of a multi-phasic mass transport problem. Zbl 1135.49025
Benamou, Jean-David; Brenier, Yann; Guittet, Kevin
2004
Topics on hydrodynamics and volume preserving maps. Zbl 1183.37140
Brenier, Yann
2003
On optimal transport of matrix-valued measures. Zbl 1460.49036
Brenier, Yann; Vorotnikov, Dmitry
2020
The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem. Zbl 1410.35102
Brenier, Yann
2018
Remarks on some linear hyperbolic equations with oscillatory coefficients. Zbl 0768.35057
Brenier, Yann
1991
Relaxation limits for a class of balance laws with kinetic formulation. Zbl 0933.35128
Brenier, Yann; Corrias, Lucilla; Natalini, Roberto
1998
A combinatorial algorithm for the Euler equations of incompressible flows. Zbl 0687.76016
Brenier, Yann
1989
Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics. Zbl 1107.74028
Brenier, Yann
2004
Rigorous derivation of the $$x-z$$ semigeostrophic equations. Zbl 1178.35299
Brenier, Yann; Cullen, Mike
2009
From conservative to dissipative systems through quadratic change of time, with application to the curve-shortening flow. Zbl 1387.35475
Brenier, Yann; Duan, Xianglong
2018
Rearrangement, convection, convexity and entropy. Zbl 1292.35226
Brenier, Yann
2013
A note on deformations of 2D fluid motions using 3D Born-Infeld equations. Zbl 1063.35130
Brenier, Yann
2004
On the hydrostatic and darcy limits of the convective Navier-Stokes equations. Zbl 1177.86005
Brenier, Yann
2009
Connections between optimal transport, combinatorial optimization and hydrodynamics. Zbl 1335.49075
Brenier, Yann
2015
Convergence of particle methods with random rezoning for the two- dimensional Euler and Navier-Stokes equations. Zbl 0832.76065
Brenier, Y.; Cottet, G.-H.
1995
Dissipative behavior of some fully nonlinear KdV-type equations. Zbl 0945.35076
Brenier, Yann; Levy, Doron
2000
A modified least action principle allowing mass concentrations for the early universe reconstruction problem. Zbl 1229.83073
Brenier, Yann
2011
Hilbertian approaches to some nonlinear conservation laws. Zbl 1223.35002
Brenier, Yann
2010
Non relativistic strings may be approximated by relativistic strings. Zbl 1110.35094
Brenier, Yann
2005
Remarks on the minimizing geodesic problem in inviscid incompressible fluid mechanics. Zbl 1282.35291
Brenier, Yann
2013
Approximate Riemann solvers and numerical flux functions. Zbl 0597.65071
Brenier, Yann; Osher, Stanley
1986
Une méthode particulaire pour les équations non linéaires de diffusion convection en dimension un. (A particle method for nonlinear one-dimensional diffusion-convection equations). Zbl 0829.65113
Brenier, Yann
1990
Optimal multiphase transportation with prescribed momentum. Zbl 1091.49034
Brenier, Yann; Puel, Marjolaine
2002
Hidden convexity in some nonlinear PDEs from geomety and physics. Zbl 1206.35099
Brenier, Y.
2010
Geometric origin and some properties of the arctangential heat equation. Zbl 1410.35081
Brenier, Yann
2019
An integrable example of gradient flow based on optimal transport of differential forms. Zbl 1401.49067
Brenier, Yann; Duan, Xianglong
2018
On the motion of an ideal incompressible fluid. Zbl 0810.35082
Brenier, Yann
1994
Optimal transportation of particles, fluids and currents. Zbl 1415.49029
Brenier, Yann
2015
A domain decomposition method for the polar factorization of vector fields. Zbl 0797.65006
Benamou, J.-D.; Brenier, Y.
1994
Extension of the Monge-Kantorovich theory to classical electrodynamics. Zbl 1357.49155
Brenier, Yann
2004
Approximation of a simple Navier-Stokes model by monotonic rearrangement. Zbl 1286.35203
Brenier, Yann
2014
On some limits in charged particle physics towards (magneto)hydrodynamic equations. (Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique.) Zbl 0997.35056
Brenier, Yann; Mauser, Norbert J.; Puel, Marjolaine
2002
Moment equations and entropy conditions for kinetic models. (Équations de moment et conditions d’entropie pour des modèles cinétiques.) Zbl 0874.35070
Brenier, Y.
1995
Some conservation laws given by kinetic models. (Quelques lois de conservations issues de modèles cinétiques.) Zbl 0873.35065
Brenier, Yann
1995
Some concepts of generalized and approximate solutions in ideal incompressible fluid mechanics related to the least action principle. Zbl 1418.35301
Brenier, Yann
2018
Méthode de transport-écoulement par deplacement de lignes de niveau appliquée aux écoulements en milieu poreux. Zbl 0544.76100
Brenier, Yann
1982
The initial value problem for the Euler equations of fluids viewed as a concave maximization problem. Zbl 1397.35189
Brenier, Yann
2018
On optimal transport of matrix-valued measures. Zbl 1460.49036
Brenier, Yann; Vorotnikov, Dmitry
2020
Geometric origin and some properties of the arctangential heat equation. Zbl 1410.35081
Brenier, Yann
2019
The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem. Zbl 1410.35102
Brenier, Yann
2018
From conservative to dissipative systems through quadratic change of time, with application to the curve-shortening flow. Zbl 1387.35475
Brenier, Yann; Duan, Xianglong
2018
An integrable example of gradient flow based on optimal transport of differential forms. Zbl 1401.49067
Brenier, Yann; Duan, Xianglong
2018
Some concepts of generalized and approximate solutions in ideal incompressible fluid mechanics related to the least action principle. Zbl 1418.35301
Brenier, Yann
2018
The initial value problem for the Euler equations of fluids viewed as a concave maximization problem. Zbl 1397.35189
Brenier, Yann
2018
Connections between optimal transport, combinatorial optimization and hydrodynamics. Zbl 1335.49075
Brenier, Yann
2015
Optimal transportation of particles, fluids and currents. Zbl 1415.49029
Brenier, Yann
2015
Topology-preserving diffusion of divergence-free vector fields and magnetic relaxation. Zbl 1294.35077
Brenier, Yann
2014
Approximation of a simple Navier-Stokes model by monotonic rearrangement. Zbl 1286.35203
Brenier, Yann
2014
Sticky particle dynamics with interactions. Zbl 1282.35236
Brenier, Y.; Gangbo, W.; Savaré, G.; Westdickenberg, M.
2013
Rearrangement, convection, convexity and entropy. Zbl 1292.35226
Brenier, Yann
2013
Remarks on the minimizing geodesic problem in inviscid incompressible fluid mechanics. Zbl 1282.35291
Brenier, Yann
2013
Weak-strong uniqueness for measure-valued solutions. Zbl 1219.35182
Brenier, Yann; De Lellis, Camillo; Székelyhidi, László jun.
2011
Upper bounds on coarsening rates in demixing binary viscous liquids. Zbl 1226.82045
Brenier, Yann; Otto, Felix; Seis, Christian
2011
A modified least action principle allowing mass concentrations for the early universe reconstruction problem. Zbl 1229.83073
Brenier, Yann
2011
Hilbertian approaches to some nonlinear conservation laws. Zbl 1223.35002
Brenier, Yann
2010
Hidden convexity in some nonlinear PDEs from geomety and physics. Zbl 1206.35099
Brenier, Y.
2010
Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations. Zbl 1177.49064
Brenier, Yann
2009
$$L^{2}$$ formulation of multidimensional scalar conservation laws. Zbl 1180.35346
Brenier, Yann
2009
The multi-water-bag equations for collisionless kinetic modeling. Zbl 1185.35292
Besse, Nicolas; Berthelin, Florent; Brenier, Yann; Bertrand, Pierre
2009
Rigorous derivation of the $$x-z$$ semigeostrophic equations. Zbl 1178.35299
Brenier, Yann; Cullen, Mike
2009
On the hydrostatic and darcy limits of the convective Navier-Stokes equations. Zbl 1177.86005
Brenier, Yann
2009
Generalized solutions and hydrostatic approximation of the Euler equations. Zbl 1143.76386
Brenier, Yann
2008
Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations. Zbl 1085.35097
Brenier, Y.
2005
Contractive metrics for scalar conservation laws. Zbl 1071.35081
Bolley, François; Brenier, Yann; Loeper, Grégoire
2005
Derivation of particle, string, and membrane motions from the born-infeld electromagnetism. Zbl 1110.78004
Brenier, Yann; Yong, Wen-An
2005
Non relativistic strings may be approximated by relativistic strings. Zbl 1110.35094
Brenier, Yann
2005
Hydrodynamic structure of the augmented Born-Infeld equations. Zbl 1055.78003
Brenier, Yann
2004
On a relaxation approximation of the incompressible Navier-Stokes equations. Zbl 1080.35064
Brenier, Yann; Natalini, Roberto; Puel, Marjolaine
2004
A geometric approximation to the Euler equations: the Vlasov-Monge-Ampère system. Zbl 1075.35046
Brenier, Y.; Loeper, G.
2004
Numerical analysis of a multi-phasic mass transport problem. Zbl 1135.49025
Benamou, Jean-David; Brenier, Yann; Guittet, Kevin
2004
Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics. Zbl 1107.74028
Brenier, Yann
2004
A note on deformations of 2D fluid motions using 3D Born-Infeld equations. Zbl 1063.35130
Brenier, Yann
2004
Extension of the Monge-Kantorovich theory to classical electrodynamics. Zbl 1357.49155
Brenier, Yann
2004
Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028
Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric
2003
Extended Monge-Kantorovich theory. Zbl 1064.49036
Brenier, Yann
2003
Remarks on the derivation of the hydrostatic Euler equations. Zbl 1040.35068
Brenier, Yann
2003
Incompressible Euler and e-MHD as scaling limits of the Vlasov/Maxwell system. Zbl 1089.35048
Brenier, Yann; Mauser, Norbert; Puel, Marjolaine
2003
$$L^p$$ approximation of maps by diffeomorphisms. Zbl 1055.26008
Brenier, Yann; Gangbo, Wilfrid
2003
Topics on hydrodynamics and volume preserving maps. Zbl 1183.37140
Brenier, Yann
2003
The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation. Zbl 1058.76586
Benamou, J.-D.; Brenier, Y.; Guittet, K.
2002
Some geometric PDEs related to hydrodynamics and electrodynamics. Zbl 1136.37355
Brenier, Yann
2002
Optimal multiphase transportation with prescribed momentum. Zbl 1091.49034
Brenier, Yann; Puel, Marjolaine
2002
On some limits in charged particle physics towards (magneto)hydrodynamic equations. (Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique.) Zbl 0997.35056
Brenier, Yann; Mauser, Norbert J.; Puel, Marjolaine
2002
Mixed $$L^2$$-Wasserstein optimal mapping between prescribed density functions. Zbl 1010.49029
Benamou, J. D.; Brenier, Y.
2001
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Zbl 0968.76069
Benamou, Jean-David; Brenier, Yann
2000
Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Zbl 0970.35110
Brenier, Y.
2000
A hierarchy of models for two-phase flows. Zbl 0998.76088
Bouchut, F.; Brenier, Y.; Cortes, Julien; Ripoll, J.-F.
2000
Derivation of the Euler equations from a caricature of Coulomb interaction. Zbl 1025.82012
Brenier, Yann
2000
Dissipative behavior of some fully nonlinear KdV-type equations. Zbl 0945.35076
Brenier, Yann; Levy, Doron
2000
Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Zbl 0910.35098
Brenier, Yann
1999
Homogeneous hydrostatic flows with convex velocity profiles. Zbl 0984.35131
Brenier, Yann
1999
A numerical method for the optimal time-continuous mass transport problem and related problems. Zbl 0916.65068
Benamou, Jean-David; Brenier, Yann
1999
Sticky particles and scalar conservation laws. Zbl 0924.35080
Brenier, Yann; Grenier, Emmanuel
1998
A kinetic formulation for multi-branch entropy solutions of scalar conservation laws. Zbl 0893.35068
Brenier, Y.; Corrias, L.
1998
Weak existence for the semigeostrophic equations formulated as a coupled Monge–Ampère/transport problem. Zbl 0915.35024
Benamou, J.-D.; Brenier, Y.
1998
Relaxation limits for a class of balance laws with kinetic formulation. Zbl 0933.35128
Brenier, Yann; Corrias, Lucilla; Natalini, Roberto
1998
A homogenized model for vortex sheets. Zbl 0962.35140
Brenier, Yann
1997
Convergence of particle methods with random rezoning for the two- dimensional Euler and Navier-Stokes equations. Zbl 0832.76065
Brenier, Y.; Cottet, G.-H.
1995
Moment equations and entropy conditions for kinetic models. (Équations de moment et conditions d’entropie pour des modèles cinétiques.) Zbl 0874.35070
Brenier, Y.
1995
Some conservation laws given by kinetic models. (Quelques lois de conservations issues de modèles cinétiques.) Zbl 0873.35065
Brenier, Yann
1995
Singular limit of the Vlasov-Poisson system in the quasi-neutral regime: The time independent case. (Limite singulière du système de Vlasov-Poisson dans le régime de quasi neutralité: Le cas indépendant du temps.) Zbl 0803.35110
Brenier, Yann; Grenier, Emmanuel
1994
On the motion of an ideal incompressible fluid. Zbl 0810.35082
Brenier, Yann
1994
A domain decomposition method for the polar factorization of vector fields. Zbl 0797.65006
Benamou, J.-D.; Brenier, Y.
1994
The dual least action problem for an ideal, incompressible fluid. Zbl 0797.76006
Brenier, Y.
1993
Polar factorization and monotone rearrangement of vector-valued functions. Zbl 0738.46011
Brenier, Yann
1991
Upstream differencing for multiphase flow in reservoir simulation. Zbl 0735.76071
Brenier, Yann; Jaffré, Jérôme
1991
Remarks on some linear hyperbolic equations with oscillatory coefficients. Zbl 0768.35057
Brenier, Yann
1991
Une méthode particulaire pour les équations non linéaires de diffusion convection en dimension un. (A particle method for nonlinear one-dimensional diffusion-convection equations). Zbl 0829.65113
Brenier, Yann
1990
The least action principle and the related concept of generalized flows for incompressible perfect fluids. Zbl 0697.76030
Brenier, Yann
1989
Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes. (A fast algorithm for the computation of the discrete Legendre-Fenchel transform). Zbl 0667.65006
Brenier, Yann
1989
A combinatorial algorithm for the Euler equations of incompressible flows. Zbl 0687.76016
Brenier, Yann
1989
The discrete one-sided Lipschitz condition for convex scalar conversation laws. Zbl 0637.65090
Brenier, Yann; Osher, Stanley
1988
Décomposition polaire et réarrangement monotone des champs de vecteurs. (Polar decomposition and increasing rearrangement of vector fields). Zbl 0652.26017
Brenier, Yann
1987
Approximate Riemann solvers and numerical flux functions. Zbl 0597.65071
Brenier, Yann; Osher, Stanley
1986
Averaged multivalued solutions for scalar conservation laws. Zbl 0565.65054
Brenier, Yann
1984
Résolution d’équations d’évolution quasilinéaires en dimension N d’espace à l’aide d’équations linéaires en dimension $$N+1$$. Zbl 0549.35055
Brenier, Yann
1983
Méthode de transport-écoulement par deplacement de lignes de niveau appliquée aux écoulements en milieu poreux. Zbl 0544.76100
Brenier, Yann
1982
Une application de la symetrisation de Steiner aux équations hyperboliques: la méthode de transport et ecroulement. Zbl 0459.35006
Brenier, Yann
1981
all top 5
### Cited by 1,960 Authors
35 Brenier, Yann 30 Santambrogio, Filippo 27 Carlier, Guillaume 26 Carrillo de la Plata, José Antonio 26 Li, Wuchen 24 Figalli, Alessio 22 Wang, Shu 20 McCann, Robert J. 17 Gangbo, Wilfrid 16 Yang, Jianwei 15 Benamou, Jean-David 15 Ghoussoub, Nassif A. 15 Kim, Young-Heon 15 Osher, Stanley Joel 14 Ambrosio, Luigi 14 Degond, Pierre 14 Loeper, Grégoire 13 Guo, Lihui 13 Peng, Yuejun 13 Yang, Hanchun 12 Liu, Hailiang 12 Natalini, Roberto 12 Savaré, Giuseppe 12 Tudorascu, Adrian 12 Zhang, Yanyan 12 Zhang, Yu 11 Berthelin, Florent 11 Chen, Yongxin 11 Han-Kwan, Daniel 11 Li, Fucai 11 Schmitzer, Bernhard 10 Cardaliaguet, Pierre 10 Feireisl, Eduard 10 Georgiou, Tryphon T. 10 Jabin, Pierre-Emmanuel 10 Monsaingeon, Léonard 10 Pass, Brendan W. 10 Perthame, Benoît 10 Shao, Zhiqiang 10 Titi, Edriss Saleh 10 Vasseur, Alexis F. 10 Vorotnikov, Dmitry A. 10 Wiedemann, Emil 9 Agueh, Martial 9 Gallouët, Thomas O. 9 Liu, Jianguo 9 Maas, Jan 9 Nedeljkov, Marko 9 Shen, Chun 9 Tchelepi, Hamdi A. 8 Cancès, Clément 8 Gosse, Laurent 8 Jin, Shi 8 Kolesnikov, Alexander V. 8 Mérigot, Quentin 8 Mielke, Alexander 8 Nguyen, Truyen Van 8 Peyré, Gabriel 8 Puel, Marjolaine 8 Seis, Christian 8 Sun, Meina 8 Tzavaras, Athanasios E. 8 Vialard, François-Xavier 8 Wang, Jinhuan 8 Wang, Zhen 8 Wolansky, Gershon 7 Budd, Christopher John 7 Choi, Young-Pil 7 De Philippis, Guido 7 Erbar, Matthias 7 Gigli, Nicola 7 Gwiazda, Piotr 7 Kitagawa, Jun 7 Lee, Paul W. Y. 7 Léonard, Christian 7 Li, Tong 7 Liu, Jiakun 7 Matthes, Daniel 7 Navoret, Laurent 7 Peletier, Mark Adriaan 7 Perrin, Charlotte 7 Pratelli, Aldo 7 Rousset, Frédéric 7 Tadmor, Eitan 7 Wang, Xu-Jia 7 Yin, Gan 7 Zhou, Hao-Min 6 Bellomo, Nicola 6 Berman, Robert J. 6 Besse, Nicolas 6 Blanchet, Adrien 6 Carlen, Eric Anders 6 Cheng, Hongjun 6 Conforti, Giovanni 6 Cullen, Michael John Priestley 6 Di Francesco, Marco 6 Fang, Shizan 6 Goudon, Thierry 6 Hynd, Ryan 6 Iacobelli, Mikaela ...and 1,860 more Authors
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### Cited in 320 Serials
85 Archive for Rational Mechanics and Analysis 69 Journal of Computational Physics 65 Calculus of Variations and Partial Differential Equations 64 Journal of Differential Equations 45 SIAM Journal on Mathematical Analysis 44 Journal of Mathematical Analysis and Applications 40 Journal of Functional Analysis 36 Journal of Mathematical Physics 35 Communications in Partial Differential Equations 33 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Discrete and Continuous Dynamical Systems 26 Journal de Mathématiques Pures et Appliquées. Neuvième Série 24 Communications in Mathematical Physics 24 Journal of Hyperbolic Differential Equations 23 Comptes Rendus. Mathématique. Académie des Sciences, Paris 22 Proceedings of the American Mathematical Society 22 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 22 Journal of Scientific Computing 19 Mathematics of Computation 19 Numerische Mathematik 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Advances in Mathematics 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 Journal of Statistical Physics 17 SIAM Journal on Scientific Computing 16 Physica D 15 Applied Mathematics Letters 14 Journal of Computational and Applied Mathematics 14 Acta Applicandae Mathematicae 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Applied Mathematics and Optimization 13 Probability Theory and Related Fields 13 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 12 Communications on Pure and Applied Mathematics 12 The Journal of Geometric Analysis 12 Computational Geosciences 12 Nonlinear Analysis. Real World Applications 12 Kinetic and Related Models 11 Computer Methods in Applied Mechanics and Engineering 11 Transactions of the American Mathematical Society 11 Journal of Mathematical Fluid Mechanics 10 The Annals of Probability 10 Journal of Optimization Theory and Applications 10 SIAM Journal on Imaging Sciences 9 Applicable Analysis 9 Quarterly of Applied Mathematics 9 SIAM Journal on Control and Optimization 9 SIAM Journal on Numerical Analysis 9 Bernoulli 9 Advances in Calculus of Variations 8 Inventiones Mathematicae 8 Mathematische Annalen 8 Chinese Annals of Mathematics. Series B 8 Journal of Mathematical Sciences (New York) 8 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 8 Foundations of Computational Mathematics 8 Discrete and Continuous Dynamical Systems. Series B 8 Communications on Pure and Applied Analysis 8 Science China. Mathematics 8 Information Geometry 7 European Journal of Applied Mathematics 7 The Annals of Applied Probability 7 Journal of Nonlinear Science 7 Bulletin des Sciences Mathématiques 7 Journal of the European Mathematical Society (JEMS) 6 Computers and Fluids 6 Journal of Fluid Mechanics 6 Journal of the American Mathematical Society 6 SIAM Journal on Applied Mathematics 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Journal of Dynamics and Differential Equations 6 Computational Optimization and Applications 6 NoDEA. Nonlinear Differential Equations and Applications 6 Advances in Computational Mathematics 6 Acta Mathematica Scientia. Series B. (English Edition) 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Annals of PDE 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 The Annals of Statistics 5 Manuscripta Mathematica 5 Geometric and Functional Analysis. GAFA 5 Stochastic Processes and their Applications 5 Bulletin of the American Mathematical Society. New Series 5 Journal of Mathematical Imaging and Vision 5 Multiscale Modeling & Simulation 5 Networks and Heterogeneous Media 5 Analysis & PDE 5 Advances in Mathematical Physics 5 SIAM/ASA Journal on Uncertainty Quantification 5 Journal de l’École Polytechnique – Mathématiques 5 Séminaire Laurent Schwartz. EDP et Applications 4 Computers & Mathematics with Applications 4 Automatica 4 Journal of Multivariate Analysis 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Potential Analysis 4 Economic Theory 4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Acta Numerica ...and 220 more Serials
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### Cited in 53 Fields
1,099 Partial differential equations (35-XX) 529 Fluid mechanics (76-XX) 487 Calculus of variations and optimal control; optimization (49-XX) 327 Numerical analysis (65-XX) 212 Probability theory and stochastic processes (60-XX) 150 Statistical mechanics, structure of matter (82-XX) 114 Operations research, mathematical programming (90-XX) 108 Differential geometry (53-XX) 100 Global analysis, analysis on manifolds (58-XX) 74 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 71 Measure and integration (28-XX) 70 Functional analysis (46-XX) 67 Dynamical systems and ergodic theory (37-XX) 57 Statistics (62-XX) 54 Biology and other natural sciences (92-XX) 51 Geophysics (86-XX) 46 Optics, electromagnetic theory (78-XX) 43 Operator theory (47-XX) 43 Computer science (68-XX) 40 Mechanics of deformable solids (74-XX) 39 Real functions (26-XX) 39 Systems theory; control (93-XX) 36 Quantum theory (81-XX) 29 Information and communication theory, circuits (94-XX) 27 Convex and discrete geometry (52-XX) 26 Mechanics of particles and systems (70-XX) 22 Ordinary differential equations (34-XX) 18 Relativity and gravitational theory (83-XX) 15 Integral equations (45-XX) 14 Classical thermodynamics, heat transfer (80-XX) 10 Combinatorics (05-XX) 10 Astronomy and astrophysics (85-XX) 9 Difference and functional equations (39-XX) 7 General and overarching topics; collections (00-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Algebraic geometry (14-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Number theory (11-XX) 4 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 General topology (54-XX) 2 Functions of a complex variable (30-XX) 2 Abstract harmonic analysis (43-XX) 2 Geometry (51-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX)
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https://asphalt.fandom.com/wiki/User_blog:Guy_Bukzi_Montag/Drop_Rates_Explained:_McLaren_720S_World_Tour | ## FANDOM
4,125 Pages
I often see players argue about drop rates of Pro Kit Boxes. Namely during the McLaren 720S World Tour I noticed two questions that made me want to find out myself:
1. Why does the box info show only 14.29 % for an item that is actually guaranteed?
2. If you need V8 engines, what is the better choice: the Pro or the Elite Supplies Box?
This blog post will answer the two questions, and while we're at it, shed some light on common misconceptions about drop rates of Pro Kit Boxes in general.
## Definitions
First, let's have a look at one of the McLaren 720 World Tour boxes, the Elite Supplies: The box contains 7 items, 4 of which are guaranteed. The other 3 items are taken randomly from a list of 9 items. So it is sure that you get between 1 and 5 blueprints, credits, tokens and one class A part, but you can't be sure, for example, to get a V8 engine because the engine is on the random list.
### Drop rate
So let's look at the percentages shown when you tap on the box info icon of the Elite Supplies. These numbers show the shares of the items you can expect if you open a very large amount of boxes. The more boxes you open, the closer you will get to the given numbers. In mathematical terms, this is called an expected value.[1] Or, in other words, the percentage shows the rate at which an item will be dropped if you open a very large amount of boxes.
However, these percentages say nothing about the probability (or chance) that you will get a desired item when you open a box.
Take the guaranteed tokens in the Elite Supplies: As they are guaranteed, they have a probability of 100 %. But as they will always make up 1 of the 7 items in the box, their drop rate is always $\tfrac{1}{7}$ = 0.142857 = 14.29 %—which is exactly the percentage provided in the box info of the game. So question number 1 from above is already answered: The box info does not show the probability of an item, but its expected value.
The drop rate or expected value of an item is its amount relative to all items in a box if a very large number of boxes is opened, expressed in percent.
Drop rates are not probabilities.
### Probability
As mentioned above, the chance of getting tokens (which are guaranteed) in an Elite Supplies box is 100 %. If you buy 100 Elite Supplies, you can be sure to have tokens in every single box.
However, when a box only consists of random items that are not guaranteed, it is possible to deduct the probability from the drop rate given in the info. For example, the which is rewarded in events, shows "Legendary: 3.06 %". If you had a very large amount of these boxes, let's say 10,000, and opened them all, the amount of Legendary items you'd get would be around 306.
Unfortunately, you can not deduce that these 306 Legendary items have an equal distribution of blueprints, engines and tech cards, because we don't know if these types of cards have additional individual probabilities assigned to them. A rough approximation would be possible if one logged all types of cards whenever a box is opened. Is there anybody who did this already?
The probability of an item is the chance of getting it in a box.
Probabilities equal drop rates if there are only random items in a box.
## The Elite Supplies Box
7 items
• 4 guaranteed
• 3 random, drawn from a list of 9 which contains:
• 1 Mid-Tech
• 2 Early Tech
• 2 Initial Tech
• 2 Class A Part
• 1 V8
What is the chance that you get a V8 engine from an Elite Box? To calculate this, we can neglect the guaranteed items. What counts is the 3 draws that are made internally from the list of the 9 random items. Technically it's an urn problem (see the Wikipedia article for further explanations): You have an urn with 9 items, one of which is a V8 engine. What is the chance to get this V8 engine if you draw 3 times?
There are three possibilies to get the V8: Either you get it at the first draw or the second or the third.
1. V8 at first draw: The probability to get the V8 at the first draw is 1 out of 9, thus $\tfrac{1}{9}$. Now 8 items are left in the urn. As you already have the V8, the next draw has a probability of $\tfrac{8}{8}$ that you don't get a V8. Now 7 items are left, and the third draw has a probability of $\tfrac{7}{7}$ (that you don't get a V8). The total probability to get a V8 at the first draw is $\tfrac{1}{9} \cdot \tfrac{8}{8} \cdot \tfrac{7}{7} = \tfrac{1}{9}$ = 11.11 %.
2. V8 at second draw: The probability that you don't get the V8 at the first draw is $\tfrac{8}{9}$. Then you get it with the second draw from 8 remaining items, thus the probability is $\tfrac{1}{8}$. Now 7 items are left, and the third draw has a probability of $\tfrac{7}{7}$ (that you don't get a V8). The total probability of this variant is $\tfrac{8}{9} \cdot \tfrac{1}{8} \cdot \tfrac{7}{7} = \tfrac{1}{9}$ = 11.11 %.
3. V8 at third draw: Analogous to the previous two examples, the probability of getting the V8 at the third draw is $\tfrac{8}{9} \cdot \tfrac{7}{8} \cdot \tfrac{1}{7} = \tfrac{1}{9}$ = 11.11 %.
The overall probability of getting the V8 with 3 draws is the sum of the probabilities of getting it at the first, second or third draw, thus
$\frac{1}{9} + \frac{1}{9} + \frac{1}{9} = \frac{3}{9} = \frac{1}{3} = 33.33 %$.
## The Pro Supplies Box
4 items
• 1 guaranteed
• 3 random, drawn from a list of 9 which contains:
• 1 Blueprint
• 2 V8
• 1 Early Tech
• 1 Initial Tech
• 1 Class A Part
• 1 Mid-Tech
• 1 20 Tokens
This time we have the chance to get either 1 or even 2 V8s, so there are more possibilities ("0" denotes no V8, "V" a V8): V00, 0V0, 00V, VV0, V0V and 0VV.
V00: $\tfrac{2}{9} \cdot \tfrac{7}{8} \cdot \tfrac{6}{7} = \tfrac{6}{36} = \tfrac{1}{6}$ = 16.67 %
0V0: $\tfrac{7}{9} \cdot \tfrac{2}{8} \cdot \tfrac{6}{7} = \tfrac{6}{36} = \tfrac{1}{6}$ = 16.67 %
00V: $\tfrac{7}{9} \cdot \tfrac{6}{8} \cdot \tfrac{2}{7} = \tfrac{6}{36} = \tfrac{1}{6}$ = 16.67 %
VV0: $\tfrac{2}{9} \cdot \tfrac{1}{8} \cdot \tfrac{7}{7} = \tfrac{1}{36}$ = 2.78 %
V0V: $\tfrac{2}{9} \cdot \tfrac{7}{8} \cdot \tfrac{1}{7} = \tfrac{1}{36}$ = 2.78 %
0VV: $\tfrac{7}{9} \cdot \tfrac{2}{8} \cdot \tfrac{1}{7} = \tfrac{1}{36}$ = 2.78 %
The overall probability of getting exactly 1 V8 with 3 draws is the sum of the first three variants: $\tfrac{1}{6} + \tfrac{1}{6} + \tfrac{1}{6} = \frac{3}{6} = \frac{1}{2}$ = 50.00 %.
The overall probability of getting exactly 2 V8s is the sum of the second three variants: $\tfrac{1}{36} + \tfrac{1}{36} + \tfrac{1}{36} = \frac{3}{36} = \frac{1}{12}$ = 8.33 %.
And the probability of getting at least one V8 (i. e. 1 or 2) is the sum of the two probabilities above:
$\frac{1}{2} + \frac{1}{12} = \frac{7}{12} = 58.33 %$
This is the answer to question number 2: The chance of getting at least 1 V8 is significantly higher (58.33 % vs. 33.33 %) if you buy a Pro Box.
Note: These probabilities only apply if there aren't any individual probabilities assigned to the random items of the list (for example that a v8 engine doesn't have the same chance to be drawn from the urn as a Mid-Tech card).
## Hidden probabilities
Can we determine if there are any hidden probabilities for certain items? The answer would be yes if we found that our calculated probabilites differ from percentages of random items in a box.
The Pro Box is a good object for such an examination because the info shows the percentages of two random items: blueprints and tokens. They are both only once in the list of 9, so their probability as well as their percentage should be equal.
The info, however, shows 21,25 % for the blueprint and 12,5 % for the token package. This is the proof that the Pro Box has its own probabilities at least for blueprints and tokens. We cannot say anything about the distribution of V8 engines, class A or tech parts, as they are all summed up under the term "Pro Kit Boxes".
## Code appendix
For those familiar with Visual Basic for Applications: I wrote a "quick and dirty" routine to simulate the draws with a very high number of rounds to get good statistical approximations of the real numbers. If you'd like to do your own drop rate calculations for a box you can copy the code into an Excel macro and see if they were correct.
The three McLaren 720S boxes are already contained; just comment out the two boxes you don't want to draw from and adjust the four constants at the beginning correspondingly.
I am not responsible for any problems the code may cause.
Sub DrawFromUrn()
'
' Draws 3 times from an urn with 9 parts without putting back.
' For more precision, this is done 100,000 times (or the value
' specified in clngAmountRounds).
' Written for the supply boxes of the McLaren 720S World Tour,
' but can be adapted for other boxes.
'
Const cintAmountDraws As Integer = 3
Const cintAmountContent As Integer = 9
Const clngAmountRounds As Long = 100000
Const cstrSearchedText As String = "V8"
Dim intRandomNumber As Integer
Dim intCounterDraws As Integer
Dim lngCounterRounds As Long
Dim strNameBox As String
Dim strContent(cintAmountContent) As String
Dim intDraw(cintAmountDraws) As Integer
Dim strMessage As String
Dim intAmountV8 As Integer
Dim lngAmountV8Total(cintAmountDraws) As Long
For lngCounterRounds = 1 To clngAmountRounds
'strNameBox = "Elite" ' 3 random items drawn from 9
'strContent(1) = "Mid-Tech"
'strContent(3) = "Early Tech"
'strContent(4) = "Early Tech"
'strContent(5) = "Initial Tech"
'strContent(6) = "Class A Part"
'strContent(7) = "Class A Part"
'strContent(8) = "V8"
'strContent(9) = "Initial Tech"
strNameBox = "Pro" ' 3 random items drawn from 9
strContent(1) = "Blueprint"
strContent(2) = "V8"
strContent(3) = "Early Tech"
strContent(4) = "Initial Tech"
strContent(5) = "Class A Part"
strContent(7) = "V8"
strContent(8) = "Mid-Tech"
strContent(9) = "20 Tokens"
'strNameBox = "Basic" ' 1 random item drawn from 6
'strContent(1) = "Blueprint"
'strContent(2) = "Class A Part"
'strContent(3) = "Early Tech"
'strContent(4) = "Initial Tech"
'strContent(5) = "Mid-Tech"
'strContent(6) = "10 Tokens"
' Reset Draws
intAmountV8 = 0
For intCounterDraws = 1 To cintAmountDraws
intDraw(intCounterDraws) = 0
Next
' Draw
For intCounterDraws = 1 To cintAmountDraws
Do
intRandomNumber = Int(cintAmountContent * Rnd + 1)
Loop Until strContent(intRandomNumber) <> ""
If strContent(intRandomNumber) = cstrSearchedText Then
intAmountV8 = intAmountV8 + 1
End If
strContent(intRandomNumber) = "" ' "Delete" drawn item
Next
lngAmountV8Total(intAmountV8) = lngAmountV8Total(intAmountV8) + 1
Next
strMessage = strNameBox & Chr(13) & Chr(13) & _
"0 " & cstrSearchedText & " " & LTrim(Str(Round(lngAmountV8Total(0) / clngAmountRounds * 100, 2))) & " %" & Chr(13) & _
"1 " & cstrSearchedText & " " & LTrim(Str(Round(lngAmountV8Total(1) / clngAmountRounds * 100, 2))) & " %" & Chr(13)
If cintAmountDraws > 2 Then
strMessage = strMessage & _
"2 " & cstrSearchedText & " " & LTrim(Str(Round(lngAmountV8Total(2) / clngAmountRounds * 100, 2))) & " %" & Chr(13)
End If
MsgBox strMessage
End Sub
## References
1. See Wikipedia: Expected value.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-05-31T11:50:43 | {"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": 0.4342164099216461, "perplexity": 1544.5361041288295}, "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-2020-24/segments/1590347413097.49/warc/CC-MAIN-20200531085047-20200531115047-00232.warc.gz"} |
https://pos.sissa.it/346/030/ | Volume 346 - 23rd International Spin Physics Symposium (SPIN2018) - Parallel Session: Spin physics in Nuclear Reactions and Nuclei (F. Becattini and o. Hen)
The neutron structure function $F_2$ at high-$x$ with BONuS at CLAS
C. Ayerbe gayoso* On behalf of the CLAS Collaboration
*corresponding author
Full text: pdf
Pre-published on: 2019 August 19
Published on: 2019 August 23
Abstract
The Barely Off-Shell Nucleon Structure (BONuS) experiment at CLAS12, at Jefferson Lab, will measure the neutron structure function $F_2$ for $0.1 < x < 0.8$ over a broad $Q^2$ range, from 1 to 14 GeV$^2 /c$, using electron scattering from deuterium with spectator-proton tagging. By selecting the low-momentum recoil protons at large backward angles, final-state interactions as the deuteron breaks up can be minimized, and the deep-inelastic kinematics for the neutron can be determined. This technique, which has been used successfully at CLAS at 6 GeV, will be extended to a beam energy of 11 GeV with significantly increased luminosity. Details of the BONuS third generation Radial Time Projection Chamber and expected high-$x$ $F_2 ^n$ results are presented.
DOI: https://doi.org/10.22323/1.346.0030
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-05-30T16:24:41 | {"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": 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": 0.4461781680583954, "perplexity": 6899.007135313864}, "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/1590347409337.38/warc/CC-MAIN-20200530133926-20200530163926-00539.warc.gz"} |
http://bimbo.ippt.gov.pl/cgi-bin/streszczenie?zmk;07.12.2006 | ## A numerical solution method for an infinitesimal elasto-plastic Cosserat model.
### prof Patrizio Neff
czwartek, 7 grudnia 2006, godz. 12:15, sala S-4
Abstract: We present a finite element implementation of a Cosserat elasto plastic model allowing for nonsymmetric stresses and we provide a numerical analysis of the introduced time incremental algorithm. The model allows the use of standard tools from convex analysis as known from classical Prandtl-Reuss plasticity. We derive the dual stress formulation and show that for vanishing Cosserat couple modulus $\mu_c\to 0$ the classical problem with symmetric stresses is approximated. Our numerical results testify to the robustness of the approximation. Notably, for positive Cosserat couple modulus there is no need for a safe load assumption. For small Cosserat couple modulus the response is numerically indistinuishable from the classical response. This is joint work with K. Chelminski, W. Mueller and C. Wieners. The paper is accepted in Math. Meth. Mod. Appl. Sci. | 2022-07-02T20:03:12 | {"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": 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": 0.4338192343711853, "perplexity": 2317.261123582679}, "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-2022-27/segments/1656104204514.62/warc/CC-MAIN-20220702192528-20220702222528-00041.warc.gz"} |
http://dlmf.nist.gov/14.18 | # §14.18 Sums
## §14.18(i) Expansion Theorem
For expansions of arbitrary functions in series of Legendre polynomials see §18.18(i), and for expansions of arbitrary functions in series of associated Legendre functions see Schäfke (1961b).
## §14.18(iii) Other Sums
### ¶ Dougall’s Expansion
For a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22).
## §14.18(iv) Compendia
For collections of sums involving associated Legendre functions, see Hansen (1975, pp. 367–377, 457–460, and 475), Erdélyi et al. (1953a, §3.10), Gradshteyn and Ryzhik (2000, §8.92), Magnus et al. (1966, pp. 178–184), and Prudnikov et al. (1990, §§5.2, 6.5). See also §18.18 and (34.3.19). | 2013-05-19T20:58:25 | {"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": 0.8999571800231934, "perplexity": 5224.15479447333}, "config": {"markdown_headings": true, "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-2013-20/segments/1368698080772/warc/CC-MAIN-20130516095440-00027-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aperthame.benoit | # zbMATH — the first resource for mathematics
## Perthame, Benoît
Compute Distance To:
Author ID: perthame.benoit Published as: Perthame, B.; Perthame, Benoit; Perthame, Benoît; Perthame, Benôıt External Links: MGP · Wikidata · GND
Documents Indexed: 272 Publications since 1984, including 5 Books
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#### Co-Authors
34 single-authored 20 Souganidis, Panagiotis E. 14 Lions, Pierre-Louis 12 Golse, François 11 Salort, Delphine 10 Tang, Min 10 Vauchelet, Nicolas 9 Jabin, Pierre-Emmanuel 9 Markowich, Peter Alexander 9 Mirrahimi, Sepideh 8 Lorz, Alexander 7 Barles, Guy 7 Bouchut, François 7 Calvez, Vincent 7 Clairambault, Jean 7 Mischler, Stéphane 7 Ryzhik, Lenya 6 Bardos, Claude Williams 5 Doumic, Marie 5 Le Tallec, Patrick 5 Zubelli, Jorge P. 4 Bristeau, Marie-Odile 4 Carrillo de la Plata, José Antonio 4 Castella, François 4 Coquel, Frédéric 4 Corrias, Lucilla 4 Nadin, Grégoire 4 Sentis, Remi 4 Stevens, Angela 4 Tadmor, Eitan 4 Vega, Luis 3 Andries, Pierre 3 Audusse, Emmanuel 3 Bourgat, Jean-François 3 Chen, Gui-Qiang G. 3 Godlewski, Edwige 3 Katsaounis, Theodoros 3 Laurençot, Philippe 3 Lorenzi, Tommaso 3 Michel, Philippe 3 Pakdaman, Khashayar 3 Qiu, Youchun 3 Quirós Gracián, Fernando 3 Rascle, Paul 3 Schmeiser, Christian 3 Simeoni, Chiara 3 Yasuda, Shugo 2 Bardi, Martino 2 Bekkal-Brikci, Fadia 2 Benamou, Jean-David 2 Berestycki, Henri 2 Bouin, Emeric 2 Bourdarias, Christian 2 Bournaveas, Nikolaos 2 Bubba, Federica 2 Cáceres, María-José 2 Cheddadi, Ibrahim 2 Deslys, Jean-Philippe 2 Després, Bruno 2 DiBenedetto, Emmanuele 2 Dolbeault, Jean 2 Drasdo, Dirk 2 El Amine, Khalid 2 Escobedo Martínez, Miguel 2 Esteban, Maria J. 2 Gasser, Ingenuin 2 Gerbeau, Jean-Frédéric 2 Gwiazda, Piotr 2 Haskovec, Jan 2 Herrero, Henar 2 James, François 2 Kang, Kyungkeun 2 Lenuzza, Natacha 2 Lucquin-Desreux, Brigitte 2 Makridakis, Charalambos G. 2 Marciniak-Czochra, Anna K. 2 Marrocco, Americo 2 Mellet, Antoine 2 Moussa, Ayman 2 Mouthon, Franck 2 Pouchol, Camille 2 Pulvirenti, Mario 2 Ribes, Edouard 2 Sainte-Marie, Jacques 2 Seguin, Nicolas 2 Stoufflet, Bruno 2 Sun, Weiran 2 Taing, Cécile 2 Tournus, Magali 2 Vasseur, Alexis F. 2 Vazquez, Juan Luis 2 Velázquez, Juan J. L. 2 Vignon-Clementel, Irene E. 2 Wakano, Joe Yuichiro 2 Zaag, Hatem 1 Almeida, Luis A. F. 1 Almeida, Luis Tadeu 1 Aoki, Kazuo 1 Batt, Jürgen 1 Belhadj, Mohamed 1 Bellomo, Nicola ...and 93 more Co-Authors
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#### Serials
12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Comptes Rendus de l’Académie des Sciences. Série I 10 Archive for Rational Mechanics and Analysis 7 Journal of Differential Equations 7 Communications in Partial Differential Equations 6 Communications in Mathematical Physics 6 SIAM Journal on Numerical Analysis 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Communications in Mathematical Sciences 5 Journal of Mathematical Biology 5 Nonlinearity 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 SIAM Journal on Mathematical Analysis 4 Communications on Pure and Applied Mathematics 4 Journal of Functional Analysis 4 Chinese Annals of Mathematics. Series B 4 Mathematical and Computer Modelling 4 Asymptotic Analysis 4 Mathematical Modelling of Natural Phenomena 4 Kinetic and Related Models 3 Mathematics of Computation 3 Transactions of the American Mathematical Society 3 Revista Matemática Iberoamericana 3 SIAM Journal on Applied Mathematics 3 Interfaces and Free Boundaries 3 Oberwolfach Reports 2 Computers & Mathematics with Applications 2 Inverse Problems 2 Journal of Computational Physics 2 Journal of Statistical Physics 2 Mathematical Biosciences 2 Mathematical Methods in the Applied Sciences 2 Transport Theory and Statistical Physics 2 Bulletin of Mathematical Biology 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Numerische Mathematik 2 Japan Journal of Applied Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Séminaire Équations aux Dérivées Partielles 2 Methods and Applications of Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Journal of Biological Dynamics 2 Networks and Heterogeneous Media 2 The Journal of Mathematical Neuroscience 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Nonlinear Analysis. Theory, Methods & Applications 1 Applicable Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Analysis and Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Optimization 1 BIT 1 Calcolo 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Theoretical Population Biology 1 Acta Applicandae Mathematicae 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applied Mathematics Letters 1 Journal of the American Mathematical Society 1 European Journal of Mechanics. B. Fluids 1 Applications of Mathematics 1 Geometric and Functional Analysis. GAFA 1 European Journal of Operational Research 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Advances in Mathematical Sciences and Applications 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of the Egyptian Mathematical Society 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Markov Processes and Related Fields 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Milan Journal of Mathematics 1 Mathematical Medicine and Biology 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oxford Lecture Series in Mathematics and its Applications 1 Series on Advances in Mathematics for Applied Sciences 1 Journal of Theoretical Biology 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 SIAM/ASA Journal on Uncertainty Quantification 1 Séminaire Laurent Schwartz. EDP et Applications 1 Philosophical Transactions A. Royal Society of London 1 Frontiers in Mathematics 1 Lecture Notes on Mathematical Modelling in the Life Sciences ...and 2 more Serials
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#### Fields
209 Partial differential equations (35-XX) 115 Biology and other natural sciences (92-XX) 77 Fluid mechanics (76-XX) 53 Statistical mechanics, structure of matter (82-XX) 37 Numerical analysis (65-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 18 Integral equations (45-XX) 11 Operator theory (47-XX) 10 Ordinary differential equations (34-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Probability theory and stochastic processes (60-XX) 7 Mechanics of deformable solids (74-XX) 7 Astronomy and astrophysics (85-XX) 5 General and overarching topics; collections (00-XX) 5 Quantum theory (81-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 4 Systems theory; control (93-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX)
#### Citations contained in zbMATH
236 Publications have been cited 6,320 times in 3,554 Documents Cited by Year
Transport equations in biology. Zbl 1185.92006
Perthame, Benoît
2007
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. Zbl 1133.65308
Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile; Klein, Rupert; Perthame, Benoît
2004
Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system. Zbl 0741.35061
Lions, P. L.; Perthame, B.
1991
Regularity of the moments of the solution of a transport equation. Zbl 0652.47031
Golse, François; Lions, Pierre-Louis; Perthame, Benoît; Sentis, Rémi
1988
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions. Zbl 1112.35023
Blanchet, Adrien; Dolbeault, Jean; Perthame, Benoit
2006
A kinetic formulation of multidimensional scalar conservation laws and related equations. Zbl 0820.35094
Lions, P. L.; Perthame, B.; Tadmor, E.
1994
Global solutions of some chemotaxis and angiogenesis system in high space dimension. Zbl 1115.35136
Corrias, L.; Perthame, Benoît; Zaag, H.
2004
Kinetic formulation of the isentropic gas dynamics and $$p$$-systems. Zbl 0799.35151
Lions, P. L.; Perthame, B.; Tadmor, E.
1994
Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Zbl 0853.76077
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
1996
Kinetic formulation of conservation laws. Zbl 1030.35002
Perthame, Benoît
2002
Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Zbl 0997.76023
Gerbeau, J.-F.; Perthame, B.
2001
Kinetic models for chemotaxis and their drift-diffusion limits. Zbl 1052.92005
Chalub, Fabio A. C. C.; Markowich, Peter A.; Perthame, Benoît; Schmeiser, Christian
2004
A kinetic scheme for the Saint-Venant system with a source term. Zbl 1008.65066
Perthame, B.; Simeoni, C.
2001
General relative entropy inequality: an illustration on growth models. Zbl 1085.35042
Michel, Philippe; Mischler, Stéphane; Perthame, Benoît
2005
The non-local Fisher-KPP equation: travelling waves and steady states. Zbl 1195.35088
Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya
2009
Exit time problems in optimal control and vanishing viscosity method. Zbl 0674.49027
Barles, G.; Perthame, B.
1988
Optimal critical mass in the two dimensional Keller-Segel model in $$R^2$$. Zbl 1056.35076
Dolbeault, Jean; Perthame, Benoît
2004
Derivation of hyperbolic models for chemosensitive movement. Zbl 1080.92014
Filbet, Francis; Laurençot, Philippe; Perthame, Benoît
2005
Discontinuous solutions of deterministic optimal stopping time problems. Zbl 0629.49017
Barles, G.; Perthame, B.
1987
The dynamics of adaptation: An illuminating example and a Hamilton–Jacobi approach. Zbl 1072.92035
Diekmann, Odo; Jabin, Pierre-Emanuel; Mischler, Stéphane; Perthame, Benoît
2005
The Gaussian-BGK model of Boltzmann equation with small Prandtl number. Zbl 0967.76082
Andries, Pierre; Le Tallec, Patrick; Perlat, Jean-Philippe; Perthame, Benoît
2000
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. Zbl 0744.76088
Perthame, B.
1992
Global existence to the BGK model of Boltzmann equation. Zbl 0694.35134
Perthame, B.
1989
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations. Zbl 1031.35077
Chen, Gui-Qiang; Perthame, Benoît
2003
Kruzkov’s estimates for scalar conservation laws revisited. Zbl 0955.65069
Bouchut, F.; Perthame, B.
1998
On positivity preserving finite volume schemes for Euler equations. Zbl 0857.76062
Perthame, Benoit; Shu, Chi-Wang
1996
Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. Zbl 0960.76051
Coquel, Frédéric; Perthame, Benoît
1998
A consistent BGK-type model for gas mixtures. Zbl 1001.82093
Andries, Pierre; Aoki, Kazuo; Perthame, Benoit
2002
A kinetic equation with kinetic entropy functions for scalar conservation laws. Zbl 0729.76070
1991
Boltzmann type schemes for gas dynamics and the entropy property. Zbl 0714.76078
Perthame, B.
1990
Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d’un opérateur de transport. (A compactness result for transport equations and application to the calculus of the limit of the principal eigenvalue of a transport operator). Zbl 0591.45007
Golse, François; Perthame, Benoît; Sentis, Rémi
1985
Exponential decay for the fragmentation or cell-division equation. Zbl 1072.35195
Perthame, Benoît; Ryzhik, Lenya
2005
PDE models for chemotactic movements: parabolic, hyperbolic and kinetic. Zbl 1099.35157
Perthame, Benoît
2004
A chemotaxis model motivated by angiogenesis. Zbl 1028.35062
Corrias, L.; Perthame, B.; Zaag, H.
2003
Gelation in coagulation and fragmentation models. Zbl 1016.82027
Escobedo, M.; Mischler, S.; Perthame, B.
2002
The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximation. Zbl 0655.35075
Bardos, C.; Golse, F.; Perthame, B.; Sentis, R.
1988
Morrey-Campanato estimates for Helmholtz equations. Zbl 0932.35048
Perthame, Benoit; Vega, Luis
1999
Dirac mass dynamics in multidimensional nonlocal parabolic equations. Zbl 1229.35113
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoît
2011
A Fourier spectral method for homogeneous Boltzmann equations. Zbl 0870.76074
Pareschi, Lorenzo; Perthame, Benoit
1996
On a boundary layer problem for the nonlinear Boltzmann equation. Zbl 0668.76089
Golse, Francois; Perthame, Benoit; Sulem, Catherine
1988
Dirac concentrations in Lotka-Volterra parabolic PDEs. Zbl 1172.35005
Perthame, Benoit; Barles, Guy
2008
Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure. Zbl 0919.35088
Perthame, B.
1998
Gelation and mass conservation in coagulation-fragmentation models. Zbl 1133.82316
Escobedo, M.; Laurençot, Ph.; Mischler, S.; Perthame, B.
2003
Equilibrium schemes for scalar conservation laws with stiff sources. Zbl 1017.65070
Botchorishvili, Ramaz; Perthame, Benoit; Vasseur, Alexis
2003
A numerical method using upwind schemes for the resolution of two-phase flows. Zbl 0893.76052
Coquel, F.; El Amine, K.; Godlewski, E.; Perthame, B.; Rascle, P.
1997
Time decay, propagation of low moments and dispersive effects for kinetic equations. Zbl 0852.35139
Perthame, B.
1996
Numerical passage from kinetic to fluid equations. Zbl 0718.76086
Coron, F.; Perthame, B.
1991
The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347
Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis
2014
Mathematical tools for kinetic equations. Zbl 1151.82351
Perthame, Benoît
2004
A limiting case for velocity averaging. Zbl 0956.45010
Perthame, B.; Souganidis, P. E.
1998
Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies. Zbl 1071.35079
Audusse, Emmanuel; Perthame, Benoît
2005
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Zbl 1274.92025
Lorz, Alexander; Lorenzi, Tommaso; Hochberg, Michael E.; Clairambault, Jean; Perthame, Benoît
2013
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states. Zbl 1259.35198
Cáceres, María J.; Carrillo, José A.; Perthame, Benoît
2011
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Zbl 1253.35186
Bouin, Emeric; Calvez, Vincent; Meunier, Nicolas; Mirrahimi, Sepideh; Perthame, Benoît; Raoul, Gaël; Voituriez, Raphaël
2012
Microreversible collisions for polyatomic gases and Boltzmann’s theorem. Zbl 0807.76067
Bourgat, J.-F.; Desvillettes, L.; Le Tallec, P.; Perthame, B.
1994
Weighted $$L^ \infty$$ bounds and uniqueness for the Boltzmann BGK model. Zbl 0786.76072
Perthame, B.; Pulvirenti, M.
1993
Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations. Zbl 0691.49028
Barles, G.; Perthame, B.
1990
Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Zbl 1334.92204
Lorz, Alexander; Lorenzi, Tommaso; Clairambault, Jean; Escargueil, Alexandre; Perthame, Benoît
2015
Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Zbl 1204.35027
Barles, Guy; Mirrahimi, Sepideh; Perthame, Benoît
2009
Dynamics of a structured neuron population. Zbl 1267.35239
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2010
General entropy equations for structured population models and scattering. Zbl 1049.35070
Michel, Philippe; Mischler, Stéphane; Perthame, Benoît
2004
On spherical symmetry solutions of the Euler-Poisson equation for the evolution of gaseous stars. Zbl 0743.35048
Makino, Tetu; Perthame, Benoît
1990
Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows. Zbl 1044.35056
Bouchut, François; Mangeney-Castelnau, Anne; Perthame, Benoît; Vilotte, Jean-Pierre
2003
Stability in a nonlinear population maturation model. Zbl 1020.92025
Mischler, Stéphane; Perthame, Benoît; Ryzhik, Lenya
2002
Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces. Zbl 1134.92006
Corrias, Lucilla; Perthame, Benoît
2008
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. Zbl 1290.35194
Audusse, Emmanuel; Bristeau, Marie-Odile; Perthame, Benoît; Sainte-Marie, Jacques
2011
Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases. Zbl 1101.76377
Andries, Pierre; Bourgat, Jean-François; le Tallec, Patrick; Perthame, Benoit
2002
Existence of solutions of the hyperbolic Keller-Segel model. Zbl 1180.35343
Perthame, Benoît; Dalibard, Anne-Laure
2009
Coupling Boltzmann and Euler equations without overlapping. Zbl 0796.76063
Bourgat, J. F.; Le Tallec, P.; Perthame, B.; Qiu, Y.
1994
Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2014
Exponential decay for the growth-fragmentation/cell-division equations. Zbl 1183.35038
Laurençot, Philippe; Perthame, Benoit
2009
Strichartz’ estimates for kinetic transport equations. Zbl 0848.35095
Castella, François; Perthame, Benoît
1996
Non-existence of global solutions to Euler-Poisson equations for repulsive forces. Zbl 0717.35049
Perthame, Benoît
1990
Relaxation and self-sustained oscillations in the time elapsed neuron network model. Zbl 1278.82046
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2013
Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Zbl 1337.35077
Perthame, Benoît; Génieys, Stephane
2007
Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. Zbl 1137.49027
Barles, Guy; Perthame, Benoît
2007
Regularity and propagation of moments in some nonlinear Vlasov systems. Zbl 0984.35102
Gasser, I.; Jabin, P.-E.; Perthame, B.
2000
A MUSCL method satisfying all the numerical entropy inequalities. Zbl 0853.65091
Bouchut, F.; Bourdarias, Ch.; Perthame, B.
1996
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation. Zbl 1219.35038
Nadin, Grégoire; Perthame, Benoît; Tang, Min
2011
Boltzmann equation with infinite energy: Renormalized solutions and distributional solutions for small initial data and initial data close to a Maxwellian. Zbl 0889.35077
Mischler, S.; Perthame, B.
1997
Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians. Zbl 0688.35052
Lions, P. L.; Perthame, B.
1987
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Zbl 1280.34066
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B.
2013
Prion dynamics with size dependency-strain phenomena. Zbl 1315.92039
Calvez, V.; Lenuzza, N.; Doumic, M.; Deslys, J.-P.; Mouthon, F.; Perthame, B.
2010
Traveling waves for the Keller-Segel system with Fisher birth terms. Zbl 1154.35459
Nadin, Gregoire; Perthame, Benoît; Ryzhik, Lenya
2008
An age-and-cyclin-structured cell population model for healthy and tumoral tissues. Zbl 1148.92014
Brikci, Fadia Bekkal; Clairambault, Jean; Ribba, Benjamin; Perthame, Benoît
2008
On the inverse problem for a size-structured population model. Zbl 1118.35072
Perthame, Benoît; Zubelli, Jorge P.
2007
Some new Godunov and relaxation methods for two-phase flow problems. Zbl 1064.76545
Coquel, F.; Godlewski, E.; Perthame, B.; In, A.; Rascle, P.
2001
Lemmes de moments, de moyenne et de dispersion. (Moments, averaging and dispersion lemmas). Zbl 0761.35085
Lions, Pierre-Louis; Perthame, Benoît
1992
The Rosseland approximation for the radiative transfer equations. Zbl 0654.65095
Bardos, C.; Golse, F.; Perthame, B.
1987
Generalized solutions of the radiative transfer equations in a singular case. Zbl 0614.35084
Golse, F.; Perthame, B.
1986
Upwinding of the source term at interfaces for Euler equations with high friction. Zbl 1213.76123
Bouchut, Francois; Ounaissa, Haythem; Perthame, Benoît
2007
Modified Keller-Segel system and critical mass for the log interaction kernel. Zbl 1126.35077
Calvez, Vincent; Perthame, Benoît; Sharifi tabar, Mohsen
2007
On the modified Enskog equation for elastic and inelastic collisions. Models with spin. Zbl 0850.70141
Esteban, Maria J.; Perthame, Benoît
1991
Conservative cross diffusions and pattern formation through relaxation. Zbl 1179.35156
Bendahmane, Mostafa; Lepoutre, Thomas; Marrocco, Americo; Perthame, Benoît
2009
Size distribution dependence of prion aggregates infectivity. Zbl 1161.92033
Calvez, Vincent; Lenuzza, Natacha; Oelz, Dietmar; Deslys, Jean-Philippe; Laurent, Pascal; Mouthon, Franck; Perthame, Benoît
2009
Line-energy Ginzburg-Landau models: zero-energy states. Zbl 1072.35051
Otto, Felix; Jabin, Pierre-Emmanuel; Perthame, Benoît
2002
High frequency limit of the Helmholtz equations. Zbl 1090.35165
Benamou, Jean-David; Castella, François; Katsaounis, Theodoros; Perthame, Benoit
2002
A BGK model for small Prandtl number in the Navier-Stokes approximation. Zbl 0943.76500
Bouchut, François; Perthame, Benoît
1993
Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. Zbl 1333.92009
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2014
Hele-Shaw limit for a system of two reaction-(Cross-)diffusion equations for living tissues. Zbl 1435.35390
Bubba, Federica; Perthame, Benoît; Pouchol, Camille; Schmidtchen, Markus
2020
The flux limited Keller-Segel system; properties and derivation from kinetic equations. Zbl 1441.35056
Perthame, Benoît; Vauchelet, Nicolas; Wang, Zhian
2020
Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations. Zbl 1423.35177
Almeida, Luis; Bubba, Federica; Perthame, Benoît; Pouchol, Camille
2019
A two-species hyperbolic-parabolic model of tissue growth. Zbl 1425.35198
Gwiazda, Piotr; Perthame, Benoît; Świerczewska-Gwiazda, Agnieszka
2019
Implicit and semi-implicit numerical schemes for the gradient flow of the formation of biological transport networks. Zbl 1437.65095
Fang, Di; Jin, Shi; Markowich, Peter; Perthame, Benoît
2019
Derivation of a voltage density equation from a voltage-conductance kinetic model for networks of integrate-and-fire neurons. Zbl 1433.35429
Perthame, Benoît; Salort, Delphine
2019
Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller-Segel equation. Zbl 1397.92101
Perthame, Benoît; Yasuda, Shugo
2018
Dynamics of concentration in a population model structured by age and a phenotypical trait. Zbl 1398.35251
Nordmann, Samuel; Perthame, Benoît; Taing, Cécile
2018
Traveling wave and aggregation in a flux-limited Keller-Segel model. Zbl 1405.92030
Calvez, Vincent; Perthame, Benoît; Yasuda, Shugo
2018
The fractional diffusion limit of a kinetic model with biochemical pathway. Zbl 1395.35015
Perthame, Benoît; Sun, Weiran; Tang, Min
2018
Super-linear propagation for a general, local cane toads model. Zbl 1407.35112
Henderson, Christopher; Perthame, Benoît; Souganidis, Panagiotis E.
2018
Long-time asymptotics for polymerization models. Zbl 1400.82316
Calvo, Juan; Doumic, Marie; Perthame, Benoît
2018
A Hele-Shaw problem for tumor growth. Zbl 1377.35245
Mellet, Antoine; Perthame, Benoît; Quirós, Fernando
2017
On interfaces between cell populations with different mobilities. Zbl 1359.35204
Lorenzi, Tommaso; Lorz, Alexander; Perthame, Benoît
2017
Toward an integrated workforce planning framework using structured equations. Zbl 1403.90462
Doumic, Marie; Perthame, Benoît; Ribes, Edouard; Salort, Delphine; Toubiana, Nathan
2017
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway. Zbl 1358.35207
Perthame, Benoît; Tang, Min; Vauchelet, Nicolas
2016
Notes on a PDE system for biological network formation. Zbl 1334.35101
Haskovec, Jan; Markowich, Peter; Perthame, Benoît; Schlottbom, Matthias
2016
Rare mutations limit of a steady state dispersal evolution model. Zbl 1387.35027
Perthame, Benoit; Souganidis, P. E.
2016
Uncertainty propagation; intrusive kinetic formulations of scalar conservation laws. Zbl 1362.35342
Despres, Bruno; Perthame, Benoit
2016
Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes. Zbl 1345.60069
Gess, Benjamin; Perthame, Benoît; Souganidis, Panagiotis E.
2016
Free boundary problems for tumor growth: a viscosity solutions approach. Zbl 1334.35360
Kim, Inwon C.; Perthame, Benoît; Souganidis, Panagiotis E.
2016
Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Zbl 1334.92204
Lorz, Alexander; Lorenzi, Tommaso; Clairambault, Jean; Escargueil, Alexandre; Perthame, Benoît
2015
Parabolic equations in biology. Growth, reaction, movement and diffusion. Zbl 1333.35001
Perthame, Benoît
2015
Asymptotic analysis of a selection model with space. Zbl 1327.35011
Mirrahimi, Sepideh; Perthame, Benoît
2015
Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience. Zbl 1336.35332
Carrillo, José Antonio; Perthame, Benoît; Salort, Delphine; Smets, Didier
2015
Mathematical analysis of a PDE system for biological network formation. Zbl 1345.35120
Haskovec, Jan; Markowich, Peter; Perthame, Benoit
2015
Incompressible limit of a mechanical model of tumour growth with viscosity. Zbl 1353.35294
Perthame, Benoît; Vauchelet, Nicolas
2015
Time fluctuations in a population model of adaptive dynamics. Zbl 1312.35011
Mirrahimi, Sepideh; Perthame, Benoît; Souganidis, Panagiotis E.
2015
A simple derivation of BV bounds for inhomogeneous relaxation systems. Zbl 1316.35183
Perthame, Benoît; Seguin, Nicolas; Tournus, Magali
2015
Data assimilation for hyperbolic conservation laws: a Luenberger observer approach based on a kinetic description. Zbl 1329.35195
Boulanger, Anne-Celine; Moireau, Philippe; Perthame, Benoît; Sainte-Marie, Jacques
2015
Dynamics of time elapsed inhomogeneous neuron network model. Zbl 1337.92014
Kang, Moon-Jin; Perthame, Benoît; Salort, Delphine
2015
Competition and boundary formation in heterogeneous media: application to neuronal differentiation. Zbl 1325.35237
Perthame, Benoît; Quiñinao, Cristóbal; Touboul, Jonathan
2015
Transversal instability for the thermodiffusive reaction-diffusion system. Zbl 1328.35097
Kowalczyk, Michal; Perthame, Benoît; Vauchelet, Nicolas
2015
The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347
Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis
2014
Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2014
Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. Zbl 1333.92009
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2014
Derivation of a Hele-Shaw type system from a cell model with active motion. Zbl 1325.35092
Perthame, Benoît; Quirós, Fernando; Tang, Min; Vauchelet, Nicholas
2014
Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient. Zbl 1366.92065
Perthame, Benoît; Tang, Min; Vauchelet, Nicolas
2014
Direct competition results from strong competition for limited resource. Zbl 1293.35346
Mirrahimi, Sepideh; Perthame, Benoît; Wakano, Joe Yuichiro
2014
Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity. Zbl 1412.92001
Cáceres, María J.; Perthame, Benoît
2014
Some mathematical aspects of tumor growth and therapy. Zbl 1373.35322
Perthame, Benoît
2014
Long-term behaviour of phenotypically structured models. Zbl 1371.92087
Lorz, Alexander; Perthame, Benoît
2014
Composite waves for a cell population system modeling tumor growth and invasion. Zbl 1321.35249
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît
2014
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Zbl 1274.92025
Lorz, Alexander; Lorenzi, Tommaso; Hochberg, Michael E.; Clairambault, Jean; Perthame, Benoît
2013
Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
Relaxation and self-sustained oscillations in the time elapsed neuron network model. Zbl 1278.82046
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2013
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Zbl 1280.34066
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B.
2013
Stochastic averaging lemmas for kinetic equations. Zbl 1323.35234
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
Optimal regularizing effect for scalar conservation laws. Zbl 1288.35343
Golse, François; Perthame, Benoît
2013
Composite waves for a cell population system modeling tumor growth and invasion. Zbl 1346.92017
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît
2013
On a voltage-conductance kinetic system for integrate & fire neural networks. Zbl 1284.35103
Perthame, Benoît; Salort, Delphine
2013
Nonlinear stability of a Vlasov equation for magnetic plasmas. Zbl 1262.35197
Charles, Frédérique; Després, Bruno; Perthame, Benoît; Sentis, Rémis
2013
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Zbl 1253.35186
Bouin, Emeric; Calvez, Vincent; Meunier, Nicolas; Mirrahimi, Sepideh; Perthame, Benoît; Raoul, Gaël; Voituriez, Raphaël
2012
Evolution of species trait through resource competition. Zbl 1279.92060
Mirrahimi, Sepideh; Perthame, Benoît; Wakano, Joe Yuichiro
2012
Regularization in Keller-Segel type systems and the De Giorgi method. Zbl 1288.35146
Perthame, Benoît; Vasseur, Alexis
2012
Analysis of a simplified model of the urine concentration mechanism. Zbl 1262.35204
Tournus, Magali; Edwards, Aurélie; Seguin, Nicolas; Perthame, Benoît
2012
A singular Hamilton-Jacobi equation modeling the tail problem. Zbl 1280.35007
Mirrahimi, Sepideh; Barles, Guy; Perthame, Benoît; Souganidis, Panagiotis E.
2012
Corrigendum to “An integro-differential equation model for alignment and orientational aggregation” [J. Differential Equations 246 (4) (2009) 1387-1421]. Zbl 1236.47045
Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L.
2012
Dirac mass dynamics in multidimensional nonlocal parabolic equations. Zbl 1229.35113
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoît
2011
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states. Zbl 1259.35198
Cáceres, María J.; Carrillo, José A.; Perthame, Benoît
2011
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. Zbl 1290.35194
Audusse, Emmanuel; Bristeau, Marie-Odile; Perthame, Benoît; Sainte-Marie, Jacques
2011
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation. Zbl 1219.35038
Nadin, Grégoire; Perthame, Benoît; Tang, Min
2011
Travelling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities. Zbl 1223.35102
Perthame, Benoît; Schmeiser, Christian; Tang, Min; Vauchelet, Nicolas
2011
A structured population model of cell differentiation. Zbl 1235.35030
Doumic, Marie; Marciniak-Czochra, Anna; Perthame, Benoît; Zubelli, Jorge P.
2011
Waves for a hyperbolic Keller–Segel model and branching instabilities. Zbl 1221.35088
Cerreti, Fiammetta; Perthame, Benoît; Schmeiser, Christian; Tang, Min; Vauchelet, Nicolas
2011
Population formulation of adaptative meso-evolution: theory and numerics. Zbl 1379.92052
Mirrahimi, Sepideh; Perthame, Benoît; Bouin, Emeric; Millien, Pierre
2011
A homogenization approach to flashing ratchets. Zbl 1209.35013
Perthame, Benoît; Souganidis, Panagiotis E.
2011
Dynamics of a structured neuron population. Zbl 1267.35239
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2010
Prion dynamics with size dependency-strain phenomena. Zbl 1315.92039
Calvez, V.; Lenuzza, N.; Doumic, M.; Deslys, J.-P.; Mouthon, F.; Perthame, B.
2010
Models of self-organizing bacterial communities and comparisons with experimental observations. Zbl 1184.35158
Marrocco, A.; Henry, H.; Holland, I. B.; Plapp, M.; Séror, S. J.; Perthame, B.
2010
Stability analysis of a simplified yet complete model for chronic myelogenous leukemia. Zbl 1203.92036
Doumic-Jauffret, Marie; Kim, Peter S.; Perthame, Benoît
2010
Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations. Zbl 1196.92031
Perthame, Benoît; Gauduchon, Mathias
2010
The non-local Fisher-KPP equation: travelling waves and steady states. Zbl 1195.35088
Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya
2009
Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Zbl 1204.35027
Barles, Guy; Mirrahimi, Sepideh; Perthame, Benoît
2009
Existence of solutions of the hyperbolic Keller-Segel model. Zbl 1180.35343
Perthame, Benoît; Dalibard, Anne-Laure
2009
Exponential decay for the growth-fragmentation/cell-division equations. Zbl 1183.35038
Laurençot, Philippe; Perthame, Benoit
2009
Conservative cross diffusions and pattern formation through relaxation. Zbl 1179.35156
Bendahmane, Mostafa; Lepoutre, Thomas; Marrocco, Americo; Perthame, Benoît
2009
Size distribution dependence of prion aggregates infectivity. Zbl 1161.92033
Calvez, Vincent; Lenuzza, Natacha; Oelz, Dietmar; Deslys, Jean-Philippe; Laurent, Pascal; Mouthon, Franck; Perthame, Benoît
2009
Numerical solution of an inverse problem in size-structured population dynamics. Zbl 1161.92020
Doumic, Marie; Perthame, Benoît; Zubelli, Jorge P.
2009
Large-time behavior of periodic entropy solutions to anisotropic degenerate parabolic-hyperbolic equations. Zbl 1176.35031
Chen, Gui-Qiang; Perthame, Benoît
2009
An integro-differential equation model for alignment and orientational aggregation. Zbl 1157.47054
Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L.
2009
Asymmetric potentials and motor effect: a homogenization approach. Zbl 1180.35081
Perthame, Benoît; Souganidis, Panagiotis E.
2009
Asymmetric potentials and motor effect: a large deviation approach. Zbl 1171.82012
Perthame, Benoît; Souganidis, Panagiotis E.
2009
Why hyperbolic and kinetic models for cell populations self-organization? Zbl 1197.35297
Perthame, Benoît
2009
Dirac concentrations in Lotka-Volterra parabolic PDEs. Zbl 1172.35005
Perthame, Benoit; Barles, Guy
2008
Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces. Zbl 1134.92006
Corrias, Lucilla; Perthame, Benoît
2008
Traveling waves for the Keller-Segel system with Fisher birth terms. Zbl 1154.35459
Nadin, Gregoire; Perthame, Benoît; Ryzhik, Lenya
2008
An age-and-cyclin-structured cell population model for healthy and tumoral tissues. Zbl 1148.92014
Brikci, Fadia Bekkal; Clairambault, Jean; Ribba, Benjamin; Perthame, Benoît
2008
Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity. Zbl 1137.35020
Perthame, Benoit; Vega, Luis
2008
Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Zbl 1134.92012
Brikci, Fadia Bekkal; Clairambault, Jean; Perthame, Benoît
2008
Global existence for a kinetic model of chemotaxis via dispersion and Strichartz estimates. Zbl 1137.92004
Bournaveas, Nikolaos; Calvez, Vincent; Gutiérrez, Susana; Perthame, Benoît
2008
Mathematical methods and modeling of biophysical phenomena. Zbl 1155.92302
Perthame, Benoit; Markowich, Peter; Zubelli, Jorge P.
2008
Analysis of a cell system with finite divisions. Zbl 1244.35153
Perthame, Benôıt; Touaoula, Tarik Mohamed
2008
Transport equations in biology. Zbl 1185.92006
Perthame, Benoît
2007
Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Zbl 1337.35077
Perthame, Benoît; Génieys, Stephane
2007
Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. Zbl 1137.49027
Barles, Guy; Perthame, Benoît
2007
On the inverse problem for a size-structured population model. Zbl 1118.35072
Perthame, Benoît; Zubelli, Jorge P.
2007
Upwinding of the source term at interfaces for Euler equations with high friction. Zbl 1213.76123
Bouchut, Francois; Ounaissa, Haythem; Perthame, Benoît
2007
Modified Keller-Segel system and critical mass for the log interaction kernel. Zbl 1126.35077
Calvez, Vincent; Perthame, Benoît; Sharifi tabar, Mohsen
2007
Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model. Zbl 1106.92053
2007
...and 136 more Documents
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#### Cited by 3,604 Authors
126 Perthame, Benoît 52 Carrillo de la Plata, José Antonio 31 Jabin, Pierre-Emmanuel 30 Bouchut, François 30 Shu, Chi-Wang 29 Zhang, Xianwen 28 Jin, Shi 27 Bellomo, Nicola 27 Calvez, Vincent 25 Kurganov, Alexander 25 Laurençot, Philippe 24 Berthon, Christophe 24 Chen, Gui-Qiang G. 24 Vauchelet, Nicolas 23 Winkler, Michael 22 Degond, Pierre 22 Fernández-Nieto, Enrique Domingo 22 Karlsen, Kenneth Hvistendahl 22 Liu, Jianguo 22 Souganidis, Panagiotis E. 21 Goudon, Thierry 21 Mischler, Stéphane 21 Pareschi, Lorenzo 21 Yang, Tong 19 Golse, François 19 Lorenzi, Tommaso 19 Lu, Yunguang 19 Markowich, Peter Alexander 19 Parés Madroñal, Carlos 19 Rein, Gerhard 18 Gosse, Laurent 18 Gwiazda, Piotr 18 Hérard, Jean-Marc 18 Yun, Seok-Bae 17 Barles, Guy 17 Bellouquid, Abdelghani 17 Chalons, Christophe 17 Lions, Pierre-Louis 17 Mai Duc Thanh 17 Natalini, Roberto 16 Filbet, Francis 16 Mirrahimi, Sepideh 15 Desvillettes, Laurent 15 Doumic, Marie 15 Ducomet, Bernard 15 Gess, Benjamin 15 Masmoudi, Nader 15 Mieussens, Luc 15 Saint-Raymond, Laure 15 Soler, Juan S. 15 Volpert, Vitaly A. 14 Andreianov, Boris 14 Coquel, Frédéric 14 Escobedo Martínez, Miguel 14 Martínez Gamba, Irene 14 Nečasová, Šárka 14 Schaeffer, Jack W. 14 Velázquez, Juan J. L. 14 Wang, Zhian 14 Xing, Yulong 13 Castro, Manuel J. 13 Chertock, Alina E. 13 Ha, Seung-Yeal 13 Huang, Feimin 13 Raoul, Gaël 13 Schmeiser, Christian 13 Zhang, Xiangxiong 12 Audusse, Emmanuel 12 Bouin, Emeric 12 Bresch, Didier 12 Gabriel, Pierre 12 Lemou, Mohammed 12 Liu, Hailiang 12 Lorz, Alexander 12 Popov, Boyan 12 Risebro, Nils Henrik 12 Tadmor, Eitan 11 Biler, Piotr 11 Chen, Zili 11 Clairambault, Jean 11 Dimarco, Giacomo 11 Hwang, Hyung Ju 11 Jüngel, Ansgar 11 Klar, Axel 11 LeFloch, Philippe Gerard 11 Lian, Ruxu 11 Mangeney, Anne 11 Puppo, Gabriella 11 Rendall, Alan D. 11 Tao, Youshan 11 Trofimchuk, Sergei I. 11 Vega, Luis 11 Zheng, Jiashan 10 Bisi, Marzia 10 Bourdarias, Christian 10 Bristeau, Marie-Odile 10 Delitala, Marcello 10 Dumbser, Michael 10 Fox, Rodney O. 10 Godlewski, Edwige ...and 3,504 more Authors
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#### Cited in 322 Serials
228 Journal of Computational Physics 191 Journal of Differential Equations 139 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 115 Journal of Mathematical Analysis and Applications 97 Communications in Partial Differential Equations 95 Archive for Rational Mechanics and Analysis 76 Journal of Mathematical Biology 71 Computers and Fluids 69 Journal of Scientific Computing 63 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 62 SIAM Journal on Mathematical Analysis 62 Kinetic and Related Models 60 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 60 Comptes Rendus. Mathématique. Académie des Sciences, Paris 56 Journal de Mathématiques Pures et Appliquées. Neuvième Série 55 Journal of Statistical Physics 53 Communications in Mathematical Physics 47 Mathematics of Computation 47 Journal of Functional Analysis 44 Discrete and Continuous Dynamical Systems 41 Applied Mathematics Letters 40 Nonlinear Analysis. Real World Applications 39 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 38 Journal of Mathematical Physics 38 Mathematical Methods in the Applied Sciences 38 Journal of Hyperbolic Differential Equations 37 Discrete and Continuous Dynamical Systems. Series B 36 Mathematical and Computer Modelling 32 Numerische Mathematik 30 Computers & Mathematics with Applications 30 Transport Theory and Statistical Physics 30 Acta Applicandae Mathematicae 30 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 29 ZAMP. Zeitschrift für angewandte Mathematik und Physik 29 Transactions of the American Mathematical Society 27 SIAM Journal on Numerical Analysis 27 European Journal of Mechanics. B. Fluids 26 Nonlinearity 26 Bulletin of Mathematical Biology 24 Applied Mathematics and Computation 24 Journal of Theoretical Biology 23 Physica D 22 SIAM Journal on Scientific Computing 21 Communications on Pure and Applied Mathematics 21 Quarterly of Applied Mathematics 20 Journal of Fluid Mechanics 20 NoDEA. Nonlinear Differential Equations and Applications 19 Computer Methods in Applied Mechanics and Engineering 19 Journal of Computational and Applied Mathematics 19 Networks and Heterogeneous Media 18 Applied Mathematics and Optimization 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 International Journal for Numerical Methods in Fluids 17 Chinese Annals of Mathematics. Series B 17 Calculus of Variations and Partial Differential Equations 16 Mathematical Biosciences 16 SIAM Journal on Applied Mathematics 16 Journal of Evolution Equations 15 Physics of Fluids 15 Multiscale Modeling & Simulation 14 Applied Mathematical Modelling 14 Mathematical Biosciences and Engineering 14 Nonlinear Analysis. Theory, Methods & Applications 13 Mathematical Modelling of Natural Phenomena 13 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 12 Applied Numerical Mathematics 12 Journal of Biological Dynamics 11 Proceedings of the American Mathematical Society 11 Stochastic Processes and their Applications 10 Applicable Analysis 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 9 European Journal of Applied Mathematics 9 The Annals of Applied Probability 9 Journal of Nonlinear Science 9 Continuum Mechanics and Thermodynamics 9 Communications on Pure and Applied Analysis 8 Advances in Mathematics 8 Japan Journal of Industrial and Applied Mathematics 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 8 Bulletin of the American Mathematical Society. New Series 8 Journal of Dynamics and Differential Equations 8 Analysis and Applications (Singapore) 8 Boundary Value Problems 8 Séminaire Laurent Schwartz. EDP et Applications 7 Journal of Engineering Mathematics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 The Annals of Probability 7 Mathematische Annalen 7 Monatshefte für Mathematik 7 Revista Matemática Iberoamericana 7 Numerical Methods for Partial Differential Equations 7 Journal of Mathematical Sciences (New York) 7 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 7 Abstract and Applied Analysis 7 Journal of Mathematical Fluid Mechanics 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Stochastic and Partial Differential Equations. Analysis and Computations 7 SMAI Journal of Computational Mathematics 6 Journal of Optimization Theory and Applications 6 Ricerche di Matematica ...and 222 more Serials
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#### Cited in 48 Fields
2,469 Partial differential equations (35-XX) 1,205 Fluid mechanics (76-XX) 908 Biology and other natural sciences (92-XX) 750 Numerical analysis (65-XX) 634 Statistical mechanics, structure of matter (82-XX) 220 Probability theory and stochastic processes (60-XX) 192 Integral equations (45-XX) 183 Calculus of variations and optimal control; optimization (49-XX) 119 Ordinary differential equations (34-XX) 107 Operator theory (47-XX) 79 Dynamical systems and ergodic theory (37-XX) 79 Geophysics (86-XX) 65 Systems theory; control (93-XX) 64 Optics, electromagnetic theory (78-XX) 62 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 61 Astronomy and astrophysics (85-XX) 57 Mechanics of deformable solids (74-XX) 50 Classical thermodynamics, heat transfer (80-XX) 37 Operations research, mathematical programming (90-XX) 34 Relativity and gravitational theory (83-XX) 33 Functional analysis (46-XX) 33 Quantum theory (81-XX) 30 Mechanics of particles and systems (70-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 21 Global analysis, analysis on manifolds (58-XX) 19 Statistics (62-XX) 16 Differential geometry (53-XX) 15 Real functions (26-XX) 10 Computer science (68-XX) 7 General and overarching topics; collections (00-XX) 6 Measure and integration (28-XX) 6 Integral transforms, operational calculus (44-XX) 5 Combinatorics (05-XX) 5 Approximations and expansions (41-XX) 5 Information and communication theory, circuits (94-XX) 4 Functions of a complex variable (30-XX) 3 History and biography (01-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 General topology (54-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Mathematics education (97-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1
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https://zbmath.org/authors/?q=ai%3Acarleson.lennart | ## Carleson, Lennart
Compute Distance To:
Author ID: carleson.lennart Published as: Carleson, Lennart; Carleson, L. External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: Wolf Prize (1992) · Abel Prize (2006)
Documents Indexed: 70 Publications since 1950, including 5 Books 3 Further Contributions Biographic References: 12 Publications Co-Authors: 15 Co-Authors with 18 Joint Publications 438 Co-Co-Authors
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### Co-Authors
52 single-authored 4 Jones, Peter Wilcox 3 Makarov, Nikolai Georgievich 2 Benedicks, Michael 2 Chang, Sun-Yung Alice 2 Garnett, John Brady 2 Lax, Peter David 1 Ahlfors, Lars Valerian 1 Akutowicz, Edwin J. 1 Atiyah, Michael Francis 1 Beurling, Arne 1 Bishop, Christopher James 1 Deligne, Pierre René 1 Engquist, Bjorn E. 1 Gamelin, Theodore W. 1 Gromov, Mikhael Leonidovich 1 Jacobs, Sigvard 1 Keel, Markus 1 Malliavin, Paul 1 Maz’ya, Vladimir Gilelevich 1 Milnor, John Willard 1 Nash, John Forbes jun. 1 Neuberger, John W. 1 Nirenberg, Louis 1 Raussen, Martin 1 Serre, Jean-Pierre 1 Sinaĭ, Yakov Grigor’evich 1 Sjölin, Per 1 Skau, Christian Fredrik 1 Szemerédi, Endre 1 Tate, John Torrence jun. 1 Tits, Jacques 1 Totik, Vilmos 1 Varadhan, S. R. Srinivasa 1 Wermer, John 1 Wiles, Andrew John 1 Yoccoz, Jean-Christophe
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### Serials
6 Arkiv för Matematik 6 Mathematica Scandinavica 4 Journal d’Analyse Mathématique 4 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 3 Acta Mathematica 3 Mathematische Zeitschrift 3 Annals of Mathematics. Second Series 2 Bulletin des Sciences Mathématiques. Deuxième Série 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 1 Communications in Mathematical Physics 1 Studia Mathematica 1 Acta Scientiarum Mathematicarum 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Publications Mathématiques 1 Pacific Journal of Mathematics 1 Notices of the American Mathematical Society 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Bulletin of the American Mathematical Society 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Nordisk Matematisk Tidskrift 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Universitext 1 Contemporary Mathematicians
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### Fields
18 Functions of a complex variable (30-XX) 9 Potential theory (31-XX) 8 History and biography (01-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Functional analysis (46-XX) 3 Measure and integration (28-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Real functions (26-XX) 1 General and overarching topics; collections (00-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
59 Publications have been cited 2,999 times in 2,558 Documents Cited by Year
Interpolations by bounded analytic functions and the corona problem. Zbl 0112.29702
Carleson, Lennart
1962
On convergence and growth of partial sums of Fourier series. Zbl 0144.06402
Carleson, Lennart
1966
Complex dynamics. Zbl 0782.30022
Carleson, Lennart; Gamelin, Theodore W.
1993
The dynamics of the Hénon map. Zbl 0724.58042
Benedicks, Michael; Carleson, Lennart
1991
An interpolation problem for bounded analytic functions. Zbl 0085.06504
Carleson, Lennart
1958
Selected problems on exceptional sets. Zbl 0189.10903
Carleson, Lennart
1967
On the existence of an external function for an inequality of J. Moser. Zbl 0619.58013
Carleson, Lennart; Chang, Sun-Yung A.
1986
Oscillatory integrals and a multiplier problem for the disc. Zbl 0215.18303
Carleson, Lennart; Sjölin, P.
1972
On iterations of $$1-\alpha x^2$$ on $$(-1,1)$$. Zbl 0597.58016
Benedicks, Michael; Carleson, Lennart
1985
The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer. Zbl 0732.01042
Beurling, Arne
1989
Sets of uniqueness for functions regular in the unit circle. Zbl 0046.30005
Carleson, Lennart
1952
On the existence of boundary values for harmonic functions in several variables. Zbl 0107.08402
Carleson, Lennart
1962
Julia and John. Zbl 0804.30023
Carleson, Lennart; Jones, Peter W.; Yoccoz, Jean-Christophe
1994
A representation formula for the Dirichlet integral. Zbl 0090.28603
Carleson, Lennart
1960
On mappings, conformal at the boundary. Zbl 0186.13701
Carleson, Lennart
1967
On coefficient problems for univalent functions and conformal dimension. Zbl 0765.30005
Carleson, Lennart; Jones, Peter W.
1992
Mergelyan’s theorem on uniform polynomial approximation. Zbl 0163.08601
Carleson, Lennart
1964
Hölder continuity of Green’s functions. Zbl 1076.30026
Carleson, Lennart; Totik, Vilmos
2004
On the support of harmonic measure for sets of Cantor type. Zbl 0593.31004
Carleson, Lennart
1985
On a class of meromorphic functions and its associated exceptional sets. Zbl 0036.04701
Carleson, Lennart
1950
Some results connected with Brennan’s conjecture. Zbl 0805.30018
Carleson, Lennart; Makarov, Nikolai G.
1994
Representations of continuous functions. Zbl 0086.27702
Carleson, Lennart
1957
Removable singularities of continuous harmonic functions in $$R^ m$$. Zbl 0141.30203
Carleson, Lennart
1963
Selected problems on exceptional sets. Translation from the English by V.P.Havin. Edited by V.G.Maz’ya. (Izbrannye problemy teorii isklyuchitel’nykh mnozhestv.) Zbl 0224.31001
Carleson, Lennart
1971
On the zeros of functions with bounded Dirichlet integrals. Zbl 0047.07601
Carleson, Lennart
1952
Two remarks on $$H^1$$ and BMO. Zbl 0357.46058
Carleson, Lennart
1976
On universal moment problems. Zbl 0114.05903
Carleson, Lennart
1961
Harmonic measures supported on curves. Zbl 0677.30017
Bishop, C. J.; Carleson, L.; Garnett, J. B.; Jones, P. W.
1989
Best uniform approximation by analytic functions. Zbl 0248.30034
Carleson, Lennart; Jacobs, Sigvard
1972
Aggregation in the plane and Loewner’s equation. Zbl 1042.82039
Carleson, Lennart; Makarov, N.
2001
Laplacian path models. Zbl 1040.30011
Carleson, Lennart; Makarov, N.
2002
On Bernstein’s approximation problem. Zbl 0044.07002
Carleson, Lennart
1951
Some analytic problems related to statistical mechanics. Zbl 0425.60091
Carleson, Lennart
1980
Interpolating sequences and separation properties. Zbl 0347.30032
Carleson, Lennart; Garnett, John
1975
An explicit unconditional basis in $$H^1$$. Zbl 0495.46020
Carleson, Lennart
1980
On the distortion of sets on a Jordan curve under conformal mapping. Zbl 0273.30014
Carleson, Lennart
1973
On nullsets for continuous analytic functions. Zbl 0042.30902
Carleson, Lennart
1951
The extension problem for quasiconformal mappings. Zbl 0304.30016
Carleson, Lennart
1974
On bounded analytic functions and closure problems. Zbl 0047.35301
Carleson, Lennart
1952
On infinite differential equations with constant coefficients. I. Zbl 0050.31101
Carleson, Lennart
1953
The Corona theorem. Zbl 0195.42104
Carleson, Lennart
1970
On $$H^\infty$$ in multiply connected domains. Zbl 0527.46048
Carleson, Lennart
1983
The analytic continuation of interpolatory functions. Zbl 0126.28803
Akutowicz, E. J.; Carleson, L.
1960
A remark on Picard’s theorem. Zbl 0133.03601
Carleson, Lennart
1961
Estimates of harmonic measures. Zbl 0521.30026
Carleson, Lennart
1982
A proof of an inequality of Carleman. Zbl 0057.04802
Carleson, Lennart
1954
On the connection between Hausdorff measures and capacity. Zbl 0078.09303
Carleson, Lennart
1958
Two remarks on the basic theorems of information theory. Zbl 0088.10603
Carleson, Lennart
1958
Wiener’s Tauberian theorem. Zbl 0881.42001
Carleson, Lennart
1997
Selected problems on exceptional sets. Reprint. Orig. publ. 1967 by Van Nostrand, Princeton, N.J. Zbl 0505.00034
Carleson, Lennart
1983
Stochastic models of some dynamical systems. Zbl 0777.58023
Carleson, Lennart
1991
Metric projections of $$L^p$$ on $$H^p$$. (Projections métriques de $$L^p$$ sur $$H^p$$.) Zbl 0269.42006
Carleson, Lennart
1973
Interpolations by bounded analytic functions and the corona problem. Zbl 0192.16801
Carleson, Lennart
1963
Lars Ahlfors and the Painlevé problem. Zbl 0959.30013
Carleson, Lennart
2000
Asymptotic paths for subharmonic functions in $$\mathbb R^n$$. Zbl 0352.31004
Carleson, Lennart
1976
Maximal functions and capacities. Zbl 0139.28701
Carleson, Lennart
1965
BMO - 10 years’ development. Zbl 0495.46021
Carleson, Lennart
1981
A remark on Denjoy’s inequality and Herman’s theorem. Zbl 0446.58014
Carleson, Lennart
1979
An example concerning analytic functions with finite Dirichlet integrals. Zbl 0449.30024
Carleson, Lennart
1979
Hölder continuity of Green’s functions. Zbl 1076.30026
Carleson, Lennart; Totik, Vilmos
2004
Laplacian path models. Zbl 1040.30011
Carleson, Lennart; Makarov, N.
2002
Aggregation in the plane and Loewner’s equation. Zbl 1042.82039
Carleson, Lennart; Makarov, N.
2001
Lars Ahlfors and the Painlevé problem. Zbl 0959.30013
Carleson, Lennart
2000
Wiener’s Tauberian theorem. Zbl 0881.42001
Carleson, Lennart
1997
Julia and John. Zbl 0804.30023
Carleson, Lennart; Jones, Peter W.; Yoccoz, Jean-Christophe
1994
Some results connected with Brennan’s conjecture. Zbl 0805.30018
Carleson, Lennart; Makarov, Nikolai G.
1994
Complex dynamics. Zbl 0782.30022
Carleson, Lennart; Gamelin, Theodore W.
1993
On coefficient problems for univalent functions and conformal dimension. Zbl 0765.30005
Carleson, Lennart; Jones, Peter W.
1992
The dynamics of the Hénon map. Zbl 0724.58042
Benedicks, Michael; Carleson, Lennart
1991
Stochastic models of some dynamical systems. Zbl 0777.58023
Carleson, Lennart
1991
The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer. Zbl 0732.01042
Beurling, Arne
1989
Harmonic measures supported on curves. Zbl 0677.30017
Bishop, C. J.; Carleson, L.; Garnett, J. B.; Jones, P. W.
1989
On the existence of an external function for an inequality of J. Moser. Zbl 0619.58013
Carleson, Lennart; Chang, Sun-Yung A.
1986
On iterations of $$1-\alpha x^2$$ on $$(-1,1)$$. Zbl 0597.58016
Benedicks, Michael; Carleson, Lennart
1985
On the support of harmonic measure for sets of Cantor type. Zbl 0593.31004
Carleson, Lennart
1985
On $$H^\infty$$ in multiply connected domains. Zbl 0527.46048
Carleson, Lennart
1983
Selected problems on exceptional sets. Reprint. Orig. publ. 1967 by Van Nostrand, Princeton, N.J. Zbl 0505.00034
Carleson, Lennart
1983
Estimates of harmonic measures. Zbl 0521.30026
Carleson, Lennart
1982
BMO - 10 years’ development. Zbl 0495.46021
Carleson, Lennart
1981
Some analytic problems related to statistical mechanics. Zbl 0425.60091
Carleson, Lennart
1980
An explicit unconditional basis in $$H^1$$. Zbl 0495.46020
Carleson, Lennart
1980
A remark on Denjoy’s inequality and Herman’s theorem. Zbl 0446.58014
Carleson, Lennart
1979
An example concerning analytic functions with finite Dirichlet integrals. Zbl 0449.30024
Carleson, Lennart
1979
Two remarks on $$H^1$$ and BMO. Zbl 0357.46058
Carleson, Lennart
1976
Asymptotic paths for subharmonic functions in $$\mathbb R^n$$. Zbl 0352.31004
Carleson, Lennart
1976
Interpolating sequences and separation properties. Zbl 0347.30032
Carleson, Lennart; Garnett, John
1975
The extension problem for quasiconformal mappings. Zbl 0304.30016
Carleson, Lennart
1974
On the distortion of sets on a Jordan curve under conformal mapping. Zbl 0273.30014
Carleson, Lennart
1973
Metric projections of $$L^p$$ on $$H^p$$. (Projections métriques de $$L^p$$ sur $$H^p$$.) Zbl 0269.42006
Carleson, Lennart
1973
Oscillatory integrals and a multiplier problem for the disc. Zbl 0215.18303
Carleson, Lennart; Sjölin, P.
1972
Best uniform approximation by analytic functions. Zbl 0248.30034
Carleson, Lennart; Jacobs, Sigvard
1972
Selected problems on exceptional sets. Translation from the English by V.P.Havin. Edited by V.G.Maz’ya. (Izbrannye problemy teorii isklyuchitel’nykh mnozhestv.) Zbl 0224.31001
Carleson, Lennart
1971
The Corona theorem. Zbl 0195.42104
Carleson, Lennart
1970
Selected problems on exceptional sets. Zbl 0189.10903
Carleson, Lennart
1967
On mappings, conformal at the boundary. Zbl 0186.13701
Carleson, Lennart
1967
On convergence and growth of partial sums of Fourier series. Zbl 0144.06402
Carleson, Lennart
1966
Maximal functions and capacities. Zbl 0139.28701
Carleson, Lennart
1965
Mergelyan’s theorem on uniform polynomial approximation. Zbl 0163.08601
Carleson, Lennart
1964
Removable singularities of continuous harmonic functions in $$R^ m$$. Zbl 0141.30203
Carleson, Lennart
1963
Interpolations by bounded analytic functions and the corona problem. Zbl 0192.16801
Carleson, Lennart
1963
Interpolations by bounded analytic functions and the corona problem. Zbl 0112.29702
Carleson, Lennart
1962
On the existence of boundary values for harmonic functions in several variables. Zbl 0107.08402
Carleson, Lennart
1962
On universal moment problems. Zbl 0114.05903
Carleson, Lennart
1961
A remark on Picard’s theorem. Zbl 0133.03601
Carleson, Lennart
1961
A representation formula for the Dirichlet integral. Zbl 0090.28603
Carleson, Lennart
1960
The analytic continuation of interpolatory functions. Zbl 0126.28803
Akutowicz, E. J.; Carleson, L.
1960
An interpolation problem for bounded analytic functions. Zbl 0085.06504
Carleson, Lennart
1958
On the connection between Hausdorff measures and capacity. Zbl 0078.09303
Carleson, Lennart
1958
Two remarks on the basic theorems of information theory. Zbl 0088.10603
Carleson, Lennart
1958
Representations of continuous functions. Zbl 0086.27702
Carleson, Lennart
1957
A proof of an inequality of Carleman. Zbl 0057.04802
Carleson, Lennart
1954
On infinite differential equations with constant coefficients. I. Zbl 0050.31101
Carleson, Lennart
1953
Sets of uniqueness for functions regular in the unit circle. Zbl 0046.30005
Carleson, Lennart
1952
On the zeros of functions with bounded Dirichlet integrals. Zbl 0047.07601
Carleson, Lennart
1952
On bounded analytic functions and closure problems. Zbl 0047.35301
Carleson, Lennart
1952
On Bernstein’s approximation problem. Zbl 0044.07002
Carleson, Lennart
1951
On nullsets for continuous analytic functions. Zbl 0042.30902
Carleson, Lennart
1951
On a class of meromorphic functions and its associated exceptional sets. Zbl 0036.04701
Carleson, Lennart
1950
all top 5
### Cited by 2,339 Authors
28 Lu, Guozhen 19 Yang, Yunyan 18 Young, Lai-Sang 15 Brudnyi, Alexander 15 Lacey, Michael T. 15 Nguyễn Văn Hoàng 15 Nicolau, Artur 14 El-Fallah, Omar 14 Izuchi, Keiji 14 Kellay, Karim 14 Weisz, Ferenc 13 Gushchin, Anatoliĭ Konstantinovich 13 Lam, Nguyen 13 Levin, Genadi M. 13 Prestini, Elena 13 Ransford, Thomas J. 12 Carleson, Lennart 12 Do Ó, João M. Bezerra 12 Girela, Daniel 12 Luzzatto, Stefano 12 Peláez, José Ángel 12 Seip, Kristian 12 Sogge, Christopher D. 12 Wick, Brett D. 11 Jones, Peter Wilcox 11 Lou, Zengjian 11 Mortini, Raymond 11 Rättyä, Jouni 11 Wang, Qiudong 10 Avkhadiev, Farit Gabidinovich 10 Bishop, Christopher James 10 Hofmann, Steve 10 Lyubich, Mikhail 10 Martell, José María (Chema) 10 Pau, Jordi 10 Tao, Terence 9 Bloshanskii, Igor L. 9 Comerford, Mark 9 Grafakos, Loukas 9 Hedenmalm, Håkan 9 Rivera-Letelier, Juan 9 Takahasi, Hiroki 9 Trent, Tavan T. 9 Tugores, Francesc Martorell 8 Alves, José Ferreira 8 Bourgain, Jean 8 Cao, Yongluo 8 Dyakonov, Konstantin M. 8 Gorkin, Pamela B. 8 Kenig, Carlos Eduardo 8 Lee, Sanghyuk 8 Przytycki, Feliks 8 Ricci, Paolo Emilio 8 Ruf, Bernhard 8 Sjölin, Per 8 Sola, Alan A. 8 Sundberg, Carl-Erik W. 8 Thiele, Christoph Martin 7 Amar, Eric 7 Fagella, Núria 7 Gonchenko, Sergey V. 7 González, María José 7 Gutlyanskiĭ, Vladimir Ya. 7 Khavin, Viktor Petrovich 7 Izuchi, Yuko 7 Jarque, Xavier 7 Makarov, Nikolai Georgievich 7 Melbourne, Ian 7 Nyström, Kaj 7 Richter, Stefan 7 Rodríguez-Piazza, Luis 7 Rohde, Steffen 7 Shirokov, Nikolaĭ Alekseevich 7 Sibony, Nessim 7 Treil, Sergei 7 Viana, Marcelo 6 Adams, David Randolph 6 Andrievskii, Vladimir V. 6 Barański, Krzysztof 6 Berger, Pierre 6 Bergweiler, Walter 6 Białas-Cież, Leokadia 6 Brennan, James E. 6 Chen, Lu 6 Chen, Peng 6 Christ, Michael 6 Colonna, Flavia 6 Díaz, Lorenzo Justiniano 6 Doubtsov, Evgueni Sergeevich 6 Fan, Dashan 6 Fornæss, John Erik 6 Lu, Shanzhen 6 Mancini, Gabriele 6 Mashreghi, Javad 6 Mayboroda, Svitlana 6 Oksasoglu, Ali 6 Qian, Ruishen 6 Queffélec, Hervé 6 Rodríguez, José Angel 6 Ryazanov, Vladimir Il’ich ...and 2,239 more Authors
all top 5
### Cited in 332 Serials
128 Journal of Functional Analysis 125 Transactions of the American Mathematical Society 108 Proceedings of the American Mathematical Society 83 Journal of Mathematical Analysis and Applications 70 Arkiv för Matematik 68 Journal d’Analyse Mathématique 58 Advances in Mathematics 50 Mathematische Annalen 49 Communications in Mathematical Physics 44 Ergodic Theory and Dynamical Systems 42 Annales de l’Institut Fourier 41 Journal of Soviet Mathematics 41 The Journal of Geometric Analysis 39 Mathematische Zeitschrift 35 Mathematical Notes 35 Integral Equations and Operator Theory 33 Journal of Approximation Theory 31 Inventiones Mathematicae 30 Acta Mathematica 29 The Journal of Fourier Analysis and Applications 29 Computational Methods and Function Theory 28 Duke Mathematical Journal 26 Acta Mathematica Sinica. English Series 25 Complex Analysis and Operator Theory 23 Bulletin of the American Mathematical Society 22 Journal of Differential Equations 22 Potential Analysis 22 Journal of Mathematical Sciences (New York) 20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 19 Chaos, Solitons and Fractals 19 Revista Matemática Iberoamericana 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 19 Calculus of Variations and Partial Differential Equations 19 St. Petersburg Mathematical Journal 18 Analysis Mathematica 18 Israel Journal of Mathematics 18 Siberian Mathematical Journal 18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 Archiv der Mathematik 17 Complex Variables and Elliptic Equations 16 Tohoku Mathematical Journal. Second Series 16 Bulletin of the American Mathematical Society. New Series 15 Journal of Statistical Physics 15 Journal of the American Mathematical Society 15 Conformal Geometry and Dynamics 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Physica D 13 Journal of the European Mathematical Society (JEMS) 13 Proceedings of the Steklov Institute of Mathematics 12 Ukrainian Mathematical Journal 12 Science in China. Series A 12 Discrete and Continuous Dynamical Systems 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 Chaos 11 Dynamical Systems 10 Mathematische Nachrichten 10 Michigan Mathematical Journal 10 Constructive Approximation 10 Geometric and Functional Analysis. GAFA 10 Indagationes Mathematicae. New Series 10 Communications on Pure and Applied Analysis 10 Science China. Mathematics 10 Analysis and Mathematical Physics 9 Rocky Mountain Journal of Mathematics 9 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 9 Topology and its Applications 9 Acta Mathematica Hungarica 9 Annals of Mathematics. Second Series 9 Stochastics and Dynamics 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Monatshefte für Mathematik 8 Nagoya Mathematical Journal 8 Journal of Dynamics and Differential Equations 8 Journal of Difference Equations and Applications 8 Doklady Mathematics 7 Nonlinearity 7 The Annals of Probability 7 Bulletin de la Société Mathématique de France 7 Collectanea Mathematica 7 Probability Theory and Related Fields 7 Linear Algebra and its Applications 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Functional Analysis and its Applications 6 Publications Mathématiques 6 Kodai Mathematical Journal 6 Memoirs of the American Mathematical Society 6 Results in Mathematics 6 Experimental Mathematics 6 Bulletin des Sciences Mathématiques 6 Annales Academiae Scientiarum Fennicae. Mathematica 6 Frontiers of Mathematics in China 6 Nonlinear Analysis. Theory, Methods & Applications 5 Bulletin of the Australian Mathematical Society 5 Lithuanian Mathematical Journal 5 Applied Mathematics and Computation 5 Czechoslovak Mathematical Journal 5 Publicacions Matemàtiques 5 International Journal of Mathematics 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Boletim da Sociedade Brasileira de Matemática. Nova Série ...and 232 more Serials
all top 5
### Cited in 55 Fields
715 Functions of a complex variable (30-XX) 581 Dynamical systems and ergodic theory (37-XX) 502 Harmonic analysis on Euclidean spaces (42-XX) 483 Functional analysis (46-XX) 319 Partial differential equations (35-XX) 286 Operator theory (47-XX) 224 Potential theory (31-XX) 193 Several complex variables and analytic spaces (32-XX) 100 Real functions (26-XX) 96 Measure and integration (28-XX) 96 Probability theory and stochastic processes (60-XX) 87 Approximations and expansions (41-XX) 75 Ordinary differential equations (34-XX) 52 Global analysis, analysis on manifolds (58-XX) 42 Abstract harmonic analysis (43-XX) 33 Number theory (11-XX) 28 Statistical mechanics, structure of matter (82-XX) 25 Numerical analysis (65-XX) 22 Sequences, series, summability (40-XX) 22 Integral transforms, operational calculus (44-XX) 22 Quantum theory (81-XX) 20 General topology (54-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 17 Differential geometry (53-XX) 16 Difference and functional equations (39-XX) 16 Systems theory; control (93-XX) 15 Special functions (33-XX) 13 History and biography (01-XX) 11 Mechanics of particles and systems (70-XX) 11 Information and communication theory, circuits (94-XX) 10 Statistics (62-XX) 9 Manifolds and cell complexes (57-XX) 8 Topological groups, Lie groups (22-XX) 8 Integral equations (45-XX) 8 Convex and discrete geometry (52-XX) 7 Group theory and generalizations (20-XX) 7 Fluid mechanics (76-XX) 6 Field theory and polynomials (12-XX) 6 Algebraic geometry (14-XX) 6 Computer science (68-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Mathematical logic and foundations (03-XX) 4 Combinatorics (05-XX) 4 Relativity and gravitational theory (83-XX) 3 Operations research, mathematical programming (90-XX) 2 Geometry (51-XX) 2 Mechanics of deformable solids (74-XX) 2 Geophysics (86-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-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. | 2022-05-28T07:35:30 | {"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": 0.4533284902572632, "perplexity": 5958.564856346396}, "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/1652663013003.96/warc/CC-MAIN-20220528062047-20220528092047-00065.warc.gz"} |
https://finalfantasy.fandom.com/wiki/Marvelous_Cheer_(weapon) | ## FANDOM
38,087 Pages
Relm: I couldn't miss the chance to practice my drawing!
This staff is garishly colored like a child's toy. Using it you feel strangely... happy.
Final Fantasy Tactics A2: Grimoire of the Rift description
Marvelous Cheer (マーベラスチアー, Māberasu Chiā?), also known as HP Shout, Cheer Staff, Marvelous Shout, or Cheerphone, is a recurring weapon in the series. It has had various forms.
## Appearances Edit
### Final Fantasy VII Edit
HP Shout is Cait Sith's ultimate weapon, found in a locker on the 64th floor of the Shinra Headquarters during the Raid on Midgar (Part 2). It provides 95 attack, 110 Atk%, 44 magic, and has eight Materia slots, four of which are linked, with zero growth. The player can find it during their first trip to in Part I, but Cloud will return it in the locker, stating there is no point in taking something that is of no use to the party.
The weapon deals more damage the more HP Cait Sith has, and its damage formula is as follows:
$Power = [(3 * Power * Cait Sith's HP) / Cait Sith's Max HP] + 1$
### Final Fantasy Tactics Advance Edit
Strange colored staff said to energize its bearer.
Description
Cheer Staff is a high-ranked staff that provides 32 attack, 5 Resistance, and 2 Evasion. It teaches Auto-Life to the White Mage for 200 AP, Judge to the Bishop for 300 AP, and Madeen to the Summoner for 300 AP.
This section about equipment in Final Fantasy Tactics Advance is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
#### Final Fantasy Tactics A2: Grimoire of the Rift Edit
Cheer Staff is a high-ranked staff that provides 32 attack and 5 Resistance. It teaches Reraise for 400 AP to the White Mage, Pilfer for 150 AP to the Bishop, and Maduin for 350 AP to the Summoner. It can be obtained from the Bazaar from the Battle-hardened Staves A category by trading a Four-Leaf Clover, Gurnat, and Hero Tonic.
### Final Fantasy Type-0 Edit
Marvelous Shout is the second strongest magic gun for Cater, increasing her Strength by 67. It is unlocked for purchase in the Sixth Arms Research Institute after completing Mission 3-Crimson on Impossible Mode, priced at 60,000 gil. In the PSP version, the weapon could be exchanged for 10 tickets on the Square Enix Members Site, and then transferred to the game.
### Pictlogica Final Fantasy ≒Edit
This section about equipment in Pictlogica Final Fantasy ≒ is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Airborne Brigade Edit
This section about equipment in Final Fantasy Airborne Brigade is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Record KeeperEdit
This section about equipment in Final Fantasy Record Keeper is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Explorers Edit
A unique staff that senses the wielder's vitality and does more damage when HP is high.
Description
This section about equipment in Final Fantasy Explorers is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
### Final Fantasy Brave ExviusEdit
A high-performance megaphone from another world which greatly boosts magical and spiritual power when equipped. It is said a black cat robot used this megaphone to issue commands to the giant moogle it rode on. Increased performance allowed more information to be relayed, making the moogle stronger.
Description
HP Shout is an Instrument that is obtained as Cait Sith's Trust Master. It provides 22 ATK, 95 MAG, and 44 SPR.
### Final Fantasy Fables: Chocobo Tales Edit
This section about an ability in Final Fantasy Fables: Chocobo Tales is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it.
## Gallery Edit
This gallery is incomplete and requires Final Fantasy Tactics A2: Grimoire of the Rift added. You can help the Final Fantasy Wiki by uploading images.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-05-27T16:09:28 | {"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": 0.25777897238731384, "perplexity": 12026.077441495749}, "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-2020-24/segments/1590347394756.31/warc/CC-MAIN-20200527141855-20200527171855-00248.warc.gz"} |
https://docs.dea.ga.gov.au/notebooks/Scientific_workflows/DEAWaterbodies/TurnWaterObservationsIntoWaterbodyPolygons.html | # Turn water observations into waterbody polygons¶
• Compatability: Notebook currently compatible with both the NCI and DEA Sandbox environments if you set your filepaths to the required datasets.
• Products used: wofs_summary
• Special requirements: This notebook requires the python_geohash library. If you are using the default dea environment, this package may not be available. You can install it locally by using pip install --user python-geohash.
• Prerequisites:
• NetCDF files with WOfS outputs that will be used to define the persistent water body polygons
• Variable name: TileFolder
• This folder can be either a custom extraction of datacube-stats, or you can choose to use the WOfS summary tiles for all of Australia (see here for further information).
• A coastline polygon to filter out polygons generated from ocean pixels.
• Optional prerequisites:
• River line dataset for filtering out polygons comprised of river segments.
• Variable name: MajorRiversDataset
• The option to filter out major rivers is provided, and so this dataset is optional if FilterOutRivers = False.
• Here we use the Bureau of Meteorology’s Geofabric v 3.0.5 Beta (Suface Hydrology Network), filtered to only keep features tagged as major rivers.
• There are some identified issues with this data layer that make the filtering using this data inconsistent (see the discussion here)
• We therefore turn this off during the production of the water bodies shapefile.
• Urban high rise polygon dataset
• Variable name: UrbanMaskFile, but this is optional and can be skipped by setting UrbanMask = False.
• WOfS has a known limitation, where deep shadows thrown by tall CBD buildings are misclassified as water. This results in ‘waterbodies’ around these misclassified shadows in capital cities. If you are not using WOfS for your analysis, you may choose to set UrbanMask = False.
## Background¶
On average, the Australian Government invests around half a billion dollars a year in monitoring, protecting and enhancing Australia’s land, coasts and oceans. DEA provides near real-time satellite information which can be used by government to better target these investments.
Water is among one the most precious natural resources and is essential for the survival of life on Earth. Within Australia, the scarcity of water is both an economic and social issue. Water is required not only for consumption but for industries and environmental ecosystems to function and flourish.
With the demand for water increasing, there is a need to better understand our water availability to ensure we are managing our water resources effectively and efficiently.
Digital Earth Australia (DEA)’s Water Observations from Space (WOfS) dataset, provides a water classified image of Australia approximately every 16 days. These individual water observations have been combined into a WOfS summary product, which calculates the frequency of wet observations (compared against all clear observations of that pixel), over the full 30 year satellite archive.
The WOfS summary product provides valuable insights into the persistence of water across the Australian landscape on a pixel by pixel basis. While knowing the wet history of a single pixel within a waterbody is useful, it is more useful to be able to map the whole waterbody as a single object.
This notebook demonstrates a workflow for mapping waterbodies across Australia as polygon objects. This workflow has been used to produce DEA Waterbodies.
## Description¶
This code follows the following workflow:
• Load the required python packages
• Set your chosen analysis parameters
• minimum number of valid observations
• wetness threshold/s
• min/max waterbody size
• optional flag to filter out waterbodies that intersect with major rivers
• if you set this flag you will need to provide a dataset to do the filtering
• set the analysis region
• set the input files for the analysis
• Generate a list of netCDF files within a specified folder location
• Opens each netCDF file and:
• Keep only pixels observed at least x times
• Keep only pixels identified as wet at least x% of the time
• Here the code can take in two wetness thresholds, to produce two initial temporary polygon files.
• Convert the raster data into polygons
• Append the polygon set to a temporary shapefile
• Remove artificial polygon borders created at tile boundaries by merging polygons that intersect across Albers Tile boundaries
• Filter the combined polygon dataset (note that this step happens after the merging of Albers tile boundary polygons to ensure that artifacts are not created by part of a polygon being filtered out, while the remainder of the polygon that sits on a separate tile is treated differently).
• Filter the polygons based on size
• Remove polygons that intersect with Australia’s coastline
• Remove erroneous ‘water’ polygons within high-rise CBD areas
• Combine the two generated wetness thresholds (optional)
• Optional filtering for proximity to major rivers (as identified by the Geofabric dataset)
• Save out the final polygon set to a shapefile
## Getting started¶
To run this analysis, work through this notebook starting with the “Load packages” cell.
Import Python packages that are used for the analysis.
## Analysis parameters¶
The following section walks you through the analysis parameters you will need to set for this workflow. Each section describes the parameter, how it is used, and what value was used for the DEA Waterbodies product.
### How frequently wet does a pixel need to be to be included? The value/s set here will be the minimum frequency (as a decimal between 0 and 1) that you want water to be detected across all analysis years before it is included.
E.g. If this was set to 0.10, any pixels that are wet at least 10% of the time across all valid observations will be included. If you don’t want to use this filter, set this value to 0.
Following the exploration of an appropriate wetness threshold for DEA Waterbodies (see here), we choose to set two thresholds here. The code is set up to loop through both wetness thresholds, and to write out two temporary shapefiles. These two shapefiles with two separate thresholds are then used together to combine polygons from both thresholds later on in the workflow.
Polygons identified by the secondary threshold that intersect with the polygons generated by the primary threshold will be extracted, and included in the final polygon dataset. This means that the location of polygons is set by the primary threshold, but the shape of these polygons is set by the secondary threshold.
Threshold values need to be provided as a list of either one or two floating point numbers. If one number is provided, then this will be used to generate the initial polygon dataset. If two thresholds are entered, the first number becomes the secondary threshold, and the second number becomes the primary threshold. If more than two numbers are entered, the code will generate an error below.
MinSize
E.g. A minimum size of 6250 means that polygons need to be at least 10 pixels to be included. If you don’t want to use this filter, set this value to 0.
MaxSize
E.g. A maximum size of 1 000 000 means that you only want to consider polygons less than 1 km2. If you don’t want to use this filter, set this number to math.inf.
NOTE: if you are doing this analysis for all of Australia, very large polygons will be generated offshore, in the steps prior to filtering by the Australian coastline. For this reason, we have used a MaxSize = Area of Kati Thanda-Lake Eyre. This will remove the huge ocean polygons, but keep large inland waterbodies that we want to map.
The total number of valid WOfS observations for each pixel varies depending on the frequency of clouds and cloud shadow, the proximity to high slope and terrain shadow, and the seasonal change in solar angle.
The count_clear parameter within the wofs_summary <https://explorer.sandbox.dea.ga.gov.au/wofs_summary>__ data provides a count of the number of valid observations each pixel recorded over the analysis period. We can use this parameter to mask out pixels that were infrequently observed. If this mask is not applied, pixels that were observed only once could be included if that observation was wet (i.e. a single wet observation means the calculation of the frequency statistic would be (1 wet observation) / (1 total observation) = 100% frequency of wet observations).
Here we set the minimum number of observations to be 128 (roughly 4 per year over our 32 year analysis). Note that this parameter does not specify the timing of these observations, but rather just the total number of valid observations (observed at any time of the year, in any year).
The Bureau of Meteorology’s Geofabric v 3.0.5 Beta (Suface Hydrology Network) can be used to filter out polygons that intersect with major rivers. This is done to remove river segments from the polygon dataset. The SH_Network AHGFNetworkStream any layer within the SH_Network_GDB_V2_1_1.zip geodatabase can be used. You may chose to filter the rivers dataset to only keep rivers tagged as major, as the full rivers dataset contains a lot of higher order streams and can remove smaller waterbodies situated on upland streams.
If you have an alternative dataset you wish to use inplace of the Bureau of Meteorology Geofabric, you can set the filepath to this file in the MajorRiversDataset variable. Any alternative dataset needs to be a vector dataset, and able to be read in by the fiona python library.
Note that we reproject this dataset to epsg 3577, Australian Albers coordinate reference system to match the coordinate reference system of the WOfS data we use. If this is not correct for your analysis, you can change this in the cell below. A list of epsg code can be found here.
If you don’t want to filter out polygons that intersect with rivers, set this parameter to False.
Note that for the Water Body Polygon dataset, we set this filter to False (FilterOutRivers = False)
The option to filter out rivers was switched off for the production of DEA Waterbodies.
Note that the Geofabric continues the streamline through on-river dams, which means these polygons are filtered out. This may not be the desired result.
[6]:
FilterOutRivers = False
This section of code allows you to choose whether to use the WOfS summary data, or your own custom analysis. There are a number of options available to you here: * All of Australia WOfS analysis * Set AllofAustraliaAllTime = True * Set CustomData = False * Set AutoGenerateTileList = False * Some of Australia WOfS analysis * Set AllofAustraliaAllTime = False * Set CustomData = False * Set AutoGenerateTileList = False * You will then need to input a list of Albers Equal Area tiles over which you would like to perform your analysis in the ListofAlbersTiles variable. * Custom analysis for any spatial extent * Set AllofAustraliaAllTime = False * Set CustomData = True * Provide a path to where the files are sitting. Note that this code assumes the files are netCDF. * Set AutoGenerateTileList = True/False * If you want to analyse all of the tiles in the custom folder, set this to True. * If you want to analyse a subset of the tiles in the custom folder, set this to False, and provide a list of tiles to the ListofAlbersTiles variable.
All of Australia analysis
If you would like to perform the analysis for all of Australia, using the published WOfS all time summaries, set AllofAustraliaAllTime = True.
The WOfS all time summaries NetCDF files used are located in /g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/. These files contain the following three variables: count_wet, count_clear and frequency.
Custom Data option
This code is set up to allow you to input your own set of custom data statistics. You can generate your own custom statistics using the datacube-stats code repository. For example, you may wish to calculate WOfS summary statistics over a specified period, rather than over the full 1987 to 2018 period provided in the WOfS summary product. Datacube-stats allows you to specify the parameters for generating statistical summaries. You will need to ensure the output format is set to netCDF to make it compatible with the code here.
If CustomData = True, you will need to specify the location of the data you would like to use for this analysis, setting TileFolder below, under the if CustomData code section below.
If CustomData = False, the code will automatically look at the published WOfS all time summaries.
Autogeneration of tile list
AutoGenerateTileList will only be used if AllOfAustraliaAllTime = False. We only want to generate a list of tiles to iterate through if it will be a subset of all of the available data.
If you would like to automatically generate a list of tiles using the outputs of an analysis (e.g. if you have run a custom datacube-stats analysis over just NSW), set AutoGenerateTileList = True and update the location of the output file directory. This will generate a tile list consisting of every available tile within that folder. Note that this option currently assumes a filename format. If you experience an error when running this step, you may need to modify the Generate_list_of_albers_tiles function loaded above.
If you would like to manually feed in a list of albers tiles (i.e. run a subset of the tiles available within a chosen folder), set AutoGenerateTileList = False, and feed in a list of tiles in the format:
ListofAlbersTiles = ['7_-34', '10_-40', '16_-34']
For testing and debugging, set CustomData = True and AutoGenerateTileList = False, then enter a list of tiles to run using the ListofAlbersTiles described above.
[8]:
AllOfAustraliaAllTime = False
CustomData = False
AutoGenerateTileList = False
[9]:
if CustomData:
# Path to the files you would like to use for the analysis
TileFolder = '/g/data/r78/cek156/datacube_stats/WOFSDamsAllTimeNSWMDB/'
else:
# Default path to the WOfS summary product
TileFolder = '/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/'
A high tide coastline for Australia is used to mask out ocean polygons. You can choose which land/sea mask you would like to use, depending on how much coastal water you would like in the final product.
We use a coastline generated using the Intertidal Extents Model (ITEM) v2 dataset. This particular coastline creates a mask by identifying any water pixels that are continuously connected to the ocean, or an estuary. Any polygons that intersect with this mask are filtered out. I.e. if a polygon identified within our workflow overlaps with this coastal mask by even a single pixel, it will be discarded. We chose this very severe ocean mask as the aim of DEA Waterbodies is not to map coastal waterbodies, but just inland ones. For a detailed description of how this coastline was created, see this notebook.
Note that the mask we use here sets ocean = 1, land = NaN. If your mask has land = 1 instead, you can either invert it, or change the code in the Filter merged polygons by: <#Filtering>__ code section below.
[11]:
# Path to the coastal mask you would like to use.
Coastline = Coastline.to_crs({'init': 'epsg:3577'})
WOfS has a known limitation, where deep shadows thrown by tall CBD buildings are misclassified as water. This results in ‘waterbodies’ around these misclassified shadows in capital cities.
To address this problem, we use the Australian Bureau of Statistics Statistical Area 3 shapefile (2016) to define a spatial footprint for Australia’s CBD areas.
We use the following polygons as our CBD filter:
SA3_CODE1
SA3_NAME16
11703
Sydney Inner City
20604
Melbourne City
30501
Brisbane Inner
30901
30910
40101
50302
Perth City
If you are not using WOfS for your analysis, you may choose to set UrbanMask = False.
[ ]:
UrbanMask = True
[12]:
if UrbanMask:
CBDs = CBDs.to_crs({'init': 'epsg:3577'})
## Generate the first temporary polygon dataset¶
This code section:
1. Checks that the AtLeastThisWet threshold has been correctly entered above
2. Sets up a for loop that allows the user to input multiple temporal datasets (see below)
3. Generates a list of netCDF files to loop through
4. Sets up a for loop for that list of files. Here we have separate data for each Landsat tile, so this loop loops through the list of tile files
5. Opens the netCDF frequency data and removes the time dimension (which in this case is only of size 1)
6. Opens the netCDF count_clear data and removes the time dimension (which in this case is only of size 1)
7. Removes any pixels not observed at least MinimumValidObs times <#valid>__
8. Sets up a for loop for the entered AtLeastThisWet thresholds <#wetnessThreshold>__
9. Masks out any data that does not meet the wetness threshold
10. Converts the data to a Boolean array, with included pixels == 1
11. Converts the raster array to a polygon dataset
12. Cleans up the polygon dataset
13. Resets the geometry to a shapely geometry
14. Merges any overlapping polygons
15. Convert the output of the merging back into a geopandas dataframe
16. Calculates the area of each polygon
17. Saves the results to a shapefile
Within this section you need to set up: - WaterBodiesShp: The name and filepath of the intermediate output polygon set - WOFSshpMerged: The filepath for the location of temp files during the code run - WOFSshpFiltered: The name and filepath of the outputs following the filtering steps - FinalName: The name and file path of the final, completed waterbodies shapefile - years to analyse: for year in range(x,y) - note that the last year is NOT included in the analysis. This for loop is set up to allow you to loop through multiple datasets to create multiple polygon outputs. If you only have one input dataset, set this to range(<year of the analysis>, <year of the analysis + 1>)
[13]:
## Set up some file names for the inputs and outputs
# The name and filepath of the intermediate output polygon set
WaterBodiesShp = f'/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/Temp'
# The name and filepath of the temp, filtered output polygon set
WOFSshpMerged = f'/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/'
WOFSshpFiltered = '/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesFiltered.shp'
# Final shapefile name
FinalName = '/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodies.shp'
[ ]:
# First, test whether the wetness threshold has been correctly set
if len(AtLeastThisWet) == 2:
print(
f'We will be running a hybrid wetness threshold. Please ensure that the major threshold is \n'
f'listed second, with the supplementary threshold entered first.'
f'**You have set {AtLeastThisWet[-1]} as the primary threshold,** \n'
f'**with {AtLeastThisWet[0]} set as the supplementary threshold.**')
elif len(AtLeastThisWet) == 1:
print(
f'You have not set up the hybrid threshold option. If you meant to use this option, please \n'
f'set this option by including two wetness thresholds in the AtLeastThisWet variable above. \n'
f'The wetness threshold we will use is {AtLeastThisWet}.')
else:
raise ValueError(
f'There is something wrong with your entered wetness threshold. Please enter a list \n'
f'of either one or two numbers. You have entered {AtLeastThisWet}. \n'
# Now perform the analysis to generate the first iteration of polygons
for year in range(1980, 1981):
### Get the list of netcdf file names to loop through
if AllOfAustraliaAllTime:
# Grab everything from the published WOfS all time summaries
Alltiles = glob.glob(f'{TileFolder}*.nc')
else:
Alltiles = Generate_list_of_tile_datasets(ListofAlbersTiles, year,
TileFolder, CustomData)
for WOFSfile in Alltiles:
try:
# Note that the netCDF files we are using here contain a variable called 'frequency',
# which is what we are using to define our water polygons.
# If you use a different netCDF input source, you may need to change this variable name here
WOFSnetCDFData = xr.open_rasterio(f'NETCDF:{WOFSfile}:frequency')
# Remove the superfluous time dimension
WOFSnetCDFData = WOFSnetCDFData.squeeze()
# Open the clear count variable to generate the minimum observation mask
# If you use a different netCDF input source, you may need to change this variable name here
WOFSvalidcount = xr.open_rasterio(f'NETCDF:{WOFSfile}:count_clear')
WOFSvalidcount = WOFSvalidcount.squeeze()
# Filter our WOfS classified data layer to remove noise
# Remove any pixels not abserved at least MinimumValidObs times
WOFSValidFiltered = WOFSvalidcount >= MinimumValidObs
for Thresholds in AtLeastThisWet:
# Remove any pixels that are wet < AtLeastThisWet% of the time
WOFSfiltered = WOFSnetCDFData > Thresholds
# Now find pixels that meet both the MinimumValidObs and AtLeastThisWet criteria
# Change all zeros to NaN to create a nan/1 mask layer
# Pixels == 1 now represent our water bodies
WOFSfiltered = WOFSfiltered.where((WOFSfiltered != 0) &
(WOFSValidFiltered != 0))
# Convert the raster to polygons
# We use a mask of '1' to only generate polygons around values of '1' (not NaNs)
WOFSpolygons = rasterio.features.shapes(
WOFSfiltered.data.astype('float32'),
transform=WOFSnetCDFData.transform)
# The rasterio.features.shapes returns a tuple. We only want to keep the geometry portion,
# not the value of each polygon (which here is just 1 for everything)
WOFSbreaktuple = (a for a, b in WOFSpolygons)
# Put our polygons into a geopandas geodataframe
PolygonGP = gp.GeoDataFrame(list(WOFSbreaktuple))
# Grab the geometries and convert into a shapely geometry
# so we can quickly calcuate the area of each polygon
PolygonGP['geometry'] = None
for ix, poly in PolygonGP.iterrows():
poly['geometry'] = shape(poly)
# Set the geometry of the dataframe to be the shapely geometry we just created
PolygonGP = PolygonGP.set_geometry('geometry')
# We need to add the crs back onto the dataframe
PolygonGP.crs = {'init': 'epsg:3577'}
# Combine any overlapping polygons
MergedPolygonsGeoms = unary_union(PolygonGP['geometry'])
# Turn the combined multipolygon back into a geodataframe
MergedPolygonsGPD = gp.GeoDataFrame(
[poly for poly in MergedPolygonsGeoms])
# Rename the geometry column
MergedPolygonsGPD.columns = ['geometry']
# We need to add the crs back onto the dataframe
MergedPolygonsGPD.crs = {'init': 'epsg:3577'}
# Calculate the area of each polygon again now that overlapping polygons
# have been merged
MergedPolygonsGPD['area'] = MergedPolygonsGPD['geometry'].area
# Save the polygons to a shapefile
schema = {
'geometry': 'Polygon',
'properties': {
'area': 'float'
}
}
# Generate our dynamic filename
FileName = f'{WaterBodiesShp}_{Thresholds}.shp'
# Append the file name to the list so we can call it later on
if os.path.isfile(FileName):
with fiona.open(FileName,
"a",
crs=from_epsg(3577),
driver='ESRI Shapefile',
schema=schema) as output:
for ix, poly in MergedPolygonsGPD.iterrows():
output.write(({
'properties': {
'area': poly['area']
},
'geometry': mapping(shape(poly['geometry']))
}))
else:
with fiona.open(FileName,
"w",
crs=from_epsg(3577),
driver='ESRI Shapefile',
schema=schema) as output:
for ix, poly in MergedPolygonsGPD.iterrows():
output.write(({
'properties': {
'area': poly['area']
},
'geometry': mapping(shape(poly['geometry']))
}))
except:
print(
f'{WOFSfile} did not run. \n'
f'This is probably because there are no waterbodies present in this tile.'
)
You have not set up the hybrid threshold option. If you meant to use this option, please
set this option by including two wetness thresholds in the AtLeastThisWet variable above.
The wetness threshold we will use is [0.95].
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_8_-32_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_19_-40_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_14_-31_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_10_-37_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_9_-34_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_20_-39_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_6_-35_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_9_-32_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_7_-36_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_18_-30_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_8_-41_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_14_-28_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_8_-34_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_6_-37_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_14_-33_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
/g/data/fk4/datacube/002/WOfS/WOfS_Stats_25_2_1/netcdf/WOFS_3577_6_-36_summary.nc did not run.
This is probably because there are no waterbodies present in this tile.
## Merge polygons that have an edge at a tile boundary¶
Now that we have all of the polygons across our whole region of interest, we need to check for artifacts in the data caused by tile boundaries.
We have created a shapefile that consists of the albers tile boundaries, plus a 1 pixel (25 m) buffer. This shapefile will help us to find any polygons that have a boundary at the edge of an albers tile. We can then find where polygons touch across this boundary, and join them up.
Within this section you need to set up: - AlbersBuffer: The file location of a shapefile that is a 1 pixel buffer around the Albers tile boundaries
NOTE: for the Australia-wide analysis, the number and size of polygons means that this cell cannot be run in this notebook. Instead, we ran this cell on raijin
#!/bin/bash
#PBS -P r78
#PBS -q hugemem
#PBS -l walltime=96:00:00
#PBS -l mem=500GB
#PBS -l jobfs=200GB
#PBS -l ncpus=7
#PBS -l wd
#PBS -lother=gdata1a
module use /g/data/v10/public/modules/modulefiles/
PYTHONPATH=$PYTHONPATH:/g/data/r78/cek156/dea-notebooks [ ]: AlbersBuffer = gp.read_file('/g/data/r78/cek156/ShapeFiles/AlbersBuffer25m.shp') for Threshold in AtLeastThisWet: print(f'Working on {Threshold} shapefile') # We are using the more severe wetness threshold as the main polygon dataset. # Note that this assumes that the thresholds have been correctly entered into the 'AtLeastThisWet' # variable, with the higher threshold listed second. WaterPolygons = gp.read_file(f'{WaterBodiesShp}_{Threshold}.shp') # Find where the albers polygon overlaps with our dam polygons BoundaryMergedDams, IntersectIndexes, NotBoundaryDams = Filter_shapefile_by_intersection( WaterPolygons, AlbersBuffer, invertMask=False, returnInverse=True) # Now combine overlapping polygons in BoundaryDams UnionBoundaryDams = BoundaryMergedDams.unary_union # Explode the multipolygon back out into individual polygons UnionGDF = gp.GeoDataFrame(crs=WaterPolygons.crs, geometry=[UnionBoundaryDams]) MergedDams = UnionGDF.explode() # Then combine our new merged polygons with the NotBoundaryDams # Combine New merged polygons with the remaining polygons that are not near the tile boundary AllTogether = gp.GeoDataFrame( pd.concat([NotBoundaryDams, MergedDams], ignore_index=True, sort=True)).set_geometry('geometry') # Calculate the area of each polygon AllTogether['area'] = AllTogether.area # Check for nans AllTogether.dropna(inplace=True) schema = {'geometry': 'Polygon', 'properties': {'area': 'float'}} print(f'Writing out {Threshold} shapefile') with fiona.open(f'{WOFSshpMerged}Union_{Threshold}.shp', "w", crs=from_epsg(3577), driver='ESRI Shapefile', schema=schema) as output: for ix, poly in AllTogether.iterrows(): output.write(({ 'properties': { 'area': poly['area'] }, 'geometry': mapping(shape(poly['geometry'])) })) ## Filter the merged polygons by:¶ • Area: Based on the MinSize and MaxSize parameters set here. • Coastline: Using the Coastline dataset loaded here. • CBD location (optional): Using the CBDs dataset loaded here. • Wetness thresholds: Here we apply the hybrid threshold described here • Intersection with rivers (optional): Using the MajorRivers dataset loaded here NOTE: for the Australia-wide analysis, the number and size of polygons means that this cell cannot be run in this notebook. Instead, we ran this cell on raijin #!/bin/bash #PBS -P r78 #PBS -q hugemem #PBS -l walltime=96:00:00 #PBS -l mem=500GB #PBS -l jobfs=200GB #PBS -l ncpus=7 #PBS -l wd #PBS -lother=gdata1a module use /g/data/v10/public/modules/modulefiles/ module load dea PYTHONPATH=$PYTHONPATH:/g/data/r78/cek156/dea-notebooks
[19]:
try:
except IndexError:
AllTogether['area'] = pd.to_numeric(AllTogether.area)
# Filter out any polygons smaller than MinSize, and greater than MaxSize
WaterBodiesBig = AllTogether.loc[((AllTogether['area'] > MinSize) &
(AllTogether['area'] <= MaxSize))]
# Filter out any ocean in the pixel
WaterBodiesLand, IntersectIndexes = Filter_shapefile_by_intersection(
# WOfS has a known bug where deep shadows from high-rise CBD buildings are misclassified
# as water. We will use the ABS sa3 dataset to filter out Brisbane, Gold Coast, Sydney,
# Melbourne, Adelaide and Perth CBDs.
# If you have chosen to set UrbanMask = False, this step will be skipped.
NotCities, IntersectIndexes = Filter_shapefile_by_intersection(
WaterBodiesLand, CBDs)
else:
print(
'You have chosen not to filter out waterbodies within CBDs. If you meant to use this option, please \n'
'set UrbanMask = True variable above, and set the path to your urban filter shapefile'
)
NotCities = WaterBodiesLand
# Check for hybrid wetness thresholds
if len(AtLeastThisWet) == 2:
# Note that this assumes that the thresholds have been correctly entered into the 'AtLeastThisWet'
# variable, with the supplementary threshold listed first.
f'{WOFSshpMerged}Union_{AtLeastThisWet[0]}.shp')
LowerThreshold['area'] = pd.to_numeric(LowerThreshold.area)
# Filter out those pesky huge polygons
LowerThreshold = LowerThreshold.loc[(LowerThreshold['area'] <= MaxSize)]
# Find where the albers polygon overlaps with our dam polygons
BoundaryMergedDams, IntersectIndexes = Filter_shapefile_by_intersection(
LowerThreshold, NotCities)
# Pull out the polygons from the supplementary shapefile that intersect with the primary shapefile
LowerThresholdToUse = LowerThreshold.loc[LowerThreshold.index.isin(
IntersectIndexes)]
# Concat the two polygon sets together
CombinedPolygons = gp.GeoDataFrame(
pd.concat([LowerThresholdToUse, NotCities], ignore_index=True))
# Merge overlapping polygons
CombinedPolygonsUnion = CombinedPolygons.unary_union
# Explode the multipolygon back out into individual polygons
UnionGDF = gp.GeoDataFrame(crs=LowerThreshold.crs,
geometry=[CombinedPolygonsUnion])
HybridDams = UnionGDF.explode()
else:
print(
'You have not set up the hybrid threshold option. If you meant to use this option, please \n'
'set this option by including two wetness thresholds in the AtLeastThisWet variable above'
)
HybridDams = NotCities
# Here is where we do the river filtering (if FilterOutRivers == True)
if FilterOutRivers:
WaterBodiesBigRiverFiltered, IntersectIndexes = Filter_shapefile_by_intersection(
HybridDams, MajorRivers)
else:
# If river filtering is turned off, then we just keep all the same polygons
WaterBodiesBigRiverFiltered = HybridDams
# We need to add the crs back onto the dataframe
WaterBodiesBigRiverFiltered.crs = {'init': 'epsg:3577'}
# Calculate the area and perimeter of each polygon again now that overlapping polygons
# have been merged
WaterBodiesBigRiverFiltered['area'] = WaterBodiesBigRiverFiltered[
'geometry'].area
WaterBodiesBigRiverFiltered['perimeter'] = WaterBodiesBigRiverFiltered[
'geometry'].length
# Calculate the Polsby-Popper value (see below), and write out too
WaterBodiesBigRiverFiltered['PPtest'] = (
(WaterBodiesBigRiverFiltered['area'] * 4 * math.pi) /
(WaterBodiesBigRiverFiltered['perimeter']**2))
# Save the polygons to a shapefile
schema = {
'geometry': 'Polygon',
'properties': {
'area': 'float',
'perimeter': 'float',
'PPtest': 'float'
}
}
with fiona.open(WOFSshpFiltered,
"w",
crs=from_epsg(3577),
driver='ESRI Shapefile',
schema=schema) as output:
for ix, poly in WaterBodiesBigRiverFiltered.iterrows():
output.write(({
'properties': {
'area': poly['area'],
'perimeter': poly['perimeter'],
'PPtest': poly['PPtest']
},
'geometry': mapping(shape(poly['geometry']))
}))
You have not set up the hybrid threshold option. If you meant to use this option, please
set this option by including two wetness thresholds in the AtLeastThisWet variable above
### Dividing up very large polygons¶
The size of polygons is determined by the contiguity of waterbody pixels through the landscape. This can result in very large polygons, e.g. where rivers are wide and unobscured by trees, or where waterbodies are connected to rivers or neighbouring waterbodies. The image below shows this for the Menindee Lakes, NSW. The relatively flat terrain in this part of Australia means that the 0.05 wetness threshold results in the connection of a large stretch of river and the individual lakes into a single large polygon that spans 154 km. This polygon is too large to provide useful insights into the changing water surface area of the Menindee Lakes, and needs to be broken into smaller, more useful polygons.
We do this by applying the Polsby-Popper test (1991). The Polsby-Popper test is an assessment of the ‘compactness’ of a polygon. This method was originally developed to test the shape of congressional and state legislative districts, to prevent gerrymandering.
The Polsby-Popper test examines the ratio between the area of a polygon, and the area of a circle equal to the perimeter of that polygon. The result falls between 0 and 1, with values closer to 1 being assessed as more compact.
\begin{align*} PPtest = \frac{polygon\ area * 4\pi}{polygon\ perimeter^2} \end{align*}
The Menindee Lakes polygon above has a PPtest value $$\approx$$ 0.00.
We selected all polygons with a PPtest value <=0.005. This resulted in a subset of 186 polygons.
The 186 polygons were buffered with a -50 meter (2 pixel) buffer to separate the polygons where they are connected bu two pixels or less. This allows us to split up these very large polygons by using natural thinning points. The resulting negatively buffered polygons was run through the multipart to singlepart tool in QGIS, to give the now separated polygons unique IDs.
These polygons were then buffered with a +50 meter buffer to return the polygons to approximately their original size. These final polygons were used to separate the 186 original polygons identified above.
The process for dividing up the identified very large polygons varied depending on the polygon in question. Where large waterbodies (like the Menindee Lakes) were connected, the buffered polygons were used to determine the cut points in the original polygons. Where additional breaks were required, the Bureau of Meteorology’s Geofabric v 3.0.5 Beta (Suface Hydrology Network) waterbodies dataset was used as an additional source of information for breaking up connected segments.
The buffering method didn’t work on large segments of river, which became a series of disconnected pieces when negatively and positively buffered. Instead, we used a combination of tributaries and man-made features such as bridges and weirs to segment these river sections.
## Final checks and recalculation of attributes¶
[11]:
WaterBodiesBigRiverFiltered = gp.read_file(WOFSshpFiltered)
[12]:
# Recalculate the area and perimeter of each polygon again following the manual checking
# step performed above
WaterBodiesBigRiverFiltered['area'] = WaterBodiesBigRiverFiltered[
'geometry'].area
WaterBodiesBigRiverFiltered['perimeter'] = WaterBodiesBigRiverFiltered[
'geometry'].length
[13]:
# Remove the PPtest column, since we don't really want this as an attribute of the final shapefile
WaterBodiesBigRiverFiltered.drop(labels='PPtest', axis=1, inplace=True)
[14]:
# Reapply the size filtering, just to check that all of the split and filtered waterbodies are
# still in the size range we want
DoubleCheckArea = WaterBodiesBigRiverFiltered.loc[(
(WaterBodiesBigRiverFiltered['area'] > MinSize) &
(WaterBodiesBigRiverFiltered['area'] <= MaxSize))]
### Generate a unique ID for each polygon¶
A unique identifier is required for every polygon to allow it to be referenced. The naming convention for generating unique IDs here is the geohash.
A Geohash is a geocoding system used to generate short unique identifiers based on latitude/longitude coordinates. It is a short combination of letters and numbers, with the length of the string a function of the precision of the location. The methods for generating a geohash are outlined here - yes, the official documentation is a wikipedia article.
Here we use the python package python-geohash to generate a geohash unique identifier for each polygon. We use precision = 9 geohash characters, which represents an on the ground accuracy of <20 metres. This ensures that the precision is high enough to differentiate between waterbodies located next to each other.
[15]:
# We need to convert from Albers coordinates to lat/lon, in order to generate the geohash
GetUniqueID = DoubleCheckArea.to_crs(epsg=4326)
# Generate a geohash for the centroid of each polygon
GetUniqueID['UID'] = GetUniqueID.apply(lambda x: gh.encode(
x.geometry.centroid.y, x.geometry.centroid.x, precision=9),
axis=1)
# Check that our unique ID is in fact unique
assert GetUniqueID['UID'].is_unique
# Make an arbitrary numerical ID for each polygon. We will first sort the dataframe by geohash
# so that polygons close to each other are numbered similarly
SortedData = GetUniqueID.sort_values(by=['UID']).reset_index()
SortedData['WB_ID'] = SortedData.index
[30]:
# The step above creates an 'index' column, which we don't actually want, so drop it.
SortedData.drop(labels='index', axis=1, inplace=True)
### Write out the final results to a shapefile¶
[32]:
BackToAlbers = SortedData.to_crs(epsg=3577)
BackToAlbers.to_file(FinalName, driver='ESRI Shapefile')
## Some extra curation¶
Following the development of timeseries for each individual polygon, it was determined that a number of polygons do not produce complete timeseries.
### Splitting polygons that cross swath boundaries¶
Three large polygons were identified that straddle Landsat swath boundaries. This is problematic, as the whole polygon will never be observed on a single day, which trips the requirement for at least 90% of a polygon to be observed in order for an observation to be valid.
There are two options for dealing with this issue: - Splitting the polygons using the swath boundaries, so that each half of the polygon will be observed in a single day. This will retain information as to the exact timing of observations. - Creating time averaged timeseries, which would group observations into monthly blocks and provide a value for each month. This would provide information for the whole polygon, but would lose the specific timing information.
We chose to go with the first option to keep the high fidelity timing information for each polygon. Three polygons were split using the swath boundaries as a guide. The split polygons were given a new WB_ID, and a new geohash was calculated for each new polygon.
[ ]:
WaterBodiesSplit = gp.read_file(
'/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesSplitEliminate.shp'
)
# We need to convert from Albers coordinates to lat/lon, in order to generate the geohash
GetUniqueID = WaterBodiesSplit.to_crs(epsg=4326)
# Only recalculate the geohash for the polygons that have changed:
ChangedWB_ID = [145126, 66034, 146567, 295902, 295903, 295904, 295905]
for ix, rowz in GetUniqueID.iterrows():
if rowz['WB_ID'] in ChangedWB_ID:
# Generate a geohash for the centroid of each polygon
GetUniqueID.loc[ix, 'WB_ID'] = gh.encode(
GetUniqueID.iloc[ix].geometry.centroid.y,
GetUniqueID.iloc[ix].geometry.centroid.x,
precision=9)
print('Changing geohash')
# Check that our unique ID is in fact unique
assert GetUniqueID['UID'].is_unique
### Save the final version of the polygons!¶
[ ]:
BackToAlbers = GetUniqueID.to_crs(epsg=3577)
BackToAlbers.to_file(
'/g/data/r78/cek156/dea-notebooks/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesFINAL.shp',
driver='ESRI Shapefile')
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github. | 2020-04-07T13:08:45 | {"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": 1, "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": 0.19252826273441315, "perplexity": 3301.1483610672376}, "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-2020-16/segments/1585371799447.70/warc/CC-MAIN-20200407121105-20200407151605-00114.warc.gz"} |
https://par.nsf.gov/biblio/10362955-intrinsic-structure-sagittarius-cm-mm | The Intrinsic Structure of Sagittarius A* at 1.3 cm and 7 mm
Abstract
Sagittarius A* (Sgr A*), the Galactic Center supermassive black hole (SMBH), is one of the best targets in which to resolve the innermost region of an SMBH with very long baseline interferometry (VLBI). In this study, we have carried out observations toward Sgr A* at 1.349 cm (22.223 GHz) and 6.950 mm (43.135 GHz) with the East Asian VLBI Network, as a part of the multiwavelength campaign of the Event Horizon Telescope (EHT) in 2017 April. To mitigate scattering effects, the physically motivated scattering kernel model from Psaltis et al. (2018) and the scattering parameters from Johnson et al. (2018) have been applied. As a result, a single, symmetric Gaussian model well describes the intrinsic structure of Sgr A* at both wavelengths. From closure amplitudes, the major-axis sizes are ∼704 ± 102μas (axial ratio ∼$1.19−0.19+0.24$) and ∼300 ± 25μas (axial ratio ∼1.28 ± 0.2) at 1.349 cm and 6.95 mm, respectively. Together with a quasi-simultaneous observation at 3.5 mm (86 GHz) by Issaoun et al. (2019), we show that the intrinsic size scales with observing wavelength as a power law, with an index ∼1.2 ± 0.2. Our results also provide estimates of the size and compact more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10362955
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
2
Page Range or eLocation-ID:
Article No. 108
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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https://phys.libretexts.org?title=TextBooks_%26_TextMaps/University_Physics_TextMaps/Map:_University_Physics_(OpenStax)/Map:_University_Physics_II_-_Thermodynamics,_Electricity,_and_Magnetism_(OpenStax)/13:_Electromagnetic_Induction/13.S:_Electromagnetic_Induction_(Summary) | $$\require{cancel}$$
# 13.S: Electromagnetic Induction (Summary)
## Key Terms
back emf emf generated by a running motor, because it consists of a coil turning in a magnetic field; it opposes the voltage powering the motor eddy current current loop in a conductor caused by motional emf electric generator device for converting mechanical work into electric energy; it induces an emf by rotating a coil in a magnetic field Faraday’s law induced emf is created in a closed loop due to a change in magnetic flux through the loop induced electric field created based on the changing magnetic flux with time induced emf short-lived voltage generated by a conductor or coil moving in a magnetic field Lenz’s law direction of an induced emf opposes the change in magnetic flux that produced it; this is the negative sign in Faraday’s law magnetic damping drag produced by eddy currents magnetic flux measurement of the amount of magnetic field lines through a given area motionally induced emf voltage produced by the movement of a conducting wire in a magnetic field peak emf maximum emf produced by a generator
## Key Equations
Magnetic flux $$\displaystyle Φ_m=∫_S\vec{B}⋅\hat{n}dA$$ Faraday’s law $$\displaystyle ε=−N\frac{dΦ_m}{dt}$$ Motionally induced emf $$\displaystyle ε=Blv$$ Motional emf around a circuit $$\displaystyle ε=∮\vec{E}⋅d\vec{l}=−\frac{dΦ_m}{dt}$$ Emf produced by an electric generator $$\displaystyle ε=NBAωsin(ωt)$$
## Summary
• The magnetic flux through an enclosed area is defined as the amount of field lines cutting through a surface area A defined by the unit area vector.
• The units for magnetic flux are webers, where $$\displaystyle 1Wb=1T⋅m^2$$.
• The induced emf in a closed loop due to a change in magnetic flux through the loop is known as Faraday’s law. If there is no change in magnetic flux, no induced emf is created.
#### 13.2 Lenz's Law
• We can use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs.
• The direction of an induced emf always opposes the change in magnetic flux that causes the emf, a result known as Lenz’s law.
#### 13.3 Motional Emf
• The relationship between an induced emf εε in a wire moving at a constant speed through a magnetic field B is given by $$\displaystyle ε=Blv$$.
• An induced emf from Faraday’s law is created from a motional emf that opposes the change in flux.
#### 13.4 Induced Electric Fields
• A changing magnetic flux induces an electric field.
• Both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday’s law.
#### 13.5 Eddy Currents
• Current loops induced in moving conductors are called eddy currents. They can create significant drag, called magnetic damping.
• Manipulation of eddy currents has resulted in applications such as metal detectors, braking in trains or roller coasters, and induction cooktops.
#### 13.6 Electric Generators and Back Emf
• An electric generator rotates a coil in a magnetic field, inducing an emf given as a function of time by $$\displaystyle ε=NBAωsin(ωt)$$ where A is the area of an N-turn coil rotated at a constant angular velocity $$\displaystyle ω$$ in a uniform magnetic field $$\displaystyle \vec{B}$$.
• The peak emf of a generator is $$\displaystyle ε_0=NBAω$$.
• Any rotating coil produces an induced emf. In motors, this is called back emf because it opposes the emf input to the motor.
#### 13.7 Applications of Electromagnetic Induction
• Hard drives utilize magnetic induction to read/write information.
• Other applications of magnetic induction can be found in graphics tablets, electric and hybrid vehicles, and in transcranial magnetic stimulation.
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2018-05-25T09:02:56 | {"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": 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": 0.6678239107131958, "perplexity": 754.6589587218768}, "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-2018-22/segments/1526794867055.20/warc/CC-MAIN-20180525082822-20180525102822-00196.warc.gz"} |
http://pdglive.lbl.gov/Reviews.action;jsessionid=65F9C9CD1E0ADC426E762577BBEAB6FD?section=BXXX000 | # Baryons Reviews
Baryon Decay Parameters ${{\mathit N}}$ and ${{\mathit \Delta}}$ Resonances (rev.) Pentaquarks (new) Baryon Magnetic Moments Pole Structure of the ${{\mathit \Lambda}{(1405)}}$ Region (new) ${{\mathit \Lambda}}$ and ${{\mathit \Sigma}}$ Resonances The ${{\mathit \Sigma}{(1670)}}$ Region Radiative Hyperon Decays ${{\mathit \Xi}}$ Resonances Charmed Baryons | 2017-05-30T05:21:09 | {"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": 0.9844805002212524, "perplexity": 14417.535919451031}, "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-2017-22/segments/1495463613796.37/warc/CC-MAIN-20170530051312-20170530071312-00394.warc.gz"} |
https://www.khronos.org/registry/vulkan/specs/1.3-extensions/man/html/VkSwapchainCreateFlagBitsKHR.html | ## C Specification
Bits which can be set in VkSwapchainCreateInfoKHR::flags, specifying parameters of swapchain creation, are:
// Provided by VK_KHR_swapchain
typedef enum VkSwapchainCreateFlagBitsKHR {
// Provided by VK_VERSION_1_1 with VK_KHR_swapchain, VK_KHR_device_group with VK_KHR_swapchain
VK_SWAPCHAIN_CREATE_SPLIT_INSTANCE_BIND_REGIONS_BIT_KHR = 0x00000001,
// Provided by VK_VERSION_1_1 with VK_KHR_swapchain
VK_SWAPCHAIN_CREATE_PROTECTED_BIT_KHR = 0x00000002,
// Provided by VK_KHR_swapchain_mutable_format
VK_SWAPCHAIN_CREATE_MUTABLE_FORMAT_BIT_KHR = 0x00000004,
} VkSwapchainCreateFlagBitsKHR;
## Description
• VK_SWAPCHAIN_CREATE_SPLIT_INSTANCE_BIND_REGIONS_BIT_KHR specifies that images created from the swapchain (i.e. with the swapchain member of VkImageSwapchainCreateInfoKHR set to this swapchain’s handle) must use VK_IMAGE_CREATE_SPLIT_INSTANCE_BIND_REGIONS_BIT.
• VK_SWAPCHAIN_CREATE_PROTECTED_BIT_KHR specifies that images created from the swapchain are protected images.
• VK_SWAPCHAIN_CREATE_MUTABLE_FORMAT_BIT_KHR specifies that the images of the swapchain can be used to create a VkImageView with a different format than what the swapchain was created with. The list of allowed image view formats is specified by adding a VkImageFormatListCreateInfo structure to the pNext chain of VkSwapchainCreateInfoKHR. In addition, this flag also specifies that the swapchain can be created with usage flags that are not supported for the format the swapchain is created with but are supported for at least one of the allowed image view formats.
## Document Notes
For more information, see the Vulkan Specification
This page is extracted from the Vulkan Specification. Fixes and changes should be made to the Specification, not directly.
Copyright 2014-2022 The Khronos Group Inc.
SPDX-License-Identifier: CC-BY-4.0 | 2022-05-18T18:36:29 | {"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": 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": 0.250805139541626, "perplexity": 8719.339677731406}, "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-2022-21/segments/1652662522309.14/warc/CC-MAIN-20220518183254-20220518213254-00175.warc.gz"} |
http://mathonline.wikidot.com/the-limit-superior-and-limit-inferior-of-functions-of-real-n | The Limit Superior and Limit Inferior of Functions of Real Numbers
# The Limit Superior and Limit Inferior of Functions of Real Numbers
Recall from The Limit Superior and Limit Inferior of Sequences of Real Numbers that if $(a_n)_{n=1}^{\infty}$ is a sequence of real numbers then we defined:
(1)
\begin{align} \quad \limsup_{n \to \infty} a_n = \lim_{n \to \infty} \sup_{k \geq n} \{ a_k \} = \inf_{n \geq 1} \left \{ \sup_{k \geq n} \{ a_k \} \right \} \end{align}
(2)
\begin{align} \quad \liminf_{n \to \infty} a_n = \lim_{n \to \infty} \inf_{k \geq n} \{ a_k \} = \sup_{n \geq 1} \left \{ \inf_{k \geq n} \{ a_k \} \right \} \end{align}
We now define the limit superior and limit inferior as $x \to \infty$ for a function $f : (a, \infty) \to \mathbb{R}$ where $a \in \mathbb{R}$:
Definition: Let $f : (a, \infty) \to \mathbb{R}$. The Limit Superior as $x \to \infty$ of $f$ is defined as $\displaystyle{\limsup_{x \to \infty} f(x) = \lim_{x \to \infty} \sup_{t \geq x} \{ f(t) \} = \inf_{x \geq a} \left \{ \sup_{t \geq x} \{ f(t) \} \right \}}$. The Limit Inferior as $x \to \infty$ of $f$ is defined as $\displaystyle{\liminf_{x \to \infty} f(x) = \lim_{x \to \infty} \inf_{t \geq x} \{ f(t) \} = \inf_{x \geq a} \left \{ \sup_{t \geq x} \{ f(t) \} \right \} }$.
We can similarly define the limit superior and limit inferior as $x \to -\infty$ for a function $f : (-\infty, b) \to \mathbb{R}$ where $b \in \mathbb{R}$:
Definition: Let $f : (-\infty, b) \to \mathbb{R}$. The Limit Superior as $x \to -\infty$ of $f$ is defined as $\displaystyle{\limsup_{x \to -\infty} f(x) = \lim_{x \to -\infty} \sup_{t \leq x} \{ f(t) \} = \inf_{x \leq b} \left \{ \sup_{t \leq x} \{ f(t) \} \right \}}$. The Limit Inferior as $x \to \infty$ of $f$ is defined as $\displaystyle{\liminf_{x \to -\infty} f(x) = \lim_{x \to -\infty} \inf_{t \leq x} \{ f(t) \} = \inf_{x \leq b} \left \{ \sup_{t \leq x} \{ f(t) \} \right \} }$.
We now prove some fundamental results regarding the limit superior and limit inferior as $x \to \infty$ of a function a function $f : (a, \infty) \to \mathbb{R}$. Analogous results can be proven for the limit superior and limit inferior as $x \to -\infty$ of a function $f : (-\infty, b) \to \mathbb{R}$.
Theorem 1: Let $f : (a, \infty) \to \mathbb{R}$ where $a \in \mathbb{R}$. Then $\displaystyle{\lim_{x \to \infty} f(x) = L}$ if and only if $\displaystyle{\limsup_{x \to \infty} f(x) = L = \liminf_{x \to \infty} f(x)}$.
• Proof: $\Rightarrow$ Suppose that $\displaystyle{\lim_{x \to \infty} f(x) = L}$. Then for all $\epsilon > 0$ there exists an $M \in \mathbb{R}$, $M \geq a$ such that if $x \geq M$ then $\: f(x) - L \: < \epsilon$. So if $x \geq M$ then:
(3)
\begin{align} \quad L - \epsilon < f(x) < L + \epsilon \end{align}
• So for $x \geq M$ we have that $L + \epsilon$ is an upper bound for $f$ and $L - \epsilon$ is a lower bound for $f$. Thus for $x \geq M$ we have that:
(4)
\begin{align} \quad L - \epsilon \leq \inf_{t \geq x} \{ f(t) \} \leq \sup_{t \geq x} \{ f(t) \} \leq L + \epsilon \quad \Leftrightarrow \quad \biggr \lvert \inf_{t \geq x} \{ f(t) \} - L \biggr \rvert < \epsilon \quad , \quad \biggr \lvert \sup_{x \geq t} \{ f(t) \} - L \biggr \rvert < \epsilon \end{align}
• Hence $\displaystyle{\liminf_{x \to \infty} f(x) = \lim_{x \to \infty} \inf_{t \geq x} \{ f(t) \} = L}$ and $\displaystyle{\limsup_{x \to \infty} f(x) = \lim_{x \to \infty} \sup_{t \geq x} \{ f(t) \} = L}$. $\blacksquare$
• $\Leftarrow$ Suppose that $\displaystyle{\limsup_{x \to \infty} f(x) = L = \liminf_{x \to \infty} f(x)}$. Let $\epsilon > 0$ be given.
• Since $\displaystyle{\limsup_{x \to \infty} f(x) = L}$ we have that there exists an $M_1 \in \mathbb{R}$, $M_1 \geq a$ such that if $x \geq M_1$ then:
(5)
\begin{align} \quad \biggr \lvert \sup_{t \geq x} \{ f(t) \} - L \biggr \rvert < \epsilon \quad \Leftrightarrow \quad L -\epsilon < \sup_{t \geq x} \{ f(t) \} < L + \epsilon \quad (*) \end{align}
• Also, since $\displaystyle{\liminf_{x \to \infty} f(x) = L}$ we have that there exists an $M_2 \in \mathbb{R}$, $M_2 \geq a$ such that if $x \geq M_2$ then:
(6)
\begin{align} \quad \biggr \lvert \inf_{t \geq x} \{ f(t) \} - L \biggr \rvert < \epsilon \quad \Leftrightarrow \quad L - \epsilon < \inf_{t \geq x} \{ f(t) \} < L + \epsilon \quad (**) \end{align}
• Let $M = \max \{ M_1, M_2 \}$. Clearly $M \geq a$ since $M_1, M_2 \geq a$. Then if $x \geq M$ we have that $(*)$ and $(**)$ hold so:
(7)
\begin{align} \quad L - \epsilon \leq \inf_{t \geq x} \{ f(t) \} \leq f(x) \leq \sup_{t \geq x} \{ f(t) \} \leq L + \epsilon \quad \Leftrightarrow \quad \biggr \lvert f(x) - L \biggr \rvert < \epsilon \end{align}
• Hence $\displaystyle{\lim_{x \to \infty} f(x) = L}$. $\blacksquare$
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2020-04-10T10:37:50 | {"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": 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": 7, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000033378601074, "perplexity": 227.6875573750011}, "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-2020-16/segments/1585371893683.94/warc/CC-MAIN-20200410075105-20200410105605-00155.warc.gz"} |
https://dakota.sandia.gov/sites/default/files/docs/6.17.0-release/user-html/usingdakota/theory/epistemic.html | # Epistemic Methods
This chapter covers theoretical aspects of methods for propagating epistemic uncertainty.
## Dempster-Shafer theory of evidence (DSTE)
In Dempster-Shafer theory, the event space is defined by a triple $$(\mathcal{S},\mathbb{S},m)$$ which defines $$\mathcal{S}$$ the universal set, $$\mathbb{S}$$ a countable collection of subsets of $$\mathcal{S}$$, and a notional measure $$m$$. $$\mathcal{S}$$ and $$\mathbb{S}$$ have a similar meaning to that in classical probability theory; the main difference is that $$\mathbb{S}$$, also known as the focal elements, does not have to be a $$\sigma$$-algebra over $$\mathcal{S}$$. The operator $$m$$ is defined to be
(149)\begin{split}\begin{aligned} m(\mathcal{U}) = \left\{ \begin{array}{rr} > 0 & \mathrm{if} \ \mathcal{U} \in \mathbb{S}\\ 0 & \mathrm{if} \ \mathcal{U} \subset \mathcal{S} \ \mathrm{and} \ \mathcal{U} \notin \mathbb{S} \end{array} \right.\end{aligned}\end{split}
(150)\begin{aligned} \displaystyle\sum_{\mathcal{U} \in \mathbb{S}} m(\mathcal{U}) = 1\end{aligned}
where $$m(\mathcal{U})$$ is known as the basic probability assignment (BPA) of the set $$\mathcal{U}$$. In the DSTE framework, belief and plausibility are defined as:
(151)$\mathrm{Bel}(\mathcal{E}) = \displaystyle\sum_{\{ \mathcal{U} \ | \ \mathcal{U} \subset \mathcal{E}, \ \mathcal{U} \in \mathbb{S}\}} m(\mathcal{U})$
(152)$\mathrm{Pl}(\mathcal{E}) = \displaystyle\sum_{\{ \mathcal{U} \ | \ \mathcal{U} \cap \mathcal{E} \neq \emptyset, \ \mathcal{U} \in \mathbb{S}\}} m(\mathcal{U})$
The belief Bel($$\mathcal{E}$$) is interpreted to be the minimum likelihood that is associated with the event $$\mathcal{E}$$. Similarly, the plausibility Pl($$\mathcal{E}$$) is the maximum amount of likelihood that could be associated with $$\mathcal{E}$$. This particular structure allows us to handle unconventional inputs, such as conflicting pieces of evidence (e.g. dissenting expert opinions), that would be otherwise discarded in an interval analysis or probabilistic framework. The ability to make use of this information results in a commensurately more informed output.
The procedure to compute belief structures involves four major steps:
1. Determine the set of $$d$$-dimensional hypercubes that have a nonzero evidential measure
2. Compute the composite evidential measure (BPA) of each hypercube
3. Propagate each hypercube through the model and obtain the response bounds within each hypercube
4. Aggregate the minimum and maximum values of the response per hypercube with the BPAs to obtain cumulative belief and plausibility functions on the response (e.g. calculate a belief structure on the response).
The first step involves identifying combinations of focal elements defined on the inputs that define a hypercube. The second step involves defining an aggregate BPA for that hypercube, which is the product of the BPAs of the individual focal elements defining the hypercube. The third step involves finding the maximum and minimum values of the response value in each hypercube, and this part can be very computationally expensive. Finally, the results over all hypercubes are aggregated to form belief structures on the response. | 2023-04-02T06:11:29 | {"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": 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": 0.9224497675895691, "perplexity": 984.1483644668042}, "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/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00470.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M049M&home=sumtabM | # ${{\boldsymbol \Upsilon}{(1S)}}$ MASS INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 9460.30 \pm0.26}$ OUR AVERAGE Error includes scale factor of 3.3.
$9460.51$ $\pm0.09$ $\pm0.05$ 1
2000
MD1 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$9459.97$ $\pm0.11$ $\pm0.07$
1984
REDE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
• • • We do not use the following data for averages, fits, limits, etc. • • •
$9460.60$ $\pm0.09$ $\pm0.05$ 2, 3
1992 B
REDE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$9460.59$ $\pm0.12$
1986
REDE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$9460.6$ $\pm0.4$ 4, 3
1984
REDE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
1 Reanalysis of BARU 1992B and ARTAMONOV 1984 using new electron mass (COHEN 1987 ).
2 Superseding BARU 1986 .
3 Superseded by ARTAMONOV 2000 .
4 Value includes data of ARTAMONOV 1982 .
References:
ARTAMONOV 2000
PL B474 427 High Precision Mass Measurements in ${{\mathit \psi}}$ and ${{\mathit \Upsilon}}$ Families Revisited
BARU 1992B
ZPHY C56 547 Determination of the ${{\mathit \Upsilon}{(1S)}}$ Leptonic Width
BARU 1986
ZPHY C30 551 New Measurement of the ${{\mathit \Upsilon}}$ Meson Mass
ARTAMONOV 1984
PL 137B 272 A High Precision Measurement of the ${{\mathit \Upsilon}}$, ${{\mathit \Upsilon}^{\,'}}$ and ${{\mathit \Upsilon}^{"}}$ Meson Masses
MACKAY 1984
PR D29 2483 Measurement of the ${{\mathit \Upsilon}}$ Mass | 2020-09-19T12:08:19 | {"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": 0.5510709881782532, "perplexity": 14508.688778880158}, "config": {"markdown_headings": true, "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-2020-40/segments/1600400191780.21/warc/CC-MAIN-20200919110805-20200919140805-00091.warc.gz"} |
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/5d19f75416b51c016e81a02f | Since Buddha’s teaching are also about universal truths of Selflessness and kindness, perhaps it will help students inculcate some of these values.
License:[Source CIET,NCERT ]July 1, 2019, 5:38 p.m. | 2020-10-26T18:56:44 | {"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": 0.9132259488105774, "perplexity": 13271.638150938727}, "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-2020-45/segments/1603107891624.95/warc/CC-MAIN-20201026175019-20201026205019-00342.warc.gz"} |
http://dlmf.nist.gov/20.15 | # §20.15 Tables
Theta functions are tabulated in Jahnke and Emde (1945, p. 45). This reference gives $\mathop{\theta_{j}\/}\nolimits\!\left(x,q\right)$, $j=1,2,3,4$, and their logarithmic $x$-derivatives to 4D for $x/\pi=0(.1)1$, $\alpha=0(9^{\circ})90^{\circ}$, where $\alpha$ is the modular angle given by
20.15.1 $\mathop{\sin\/}\nolimits\alpha={\mathop{\theta_{2}\/}\nolimits^{2}}\!\left(0,q% \right)/{\mathop{\theta_{3}\/}\nolimits^{2}}\!\left(0,q\right)=k.$ Defines: $\alpha$: modular angle (locally) Symbols: $\mathop{\theta_{\NVar{j}}\/}\nolimits\!\left(\NVar{z},\NVar{q}\right)$: theta function, $\mathop{\sin\/}\nolimits\NVar{z}$: sine function and $q$: nome Referenced by: §20.15, §20.15 Permalink: http://dlmf.nist.gov/20.15.E1 Encodings: TeX, pMML, png See also: Annotations for 20.15
Spenceley and Spenceley (1947) tabulates $\mathop{\theta_{1}\/}\nolimits\!\left(x,q\right)/\mathop{\theta_{2}\/}% \nolimits\!\left(0,q\right)$, $\mathop{\theta_{2}\/}\nolimits\!\left(x,q\right)/\mathop{\theta_{2}\/}% \nolimits\!\left(0,q\right)$, $\mathop{\theta_{3}\/}\nolimits\!\left(x,q\right)/\mathop{\theta_{4}\/}% \nolimits\!\left(0,q\right)$, $\mathop{\theta_{4}\/}\nolimits\!\left(x,q\right)/\mathop{\theta_{4}\/}% \nolimits\!\left(0,q\right)$ to 12D for $u=0(1^{\circ})90^{\circ}$, $\alpha=0(1^{\circ})89^{\circ}$, where $u=2x/(\pi{\mathop{\theta_{3}\/}\nolimits^{2}}\!\left(0,q\right))$ and $\alpha$ is defined by (20.15.1), together with the corresponding values of $\mathop{\theta_{2}\/}\nolimits\!\left(0,q\right)$ and $\mathop{\theta_{4}\/}\nolimits\!\left(0,q\right)$.
Lawden (1989, pp. 270–279) tabulates $\mathop{\theta_{j}\/}\nolimits\!\left(x,q\right)$, $j=1,2,3,4$, to 5D for $x=0(1^{\circ})90^{\circ}$, $q=0.1(.1)0.9$, and also $q$ to 5D for $k^{2}=0(.01)1$.
Tables of Neville’s theta functions $\mathop{\theta_{s}\/}\nolimits\!\left(x,q\right)$, $\mathop{\theta_{c}\/}\nolimits\!\left(x,q\right)$, $\mathop{\theta_{d}\/}\nolimits\!\left(x,q\right)$, $\mathop{\theta_{n}\/}\nolimits\!\left(x,q\right)$ (see §20.1) and their logarithmic $x$-derivatives are given in Abramowitz and Stegun (1964, pp. 582–585) to 9D for $\varepsilon,\alpha=0(5^{\circ})90^{\circ}$, where (in radian measure) $\varepsilon=x/{\mathop{\theta_{3}\/}\nolimits^{2}}\!\left(0,q\right)=\pi x/(2% \!\mathop{K\/}\nolimits\!\left(k\right))$, and $\alpha$ is defined by (20.15.1).
For other tables prior to 1961 see Fletcher et al. (1962, pp. 508–514) and Lebedev and Fedorova (1960, pp. 227–230). | 2017-05-26T05:29:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 35, "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": 0.9874045848846436, "perplexity": 2750.2098332146893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2017-22/segments/1495463608642.30/warc/CC-MAIN-20170526051657-20170526071657-00477.warc.gz"} |
https://par.nsf.gov/biblio/10126576-sami-galaxy-survey-first-detection-transition-spin-orientation-respect-cosmic-filaments-stellar-kinematics-galaxies | The SAMI Galaxy Survey: first detection of a transition in spin orientation with respect to cosmic filaments in the stellar kinematics of galaxies
ABSTRACT
We present the first detection of mass-dependent galactic spin alignments with local cosmic filaments with >2σ confidence using IFS kinematics. The 3D network of cosmic filaments is reconstructed on Mpc scales across GAlaxy and Mass Assembly fields using the cosmic web extractor DisPerSe. We assign field galaxies from the SAMI survey to their nearest filament segment in 3D and estimate the degree of alignment between SAMI galaxies’ kinematic spin axis and their nearest filament in projection. Low-mass galaxies align their spin with their nearest filament while higher mass counterparts are more likely to display an orthogonal orientation. The stellar transition mass from the first trend to the second is bracketed between $10^{10.4}$ and $10^{10.9}\, \mathrm{ M}_{\odot }$, with hints of an increase with filament scale. Consistent signals are found in the Horizon-AGN cosmological hydrodynamic simulation. This supports a scenario of early angular momentum build-up in vorticity rich quadrants around filaments at low stellar mass followed by progressive flip of spins orthogonal to the cosmic filaments through mergers at high stellar mass. Conversely, we show that dark matter only simulations post-processed with a semi-analytical model treatment of galaxy formation struggles to reproduce this alignment signal. This suggests that gas physics more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10126576
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
491
Issue:
2
Page Range or eLocation-ID:
p. 2864-2884
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
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1. ABSTRACT
We study the alignments of galaxy spin axes with respect to cosmic web filaments as a function of various properties of the galaxies and their constituent bulges and discs. We exploit the SAMI Galaxy Survey to identify 3D spin axes from spatially resolved stellar kinematics and to decompose the galaxy into the kinematic bulge and disc components. The GAMA survey is used to reconstruct the cosmic filaments. The mass of the bulge, defined as the product of stellar mass and bulge-to-total flux ratio Mbulge = M⋆ × (B/T), is the primary parameter of correlation with spin–filament alignments: galaxies with lower bulge masses tend to have their spins parallel to the closest filament, while galaxies with higher bulge masses are more perpendicularly aligned. M⋆ and B/T separately show correlations, but they do not fully unravel spin–filament alignments. Other galaxy properties, such as visual morphology, stellar age, star formation activity, kinematic parameters, and local environment, are secondary tracers. Focussing on S0 galaxies, we find preferentially perpendicular alignments, with the signal dominated by high-mass S0 galaxies. Studying bulge and disc spin–filament alignments separately reveals additional information about the formation pathways of the corresponding galaxies: bulges tend to have more perpendicular alignments, while discs showmore »
2. ABSTRACT
We select a volume-limited sample of galaxies derived from the SDSS DR7 to study the environment of low surface brightness (LSB) galaxies at different scales, as well as several physical properties of the dark matter haloes where the LSB galaxies of the sample are embedded. To characterize the environment, we make use of a number of publicly available value-added galaxy catalogues. We find a slight preference for LSB galaxies to be found in filaments instead of clusters, with their mean distance to the nearest filament typically larger than for high surface brightness (HSB) galaxies. The fraction of isolated central LSB galaxies is higher than the same fraction for HSB ones, and the density of their local environment lower. The stellar-to-halo mass ratio using four different estimates is up to ∼20 per cent for HSB galaxies. LSB central galaxies present more recent assembly times when compared with their HSB counterparts. Regarding the λ spin parameter, using six different proxies for its estimation, we find that LSB galaxies present systematically larger values of λ than the HSB galaxy sample, and constructing a control sample with direct kinematic information drawn from ALFALFA, we confirm that the spin parameter of LSB galaxies is 1.6–2 times largermore »
3. ABSTRACT
Using data from the SAMI Galaxy Survey, we investigate the correlation between the projected stellar kinematic spin vector of 1397 SAMI galaxies and the line-of-sight motion of their neighbouring galaxies. We calculate the luminosity-weighted mean velocity difference between SAMI galaxies and their neighbours in the direction perpendicular to the SAMI galaxies’ angular momentum axes. The luminosity-weighted mean velocity offset between SAMI galaxies and neighbours, which indicates the signal of coherence between the rotation of the SAMI galaxies and the motion of neighbours, is 9.0 ± 5.4 km s−1 (1.7σ) for neighbours within 1 Mpc. In a large-scale analysis, we find that the average velocity offsets increase for neighbours out to 2 Mpc. However, the velocities are consistent with zero or negative for neighbours outside 3 Mpc. The negative signals for neighbours at a distance around 10 Mpc are also significant at the ∼2σ level, which indicate that the positive signals within 2 Mpc might come from the variance of large-scale structure. We also calculate average velocities of different subsamples, including galaxies in different regions of the sky, galaxies with different stellar masses, galaxy type, λRe, and inclination. Although subsamples of low-mass, high-mass, early-type, and low-spin galaxies show the 2–3σ signal of coherencemore »
4. ABSTRACT
Most dynamical models of galaxies to date assume axisymmetry, which is not representative of a significant fraction of massive galaxies. We have built triaxial orbit-superposition Schwarzschild models of galaxies observed by the SAMI Galaxy Survey, in order to reconstruct their inner orbital structure and mass distribution. The sample consists of 153 passive galaxies with total stellar masses in the range 109.5 to $10^{12} \, {\rm M}_{\odot }$. We present an analysis of the internal structures and intrinsic properties of these galaxies as a function of their environment. We measure their environment using three proxies: central or satellite designation, halo mass and local 5th nearest neighbour galaxy density. We find that although these intrinsic properties correlate most strongly with stellar mass, environment does play a secondary role: at fixed stellar mass, galaxies in the densest regions are more radially anisotropic. In addition, central galaxies, and galaxies in high local densities show lower values of edge-on spin parameter proxy λRe, EO. We also find suggestions of a possible trend of the fractions of orbits with environment for lower mass galaxies (between 109.5 and $10^{11} \, {\rm M}_{\odot }$) such that, at fixed stellar mass, galaxies in higher local densities and halomore »
5. It is now well established that galaxies have different morphologies, gas contents, and star formation rates (SFR) in dense environments like galaxy clusters. The impact of environmental density extends to several virial radii, and galaxies appear to be pre-processed in filaments and groups before falling into the cluster. Our goal is to quantify this pre-processing in terms of gas content and SFR, as a function of density in cosmic filaments. We have observed the two first CO transitions in 163 galaxies with the IRAM-30 m telescope, and added 82 more measurements from the literature, thus forming a sample of 245 galaxies in the filaments around the Virgo cluster. We gathered HI-21cm measurements from the literature and observed 69 galaxies with the Nançay telescope to complete our sample. We compare our filament galaxies with comparable samples from the Virgo cluster and with the isolated galaxies of the AMIGA sample. We find a clear progression from field galaxies to filament and cluster galaxies for decreasing SFR, increasing fraction of galaxies in the quenching phase, an increasing proportion of early-type galaxies, and decreasing gas content. Galaxies in the quenching phase, defined as having a SFR below one-third of that of the main sequencemore » | 2023-04-01T02:23:04 | {"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": 0.7117884755134583, "perplexity": 2992.762669732078}, "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/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00427.warc.gz"} |
https://mooseframework.inl.gov/modules/level_set/example_rotate.html | # Rotating Circle
The second example is a typical benchmark problem for the level set equation: a rotating bubble. The problem involves initializing (see Theory) with a "bubble" of radius 0.15 at for . This bubble is then advected with the given velocity field , so that, at , the bubble should return to its original position.
## Level Set Equation
Figure 1 show the results of solving the rotating bubble problem with the level set equation alone, which initially behaves in a consistent manner. However, near the end of the simulation node-to-node oscillations appear in the solution, which is evident in the contour lines shown in Figure 1. As expected, these oscillations influence the area of the region encapsulated by the 0.5 level set contour as shown in Figure 4 and discussed in the Area Comparison section.
The complete input file for running this portion of the example is included below and it may be executed as follows.
cd ~/projects/moose/module/level_set/examples/rotating_circle
../../level_set-opt -i rotating_circle.i
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 32
ny = 32
uniform_refine = 2
[]
[AuxVariables]
[./vel_x]
[../]
[./vel_y]
[../]
[]
[AuxKernels]
[./vel_x]
type = FunctionAux
function = 4*y
variable = vel_x
execute_on = initial
[../]
[./vel_y]
type = FunctionAux
function = -4*x
variable = vel_y
execute_on = initial
[../]
[]
[Variables]
[./phi]
[../]
[]
[Functions]
[./phi_exact]
type = LevelSetOlssonBubble
epsilon = 0.03
center = '0 0.5 0'
[../]
[]
[ICs]
[./phi_ic]
type = FunctionIC
function = phi_exact
variable = phi
[../]
[]
[Kernels]
[./time]
type = TimeDerivative
variable = phi
[../]
velocity_x = vel_x
velocity_y = vel_y
variable = phi
[../]
[]
[Postprocessors]
[./area]
type = LevelSetVolume
threshold = 0.5
variable = phi
location = outside
execute_on = 'initial timestep_end'
[../]
[./cfl]
type = LevelSetCFLCondition
velocity_x = vel_x
velocity_y = vel_y
execute_on = 'initial' #timestep_end'
[../]
[]
[Executioner]
type = Transient
solve_type = PJFNK
start_time = 0
end_time = 1.570796
scheme = crank-nicolson
petsc_options_iname = '-pc_type -pc_sub_type'
petsc_options_value = 'asm ilu'
[./TimeStepper]
type = PostprocessorDT
postprocessor = cfl
scale = 0.8
[../]
[]
[Outputs]
csv = true
exodus = true
[]
(modules/level_set/examples/rotating_circle/circle_rotate.i)
## Level Set Equation with SUPG
Adding SUPG stabilization—set the theory for details—mitigates the oscillations present in the first step, as shown in Figure 2. Adding the SUPG stabilization is trivial simply add the time and advection SUPG kernels to the input file (circle_rotate_supg.i) shown previously, the kernels block will then appear as:
[AuxKernels]
[./vel_x]
type = FunctionAux
function = 4*y
variable = vel_x
execute_on = initial
[../]
[./vel_y]
type = FunctionAux
function = -4*x
variable = vel_y
execute_on = initial
[../]
[]
(modules/level_set/examples/rotating_circle/circle_rotate_supg.i)
Adding the stabilization improve the numerical solution but it suffers from a loss of conservation of the phase field variable, as discussed in the Area Comparison section and shown in Figure 4.
## Level Set Equation with Reinitialization
Adding reinitializtion, in this case the scheme proposed by Olsson et al. (2007), requires the use of the MOOSE MultiApp. The enable reinitialization two input files are required: a master and sub-application.
The master input file must add the necessary MultiApps and Transfers blocks. For the problem at hand (circle_rotate_master.i) this easily accomplished by adding the following to the input file from the first step (i.e., do not include the SUPG kernels).
[MultiApps]
[./reinit]
type = LevelSetReinitializationMultiApp
input_files = 'circle_rotate_sub.i'
execute_on = 'timestep_end'
[../]
[]
[Transfers]
[./to_sub]
type = MultiAppCopyTransfer
source_variable = phi
variable = phi
direction = to_multiapp
multi_app = reinit
execute_on = 'timestep_end'
[../]
[./to_sub_init]
type = MultiAppCopyTransfer
source_variable = phi
variable = phi_0
direction = to_multiapp
multi_app = reinit
execute_on = 'timestep_end'
[../]
[./from_sub]
type = MultiAppCopyTransfer
source_variable = phi
variable = phi
direction = from_multiapp
multi_app = reinit
execute_on = 'timestep_end'
[../]
[]
(modules/level_set/examples/rotating_circle/circle_rotate_master.i)
Next, the sub-application input file must be created, which is shown below. This input file mimics the master input file closely, with three notable exceptions. First, the Kernels block utilize the time derivative and a new object, LevelSetOlssonReinitialization, that implements the reinitialization scheme of Olsson et al. (2007). Second, the Problem is set to use the LevelSetReinitializationProblem. Finally, the UserObjects block includes a terminator, LevelSetOlssonTerminator, which is responsible for stopping the reinitialization solve when steady-state is achieved according to the criteria defined by Olsson et al. (2007).
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 32
ny = 32
uniform_refine = 2
[]
[Variables]
[./phi]
[../]
[]
[AuxVariables]
[./phi_0]
[../]
[./marker]
[../]
[]
[Kernels]
[./time]
type = TimeDerivative
variable = phi
[../]
[./reinit]
type = LevelSetOlssonReinitialization
variable = phi
phi_0 = phi_0
epsilon = 0.03
[../]
[]
[Problem]
type = LevelSetReinitializationProblem
[]
[UserObjects]
[./arnold]
type = LevelSetOlssonTerminator
tol = 1
min_steps = 3
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
start_time = 0
num_steps = 100
nl_abs_tol = 1e-14
scheme = crank-nicolson
line_search = none
petsc_options_iname = '-pc_type -pc_sub_type'
petsc_options_value = 'asm ilu'
dt = 0.003
[]
[Outputs]
[]
(modules/level_set/examples/rotating_circle/circle_rotate_sub.i)
Figure 3 shows the results of the bubble problem with reinitialization, the result looks similar to the SUPG result. However, if you consider the area conservation discussed in the Area Comparison section, the reinitialization scheme yields the superior solution for this problem.
Figure 1: Results from solving the rotating circle problem with the level set equation alone.
Figure 2: Results from solving the rotating circle problem with the level set equation using SUPG stabilization.
Figure 3: Results from solving the rotating circle problem with the level set equation with reinitialization.
## Area Comparison
Figure 4 is a plot of the area of the circle during the three simulations. Note that in the unstabilized, un-reinitialized level set equation, both area conservation and stability issues are readily apparent. The instabilities are especially obvious in Figure 4, where the drastic area changes are due to numerical oscillations in the solution field. Adding SUPG stabilization helps ameliorate the stability concern but it suffers from loss of area conservation. The re-initialization scheme is both stable and area-conserving.
Figure 4: Comparison of area inside the bubble during simulations.
The re-initialization methods performs well, but it is computationally expensive and picking the pseudo timestep size , steady-state criteria , and interface thickness correctly for the re-initialization problem is a non-trivial difficulty. Nevertheless, the level set module provides a valuable starting point and proof-of-concept for other researchers interested in the method, and the existing algorithm can no doubt be tuned to the needs of specific applications in terms of conservation and computational cost requirements.
## References
1. Elin Olsson, Gunilla Kreiss, and Sara Zahedi. A conservative level set method for two phase flow ii. Journal of Computational Physics, 225(1):785–807, 2007. URL: http://dx.doi.org/10.1016/j.jcp.2006.12.027.[BibTeX] | 2019-05-23T14:55:47 | {"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": 0.6750518679618835, "perplexity": 3220.4298347924805}, "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-2019-22/segments/1558232257259.71/warc/CC-MAIN-20190523143923-20190523165923-00450.warc.gz"} |
https://studenttheses.uu.nl/handle/20.500.12932/1275?show=full | dc.rights.license CC-BY-NC-ND dc.contributor.advisor Behrends, T. dc.contributor.author Kuppevelt, H.N. van dc.date.accessioned 2021-09-08T18:01:03Z dc.date.available 2021-09-08T18:01:03Z dc.date.issued 2021 dc.identifier.uri https://studenttheses.uu.nl/handle/20.500.12932/1275 dc.description.abstract Ecological damage by phosphate (P) pollution in aquatic environments is a growing problem. Legacy P released from sediments impedes the restoration of water quality of freshwater systems even with no external influx of P. The internal P loading causes prolonged eutrophication which in turn causes anoxia and very harmful for aquatic organisms. Internal P loading can persist for a very long time, so for restoration purposes it is necessary to mitigate internal loading effectively. A promising method is the fixation of P in the sediment with iron (Fe) compounds. In this study, we investigate the ditch system in Bovenlanden, a wet peat meadow in the Western peat area in the Netherlands. In two ditches of the system, iron-containing by-products from drinking water treatment, predominately consisting of iron (oxy)hydroxides, have been added six months before in order to mitigate internal P loading. Here, we evaluate the effect of Fe treatment on the P and Fe dynamics and composition of the sediment, and on the benthic fluxes of P and Fe. We used a sequential extraction procedure to identify iron speciation in the sediment and examine P associated with Fe phases. Benthic fluxes were monitored under laboratory conditions in sediment cores from treated and non-treated ditches in the area, under both oxic and anoxic conditions. We found Fe concentrations up to an order of magnitude larger in the treated sediment compared to untreated sediment. The Fe in the treated sediment was mainly extracted by HCl. Most P was extracted by HCl as well, in both treated and untreated cores. Coinciding with elevated solid Fe content, Fe concentrations in the porewater of the treated cores were high, ranging from 30uM up to 350 uM. In contrast, P concentrations were lowered significantly (< 5 $\mu$M) at depth intervals with high Fe contents, compared to the high P concentrations in the non-treated cores (5-100 uM). The difference in dissolved P and Fe in the porewater was reflected by the benthic flux results, where P fluxes have decreased an order of magnitude as result of Fe treatment. This shows that within the timescale of this study, the treatment of peaty ditches with Fe-containing by-products is an effective way to suppress internal P loading. dc.description.sponsorship Utrecht University dc.format.extent 30459293 dc.format.mimetype application/pdf dc.language.iso en dc.title Addition of iron (oxy)hydroxides to ditches in a peat meadow reduces the internal phosphorus loading dc.type.content Master Thesis dc.rights.accessrights Open Access dc.subject.keywords Phosphorous; Water quality; Eutrophication; Internal P loading; Nutrient cycling; Benthic flux; Sequential extractions; dc.subject.courseuu Earth Structure and Dynamics
| 2022-12-04T01:40:36 | {"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": 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": 0.4501343071460724, "perplexity": 10704.483333218643}, "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/1669446710953.78/warc/CC-MAIN-20221204004054-20221204034054-00031.warc.gz"} |
http://dlmf.nist.gov/5.21 | # §5.21 Methods of Computation
An effective way of computing $\mathop{\Gamma\/}\nolimits\!\left(z\right)$ in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3). Or we can use forward recurrence, with an initial value obtained e.g. from (5.7.3). For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3).
Similarly for $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(z\right)$, $\mathop{\psi\/}\nolimits\!\left(z\right)$, and the polygamma functions.
Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. See Schmelzer and Trefethen (2007).
For a comprehensive survey see van der Laan and Temme (1984, Chapter III). See also Borwein and Zucker (1992).
For the computation of the $q$-gamma and $q$-beta functions see Gabutti and Allasia (2008). | 2017-01-20T20:06:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 5, "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": 0.9145532846450806, "perplexity": 1316.801168165064}, "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-2017-04/segments/1484560280872.69/warc/CC-MAIN-20170116095120-00077-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10343940-observation-exotic-narrow-doubly-charmed-tetraquark | This content will become publicly available on July 1, 2023
Observation of an exotic narrow doubly charmed tetraquark
Abstract Conventional, hadronic matter consists of baryons and mesons made of three quarks and a quark–antiquark pair, respectively 1,2 . Here, we report the observation of a hadronic state containing four quarks in the Large Hadron Collider beauty experiment. This so-called tetraquark contains two charm quarks, a $$\overline{{{{{u}}}}}$$ u ¯ and a $$\overline{{{{{d}}}}}$$ d ¯ quark. This exotic state has a mass of approximately 3,875 MeV and manifests as a narrow peak in the mass spectrum of D 0 D 0 π + mesons just below the D *+ D 0 mass threshold. The near-threshold mass together with the narrow width reveals the resonance nature of the state.
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; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
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Publication Date:
NSF-PAR ID:
10343940
Journal Name:
Nature Physics
Volume:
18
Issue:
7
Page Range or eLocation-ID:
751 to 754
ISSN:
1745-2473
2. A bstract The p T -differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity ( | y | < 0 . 5) in proton-proton collisions at $$\sqrt{s}$$ s = 5 . 02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19 . 3 ± 0 . 4) nb − 1 . D mesons were reconstructed from their decays D 0 → K − π + , D + → K − π + π + , and $${\mathrm{D}}_{\mathrm{s}}^{+}\tomore » 3. A bstract The production of prompt D 0 , D + , and D *+ mesons was measured at midrapidity (| y | < 0.5) in Pb–Pb collisions at the centre-of-mass energy per nucleon–nucleon pair$$ \sqrt{s_{\mathrm{NN}}} $$s NN = 5 . 02 TeV with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decay channels and their production yields were measured in central (0–10%) and semicentral (30–50%) collisions. The measurement was performed up to a transverse momentum ( p T ) of 36 or 50 GeV/c depending on the D meson species andmore » 4. Abstract Mesons comprising a beauty quark and strange quark can oscillate between particle ($${B}_{\mathrm{s}}^{0}$$B s 0 ) and antiparticle ($${\overline{B}}_{\mathrm{s}}^{0}$$B ¯ s 0 ) flavour eigenstates, with a frequency given by the mass difference between heavy and light mass eigenstates, Δ m s . Here we present a measurement of Δ m s using$${B}_{\mathrm{s}}^{0}\to {D}_{\mathrm{s}}^{-}$$B s 0 → D s − π + decays produced in proton–proton collisions collected with the LHCb detector at the Large Hadron Collider. The oscillation frequency is found to be Δ m s = 17.7683 ± 0.0051 ± 0.0032 ps −1 , where the firstmore » 5. A bstract The inclusive J/ ψ elliptic ( v 2 ) and triangular ( v 3 ) flow coefficients measured at forward rapidity (2 . 5 < y < 4) and the v 2 measured at midrapidity (| y | < 0 . 9) in Pb-Pb collisions at$$ \sqrt{s_{\mathrm{NN}}} s NN = 5 . 02 TeV using the ALICE detector at the LHC are reported. The entire Pb-Pb data sample collected during Run 2 is employed, amounting to an integrated luminosity of 750 μ b − 1 at forward rapidity and 93 μ b − 1 at midrapidity.more » | 2022-09-26T13:04:09 | {"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": 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": 0.9189313650131226, "perplexity": 2818.918030524587}, "config": {"markdown_headings": false, "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/1664030334871.54/warc/CC-MAIN-20220926113251-20220926143251-00269.warc.gz"} |
https://www.federalreserve.gov/pubs/feds/2013/201343/index.html | Finance and Economics Discussion Series: 2013-43 Screen Reader version
Sequential Monte Carlo Sampling for DSGE Models
Abstract:
We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples-an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohé and Uribe's (2012) news shock model-we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely-used random-walk Metropolis-Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters (2007) model improves its marginal data density and that a slight modification of the prior for the news shock model leads to important changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.
JEL CLASSIFICATION: C11, C15, E10
KEY WORDS: Bayesian analysis, DSGE models, monte carlo methods, parallel computing
1 Introduction
Bayesian methods are now widely used to estimate dynamic stochastic general equilibrium (DSGE) models. Bayesian methods combine the likelihood function of a DSGE model with a prior distribution for its parameters to form a posterior distribution that can then be used for inference and decision making. Because it is infeasible to compute moments of the posterior distribution analytically, simulation methods must be used to characterize the posterior. Starting with Schorfheide (2000) and Otrok (2001), the random walk Metropolis-Hastings (RWMH) algorithm - an iterative simulation technique belonging to the class of algorithms known as Markov chain Monte Carlo (MCMC) algorithms - has been the workhorse simulator for DSGE models. Herbst (2011) reports that 95% of papers published from 2005 to 2010 in eight top economics journals use the RWMH algorithm to implement Bayesian estimation of DSGE models.
While the complexity of DSGE models has increased over time, the efficacy of the RWMH algorithm has declined. It is well documented, e.g., Chib and Ramamurthy (2010) and Herbst (2011), that the sequences of DSGE model parameter draws generated by the RWMH algorithm can be very slow to converge to the posterior distribution. This problem is not limited to DSGE model applications; it is important for many areas of applied Bayesian research. Parameter draws may exhibit high serial correlation such that averages of these draws converge very slowly to moments of posterior distributions, or the algorithm may get stuck near local mode and fail to explore the posterior distribution in its entirety (see, for instance, Neal (2003)).
In this paper, we explore an alternative class of algorithms, namely, so-called sequential Monte Carlo (SMC) algorithms, to generate draws from posterior distributions associated with DSGE models. SMC techniques are typically used for solving intractable integration problems (such as filtering nonlinear state space systems); however, they can be used to estimate static model parameters - a point raised by Chopin (2002). The SMC method employed here amounts to recursively constructing importance samplers for a sequence of distributions that begin at an easy-to-sample initial distribution and end at the posterior, supplemented by a series of intermediate "bridge" distributions. The draws from these distributions are called particles and each particle is associated with an importance weight. The particles that represent bridge distribution are "mutated" into particles for bridge distribution using the Metropolis-Hastings (MH) algorithm.
The contributions of this paper are threefold. First, we tailor a generic SMC algorithm to make it suitable for the analysis of a large-scale DSGE model. More specifically, building on insights from the application of RWMH algorithms to DSGE models, we use random blocking of parameters as well as mixture proposal distributions during the MH mutation step of the algorithm. Without these modifications, the algorithm failed to explore the posterior surface of large-scale DSGE models. We also made the proposal distribution adaptive, that is, its mean and covariance matrix in iteration is a function of the particles generated in iteration . Second, we present a strong law of large numbers (SLLN) and a central limit theorem (CLT) for the specific version of our algorithm. In particular, we show that, under some regularity conditions, the adaptive determination of the proposal distribution in the mutation step of our algorithm does not affect the limit distribution of the SMC approximation of posterior moments.
Third, we provide two empirical illustrations involving large-scale DSGE models, namely the widely used Smets and Wouters (2007) model (hereafter SW model) and a DSGE model with anticipated (news) shocks developed by Schmitt-Grohe and Uribe (2012) (hereafter SGU model). We find that the SMC algorithm is more stable than the RWMH algorithm if applied repeatedly to generate draws from the same posterior distribution, providing a better approximation of multimodal posterior distributions, in particular. We estimate the SW model under the prior used by Smets and Wouters (2007) as well as a more diffuse prior. While the fit of the model, measured by the marginal data density, substantially improves under the diffuse prior, the posterior surface becomes multimodal and the standard RWMH algorithm does a poor job in capturing this multimodality. We also introduce a small modification to the prior distribution used by SGU to estimate their news shock model and find that conclusions about the importance of news shocks for business cycles can change dramatically. While SGU report that anticipated shocks explain about 70% of the variance of hours worked, under our slightly modified prior the posterior distribution becomes bimodal and most of the posterior probability concentrates near the mode that implies that the contribution of anticipated shocks to hours is only 30%. The RWMH algorithm is unable to characterize this multimodal posterior reliably.
We build on several strands of the existing literature. There exists an extensive body of work in the statistical literature on applying SMC methods to posterior inference for static model parameters as in Chopin (2002). Textbook treatments can be found in Cappe and Moulines, and Ryden (2005) and Liu (2008) and a recent survey is provided by Creal (2012). The theoretical analysis in our paper builds heavily on Chopin (2004), by modifying his proofs to suit our particular version of the SMC algorithm. So far as we know, ours is the second paper that uses SMC to implement Bayesian inference in DSGE models. Creal (2007) presents a basic algorithm, which he applies to the small-scale DSGE model of Rabanal and Rubio-Ramirez (2005). While we used his algorithm as a starting point, the application to large-scale DSGE models required substantial modifications including the more elaborate adaptive mutation step described above as well as a different sequence of bridge distributions. Moreover, our implementation exploits parallel computation to substantially speed up the algorithm, which is necessary for the practical implementation of this algorithm on modern DSGE models.
In complementary research,Durham and Geweke (2012) use an SMC algorithm to estimate an EGARCH model as well as several other small-scale reduced-form time series models. They employ a graphical processing unit (GPU) to implement an SMC algorithm using the predictive likelihood distribution as the bridge distribution. For our applications, the use of GPUs appeared impractical because the solution and likelihood evaluation of DSGE models involves high-dimensional matrix operations that are not readily available in current GPU programming languages. Durham and Geweke (2012) also propose an adaptive tuning scheme for the sequence of the bridge distributions and the proposal distributions used in the particle mutation step. They suggest determining the tuning parameters in a preliminary run of the SMC algorithm to ensure that the adaptive tuning scheme does not invalidate the CLT for the SMC approximation. Our theoretical analysis suggests that this is unnecessary, provided that the tuning scheme satisfies certain regularity conditions. The authors propose a version of the SMC algorithm that divides particles into groups and carries out independent computations for each group. The variation across groups provides a measure of numerical accuracy. By running the SMC multiple times, we employ an evaluation scheme in our paper that is similar in spirit to theirs.
Other authors have explored alternatives to the version of the RWMH algorithm that has become standard in DSGE model applications. Several papers that have tried to improve upon the RWMH, including Chib and Ramamurthy (2010), Curdia and Reis (2010), Kohn, Giordani, and Strid (2010), and Herbst (2011). These papers propose alternative MCMC algorithms that improve upon the standard single-block RWMH algorithm by grouping parameters into blocks and cycling over conditional posterior distributions (the so-called Metropolis-within-Gibbs algorithm) and by changing the proposal distribution that is used to generate proposed draws in the Metropolis steps. Each of these algorithms, however, is an MCMC technique and remains to some extent susceptible to the above criticism of highly correlated draws.
On the computational front, multiple processor and core environments are becoming more readily available. While likelihood evaluation routines and MCMC algorithms can be written to take advantage of this,1 neither is "embarrassingly parallelizable," that is, neither naturally exploits the parallel computing framework. This computational challenge might bias researchers to simulate too few draws in their MCMC chains, exacerbating the statistical problem discussed above. SMC algorithms, on the other hand, can easily take advantage of a parallel processing environment. In the extreme case, each draw (or particle) from the initial distribution can be assigned to a separate processor and then converted into a sequence of draws from the "bridge" distributions. While, some communication between the processors is necessary to normalize the particle weights and to potentially eliminate particle degeneracy by a re-sampling step, but the most time-consuming task-namely the evaluation of the likelihood function-can be executed in parallel.
The remainder of this paper is organized as follows. In Section 2, we review some basic insights underlying SMC methods. The SMC algorithm tailored to DSGE model applications is presented in Section 3 and its theoretical properties are studied in Section 4. Section 5 contains three numerical illustrations, one pertaining to a stylized state space model, to motivate estimation problems inherent to DSGE models, and two based on DSGE model posteriors obtained from actual U.S. data. Section 6 concludes. The proofs for Section 4 and a detailed description of the DSGE models estimated in Section 5 as well as additional empirical results are relegated to the Online Appendix.
2 Sequential Monte Carlo Methods
Let denote the likelihood function and the prior density. The object of interest is the posterior density given by
(1)
The parameter vector has support . To economize on notation, we abbreviate this density by . Moreover, we denote the numerator in (1) by and the denominator by , which does not depend on . Using this more compact notation
(2)
While for linearized DSGE models with Gaussian innovations and a regular prior density the function can be evaluated to machine accuracy without the use of simulation approximations, the normalization constant is unknown and closed-form expressions for posterior moments under are unavailable. Thus, posterior expectations of and transformations have to be approximated numerically with Monte Carlo (MC) simulation methods. Most of the Bayesian DSGE literature applies Markov chain Monte Carlo (MCMC) techniques. As we will argue later, the increasing complexity of DSGE models combined with the emerging parallel framework for scientific computing makes MCMC less attractive for sampling. Instead, sequential Monte Carlo (SMC) methods, we will argue, are an appealing alternative simulation technique. We describe the basics of SMC below. More elaborate explications can be found in Chopin (2002), De Moral, Doucet, and Jasra (2006), and Creal (2012).
One of the important steps in all SMC algorithms involves importance sampling: we might try to approximate using a different, tractable density that is easy to sample from. Importance sampling is based on the identity
(3)
Suppose that , . Then, under suitable regularity conditions, see Geweke (1989), the Monte Carlo estimate
(4)
converges almost surely (a.s.) to as . The set of pairs provides a particle approximation of . The 's are the (normalized) importance weights assigned to each particle value . The accuracy of the approximation is driven by the "closeness" of to and is reflected in the distribution of the weights. If the distribution of weights is very uneven, the Monte Carlo approximation is inaccurate. Uniform weights arise if , which means that we are sampling directly from .
Importance sampling was first used for posterior inference in DSGE models by DeJong, Ingram, and Whiteman (2000). However, in practice, it is extremely difficult to find densities that lead to efficient importance samplers. This task is particularly challenging if the posterior has a non-normal shape, containing several peaks and valleys. The essence of the SMC methods employed in this paper is to construct sequential particle approximations to intermediate distributions, indexed by :2
(5)
where and . Note that for . Since priors in DSGE models are typically specified such that draws can either be generated by direct sampling or with an efficient acceptance sampler, the initialization of the SMC algorithm is straightforward. Thus, provided it is possible to use the approximation of to assist in the construction of a particle approximation for , one can use iterative approximations to estimate . A function (here the likelihood) raised to a power less than one is called a tempered function. The process of estimating the parameters of a function through a sequence of tempered functions is known as simulated tempering. This estimation framework has a long history in statistics; see Liu (2008) and the references therein. It is common to refer to the sequence of tempering parameters as the tempering schedule (or heating schedule, due to its connection to simulated annealing.)
3 An SMC Algorithm for DSGE Models
We begin with the description of the basic algorithm in Section 3.1. This algorithm consists of three steps, using Chopin (2004)'s terminology: correction, that is, reweighting the particles to reflect the density in iteration ; selection, that is, eliminating any particle degeneracy by resampling the particles; and mutation, that is, propagating the particles forward using a Markov transition kernel to adapt to the current bridge density. Section 3.2 provides details on the choice of the transition kernel in the mutation step, and the adaptive choice of various tuning parameters is discussed in Section 3.3. Finally, we provide a summary of the key aspects of our algorithm in Section 3.4.
3.1 The Basic Algorithm
To avoid confusion as to whether is drawn from or , we equip the parameter vector with a subscript . Thus, is associated with the density .
Algorithm 1 (Simulated Tempering SMC)
1. Initialization. (). Draw the initial particles from the prior:
2. Recursion. For ,
1. Correction. Reweight the particles from stage by defining the incremental and normalized weights
An approximation of is given by
(6)
2. Selection. Compute the effective sample size .
Case (i): If , resample the particles via multinomial resampling. Let denote draws from a multinomial distribution characterized by support points and weights and set . Case (ii): If , let and , . An approximation of is given by
(7)
3. Mutation. Propagate the particles via steps of a MH algorithm with transition density and stationary distribution (see Algorithm 2 for details below). An approximation of is given by
(8)
3. For ( the final importance sampling approximation of is given by:
(9)
Our basic SMC algorithm requires tuning in two dimensions. First, the user has to specify the number of particles . Under suitable regularity conditions discussed in Section 4, the SMC approximations of posterior moments satisfy a CLT, which implies that the precision (i.e. inverse variance) of the approximation increases in proportion to . Second, the user has to determine the tempering schedule . All other things equal, increasing the number of stages of the tempering schedule, , will decrease the distance between bridge distributions and thus make it easier to maintain particle weights that are close to being uniform. The cost of increasing is that each stage requires additional likelihood evaluations. To control the shape of the tempering schedule, we introduce a parameter :
A large value of implies that the bridge distributions will be very similar (and close to the prior) for small values of and very different at a later stage when is large. In the DSGE model applications, we found a value of to be very useful, because for smaller values the information from the likelihood function will dominate the priors too quickly and only a few particles will survive the correction and selection steps. Conversely, if is much larger than 2, it makes some of the bridge distributions essentially redundant and leads to unnecessary computations. The choice of does not affect the overall number of likelihood evaluations.
Algorithm 1 is initialized by generating draws from the prior distribution. This initialization will work well as long as the prior is sufficiently diffuse to assign non-trivial probability mass to the area of the parameter space in which the likelihood function peaks.3 If the particles are initialized based on a more general distribution with density , then for the incremental weights have to be corrected by the ratio . In the selection step, the resampling is only executed if the effective sample size , which is a function of the variance of the particle weights, falls below some threshold. We discuss the rationale for this threshold rule in more detail in Section 4.
3.2 The Transition Kernel for the Mutation Step
The transition kernel is generated through a sequence of Metropolis-Hastings steps. It is indexed by a vector of tuning parameters . The transition kernel is constructed such that for each the posterior is an invariant distribution. The MH steps are summarized in the following algorithm. Let denote a particular set of values for the parameter vector and be a covariance matrix that is conformable with the parameter vector . In Section 3.3 we will replace and by estimates of and .
Algorithm 2 (Particle Mutation) In Step 2(c) at iteration of Algorithm 1:
1. Randomly partition4 the parameter vector into equally sized blocks, denoted by , . Moreover, let and be the partitions of and that correspond to the subvector .
2. For each particle , run steps of the following MH algorithm. For to :
For to :
1. Let be the parameter value for in the -th iteration (initialization for : ) and let .
2. Generate a proposal draw from the mixture distribution
and denote the density of the proposal distribution by .
3. Define the acceptance probability
and let
3. Let for .
The particle-mutation algorithm uses several insights from the application of RWMH algorithms to DSGE models. First, Chib and Ramamurthy (2010) have documented that in DSGE model applications, blocking of parameters can dramatically reduce the persistence in Markov chains generated by the MH algorithm. determines the number of partitions of the parameter vector. For simple models with elliptical posteriors, blocking the parameter vector is unnecessary. When the posterior becomes complex or the dimensionality of the parameter vector is large, however, moving all the parameters in a single block precludes all but the smallest moves, which could hamper the mutation step. Second, Kohn, Giordani, and Strid (2010) have proposed an adaptive MH algorithm for DSGE model posteriors in which the proposal density is a mixture of a random-walk proposal, an independence proposal, and a -copula estimated from previous draws of the chain. Adopting this general idea, our proposal density in Step 2(a) of Algorithm 2 is also a mixture. The first component corresponds to a random-walk proposal with non-diagonal covariance matrix, the second component is a random-walk proposal with diagonal covariance matrix, and the third component is an independence proposal density.
The tuning parameter controls the weight of the mixture components. The parameter scales the covariance matrices of the proposal densities.5 The number of MH steps affects the probability that the particle mutation step is successful in the sense that . In practice, the effect of increasing turned out to be similar to the effect of raising and thereby reducing the distance between bridge distributions. In the applications in Section 5, we set .
3.3 Adaption of the Transition Kernel
To achieve a good performance of the SMC algorithm, it is important to choose some of the tuning parameters adaptively, that is, tuning parameters for iteration are chosen based on the particles generated in iteration . We collect the adaptively chosen parameters in the vector :
(11)
In the implementation of the mutation algorithm we fix the remaining tuning parameters, which are , , and . We also fix the tuning parameters , , and for Algorithm 1 ex ante. We use importance sampling approximations of and to specify and and we adjust the scaling factor to ensure that the acceptance rate in the MH step is approximately 25%, along the lines of Durham and Geweke (2012). At each iteration , we replace in (11) with
(12)
where is measurable with respect to the -algebra generated by the particles .6 The following algorithm describes how is constructed at each iteration .
Algorithm 3 (Adaptive Particle Mutation) Prior to Step 1 of Algorithm 2:
1. Compute importance sampling approximations and of and based on the particles .
2. Compute the average empirical rejection rates , based on the Mutation step in iteration . The averages are computed across the blocks and across the three mixture components separately.
3. Adjust the scaling factor according to
where is given by
4. Execute Algorithm 2 by replacing with .
Note that , which means that the scaling factor stays constant whenever the target acceptance rate is achieved. If the acceptance rate is below (above) 25% the scaling factor is decreased (increased). To satisfy the regularity conditions for the theoretical analysis in Section 4, we chose a function that is differentiable.
3.4 Further Discussion
Our implementation of the SMC algorithm differs from that in Creal (2007) in two important dimensions. First, our mutation step is more elaborate. The mixture proposal distribution proved to be important for adapting the algorithm to large-scale DSGE models with complicated multimodal posterior surfaces. The random blocking scheme is important for avoiding bad blocks as the correlation structure of the tempered posterior changes. Moreover, the introduction of the tempering parameter, , is crucial. Creal (2007) uses a linear cooling schedule (i.e., ). Even for a large number of stages () at , the information contained in dominates the information contained in the prior. This means that initializing the algorithm from the prior is impractical, as sample impoverishment occurs immediately. In light of this, Creal (2007) initializes the simulator from a student- distribution centered at the posterior mode. The initialization presumes prior knowledge of the mode(s) of the posterior and is not well suited in applications where there are many modes or the posterior is severely non-elliptical. Instead, by using a , we are able to add information from the likelihood to the prior slowly. This allows us to initialize the algorithm from the prior, working without presupposition about the shape of the posterior. Collectively, these additional tuning parameters yield a degree of flexibility that is crucial for the implementation of SMC algorithms on large-scale DSGE models.
Second, our implementation exploits parallel computing to substantially speed up the algorithm. The potential for parallelisation is a key advantage of SMC over MCMC routines. In Algorithm 2, step 2 involves MH steps. Here, the principal computational bottleneck is the evaluation of the likelihood itself.7 The total number of likelihood evaluations in the SMC algorithm is equal to . For some of the examples considered in this paper, that number can be in the tens of millions. In our experience, the standard number of draws in an MCMC estimation of a DSGE model is rarely more than one million. So it would appear that the SMC algorithm would take a prohibitively long time to run. With SMC methods, however, one can exploit the fact that the likelihood evaluations in Step 2 of Algorithm 2 can be executed independently for each of the particles. Given access to a multiple processor8 environment, this feature is very useful. Because multiple core/processor setups are quite common, parallelization can be achieved easily in many programming languages, e.g., via the MATLAB command parfor, even on a single machine.
In our implementation, we use multiple machines (distributed memory) communicating via a Message Passing Interface (MPI). To get a sense of gains from parallelization, let be the running time of an algorithm using processors. The relative speedup is given by . For example, for the standard SW model in Section 5.2, , which means that using 24 processors speeds up the algorithm by a factor of 15. A back-of-the-envelope calculation suggests that, for the specific model and computational setup used here, about 97% of the SMC algorithm's time is spent in Step 2 of Algorithm 2. This means that parallelization is extremely efficient.9
4 Theoretical Properties
We proceed with a formal analysis of Algorithm 1 and provide some regularity conditions under which the SMC approximations satisfy a SLLN and CLT. The main results are summarized in four theorems. The first three theorems establish a SLLN/CLT for the correction, selection, and mutation steps of Algorithm 1. The fourth theorem shows that the adaptive choice of the transition kernel discussed in Section 3.3 does not, under some regularity conditions, affect the asymptotic variance of the SMC approximation. The first three theorems (and their proofs) essentially correspond to Lemmas A.1, A.2, and A.3 in Chopin (2004). We make three modifications: (i) while our proofs closely follow the proofs in Chopin (2004), we use our specific assumptions about the prior and likelihood function; (ii) our algorithm executes the three steps in a different order; and (iii) we resample only if ESS falls below the threshold , which requires an adjustment in some of the asymptotic variance formulas. Although the first three theorems are not new, we think that it is worthwhile to reproduce them, because the asymptotic variance formulas provide valuable insights for practitioners into the behavior of the algorithm. To the best of our knowledge, the fourth theorem is new. It states that the adaptive choice of has no effect on the limit distribution of the SMC approximation. This asymptotic variance, of course, depends on , which we define to be the probability limit of in (12). Detailed proofs of the four theorems are provided in the Online Appendix. We begin with some assumptions on the prior and the likelihood function:10
Assumption 1 Suppose that (i) the prior is proper: ; (ii) the likelihood function is uniformly bounded: ; and (iii) .
For the analysis of a DSGE model, the restriction to proper prior distributions does not pose a real constraint on the researcher. In fact, most priors used in the literature are fairly informative and many parameters have a bounded domain. We also assume that the likelihood function is bounded from above and that there exists a set of parameters with non-zero measure under the prior distribution for which the likelihood function is strictly positive, meaning that the marginal tempered data density is positive at the observed data. Throughout this section, we will assume that the object of interest is the posterior mean of the scalar function . Extensions to vector-valued functions are straightforward. The convergence of the sequential Monte Carlo approximations requires the existence of moments. We define the classes of functions and as
and our convergence results will apply to functions in these two classes. Assumption 1 implies that for functions in posterior moments exist for all values of the tempering parameter .11
We follow Chopin (2004) and state the convergence results in an inductive manner, starting from the following assumption:
Assumption 2
(i)
for every .
(ii)
for every .
It is straightforward to verify that Assumption 2 is satisfied for . Recall that . According to Step 1 of Algorithm 1, the particles are obtained using an sample from the prior distribution. Thus, for and , the moment conditions for the SLLN and the CLT for random variables are satisfied and . To present the subsequent results, it is convenient to normalize the incremental weights as follows. Let
such that . Theorem 1 summarizes the convergence results for the Monte Carlo approximations obtained after the correction step:
Theorem 1 [Correction Step] Suppose that Assumptions 1 and 2 are satisfied. Then, defined in (6) converges as follows: (i) for every ; (ii) , where , for every .
The asymptotic variance has the familiar form of the variance of an importance sampling approximation where the s correspond to the importance sampling weights. As discussed, for instance, in Liu (2008), a crude approximation of is given by , which provides a rationale for monitoring (see the selection step of Algorithm 1).12 However, does not directly measure the overall asymptotic variance of the SMC approximation. For the subsequent selection step, we distinguish between the case in which the particles are resampled, i.e. , and the case in which the resampling is skipped.
Theorem 2 [Selection Step] Suppose that Assumptions 1 and 2 are satisfied. Then, defined in (7) converges as follows: (i) for every ; (ii) for every . Case (a): if the particles are resampled, then . Case (b): if the particles not are resampled, then .
A comparison of in cases (a) and (b) highlights that the resampling adds noise to the Monte Carlo approximation. However, it also equalizes the particle weights and thereby reduces the variance in the correction step of iteration . The rule of resampling whenever tries to strike a balance between this trade-off. To obtain the convergence results for the mutation step, we need the following additional assumption on the transition kernel:
Assumption 3 is an invariant distribution associated with the transition kernel, that is: .
Theorem 3 [Mutation Step] Suppose that Assumptions 1, 2, and 3 are satisfied. Then, defined in (8) converges as follows: (i) for every ; (ii) for every . Case (a): if the particles were resampled in the preceeding selection step, then . Case (b): If the last resampling was executed in iteration , then , where
The asymptotic variance consists of two terms. The first term captures the average conditional variance of the Markov transition kernel . If the particle weights are not equal to one, then the conditional variance needs to be scaled by the weights, which are functions of the particles from the previous iterations. The second term captures the variance of the average of the conditional expectations , which are functions of the resampled particles . The variance depends on the tuning parameter of the Markov transition kernel.
To study the effect of choosing the tuning parameters adaptively by replacing it with , where is measurable with respect to the -algebra generated by , we use the following decomposition
(13)
Since by Assumption 3, we deduce that for all . We now make the high-level assumption that approaches a limit value as and that is differentiable with respect to .
Assumption 4 Suppose the following conditions are satisfied:
(iii)
(iv)
and are twice differentiable and there exist constants and , independent of and , such that and .
Theorem 4 If Assumption 4 is satisfied then the fixed tuning parameters in Algorithm 2 can be replaced by the adaptive tuning parameters in Algorithm 3 without affecting the limit distribution in Theorem 3.
Since for all , it is also the case that the expected values of the derivatives with respect to are equal to zero: and The proof relies on the insight that
The first is obtained by noting that according to Theorem 2, . In the remainder of this section, we will verify Assumption 4 for a special case of Algorithm 2.
Example: Suppose that , , and . The transition density can be expressed as
(14)
where is the proposal density, is the dirac function,13 and
The function is the probability that the proposed draw is rejected. The function is given by
(15)
Under the restriction , the conditional acceptance probability does not depend on , that is, , and the proposal density takes the form
Its derivatives are given by
The derivatives of the log density with respect to , and are polynomial functions of and therefore integrable with respect to under the Gaussian proposal density . Thus, the differentiability condition of Assumption 4 is satisfied.
We now verify that is stochastically bounded. Let and define as the Monte Carlo approximation of based on the particles . Then, Theorem 1 implies that . The empirical rejection rate in iteration is given by
and has expected value
The arguments used in the proof of Theorem 3 can be modified to verify that conditional on , converges in distribution to a Gaussian limit and is therefore . Using the relationship between and the rejection rate in iteration specified in Algorithm 3, we deduce that .
Verifying the regularity conditions for the general transition kernel associated with Algorithm 2 is more tedious. For or , the representation of the transition kernel's density in (14) involves additional point masses and the expression for in (15) becomes more complicated. For , it is no longer true that the conditional acceptance probability is invariant to . Due to the operator in the definition of , there are points at which the function is no longer differentiable with respect to . Thus, rather than verifying the differentiability of the integrants in (15) directly one has to integrate with respect to separately over the regions and and show that the boundary is a smooth function of .
5 Applications
We now consider three applications of the proposed SMC algorithm and provide comparisons to a standard RWMH algorithm. Section 5.1 evaluates the posterior distribution of a small stylized state-space model based on simulated data. In Section 5.2 we consider the SW model. Typically, the SW model is estimated under a fairly informative prior distribution that leads to a well-behaved posterior distribution when combined with U.S. data. However, under a less informative prior the posterior distribution becomes more irregular and provides an interesting application for our algorithm. Finally, in Section 5.3 we apply the algorithm to a real business cycle model proposed by Schmitt-Grohe and Uribe (2012) which, in addition to standard shocks, is driven by a large number of anticipated shocks, e.g., news about future changes in technology. These news shocks make parameter identification more difficult. The SW model and the SGU model are estimated based on actual U.S. data.
5.1 A Stylized State-Space Model
To illustrate the difficulties that can arise when generating draws from the posterior density , consider the following stylized state-space model discussed in Schorfheide (2010):
(16)
The mapping between some structural parameters and the reduced-form parameters is assumed to be
(17)
The first state, , looks like a typical exogenous driving force of a DSGE model, e.g., total factor productivity, while the second state evolves like an endogenous state variable, e.g., the capital stock, driven by the exogenous process and past realizations of itself. The mapping from structural to reduced-form parameters is chosen to highlight the identification problems endemic to DSGE models. First, is not identifiable when is close to 0, since it enters the model only multiplicatively. Second, there is a global identification problem. Root cancellation in the AR and MA lag polynomials for causes a bimodality in the likelihood function. To illustrate this, we
Figure 1: State Space Model: Log Likelihood Function and Posterior Draws
Notes: The left panel shows a contour plot of the log likelihood function overlaid with draws from the RWMH (red) and SMC (red) algorithms. The right panel shows sequential density estimates of πn1) using output from the SMC algorithm. Here n = 1, φ...,50, φ1 = 0, and φ 50= 1. simulate observations given . This parameterization is observationally equivalent to . Moreover, we use a prior distribution that is uniform on the square and .
Tuning of Algorithms. The SMC algorithm is configured as follows. We set , , and . Since this is a very simple (and correctly specified) model, we use only block, , and set . The SMC algorithm works extremely well for this small problem, so changing the hyperparameters does not change the results or running time very much. For comparison, we also run the standard RWMH algorithm with a proposal density that is a bivariate independent normal scaled to achieve a 25% acceptance rate. Changing this proposal variance does not materially affect the results.
Results. The left panel of Figure 1 plots the contours of the posterior density overlaid with draws from the SMC algorithm (black) and the RWMH (red). It is clear that the RWMH algorithm fails to mix on both modes, while the SMC does a good job of capturing the structure of the posterior. To understand the evolution of the particles in the SMC algorithm, in the right panel of Figure 1 we show estimates of the sequence of (marginal) densities , where and . The density for starts out very flat, reflecting the fact that for low the uniform prior dominates the scaled likelihood. As increases, the bimodal structure quickly emerges and becomes very pronounced as approaches one. This plot highlights some of the crucial features of SMC. The general characteristics of the posterior are established relatively quickly in the algorithm. For larger DSGE models, this feature will guide our choice set , as the early approximations are crucial for the success of the algorithm. As the algorithm proceeds, the approximation at step provides a good importance sample for the distribution at step .
5.2 The Smets-Wouters Model
The SW model is a medium-scale macroeconomic model that has become an important benchmark in the DSGE model literature. The model is typically estimated with data on output, consumption, investment, hours, wages, inflation, and interest rates. The details of the model, which we take exactly as presented in SW, are summarized in the Online Appendix. In our subsequent analysis, we consider two prior distributions. The first prior, which we refer to as the standard prior, is the one used by SW and many of the authors that build on their work. Our second prior is less informative than SW's prior and we will refer to it as the diffuse prior. However, the second prior is still proper.
Comparison Among Algorithms. We compute posterior moments based on our proposed SMC algorithm as well as a standard RWMH algorithm. To assess the precision of the Monte Carlo approximations, we run both algorithms 20 times and compute means and standard deviations of posterior moment estimates across runs. To the extent that the number of particles is large enough for the CLTs presented in Section 4 to be accurate, the standard deviations reported below for the SMC can be interpreted as simulation approximations of the asymptotic variance (for ) that appears in Theorem 3. We have taken some care to ensure an "apples-to-apples" comparison by constraining the processing time to be roughly the same across algorithms. Given our choice of tuning parameters (see below), the SMC algorithm for the SW model with the standard prior (diffuse prior), runs about 1 hour and 40 minutes (2 hours and 30 minutes) using two twelve-core Intel Xeon X5670 CPUs (24 processors in total) in parallel. The code is written in Fortran 95 and uses the distributed-memory communication interface MPI.
When comparing the SMC and RWMH algorithms, it is important to avoid giving the SMC algorithm an advantage simply because it can more easily exploit parallel programming techniques. In principle, we could instead run 24 copies of the RWMH on separate processor cores and merge the results afterwards. This may reduce sampling variance if each of the RWMH chains has reliably converged to the posterior distribution. However, if there is a bias in the chains - because of, say, the failure to mix on a mode in a multimodal posterior or simply a slowly converging chain - then merging chains will not eliminate that bias. Moreover, choosing the length of the "burn-in" phase may become an issue as discussed in Rosenthal (2000). Instead, we use a poor-man's parallelization of the RWMH algorithm. It is possible to parallelize MH algorithms via pre-fetching as discussed in Strid (2009). Pre-fetching tries to anticipate the points in the parameter space that the MH algorithm is likely to visit in the next iterations and executes the likelihood evaluation for these parameter values in parallel. Once the likelihood values have been computed one can quickly determine the next draws. While coding the parallel MCMC algorithm efficiently is quite difficult, the simulation results reported in Strid (2009) suggest that a parallelization using 24 processors would lead to a speedup factor of eight at best. Thus, in our poor-man's parallelization, we simply increase the running time of the RWMH algorithm on a single CPU by a factor of eight. This results in approximately 10 million draws.
Tuning of Algorithms. The hyperparameters of the SMC algorithm for the estimation under the standard prior are , , , , , and . The total product of the number of particles, stages, and blocks was chosen by the desired run time of the algorithm. The choice of at 500 was somewhat arbitrary, but it ensured that the bridge distributions were never too "different." The parameter was calibrated by examining the correction step at . Essentially, we increased until the effective sample size after adding the first piece of information from the likelihood was at least ; roughly speaking, 80% of the initial particles retained substantial weight. We settled on the number of blocks by examining the behavior of the adaptive scaling parameter in a preliminary run. Setting ensured that the proposal variances were never scaled down too much for sufficient mutation. For the estimation under the diffuse prior, we increase the number of blocks to . For the RWMH algorithm, we scale the proposal covariance to achieve an acceptance rate of approximately 30% over 5 million draws after a burn-in period of 5 million. Each RWMH chain was initialized with a draw from the prior distribution.
Results from the Standard Prior. It turns out that with the standard prior, the results for the RWMH algorithm and the SMC algorithm are close, both for the posterior means and for the 5% and 95% quantiles of the posterior distribution. The Online Appendix contains a table
Notes: This Figure shows estimates of the mean, 5th and 95th percentile for the RWMH (black) and SMC (red) simulators for the SW model under the standard prior (left) and diffuse prior (right). The boxes are centered at the mean estimate (across 20 simulations) for each statistic while the shaded region shows plus and minus two standard deviations around this mean.
with posterior means as well as 90% equal-tail-probability credible intervals obtained from the two algorithms. A visual comparison of the RWMH and SMC algorithm under the standard prior is provided in the left panel of Figure 2. For seven selected parameters, Figure 2 presents the estimates of the mean, 5th, and 95th percentiles of the posterior distribution. The shaded region covers plus and minus two standard deviations (across runs) around the point estimates for each of the three statistics. The RWMH estimates are shown in black, while the SMC estimates are in red. The figure shows that both simulators are capturing the distribution, although the SMC algorithm is more precise, as indicated by the size of the red boxes relative to the black ones.
The parameter where this difference is most stark is , which is the moving average term in the exogenous ARMA(1,1) price-markup shock process. For , the black boxes representing the noise around estimates of the mean, 5th, and 95th percentiles overlap, which indicates substantial convergence problems. A close inspection of the output from the posterior simulators shows the reason for this. On two of the twenty runs for the RWMH algorithm, the simulator becomes trapped in a region with relatively low posterior density. That is, there is a local mode on which the RWMH gets stuck. Note that this mode is small, so that it can be safely ignored when characterizing the posterior distribution, unlike the multimodal posterior distributions seen below. Perhaps most
Table 1: SW MODEL: LOG MDD ESTIMATES
Algorithm (Method) MEAN(Log MDD) STD(Log MDD) Standard Prior: SMC (Particle Estimate) -901.739 0.33 Standard Prior: RWMH (Modified Harmonic Mean) -902.626 2.34 Diffuse Prior: SMC (Particle Estimate) -873.46 0.24 Diffuse Prior: RWMH (Modified Harmonic Mean) -874.56 1.20
Note Means and standard deviations are over 20 runs for each algorithm.
disturbing is that output from these simulators "looks" fine, in the sense that there are no abrupt shifts in acceptance rates, recursive means, or other summary statistics routinely used as indications of convergence. The SMC algorithm easily avoids getting trapped in the vicinity of this mode, as the relatively small weight on particles in this region ensures they are dropped during a resampling step or mutated.
In addition to the posterior distribution of the parameters, the so-called marginal data density (MDD) plays an important role in DSGE model applications, because it determines the posterior model probability. The MDD is the normalization constant that appears in the denominator of (1) and as constant in (2). The top panel of Table 1 shows estimates of the marginal data densities (MDD) associated with the posterior simulators. While the SMC algorithm delivers an estimate of the MDD as a by-product of the simulation, for the RWMH an auxiliary estimator must be used. We use the modified harmonic mean estimator of Geweke (1999). The estimates in Table 1 indicate that the SMC algorithm is a more stable estimator of the MDD. The high standard deviation of the RWMH-based estimate is driven by the two runs that get stuck in a local mode. These runs produce MDD estimates of about -902.6, a much worse fit relative to the SMC algorithm.
The Diffuse Prior. Some researchers argue that the prior distributions used by SW are implausibly tight, in the sense that they seem hard to rationalize based on information independent of the information in the estimation sample. For instance, the tight prior on the steady-state inflation rate is unlikely to reflect a priori beliefs of someone who has seen macroeconomic data only from the 1950s and 1960s. At the same time, this prior has a strong influence on the empirical performance of the model, as discussed in Del Negro and Schorfheide (2013). Closely related, Muller (2011) derives an analytical approximation for the sensitivity of posterior means to shifts in prior means and finds evidence that the stickiness of prices and wages is driven substantially by the priors.
One side benefit of tight prior distributions is that they tend to smooth out the posterior surface by down-weighting areas of the parameter space that exhibit local peaks in the likelihood function but are deemed unlikely under the prior distribution. Moreover, if the likelihood function contains hardly any information about certain parameters and is essentially flat with respect to these parameters, tight priors induce curvature in the posterior. In both cases, the prior information stabilizes the posterior computations. For simulators such as the RWMH this is crucial, as they work best when the posterior is well-behaved. With a view toward comparing the effectiveness of the different posterior simulators, we relax the priors on the SW model substantially. For parameters which previously had a Beta prior distribution, we now use a uniform distribution. Moreover, we scale the prior variances of the other parameters by a factor of three - with the exception that we leave the priors for the shock standard deviations unchanged. A table with the full specification of the prior is available in the Online Appendix.
Table 2: SW MODEL WITH DIFFUSE PRIOR: POSTERIOR COMPARISON
SMC:Parameter SMC: Mean [0.05, 0.95] SMC: STD(Mean) SMC: Neff RWMH: Mean [0.05, 0.95] RWMH: STD(Mean) Neff 3.06 [ 1.40, 5.26] 0.04 1058 3.04 [ 1.41, 5.14] 0.15 60 -0.06 [-2.99, 2.92] 0.07 732 -0.01 [-2.92, 2.93] 0.16 177 0.11 [ 0.01, 0.29] 0.00 637 0.12 [ 0.01, 0.29] 0.02 19 0.70 [ 0.59, 0.78] 0.00 522 0.69 [ 0.58, 0.78] 0.03 5 1.71 [ 1.50, 1.94] 0.01 514 1.69 [ 1.48, 1.91] 0.04 10 2.78 [ 2.12, 3.52] 0.02 507 2.76 [ 2.11, 3.51] 0.03 159 0.19 [ 0.03, 0.44] 0.01 440 0.21 [ 0.03, 0.48] 0.08 3 8.12 [ 4.27, 12.59] 0.16 266 7.98 [ 4.16, 12.50] 1.03 6 0.14 [ 0.09, 0.23] 0.00 126 0.15 [ 0.11, 0.20] 0.04 1 0.72 [ 0.60, 0.82] 0.01 91 0.73 [ 0.62, 0.82] 0.03 5 0.73 [ 0.37, 0.97] 0.02 87 0.72 [ 0.39, 0.96] 0.03 36 0.77 [ 0.47, 0.98] 0.02 77 0.80 [ 0.54, 0.96] 0.10 3 0.69 [ 0.21, 0.99] 0.04 49 0.69 [ 0.21, 0.99] 0.09 11 0.63 [ 0.09, 0.97] 0.05 49 0.63 [ 0.09, 0.98] 0.09 11 0.93 [ 0.80, 0.99] 0.01 43 0.93 [0.82, 0.99] 0.02 8
Notes: Means and standard deviations are over 20 runs for each algorithm. The RWMH algorithms use 10 million draws with the first 5 million discarded. The SMC algorithms use 12,000 particles and 500 stages. The two algorithms utilize approximately the same computational resources. We define .
Results from the Diffuse Prior. Table 2 summarizes the output of the posterior simulators under the diffuse prior, focusing on parameters for which the standard deviation (STD) of the posterior mean approximation under the RWMH algorithm is greater than 0.02 (the results for the remaining parameters are reproduced in the Online Appendix). While the average estimated mean of the posterior seems to be roughly the same across the algorithms, the variance across simulations is substantially higher under the RWMH algorithm. For instance, the standard deviation of the estimate of the mean for , the autoregressive coefficient for the wage markup, is 0.09. Given the point estimate of 0.69, this means that any given run of the simulator could easily return a mean between 0.5 and 0.9, even after simulating a Markov chain of length 10 million. In almost all cases, the SMC estimates are about half as noisy, usually substantially less so.
Suppose we were able to generate draws from the marginal posterior distribution for a parameter . The variance of the mean of these draws would be given by . Thus, we define , where is an estimate of the posterior variance of obtained from the output of the SMC algorithm and is the variance of the posterior mean estimate across the 20 runs of each algorithm. The effective sample sizes are also reported in Table 2. The differences across the two algorithms are striking. The SMC algorithm is substantially more efficient, generating effective sample sizes that are one to two orders of magnitudes larger. for the inverse Frisch elasticity of labor supply is 1058 for the SMC algorithm and only 60 for the RWMH. The least efficient numerical approximation is obtained for the posterior mean of the parameters governing the wage (, , , ) and price (, , ) stickiness. Under the SMC algorithm, ranges from 43 to 126, whereas for the RWMH algorithm, the effective sample size ranges from 1 to 36.
We return to Figure 2, which graphically illustrates the precision of the algorithms estimates of the mean, 5th, and 95th percentiles of selected parameters. For the diffuse prior, the differences across algorithms are more pronounced. First, note that relative to the analysis with the standard prior, the posterior distributions are now more spread out. Second, the precision of the estimates is much lower for the RWMH simulations than for the SMC simulations, as the black boxes are generally much larger than the red boxes. In fact, the performance of the RWMH algorithm is so poor that for the parameters restricted to the unit intervals, the boxes overlap substantially, meaning that there is sufficient noise in the RWMH algorithm to tangle the, say, 5th and 95th percentile of the posterior distribution for . Moreover, the figure confirms the message from Table 2: some of the worst-performing aspects of the RWMH algorithm are associated with the parameters controlling the movements of wages and prices.
Figure 3:SW Model with Diffuse Prior: Bivariate Contour Plots
Notes: This figure shows contour plots for bivariate kernel density estimates of the posteriors for (left) and (right) from the SMC simulator. The black solid line is the line.
To examine the posterior distribution more closely, we plot joint kernel density estimates of parameters from the wage and price block of the model. The two panels of Figure 3 display joint density estimates of and . is the autocorrelation parameter in the exogenous wage-markup shock process, whereas is the wage-Calvo parameter that determines the degree of nominal wage rigidity. The parameters and are the autoregressive and moving-average coefficients of the exogenous price-markup shock process. The black line shows the line. It is clear that both panels display multimodal, irregular posterior distributions, exacerbated by hard parameter boundaries.14 For the left panel, it is clear that when the autoregressive coefficient for the exogenous wage-markup parameter, , is very close to one, the endogenous wage stickiness of the model, embodied in the wage-Calvo parameter , is less important. On the other hand, when is close to one, the exogenous persistence of wage movements is much lower. The right panel in Figure 3 shows identification problems related to the coefficients of the ARMA(1,1) price-markup shock process.
Motivated by the bimodal features of the bivariate posteriors displayed in Figure 3, we graph estimates of posterior probabilities associated with particular regions in the parameter space in Figure 4. According to Figure 3 there exists a mode for
Figure 4: SW Model with Diffuse Prior: Posterior Probability Statements
Notes: This Figure shows estimates of various posterior probability statements. The black (RWMH) and red (SMC) boxes are centered at the mean (across the 20 simulations) estimate of each probability statement. The shaded region shows plus and minus two standard deviations around this mean.
which ( ) and a mode for which ( ). To measure the posterior probabilities associated with these regions it is necessary for the posterior simulator to mix draws from the two modal regions in the right proportion. Figur 4 shows that the RWMH algorithm has severe difficulties approximating the posterior probabilities precisely. The RWMH estimates are highly variable, and in the case of range from 0 to 1, whereas the SMC algorithm fairly precisely determines this probability to be around 0.95.
Table 3: SW MODEL WITH DIFFUSE PRIOR: TWO MODES
Parameter Mode 1 Mode 2 0.844 0.962 0.812 0.918 0.997 0.394 0.978 0.267 0.591 0.698 0.001 0.085 0.909 0.999 0.612 0.937 Log Posterior -804.14 -803.51
To further explore the multimodal shape of the posterior under the diffuse prior, Table 3 lists the values of the key wage and price parameters at two modes of the joint posterior density captured by the SMC algorithm.15 With respect to wages, the modes identify two different drivers of fit. At Mode 1, the values of the wage Calvo parameter, , and wage indexation parameter, , are relatively low, while the parameters governing the exogenous wage markup process, and , are high. That is, model dynamics for wages near this mode are driven by the exogenous persistence of the shock. At Mode 2, the relative importance of the parameters is reversed. The persistence of wages is driven by the parameters that control the strength of the endogenous propagation, echoing the shape in Figure 3. The exogenous wage markup process is much less persistent. We see that the data support both endogenous and exogenous persistence mechanisms. Thus, a researcher's priors can heavily influence the assessment of the importance of nominal rigidities, echoing a conclusion reached by Del Negro and Schorfheide (2008).
Finally, we return to the marginal data densities, which for the SW model with diffuse prior are reported in the bottom panel of Table 1. The SMC estimate is much more precise, which is unsurprising, given the difficulties of using the modified harmonic mean estimator on a bimodal distribution. The modified harmonic mean estimator actually performs better on the model with diffuse prior than on model with standard prior, mostly because the "height" of the different modes is more similar. Still, the high standard deviation of the estimate indicates severe problems in the algorithm. Finally, as a substantive point, it should be noted that the diffuse prior model has an MDD that is about 30 log points higher than the standard prior SW model. This is a large difference in favor of the diffuse prior model and it highlights the strong tension between the standard prior and the data. This point may apply more generally to DSGE models.
5.3 The Schmitt-Grohe and Uribe News Model
The final application is SGU's "news" model, which has been used to examine the extent to which anticipated shocks (i.e., news) to technology, government spending, wage markups, and preferences explain movements in major macroeconomic time series at business cycle frequencies. The core of the SGU model is a real business cycle model with real rigidities in investment, capital utilization, and wages. While there is not enough space to go through the complete model here, we summarize the key features below. The complete equilibrium conditions for this model are summarized in the Online Appendix.
Important Model Features. We focus on two key features of the SGU model. First, the model has seven exogenous processes in total: stationary and nonstationary technology, stationary and nonstationary investment specific technology, government spending, wage markup, and preference shocks. Each of the seven processes is driven by three (independent) innovations, one of which is realized contemporaneously, and two of which are realized four and eight quarters ahead. So, the determination of a given exogenous process looks like:
Each innovation is scaled by its own variance, , for horizons . Given the model's seven exogenous processes, there are 21 shocks in total, plus a measurement error for output. This framework allows one to capture anticipated changes in, say, productivity as a driver of the business cycle. This can lead to expectation-driven booms, which are, strictly speaking, ruled out in most DSGE models. In forward-looking models, anticipated shocks can have large effects, so it is crucial for the econometrician to recover plausible values for the size of these shocks. The second key feature of the SGU model is that households have nonstandard preferences. Specifically, the representative agent has constant-relative-risk-aversion (CRRA) preferences defined over , a bundle of consumption (), labor (), and the additional variable :
The parameter controls the degree to which households display (internal) habit formation, and the parameters and are related to the level and elasticity of labor supply, respectively. The variable reflects a geometric average of past habit-adjusted consumption:
The presence of , owing to Jaimovich and Rebelo (2009), nests two popular specifications for preferences. As , preferences take the form introduced by King, Plosser, and Rebelo (1988). Here, the labor choice will be related to the intertemporal consumption-savings decision; that is, there will be a wealth effect on labor supply. This is the standard form of preferences used in most estimated DSGE models. In a model with anticipated shocks, it might be problematic because, if there is a large wealth effect, hours today might fall in response to positive news about future economic conditions. On the other hand, as , preferences take the form of , Hercowitz, and Huffman (1988). Labor supply depends only on the current real wage: the wealth effect on labor supply is eliminated. Jaimovich and Rebelo (2009) highlight how crucial this style of preference - coupled with specific adjustment costs - is to generating comovements in response to the news about technology shocks. It is important to note that must lie strictly above zero to be compatible with a balanced growth path for the economy.
The model is estimated on seven economic time series: real GDP growth, real consumption growth, real investment growth, real government spending growth, hours, TFP growth and the relative price of investment. The estimation period is 1955:Q1 to 2006:Q4. This model is an interesting application for the SMC algorithm for several reasons. First, the scale of the model is quite large. There are almost 100 states and 35 estimated parameters. Second, the model contains many parameters for which the priors are quite diffuse, relative to standard priors used in macroeconometrics. In particular, this is true for the variances of the shocks. Also, the prior for the Jaimovich-Rebelo parameter, , is uniform across . We estimate the SGU model under the prior specified by SGU (tabulated in the Online Appendix) and a modified version of this prior in which we change the distribution of the preference parameter .
Tuning of Algorithms. We run the same comparison as in previous sections. For each posterior simulator, we compute 20 runs of the algorithm. For the SMC runs, we use particles, stages, , blocks, , and . We choose the tuning parameters in a way similar to that for the SW model. We use many more particles because the parameter space is larger and the prior is more diffuse compared to the SW model. Given the high-dimensional parameter vector, we increase the number of blocks from 3 to 6 to ensure that mutation can still occur. For the RWMH algorithm, we simulate chains of length 10 million, considering only the final 5 million draws. For the proposal density we use a covariance matrix computed from an earlier run, scaled so that the acceptance rate is roughly 32%. The SMC algorithm takes about 14 hours to run while the RWMH algorithm takes about 4 days. This suggests that a parallelized RWMH algorithm with a speed-up factor of 6.85 would take roughly as long as the SMC algorithm. This is in line with the estimates of Strid (2009), so we take it that the algorithms are on roughly equal footing in terms of computing power.
Table 4: POSTERIOR COMPARISON FOR NEWS MODEL
SMC: Parameter SMC: Mean SMC:[0.05, 0.95] SMC: STD(Mean) SMC: N eff RWMH: Mean RWMH:[0.05, 0.95] RWMH: STD(Mean) Neff 3.14 [ 0.21, 7.98] 0.04 4190 3.08 [ 0.21, 7.80] 0.24 108 0.41 [ 0.03, 0.99] 0.01 1830 0.41 [ 0.03, 0.98] 0.03 108 5.59 [ 0.75, 10.59] 0.09 1124 5.68 [ 0.87, 10.54] 0.30 102 4.13 [ 3.19, 5.18] 0.02 671 4.14 [ 3.22, 5.19] 0.05 146 12.27 [ 9.07, 15.84] 0.09 640 12.36 [ 9.05, 16.12] 0.09 616 1.04 [ 0.06, 2.79] 0.04 626 0.92 [ 0.06, 2.39] 0.04 625 0.62 [ 0.06, 1.08] 0.01 609 0.60 [ 0.06, 1.07] 0.03 111 9.32 [ 7.48, 11.33] 0.05 578 9.33 [ 7.49, 11.40] 0.09 208 2.43 [ 0.15, 5.95] 0.09 406 2.44 [ 0.15, 6.04] 0.04 2066 3.82 [ 0.50, 6.77] 0.10 384 3.80 [ 0.51, 6.78] 0.22 73 2.65 [ 0.17, 6.22] 0.11 335 2.62 [ 0.17, 6.07] 0.18 126 4.26 [ 0.28, 5.91] 0.24 49 4.33 [ 0.84, 5.92] 0.49 12 1.36 [ 0.03, 5.14] 0.24 46 1.34 [ 0.04, 4.83] 0.49 11
Notes: Means and standard deviations are over 20 runs for each algorithm. The RWMH algorithms use 10 million draws with the first 5 million discarded. The SMC algorithms use 30,048 particles and 500 stages. The two algorithms utilize approximately the same computational resources. We define .
Results from the SGU Prior. Table 4 displays the posteriors for some of the parameters of the SGU model with the standard prior. It is clear that the average posterior means from the RWMH and SMC algorithms are roughly the same, with a few exceptions, but that the posteriors generated by the RWMH algorithm are substantially noisier. Mean estimates of parameters associated with news about the wage markup, and , have standard deviations about twice as large under the RWMH simulator relative to the SMC simulator. Related, in terms of coverage, the posterior credible interval for the standard deviation of the contemporaneous wage markup shock, , has a 95% quantile estimate of 2.79 under the SMC algorithm and 2.39 under the RWMH algorithm. Furthermore, the estimate of the mean of the Jaimovich-Rebelo parameter, , under the SMC algorithm is outside the 90% credible interval generated by the RWMH algorithm (not listed in Tabl 4). Estimates related to news about the investment specific technology shock, and , similarly contain much more Monte Carlo noise under the RWMH. Using the numeric efficiency measure discussed in Section 5.2, there are about 3 times as many independent draws in the SMC samples relative to the RWMH samples, based on the median parameter.
To shed light on the relative performance of the simulators, Figure 5 displays histograms for the
Figure 5: News Model: RWMH and SMC Histogram of Wage Markup Process
marginal posterior of parameters associated with the wage markup process. For each of the 20 runs we compute separate histograms. Each box is centered at the mean relative histogram height across the 20 runs for the RWMH (black) and SMC (red) algorithms. The shaded rectangles span plus and minus two standard deviations (across the 20 runs) about this mean. We choose evenly-sized bins for the histograms, restricting the span of the bins to a range with non-trivial posterior density. In the upper left panel, the histogram estimates for , the persistence of the wage markup, shows that the RWMH and SMC algorithm capture roughly the same posterior shape. The size of the black boxes relative to the red boxes shows that the SMC estimator is much more precise. For the parameter , the standard deviation of unanticipated markup shock, the posteriors appear very slightly different, as the SMC algorithm has a long tail, consistent with the difference in credible intervals discussed above.
Finally, the bottom two panels of Figure 5 indicate that the RWMH has the most trouble with the multimodalities and irregularities associated with the variances of the news shocks. Looking
Figure 6: News Model: RWMH and SMC Histograms of γ.
Notes: The boxes show estimates of histograms from each of the simulators. The RWMH algorithm is in red and the SMC is in black. The left panel shows output from the standard prior model and the right panel shows output from the di use prior model. Each box is centered at the mean of the number of elements in each, while the height of the box indicates plus or minus two standard deviations around this mean.
at the size of the boxes, it is clear that these bimodal distributions are more precisely estimated using SMC. For instance, , the size of the four-quarter-ahead news about wage markups, has two sharp peaks, one roughly at 0.35, and another at 4.9. The reason for the two peaks is a (global) identification problem. The model has difficulty distinguishing markup news at 4-quarter-ahead frequency from 8-quarter ahead. This is borne out by the density of , which has a similar bimodal shape as the density of , although the heights are peaked differently.16 Indeed, the posterior correlation of the two parameters is -0.9. The Online Appendix plots a kernel density estimate of the bivariate posterior. In this particular instance, the economic effects of anticipated shocks are unchanged by the failure of the RWMH to mix properly, precisely because of the identification problem: the effects of an eight- and four-periods-ahead shock are very similar. On the other hand, fine parsings of the structural results are incorrect under RWMH. For instance, Table 6 of SGU reports that eight-periods-ahead shocks are responsible for about five percent of the variation in hours worked. Our RWMH runs that do not mix on the second are consistent with that result. The SMC algorithm, which properly reflects the bimodal structure of the shock variances, puts that number close to 20% and, in general, places more importance on longer run news about wages.
With respect to the Jaimovich-Rebelo parameter, , the posteriors generated by the RWMH and the SMC algorithm yield small but interesting differences. The left panel of Figure 6 displays the histograms for the posterior for . The histograms are set up as in Figure 5, with the exception that the left panel has a different scale for the smallest bin. The RWMH algorithm essentially finds a "pointmass" very close to zero. All of the draws from the RWMH runs are less than 0.03, which we refer to as Mode 1. The SMC algorithm also finds significant posterior probability mass near zero, but in addition it detects a small mode (Mode 2) around , comprising about 3% of the total posterior. This can be seen again by looking at the red boxes to the right of 0.1, vs. the non-existent black boxes. Keep in mind though, that the scale for Mode 2 is magnified relative to Mode 1.
The two modes have very different economic implications. Near Mode 2 the wealth effect associated with an increase in income is nonzero. This changes the dynamics of the news model: positive news about the future tend to decrease labor supplied today, because consumers anticipate higher income in the future. Indeed, a parameter value of implies that the importance of anticipated shocks for hours is substantially diminished. To compensate for the reduced importance of anticipated shocks, values of are associated with high standard deviations of the unanticipated wage-markup shock. Overall, a variance decomposition implies that conditional on , unanticipated movements in the wage markup account for about 50% of the movement in hours, compared with just 10% of the movement when . Thus, for parameters near Mode 2, movements in hours are not principally driven by news.
Results from a Modified Prior. To highlight this potential pitfall more clearly, we re-estimate the news model under a different prior for , namely, Relative to the uniform prior, this prior places more mass on the region near 1. Its probability density function is a 45-degree line. A possible justification for this prior is that it places more weight on the "standard" utility functions used in the macroeconomics literature. Mechanically, this prior causes Mode 2 in the original SGU model to become more important. Indeed, now most of the mass resides in this region, although the peak at is still important. The heights of the two modes in the posterior distribution of is approximately equal under the modified prior. The right panel of Figure 6displays the histogram estimates for under the new prior for 20 runs each of the RWMH (black) and the SMC (red) algorithms. One can see that the estimates for are now extremely noisy, place anywhere from 0 to 1 probability mass in the region for the RWMH, indicating that some runs of the RWMH did not mix on both modes. The reason for this is that the peak around
Figure 7: News Model: Anticipated Shocks' Variance Shares for Hours
Notes: The boxes show estimates of histograms for the share of long-run variance in hours attributable to news shocks from each of the simulators. The RWMH algorithm is in red and the SMC is in black. The prior share is shown with the blue line. The left panel shows output from the standard prior model and the right panel shows output from the modified prior model. Each box is centered at the mean of the number of elements in each, while the height of the box indicates plus or minus two standard deviations around this mean.
is extremely sharp and the valley around is very deep. If the RWMH gets to this region, it is extremely unlikely to ever leave it. On the other hand, the SMC algorithm mixes on both modes easily.
To see how this translates into problems for substantive economic inference, Figure 7 plots the histograms for the share of the long-run variance in hours accounted for by anticipated shocks under both priors along with the prior shares. Under the standard prior, both simulators generate roughly the same posterior variance shares, although the SMC has a slightly longer left tail due to the small second mode, and to be sure, this tail is relatively imprecisely estimated (as it is small). Once the prior for is changed to a distribution, the problems associated with the RWMH are exacerbated and inference is substantially changed. As with the posterior for , the RWMH places anywhere from 0 to 1 probability mass on the anticipated shocks accounting for 80% of the long-run movements in hours. The bimodal shape of the posterior distribution distribution of the news shock share under the modified prior is much more precisely estimated by the SMC algorithm and the economic inference is not overwhelmed by Monte Carlo noise. Relative to the standard prior, news shocks are much less important in determining the behavior of hours.
Algorithm (Method) MEAN(Log MDD) STD(Log MDD) SGU Prior: SMC (Particle Estimate) -1802.15 0.23 SGU Prior: RWMH (Modified Harmonic Mean) -1800.77 0.35 Modified Prior: SMC (Particle Estimate) -1805.00 0.11 Modified Prior: RWMH (Modified Harmonic Mean) -1836.42 7.72
Notes: Means and standard deviations are over 20 runs for each algorithm.
Finally, we report log marginal data density estimates in Table 5. As in the case of the Smets-Wouters model, the modified harmonic mean estimate computed from the output of the RWMH algorithm is more noisy, in particular under the modified prior. It turns out that the data slightly favor the model specification with the original SGU prior distribution, but further modifications, e.g. larger prior variances, may easily overturn this ranking. While the analysis under the modified prior was designed to highlight the merit of the SMC sampler, it makes an empirical point as well: Conclusions about the importance of news as a drivers of the business cycle are very sensitive to prior choices. By pushing the prior for towards more standard values in the literature, we were able to reduce the effect of news on hours substantially. This result signals cautious interpretation of DSGE model-based estimates of the importance (or lack thereof) of news on the business cycle.
6 Conclusion
This paper has presented an alternative simulation technique for estimating Bayesian DSGE models. We showed that, when properly tailored to DSGE models, a sequential Monte Carlo technique can be more effective than the random-walk Metropolis Hastings algorithm. The RWMH is poorly suited to dealing with complex and large posteriors, while SMC algorithms, by slowly building a particle approximation of the posterior, can overcome the problems inherent in multimodality. This is important for DSGE models, where the parameters enter the likelihood in a highly nonlinear fashion and identification problems may be present. We have seen in both the SW model and the SGU model that when priors are not very informative, the posterior can possess multimodalities. It is difficult to correctly characterize the posterior with the RWMH in this case. Moreover, the SMC algorithm has an embarrassingly parallelizable structure. Within each tempering iteration, likelihoods can be evaluated simultaneously. In most programming languages, this kind of parallelism can be employed easily, for example, MATLAB's parfor command. Finally, we have shown that the sequential Monte Carlo methods can be used for very large DSGE models. Indeed, it is on large complex distributions that returns to using an SMC algorithm over an MCMC algorithm are highest.
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Footnotes
* Correspondence: E. Herbst: Board of Governors of the Federal Reserve System, 20th Street and Constitution Avenue N.W., Washington, D.C. 20551. Email: [email protected]. F. Schorfheide: Department of Economics, 3718 Locust Walk, University of Pennsylvania, Philadelphia, PA 19104-6297. Email: [email protected]. Many thanks to Stephanie Schmitt-Grohé and Martín Uribe for graciously sharing their code. We are also thankful for helpful comments and suggestions from Fabio Canova (Co-Editor), two anonymous referees, Garland Durham, Jesus Fernandez-Villaverde, John Roberts, and seminar participants at the Board of Governors, the 2012 Conference on Computational and Financial Econometrics, ECARES/ULB, and University of Pennsylvania. Schorfheide gratefully acknowledges financial support from the National Science Foundation under Grant SES 1061725. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Philadelphia, the Federal Reserve Board of Governors, or the Federal Reserve System. Return to Text
1. For instance, one can run separate Markov chains on each processor and subsequently merge the draws. Return to Text
2. Using the notation that and one could define an integer-valued sequence with and and define . This data-point tempering approach is attractive for applications in which is sequentially estimated on an increasing sample. Return to Text
3. There exist papers in the DSGE model estimation literature in which the posterior mean of some parameters is several prior standard deviations away from the prior mean. For such applications it might be necessary to choose and to use an initial distribution that is also informed by the tempered likelihood function . Return to Text
4. We assign draws to each parameter, sort the parameters according to the assigned random numbers, and then let the -th block consist of parameters . Return to Text
5. In principle one could use separate scaling factors for the three mixture components but in our applications a single scaling factor was sufficient. Return to Text
6. We use "tilde" instead of "hat" for and because the approximations are based on the correction step in Algorithm 1. Return to Text
7. We speed up the evaluation of the likelihood of the DSGE model by using the Chandrasekhar recursions to compute the predictive decomposition of the likelihood. See Herbst (2012) for details. Return to Text
8. We use the term processor to refer to the basic physical unit capable of executing a single thread. Return to Text
9. We perform this calculation as follows. Divide the algorithm instructions in two parts: a fraction of serial (i.e., non-parallelizable) instructions and instructions which can be executed in parallel. Amdahl's Law, see Amdahl (1967), states that the best expected improvement from using processors/cores/threads is . Using the runtimes for our algorithm for various s, we can come up with an (admittedly crude) estimate for . Return to Text
10. Our Assumptions correspond to Conditions 3 and 4 in Durham and Geweke (2012). Return to Text
11. In principle the classes of functions can be enlarged to functions for which posterior moments exist only if . In this case one could start the algorithm from using a proposal density that delivers uniformly bounded importance weights. Return to Text
12. Creal, Koopman, and Shephard (2009) suggest various visual indicators of weight performance: (i) a scatter plot of the top 100 weights should be free of outliers; (ii) the histogram of the remaining weights should not be sharply skewed, indicating that many of the particles have very little weight; and (iii) recursive estimates of the variance of the weights should be stable. Return to Text
13. It has the properties that for and . Return to Text
14. We did some exercises using parameters transformed to unbounded space. The results were essentially unchanged. Return to Text
15. Note that these two modes of the joint posterior are different from the two modes in the marginal posteriors for and seen in Figure 3. Return to Text
16. To examine whether the bimodality is specific to the U.S. data that are used to estimate the SGU model, we re-estimated the model based on simulated data. The posterior obtained from simulated data exhibits a similar bimodal shape as the posterior given the actual data. Return to Text
This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text | 2016-12-09T09:47:52 | {"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": 0.807898759841919, "perplexity": 998.1223032458939}, "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-2016-50/segments/1480698542693.41/warc/CC-MAIN-20161202170902-00121-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://dlmf.nist.gov/10.25 | # §10.25 Definitions
## §10.25(i) Modified Bessel’s Equation
This equation is obtained from Bessel’s equation (10.2.1) on replacing by , and it has the same kinds of singularities. Its solutions are called modified Bessel functions or Bessel functions of imaginary argument.
## §10.25(ii) Standard Solutions
10.25.2
This solution has properties analogous to those of , defined in §10.2(ii). In particular, the principal branch of is defined in a similar way: it corresponds to the principal value of , is analytic in , and two-valued and discontinuous on the cut .
The defining property of the second standard solution of (10.25.1) is
10.25.3
as in . It has a branch point at for all . The principal branch corresponds to the principal value of the square root in (10.25.3), is analytic in , and two-valued and discontinuous on the cut .
Both and are real when is real and .
For fixed each branch of and is entire in .
### ¶ Branch Conventions
Except where indicated otherwise it is assumed throughout the DLMF that the symbols and denote the principal values of these functions.
### ¶ Symbol
Corresponding to the symbol introduced in §10.2(ii), we sometimes use to denote , , or any nontrivial linear combination of these functions, the coefficients in which are independent of and .
## §10.25(iii) Numerically Satisfactory Pairs of Solutions
Table 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1). It is assumed that . When , is replaced by .
Table 10.25.1: Numerically satisfactory pairs of solutions of the modified Bessel’s equation.
Pair Region | 2013-05-24T17:26:50 | {"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": 0.948545515537262, "perplexity": 1035.8735959488897}, "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/1368704818711/warc/CC-MAIN-20130516114658-00091-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://dlmf.nist.gov/30.3 | # §30.3 Eigenvalues
## §30.3(i) Definition
With $\mu=m=0,1,2,\dots$, the spheroidal wave functions $\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits\!\left(x,\gamma^{2}\right)$ are solutions of Equation (30.2.1) which are bounded on $(-1,1)$, or equivalently, which are of the form $(1-x^{2})^{\frac{1}{2}m}g(x)$ where $g(z)$ is an entire function of $z$. These solutions exist only for eigenvalues $\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)$, $n=m,m+1,m+2,\dots$, of the parameter $\lambda$.
## §30.3(ii) Properties
The eigenvalues $\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)$ are analytic functions of the real variable $\gamma^{2}$ and satisfy
30.3.1 $\mathop{\lambda^{m}_{m}\/}\nolimits\!\left(\gamma^{2}\right)<\mathop{\lambda^{% m}_{m+1}\/}\nolimits\!\left(\gamma^{2}\right)<\mathop{\lambda^{m}_{m+2}\/}% \nolimits\!\left(\gamma^{2}\right)<\cdots,$
30.3.2 $\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)=n(n+1)-\tfrac{1}{% 2}\gamma^{2}+\mathop{O\/}\nolimits\!\left(n^{-2}\right),$ $n\to\infty$,
30.3.3 $\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(0\right)=n(n+1),$
30.3.4 $-1<\frac{d\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)}{d(% \gamma^{2})}<0.$
## §30.3(iii) Transcendental Equation
If $p$ is an even nonnegative integer, then the continued-fraction equation
30.3.5 $\beta_{p}-\lambda-\cfrac{\alpha_{p-2}\gamma_{p}}{\beta_{p-2}-\lambda-\cfrac{% \alpha_{p-4}\gamma_{p-2}}{\beta_{p-4}-\lambda-\cdots}}=\cfrac{\alpha_{p}\gamma% _{p+2}}{\beta_{p+2}-\lambda-\cfrac{\alpha_{p+2}\gamma_{p+4}}{\beta_{p+4}-% \lambda-\cdots}},$ Symbols: $\alpha_{k}$: coefficent, $\beta_{k}$: coefficent and $\gamma_{k}$: coefficent A&S Ref: 21.7.4 Referenced by: §30.3(iii), §30.3(iii) Permalink: http://dlmf.nist.gov/30.3.E5 Encodings: TeX, pMML, png
where $\alpha_{k}$, $\beta_{k}$, $\gamma_{k}$ are defined by
30.3.6 $\displaystyle\alpha_{k}$ $\displaystyle=-(k+1)(k+2),$ $\displaystyle\beta_{k}$ $\displaystyle=(m+k)(m+k+1)-\gamma^{2},$ $\displaystyle\gamma_{k}$ $\displaystyle=\gamma^{2},$ Defines: $\alpha_{k}$: coefficent (locally), $\beta_{k}$: coefficent (locally) and $\gamma_{k}$: coefficent (locally) Symbols: $m$: nonnegative integer and $\gamma^{2}$: real parameter Referenced by: §30.4(iii) Permalink: http://dlmf.nist.gov/30.3.E6 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png
has the solutions $\lambda=\mathop{\lambda^{m}_{m+2j}\/}\nolimits\!\left(\gamma^{2}\right)$, $j=0,1,2,\dots$. If $p$ is an odd positive integer, then Equation (30.3.5) has the solutions $\lambda=\mathop{\lambda^{m}_{m+2j+1}\/}\nolimits\!\left(\gamma^{2}\right)$, $j=0,1,2,\dots$. If $p=0$ or $p=1$, the finite continued-fraction on the left-hand side of (30.3.5) equals 0; if $p>1$ its last denominator is $\beta_{0}-\lambda$ or $\beta_{1}-\lambda$.
In equation (30.3.5) we can also use
30.3.7 $\displaystyle\alpha_{k}$ $\displaystyle=\gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)},$ $\displaystyle\beta_{k}$ $\displaystyle=(k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k% +2m+3)},$ $\displaystyle\gamma_{k}$ $\displaystyle=\gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}.$
## §30.3(iv) Power-Series Expansion
30.3.8 $\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)=\sum_{k=0}^{% \infty}\ell_{2k}\gamma^{2k},$ $|\gamma^{2}|.
For values of $r_{n}^{m}$ see Meixner et al. (1980, p. 109).
30.3.9 $\displaystyle\ell_{0}$ $\displaystyle=n(n+1),$ $\displaystyle 2\ell_{2}$ $\displaystyle=-1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)},$ $\displaystyle 2\ell_{4}$ $\displaystyle=\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n% -m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}.$ Symbols: $m$: nonnegative integer, $n\geq m$: integer degree and $\ell_{j}$: coefficients A&S Ref: 21.7.5 Permalink: http://dlmf.nist.gov/30.3.E9 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png
30.3.10 $\ell_{6}=(4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3% )^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1% )(2n+3)}\right),$
30.3.11 $\ell_{8}=2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D,$
30.3.12 $\displaystyle A$ $\displaystyle=\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)^{2}(2n-3)(2n-1)^{7}(2n+1)% (2n+3)^{2}}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)^{2}(2n+1)(2n+3)^{7}(2n+% 5)(2n+7)^{2}},$ $\displaystyle B$ $\displaystyle=\frac{(n-m-3)(n-m-2)(n-m-1)(n-m)(n+m-3)(n+m-2)(n+m-1)(n+m)}{(2n-% 7)(2n-5)^{2}(2n-3)^{3}(2n-1)^{4}(2n+1)}-\frac{(n-m+1)(n-m+2)(n-m+3)(n-m+4)(n+m% +1)(n+m+2)(n+m+3)(n+m+4)}{(2n+1)(2n+3)^{4}(2n+5)^{3}(2n+7)^{2}(2n+9)},$ $\displaystyle C$ $\displaystyle=\frac{(n-m+1)^{2}(n-m+2)^{2}(n+m+1)^{2}(n+m+2)^{2}}{(2n+1)^{2}(2% n+3)^{7}(2n+5)^{2}}-\frac{(n-m-1)^{2}(n-m)^{2}(n+m-1)^{2}(n+m)^{2}}{(2n-3)^{2}% (2n-1)^{7}(2n+1)^{2}},$ $\displaystyle D$ $\displaystyle=\frac{(n-m-1)(n-m)(n-m+1)(n-m+2)(n+m-1)(n+m)(n+m+1)(n+m+2)}{(2n-% 3)(2n-1)^{4}(2n+1)^{2}(2n+3)^{4}(2n+5)}.$
Further coefficients can be found with the Maple program SWF9; see §30.18(i). | 2015-10-04T12:46:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 117, "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": 0.9804905652999878, "perplexity": 5560.281247403126}, "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-2015-40/segments/1443736673632.3/warc/CC-MAIN-20151001215753-00169-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://pos.sissa.it/390/496/ | Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Strong Interactions and Hadron Physics
Search for a colorless C-odd three-gluon state from comparison of elastic proton proton and proton antiproton scattering
C. Royon
Full text: Not available
Abstract
We analyze the differences between the $pp$ and $p\bar{p}$ differential elastic cross section measurements by the
D0 and TOTEM Collaborations at the Tevatron, Fermilab, and the LHC, CERN that lead to a significance larger than 3$\sigma$ of the existence of the
colourless $C$-odd three-gluon state, the odderon.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-11-29T10:22:18 | {"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": 0.3398647904396057, "perplexity": 4661.432746370084}, "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-2020-50/segments/1606141197593.33/warc/CC-MAIN-20201129093434-20201129123434-00538.warc.gz"} |
https://predict.cdc.gov/post/5c4f6d687620e103b6dcd015 | # Aedes Challenge 2019
### Aedes Forecasting Challenge 2019
Aedes aegypti and Ae. albopictus are the vectors of chikungunya, dengue, yellow fever, and Zika viruses, the most important arboviruses globally. These vectors are present across broad regions of the United States, but their spatiotemporal distribution is dynamic and not well understood. Data are limited and current models based on those data have not been evaluated on external data. Evaluating model-based, county-level forecasts on future data can help clarify model accuracy and utility, the seasonal and geographical dynamics of these species, and key directions for future research. These advances can contribute to improved preparedness for arboviral invasion in the U.S. and in other regions where Aedes suitability may be limited and changing.
Challenge
This is an open forecasting challenge to predict the monthly presence of Ae. aegypti and Ae. albopictus in a subset of U.S. counties during the 2019 calendar year. The forecasting targets are described on the Targets page. The subset of counties are listed on the Data page along with historical data for each county. Participation guidelines are described on the Participation page and evaluation criteria are described on the Evaluation page.
Timeline
• Project announcement and data release: February 4, 2019.
• Data release completed: March 1, 2019.
• Registration deadline: Teams may register up to Wednesday, March 27, 2019.
• Forecast deadlines: The first forecast should be for April, 2019 and is due on March 31, 2019 at 11:59 Eastern Standard Time (UTC−05:00). Forecasts for May through December are due at 11:59 EST on the final day of the preceding month (i.e. the 30th or 31st) with the last forecast due on November 30, 2019 (forecast for December, 2019). More details are available on the Participation page.
• Forecast evaluation: Early 2020, as soon as final surveillance data for 2019 are available.
### Targets
Forecasts will be made on a monthly basis for the presence of Aedes aegypti or Ae. albopictus in a subset of US counties.
### Monthly presence of Ae. aegyptiorAe. albopictus
DEFINITION
Presence of either species for a given calendar month and county will be determined by collection data for adult mosquitoes from that month and county. If any adult mosquito of the species is collected on any day of the month, the species will be considered “present” for that month. If no adults are reported and trapping effort is reported and consistent with historical data for that county, the species will be considered “absent”. Final determinations will be made when final collection data from counties are available (December 2019 or later). Note that collection efforts are highly variable across counties and “absence”, as defined here, does not necessarily mean that the species is truly absent.
MOTIVATION
Because of their role as vectors for arboviruses, Ae. aegypti and Ae. albopictus mosquitoes are targeted by many mosquito surveillance and control programs. Forecasts of where and when these mosquitoes are likely be found can help mosquito control agencies efficiently plan and implement these programs.
### Mosquito surveillance data
The data are now complete for 95 counties in 8 states (as of March 1, 2019 - previously only a subset had been provided). There are at least two years of historical data for each participating county (2017-2018), but some have many more. The surveillance methods employed for each county are different and may vary over time (e.g. many counties do not trap in the winter months). The compiled data include indicators of trapping effort including trap type, number of collections, and number of trap nights by county. Forecasters should assume that trapping effort for each county will be similar in 2019 to what was reported for 2018. Forecasts for counties with substantially different trapping effort in 2019 will be analyzed separately and not included in overall scores.
The data are provided in standardized csv files below with one file for each state (including all participating counties). A detailed description of the fields included in these csv files is also included below.
Other data sources may also be used for forecasting. There are no restrictions as to what data may be used. Forecasters may use as many data sources as they wish, but all should be listed in the model description (see Participation page). Links to potentially useful environmental data sources are included below on this page.
DATA USE
Data providers are indicated for each state. These data providers and the 2019 Epidemic Prediction Initiative Aedes Forecasting Challenge should be acknowledged when using these data.
### California
41 counties: Alameda, Butte, Colusa, Contra Costa, Fresno, Glenn, Imperial, Inyo, Kern, Kings, Lake, Los Angeles, Madera, Marin, Merced, Mono, Monterey, Napa, Orange, Placer, Riverside, Sacramento, San Benito, San Bernardino, San Diego, San Francisco, San Joaquin, San Luis Obispo, San Mateo, Santa Barbara, Santa Clara, Santa Cruz, Shasta, Solano, Sonoma, Stanislaus, Sutter, Tulare, Ventura, Yolo, Yuba
Data providers: Alameda County Vector Control Services District, Alameda County Mosquito Abatement District, Antelope Valley Mosquito and Vector Control District, Butte County Mosquito and Vector Control District, Colusa Mosquito Abatement District, Consolidated Mosquito Abatement District, Contra Costa Mosquito and Vector Control District, Coachella Valley Mosquito and Vector Control District, Delano Mosquito Abatement District, Delta Vector Control District, East Side Mosquito Abatement District, Fresno Mosquito and Vector Control District, Fresno Westside Mosquito Abatement District, Greater LA County Vector Control District, Imperial County Vector Control, Owens Valley Mosquito Abatement Program, Kern Mosquito and Vector Control District, Kings Mosquito Abatement District, Los Angeles West Vector and Vector-borne Disease Control District, Lake County Vector Control District, Long Beach Vector Control Program, Madera County Mosquito and Vector Control District, Marin-Sonoma Mosquito and Vector Control District, Merced County Mosquito Abatement District, City of Moorpark Vector Control, Napa County Mosquito Abatement District, North Salinas Valley Mosquito Abatement District, Northwest Mosquito and Vector Control District, Orange County Mosquito and Vector Control District, Placer Mosquito and Vector Control District, Riverside County Department of Environmental Health Vector Control Program, San Bernardino County Mosquito and Vector Control, San Diego County Dept of Environmental Health Vector Control, San Mateo County Mosquito and Vector Control District, Sacramento-Yolo Mosquito and Vector Control District, Mosquito and Vector Management District of Santa Barbara County, San Benito County Agricultural Commission, Santa Cruz County Mosquito and Vector Control District, San Francisco Public Health Environmental Health Section, San Gabriel Valley Mosquito and Vector Control District, Shasta Mosquito and Vector Control District, Oroville Mosquito Abatement District, San Joaquin County Mosquito and Vector Control District, Solano County Mosquito Abatement District, Santa Clara County Vector Control District, Sutter-Yuba Mosquito and Vector Control District, Tulare Mosquito Abatement District , Turlock Mosquito Abatement District, Ventura County Environmental Health Division, West Side Mosquito and Vector Control District, West Valley Mosquito and Vector Control District, California Vector-borne Disease Surveillance (CalSurv) Gateway University of California Davis
### Connecticut
2 counties: Fairfield, New Haven
Data provider: Connecticut Agricultural Experiment Station
### Florida
25 counties: Calhoun, Collier, Escambia, Gadsden, Hillsborough, Holmes, Jackson, Jefferson, Lee, Liberty, Madison, Manatee, Martin, Miami-Dade, Okaloosa, Osceola, Pasco, Pinellas, Polk, Santa Rosa, St. Johns, Taylor, Wakulla, Walton, Washington
Data providers: Florida State University, Collier Mosquito Control District, Escambia County Mosquito Control, Hillsborough County Public Works Department, Lee County Mosquito Control District, Manatee County Mosquito Control District, Martin County Public Works Department, Miami-Dade County Department of Solid Waste Management, Osceola County Public Works, Pasco County Mosquito Control District, Pinellas County Mosquito Control, Polk County Mosquito Control, Anastasia Mosquito Control District, South Walton County Mosquito Control District
### New Jersey
8 counties: Cumberland, Essex, Mercer, Monmouth, Morris, Salem, Sussex, Warren
Data providers: Cumberland County Mosquito Control Division, Essex County Mosquito Control, Mercer County Mosquito Control, Monmouth County Mosquito Control, Morris County Division of Mosquito Control, Salem County Mosquito Control, Sussex County Office of Mosquito Control, Warren County Mosquito Control Commission
### New York
8 counties: Bronx, Kings, Nassau, New York, Queens, Richmond, Rockland, Westchester
Data providers: New York City Department of Health and Mental Hygiene, Nassau County Department of Health, Rockland County Department of Health, Westchester County Department of Health, New York State Department of Health, Columbia University
### North Carolina
5 counties: Forsyth, New Hanover, Pitt, Transylvania, Wake
Data providers: Forsyth County Department of Public Health, New Hanover County Vector Control,Pitt County Environment Health, Transylvania Public Health, North Carolina State University
### Texas
3 counties: Cameron, Hidalgo, Tarrant
Data providers: City of Brownsville Public Health, Hidalgo County Health and Human Services, Tarrant County Public Health
### Wisconsin
3 counties: Dane, Milwaukee, Waukesha
### Data Dictionary
The dataset includes monthly adult Ae. aegypti and Ae. albopictus trapping data by trap type. This includes data on the total trapping effort (number of sites, trap nights, and collections) and the collections of both species (number of positive collections and number of adults collected). Each line represents all collections for a single county in a single month with a single trap type. Note that some counties have multiple lines for a single month because they employed more than one trap type.
DESCRIPTION OF VARIABLES
state
State of collection
Examples: Florida, California
statefp
Two digit FIPS code for state of collection https://www.census.gov/geo/reference/codes/cou.html.
Examples: 12, 06
county
County of collection, without the word "County"
Examples: Broward, Los Angeles
countyfp
Three digit FIPS code for county of collection https://www.census.gov/geo/reference/codes/cou.html
Examples: 011, 037
year
Four digit year of collection
Examples: 2016, 2017
month
Numeric month of collection (1-12)
Examples: 1, 10
trap_type
Type of trap used for collection, includes:
• BGS: BG sentinel traps including those baited with CO2
• GAT: Traps that target gravid Aedes females with enclosed water containers including BGGAT and AGO traps.
• GRAV: Traps that target gravid females with open water containers including CDC gravid traps. These traps target Culex species but may also detect Aedes species.
• CO2: Traps baited with CO2 including CDC and ABC light traps and Fay-Prince traps (BG sentinel traps using CO2 are classified as BGS) .
For collections where only presence or absence was recorded, “-PRES” is included at the end of the trap type name.
num_sites
Number of distinct trap sites
num_collection_events
Number of distinct trap collections. This may be less than the number of trap nights when a trap was set for multiple nights.
num_trap_nights
Cumulative number of nights distinct traps were run at all sites
num_aegypti_collected
Number of collected mosquitoes identified as Aedes aegypti. This may not be available and marked as NA in the case that collections were classified as present or absent rather than counting the number of mosquitoes. If only presence or absence was recorded for a trap, that is indicated in num_collections_aegypti.
num_albopictus_collected
Number of collected mosquitoes identified as Aedes albopictus. This may not be available and marked as NA in the case that collections were classified as present or absent rather than counting the number of mosquitoes. If only presence or absence was recorded for a trap, that is indicated in num_collections_albopictus.
num_collections_aegypti
Number of collections where Aedes aegypti were detected.
num_collections_albopictus
Number of collections where Aedes albopictus were detected.
### Environmental data
This list includes potential sources of useful environmental data. There is no obligation to use any particular data source or to limit data sources to these.
### Participation guidance
How to participate
To participate in the challenge, one team member must register on this website and, after logging in, register specifically for the Aedes Forecasting Challenge (instructions for registration). The forecast submissions will be made using this account. Only one forecast can be submitted for each deadline per account and the same account must be used for all submissions. If teams wish to submit different forecasts (e.g. from different models), they need to use multiple accounts.
Full participation requires: Electronic submission of forecasts for all included counties and months by the respective deadlines (details below and Evaluation page). Submission of a model description document by email (details below).
### Electronic submission
Forecast format
Forecasts should be made for each month in csv files matching the format in this submission template. Each csv should contain forecasts for all counties and both species, but only for a single month. For internal record keeping, teams may find it useful to include the month in the file name.
The forecast file includes one line for each forecast. That line includes:
• location: “State” and “County” as written in the data files with a hyphen: “State-County”. For example, “California-San Diego” or “Connecticut-Fairfield”. Omit the word “County” and include spaces between words within the county or state name. The template provided above should match the state and county fields in the provided surveillance data.
• target: “Ae. aegypti” or “Ae. albopictus”
• type: “binary” for all. Indicates that it is a yes or no forecast.
• unit: “present” for all. Indicates the forecasts are for the observation of the species. I.e. a forecast of 0.8 indicates 80% chance of being trapped and reported (and 20% chance of not being trapped and reported).
• value: A probability for the observation of a specific species in that particular month and county. The value indicates the probability on a scale from 0 to 1, where 0 is certain absence, 0.5 is an equal chance of absence or presence (50/50), and 1.0 is certain presence). In the template, the values are 0.5 for all species and counties. These should be changed to reflect the forecast of each team. Note: when a forecast has high confidence but not absolute certainty, it may be beneficial to assign a very small probability to the unexpected outcome to prevent a very low score should that occur, e.g. 0.999 instead of 1.0 for presence or 0.001 instead of 0 for absence. See the Evaluation page for details on scoring.
Submission process
Registered participants will have access to a Submit page. The individual csv files can be uploaded on that page any time before the specific deadlines. Take care to match the forecast time frame as there is no built in check for this. The due dates correspond to 11:59 PM EST the day before the forecasted month begins. For example, forecasts for April are due by 11:59 PM EST on March 31 and should be submitted in the row showing that due date. If you do not see the due date, check the “previous submissions” and “future submissions”. Likewise, forecasts for May have the due date April 30. Forecasts may be submitted and updated at any time prior to the due date. Successful submission can be checked by clicking on the “Open JSON” link (the JSON format is a format used by the server). Note that if you are in a different time zone, the date displayed for each deadline may be one day off, but the deadline is still 11:59 PM on the last day of the month in the Eastern Standard Time Zone.
### Model description
Each team should select their best model for forecasts and submit a brief model description (details below) by email to [email protected] prior to the first forecast deadline. Teams may update their model during the challenge provided they submit an updated model description. The description should include the following components:
1. Date
2. Team name: This should match the registration name and may be used in forecast visualizations on the website (predict.cdc.gov).
3. Team members: List every person involved with the forecasting effort and their institution. Identify a team leader and include the email address of the team leader.
4. Agreement: Include the following statement: “By submitting these forecasts, I (we) indicate my (our) full and unconditional agreement to abide by the project's rules and data use agreements.” See the participation agreement below.
5. Model description (no more than 400 words): Is the model mechanistic, statistical? Is it an instance of a known class of models? The description should include sufficient detail for another modeler to understand the approach being applied. It may include equations, but that is not necessary. If multiple models are used, describe each model and how they were combined.
6. Data sources: What data were used in the model? Historical case data? Weather data? Other data?
7. Computational resources: What programming languages/software tools were used to write and execute the forecasts?
8. Publications: Does the model derive directly from previously published work? If so please include references.
### Participation agreement
All participants provide consent for their forecasts to be published in real-time on the CDC’s Epidemic Prediction Initiative website (https://predict.cdc.gov/), GitHub page (https://github.com/cdcepi), and, after the season ends, in a scientific journal describing the results of the challenge. The forecasts can be attributed to a team name (e.g., John Doe University) or anonymous (e.g., Team A) based on individual team preference. Team names should be limited to 25 characters for display online. The team name registered with the EPI website will be displayed alongside a team’s forecasts. Any team may publish results from their forecast at any time, but no participating team may publish the results of another team’s model in any form without the team’s consent. Any mosquito surveillance data used should acknowledge the sources of those data as stated on the Data page. The manuscript describing the accuracy of forecasts across teams will be coordinated by a representative from CDC.
### Evaluation
All forecasts will be scored by comparison to data reported by participating counties in 2019. Those data will be collected from participating counties when the data are complete for the year (late 2019 or early 2020). Forecasts will be ranked by average logarithmic score (see below) across all counties and months for each species separately. If reported trapping effort in 2019 is substantially different from 2018 for some counties/months, those counties/months may be removed from the analysis. Forecasts for counties without trapping data for a given month (e.g. November and December) will not be scored.
The top ranked team will be announced publicly by CDC in early 2020.
Eligibility
To be eligible for an overall ranking, teams must: Submit forecasts for every county listed on the Data page and for every month of the challenge: April, May, June, July, August, September, October, November, and December. Submit forecasts electronically prior to the respective deadline (the day before each new month starts). Submit a model description (see Participation page). Forecasts from teams that do not submit all required forecasts may still be evaluated, but they will not be ranked for overall performance. Teams may consider submitting some naive forecasts (e.g. 0.5) if they have difficulty producing all forecasts by the deadlines.
Results
Preliminary results will be distributed to all teams in early 2020. A joint manuscript will be prepared by the project organizers to disseminate all forecasts, findings of this analysis, and the general performance of submitted forecasts. Participants may publish their own forecasts and results at any time.
### Logarithmic Score
All forecasts are probabilistic, a probability, ;;p;;, of the mosquito species being reported in a specific month in a specific county. Reported data from 2019 will be used to classify presence for each species, county, and month combination, ;;x;;, as present (1) or absent (0) following the definition on the Targets page. The logarithmic score is calculated as:
$$S(p,x) = x\text{ln}(p) + (1-x)\text{ln}(p - 1)$$
Logarithmic scores (;;S;;) can be averaged across many different predictions. In this case they will be averaged for all included counties and months for each species separately.
Example: A forecast predicts there is a probability of 0.2 (i.e. a 20% chance) that Ae. aegypti is reported in County X in June 2019. Collection of an adult Ae. aegypti in June is reported later in 2019. The logarithmic score is therefore ;;\text{ln}(0.2) = -1.6;;. Alternatively, if no Ae. aegypti were reported, the logarithmic score would be higher, ;;\text{ln}(1 - 0.2) = \text{ln}(0.8) = -0.22;;.
Notes
• A 50/50 chance or a probability of 0.5 gives a logarithmic score of -0.69 regardless of whether the species was observed or not.
• A forecast probability of 0 will give a logarithmic score of -Infiniti if the species is reported. The same is true for a probability of 1 when the species is not reported. Even a small probability for unlikely events can substantially improve average scores. For example, a forecast probability of 0.01 will give a logarithmic score of -4.6 if the species is observed.
References | 2020-10-20T09:14:06 | {"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": 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": 0.2029722034931183, "perplexity": 8477.34061987221}, "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-2020-45/segments/1603107871231.19/warc/CC-MAIN-20201020080044-20201020110044-00220.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?init=0&node=M144&home=MXXX025 | ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit c}}}$ MESONS(including possibly non- ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ states)
#### ${{\mathit h}_{{c}}{(1P)}}$
$I^G(J^{PC})$ = $0^-(1^{+ -})$
Quantum numbers are quark model prediction, ${}^{C} =$ established by ${{\mathit \eta}_{{c}}}{{\mathit \gamma}}$ decay.
${{\mathit h}_{{c}}{(1P)}}$ MASS $3525.38 \pm0.11$ MeV
${{\mathit h}_{{c}}{(1P)}}$ WIDTH $0.7 \pm0.4$ MeV
${{\mathit h}_{{c}}{(1P)}}$ PARTIAL WIDTHS
$\Gamma_{1}$ ${{\mathit J / \psi}{(1S)}}{{\mathit \pi}^{0}}$ 382
$\Gamma_{2}$ ${{\mathit J / \psi}{(1S)}}{{\mathit \pi}}{{\mathit \pi}}$ not seen 312
$\Gamma_{3}$ ${{\mathit J / \psi}{(1S)}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $<2.3\times 10^{-3}$ CL=90% 305
$\Gamma_{4}$ ${{\mathit p}}{{\overline{\mathit p}}}$ $<1.5\times 10^{-4}$ CL=90% 1492
$\Gamma_{5}$ ${{\mathit p}}{{\overline{\mathit p}}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $(2.9\pm{0.6})\times 10^{-3}$ 1390
$\Gamma_{6}$ ${{\mathit p}}{{\overline{\mathit p}}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $<5\times 10^{-4}$ CL=90% 1394
$\Gamma_{7}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $(1.6\pm{0.5})\times 10^{-3}$ 1749
$\Gamma_{8}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ $(7.2\pm{2.3})\times 10^{-3}$ 1695
$\Gamma_{9}$ 2 ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $(8.1\pm{1.8})\times 10^{-3}$ 1716
$\Gamma_{10}$ 3 ${{\mathit \pi}^{+}}$3 ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $<9\times 10^{-3}$ CL=90% 1661
$\Gamma_{11}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $<6\times 10^{-4}$ CL=90% 1640
$\Gamma_{12}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $(3.2\pm{0.8})\times 10^{-3}$ 1606
$\Gamma_{13}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ $<2.3\times 10^{-3}$ CL=90% 1480
$\Gamma_{14}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}$ $<6\times 10^{-4}$ CL=90% 1670
$\Gamma_{15}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ $<2.1\times 10^{-3}$ CL=90% 1532
$\Gamma_{16}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \eta}}$ $<9\times 10^{-4}$ CL=90% 1574
$\Gamma_{17}$ 2 ${{\mathit K}^{+}}$2 ${{\mathit K}^{-}}{{\mathit \pi}^{0}}$ $<2.4\times 10^{-4}$ CL=90% 1339
$\Gamma_{18}$ ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}$ $<6\times 10^{-4}$ CL=90% 1668
$\Gamma_{19}$ ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $(2.8\pm{1.0})\times 10^{-3}$ 1604
FOOTNOTES | 2023-03-23T14:52:15 | {"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": 0.5971623063087463, "perplexity": 3530.237987550699}, "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/1679296945168.36/warc/CC-MAIN-20230323132026-20230323162026-00763.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M192M&home=MXXX025 | #### ${{\boldsymbol X}{(4250)}^{\pm}}$ MASS
VALUE (MeV) DOCUMENT ID TECN COMMENT
$4248$ ${}^{+44}_{-29}$ ${}^{+180}_{-35}$ 1
2008
BELL ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \chi}_{{c1}}{(1P)}}$
1 From a Dalitz plot analysis with two Breit-Wigner amplitudes.
References:
MIZUK 2008
PR D78 072004 Observation of Two Resonancelike Structures in the ${{\mathit \pi}^{+}}{{\mathit \chi}_{{c1}}}$ Mass Distribution in Exclusive ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \chi}_{{c1}}}$ Decays | 2021-11-26T23:00:30 | {"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": 0.9700894951820374, "perplexity": 12954.96524358306}, "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/1637964358074.14/warc/CC-MAIN-20211126224056-20211127014056-00341.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Aavila.artur | ## Avila Cordeiro de Melo, Artur
Compute Distance To:
Author ID: avila.artur Published as: Avila, Artur; Avila, A. Homepage: http://w3.impa.br/~avila/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Awards: Clay Research Award (2006) · EMS Prize (2008) · Fields Medal (2014)
Documents Indexed: 94 Publications since 2001, including 1 Book 1 Contribution as Editor · 1 Further Contribution Biographic References: 8 Publications Co-Authors: 54 Co-Authors with 83 Joint Publications 950 Co-Co-Authors
all top 5
### Co-Authors
12 single-authored 10 Bochi, Jairo 10 Viana, Marcelo 8 Jitomirskaya, Svetlana Yakovlevna 7 Lyubich, Mikhail 7 Wilkinson, Amie 6 Damanik, David 6 Moreira, Carlos Gustavo Tamm de Araujo 5 Yoccoz, Jean-Christophe 4 Fayad, Bassam R. 3 Forni, Giovanni 3 Gouëzel, Sébastien 3 Hubert, Pascal 3 Kocsard, Alejandro 3 Krikorian, Raphaël 3 Matheus, Carlos 3 Santamaria, Jimmy 2 Buff, Xavier 2 Chéritat, Arnaud 2 Crovisier, Sylvain 2 de Melo, Welington 2 Delecroix, Vincent 2 Leguil, Martin 2 Shen, Weixiao 2 Skripchenko, Alexandra 2 Ulcigrai, Corinna 2 Zhou, Qi 1 Abdenur, Flavio 1 Bufetov, Aleksandr Igorevich 1 Candela, Pablo 1 Cheraghi, Davoud 1 de Simoi, Jacopo 1 Dolgopyat, Dmitry 1 Duryev, Eduard 1 Eskin, Alex 1 Kahn, Jeremy Adam 1 Kaloshin, Vadim Yu. 1 Khanin, Konstantin M. 1 Last, Yoram 1 Le Calvez, Patrice 1 Liu, Xiaochuan 1 Martens, Marco 1 Marx, Christoph A. 1 Möller, Martin 1 Rassias, Michael Th. 1 Ravotti, Davide 1 Resende, Maria João 1 Roblin, Thomas 1 Sadel, Christian 1 Sarig, Omri M. 1 Simon, Barry 1 Tsujii, Masato 1 Xu, Disheng 1 You, Jiangong 1 Zhang, Zhenghe 1 Zhang, Zhiyuan
all top 5
### Serials
8 Annals of Mathematics. Second Series 7 Inventiones Mathematicae 6 Journal of the European Mathematical Society (JEMS) 4 Communications in Mathematical Physics 4 Acta Mathematica 4 Duke Mathematical Journal 4 Publications Mathématiques 4 Journal of the American Mathematical Society 3 Bulletin de la Société Mathématique de France 3 Geometric and Functional Analysis. GAFA 3 Journal of Modern Dynamics 2 Israel Journal of Mathematics 2 Nonlinearity 2 Advances in Mathematics 2 Commentarii Mathematici Helvetici 2 Journal of Differential Geometry 2 Mathematische Annalen 2 Ergodic Theory and Dynamical Systems 2 Portugaliae Mathematica. Nova Série 2 Bulletin of the Brazilian Mathematical Society. New Series 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Mathematical Research Letters 1 Discrete and Continuous Dynamical Systems 1 European Mathematical Society Newsletter 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Oberwolfach Reports 1 Astérisque 1 Analysis & PDE 1 Pure and Applied Functional Analysis
all top 5
### Fields
84 Dynamical systems and ergodic theory (37-XX) 17 Operator theory (47-XX) 10 Quantum theory (81-XX) 7 Measure and integration (28-XX) 7 Several complex variables and analytic spaces (32-XX) 5 Ordinary differential equations (34-XX) 4 Difference and functional equations (39-XX) 4 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX)
### Citations contained in zbMATH Open
86 Publications have been cited 1,419 times in 868 Documents Cited by Year
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
2009
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
2006
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
2007
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
2010
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
2006
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
2007
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
2010
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
2015
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031
Avila, Artur; Last, Yoram; Simon, Barry
2010
An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104
Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
2016
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
2009
On the regularization of conservative maps. Zbl 1211.37029
Avila, Artur
2010
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
2013
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
2014
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
2015
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
2017
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Density of positive Lyapunov exponents for $$\text{SL}(2,\mathbb R)$$-cocycles. Zbl 1236.37031
Avila, Artur
2011
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
2015
Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029
Avila, Artur; Moreira, Carlos Gustavo
2005
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
2012
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019
Avila, A.; Jitomirskaya, S.; Marx, C. A.
2017
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
2016
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
2004
Uniformly hyperbolic finite-valued $$\mathrm{SL}(2,\mathbb R)$$-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
2010
Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016
Avila, Artur; Gouëzel, Sébastien
2013
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
2002
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
2007
Symplectic and isometric $$\mathrm{SL}(2,\mathbb{R})$$-invariant subbundles of the Hodge bundle. Zbl 1387.14093
Avila, Artur; Eskin, Alex; Möller, Martin
2017
On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
2015
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
2006
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060
Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O.
2015
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
2011
A generic $$C^1$$ map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
2006
On rigidity of critical circle maps. Zbl 1314.37028
Avila, Artur
2013
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
2011
Nonuniform center bunching and the genericity of ergodicity among $$C^1$$ partially hyperbolic symplectomorphisms. Zbl 1191.37017
Avila, Artur; Bochi, Jairo; Wilkinson, Amie
2009
Cocycles over partially hyperbolic maps. Zbl 1350.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
$$C^1$$ density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
2021
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
2018
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
2011
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
2005
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
2006
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
2016
Robust transitivity and topological mixing for $$C^1$$-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
2004
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
2003
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2018
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
2012
$$\mathrm{SL}(2,\mathbb R)$$-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2013
A uniform dichotomy for generic $$\mathrm{SL}(2,\mathbb R)$$ cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
2007
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
2002
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
2007
Density of positive Lyapunov exponents for quasiperiodic SL$$(2, \mathbb R)$$-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
2009
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012
Avila, Artur; Candela, Pablo
2016
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
2020
Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022
Avila, Artur; Moreira, Carlos Gustavo
2005
Convergence of an exact quantization scheme. Zbl 1068.81041
Avila, Artur
2004
Some monoids of Pisot matrices. Zbl 1445.15016
Avila, Artur; Delecroix, Vincent
2019
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
2005
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
2018
Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002
Avila, Artur; Leguil, Martin
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2018
The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2019
Bifurcations of unimodal maps. Zbl 1070.37018
Avila, Artur; Moreira, Carlos Gustavo
2003
Uniform exponential growth for some $$SL(2,\mathbb R)$$ matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
2009
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
Generic expanding maps without absolutely continuous invariant $$\sigma$$-finite measure. Zbl 1139.28005
Avila, Artur; Bochi, Jairo
2007
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
2011
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
2020
Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028
Avila, Artur
2002
Non-differentiable irrational curves for $$C^1$$ twist map. Zbl 07457813
2022
Stable accessibility with $$2$$ dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
2020
Non-differentiable irrational curves for $$C^1$$ twist map. Zbl 07457813
2022
$$C^1$$ density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
2021
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
2020
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
2020
Stable accessibility with $$2$$ dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
2020
Some monoids of Pisot matrices. Zbl 1445.15016
Avila, Artur; Delecroix, Vincent
2019
The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2019
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
2018
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2018
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
2018
Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002
Avila, Artur; Leguil, Martin
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2018
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
2017
Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019
Avila, A.; Jitomirskaya, S.; Marx, C. A.
2017
Symplectic and isometric $$\mathrm{SL}(2,\mathbb{R})$$-invariant subbundles of the Hodge bundle. Zbl 1387.14093
Avila, Artur; Eskin, Alex; Möller, Martin
2017
An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104
Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
2016
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
2016
On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
2016
Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012
Avila, Artur; Candela, Pablo
2016
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
2015
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
2015
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
2015
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
2015
The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060
Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O.
2015
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
2013
Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016
Avila, Artur; Gouëzel, Sébastien
2013
On rigidity of critical circle maps. Zbl 1314.37028
Avila, Artur
2013
Cocycles over partially hyperbolic maps. Zbl 1350.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
$$\mathrm{SL}(2,\mathbb R)$$-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2013
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
2012
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
2012
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Density of positive Lyapunov exponents for $$\text{SL}(2,\mathbb R)$$-cocycles. Zbl 1236.37031
Avila, Artur
2011
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
2011
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
2011
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
2011
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
2011
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
2010
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
2010
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031
Avila, Artur; Last, Yoram; Simon, Barry
2010
On the regularization of conservative maps. Zbl 1211.37029
Avila, Artur
2010
Uniformly hyperbolic finite-valued $$\mathrm{SL}(2,\mathbb R)$$-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
2010
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
2009
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
2009
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Nonuniform center bunching and the genericity of ergodicity among $$C^1$$ partially hyperbolic symplectomorphisms. Zbl 1191.37017
Avila, Artur; Bochi, Jairo; Wilkinson, Amie
2009
Density of positive Lyapunov exponents for quasiperiodic SL$$(2, \mathbb R)$$-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
2009
Uniform exponential growth for some $$SL(2,\mathbb R)$$ matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
2009
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
2007
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
2007
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
2007
A uniform dichotomy for generic $$\mathrm{SL}(2,\mathbb R)$$ cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
2007
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
2007
Generic expanding maps without absolutely continuous invariant $$\sigma$$-finite measure. Zbl 1139.28005
Avila, Artur; Bochi, Jairo
2007
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
2006
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
2006
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
2006
A generic $$C^1$$ map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
2006
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
2006
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029
Avila, Artur; Moreira, Carlos Gustavo
2005
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
2005
Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022
Avila, Artur; Moreira, Carlos Gustavo
2005
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
2005
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
2004
Robust transitivity and topological mixing for $$C^1$$-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
2004
Convergence of an exact quantization scheme. Zbl 1068.81041
Avila, Artur
2004
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
2003
Bifurcations of unimodal maps. Zbl 1070.37018
Avila, Artur; Moreira, Carlos Gustavo
2003
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
2002
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
2002
Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028
Avila, Artur
2002
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### Cited by 803 Authors
46 Avila Cordeiro de Melo, Artur 31 Damanik, David 27 Jitomirskaya, Svetlana Yakovlevna 15 Bochi, Jairo 15 You, Jiangong 14 Viana, Marcelo 12 Fillman, Jake 12 Matheus, Carlos 12 Zhou, Qi 11 Liu, Wencai 10 Forni, Giovanni 10 Rodriguez-Hertz, Federico 10 Ulcigrai, Corinna 10 Varandas, Paulo 10 Yang, Jiagang 9 Bessa, Mário 9 Breuer, Jonathan 9 Gorodetskii, Anton Semenovich 9 Xu, Junxiang 9 Yoccoz, Jean-Christophe 9 Zhang, Dongfeng 8 Araújo, Vítor 8 Crovisier, Sylvain 8 Hubert, Pascal 8 Kanigowski, Adam 8 Lubinsky, Doron S. 8 Lyubich, Mikhail 8 Tahzibi, Ali 8 Wang, Jing 8 Wilkinson, Amie 8 Zhao, Xin 7 Baladi, Viviane 7 Bjerklöv, Kristian 7 Bufetov, Aleksandr Igorevich 7 Chaika, Jonathan 7 Eskin, Alex 7 Ferenczi, Sébastien 7 Han, Rui 7 Krüger, Helge 7 Rodriguez Hertz, Jana 7 Wright, Alex 7 Yuan, Xiaoping 6 Butterley, Oliver 6 Carrasco, Pablo D. 6 de Melo, Welington 6 Guarino, Pablo 6 Hou, Xuanji 6 Kaloshin, Vadim Yu. 6 Masur, Howard A. 6 Rempe-Gillen, Lasse 6 Sadovskaya, Victoria 6 Xu, Disheng 5 Backes, Lucas H. 5 Bruin, Henk 5 Damjanović, Danijela 5 Gan, Zheng 5 Gelfert, Katrin Grit 5 Goldstein, Michael 5 Gouëzel, Sébastien 5 Oertel-Jäger, Tobias Hendrik 5 Kocsard, Alejandro 5 Krikorian, Raphaël 5 Last, Yoram 5 Marx, Christoph A. 5 Melbourne, Ian 5 Mirzakhani, Maryam 5 Morris, Ian D. 5 Ong, Darren C. 5 Poletti, Mauricio 5 Pollicott, Mark 5 Rams, Michał 5 Shen, Weixiao 5 Skripchenko, Alexandra 5 Smania, Daniel 5 Tao, Kai 5 van Strien, Sebastian J. 5 Yang, Fan 5 Zhang, Zhiyuan 4 Berger, Pierre 4 Bialy, Misha 4 Boissy, Corentin 4 Buff, Xavier 4 Cao, Yongluo 4 Chéritat, Arnaud 4 Dolgopyat, Dmitry 4 Dudko, Artem 4 Fayad, Bassam R. 4 Ge, Lingrui 4 Iommi, Godofredo 4 Khanin, Konstantin M. 4 Klein, Silvius 4 Kocić, Saša 4 Lanneau, Erwan 4 Liang, Jinhao 4 Liverani, Carlangelo 4 Lukic, Milivoje 4 Marin, Karina 4 Qu, Yanhui 4 Ravotti, Davide 4 Rocha, Jorge ...and 703 more Authors
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https://docs.dea.ga.gov.au/notebooks/Scientific_workflows/DEAWaterbodies/DEAWaterbodiesToolkit/IdentifyTimeWaterbodyExceedsXpc.html | # Identify the time a waterbody exceeds X% wet surface area¶
• Compatability: Notebook currently compatible with the NCI environment only. You can make this notebook Sandbox compatible by pointing it to the DEA Waterbodies timeseries located in AWS.
• Products used: None.
• Prerequisites: This notebook explores the individual waterbody timeseries csvs contained within the DEA Waterbodies dataset. It has been designed with that very specific purpose in mind, and is not intended as a general analysis notebook. This notebook in its current form assumes that the RemoveRiversfromWaterBodyPolygons.ipynb <RemoveRiversfromWaterBodyPolygons.ipynb>__ notebook has already been run. You can choose to run this notebook on the non-river filtered polygons, but rivers will produce erroneous results when performing the wet area detection as they are long-standing features in the landscape and a ‘first observed’ analysis will inevitably be limited by observation availability and not reflect the actual feature.
## Description¶
This notebook loops through all of the individual DEA Waterbodies timeseries files and finds the quarter (JFM/AMJ/JAS/OND) that each waterbody is first/last observed at having at least SurfaceAreaThreshold% of the total surface area of the waterbody observed as wet. This attribute is used as a proxy for construction date for built waterbody structures. This date is then appended to the waterbody polygon shapefile as an attribute.
1. Load in the required modules
2. Set up the file paths for inputs/outputs
3. Read in the DEA Waterbodies shapefile
4. Loop through each timeseries and find the quarter where the waterbody is first/last observed at having at least X% of the total surface area of the waterbody observed as wet
5. Append this date to the shapefile
6. Write out an updated shapefile
7. Load in the shapefile again (done as a separate step so you can choose to start to run the notebook from here without re-doing the analysis)
8. Groupby the dates and sum the area of all the polygons first/last observed in that quarter
9. Plot the results
## Getting started¶
To run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.
Import Python packages that are used for the analysis.
[2]:
%matplotlib inline
import matplotlib.pyplot as plt
import fiona
import geopandas as gp
import numpy as np
import pandas as pd
from pandas.plotting import register_matplotlib_converters
register_matplotlib_converters()
### Analysis parameters¶
• WaterBodyRiverFiltered: file path to the DEA Waterbodies shapefile to read in
• CSVFolder: file path to the folder of DEA Waterbodies timeseries
• SurfaceAreaThreshold: e.g. 50. Select the percentage of the total surface area of the waterbody that must have been observed as wet as a single time period.
• FirstorLastIndex: e.g. {‘First’: 0} for first, or {‘Last’: -1} for last. Set which index to pull out depending on whether you want to find the first time the surface area wetness threshold was met, or the last time it was.
[3]:
WaterBodyRiverFiltered = '/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesFINALRiverFiltered.shp'
CSVFolder = '/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/timeseries_aus_uid/'
SurfaceAreaThreshold = 50
FirstorLastIndex = {'First': 0}
### Read in data and loop through each timeseries¶
[3]:
WaterBodyRiverFilteredShapes = gp.read_file(WaterBodyRiverFiltered)
# Set up an empty attribute to write into
WaterBodyRiverFilteredShapes[f'Time {list(FirstorLastIndex.keys())[0]} Exceeds {SurfaceAreaThreshold}%'] = -999
[4]:
PolygonsThatDidntWork = []
for shapes in fiona.open(WaterBodyRiverFiltered):
polyName = shapes['properties']['UID']
# Read in the correct csv file
try:
except:
continue
# Change the date column to an actual datetime object
Timeseries['Observation Date'] = pd.to_datetime(
Timeseries['Observation Date'])
Timeseries = Timeseries.set_index(['Observation Date'])
# Aggregate the timeseries quarterly
QuartelyAveraged = Timeseries.resample('Q', label='left').agg('max')
try:
# Find the first time that the timeseries is greater than or equal to 50%
IndexExceeds = np.where(
QuartelyAveraged['Wet pixel percentage'] >=
SurfaceAreaThreshold)[0][list(FirstorLastIndex.values())[0]]
TimeExceeds = QuartelyAveraged.iloc[IndexExceeds]
DateString, BitToThrowOut = str(TimeExceeds.name).split(' ')
except:
print('Another one that didn\'t work...')
PolygonsThatDidntWork.append(polyName)
continue
# Put the values back into the dataframe
WaterBodyRiverFilteredShapes.at[WaterBodyRiverFilteredShapes.loc[
WaterBodyRiverFilteredShapes['UID'] ==
polyName].index, f'{list(FirstorLastIndex.keys())[0]}{SurfaceAreaThreshold}%'] = DateString
WaterBodyRiverFilteredShapes.to_file(
f'/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesFINALRiverFilteredTimeseries{list(FirstorLastIndex.keys())[0]}{SurfaceAreaThreshold}.shp'
)
Another one that didn't work...
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Can't open/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/timeseries_aus_uid/qv6p/qv6p0jr15.csv
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Can't open/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/timeseries_aus_uid/qvzf/qvzfjh7uf.csv
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## Calculate some statistics on the timing of waterbodies wet observations¶
Load back in the new appended shapefile and add up the total surface area of waterbodies that were first/last seen as at least X% wet in each quarter through time.
Note that this notebook can be run starting from this point, ignoring the processing cell above if it has previously been run.
[9]:
AllTheData = gp.read_file(f'/g/data/r78/cek156/dea-notebooks/Scientific_workflows/DEAWaterbodies/AusAllTime01-005HybridWaterbodies/AusWaterBodiesFINALRiverFilteredTimeseries{list(FirstorLastIndex.keys())[0]}{SurfaceAreaThreshold}.shp')
### Group the data by quarter, remove missing values and convert to $$km^2$$¶
[10]:
# Group all the waterbodies by quarters and sum them up
GroupedData = AllTheData.groupby(by=f'{list(FirstorLastIndex.keys())[0]}{SurfaceAreaThreshold}%').sum()
# Drop the -999 missing values
CleanedData = GroupedData.drop('-999')
[11]:
# Convert the quarter dates to a pandas datetime object
CleanedData.index = pd.to_datetime(CleanedData.index)
# Convert from m2 to km2
CleanedData['area'] = CleanedData['area'] / 1000000
### Plot the results¶
[20]:
plt.figure(figsize=[10, 8])
plt.plot(CleanedData.area.cumsum())
plt.xlim('1992-01-01', '2018-01-01')
plt.ylim(40000, 55000)
plt.ylabel('Total area of water bodies ($km^2$)')
plt.xlabel(f'Time each waterbody {list(FirstorLastIndex.keys())[0]} observed at having at least {SurfaceAreaThreshold}% \n'
'of the total surface area of the waterbody observed as wet')
plt.title(f'Total area of waterbodies {list(FirstorLastIndex.keys())[0]} observed as {SurfaceAreaThreshold}% wet each quarter')
plt.rcParams["font.size"] = "14"
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github. | 2020-02-27T07:40:39 | {"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": 1, "mathjax_display_tex": 1, "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": 0.1876131147146225, "perplexity": 8523.098868599911}, "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/1581875146665.7/warc/CC-MAIN-20200227063824-20200227093824-00507.warc.gz"} |
https://malegislature.gov/Laws/GeneralLaws/PartIV/TitleI/Chapter269/Section11A | # General Laws
## Section 11A Definitions
Section 11A. For the purposes of this section and sections eleven B, eleven C and eleven D, the following words shall have the following meanings:?
''Firearm'', a firearm as defined in section one hundred and twenty-one of chapter one hundred and forty, or a rifle or shotgun.
''Serial number'', the number stamped or placed upon a firearm by the manufacturer in the original process of manufacture.
''Identification number'', the number stamped or placed upon a firearm by the colonel of the state police under authority of section eleven D. | 2016-05-01T06:20:04 | {"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": 0.8028081059455872, "perplexity": 4839.528490966163}, "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-2016-18/segments/1461860114285.77/warc/CC-MAIN-20160428161514-00120-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Akabluchko.zakhar-a | # zbMATH — the first resource for mathematics
## Kabluchko, Zakhar A.
Compute Distance To:
Author ID: kabluchko.zakhar-a Published as: Kabluchko, Z.; Kabluchko, Z. A.; Kabluchko, Zakhar; Kabluchko, Zakhar A. Homepage: https://www.uni-muenster.de/Stochastik/Arbeitsgruppen/Kabluchko/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · GND
Documents Indexed: 82 Publications since 2001 Reviewing Activity: 83 Reviews
all top 5
#### Co-Authors
14 single-authored 13 Zaporozhets, Dmitry 11 Marynych, Alexander V. 9 Thäle, Christoph 8 Iksanov, Aleksander M. 7 Schlather, Martin 5 Engelke, Sebastian 5 Prochno, Joscha 5 Vysotsky, Vladislav V. 4 Alsmeyer, Gerold 3 Lifshits, Mikhail A. 3 Munk, Axel 2 Dombry, Clément 2 Flasche, Hendrik 2 Grübel, Rudolf 2 Proskurin, Daniil P. 2 Sulzbach, Henning 2 Temesvari, Daniel 1 Ballani, Felix 1 Davies, Patrick Laurie 1 de Haan, Laurens 1 Denker, Manfred 1 Götze, Friedrich W. 1 Grote, Julian 1 Gusakova, Anna Grigorevna 1 Hashorva, Enkelejd 1 Hotz, Thomas 1 Hug, Daniel 1 Ibragimov, Il’dar Abdullovich 1 Kim, Chesoong 1 Klimovsky, Anton 1 Last, Günter 1 Litvak, Aleksandr Evgen’evich 1 Löwe, Matthias 1 Malinowski, Alexander 1 Marnitz, Philipp 1 Oesting, Marco 1 Samoĭlenko, Yuriĭ Stefanovych 1 Schubert, Kristina 1 Seidel, Hauke 1 Shevchenko, Georgiy M. 1 Spodarev, Evgueni 1 Stichtenoth, Rahel 1 Stoev, Stilian A. 1 Wang, Yizao 1 Wübker, Achim
all top 5
#### Serials
9 Stochastic Processes and their Applications 5 Bernoulli 5 Extremes 4 The Annals of Probability 4 The Annals of Applied Probability 4 Journal of Mathematical Sciences (New York) 3 Journal of Applied Probability 3 Proceedings of the American Mathematical Society 3 Transactions of the American Mathematical Society 3 Statistics & Probability Letters 3 Journal of Theoretical Probability 3 Electronic Journal of Probability 3 Electronic Communications in Probability 2 Advances in Applied Probability 2 Advances in Mathematics 2 Probability Theory and Related Fields 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Communications in Contemporary Mathematics 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Israel Journal of Mathematics 1 Journal of Statistical Physics 1 Studia Mathematica 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 Reviews in Mathematical Physics 1 Journal of Approximation Theory 1 Mathematische Nachrichten 1 Mathematika 1 Probability and Mathematical Statistics 1 Discrete & Computational Geometry 1 Geometric and Functional Analysis. GAFA 1 Computational Statistics and Data Analysis 1 Izvestiya: Mathematics 1 Methods of Functional Analysis and Topology 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Journal of Integer Sequences 1 Theory of Stochastic Processes
all top 5
#### Fields
76 Probability theory and stochastic processes (60-XX) 17 Convex and discrete geometry (52-XX) 7 Functions of a complex variable (30-XX) 7 Functional analysis (46-XX) 4 Real functions (26-XX) 3 Number theory (11-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX)
#### Citations contained in zbMATH
67 Publications have been cited 528 times in 291 Documents Cited by Year
Stationary max-stable fields associated to negative definite functions. Zbl 1208.60051
Kabluchko, Zakhar; Schlather, Martin; de Haan, Laurens
2009
Spectral representations of sum- and max-stable processes. Zbl 1224.60120
Kabluchko, Zakhar
2009
Simulation of Brown-Resnick processes. Zbl 1329.60157
Oesting, Marco; Kabluchko, Zakhar; Schlather, Martin
2012
Asymptotic distribution of complex zeros of random analytic functions. Zbl 1295.30008
Kabluchko, Zakhar; Zaporozhets, Dmitry
2014
Extremes of independent Gaussian processes. Zbl 1329.60152
Kabluchko, Zakhar
2011
Extremes of the standardized Gaussian noise. Zbl 1225.60084
Kabluchko, Zakhar
2011
Ergodic properties of max-infinitely divisible processes. Zbl 1205.60101
Kabluchko, Zakhar; Schlather, Martin
2010
Stochastic integral representations and classification of sum- and max-infinitely divisible processes. Zbl 1339.60065
Kabluchko, Zakhar; Stoev, Stilian
2016
Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. Zbl 1414.60038
Engelke, Sebastian; Malinowski, Alexander; Kabluchko, Zakhar; Schlather, Martin
2015
Extremes of independent chi-square random vectors. Zbl 1329.60028
Hashorva, Enkelejd; Kabluchko, Zakhar; Wübker, Achim
2012
Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Zbl 1373.52009
Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry
2017
Ergodic decompositions of stationary max-stable processes in terms of their spectral functions. Zbl 1367.60056
Dombry, Clément; Kabluchko, Zakhar
2017
Locally adaptive image denoising by a statistical multiresolution criterion. Zbl 1239.62116
Hotz, Thomas; Marnitz, Philipp; Stichtenoth, Rahel; Davies, Laurie; Kabluchko, Zakhar; Munk, Axel
2012
An equivalent representation of the Brown-Resnick process. Zbl 1234.60056
Engelke, S.; Kabluchko, Z.; Schlather, M.
2011
Maxima of independent, non-identically distributed Gaussian vectors. Zbl 1322.60073
Engelke, Sebastian; Kabluchko, Zakhar; Schlather, Martin
2015
Random tessellations associated with max-stable random fields. Zbl 1388.60092
Dombry, Clément; Kabluchko, Zakhar
2018
Critical points of random polynomials with independent identically distributed roots. Zbl 1314.30008
Kabluchko, Zakhar
2015
Exact convergence rate for the maximum of standardized Gaussian increments. Zbl 1189.60063
Kabluchko, Zakhar; Munk, Axel
2008
An Erdős-Rényi law for mixing processes. Zbl 1125.60023
Denker, Manfred; Kabluchko, Zakhar
2007
Local universality for real roots of random trigonometric polynomials. Zbl 1361.30009
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander
2016
Roots of random polynomials whose coefficients have logarithmic tails. Zbl 1364.26019
Kabluchko, Zakhar; Zaporozhets, Dmitry
2013
Stationary systems of Gaussian processes. Zbl 1230.60054
Kabluchko, Zakhar
2010
Shao’s theorem on the maximum of standardized random walk increments for multidimensional arrays. Zbl 1188.60014
Kabluchko, Zakhar; Munk, Axel
2009
Expected intrinsic volumes and facet numbers of random beta-polytopes. Zbl 1414.52003
Kabluchko, Zakhar; Temesvari, Daniel; Thäle, Christoph
2019
High-dimensional limit theorems for random vectors in $$\ell_p^n$$-balls. Zbl 1412.52007
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2019
Limit theorems for random simplices in high dimensions. Zbl 07004723
Grote, Julian; Kabluchko, Zakhar; Thäle, Christoph
2019
A functional central limit theorem for branching random walks, almost sure weak convergence and applications to random trees. Zbl 1367.60028
Grübel, Rudolf; Kabluchko, Zakhar
2016
Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls. Zbl 1366.60025
Kabluchko, Zakhar; Zaporozhets, Dmitry
2016
Limiting distribution for the maximal standardized increment of a random walk. Zbl 1323.60074
Kabluchko, Zakhar; Wang, Yizao
2014
Distribution of levels in high-dimensional random landscapes. Zbl 1246.60036
Kabluchko, Zakhar
2012
Edgeworth expansions for profiles of lattice branching random walks. Zbl 1387.60075
Grübel, Rudolf; Kabluchko, Zakhar
2017
Fractionally integrated inverse stable subordinators. Zbl 1353.60032
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander; Shevchenko, Georgiy
2017
Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Zbl 1337.60021
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander
2016
Max-stable processes and stationary systems of Lévy particles. Zbl 1330.60065
Engelke, Sebastian; Kabluchko, Zakhar
2015
Complex random energy model: zeros and fluctuations. Zbl 1292.60052
Kabluchko, Zakhar; Klimovsky, Anton
2014
Random marked sets. Zbl 1266.60091
Ballani, F.; Kabluchko, Z.; Schlather, M.
2012
Sanov-type large deviations in Schatten classes. Zbl 1445.60012
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2020
Cones generated by random points on half-spheres and convex hulls of Poisson point processes. Zbl 1428.52007
Kabluchko, Zakhar; Marynych, Alexander; Temesvari, Daniel; Thäle, Christoph
2019
General Edgeworth expansions with applications to profiles of random trees. Zbl 1382.60068
Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
2017
A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk. Zbl 1356.60055
Iksanov, Alexander; Kabluchko, Zakhar
2016
Functional limit theorems for sums of independent geometric Lévy processes. Zbl 1225.60056
Kabluchko, Zakhar
2011
Extremes of space-time Gaussian processes. Zbl 1181.60075
Kabluchko, Zakhar
2009
Convex hulls of random walks: expected number of faces and face probabilities. Zbl 1377.52007
Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry
2017
Inclusion-exclusion principles for convex hulls and the Euler relation. Zbl 1376.52010
Kabluchko, Zakhar; Last, Günter; Zaporozhets, Dmitry
2017
Renewal shot noise processes in the case of slowly varying tails. Zbl 1374.60174
Kabluchko, Zakhar; Marynych, Alexander
2016
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields. Zbl 1339.60038
Zaporozhets, D.; Kabluchko, Z.
2014
Scan statistics of Lévy noises and marked empirical processes. Zbl 1162.60016
Kabluchko, Zakhar; Spodarev, Evgeny
2009
Limiting distribution of the continuity modulus for Gaussian processes with stationary increments. Zbl 1159.60324
Kabluchko, Zakhar
2009
On the extension of higher-dimensional noncommutative tori. Zbl 0980.46050
Kabluchko, Zakhar A.
2001
Limit theorems for the least common multiple of a random set of integers. Zbl 07110634
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2019
A functional limit theorem for the profile of random recursive trees. Zbl 1406.60051
Iksanov, Alexander; Kabluchko, Zakhar
2018
A leader-election procedure using records. Zbl 1392.60025
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2017
Mean width of regular polytopes and expected maxima of correlated Gaussian variables. Zbl 1381.52010
Kabluchko, Zakhar; Litvak, A. E.; Zaporozhets, D.
2017
Least energy approximation for processes with stationary increments. Zbl 1419.60030
Kabluchko, Zakhar; Lifshits, Mikhail
2017
Limit laws for sums of independent random products: the lattice case. Zbl 1251.60040
Kabluchko, Zakhar
2012
Beta polytopes and Poisson polyhedra: $$f$$-vectors and angles. Zbl 1448.52005
Kabluchko, Zakhar; Thäle, Christoph; Zaporozhets, Dmitry
2020
Exact asymptotic volume and volume ratio of Schatten unit balls. Zbl 07227729
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2020
Angle sums of random simplices in dimensions $$3$$ and $$4$$. Zbl 1441.52006
Kabluchko, Zakhar
2020
Some extensions of linear approximation and prediction problems for stationary processes. Zbl 1422.60055
Ibragimov, Ildar; Kabluchko, Zakhar; Lifshits, Mikhail
2019
Expected volumes of Gaussian polytopes, external angles, and multiple order statistics. Zbl 07076088
Kabluchko, Zakhar; Zaporozhets, Dmitry
2019
Distances between zeroes and critical points for random polynomials with i.i.d. zeroes. Zbl 1420.30003
Kabluchko, Zakhar; Seidel, Hauke
2019
Weak convergence of the number of vertices at intermediate levels of random recursive trees. Zbl 1405.60031
Iksanov, Alexander; Kabluchko, Zakhar
2018
An inclusion-exclusion identity for normal cones of polyhedral sets. Zbl 1390.52019
Hug, Daniel; Kabluchko, Zakhar
2018
Monotonicity of expected $$f$$-vectors for projections of regular polytopes. Zbl 1382.52004
Kabluchko, Zakhar; Thäle, Christoph
2018
Leader election using random walks. Zbl 1355.60057
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2016
Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers. Zbl 1367.11029
Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
2016
A characterization of the normal distribution using stationary max-stable processes. Zbl 1333.60100
Engelke, Sebastian; Kabluchko, Zakhar
2016
Sanov-type large deviations in Schatten classes. Zbl 1445.60012
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2020
Beta polytopes and Poisson polyhedra: $$f$$-vectors and angles. Zbl 1448.52005
Kabluchko, Zakhar; Thäle, Christoph; Zaporozhets, Dmitry
2020
Exact asymptotic volume and volume ratio of Schatten unit balls. Zbl 07227729
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2020
Angle sums of random simplices in dimensions $$3$$ and $$4$$. Zbl 1441.52006
Kabluchko, Zakhar
2020
Expected intrinsic volumes and facet numbers of random beta-polytopes. Zbl 1414.52003
Kabluchko, Zakhar; Temesvari, Daniel; Thäle, Christoph
2019
High-dimensional limit theorems for random vectors in $$\ell_p^n$$-balls. Zbl 1412.52007
Kabluchko, Zakhar; Prochno, Joscha; Thäle, Christoph
2019
Limit theorems for random simplices in high dimensions. Zbl 07004723
Grote, Julian; Kabluchko, Zakhar; Thäle, Christoph
2019
Cones generated by random points on half-spheres and convex hulls of Poisson point processes. Zbl 1428.52007
Kabluchko, Zakhar; Marynych, Alexander; Temesvari, Daniel; Thäle, Christoph
2019
Limit theorems for the least common multiple of a random set of integers. Zbl 07110634
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2019
Some extensions of linear approximation and prediction problems for stationary processes. Zbl 1422.60055
Ibragimov, Ildar; Kabluchko, Zakhar; Lifshits, Mikhail
2019
Expected volumes of Gaussian polytopes, external angles, and multiple order statistics. Zbl 07076088
Kabluchko, Zakhar; Zaporozhets, Dmitry
2019
Distances between zeroes and critical points for random polynomials with i.i.d. zeroes. Zbl 1420.30003
Kabluchko, Zakhar; Seidel, Hauke
2019
Random tessellations associated with max-stable random fields. Zbl 1388.60092
Dombry, Clément; Kabluchko, Zakhar
2018
A functional limit theorem for the profile of random recursive trees. Zbl 1406.60051
Iksanov, Alexander; Kabluchko, Zakhar
2018
Weak convergence of the number of vertices at intermediate levels of random recursive trees. Zbl 1405.60031
Iksanov, Alexander; Kabluchko, Zakhar
2018
An inclusion-exclusion identity for normal cones of polyhedral sets. Zbl 1390.52019
Hug, Daniel; Kabluchko, Zakhar
2018
Monotonicity of expected $$f$$-vectors for projections of regular polytopes. Zbl 1382.52004
Kabluchko, Zakhar; Thäle, Christoph
2018
Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Zbl 1373.52009
Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry
2017
Ergodic decompositions of stationary max-stable processes in terms of their spectral functions. Zbl 1367.60056
Dombry, Clément; Kabluchko, Zakhar
2017
Edgeworth expansions for profiles of lattice branching random walks. Zbl 1387.60075
Grübel, Rudolf; Kabluchko, Zakhar
2017
Fractionally integrated inverse stable subordinators. Zbl 1353.60032
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander; Shevchenko, Georgiy
2017
General Edgeworth expansions with applications to profiles of random trees. Zbl 1382.60068
Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
2017
Convex hulls of random walks: expected number of faces and face probabilities. Zbl 1377.52007
Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry
2017
Inclusion-exclusion principles for convex hulls and the Euler relation. Zbl 1376.52010
Kabluchko, Zakhar; Last, Günter; Zaporozhets, Dmitry
2017
A leader-election procedure using records. Zbl 1392.60025
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2017
Mean width of regular polytopes and expected maxima of correlated Gaussian variables. Zbl 1381.52010
Kabluchko, Zakhar; Litvak, A. E.; Zaporozhets, D.
2017
Least energy approximation for processes with stationary increments. Zbl 1419.60030
Kabluchko, Zakhar; Lifshits, Mikhail
2017
Stochastic integral representations and classification of sum- and max-infinitely divisible processes. Zbl 1339.60065
Kabluchko, Zakhar; Stoev, Stilian
2016
Local universality for real roots of random trigonometric polynomials. Zbl 1361.30009
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander
2016
A functional central limit theorem for branching random walks, almost sure weak convergence and applications to random trees. Zbl 1367.60028
Grübel, Rudolf; Kabluchko, Zakhar
2016
Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls. Zbl 1366.60025
Kabluchko, Zakhar; Zaporozhets, Dmitry
2016
Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Zbl 1337.60021
Iksanov, Alexander; Kabluchko, Zakhar; Marynych, Alexander
2016
A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk. Zbl 1356.60055
Iksanov, Alexander; Kabluchko, Zakhar
2016
Renewal shot noise processes in the case of slowly varying tails. Zbl 1374.60174
Kabluchko, Zakhar; Marynych, Alexander
2016
Leader election using random walks. Zbl 1355.60057
Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
2016
Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers. Zbl 1367.11029
Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
2016
A characterization of the normal distribution using stationary max-stable processes. Zbl 1333.60100
Engelke, Sebastian; Kabluchko, Zakhar
2016
Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. Zbl 1414.60038
Engelke, Sebastian; Malinowski, Alexander; Kabluchko, Zakhar; Schlather, Martin
2015
Maxima of independent, non-identically distributed Gaussian vectors. Zbl 1322.60073
Engelke, Sebastian; Kabluchko, Zakhar; Schlather, Martin
2015
Critical points of random polynomials with independent identically distributed roots. Zbl 1314.30008
Kabluchko, Zakhar
2015
Max-stable processes and stationary systems of Lévy particles. Zbl 1330.60065
Engelke, Sebastian; Kabluchko, Zakhar
2015
Asymptotic distribution of complex zeros of random analytic functions. Zbl 1295.30008
Kabluchko, Zakhar; Zaporozhets, Dmitry
2014
Limiting distribution for the maximal standardized increment of a random walk. Zbl 1323.60074
Kabluchko, Zakhar; Wang, Yizao
2014
Complex random energy model: zeros and fluctuations. Zbl 1292.60052
Kabluchko, Zakhar; Klimovsky, Anton
2014
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields. Zbl 1339.60038
Zaporozhets, D.; Kabluchko, Z.
2014
Roots of random polynomials whose coefficients have logarithmic tails. Zbl 1364.26019
Kabluchko, Zakhar; Zaporozhets, Dmitry
2013
Simulation of Brown-Resnick processes. Zbl 1329.60157
Oesting, Marco; Kabluchko, Zakhar; Schlather, Martin
2012
Extremes of independent chi-square random vectors. Zbl 1329.60028
Hashorva, Enkelejd; Kabluchko, Zakhar; Wübker, Achim
2012
Locally adaptive image denoising by a statistical multiresolution criterion. Zbl 1239.62116
Hotz, Thomas; Marnitz, Philipp; Stichtenoth, Rahel; Davies, Laurie; Kabluchko, Zakhar; Munk, Axel
2012
Distribution of levels in high-dimensional random landscapes. Zbl 1246.60036
Kabluchko, Zakhar
2012
Random marked sets. Zbl 1266.60091
Ballani, F.; Kabluchko, Z.; Schlather, M.
2012
Limit laws for sums of independent random products: the lattice case. Zbl 1251.60040
Kabluchko, Zakhar
2012
Extremes of independent Gaussian processes. Zbl 1329.60152
Kabluchko, Zakhar
2011
Extremes of the standardized Gaussian noise. Zbl 1225.60084
Kabluchko, Zakhar
2011
An equivalent representation of the Brown-Resnick process. Zbl 1234.60056
Engelke, S.; Kabluchko, Z.; Schlather, M.
2011
Functional limit theorems for sums of independent geometric Lévy processes. Zbl 1225.60056
Kabluchko, Zakhar
2011
Ergodic properties of max-infinitely divisible processes. Zbl 1205.60101
Kabluchko, Zakhar; Schlather, Martin
2010
Stationary systems of Gaussian processes. Zbl 1230.60054
Kabluchko, Zakhar
2010
Stationary max-stable fields associated to negative definite functions. Zbl 1208.60051
Kabluchko, Zakhar; Schlather, Martin; de Haan, Laurens
2009
Spectral representations of sum- and max-stable processes. Zbl 1224.60120
Kabluchko, Zakhar
2009
Shao’s theorem on the maximum of standardized random walk increments for multidimensional arrays. Zbl 1188.60014
Kabluchko, Zakhar; Munk, Axel
2009
Extremes of space-time Gaussian processes. Zbl 1181.60075
Kabluchko, Zakhar
2009
Scan statistics of Lévy noises and marked empirical processes. Zbl 1162.60016
Kabluchko, Zakhar; Spodarev, Evgeny
2009
Limiting distribution of the continuity modulus for Gaussian processes with stationary increments. Zbl 1159.60324
Kabluchko, Zakhar
2009
Exact convergence rate for the maximum of standardized Gaussian increments. Zbl 1189.60063
Kabluchko, Zakhar; Munk, Axel
2008
An Erdős-Rényi law for mixing processes. Zbl 1125.60023
Denker, Manfred; Kabluchko, Zakhar
2007
On the extension of higher-dimensional noncommutative tori. Zbl 0980.46050
Kabluchko, Zakhar A.
2001
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49 Kabluchko, Zakhar A. 22 Hashorva, Enkelejd 12 Zaporozhets, Dmitry 11 Schlather, Martin 11 Wang, Yizao 10 Marynych, Alexander V. 10 Stoev, Stilian A. 9 Iksanov, Aleksander M. 9 Thäle, Christoph 8 Dombry, Clément 8 Engelke, Sebastian 8 Tan, Zhongquan 7 Dębicki, Krzysztof 7 Molchanov, Ilya S. 7 Munk, Axel 7 Oesting, Marco 6 Gao, Zhiqiang 6 Prochno, Joscha 6 Strokorb, Kirstin 5 Davis, Richard A. 5 Huser, Raphaël 5 Peng, Zuoxiang 5 Pritsker, Igor E. 5 Vysotsky, Vladislav V. 4 Bacro, Jean-Noël 4 Davison, Anthony C. 4 Hintermüller, Michael 4 Klüppelberg, Claudia 4 Liu, Quansheng 4 Mikosch, Thomas 4 Padoan, Simone A. 4 Roy, Parthanil 4 Weng, Zhichao 3 Arias-Castro, Ery 3 Buhl, Sven 3 Eyi-Minko, Frédéric 3 Frick, Klaus 3 Gaetan, Carlo 3 Genton, Marc G. 3 Hug, Daniel 3 Koch, Erwan 3 Liao, Xin 3 Lifshits, Mikhail A. 3 Marnitz, Philipp 3 Opitz, Thomas 3 Poly, Guillaume 3 Rautenberg, Carlos N. 3 Ribatet, Mathieu 3 Robert, Christian Yann 3 Samorodnitsky, Gennady Pinkhosovich 3 Segers, Johan 3 So, Mike K. P. 3 Sulzbach, Henning 3 Takahasi, Hiroki 3 Temesvari, Daniel 2 Alonso-Gutiérrez, David 2 Angst, Jürgen 2 Ballani, Felix 2 Beneš, Viktor 2 Bissantz, Nicolai 2 Bloom, Thomas 2 Chan, Raymond K. S. 2 Chasapis, Giorgos 2 Chown, Justin 2 Cooley, Daniel S. 2 Davies, Patrick Laurie 2 Dette, Holger 2 Dieker, A. B. 2 Falk, Michael 2 Flasche, Hendrik 2 Götze, Friedrich W. 2 Ibragimov, Il’dar Abdullovich 2 Ji, Lanpeng 2 Kiriliouk, Anna 2 Klimovsky, Anton 2 Krupskii, Pavel 2 Meiners, Matthias 2 Nishry, Alon 2 Owada, Takashi 2 Papastathopoulos, Ioannis 2 Popescu, Gelu 2 Račkauskas, Alfredas Yurgevich 2 Reich, Brian James 2 Rhodes, Rémi 2 Ribereau, Pierre 2 Schneider, Rolf G. 2 Šedivý, Ondřej 2 Sodin, Mikhail 2 Soulier, Philippe 2 Staněk, Jakub 2 Steinerberger, Stefan 2 Steinkohl, Christina 2 Stucki, Kaspar 2 Tawn, Jonathan A. 2 Thibaud, Emeric 2 Toulemonde, Gwladys 2 Uribe Bravo, Gerónimo 2 Vargas, Vincent 2 Werner, Frank 2 Williams, Noah ...and 220 more Authors
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https://read.dukeupress.edu/demography/article/59/2/607/294500/Death-by-Robots-Automation-and-Working-Age | ## Abstract
The decline of manufacturing employment is frequently invoked as a key cause of worsening U.S. population health trends, including rising mortality due to “deaths of despair.” Increasing automation—the use of industrial robots to perform tasks previously done by human workers—is one structural force driving the decline of manufacturing jobs and wages. In this study, we examine the impact of automation on age- and sex-specific mortality. Using exogenous variation in automation to support causal inference, we find that increases in automation over the period 1993–2007 led to substantive increases in all-cause mortality for both men and women aged 45–54. Disaggregating by cause, we find evidence that automation is associated with increases in drug overdose deaths, suicide, homicide, and cardiovascular mortality, although patterns differ by age and sex. We further examine heterogeneity in effects by safety net program generosity, labor market policies, and the supply of prescription opioids.
## Introduction
Today, a person born in the United States is expected to die an average of three years sooner than persons born in other high-income countries (Ho and Hendi 2018). This was not always the case: U.S. life expectancy diverged from that in peer countries starting around 1980, relative stagnation that recently culminated in a decline in expected longevity for the first time on record (Woolf and Schoomaker 2019). Demographic evidence reveals that this deterioration in U.S. population health is driven primarily by rising mortality among less educated, working-age adults. Increasing premature death in this subgroup—from suicide, drug overdose, and other so-called “deaths of despair”—has received widespread attention in both academic and popular discourse (Case and Deaton 2017).
The most common explanations attribute this troubling trend to structural changes in the U.S. economy, which reduced opportunity and increased precarity for working-age adults without a four-year college degree. A growing body of empirical research supports this contention (Coile and Duggan 2019; Naik et al. 2019; Seltzer 2020; Venkataramani, O'Brien et al. 2020). Much of this work examines the impact of the decline in domestic manufacturing, a sector that historically served as a path to the middle class for those without a college degree (Cherlin 2014). For example, Venkataramani, Bair et al. (2020) found that sharp reductions in local manufacturing jobs following automobile assembly plant closures led to an acute increase in opioid overdose mortality. Other studies have linked exposure to competition from foreign manufacturing—which reduces wages and employment opportunities for domestic manufacturing workers—to increases in mortality among working-age men with less education (Adda and Fawaz 2020; Autor et al. 2019; Pierce and Schott 2020).
This article examines the mortality impact of another structural force behind the decline of manufacturing: automation. Since the 1980s, technological improvements, coupled with the pressures of an increasingly competitive global marketplace, have fueled the adoption of industrial robots on plant floors (Acemoglu and Restrepo 2020; Autor and Salomons 2018). Although automation in some sectors may augment opportunities and raise wages by increasing the productivity of human workers (Autor 2015; Eggleston et al. 2021), this specific class of industrial robots displaced workers. According to work by Acemoglu and Restrepo (2020), adoption of industrial robots led to the loss of an estimated 420,000–750,000 jobs over the 1990s and 2000s, the majority of which were in manufacturing; workers fortunate enough to keep their jobs still experienced meaningful declines in wages (Acemoglu and Restrepo 2020).
The decline in economic opportunities due to automation has been borne primarily by less educated workers, the same group that has faced rising mortality rates. This suggests a causal link between automation and mortality, which we argue may operate through “material” pathways by impacting current employment, wages, and access to health care, as well as through “despair” pathways by reducing future economic opportunities. Although a recent consensus study report from the National Academies of Sciences, Engineering, and Medicine (2021:6) identifies “technological advances that replace workers” as one potential driver of increasing working-age mortality, this association has not been examined in the literature. With the adoption of industrial robots projected to increase twofold to fourfold in the coming decade (Acemoglu and Restrepo 2020)—a trend that may be further exacerbated by responses to the COVID-19 pandemic (Chernoff and Warman 2020)—understanding the potential consequences of automation on mortality outcomes is critical for policymakers. It is also instructive to examine heterogeneity in these relationships to identify policies that may mitigate any adverse consequences of continued automation on population health.
We use newly available measures of the adoption of industrial robots across U.S. commuting zones between 1993 and 2007 to examine the impacts of one key form of automation on mortality. Specifically, we apply the instrumental variable strategy used by Acemoglu and Restrepo (2020), who created a plausibly exogenous measure of robot penetration by combining information on preexisting employment shares in different industries in each commuting zone with the trajectory of robot adoption in each of those industries from a set of European countries. This method addresses confounding from omitted factors that may affect both automation and mortality. For example, health may have been worsening among workers even prior to automation, which may induce firms to replace sicker workers with robots. In the absence of the instrumental variable, such a process may lead us to erroneously draw a relationship between automation and population health. Combining this instrument with restricted-access U.S. death certificate data from 1993–2007, we estimate the causal effect of commuting zone–level automation on cause-specific, county-level mortality among working-age adults by age and sex in a series of first-differences models.
We find that increases in automation led to substantive increases in mortality, with positive and statistically significant effects on all-cause mortality for both men and women aged 45–54, the same age-group that has seen mortality increase in recent years. Point estimates indicate that each additional robot per 1,000 workers led to just over eight additional deaths per 100,000 males aged 45–54 and just under four additional deaths per 100,000 females in the same age-group. Automation, therefore, contributed to the slowdown in mortality improvements over this study period, portending the absolute increase observed for some subgroups in recent years (Case and Deaton 2017). Disaggregating by cause, we find that automation led to increases in drug overdose mortality for men of all age-groups and for younger (20–29) women; our estimates indicate that automation explains 12% of the overall increase in drug overdose mortality among all working-age adults over the study period. Automation also led to a substantial increase in suicide mortality for males aged 45–54, contributing to the secular rise in suicide mortality for middle-aged males observed in recent decades (Hedegaard et al. 2020). We also see evidence that automation was associated with increased homicide, cancer, and cardiovascular mortality in specific age–sex groups. Our findings are robust to accounting for preexisting trends in mortality and removing “outlier” commuting zones with exceptionally high penetration of industrial robots during the study period.
This study is among the first to demonstrate a causal association between long-run secular trends of automation-induced deindustrialization and working-age mortality.1 Our findings are consistent with a large body of work correlating declines in manufacturing with worsening individual and population health, including mortality (e.g., Seltzer 2020). They are also in line with research identifying the causal effect of long-run manufacturing decline on mortality in specific communities (e.g., Sullivan and von Wachter 2009), in response to increased exposure to foreign trade (Adda and Fawaz 2020; Autor et al. 2019; Pierce and Schott 2020), or from acute shocks, such as plant closures (e.g., Browning and Heinesen 2012; Venkataramani, Bair et al. 2020).
We go on to examine three contextual features of places that both theory and prior work suggest could moderate the relationship between automation and mortality: social safety net policies, labor market policies, and prescription opioid supply. Several recent studies emphasized the role of state policy variation in explaining levels and trends in health disparities, including mortality (see Montez 2017; Montez et al. 2020; Montez et al. 2019). Similarly, we find evidence that the generosity of state safety net programs—Medicaid and Unemployment Insurance (UI)—mitigated the effect of automation on mortality among middle-aged males, specifically deaths due to suicide and drug overdose. We also find evidence that state labor market policies moderated the effect of automation on mortality for middle-aged males: the effect of automation on drug overdose mortality and suicide mortality was more pronounced in states with “right-to-work” (RTW) laws and in states with lower minimum wage rates. Taken together, these findings demonstrate the central importance of public policies in moderating the effects of deindustrialization on deaths of despair.
We also examine effect heterogeneity as a function of the supply of prescription opioids in a local area, constructing estimates from national prescription drug surveillance data. We find suggestive—but imprecisely estimated—evidence that the effect of automation on drug overdose mortality may be higher in areas with higher per capita supply of prescription opioids. This evidence may inform ongoing debates over the relative roles of supply versus demand factors in driving the opioid overdose epidemic (Currie et al. 2018; Currie and Schwandt 2020; Hollingsworth et al. 2017; Seltzer 2020).
In the following sections, we describe the mechanisms through which automation may impact working-age mortality, drawing on a growing body of research demonstrating the impact of the economy on individual and population health. We then describe our three potential contextual moderators before turning to our data, methods, and results.
## Theoretical Pathways
Theory and empirical research suggest two pathways through which the rise of industrial automation may impact working-age mortality: what we term the “material” pathway and the “despair” pathway. These pathways are not mutually exclusive, but rather complementary, inviting us to consider how the same structural economic trends may yield increases in mortality from causes as distinct as suicide and cardiovascular disease.
### Material Pathway
The first pathway through which automation may impact working-age mortality is by shaping material outcomes known to impact individual and population health, including employment and wages. Acemoglu and Restrepo (2020) found that the rise of industrial robots had substantial negative effects on employment both directly through displacement of manufacturing workers and indirectly by depressing local economic demand, thereby reducing jobs in other industries, such as the service sector. In addition to lower employment rates, they found a substantial negative effect on average wages in the commuting zone, experienced even by those who remain employed. These direct and indirect effects of automation on employment and wages, in turn, are likely to impact health outcomes. Previous research has established a link between manufacturing decline and working-age mortality, examining both long-term secular trends (e.g., Seltzer 2020) and acute declines in employment opportunities due to plant closures (e.g., Venkataramani, Bair et al. 2020). Moreover, a large body of work across the social sciences has found income and employment to be key determinants of health; individuals with higher incomes live longer (Chetty et al. 2016), and areas with higher average income have higher average life expectancy (Dwyer-Lindgren et al. 2017).
Employment and wages are not the only mechanisms through which automation may impact material outcomes with consequences for health. For example, most working-age persons in the United States rely on employer-provided health insurance benefits; manufacturing is one sector in which less educated workers were historically provided such nonwage benefits. To the extent that automation decreases the total number of jobs that provide health insurance coverage, it may decrease health care access and utilization, particularly for preventative and diagnostic visits (see Freeman et al. 2008 for a review). This, in turn, could drive increased mortality for conditions such as cancer and heart disease. At the community level, increasing automation and worker displacement may lead to lower tax revenues, thus reducing public-sector spending on everything from health to education.2 To the extent automation reduces public-sector investment in health care services, we would expect that to increase mortality on the margins.
It is possible that automation may also improve health for some subsets of the population, particularly if tasks done by industrial robots allow existing workers to focus on less dangerous or taxing tasks. For example, recent work suggests that adoption of industrial robots may improve self-reported health among some types of workers, likely owing to reductions in physical tasks (Gihleb et al. 2020; Gunadi and Ryu 2021). However, given the substantial negative estimated effect of automation on the material economic outcomes of affected workers and their communities, we expect to find an association between the changing intensity of robot penetration and working-age mortality across U.S. counties.
### Despair Pathway
The second pathway through which automation may impact working-age mortality is by shaping the real and perceived economic opportunity of residents in affected areas. Analyzing the social and economic correlates of recent trends in mortality for different subpopulations, Siddiqi and colleagues (2019) found that the material pathways described here cannot entirely account for worsening mortality among middle-aged White individuals, given that the same adverse trends also impacted Black Americans who, in contrast, did not experience the same increases in mortality until more recently. The authors attributed increasing mortality among the former group to perceived status loss due to declining relative group position, specifically vis-à-vis racial and ethnic minorities. In addition, recent work demonstrates that occupational expectations are stronger predictors of death from drug overdose and suicide than actual occupational attainment (Muller et al. 2020). These findings are consistent with emerging work showing that area-level prospects for social mobility are strongly associated with a range of individual- and area-level measures of health behaviors and physical and mental health outcomes, even after adjusting for socioeconomic status (Venkataramani, Daza, and Emanuel 2020; Venkataramani et al. 2016), as well as with evidence that mortality among middle-aged White individuals increased more in areas characterized by low economic mobility (O'Brien et al. 2017). How people understand and conceive of their position in the social hierarchy, and the opportunities and possibilities available to them, can impact health outcomes regardless of the material reality.
We argue that the decline of manufacturing employment is likely to have a negative impact on perceived economic opportunity and future expectations, particularly for residents of the industrial heartland. Historically, regions of the United States with high levels of manufacturing employment have been characterized by high rates of intergenerational economic mobility—the likelihood that children will achieve the American dream of doing better than their parents in adulthood (Berger and Engzell 2020). Indeed, recent work finds that the decline in manufacturing is a key driver of declining rates of economic mobility in many parts of the industrial Midwest and Northeast (Connor and Storper 2020). To the extent that automation reduces local area economic opportunity, or the perception thereof, we might expect increased mortality from drug overdose, suicide, and other so-called “deaths of despair” (Case and Deaton 2017). Compounding these forces is the fact that areas facing deindustrialization also experience shifts in key social factors—for example, changes in marriage markets and destruction of social capital—that may further worsen health outcomes (Cherlin 2014; Wilson 1996).
The material and despair pathways through which automation may impact mortality are complementary and mutually reinforcing; they also reveal how the determinants of health and mortality cannot be neatly categorized as processes occurring at either the individual or the ecological levels. Automation is a technological shock that has implications for both individuals and their communities. Whether and to what extent the material hit to an individual—say, in the form of job loss or lower wages—translates into heightened mortality risk are likely to vary as a function of the overall economic health of the local area. At the same time, residing in an area hit hard by automation-driven deindustrialization may heighten mortality risk even among those whose own immediate material reality is unchanged by dimming prospects for economic mobility and weakening of the public sector. In the following analysis, we estimate change in mortality at the county level, capturing the net effect of these distinct but related pathways.
## Potential Contextual Moderators
The United States is a large and heterogeneous country. Therefore, we expect the effect of technological adoption on population health to vary systematically across places. We consider three aspects of local context that may moderate the relationship between automation and working-age mortality: social safety net policies, labor market policies, and prescription opioid supply.
### Social Safety Net Policies
Evidence suggests that cross-state variation in the generosity of social safety net programs is an important determinant of spatial patterns in population health (Montez 2017; Montez et al. 2020). In the context of this analysis, we might expect social safety net program generosity to moderate the relationship between automation and mortality by blunting the social and economic hit to workers, families, and their communities. Our measures of program generosity are taken from Fox et al. (2020), who created summary indices for each social program that are based on program generosity, eligibility requirements, and administrative burdens to accessing benefits.3 In addition to a composite measure capturing the overall generosity of state social safety net policies, we consider two specific programs that exhibit substantial variation across state lines: Medicaid and UI. We use measures from the earliest year available (2000) in their data.
Our prior is that the generosity of state Medicaid programs is the most likely element to moderate the relationship between automation and mortality; during our study period, there was considerable cross-state variation in Medicaid income eligibility thresholds for working-age adults. Research has found that variation in Medicaid policy impacted spatial patterns in both all-cause and drug overdose mortality (Miller et al. 2021; Sommers et al. 2012; Venkataramani and Chatterjee 2019). Although generosity of (and eligibility for) UI varies across state lines, it is a time-limited social benefit. Even so, work by Kuka (2020) found a causal association between UI generosity and health insurance coverage and utilization, particularly during periods of high unemployment. She also found that UI generosity was associated with higher self-rated health. Similarly, Cylus et al. (2014) showed that more generous UI benefits at the state level were associated with lower suicide rates, particularly during periods of high unemployment. Moreover, other evidence suggests that UI program generosity is associated with improved job matching for unemployed workers (Farooq et al. 2020), which may both reduce despair and improve material outcomes for workers in ways that benefit health.
### Labor Market Policies
Beyond the social safety net, there is substantial variation in state labor market policies. We consider two: minimum wage rates and RTW laws. Evidence on the effect of state minimum wage rates on health outcomes of the working-age population is mixed, with most studies finding no discernible effects (see Leigh et al. 2019 for a review). There is, however, growing evidence linking higher minimum wage rates to reductions in mortality from suicide among working-age adults (Dow et al. 2020; Gertner et al. 2019). Moreover, correlational analyses have found that reports of unmet medical needs among low-skilled workers were lower in states with higher minimum wages, net of individual and contextual covariates (McCarrier et al. 2011). In our conceptual framework, higher minimum wages may moderate the effect of automation on mortality by mitigating the wage loss associated with a decline in manufacturing employment. Our analysis tests for effect heterogeneity as a function of the state minimum wage rate in nominal dollars in the year 2000 (obtained from University of Kentucky Center for Poverty Research 2021).
We also consider the potential moderating effect of state RTW laws. Such laws are state-level prohibitions on unions that require nonmembers who benefit from union-negotiated benefits to contribute to the cost of union representation. The empirical evidence on the effects of RTW laws on labor market indicators such as aggregate employment and wages is mixed and inconclusive (see Collins 2012 for a review), although there is evidence that they reduce labor organizing (Ellwood and Fine 1987) and private-sector unionization rates (Eren and Ozbeklik 2016). To the extent that these laws shape the quality and/or quantity of jobs available to displaced workers, they may moderate the association between automation and working-age mortality. We explore this using a binary indicator for whether the state had a RTW law as of 2000 with data taken from Caughey and Warshaw (2016).
### Prescription Opioid Supply
Several studies have found a positive association between local-area, prescription opioid supply and drug overdose rates (see, e.g., Alpert et al. 2019; Currie and Schwandt 2020; Monnat 2019; Ruhm 2019). Therefore, we also consider the possibility that the local opioid supply may moderate the effect of automation on mortality. Specifically, we hypothesize that any effect of robot adoption on drug overdose mortality is likely to be higher in local areas with a greater supply of prescription opioids. To examine this, we amassed data on the prevalence of oxycodone prescriptions across counties in the United States, as reported to the Automated Reports and Consolidated Ordering System (ARCOS), which is maintained by the U.S. Department of Justice and collects information on controlled substance transactions from manufacturers and distributors. We used these data to calculate the (logged) milligram equivalent of morphine of oxycodone prescribed per working-age adult between ages 20–64 in each U.S. county in 2000.
## Methods
### Data
For our main exposure—commuting zone–level exposure to automation—data were obtained from Acemoglu and Restrepo (2020). This measure captures the predicted increase in industrial robots per 1,000 workers over the period 1993–2007. The measure is constructed using 1970 U.S. commuting zone–level data4 on employment shares across 19 different industries, as well as data on the growth in industrial robots in each of these industries for five European countries (Denmark, Finland, France, Italy, and Sweden). The use of data from these countries—which adopted industrial robots sooner than the United States did—allowed Acemoglu and Restrepo (2020) to limit bias from endogenous, commuting zone, labor demand factors that may have jointly influenced automation and our outcomes of interest (e.g., worsening health leading both to firms adopting automation technologies and to increased working-age mortality; see Currie et al. 2018; Krueger 2017). This type of measure is known as a “shift-share instrument” in the econometrics literature (Goldsmith-Pinkham et al. 2020). Figure 1 maps the predicted change in automation across commuting zones between 1993 and 2007 as estimated by Acemoglu and Restrepo (2020).
We constructed county-specific, age-adjusted mortality rates by age-group, sex, and cause using restricted-access, death certificate data obtained from the U.S. National Center for Health Statistics and annual age- and sex-specific population estimates from the U.S. Census Bureau. We examine sex-specific mortality rates for the 20–29, 30–44, 45–54, and 55–64 age-groups, given evidence of heterogeneous impacts by age and sex in other work. For each group, we compute mortality rates from all causes, as well as from drug overdoses, suicides, homicides, cardiovascular diseases, respiratory illnesses, cancers, and unintentional injuries (excluding drug overdoses; see Table A1 of the online appendix for relevant ICD-9 and ICD-10 codes, and Table A2 for mortality rates by age and sex in 1993). To best match the automation data, we compute changes in mortality rates for each demographic group and cause (per 100,000) between 1993 and 2007. For each baseline and endline year, we use the surrounding three-year average for mortality rates to improve the precision of measurement (Woolf and Schoomaker 2019).
### Analytic Strategy
To estimate the impact of automation on working-age mortality, we estimate versions of the following first-differences model:
$ΔYi,j,r,t1−t0=α1×ΔAutomationj,r,t1−t0+β×BaselineCharj,r,t0+θr+ei,j,r,t,$
(1)
where i indexes the county, j indexes the commuting zone, and t1 and t0 index 2007 and 1993, respectively. $ΔYi,j,r,t1−t0$ represents the change in mortality at the county level and $ΔAutomationj,r,t1−t0$ represents the change in the number of industrial robots per 1,000 workers at the commuting zone level. This specification corresponds to the “long-difference” model used by Acemoglu and Restrepo (2020).
$α1$, which captures the association between exposure to automation and mortality, is our parameter of interest. This parameter captures health impacts accruing from both the material and despair pathways—that is, the effects of automation-led job and benefit loss, diminished wages among still-employed workers (Elser et al. 2019), reduced physical exertion and injury risk among still employed workers (Gihleb et al. 2020; Gunadi and Ryu 2021), reduced economic opportunities and future expectations, and the effects of shifting social factors (e.g., changes to marriage markets, destruction of social capital) (Cherlin 2014; Wilson 1996). Our research design and data limitations do not allow us to assess the specific contribution of each of these pathways, and we flag this as an important area for future research.
Shift-share instrumental variables may be susceptible to bias if the baseline characteristics (here, commuting zone industrial shares in 1970) used to create the instrument are correlated with other baseline characteristics, the subsequent trends of which may also affect the outcomes of interest (e.g., educational attainment) (Goldsmith-Pinkham et al. 2020). To address this concern, we follow Acemoglu and Restrepo (2020)'s preferred specification and adjust a rich set of baseline characteristics (denoted by the vector $BaselineCharj,r,t0$) measured in 1990, including commuting zone demographic (age distribution, race/ethnicity population shares) and socioeconomic characteristics (shares completing high school and college education, share employed in manufacturing, share employed in routine occupations, and exposure to foreign trade). We also include a vector of fixed effects for the nine census divisions (denoted by $θr$), given regional patterns in the evolution of automation and our main outcomes (see Figure 1). We estimate the foregoing model for mortality outcomes separately by age–sex groups and cause. In all analyses, we cluster standard errors at the state level to account for potential geographic correlation in the exposure and outcomes, and weight by appropriate (age–sex group) population size. Clustering at the commuting zone level produces substantively identical results (see Table A3 in the online appendix).
We test for potential contextual moderators by estimating models that include an interaction term between our contextual measure (e.g., state minimum wage rate) and the automation measure. We also include in our models all interactions between the focal contextual measure and the full set of covariates, to reduce the possibility that the interaction effects of interest are confounded by other interactions between the contextual measure and observable characteristics potentially correlated with our automation measure. Specifically, we estimate versions of the following equation:
$ΔYi,j,r,t1−t0=γ1×ΔAutomationj,r,t1−t0+γ2×ΔAutomationj,r,t1−t0×StateContextj,r+γ3×StateContextj,r+δ×BaselineCharj,r,t0+ϑ×BaselineCharj,r,t0×StateContextj,r+θr+θr×StateContextj,r+ui,j,r,t.$
(2)
The key parameter of interest here is $γ2$, which captures the interaction between the focal contextual measure ($StateContextj,r$) and our automation instrument. We estimate this model specifically for men and women aged 45–54, for whom increases in midlife mortality have been most prominent and for whom we find large impacts of automation on all-cause mortality in our main analyses. For the ease of interpretation, we report marginal effects of automation on mortality evaluated at high and low values of the contextual measure $StateContextj,r$ (we report estimated coefficients on the interaction term in Tables A9–A14 in the online appendix).
## Results
### Impacts of Automation on Mortality
#### Main Findings
Figure 2 plots estimated coefficients of the effects of automation on mortality by cause for males of four age-groups (Table A3 of the online appendix reports the coefficients and standard errors). Across all age-groups, the estimated effect of automation on all-cause mortality was positive and substantial in magnitude; however, only for males aged 45–54 was the point estimate statistically distinguishable from zero at conventional alpha levels (p < .05). Among this group, an increase of one robot per 1,000 workers was associated with a statistically significant eight additional deaths per 100,000 persons (relative to a scenario in which there was no increase in industrial robots). This is a sizable relative increase in mortality, notably among the exact demographic subgroup identified by Case and Deaton (2017) as suffering from increased deaths of despair. The average increase in automation over the study period (two robots per 1,000 workers) was thus associated with 16 additional deaths per 100,000 persons, equivalent to roughly 25% of the overall secular decline seen in this age-group between 1993 and 2007 (64 deaths per 100,000).
Disaggregating by cause, we find evidence that increases in robot penetration led to significant increases in drug overdose mortality across all four age-groups. The average increase in automation across commuting zones of two robots per 1,000 workers can account for 13.5% of the overall increase (14 deaths per 100,000) in drug overdose deaths between 1993 and 2007 among men aged 20–29 (p < .05), 20.1% of the overall increase (11 per 100,000) among those aged 30–44 (p < .05), 8.2% of the overall increase (22 per 100,000) among those aged 45–54 (p < .10), and 12.0% of the overall increase (11 per 100,000) among those aged 55–65 (p < .10). To place these findings in context, we note that the relative share of drug overdose deaths explained by automation was somewhat smaller than the share explained by local exposure to international trade. For example, Pierce and Schott (2020) noted that local economic shocks resulting from the United States granting permanent trade relations with China could account for approximately 40% of the growth in drug overdose mortality in the early 2000s.
Estimates for other causes of death varied by age-group. Among men aged 30–44, we find evidence that automation led to increases in homicide deaths. Among those aged 45–54, we see evidence of impacts on suicide mortality rates, with the average increase in robot penetration of two per 1,000 workers, accounting for 51% of the overall increase in suicide deaths (five deaths per 100,000) in this age-group over the study period. In addition to increasing deaths of despair, we also find evidence that automation was associated with elevated risk of cardiovascular mortality, particularly among males aged 55–64, for whom each additional robot per 1,000 workers was associated with an additional five deaths per 100,000.5 This finding is consistent with an emerging literature linking area-level economic prosperity with cardiovascular disease outcomes (Khatana et al. 2021).
Figure 3 presents the corresponding analysis for females. Here the estimated effect sizes were generally smaller but follow a similar pattern: automation was associated with an increase in all-cause mortality among working-age females, with statistically significant effects among those aged 20–29 (p < .05) and 45–54 (p < .01). In the latter group, the average increase in automation led to a relative increase in mortality equal to about 59% of the overall decline in all-cause mortality observed over the study period (13 deaths per 100,000). As with men, drug overdose mortality among women aged 20–29 increased with automation. Among women aged 30–44, we find that automation was associated with higher cancer mortality rates.6 The largest absolute impact was on cardiovascular mortality for women aged 55–64, with each additional robot per 1,000 workers associated with an increase of just under four deaths per 100,000.
Taken together, our findings reveal a direct link between the rise of automation and the mortality among adults aged 45–54, operating largely through increasing deaths from drug overdose and suicide. We also see that automation led to a relative increase in overall mortality among younger females and, for certain age–sex groups, increased mortality from causes as varied as cancer and cardiovascular disease.
#### Robustness Checks
Following Acemoglu and Restrepo (2020), we checked that our findings were not being driven by a subset of commuting zones where adoption of industrial robots distinctly outpaced the rest of the United States. We reestimated our models after removing these “outlier” commuting zones and found similar substantive effects (Table A4, column 1, in the online appendix).7 We also examined the effect of automation in areas with high levels of manufacturing employment, defined as counties in the top quartile of the share of residents employed in manufacturing in 1980 (Table A4, column 2). Notably, we find the estimated effect of automation on drug overdose mortality and suicide mortality to be substantially larger (and statistically different) when we restrict our sample to communities in which manufacturing workers tended to live, consistent with the fact that automation affected these workers the most (Acemoglu and Restrepo 2020).
A key threat to inference in our research design is preexisting trends in the outcome of interest. Namely, areas with greater adoption of industrial robots over the study period may have already experienced worsening mortality. We address this possibility by estimating models regressing changes in cause-specific mortality rates between 1981 and 1992 on automation between 1993 and 2007 (conditional on the same covariates in our main specification). Large, positive estimates on automation in these models would be consistent with upward-biasing preexisting trends. As seen in column 3 of Table A4 (online appendix), we find no evidence of preexisting trends of increasing mortality rates. If anything, some of the estimates suggest pretrends in the opposite direction. To correct for this, we estimate versions of our main model for each cause of death while adjusting for the 1981–1992 pretrends; our results are substantively unchanged by inclusion of this covariate (Table A4, column 4).
### Contextual Moderators
To test for potential contextual moderators of the effect of automation on mortality, we estimate versions of our core model that additionally include interaction terms between the contextual measure and automation (as well as interactions between the contextual measure and each of the covariates; see Eq. (2)). For safety net and labor market policies, we focus on outcomes for males aged 45–54, for whom the effect of robots on mortality was largest (for corresponding analysis for females aged 45–54, see Table A8 in the online appendix). For opioid supply, we examine all-cause and drug overdose mortality for all working-age males and females.
#### Safety Net Programs
We examine effect heterogeneity using a composite index of the overall generosity of state social safety net programs, as well as indices of the generosity of two specific programs that vary across state lines: Medicaid and UI. Note that our policy generosity variables are measured in 2000, and because this time point falls in the middle of the study period, estimates on interaction terms cannot be interpreted causally if program generosity was responsive to economic shocks. Even if they were not, program generosity may be correlated with other policy choices or state-level factors. Consequently, we consider this exercise to be descriptive.
Table 1 presents estimates from our safety net policy heterogeneity models. Each set of rows shows the marginal effects (and standard errors) obtained from a separate regression model, with margins evaluated at the 25th and 75th percentile of the national distribution of overall safety net program generosity, as well as specifically for Medicaid and UI program generosity. Estimates of the interaction term between automation and safety net programs—which effectively test whether the differences between effects in low versus high program generosity areas are statistically significant—are presented in Tables A9–A11 of the online appendix. Focusing on coefficient magnitudes, UI generosity appeared to moderate the effect of automation on all-cause mortality for men aged 45–54. Point estimates indicated that in states with relatively less generous UI benefits, an additional robot per 1,000 workers was associated with an increase in all-cause mortality of about 16 deaths per 100,000, compared with about 10 deaths per 100,000 in states with relatively more generous UI programs; however, these differences were not statistically significant (Table A11 in the online appendix).
Turning to cause-specific mortality, we find strong evidence that state safety net generosity—overall, and for both UI and Medicaid in particular—moderated the effect of automation on suicide mortality (with estimates on the key interaction term between automation and program generosity being statistically significant; see Tables A9–A11 in the online appendix). We also find evidence that state Medicaid program generosity substantially mitigates the effect of automation on drug overdose mortality, an interaction effect that was precisely estimated (Table A10 in the online appendix) and consistent with prior work. Notably, we find no evidence that these programs moderated the effect of automation on other causes of death. Taken together, these findings suggest that social safety policies may play a uniquely important role in blunting the effect of automation on drug overdose and suicide deaths.
#### Labor Market Policies
We next examine state labor market policy, specifically RTW laws and minimum wage rates. Estimates presented in the right panel of Table 1 reveal that the effect of automation on middle-aged male all-cause mortality is higher in states with a RTW law than in those without (with the interaction between automation and RTW being statistically significant for all-cause mortality at the 10% level; see Table A12 in the online appendix). Point estimates suggest that every additional robot per 1,000 workers was associated with an increase of 28 deaths per 100,000 in RTW states, compared with about nine deaths per 100,000 in the rest of the country. This appears to be driven in part by higher rates of suicide mortality in RTW states in response to automation. We see a similar pattern when we examine state minimum wage rates: the effect of automation on suicide mortality was higher in states with relatively lower minimum wage rates (Table A13, online appendix). This again provides suggestive evidence that public policy—specifically state labor market policies—may play an important role in blunting the effect of automation on suicide deaths.
#### Local Supply of Prescription Opioids
Finally, Table 2 examines heterogeneity in the effect of automation on all-cause and drug overdose mortality as a function of the county-level supply of prescription opioids (logged milligram equivalents of morphine per capita) for the year 2000. Here, we find that for both males and females of working age, the effect of automation on drug overdose mortality was higher in areas with a relatively greater supply of prescription opioids. However, this interaction effect was not statistically significant (see Table A14, online appendix). The direction of this finding suggests that opioid supply and economic demand may have worked interactively to produce the opioid crisis, a finding that warrants further exploration in contexts where there may be greater statistical power to detect true differences.
## Discussion and Conclusion
Technological change has led to increasing automation of routine tasks, a trend that is expected to continue in the coming decades. Since the 1990s, adoption of labor-displacing automation technologies in U.S. labor markets has coincided with rising rates of mortality, particularly among individuals with lower levels of education. Our study suggests a causal link between these trends, with (average) increases in automation accounting for a slowdown in mortality improvements equivalent to 25% of the overall decline in mortality among males aged 45–54 and 59% of the decline for females aged 45–54 observed during the study period, portending the stagnation and reversal in longevity seen in more recent years. We find that this increase is driven in large part by increased mortality from so-called deaths of despair, including drug overdose and suicide. The effect of automation on despair mortality, in turn, appears to vary as a function of state safety net generosity, prevailing minimum wage rates and right to work laws, and the local level of prescription opioid supply.
Our findings have implications for policymakers and researchers. First, they add causal evidence in support of the theory that declining economic opportunity—whether through automation or increased exposure to foreign trade—is a major driver of worsening population health and declines in expected longevity among working-age persons without a college degree (Monnat 2019; Seltzer 2020). Second, the mortality consequences of fading opportunity are heterogeneous by sex, age, and cause of death. For example, while the largest impacts were for men aged 45–54, we also find important impacts on drug overdose, cancer, and all-cause mortality for younger women. This reveals that the impact of automation on mortality extends well beyond its direct effect on displaced workers to shape the population health of entire communities. This, in turn, motivates future research to identify and decompose potential indirect or ecological effects: for example, areas hit hard by the forces of deindustrialization face the double whammy of fewer high-quality jobs and the resulting deterioration in the wealth of tax bases used to fund the public sector.
Third, our findings also reveal that public policy plays an important role in mitigating the effect of deindustrialization on population health. Efforts to blunt the economic impacts of automation on workers through enhanced social safety net programs can make a difference—as can policies that improve local labor market opportunities and the quality of jobs available to workers (and “would-be workers”) displaced by automation, such as higher minimum wage laws or rules that make it easier for workers to unionize. At the same time, constraining the supply of prescription opioids is critical to reducing the likelihood that the economic punch to individuals and communities from the arrival of industrial robots and reduction in manufacturing employment translates into higher rates of drug overdose mortality.
Deindustrialization driven by foreign competition and automation is expected to continue—perhaps even accelerate—in coming years. Counteracting these forces will require significant public-sector investment in displaced workers. It will also require national investments in these distressed communities. To mitigate the negative health effects of this structural change to the economy, policymakers should consider targeting income support to this population, either by expanding eligibility and/or generosity of existing programs or by introducing new transfer programs. At the same time, our findings suggest there may be real health gains to investing in industrial policies that increase the number of quality jobs as well as programs to help workers develop new skills and transition to new sectors (Katz et al. 2020). Efforts to improve the economic well-being of workers displaced by structural shifts to the economy—from automation or foreign trade—will have substantial benefits for population health.
## Acknowledgments
The authors thank David Asch, J. Michael Collins, Kosali Simon, Justin Sydnor, and seminar participants at the Social Security Administration, University of Wisconsin–Madison, and University of Pennsylvania for helpful comments and suggestions. They also thank Ashley Fox for providing access to her database on state welfare program generosity and administrative burdens. The research reported here was performed pursuant to a grant from the U.S. Social Security Administration (SSA) funded as part of the Retirement and Disability Consortium. The opinions and conclusions expressed are solely those of the authors and do not represent the opinions or policy of SSA or any agency of the federal government. Neither the U.S. Government, nor any agency thereof, nor any of their employees makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of the contents of this report. Reference to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply endorsement, recommendation, or favoring by the U.S. Government or any agency thereof.
## Notes
1
Closest to the present paper is a recent working paper (Gihleb et al. 2020) examining the causal impact of industrial robot adoption in the United States and Germany on a range of outcomes; it found that automation was associated with an overall increase in alcohol and suicide mortality. However, their analysis pooled all ages (including non-working-age adults) and genders, and included data from a more limited time frame and more limited set of counties. Moreover, they did not consider other causes of death. Our study also relates to work by Patel and colleagues (2018), who found that county-level measures of automation were associated with worse self-reported health, though this analysis is descriptive and precludes causal interpretations. Finally, Gunadi and Ryu (2021) assessed causal relationships between automation and self-reported health specifically among low-skill workers, finding improvements in health as a result of reallocation of workers to less physically intensive tasks.
2
Feler and Senses (2017) found exactly that in their analysis of the impact of foreign trade exposure on the local provision of public goods.
3
For example, the Medicaid generosity index combines multiple measures of generosity (based on coverage of optional benefits, e.g., dental, vision, psychologists), eligibility requirements (i.e., income eligibility thresholds for children, pregnant women, parents, and nonparents), and administrative burdens (e.g., presence of asset tests, face-to-face interviews, presumptive eligibility, continuous enrollment). This index ranges from 0 to 100; see Fox et al. (2020) for details. Fox et al. also constructed indices for the Temporary Assistance for Needy Families (TANF) and Supplemental Nutrition Assistance Program (SNAP). However, we did not consider these programs in our analysis given either the limited scope of the program (TANF) or the relative lack of cross-state variation in generosity during the study period (SNAP).
4
Acemoglu and Restrepo (2020) used 1970 values to address potential bias from mean reversion in industrial employment shares in the 1980s.
5
In absolute terms, this is the largest effect for a specific cause of death across all age–sex groups. However, given that the baseline rates for cardiovascular disease mortality are an order of magnitude larger than for other disease (except for cancer), these effects are in fact smaller in relative (e.g., percentage increase) terms than, for example, the automation-driven increase in drug overdose deaths among men in any age-group.
6
Given small sample sizes, we follow standard practice and aggregate cancers from all causes into a single statistic for the purposes of this analysis.
7
We also note that Acemoglu and Restrepo (2020) found that the bulk of the effects of automation on labor market outcomes were unlikely to be explained by migration, and that migration in general appeared to play a minor role in other studies examining the link between economic opportunity and health (Autor et al. 2019; Ganong and Shoag 2017; Sullivan and von Wachter 2020).
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This is an open access article distributed under the terms of a Creative Commons license (CC BY-NC-ND 4.0). | 2023-03-31T14:01:05 | {"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": 0.47636520862579346, "perplexity": 6483.955892279419}, "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/1679296949642.35/warc/CC-MAIN-20230331113819-20230331143819-00767.warc.gz"} |
https://www.usgs.gov/publications/evaluating-management-alternatives-wyoming-elk-feedgrounds-consideration-chronic | # Evaluating management alternatives for Wyoming elk feedgrounds in consideration of chronic wasting disease
March 9, 2023
Executive Summary
The authors used decision and modeling analyses to evaluate management alternatives for a decision on whether to permit Cervus canadensis (elk) feeding on two sites on Bridger-Teton National Forest, Dell Creek and Forest Park. Supplemental feeding of elk could increase the transmission of chronic wasting disease (CWD) locally and disease spread regionally, potentially impacting elk populations over time with wider implications for Odocoileus hemionus (mule deer) and Odocoileus virginianus (white-tailed deer) populations and hunting, tourism, and regional revenue. Supplemental feeding is thought to improve overwinter elk survival and reduce the commingling of elk with cattle during months when brucellosis transmission risk is highest. We worked with the U.S. Department of Agriculture Forest Service to identify their fundamental objectives and associated performance metrics related to this feedground decision. We then developed disease and habitat selection models to quantify the effect of four management alternatives on select performance metrics. The four alternatives were to continue to permit feeding, phaseout permits to feed in three years, permit feeding on an emergency basis, or stop permitting feeding. In this report, we present methods and summarized results on disease and habitat selection models and summaries of other performance metrics analyzed by BIO-WEST, Inc. and Cirrus Ecological Solutions as part of an Environmental Impact Statement.
Data from Wyoming Game and Fish Department (WGFD) supported the assumption that supplemental elk feeding allows for larger elk populations in a region. We documented herd units (HU) with feedgrounds having 2.2 times higher densities of elk per area of winter range when compared against HUs without feedgrounds, after accounting for differences in sightability of elk counts on and off feedgrounds. Thus, throughout our analyses, we assumed feedground closures would reduce elk carrying capacity and previously fed elk population segments would decline by 50 percent because of feedground closures. We used a panel of experts to help estimate CWD transmission in fed and unfed elk population segments. In aggregate, the expert panel estimated that median values of direct and indirect transmission of CWD are expected to be 1.9 and 4 times higher, respectively, in fed elk populations compared to unfed elk. We used these disease transmission estimates in combination with local elk demographic rates and carrying capacity estimates to project disease and population dynamics.
In year 20, we predicted CWD prevalence would increase to 40 percent (5th and 95th percentiles = [32 percent, 51 percent]), and 14 percent (5th and 95th percentiles = [3.9 percent, 29 percent] on average for fed and unfed elk population segments, respectively, given a starting prevalence of 1.6 percent. The prevalence estimates for the unfed elk population segments are in the range of previous observations of CWD in elk in the western United States. The average CWD prevalence from 2016 to 2018 in the unfed elk population of Wind Cave National Park in South Dakota was 18 percent overall but up to 30 percent in some regions (Sargeant and others, 2021). Meanwhile, CWD prevalence in the Iron Mountain and Laramie Peak elk herds in Wyoming from 2016 to 2018 was 14 percent and 7 percent, respectively, despite being present since at least 2002 (Wyoming Game and Fish Department, 2020b).
Elk that are fed at Forest Park and Dell Creek constitute 14–19 percent of the total elk on their respective HUs. As a result, the differences between management alternatives are modest when considering the closure of only one feedground on an HU. The no feeding alternative for Forest Park resulted in a CWD prevalence of 16 percent in the Afton HU compared to 19 percent with continued feeding by year 20. In the Upper Green River HU, no feeding on Dell Creek resulted in a CWD prevalence of 30 percent compared to 34 percent with continued feeding. In terms of disease-associated mortality, we predicted the closure of Forest Park and Dell Creek feedgrounds would reduce the total number of CWD mortalities by 9 percent in the Afton HU and 20 percent in the Upper Green River HU during the 20-year timespan.
Our spatial analyses predicted that management alternative effects vary by HU as a function of private property and other wildlife winter ranges proximity relative to feedground location. The predicted number of elk abortions on private land, as a proxy for brucellosis risk to cattle, may increase by 8–10 percent in the absence of feeding at Dell Creek and Forest Park. On the Afton HU, the no feeding alternative resulted in the lowest use of mule deer and Alces alces (moose) winter range by elk. In the Upper Green River HU, the no feeding alternative resulted in less use of moose winter range compared to continued feeding, but higher elk use of mule deer winter range.
Eight feedgrounds are located on Bridger-Teton National Forest, all of which have permits that have expired or will expire prior to 2028. In addition, WGFD could change their management of feedgrounds in light of new information; therefore, we also assessed the cumulative effects of continued feeding, phaseout, and no feeding management alternatives across five HUs south of Jackson, Wyoming (Afton HU, Fall Creek HU, Piney HU, Pinedale HU, and Upper Green River HU). These five HUs ranged from about 60 to 95 percent of the elk herd using feedgrounds, which corresponded to a CWD prevalence at year 20 of 21–38 percent if all feedgrounds in those five HUs remained open relative to 13 percent if all feedgrounds were closed. For all management alternatives, we predicted a 30–58 percent decline in elk populations at the HU level over 20 years because of increasing CWD prevalence or from reductions in populations because of feedground closures. We predicted feedground closures may result in more immediate reductions in population size relative to alternatives that continue feeding (for example, continued feeding and emergency feeding alternatives); however, over longer periods of time, CWD-associated mortality leads to larger population reductions. The no feeding alternative resulted in higher elk population sizes compared to the continued feeding alternative after 10–15 years of implementation. Delayed action under a phaseout alternative resulted in roughly doubling CWD prevalence relative to no feeding on HUs with a large population of fed elk.
Summarizing our cumulative results across all five of the analyzed HUs, we predicted continued feeding will lead to fewer elk by year 20 (mean =10,400, standard deviation [SD] = 800) compared to no feeding at U.S. Department of Agriculture Forest Service sites (11,300, SD = 600). The closure of all feedgrounds was projected to result in the largest elk populations at year 20 (11,800, SD = 600). Continued feeding at all sites, however, resulted in the largest cumulative harvest of 55,400 (SD = 3,500) compared to 51,000 (SD = 1,600) for no feeding at all current feedground sites on the five HUs. Continued feeding also resulted in the lowest brucellosis costs to producers ($199,000, SD =$7,400) compared to phasing out all feedgrounds in three years ($218,000, SD =$7,500). Assuming moderate reductions in hunter interest because of increasing CWD prevalence in elk, we predicted that no feeding resulted in a regional revenue of $162 million (SD =$4.0 million) compared to $176 million (SD =$8.0 million) for continued feeding over the 20-year timeframe.
Recent CWD detections in mule deer and elk in Grand Teton National Park has elevated the importance of the current decision on whether, and how, to permit elk feeding on Forest Park and Dell Creek and the management of the other feedgrounds. Aggressive male harvest has slowed, but not stopped, the increasing prevalence of CWD in mule deer (Conner and others, 2021). It is unclear whether harvest management can be an effective tool to slow the spread of CWD in elk. There are also no effective treatments or vaccines for CWD, and it is unlikely that any will be developed that can be easily deployed in the near future. Thus, reducing artificial aggregations is one of the few management approaches suggested by the Western Association of Fish and Wildlife Agencies (Almberg and others, 2017).
Future surveillance and monitoring can be designed to resolve uncertainties that can improve future decision-making. If feedgrounds close, research could quantify elk population reductions in the absence of feeding, the redistribution of fed elk to other places, or the consequences of elk movement on private property. If feedgrounds remain open, research could assess how rapidly CWD spreads in artificial aggregations of elk; however, surveillance programs would need to be designed with sufficient power to detect initial changes of CWD prevalence. Delaying action on feedground management was projected to be costly. Results of the phaseout alternative relative to the no feeding alternative suggested a three-year delay was enough for substantial long-term changes in CWD prevalence. The long-term persistence of infectious CWD prions in the environment suggests that feedground management decisions may have long-lasting consequences.
Our results indicated tradeoffs in the ability of a management agency to achieve all their objectives, and all management alternatives resulted in significant reductions in elk population size. This report contains the foundational elements for formal decision analysis methods, which can be implemented to help decision makers transparently evaluate the consequences of decision alternatives and identify the set of actions that best achieve agency and stakeholder priorities.
## Citation Information
Publication Year 2023 Evaluating management alternatives for Wyoming elk feedgrounds in consideration of chronic wasting disease 10.3133/ofr20231015 Jonathan D. Cook, Paul C. Cross, Emily M. Tomaszewski, Eric K. Cole, Evan H. Campbell Grant, James M. Wilder, Michael C. Runge Report USGS Numbered Series Open-File Report 2023-1015 ofr20231015 USGS Publications Warehouse Northern Rocky Mountain Science Center | 2023-03-26T23:35:33 | {"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": 0.37829679250717163, "perplexity": 8162.771887710039}, "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/1679296946535.82/warc/CC-MAIN-20230326204136-20230326234136-00312.warc.gz"} |
https://control.com/textbook/problem-solving-and-diagnostic-strategies/general-problem-solving-techniques/ | # General Problem-solving Techniques
## Chapter 7 - Problem-solving and Diagnostic Strategies in Control System Analysis
A variety of problem-solving techniques have been presented for students over the years which are all helpful in tackling problems both in the classroom and in the real world. Several of these techniques are presented here in this section.
### Identifying and classifying all “known” conditions
An important step in solving certain types of problems, especially quantitative problems where calculations are necessary to obtain precise answers, it is often useful to list all the known quantities available to us relevant to the problem. Similarly, taking the time to list all relevant (and possibly relevant) mathematical formulae we might apply to the solution is a helpful step.
One way to save time applying the latter suggestion in a classroom setting is to keep a concise reference card or file filled with formulae you’ve been learning within that course. This reference may be referred to as often as necessary, without having to re-write the equations for each and every problem, thus eliminating unnecessary effort.
### Re-cast the problem in a different format
Many people find it easier to grasp the nature of a problem – and by extension, that problem’s solution – if they can look at an illustration of the problem. Therefore, a helpful step in solving problems described to you in words is to translate those words into a picture to look at.
If you are one of those people for whom drawing is a challenge, take heart in the fact that this is a skill you can build. Practice is the key to honing this skill. With this in mind, make it a habit to sketch some kind of illustration for every problem you are asked to solve. If you are working in teams to solve a problem, a collaborative sketch goes a long way toward coordinating problem-solving efforts and ensuring everyone on the team has the same view of the problem.
For some people, describing a problem verbally is helpful in solving it. If your brain tends to work like this – understanding concepts and situations better when they are cast into clear prose – then you may find it helpful to first draft an explanatory paragraph of the problem in your own words. This is also an exercise lending itself well to team-based problem solving, as the entire team can help each other describe the nature of the problem.
### Working backwards from a known solution
Sometimes we may gain insight into the solution of a problem by assuming we already know the answer to a similar problem, then working “backward” to find the problem from that assumed solution.
An application of this problem-solving strategy is found learning how to decode binary bits that have been encoded using the Manchester standard. With Manchester encoding, binary bits are represented by the rising and falling edges of square-shaped waveforms rather than high and low states themselves. For example:
Seeing this example, we note how each binary “0” bit is represented by a falling edge, while each “1” bit is represented by a rising edge.
Where most students encounter trouble is in situations where they have been given a Manchester encoded waveform and must decode it into its representative bit stream. Take this for example:
Most students’ first inclination is to ask their instructor or their classmates for an algorithm to decode the waveform. “What steps should I take to figure out where the data bits are?” they will ask. This sort of “give me the answer” mind-set should always be discouraged, because it is the polar opposite of true problem-solving technique, where the student methodically searches for patterns and develops algorithms on their own.
A better approach is to encourage the strategy of working the problem backwards: begin with a known series of binary bits, and then develop a Manchester waveform from that. The act of encoding a binary string provides insight that will be useful in decoding the next Manchester waveform they encounter.
For example, let’s begin with the binary string 100011101:
We may begin the process of encoding this into Manchester format by sketching the rising- and falling-edges we know we will need for each bit:
Next, we can try connecting the tops and bottoms of these pulse edges to form a complete waveform. Soon, however, we will find that this is only possible where opposite bit states are adjacent to each other. Where identical bits follow in sequence, we are faced with sequential rising edges or sequential falling edges, which we cannot simply bridge at the tops or bottoms to make a full pulse:
This observation leads to the realization of why we need reversals in a Manchester waveform. The only way to connect repeating bits’ edges together is if the waveform goes through another rising or falling edge in order to be properly set up for the next edge we need to represent a bit:
Here we see the power and utility of working a problem “backwards”: it reveals to us the reason why things are the way they are. Without this understanding, problem-solving is nothing more than rote recall of algorithms, and limited in application. Any problem becomes simpler to solve once we fully understand its rationale.
Once we realize the purpose for reversals in a Manchester waveform, it becomes obvious to see that these reversals always fall between the bit transitions, and thus are always out of step with the frequency of the bits. Those edge transitions representing real data bits must always fall along a regular timed interval, with reversals being “half-steps” in between those intervals. We need only to look for the widest-spaced intervals in a Manchester waveform to distinguish those pulse edges representing real data bits, and then we know to ignore any pulse edges out of step with them.
Returning to our sample problem, where we were given a Manchester waveform and asked to decode it:
First, we identify the real data bit edges by widest spacing:
Now that we know which pulse edges represent bits, we may ignore those that do not (the reversals), and decode the waveform:
### Using thought experiments
One of the most powerful problem-solving techniques available for general use is something called a thought experiment. Scientists use experiments to confirm or refute hypotheses, testing their explanations by seeing whether or not they can successfully predict the outcome of a certain situation by comparing their predictions against real outcomes. While this technique is extremely useful, it might not always be practical or expedient. A useful alternative to real experiments is to mentally “model” the system and then imagine changing certain elements or variables within that model to deduce the effects.
Albert Einstein famously applied “thought experiments” to the formulation of his Theory of Relativity, for the very simple reason that he lacked the resources and technology to actually test his ideas in real life. Working as a patent clerk, he would imagine what might happen if an observer were to travel at or near the speed of light. One particular example of this is the anecdote of Einstein observing a clock tower as he rode a trolley traveling away from the tower. “What would an observer see,” he wondered, “as he viewed the clock’s face while traveling away from it at the speed of light?” Concluding that the clock’s face would appear to be frozen in time was one of the surprising “experimental” results leading Einstein to a more rigorous examination of physical effects at extremely high velocities.
“Thought experiments” are useful in solving a wide variety of problems, because they allow us to test our understanding of a system’s behavior. By imagining certain conditions or variables changing in a system and then asking ourselves what the effects will be, we probe our own understanding of that system, often times with the result being that we are able to predict its behavior under conditions that baffle us at first.
You will find “thought experiments” scattered throughout this book, used both as illustrations of problem-solving strategies and also as a tool to explain how certain technologies function. An example of this is the section explaining non-dispersive analyzers, which are instruments employing the absorption of light by certain species of chemicals in order to detect the presence and measure the quantities of those chemicals. Beginning in section 23.6 on page , a series of “thought experiments” are used to explore the principles used to identify chemicals by light absorption. This series of virtual experiments becomes most valuable when this section explores the analyzer’s ability to selectively measure the presence of one light-absorbing chemical to the exclusion of other light-absorbing chemicals within the same mixture.
Suppose you were asked to solve this multiplication problem, without the use of a calculating machine of any kind, but with access to paper and a writing tool:
Your primary school education should have prepared you to solve elementary arithmetic problems of this kind, by a process of digit-by-digit multiplication and addition, to arrive at an answer of 1,955,096. The procedure, while tedious, is rather simple: manually multiply the top numeral three times over by successive digits of the bottom numeral, noting any “carried” quantities as you do so, then sum those three subtotals together (padded with zeros to represent the place of the bottom numeral’s digit) to arrive at the final product.
Now suppose you were asked to solve the exact same multiplication problem, but this time doing the same digit-by-digit arithmetic all in your mind, without the use of a writing tool to annotate your work. Suddenly this elementary task becomes nearly impossible for anyone who isn’t a mathematical savant. What made the difference between this problem as an elementary exercise and this same problem as a nearly impossible feat? The answer to this question is short-term memory: most people do not possess a good enough short-term memory to mentally manage all the intermediate calculations necessary to complete the calculation. This is why people learn to annotate their work when performing manual multiplication, so they don’t have to rely on their limited short-term memories. The freedom to write your steps on paper converts what would otherwise be a Herculean feat of arithmetic into a rather trivial exercise.
Annotating your intermediate steps as you solve a problem is actually an excellent general problem-solving strategy, applicable to far more than just arithmetic. Some examples of annotating intermediate steps are listed here:
• Reading a complex document: annotating your thoughts, questions, and epiphanies as you read the text allows you to derive a better understanding of the text as a whole.
• Learning a new computer application: noting how features are accessed and identifying the necessary conditions for each feature to work helps you navigate the software more efficiently.
• Following a route on a map: marking where you started, where your destination is, and where you have traveled thus far helps you see how far you still need to go, and which alternative routes are open to you.
• Analyzing an electric circuit: annotating all calculated voltages, currents, and impedances on the diagram helps you keep track of what you know about the circuit and where to go next in your analysis.
• Troubleshooting a system fault: noting all your diagnostic steps and conclusions along the way helps you confirm or disprove hypotheses.
Sadly, many students attempt to solve new types of problems analogously to performing multiplication without paper and pencil: they attempt to mentally manage all their intermediate steps, not writing anything down that would help them later. As a result, students tend to get “lost” when trying to solve new problems simply because they cannot readily reference of all their thoughts along the way. Most people simply give up when they begin to feel “lost” in solving a problem, thinking that if they cannot mentally picture the solution in its entirety then they have no hope of attaining it. Let’s face it: how soon would you give up on multiplying 3418 $$\times$$ 572 without a calculator if you believed the only alternative was to manage all the arithmetic in your head?
One reason why students default to the “mental-only” approach when approaching new problems is that their educational experience has only presented annotation for specific types of problems. Thus, marking all the carry digits and subtotals is something they “only do” when performing multiplication by hand; marking calculated voltages and currents on a schematic diagram is something they “only do” when solving DC resistor circuits; taking notes when reading is something they “only do” when completing a book report. In other words, students see annotation only in very specific contexts, and so they may fail to see just how widely applicable annotation is as a problem-solving strategy. What teachers should do is model and encourage annotation as a problem-solving technique for all types of problems, not just for some types of problems.
To illustrate how this might be done in the context of control system analysis, let us suppose we were asked to determine the effect of flow transmitter FT-24 failing with a low (no-flow) signal in this ratio control system, part of a process for manufacturing ammonium nitrate fertilizer:
Before it is possible to analyze the effects of a transmitter failure, we must first determine what the system ought to do in normal operation. Natural questions to ask might include the following:
• Where do the instrument signals come from and where do they go to?
• What does each instrument signal represent?
• What is the direction of action for each controller in the system?
With just a basic understanding of ratio control systems, we may answer all of these questions by close examination of the P&ID segment, and also annotate those thoughts and conclusions on the diagram in order to help us analyze the system’s response. Starting with the first two questions of where signals originate and terminate and what each signal represents, we may annotate this with arrows and text (shown in red):
We know that all transmitters output data, and so all signal arrows should point away from all transmitters and toward all controllers. We know that all valves receive data, which means arrows must point toward the control valve. The first tag letter of each transmitter (AIT, FT) tells us its measurement function: chemical pH and flow, respectively. The fact that FT-23 is mounted on the same pipe as FV-23 tells us FT-23 must send controller FFC-23 its process variable (captive flow), making the other flow signal (from FT-24) the “wild” flow in this ratio control scheme. AIC-28’s task is to control pH exiting the neutralizer, so we know its output signal must call for a neutralizing reagent, in this case nitric acid. This tells us the signal between AIC-28 and FFC-23 must be a cascade output-setpoint link, with AIC-28 as the master controller and FFC-23 as the slave controller.
Now we turn to the question of controller action, since we know the direction of each controller’s action (e.g. direct or reverse) is significant to how each controller will react to any given change in signal. Here, ‘thought experiments’’ are useful as we imagine the process variable changing due to some load condition, and then determine how the controller must respond to bring that process variable back to setpoint.
When we annotate the action of each controller, it is best to use symbols more descriptive than the words “direct” and “reverse,” especially due to the confusion this often causes when distinguishing the effects of a changing PV signal versus a changing SP signal. In this case, we will write a short formula next to each controller denoting its action according to how the error is calculated ($$e = \hbox{PV} - \hbox{SP}$$ for direct action and $$e = \hbox{SP} - \hbox{PV}$$ for reverse action). We may also write “+” and “$$-$$” symbols next to each input on each controller to further reinforce the direction of each signal’s influence:
FFC-23 is the best controller to start with, since it is the slave controller (in the “inner-most” control loop of this cascade/ratio system). Here, we see that FFC-23 must be reverse-acting, for if FT-23 reports a higher flow we will want FV-23 to close down. This means the remote SP input must have a non-inverting effect on the output: a greater signal from AIC-28 will increase nitric acid flow into the neutralizer. Following this reasoning, we see that AIC-28 should be direct-acting, calling for more nitric acid flow into the neutralizer as product pH becomes more alkaline (pH increases).
The purpose of the ratio control strategy is to balance the “wild” flow of ammonia into the neutralizer with a proportional flow of nitric acid. This is in keeping with principles of chemical reactions (stoichiometry) and mass balance. Therefore, we would expect an increase in ammonia flow to call for a proportionate increase in nitric acid flow, giving the wild flow signal a non-inverting effect on FFC-23.
Only at this point in time are we fully ready to analyze the effects of FT-24 failing with a low-flow signal. Once again, we may annotate the failure on the diagram as well, arbitrarily electing to use blue “up” and “down” arrows and bold text to indicate the directions of change for each signal immediately following the failure of FT-24:
As FT-24’s signal fails low, the “wild” flow signal to FFC-23 goes low as well. Since we have already determined that input has a non-inverting effect on the ratio controller, we may conclude control valve FV-23 will close as a result, decreasing the flow of nitric acid into the neutralizer. This analysis becomes trivial after we’ve done the work of annotating the diagram with our own notes showing how the instruments are supposed to function. Without this set-up, the task of analyzing the effects of FT-24 failing low would be much more difficult.
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Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License | 2020-02-24T02:44:37 | {"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": 0.5983912944793701, "perplexity": 885.3279867559479}, "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/1581875145869.83/warc/CC-MAIN-20200224010150-20200224040150-00033.warc.gz"} |
https://pos.sissa.it/304/021/ | Volume 304 - The 15th International Conference on Flavor Physics & CP Violation (FPCP2017) - Neutrinos
Precise Measurements of Oscillation Parameters $\Theta_{13}$ and $\Delta m^2_{ee}$
Y. Guo, Q. Zhang* on behalf of the Daya Bay collaboration
Full text: pdf
Pre-published on: October 01, 2017
Published on: November 08, 2017
Abstract
The precision of neutrino mixing angle $\theta$$_{13} is of key significance in constraining the leptonic CP phase and testing neutrino oscillation theory. \theta$$_{13}$ is the smallest and the last known neutrino oscillation angle, and its precise measurements were reviewed in this paper. Its two typical measurement approaches, long-baseline accelerator neutrino experiment and short-baseline reactor neutrino experiment, are summarized. Then, their related typical experiments and the corresponding results were also overviewed. Daya Bay is the first experiment to exclude $\theta$$_{13}=0 with a significance of more than 5 standard deviations and has given the most accurate measurement of sin^{2}2$$\theta$$_{13}$ =0.0841±0.0027(stat.)±0.0019(syst.).In addition, |$\Delta$m$_{ee}^{2}$|=2.50±0.06 (stat.)± 0.06 (syst.)×10-3eV$^{2}$ has been also obtained in Daya Bay experiment, which is comparable with $\Delta$m$_{32}^{2}$ measured in long-baseline accelerator neutrino experiment.
DOI: https://doi.org/10.22323/1.304.0021
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-07-03T11:03:32 | {"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": 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": 0.678490161895752, "perplexity": 3720.745319890061}, "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/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00079.warc.gz"} |
https://par.nsf.gov/biblio/10288780-progress-calibration-surface-brightnesscolor-relations-early-late-type-stars | Progress on the calibration of surface brightness–color relations for early- and late-type stars
Context. Surface brightness-color relations (SBCRs) are widely used for estimating angular diameters and deriving stellar properties. They are critical to derive extragalactic distances of early-type and late-type eclipsing binaries or, potentially, for extracting planetary parameters of late-type stars hosting planets. Various SBCRs have been implemented so far, but strong discrepancies in terms of precision and accuracy still exist in the literature. Aims. We aim to develop a precise SBCR for early-type B and A stars using selection criteria, based on stellar characteristics, and combined with homogeneous interferometric angular diameter measurements. We also improve SBCRs for late-type stars, in particular in the Gaia photometric band. Methods. We observed 18 early-type stars with the VEGA interferometric instrument, installed on the CHARA array. We then applied additional criteria on the photometric measurements, together with stellar characteristics diagnostics in order to build the SBCRs. Results. We calibrated a SBCR for subgiant and dwarf early-type stars. The RMS of the relation is σ F V 0 = 0.0051 mag, leading to an average precision of 2.3% on the estimation of angular diameters, with 3.1% for V − K < −0.2 mag and 1.8% for V − K > −0.2 mag. We found that the conversion between more »
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10288780
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Astronomy & Astrophysics
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652
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A26
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0004-6361
5. ABSTRACT We characterize ${\sim } 71\, 200$ W Ursae Majoris (UMa) type (EW) contact binaries, including ${\sim } 12\, 600$ new discoveries, using All-Sky Automated Survey for SuperNovae (ASAN-SN)V-band all-sky light curves along with archival data from Gaia, 2MASS, AllWISE, LAMOST, GALAH, RAVE, and APOGEE. There is a clean break in the EW period–luminosity relation at $\rm \log (\it P/{\rm d})\,{\simeq }\,{\rm -0.30}$, separating the longer period, early-type EW binaries from the shorter period, late-type systems. The two populations are even more cleanly separated in the space of period and effective temperature, by $T_{\rm eff}=6710\,{\rm K}-1760\,{\rm K}\, \log (P/0.5\,{\rm d})$. Early-type and late-type EW binaries follow opposite trends in Teff with orbital period. For longer periods, early-type EW binaries are cooler, while late-type systems are hotter. We derive period–luminosity relationships in the WJK, V, Gaia DR2 G, J, H, Ks, and W1 bands for the late-type and early-type EW binaries separated by both period and effective temperature, and by period alone. The dichotomy of contact binaries is almost certainly related to the Kraft break and the related changes in envelope structure, winds, and angular momentum loss. | 2022-11-28T22:03:16 | {"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": 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": 0.685730516910553, "perplexity": 7674.0456360204025}, "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/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00859.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Avasseur.alexis-f | Vasseur, Alexis F.
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Author ID: vasseur.alexis-f Published as: Vasseur, Alexis; Vasseur, Alexis F.; Vasseur, A. more...less Homepage: http://www.ma.utexas.edu/users/vasseur/ External Links: MGP · Wikidata · dblp · IdRef · theses.fr
Documents Indexed: 100 Publications since 1996 Co-Authors: 57 Co-Authors with 86 Joint Publications 1,395 Co-Co-Authors
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14 single-authored 11 Kang, Moon-Jin 8 Goudon, Thierry 7 Mellet, Antoine 6 Caffarelli, Luis Ángel 5 Yu, Cheng 4 Choi, Kyudong 3 Berthelin, Florent 3 Chan, Chi Hin 3 Collet, Jean-François 3 Kwon, Young-Sam 3 Michoski, C. E. 3 Novack, Matthew D. 3 Poupaud, Frédéric 3 Serre, Denis 3 Wang, Yi 2 Allen, Mark G. 2 Bresch, Didier 2 Caputo, M. Cristina 2 Ducomet, Bernard 2 Feireisl, Eduard 2 Martínez Gamba, Irene 2 Krupa, Sam G. 2 Lacroix-Violet, Ingrid 2 Leger, Nicholas 2 Nečasová, Šárka 2 Perthame, Benoît 2 Schmitz, Phillip G. 2 Stokols, Logan F. 2 Vishik, Misha M. 1 Akopian, Sona 1 Baer, Eric 1 Besnard, D. C. 1 Bjorland, Clayton 1 Bostan, Mihai 1 Botchorishvili, Ramaz 1 Chainais-Hillairet, Claire 1 Chen, Robin Ming 1 Ducros, Frédéric 1 Gisclon, Marguerite 1 Golse, François 1 Hariz, Sara 1 Imbert, Cyril 1 Jabin, Pierre-Emmanuel 1 Jüngel, Ansgar 1 Kreml, Ondřej 1 Lafleche, Laurent 1 Loeper, Grégoire 1 Loreaux, Philippe 1 Merlet, Benoît 1 Mimouni, Stéphane 1 Mischler, Stéphane 1 Mouhot, Clément 1 Puel, Marjolaine 1 Tzavaras, Athanasios E. 1 Wen, Huanyao 1 Yang, Jincheng 1 Yao, Lei
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10 Archive for Rational Mechanics and Analysis 8 SIAM Journal on Mathematical Analysis 5 Communications in Mathematical Physics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Communications in Mathematical Sciences 3 Indiana University Mathematics Journal 3 Communications in Partial Differential Equations 3 Journal of Mathematical Fluid Mechanics 2 Journal of Computational Physics 2 Journal of Statistical Physics 2 Inventiones Mathematicae 2 Journal of Differential Equations 2 SIAM Journal on Numerical Analysis 2 Asymptotic Analysis 2 Methods and Applications of Analysis 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Hyperbolic Differential Equations 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Monatshefte für Mathematik 1 Chinese Annals of Mathematics. Series B 1 Physica D 1 Journal of the American Mathematical Society 1 Applications of Mathematics 1 SIAM Journal on Applied Mathematics 1 Journal of Nonlinear Science 1 Séminaire Équations aux Dérivées Partielles 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Annals of Mathematics. Second Series 1 Multiscale Modeling & Simulation 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Discrete and Continuous Dynamical Systems. Series S 1 Analysis & PDE 1 Journal de l’École Polytechnique – Mathématiques
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Fields
93 Partial differential equations (35-XX) 53 Fluid mechanics (76-XX) 15 Statistical mechanics, structure of matter (82-XX) 8 Numerical analysis (65-XX) 5 Geophysics (86-XX) 3 Integral equations (45-XX) 3 Operator theory (47-XX) 3 Biology and other natural sciences (92-XX) 2 Real functions (26-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)
Citations contained in zbMATH Open
90 Publications have been cited 2,035 times in 1,368 Documents Cited by Year
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063
Caffarelli, Luis A.; Vasseur, Alexis
2010
On the barotropic compressible Navier-Stokes equations. Zbl 1149.35070
Mellet, A.; Vasseur, A.
2007
Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. Zbl 1141.76054
Mellet, A.; Vasseur, A.
2008
A parabolic problem with a fractional time derivative. Zbl 1338.35428
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016
Asymptotic analysis for a Vlasov-Fokker-Planck compressible Navier-Stokes system of equations. Zbl 1155.35415
Mellet, A.; Vasseur, A.
2008
Strong traces for solutions of multidimensional scalar conservation laws. Zbl 0999.35018
Vasseur, Alexis
2001
Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations. Zbl 1136.76042
Mellet, A.; Vasseur, A.
2007
Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098
Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis
2011
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. I: Light particles regime. II: Fine particles regime. Zbl 1085.35117
Goudon, Thierry; Jabin, Pierre-Emmanuel; Vasseur, Alexis
2004
A new proof of partial regularity of solutions to Navier-Stokes equations. Zbl 1142.35066
Vasseur, Alexis F.
2007
Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations. Zbl 1354.35115
Vasseur, Alexis F.; Yu, Cheng
2016
Equilibrium schemes for scalar conservation laws with stiff sources. Zbl 1017.65070
Botchorishvili, Ramaz; Perthame, Benoit; Vasseur, Alexis
2003
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation. Zbl 1431.35016
Golse, François; Imbert, Cyril; Mouhot, Clément; Vasseur, Alexis
2019
Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-$$BV$$ perturbations. Zbl 1261.35090
Leger, Nicholas; Vasseur, Alexis
2011
From kinetic equations to multidimensional isentropic gas dynamics before shocks. Zbl 1130.35090
Berthelin, F.; Vasseur, A.
2005
Global weak solutions to the compressible quantum Navier-Stokes equations with damping. Zbl 1343.35189
Vasseur, Alexis F.; Yu, Cheng
2016
Regularity analysis for systems of reaction-diffusion equations. Zbl 1191.35202
Goudon, Thierry; Vasseur, Alexis
2010
Global weak solution to the viscous two-fluid model with finite energy. Zbl 1450.76033
Vasseur, Alexis; Wen, Huanyao; Yu, Cheng
2019
Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations. Zbl 1198.35175
Chan, Chi Hin; Vasseur, Alexis
2007
Strong traces for solutions to scalar conservation laws with general flux. Zbl 1121.35078
Kwon, Young-Sam; Vasseur, Alexis
2007
Classical and quantum transport in random media. Zbl 1035.82037
Poupaud, Frédéric; Vasseur, Alexis
2003
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity. Zbl 1212.35354
Vasseur, Alexis
2009
Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2017
Recent results on hydrodynamic limits. Zbl 1185.35003
Vasseur, Alexis F.
2008
Global weak solutions to the compressible quantum Navier-Stokes equation and its semi-classical limit. Zbl 1392.35228
Lacroix-Violet, Ingrid; Vasseur, Alexis
2018
Asymptotic analysis of Vlasov-type equations under strong local alignment regime. Zbl 1331.35345
Kang, Moon-Jin; Vasseur, Alexis F.
2015
From discrete velocity Boltzmann equations to gas dynamics before shocks. Zbl 1168.82322
Berthelin, Florent; Tzavaras, Athanasios E.; Vasseur, Alexis
2009
Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations. Zbl 1181.35209
Gamba, Irene M.; Jüngel, Ansgar; Vasseur, Alexis
2009
Global regularity of solutions to systems of reaction-diffusion with sub-quadratic growth in any dimension. Zbl 1181.35295
Caputo, M. Cristina; Vasseur, Alexis
2009
$$L^2$$-type contraction for systems of conservation laws. (Contraction de type $$L^2$$ pour des systèmes de lois de conservation.) Zbl 1310.62079
Serre, Denis; Vasseur, Alexis F.
2014
The Becker-Döring system and its Lifshitz-Slyozov limit. Zbl 1025.45005
Collet, Jean-François; Goudon, Thierry; Poupaud, Frédéric; Vasseur, Alexis
2002
The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039
Caffarelli, Luis A.; Vasseur, Alexis F.
2010
Time regularity for the system of isentropic gas dynamics with $$\gamma=3$$. Zbl 0940.35169
Vasseur, A.
1999
Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method. Zbl 1316.35195
Choi, Kyudong; Vasseur, Alexis F.
2015
Stability of the isentropic Riemann solutions of the full multidimensional Euler system. Zbl 1325.35148
Feireisl, E.; Kreml, O.; Vasseur, A.
2015
Bjorland, Clayton; Vasseur, Alexis
2011
Solutions of the 4-species quadratic reaction-diffusion system are bounded and $$C^\infty$$-smooth, in any space dimension. Zbl 1423.35164
Caputo, M. Cristina; Goudon, Thierry; Vasseur, Alexis F.
2019
Relative entropy and contraction for extremal shocks of conservation laws up to a shift. Zbl 1357.35219
Vasseur, Alexis F.
2016
$$L^{2}$$-contraction for shock waves of scalar viscous conservation laws. Zbl 1368.35183
Kang, Moon-Jin; Vasseur, Alexis F.
2017
Criteria on contractions for entropic discontinuities of systems of conservation laws. Zbl 1354.35077
Kang, Moon-Jin; Vasseur, Alexis F.
2016
Well-posedness of scalar conservation laws with singular sources. Zbl 1084.35046
Vasseur, Alexis
2002
New perspectives in fluid dynamics: mathematical analysis of a model proposed by Howard Brenner. Zbl 1221.35276
Feireisl, Eduard; Vasseur, Alexis
2010
About the relative entropy method for hyperbolic systems of conservation laws. Zbl 1355.35138
Serre, Denis; Vasseur, Alexis F.
2016
The inviscid limit to a contact discontinuity for the compressible Navier-Stokes-Fourier system using the relative entropy method. Zbl 1333.35165
Vasseur, Alexis; Wang, Yi
2015
$$L^2$$-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws. Zbl 1417.35129
Kang, Moon-Jin; Vasseur, Alexis F.; Wang, Yi
2019
On spherically symmetric motions of a viscous compressible barotropic and selfgravitating gas. Zbl 1270.35338
Ducomet, Bernard; Nečasová, Šárka; Vasseur, Alexis
2011
Nonlinear stability of viscous shock wave to one-dimensional compressible isentropic Navier-Stokes equations with density dependent viscous coefficient. Zbl 1360.35152
Vasseur, Alexis F.; Yao, Lei
2016
The relative entropy method for the stability of intermediate shock waves; the rich case. Zbl 1347.35169
Serre, Denis; Vasseur, Alexis
2016
Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas. Zbl 0920.65060
Vasseur, Alexis
1998
Estimates on fractional higher derivatives of weak solutions for the Navier-Stokes equations. Zbl 1297.76047
Choi, Kyudong; Vasseur, Alexis F.
2014
Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with $$\gamma=3$$. Zbl 1020.65054
Vasseur, Alexis
1999
Global in time classical solutions to the 3D quasi-geostrophic system for large initial data. Zbl 1417.35137
Novack, Matthew D.; Vasseur, Alexis F.
2018
On global motions of a compressible barotropic and self-gravitating gas with density-dependent viscosities. Zbl 1244.76105
Ducomet, Bernard; Nečasová, Šárka; Vasseur, Alexis
2010
A discontinuous Galerkin method for viscous compressible multifluids. Zbl 1303.76088
Michoski, C.; Evans, J. A.; Schmitz, P. G.; Vasseur, A.
2010
Global weak solutions to the inviscid 3D quasi-geostrophic equation. Zbl 1328.35177
Puel, Marjolaine; Vasseur, Alexis F.
2015
Some remarks on large-time asymptotic of the Lifshitz-Slyozov equations. Zbl 1067.82046
Collet, Jean-François; Goudon, Thierry; Vasseur, Alexis
2002
Electric turbulence in a plasma subject to a strong magnetic field. Zbl 1080.35153
Loeper, G.; Vasseur, A.
2004
The De Giorgi method for elliptic and parabolic equations and some applications. Zbl 1353.35096
Vasseur, Alexis F.
2016
Existence and uniqueness of strong solutions for a compressible multiphase Navier-Stokes miscible fluid-flow problem in dimension $$n=1$$. Zbl 1166.76047
Michoski, C.; Vasseur, A.
2009
Boundary value problems for the stationary Vlasov-Boltzmann-Poisson equation. Zbl 1236.82062
Bostan, Mihai; Gamba, Irene M.; Thierry; Vasseur, Alexis
2010
De Giorgi techniques applied to Hamilton-Jacobi equations with unbounded right-hand side. Zbl 1415.35095
Stokols, Logan F.; Vasseur, Alexis F.
2019
Higher derivatives estimate for the 3D Navier-Stokes equation. Zbl 1396.35046
Vasseur, Alexis
2010
The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249
Caffarelli, Luis A.; Vasseur, Alexis
2012
On uniqueness of solutions to conservation laws verifying a single entropy condition. Zbl 1453.35122
Krupa, Sam G.; Vasseur, Alexis F.
2019
Regularization in Keller-Segel type systems and the De Giorgi method. Zbl 1288.35146
Perthame, Benoît; Vasseur, Alexis
2012
Asymptotic limit to a shock for BGK models using relative entropy method. Zbl 1316.35196
Kwon, Young-Sam; Vasseur, Alexis F.
2015
Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. Zbl 1443.92058
Choi, Kyudong; Kang, Moon-Jin; Kwon, Young-Sam; Vasseur, Alexis F.
2020
Study of a generalized fragmentation model for sprays. Zbl 1188.35134
Leger, Nicholas; Vasseur, Alexis F.
2009
Blow-up solutions to 3D Euler are hydrodynamically unstable. Zbl 1446.35114
Vasseur, Alexis F.; Vishik, Misha
2020
Stability and uniqueness for piecewise smooth solutions to a nonlocal scalar conservation law with applications to Burgers-Hilbert equation. Zbl 1453.35123
Krupa, Sam G.; Vasseur, Alexis F.
2020
Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system. Zbl 1460.76614
Kang, Moon-Jin; Vasseur, Alexis F.
2021
$$L^p$$ estimates for quantities advected by a compressible flow. Zbl 1172.35056
Mellet, Antoine; Vasseur, Alexis
2009
A bound from below for the temperature in compressible Navier-Stokes equations. Zbl 1173.35100
Mellet, Antoine; Vasseur, Alexis
2009
Quantum hydrodynamics with trajectories: the nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry. Zbl 1287.76244
Michoski, C.; Evans, J. A.; Schmitz, P. G.; Vasseur, A.
2009
De Giorgi techniques applied to the Hölder regularity of solutions to Hamilton-Jacobi equations. Zbl 1390.35048
Chan, Chi Hin; Vasseur, Alexis
2017
Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities. Zbl 1442.35339
Kang, Moon-Jin; Vasseur, Alexis F.
2020
Global well-posedness of large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. Zbl 1448.92036
Choi, Kyudong; Kang, Moon-Jin; Vasseur, Alexis F.
2020
Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems. Zbl 1460.76661
Kang, Moon-Jin; Vasseur, Alexis F.
2021
The inviscid three dimensional quasi-geostrophic system on bounded domains. Zbl 1435.35308
Novack, Matthew D.; Vasseur, Alexis F.
2020
On a model for mixture flows: derivation, dissipation and stability properties. Zbl 1339.35319
Goudon, Thierry; Vasseur, Alexis
2016
Existence and properties of semidiscrete shock profiles for the isentropic gas dynamic system with $$\gamma=3$$. Zbl 1002.76062
Vasseur, Alexis
2001
A bound from below on the temperature for the Navier-Stokes-Fourier system. Zbl 1285.35075
Baer, Eric; Vasseur, Alexis
2013
A rigorous derivation of the coupling of a kinetic equation and Burgers’ equation. Zbl 1256.35047
Vasseur, Alexis F.
2012
Inviscid limit to the shock waves for the fractal Burgers equation. Zbl 1462.35200
Akopian, Sona; Kang, Moon-Jin; Vasseur, Alexis
2020
Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics. Zbl 07436485
Chen, Robin Ming; Vasseur, Alexis F.; Yu, Cheng
2021
On the exponential decay for compressible Navier-Stokes-Korteweg equations with a drag term. Zbl 07451596
Bresch, D.; Gisclon, M.; Lacroix-Violet, I.; Vasseur, A.
2022
On the convergence of numerical schemes for the Boltzmann equation. Zbl 1038.82082
Horsin, T.; Mischler, S.; Vasseur, A.
2003
Positive lower bound for the numerical solution of a convection-diffusion equation. Zbl 1372.65291
Chainais-Hillairet, Claire; Merlet, Benoît; Vasseur, Alexis F.
2017
Hölder regularity up to the boundary for critical SQG on bounded domains. Zbl 1439.35480
Stokols, Logan F.; Vasseur, Alexis F.
2020
Global existence of entropy-weak solutions to the compressible Navier-Stokes equations with non-linear density dependent viscosities. Zbl 07509409
Bresch, Didier; Vasseur, Alexis F.; Yu, Cheng
2022
On the exponential decay for compressible Navier-Stokes-Korteweg equations with a drag term. Zbl 07451596
Bresch, D.; Gisclon, M.; Lacroix-Violet, I.; Vasseur, A.
2022
Global existence of entropy-weak solutions to the compressible Navier-Stokes equations with non-linear density dependent viscosities. Zbl 07509409
Bresch, Didier; Vasseur, Alexis F.; Yu, Cheng
2022
Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system. Zbl 1460.76614
Kang, Moon-Jin; Vasseur, Alexis F.
2021
Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems. Zbl 1460.76661
Kang, Moon-Jin; Vasseur, Alexis F.
2021
Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics. Zbl 07436485
Chen, Robin Ming; Vasseur, Alexis F.; Yu, Cheng
2021
Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. Zbl 1443.92058
Choi, Kyudong; Kang, Moon-Jin; Kwon, Young-Sam; Vasseur, Alexis F.
2020
Blow-up solutions to 3D Euler are hydrodynamically unstable. Zbl 1446.35114
Vasseur, Alexis F.; Vishik, Misha
2020
Stability and uniqueness for piecewise smooth solutions to a nonlocal scalar conservation law with applications to Burgers-Hilbert equation. Zbl 1453.35123
Krupa, Sam G.; Vasseur, Alexis F.
2020
Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities. Zbl 1442.35339
Kang, Moon-Jin; Vasseur, Alexis F.
2020
Global well-posedness of large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. Zbl 1448.92036
Choi, Kyudong; Kang, Moon-Jin; Vasseur, Alexis F.
2020
The inviscid three dimensional quasi-geostrophic system on bounded domains. Zbl 1435.35308
Novack, Matthew D.; Vasseur, Alexis F.
2020
Inviscid limit to the shock waves for the fractal Burgers equation. Zbl 1462.35200
Akopian, Sona; Kang, Moon-Jin; Vasseur, Alexis
2020
Hölder regularity up to the boundary for critical SQG on bounded domains. Zbl 1439.35480
Stokols, Logan F.; Vasseur, Alexis F.
2020
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation. Zbl 1431.35016
Golse, François; Imbert, Cyril; Mouhot, Clément; Vasseur, Alexis
2019
Global weak solution to the viscous two-fluid model with finite energy. Zbl 1450.76033
Vasseur, Alexis; Wen, Huanyao; Yu, Cheng
2019
Solutions of the 4-species quadratic reaction-diffusion system are bounded and $$C^\infty$$-smooth, in any space dimension. Zbl 1423.35164
Caputo, M. Cristina; Goudon, Thierry; Vasseur, Alexis F.
2019
$$L^2$$-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws. Zbl 1417.35129
Kang, Moon-Jin; Vasseur, Alexis F.; Wang, Yi
2019
De Giorgi techniques applied to Hamilton-Jacobi equations with unbounded right-hand side. Zbl 1415.35095
Stokols, Logan F.; Vasseur, Alexis F.
2019
On uniqueness of solutions to conservation laws verifying a single entropy condition. Zbl 1453.35122
Krupa, Sam G.; Vasseur, Alexis F.
2019
Global weak solutions to the compressible quantum Navier-Stokes equation and its semi-classical limit. Zbl 1392.35228
Lacroix-Violet, Ingrid; Vasseur, Alexis
2018
Global in time classical solutions to the 3D quasi-geostrophic system for large initial data. Zbl 1417.35137
Novack, Matthew D.; Vasseur, Alexis F.
2018
Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2017
$$L^{2}$$-contraction for shock waves of scalar viscous conservation laws. Zbl 1368.35183
Kang, Moon-Jin; Vasseur, Alexis F.
2017
De Giorgi techniques applied to the Hölder regularity of solutions to Hamilton-Jacobi equations. Zbl 1390.35048
Chan, Chi Hin; Vasseur, Alexis
2017
Positive lower bound for the numerical solution of a convection-diffusion equation. Zbl 1372.65291
Chainais-Hillairet, Claire; Merlet, Benoît; Vasseur, Alexis F.
2017
A parabolic problem with a fractional time derivative. Zbl 1338.35428
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016
Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations. Zbl 1354.35115
Vasseur, Alexis F.; Yu, Cheng
2016
Global weak solutions to the compressible quantum Navier-Stokes equations with damping. Zbl 1343.35189
Vasseur, Alexis F.; Yu, Cheng
2016
Relative entropy and contraction for extremal shocks of conservation laws up to a shift. Zbl 1357.35219
Vasseur, Alexis F.
2016
Criteria on contractions for entropic discontinuities of systems of conservation laws. Zbl 1354.35077
Kang, Moon-Jin; Vasseur, Alexis F.
2016
About the relative entropy method for hyperbolic systems of conservation laws. Zbl 1355.35138
Serre, Denis; Vasseur, Alexis F.
2016
Nonlinear stability of viscous shock wave to one-dimensional compressible isentropic Navier-Stokes equations with density dependent viscous coefficient. Zbl 1360.35152
Vasseur, Alexis F.; Yao, Lei
2016
The relative entropy method for the stability of intermediate shock waves; the rich case. Zbl 1347.35169
Serre, Denis; Vasseur, Alexis
2016
The De Giorgi method for elliptic and parabolic equations and some applications. Zbl 1353.35096
Vasseur, Alexis F.
2016
On a model for mixture flows: derivation, dissipation and stability properties. Zbl 1339.35319
Goudon, Thierry; Vasseur, Alexis
2016
Asymptotic analysis of Vlasov-type equations under strong local alignment regime. Zbl 1331.35345
Kang, Moon-Jin; Vasseur, Alexis F.
2015
Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method. Zbl 1316.35195
Choi, Kyudong; Vasseur, Alexis F.
2015
Stability of the isentropic Riemann solutions of the full multidimensional Euler system. Zbl 1325.35148
Feireisl, E.; Kreml, O.; Vasseur, A.
2015
The inviscid limit to a contact discontinuity for the compressible Navier-Stokes-Fourier system using the relative entropy method. Zbl 1333.35165
Vasseur, Alexis; Wang, Yi
2015
Global weak solutions to the inviscid 3D quasi-geostrophic equation. Zbl 1328.35177
Puel, Marjolaine; Vasseur, Alexis F.
2015
Asymptotic limit to a shock for BGK models using relative entropy method. Zbl 1316.35196
Kwon, Young-Sam; Vasseur, Alexis F.
2015
$$L^2$$-type contraction for systems of conservation laws. (Contraction de type $$L^2$$ pour des systèmes de lois de conservation.) Zbl 1310.62079
Serre, Denis; Vasseur, Alexis F.
2014
Estimates on fractional higher derivatives of weak solutions for the Navier-Stokes equations. Zbl 1297.76047
Choi, Kyudong; Vasseur, Alexis F.
2014
A bound from below on the temperature for the Navier-Stokes-Fourier system. Zbl 1285.35075
Baer, Eric; Vasseur, Alexis
2013
The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249
Caffarelli, Luis A.; Vasseur, Alexis
2012
Regularization in Keller-Segel type systems and the De Giorgi method. Zbl 1288.35146
Perthame, Benoît; Vasseur, Alexis
2012
A rigorous derivation of the coupling of a kinetic equation and Burgers’ equation. Zbl 1256.35047
Vasseur, Alexis F.
2012
Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098
Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis
2011
Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-$$BV$$ perturbations. Zbl 1261.35090
Leger, Nicholas; Vasseur, Alexis
2011
Bjorland, Clayton; Vasseur, Alexis
2011
On spherically symmetric motions of a viscous compressible barotropic and selfgravitating gas. Zbl 1270.35338
Ducomet, Bernard; Nečasová, Šárka; Vasseur, Alexis
2011
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063
Caffarelli, Luis A.; Vasseur, Alexis
2010
Regularity analysis for systems of reaction-diffusion equations. Zbl 1191.35202
Goudon, Thierry; Vasseur, Alexis
2010
The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039
Caffarelli, Luis A.; Vasseur, Alexis F.
2010
New perspectives in fluid dynamics: mathematical analysis of a model proposed by Howard Brenner. Zbl 1221.35276
Feireisl, Eduard; Vasseur, Alexis
2010
On global motions of a compressible barotropic and self-gravitating gas with density-dependent viscosities. Zbl 1244.76105
Ducomet, Bernard; Nečasová, Šárka; Vasseur, Alexis
2010
A discontinuous Galerkin method for viscous compressible multifluids. Zbl 1303.76088
Michoski, C.; Evans, J. A.; Schmitz, P. G.; Vasseur, A.
2010
Boundary value problems for the stationary Vlasov-Boltzmann-Poisson equation. Zbl 1236.82062
Bostan, Mihai; Gamba, Irene M.; Thierry; Vasseur, Alexis
2010
Higher derivatives estimate for the 3D Navier-Stokes equation. Zbl 1396.35046
Vasseur, Alexis
2010
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity. Zbl 1212.35354
Vasseur, Alexis
2009
From discrete velocity Boltzmann equations to gas dynamics before shocks. Zbl 1168.82322
Berthelin, Florent; Tzavaras, Athanasios E.; Vasseur, Alexis
2009
Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations. Zbl 1181.35209
Gamba, Irene M.; Jüngel, Ansgar; Vasseur, Alexis
2009
Global regularity of solutions to systems of reaction-diffusion with sub-quadratic growth in any dimension. Zbl 1181.35295
Caputo, M. Cristina; Vasseur, Alexis
2009
Existence and uniqueness of strong solutions for a compressible multiphase Navier-Stokes miscible fluid-flow problem in dimension $$n=1$$. Zbl 1166.76047
Michoski, C.; Vasseur, A.
2009
Study of a generalized fragmentation model for sprays. Zbl 1188.35134
Leger, Nicholas; Vasseur, Alexis F.
2009
$$L^p$$ estimates for quantities advected by a compressible flow. Zbl 1172.35056
Mellet, Antoine; Vasseur, Alexis
2009
A bound from below for the temperature in compressible Navier-Stokes equations. Zbl 1173.35100
Mellet, Antoine; Vasseur, Alexis
2009
Quantum hydrodynamics with trajectories: the nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry. Zbl 1287.76244
Michoski, C.; Evans, J. A.; Schmitz, P. G.; Vasseur, A.
2009
Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. Zbl 1141.76054
Mellet, A.; Vasseur, A.
2008
Asymptotic analysis for a Vlasov-Fokker-Planck compressible Navier-Stokes system of equations. Zbl 1155.35415
Mellet, A.; Vasseur, A.
2008
Recent results on hydrodynamic limits. Zbl 1185.35003
Vasseur, Alexis F.
2008
On the barotropic compressible Navier-Stokes equations. Zbl 1149.35070
Mellet, A.; Vasseur, A.
2007
Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations. Zbl 1136.76042
Mellet, A.; Vasseur, A.
2007
A new proof of partial regularity of solutions to Navier-Stokes equations. Zbl 1142.35066
Vasseur, Alexis F.
2007
Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations. Zbl 1198.35175
Chan, Chi Hin; Vasseur, Alexis
2007
Strong traces for solutions to scalar conservation laws with general flux. Zbl 1121.35078
Kwon, Young-Sam; Vasseur, Alexis
2007
From kinetic equations to multidimensional isentropic gas dynamics before shocks. Zbl 1130.35090
Berthelin, F.; Vasseur, A.
2005
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. I: Light particles regime. II: Fine particles regime. Zbl 1085.35117
Goudon, Thierry; Jabin, Pierre-Emmanuel; Vasseur, Alexis
2004
Electric turbulence in a plasma subject to a strong magnetic field. Zbl 1080.35153
Loeper, G.; Vasseur, A.
2004
Equilibrium schemes for scalar conservation laws with stiff sources. Zbl 1017.65070
Botchorishvili, Ramaz; Perthame, Benoit; Vasseur, Alexis
2003
Classical and quantum transport in random media. Zbl 1035.82037
Poupaud, Frédéric; Vasseur, Alexis
2003
On the convergence of numerical schemes for the Boltzmann equation. Zbl 1038.82082
Horsin, T.; Mischler, S.; Vasseur, A.
2003
The Becker-Döring system and its Lifshitz-Slyozov limit. Zbl 1025.45005
Collet, Jean-François; Goudon, Thierry; Poupaud, Frédéric; Vasseur, Alexis
2002
Well-posedness of scalar conservation laws with singular sources. Zbl 1084.35046
Vasseur, Alexis
2002
Some remarks on large-time asymptotic of the Lifshitz-Slyozov equations. Zbl 1067.82046
Collet, Jean-François; Goudon, Thierry; Vasseur, Alexis
2002
Strong traces for solutions of multidimensional scalar conservation laws. Zbl 0999.35018
Vasseur, Alexis
2001
Existence and properties of semidiscrete shock profiles for the isentropic gas dynamic system with $$\gamma=3$$. Zbl 1002.76062
Vasseur, Alexis
2001
Time regularity for the system of isentropic gas dynamics with $$\gamma=3$$. Zbl 0940.35169
Vasseur, A.
1999
Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with $$\gamma=3$$. Zbl 1020.65054
Vasseur, Alexis
1999
Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas. Zbl 0920.65060
Vasseur, Alexis
1998
all top 5
Cited by 1,500 Authors
56 Vasseur, Alexis F. 20 Mai Duc Thanh 19 Goudon, Thierry 17 Kang, Moon-Jin 16 Kwon, Young-Sam 15 Choi, Young-Pil 15 Jiu, Quansen 15 Lian, Ruxu 15 Wang, Yi 13 Constantin, Peter 12 Guo, Zhenhua 12 Novotný, Antonín 12 Zatorska, Ewelina 11 Bresch, Didier 11 Caffarelli, Luis Ángel 11 Feireisl, Eduard 11 Ha, Seung-Yeal 11 Silvestre, Luis E. 11 Vazquez, Juan Luis 11 Vicol, Vlad C. 11 Wang, Yanqing 11 Yao, Lei 11 Yu, Cheng 10 Dong, Hongjie 10 Jin, Shi 10 Li, Hailiang 10 Liu, Jianguo 10 Trivisa, Konstantina 10 Wen, Huanyao 10 Xin, Zhouping 10 Zhu, Changjiang 9 Andreianov, Boris 9 Haspot, Boris 9 Imbert, Cyril 9 Karlsen, Kenneth Hvistendahl 9 Pierre, Michel 9 Tang, Bao Quoc 9 Yang, Jianwei 8 Berthelin, Florent 8 Cuong, Dao Huy 8 Gala, Sadek 8 Nečasová, Šárka 8 Perthame, Benoît 8 Xue, Liutang 8 Zhu, Shengguo 7 Dai, Wei 7 Desvillettes, Laurent 7 Dong, Boqing 7 Fellner, Klemens 7 Friedlander, Susan Jean 7 Gosse, Laurent 7 Jabin, Pierre-Emmanuel 7 Pokorný, Milan 7 Quirós Gracián, Fernando 7 Rosini, Massimiliano Daniele 7 Seguin, Nicolas 7 Sire, Yannick 7 Stinga, Pablo Raúl 7 Wang, Dehua 7 Wang, Pengyan 7 Yu, Xinwei 6 Antonelli, Paolo 6 Carrillo de la Plata, José Antonio 6 Dai, Mimi 6 Jia, Yan 6 Kuznetsov, Ivan V. 6 Li, Fucai 6 Li, Lei 6 Li, Yachun 6 Liu, Jian 6 Miao, Changxing 6 Morgan, Jeff J. 6 Novack, Matthew D. 6 Peng, Shaolong 6 Ryzhik, Lenya 6 Shvydkoy, Roman V. 6 Soler, Juan S. 6 Spirito, Stefano 6 Tang, Tong 6 Valdinoci, Enrico 6 Wu, Gang 6 Wu, Jiahong 6 Zhang, Zhifei 5 Alonso Rodríguez, Ana 5 Bal, Guillaume 5 Beirão da Veiga, Hugo 5 Chamorro, Diego 5 Chen, Gui-Qiang G. 5 de Pablo, Arturo 5 Desjardins, Benoît 5 Dipierro, Serena 5 Donadello, Carlotta 5 Dong, Jianwei 5 Dou, Changsheng 5 Fan, Jishan 5 Huang, Bingkang 5 Jung, Jinwook 5 Kang, Kyungkeun 5 Kim, Jeongho 5 Kukavica, Igor ...and 1,400 more Authors
all top 5
Cited in 209 Serials
112 Journal of Differential Equations 60 SIAM Journal on Mathematical Analysis 56 Archive for Rational Mechanics and Analysis 50 Journal of Mathematical Fluid Mechanics 42 Journal of Mathematical Analysis and Applications 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 37 Journal of Mathematical Physics 35 Communications in Mathematical Physics 35 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 30 Discrete and Continuous Dynamical Systems 29 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 26 Journal of Functional Analysis 24 Journal of Computational Physics 24 Journal of Evolution Equations 22 ZAMP. Zeitschrift für angewandte Mathematik und Physik 22 Advances in Mathematics 22 Nonlinear Analysis. Real World Applications 20 Applied Mathematics Letters 20 Journal of Hyperbolic Differential Equations 19 Discrete and Continuous Dynamical Systems. Series B 18 Nonlinearity 18 Calculus of Variations and Partial Differential Equations 17 Communications on Pure and Applied Analysis 17 Kinetic and Related Models 14 Mathematical Methods in the Applied Sciences 13 Communications in Partial Differential Equations 12 Journal of Statistical Physics 12 Applied Mathematics and Computation 11 Discrete and Continuous Dynamical Systems. Series S 10 Transactions of the American Mathematical Society 9 Computers & Mathematics with Applications 9 Mathematics of Computation 9 Quarterly of Applied Mathematics 9 Acta Applicandae Mathematicae 9 Physica D 9 Journal of Scientific Computing 9 Journal of Nonlinear Science 9 Boundary Value Problems 8 Applicable Analysis 8 Acta Mathematicae Applicatae Sinica. English Series 8 NoDEA. Nonlinear Differential Equations and Applications 7 Proceedings of the American Mathematical Society 7 Advances in Nonlinear Analysis 6 Chinese Annals of Mathematics. Series B 6 SIAM Journal on Applied Mathematics 6 Stochastic Processes and their Applications 6 Abstract and Applied Analysis 6 Fractional Calculus & Applied Analysis 6 Journal of the European Mathematical Society (JEMS) 6 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 6 Complex Variables and Elliptic Equations 6 Annals of PDE 5 Physics Letters. A 5 Inventiones Mathematicae 5 Mathematische Annalen 5 Numerische Mathematik 5 SIAM Journal on Numerical Analysis 5 Asymptotic Analysis 5 Journal of Dynamics and Differential Equations 5 Journal of Applied Mathematics 5 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 5 Science China. Mathematics 4 Monatshefte für Mathematik 4 Applied Numerical Mathematics 4 The Journal of Geometric Analysis 4 Potential Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Journal of Inequalities and Applications 4 Annals of Mathematics. Second Series 4 Communications in Contemporary Mathematics 4 Advanced Nonlinear Studies 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Analysis & PDE 3 Computers and Fluids 3 Communications on Pure and Applied Mathematics 3 Journal of Mathematical Biology 3 Applied Mathematics and Optimization 3 Journal of Computational and Applied Mathematics 3 Pacific Journal of Mathematics 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 SIAM Journal on Scientific Computing 3 Journal of Mathematical Sciences (New York) 3 Advances in Computational Mathematics 3 Acta Mathematica Sinica. English Series 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Multiscale Modeling & Simulation 3 Networks and Heterogeneous Media 3 Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 3 Journal of Elliptic and Parabolic Equations 2 Computer Methods in Applied Mechanics and Engineering 2 Journal d’Analyse Mathématique 2 Rocky Mountain Journal of Mathematics 2 Chaos, Solitons and Fractals 2 The Annals of Probability 2 Ricerche di Matematica 2 Revista Matemática Iberoamericana 2 Journal of the American Mathematical Society ...and 109 more Serials
all top 5
Cited in 43 Fields
1,266 Partial differential equations (35-XX) 647 Fluid mechanics (76-XX) 112 Numerical analysis (65-XX) 108 Statistical mechanics, structure of matter (82-XX) 71 Probability theory and stochastic processes (60-XX) 67 Geophysics (86-XX) 58 Real functions (26-XX) 55 Biology and other natural sciences (92-XX) 52 Operator theory (47-XX) 42 Integral equations (45-XX) 29 Ordinary differential equations (34-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 24 Mechanics of deformable solids (74-XX) 24 Classical thermodynamics, heat transfer (80-XX) 23 Quantum theory (81-XX) 21 Global analysis, analysis on manifolds (58-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 20 Functional analysis (46-XX) 19 Dynamical systems and ergodic theory (37-XX) 15 Systems theory; control (93-XX) 12 Differential geometry (53-XX) 11 Operations research, mathematical programming (90-XX) 10 Potential theory (31-XX) 9 Optics, electromagnetic theory (78-XX) 7 Astronomy and astrophysics (85-XX) 6 Mechanics of particles and systems (70-XX) 5 Measure and integration (28-XX) 5 Functions of a complex variable (30-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Relativity and gravitational theory (83-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-06-30T04:08:48 | {"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": 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": 0.5315595269203186, "perplexity": 7091.41826911472}, "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-2022-27/segments/1656103661137.41/warc/CC-MAIN-20220630031950-20220630061950-00673.warc.gz"} |
https://huggingface.co/datasets/albertvillanova/tmp-mention/blob/main/README.md | # Datasets: albertvillanova /tmp-mention
ArXiv:
ddff094
license: cc-by-4.0
tags:
- zenodo
# Dataset Card for MultiLingual LibriSpeech
## Dataset Description
### Dataset Summary
Deprecated: Not every model supports a fast tokenizer. Take a look at this table to check if a model has fast tokenizer support.
Multilingual LibriSpeech (MLS) dataset is a large multilingual corpus suitable for speech research. The dataset is derived from read audiobooks from LibriVox and consists of 8 languages - English, German, Dutch, Spanish, French, Italian, Portuguese, Polish.
• automatic-speech-recognition, audio-speaker-identification: The dataset can be used to train a model for Automatic Speech Recognition (ASR). The model is presented with an audio file and asked to transcribe the audio file to written text. The most common evaluation metric is the word error rate (WER). The task has an active leaderboard which can be found at https://paperswithcode.com/dataset/multilingual-librispeech and ranks models based on their WER.
Deprecated: Not every model supports a fast tokenizer. Take a look at this table to check if a model has fast tokenizer support.
⚠ In general, just avoid the red boxes.
In general, just avoid the red boxes.
Error:
[!WARNING] This is a warning
Warning: Be very careful here.
This is a warning This is a warning This is a warning
Warning This is a warning | 2023-04-01T21:18:00 | {"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": 0.19935427606105804, "perplexity": 3236.030432286791}, "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-2023-14/segments/1679296950247.65/warc/CC-MAIN-20230401191131-20230401221131-00246.warc.gz"} |
http://fuelcycle.org/cep/cep23.html | # CEP 23 - Defining Time Step Length, High Noon for Blue Moon¶
CEP: 23 Defining Time Step Length, High Noon for Blue Moon 2014-12-01 Anthony Scopatz Paul P. H. Wilson Draft Standards Track 2014-12-01
## Motivation¶
Cyclus is a discrete time simulator whose assumed default time step is months. Months are the worst unit ever. This proposal adds precision and flexibility to what we mean by $$\delta t$$. Namely, this CEP moves from months to seconds and allows the user to set the time step length, preserving a default length of a Julian month.
## Discussion¶
Cyclus lacks a canonical time system. This CEP seeks to unambiguously define the seconds as the default time unit. This allows agents to unambiguously communicate with each other and to determine their own time scales internally. This CEP also adds the capability for users to specify a time step length ($$\delta t$$) of their choosing. The default time step, if unspecified, will be a well-defined month, improving on the historically nebulous month.
This CEP is motivated by our past woes with months. Months are an awful time step because there is no single definition for what a month is and all definitions lack a physical basis. Days and years map nicely (enough) onto a solar cycle. A lunar cycle is 29.53059 days with 7.4 days per phase. This does not map on well to any solar equivalent. In fact, a 12 month lunar year is only 354.36708 days, which is a far cry from a solar year. This is why many lunar calendars are, in fact, lunisolar. Various strategies for dealing with this time defect are either to add an extra months occasionally or to have non-month days between years.
As physically impossible as it is to perfectly sync the sun and the moon, it is an even worse idea to implement a full Gregorian calendar. Like with time zones, the opportunities for failure are nearly endless. Furthermore, going with a real calendar breaks with the current notion that all time steps have an equal $$\delta t$$.
## Specification¶
This CEP defines the default time step as the average length of a Julian month as measured in seconds, the proper unit for time:
$\delta t = \frac{365.25 [d]}{12} = \frac{31557600 [s]}{12} = 2629800 [s/m]$
Furthermore, this actual time step should be able to be set by the user in the input file. The following changes to the master schema(s) are thus needed:
<element name ="control">
<interleave>
. . .
<optional>
<element name="dt"><data type="unsignedLong"/</element>
</optional>
<optional>
<element name="dt_units"><data type="token"/</element>
</optional>
</interleave>
</element>
This information would be added to the context with the following members:
class Context {
public:
// Returns the time step in seconds
inline uint64_t dt() { return dt_; };
// Returns the time step in [units], given as string
uint64_t dt(std::string units);
// Returns the time step in [units], given as TimeUnits enum
uint64_t dt(TimeUnits units);
private:
uint64_t dt_; // the length of the time step, in seconds.
}
All archetypes and toolkit code should then ask the context what the time step size is whenever they actually need the current. As per CEP20, the time step length is fixed for the entire simulation and may not change.
Furthermore, TimeUnits will be a fixed set of time increments that will not be able to be set by the users. An initial set of time units are: s, min, hr, d, month (as defined above), y, ky, My, Gy.
### Best Practices¶
Along with this CEP comes the best practice that archetypes which model time-dependent behavior should not assume a nominal time step. Archetypes should always get the time step length from the context. Since the time step is fixed, this need only be done once per prototype.
From here, we also define two broad archetype classifications: those which care about actual real physical time and those which simply function per simulation time step.
When an archetype uses real time, due to physics calculations or other needs, the archetype should now check that $$\delta t$$ is within a valid range that they define. This is because users will now be able to set the time step. This validation check maybe performed in any of the archetype’s member functions. If a static range is known ahead of time, then this check is most appropriate in the constructor. If the time step length is outside of the valid range of the agent, then an exception should be raised. We recommend something along the lines of:
if (context().dt() > max_dt)
throw cyclus::ValidationError("time step exceeds valid range!");
On the other hand, if the archtype only models per time step behavior, then state variables should be expressible by default in terms of number of time steps, not in terms of seconds. If other time values are desirable, the user should explicitly give the time units. For any time-based variable, the default associated units should be provided by the metadata.
## Implementation¶
The implementation of this code should be fairly straight forward. Unlike time itself, there is no funny business here.
## Document History¶
This document is released under the CC-BY 4.0 license. | 2022-01-25T13:51:32 | {"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": 1, "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": 0.5602593421936035, "perplexity": 1704.651652375912}, "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-2022-05/segments/1642320304835.96/warc/CC-MAIN-20220125130117-20220125160117-00165.warc.gz"} |
https://par.nsf.gov/biblio/10184314-properties-circumgalactic-medium-cosmic-ray-dominated-galaxy-haloes | Properties of the circumgalactic medium in cosmic ray-dominated galaxy haloes
ABSTRACT We investigate the impact of cosmic rays (CRs) on the circumgalactic medium (CGM) in FIRE-2 simulations, for ultra-faint dwarf through Milky Way (MW)-mass haloes hosting star-forming (SF) galaxies. Our CR treatment includes injection by supernovae, anisotropic streaming and diffusion along magnetic field lines, and collisional and streaming losses, with constant parallel diffusivity $\kappa \sim 3\times 10^{29}\, \mathrm{cm^2\ s^{-1}}$ chosen to match γ-ray observations. With this, CRs become more important at larger halo masses and lower redshifts, and dominate the pressure in the CGM in MW-mass haloes at z ≲ 1–2. The gas in these ‘CR-dominated’ haloes differs significantly from runs without CRs: the gas is primarily cool (a few ${\sim}10^{4}\,$ K), and the cool phase is volume-filling and has a thermal pressure below that needed for virial or local thermal pressure balance. Ionization of the ‘low’ and ‘mid’ ions in this diffuse cool gas is dominated by photoionization, with O vi columns ${\gtrsim}10^{14.5}\, \mathrm{cm^{-2}}$ at distances ${\gtrsim}150\, \mathrm{kpc}$. CR and thermal gas pressure are locally anticorrelated, maintaining total pressure balance, and the CGM gas density profile is determined by the balance of CR pressure gradients and gravity. Neglecting CRs, the same haloes are primarily warm/hot ($T\gtrsim 10^{5}\,$K) with thermal pressure balancing gravity, more »
Authors:
; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10184314
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
496
Issue:
4
Page Range or eLocation-ID:
4221 to 4238
ISSN:
0035-8711
1. ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$, $M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore »
3. ABSTRACT Heating of virialized gas by streaming cosmic rays (CRs) may be energetically important in galaxy haloes, groups, and clusters. We present a linear thermal stability analysis of plasmas heated by streaming CRs. We separately treat equilibria with and without background gradients, and with and without gravity. We include both CR streaming and diffusion along the magnetic-field direction. Thermal stability depends strongly on the ratio of CR pressure to gas pressure, which determines whether modes are isobaric or isochoric. Modes with $\boldsymbol {k \cdot B }\ne 0$ are strongly affected by CR diffusion. When the streaming time is shorter than the CR diffusion time, thermally unstable modes (with $\boldsymbol {k \cdot B }\ne 0$) are waves propagating at a speed ∝ the Alfvén speed. Halo gas in photoionization equilibrium is thermally stable independent of CR pressure, while gas in collisional ionization equilibrium is unstable for physically realistic parameters. In gravitationally stratified plasmas, the oscillation frequency of thermally overstable modes can be higher in the presence of CR streaming than the buoyancy/free-fall frequency. This may modify the critical tcool/tff at which multiphase gas is present. The criterion for convective instability of a stratified, CR-heated medium can be written in the familiar Schwarzschild formmore » | 2022-12-03T22:10:03 | {"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": 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": 0.7193214297294617, "perplexity": 5471.053208909558}, "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/1669446710941.43/warc/CC-MAIN-20221203212026-20221204002026-00073.warc.gz"} |
https://mooseframework.inl.gov/source/action/ConservedAction.html | # ConservedAction
Set up the variable(s) and the kernels needed for a conserved phase field variable. Note that for a direct solve, the element family and order are overwritten with hermite and third.
This action simplifies the input file syntax for creating a conserved phase field variable in the phase field module. It creates the variables and kernels needed to solve for a conserved variable. Three solving approaches (solve_type) are supported: - direct - reverse_split - forward_split
## Variables
In each approach, the name of the conserved variable is the block name.
### direct
The direct solve has a second order spatial derivative term in the CHInterface residual, and therefore requires a higher order element. For this reason, the variable is always created to be a third-order Hermite, no matter the family and order passed into the action.
### reverse_split
The reverse_split adds two variables. It adds a conserved variable and a coupled variable which stores the chemical potential. Both variables have the same family and order.
### forward_split
The forward_split adds two variables. It adds conserved variable and a coupled variable which stores the Laplacian of the conserved variable. Both variables have the same family and order.
## Kernels
The kernels that are added depend on the solution approach:
### reverse_split
Conserved variable - CoupledTimeDerivative
Coupled variable - SplitCHWRes - SplitCHParsed
### forward_split
Conserved variable - TimeDerivative - MatDiffusion
Coupled variable - MatDiffusion - CoupledMaterialDerivative - CoefReaction
## Input Parameters
• kappaThe kappa used with the kernel
C++ Type:MaterialPropertyName
Options:
Description:The kappa used with the kernel
• free_energyBase name of the free energy function F defined in a free energy material
C++ Type:MaterialPropertyName
Options:
Description:Base name of the free energy function F defined in a free energy material
• solve_typeSplit or direct solve?
C++ Type:MooseEnum
Options:DIRECT REVERSE_SPLIT FORWARD_SPLIT
Description:Split or direct solve?
• mobilityThe mobility used with the kernel
C++ Type:MaterialPropertyName
Options:
Description:The mobility used with the kernel
### Required Parameters
• inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector
Options:
Description:If specified blocks matching these identifiers will be skipped.
• active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector
Options:
Description:If specified only the blocks named will be visited and made active
• argsVector of variable arguments this kernel depends on
C++ Type:std::vector
Options:
Description:Vector of variable arguments this kernel depends on
• orderFIRSTSpecifies the order of the FE shape function to use for this variable
Default:FIRST
C++ Type:MooseEnum
Options:CONSTANT FIRST SECOND THIRD FOURTH
Description:Specifies the order of the FE shape function to use for this variable
• familyLAGRANGESpecifies the family of FE shape functions to use for this variable
Default:LAGRANGE
C++ Type:MooseEnum
Options:LAGRANGE MONOMIAL HERMITE SCALAR HIERARCHIC CLOUGH XYZ SZABAB BERNSTEIN L2_LAGRANGE L2_HIERARCHIC NEDELEC_ONE LAGRANGE_VEC
Description:Specifies the family of FE shape functions to use for this variable
### Optional Parameters
• scaling1Specifies a scaling factor to apply to this variable
Default:1
C++ Type:double
Options:
Description:Specifies a scaling factor to apply to this variable
• implicitTrueWhether kernels are implicit or not
Default:True
C++ Type:bool
Options:
Description:Whether kernels are implicit or not
• use_displaced_meshFalseWhether to use displaced mesh in the kernels
Default:False
C++ Type:bool
Options:
Description:Whether to use displaced mesh in the kernels | 2018-12-17T11:40:27 | {"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": 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": 0.30163177847862244, "perplexity": 5888.236213445576}, "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-2018-51/segments/1544376828507.57/warc/CC-MAIN-20181217113255-20181217135255-00600.warc.gz"} |
https://par.nsf.gov/biblio/10388034-design-characterization-new-ghz-detectors-cosmology-large-angular-scale-surveyor-class | This content will become publicly available on August 31, 2023
Design and characterization of new 90 GHz detectors for the Cosmology Large Angular Scale Surveyor (CLASS)
The Cosmology Large Angular Scale Surveyor (CLASS) is a polarization-sensitive telescope array located at an altitude of 5,200 m in the Chilean Atacama Desert. CLASS is designed to measure "E-mode" (even parity) and "B-mode" (odd parity) polarization patterns in the Cosmic Microwave Background (CMB) over large angular scales with the aim of improving our understanding of inflation, reionization, and dark matter. CLASS is currently observing with three telescopes covering four frequency bands: one at 40 GHz (Q); one at 90 GHz (W1); and one dichroic system at 150/220 GHz (G). In these proceedings, we discuss the updated design and in-lab characterization of new 90 GHz detectors. The new detectors include design changes to the transition-edge sensor (TES) bolometer architecture, which aim to improve stability and optical efficiency. We assembled and tested four new detector wafers, to replace four modules of the W1 focal plane. These detectors were installed into the W1 telescope, and will achieve first light in the austral winter of 2022. We present electrothermal parameters and bandpass measurements from in-lab dark and optical testing. From in-lab dark tests, we also measure a median NEP of 12.3 aW√ s across all four wafers about the CLASS signal band, which more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Editors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10388034
Journal Name:
Proceedings Volume 12190, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI
Volume:
12190
Page Range or eLocation-ID:
121901J
The Cosmology Large Angular Scale Surveyor (CLASS) observes the polarized cosmic microwave background (CMB) over the angular scales of 1° ≲θ≤ 90° with the aim of characterizing primordial gravitational waves and cosmic reionization. We report on the on-sky performance of the CLASSQ-band (40 GHz),W-band (90 GHz), and dichroicG-band (150/220 GHz) receivers that have been operational at the CLASS site in the Atacama desert since 2016 June, 2018 May, and 2019 September, respectively. We show that the noise-equivalent power measured by the detectors matches the expected noise model based on on-sky optical loading and lab-measured detector parameters. Using Moon, Venus, and Jupiter observations, we obtain power to antenna temperature calibrations and optical efficiencies for the telescopes. From the CMB survey data, we compute instantaneous array noise-equivalent-temperature sensitivities of 22, 19, 23, and 71$μKcmbs$for the 40, 90, 150, and 220 GHz frequency bands, respectively. These noise temperatures refer to white noise amplitudes, which contribute to sky maps at all angular scales. Future papers will assess additional noise sources impacting larger angular scales. | 2023-03-22T13:24:22 | {"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": 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": 0.46888190507888794, "perplexity": 5874.280095904023}, "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-20230322114226-20230322144226-00222.warc.gz"} |
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