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https://en.wikipedia.org/wiki/Juan%20Pablo%20Dom%C3%ADnguez
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Juan Pablo Domínguez Chonteco (born 30 October 1998) is a Mexican professional footballer who plays as a midfielder for Liga MX club Toluca.
Career statistics
Club
References
External links
Living people
1998 births
Men's association football midfielders
Atlante F.C. footballers
Club Necaxa footballers
Liga MX players
Liga de Expansión MX players
People from Ecatepec de Morelos
Footballers from the State of Mexico
Mexican men's footballers
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https://en.wikipedia.org/wiki/Tajikistan%20women%27s%20national%20football%20team%20results
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This page details the match results and statistics of the Tajikistan women's national football team.
Tajikistan women's national football team is the representative of Tajikistan in international women's association football, It is governed by the Tajikistan Football Federation (FFT) and it competes as a member of the Asian Football Confederation (AFC).
the national team's first activity was in 2017. where the team started its women's football journey with an International Friendly against Kyrgyzstan as a preparation for their 2018 AFC Women's Asian Cup qualification campaign, in which they played in an international tournament for the first time. Tajikistan opened their qualification tournament with a promising win against Iraq. however, the Tajiks lost their four next games finishing fifth ahead of Iraq whom they have beaten on the first day. the team is currently ranked 144th in the FIFA Women's World Rankings, ranked 30th in the Asian continent.
Record per opponent
Key
The following table shows Tajikistan' all-time official international record per opponent:
Results
2017
2018
2019
2021
2022
2023
See also
Tajikistan national football team results
Football in Tajikistan
References
External links
Tajikistan results on The Roon Ba
Tajikistan results on Globalsports
Tajikistan results on soccerway
2010s in Tajikistan
2020s in Tajikistan
Women's national association football team results
results
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https://en.wikipedia.org/wiki/Perdita%20Stevens
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Perdita Emma Stevens (born 1966) is a British mathematician, theoretical computer scientist, and software engineer who holds a personal chair in the mathematics of software engineering as part of the School of Informatics at the University of Edinburgh. Her research includes work on model-driven engineering, including model transformation, model checking, and the Unified Modeling Language.
Education and career
Stevens read mathematics at the University of Cambridge, earning a bachelor's degree in 1987. She went to the University of Warwick for graduate study in abstract algebra, earning a master's degree in 1988 and completing a PhD in 1992. Her doctoral dissertation, Integral Forms for Weyl Modules of , was supervised by Sandy Green.
After working in industry as a software engineer, Stevens joined the Department of Computer Science at the University of Edinburgh in 1984. She became a reader there in 2003 and in 2014 was given a personal chair as Professor of Mathematics of Software Engineering.
Books
Stevens is the author of books including:
Using UML: Software Engineering with Objects and Components (with Rob Pooley, Addison-Wesley, 1999; 2nd ed., 2006)
How to Write Good Programs: A Guide for Students (Cambridge University Press, 2020)
References
External links
Home page
1966 births
Living people
British mathematicians
British women mathematicians
British computer scientists
British women computer scientists
British software engineers
Alumni of the University of Cambridge
Alumni of the University of Warwick
Academics of the University of Edinburgh
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Zhejiang
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The COVID-19 pandemic reached the province of Zhejiang, China.
Statistics
Distribution of cases in prefecture-level cities
The following is the distribution of confirmed cases in prefecture-level cities, and the sources of the data are the official websites of prefecture-level cities.
Timeline
2020
2021
2022
2023
On Jan. 9, authorities in Zhejiang province said the province had passed the peak of its first wave of infections.
References
Zhejiang
COVID-19 pandemic in mainland China
History of Zhejiang
Health in Zhejiang
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Shandong
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The COVID-19 pandemic reached the province of Shandong, China.
Statistics
Timeline
2020
On January 22, 1 new case was reported, and a total of 2 cases were reported. The new addition is a 38-year-old male, who works in Zhoushan, Zhejiang, and has close contact with a confirmed patient. He went to Weihai to visit relatives on the 18th and was quarantined on the 20th when he had a fever.
On January 23, 4 new cases were reported throughout the day on the 22nd. Linyi City reported two confirmed cases for the first time, and Qingdao City added two confirmed cases.
On January 24, the Shandong Provincial Health Commission notified six new confirmed cases, including 2 in Jinan, 2 in Yantai, and 1 in Jining, all of which were confirmed cases for the first time; 1 new confirmed case in Qingdao.
2021
On January 1, Qingdao City reported a confirmed case imported from the UK.
On January 2, Yantai City announced that an employee of an enterprise in another city was diagnosed as a confirmed case on January 1, and some of the auto parts packaging samples it distributed tested positive for nucleic acid. Some of the products flowed into Yantai City. After the inspection and review by the city and district CDC, one of the samples of the outer packaging of the goods from one of the enterprises was positive.
On January 4, the Shandong Provincial Center for Disease Control and Prevention conducted a whole-genome sequencing analysis of a sample of a British imported case reported in Qingdao, which was highly homologous to the sequence of the British variant strain. Since then, Shandong Province has become the third first-level administrative region in mainland China where the British variant was found after Shanghai and Guangdong.
On January 8, Rizhao City reported a confirmed case imported from Angola.
On January 16, Qingdao City reported a confirmed case imported from the United States.
On January 20, Qingdao City reported one new imported confirmed case from outside the province.
2022
January
On January 1, Shandong Province reported two newly imported confirmed cases, imported from Japan and the United Arab Emirates (2 cases in Jinan, of which imported cases from the United Arab Emirates were asymptomatic infections).
On January 2, Shandong Province reported one newly imported confirmed case, which was imported from the UAE (1 case in Jinan).
On January 3, Shandong Province reported one newly imported confirmed case, which was imported from Finland (1 case in Weihai).
On January 4, Shandong Province reported one newly imported confirmed case, which was imported from the UAE (1 case in Jinan).
On January 5, Shandong Province reported one newly imported confirmed case imported from Japan (1 case in Linyi).
On January 8, Shandong Province reported one newly imported confirmed case, which was imported from South Korea (1 case in Qingdao).
On January 14, Shandong Province reported three newly imported confirmed cases imported from South Korea (3 cases
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Hebei
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The COVID-19 pandemic reached the province of Hebei, China.
Statistics
Timeline
2020
On January 22, Shijiazhuang City, Hebei Province, reported the first confirmed case. Patient Li, male, 72 years old, from Wuhan, came to Shijiazhuang to visit relatives on January 18. The patient was isolated and treated in a designated hospital, and his condition was stable. Six of his close contacts have been isolated for medical observation, and there are no abnormalities such as fever.
On January 23, the Hebei Provincial Health Commission stated that an 80-year-old man surnamed Chen was diagnosed with the new coronavirus. The patient passed away on the 22nd, the first death case outside Hubei.
On January 25, Hebei Province reported six new confirmed cases of pneumonia caused by a new type of coronavirus. Among them: Baoding City and Chengde City each had 1 case, which was the first confirmed case reported; other newly established cases were 3 cases in Shijiazhuang City and 1 case in Cangzhou City.
On January 26, Hebei Province reported five new confirmed cases of pneumonia caused by the new coronavirus, including 2 cases in Handan City, 2 cases in Baoding City, and 1 in Shijiazhuang City. Handan City reported the first confirmed case.
On January 27, Hebei Province reported five new confirmed cases of pneumonia caused by a new coronavirus infection, including 2 cases in Langfang City, 2 cases in Shijiazhuang City, and 1 case in Xingtai City. Langfang City and Xingtai City reported the first confirmed cases.
On January 28, Hebei Province reported 15 new confirmed cases of pneumonia caused by new coronavirus infection, including 4 cases in Langfang City, 3 cases in Cangzhou City, 2 cases in Handan City, 2 cases in Shijiazhuang City, 2 cases in Hengshui City, 1 case in Tangshan City, and 1 case in Xingtai City. Hengshui and Tangshan reported the first confirmed cases.
On January 29, Hebei Province reported 15 new confirmed cases of pneumonia caused by new coronavirus infection, including 3 cases in Baoding City, 3 cases in Cangzhou City, 3 cases in Langfang City, 2 cases in Tangshan City, 1 case in Shijiazhuang City, and 1 case in Hengshui City. 1 point in Zhangjiakou City and 1 point in Xingtai City.
On January 30, Hebei Province reported 17 new confirmed cases of pneumonia caused by the new coronavirus, including 5 cases in Zhangjiakou City, 4 cases in Cangzhou City, 2 cases in Handan City, 2 cases in Xingtai City, 1 case in Shijiazhuang City, and 1 case in Baoding City. There was 1 case in Chengde City and 1 case in Hengshui City.
On January 31, Hebei Province reported 17 new confirmed cases of pneumonia caused by the new coronavirus, including 6 cases in Cangzhou City, 4 cases in Tangshan City, 4 cases in Baoding City, 2 cases in Xingtai City, and 1 case in Handan City.
2021
On January 2, 1 new case in Hebei Province.Reported by Gaocheng District, Shijiazhuang City. The patient is a 61-year-old woman who attended a wedding on December 28.
On Jan
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Shanxi
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The COVID-19 pandemic reached the province of Shanxi, China.
Statistics
Timeline
2020
On January 22, the first confirmed case of pneumonia with a new type of coronavirus infection appeared in Shanxi Province, and six close contacts have been tracked and medically observed.
2021
On January 3, Shanxi Province added 1 newly imported confirmed case (imported from Poland).
2022
On January 22, Yungang District of Datong City conducted a nucleic acid test on a returnee from Fengtai District of Beijing, and the result was positive. In the early morning of January 23, the results of the review by the Municipal Center for Disease Control and Prevention and the Fourth People's Hospital of the Municipality were all positive.
References
Shanxi
COVID-19 pandemic in mainland China
History of Shanxi
Health in Shanxi
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https://en.wikipedia.org/wiki/The%20Geometry%20of%20Love
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"The Geometry of Love" is a work of short fiction by John Cheever which first appeared in The Saturday Evening Post on January 1, 1966. The story was collected in The World of Apples, published in 1973 by Alfred A. Knopf.
Plot
Charlie Mallory, an engineer, lives in New York City with his wife Matilda, a homemaker, and their two young children. Cheever refers to his protagonist as Mallory throughout the story. The Mallorys are emotionally estranged, and Matilda punishes her uxorious with accusatory invective that leave him dismayed and disheartened.
When a delivery truck passes him bearing the name EUCLID'S DRY CLEANING AND DYEING on its side panel, Mallory has an epiphany: he decides to formulate an escape from his troubled life by way of Euclidean geometry. As an engineer, he possesses superior skills at drawing these mathematical diagrams. He proceeds to represent his existence in terms of theorems and postulates, allowing him to assert a measure of control over the chaos of his daily affairs. Mallory's methods, in particular, permit him to endure Matilda's mood swings with equanimity. Immensely satisfied with his results, Mallory considers writing a treatise on his system and considers calling it Euclidean Emotion: The Geometry of Sentiment.
Mallory's proficiency at reducing the troubling complexities of his emotional and physical surroundings to linear representations soon rebounds on him. On a business trip to Chicago, he attempts to deflect the depressing landscape of Gary, Indiana by configuring it into a parallelogram. By a geometric miscalculation, he causes the city to vanish entirely from his sight.
A few weeks later, Mallory collapses in his office. He is rushed to the hospital where a portion of his intestines are removed. Matilda visits her gravely ill husband, gushing with false cheeriness. She considers his convalescence in the posh hospital an act of self-indulgence. Mallory is devastated by Matilda's detachment from his suffering and doubts that he can survive another such encounter.
Obtaining his slide rule and notebook from the nurse he devises "a simple, geometric analogy between his love for Matilda and his fear of death." The formula is a success and shields Mallory from Matilda's suffocating insinuations during her next visit. When she departs, he attempts to shave his face. His cadaverous visage in the mirror spurs him to enlist geometry to counter his death-like appearance. Proceeding with caution— wary of his miscalculation at the city of Gary— Mallory conjures his fateful diagram.
That evening, after Matilda returns home, she is informed by her housekeeper that Mallory is dead.
Publication background
Cheever wrote "The Geometry of Love" in September 1965, over a year after completing his last short story "The Swimmer", the latter considered one his finest works of short fiction.
The New Yorker's leading editor William Maxwell, who had for years championed Cheever's literary output, declined to accept "The Ge
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https://en.wikipedia.org/wiki/Jos%C3%A9%20Gonz%C3%A1lez%20%28footballer%2C%20born%202004%29
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José Daniel González Pichardo (born 12 November 2004) is a Mexican professional footballer who plays as a forward for Liga MX club UNAM.
Career statistics
Club
References
External links
Living people
2004 births
Mexican men's footballers
Men's association football forwards
Club Universidad Nacional footballers
Liga MX players
Liga de Expansión MX players
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Madhava%27s%20correction%20term
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Madhava's correction term is a mathematical expression attributed to Madhava of Sangamagrama (c. 1340 – c. 1425), the founder of the Kerala school of astronomy and mathematics, that can be used to give a better approximation to the value of the mathematical constant (pi) than the partial sum approximation obtained by truncating the Madhava-Leibniz infinite series for . The Madhava-Leibniz infinite series for is
Taking the partial sum of the first terms we have the following approximation to :
Denoting the Madhava correction term by , we have the following better approximation to :
Three different expressions have been attributed to Madhava as possible values of , namely,
In the extant writings of the mathematicians of the Kerala school there are some indications regarding how the correction terms and have been obtained, but there are no indications on how the expression has been obtained. This has led to a lot of speculative work on how the formulas might have been derived.
Correction terms as given in Kerala texts
The expressions for and are given explicitly in the Yuktibhasha, a major treatise on mathematics and astronomy authored by the Indian astronomer Jyesthadeva of the Kerala school of mathematics around 1530, but that for appears there only as a step in the argument leading to the derivation of .
The Yuktidipika-Laghuvivrthi commentary of Tantrasangraha, a treatise written by Nilakantha Somayaji an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics and completed in 1501, presents the second correction term in the following verses (Chapter 2: Verses 271 - 274):
English translation of the verses:
"To the diameter multiplied by 4 alternately add and subtract in order the diameter multiplied by 4 and divided separately by the odd numbers 3, 5, etc. That odd number at which this process ends, four times the diameter should be multiplied by the next even number, halved and [then] divided by one added to that [even] number squared. The result is to be added or subtracted according as the last term was subtracted or added. This gives the circumference more accurately than would be obtained by going on with that process."
In modern notations this can be stated as follows (where is the diameter of the circle):
Circumference
If we set , the last term in the right hand side of the above equation reduces to .
The same commentary also gives the correction term in the following verses (Chapter 2: Verses 295 - 296):
English translation of the verses:
"A subtler method, with another correction. [Retain] the first procedure involving division of four times the diameter by the odd numbers, 3, 5, etc. [But] then add or subtract it [four times the diameter] multiplied by one added to the next even number halved and squared, and divided by one added to four times the preceding multiplier [with this] multiplied by the even number halved."
In modern notations, this can be stated as follo
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https://en.wikipedia.org/wiki/Mary%20Croarken
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Mary G. Croarken is a British independent scholar and author in the history of mathematics and the history of computing.
Education and career
Croarken earned a degree in computer science from the University of Warwick in 1982 and a doctorate in the history of science there in 1986, supervised by Martin Campbell-Kelly, who describes her as one of his two most successful students.
After leaving academia to raise a family in Norwich, she became a health research manager in the National Health Service, while continuing to work in the history of science as an independent scholar. She has been a research fellow at the National Maritime Museum in Greenwich and in the computer science department at the University of Warwick.
Books
Croarken is the author of the book Early Scientific Computing in Britain (Clarendon Press, 1990). She is a co-editor of The History of Mathematical Tables: from Sumer to Spreadsheets (Oxford University Press, 2003) and of Mathematics at the Meridian: The History of Mathematics at Greenwich (Chapman & Hall / CRC, 2020)
References
Year of birth missing (living people)
Living people
British historians of mathematics
British women historians
Alumni of the University of Warwick
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https://en.wikipedia.org/wiki/Laura%20Gardini
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Laura Gardini (born 1952) is an Italian mathematician who studies chaos in dynamical systems, with applications in mathematical finance. She is professor in mathematics for economic applications at the University of Urbino.
Education and career
Gardini is originally from Ravenna, where she was born on August 21, 1952. She graduated cum laude from the University of Bologna in 1975, and became a researcher for the Ente Nazionale Idrocarburi (ENI), an Italian national energy association. During this period she also taught mechanics in the Faculty of Engineering of the University of Ancona. In 1988 she moved to the University of Urbino as a researcher in mathematics for economic applications; she became associate professor there in 1992 and full professor in 1994.
She is co-editor-in-chief of the Elsevier journal Mathematics and Computers in Simulation. She is one of the founders of an annual workshop on dynamical systems in economics and finance, held at the University of Urbino since 2000.
Recognition
A festschrift in honor of her 60th birthday, Global Analysis of Dynamic Models in Economics and Finance: Essays in Honour of Laura Gardini, was published in 2013.
Books
Gardini is the coauthor of books including:
Chaotic Dynamics in Two-Dimensional Noninvertible Maps (with Christian Mira, Alexandra Barugola, and Jean-Claude Cathala, World Scientific, 1996)
Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions (with Ralph H. Abraham and Christian Mira, Springer, 1997).
Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures (with Viktor Avrutin, Iryna Sushko, and Fabio Tramontana, World Scientific, 2019)
Appunti di matematica finanziaria (with Rita Laura D'Ecclesia, 1998; 8th ed., Giappichelli, 2019)
References
External links
People from Ravenna
1952 births
Living people
Italian mathematicians
Italian women mathematicians
Italian economists
Italian women economists
Mathematical economists
University of Bologna alumni
Academic staff of the University of Urbino
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https://en.wikipedia.org/wiki/Mathieu%20Le%20Scornet
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Mathieu Le Scornet (born 2 May 1983) is a French football manager. He was the interim manager of Ligue 1 club Strasbourg for 6 games in 2023.
Managerial statistics
References
External links
1983 births
Living people
People from Metz
Sportspeople from Metz
French football managers
RC Strasbourg Alsace managers
Ligue 1 managers
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https://en.wikipedia.org/wiki/Iryna%20Sushko
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Iryna Sushko (born 1967) is a Ukrainian mathematician who works as a senior research fellow in the Institute of Mathematics of the National Academy of Sciences of Ukraine and as a visiting professor at the Kyiv School of Economics. Her research concerns nonlinear dynamical systems and their applications in economics and radio engineering.
Education and career
Sushko was born in 1967, near Kyiv. She earned a master's degree in cybernetics from the Taras Shevchenko National University of Kyiv in 1989. After postgraduate study at the National Academy of Sciences of Ukraine, she earned a candidate (PhD) degree in physics and mathematics in 1993, supervised by Oleksandr Mykolayovych Sharkovsky. She became a research fellow at the National Academy of Sciences in 1993 and was promoted to senior research fellow in 2002.
In 2004–2005 she visited the University of Urbino as a Marie Curie Fellow of the European Community. Since 2009 to 2020 she has also held a position as a visiting professor at the Kyiv School of Economics.
Books
Sushko is the co-author of Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures (with Viktor Avrutin, Laura Gardini, and Fabio Tramontana, World Scientific, 2019)
She is also a co-editor of several edited volumes, including Oligopoly and Complex Dynamics: Models and Tools (Springer, 2002), Business Cycle Dynamics: Models and Tools (Springer, 2006), and Global Analysis of Dynamic Models for Economics, Finance and Social Sciences (Springer, 2013).
References
External links
Personal home page
Home page at Kyiv School of Economics
1967 births
Living people
Ukrainian women mathematicians
Ukrainian women economists
Taras Shevchenko National University of Kyiv alumni
20th-century Ukrainian mathematicians
20th-century women mathematicians
20th-century Ukrainian economists
21st-century Ukrainian mathematicians
21st-century women mathematicians
21st-century Ukrainian economists
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https://en.wikipedia.org/wiki/Gauss%20composition%20law
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In mathematics, in number theory, Gauss composition law is a rule, invented by Carl Friedrich Gauss, for performing a binary operation on integral binary quadratic forms (IBQFs). Gauss presented this rule in his Disquisitiones Arithmeticae, a textbook on number theory published in 1801, in Articles 234 - 244. Gauss composition law is one of the deepest results in the theory of IBQFs and Gauss's formulation of the law and the proofs its properties as given by Gauss are generally considered highly complicated and very difficult. Several later mathematicians have simplified the formulation of the composition law and have presented it in a format suitable for numerical computations. The concept has also found generalisations in several directions.
Integral binary quadratic forms
An expression of the form , where are all integers, is called an integral binary quadratic form (IBQF). The form is called a primitive IBQF if are relatively prime. The quantity is called the discriminant of the IBQF . An integer is the discriminant of some IBQF if and only if . is called a fundamental discriminant if and only if one of the following statements holds
and is square-free,
where and is square-free.
If and then is said to be positive definite; if and then is said to be negative definite; if then is said to be indefinite.
Equivalence of IBQFs
Two IBQFs and are said to be equivalent (or, properly equivalent) if there exist integers α, β, γ, δ such that
and
The notation is used to denote the fact that the two forms are equivalent. The relation "" is an equivalence relation in the set of all IBQFs. The equivalence class to which the IBQF belongs is denoted by .
Two IBQFs and are said to be improperly equivalent if
and
The relation in the set of IBQFs of being improperly equivalent is also an equivalence relation.
It can be easily seen that equivalent IBQFs (properly or improperly) have the same discriminant.
Gauss's formulation of the composition law
Historical context
The following identity, called Brahmagupta identity, was known to the Indian mathematician Brahmagupta (598–668) who used it to calculate successively better fractional approximations to square roots of positive integers:
Writing this identity can be put in the form
where .
Gauss's composition law of IBQFs generalises this identity to an identity of the form where are all IBQFs and are linear combinations of the products .
The composition law of IBQFs
Consider the following IBQFs:
If it is possible to find integers and such that the following six numbers
have no common divisors other than ±1, and such that if we let
the following relation is identically satisfied
,
then the form is said to be a composite of the forms and . It may be noted that the composite of two IBQFs, if it exists, is not unique.
Example
Consider the following binary quadratic forms:
Let
We have
.
These six numbers have no common divisors other t
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Shaanxi
|
The COVID-19 pandemic reached the province of Shaanxi, China.
Statistics
Timeline
2020
On the evening of January 24, the Shaanxi Provincial Health Committee reported that there were 2 new confirmed cases of pneumonia caused by a new type of coronavirus in Shaanxi, including 1 in Ankang City and 1 in Yan'an City.
On January 25, Shaanxi Province reported 10 new cases. One of the patients was a 9-year-old girl from Wuhan. She visited relatives in Tongchuan City on Monday. She developed symptoms the next day and went to the hospital for medical treatment after self-medication was ineffective. She is currently in the local infectious disease hospital. Isolation treatment, stable condition.
On January 27, Shaanxi Province notified 13 new confirmed cases of new pneumonia and 2 new severe patients.
On January 28, Shaanxi Province reported 11 new confirmed cases of new pneumonia. Among the newly confirmed cases, there were 3 cases in Xi'an City, 3 cases in Baoji City, 2 cases in Weinan City, 1 case in Hanzhong City, 1 case in Ankang City, and 1 case in Shangluo City. 1 case.
On January 29, Shaanxi Province reported 10 new confirmed cases of new pneumonia. Among the newly confirmed cases, there were 3 cases in Xi'an City, 1 case in Baoji City, 1 case in Xianyang City, 1 case in Yan'an City, 2 cases in Hanzhong City, and 2 cases in Ankang City. 2 cases.
On January 30, Shaanxi Province reported 7 new confirmed cases of new pneumonia and 1 new severe patient. Among the newly confirmed cases, 4 were in Xi'an, 1 in Weinan, 1 in Yulin, and 1 in Hancheng.
On January 31, Shaanxi Province notified 24 new confirmed cases of new pneumonia. Among the newly confirmed cases, 10 were in Xi'an, 1 in Xianyang, 1 in Weinan, 4 in Yan'an, 5 in Hanzhong, and 3 in Ankang.
2021
On January 1, 1 newly imported confirmed case was reported (from Spain).
2022
On January 1, 123 local confirmed cases were newly reported in Shaanxi Province (122 in Xi'an City, 1 in Yan'an City), and 1 case was cured and discharged.
References
Shaanxi
COVID-19 pandemic in mainland China
History of Shaanxi
Health in Shaanxi
zh:2019冠状病毒病陕西省疫情
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https://en.wikipedia.org/wiki/Pseudogamma%20function
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In mathematics, a pseudogamma function is a function that interpolates the factorial. The gamma function is the most famous solution to the problem of extending the notion of the factorial beyond the positive integers only. However, it is clearly not the only solution, as, for any set of points, an infinite number of curves can be drawn through those points. Such a curve, namely one which interpolates the factorial but is not equal to the gamma function, is known as a pseudogamma function. The two most famous pseudogamma functions are Hadamard's gamma function:
where is the Lerch zeta function. We also have the Luschny factorial:
where denotes the classical gamma function
and denotes the digamma function. Other related pseudo gamma functions are also known, for instance see.
References
Functions and mappings
Factorial and binomial topics
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https://en.wikipedia.org/wiki/Mike%20West%20%28statistician%29
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Mike West is an English and American statistician. West works primarily in the field of Bayesian statistics, with research contributions ranging from theory to applied research in areas including finance, commerce, macroeconomics, climatology, engineering, genomics and other areas of biology. Since 1999, West has been the Arts & Sciences Distinguished Professor of Statistics & Decision Sciences in the Department of Statistical Science at Duke University.
Education and career
West earned a BSc in Mathematics in 1978, and then PhD in Mathematics (Statistics) in 1982, from the University of Nottingham. He worked at Warwick University before joining Duke University in 1988, where he became the Director of the Institute of Statistics and Decision Sciences (ISDS) from 1990 to 2001.
West has made significant contributions to Bayesian theory and methods for time series analysis and forecasting. He has also conducted research on non-parametric Bayesian analysis with methodological and applied research that include implementations of Dirichlet process mixture models starting with a paper published in 1995. His research with molecular geneticists and clinical researchers involved developing predictive models for identifying types of breast cancer using gene expression data, contributing to the popularisation of biomarker discovery through gene expression profiling.
West has been a consultant with various companies, banks, government agencies and academic centres, co-founder of a biotech company, and board member of several financial and IT companies. West has also served the international statistics profession in founding roles and as a board member in a number of national and international centres and institutes as well as professional societies.
Elected positions & honours
President of the International Society for Bayesian Analysis in 2009-2010.
Elected Fellow of the Royal Statistical Society in 1982, of the Institute of Mathematical Statistics in 1993, of the American Statistical Association in 1993, of the International Statistical Institute in 1997, and elected inaugural fellow of the International Society for Bayesian Analysis in 2012.
Founding Chair of the International Society for Bayesian Analysis (ISBA) section on Economics, Finance, and Business in 2012-2013
Chair of the American Statistical Association section on Bayesian Statistical Science in 2010.
Books
Time Series: Modeling, Computation & Inference. Chapman & Hall/CRC Press
2021, 2nd edition, R. Prado, M.A.R. Ferreira and M. West
2010, 1st edition, R. Prado and M. West
Bayesian Forecasting and Dynamic Models, Springer Verlag
1997, 2nd edition, M. West and P. J. Harrison
1989, 1st edition, M. West and P. J. Harrison
Applied Bayesian Forecasting and Time Series Analysis, Chapman-Hall
1994, A. Pole, M. West, and P. J. Harrison
Selected awards & recognition
Bruno de Finetti Lecture Award of the International Society of Bayesian Analysis (ISBA), 2022
Akaike Memorial Lecture Awa
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https://en.wikipedia.org/wiki/Steve%20MacEachern
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Steve MacEachern is an American Statistician. MacEachern is a Distinguished Arts & Sciences Professor of Statistics at the Ohio State University. He received his B.A. in Mathematics from Carleton College in 1982 and his Ph.D. in Statistics from the University of Minnesota in 1988. His doctoral work focused on nonparametric Bayesian methods under the guidance of Don Berry.
MacEachern joined the faculty at Ohio State in 1988 and has been a member of the Department of Statistics ever since. He has a courtesy appointment as a Professor in the Department of Psychology. He is best known for Bayesian modeling and computation, with a particular emphasis on dependent Dirichlet processes. He has published extensively in leading statistical journals, and his work has had a significant impact on the field.
MacEachern has received numerous honors throughout his career, including being elected as a Fellow of the American Statistical Association in 2006, of the International Society for Bayesian Analysis in 2020 and of the Institute of Mathematical Statistics in 2021. He served as President of the International Society for Bayesian Analysis in 2016.
References
American statisticians
Year of birth missing (living people)
Living people
University of Minnesota alumni
Carleton College alumni
Ohio State University faculty
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https://en.wikipedia.org/wiki/Gaussian%20brackets
|
In mathematics, Gaussian brackets are a special notation invented by Carl Friedrich Gauss to represent the convergents of a simple continued fraction in the form of a simple fraction. Gauss used this notation in the context of finding solutions of the indeterminate equations of the form .
This notation should not be confused with the widely prevalent use of square brackets to denote the greatest integer function: denotes the greatest integer less than or equal to . This notation was also invented by Gauss and was used in the third proof of the quadratic reciprocity law. The notation , denoting the floor function, is now more commonly used to denote the greatest integer less than or equal to .
The notation
The Gaussian brackets notation is defined as follows:
The expanded form of the expression can be described thus: "The first term is the product of all n members; after it come all possible products of (n -2) members in which the numbers have alternately odd and even indices in ascending order, each starting with an odd index; then all possible products of (n-4) members likewise have successively higher alternating odd and even indices, each starting with an odd index; and so on. If the bracket has an odd number of members, it ends with the sum of all members of odd index; if it has an even number, it ends with unity."
With this notation, one can easily verify that
Properties
The bracket notation can also be defined by the recursion relation:
The notation is symmetric or reversible in the arguments:
The Gaussian brackets expression can be written by means of a determinant:
The notation satisfies the determinant formula (for use the convention that ):
Let the elements in the Gaussian bracket expression be alternatively 0. Then
Applications
The Gaussian brackets have been used extensively by optical designers as a time-saving device in computing the effects of changes in surface power, thickness, and separation of focal length, magnification, and object and image distances.
References
Additional reading
The following papers give additional details regarding the applications of Gaussian brackets in optics.
Carl Friedrich Gauss
Continued fractions
|
https://en.wikipedia.org/wiki/Daisy%20Cave
|
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Daisy Cave, also known as CA-SMI-261, is an archeological site located on San Miguel Island in California. San Miguel Island is the westernmost island in a larger island chain dubbed the Channel Islands. The island sits between the Santa Barbara Channel and the Pacific Ocean and is often notably battered by winds all year round, but the Daisy Cave itself provides solace from the weather and has served as an effective shelter time and time again. The cave appears to have multiple archaeological deposits, in which artifacts ranging from the "terminal Pleistocene to the present." San Miguel was once part of a larger 'Superisland,' connected with Santa Rosa, Santa Cruz and Anacapa to make up Santarosae. Santarosae existed as the 'superisland' until as recent as 10,000 years ago, with some estimation.
Excavation
The first excavations of the Daisy Cave are estimated to have occurred around the early 1900s. These initial excavations are not well documented, nor well executed; therefore, the 1967 excavation led by Charles Rozaire is largely considered to be the first true scientific excavation. Rozaire (curator of archeology at the Los Angeles County Museum of Natural History) and his team excavated about 20% of the deposits within the Daisy Cave, but the technology at the time would hardly lend credence to the true age and significance of his findings. Within this first excavation, the remains of about 26 people were found, as well as other various artifacts and remains.
The next excavation would occur in 1985, when Daniel A. Guthrie, Don P. Morris and Pandora E. Snethkamp conducted another, smaller excavation. They would discover "invaluable faunal and artifactal remains," and this was the first time that evidence was dated to be from the Pleistocene, rather than being from the last 3000 years as Rozaire had suggested. The quality of the evidence was invaluable, but the quantity was lacking, these scholars also took the opportunity to correctly date the artifacts that Rozaire had recovered in his excavation back in 1967.
Most recently in 1989, Don P. Morris, S. Hammersmith, and Jon. M Erlandson completed a map of the Daisy Cave and scheduled further site studies and investigations. Erlandson planned investigations for the summers of 1992, 1993, 1994 and 1996. These efforts "completed the stratigraphically controlled excavation of three 50 cm x 100 cm wide test units in the deposits outside the rockshelter and an exploratory sounding extending Rozaire's test pit inside the cave deeper into stratified sediments beneath the cave floor."
Artifacts
The Daisy Cave serves as a time capsule into the lives of Paleo-Indians, Paleo-Coastal peoples, and other maritime populations (ordered sequentially). Each of the
|
https://en.wikipedia.org/wiki/Superabundance
|
Superabundance may refer to:
Superabundance (album), a 2008 album by Young Knives
Superabundance (algebraic geometry), an inequality in the Riemann–Roch theorem for surfaces
Myth of superabundance, the belief that Earth has ample resources to satisfy humanity's needs
|
https://en.wikipedia.org/wiki/Shiv%20Vilas%20Palace
|
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}Shiv Vilas Palace, also known as the New palace, is a royal residential palace in Indore, built by Maharaja Shivajirao Holkar of the Holkar dynasty and served as the official residence of the Holkars from 1894 to 1920. This palace was built beside their old residence, the Rajwada. The construction was started in 1890 and exhibits Neoclassical architecture. The starting year of construction (1890) coincided with the birth of Maharaja Shivajirao's son and successor, Tukojirao Holkar III. It currently houses a hospital and a few offices. The Shiv Vilas Palace was constructed while the construction of the Lalbagh Palace was in progress and upon its completion, the official residence was shifted to it. Recently, city tours have started to include the palace in their itineraries.
References
Gallery
Palaces in Madhya Pradesh
Buildings and structures in Indore
Tourist attractions in Indore
|
https://en.wikipedia.org/wiki/Clayton%20Community%20Centre
|
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"geometry": {
"type": "Point",
"coordinates": [
-122.704679,
49.132953
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}Clayton Community Centre is a community recreation center located in Surrey, British Columbia, Canada. The building is the largest largest Passive House green building in Canada The building uses up to 90% less energy than similar buildings.
The facility contains music studios, an indoor cycling studio, weight room, gymnasiums, demonstration kitchen, preschool, woodworking shop and demo kitchen as well as a 14,000 square foot branch of Surrey Libraries
References
Buildings and structures in Surrey, British Columbia
Sports venues completed in 2016
|
https://en.wikipedia.org/wiki/Freddy%20Delbaen
|
Freddy Delbaen (born 21 November 1946 in Duffel, Belgium) is a Belgian-Swiss mathematician. He is professor emeritus of financial mathematics at ETH Zurich.
Delbaen made fundamental contributions to the mathematical theory of arbitrage including proving, together with Walter Schachermayer, a general version of the fundamental theorem of asset pricing. He also introduced in a jointly written paper the notion of the risk measure.
His research includes topics in financial mathematics, probability theory, functional analysis and actuarial mathematics.
Life
Delbaen was born in 1946 in Duffel in the province of Antwerp. He studied mathematics at the Free University of Brussels and received his doctorate there in 1971 under the supervision of Lucien Waelbroeck.
From 1971 to 1995 he was a professor at the Free University of Brussels and at the University of Antwerp. In 1995, Delbaen became a full professor at the ETH Zurich, remaining there until his retirement in 2008. He is still a professor emeritus at ETH and, since 2011, also a guest lecturer at the University of Zurich.
Delbaen is a Fellow of the Institute of Mathematical Statistics since 2011 and the American Mathematical Society since 2013. He is also a member of Academia Europaea since 2020.
Research
Together with Walter Schachermayer, he proved a general form of the fundamental theorem of asset pricing for (locally) bounded semimartingales, replacing the condition of "no arbitrage" with the term no free lunch with vanishing risk (NFLVR). The two also proved a version for unbounded price processes.
In a joint paper with P. Artzner, J. M. Eber and D. Heath, he introduced the concept of (coherent) risk measure on a finite probability space. Delbaen later generalized the concept to general probability spaces.
Selected publications
Books
Monetary Utility Functions (2012). Finance and Insurance, Osaka University Lecture Notes Series.
with Walter Schachermayer: The Mathematics of Arbitrage (2005). Springer Finance
References
External links
Homepage at ETH Zurich
1946 births
Living people
20th-century Belgian mathematicians
21st-century Belgian mathematicians
20th-century Swiss mathematicians
21st-century Swiss mathematicians
Academic staff of ETH Zurich
Vrije Universiteit Brussel alumni
Fellows of the Institute of Mathematical Statistics
Fellows of the American Mathematical Society
People from Duffel
|
https://en.wikipedia.org/wiki/Fax%C3%A9n%20integral
|
In mathematics, the Faxén integral (also named Faxén function) is the following integral
The integral is named after the Swedish physicist Olov Hilding Faxén, who published it in 1921 in his PhD thesis.
n-dimensional Faxén integral
More generally one defines the -dimensional Faxén integral as
with
and
for and
The parameter is only for convenience in calculations.
Properties
Let denote the Gamma function, then
For one has the following relationship to the Scorer function
Asymptotics
For we have the following asymptotics
References
Mathematical analysis
Functions and mappings
Definitions of mathematical integration
|
https://en.wikipedia.org/wiki/Khaled%20Abdelfattah
|
Khaled Mohamed Abdelfattah Ibrahim (; born 22 January 1999) is an Egyptian footballer who plays for Al Ahly as a centre back.
Career statistics
Club
.
Honours
Al Ahly
Egyptian Premier League: 2022–23
Egypt Cup: 2021–22
Egyptian Super Cup: 2022-23
CAF Champions League: 2022–23
References
1999 births
Living people
Egyptian men's footballers
Al Ahly SC players
Men's association football defenders
Egyptian Premier League players
|
https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Jiangxi
|
The COVID-19 pandemic reached the province of Jiangxi, China.
Statistics
Timeline
2020
On January 23, Jiangxi Province reported 1 new confirmed case, which was a severe case, and it was also the first confirmed case reported in Nanchang City.
On January 24, Jiangxi Province reported 4 new confirmed cases, including 1 in Nanchang, 1 in Ji'an, 1 in Jiujiang, and 1 in Xinyu.
On January 25, Jiangxi Province reported 11 new confirmed cases, including 3 in Fuzhou, 2 in Ganzhou, 2 in Shangrao, 1 in Nanchang, 1 in Jiujiang, 1 in Jingdezhen, and 1 in Yichun. ; Jingdezhen City, Ganzhou City, Yichun City, and Shangrao City were the first confirmed cases.
On January 26, Jiangxi Province reported 18 new confirmed cases (including 2 severe cases), including 5 cases in Ganzhou City, 4 cases in Yichun City, 4 cases in Shangrao City, 2 cases in Fuzhou City, 1 case in Nanchang City, and 1 case in Pingxiang City with 1 case in Ji'an City.
On January 28, Jiangxi Province reported 24 new confirmed cases and 2 cured and discharged cases. Among the newly confirmed cases, there were 9 in Nanchang, 5 in Jiujiang, 4 in Yichun, 3 in Ganzhou, 1 in Yingtan, 1 in Shangrao, and 1 in Fuzhou. Yingtan reported the first confirmed case. Among the discharged cases, 1 in Ji'an City and 1 in Pingxiang City.
On January 30, Jiangxi Province reported 53 new confirmed cases of pneumonia caused by a new type of coronavirus. Among the newly confirmed cases, 21 were in Nanchang, 15 in Jiujiang, 5 in Ganzhou, 4 in Fuzhou, 3 in Pingxiang, 2 in Yingtan, 2 in Shangrao, and 1 in Ji'an.
On January 31, Jiangxi Province reported 78 new confirmed cases of new coronavirus-infected pneumonia and 4 new discharged cases. Among the newly confirmed cases, 21 were in Nanchang, 17 in Xinyu, 12 in Yichun, 11 in Jiujiang, 6 in Ganzhou, 3 in Pingxiang, 3 in Ji'an, 2 in Fuzhou, and 1 in Jingdezhen. , 1 case in Yingtan City, and 1 case in Shangrao City. Among the newly discharged cases, 1 was in Nanchang, 1 in Jingdezhen, 1 in Xinyu, and 1 in Shangrao.
In the afternoon of the same day, Jiangxi Province stated at a press conference that because an employee surnamed Huang of Xinyu Fourth Hospital was diagnosed with infection on January 23, some medical staff who had contact with him also developed symptoms. The case was related to Huang, so it was decided to temporarily close Xinyu Fourth Hospital.
2021
From 00:00 to 24:00 on March 20, Jiangxi Province reported a new confirmed case of imported novel coronavirus pneumonia. The newly imported confirmed case was a Chinese nationals working in Zimbabwe. He entered the country from Nanjing on March 1, and returned to Jiangxi after the centralized isolation was lifted on March 15. On March 16, the nucleic acid test was positive, and he was transferred to a designated hospital for investigation. The expert group diagnosed him as an asymptomatic infection of the new coronavirus. Relevant symptoms appeared on March 20, and the expert group diagnosed it as a conf
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Hunan
|
The COVID-19 pandemic reached the province of Hunan, China.
Statistics
Timeline
2020
On January 21, 2020, the National Health and Medical Commission confirmed the first confirmed case of imported new coronavirus pneumonia in Changsha City, Hunan Province. The patient was from Wuhan. During his visit to Changsha, he suffered from fever and cough and went to a doctor in Changsha on the 16th. This was the first confirmed case of new pneumonia in Hunan Province.
On January 22, the Hunan Provincial Health Commission reported 3 new cases, bringing the total to 4 cases. Added 2 females and 1 male, from Huaihua, aged between 30-40 years old, colleagues in the same company. Two women had been to Wuhan, and one man was a close contact.
On January 23, 5 new confirmed cases of pneumonia with new coronavirus infection were reported, including 3 cases in Changsha City, 1 case in Yongzhou City, and 1 case in Chenzhou City. All five patients had a history of Wuhan exposure. The five patients were in stable condition and were treated in isolation at a designated local hospital. At the time, the close contacts had no abnormal conditions such as fever.
On January 24, 15 new confirmed cases were reported, bringing the total to 24 cases. Zhuzhou City, Xiangtan City, Yueyang City, and Loudi City reported the first confirmed cases. Among the newly confirmed cases, there was 1 in Zhuzhou City, 1 in Xiangtan City, 3 in Yueyang City, 3 in Loudi City, 4 in Changsha City, and 3 in Yongzhou City.
On January 25, 19 new confirmed cases were reported, bringing the total to 43 cases. Hengyang City, Shaoyang City, Changde City, and Yiyang City reported the first confirmed cases. Among the newly confirmed cases, there were 3 cases in Hengyang City, 1 case in Xiangtan City, 2 cases in Shaoyang City, 2 cases in Yueyang City, 3 cases in Changde City, 4 cases in Yiyang City, 2 cases in Huaihua City, and 2 cases in Loudi City.
On January 26, there were 26 new confirmed cases and 6 new severe cases. A total of 69 cases had been reported, including 20 severe cases. Among the newly confirmed cases, 10 were in Changsha, 2 in Zhuzhou, 1 in Xiangtan, 1 in Yueyang, 4 in Changde, 2 in Chenzhou, 3 in Huaihua, and 3 in Xiangxi Autonomous Prefecture.
On January 28, there were 43 new confirmed cases and 10 new severe cases. A total of 143 cases had been reported, including 31 severe cases (another severe case was converted to a normal case). Among the newly confirmed cases, there were 2 cases in Changsha City, 3 cases in Hengyang City, 2 cases in Zhuzhou City, 2 cases in Xiangtan City, 3 cases in Shaoyang City, 10 cases in Yueyang City, 7 cases in Changde City, 3 cases in Yiyang City, and 1 case in Chenzhou City , 3 cases in Yongzhou City, 5 cases in Huaihua City, and 2 cases in Loudi City; among the new severe cases, 1 case was in Changsha City, 1 case in Hengyang City, 2 cases in Shaoyang City, 2 cases in Changde City, 1 case in Yiyang City, and 2 cases in Huaihua City. There was 1 case
|
https://en.wikipedia.org/wiki/2023%20California%20wildfires
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The 2023 California wildfire season is a series of significant wildfires that have burned in the U.S. state of California since the beginning of the calendar year. According to statistics published by the California Department of Forestry and Fire Protection (Cal Fire), , a total of 6,001 fires have burned a total of . This is below the state's five-year average of burned during the same period. The 2023 fire season follows the 2022 season, during which the number of fires and the resulting burned acreage were both below average.
Season outlook
Climate
California saw a series of powerful atmospheric rivers between December 2022 and March 2023, which much improved drought conditions in the state and boosted the snowpack in the Sierra Nevada to more than 200% of average for the date. Some researchers noted that the resulting vegetation growth could prove dangerous if dry and warm conditions return during spring and summer, obviating the gains from early storms, but in general, according to the California Department of Forestry and Fire Protection (Cal Fire), increased precipitation reduces the risk of a worse wildfire season.
Cal Fire predicted that "critically dry fuel moisture alignments are not likely to be reached for any great length of time or over a larger area" between March and June 2023. Critical fuel moisture refers to the point at which fuel characteristics—like vegetation mortality or dryness—are favorable for large fire growth.
Timing of peak fire season
In Northern California, fire season typically peaks in the summer with increasingly warm and dry conditions and aided by occasional dry cold frontal passages that may bring winds and/or lightning. Activity usually continues until late fall brings Pacific moisture to the northern portion of the state, though northeast wind events may pose a threat. In Southern California, fire season typically peaks in late spring through early fall, when Pacific moisture recedes. Offshore wind events such as Santa Ana winds mean that large fires are possible year-round, but their frequency is most heightened in the fall, when fuels are also driest.
Preparation
In January, U.S. Agriculture Secretary Tom Vilsack announced the allocation of $930 million in funding from the Infrastructure Investment and Jobs Act and the Inflation Reduction Act to ten western states, including California, for fuel reduction programs and other measures to curtail wildfire risks. The allocation was reported to represent a significant increase in funding for programs like tree clearing, brush thinning and removal, and controlled burns in Southern California, whose four National Forests previously received about $1.2 million annually for those purposes.
On January 31, California senators Dianne Feinstein and Alex Padilla (as well as senators Steve Daines of Montana and Ron Wyden of Oregon) introduced a bill to the U.S. Senate entitled the Wildfire Emergency Act, recognizing the "threat of wildfire" as an emergency in
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https://en.wikipedia.org/wiki/Mixed%20White%20and%20Black%20Caribbean%20%28United%20Kingdom%20ethnicity%20category%29
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Mixed White and Black Caribbean is an ethnic group category that was first introduced by the United Kingdom's Office for National Statistics for the 2001 Census. Colloquially it refers to British citizens or residents whose parents are of a White ethnic background and Black Caribbean ethnic background. This classification is only used in England and Wales, as Scotland and Northern Ireland do not have sub categories for their mixed group options.
They have a total population of 513,042, representing 0.9% of England and Wales, an increase from 426,715 in 2011 and 237,420 in 2001.
Demographics
The White and Black Caribbean Mixed population has increased with each decennial census, starting from 237,420 people with the category's introduction in 2001, rising to 426,715 in 2011 to now 513,042 in 2021 in England and Wales.
Religion
See also
Mixed (United Kingdom ethnicity category)
Mixed White and Black African people in the United Kingdom
References
Afro-Caribbean culture in England
Sub-ethnic groups
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https://en.wikipedia.org/wiki/Mixed%20White%20and%20Asian%20%28United%20Kingdom%20ethnicity%20category%29
|
Mixed White and Asian is an ethnic group category that was first introduced by the United Kingdom's Office for National Statistics for the 2001 Census. Colloquially it refers to British citizens or residents whose parents are of a White (unspecificed) ethnic background and Asian (unspecified) ethnic background. This classification is only used in England and Wales, as Scotland and Northern Ireland do not have sub categories for their mixed group options.
They have a total population of 488,225 representing 0.8% of England and Wales, an increase from 341,727 in 2011 and 189,015 in 2001.
Demographics
The White and Asian Mixed population has increased with each decennial census, starting from 189,015 people with the category's introduction in 2001, rising to 341,727 in 2011 to now 488,225 in 2021 in England and Wales.
Religion
See also
Mixed (United Kingdom ethnicity category)
Mixed White and Black African people in the United Kingdom
Mixed White and Black Caribbean (United Kingdom ethnicity category)
References
Asian-British culture in England
Sub-ethnic groups
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https://en.wikipedia.org/wiki/2022%20Melaka%20United%20F.C.%20season
|
The 2022 season was Melaka United Football Club's 98th season in club history and 6th season in the Malaysia Super League.
Players
First-team squad
Squad statistics
Appearances
|-
|colspan="17"|Players who left the club during the season
|-
|}
Competitions
Malaysia Super League
Malaysia FA Cup
References
Melaka United F.C.
Melaka United F.C. seasons
Melaka United
Malaysian football club seasons by club
|
https://en.wikipedia.org/wiki/Multiple%20orthogonal%20polynomials
|
In mathematics, the multiple orthogonal polynomials (MOPs) are orthogonal polynomials in one variable that are orthogonal with respect to a finite family of measures. The polynomials are divided into two classes named type 1 and type 2.
In the literature, MOPs are also called -orthogonal polynomials, Hermite-Padé polynomials or polyorthogonal polynomials. MOPs should not be confused with multivariate orthogonal polynomials.
Multiple orthogonal polynomials
Consider a multiindex and positive measures over the reals. As usual .
MOP of type 1
Polynomials for are of type 1 if the -th polynomial has at most degree such that
and
Explanation
This defines a system of equations for the coefficients of the polynomials .
MOP of type 2
A monic polynomial is of type 2 if it has degree such that
Explanation
If we write out, we get the following definition
Literature
López-Lagomasino, G. (2021). An Introduction to Multiple Orthogonal Polynomials and Hermite-Padé Approximation. In: Marcellán, F., Huertas, E.J. (eds) Orthogonal Polynomials: Current Trends and Applications. SEMA SIMAI Springer Series, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-56190-1_9
References
Orthogonal polynomials
|
https://en.wikipedia.org/wiki/Magnetic%20topology
|
In plasma physics, the magnetic topology of a plasma is the structure and linkage of its magnetic field.
The magnetic topology of a plasma can be changed through magnetic diffusion and reconnection. In the limit of a large magnetic Reynolds number, however, diffusion and reconnection of the magnetic field cannot occur, and the magnetic topology is preserved.
References
Plasma physics
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Anhui
|
The COVID-19 pandemic reached the province of Anhui, China, in 2020.
Statistics
Timeline
2020
On January 21, 2020, the Hefei Municipal Health Commission reported that a suspected case of infection with the new coronavirus was found. The patient had been engaged in the operation and management of beef frozen products in Wuhan, and drove back to Anhui from Wuhan on January 17. He had been receiving isolation treatment in a designated hospital, his condition was stable, and close contacts were placed under medical observation. The patient's laboratory test results were reviewed as required.
At 16:00 on January 22, confirmed by the National Health and Health Commission, Anhui Province received the first case of pneumonia infected by a new type of coronavirus reported by Hefei City as a confirmed case. In addition, as of 16:00 on January 22, the Provincial Health and Health Commission received a total of 4 suspected cases of pneumonia caused by new coronavirus infection reported by 2 cities in the province (3 cases in Hefei City and 1 case in Lu'an City).
At 10 o'clock on January 23, Anhui Province reported 8 new confirmed cases of pneumonia caused by a new type of coronavirus infection. Among them, Lu'an City, Chuzhou City, Fuyang City, and Bozhou City reported the first confirmed cases, and Hefei City had 4 new confirmed cases.
On January 24, Anhui Province reported 6 new confirmed cases of pneumonia caused by a new type of coronavirus, including 1 case each in Anqing City, Chizhou City, and Bengbu City, which was the first confirmed case report. 1 newly reported confirmed case.
On January 25, Anhui Province reported 24 new confirmed cases of pneumonia caused by the new coronavirus, including 4 cases in Hefei City, 3 cases in Tongling City, 3 cases in Anqing City, 4 cases in Ma'anshan City, 5 cases in Fuyang City, and 3 cases in Bozhou City. 1 case in Wuhu City, 1 case in Chuzhou City, Tongling City, Maanshan City, and Wuhu City were the first case reports.
Since January 26, all buses in Zongyang County, Tongling City were suspended. On the same day, Anhui Province reported 21 new confirmed cases of pneumonia caused by the new coronavirus, including 3 in Hefei, 3 in Ma'anshan, 3 in Fuyang, 2 in Bozhou, 2 in Wuhu, 2 in Suzhou, 1 in Xuancheng, and 1 in Lu'an. 1 case, 1 case in Huaibei, 1 case in Huainan, 1 case in Anqing, and 1 case in Huangshan. Suzhou City, Xuancheng City, Huaibei City, Huainan City, and Huangshan City were the first case reports.
References
Anhui
COVID-19 pandemic in mainland China
History of Anhui
Health in Anhui
|
https://en.wikipedia.org/wiki/Sobolev%20orthogonal%20polynomials
|
In mathematics, Sobolev orthogonal polynomials are orthogonal polynomials with respect to a Sobolev inner product, i.e. an inner product with derivatives.
By having conditions on the derivatives, the Sobolev orthogonal polynomials in general no longer share some of the nice features that classical orthogonal polynomials have.
Sobolev orthogonal polynomials are named after Sergei Lvovich Sobolev.
Definition
Let be positive Borel measures on with finite moments. Consider the inner product
and let be the corresponding Sobolev space. The Sobolev orthogonal polynomials are defined as
where denotes the Kronecker delta. One says that these polynomials are sobolev orthogonal.
Explanation
Classical orthogonal polynomials are Sobolev orthogonal polynomials, since their derivatives are also orthogonal polynomials.
Sobolev orthogonal polynomials in general are no longer commutative in the multiplication operator with respect to the inner product, i.e.
Consequently neither Favard's theorem, the three term recurrence or the Christoffel-Darboux formula hold. There exist however other recursion formulas for certain types of measures.
There exist a lot of literature for the case .
Literature
References
Orthogonal polynomials
Sobolev spaces
|
https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Ningxia
|
The COVID-19 pandemic reached the Ningxia Hui Autonomous Region, China in 2020.
Statistics
Timeline
2020
During the period from January 24 to 26, 1 new confirmed case was reported every day.
On January 26, Ningxia newly reported 3 confirmed cases and excluded 1 suspected case.
On January 27, Ningxia newly reported 4 confirmed cases.
On January 28, one new confirmed case was reported in Ningxia
On January 29, Ningxia newly reported 5 confirmed cases.
On January 30, Ningxia newly reported 4 confirmed cases.
On January 31, Ningxia newly reported 5 confirmed cases.
May 2021
On May 8, a new confirmed case was added in Yinchuan City. The patient entered Shanghai on April 23. After 14 days of centralized isolation medical observation and three negative nucleic acid tests, he was released from isolation on May 7 and returned to Shanghai from Shanghai. The nucleic acid test result was positive on the first day of his return, and he was diagnosed the next day.
July 2021
On July 30, Yinchuan City organized a follow-up investigation of Zhang Moumou, a close contact of a confirmed case in Chengdu, according to the requirements of the relevant provincial and municipal investigation letters. The nucleic acid test was positive, and he was immediately transferred to the Fourth People's Hospital of Ningxia Hui Autonomous Region for isolation diagnosis and treatment. Diagnosed by the diagnosis and treatment expert group as a confirmed case of new coronary pneumonia, the clinical type is common type.
2022
On April 28, Ningxia reported 1 new case of asymptomatic infection of new coronary pneumonia (in Yinchuan, a close contact of an asymptomatic infection who returned to Ningxia after entering the quarantine on April 25).
References
Ningxia
COVID-19 pandemic in mainland China
History of Ningxia
Health in Ningxia
zh:2019冠状病毒病宁夏回族自治区疫情
|
https://en.wikipedia.org/wiki/Bou%C3%A9%E2%80%93Dupuis%20formula
|
In stochastic calculus, the Boué–Dupuis formula is variational representation for Wiener functionals. The representation has application in finding large deviation asymptotics.
The theorem was proven in 1998 by Michelle Boué and Paul Dupuis. In 2000 the result was generalized to infinite-dimensional Brownian motions and in 2009 extended to abstract Wiener spaces.
Boué–Dupuis formula
Let be the classical Wiener space and be a -dimensional standard Brownian motion. Then for all bounded and measurable functions
we have the following variational representation
where:
The expectation is with respect to the probability space of .
The infimum runs over all processes which are progressively measurable with respect to the augmented filtration generated by
denotes the -dimensional Euclidean norm.
References
Stochastic calculus
Wiener process
Probability theorems
Calculus of variations
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https://en.wikipedia.org/wiki/Bad%20control
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In statistics, bad controls are variables that introduce an unintended discrepancy between regression coefficients and the effects that said coefficients are supposed to measure. These are contrasted with confounders which are "good controls" and need to be included to remove omitted variable bias. This issue arises when a bad control is an outcome variable (or similar to) in a causal model and thus adjusting for it would eliminate part of the desired causal path. In other words, bad controls might as well be dependent variables in the model under consideration. Angrist and Pischke (2008) additionally differentiate two types of bad controls a simple bad-control scenario and proxy-control scenario where the included variable partially controls for omitted factors but is partially affected by the variable of interest. Pearl (1995) provides a graphical method for determining good controls using causality diagrams and the back-door criterion and front-door criterion.
Examples
Simple bad control
A simplified example studies effect of education on wages . In this gedankenexperiment two levels of education are possible: lower and higher and two types of jobs are performed: white-collar and blue-collar work. When considering the causal effect of education on wages of an individual, it might be tempting to control for the work-type , however, work type is a mediator () in the causal relationship between education and wages (see causal diagram) and thus, controlling for it precludes causal inference from the regression coefficients.
Bad proxy-control
Another example of bad control is when attempting to control for innate ability when estimating effect of education on wages . In this example, innate ability (thought of as for example IQ at pre-school age) is a variable influencing wages , but its value is unavailable to researchers at the time of estimation. Instead they choose before-work IQ test scores , or late ability, as a proxy variable to estimate innate ability and perform regression from education to wages adjusting for late ability. Unfortunately, late ability (in this thought experiment) is causally determined by education and innate ability and, by controlling for it, researchers introduced collider bias into their model by opening a back-door path previously not present in their model. On the other hand, if both links and are strong, one can expect strong (non-causal) correlation between and and thus large omitted-variable bias if is not controlled for. This issue, however, is separate from the causality problem.
References
Statistical concepts
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https://en.wikipedia.org/wiki/David%20Earn
|
David J. D. Earn is a Canadian mathematical epidemiologist. He is the Faculty of Science Research Chair in Mathematical Epidemiology in the Department of Mathematics and Statistics at McMaster University. In 2022, Earn was elected a Fellow of the Canadian Academy of Health Sciences.
Early life and education
Earn was born and raised in Winnipeg, Manitoba, Canada. He completed his Bachelor of Science degree and Master's degree at the University of Toronto before completing his Ph.D. at the University of Cambridge under the guidance of Donald Lynden-Bell. Following his PhD, Earn accepted and completed post-doctoral fellowships at Cambridge, Hebrew University of Jerusalem, and Princeton University.
Career
Following his fellowships, Earn joined the faculty at McMaster University as a professor of applied mathematics in January 2000. In this role, he began co-developing a new mathematical model to enable scientists to predict epidemics of infectious diseases with researchers from the University of Florida and University of Cambridge. The model made the prediction that increases or decreases in birth rates or vaccination rates should cause dramatic changes in patterns of epidemics. In developing the model, Earn studied historical data on the outbreaks of measles in London, Liverpool, New York, and Baltimore. Later that year, Earn began developing a mathematical formula to help eliminate measles and other infectious diseases by increasing vaccinations. He hypothesized that upping vaccines for measles once every year, rather than only for children at 13 months, would cause epidemics and low-disease periods to occur simultaneously and annually at the same time and eventually die out. Beyond eradicating infectious diseases in humans, Earn also worked to determine if conservation corridors are a benefit or a threat to endangered species.
As a professor at McMaster and investigator with the Michael G. DeGroote Institute for Infectious Disease Research, Earn co-discovered three factors that contributed to the Spanish flu's waves of infection. His research team determined that the closing and opening of schools, temperature changes and changes in human behaviour were important contributors. He also published a study that investigated whether closing schools could help slow the spread of infectious disease and should be considered as a control measure during pandemic outbreaks. His efforts were recognized with the 2013 Synergy Award from McMaster.
During the COVID-19 pandemic, Earn co-authored a paper entitled "The origins and potential future of SARS-CoV-2 variants of concern in the evolving COVID-19 pandemic." He was also selected to sit on the Ontario COVID-19 Science Advisory Table. In May 2021, Earn was appointed as the Faculty of Science Research Chair in Mathematical Epidemiology. The following year, he was elected a Fellow of the Canadian Academy of Health Sciences for his overall work in infectious disease but was specifically recognized for being "
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https://en.wikipedia.org/wiki/Clarke%20generalized%20derivative
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In mathematics, the Clarke generalized derivatives are types generalized of derivatives that allow for the differentiation of nonsmooth functions. The Clarke derivatives were introduced by Francis Clarke in 1975.
Definitions
For a locally Lipschitz continuous function the Clarke generalized directional derivative of at in the direction is defined as
where denotes the limit supremum.
Then, using the above definition of , the Clarke generalized gradient of at (also called the Clarke subdifferential) is given as
where represents an inner product of vectors in
Note that the Clarke generalized gradient is set-valued—that is, at each the function value is a set.
More generally, given a Banach space and a subset the Clarke generalized directional derivative and generalized gradients are defined as above for a locally Lipschitz contininuous function
See also
Subgradient method — Class of optimization methods for nonsmooth functions.
Subderivative
References
Generalizations of the derivative
Convex optimization
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https://en.wikipedia.org/wiki/Eicke%20Weber
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Eicke Richard Weber (born 28 October 1949 in Münnerstadt) is a German physicist.
Life
Scientific activity
Weber grew up from 1955 in Cologne, where he also took his Abitur. He studied mathematics and physics at the University of Cologne from 1967. After graduating in 1972, he took on an assistant position at the RWTH Aachen and finished his doctorate in physics in 1976 with the topic Point Defects in Deformed Silicon and received his Ph.D. His habilitation followed in 1983 with the topic Transition Metals in Silicon. Weber joined the faculty of the Department of Materials Science and Engineering, University of California, Berkeley, first as Assistant in 1983, than Associate and since 2001 as Full Professor, and stayed there for 23 years, until he accepted in 2006 a call from the Fraunhofer society. He spent one research semester each as a visiting professor at Tōhoku-Gakuin University in Sendai, and Kyoto University in Japan. In Berkeley, he served 2004–06 as founding Chair of the Interdisciplinary Nanoscale Science and Engineering Graduate Group. From July 2006 to December 2016, he was director of the Fraunhofer Institute for Solar Energy Systems (ISE) in Freiburg, Germany. In addition to his position as Director of ISE, he held the Chair of Physics/Solar Energy at the Albert Ludwigs University of Freiburg. From 2012 to 2016, he served also as executive director of the Centre for Renewable Energies at the University of Freiburg. He then worked as the Director of the Berkeley Education Alliance for Research in Singapore (BEARS) from January 2017 to May 2018.
In 2002, Weber and colleagues founded the (GSO), of which he remains president today. In 2013, he and colleagues founded the German Energy Storage Association, until 2016 he was BVES President, since then Honorary President. In 2016, he was appointed to the Economic Senate of the German Association of Small and Medium-Sized Businesses (BVMW), since March 2020 he is heading the BVMW Commission for Energy and Sustainable Economy.
In the course of his scientific work, he has authored or co-authored 618 papers.
Politics
In 2016, he ran unsuccessfully for the Free Democratic Party in the state elections in Baden-Württemberg in the electoral district Freiburg II. He is co-president of the European Solar Manufacturing Council (ESMC), an interest group of companies and research institutions for the production of photovoltaic systems in the European Union. As such, he considers the complete supply of Germany by green electricity by 2030 to be plausible, provided that appropriate measures are taken.
Offices
since 2003: President of the German Scholars Organization
2004–2006: Chair of the Berkeley Nanoscale Science and Engineering Graduate Group
2008–2014: Director of the SEMI International Board of Directors
2008–2012 Member of the Meyer Burger Board of Directors, from 2010 of the Technology Advisory Board
2011–2013: Member of the Q-Cells Supervisory Board
2013–2016: President of the
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https://en.wikipedia.org/wiki/Abdellatif%20Ben%20Ammar
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Abdellatif Ben Ammar (; 25 April 1943 – 6 February 2023) was a Tunisian film director and screenwriter.
Biography
Born in Tunis on 25 April 1943, Ben Ammar studied mathematics at the . He then turned to cinema and earned a diploma in filmmaking from the Institut des hautes études cinématographiques in Paris in 1965.
Upon his return to Tunisia, Ben Ammar was hired by the Tunisian Company for Cinematic Production and Expansion and began shooting short films and assisting Tunisian and foreign directors. In 1970, he released his first feature film, A Simple Story, then founded the film studio Latif Productions alongside Abdellatif Layouni. He also founded a post-production company, Ben Duran.
Ben Ammar died in Tunis on 6 February 2023, at the age of 79.
Filmography
2 + 2 = 5 (1966)
Le Cerveau (1967)
Opération yeux (1967)
L'Espérance (1968)
A Simple Story (1970)
Sur les traces de Baal (1971)
Mosquées de Kairouan (1972)
(1973)
Sadiki (1975)
Kairouan, la Grande Mosquée (1979)
Aziza (1980)
Le Chant de la noria (2002)
Farhat Hached (2002)
Khota Fawka Assahab (2003)
Les Palmiers blessés (2010)
Distinctions
Tanit de bronze at the Carthage Film Festival for A Simple Story (1970)
Tanit de bronze at the Carthage Film Festival for Sejnane (1974)
Special jury prize of the Panafrican Film and Television Festival of Ouagadougou for Sejnane (1976)
Tanit d'or at the Carthage Film Festival for Aziza (1980)
Selection for the Directors' Fortnight at the Cannes Film Festival for Aziza (1980)
References
1943 births
2023 deaths
Tunisian male writers
People from Tunis
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https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Tianjin
|
The COVID-19 pandemic reached the municipality of Tianjin, China, in January 2020.
Statistics
2020
On January 21, 2020, 2 confirmed cases were reported. A 60-year-old woman and a 58-year-old man were quarantined after returning to Tianjin from Wuhan on January 19 and January 14.
At 12 o'clock on January 22, two new confirmed cases were reported, both of whom had received isolation treatment in designated hospitals, and their vital signs were stable. Among the patients, there was one female, 67 years old, and one male, 40 years old, both of whom had a work history in Wuhan.
On January 24, the Tianjin Center for Disease Control and Prevention announced two confirmed cases. The patient was an employee of the crew workshop of the Tianjin High-speed Train Passenger Transport Section and was a colleague of one of the patients who was diagnosed on January 21. On the same day, the Tianjin Municipal Health Commission reported a new confirmed case of pneumonia caused by a new type of coronavirus infection. The patient was a 46-year-old male patient.
On January 25, the Tianjin Municipal Health and Health Commission announced three new cases, one new case, and one confirmed case three times. As of the afternoon of January 25, a total of 10 cases of pneumonia caused by the new coronavirus infection had been found in Tianjin, including 7 males and 3 females; 7 severe cases and 3 mild cases; no critical cases.
On January 26, the Tianjin Municipal Health Commission announced that there were 3 new confirmed cases of pneumonia caused by a new type of coronavirus infection.
2021
On January 1, 2021, Tianjin added 3 new confirmed cases of imported new coronary pneumonia.
2022
On January 1, 5 new confirmed cases of imported new coronary pneumonia were reported in Tianjin.
References
Tianjin
COVID-19 pandemic in mainland China
History of Tianjin
Health in Tianjin
zh:2019冠狀病毒病天津市疫情
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https://en.wikipedia.org/wiki/Big-line-big-clique%20conjecture
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The big-line-big-clique conjecture is an unsolved problem in discrete geometry, stating that finite sets of many points in the Euclidean plane either have many collinear points, or they have many points that are all mutually visible to each other (no third point blocks any two of them from seeing each other).
Statement and history
More precisely, the big-line big-clique conjecture states that, for any positive integers and there should exist another number , such that every set of points contains collinear points (a "big line"), mutually-visible points (a "big clique"), or both.
The big-line-big-clique conjecture was posed by Jan Kára, Attila Pór, and David R. Wood in a 2005 publication. It has led to much additional research on point-to-point visibility in point sets.
Partial results
Finite point sets in general position (no three collinear) do always contain a big clique, so the conjecture is true for . Additionally, finite point sets that have no five mutually-visible points (such as the intersections of the integer lattice with convex sets) do always contain many collinear points, so the conjecture is true for .
Generalizing the integer lattice example, projecting a -dimensional system of lattice points of size
onto the plane, using a generic linear projection, produces a set of points with no collinear points and no mutually visible points. Therefore, when exists, it must be greater than .
Related problems
The visibilities among any system of points can be analyzed by using the visibility graph of the points, a graph that has the points as vertices and that connects two points by an edge whenever the line segment connecting them is disjoint from the other points. The "big cliques" of the big-line-big-clique conjecture are cliques in the visibility graph. However, although a system of points that is entirely collinear can be characterized by having a bipartite visibility graph, this characterization does not extend to subsets of points: a subset can have a bipartite induced subgraph of the visibility graph without being collinear.
According to the solution of the happy ending problem, every subset of points with no three in line includes a large subset forming the vertices of a convex polygon. More generally, it can be proven using the same methods that every set of sufficiently many points either includes collinear points or points in convex position. However, some of these pairs of convex points could be blocked from visibility by points within the convex polygon they form.
Another related question asks whether points in general position (or with no lines of more than some given number of points) contain the vertices of an empty convex polygon or hole. This is a polygon whose vertices belong to the point set, but that has no other points in the intersection of the point set with its convex hull. If a hole of a given size exists, its vertices all necessarily see each other. All sufficiently large sets of points in general p
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https://en.wikipedia.org/wiki/Formal%20distribution
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In mathematics, a formal distribution is an infinite sum of powers of a formal variable, usually denoted in the theory of formal distributions. The coefficients of these infinite sums can be many different mathematical structures, such as vector spaces or rings, but in applications most often take values in an algebra over a field. These infinite sums are allowed to have infinitely many positive and negative powers, and are not required to converge, and so do not define functions of the formal variable. Rather, they are interpreted as distributions, that is, linear functionals on an appropriate space of test functions. They are closely related to formal Laurent series, but are not required to have finitely many negative powers. In particular, this means even if the coefficients are ring-valued, it is not necessarily possible to multiply two formal distributions.
They are important in the study of vertex operator algebras, since the vertex operator playing a central role in the theory takes values in a space of endomorphism-valued formal distributions.
Definition over a C-algebra
Let be an algebra over , as is the case for applications to vertex algebras. An -valued formal distribution in variables is an arbitrary series
with each . These series form a vector space, denoted . While it can be possible to multiply some pairs of elements in the space of formal distributions, in general there is no product on the whole space.
In practice, the number of variables considered is often just one or two.
Products
If the variables in two formal distributions are disjoint, then the product is well-defined.
The product of a formal distribution by a Laurent polynomial is also well-defined.
Formal distributions in a single variable
For this section we consider .
Formal residue
The formal residue is a linear map , given by
The formal residue of can also be written or . It is named after residues from complex analysis, and when is a meromorphic function on a neighborhood of zero in the complex plane, the two notions coincide.
Formal derivative
The formal derivative is a linear map . For an element , its action is given by
extended linearly to give a map for the whole space.
In particular, for any formal distribution ,
Interpretation as distribution
This then motivates why they are named distributions: considering the space of 'test functions' to be the space of Laurent polynomials, any formal distribution defines a linear functional on the test functions. If is a Laurent polynomial, the formal distribution defines a linear functional by
Formal distributions in two variables
For this section we consider .
Delta distribution
One of the most important distributions is the delta function, and indeed it can be realized as a formal distribution in two variables.
It is defined
and satisfies, for any formal distribution
where now, the subscript on is necessary to identify for which variable one reads the residue from.
Expansions of
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https://en.wikipedia.org/wiki/SaTScan
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SaTScan is a software tool that employs scan statistics for the spatial and temporal analysis of clusters of events. The software is trademarked by Martin Kulldorff, and was designed originally for public health and epidemiology to identify clusters of cases in both space (geographical location) and time and to perform statistical analysis to determine if these clusters are significantly different from what would be expected by chance The software provides a user-friendly interface and a range of statistical methods, making it accessible to researchers and practitioners. While not a full Geographic Information System, the outputs from SaTScan can be integrated with software such as ArcGIS or QGIS to visualize and analyze spatial data, and to map the distribution of various phenomena.
Analysis
SaTScan employs scan statistics to identify clusters of space and time phenomena. Scan statistics use regular shapes (usually circles) of varying sizes to evaluate a study area. Within each circle, the software computes if the phenomena within the circle is significantly different than expected compared to the area outside the circle.
SaTScan can analyze data retrospectively or prospectively. It can look at the data spatially, temporally, or simultaneously incorporate both space and time. SaTScan can incorporate numerous probability models, including Poisson distribution, Bernoulli distribution, Monte Carlo method, and multinomial distribution. Using these, it can look for areas of higher and lower occurrences of phenomena than expected.
Results are output into a variety of formats, including ESRI Shapefile, HTML, and KML.
History
SaTScan was developed by a group of epidemiologists and statisticians led by Martin Kulldorff, a Swedish biostatistician professor of medicine at Harvard Medical School. Version 1.0 of the software was first released in 1997 and has since become a widely used tool in the field of public health research and practice.
SaTScan was developed in response to a growing need for sophisticated tools to analyze disease outbreaks. Before the development of SaTScan, few tools were available that could effectively analyze the spatial and temporal patterns of disease, making it difficult for public health authorities to respond effectively to outbreaks.
Since its release, SaTScan has been used in many public health research studies, including infectious diseases, cancers, and other conditions. Public health authorities and disease surveillance systems have also adopted the software in many countries, and it has broad applications for other types of data.
SaTScan was used extensively by researchers during the COVID-19 pandemic.
Applications
Epidemiology
SaTScan was originally developed for epidemiology and public health. Since its release, SaTScan has been used in many public health research studies involving GIS, including infectious diseases, cancers, and other conditions. Public health authorities and disease surveillance systems ha
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https://en.wikipedia.org/wiki/Ker-Chau%20Li
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Ker-Chau Li () is a Taiwanese statistician.
In 1975, Li graduated from National Taiwan University with a Bachelor of Science degree in mathematics. He then pursued graduate study in statistics at the University of California, Berkeley, completing a master's of science in 1979, followed by a doctorate in 1981. Li's doctoral dissertation, Contributions to Robust Design and Estimation Problems, was advised by Jack Kiefer. Li began his teaching career as an assistant professor in the statistics department of Purdue University, then joined the mathematics department of the University of California, Los Angeles in 1984. He was promoted to a full professorship in 1989, and transferred to the newly established UCLA statistics department in 1999. In 2009, Li was appointed a distinguished professor. In his native Taiwan, Li served as editor of the Statistica Sinica, and from 2006, served as director and distinguished research fellow of Academia Sinica's Institute of Statistical Science, stepping down from the former position in 2012.
Honors and awards
Li was elected a fellow of the Institute of Mathematical Statistics in 1989, awarded a Guggenheim Fellowship in 1993, and elected member of Academia Sinica and fellow of The World Academy of Sciences in 2012 and 2014, respectively.
References
Living people
Taiwanese statisticians
National Taiwan University alumni
University of California, Los Angeles faculty
University of California, Berkeley alumni
Members of Academia Sinica
Purdue University faculty
Year of birth missing (living people)
TWAS fellows
Fellows of the Institute of Mathematical Statistics
Mathematics journal editors
Mathematical statisticians
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https://en.wikipedia.org/wiki/Ashkan%20Nikeghbali
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Ashkan Nikeghbali Cisakht (; born 1975) is a mathematician and university professor . He holds the chair of Financial Mathematics at the University of Zurich.
Academic career
Nikeghbali obtained his PhD at the Pierre and Marie Curie University in 2005 with the thesis "Temps aléatoires, filtrations et sous-martingales: quelques développements récents", supervised by Marc Yor. Prior to that, he was a researcher from February 2004 to July 2004 at the Isaac Newton Institute on the topic of "Random matrix approaches in number theory." After completing his PhD, Nikeghbali first worked as a postdoctoral researcher at the American Institute of Mathematics (under the direction of Brian Conrey) at Rochester University. In June 2006, he was appointed Heinz-Hopf Lecturer at ETH Zurich. In March 2007, Nikeghbali was appointed assistant professor at the Institute of Mathematics at the University of Zurich. He was promoted to Extraordinary Professor of Applied Mathematics there in 2009.
Research
Nikeghbali's research focuses on financial mathematics, probability theory, and analytic number theory. In particular, he works in the areas of portfolio theory, stochastic processes, random operators and matrices, and the application of stochastics in number theory and combinatorics.
In asymptotic probability theory, Nikeghbali, together with Féray, Méliot, and Kowalski introduced the concept of Mod-Ф convergence. In number theory, he, together with Chhaibi and Najnudel, introduced the concept of stochastic zeta function.
Nikeghbali supervised at least six PhD students during his time at the University of Zurich.
Other activities
Member of the world.minds community since 2008. Member of the Scientific Advisory Board of swissQuant. Member of the advisory board of EVMTech. Strategy advisor for data analysis and modeling of stochastic processes at Roche Holding in Basel.
Awards
Honorary doctorate from the University of Alba Iulia in Romania.
Publications
References
External links
1975 births
21st-century mathematicians
Probability theorists
Number theorists
Pierre and Marie Curie University alumni
People associated with the University of Zurich
Living people
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https://en.wikipedia.org/wiki/Margaret%20Sullivan%20Pepe
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Margaret Patricia O'Sullivan Pepe (born June 24, 1961) is an Irish biostatistician specializing in the evaluation of tests and biomarkers for disease screening. She is a professor of biostatistics at the University of Washington School of Public Health and a researcher at the Fred Hutchinson Cancer Research Center.
Life
Pepe was born June 24, 1961, in Cork, Ireland to Seamus O'Sullivan. She attended Mount Mercy College, Cork. She completed a B.Sc. in mathematics science at the University College Cork in 1981. Pepe earned a M.S. in statistics in 1984 and a Ph.D. in biostatistics at the University of Washington School of Public Health in 1986. Her dissertation was titled, A new class of statistics for the two-sample survival analysis problem. Thomas R. Fleming was her doctoral advisor.
In 1997, she won the Mortimer Spiegelman Award.
Pepe is a professor of biostatistics at the University of Washington School of Public Health. She is a researcher at the Fred Hutchinson Cancer Research Center.
Selected works
References
Living people
1961 births
21st-century American mathematicians
21st-century women mathematicians
American women statisticians
Biostatisticians
American medical researchers
Women medical researchers
21st-century American women scientists
21st-century American biologists
American women biologists
Alumni of University College Cork
University of Washington School of Public Health alumni
University of Washington faculty
Irish emigrants to the United States
21st-century Irish women scientists
21st-century Irish mathematicians
Irish statisticians
Expatriate academics in the United States
Scientists from Cork (city)
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https://en.wikipedia.org/wiki/2010%20Home%20United%20FC%20season
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The 2010 Home United FC season involves Home United competing in the 2010 S.League.
Squad
S.League squad
Transfers
Pre-season transfers
In
Out
Mid-season transfers
In
Out
Team statistics
Appearances and goals
Numbers in parentheses denote appearances as substitute.
Competitions
S.League
League table
Singapore Cup
Singapore League Cup
References
Home United
2010
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https://en.wikipedia.org/wiki/Austin%20FC%20record%20by%20opponent
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All-time league record
Statistics correct as of match played on October 7, 2023.
All-time MLS Cup record
Statistics correct as of match played on October 30, 2022.
All-time CONCACAF Champions League record
Statistics correct as of match played on March 14, 2023.
All-time Leagues Cup record
Statistics correct as of match played on July 21, 2023.
All-time U.S. Open Cup record
Statistics correct as of match played on May 24, 2023.
References
American soccer clubs records and statistics
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https://en.wikipedia.org/wiki/Piecewise%20algebraic%20space
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In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation was for the proof of Deligne's conjecture on Hochschild cohomology. Robert Hardt, Pascal Lambrechts, Victor Turchin, and Ismar Volić later developed the theory.
References
Maxim Kontsevich and Yan Soibelman. “Deformations of algebras over operads and the Deligne conjecture”. In: Conférence Moshé Flato 1999, Vol. I (Dijon). Vol. 21. Math. Phys. Stud. Dordrecht: Kluwer Acad. Publ., 2000, pp. 255–307. arXiv: math/0001151.
Algebraic geometry
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https://en.wikipedia.org/wiki/Deligne%27s%20conjecture%20on%20Hochschild%20cohomology
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In deformation theory, a branch of mathematics, Deligne's conjecture is about the operadic structure on Hochschild cochain complex. Various proofs have been suggested by Dmitry Tamarkin, Alexander A. Voronov, James E. McClure and Jeffrey H. Smith, Maxim Kontsevich and Yan Soibelman, and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex. It is of importance in relation with string theory.
See also
piecewise algebraic space
References
Further reading
https://ncatlab.org/nlab/show/Deligne+conjecture
https://mathoverflow.net/questions/374/delignes-conjecture-the-little-discs-operad-one
Algebraic topology
String theory
Conjectures
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https://en.wikipedia.org/wiki/Bradley%20Thiessen%20%28statistician%29
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Bradley Adam Thiessen is an American statistician and academic administrator serving as the interim president of the New College of Florida. He is the chief of staff and a professor of statistics.
Life
Theissen earned a bachelor's degree in secondary mathematics education at the St. Ambrose University. He earned a master's degree and Ph.D. in educational measurement and statistics from the University of Iowa. His 2008 dissertation was titled, Relationship between test security policies and test score manipulations. Timothy Neri Ansley was his doctoral advisor.
Thiessen worked at the St. Ambrose University for 12 years as the university assessment coordinator and a faculty member in the department of mathematics and statistics. He joined the New College of Florida in July 2016 as the president's chief of staff and a professor of statistics. In August 2016, he became its first director of institutional performance assessment. On January 2, 2020, he became the director of institutional research at the University of Hawaiʻi at Hilo. On January 31 2023, Thiessen was appointed as the interim president of the New College of Florida by the board of trustees, succeeding Patricia Okker. He will serve until March 2023 when he is replaced by Richard Corcoran.
References
Living people
Year of birth missing (living people)
Place of birth missing (living people)
American statisticians
St. Ambrose University alumni
University of Iowa alumni
St. Ambrose University faculty
University of Hawaiʻi faculty
Presidents of New College of Florida
21st-century American mathematicians
Mathematicians from Iowa
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https://en.wikipedia.org/wiki/Brownian%20sheet
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In mathematics, a brownian sheet is a multiparametric generalization of the brownian motion to a gaussian random field. This means we generalize the "time" parameter of a brownian motion from to .
The exact dimension of the space of the new time parameter varies from authors. We follow John B. Walsh and define the -brownian sheet, while some authors define the brownian sheet specifically only for , what we call the -brownian sheet.
(n,d)-Brownian sheet
A -dimensional gaussian process is called a -brownian sheet if
it has zero mean, i.e. for all
for the covariance function
for .
Properties
From the definition follows
almost surely.
Examples
-brownian sheet is the brownian motion in .
-brownian sheet is the brownian motion in .
Existence of abstract Wiener measure
Let denote the Sobolev space of degree , and let denote the space of continuous functions such that
Then by Sobolev embedding, embeds continuously into a dense subspace of .
There exists a probability measure on such that the triple
is an abstract Wiener space . For any , the elements of are almost surely Hölder continuous of exponent , and for any , the elements of are almost surely not Hölder continuous of exponent .
This handles of a Brownian sheet in the case . For higher dimensional , the construction is similar.
See also
Gaussian free field
Literature
.
References
Wiener process
Robert Brown (botanist, born 1773)
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https://en.wikipedia.org/wiki/Math%20walk
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A math walk, or math trail, is a type of themed walk in the US, where direct experience is translated into the language of mathematics or abstract mathematical sciences such as information science, computer science, decision science, or probability and statistics. Some sources specify how to create a math walk whereas others define a math walk at a specific location such as a junior high school or in Boston. The journal The Mathematics Teacher includes a special section titled "Mathematical Lens" in many issues with the metaphor of lens capturing seeing the world as mathematics.
Informal learning
The idea that "math is everywhere", which is emphasized on a math walk, is captured by the philosophy of mathematicism with its early adherents, Pythagoras and Plato. The math walk also implicitly involves experiencing math via modeling since mathematics serves to model what we sense. The math walk is a form of informal learning, often in an outside environment or in a museum. This type of learning is contrasted with formal learning, which tends to be more structured and performed in a classroom. Math walks have been shown to encourage students to think more deeply about mathematics, and to connect school content to the real world.
Maps and object discovery
There are different approaches to designing a math walk. The walk can be guided or unguided. In a guided walk, the learners are guided by a person knowledgeable in the topic of mathematics. In an unguided walk, learners are provided with a map. The map identifies walking stops and identifiers, such as QR codes or bluetooth beacons, to provide additional information on how the objects experienced during a math walk are translated into mathematical language.
Example math walk scene
A walk can involve translation only, or translation and problem solving. For example, considering a window on a building involves first perceiving the window. After perception, there is a translation of the form of the window to mathematical language, such as the array where is the window's width and is the window's length. The array is a mathematical model of the window. This modeling is pure translation, without explicit problem solving. Questions such as "what is the area of the window?" require not only translation, but also the problem of solving for area: .
A photo of the railroad tracks in Fernandina Beach Historic District captures a stop on a math walk. The walk's information can focus on discrete items. These items reflect counting and number sense. Examples of discrete items are the cloud structures, the distant red harbor cranes, power line poles, wooden railroad ties, the diagonal lines in the road, and the cross walk across the rails.
The counting of the ties leads to the idea of iteration in computer programming and, more generally, to discrete mathematics, the core of computer science. For iteration, we can use a programming language such as Python or C to encode the syntactical form of the iterat
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https://en.wikipedia.org/wiki/Yu%20Takeuchi
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(Tokyo, 16 March 1927 - Bogotá, 25 December 2014) was a Colombian nationalized Japanese physicist and mathematician, teacher and promoter of mathematics in Colombia.
Biography
Takeuchi studied theoretical physics at the Imperial University of Tokyo (now University of Tokyo) and was a professor at the Ibaraki University. He arrived in Colombia through a cultural exchange program sponsored by the National University of Colombia and the Japanese government in 1959, and he would go on to teach at the university until 1989. Along with five other Japanese professors, Takeuchi arrived in Colombia, entering through Buenaventura, without knowing how to speak Spanish. The hiring process was arranged by the Japanese embassy. His selection was made from a pool of 30 teachers, as Ramón García Piment indicated in an interview with UN Radio.
Although Takeuchi graduated as a physicist due to family influence, his interest was to learn and teach mathematics. He taught courses on vector analysis, calculus, and sequences, with the latter being his main interest. He is known for being the founder of the magazine Matemáticas: Enseñanza Universitaria and was part of the first class of the master's degree in mathematics at the National University of Colombia in 1972.
According to Ignacio Mantilla, a former student of Yu Takeuchi and former rector of the National University of Colombia, in the event commemorating 100 years of relations between Colombia and Japan in 2008, Takeuchi was recognized as the most influential Japanese figure in Colombia.
Since 2016, the Takeuchi family and the Colombian Academy of Exact, Physical, and Natural Sciences have awarded the Yu Takeuchi Prize in honor and memory of him.
Work as a Educator
Since he started working as a teacher in Colombia, Takeuchi became very aware of the backwardness and lack of updating of mathematics in the country and the need to train teachers at all levels of education. Therefore, he also dedicated himself to traveling throughout the national territory, disseminating Modern Mathematics through seminars, workshops, and collaborations of all kinds.
Printing press
By the 1960s, many students at the Faculty of Sciences of the National University of Colombia did not have the economic resources to acquire textbooks, few of which were in Spanish. Takeuchi knew of this difficulty, so he had a printing press in the garage of his house, where with the collaboration of his wife and children, he produced various hand-made and low-cost texts that were easily accessible to the university community. According to the professor, his greatest desire was to transmit mathematical knowledge at all costs, which Colombia lacked in those years.
Iván Castro Chadid, a close colleague of Takeuchi, remembers: Actually, this was what he did with his publications as he himself stated: "I wrote texts for everyone, seeking the popularization of mathematics." Usually, these books were made up of 60 paragraphs, so that each paragraph
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https://en.wikipedia.org/wiki/Robert%20Strawderman
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Robert L. Strawderman is an academic biostatistician and researcher who holds the Donald M. Foster, MD Distinguished Professorship in Biostatistics at the University of Rochester. He has served as chair of the Department of Biostatistics and Computational Biology since 2012. Strawderman's principal research interests include semiparametric methods for missing and censored data and statistical learning methods for risk and outcome prediction. Contributions in numerous other areas include inference and variable selection in the areas of dynamic treatment regimes and causal inference in mediation analysis and for recurrent events.
Education and Career Highlights
Strawderman graduated from Rutgers University in New Brunswick, New Jersey with a B.A. in mathematics in 1988, and completed a M.Sc. and Sc.D. in biostatistics at Harvard University in 1990 and 1992, respectively. He completed his dissertation under the direction of Anastasios A. (Butch) Tsiatis. Strawderman then joined the faculty of the Department of Biostatistics at the University of Michigan (Ann Arbor, MI) in 1992 as an assistant professor. Strawderman moved to Cornell University (Ithaca, NY) in 2000 as an associate professor in the Departments of Statistical Science and Biological Statistics and Computational Biology, becoming Professor in 2005. Strawderman later joined the University of Rochester to become chair of the Department of Biostatistics and Computational Biology within the School of Medicine and Dentistry in 2012, where he was initially appointed as a Dean's Professor and later named as the inaugural recipient of the Foster distinguished professorship in 2014.
Strawderman served as an Associate Editor for the Journal of the American Statistical Association (Theory & Methods) from 1997 through 2017, as well as for the Electronic Journal of Statistics from 2007 through 2013. He additionally served as officer for the Caucus of Academic Representatives (chair, 2017–2018), a committee formed by the American Statistical Association to "promote the statistics discipline within the academic community and provide resources for academic statisticians to successfully advocate for the discipline."
In 2006, Strawderman was elected as a Fellow of the American Statistical Association for "outstanding contributions to statistical methodology in the areas of failure time and recurrent event data and small sample inference; for excellence in collaborative research and teaching; and, for editorial service"; in 2012, he was elected as a Fellow of the Institute of Mathematical Statistics for "innovative methodological contributions to survival analysis, recurrent events, and small sample asymptotics and their applications; for excellence in editorial service." Strawderman is also the 2008 recipient of the Distinguished Alumni Award from the Department of Biostatistics at Harvard University.
References
External links
Biostatisticians
American statisticians
University of Rochester facul
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https://en.wikipedia.org/wiki/Christina%20T%C3%B8nnesen-Friedman
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Christina Wiis Tønnesen-Friedman is a Danish-American mathematician specializing in Riemannian geometry, especially of Kähler manifolds and Sasakian manifolds. She is Marie Louise Bailey Professor of Mathematics at Union College in Schenectady, New York.
Education
Tønnesen-Friedman studied mathematics and chemistry at Odense University, earning a candidate degree in 1995 and completing her Ph.D. in mathematics in 1997. Her doctoral dissertation, Extremal Kähler Metrics on Ruled Surfaces, was co-advised by Claude LeBrun and Henrik Laurberg Pedersen.
Career
Tønnesen-Friedman became a research assistant professor at Aarhus University in 1997. In 2001, she moved to Union College as an assistant professor of mathematics. She was tenured as an associate professor in 2007, promoted to full professor in 2012, and chaired the mathematics department at Union College from 2017 to 2021.
References
External links
Home page
Year of birth missing (living people)
Living people
Danish mathematicians
Danish women mathematicians
American mathematicians
American women mathematicians
Union College (New York) faculty
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https://en.wikipedia.org/wiki/Stephen%20Blyth
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Stephen James Blyth is a British mathematician and academic. Since October 2022, he has been Principal of Lady Margaret Hall, Oxford. He had been Professor of the Practice of Statistics at Harvard University since 2012, and was also chief executive officer of the Harvard Management Company between January 2015 and July 2016.
Biography
Blyth matriculated into Christ's College, Cambridge, in 1985 to study the Mathematical Tripos. He graduated with a first class honours Bachelor of Arts (BA) degree, and was the 3rd wrangler in that year. He then moved to the United States, where he studied statistics at Harvard University. He was awarded a Master of Arts (AM) degree in 1989. His doctoral dissertation was titled "Local Regression Coefficients and the Correlation Curve" and his advisor was Kjell Doksum. His Doctor of Philosophy (PhD) degree was awarded in 1992.
After graduating with his PhD, he returned to England and was a lecturer in the Department of Mathematics at Imperial College London from 1992 to 1994. He then moved into the financial industry, working at HSBC , Morgan Stanley and Deutsche Bank. In 2006, he returned to Harvard University where he joined the faculty. He taught statistics in the Harvard Faculty of Arts and Sciences, rising to become Professor of the Practice of Statistics in 2012. He also worked with the Harvard Management Company (HMC) which manages Harvard University's endowment and related financial assets. By 2014, he was managing director and head of public markets. In September 2014, he was announced as the next president and chief executive officer of the Harvard Management Company: he took up the post on 1 January 2015. He took medical leave from 23 May 2016, and stepped down as CEO on 27 July 2016.
In December 2021, Blyth was announced as the next Principal of Lady Margaret Hall, Oxford. He took up the post on 1 October 2022 and was installed during a service in the College Chapel on 7 October 2022.
Selected works
References
Living people
Year of birth missing (living people)
British mathematicians
British statisticians
Harvard University faculty
Principals of Lady Margaret Hall, Oxford
Alumni of Christ's College, Cambridge
Harvard University alumni
Academics of Imperial College London
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https://en.wikipedia.org/wiki/Yan%27s%20theorem
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In probability theory, Yan's theorem is a separation and existence result. It is of particular interest in financial mathematics where one uses it to prove the Kreps-Yan theorem.
The theorem was published by Jia-An Yan. It was proven for the L1 space and later generalized by Jean-Pascal Ansel to the case .
Yan's theorem
Notation:
is the closure of a set .
.
is the indicator function of .
is the conjugate index of .
Statement
Let be a probability space, and be the space of non-negative and bounded random variables. Further let be a convex subset and .
Then the following three conditions are equivalent:
For all with exists a constant , such that .
For all with exists a constant , such that .
There exists a random variable , such that almost surely and
.
Literature
Freddy Delbaen and Walter Schachermayer: The Mathematics of Arbitrage (2005). Springer Finance
References
Probability
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https://en.wikipedia.org/wiki/Thomas%20A.%20Garrity
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Thomas Anthony Garrity (born 1959) is an American mathematician. He teaches at Williams College, where he is the Webster Atwell Class of 1921 Professor of Mathematics.
Early life and education
Thomas Anthony Garrity born in 1959 in the United States. He completed his bachelor's degree in mathematics at the University of Texas at Austin in 1981. He attended Brown University for doctoral studies, completing a PhD in mathematics in 1986 under the supervision of professor William Fulton. Garrity's doctoral thesis was titled On Ample Vector Bundles and Negative Curvature.
Career
Garrity is currently a professor of mathematics at Williams College, where he has taught since 1989.
Bibliography
His notable books include:
Algebraic Geometry: A Problem Solving Approach
All the Mathematics You Missed
The United States of Mathematics Presidential Debate
References
External links
Website
Mathematics Genealogy Project
American mathematicians
1959 births
Living people
University of Texas at Austin alumni
Brown University alumni
Williams College faculty
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https://en.wikipedia.org/wiki/Dimension%20doubling%20theorem
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In probability theory, the dimension doubling theorems are two results about the Hausdorff dimension of an image of a Brownian motion. In their core both statements say, that the dimension of a set under a Brownian motion doubles almost surely.
The first result is due to Henry P. McKean jr and hence called McKean's theorem (1955). The second theorem is a refinement of McKean's result and called Kaufman's theorem (1969) since it was proven by Robert Kaufman.
Dimension doubling theorems
For a -dimensional Brownian motion and a set we define the image of under , i.e.
McKean's theorem
Let be a Brownian motion in dimension . Let , then
-almost surely.
Kaufman's theorem
Let be a Brownian motion in dimension . Then -almost surley, for any set , we have
Difference of the theorems
The difference of the theorems is the following: in McKean's result the -null sets, where the statement is not true, depends on the choice of . Kaufman's result on the other hand is true for all choices of simultaneously. This means Kaufman's theorem can also be applied to random sets .
Literature
References
Wiener process
Probability theorems
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https://en.wikipedia.org/wiki/2023%20Paysandu%20Sport%20Club%20season
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The 2023 season was Paysandu's 110th season in the club's history. Paysandu competed in the Campeonato Paraense, Copa Verde, Série C and Copa do Brasil.
Current squad
Statistics
Overall
{|class="wikitable"
|-
|Games played || 48 (14 Campeonato Paraense, 7 Copa Verde, 2 Copa do Brasil, 25 Série C)
|-
|Games won || 22 (9 Campeonato Paraense, 2 Copa Verde, 0 Copa do Brasil, 11 Série C)
|-
|Games drawn || 11 (3 Campeonato Paraense, 2 Copa Verde, 0 Copa do Brasil, 6 Série C)
|-
|Games lost || 15 (2 Campeonato Paraense, 3 Copa Verde, 2 Copa do Brasil, 8 Série C)
|-
|Goals scored || 59
|-
|Goals conceded || 57
|-
|Goal difference || +2
|-
|Best results || 4–1 (A) v Tuna Luso - Campeonato Paraense - 2023.04.16
|-
|Worst result || 0–5 (A) v Ypiranga - Série C - 2023.05.11
|-
|Top scorer || Mário Sérgio (22)
|-
Goalscorers
Managers performance
Official Competitions
Campeonato Paraense
First Stage
Quarter-finals
Semi-finals
Matches for third place
Record
Copa Verde
Round of 16
Quarter-finals
Semi-finals
Finals
Record
Copa do Brasil
Third round
Record
Série C
First stage
Results summary
First stage
Second stage
Record
References
External links
Paysandu Sport Club seasons
Paysandu
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https://en.wikipedia.org/wiki/Factorization%20algebra
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In mathematics and mathematical physics, a factorization algebra is an algebraic structure first introduced by Beilinson and Drinfel'd in an algebro-geometric setting as a reformulation of chiral algebras, and also studied in a more general setting by Costello to study quantum field theory.
Definition
Prefactorization algebras
A factorization algebra is a prefactorization algebra satisfying some properties, similar to sheafs being a presheaf with extra conditions.
If is a topological space, a prefactorization algebra of vector spaces on is an assignment of vector spaces to open sets of , along with the following conditions on the assignment:
For each inclusion , there's a linear map
There is a linear map for each finite collection of open sets with each and the pairwise disjoint.
The maps compose in the obvious way: for collections of opens , and an open satisfying and , the following diagram commutes.
So resembles a precosheaf, except the vector spaces are tensored rather than (direct-)summed.
The category of vector spaces can be replaced with any symmetric monoidal category.
Factorization algebras
To define factorization algebras, it is necessary to define a Weiss cover. For an open set, a collection of opens is a Weiss cover of if for any finite collection of points in , there is an open set such that .
Then a factorization algebra of vector spaces on is a prefactorization algebra of vector spaces on so that for every open and every Weiss cover of , the sequence
is exact. That is, is a factorization algebra if it is a cosheaf with respect to the Weiss topology.
A factorization algebra is multiplicative if, in addition, for each pair of disjoint opens , the structure map
is an isomorphism.
Algebro-geometric formulation
While this formulation is related to the one given above, the relation is not immediate.
Let be a smooth complex curve. A factorization algebra on consists of
A quasicoherent sheaf over for any finite set , with no non-zero local section supported at the union of all partial diagonals
Functorial isomorphisms of quasicoherent sheaves over for surjections .
(Factorization) Functorial isomorphisms of quasicoherent sheaves
over .
(Unit) Let and . A global section (the unit) with the property that for every local section (), the section of extends across the diagonal, and restricts to .
Example
Associative algebra
Any associative algebra can be realized as a prefactorization algebra on . To each open interval , assign . An arbitrary open is a disjoint union of countably many open intervals, , and then set . The structure maps simply come from the multiplication map on . Some care is needed for infinite tensor products, but for finitely many open intervals the picture is straightforward.
See also
Vertex algebra
References
Algebra
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https://en.wikipedia.org/wiki/List%20of%20functional%20urban%20areas%20in%20New%20Zealand
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This is a list of functional urban areas in New Zealand, as defined by Statistics New Zealand.
Under the Statistical standard for geographic areas 2023 and Statistical standard for geographic areas 2018, a functional urban area an urban area, rural settlement or rural statistical area where there is a major, large medium or small urban core with more than 5,000 residents. They may also have urban cores, satellite urban areas, rural settlements and rural hinterland ares where at least 40% of workers commute to the urban core or associated secondary urban core for work. Functional urban areas are based on linkages between where people live and where they work, shop, access health care, and take part in recreation activities.
As of 2023, there are 53 functional urban areas in New Zealand.
Metropolitan areas
Auckland (1,547,619) – Auckland, Hibiscus Coast, Pukekohe, Beachlands-Pine Harbour, Clarks Beach, Helensville, Kumeu-Huapai, Maraetai, Muriwai, Parakai, Patumāhoe, Pōkeno, Riverhead, Tuakau, Waimauku, Waiuku
Christchurch (470,814) – Christchurch, Kaiapoi, Rangiora, Rolleston, Diamond Harbour, Leeston, Lincoln, Lyttelton, Pegasus, Prebbleton, West Melton, Woodend
Wellington (414,033) – Wellington, Lower Hutt, Porirua, Upper Hutt, Featherston, Greytown
Hamilton (198,957) – Hamilton, Ngāruawāhia
Tauranga (156,096) – Tauranga, Ōmokoroa
Dunedin (125,007) – Dunedin, Mosgiel, Brighton, Waikouaiti
Large regional centres
Palmerston North (92,004) – Palmerston North, Ashhurst
Whangārei (84,117) – Whangārei, Hikurangi, Ngunguru, One Tree Point, Ruakākā
Nelson (79,998) – Nelson, Richmond, Brightwater, Hope, Māpua, Wakefield
New Plymouth (79,074) – New Plymouth, Inglewood, Ōakura, Waitara
Hastings (75,255) – Hastings, Havelock North, Clive
Rotorua (67,179) – Rotorua, Ngongotahā
Napier (64,767)
Invercargill (54,084)
Kāpiti Coast (46,683) – Paraparaumu, Waikanae, Paekākāriki
Whanganui (44,403)
Gisborne (39,447)
Medium regional centres
Timaru (38,559) – Timaru, Pleasant Point, Temuka
Masterton (32,043) – Masterton, Carterton
Blenheim (30,099)
Taupō (28,068)
Levin (25,803) – Levin, Shannon
Queenstown (24,693) – Queenstown, Arrowtown, Arthurs Point, Lake Hayes
Whakatāne (21,828) – Whakatāne, Ōhope
Ashburton (21,672)
Cambridge (21,261)
Te Awamutu (19,677) – Te Awamutu, Kihikihi, Pirongia
Feilding (17,727)
Oamaru (15,255)
Tokoroa (13,710)
Greymouth (11,604) – Greymouth, Runanga
Small regional centres (Population 5000+)
Warkworth (14,037) – Warkworth, Snells Beach
Wānaka (12,633) – Wānaka, Lake Hāwea
Kerikeri (12,699)
Kaitaia (12,291)
Hāwera (11,718)
Gore (10,053) – Gore, Mataura
Te Puke (9,918)
Motueka (9,501)
Thames (9,288)
Morrinsville (9,195)
Alexandra (8,526) – Alexandra, Clyde
Huntly (8,052)
Matamata (8,019)
Kawerau (7,419)
Cromwell (7,305)
Stratford (7,023)
Ōtaki (6,984) – Ōtaki, Ōtaki Beach
Dannevirke (6,360)
Marton (5,676)
Whitianga (5,622)
Katikati (5,442)
Waihi (5,403)
See also
List of statistical areas in New Zealand
List of cities in New Zealan
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https://en.wikipedia.org/wiki/%C3%89mery%20topology
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In martingale theory, Émery topology is a topology on the space of semimartingales. The topology is used in financial mathematics. The class of stochastic integrals with general predictable integrands coincides with the closure of the set of all simple integrals.
The topology was introduced in 1979 by the french mathematician Michel Émery.
Definition
Let be a filtred probability space, where the filtration satisfies the usual conditions and . Let be the space of real semimartingales and the space of simple predictable processes with .
We define the quasinorm
Then with the metric is a complete space and the induced topology is called Émery topology.
References
probability
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https://en.wikipedia.org/wiki/Ljung%20and%20Annelund
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Ljung and Annelund () is a locality situated in Herrljunga Municipality, Västra Götaland County, Sweden. It had 1,215 inhabitants in 2020. The locality was formed by Statistics Sweden from the separate localities of Ljung and Annelund between 2010 and 2015.
The locality is home to a train station named Ljung on the Älvsborg Line.
Sports
The following sports clubs are located in Ljung and Annelund:
Annelunds IF
References
Populated places in Västra Götaland County
Populated places in Herrljunga Municipality
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https://en.wikipedia.org/wiki/Matias%20D.%20Cattaneo
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Matias Damian Cattaneo (born May 16, 1978) is a Professor of Operations Research and Financial Engineering at Princeton University. His research focuses on statistics, econometrics, data science and decision science, with applications to program evaluation and causal inference. He is best known for his work on Regression Discontinuity Designs.
Cattaneo is a co-editor of Econometric Theory and an associate editor with the Journal of the American Statistical Association, Econometrica, and Operations Research.
Education and academic career
Cattaneo received his Licentiate from UBA in 2000, and his Ph.D. from the University of California, Berkeley in 2008, under supervision of James L. Powell. From 2008 to 2019, Cattaneo taught at the University of Michigan. In 2019, Cattaneo joined Princeton University as a Professor in the Department of Operations Research and Financial Engineering.
Honors and awards
Fellow, American Statistical Association, 2023.
Fellow, Institute of Mathematical Statistics, 2022.
Fellow, International Association for Applied Econometrics, 2022.
Stata Journal Editors’ Prize, 2019.
Publications
References
External links
Cattaneo's faculty page at Princeton University
Cattaneo's Google Scholar profile
1978 births
Living people
Princeton University faculty
University of Buenos Aires alumni
University of California, Berkeley alumni
Operations researchers
Econometricians
Scientists from Buenos Aires
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
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https://en.wikipedia.org/wiki/Martin%20Z.%20Bazant
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Martin Zdenek Bazant is an American chemical engineer, mathematician, physicist, and academic. He is the E. G. Roos (1944) Professor of Chemical Engineering and Mathematics at the Massachusetts Institute of Technology (MIT). From 2016 to 2020, he served as executive officer of the department of chemical engineering.
Bazant is well recognized for his teaching and research in electrochemistry, electrokinetics, transport phenomena, and applied mathematics. He was elected President of the International Electrokinetics Society and Fellow of the American Physical Society, the International Society of Electrochemistry, and the Royal Society of Chemistry. He is also the chief scientific advisor of Saint-Gobain Research North America and chief scientist and co-founder of Lithios.
Education
Bazant earned a B.S. in mathematics and physics in 1992 and an M.S. in applied mathematics in 1993 from the University of Arizona. Subsequently, he undertook research in physics for a Ph.D. at Harvard University, under the supervision of E. Kaxiras, and graduated in 1997. His dissertation was titled, Interatomic Forces in Covalent Solids. He then spent a year at Harvard as a postdoctoral fellow in engineering and applied sciences under the guidance of Howard A. Stone.
Career
Bazant began his academic career in 1998 as an instructor of applied mathematics at Massachusetts Institute of Technology. He was appointed as assistant professor of mathematics in 2000 and promoted to associate professor in 2003. He joined the department of chemical engineering in 2009 and built an experimental laboratory to compliment his theoretical research. He was promoted to full professor in 2012 and named the inaugural Edwin G. Roos (1944) Chair Professor of Chemical Engineering in 2015. He has held visiting faculty positions as the Paris Sciences chair at ESPCI Paris (2001, 2007-2008) and as the Global Climate and Energy Project chair at Stanford University (2015-2016).
Bazant was the executive officer of the department of chemical engineering at MIT from 2016 to 2020 and then created the new role of digital learning officer. He has co-founded multiple research centers and serves as director of D3BATT: Data-Driven Design of Rechargeable Batteries and of the Center for Battery Sustainability.
After organizing the 13th International Electrokinetics Symposium (ELKIN) in 2019, he co-founded the International Electrokinetics Society and became its first president. He served as associate editor of SIAM Journal on Applied Mathematics from 2011 to 2021. He has consulted for Saint-Gobain Research North America on ceramics and plastics since 2008 and became chief scientific advisor in 2013.
Bazant co-founded two MIT startup companies: ICEO in 2005, which developed induced-charge electro-osmotic microfluidic devices, and Lithios in 2022, developing electrochemical lithium extraction.
Teaching
Bazant has created many open educational resources, including OpenCourseWare for Random Walks and Diff
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https://en.wikipedia.org/wiki/Eustachy%20%C5%BByli%C5%84ski
|
Eustachy Karol Żyliński (19 September 1889 – 4 July 1954) was a Polish mathematician and university professor known for his work on number theory, algebra, and logic. He was a member of the Lwów School of Mathematics.
Biography
Early life and career (1889–1919)
Żyliński was born in to a landless noble family. In 1907 he graduated with a gold medal from the gymnasium in Kiev, and in 1911 with a first-degree diploma from the Faculty of Physics and Mathematics of the University of Imperial Saint Vladimir University in Kiev, where he then worked from 1912to 1914, while doing internships in Göttingen, Cambridge and Marburg. In 1914 he obtained a master's degree (equivalent to today's PhD).
In 1916 he was drafted into the Imperial Russian army. He graduated from a military-engineering school in Kiev and an electrical engineering school in St. Petersburg in 1917 put himself at the disposal of the 1st Polish Corps. From 1918, as an associate professor, he lectured at the Polish University College and the Higher Technical Institute in Kiev. In 1919 he stayed in Warsaw, performing military service as an officer of the Polish Army.
Lwów School of Mathematics (1919–1945)
From October 1919, he was associate professor at the Jan Kazimierz University in Lwów and in July 1922 Żyliński was appointed full professor at University in Lwów, and then head of the Department of Mathematics A at the Faculty of Philosophy. In 1925, he proved that "there are exactly two binary functors (namely, binegation and the Sheffer stroke) each of which is sufficient for defining all other unary and binary functors of classical propositional logic." His colleagues included mathematicians such as Stefan Banach and Hugo Steinhaus. 1929 he was dean of the Faculty of Mathematics and Natural Sciences of the Jagiellonian University and was the promoter of Władysław Orlicz's doctoral dissertation.
During the Soviet occupation of Lwów he worked as the head of the Algebra Department at the University of Lwów, and during the German occupation (1941–1944) he took part in clandestine teaching at the Jagiellonian University.
Postwar career (1945–1954)
After Lwów was reoccupied by the Red Army, he started working at the university. From March 15, 1945, Żyliński was a member of the Union of Polish Patriots in Lviv but was removed from the union in 1946. After the deportation from of Poles Lviv, he initially settled in Łódź. At that time, he worked at the Ministry of Foreign Affairs, and was also nominated as consul general in Kiev, but did not assume this office. In 1947 he moved to Gliwice, where in the years 1946–1951 he was the head of the Department of Mathematics at the Faculty of Engineering and Construction of the Silesian University of Technology. In 1951 he retired and returned to Lodz. Żyliński died there in 1954 of a cerebral hemorrhage.
References
Polish mathematicians
Polish scientists
Lwów School of Mathematics
Polish academics
Members of the Lwów Scientific Society
20th-c
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https://en.wikipedia.org/wiki/Andr%C3%A1s%20M%C3%A1t%C3%A9%20G%C3%B6m%C3%B6ri
|
András Máté Gömöri (born August 29, 1992) is an Hungarian actor, bodybuilder and powerlifter
Personal life
András Máté Gömöri was only 10 years old when he lost his mother, a mathematics teacher, and 16 when his father, an army officer and engineer, passed away. He has two brothers, Péter and Gergely, who are 16 and 12 years his elders respectively. He moved to Kisgyőr with his father, who at the time was living on disability benefits due to heart disease. This is where he spent his childhood, and where his father met Gömöri’s future stepmother, Judit. He moved to a dormitory in Miskolc when he began his studies in Bláthy Ottó Electrical Engineering Vocational Secondary School (Bláthy Ottó Villamosipari Technikum). He spent a lot of time with his elder brother who lived in Miskolc, and later with his other brother, who lived in Pest.
He married Lilla Polyák in the summer of 2018.
Acting career
He was still a child when he got his first role in 2004 in the National Theatre of Miskolc.
He began his studies in the Pesti Magyar Academy of Drama at the Magyar Theatre — the successor of the Nemzeti Stúdió (Academy of the National Theatre) — in 2011, but his attraction gradually shifted from plays to musical theatre. In 2012 he applied for an acting student spot in the Pesti Broadway Studio at the Budapest Operetta Theater, but was offered the main role of Rudolph in the musical Elisabeth instead. From then on, he has acted in musicals such as Romeo and Juliet, Fame, Gone with the Wind, Flowers for Algernon, The Hunchback of Notre Dame, Singin' in the Rain, and Jekyll and Hyde.
In October 2018 he also debuted in prose in the drama The Night of the Tribades in the Pinceszínház located in Budapest.
Between 2017 and 2020 he completed the drama instructor and actor program of the University of Theatre and Film Arts in Budapest. His thesis explored the portrayal of negative characters.
Since 2014 he has appeared in various television series and the Hungarian movie Budapest Noir. For six months in 2018 he hosted the morning show on the television channel FEM3, and from January 2020 he has been hosting a lifestyle show at the channel TV2. He has also been involved with several events and galas.
In 2019 he was nominated for Playboy’s (Marquard Media Hungary) Man of the Year award in the performance arts category.
Sports career
At school, in addition to playing volleyball and football, he did athletics and participated in triathlons. Later on, he turned to archery, and started competing in 2004. It was around 2010 that he was introduced to gym workouts, which started to play a significant role in his life after moving to Budapest. In 2012, he was already an avid bodybuilder, swimmer and runner. In 2014 he was presented with the Fittest Actor of the Year award at the third Fitbalance Award Gala, which he won again in 2019.
Bodybuilding career
In his first natural bodybuilding competition, which was held by the INBA (International Natural Bodybuilding
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https://en.wikipedia.org/wiki/Koml%C3%B3s%27%20theorem
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Komlós' theorem is a theorem from probability theory and mathematical analysis about the Cesàro convergence of a subsequence of random variables (or functions) and their subsequences to an integrable random variable (or function). It's also an existence theorem for an integrable random variable (or function). There exist a probabilistic and an analytical version for finite measure spaces.
The theorem was proven in 1967 by János Komlós. There exists also a generalization from 1970 for general measure spaces by Srishti D. Chatterji.
Komlós' theorem
Probabilistic version
Let be a probability space and be a sequence of real-valued random variables defined on this space with
Then there exists a random variable and a subsequence , such that for every arbitrary subsequence when then
-almost surely.
Analytic version
Let be a finite measure space and be a sequence of real-valued functions in and . Then there exists a function and a subsequence such that for every arbitrary subsequence
if then
-almost everywhere.
Explanations
So the theorem says, that the sequence and all its subsequences converge in Césaro.
Literature
Kabanov, Yuri & Pergamenshchikov, Sergei. (2003). Two-scale stochastic systems. Asymptotic analysis and control. 10.1007/978-3-662-13242-5. Page 250.
References
Probability theorems
Theorems in analysis
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https://en.wikipedia.org/wiki/John%20H.%20C.%20Coffin
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John Huntington Crane Coffin (September 14, 1815 – January 8, 1890) was an American astronomer and educator. He was a professor of mathematics with the United States Navy and the United States Naval Academy. During the American Civil War, Coffin was the head of instruction at the Naval Academy. He served as the superintendent of American Ephemeris and Nautical Almanac from 1866 to 1877.
Early life
John Huntington Crane Coffin was born on September 14, 1815, in Wiscasset, Maine, to Mary (née Porter) and Nathanael Coffin. His mother was the niece of Rufus King, U.S. minister to Great Britain. He graduated Bowdoin College in 1834 with a Bachelor of Arts. In 1834, Coffin went on a sea voyage with his uncle Captain King Porter and learned navigation and seamanship. He graduated with a Master of Arts from Bowdoin College in 1837. His sister married William Smyth, professor at Bowdoin College.
Career
In 1836, Coffin became a professor of mathematics with the United States Navy. He taught midshipmen at sea and on land at the Norfolk Navy Yard. During this time, Coffin also served on the USS Vandalia, the USS Constellation and on surveys in Florida. Coffin was retained as a senior professor in 1848 when the corps was reduced.
Coffin was stationed at the United States Naval Observatory in Washington, D.C., starting in January 1845. He was in charge of the mural circle and remained there until 1853, after suffering an eye disease.
In 1853, Coffin became the head of the mathematics department at the United States Naval Academy. In 1860, Coffin also became head of the navigation and astronomy department, replacing the retiring William Chauvenet. Following the outbreak of the Civil War, the Naval Academy moved to Newport, Rhode Island, and Coffin was the head of all departments during that period. His textbook "Navigation and Nautical Almanac" was used for over thirty years in instruction at the Naval Academy.
Coffin served as the superintendent of the American Ephemeris and Nautical Almanac starting on May 1, 1866. In 1867, he moved from Cambridge, Massachusetts, to Washington, D.C., when the almanac moved its place of publication. He retired on September 15, 1877.
Coffin was elected as a member of the American Academy of Arts and Sciences in 1851. He became an associate fellow. He was also a member of the American Philosophical Society. In 1863, Coffin was appointed as one of the first members of the National Academy of Sciences by the U.S. Congress.
Personal life
Coffin married Louisa Harrison of Maryland in the spring of 1845. They had two sons and three daughters, including Helen Olcott Paine, Richard Harrison and Louisa Harrison. His wife died in 1871.
Coffin died on January 8, 1890, in Washington, D.C. He was buried at Oak Hill Cemetery in Washington, D.C.
Selected publications
"Observations with the Mural Circle at the United States Naval Observatory, with Explanations, Formulas, Tables, and Discussions, 1845-1849"
"Personal Errors in Obser
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https://en.wikipedia.org/wiki/Weronika%20Lizakowska
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Weronika Lizakowska (born 2 November 1998) is a Polish track and field athlete who competes as a middle-distance runner.
Early life
Lizakowdska graduated with a bachelor's degree in mathematics from the University of Gdańsk.
Career
Junior career
In 2015, Lizakowdska took first place in the 1500m run at the 21st National Youth Olympics held in Łódź. In 2016, she competed at the 2016 European Cross Country Championships that took place in Chia, Sardinia, Italy. She was selected for the Polish team to compete in the 1500m at the European U20 Championships held in Grosseto, Italy in 2017. She won gold over 3km in 2018 at the Polish Academic Championships.
Senior career
Competing for the Kościerzyna Student Sports Club, Remus Kościerzyna, she finished third at the Polish national championships in 2022 in the 10,000m. In February 2023, she finished third in the Polish indoor national championships in Ostrava, running a new personal best. Subsequently, she was selected for the Polish team to compete at the European Athletics Indoor Championships held in Istanbul. In August 2023, she finished fourth in the 1500 metres at the University Games, held in Chengdu, China.
In October 2023, she finished thirteenth at the 2023 World Athletics Road Running Championships in Riga, running 4:37.04 in the mile road race.
Personal life
Alongside her running career, she works part-time as a private mathematics teacher and by March 2023 was undertaking a master's degree in Pedagogy.
References
External links
1998 births
Living people
Polish female middle-distance runners
21st-century Polish sportswomen
University of Gdańsk alumni
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https://en.wikipedia.org/wiki/Resilience%20%28mathematics%29
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In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady state. It is a measure of the stability and robustness of a system in the face of changes or disturbances. If a system is not resilient enough, it is more susceptible to perturbations and can more easily undergo a critical transition. A common analogy used to explain the concept of resilience of an equilibrium is one of a ball in a valley. A resilient steady state corresponds to a ball in a deep valley, so any push or perturbation will very quickly lead the ball to return to the resting point where it started. On the other hand, a less resilient steady state corresponds to a ball in a shallow valley, so the ball will take a much longer time to return to the equilibrium after a perturbation.
The concept of resilience is particularly useful in systems that exhibit tipping points, whose study has a long history that can be traced back to catastrophe theory. While this theory was initially overhyped and fell out of favor, its mathematical foundation remains strong and is now recognized as relevant to many different systems.
History
In 1973, Canadian ecologist C. S. Holling proposed a definition of resilience in the context of ecological systems. According to Holling, resilience is "a measure of the persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between populations or state variables". Holling distinguished two types of resilience: engineering resilience and ecological resilience. Engineering resilience refers to the ability of a system to return to its original state after a disturbance, such as a bridge that can be repaired after an earthquake. Ecological resilience, on the other hand, refers to the ability of a system to maintain its identity and function despite a disturbance, such as a forest that can regenerate after a wildfire while maintaining its biodiversity and ecosystem services. With time, the once well-defined and unambiguous concept of resilience has experienced a gradual erosion of its clarity, becoming more vague and closer to an umbrella term than a specific concrete measure.
Definition
Mathematically, resilience can be approximated by the inverse of the return time to an equilibrium given by
where is the maximum eigenvalue of matrix .
The largest this value is, the faster a system returns to the original stable steady state, or in other words, the faster the perturbations decay.
Applications and examples
In ecology, resilience might refer to the ability of the ecosystem to recover from disturbances such as fires, droughts, or the introduction of invasive species. A resilient ecosystem would be one that is able to adapt to these changes and continue functioning, while a less resilient ecosystem might experience irreversible damage or collapse. The exact definition of resilience has remained vague for pra
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https://en.wikipedia.org/wiki/Masovian%20Regional
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Masovian Regional is statistical area of the Nomenclature of Territorial Units for Statistics, level NUTS 2. It includes all of Masovian Voivodeship excluding Warsaw metropolitan area.
Economy
The Gross domestic product (GDP) of the region was 30.2 billion € in 2021, accounting for only around 5% of Polish economic output. GDP per capita was around €12,900 .
References
NUTS 2 statistical regions of the European Union
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https://en.wikipedia.org/wiki/2023%20ICC%20Women%27s%20T20%20World%20Cup%20statistics
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This is a list of statistics for the 2023 ICC Women's T20 World Cup.
Team statistics
Highest team totals
Largest winning margin
By runs
By wickets
By balls remaining
Lowest team totals
Notes: This is a list of completed innings only; low totals in matches with reduced overs are omitted except when the team was all out. Successful run chases in the second innings are not counted.
Smallest winning margin
By runs
Individual statistics
Batting
Most runs
Highest scores
Most boundaries
Bowling
Most wickets
Best bowling figures
Fielding
Most dismissals
This is a list of wicket-keepers with the most dismissals in the tournament.
Most catches
This is a list of the fielders who took the most catches in the tournament.
Other statistics
Highest partnerships
The following tables are lists of the highest partnerships for the tournament.
References
External links
Official 2023 World Cup site
Cricket World Cup at icc-cricket.com
statistics
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https://en.wikipedia.org/wiki/Curtis%20Stewart%20%28violinist%29
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Curtis Stewart is an American violinist and composer.
Life and career
Stewart graduated from the Eastman School of Music and University of Rochester with a degree in Mathematics and Violin Performance, and Lehman college with a masters in music education. He has soloed at Carnegie Hall, Lincoln Center, Kennedy Center, and the 2022 GRAMMY Awards, among many others.
Stewart founded the string ensemble PUBLIQuartet in 2010, was finalist at the Concert Artists Guild Competition in 2013. He taught music at the Fiorello H. LaGuardia High School, and the Juilliard School. He received the Centennial Award from the Eastman School of Music in 2022. He is currently the artistic director of the American Composers Orchestra.
Selected discography
Of Love (2023)
Of Power (2021)
Of Colors (2016)
Awards and nominations
References
External links
Living people
Year of birth missing (living people)
American violinists
21st-century violinists
American classical violinists
20th-century classical composers
American male classical composers
Eastman School of Music alumni
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https://en.wikipedia.org/wiki/Buffered%20probability%20of%20exceedance
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Buffered probability of exceedance (bPOE) is a function of a random variable used in statistics and risk management, including financial risk. The bPOE is the probability of a tail with known mean value . The figure shows the bPOE at threshold (marked in red) as the blue shaded area. Therefore, by definition, bPOE is equal to one minus the confidence level at which the Conditional Value at Risk (CVaR) is equal to . bPOE is similar to the probability of exceedance of the threshold , but the tail is defined by its mean rather than the lowest point of the tail.
bPOE has its origins in the concept of buffered probability of failure (bPOF), developed by R. Tyrrell Rockafellar and Johannes Royset to measure failure risk. It was further developed and defined as the inverse CVaR by Matthew Norton, Stan Uryasev, and Alexander Mafusalov. Similar to CVaR, bPOE considers not only the probability that outcomes (losses) exceed the threshold , but also the magnitude of these outcomes (losses).
Formal definition
There are two slightly different definitions of bPOE, so called Lower bPOE and Upper bPOE.
For a random variable, the Lower bPOE, , at threshold is given by:
where .
bPOE can be expressed as the inverse function of CVaR:
,
where is the CVaR of with confidence level .
References
Statistics
Risk management
Extreme value data
Reliability analysis
Stochastic processes
Survival analysis
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https://en.wikipedia.org/wiki/Tuza%27s%20conjecture
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Tuza's conjecture is an unsolved problem in graph theory, a branch of mathematics, concerning triangles in undirected graphs.
Statement
In any graph , one can define two quantities and based on the triangles in . The quantity is the "triangle packing number", the largest number of edge-disjoint triangles that it is possible to find in . It can be computed in polynomial time as a special case of the matroid parity problem. The quantity is the size of the smallest "triangle-hitting set", a set of edges that touches at least one edge from each triangle.
Clearly, . For the first inequality, , any triangle-hitting set must include at least one edge from each triangle of the optimal packing, and none of these edges can be shared between two or more of these triangles because the triangles are disjoint. For the second inequality, , one can construct a triangle-hitting set of size by choosing all edges of the triangles of an optimal packing. This must hit all triangles in , even the ones not in the packing, because otherwise the packing could be made larger by adding any unhit triangle.
Tuza's conjecture asserts that the second inequality is not tight, and can be replaced by . That is, according to this unproven conjecture, every undirected graph has a triangle-hitting set whose size is at most twice the number of triangles in an optimal packing.
History and partial results
Zsolt Tuza formulated Tuza's conjecture in 1981. If true, it would be best possible: there are infinitely many graphs for which , including all of the block graphs whose blocks are cliques of 2, 4, or 5 vertices.
The conjecture is known to hold for planar graphs, and more generally for sparse graphs of degeneracy at most six. (Planar graphs have degeneracy at most five.) It is also known to hold for graphs of treewidth at most six, for threshold graphs, for sufficiently dense graphs, and for chordal graphs that contain a large clique. For random graphs in the Erdős–Rényi–Gilbert model, it is true with high probability.
Although Tuza's conjecture remains unproven, the bound can be improved, for all graphs, to .
See also
Mantel's theorem
Triangle removal lemma
References
External links
Unsolved problems in graph theory
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https://en.wikipedia.org/wiki/Matrix%20F-distribution
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In statistics, the matrix F distribution (or matrix variate F distribution) is a matrix variate generalization of the F distribution which is defined on real-valued positive-definite matrices. In Bayesian statistics it can be used as the semi conjugate prior for the covariance matrix or precision matrix of multivariate normal distributions, and related distributions.
Density
The probability density function of the matrix distribution is:
where and are positive definite matrices, is the determinant, Γp(·) is the multivariate gamma function, and is the p × p identity matrix.
Properties
Construction of the distribution
The standard matrix F distribution, with an identity scale matrix , was originally derived by. When considering independent distributions,
and , and define , then .
If and , then, after integrating out , has a matrix F-distribution, i.e.,
This construction is useful to construct a semi-conjugate prior for a covariance matrix.
If and , then, after integrating out , has a matrix F-distribution, i.e.,This construction is useful to construct a semi-conjugate prior for a precision matrix.
Marginal distributions from a matrix F distributed matrix
Suppose has a matrix F distribution. Partition the matrices and conformably with each other
where and are matrices, then we have .
Moments
Let .
The mean is given by:
The (co)variance of elements of are given by:
Related distributions
The matrix F-distribution has also been termed the multivariate beta II distribution. See also, for a univariate version.
A univariate version of the matrix F distribution is the F-distribution. With (i.e. univariate) and , and , the probability density function of the matrix F distribution becomes the univariate (unscaled) F distribution:
In the univariate case, with and , and when setting , then follows a half t distribution with scale parameter and degrees of freedom . The half t distribution is a common prior for standard deviations
See also
Inverse matrix gamma distribution
Matrix normal distribution
Wishart distribution
Inverse Wishart distribution
Complex inverse Wishart distribution
References
Analysis of variance
Multivariate continuous distributions
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https://en.wikipedia.org/wiki/Sophie%20Achard
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Sophie Achard (born 1977) is a French statistician and neuroscientist whose research concerns the statistics of the pattern of connectivity in the brain. She is a director of research for the French National Centre for Scientific Research (CNRS), affiliated with the French Institute for Research in Computer Science and Automation (Inria) laboratory at Grenoble Alpes University.
Education and career
Achard studied mathematics, statistics, and numerical analysis at Jean Monnet University, earning a bachelor's degree in 1999. She earned a master's degree through research on the statistics of mixture models at Joseph Fourier University in Grenoble 2000, and completed a Ph.D. there in 2003. Her doctoral dissertation, Mesures de dépendance pour la séparation aveugle de sources : application aux mélanges post non linéaires, was directed by Dinh-Tuan Pham and Christian Jutten.
After postdoctoral research in the Brain Mapping Unit at the University of Cambridge with Edward Bullmore from 2004 to 2007, she returned to Grenoble as a CNRS researcher in 2008, and was promoted to director of research in 2017.
Recognition
Achard received the CNRS Silver Medal in 2023.
References
External links
Home page
1977 births
Living people
French statisticians
Women statisticians
French neuroscientists
French women neuroscientists
Jean Monnet University alumni
Research directors of the French National Centre for Scientific Research
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https://en.wikipedia.org/wiki/Bogomolov%E2%80%93Sommese%20vanishing%20theorem
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In algebraic geometry, the Bogomolov–Sommese vanishing theorem is a result related to the Kodaira–Itaka dimension. It is named after Fedor Bogomolov and Andrew Sommese. Its statement has differing versions:
This result is equivalent to the statement that:
for every complex projective snc pair and every invertible sheaf
with .
Therefore, this theorem is called the vanishing theorem.
See also
Bogomolov–Miyaoka–Yau inequality
Vanishing theorem (disambiguation)
Notes
References
Further reading
Theorems in algebraic geometry
Theorems in complex geometry
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https://en.wikipedia.org/wiki/Dividing%20a%20square%20into%20similar%20rectangles
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Dividing a square into similar rectangles (or, equivalently, tiling a square with similar rectangles) is a problem in mathematics.
Three rectangles
There is only one way (up to rotation and reflection) to divide a square into two similar rectangles.
However, there are three distinct ways of partitioning a square into three similar rectangles:
The trivial solution given by three congruent rectangles with aspect ratio 3:1.
The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ratio 3:2.
The solution in which the three rectangles are all of different sizes and where they have aspect ratio ρ2, where ρ is the plastic number.
The fact that a rectangle of aspect ratio ρ2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ρ2 related to the Routh–Hurwitz theorem: all of its conjugates have positive real part.
Generalization to n rectangles
In 2022, the mathematician John Baez brought the problem of generalizing this problem to n rectangles to the attention of the Mathstodon online mathematics community.
The problem has two parts: what aspect ratios are possible, and how many different solutions are there for a given n. Frieling and Rinne had previously published a result in 1994 that states that the aspect ratio of rectangles in these dissections must be an algebraic number and that each of its conjugates must have a positive real part. However, their proof was not a constructive proof.
Numerous participants have attacked the problem of finding individual dissections using exhaustive computer search of possible solutions. One approach is to exhaustively enumerate possible coarse-grained placements of rectangles, then convert these to candidate topologies of connected rectangles. Given the topology of a potential solution, the determination of the rectangle's aspect ratio can then trivially be expressed as a set of simultaneous equations, thus either determining the solution exactly, or eliminating it from possibility.
, the following results have been obtained for the number of distinct valid dissections for different values of n:
See also
Squaring the square
References
External links
Python code for dissection of a square into n similar rectangles via "guillotine cuts" by Rahul Narain
Geometry
Mathematical problems
Recreational mathematics
Tessellation
Geometric dissection
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https://en.wikipedia.org/wiki/List%20of%20FC%20Shakhtar%20Donetsk%20managers
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Below is a list of the head coaches of the Shakhtar football club (Donetsk, Ukraine), their statistics and achievements in the club.
"Miner" ("Coal Miners" (1936), "Stakhanovets" (1936–46 years), "Shakhtar" (since 1946)) is a Ukrainian football club from the city of Donetsk playing in the Premier League of Ukraine. The first and only among Ukrainian clubs to win the UEFA Cup. Winner of the USSR Super Cup, four-time winner of the USSR Cup, thirteen-time champion of Ukraine, thirteen-time winner of the Ukrainian Cup, nine-time winner of the Ukrainian Super Cup.
The first official match in the Soviet Top League "Coal miners" played in Kazan against the local team "Dynamo" and lost with a score of 1:4. The first coach of the club was Nikolay Grigoryevich Naumov. The club has been led by 34 head coaches throughout its history, he last of which, on June 14, 2022, was the Croatian coach – Igor Jovićević.
Most matches (574 or according to other information 573) the club spent under the coach - Mircea Lucescu, who headed Shakhtar Donetsk from 2004 to 2016. Lucescu also ranks first in the number of victories - 389.
List of coaches
Information correct as of April 3, 2023. Only official matches are included in the statistics.
References
External links
Official website
List of head coaches (Segodnya.ua)
List of head coaches (Footballfacts.ru)
Football clubs in Donetsk
Lists of football managers in Ukraine by club
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https://en.wikipedia.org/wiki/2023%20New%20South%20Wales%20Waratahs%20season
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Coaching and squad
The squad for the 2023 Super Rugby Pacific season is:
Season fixture
Statistics
(As of round five; 24 March 2023)
Notes
References
External links
Waratahs Official website
Australia Super Rugby website
SANZAR website
2023
2023 in Australian rugby union
Waratahs
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https://en.wikipedia.org/wiki/Sofascore
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Sofascore is an application for following sports statistics and results. The app is owned and developed by SofaIT from Zagreb, Croatia. In 2020, the app had 20 million users. It covers 20 different sports and around 11,000 different leagues and tournaments, and is available in more than 30 different languages.
The app founders are Ivan Bešlić and Zlatko Hrkać, who previously worked on other Internet projects during the era of "blogs and forums". They started the app for collecting sports results in 2010. After noticing large traffic on their site, Google invited them to Dublin in 2011. That year they formed a small office for programme developers. In 2012, just before the UEFA Euro 2012, they changed the app's name to Sofascore in order to develop a brand.
They developed a system of assessment of athletes' performances which differentiated them from other similar existing apps and gave them leverage in the market. The system also enables the tracking and assessment of young players from lower-tier leagues, that otherwise wouldn't get attention.
Most users are from footballing countries like Germany, Italy, France, and the United Kingdom. The app is also much used in South America and Africa. In Africa, a special version of the app is available for low internet connectivity.
As of 2023, Luka Modrić is a brand ambassador of Sofascore
Footnotes
References
Internet properties established in 2010
2010 establishments in Croatia
Croatian sport websites
iOS software
Companies based in Zagreb
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https://en.wikipedia.org/wiki/Ville%27s%20inequality
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In probability theory, Ville's inequality provides an upper bound on the probability that a supermartingale exceeds a certain value. The inequality is named after Jean Ville, who proved it in 1939.
The inequality has applications in statistical testing.
Statement
Let be a non-negative supermartingale. Then, for any real number
The inequality is a generalization of Markov's inequality.
References
Probabilistic inequalities
Martingale theory
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https://en.wikipedia.org/wiki/Bikash%20Debbarma
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Bikash Debbarma is an Indian politician from Tripura. He is currently serving as Minister of Tribal Welfare, Handloom, Handicrafts and Sericulture and Statistics in Government of Tripura under Second Saha Ministry.
Political career
He became the MLA from Krishnapur Assembly constituency by defeating Mahendra Debbarma of Tipra Motha Party by a margin of 2,638 votes in 2023. He was also a BJP's Janajati Morcha President in Tripura.
References
Living people
Tripura MLAs 2023–2028
State cabinet ministers of Tripura
Bharatiya Janata Party politicians from Tripura
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Wu%E2%80%93Yang%20dictionary
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In topology and high energy physics, the Wu–Yang dictionary refers to the mathematical identification that allows back-and-forth translation between the concepts of gauge theory and those of differential geometry. It was devised by Tai Tsun Wu and C. N. Yang in 1975 when studying the relation between electromagnetism and fiber bundle theory. This dictionary has been credited as bringing mathematics and theoretical physics closer together.
A crucial example of the success of the dictionary is that it allowed the understanding of monopole quantization in terms of Hopf fibrations.
History
In 1931, Paul Dirac published his quantization conditions for magnetic monopoles. Unaware of any connection, the same year, mathematician Heinz Hopf independently proposed his epynomous fibration of a 3-sphere.
Equivalences between fiber bundle theory and gauge theory were hinted at the end of the 1960s. In 1967, mathematician Andrzej Trautman started a series of lectures aimed at physicists and mathematicians at King's College London regarding these connections.
Theoretical physicists Tsun Wu and C. N. Yang working in Stony Brook University, published a paper in 1975 on the mathematical framework of electromagnetism and the Aharonov–Bohm effect in terms of fiber bundles. A year later, mathematician Isadore Singer came to visit and brought a copy back to the University of Oxford. Singer showed the paper to Michael Atiyah and other mathematicians, sparking a close collaboration between physicists and mathematicians.
Yang also recounts a conversation that he had with one of the mathematicians that founded fiber bundle theory, Shiing-Shen Chern:
Using these equivalences, Trautman demonstrated an equivalence between Dirac quantization condition and Hopf fibration in 1977. Mathematician Jim Simons discussing this equivalence with Yang expressed that “Dirac had discovered trivial and nontrivial bundles before mathematicians.”
Description
Summarized version
The Wu-Yang dictionary relates terms in particle physics with terms in mathematics, specifically fiber bundle theory. Many versions and generalization of the dictionary exist. Here is an example of a dictionary, which puts each physics term next to its mathematical analogue:
Original version for electromagnetism
Wu and Yang considered the description of an electron traveling around a cylinder in the presence of a magnetic field inside the cylinder (outside the cylinder the field vanishes i.e. ). According to the Aharonov–Bohm effect, the interference patterns shift by a factor , where is the magnetic flux and is the magnetic flux quantum. For two different fluxes a and b, the results are identical if , where is an integer. We define the operator as the operator that brings the electron wave function from one configuration to the other . For an electron that takes a path from point P to point Q, we define the phase factor as
,
where is the electromagnetic four-potential. For the case of a SU2 gauge f
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https://en.wikipedia.org/wiki/Sectorial%20operator
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In mathematics, more precisely in operator theory, a sectorial operator is a linear operator on a Banach space, whose spectrum in an open sector in the complex plane and whose resolvent is uniformly bounded from above outside any larger sector. Such operators might be unbounded.
Sectorial operators have applications in the theory of elliptic and parabolic partial differential equations.
Sectorial operator
Let be a Banach space. Let be a (not necessarily bounded) linear operator on and its spectrum.
For the angle , we define the open sector
,
and set if .
Now, fix an angle .
The operator is called sectorial with angle if
and if
.
for every larger angle . The set of sectorial operators with angle is denoted by .
Remarks
If , then is open and symmetric over the positive real axis with angular aperture .
Bibliography
References
Functional analysis
Operator theory
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https://en.wikipedia.org/wiki/Stochastic%20analysis%20on%20manifolds
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In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore a synthesis of stochastic analysis and differential geometry.
The connection between analysis and stochastic processes stems from the fundamental relation that the infinitesimal generator of a continuous strong Markov process is a second-order elliptic operator. The infinitesimal generator of Brownian motion is the Laplace operator and the transition probability density of Brownian motion is the minimal heat kernel of the heat equation. Interpreting the paths of Brownian motion as characteristic curves of the operator, Brownian motion can be seen as a stochastic counterpart of a flow to a second-order partial differential operator.
Stochastic analysis on manifolds investigates stochastic processes on non-linear state spaces or manifolds. Classical theory can be reformulated in a coordinate-free representation. In that, it is often complicated (or not possible) to formulate objects with coordinates of . Thus, we require an additional structure in form of a linear connection or Riemannian metric to define martingales and Brownian motion on manifolds. Therefore, controlled by the Riemannian metric, Brownian motion will be a local object by definition. However, its stochastic behaviour determines global aspects of the topology and geometry of the manifold.
Brownian motion is defined to be the diffusion process generated by the Laplace-Beltrami operator with respect to a manifold and can be constructed as the solution to a non-canonical stochastic differential equation on a Riemannian manifold. As there is no Hörmander representation of the operator if the manifold is not parallelizable, i.e. if the tangent bundle is not trivial, there is no canonical procedure to construct Brownian motion. However, this obstacle can be overcome if the manifold is equipped with a connection: We can then introduce the stochastic horizontal lift of a semimartingale and the stochastic development by the so-called Eells-Elworthy-Malliavin construction.
The latter is a generalisation of a horizontal lift of smooth curves to horizontal curves in the frame bundle, such that the anti-development and the horizontal lift are connected by a stochastic differential equation. Using this, we can consider an SDE on the orthonormal frame bundle of a Riemannian manifold, whose solution is Brownian motion, and projects down to the (base) manifold via stochastic development. A visual representation of this construction corresponds to the construction of a spherical Brownian motion by rolling without slipping the manifold along the paths (or footprints) of Brownian motion left in Euclidean space.
Stochastic differential geometry provides insight into classical analytic problems, and offers new approaches to prove results by means of probability. For example, one can apply Brownian motion to the Dirichlet problem at infini
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https://en.wikipedia.org/wiki/Michael%20W.%20Davis
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Michael W. Davis (born April 26, 1949) is an American mathematician, author and academic. He is a Professor Emeritus of mathematics at the Ohio State University.
Davis is most known for his work in the fields of geometry and topology, with a focus on the methods for constructing aspherical manifolds and spaces. He is the author of two books that include The Geometry and Topology of Coxeter Groups and Multiaxial Actions on Manifolds. His notable contributions to the field of mathematics include the creation of several mathematical concepts, such as the Charney-Davis Conjecture, Davis-Moussong complex, Davis manifolds, Davis-Januszkiewicz space, and the reflection group trick.
Early life and education
Davis attended Princeton University where he earned a bachelor's degree in 1971. He then completed a PhD in mathematics at the same institution under the supervision of Wu-Chung Hsiang in 1975 with a thesis titled "Smooth Actions of the Classical Groups".
Career
Following his PhD, Davis held an appointment as a Moore Instructor of Mathematics at the Massachusetts Institute of Technology from 1974 to 1976. Starting in 1977, he worked as an assistant professor at Columbia University until 1982. Later, in 1983 he was appointed as an associate professor in the Department of Mathematics at Ohio State University and was promoted to Professor in 1988, a position in which he served until his retirement in 2022. Since 2022, he has been Professor Emeritus at Ohio State University.
In June, 2009 an international conference on geometric group theory was held in honor of his 60th birthday. He became a Fellow of the American Mathematical Society in 2015.
Research
Davis has worked in the fields of topology and geometric group theory. At the beginning of his career, his research concerned Lie group actions on manifolds. Later, he started working on aspherical spaces and co-authored a foundational paper on toric topology.
Aspherical manifolds and nonpositive curvature
Davis is most known for his seminal works in the area of aspherical manifolds. He is credited with pioneering the use of reflection groups in the construction of aspherical manifolds, which led to the creation of numerous examples of aspherical manifolds with universal covers not homeomorphic to Euclidean space. In collaborations with Januszkiewicz and Charney, he established the "hyperbolization" method for using nonpositive curvature to construct aspherical manifolds. His contributions also include the construction in 1998 of exotic Poincare duality groups by using the Reflection Group trick in 1998.
Coxeter groups
Davis has conducted research on Coxeter groups, Artin groups, and buildings. In his book, The Geometry and Topology of Coxeter Groups, he constructs the Davis complexes for Coxeter groups and he describes foundational results about these spaces to establish properties at infinity of Coxeter groups. In his book he also discusses the recent work on L2-cohomology of Coxeter groups, Artin
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https://en.wikipedia.org/wiki/Mahbanoo%20Tata
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Mahbanoo Tata (26 April 1942 – 7 August 2023) was an Indian-born Iranian statistician. She was widely regarded as the founder of statistics in Iran.
Education
A Zoroastrian (Parsi) from Bombay, she attended her local university to obtain her bachelor's and master's degrees before attending Purdue University where she studied and graduated with a Ph.D. in statistics in 1967. After completing her education, she pursued a career in academia, eventually becoming a professor of statistics at several universities in Iran.
Career
Tata came to Iran after five years of teaching at Michigan State University and spent two years as a statistics professor at Sharif University of Technology. Thereafter, over the course of the following 16 years, she established statistics as a subject at the Institute of Education, Statistics and Informatics, the Higher School of Computer Planning and Application, Iran Azad University, and Allameh Tabatabai University.
In 1989, she moved to Kerman to work in the statistics department of the Department of Mathematics and Computer Science at Shahid Bahonar University of Kerman. She oversaw the same department for many years.
Tata was a member of scientific organisations including the International Institute of Statistics, the Iranian Society of Mathematicians, and the Iranian Society of Statistics. She was named as "Mother of Statistics of Iran" for all the contributions she made to Iran's statistical expertise.
Death
Mahbanoo Tata died on 7 August 2023, at the age of 81.
References
1942 births
2023 deaths
Indian statisticians
20th-century Indian women
Iranian statisticians
Women statisticians
Indian expatriates in the United States
Indian women mathematicians
Iranian women scientists
Academic staff of Shahid Bahonar University of Kerman
Academic staff of Sharif University of Technology
Parsi people from Mumbai
Scientists from Mumbai
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https://en.wikipedia.org/wiki/Quasi-free%20algebra
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In abstract algebra, a quasi-free algebra is an associative algebra that satisfies the lifting property similar to that of a formally smooth algebra in commutative algebra. The notion was introduced by Cuntz and Quillen for the applications to cyclic homology. A quasi-free algebra generalizes a free algebra, as well as the coordinate ring of a smooth affine complex curve. Because of the latter generalization, a quasi-free algebra can be thought of as signifying smoothness on a noncommutative space.
Definition
Let A be an associative algebra over the complex numbers. Then A is said to be quasi-free if the following equivalent conditions are met:
Given a square-zero extension , each homomorphism lifts to .
The cohomological dimension of A with respect to Hochschild cohomology is at most one.
Let denotes the differential envelope of A; i.e., the universal differential-graded algebra generated by A. Then A is quasi-free if and only if is projective as a bimodule over A.
There is also a characterization in terms of a connection. Given an A-bimodule E, a right connection on E is a linear map
that satisfies and . A left connection is defined in the similar way. Then A is quasi-free if and only if admits a right connection.
Properties and examples
One of basic properties of a quasi-free algebra is that the algebra is left and right hereditary (i.e., a submodule of a projective left or right module is projective or equivalently the left or right global dimension is at most one). This puts a strong restriction for algebras to be quasi-free. For example, a hereditary (commutative) integral domain is precisely a Dedekind domain. In particular, a polynomial ring over a field is quasi-free if and only if the number of variables is at most one.
An analog of the tubular neighborhood theorem, called the formal tubular neighborhood theorem, holds for quasi-free algebras.
References
Bibliography
Maxim Kontsevich, Alexander Rosenberg, Noncommutative spaces, preprint MPI-2004-35
Further reading
https://ncatlab.org/nlab/show/quasi-free+algebra
Abstract algebra
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https://en.wikipedia.org/wiki/Q-category
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In mathematics, a Q-category or almost quotient category is a category that is a "milder version of a Grothendieck site." A Q-category is a coreflective subcategory. The Q stands for a quotient.
The concept of Q-categories was introduced by Alexander Rosenberg in 1988. The motivation for the notion was its use in noncommutative algebraic geometry; in this formalism, noncommutative spaces are defined as sheaves on Q-categories.
Definition
A Q-category is defined by the formula where is the left adjoint in a pair of adjoint functors and is a full and faithful functor.
Examples
The category of presheaves over any Q-category is itself a Q-category.
For any category, one can define the Q-category of cones.
There is a Q-category of sieves.
References
Alexander Rosenberg, Q-categories, sheaves and localization, (in Russian) Seminar on supermanifolds 25, Leites ed. Stockholms Universitet 1988.
Further reading
Category theory
Noncommutative geometry
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https://en.wikipedia.org/wiki/2022%20Sport%20Club%20do%20Recife%20season
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The 2022 season was Sport Recife's 118th season in the club's history. Sport competed in the Campeonato Pernambucano, Copa do Nordeste, Série B and Copa do Brasil.
Final squad
Statistics
Overall
{|class="wikitable"
|-
|Games played || 61 (10 Campeonato Pernambucano, 12 Copa do Nordeste, 1 Copa do Brasil, 38 Campeonato Brasileiro)
|-
|Games won || 24 (4 Campeonato Pernambucano, 5 Copa do Nordeste, 0 Copa do Brasil, 15 Campeonato Brasileiro)
|-
|Games drawn || 21 (5 Campeonato Pernambucano, 4 Copa do Nordeste, 0 Copa do Brasil, 12 Campeonato Brasileiro)
|-
|Games lost || 16 (1 Campeonato Pernambucano, 3 Copa do Nordeste, 1 Copa do Brasil, 11 Campeonato Brasileiro)
|-
|Goals scored || 75
|-
|Goals conceded || 52
|-
|Goal difference || +23
|-
|Best results || 7–0 (H) v Sete de Setembro - Campeonato Pernambucano - 2022.01.26
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|Worst result || 1–4 (A) v Sampaio Corrêa - Campeonato Brasileiro Série B - 2022.07.221–4 (A) v Ituano - Campeonato Brasileiro Série B - 2022.08.09
|-
|Top scorer || Luciano Juba (10)
|-
Goalscorers
Managers performance
Home record
Overview
Competitions
Copa do Nordeste
Group stage
Quarter-final
Semi-final
Finals
Record
Campeonato Pernambucano
First stage
Quarter-final
Record
Copa do Brasil
First stage
Record
Série B
Record
References
External links
Sport Club do Recife seasons
Sport Recife
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