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https://en.wikipedia.org/wiki/Takaya%20Kuroishi
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is a Japanese footballer currently playing as a forward for Mito HollyHock.
Career statistics
Club
.
Notes
References
External links
1997 births
Living people
Japanese men's footballers
Men's association football forwards
Japan Football League players
J2 League players
Reilac Shiga FC players
Vanraure Hachinohe players
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https://en.wikipedia.org/wiki/Lifting-the-exponent%20lemma
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In elementary number theory, the lifting-the-exponent lemma (LTE lemma) provides several formulas for computing the p-adic valuation of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of in such expressions. It is related to Hensel's lemma.
Background
The exact origins of the LTE lemma are unclear; the result, with its present name and form, has only come into focus within the last 10 to 20 years. However, several key ideas used in its proof were known to Gauss and referenced in his Disquisitiones Arithmeticae. Despite chiefly featuring in mathematical olympiads, it is sometimes applied to research topics, such as elliptic curves.
Statements
For any integers , a positive integer , and a prime number such that and , the following statements hold:
When is odd:
If , then .
If is odd and , then .
When :
If and is even, then .
If and is odd, then . (Follows from the general case below.)
Corollary:
If , then and thus .
For all :
If and , then .
If , and odd, then .
Outline of proof
Base case
The base case when is proven first. Because ,
The fact that completes the proof. The condition for odd is similar.
General case (odd p)
Via the binomial expansion, the substitution can be used in (1) to show that because (1) is a multiple of but not . Likewise, .
Then, if is written as where , the base case gives .
By induction on ,
A similar argument can be applied for .
General case (p = 2)
The proof for the odd case cannot be directly applied when because the binomial coefficient is only an integral multiple of when is odd.
However, it can be shown that when by writing where and are integers with odd and noting that
because since , each factor in the difference of squares step in the form is congruent to 2 modulo 4.
The stronger statement when is proven analogously.
In competitions
Example problem
The LTE lemma can be used to solve 2020 AIME I #12:
Let be the least positive integer for which is divisible by Find the number of positive integer divisors of .
Solution. Note that . Using the LTE lemma, since and but , . Thus, . Similarly, but , so and .
Since , the factors of 5 are addressed by noticing that since the residues of modulo 5 follow the cycle and those of follow the cycle , the residues of modulo 5 cycle through the sequence . Thus, iff for some positive integer . The LTE lemma can now be applied again: . Since , . Hence .
Combining these three results, it is found that , which has positive divisors.
References
Lemmas in number theory
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https://en.wikipedia.org/wiki/Keishi%20Murakami
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is a Japanese footballer currently playing as a defender for Gamba Osaka.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
Japanese men's footballers
Men's association football defenders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/Ryusei%20Sugano
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is a Japanese footballer currently playing as a midfielder for Gamba Osaka U-23.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
Japanese men's footballers
Men's association football midfielders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/Kanta%20Nagakawa
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is a Japanese footballer currently studying at the Momoyama Gakuin University.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
Momoyama Gakuin University alumni
Japanese men's footballers
Men's association football midfielders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/Josu%C3%A9%20Villafranca
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Josué Isaias Villafranca Quiñónez (born 16 December 1999) is a Honduran footballer currently playing as a forward for CF Intercity on loan from F.C. Motagua.
Career statistics
Club
Notes
References
Living people
1999 births
Honduran men's footballers
Honduras men's youth international footballers
Men's association football forwards
Liga Nacional de Fútbol Profesional de Honduras players
F.C. Motagua players
C.D. Real de Minas players
C.D.S. Vida players
Tercera División players
Honduran expatriate men's footballers
Expatriate men's footballers in Spain
Honduran expatriate sportspeople in Spain
Honduras men's under-20 international footballers
People from El Paraíso Department
CF Intercity players
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https://en.wikipedia.org/wiki/Jonathan%20N%C3%BA%C3%B1ez%20%28Honduran%20footballer%29
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Jonathan Adid Núñez García (born 26 November 2001) is a Honduran professional footballer who plays as a midfielder for Motagua.
Career statistics
Club
Notes
References
Living people
2001 births
Honduran men's footballers
Honduras men's under-20 international footballers
Men's association football midfielders
Liga Nacional de Fútbol Profesional de Honduras players
F.C. Motagua players
Footballers at the 2020 Summer Olympics
Olympic footballers for Honduras
Footballers from La Ceiba
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https://en.wikipedia.org/wiki/Axel%20G%C3%B3mez
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Axel Daniel Gómez Guzmán (born 28 June 2000) is a Honduran professional footballer currently playing as a left-back.
Career statistics
Club
Notes
References
Living people
2000 births
Honduran men's footballers
Honduras men's youth international footballers
Men's association football defenders
Liga Nacional de Fútbol Profesional de Honduras players
C.D. Olimpia players
Honduras men's under-20 international footballers
Footballers from Tegucigalpa
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https://en.wikipedia.org/wiki/Khatri%E2%80%93Rao%20product
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In mathematics, the Khatri–Rao product of matrices is defined as
in which the ij-th block is the sized Kronecker product of the corresponding blocks of A and B, assuming the number of row and column partitions of both matrices is equal. The size of the product is then .
For example, if A and B both are partitioned matrices e.g.:
we obtain:
This is a submatrix of the Tracy–Singh product
of the two matrices (each partition in this example is a partition in a corner of the Tracy–Singh product) and also may be called the block Kronecker product.
Column-wise Kronecker product
A column-wise Kronecker product of two matrices may also be called the Khatri–Rao product. This product assumes the partitions of the matrices are their columns. In this case , , and for each j: . The resulting product is a matrix of which each column is the Kronecker product of the corresponding columns of A and B. Using the matrices from the previous examples with the columns partitioned:
so that:
This column-wise version of the Khatri–Rao product is useful in linear algebra approaches to data analytical processing and in optimizing the solution of inverse problems dealing with a diagonal matrix.
In 1996 the Column-wise Khatri–Rao product was proposed to estimate the angles of arrival (AOAs) and delays of multipath signals and four coordinates of signals sources at a digital antenna array.
Face-splitting product
The alternative concept of the matrix product, which uses row-wise splitting of matrices with a given quantity of rows, was proposed by V. Slyusar in 1996.
This matrix operation was named the "face-splitting product" of matrices or the "transposed Khatri–Rao product". This type of operation is based on row-by-row Kronecker products of two matrices. Using the matrices from the previous examples with the rows partitioned:
the result can be obtained:
Main properties
Examples
Theorem
If , where are independent components a random matrix with independent identically distributed rows , such that
and ,
then for any vector
with probability if the quantity of rows
In particular, if the entries of are can get
which matches the Johnson–Lindenstrauss lemma of when is small.
Block face-splitting product
According to the definition of V. Slyusar the block face-splitting product of two partitioned matrices with a given quantity of rows in blocks
can be written as :
The transposed block face-splitting product (or Block column-wise version of the Khatri–Rao product) of two partitioned matrices with a given quantity of columns in blocks has a view:
Main properties
Transpose:
Applications
The Face-splitting product and the Block Face-splitting product used in the tensor-matrix theory of digital antenna arrays. These operations used also in:
Artificial Intelligence and Machine learning systems to minimization of convolution and tensor sketch operations,
A popular Natural Language Processing models, and hypergraph models of similarity,
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https://en.wikipedia.org/wiki/Dolni%20Disan
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Dolni Disan () is a village in the municipality of Negotino, North Macedonia. It is located in the Povardarie wine-growing region.
Demographics
According to the statistics of Bulgarian ethnographer Vasil Kanchov from 1900, 1556 inhabitants lived in Dolni Disan, 1200 Muslim Bulgarians, 350 Christian Bulgarians and 6 Romani. According to the 2002 census, the village had a total of 931 inhabitants. Ethnic groups in the village include:
Macedonians 903
Turks 15
Serbs 6
Other 7
References
Villages in Negotino Municipality
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https://en.wikipedia.org/wiki/Pepeli%C5%A1te
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Pepelište () is a village in the municipality of Negotino, North Macedonia. It is located in the Povardarie wine-growing region, along the river Vardar.
Demographics
According to the statistics of Bulgarian ethnographer Vasil Kanchov from 1900 the settlement is recorded as "Pepelišta" in which 984 inhabitants lived. 850 of them being Muslim Bulgarians, 80 being Christian Bulgarians and 54 being Romani. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is shown as a Muslim Bulgarian village.According to the 2002 census, the village had a total of 1,070 inhabitants. Ethnic groups in the village include:
Macedonians 796
Turks 33
Serbs 194
Romani 25
Albanians
Others 22
References
Villages in Negotino Municipality
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https://en.wikipedia.org/wiki/Timjanik
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Timjanik () is a village in the municipality of Negotino, North Macedonia. It is located in the Povardarie wine-growing region.
Demographics
According to the statistics of Bulgarian ethnographer Vasil Kanchov from 1900 the settlement is recorded as "Tamjanik" and having 1250 inhabitants with 1150 being Muslim Bulgarians and 100 being Christian Bulgarians. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is shown as a fully Muslim Bulgarian village. As of the 2021 census, Timjanik had 1,138 residents with the following ethnic composition:
Macedonians 1,077
Persons for whom data are taken from administrative sources 27
Serbs 17
Turks 13
Others 4
According to the 2002 census, the village had a total of 1,155 inhabitants. Ethnic groups in the village include:
Macedonians 1,096
Turks 9
Serbs 49
Others 1
References
Villages in Negotino Municipality
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https://en.wikipedia.org/wiki/Tremnik
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Tremnik () is a village in the municipality of Negotino, North Macedonia. It is located in the Povardarie wine-growing region.
Demographics
According to the statistics of the Bulgarian ethnographer Vasil Kanchov from 1900, 657 inhabitants lived in Tremnik, 554 Muslim Bulgarians, 93 Christian Bulgarians and 10 Romani. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is shown as a fully Muslim Bulgarian village. According to the 2002 census, the village had a total of 827 inhabitants. Ethnic groups in the village include:
Macedonians 618
Turks 85
Serbs 121
Others 3
References
Villages in Negotino Municipality
Turkish communities in North Macedonia
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https://en.wikipedia.org/wiki/COVID-19%20datasets
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COVID-19 datasets are public databases for sharing case data and medical information related to the COVID-19 pandemic.
Aggregate statistics
United States
Volunteer/non-government
U.S. Department of Health & Human Services
Global
Johns Hopkins Coronavirus Resource Center: Global aggregated data including cases, testing, contact tracing, and vaccine development
World Health Organization (WHO) Coronavirus Disease Dashboard: a database of confirmed cases and deaths reported globally and broken down by region. This database is part of the WHO Health Data Platform.
COVID-19 Africa Open Data Project: a volunteer-run database and dashboard reporting region, country and district level case counts, deaths, healthcare worker infections, healthcare services and urgent needs.
Data hubs
Health Data Research UK provides a searchable registry of health data resources from the United Kingdom, including COVID-19 related datasets.
NIH Open Access Datasets: The National Institutes of Health provide open-access data and computational resources related to COVID-19.
COVID-19 Open Research Dataset (CORD-19): The Semantic Scholar project of the Allen Institute for AI hosts CORD-19, a public dataset of academic articles about COVID-19 and related research. The dataset is updated daily and includes both peer-reviewed articles and preprints. CORD-19 was originally released on March 16, 2020, by researchers and leaders from the Allen Institute for AI, Chan Zuckerberg Initiative, Georgetown University's Center for Security and Emerging Technhology, Microsoft, and the National Library of Medicine. The dataset is created through the use of text mining of the current research literature.
Topic-specific and special-interest resources
Genomics
Consensus genome data for SARS-CoV-2 is available through GISAID for registered users and included in an interactive Phylogenetic tree dashboard on Nextstrain, an open-source pathogen genome data project.
Imaging (Radiology)
Characteristic imaging features on chest radiographs and computed tomography (CT) of people who are symptomatic include asymmetric peripheral ground-glass opacities without pleural effusions. The University of Montreal and Mila created the "COVID-19 Image Data Collection" in March which is a public data repository of chest imaging. The Medical Imaging Databank in Valencian Region released a large dataset of chest imaging from Spain. The Italian Radiological Society is compiling an international online database of imaging findings for confirmed cases. Online radiology case sharing platforms such as Eurorad and Radiopaedia serve as platforms for sharing COVID-19 case data and imaging.
References
datasets
Datasets
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https://en.wikipedia.org/wiki/Peter%20Henrici%20Prize
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The Peter Henrici Prize (; ; ) is a prize awarded jointly by ETH Zurich and the Society for Industrial and Applied Mathematics (SIAM) for "original contributions to applied analysis and numerical analysis and/or for exposition appropriate for applied mathematics and scientific computing". The prize is named in honor of the Swiss numerical analyst Peter Henrici, who was a professor at ETH Zurich for 25 years.
Description
The prize, initiated in 1999 with funds contributed by ETH Zurich, is awarded every four years. It consists of a certificate containing the citation and (as of 2023) a cash prize of $5,000 (US). The winner is chosen by a prize committee, consisting of four members, two members chosen by SIAM and two others by ETH Zurich. "The prize may be awarded to any member of the scientific community who meets the general guideline of the prize description."
Award ceremony
The award is presented every four years at the International Congress on Industrial and Applied Mathematics (ICIAM). The presentation of the prize is made by the SIAM president. The recipient is requested to give a lecture at the conference.
Prize winners
1999 : Germund Dahlquist
2003 : Ernst Hairer and Gerhard Wanner
2007 : Gilbert Strang
2011 : Bjorn Engquist
2015 : Eitan Tadmor
2019 : Weinan E
See also
Alice Roth Lecture Series
References
Awards established in 1999
Awards of the Society for Industrial and Applied Mathematics
Numerical analysis
ETH Zurich
1999 establishments in Switzerland
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https://en.wikipedia.org/wiki/Mirror%20symmetry%20conjecture
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In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus algebraic curves of degree on a Calabi-Yau variety and integrals on a dual variety . These relations were original discovered by Candelas, de la Ossa, Green, and Parkes in a paper studying a generic quintic threefold in as the variety and a construction from the quintic Dwork family giving . Shortly after, Sheldon Katz wrote a summary paper outlining part of their construction and conjectures what the rigorous mathematical interpretation could be.
Constructing the mirror of a quintic threefold
Originally, the construction of mirror manifolds was discovered through an ad-hoc procedure. Essentially, to a generic quintic threefold there should be associated a one-parameter family of Calabi-Yau manifolds which has multiple singularities. After blowing up these singularities, they are resolved and a new Calabi-Yau manifold was constructed. which had a flipped Hodge diamond. In particular, there are isomorphisms
but most importantly, there is an isomorphism
where the string theory (the A-model of ) for states in is interchanged with the string theory (the B-model of ) having states in . The string theory in the A-model only depended upon the Kahler or symplectic structure on while the B-model only depends upon the complex structure on . Here we outline the original construction of mirror manifolds, and consider the string-theoretic background and conjecture with the mirror manifolds in a later section of this article.
Complex moduli
Recall that a generic quintic threefold in is defined by a homogeneous polynomial of degree . This polynomial is equivalently described as a global section of the line bundle . Notice the vector space of global sections has dimension but there are two equivalences of these polynomials. First, polynomials under scaling by the algebraic torus (non-zero scalers of the base field) given equivalent spaces. Second, projective equivalence is given by the automorphism group of , which is dimensional. This gives a dimensional parameter space since , which can be constructed using Geometric invariant theory. The set corresponds to the equivalence classes of polynomials which define smooth Calabi-Yau quintic threefolds in , giving a moduli space of Calabi-Yau quintics. Now, using Serre duality and the fact each Calabi-Yau manifold has trivial canonical bundle , the space of deformations has an isomorphism with the part of the Hodge structure on . Using the Lefschetz hyperplane theorem the only non-trivial cohomology group is since the others are isomorphic to . Using the Euler
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https://en.wikipedia.org/wiki/Martina%20Z%C3%A4hle
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Martina Zähle (born 1950) is a German mathematician specializing in geometric measure theory and stochastic geometry. She is a professor of mathematics at the University of Jena, where she holds the chair for geometry.
Zähle completed her doctorate in 1978 at the University of Jena. Her dissertation, Ergodizitätseigenschaften von Strömungsmodellen mit Anwendungen in der Bedienungstheorie, was supervised by Joseph Mecke. She earned a habilitation at Jena in 1982.
She is the coauthor of the book Curvature Measures of Singular Sets (with Jan Rataj, Springer, 2019).
References
Living people
20th-century German mathematicians
German women mathematicians
University of Jena alumni
Academic staff of the University of Jena
1950 births
20th-century German women
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https://en.wikipedia.org/wiki/Kang%20Hyeon
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Kang Hyeon (; born 30 January 1998) is a South Korean footballer who currently plays as a midfielder for Yeoju.
Career statistics
Club
References
1998 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Men's association football midfielders
2. Liga (Austria) players
Kapfenberger SV players
South Korean expatriate sportspeople in Austria
Expatriate men's footballers in Austria
South Korean expatriate sportspeople in Croatia
Expatriate men's footballers in Croatia
South Korean expatriate sportspeople in Thailand
Expatriate men's footballers in Thailand
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https://en.wikipedia.org/wiki/Park%20Seon-hong
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Park Seon-hong (; born 5 November 1993) is a South Korean footballer who plays as a midfielder for Nakhon Si United.
Career statistics
Club
References
1993 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Jeonju University alumni
Men's association football midfielders
K League 1 players
Gwangju FC players
South Korean expatriate sportspeople in Thailand
Expatriate men's footballers in Thailand
Park Seon-hong
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https://en.wikipedia.org/wiki/Moacir%20%28footballer%2C%20born%201993%29
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Moacir Da Rosa Wilmsen (born 13 March 1993), commonly known as Moacir, is a Brazilian footballer.
Career statistics
Club
Notes
References
1993 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
Sociedade Esportiva e Recreativa Caxias do Sul players
Caxias Futebol Clube players
Grêmio Esportivo Juventus players
Clube Esportivo Aimoré players
Pembroke Athleta F.C. players
Angthong F.C. players
Brazilian expatriate sportspeople in Malta
Expatriate men's footballers in Malta
Brazilian expatriate sportspeople in Thailand
Expatriate men's footballers in Thailand
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https://en.wikipedia.org/wiki/Ailton%20%28footballer%2C%20born%201994%29
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Ailton Machado de Souza Rosa (born 17 April 1994), commonly known as Ailton, is a Brazilian footballer who plays as midfielder for Samut Sakhon City in the Thai League 3.
Career statistics
Club
Notes
References
1994 births
Living people
Brazilian expatriate men's footballers
Men's association football midfielders
Segunda División B players
Thai League 2 players
Thai League 3 players
São Paulo FC players
Quissamã Futebol Clube players
Esporte Clube Passo Fundo players
Clube Náutico Marcílio Dias players
Santos FC players
CP Cacereño players
Desportivo Brasil players
Comunicaciones F.C. players
CR Vasco da Gama players
Nova Iguaçu FC players
Irodotos FC players
Al-Mujazzal Club players
Oman Club players
Muangkan United F.C. players
Kasetsart F.C. players
Sheikh Russel KC players
Samut Sakhon City F.C. players
Brazilian expatriate sportspeople in Spain
Expatriate men's footballers in Spain
Brazilian expatriate sportspeople in Guatemala
Expatriate men's footballers in Guatemala
Brazilian expatriate sportspeople in Greece
Expatriate men's footballers in Greece
Brazilian expatriate sportspeople in Saudi Arabia
Expatriate men's footballers in Saudi Arabia
Brazilian expatriate sportspeople in Oman
Expatriate men's footballers in Oman
Brazilian expatriate sportspeople in Thailand
Expatriate men's footballers in Thailand
Footballers from Rio de Janeiro (city)
Brazilian men's footballers
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https://en.wikipedia.org/wiki/Rafinha%20%28footballer%2C%20born%20March%201992%29
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Rafael de Sá Rodrigues (born 23 March 1992), commonly known as Rafinha, is a Brazilian footballer who plays for PSCS Cilacap in the Liga 2.
Career statistics
Club
Notes
References
1992 births
Living people
Footballers from Recife
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
Campeonato Brasileiro Série B players
Meistriliiga players
Lao Premier League players
Rafinha
Liga 2 (Indonesia) players
Duque de Caxias Futebol Clube players
Esporte Clube Tigres do Brasil players
Mogi Mirim Esporte Clube players
Nõmme Kalju FC players
Mesquita Futebol Clube players
F.C. Chanthabouly players
Master 7 FC players
PSCS Cilacap players
Brazilian expatriate sportspeople in Estonia
Expatriate men's footballers in Estonia
Brazilian expatriate sportspeople in Laos
Expatriate men's footballers in Laos
Brazilian expatriate sportspeople in Thailand
Expatriate men's footballers in Thailand
Expatriate men's footballers in Indonesia
Brazilian expatriate sportspeople in Indonesia
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https://en.wikipedia.org/wiki/Adri%C3%A1n%20S%C3%A1nchez%20%28footballer%29
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Adrián Guillermo Sánchez (born 14 May 1999) is an Argentine footballer playing as a midfielder for Curicó Unido, on loan from Boca Juniors.
Career statistics
Club
Notes
References
1999 births
Living people
Argentine men's footballers
Men's association football midfielders
Uruguayan Primera División players
Boca Juniors footballers
Cerro Largo F.C. players
Footballers from Buenos Aires Province
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https://en.wikipedia.org/wiki/Ransford%20Koufie
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Ransford Koufie (born 21 August 2002) is a Ghanaian footballer who currently plays as a midfielder for Golden Kick.
Career statistics
Club
Notes
References
2002 births
Living people
Ghanaian men's footballers
Ghana men's youth international footballers
Men's association football midfielders
Ghana Premier League players
International Allies F.C. players
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https://en.wikipedia.org/wiki/Prince%20Kwabena%20Adu
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Prince Kwabena Adu (born 23 September 2003) is a Ghanaian footballer who plays for Kryvbas Kryvyi Rih. He was included in The Guardian's "Next Generation 2020".
Career statistics
Club
References
External links
2003 births
Living people
People from Sunyani District
Ghanaian men's footballers
Ghana men's youth international footballers
Men's association football forwards
Ghanaian expatriate men's footballers
Expatriate men's footballers in Belarus
Expatriate men's footballers in Ukraine
Ghana Premier League players
Bechem United F.C. players
FC Isloch Minsk Raion players
FC Kryvbas Kryvyi Rih players
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https://en.wikipedia.org/wiki/Birth%20process
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In probability theory, a birth process or a pure birth process is a special case of a continuous-time Markov process and a generalisation of a Poisson process. It defines a continuous process which takes values in the natural numbers and can only increase by one (a "birth") or remain unchanged. This is a type of birth–death process with no deaths. The rate at which births occur is given by an exponential random variable whose parameter depends only on the current value of the process
Definition
Birth rates definition
A birth process with birth rates and initial value is a minimal right-continuous process such that and the interarrival times are independent exponential random variables with parameter .
Infinitesimal definition
A birth process with rates and initial value is a process such that:
is independent of
(The third and fourth conditions use little o notation.)
These conditions ensure that the process starts at , is non-decreasing and has independent single births continuously at rate , when the process has value .
Continuous-time Markov chain definition
A birth process can be defined as a continuous-time Markov process (CTMC) with the non-zero Q-matrix entries and initial distribution (the random variable which takes value with probability 1).
Variations
Some authors require that a birth process start from 0 i.e. that , while others allow the initial value to be given by a probability distribution on the natural numbers. The state space can include infinity, in the case of an explosive birth process. The birth rates are also called intensities.
Properties
As for CTMCs, a birth process has the Markov property. The CTMC definitions for communicating classes, irreducibility and so on apply to birth processes. By the conditions for recurrence and transience of a birth–death process, any birth process is transient. The transition matrices of a birth process satisfy the Kolmogorov forward and backward equations.
The backwards equations are:
(for )
The forward equations are:
(for )
(for )
From the forward equations it follows that:
(for )
(for )
Unlike a Poisson process, a birth process may have infinitely many births in a finite amount of time. We define and say that a birth process explodes if is finite. If then the process is explosive with probability 1; otherwise, it is non-explosive with probability 1 ("honest").
Examples
A Poisson process is a birth process where the birth rates are constant i.e. for some .
Simple birth process
A simple birth process is a birth process with rates . It models a population in which each individual gives birth repeatedly and independently at rate . Udny Yule studied the processes, so they may be known as Yule processes.
The number of births in time from a simple birth process of population is given by:
In exact form, the number of births is the negative binomial distribution with parameters and . For the special case , this is the geometric distribution wi
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https://en.wikipedia.org/wiki/Robert%20Riley%20%28mathematician%29
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Robert F. Riley (December 22, 1935–March 4, 2000) was an American mathematician. He is known for his work in low-dimensional topology using computational tools and hyperbolic geometry, being one of the inspirations for William Thurston's later breakthroughs in 3-dimensional topology.
Career
Riley earned a bachelor's degree in mathematics from MIT in 1957; shortly thereafter he dropped out of the graduate program and went on to work in industry, eventually moving to Amsterdam in 1966. In 1968 he took a temporary position at the University of Southampton. He defended his Ph.D. at this institution in 1980, under the nominal direction of David Singerman. For the next two years he occupied a postdoctoral position in Boulder where William Thurston was employed at the time, before moving on to Binghamton University as a professor.
Mathematical work
Riley's research was in geometric topology, especially in knot theory, where he mostly studied representations of knot groups. Early on, following work of Ralph Fox, he was interested in morphisms to finite groups. Later on in Southampton, considering -representations sending peripheral elements to parabolics led him to discover the hyperbolic structure on the complement of the figure-eight knot and some others. This was one of the few examples of hyperbolic 3-manifolds that were available at the time, and as such it was one of the motivations which led to William Thurston's geometrisation conjecture, which includes as a particular case a criterion for a knot complement to support a hyperbolic structure. One notable feature of Riley's work is that it relied much on the assistance of a computer.
Selected publications
Notes
References
2000 deaths
Topologists
20th-century American mathematicians
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https://en.wikipedia.org/wiki/Truncated%20projective%20plane
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In geometry, a truncated projective plane (TPP), also known as a dual affine plane, is a special kind of a hypergraph or geometric configuration that is constructed in the following way.
Take a finite projective plane.
Remove one of the points (vertices) in the plane.
Remove all lines (edges) containing that point.
These objects have been studied in many different settings, often independent of one another, and so, many terminologies have been developed. Also, different areas tend to ask different types of questions about these objects and are interested in different aspects of the same objects.
Example: the Pasch hypergraph
Consider the Fano plane, which is the projective plane of order 2. It has 7 vertices {1,2,3,4,5,6,7} and 7 edges {123, 145, 167, 246, 257, 347, 356}.
It can be truncated e.g. by removing the vertex 7 and the edges containing it. The remaining hypergraph is the TPP of order 2. It has 6 vertices {1,2,3,4,5,6} and 4 edges {123, 154, 624, 653}. It is a tripartite hypergraph with sides {1,6},{2,5},{3,4} (which are exactly the neighbors of the removed vertex 7). It is also called the Pasch hypergraph, due to its connection with Pasch's axiom.
It is a 2-regular hypergraph (each vertex is in exactly two edges), and its maximum matching is of size 1 (every two of its edges intersect).
Combinatorics of dual affine planes
A finite projective plane of order has + 1 points on every line ( in the hypergraph description). There are total points and an equal number of lines. Each point is on + 1 lines. Every two distinct points lie on a unique line and every two distinct lines meet at a unique point.
By removing a point and all the lines that pass through that point, the configuration that is left has points, 2 lines, each point is on lines and each line contains + 1 points. Each pair of distinct lines still meet at a unique point, but two distinct points are on at most one line. This dual affine plane is thus a configuration of type ().
The points can be partitioned into + 1 sets of points apiece, where no two points in the same partition set are joined by a line. These sets are the analogs of classes of parallel lines in an affine plane, and some authors refer to the points in a partition piece as parallel points in keeping with the dual nature of the structure.
Projective planes constructed from finite fields (Desarguesian planes) have automorphism groups that act transitively on the points of the plane, so for these planes the point removed to form the dual affine plane is immaterial, the results of choosing different points are isomorphic. However, there do exist non-Desarguesian planes and the choice of point to remove in them may result in non-isomorphic dual affine planes having the same parameters.
An affine plane is obtained by removing a line and all the points on that line from a projective plane. Since a projective plane is a self-dual configuration, the dual configuration of an affine plane is obtained f
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https://en.wikipedia.org/wiki/Mathematical%20Models%20%28Fischer%29
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Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary is a book on the physical models of concepts in mathematics that were constructed in the 19th century and early 20th century and kept as instructional aids at universities. It credits Gerd Fischer as editor, but its photographs of models are also by Fischer. It was originally published by Vieweg+Teubner Verlag for their bicentennial in 1986, both in German (titled Mathematische Modelle. Aus den Sammlungen von Universitäten und Museen. Mit 132 Fotografien. Bildband und Kommentarband) and (separately) in English translation, in each case as a two-volume set with one volume of photographs and a second volume of mathematical commentary. Springer Spektrum reprinted it in a second edition in 2017, as a single dual-language volume.
Topics
The work consists of 132 full-page photographs of mathematical models, divided into seven categories, and seven chapters of mathematical commentary written by experts in the topic area of each category.
These categories are:
Wire and thread models, of hypercubes of various dimensions, and of hyperboloids, cylinders, and related ruled surfaces, described as "elementary analytic geometry" and explained by Fischer himself.
Plaster and wood models of cubic and quartic algebraic surfaces, including Cayley's ruled cubic surface, the Clebsch surface, Fresnel's wave surface, the Kummer surface, and the Roman surface, with commentary by W. Barth and H. Knörrer.
Wire and plaster models illustrating the differential geometry and curvature of curves and surfaces, including surfaces of revolution, Dupin cyclides, helicoids, and minimal surfaces including the Enneper surface, with commentary by M. P. do Carmo, G. Fischer, U. Pinkall, H. and Reckziegel.
Surfaces of constant width including the surface of rotation of the Reuleaux triangle and the Meissner bodies, described by J. Böhm.
Uniform star polyhedra, described by E. Quaisser.
Models of the projective plane, including the Roman surface (again), the cross-cap, and Boy's surface, with commentary by U. Pinkall that includes its realization by Roger Apéry as a quartic surface (disproving a conjecture of Heinz Hopf).
Graphs of functions, both with real and complex variables, including the Peano surface, Riemann surfaces, exponential function and Weierstrass's elliptic functions, with commentary by J. Leiterer.
Audience and reception
This book can be viewed as a supplement to Mathematical Models by Martyn Cundy and A. P. Rollett (1950), on instructions for making mathematical models, which according to reviewer Tony Gardiner "should be in every classroom and on every lecturer's shelf" but in fact sold very slowly. Gardiner writes that the photographs may be useful in undergraduate mathematics lectures, while the commentary is best aimed at mathematics professionals in giving them an understanding of what each model depicts. Gardiner also suggests using the book as a source of
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https://en.wikipedia.org/wiki/EM%20algorithm%20and%20GMM%20model
|
In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model.
Background
In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the Control Group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia.
is a random vector such as , and from medical studies it is known that are normally distributed in each group, i.e. .
is denoted as the group where belongs, with when belongs to Anemia Group and when belongs to Control Group. Also where , and . See Categorical distribution.
The following procedure can be used to estimate .
A maximum likelihood estimation can be applied:
As the for each are known, the log likelihood function can be simplified as below:
Now the likelihood function can be maximized by making partial derivative over , obtaining:
If is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if is unknown it is much more complicated.
Being a latent variable (i.e. not observed), with unlabeled scenario, the Expectation Maximization Algorithm is needed to estimate as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed.
In machine learning, the latent variable is considered as a latent pattern lying under the data, which the observer is not able to see very directly. is the known data, while are the parameter of the model. With the EM algorithm, some underlying pattern in the data can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important.
EM algorithm in GMM
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the can be randomly initialized. In the E-step, the algorithm tries to guess the value of based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of of the E-step. These two steps are repeated until convergence is reached.
The algorithm in GMM is:
Repeat until convergence:
1. (E-step) For each , set
2. (M-step) Update the parameters
With Bayes Rule, the following result is obtained by the E-step:
According to GMM setting, these following formulas are obtained:
In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.
References
Machine learning
Regression models
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https://en.wikipedia.org/wiki/Zsombor%20Nagy
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Zsombor Nagy (born 21 March 1998) is a Hungarian professional footballer who plays for Szeged on loan from MTK Budapest FC.
Career statistics
.
References
1998 births
Living people
People from Szeged
Hungarian men's footballers
Men's association football defenders
Dorogi FC footballers
MTK Budapest FC players
Szeged-Csanád Grosics Akadémia footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
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https://en.wikipedia.org/wiki/Salman%20Dawood
|
Salman Dawood is a former Iraqi football midfielder who played for Iraq between 1964 and 1967. He played 7 matches and scored 1 goal.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
Iraqi men's footballers
Iraq men's international footballers
Living people
Men's association football midfielders
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Motonobu%20Ogino
|
is a Japanese footballer currently playing as a midfielder for Gamba Osaka U-23.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
Japanese men's footballers
Men's association football midfielders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/2020%20Perak%20FA%20season
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The 2020 season was Perak's 17th consecutive season in Malaysia Super League, the top flight of Malaysian football.
Players
Current squad
Statistics
Appearances and goals
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!colspan="14"|Players away from the club on loan:
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!colspan="14"|Players who left Perak during the season:
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Perak II
Squad statistics
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References
Perak F.C.
Perak F.C. seasons
Perak
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https://en.wikipedia.org/wiki/Shin%20Won-ho%20%28footballer%29
|
Shin Won-ho (; born 19 May 2001) is a South Korean professional footballer who plays as a left-back for K League 2 club Cheonan City.
Career statistics
Club
.
Notes
References
External links
Profile at Gamba Osaka
2001 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
South Korean expatriate men's footballers
Men's association football defenders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
K League 1 players
Suwon Samsung Bluewings players
K League 2 players
Cheonan City FC players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
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https://en.wikipedia.org/wiki/Kei%20Sakamoto
|
is a Japanese footballer currently playing as a defender for Gainare Tottori.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Japanese men's footballers
Men's association football defenders
J3 League players
Gainare Tottori players
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https://en.wikipedia.org/wiki/Szabolcs%20Mezei
|
Szabolcs Mezei (born 27 September 2000) is a Hungarian football player who plays as winger for Paks in OTP Bank Liga.
Career statistics
.
References
2000 births
Footballers from Békéscsaba
21st-century Hungarian people
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
MTK Budapest FC players
Békéscsaba 1912 Előre footballers
Paksi FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
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https://en.wikipedia.org/wiki/Issei%20Tone
|
is a Japanese footballer currently playing as a defender for Iwate Grulla Morioka.
Career statistics
Club
.
Notes
References
External links
1996 births
Living people
Association football people from Osaka Prefecture
Tokai Gakuen University alumni
Japanese men's footballers
Men's association football defenders
J2 League players
J3 League players
Kataller Toyama players
Iwate Grulla Morioka players
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https://en.wikipedia.org/wiki/Yuhi%20Takemoto
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is a Japanese footballer currently playing as a midfielder for Roasso Kumamoto.
Career statistics
Club
.
Notes
References
External links
1997 births
Living people
Association football people from Hiroshima Prefecture
Ritsumeikan University alumni
Japanese men's footballers
Men's association football midfielders
J2 League players
J3 League players
Roasso Kumamoto players
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https://en.wikipedia.org/wiki/Kanta%20Wada
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is a Japanese footballer currently playing as a midfielder for YSCC Yokohama.
Career statistics
Club
.
Notes
References
External links
1996 births
Living people
Sportspeople from Ibaraki Prefecture
Association football people from Ibaraki Prefecture
Niigata University of Health and Welfare alumni
Japanese men's footballers
Men's association football midfielders
J3 League players
YSCC Yokohama players
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https://en.wikipedia.org/wiki/Wataru%20Ise
|
is a Japanese footballer who plays as a defender for Nara Club.
Career statistics
Club
.
Notes
References
External links
Profile at Nara Club
1996 births
Living people
Japanese men's footballers
Men's association football defenders
Komazawa University alumni
Japan Football League players
J3 League players
Minebea Mitsumi FC players
Vanraure Hachinohe players
Nara Club players
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https://en.wikipedia.org/wiki/Solomon%20Sakuragawa
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is a Japanese footballer currently playing as a forward for JEF United Chiba. He is of Nigerian descent.
Career statistics
.
Notes
References
External links
2001 births
Living people
Japanese men's footballers
Japan men's youth international footballers
Men's association football forwards
J2 League players
JEF United Chiba players
Japanese people of Nigerian descent
Association football people from Chiba (city)
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https://en.wikipedia.org/wiki/Kento%20Hashimoto%20%28footballer%2C%20born%201999%29
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is a Japanese footballer currently playing as a left-back for Yokohama FC from 2023, on loan from Renofa Yamaguchi as a designated special player.
Career statistics
Club
.
Notes
References
External links
1999 births
Living people
Association football people from Kanagawa Prefecture
Keio University alumni
Japanese men's footballers
Men's association football defenders
J1 League players
J2 League players
Renofa Yamaguchi FC players
Yokohama FC players
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https://en.wikipedia.org/wiki/Dan%20Kalman
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Daniel "Dan" Simon Kalman (born March 21, 1952 in Oakland, California) is an American mathematician and winner of nine awards for expository writing in mathematics.
Education and career
After graduating from Oakland High School in 1970, Kalman matriculated at Harvey Mudd College, where he graduated in 1974. From 1974 to 1980 he was a graduate student at the University of Wisconsin–Madison, where he received his PhD in 1980. He was from 1978 to 1979 an instructor at Lawrence University in Appleton, Wisconsin, and from 1979 to 1983 an assistant professor at the University of Wisconsin–Green Bay. After teaching as a visiting lecturer from 1983 to 1985 at Augustana College in Sioux Falls, South Dakota, Kalman worked from 1985 to 1993 as a member of the technical staff of The Aerospace Corporation in Los Angeles. At Washington, D.C.'s American University he was from 1993 to 1998 an assistant professor, from 1998 to 2003 an associate professor, and from 2003 to 2018 a full professor, retiring in 2018 as professor emeritus. From 1996 to 1997 he was Associate Executive Director of the Mathematical Association of America (MAA) in Washington, D.C.
The MAA has given Kalman nine awards for outstanding expository articles or books. He won the George Pólya Award in 1994 and in 2003, the Trevor Evans Award in 1997 and (with coauthor Nathan Carter) in 2012, the Carl B. Allendoerfer Award (with coauthors Robert Mena and Shariar Shariari) in 1998 and (alone) in 2003, the Lester R. Ford Award in 2009 and (with coauthor Mark McKinzie) in 2013, and the Beckenbach Book Prize in 2012.
Selected publications
Articles
(1994 George Polya Award, independently awarded to Charles Groetsch in the same year)
(over 450 citations)
with Robert Mena and Shahriar Shahriari:
with James White:
with Jane Day:
with James White:
(2003 George Pólya Award)
with Robert Mena: (over 230 citations)
(2009 Lester R. Ford Award)
(slides from a talk)
with Mark McKinzie:
Books
with Sacha Forgoston and Albert Goetz:
(2012 Beckenbach Book Prize)
References
External links
1952 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvey Mudd College alumni
University of Wisconsin–Madison alumni
American University faculty and staff
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https://en.wikipedia.org/wiki/Basil%20Fadhel
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Basil Fadhel (born 10 May 1963) is an Iraqi former football midfielder who played for Iraq.He played for the national team in the 1989 Peace and Friendship Cup.
Statistics
International goals
Scores and results list Iraq's goal tally first.
References
Iraqi men's footballers
Iraq men's international footballers
Men's association football midfielders
1963 births
Living people
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https://en.wikipedia.org/wiki/Kazuki%20Fujimoto
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is a Japanese footballer currently playing as a forward for Oita Trinita.
Career statistics
Club
.
Notes
References
External links
1998 births
Living people
Association football people from Fukuoka (city)
National Institute of Fitness and Sports in Kanoya alumni
Japanese men's footballers
Men's association football forwards
J1 League players
Sagan Tosu players
Oita Trinita players
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https://en.wikipedia.org/wiki/Tatsuya%20Shirai
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is a Japanese footballer currently playing as a defender for FC Imabari.
Career statistics
Club
.
Notes
References
External links
1997 births
Living people
Japanese men's footballers
Men's association football defenders
Kanagawa University alumni
J3 League players
SC Sagamihara players
Association football people from Kawasaki, Kanagawa
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https://en.wikipedia.org/wiki/Mihai%20Udrea
|
Mihai Răzvan Udrea (born 20 July 2001) is a Romanian professional footballer who plays as a goalkeeper for Liga I club FCSB.
Career statistics
Club
Honours
Club
FCSB
Cupa României: 2019–20
References
2001 births
Living people
Romanian men's footballers
Men's association football goalkeepers
Liga I players
FC Steaua București players
Liga II players
FC Unirea Constanța players
Liga III players
FCSB II players
ACS Viitorul Târgu Jiu players
Footballers from Craiova
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https://en.wikipedia.org/wiki/Mahmoud%20Assad
|
Mahmoud Assad is a former Iraqi football forward who played for Iraq between 1966 and 1967. He played in the 1966 Arab Nations Cup and scored 1 goal.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
Iraqi men's footballers
Iraq men's international footballers
Living people
Men's association football forwards
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Kosei%20Okazawa
|
is a Japanese footballer who plays as a defensive midfielder for J3 League club FC Ryukyu, on loan from Cerezo Osaka.
Career statistics
Club
.
References
External links
2003 births
Living people
Japanese men's footballers
Men's association football midfielders
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
FC Ryukyu players
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https://en.wikipedia.org/wiki/Bert%20Knott
|
Herbert Knott (5 December 1914 – June 1986) was an English professional footballer who played in the Football League for Walsall and Hull City as an inside forward.
Career statistics
Honours
Margate
Kent League First Division: 1946–47
References
English men's footballers
English Football League players
Lincoln City F.C. wartime guest players
Sheffield United F.C. wartime guest players
Hull City A.F.C. wartime guest players
Reading F.C. wartime guest players
Norwich City F.C. wartime guest players
Notts County F.C. wartime guest players
Millwall F.C. wartime guest players
Clapton Orient F.C. wartime guest players
1914 births
1986 deaths
People from Goole
Men's association football inside forwards
Goole Town F.C. players
Arsenal F.C. players
Hendon F.C. players
Margate F.C. players
Brentford F.C. players
Stourbridge F.C. players
Walsall F.C. players
Brierley Hill Alliance F.C. players
Hull City A.F.C. players
Bradford (Park Avenue) A.F.C. players
Hinckley Athletic F.C. players
Kent Football League (1894–1959) players
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https://en.wikipedia.org/wiki/Arthur%20Barraclough
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Arthur Barraclough (7 November 1916 – 2005) was an English professional footballer who played in the Football League for Swindon Town as an outside left.
Career statistics
References
English men's footballers
English Football League players
1916 births
2005 deaths
Footballers from West Yorkshire
Men's association football outside forwards
Peterborough United F.C. players
Midland Football League players
Chelsea F.C. players
Swindon Town F.C. players
Clapton Orient F.C. wartime guest players
Notts County F.C. wartime guest players
Doncaster Rovers F.C. wartime guest players
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https://en.wikipedia.org/wiki/Yuma%20Matsumoto
|
is a Japanese footballer who playing as a midfielder and currently plays for FC Imabari.
Career statistics
Club
.
Notes
References
External links
Profile at FC Imabari
1999 births
Living people
Japanese men's footballers
Men's association football midfielders
Niigata University of Health and Welfare alumni
J3 League players
Kashiwa Reysol players
Kataller Toyama players
FC Imabari players
|
https://en.wikipedia.org/wiki/List%20of%20FC%20Ararat-Armenia%20records%20and%20statistics
|
Football Club Ararat-Armenia is an Armenian professional football club based in Yerevan. The club was formed in 2017 as FC Avan Academy before changing their name to FC Ararat-Moskva at the beginning of 2018, and then FC Ararat-Armenia upon gaining promotion to the Armenian Premier League in the summer of 2018.This article encompasses the major records set by the club and their players in the Armenian Premier League, Armenian Cup and European competitions. The player records section includes details of the club's goalscorers and those who have made more than 50 appearances in first-team competitions.
Players
Most appearances
Players played over 50 competitive, professional matches only. Appearances as substitute (goals in parentheses) included in total.
Goal scorers
Competitive, professional matches only, appearances including substitutes appear in brackets.
Clean Sheets
Competitive, professional matches only, appearances including substitutes appear in brackets.
Internationals
Current players
Away on loan
Former players
Team
Record wins
Record win: 11–2
v Sevan, 2019–20 Armenian Cup, 27 November 2019.
Record League win: 8–0
v Erebuni, 2017–18 Armenian First League, 12 March 2018.
Record Armenian Cup win: 11–2
v Sevan, 2019–20 Armenian Cup, 27 November 2019.
Record home win: 8–0
v Erebuni, 2017–18 Armenian First League, 12 March 2018.
Record away win: 11–2
v Sevan, 2019–20 Armenian Cup, 27 November 2019.
Record defeats
Record defeat: 0–4
v Gandzasar Kapan, 2017–18 Armenian Cup Quarter-Final 2nd leg, 11 October 2017.
Record League defeat: 1–5
v Lori, 2017–18 Armenian First League, 3 September 2017.
Record Armenian Cup defeat: 0–4
v Gandzasar Kapan, 2017–18 Armenian Cup Quarter-Final 2nd leg, 11 October 2017.
Record European defeat: 1–3
v AIK, 2019–20 UEFA Champions League First qualifying round 2nd leg, 17 July 2019.
Record home defeat: 0–4
v Gandzasar Kapan, 2017–18 Armenian Cup Quarter-Final 2nd leg, 11 October 2017.
Record away defeat: 0–3
v Gandzasar Kapan, 2017–18 Armenian Cup Quarter-Final 1st leg, 13 September 2017.
Wins/draws/losses in a season
Most wins in a league season: 18 – 2018–19
Most draws in a league season: 7 – 2018–19, 2019–20
Most defeats in a league season: 9 – 2017-18
Fewest wins in a league season: 14 – 2017-18
Fewest draws in a league season: 4 – 2017-18
Fewest defeats in a league season: 6 – 2019–20
Goals
Most League goals scored in a season: 85 – 2019-20
Most League goals scored in a season: 65 – 2017–18
Fewest League goals scored in a season: 45 – 2019-20
Most League goals conceded in a season: 41 – 2017–18
Fewest League goals conceded in a season: 23 – 2019-20
Points
Most points in a season:
76 in 36 matches, 2022–23 Armenian Premier League
Fewest points in a season:
38 in 24 matches, 2020–21 Armenian First League
References
FC Ararat-Armenia
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https://en.wikipedia.org/wiki/Bright%20Machida
|
is a Japanese footballer currently playing as a forward for FC Gifu.
Career statistics
Club
.
Notes
References
External links
1996 births
Living people
Japanese men's footballers
Men's association football forwards
Tokyo International University alumni
J3 League players
Japan Soccer College players
FC Gifu players
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https://en.wikipedia.org/wiki/Soya%20Takada
|
is a Japanese footballer currently playing as a forward for Tokushima Vortis, on loan from Omiya Ardija.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Sportspeople from Saitama Prefecture
Association football people from Saitama Prefecture
Japanese men's footballers
Japan men's youth international footballers
Men's association football forwards
J2 League players
Omiya Ardija players
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https://en.wikipedia.org/wiki/Misaki%20Haruyama
|
is a Japanese footballer currently playing as a forward for Machida Zelvia.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Sportspeople from Sendai
Association football people from Miyagi Prefecture
Japanese men's footballers
Japan men's youth international footballers
Men's association football forwards
J2 League players
FC Machida Zelvia players
|
https://en.wikipedia.org/wiki/Set%20theory%20%28disambiguation%29
|
Set theory is a branch of mathematics concerning mathematical sets. A set theory may also refer to a specific formalization of the mathematics of sets; for a listing of different alternative set theories in this sense, see alternative set theory.
Set theory may also refer to:
Set theory (music), a theory providing concepts for categorizing musical objects and describing their relationships
Set Theory: An Introduction to Independence Proofs, a book by Kenneth Kunen
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https://en.wikipedia.org/wiki/Charlie%20Brooks%20%28footballer%29
|
Charles Edward Brooks (12 January 1911 – October 1980) was an English professional footballer who played in the Football League for Clapton Orient as a right back.
Career statistics
References
English men's footballers
English Football League players
Leyton Orient F.C. players
1911 births
1980 deaths
Men's association football fullbacks
Sportspeople from Folkestone
Arsenal F.C. players
Nunhead F.C. players
Folkestone F.C. players
Crystal Palace F.C. players
Clapton Orient F.C. wartime guest players
People from Brabourne
Footballers from Kent
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https://en.wikipedia.org/wiki/Leonard%20Gross
|
Leonard Gross (born February 24, 1931) is an American mathematician and Professor Emeritus of Mathematics at Cornell University.
Gross has made fundamental contributions to mathematics and the mathematically rigorous study of quantum field theory.
Education and career
Leonard Gross graduated from James Madison High School in December 1948. He was awarded an Emil Schweinberg scholarship that enabled him to attend college. He studied at City College of New York for one term and then studied electrical engineering at Cooper Union for two years. He then transferred to the University of Chicago, where he obtained a master's degree in physics and mathematics (1954) and a Ph.D. in mathematics (1958).
Gross taught at Yale University and was awarded a National Science Foundation Fellowship in 1959. He joined the faculty of the mathematics department of Cornell University in 1960. Gross was a member of the Institute for Advanced Study in 1959 and in 1983 and has held other visiting positions. He has supervised 35 doctoral students.
Gross serves on the editorial boards of the Journal of Functional Analysis, and Potential Analysis.
Research
Gross's scientific work has centered on the mathematically rigorous study of quantum field theories and related mathematical theories such as statistical mechanics. His early works developed the foundations of integration on infinite-dimensional spaces and analytic tools needed for quantum fields corresponding to classical fields described by linear equations. His later works have been devoted to Yang–Mills theory and related mathematical theories such as analysis on loop groups.
Abstract Wiener spaces
Gross's earliest mathematical works were on integration and harmonic analysis on infinite-dimensional spaces. These ideas, and especially the need for a structure within which
potential theory in infinite dimensions could be studied, culminated in Gross's construction of abstract Wiener spaces in 1965. This structure has since become a standard framework for infinite-dimensional analysis.
Logarithmic Sobolev inequalities
Gross was one of the initiators of the study of logarithmic Sobolev inequalities, which he discovered in 1967 for his work in constructive quantum field theory and published later in two foundational papers established these inequalities for the Bosonic and Fermionic cases. The inequalities were named by Gross, who established the inequalities in dimension-independent form, a key feature especially in the context of applications to infinite-dimensional settings such as for quantum field theories. Gross's logarithmic Sobolev inequalities proved to be of great significance well beyond their original intended scope of application, for example in the proof of the Poincaré conjecture by Grigori Perelman.
Analysis on loop groups and Lie groups
Gross has done important work in the study of loop groups, for example proving the Gross ergodicity theorem for the pinned Wiener measure under the acti
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https://en.wikipedia.org/wiki/Plane%E2%80%93plane%20intersection
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In analytic geometry, the intersection of two planes in three-dimensional space is a line.
Formulation
The line of intersection between two planes and where are normalized is given by
where
Derivation
This is found by noticing that the line must be perpendicular to both plane normals, and so parallel to their cross product (this cross product is zero if and only if the planes are parallel, and are therefore non-intersecting or entirely coincident).
The remainder of the expression is arrived at by finding an arbitrary point on the line. To do so, consider that any point in space may be written as , since is a basis. We wish to find a point which is on both planes (i.e. on their intersection), so insert this equation into each of the equations of the planes to get two simultaneous equations which can be solved for and .
If we further assume that and are orthonormal then the closest point on the line of intersection to the origin is . If that is not the case, then a more complex procedure must be used.
Dihedral angle
Given two intersecting planes described by and , the dihedral angle between them is defined to be the angle between their normal directions:
References
Euclidean geometry
Computational physics
Geometric algorithms
Geometric intersection
Planes (geometry)
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https://en.wikipedia.org/wiki/Mireille%20Martin-Deschamps
|
Mireille Martin-Deschamps is a French mathematician who studies the algebraic geometry of space curves. She was president of the Société mathématique de France.
Education and career
Martin-Deschamps studied at the École normale supérieure de jeunes filles from 1965 to 1969, and completed a doctorate in 1976 at Paris-Sud University, supervised by Pierre Samuel. She was a researcher for the French National Centre for Scientific Research from 1969 until 2003, when she became a professor at Versailles Saint-Quentin-en-Yvelines University. She retired in 2010, and the university held a colloquium in honor of her retirement.
She was president of the Société mathématique de France from 1998 to 2001. As well, she served on the executive committee of the European Mathematical Society beginning in 2006.
Research
Martin-Deschamps's doctoral work was in algebraic geometry in the style of Alexander Grothendieck. Her later work involved Hilbert schemes of space curves in projective space.
References
Year of birth missing (living people)
Living people
French mathematicians
French women mathematicians
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https://en.wikipedia.org/wiki/Ben%20Martino
|
Ben Martino (born September 13, 2002), is an American professional soccer player who plays as a goalkeeper for Nashville SC in Major League Soccer.
Career statistics
Club
Notes
References
2002 births
Living people
Men's association football goalkeepers
American men's soccer players
Homegrown Players (MLS)
Nashville SC players
Philadelphia Union II players
Soccer players from Pennsylvania
USL Championship players
Virginia Tech Hokies men's soccer players
MLS Next Pro players
Huntsville City FC players
|
https://en.wikipedia.org/wiki/Shori%20Murata
|
is a Japanese professional footballer who plays as a defensive midfielder for Cambodian Premier League club Tiffy Army.
Career statistics
Club
Notes
References
1993 births
Living people
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football midfielders
Kanto Gakuin University alumni
Athletic 220 FC players
F.C. Chanthabouly players
Yangon United F.C. players
Persiraja Banda Aceh players
Lao Premier League players
Myanmar National League players
Liga 1 (Indonesia) players
Expatriate men's footballers in Laos
Japanese expatriate sportspeople in Laos
Expatriate men's footballers in Mongolia
Japanese expatriate sportspeople in Mongolia
Expatriate men's footballers in Myanmar
Japanese expatriate sportspeople in Myanmar
Expatriate men's footballers in Indonesia
Japanese expatriate sportspeople in Indonesia
Expatriate men's footballers in Cambodia
Japanese expatriate sportspeople in Cambodia
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https://en.wikipedia.org/wiki/Itsuki%20Kurata
|
is a Japanese footballer currently playing as a left-back for Codru Lozova.
Career statistics
Club
.
Notes
References
1999 births
Living people
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football defenders
Sakushin Gakuin University alumni
Moldovan Super Liga players
Tokyo Musashino United FC players
FC Codru Lozova players
Expatriate men's footballers in Moldova
Japanese expatriate sportspeople in Moldova
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https://en.wikipedia.org/wiki/Diego%20Corvalan
|
Diego Miguel Corvalan Couceiro (born 17 February 2002) is a Swiss professional footballer who plays as a right-back for YF Juventus.
Career statistics
Club
Notes
References
2002 births
Footballers from Zürich
Swiss people of Argentine descent
Sportspeople of Argentine descent
Living people
Swiss men's footballers
Switzerland men's youth international footballers
Men's association football defenders
FC Zürich players
SC Young Fellows Juventus players
FC Baden players
Swiss Super League players
Swiss Promotion League players
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https://en.wikipedia.org/wiki/Silvan%20Wallner
|
Silvan Jeremy Wallner (born 15 January 2002) is a Swiss professional footballer who plays as a defender for Zürich.
Career statistics
Club
References
2002 births
Living people
Swiss men's footballers
Switzerland men's youth international footballers
Men's association football defenders
Swiss Super League players
Swiss Challenge League players
Swiss Promotion League players
FC Zürich players
FC Wil players
Swiss people of Austrian descent
Footballers from Zürich
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https://en.wikipedia.org/wiki/Soheil%20Arghandewall
|
Soheil Arghandewall (born 19 August 2001) is a German professional footballer who plays as a midfielder for Swiss club YF Juventus.
Career statistics
References
2001 births
Footballers from Münster
Living people
German men's footballers
German people of Afghan descent
Men's association football midfielders
SC Preußen Münster players
FC Zürich players
SC Young Fellows Juventus players
Swiss Super League players
Swiss Promotion League players
German expatriate men's footballers
German expatriate sportspeople in Switzerland
Expatriate men's footballers in Switzerland
21st-century German people
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https://en.wikipedia.org/wiki/Enit%20Sadiku
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Enit Sadiku (born 14 July 1998) is a Swiss professional footballer who plays as a right-back for FC Uster.
Career statistics
Club
Notes
References
1998 births
Swiss people of Kosovan descent
Footballers from Zürich
Living people
Swiss men's footballers
Men's association football defenders
FC Zürich players
Swiss Promotion League players
Swiss Super League players
Swiss 1. Liga (football) players
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https://en.wikipedia.org/wiki/Basil%20Erne
|
Basil Erne (born 2 June 2000) is a Swiss professional footballer who plays as a left-back for Swiss club Zürich U21.
Career statistics
Club
Notes
References
2000 births
People from Meilen District
Living people
Swiss men's footballers
Men's association football defenders
FC Zürich players
Swiss Super League players
Swiss Promotion League players
Footballers from the canton of Zürich
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https://en.wikipedia.org/wiki/Elivelton%20%28footballer%2C%20born%201995%29
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Elivelton Ubiratan Oliveira de Lima (born 13 October 1995), commonly known as Elivelton, is a Brazilian footballer who plays for Sergipe.
Career statistics
Club
References
1995 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football defenders
Campeonato Brasileiro Série B players
Paraná Clube players
Boa Esporte Clube players
Paraná Soccer Technical Center players
FC Cascavel players
FC Tucson players
Lagarto Futebol Clube players
Club Sportivo Sergipe players
Brazilian expatriate sportspeople in the United States
Expatriate men's soccer players in the United States
Footballers from Curitiba
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https://en.wikipedia.org/wiki/Ezra%20Brown
|
Ezra Abraham "Bud" Brown (born January 22, 1944, in Reading, Pennsylvania) is an American mathematician active in combinatorics, algebraic number theory, elliptic curves, graph theory, expository mathematics and cryptography. He spent most of his career at Virginia Tech where he is now Alumni Distinguished Professor Emeritus of Mathematics.
Education and career
Brown earned a BA at Rice University in 1965. He then studied mathematics at Louisiana State University (LSU), getting an MS in 1967 and a PhD in 1969 with the dissertation "Representations of Discriminantal Divisors by Binary Quadratic Forms" under Gordon Pall. He joined Virginia Tech in 1969 becoming Assistant Professor (1969–73), Associate Professor (1973–81), Professor (1981–2005), and Alumni Distinguished Professor of Mathematics and Distinguished Professor of Mathematics (2005–2017). He retired from Virginia Tech in 2017.
Brown became interested in elliptic curves while at LSU and this has remained one of his principal areas of research along with quadratic forms and algebraic number theory in general.
His books include The Unity of Combinatorics (MAA, 2020), co-authored with Richard K. Guy.
Personal life
While at LSU he met his future wife Jo. Brown remained at Virginia Tech until his retirement in 2017.
At the age of 16 Brown taught himself to play the piano, and in college he acted in several musicals and joined an a cappella chorus. In 1989, he joined the Blacksburg Master Chorale and the chorus of Opera Roanoke. Starting in 2011 he took his love of music and math to MathFest where he an his fellow mathematicians composed new words to old show tunes and even took part in a Gilbert-and-Sullivan Singalong at MathFest 2016 with his "Biscuits of Number Theory" co-editor Art Benjamin.
Brown and his mathematical grandfather, L. E. Dickson, have the same birthday.
Selected publications
papers
2018 "Five Families Around a Well: A New Look at an Old Problem" (with Matthew Crawford)
2015 "Many More Names of (7,3,1)]"
2012 "Why Ellipses Are Not Elliptic Curves" (with Adrian Rice)
2009 "Kirkman's Schoolgirls Wearing Hats and Walking Through Fields of Numbers" (with Keith Mellinger)
2005 "Phoebe Floats!"Phoebe Floats!
2004 "The Fabulous (11, 5, 2) Biplane"
2002 "The Many Names of (7,3,1)"
2000 "Three Fermat Trails to Elliptic Curves"
1999 "Square Roots from 1; 24, 51, 10 to Dan Shanks"
books
2020 (with Richard K. Guy) The Unity of Combinatorics, American Mathematical Society,
2009 (co-edited with Arthur T. Benjamin) Biscuits of Number Theory, MAA Publications,
1990 (translation from German) Regiomontanus: His Life and Work
Awards
2022 MAA Chauvenet Prize (with Matthew Crawford) for "Five Families Around a Well: A New Look at an Old Problem"
2014 MAA Sister Helen Christensen Service Award
2013 MAA Allendoerfer Award (with Adrian Rice) for "Why Ellipses Are Not Elliptic Curves"
2010 MAA Allendoerfer Award (with Keith Mellinger) for "Kirkman's Schoolgirls Weari
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https://en.wikipedia.org/wiki/Logarithmic%20Sobolev%20inequalities
|
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known.
Gross proved the inequality:
where is the -norm of , with being standard Gaussian measure on Unlike classical Sobolev inequalities, Gross's log-Sobolev inequality does not have any dimension-dependent constant, which makes it applicable in the infinite-dimensional limit.
In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f
where is the entropy functional.
Notes
References
Axiomatic quantum field theory
Sobolev spaces
Logarithms
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https://en.wikipedia.org/wiki/A%20Topological%20Picturebook
|
A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
Topics
Although the book includes some computer-generated images, most of it is centered on hand drawing techniques. After an introductory chapter on topological surfaces, the cusps in the outlines of surfaces formed when viewing them from certain angles, and the self-intersections of immersed surfaces, the next two chapters are centered on drawing techniques: chapter two concerns ink, paper, cross-hatching, and shading techniques for indicating the curvature of surfaces, while chapter three provides some basic techniques of graphical perspective.
The remaining five chapters of the book provide case studies of different visualization problems in mathematics, called by the book "picture stories". The mathematical topics visualized in these chapters include the Penrose triangle and related optical illusions; the Roman surface and Boy's surface, two different immersions of the projective plane, and deformations between them; sphere eversion and the Morin surface; group theory, the mapping class groups of surfaces, and the braid groups; and knot theory, Seifert surfaces, the Hopf fibration of space by linked circles, and the construction of knot complements by gluing polyhedra.
Audience and reception
Reviewer Athanase Papadopoulos calls the book "a drawing manual for mathematicians". However, reviewer Dave Auckly disagrees, writing that, although the book explains the principles of Francis's own visualizations, it is not really a practical guide to constructing visualizations more generally. Auckly also calls the chapter on perspective "a bizarre mix of mathematical formulas and artistic constructions". Nevertheless, he reviews it positively as "mathematics book loaded with pictures", aimed at undergraduates interested in mathematics.
More generally, Bill Satzer suggests that the book can provide inspiration for other mathematical illustrators, and for how mathematics is taught and imagined, and Dušan Repovš sees the book as an encouragement to professional mathematicians to more heavily illustrate their work. Jeffrey Weeks sees the book as an embodiment of the principle that abstract mathematical results can often be best appreciated through concrete examples. Thomas Banchoff writes that most readers from a general audience will be "captivated" by the intricate artworks of the book, and professional mathematicians will find sufficient depth in its explanation of these works. However, Weeks writes that the book fails at another stated purpose, allowing artists to appreciate the mathematics behind the artworks it presents, because the mathematics is too advanced for easy understanding by a general audience.
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https://en.wikipedia.org/wiki/Parfait%20Guiagon
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Parfait Guiagon (born 22 February 2001) is an Ivorian professional footballer who plays as a midfielder for Charleroi. He was included in The Guardian's "Next Generation 2018".
Career statistics
Club
Notes
References
2001 births
Living people
Ivorian men's footballers
Africa Sports d'Abidjan players
Maccabi Tel Aviv F.C. players
Beitar Tel Aviv Bat Yam F.C. players
Maccabi Netanya F.C. players
R. Charleroi S.C. players
Israeli Premier League players
Liga Leumit players
Belgian Pro League players
Ivorian expatriate men's footballers
Expatriate men's footballers in Israel
Expatriate men's footballers in Belgium
Ivorian expatriate sportspeople in Israel
Ivorian expatriate sportspeople in Belgium
Footballers at the 2020 Summer Olympics
Men's association football midfielders
Olympic footballers for Ivory Coast
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https://en.wikipedia.org/wiki/Jeong%20Ho-jin
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Jeong Ho-jin (; born 6 August 1999) is a South Korean footballer who plays as a midfielder for Jeonnam Dragons.
Career statistics
Club
References
1999 births
Living people
South Korean men's footballers
South Korea men's under-20 international footballers
Men's association football midfielders
Korea University alumni
K League 2 players
K League 1 players
Jeonnam Dragons players
Suwon Samsung Bluewings players
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https://en.wikipedia.org/wiki/Aniekeme%20Okon
|
Aniekeme Asuquo Okon (born 8 May 1999) is a Nigerian footballer who plays as a forward for Kano Pillars.
Career statistics
Club
Notes
References
1999 births
Living people
Nigerian men's footballers
Nigeria men's youth international footballers
Nigerian expatriate men's footballers
Men's association football forwards
Akwa United F.C. players
Altay S.K. footballers
Kano Pillars F.C. players
Nigeria Professional Football League players
Nigerian expatriate sportspeople in Turkey
Expatriate men's footballers in Turkey
Nigeria men's under-20 international footballers
People from Uyo
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https://en.wikipedia.org/wiki/Asenele%20Velebayi
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Asenele Velebayi (born 11 December 2002) is a South African soccer player currently playing as a midfielder for Ajax Cape Town.
Career statistics
Club
Notes
References
2002 births
Living people
South African men's soccer players
Men's association football midfielders
National First Division players
Cape Town Spurs F.C. players
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https://en.wikipedia.org/wiki/Luthando%20Mateza
|
Luthando Mateza (born 8 February 1998) is a South African soccer player who plays as a midfielder for Steenberg United.
Career statistics
Notes
References
1998 births
Living people
South African men's soccer players
Men's association football midfielders
South African Premier Division players
Cape Town Spurs F.C. players
Steenberg United F.C. players
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https://en.wikipedia.org/wiki/Suvodol%2C%20Demir%20Hisar
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Suvodol () is a village in the municipality of Demir Hisar, North Macedonia.
Demographics
In statistics gathered by Vasil Kanchov in 1900, the village of Suvodol was inhabited by 120 Muslim Albanians.
According to the 2002 census, the village had a total of 415 inhabitants. Ethnic groups in the village include:
Macedonians 369
Turks 13
Serbs 1
Albanians 31
Others 1
References
Villages in Demir Hisar Municipality
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https://en.wikipedia.org/wiki/George%20Goodyear%20%28footballer%29
|
George William Goodyear (5 July 1916 – 16 July 2001) was an English professional footballer who played in the Football League for Southend United and Luton Town as a wing half.
Career statistics
References
Clapton Orient F.C. wartime guest players
English Football League players
English men's footballers
1916 births
2001 deaths
Men's association football wing halves
Footballers from Luton
Hitchin Town F.C. players
Southend United F.C. players
Luton Town F.C. players
Crystal Palace F.C. players
Biggleswade Town F.C. players
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https://en.wikipedia.org/wiki/Judith%20Covington
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Judith Lynnette Covington is an American mathematician and mathematics educator who works as a professor of mathematics at Louisiana State University Shreveport (LSUS).
Education and career
Covington earned her Ph.D. in 1993 at the University of Louisiana at Lafayette, with a dissertation in topological group theory jointly supervised by Victor P. Schneider and Bradd Clark, and in the same year joined the LSUS faculty. In the mid-1990s, she became one of the first cohort of fellows of Project NExT, a professional development program of the Mathematical Association of America, and she has continued to be associated with Project NExT as part of its leadership team since then.
Beyond her work in teacher education at LSUS, she has also contributed to local mathematics education by founding the North Louisiana Math Teachers' Circle in 2010, and she was elected as the governor of the Louisiana–Mississippi section of the Mathematical Association of America in 2016.
Recognition
In 2004 Covington was named LSUS Elmer and Barbara Simon Distinguished Teaching Professor. The Louisiana–Mississippi section of the Mathematical Association of America gave her their Distinguished Teaching Award in 2012. In 2015 Covington was one of three winners of the Deborah and Franklin Haimo Awards for Distinguished College or University Teaching of Mathematics of the Mathematical Association of America.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Mathematics educators
University of Louisiana at Lafayette alumni
Louisiana State University Shreveport faculty
20th-century American women
21st-century American women
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https://en.wikipedia.org/wiki/Edmund%20Arko-Mensah
|
Edmund Arko-Mensah (born 9 September 2001) is a Ghanaian footballer who plays as a left-back for Veikkausliiga side FC Honka.
Career statistics
Club
Notes
References
2001 births
Living people
Ghanaian men's footballers
Ghanaian expatriate men's footballers
Ghana men's youth international footballers
Men's association football defenders
Legon Cities FC players
Berekum Chelsea F.C. players
FC Honka players
Ghana Premier League players
Veikkausliiga players
Expatriate men's footballers in Finland
Ghanaian expatriate sportspeople in Finland
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https://en.wikipedia.org/wiki/Jiro%20Nakamura
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is a Japanese professional footballer who plays as a winger for J1 League club Gamba Osaka.
Career statistics
Club
.
Notes
References
External links
Profile at Gamba Osaka
2003 births
Living people
Japanese men's footballers
Japan men's youth international footballers
Men's association football midfielders
J3 League players
J1 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/Shohei%20Ogushi
|
is a Japanese footballer currently studying at the Kyoto Sangyo University.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
Association football people from Hyōgo Prefecture
Kyoto Sangyo University alumni
Japanese men's footballers
Japan men's youth international footballers
Men's association football defenders
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
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https://en.wikipedia.org/wiki/Temma%20Nomura
|
is a Japanese footballer currently playing as a left-back.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Japanese men's footballers
Komazawa University alumni
Men's association football defenders
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
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https://en.wikipedia.org/wiki/Kaito%20Hayashida
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is a Japanese footballer who plays as a defender for the University of Tsukuba.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Association football people from Hyōgo Prefecture
University of Tsukuba alumni
Japanese men's footballers
Japan men's youth international footballers
Men's association football defenders
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
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https://en.wikipedia.org/wiki/Teruki%20Origuchi
|
is a Japanese footballer.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Japanese men's footballers
Men's association football goalkeepers
Fuji University alumni
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
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https://en.wikipedia.org/wiki/Yoshihito%20Iizuka
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is a Japanese footballer currently playing as a goalkeeper and studying at the Sakushin Gakuin University.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Japanese men's footballers
Sakushin Gakuin University alumni
Men's association football goalkeepers
J3 League players
FC Tokyo players
FC Tokyo U-23 players
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https://en.wikipedia.org/wiki/Closed%20graph%20theorem%20%28functional%20analysis%29
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In mathematics, particularly in functional analysis and topology, the closed graph theorem is a result connecting the continuity of certain kinds of functions to a topological property of their graph. In its most elementary form, the closed graph theorem states that a linear function between two Banach spaces is continuous if and only if the graph of that function is closed.
The closed graph theorem has extensive application throughout functional analysis, because it can control whether a partially-defined linear operator admits continuous extensions. For this reason, it has been generalized to many circumstances beyond the elementary formulation above.
Preliminaries
The closed graph theorem is a result about linear map between two vector spaces endowed with topologies making them into topological vector spaces (TVSs). We will henceforth assume that and are topological vector spaces, such as Banach spaces for example, and that Cartesian products, such as are endowed with the product topology.
The of this function is the subset
of where denotes the function's domain.
The map is said to have a (in ) if its graph is a closed subset of product space (with the usual product topology).
Similarly, is said to have a if is a sequentially closed subset of
A is a linear map whose graph is closed (it need not be continuous or bounded).
It is common in functional analysis to call such maps "closed", but this should not be confused the non-equivalent notion of a "closed map" that appears in general topology.
Partial functions
It is common in functional analysis to consider partial functions, which are functions defined on a dense subset of some space
A partial function is declared with the notation which indicates that has prototype (that is, its domain is and its codomain is ) and that is a dense subset of
Since the domain is denoted by it is not always necessary to assign a symbol (such as ) to a partial function's domain, in which case the notation or may be used to indicate that is a partial function with codomain whose domain is a dense subset of
A densely defined linear operator between vector spaces is a partial function whose domain is a dense vector subspace of a TVS such that is a linear map.
A prototypical example of a partial function is the derivative operator, which is only defined on the space of once continuously differentiable functions, a dense subset of the space of continuous functions.
Every partial function is, in particular, a function and so all terminology for functions can be applied to them. For instance, the graph of a partial function is (as before) the set
However, one exception to this is the definition of "closed graph". A function is said to have a closed graph (respectively, a sequentially closed graph) if is a closed (respectively, sequentially closed) subset of in the product topology; importantly, note that the product space is and as it was defined above
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https://en.wikipedia.org/wiki/Jake%20Iceton
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Jacob Iceton (22 October 1903 – 1981) was an English professional footballer who played in the Football League for Fulham, Clapton Orient and Aldershot as a goalkeeper.
Career statistics
Honours
Fulham
Football League Third Division South: 1931–32
References
English Football League players
English men's footballers
Leyton Orient F.C. players
Men's association football goalkeepers
1903 births
1981 deaths
Footballers from County Durham
Cockfield F.C. players
Hull City A.F.C. players
Shildon A.F.C. players
Fulham F.C. players
Aldershot F.C. players
Worcester City F.C. players
Clapton Orient F.C. wartime guest players
People from West Auckland
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https://en.wikipedia.org/wiki/Noah%20Henchoz
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Noah Henchoz (born 22 February 2002) is a Swiss professional footballer who plays as a defender for Servette.
Career statistics
Club
Notes
References
2002 births
Living people
Sportspeople from the canton of Geneva
Swiss men's footballers
Switzerland men's youth international footballers
Men's association football defenders
Étoile Carouge FC players
Servette FC players
Swiss Super League players
2. Liga Interregional players
Swiss Promotion League players
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https://en.wikipedia.org/wiki/Nick%20Perc
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Nick Perc (born 27 May 2003) is a Slovenian footballer who plays as a forward for Slovenian PrvaLiga side Domžale.
Career statistics
Club
References
External links
Nick Perc at NZS
2003 births
Living people
Slovenian men's footballers
Slovenia men's youth international footballers
Slovenia men's under-21 international footballers
Men's association football forwards
Slovenian PrvaLiga players
NK Celje players
NK Domžale players
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https://en.wikipedia.org/wiki/Eric%20Lambert%20%28English%20footballer%29
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Eric Victor Lambert (4 August 1920 – 1979) was an English professional footballer who played in the Football League for Hartlepools United as a full back.
Career statistics
References
English Football League players
Clapton Orient F.C. wartime guest players
Men's association football fullbacks
1979 deaths
English men's footballers
1920 births
Footballers from Derby
Nottingham Forest F.C. players
Derby County F.C. players
Hartlepool United F.C. players
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https://en.wikipedia.org/wiki/Eddie%20Lewis%20%28footballer%2C%20born%201926%29
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Edward Lewis (born 21 June 1926) was an English professional footballer who played in the Football League for Leyton Orient as a goalkeeper.
Career statistics
References
1926 births
English Football League players
Clapton Orient F.C. wartime guest players
English men's footballers
Men's association football goalkeepers
Footballers from West Bromwich
Leyton Orient F.C. players
Possibly living people
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https://en.wikipedia.org/wiki/Conceptual%20question
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Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require plugging in numerical values into previously discussed formulas. Such "plug-and-chug" numerical problems can often be solved correctly by just matching the pattern of the problem to a previously discussed problem and changing the numerical inputs, which requires significant amounts of time to perform the calculations but does not test or deepen the understanding of how the concepts and formulas should work together. Conceptual questions, therefore, provide a good complement to conventional numerical problems because they need minimal or no calculations and instead encourage the students to engage more deeply with the underlying concepts and how they relate to formulas.
Conceptual problems are often formulated as multiple-choice questions, making them easy to use during in-class discussions, particularly when utilizing active learning, peer instruction, and audience response. An example of a conceptual question in undergraduate thermodynamics is provided below:
During adiabatic expansion of an ideal gas, its temperatureincreases
decreases
stays the same
Impossible to tell/need more information
The use of conceptual questions in physics was popularized by Eric Mazur, particularly in the form of multiple-choice tests that he called ConcepTests. In recent years, multiple websites that maintain lists of conceptual questions have been created by instructors for various disciplines. Some books on physics provide many examples of conceptual questions as well.
Multiple conceptual questions can be assembled into a concept inventory to test the working knowledge of students at the beginning of a course or to track the improvement in conceptual understanding throughout the course.
References
Science education
Technology education
Engineering education
Mathematics education
Educational evaluation methods
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https://en.wikipedia.org/wiki/Andorra%20national%20football%20team%20records%20and%20statistics
|
The following tables show the Andorra national football team's all-time international record. The statistics are composed of FIFA World Cup, UEFA European Football Championship, UEFA Nations League, as well as numerous international friendly tournaments and matches.
Performances
''Last match updated was against on 17 November 2019
Performance by competition
Individual records
Player records
Manager records
Team records
Competition records
FIFA World Cup
Head-to-head record
References
Andorra national football team records and statistics
National association football team records and statistics
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https://en.wikipedia.org/wiki/Weverson%20%28footballer%2C%20born%202000%29
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Weverson Moreira da Costa (born 5 July 2000), simply known as Weverson, is a Brazilian footballer who plays as a left-back for Portuguese club Arouca.
Career statistics
Honours
São Paulo
Copa São Paulo de Futebol Jr.: 2019
References
2000 births
Footballers from Brasília
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Men's association football defenders
São Paulo FC players
Red Bull Bragantino players
F.C. Arouca players
Campeonato Brasileiro Série A players
Primeira Liga players
Brazilian expatriate men's footballers
Expatriate men's footballers in Portugal
Brazilian expatriate sportspeople in Portugal
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https://en.wikipedia.org/wiki/George%20Lunn%20%28footballer%29
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George Lunn (28 June 1915 – January 2000) was an English professional footballer who played in the Football League for Watford as a centre half.
Career statistics
References
English Football League players
Clapton Orient F.C. wartime guest players
English men's footballers
Men's association football wing halves
1915 births
2000 deaths
People from Bolton upon Dearne
Frickley Athletic F.C. players
Chester City F.C. wartime guest players
Doncaster Rovers F.C. wartime guest players
Fulham F.C. wartime guest players
Northampton Town F.C. wartime guest players
Rochdale A.F.C. wartime guest players
Southport F.C. wartime guest players
Stockport County F.C. wartime guest players
Wrexham F.C. wartime guest players
Watford F.C. wartime guest players
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https://en.wikipedia.org/wiki/IMA%20Journal%20of%20Numerical%20Analysis
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The IMA Journal of Numerical Analysis is a quarterly peer-reviewed scientific journal published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. It was established in 1981 and covers all aspects of numerical analysis, including theory, development or use of practical algorithms, and interactions between these aspects. The editors-in-chief are C.M. Elliott (University of Warwick), A. Iserles (University of Cambridge), and E. Süli (University of Oxford).
Abstracting and indexing
The journal is abstracted and indexed in:
According to the Journal Citation Reports, the journal has a 2019 impact factor of 2.275.
References
External links
Mathematics journals
Hybrid open access journals
Oxford University Press academic journals
Academic journals established in 1981
Quarterly journals
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