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https://en.wikipedia.org/wiki/Approximate%20fibration
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In algebraic topology, a branch of mathematics, an approximate fibration is a sort of fibration such that the homotopy lifting property holds only approximately. The notion was introduced by Coram and Duvall in 1977.
A manifold approximate fibration is a proper approximate fibration between manifolds. Some authors believe that manifold approximate fibrations are the "correct bundle theory for topological manifolds and singular spaces".
References
Further reading
nLab - approximate fibration
Algebraic topology
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https://en.wikipedia.org/wiki/Willard%20D.%20James
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Willard Donald James is an American mathematician most known for his work on the James-Stein estimator. He graduated with a Ph.D. in mathematics from University of Illinois in 1957 and was recruited to California State University, Long Beach in 1967 from which he retired as a Professor Emeritus in 1987.
References
Living people
20th-century American mathematicians
21st-century American mathematicians
University of Illinois alumni
California State University, Long Beach faculty
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Le%20Potier%27s%20vanishing%20theorem
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In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundle. The theorem states the following
In case of r = 1, and let E is an ample (or positive) line bundle on X, this theorem is equivalent to the Nakano vanishing theorem. Also, found another proof.
generalizes Le Potier's vanishing theorem to k-ample and the statement as follows:
gave a counterexample, which is as follows:
See also
vanishing theorem
Barth–Lefschetz theorem
Note
References
Further reading
External links
(OpenContent book)
Theorems in algebraic geometry
Theorems in complex geometry
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https://en.wikipedia.org/wiki/Metric%20lattice
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In the mathematical study of order, a metric lattice is a lattice that admits a positive valuation: a function satisfying, for any , and
Relation to other notions
A Boolean algebra is a metric lattice; any finitely-additive measure on its Stone dual gives a valuation.
Every metric lattice is a modular lattice, c.f. lower picture. It is also a metric space, with distance function given by With that metric, the join and meet are uniformly continuous contractions, and so extend to the metric completion (metric space). That lattice is usually not the Dedekind-MacNeille completion, but it is conditionally complete.
Applications
In the study of fuzzy logic and interval arithmetic, the space of uniform distributions is a metric lattice. Metric lattices are also key to von Neumann's construction of the continuous projective geometry. A function satisfies the one-dimensional wave equation if and only if it is a valuation for the lattice of spacetime coordinates with the natural partial order. A similar result should apply to any partial differential equation solvable by the method of characteristics, but key features of the theory are lacking.
References
Lattice theory
Metric spaces
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https://en.wikipedia.org/wiki/Gustavo%20Guti%C3%A9rrez%20%28footballer%29
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Gustavo Guadalupe Gutiérrez Muñoz (born 1 November 1996) is a Mexican professional footballer who plays as a goalkeeper.
Career statistics
Club
References
External links
Living people
1996 births
Men's association football goalkeepers
Liga MX players
Deportivo Toluca F.C. players
Footballers from Jalisco
People from Tepatitlán
Mexican men's footballers
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https://en.wikipedia.org/wiki/Alan%20Rodr%C3%ADguez%20%28Mexican%20footballer%29
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Alan Omar Rodríguez Ortiz (born 20 March 1996) is a Mexican professional footballer who plays as a midfielder.
Career statistics
Club
References
External links
Living people
1996 births
Mexican men's footballers
Men's association football midfielders
Ascenso MX players
Liga MX players
Liga Premier de México players
Deportivo Toluca F.C. players
Loros UdeC footballers
Tlaxcala F.C. players
Footballers from Jalisco
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https://en.wikipedia.org/wiki/Aldo%20Llanas
|
Aldo Emmanuel Llanas Valdez (born 7 February 2003) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club Toluca.
Career statistics
Club
Notes
References
External links
Living people
2003 births
Men's association football midfielders
Mexican men's footballers
Liga MX players
Deportivo Toluca F.C. players
Footballers from Coahuila
Sportspeople from Monclova
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https://en.wikipedia.org/wiki/MISSY
|
The Microdata Information System (MISSY) is a database-driven online system that provides structured metadata about selected research data of official statistics free of charge as part of the service infrastructure of the German Microdata Lab (GML) at GESIS – Leibniz Institute for the Social Sciences. MISSY is targeted at empirically working scientists who use official microdata for their research.
Documented data
Metadata for the following microdata are provided and regularly updated in MISSY:
German Microcensus (MZ)
European Union Statistics on Income and Living Conditions (EU-SILC)
European Union Labour Force Survey (EU-LFS)
All documentation in MISSY refers to microdata available for scientific purposes (Scientific Use Files).
Coverage
The metadata offered in MISSY includes aspects of information relevant for an analysis of the data collected in the respective surveys.
The MISSY metadata schema is based on the recommendations of the international documentation standard of the Data Documentation Initiative (DDI) and work by GML. In MISSY, the research-relevant metadata on official microdata are digitally prepared and available via a database, from where they may be automatically exported to statistical software or social science classification systems. The system supports comparisons between survey years, countries, and research-relevant variables. MISSY data adheres to FAIR criteria (findable, accessible, interoperable, and reusable) standards.
External links
Microdata Information System MISSY
Homepage of GESIS
German Microdata Lab
Data access European microdata
Data access German Microcensus
References
Databases in Germany
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https://en.wikipedia.org/wiki/Jaziel%20Mart%C3%ADnez
|
Jaziel Ismael Martínez Huerta (born 3 October 2000) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club Atlas, on loan from Monterrey.
Career statistics
Club
Honours
Monterrey
CONCACAF Champions League: 2021
References
External links
Living people
2000 births
Mexican men's footballers
Men's association football midfielders
Liga de Expansión MX players
Liga MX players
C.F. Monterrey players
Raya2 Expansión players
Footballers from Coahuila
Sportspeople from Saltillo
|
https://en.wikipedia.org/wiki/Jayden%20Addai
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Jayden Osei Addai (born 26 August 2005) is a Dutch footballer who currently plays as a forward for Jong AZ.
Personal life
Born in the Netherlands, Addai is of Ghanaian descent.
Career statistics
Club
Notes
References
2005 births
Living people
Dutch men's footballers
Netherlands men's youth international footballers
Dutch people of Ghanaian descent
Men's association football forwards
Eerste Divisie players
AZ Alkmaar players
Jong AZ players
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https://en.wikipedia.org/wiki/List%20of%20Inverness%20Caledonian%20Thistle%20F.C.%20records%20and%20statistics
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Inverness Caledonian Thistle are a Scottish professional association football club based in Inverness. They have played at their home ground, the Caledonian Stadium, since 1996, prior to that they played at Telford Street Park. Inverness CT joined the Scottish Football League in 1994, and the Scottish Premier League in 2004 as well as the Scottish Premiership in 2013.
The club's record appearance maker is Ross Tokely, who made 545 appearances between 1996 and 2012. Billy Mckay is the club's record goalscorer, scoring 102 goals in major competitions during his 3 spells with Inverness CT, passing previous record holder Dennis Wyness in a 3–2 loss to Airdrieonians in July 2023.
This list encompasses the major honours won by Inverness CT, records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Inverness CT players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at the Caledonian Stadium are also included in the list.
Honours
Inverness's first trophy was the Scottish Challenge Cup in 2003, which was won after a 2–0 win against Airdrie United. Their first national trophy win was the Scottish Cup in 2015, beating Falkirk 2–1. Inverness CT are yet to lift the Scottish League Cup, however they came close in 2014, losing 4–2 on Penalties to Aberdeen after a tight 0–0 draw. Inverness claimed their second Scottish Cup Final in 2023, where they lost 3–1 to Celtic.
Inverness's most recent trophy win was in 2020, when they shared the Scottish Challenge Cup with Raith Rovers due to the final being cancelled due to the Coronavirus Pandemic.
National
League
Scottish First Division/Scottish Championship (Second Tier)
Winners (2): 2003–04, 2009–10
Runners-up (1): 2019–20
Scottish Second Division (Third Tier)
Runners-up (1): 1998–99
Scottish Third Division (Fourth Tier)
Winners (1): 1996–97
Scottish Cup
Winners (1): 2014–15
Runners-up (1): 2022–23
Scottish League Cup
Runners-up (1): 2013–14
Scottish Challenge Cup
Winners (3): 2003–04, 2017–18, 2019–20
Runners-up (2): 1999–00, 2009–10
Regional
North of Scotland Cup (4): 1999–00, 2007–08, 2009–10, 2011–12
Inverness Cup (8): 1995–96, 1997–98, 1998–99, 1999–00, 2001–02, 2004–05, 2009–10, 2023–24
Other cups
Chic Allan Memorial Cup (2): 1994–95, 1998–99
Football Times Cup (1): 1998–99
PCT Cup (1): 1998–99
Player records
Appearances
Ross Tokely is the club's all time record appearance holder with 545 appearances in all competitions, including playoffs and Challenge Cups.
Most appearances in all competitions: Ross Tokely, 545.
Most League appearances: Ross Tokely, 456.
Most Scottish Cup appearances: Ross Tokely, 42.
Most League Cup appearances: Ross Tokely, 32
Most European appearances: 12 Players, 2
Youngest first-team player: D
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https://en.wikipedia.org/wiki/Kuratowski%27s%20intersection%20theorem
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In mathematics, Kuratowski's intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection. Kuratowski's result is a generalisation of Cantor's intersection theorem. Whereas Cantor's result requires that the sets involved be compact, Kuratowski's result allows them to be non-compact, but insists that their non-compactness "tends to zero" in an appropriate sense. The theorem is named for the Polish mathematician Kazimierz Kuratowski, who proved it in 1930.
Statement of the theorem
Let (X, d) be a complete metric space. Given a subset A ⊆ X, its Kuratowski measure of non-compactness α(A) ≥ 0 is defined by
Note that, if A is itself compact, then α(A) = 0, since every cover of A by open balls of arbitrarily small diameter will have a finite subcover. The converse is also true: if α(A) = 0, then A must be precompact, and indeed compact if A is closed. Also, if A is a subset of B, then α(A) ≤ α(B). In some sense, the quantity α(A) is a numerical description of "how non-compact" the set A is.
Now consider a sequence of sets An ⊆ X, one for each natural number n. Kuratowski's intersection theorem asserts that if these sets are non-empty, closed, decreasingly nested (i.e. An+1 ⊆ An for each n), and α(An) → 0 as n → ∞, then their infinite intersection
is a non-empty compact set.
The result also holds if one works with the ball measure of non-compactness or the separation measure of non-compactness, since these three measures of non-compactness are mutually Lipschitz equivalent; if any one of them tends to zero as n → ∞, then so must the other two.
References
Compactness theorems
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https://en.wikipedia.org/wiki/CISH
|
CISH or cish may refer to:
Chromogenic in situ hybridization, a technique in molecular biology
CISH (gene), coding for the cytokine-inducible SH2-containing protein
cish (mathematics), a hyperbolic function in mathematics
International Committee of Historical Sciences, also referred to as Comité International des Sciences Historiques (CISH) outside the anglosphere
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https://en.wikipedia.org/wiki/Bretagnolle%E2%80%93Huber%20inequality
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In information theory, the Bretagnolle–Huber inequality bounds the total variation distance between two probability distributions and by a concave and bounded function of the Kullback–Leibler divergence . The bound can be viewed as an alternative to the well-known Pinsker's inequality: when is large (larger than 2 for instance.), Pinsker's inequality is vacuous, while Bretagnolle–Huber remains bounded and hence non-vacuous. It is used in statistics and machine learning to prove information-theoretic lower bounds relying on hypothesis testing
Formal statement
Preliminary definitions
Let and be two probability distributions on a measurable space .
Recall that the total variation between and is defined by
The Kullback-Leibler divergence is defined as follows:
In the above, the notation stands for absolute continuity of with respect to , and stands for the Radon–Nikodym derivative of with respect to .
General statement
The Bretagnolle–Huber inequality says:
Alternative version
The following version is directly implied by the bound above but some authors prefer stating it this way.
Let be any event. Then
where is the complement of .
Indeed, by definition of the total variation, for any ,
Rearranging, we obtain the claimed lower bound on .
Proof
We prove the main statement following the ideas in Tsybakov's book (Lemma 2.6, page 89), which differ from the original proof (see C.Canonne's note for a modernized retranscription of their argument).
The proof is in two steps:
1. Prove using Cauchy–Schwarz that the total variation is related to the Bhattacharyya coefficient (right-hand side of the inequality):
2. Prove by a clever application of Jensen’s inequality that
Step 1:
First notice that
To see this, denote and without loss of generality, assume that such that . Then we can rewrite
And then adding and removing we obtain both identities.
Then
because
Step 2:
We write and apply Jensen's inequality:
Combining the results of steps 1 and 2 leads to the claimed bound on the total variation.
Examples of applications
Sample complexity of biased coin tosses
Source:
The question is
How many coin tosses do I need to distinguish a fair coin from a biased one?
Assume you have 2 coins, a fair coin (Bernoulli distributed with mean ) and an -biased coin (). Then, in order to identify the biased coin with probability at least (for some ), at least
In order to obtain this lower bound we impose that the total variation distance between two sequences of samples is at least . This is because the total variation upper bounds the probability of under- or over-estimating the coins' means. Denote and the respective joint distributions of the coin tosses for each coin, then
We have
The result is obtained by rearranging the terms.
Information-theoretic lower bound for k-armed bandit games
In multi-armed bandit, a lower bound on the minimax regret of any bandit algorithm can be
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https://en.wikipedia.org/wiki/Ryota%20Takada
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is a Japanese footballer who plays as a defender for J2 League club Blaublitz Akita.
Career statistics
Club
.
Notes
References
2000 births
Living people
Sportspeople from Miyazaki Prefecture
Association football people from Miyazaki Prefecture
Hannan University alumni
Japanese men's footballers
Men's association football defenders
J2 League players
Blaublitz Akita players
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https://en.wikipedia.org/wiki/Thom%E2%80%93Sebastiani%20Theorem
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In complex analysis, a branch of mathematics, the Thom–Sebastiani Theorem states: given the germ defined as where are germs of holomorphic functions with isolated singularities, the vanishing cycle complex of is isomorphic to the tensor product of those of . Moreover, the isomorphism respects the monodromy operators in the sense: .
The theorem was introduced by Thom and Sebastiani in 1971.
Observing that the analog fails in positive characteristic, Deligne suggested that, in positive characteristic, a tensor product should be replaced by a (certain) local convolution product.
References
Theorems in complex analysis
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https://en.wikipedia.org/wiki/List%20of%20Newcastle%20KB%20United%20records%20and%20statistics
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Newcastle KB United was an Australian semi-professional association football club based in Newcastle. The club was formed in 1977 was admitted into the National Soccer League in 1978. The club had never qualified for the Finals series in the National Soccer League in all seven seasons of existence until they became defunct after playing seven rounds of the 1984 National Soccer League season and being replaced by another Newcastle club Newcastle Rosebud United (now Adamstown Rosebud).
The list encompasses the records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Newcastle KB United players on the international stage. Attendance records in Newcastle are also included.
The club's record appearance maker is Craig Mason, who made 152 appearances between 1978 and 1984. Ken Boden is Newcastle KB United's record goalscorer, scoring 30 goals in total.
Player records
Appearances
Most NSL appearances: Craig Mason, 142
Most NSL Cup appearances: Colin Curran and Roy Drinkwater, 11
Most separate spells with the club: Bob Mountford, 3 (1978; 1981 and 1983)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in a season: Ken Boden, 15 goals (in the 1978 and 1979 season)
Most league goals in a season: Ken Boden, 14 goals in the National Soccer League, 1978
Top goalscorers
Ken Boden was the all-time top goalscorer for Newcastle KB United.
Competitive matches only. Numbers in brackets indicate appearances made.
Club records
Matches
Firsts
First National Soccer League match: Newcastle KB United 1–4 Sydney City, National Soccer League, 5 March 1978
First NSL Cup match: Weston Bears 1–2 Newcastle KB United, First round, 17 May 1978
Record wins
Record NSL win: 5–0 against Canberra City, 20 August 1983
Record NSL Cup win:
3–0 against Sydney Olympic, Second round, 19 May 1979
3–0 against Edgeworth Eagles, First round, 25 April 1980
Record defeats
Record NSL defeat:
0–4 against Canberra City, 12 April 1980
0–4 against Heidelberg United, 25 May 1980
0–4 against Sydney City, 18 April 1982
Record NSL Cup defeat:
0–2 against Brisbane City, Semi-finals, 1 October 1978
1–3 against Marconi Fairfield, Second round, 5 July 1980
1–3 against Sydney Olympic, Second round, 4 April 1983
Record consecutive results
Record consecutive wins: 4, from 23 April 1983 to 22 May 1983
Record consecutive defeats:
4, from 28 April 1979 to 3 June 1979
4, from 19 April 1981 to 10 May 1981
Record consecutive draws: 5, from 15 July 1979 to 12 August 1979
Record consecutive matches without a defeat: 9, from 1 July 1979 to 25 August 1979
Record consecutive league matches without a defeat: 10, from 12 August 1978 to 22 April 1979
Record consecutive matches without a win: 9, from 21 March 1982 to
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https://en.wikipedia.org/wiki/Subgroup%20distortion
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In geometric group theory, a discipline of mathematics, subgroup distortion measures the extent to which an overgroup can reduce the complexity of a group's word problem. Like much of geometric group theory, the concept is due to Misha Gromov, who introduced it in 1993.
Formally, let generate group , and let be an overgroup for generated by . Then each generating set defines a word metric on the corresponding group; the distortion of in is the asymptotic equivalence class of the function where is the ball of radius about center in and is the diameter of .
Subgroups with constant distortion are called quasiconvex.
Examples
For example, consider the infinite cyclic group , embedded as a normal subgroup of the Baumslag–Solitar group . Then is distance from the origin in , but distance from the origin in . In particular, is at least exponentially distorted with base .
Similarly, the same infinite cyclic group, embedded in the free abelian group on two generators , has linear distortion; the embedding in itself as only produces constant distortion.
Elementary properties
In a tower of groups , the distortion of in is at least the distortion of in .
A normal abelian subgroup has distortion determined by the eigenvalues of the conjugation overgroup representation; formally, if acts on with eigenvalue , then is at least exponentially distorted with base . For many non-normal but still abelian subgroups, the distortion of the normal core gives a strong lower bound.
Known values
Every computable function with at most exponential growth can be a subgroup distortion, but Lie subgroups of a nilpotent Lie group always have distortion for some rational .
The denominator in the definition is always ; for this reason, it is often omitted. In that case, a subgroup that is not locally finite has superadditive distortion; conversely every superadditive function (up to asymptotic equivalence) can be found this way.
In cryptography
The simplification in a word problem induced by subgroup distortion suffices to construct a cryptosystem, algorithms for encoding and decoding secret messages. Formally, the plaintext message is any object (such as text, images, or numbers) that can be encoded as a number . The transmitter then encodes as an element with word length . In a public overgroup with that distorts , the element has a word of much smaller length, which is then transmitted to the receiver along with a number of "decoys" from , to obscure the secret subgroup . The receiver then picks out the element of , re-expresses the word in terms of generators of , and recovers .
References
Geometric group theory
Low-dimensional topology
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https://en.wikipedia.org/wiki/Sue-Jane%20Wang
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Sue-Jane Wang is a biostatistician at the United States Food and Drug Administration (FDA), where she works as the Biostatistics Lead and as the liaison from the Office of Biostatistics to the FDA Center for Drug Evaluation and Research (CDER) Biomarker Qualification Program. She is also deputy division director for biometrics in the Office of Biostatistics.
Education and career
Wang earned a master's degree in statistics from the University of Missouri in 1984, a second master's degree in biostatistics from the University of California, Los Angeles in 1986, and a Ph.D. in biostatistics from the University of Southern California in 1993.
She has been a senior expert statistician at the FDA since 2004, and a former distinguished faculty member in CDER. For many years she was Associate Director for Adaptive Design and Pharmacogenomics.
She was editor-in-chief of the Journal of Pharmaceutical Statistics from 2006 to 2008, and of the International Chinese Statistics Association Bulletin from 2000 to 2002.
Recognition
In 2011, Wang was elected to be a Fellow of the American Statistical Association. She is also an Elected Member of the International Statistical Institute.
References
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
Biostatisticians
University of Missouri alumni
University of California, Los Angeles alumni
University of Southern California alumni
Fellows of the American Statistical Association
Elected Members of the International Statistical Institute
21st-century American mathematicians
21st-century American women scientists
Food and Drug Administration people
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https://en.wikipedia.org/wiki/Lamp%20cord%20trick
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In topology, a branch of mathematics, and specifically knot theory, the lamp cord trick is an observation that two certain spaces are homeomorphic, even if one of the components is knotted. The spaces are , where is a hollow ball homeomorphic to and a tube connecting the boundary components of . The name comes from R. H. Bing's book "The Geometric Topology of 3-manifolds".
References
Lucien Grillet, La Conjecture de Smith en faible régularité.
Knot theory
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https://en.wikipedia.org/wiki/Asma%20Hassannezhad
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Asma Hassannezhad is an Iranian mathematician whose research concerns geometric analysis, spectral geometry, and differential geometry. She is a lecturer in pure mathematics in the School of Mathematics at the University of Bristol, where she is also a member of the Institute of Probability, Analysis and Dynamics and the Institute of Pure Mathematics.
Education
Hassannezhad has a bachelor's and master's degree from Sharif University of Technology in Iran. She completed her Ph.D. in 2012, jointly through Sharif University, the University of Neuchâtel in Switzerland, and the University of Tours in France. Her dissertation, Bornes supérieures pour les valeurs propres d'opérateurs naturels sur Les variétés riemanniennes compactes, was jointly supervised by Bruno Colbois of Neuchâtel, Ahmad El Soufi of Tours, and Alireza Ranjbar-Motlagh of Sharif.
Recognition
Hassannezhad was the 2022 winner of the Anne Bennett Prize "for her
outstanding work in spectral geometry and her substantial contributions toward the
advancement of women in mathematics".
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century Iranian mathematicians
Iranian women scientists
Women mathematicians
Sharif University of Technology alumni
University of Neuchâtel alumni
University of Tours alumni
Academics of the University of Bristol
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https://en.wikipedia.org/wiki/Vladimir%20Antonovich%20Kovalevsky
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Vladimir Antonovich Kovalevsky (born 1927) is a physicist. His research interests include digital geometry, digital topology, computer vision, image processing and pattern recognition.
Scientific activity
Vladimir A. Kovalevsky received his diploma in physics from Kharkiv University (Ukraine) in 1950, his first doctoral degree in technical sciences from the Central Institute of Metrology (Leningrad) in 1957 and his second doctoral degree in computer science from the Institute of Cybernetics of the Academy of Sciences of the Ukraine (Kiev) in 1968. From 1961 to 1983 he served as Head of Department of Pattern Recognition at that Institute. In 1983 he moved to the GDR. He worked as teaching professor or as scientific collaborator on universities in Germany (Zentralinstitut für Kybernetik at the ADW, Berlin University of Applied Sciences and Technology, University of Rostock, Technische Universität Dresden), USA (University of Pennsylvania, Drexel University), Mexico (National Autonomous University of Mexico), New Zealand (University of Auckland, Manukau Institute of Technology) and Korea (Chonbuk National University).
Over a period of nearly 40 years, Vladimir A. Kovalevsky made many fundamental and pioneering contributions to nearly every area of the above-mentioned fields. The research on digital image analysis (specifically on digital geometry and digital topology) is an important insertion to image processing and image analysis. He developed the statistically founded correlation method of recognizing optical patterns and the department “Pattern Recognition” at the Institute of Cybernetics, Kiew, has constructed in 1968 the optical character reading machine “Chars” implementing this method. The machine could read typed pages with high security.
He suggested 1989 using topological knowledge, especially those of abstract cell complexes, in image processing. This has improved the definitions and the processing of boundaries and edges in two- and three-dimensional digital images. Vladimir A. Kovalevsky invented new efficient algorithms for edge detection in color images which can detect edges between subsets of different colors but the same lightness. He suggested efficient algorithms for tracing and encoding boundaries and also new definitions and recognition algorithms for recognizing digital straight segments. Kovalevsky developed as programmer many projects implementing these algorithms. The results of his research are described in his monographs.
Publications
Image Pattern Recognition. Springer, 1980, ISBN 978-1-4612-6033-2
Finite Topology as Applied to Image Analysis. In: Computer Vision, Graphics and Image Processing, vol. 46 (1989) pp. 141–161
Geometry of Locally Finite Spaces. Verlag Dr. Baerbel Kovalevski, Berlin, 2008, ISBN 978-3-9812252-0-4
Modern Algorithms for Image Processing. Apress, 2019, ISBN 978-1-4842-4236-0
Image Processing with Cellular Topology. Springer, 2021, ISBN 978-981-16-5771-9
References
External links
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https://en.wikipedia.org/wiki/Ring%20theory%20%28disambiguation%29
|
Ring theory is a branch of algebra.
Ring theory can also refer to:
Ring theory (psychology), a theory in psychology
Chiastic structure, a literary technique
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https://en.wikipedia.org/wiki/Jessica%20Fintzen
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Jessica Fintzen is a German mathematician whose research concerns the representation theory of algebraic groups over the -adic numbers, with connections to the Langlands program. She is jointly appointed at the University of Cambridge, Duke University, and the University of Bonn.
Education and career
Fintzen competed for Germany in the 2008 International Mathematical Olympiad, earning a bronze medal, and earned a bachelor's degree in mathematics from Jacobs University Bremen in 2011. She went to Harvard University for graduate study in mathematics, completing her Ph.D. in 2016. Her dissertation concerned the Moy–Prasad filtration and was supervised by Benedict Gross.
After postdoctoral research at the Institute for Advanced Study, University of Michigan, and Trinity College, Cambridge, she became an assistant professor of mathematics at Duke University and was promoted to full professor there in 2022. She has also been Royal Society University Research Fellow and Lecturer at the University of Cambridge since 2020. In 2022 she became a full professor at the University of Bonn.
Recognition
Fintzen won the 2018 Friedrich Hirzebruch Dissertation prize of the German Academic Scholarship Foundation and Theodor Pfizer Foundation, and the 2018 Association for Women in Mathematics Dissertation Prize. She was named as a Sloan Research Fellow in 2021. In 2022, Fintzen won the Whitehead Prize, "for her groundbreaking work in representation theory, in particular as it relates to number theory via the (local) Langlands program".
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century German mathematicians
German women mathematicians
Harvard Graduate School of Arts and Sciences alumni
Duke University faculty
Academics of the University of Cambridge
Academic staff of the University of Bonn
Jacobs University Bremen
21st-century women mathematicians
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https://en.wikipedia.org/wiki/Institute%20of%20Statistics%20and%20Economic%20Studies
|
The Institute of Statistics and Economic Studies - New Caledonia (ISEE-NC) () is a public institution in New Caledonia that collects, produces and analyzes statistical information.
References
External links
National statistical services
Government of New Caledonia
1985 establishments in New Caledonia
Organizations established in 1985
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https://en.wikipedia.org/wiki/2022%20FIVB%20Volleyball%20Men%27s%20World%20Championship%20statistics
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The final tournament was held in Poland and Slovenia from 26 August to 11 September 2022.
Italy claimed their fourth title, defeating the reigning world champions Poland and Brazil won the third place match, defeating Slovenia in four sets.
Preliminary round
The top two teams in each pool and the top four of the third placed teams will qualify for the final round.
Combined ranking
Tournament statistics
Attendance
Matches played : 52
Attendance (preliminary round) (played 36) : 86,520 (2,403 per match)
Attendance (final round) (played 16) : 108,092 (6,776 per match)
Total attendance on tournament : 194,612 (3,743 per match)
Arena Stožice total attendance (played 30) : 71,038 (2,368 per match)
Arena Spodek, Katowice, Poland total attendance (played 16) : 83,413 (5,213 per match)
Arena Gliwice, Gliwice, Poland total attendance (played 6) : 40,161 (6,694 per match)
Most attendance : 12,258 - v. , Gliwice, Gliwice on 8 September 2022.
Fewest attendance : 90 - v. , Arena Stožice, Ljubljana on 27 August 2022.
Matches
Most matches wins : 7 -
Fewest matches wins : 0 - , , , , ,
Most matches lost : 3 - , , , , ,
Fewest matches lost : 0 -
Most points played in match : 254 - vs. 2 : 3 (124/130)
Fewest points played in match : 113 - vs. 3 : 0 (75/38)
Longest match played (duration) : 159 min. - vs. (2h,39m)
Shortest match played (duration) : 59 min. - vs. (0h,59m)
Sets
Total sets (preliminary round) : 126 (3.5 per match)
Total sets (final round) : 64 (4.0 per match)
Total sets scored : 190 (3.65 per match)
Most sets played : 27 - ,
Most sets wins : 21 -
Fewest sets wins : 0 - ,
Most sets lost : 11 - ,
Fewest sets lost : 4 -
Highest set ratio : 5.250 - (21/4)
Lowest set ratio : 0.000 - , (0/9)
Points
Total points (preliminary round) : 5,682 (158 per match)
Total points (final round) : 2,834 (177 per match)
Total points scored : 8,516 (164 per match)
Most points wins : 641 -
Fewest points wins : 153 -
Most points lost : 584 -
Fewest points lost : 225 -
Highest points ratio : 1.228 - (620/508)
Lowest points ratio : 0.680 - (153/225)
Squads
Coaches
Oldest coach: Antonio Giacobbe – 75 years at the start of the tournament.
Youngest coach: Michał Winiarski – 38 years at the start of the tournament.
Players
Appearance record: Luciano de Cecco and Marko Podraščanin participated in the World Championship for the fifth time.
Oldest player: At 38 years and 61 days, Mitja Gasparini is the oldest player ever to be nominated for a 2022 FIVB Volleyball Men's World Championship finals.
Youngest player: At 17 years and 343 days Mahdi Ben Tahar is the youngest player ever to be nominated for a 2022 FIVB Volleyball Men's World Championship finals.
Tallest player: At 2.15 m (7 ft 0.65 in), Yvan Arthur Kody Bitjaa is the tallest player ever to be nominated for a 2022 FIVB Volleyball Men's World Championship finals.
Shortest player: At 1.70 m (5 ft 7 in), José Roberto Mendoza Perdomo
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https://en.wikipedia.org/wiki/List%20of%20Norwegian%20mathematicians
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A mathematician is a scholar in the fields of mathematics. They solve and research mathematical problems which can be applied in real life or completely abstract (pure). This article covers notable mathematicians from Norway.
A pioneer of modern mathematics, Niels Henrik Abel contributed greatly towards various fields of mathematics during his short life. He died in 1829, aged 26, from tuberculosis. German mathematician Felix Klein spoke of his reluctance "to part from this ideal type of researcher". In 2001, the Abel Prize was established in his honour.
Other notable mathematicians include (in alphabetical order) Carl Anton Bjerknes, Vilhelm Bjerknes, Bernt Michael Holmboe, who is known for being Abel's teacher and tutor, Sophus Lie, Idun Reiten, Atle Selberg, Thoralf Skolem and Carl Størmer.
Alphabetical order
"Aa" appears under "å" as they are considered different representations of the same letter.
See also
Archiv for Mathematik og Naturvidenskab
Bjerknes (lunar crater)
Bjerknes (Martian crater)
List of things named after Niels Henrik Abel
Abel Prize
Selberg class
Weather forecasting
Aanderaa–Karp–Rosenberg conjecture
Notes
References
External links
Abel Prize
Norwegian mathematicians
Mathematics-related lists
Norwegian
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https://en.wikipedia.org/wiki/Chrysoula%20Tsogka
|
Chrysoula Tsogka is a Greek applied mathematician whose research involves remote sensing, wave propagation, and imaging through complex media. She is a professor of applied mathematics at the University of California, Merced.
Education
Tsogka studied chemical engineering at the National Technical University of Athens, graduating with a bachelor's degree in 1995. She went to Paris Dauphine University for graduate study in applied mathematics, earning a master's degree in 1996 and completing her Ph.D. in 1999. Her dissertation, Mathematical and Numerical Modeling of 3D Elastic Wave Propagation in Complex Media with Cracks, was supervised by Patrick Joly.
Career
After working as a researcher for CNRS in the Laboratoire de Mecanique et d’Acoustique, and as a visiting researcher at Stanford University, she became an assistant professor at the University of Chicago in 2004. She moved to the University of Crete as an associate professor in 2007, and was promoted to full professor in 2014. She took her present position at the University of California, Merced in 2019.
References
External links
Home page
Year of birth missing (living people)
Living people
Greek mathematicians
Greek women mathematicians
Applied mathematicians
National Technical University of Athens alumni
University of Chicago faculty
Academic staff of the University of Crete
University of California, Merced faculty
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https://en.wikipedia.org/wiki/Iker%20Moreno
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Iker Moreno Diez De Bonilla (born 14 September 2003) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club Atlético San Luis.
Career statistics
Club
References
External links
Living people
2003 births
Men's association football midfielders
Mexican men's footballers
Liga MX players
Club América footballers
Footballers from Guanajuato
People from Celaya
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https://en.wikipedia.org/wiki/Sergio%20de%20los%20R%C3%ADos
|
Sergio de los Ríos Peztña (born 28 June 2003) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club América.
Career statistics
Club
Honours
Mexico U20
Revelations Cup: 2022
References
External links
Living people
2003 births
Men's association football midfielders
Mexican men's footballers
Liga MX players
Club América footballers
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Francisco%20Garc%C3%ADa%20%28footballer%2C%20born%202003%29
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Francisco Manuel García Flores (born 8 October 2003) is a Mexican professional footballer who plays as a forward for Liga MX club América.
Career statistics
Club
References
External links
Living people
2003 births
Men's association football forwards
Mexican men's footballers
Liga MX players
Club América footballers
Footballers from Tijuana
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https://en.wikipedia.org/wiki/Aldo%20L%C3%B3pez
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Aldo López Vargas (born 23 May 2000) is a Mexican professional footballer who plays as a midfielder for Liga MX club Santos Laguna.
Career statistics
Club
References
External links
2000 births
Living people
Mexican men's footballers
Men's association football midfielders
Atlas F.C. footballers
Liga de Expansión MX players
Liga MX players
Santos Laguna footballers
C.D.S. Tampico Madero footballers
Footballers from Chihuahua
Sportspeople from Chihuahua City
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https://en.wikipedia.org/wiki/Jacques-Fran%C3%A7ois%20Le%20Poivre
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Jacques-François Le Poivre (11 February 1652 – 6 December 1710) was a Belgian mathematician and geometer who was a pioneer of projective geometry. He is largely known from a single book in French on conic sections, Traité des sections du cylindrie et du cône considérées dans le solide et dans le plan, avec des démonstrations simples & nouvelles (1704).
Le Poivre was born in Mons to son of Jacques and Catherine Demeurs. The Le Poivre family had many engineers including Pierre Le Poivre (1546-1626), an architect and military engineer. Jacques-François too studied mathematics and geometry and worked as a clerk and surveyor for the city of Mons. In 1700 he moved to Paris and in 1704 he published a treatise in two parts on cylindrical and conic sections. This work largely escaped serious study and some reviewers considered it to be plagiarism of Philippe de la Hire. In any case, de la Hire's work was more well-known. In part 2, his method of central projection was essentially the same as used by de La Hire in his 1673 work Nouvelle méthode en géométrie, pour les sections des superficies coniques et cylindriques but it has been suggested that Le Poivre independently discovered this since the book included several original theorems. A second edition of the Traité was published in 1708. An earlier work on an introduction to arithmetic that Le Poivre published in 1687 has never been located. He was a friend of Guillaume de l'Hôpital and a simple proof of the intersecting chords theorem by Le Poivre impressed l'Hôpital and may have made its way into l'Hôpital's Traité analytique des sections coniques. A biography claimed that Le Poivre was a poet.
References
External links
Traité des sections du cylindrie et du cône considérées dans le solide et dans le plan, avec des démonstrations simples & nouvelles (1704) - at the German national library
Scientists from Paris
People from Mons
1710 deaths
Belgian mathematicians
1652 births
Belgian emigrants to France
Geometers
Belgian surveyors
17th-century French mathematicians
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https://en.wikipedia.org/wiki/Joseph%20Melia
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Joseph Melia is a philosopher working in the areas of philosophy of mathematics, modal logic and possible worlds. He has made important contributions to the debate over the Quine–Putnam indispensability argument, where he argues for a "weaseling" approach to mathematical nominalism. He has also argued against modalism and the modal realism of David Lewis.
References
Philosophers of mathematics
20th-century British philosophers
Year of birth missing (living people)
Living people
21st-century British philosophers
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https://en.wikipedia.org/wiki/Mary%20Frecker
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Mary Irene Frecker is an American mechanical engineer whose research focuses on topology optimization of adaptive structures, compliant mechanisms, and self-folding origami mechanisms, with applications including the design of medical devices. She is a professor of mechanical and biomechanical engineering in the Penn State College of Engineering, Riess Chair of Engineering, head of the mechanical engineering department, and director of the Penn State Center for Biodevices.
Education and career
Frecker majored in mechanical engineering at the University of Dayton, graduating in 1991. She went to the University of Michigan for graduate study in mechanical engineering, earning a master's degree in 1994 and completing her Ph.D. in 1997. Her dissertation was Optimal design of compliant mechanisms, supervised by Noboru Kikuchi and Sridhar Kota.
She joined the Pennsylvania State University in 1997 as an assistant professor and the Pearce Endowed Development Professor in Mechanical Engineering. In 2020, she was named to the Leighton Riess Chair in Engineering and became the director of the Penn State Center for Biodevices. She was named as head of the Department of Mechanical Engineering, succeeding Karen Thole, in 2021.
Recognition
Frecker was elected as an ASME Fellow in 2009. In 2021, the American Society of Mechanical Engineers gave her their Adaptive Structures and Material Systems Award.
References
External links
Penn State Engineering Design and Optimization Group
Year of birth missing (living people)
Living people
American mechanical engineers
American women engineers
University of Dayton alumni
University of Michigan alumni
Pennsylvania State University faculty
Fellows of the American Society of Mechanical Engineers
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https://en.wikipedia.org/wiki/Silver%27s%20dichotomy
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In descriptive set theory, a branch of mathematics, Silver's dichotomy (also known as Silver's theorem) is a statement about equivalence relations, named after Jack Silver.
Statement and history
A relation is said to be coanalytic if its complement is an analytic set. Silver's dichotomy is a statement about the equivalence classes of a coanalytic equivalence relation, stating any coanalytic equivalence relation either has countably many equivalence classes, or else there is a perfect set of reals that are each incomparable to each other. In the latter case, there must be uncountably many equivalence classes of the relation.
The first published proof of Silver's dichotomy was by Jack Silver, appearing in 1980 in order to answer a question posed by Harvey Friedman. One application of Silver's dichotomy appearing in recursive set theory is since equality restricted to a set is coanalytic, there is no Borel equivalence relation such that , where denotes Borel-reducibility. Some later results motivated by Silver's dichotomy founded a new field known as invariant descriptive set theory, which studies definable equivalence relations. Silver's dichotomy also admits several weaker recursive versions, which have been compared in strength with subsystems of second-order arithmetic from reverse mathematics, while Silver's dichotomy itself is provably equivalent to over .
References
Set theory
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https://en.wikipedia.org/wiki/List%20of%20Canberra%20Cosmos%20FC%20records%20and%20statistics
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Canberra Cosmos Football Club was an Australian semi-professional association football club based in Canberra. The club was formed and admitted into the National Soccer League in 1995. The club had never qualified for the Finals series in the National Soccer League in all six seasons of existence until they became defunct in September 2001.
The list encompasses the records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Canberra Cosmos players on the international stage. Attendance records in Canberra are also included.
The club's record appearance maker was Toplica Popovich, who made 126 appearances between 1995 and 2001. Peter Buljan was Canberra Cosmos' record goalscorer, scoring 21 goals in total.
Player records
Appearances
Most league appearances: Toplica Popovich, 123
Most NSL Cup appearances: John Koch, 5
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in a season: Ivo de Jesus, 12 goals (in the 1999–2000 season)
Most league goals in a season: Ivo de Jesus, 12 goals in the National Soccer League, 1999–2000
Top goalscorers
Peter Buljan was the all-time top goalscorer for Canberra Cosmos.
Competitive matches only. Numbers in brackets indicate appearances made.
International
This section refers only to caps won while a Canberra Cosmos player.
First capped player: Paul Wade, for Australia against New Zealand on 15 November 1995
Most capped player: Paul Wade with 8 caps
Club records
Matches
Firsts
First National Soccer League match: Adelaide City 2–0 Canberra Cosmos, National Soccer League, 8 October 1995
First NSL Cup match: West Adelaide 1–1 Canberra Cosmos, First round, 3 January 1996
Record wins
Record NSL win: 8–1 against Sydney Olympic, National Soccer League, 5 January 1998
Record NSL Cup win: 1–0 against West Adelaide, First round, 20 January 1996
Record defeats
Record NSL defeat: 0–8 against Wollongong Wolves, National Soccer League, 5 December 1997
Record NSL Cup defeat: 1–3 against South Melbourne, Semi-finals, 25 January 1996
Record consecutive results
Record consecutive wins: 3, from 22 April 2000 to 29 April 2000
Record consecutive defeats: 16, from 30 March 1998 to 10 January 1999
Record consecutive draws: 3, from 23 January 2000 to 28 January 2000
Record consecutive NSL matches without a defeat: 4, from 22 April 2000 to 7 May 2000
Record consecutive matches without a win: 23, from 22 February 1998 to 24 January 1999
Goals
Most NSL goals scored in a season: 49 in 30 matches, National Soccer League, 2000–01
Fewest NSL goals scored in a season: 21 in 28 matches, National Soccer League, 1998–99
Most NSL goals conceded in a season: 69 in 26 matches, National Soccer League, 1996–97
Fewest NSL goals conceded in a season:
55 in
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https://en.wikipedia.org/wiki/Eagle%20Point%2C%20Saskatchewan
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Eagle Point is an unincorporated community and cluster subdivision within northern Saskatchewan, Canada. It is recognized as a designated place by Statistics Canada.
Geography
Eagle Point is on the western shore of Lac la Ronge.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Eagle Point had a population of 105 living in 33 of its 36 total private dwellings, a change of from its 2016 population of 91. With a land area of , it had a population density of in 2021.
References
Division No. 18, Saskatchewan
Designated places in Saskatchewan
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https://en.wikipedia.org/wiki/Napatak%2C%20Saskatchewan
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Napatak is an unincorporated community and resort subdivision within northern Saskatchewan, Canada. It is recognized as a designated place by Statistics Canada.
Geography
Napatak is on the western shore of Lac la Ronge.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Napatak had a population of 118 living in 54 of its 116 total private dwellings, a change of from its 2016 population of 134. With a land area of , it had a population density of in 2021.
References
Division No. 18, Saskatchewan
Designated places in Saskatchewan
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https://en.wikipedia.org/wiki/Potato%20Lake%2C%20Saskatchewan
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Potato Lake is an unincorporated community and cluster subdivision within northern Saskatchewan, Canada. It is recognized as a designated place by Statistics Canada.
Geography
Potato Lake is along Highway 2 on the western shore of Potato Lake.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Potato Lake had a population of 43 living in 19 of its 20 total private dwellings, a change of from its 2016 population of 45. With a land area of , it had a population density of in 2021.
References
Division No. 18, Saskatchewan
Designated places in Saskatchewan
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https://en.wikipedia.org/wiki/Ramsey%20Bay%2C%20Saskatchewan
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Ramsey Bay is an unincorporated community and resort subdivision within northern Saskatchewan, Canada. It is recognized as a designated place by Statistics Canada.
Geography
Ramsey Bay is on the western shore of Weyakwin Lake.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Ramsey Bay had a population of 159 living in 69 of its 210 total private dwellings, a change of from its 2016 population of 79. With a land area of , it had a population density of in 2021.
References
Division No. 18, Saskatchewan
Designated places in Saskatchewan
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https://en.wikipedia.org/wiki/McShane%20integral
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In the branch of mathematics known as integration theory, the McShane integral, created by Edward J. McShane, is a modification of the Henstock-Kurzweil integral. The McShane integral is equivalent to the Lebesgue integral.
Definition
Free tagged partition
Given a closed interval of the real line, a free tagged partition of is a set
where
and each tag .
The fact that the tags are allowed to be outside the subintervals is why the partition is called free. It's also the only difference between the definitions of the Henstock-Kurzweil integral and the McShane integral.
For a function and a free tagged partition , define
Gauge
A positive function is called a gauge in this context.
We say that a free tagged partition is -fine if for all
Intuitively, the gauge controls the widths of the subintervals. Like with the Henstock-Kurzweil integral, this provides flexibility (especially near problematic points) not given by the Riemann integral.
McShane integral
The value is the McShane integral of if for every we can find a gauge such that for all -fine free tagged partitions of ,
Examples
It's clear that if a function is integrable according to the McShane definition, then is also Henstock-Kurzweil integrable. Both integrals coincide in the regard of its uniqueness.
In order to illustrate the above definition we analyse the McShane integrability of the functions described in the following examples, which are already known as Henstock-Kurzweil integrable (see the paragraph 3 of the site of this Wikipedia "Henstock-Kurzweil integral").
Example 1
Let be such that and if
As is well known, this function is Riemann integrable and the correspondent integral is equal to We will show that this is also McShane integrable and that its integral assumes the same value.
For that purpose, for a given , let's choose the gauge such that and if
Any free tagged partition of can be decomposed into sequences like
, for ,
, for , and
, where , such that
This way, we have the Riemann sum
and by consequence
Therefore if is a free tagged -fine partition we have
, for every , and
, for every .
Since each one of those intervals do not overlap the interior of all the remaining, we obtain
Thus is McShane integrable and
The next example proves the existence of a distinction between Riemann and McShane integrals.
Example 2
Let the well known Dirichlet's function given by
which one knows to be not Riemann integrable. We will show that is integrable in the MacShane sense and that its integral is zero.
Denoting by the set of all rational numbers of the interval , for any let's formulate the following gauge
For any -fine free tagged partition consider its Riemann sum
.
Taking into account that whenever is irrational, we can exclude in the sequence of ordered pairs which constitute , the pairs where is irrational. The remainder are subsequences of the type such that , Since each one of those intervals do
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https://en.wikipedia.org/wiki/Jennifer%20Hill
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Jennifer Lynn Hill (born 1969) is an American statistician specializing in causal inference with applications to social statistics. She is a professor of applied statistics at New York University in the Steinhardt School of Culture, Education, and Human Development.
Education and career
Hill majored in economics at Swarthmore College, graduating in 1991. She earned a master's degree in statistics at Rutgers University in 1995, and completed a Ph.D. in statistics at Harvard University in 2000. Her dissertation, Applications of Innovative Statistical Methodology for the Social Sciences, was jointly supervised by political scientist Gary King and statistician Donald Rubin.
She became an assistant professor in the Columbia University School of International and Public Affairs in 2002. She moved to the New York University Steinhardt School of Culture, Education, and Human Development in 2008, as an associate professor and founding co-director of the Center for Practice and Research at the Intersection of Information, Society, and Methodology (PRIISM). She was promoted to full professor in 2015.
Books
Hill is the coauthor, with Andrew Gelman, of the book Data Analysis using Regression and Multilevel/Hierarchical Models (Cambridge University Press, 2007). With Gelman and Aki Vehtari, she is coauthor of Regression and Other Stories (Cambridge University Press, 2020).
Recognition
Hill was the 2020–2021 winner of the New York University Distinguished Teaching Award.
Personal life
With other statistics professors Bradley Carlin, Mark Glickman, Donald Hedeker, and Michael I. Jordan, Hill was a member of a music band, the Imposteriors.
References
External links
Home page
The Imposteriors
Living people
American statisticians
American women statisticians
Swarthmore College alumni
Rutgers University alumni
Harvard University alumni
Columbia School of International and Public Affairs faculty
Steinhardt School of Culture, Education, and Human Development faculty
1969 births
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https://en.wikipedia.org/wiki/John%20Truss
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John Kenneth Truss (born April 1947) is a mathematician and emeritus professor of pure mathematics at the University of Leeds where he specialises in mathematical logic, infinite permutation groups, homogeneous structures and model theory. Truss began his career as a junior research fellow at the University of Oxford before holding a series of academic positions and lastly joining the University of Leeds. He has written books on discrete mathematics (1991) and mathematical analysis (1997) and was co-editor in chief of the Journal of the London Mathematical Society until June 2003. He is the father of the former Prime Minister of the United Kingdom, Liz Truss.
Early life and family
John Truss was born in April 1947. He graduated from King's College, Cambridge in 1968 and earned his PhD at the University of Leeds in 1973 for a dissertation titled "Some Results about Cardinal Numbers without the Axiom of Choice" which was supervised by Frank Drake. In 1969, he married Priscilla Mary Grasby, a nurse, who he had met while they were students at Cambridge. Together, they have a daughter, Liz Truss, and three sons. Liz Truss has described her parents' politics as "to the left of Labour". Truss and his wife were both supporters of the Campaign for Nuclear Disarmament. They divorced in 2003.
Career
Truss's first academic position was as a junior research fellow at the Mathematical Institute of the University of Oxford. He then taught at a school in Kidderminster, Worcestershire, before lecturing at Paisley College of Technology from 1979 to 1985. In 1987, he worked at Simon Fraser University in British Columbia, Canada, and later at the University of Leeds where in 1988 with Frank Drake he edited the collected papers of Logic Colloquium '86, held at the University of Hull in 1986.
In 1990, Peter Cameron paid tribute to Truss in his notes on Oligomorphic Permutation Groups in the London Mathematical Society Lecture Notes Series No. 152, for saving him from "making some rash conjectures (by disproving them)", and "notably" for his contribution to the question of what are the possible cycle structures of automorphisms of M? In 1991, Truss published Discrete Mathematics for Computer Scientists which John Bayliss described in The Mathematical Gazette as "masterful and thorough" and getting "rapidly to the heart of some very exciting topics" but felt that it was more of a mathematician's book than a book for computer scientists as claimed by the author. Nonethless, Bayliss felt that the approach taken by Truss in organising and presenting his material was highly successful in condensing different strands of mathematics so that the author had shown that "discrete mathematics has come of age and is no longer a collection of disparate topics."
In 1999, Truss and S. Barry Cooper, also of the University of Leeds, jointly edited two volumes of papers in the London Mathematical Society Lecture Notes Series arising from the European meeting of the Association for Sy
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https://en.wikipedia.org/wiki/Leibniz%20theorem
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Leibniz theorem (named after Gottfried Wilhelm Leibniz) may refer to one of the following:
Product rule in differential calculus
General Leibniz rule, a generalization of the product rule
Leibniz integral rule
The alternating series test, also called Leibniz's rule
The Fundamental theorem of calculus, also called Newton-Leibniz theorem.
Leibniz formula for π
See also
Leibniz (disambiguation)
Leibniz' law (disambiguation)
List of things named after Gottfried Leibniz
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https://en.wikipedia.org/wiki/Jan%20Kohlhaase
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Jan Kohlhaase (1976) is a German mathematician specialising in the representation theory of p-adic Lie groups and arithmetic geometry.
Education and career
From 1997 to 2002, Kohlhaase studied mathematics and physics at the University of Hamburg and at Purdue University. In 2005 he obtained his PhD at the University of Münster under the supervision of Peter Schneider. He subsequently worked at IHES, the University of Münster as well as the University of Heidelberg. Kohlhaase habilitated at the University of Münster in 2011, and was appointed professor for arithmetic geometry at the University of Duisburg-Essen in 2014.
References
1976 births
Living people
20th-century German mathematicians
21st-century German mathematicians
Arithmetic geometers
Academic staff of the University of Duisburg-Essen
Place of birth missing (living people)
University of Münster alumni
University of Hamburg alumni
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https://en.wikipedia.org/wiki/2022%E2%80%9323%20PFC%20Ludogorets%20Razgrad%20season
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The 2022–23 season was Ludogorets Razgrad's twelfth consecutive season in the Bulgarian First League, of which they are defending champions. This article shows player statistics and all matches (official and friendly) that the club has played during the season.
In addition to successfully defending the league title for a record time, Ludogorets won the Bulgarian Cup and the Bulgarian Supercup, achieving the domestic treble for a second time in the club's history.
Squad
Transfers
In
Out
Loans out
Friendlies
Competitions
Overview
First League
Regular stage
Table
Results summary
Results by round
Results
Championship stage
Table
Results summary
Results by round
Matches
Bulgarian Cup
Bulgarian Supercup
UEFA Champions League
Qualifying rounds
UEFA Europa League
Qualifying rounds
Group stage
UEFA Europa Conference League
Knockout phase
Squad statistics
Appearances and goals
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|colspan="18"|Players away from the club on loan:
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|colspan="18"|Players who appeared for Ludogorets Razgrad that left during the season:
|}
Goalscorers
Clean sheets
Disciplinary record
References
Ludogorets Razgrad
PFC Ludogorets Razgrad seasons
Ludogorets Razgrad
Bulgarian football championship-winning seasons
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https://en.wikipedia.org/wiki/Orthogonality%20%28mathematics%29
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In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms.
Two elements u and v of a vector space with bilinear form B are orthogonal when . Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis.
The concept has been used in the context of orthogonal functions, orthogonal polynomials, and combinatorics.
Definitions
In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i.e., they form a right angle.
Two vectors x and y in an inner product space V are orthogonal if their inner product is zero. This relationship is denoted .
An orthogonal matrix is a matrix whose column vectors are orthonormal to each other.
An orthonormal basis is a basis whose vectors are both orthogonal and normalized (they are unit vectors).
A conformal linear transformation preserves angles and distance ratios, meaning that transforming orthogonal vectors by the same conformal linear transformation will keep those vectors orthogonal.
Two vector subspaces A and B of an inner product space V are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace of V that is orthogonal to a given subspace is its orthogonal complement.
Given a module M and its dual M∗, an element m′ of M∗ and an element m of M are orthogonal if their natural pairing is zero, i.e., . Two sets and are orthogonal if each element of S′ is orthogonal to each element of S.
A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent.
A set of vectors in an inner product space is called pairwise orthogonal if each pairing of them is orthogonal. Such a set is called an orthogonal set.
In certain cases, the word normal is used to mean orthogonal, particularly in the geometric sense as in the normal to a surface. For example, the y-axis is normal to the curve at the origin. However, normal may also refer to the magnitude of a vector. In particular, a set is called orthonormal (orthogonal plus normal) if it is an orthogonal set of unit vectors. As a result, use of the term normal to mean "orthogonal" is often avoided. The word "normal" also has a different meaning in probability and statistics.
A vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two vectors results in zero, then they are orthogonal. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality. In the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ.
Euclidean vector spaces
In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (π/2 radians), or one of the vectors is zero. Hence orthogonality of vectors is an extension of the
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https://en.wikipedia.org/wiki/Frederic%20Wan
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Frederic Yui-Ming Wan is a Chinese-American applied mathematician, academic, author and consultant. He is a Professor Emeritus of Mathematics at the University of California, Irvine (UCI), and an Affiliate Professor of Applied Mathematics at the University of Washington (UW).
Wan is most known for his research in applied mathematics, theoretical mechanics, resource economics, and biomathematics. He is the author of more than 150 archival journal research publications and 6 books. These and some of his educational and service programs have been recognized by his election as a Fellow of the American Academy of Mechanics (AAM), American Society of Mechanical Engineers (ASME), American Association for the Advancement of Science (AAAS), and Society for Industrial and Applied Mathematics (SIAM). There are two Lecture Series (at UCI and UW, respectively) in honor of him and his wife Julia and a conference room in his name in Lewis Hall at UW that houses the Department of Applied Mathematics.
Early life and education
Wan was born in 1936 in Shanghai, China to Olga Jung Wan and Wai-nam Wan. While his parents relocated to Paris France to work in the Chinese Embassy in the same year, Wan grew up in the care of his grandparents and went to school in Saigon and Cholon before he left for Seattle in 1954 as a derived citizen of an American mother.
Wan graduated from Garfield High School of Seattle in 1955, and headed for undergraduate study at the Massachusetts Institute of Technology (MIT). In his freshman year, Wan pledged and was initiated into the Theta Deuteron chapter of the Theta Delta Chi fraternity at MIT. He received an S.B. degree in mathematics in 1959 and earned his S.M. and Ph.D. degrees in mathematics at the same institute in 1963 and 1965, respectively. His doctoral dissertation, "Twisting and Stretching of Helicoidal Shells", was supervised by E. Reissner.
Career
After receiving his SB at MIT, Wan served as a Research Staff Member at the MIT Lincoln Laboratory from 1959 to 1965. Upon receiving his Ph.D. in mathematics, he held a postdoctoral appointment as an instructor of mathematics at MIT, was promoted to assistant professor of Applied Mathematics in 1967, and to associate professor in 1969. From 1974 till 1983, he served as a professor of mathematics at the University of British Columbia (UBC), but left in 1983 for the University of Washington (UW) as Professor of Applied Mathematics. In 1995, he moved to the University of California, Irvine (UCI), as a Professor Mathematics with a joint appointment as Professor of Mechanical and Aerospace Engineering. From 1999 till 2005, he also held an appointment as Professor of Civil and Environmental Engineering. He retired from his regular faculty position at UCI in 2017 and became Professor Emeritus of Mathematics.
Along with academic appointments, Wan also held a number of administrative positions in his career. In relocating to UBC in 1974, Wan also accepted the appointment as the first Dire
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https://en.wikipedia.org/wiki/Jes%C3%BAs%20Daniel%20Hern%C3%A1ndez
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Jesús Daniel Hernández Casiano (born 1 August 2001) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club Pachuca.
Career statistics
Club
Honours
Pachuca
Liga MX: Apertura 2022
References
External links
2001 births
Living people
Mexican men's footballers
Men's association football midfielders
Liga MX players
C.F. Pachuca players
Footballers from Guerrero
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https://en.wikipedia.org/wiki/Beatrice%20Meini
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Beatrice Meini (born 1968) is an Italian computational mathematician and numerical analyst specializing in numerical linear algebra and its applications to Markov chains, matrix equations, and queueing theory. She is Professor of Numerical Analysis in the Department of Mathematics at the University of Pisa.
Education and career
Meini was born on 5 December 1968 in Pontedera, in the province of Pisa. She earned a laurea in mathematics from the University of Pisa in 1993, and completed her Ph.D. there in 1998. Her dissertation, Fast Algorithms For The Numerical Solution of Structured Markov Chains, was supervised by Dario Bini.
After postdoctoral research with the Italian National Research Council (CNR) and at the University of Pisa, she became an associate professor of numerical analysis at the University of Pisa in 2005, and a full professor in 2016.
Books
Meini is the coauthor of books including:
Numerical Methods for Structured Markov Chains (Oxford University Press, 2005, with Dario Bini and Guy Latouche)
Numerical Solution of Algebraic Riccati Equations (Society for Industrial and Applied Mathematics, 2011, with Dario Bini and Bruno Iannazzo)
References
External links
Home page
1968 births
Living people
People from Pontedera
Italian mathematicians
Italian women mathematicians
Numerical analysts
Queueing theorists
University of Pisa alumni
Academic staff of the University of Pisa
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https://en.wikipedia.org/wiki/Illian%20Hern%C3%A1ndez
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Illian Gerardo Hernández Vargas (born 12 April 2000) is a Mexican professional footballer who plays as a forward for Liga MX club Pachuca.
Career statistics
Club
Honours
Pachuca
Liga MX: Apertura 2022
References
External links
2000 births
Living people
Mexican men's footballers
Men's association football forwards
Ascenso MX players
Liga MX players
Liga Premier de México players
C.F. Pachuca players
Mineros de Zacatecas players
Footballers from Zacatecas
People from Fresnillo
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https://en.wikipedia.org/wiki/Jahaziel%20Marchand
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Jahaziel Marchand Herrera (born 28 September 2001) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club Pachuca.
Career statistics
Club
Honours
Pachuca
Liga MX: Apertura 2022
References
External links
2001 births
Living people
Mexican men's footballers
Men's association football midfielders
Liga MX players
C.F. Pachuca players
Footballers from Chihuahua
Sportspeople from Ciudad Juárez
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https://en.wikipedia.org/wiki/List%20of%20Football%20Kingz%20FC%20records%20and%20statistics
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Football Kingz Football Club was a New Zealand professional association football club based in Auckland. The club was formed and admitted into the National Soccer League in 1995. The club had never qualified for the Finals series in the National Soccer League in all five seasons of existence until they became defunct in 2004.
The list encompasses the records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Football Kingz players on the international stage. Attendance records in Newcastle are also included.
The club's record appearance maker was Harry Ngata, who made 128 appearances between 1999 and 2004. Harry Ngata was also Football Kingz's record goalscorer, scoring 29 goals in total.
Player records
Appearances
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in a season: Dennis Ibrahim, 12 goals (in the 2000–01 season)
Top goalscorers
Peter Buljan was the all-time top goalscorer for Football Kingz.
Competitive matches only. Numbers in brackets indicate appearances made.
Club records
Matches
First National Soccer League match: Football Kingz 0–3 Carlton, National Soccer League, 1 October 1999
Record win:
4–0 against Parramatta Power, National Soccer League, 19 April 2000
5–1 against Newcastle United, National Soccer League, 27 October 2000
Record defeat: 0–7 against Parramatta Power, National Soccer League, 5 December 1997
Record consecutive wins:
3, from 15 November 2002 to 6 December 2002
Record consecutive defeats: 7, from 15 February 2002 to 7 April 2002
Record consecutive draws: 2, from 11 October 2002 to 20 October 2002
Record consecutive NSL matches without a defeat: 6, from 23 February 2001 to 6 April 2001
Record consecutive matches without a win: 10, from 2 February 2002 to 22 September 2002
Goals
Most NSL goals scored in a season: 57 in 34 matches, National Soccer League, 1999–2000
Fewest NSL goals scored in a season: 25 in 24 matches, National Soccer League, 2003–04
Most NSL goals conceded in a season: 59 in 34 matches, National Soccer League, 1999–2000
Fewest NSL goals conceded in a season: 45 in 24 matches, National Soccer League, 2002–03
Points
Most points in a season: 50 in 34 matches, National Soccer League, 1999–2000
Fewest points in a season: 14 in 24 matches, National Soccer League, 2001–02
Attendances
Highest attendance: 13,111, against Marconi Fairfield, National Soccer League, 1 November 1996
Lowest attendance: 892, against South Melbourne, National Soccer League, 14 February 2004
References
Football Kingz
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https://en.wikipedia.org/wiki/Von%20Neumann%27s%20elephant
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Von Neumann's elephant is a problem in recreational mathematics, consisting of constructing a planar curve in the shape of an elephant from only four fixed parameters. It originated from a discussion between physicists John von Neumann and Enrico Fermi.
History
In a 2004 article in the journal Nature, Freeman Dyson recounts his meeting with Fermi in 1953. Fermi evokes his friend von Neumann who, when asking him how many arbitrary parameters he used for his calculations, replied, "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk." By this he meant that the Fermi simulations relied on too many input parameters, presupposing an overfitting phenomenon.
Solving the problem (defining four complex numbers to draw an elephantine shape) subsequently became an active research subject of recreational mathematics. A 1975 attempt through least-squares function approximation required dozens of terms. The best approximation was found by three physicists in 2010.
Construction
The construction is based on complex Fourier analysis.
The curve found in 2010 is parameterized by:
The four fixed parameters used are complex, with affixes , , , .
The affix point is added to make the eye of the elephant and this value serves as a parameter for the movement of the "trunk".
See also
Epicycloid
Curve fitting
References
External links
"Fitting an Elephant" at the Wolfram Demonstrations Project site
Curves
Recreational mathematics
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https://en.wikipedia.org/wiki/Sebasti%C3%A1n%20Mart%C3%ADnez%20%28footballer%2C%20born%202003%29
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Sebastián Martínez Cruz (born 25 April 2003) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club América.
Career statistics
Club
References
External links
Living people
2003 births
Men's association football midfielders
Liga MX players
Club América footballers
Mexican men's footballers
Footballers from Torreón
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https://en.wikipedia.org/wiki/HockeyDB
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HockeyDB, originally known as the Internet Hockey Database, is a Canadian-American website dedicated to the specialization of statistics behind the game of ice hockey. It is one of the largest repositories of hockey data on the internet, gathering more than 1.3 million unique visitors a month.
History
HockeyDB was founded by Ralph Slate in 1996, through the old Usenet. With the database being founded two years before Google was incorporated, it has become a go-to database for every level of hockey fan. The website covers hockey statistics of leagues across the world, from the National Hockey League to the Austrian Hockey League and many more. The website created different ways to look at NHL players, as well as having the standings and statistics for nearly every professional hockey player to play the game.
Hockey statistics on the website are updated on a regular basis and include daily morning reports, which detail the current standings of world-wide leagues, daily hockey transactions, and all-time records. The NHL player list is categorized in many ways, from One Game Wonders to Playoff-only Players to the Pack Your Bag Club. The website also allows you to search the player list by league and by team.
Slate has been interviewed on multiple occasions on the success of HockeyDB. In 2017, Slate stated that he has compiled a set of encyclopedias’ worth of digital information: some 186,531 players, 7,220 teams, 416 leagues, 2,131 logos, and 6,071 sets of hockey cards.
In 2018, Slate was interviewed by FanSided writer Michael Joubran to discuss more about the website that connects fans to the statistics of their favorite players, past and present. In that interview, Slate dropped an easter egg, saying “if I have more than one photo of a player [on the website], clicking on the player’s photo will cycle through them all.”
Popularity
Peter Alper joined the HockeyDB team in 2019. He is responsible for creating the site's first Twitter account. As of September 2022, the HockeyDB Twitter account has amassed over 41,000 followers. The account is known for using images and statistics from the website to spark conversation on social media. Some discussions include who has the best hockey headshot, who were the best hockey players on Wall Street, and who were the biggest busts in the last 10 years of NHL Drafts.
References
External links
Website
Twitter
Sport websites
Ice hockey websites
American sport websites
Canadian sport websites
Sport Internet forums
Internet properties established in 1996
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https://en.wikipedia.org/wiki/Pedro%20Pedraza
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Pedro Pedraza Reyna (born 30 April 2000) is a Mexican professional footballer who plays as a midfielder for Liga MX club Pachuca.
Career statistics
Club
Honours
Pachuca
Liga MX: Apertura 2022
References
External links
2000 births
Living people
Men's association football midfielders
Ascenso MX players
Liga de Expansión MX players
Liga MX players
Liga Premier de México players
C.F. Pachuca players
Mineros de Zacatecas players
Footballers from Nuevo León
Footballers from Monterrey
Mexican men's footballers
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https://en.wikipedia.org/wiki/Jes%C3%BAs%20Garza
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Jesús Ángel Garza García (born 6 June 2000) is a Mexican professional footballer who plays as a defender for Liga MX club Tigres UANL.
Career statistics
Club
Honours
Tigres UANL
Liga MX: Clausura 2023
Campeón de Campeones: 2023
Campeones Cup: 2023
References
External links
2000 births
Living people
Men's association football midfielders
Liga MX players
Tigres UANL footballers
Footballers from Nuevo León
Footballers from Monterrey
Mexican men's footballers
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https://en.wikipedia.org/wiki/David%20Ayala%20%28footballer%2C%20born%202000%29
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David René Ayala Hernández (born 6 April 2000) is a Mexican professional footballer who plays as a midfielder for Liga MX club Tigres UANL.
Career statistics
Club
Honours
Tigres UANL
Liga MX: Clausura 2023
References
External links
2000 births
Living people
Men's association football midfielders
Liga MX players
Tigres UANL footballers
Footballers from the State of Mexico
People from Naucalpan
Mexican men's footballers
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https://en.wikipedia.org/wiki/P%C3%A1vel%20P%C3%A9rez
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Pável Uriel Pérez Hernández (born 26 June 1998) is a Mexican professional footballer who plays as a midfielder for Liga MX club Guadalajara.
Career statistics
Club
Honours
Tepatitlán
Liga de Expansión MX: Guardianes 2021
Campeón de Campeones: 2021
References
External links
1998 births
Living people
Men's association football midfielders
Liga de Expansión MX players
Liga MX players
Tercera División players
C.D. Guadalajara footballers
Tepatitlán F.C. players
CD Toledo players
Footballers from Jalisco
People from Tala, Jalisco
Mexican men's footballers
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https://en.wikipedia.org/wiki/Countable%20Borel%20relation
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In descriptive set theory, specifically invariant descriptive set theory, countable Borel relations are a class of relations between standard Borel space which are particularly well behaved. This concept encapsulates various more specific concepts, such as that of a hyperfinite equivalence relation, but is of interest in and of itself.
Motivation
A main area of study in invariant descriptive set theory is the relative complexity of equivalence relations. An equivalence relation on a set is considered more complex than an equivalence relation on a set if one can "compute using " - formally, if there is a function which is well behaved in some sense (for example, one often requires that is Borel measurable) such that . Such a function If this holds in both directions, that one can both "compute using " and "compute using ", then and have a similar level of complexity. When one talks about Borel equivalence relations and requires to be Borel measurable, this is often denoted by .
Countable Borel equivalence relations, and relations of similar complexity in the sense described above, appear in various places in mathematics (see examples below, and see for more). In particular, the Feldman-Moore theorem described below proved useful in the study of certain Von Neumann algebras (see ).
Definition
Let and be standard Borel spaces. A countable Borel relation between and is a subset of the cartesian product which is a Borel set (as a subset in the Product topology) and satisfies that for any , the set is countable.
Note that this definition is not symmetric in and , and thus it is possible that a relation is a countable Borel relation between and but the converse relation is not a countable Borel relation between and .
Examples
A countable union of countable Borel relations is also a countable Borel relation.
The intersection of a countable Borel relation with any Borel subset of is a countable Borel relation.
If is a function between standard Borel spaces, the graph of the function is a countable Borel relation between and if and only if is Borel measurable (this is a consequence of the Luzin-Suslin theorem and the fact that ). The converse relation of the graph, , is a countable Borel relation if and only if is Borel measurable and has countable fibers.
If is an equivalence relation, it is a countable Borel relation if and only if it is a Borel set and all equivalence classes are countable. In particular hyperfinite equivalence relations are countable Borel relations.
The equivalence relation induced by the continuous action of a countable group is a countable Borel relation. As a concrete example, let be the set of subgroups of , the Free group of rank 2, with the topology generated by basic open sets of the form and for some (this is the Product topology on ). The equivalence relation is then a countable Borel relation.
Let be the space of subsets of the naturals, again with the product topology
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https://en.wikipedia.org/wiki/Random%20polytope
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In mathematics, a random polytope is a structure commonly used in convex analysis and the analysis of linear programs in d-dimensional Euclidean space . Depending on use the construction and definition, random polytopes may differ.
Definition
There are multiple non equivalent definitions of a Random polytope. For the following definitions. Let K be a bounded convex set in a Euclidean space:
The convex hull of random points selected with respect to a uniform distribution inside K.
The nonempty intersection of half-spaces in .
The following parameterization has been used: such that (Note: these polytopes can be empty).
Properties definition 1
Let be the set of convex bodies in . Assume and consider a set of uniformly distributed points in . The convex hull of these points, , is called a random polytope inscribed in . where the set stands for the convex hull of the set. We define to be the expected volume of . For a large enough and given .
vol vol
Note: One can determine the volume of the wet part to obtain the order of the magnitude of , instead of determining .
For the unit ball , the wet part is the annulus where h is of order : vol
Given we have is the volume of a smaller cap cut off from by aff, and is a facet if and only if are all on one side of aff .
.
Note: If (a function that returns the amount of d-1 dimensional faces), then and formula can be evaluated for smooth convex sets and for polygons in the plane.
Properties definition 2
Assume we are given a multivariate probability distribution on that is
Absolutely continuous on with respect to Lebesgue measure.
Generates either 0 or 1 for the s with probability of each.
Assigns a measure of 0 to the set of elements in that correspond to empty polytopes.
Given this distribution, and our assumptions, the following properties hold:
A formula is derived for the expected number of dimensional faces on a polytope in with constraints: . (Note: where ). The upper bound, or worst case, for the number of vertices with constraints is much larger: .
The probability that a new constraint is redundant is: . (Note: , and as we add more constraints, the probability a new constraint is redundant approaches 100%).
The expected number of non-redundant constraints is: . (Note: ).
Example uses
Minimal caps
Macbeath regions
Approximations (approximations of convex bodies see properties of definition 1)
Economic cap covering theorem (see relation from properties of definition 1 to floating bodies)
References
Metric geometry
Convex analysis
Computational geometry
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https://en.wikipedia.org/wiki/Deafness%20in%20Denmark
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Though official statistics are not available, the Danish Deaf Association estimates that there are currently about 5,000 deaf users of Danish Sign Language, which is equivalent to nearly 0.1% of the country's population. As many as 20,000 people are thought to use the language daily in their professional or personal life.
Language emergence
Danish Sign Language (DSL) is the main sign language used in Denmark, written in Danish as dansk tegnsprog. In Greenland, part of the Realm of Denmark, a very similar form of sign is used that some might classify as a distinct language. Danish Sign Language can be traced back to the creation of Denmark's first school for the deaf, opened in 1807. The founder of the school studied deaf education in Paris, and as deaf students came together as a large community for the first time, their local home signs converged with French Sign Language. Thus, Danish Sign Language is a deaf-community sign language.
Significant organizations
Danish Deaf Association
Founded in 1935, the Danish Deaf Association, or Danske Døves Landsforbund (DDL), is privately run but receives monetary support from the government. The organization fought for the inclusion of sign language interpretation for broadcast news, encouraged the Ministry of Education to offer classes in sign language interpretation for people with no prior knowledge of the language, and acquired a grant that allowed them to produce an online Danish Sign Language dictionary. Its members continue to push for greater equality between the deaf and hearing communities in Denmark and for the recognition of Danish Sign Language.
Danish Deaf Youth Association
The Danish Deaf Youth Association, or Danske Døves Ungdomsforbund (DDU), operates mostly as a subsidiary of the Danish Deaf Association. It was formed within the DDL in 1969 and was independently recognized in 1994.
Danish Deaf Sports Association
The Danish Deaf Sports Association [Dansk Døve-Idrætsforbund (DDI)] originated in 1922 and exists under the Danish Sports Association. It provides access to sports at any level—from grassroots to internationally competitive—to those who are hearing-impaired.
Center for Sign Language / Center for the Deaf
The Danish Center for Sign Language (Center for Tegnsprog), also called the Center for the Deaf (CFD), was established in 1972, and has gone by several different names throughout its years, including the Center for Total Communication of the Deaf (Døves Center for Total Kommunikation). The CFD is a nonprofit organization and the most extensive of its kind for hearing impaired people in Denmark. It provides support for housing, job seeking, and mental health services, with special consideration for those with further impairments. All staff are trained in sign language.
Human/Civil rights
Deaf people in Denmark have quite a few protections under the law. Denmark ratified the United Nations Convention on the Rights of Persons with Disabilities (CRPD) in 2009 and the Optio
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https://en.wikipedia.org/wiki/Juan%20Pablo%20Mart%C3%ADnez
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Juan Pablo Martínez Rodríguez (born 4 February 1999) is a Mexican professional footballer who plays as a full-back for Botafogo-SP, on loan from Liga MX club Atlético San Luis.
Career statistics
Club
References
External links
Living people
1999 births
Men's association football defenders
Atlético San Luis footballers
Liga de Expansión MX players
Liga MX players
Tigres UANL footballers
Venados F.C. players
Footballers from Nuevo León
People from Guadalupe, Nuevo León
Mexican men's footballers
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https://en.wikipedia.org/wiki/2022%20FIVB%20Volleyball%20Women%27s%20World%20Championship%20statistics
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The final tournament was held in Netherlands and Poland from 23 September to 15 October 2022.
Serbia won their second title for the consecutive edition, beating Brazil in straight sets.
First round
The top four teams in each pool will qualify for the second phase.
Pool A
Total matches played : 15
Total sets played : 50 (3.33 per match)
Total points played : 2,158 (144 per match)
Pool B
Total matches played : 15
Total sets played : 56 (3.73 per match)
Total points played : 2,394 (160 per match)
Pool C
Total matches played : 15
Total sets played : 52 (3.47 per match)
Total points played : 2,241 (149 per match)
Pool D
Total matches played : 15
Total sets played : 52 (3.47 per match)
Total points played : 2,300 (153 per match)
Second round
The top four teams will qualify for the final phase.
Pool E
Total matches played : 16
Total sets played : 57 (3.56 per match)
Total points played : 2,474 (155 per match)
Pool F
Total matches played : 16
Total sets played : 61 (3.81 per match)
Total points played : 2,709 (169 per match)
Final round
Total matches played : 8
Total sets played : 31 (3.88 per match)
Total points played : 1,375 (172 per match)
Tournament statistics
Host cities
Netherlands : Arnhem, Rotterdam, Apeldoorn
Poland : Gdańsk, Łódź, Gliwice
Venues
Arnhem : GelreDome (21,248)
Rotterdam : Rotterdam Ahoy (16,426)
Apeldoorn : Omnisport (6,525)
Gdańsk : Ergo Arena (11,409)
Łódź : Atlas Arena (13,805)
Gliwice : Gliwice Arena (13,752)
Attendance
Matches played : 100
Attendance (first round) (played 60) : 120,879 (2,015 per match)
Attendance (second round) (played 32) : 68,430 (2,138 per match)
Attendance (final round) (played 8) : 42,206 (5,276 per match)
Total attendance on tournament : 231,515 (2,315 per match)
Arena GelreDome total attendance (played 39) : 91,359 (2,343 per match)
Arena Rotterdam Ahoy total attendance (played 16) : 31,115 (1,945 per match)
Arena Omnisport total attendance (played 5) : 26,587 (5,317 per match)
Ergo Arena total attendance (played 12) : 25,515 (2,126 per match)
Atlas Arena total attendance (played 25) : 41,320 (1,653 per match)
Gliwice Arena total attendance (played 3) : 15,619 (5,206 per match)
Most attendance : 10,000 - v. , GelreDome, Arnhem on 30 September 2022.10,000 - v. , GelreDome, Arnhem on 1 October 2022. 10,000 - v. , GelreDome, Arnhem on 2 October 2022.
Fewest attendance : 101 - v. , Atlas Arena, Łódź on 4 October 2022.
Matches
Most matches wins : 12 -
Fewest matches wins : 0 - , , ,
Most matches lost : 7 -
Fewest matches lost : 0 -
Longest match played (duration) : 137 min. - vs. (2h,17m)
Shortest match played (duration) : 58 min. - vs. (0h,58m) 58 min. - vs. (0h,58m) 58 min. - vs. (0h,58m)
Sets
Total sets (first round) : 210 (3.50 per match)
Total sets (second round) : 118 (3.69 per match)
Total sets (final round) : 31 (3.88 per match)
Total sets scored : 359 (3.60 per match)
Most sets played : 45 - (31/14)
Most sets wins : 36 - (3
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https://en.wikipedia.org/wiki/Paul%20Bell%C3%B3n
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Paul Bellón Saracho (born 4 June 1997) is a Mexican professional footballer who plays as a centre-back for Liga MX club León.
Career statistics
Club
Honours
León
CONCACAF Champions League: 2023
References
External links
Living people
1997 births
Men's association football defenders
Ascenso MX players
Club León footballers
Leones Negros UdeG footballers
Liga de Expansión MX players
Liga MX players
Footballers from Jalisco
People from Guadalajara, Jalisco
Mexican men's footballers
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https://en.wikipedia.org/wiki/Ram%20Kishore%20Saxena
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Ram Kishore Saxena D.Sc , FNASc (11 November 1936) is an Indian mathematician and Emeritus professor, UGC Jai Narain Vyas University and former Professor and Head, Department of Mathematics.
Published work
Saxena has published 356 research papers; under his supervision many scholars has done PhD and post-doctoral research. Saxena has published books.
References
Indian mathematicians
Living people
1936 births
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https://en.wikipedia.org/wiki/Six%20Ideas%20that%20Shaped%20Physics
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Six Ideas that Shaped Physics is a textbook in calculus based physics, notable for covering special relativity, quantum mechanics, and thermodynamics – topics usually reserved for upper division classes.
Contents
The books opens with 20th century physics, starting with the conservation laws implied by Noether's theorem, it then proceeds to present Newtonian mechanics and the laws of motion as a consequence of underlying physical symmetry, reversing the chronological order in which the study of Physics developed as a scientific discipline. The courses include Unit C: Conservation Laws Constrain Interactions (14 chapters), Unit N: The Laws of Physics are Universal (12 chapters), Unit R: The Laws of Physics are Frame-Independent (9 chapters), Unit E: Electric and Magnetic Fields are Unified (20 chapters), Unit Q: Particles Behave Like Waves (15 chapters), and Unit T: Some Processes are Irreversible (11 chapters).
Editions
First published in 1998, it has been widely adopted and is now in the Fourth edition. It was written by professor Thomas Moore based on his introductory course in college physics at Pomona College.
The impetus for the project came from the 1987-1996 Introductory University Physics Project (IUPP), which found that most college texts neglected to teach topics in 20th century physics
References
Physics textbooks
1998 non-fiction books
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https://en.wikipedia.org/wiki/%C3%93scar%20Villa%20%28footballer%2C%20born%202001%29
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Óscar Eduardo Villa Domínguez (born 24 February 2001) is a Mexican professional footballer who plays as a full-back for Liga MX club León.
Career statistics
Club
Honours
León
Leagues Cup: 2021
CONCACAF Champions League: 2023
Mexico U23
Central American and Caribbean Games: 2023
References
External links
Living people
2001 births
Mexican men's footballers
Mexico men's youth international footballers
Men's association football defenders
Club León footballers
Liga MX players
Footballers from Veracruz
People from Pánuco, Veracruz
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https://en.wikipedia.org/wiki/Michael%20Thaddeus
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Michael Thaddeus (born January 12, 1967) is an American mathematician and a professor of mathematics at Columbia University. He is best known for having been a whistleblower in exposing deliberately misleading data submitted by Columbia University to U.S. News & World Report (USNWR)'s Best Colleges Ranking which exaggerated the university's college ranking.
Early life and education
Thaddeus was born on January 12, 1967, in New York City, and grew up in Morningside Heights. His father, Patrick, and his mother, Janice, both obtained doctorates from Columbia University. Thaddeus was educated at St. Hilda's & St. Hugh's School before enrolling at Hunter College High School in 1980, where he graduated in 1984.
Thaddeus matriculated at Harvard University, where his sister was also a student, with the intent to study biology but switched to mathematics. He graduated in 1988 and attained a Rhodes Scholarship to study at St John's College, Oxford, where he earned his Doctor of Philosophy (DPhil). His dissertation, Algebraic Geometry and the Verlinde Formula, was published in 1992 under the supervision of Simon Donaldson.
Academic career
In 1994, Thaddeus was elected to become a junior fellow at the Harvard Society of Fellows. He was a postdoctoral researcher at the Mittag-Leffler Institute and the Simons Laufer Mathematical Sciences Institute from 1994 and 1997. In 1998, Thaddeus joined the mathematics faculty of Columbia University. He has lectured at multiple institutions including Hunter College, Virginia Tech, and Creighton University, among others. He specializes in algebraic geometry.
Thaddeus was a member of the School of Mathematics at the Institute for Advanced Study in 2001. From 2017 to 2020, he was the chair of the math department at Columbia University.
Columbia rankings exposé
Thaddeus' exposé, An Investigation of the Facts Behind Columbia’s U.S. News Ranking, was published in February 2022, identifying discrepancies such as shrunken class sizes and the exaggeration of faculty credentials. Due to Thaddeus' analysis, Columbia later dropped from having been ranked 2nd to being ranked 18th, sparking speculation about the integrity of college rankings.
Selected publications
References
1967 births
Living people
Harvard College alumni
Columbia University faculty
Alumni of Corpus Christi College, Oxford
Alumni of St John's College, Oxford
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https://en.wikipedia.org/wiki/Edgar%20Fuller
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Edgar Fuller is an American mathematician. He is a distinguished professor in the department of mathematics and statistics at Florida International University.
References
Living people
Place of birth missing (living people)
Year of birth missing (living people)
American mathematicians
21st-century American mathematicians
Florida International University faculty
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https://en.wikipedia.org/wiki/Javier%20Ibarra
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Javier Eduardo Ibarra de la Rosa (born 6 February 1998) is a Mexican professional footballer who plays as a midfielder for Liga de Expansión MX club Atlético Morelia.
Career statistics
Club
Honours
Atlético Morelia
Liga de Expansión MX: Clausura 2022
References
External links
Living people
1998 births
Mexico men's youth international footballers
Men's association football midfielders
Ascenso MX players
Atlante F.C. footballers
Atlético Morelia players
C.F. Monterrey players
Club León footballers
Liga de Expansión MX players
Liga MX players
Querétaro F.C. footballers
Footballers from Coahuila
Mexican men's footballers
People from Monclova
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https://en.wikipedia.org/wiki/Florence%20Calvert%20Thorne
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Florence Calvert Thorne (July 28, 1877 – March 16, 1973) was an American labour activist and long-time member of the American Federation of Labor, where she established vital statistics reporting that would go on to inform New Deal social programs.
Early life and education
Thorne was born July 28, 1877, in Hannibal, Missouri. She graduated from high school as valedictorian of her class in 1896. Thorne studied English and classical languages in at Oberlin College, graduating in 1899. She taught for a year in Georgia before continuing her studies at the University of Chicago, where she received a PhD in 1909. Thorne attended classes at the school during the summer and taught as a means of supporting herself financially in Hannibal during the school year.
Career
Thorne's relationship with the American Federation of Labor began during her doctoral studies, when she contacted the organization while writing a these titled "American Federation of Labor in Politics". In 1912 AFL President Samuel Gompers, who had been impressed with her graduate research, offered Thorne a job editing The American Federationist. She would go on to become a primary contributor to the publication, as well as a close colleague and confidante of Gompers.
A supporter of the United States' involved in World War I, Thorne left her role with AFL in 1917 to take a position on the Advisory Committee of the Council of National Defense's Subcommittee on Women in Industry. A year later she joined the Department of Labor as assistant director of the working conditions service which, at the time, was tasked with establishing and maintaining labor standards in war related industries. After the end of the war, Thorne returned to the AFL, significantly contributing to Gompers' autobiography, Seventy Years of Life and Labor: An Autobiography, conducting much of the research and authoring the Appendix regarding the last months of his life. She was at his bedside when he died in 1924.
Under the tenure of AFL president William Green, Thorne edited the AFL newsletter for several years before being named the director of the organization's newly established research department in 1933. She remained in the role until her retirement from the AFL. The research department was founded based on Thorne's management of volunteer data collection, which included the tracking of unemployment reporting by local unions. Part of her work as head of the research department involved assessing and providing vital statistics information to union heads in order to assist with collective bargaining. During her time with the research department, Thorne researched and conducted studies on topics including affordable housing, compensation, health and medical care, and child labor.
The type of reporting Thorne established went on inform New Deal programs, despite Thorne, like Grompers, being opposed to government legislation in favour of improvements gained through the activism of trade-union organizers. She retire
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https://en.wikipedia.org/wiki/Luis%20Cervantes
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Luis Roberto Cervantes Godínez (born 9 February 2001) is a Mexican professional footballer who plays as a full-back for Liga MX club León.
Career statistics
Club
Notes
Honours
Club Domestic
Liga MX 2021–22 Apertura Runner-up
References
External links
Living people
2001 births
Mexican men's footballers
Men's association football defenders
Club León footballers
Liga MX players
Footballers from Guanajuato
People from Guanajuato City
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https://en.wikipedia.org/wiki/Rafael%20Guerrero
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Rafael Guerrero Ramírez (born 13 January 2003) is a Mexican professional footballer who plays as a centre-back for Liga MX club Cruz Azul.
Career statistics
Club
Honours
Cruz Azul
Supercopa de la Liga MX: 2022
Mexico U23
Central American and Caribbean Games: 2023
References
External links
Living people
2003 births
Mexican men's footballers
Men's association football defenders
Cruz Azul footballers
Liga MX players
Footballers from Tijuana
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https://en.wikipedia.org/wiki/Jorge%20Garc%C3%ADa%20%28footballer%2C%20born%202002%29
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Jorge Luis García Rivas (born 22 January 2002) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club Cruz Azul.
Career statistics
Club
Honours
Cruz Azul
Liga MX: Guardianes 2021
Copa MX: Apertura 2018
Supercopa de la Liga MX: 2022
References
External links
Living people
2002 births
Mexico men's youth international footballers
Men's association football defenders
Cruz Azul footballers
Liga MX players
Footballers from Hidalgo (state)
Sportspeople from Pachuca
Mexican men's footballers
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https://en.wikipedia.org/wiki/Cristian%20Jim%C3%A9nez%20%28footballer%2C%20born%202002%29
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Cristian Ramón Jiménez Ducloux (born 18 July 2002) is a Mexican professional footballer who plays as an attacking midfielder for Liga MX club Cruz Azul.
Career statistics
Club
Honours
Cruz Azul
Campeón de Campeones: 2021
References
External links
Living people
2002 births
Mexican men's footballers
Men's association football midfielders
Cruz Azul footballers
Liga MX players
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Emilio%20Mart%C3%ADnez%20%28footballer%2C%20born%202003%29
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Emilio Martínez González (born 2 February 2003) is a Mexican professional footballer who plays as a right-back for Liga MX club Necaxa.
Career statistics
Club
Honours
Mexico U20
Revelations Cup: 2021
References
External links
Living people
2003 births
Mexican men's footballers
Mexico men's youth international footballers
Men's association football defenders
Club Puebla players
Liga MX players
Footballers from Veracruz
Sportspeople from Córdoba, Veracruz
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https://en.wikipedia.org/wiki/Alberto%20Herrera
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Alberto Herrera Rodríguez (born 23 February 2001) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club Puebla.
Career statistics
Club
References
External links
Living people
2001 births
Men's association football midfielders
Club Puebla players
Liga MX players
Footballers from Tamaulipas
People from Ciudad Madero
Mexican men's footballers
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https://en.wikipedia.org/wiki/Arturo%20Palma
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Arturo Adolfo Palma Cisneros (born 16 January 2002) is a Mexican professional footballer who plays as an attacking midfielder.
Career statistics
Club
References
External links
Living people
2002 births
Mexican men's footballers
Men's association football midfielders
Club Necaxa footballers
Liga MX players
Querétaro F.C. footballers
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Diego%20G%C3%B3mez%20%28Mexican%20footballer%29
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Diego Esaú Gómez Medina (born 10 September 2003) is a Mexican professional footballer who plays as a midfielder for Liga MX club Necaxa.
Career statistics
Club
References
External links
Living people
2003 births
Mexican men's footballers
Mexico men's youth international footballers
Men's association football midfielders
Club Necaxa footballers
Liga MX players
Footballers from Aguascalientes
People from Pabellón de Arteaga Municipality
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https://en.wikipedia.org/wiki/Plug-in%20electric%20vehicles%20in%20Finland
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, there were about 27,000 battery electric vehicles and 84,000 plug-in hybrid vehicles in Finland. , 31% of new cars sold in Finland were electric.
Statistics
, the Volkswagen ID.4 was the best-selling electric vehicle in Finland.
Government policy
, the Finnish government offers tax rebates of up to €2,000 for electric vehicle purchases.
Charging stations
, there were 1,302 public charging station locations in Finland.
Public opinion
In a 2022 poll conducted by Tori Auto, slightly more than half of respondents in Finland said that they were unwilling to buy an electric car for their next vehicle purchase, compared with 30% for Norway and Sweden, and 23% for Denmark.
By region
Central Finland
, 18% of new cars registered in Central Finland were electric.
North Ostrobothnia
, there were about 900 electric vehicles in Oulu.
Pirkanmaa
, there were about 1,500 electric vehicles in Tampere.
Satakunta
, about 11% of new cars registered in Satakunta were electric.
Southwest Finland
, there were about 1,000 electric vehicles in Turku.
Uusimaa
, there were about 6,000 electric vehicles in Helsinki.
Åland
, there were 16 public charging stations in Åland.
References
Finland
Road transport in Finland
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https://en.wikipedia.org/wiki/Denzell%20Garc%C3%ADa
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Denzell Arturo García Bojórquez (born 15 August 2003) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club Juárez.
Career statistics
Club
Honours
Mexico U23
Central American and Caribbean Games: 2023
References
External links
Living people
2003 births
Mexican men's footballers
Men's association football midfielders
Club Necaxa footballers
Liga MX players
Footballers from Sinaloa
People from Ahome Municipality
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https://en.wikipedia.org/wiki/Geometry%20E
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The Geometry E is a battery-powered subcompact crossover produced by Chinese auto manufacturer Geely under the Geometry brand.
Overview
The Geometry E is officially the third brand new model of the Geometry brand, while replacing the short-lived Geometry EX3 sold in 2021 alone. It was developed based on the same platform as the Geely Vision X3 and the Geometry EX3 rebadged variant, and comes in three trims; Cute Tiger, Linglong Tiger, and Thunder Tiger. Pricing of the Geometry E starts at $12,947 (86,800 yuan) for the base model, while the Linglong Tiger and Thunder Tiger costs around $14,588 and $15,483 respectively.
The battery of the Geometry E is a base 33.5 kWh and a longer-range 39.4 kWh lithium iron phosphate battery providing a NEDC range of respectively. The electric motor is a TZ160XS601 drive motor produced by GLB Intelligent Power Technologies capable of producing 60 kW and 130 Nm of torque, giving it a top speed of 121 km/h. Charge time for the Geometry E from 0-80% is 30 minutes.
The interior of the Geometry E features two 10.25-inch infotainment screens and a central control screen as standard.
References
External links
Geometry Official Website
Geometry vehicles
Crossover sport utility vehicles
Hatchbacks
Front-wheel-drive vehicles
Subcompact cars
Cars introduced in 2022
2020s cars
Cars of China
Production electric cars
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https://en.wikipedia.org/wiki/Denmark%20women%27s%20national%20football%20team%20records%20and%20statistics
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This article comprises an overview of the Denmark women's national football team records and statistics, from their first official match against Sweden in 1974 to the present day.
Most appearances
Players denoted in bold are still playing or available for selection. The 25 most capped players for Denmark are:
Goalscorers
Top goalscorers
Players still playing or available for selection are in bold. With 74 goals, Pernille Harder is currently the number one goalscorer in Danish football history. The players with 10 goals or more for Denmark are:
Team captains
As of 31 October 2023, the ten players with the most caps as Danish team captains are:
References
Denmark women's national football team
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https://en.wikipedia.org/wiki/Matemateca
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Matemateca (Matemateca IME-USP) is a collection of objects related to mathematics and mathematics teaching that is housed in the Institute of Mathematics and Statistics of the University of São Paulo. It is an initiative that dates to 2003, when professors connected to IME mobilized and counted with the support of Pró-Reitorias de Graduação e de Cultura e Extensão da Universidade de São Paulo and CNPQ (National Research Council) to organize the collection. Matemateca organizes exhibitions open to the public.
The professors in the Department of Mathematics of IME-USP (Institute of Mathematics and Statistics of the University of São Paulo) who initiated the project were Deborah Raphael, Eduardo Colli, and Sônia Garcia; Artur Simões Rozestraten from the Laboratory for Models and Tests (LAME) in the Department of Architectural Technology of the FAU-USP ( Faculty of Architecture and Urbanism of the University of São Paulo) partners with the IME.
History
In August 2002 the French itinerant exhibition of the Cité des sciences et de I'industrie, visited IME, causing in some teachers the desire of building a collection with the purpose of divulging to students of the exact area mathematical contents that are not covered in graduation courses. Matemateca's debut took place during the First Week of Graduation of the Institute of Mathematics and Statistics of the University of São Paulo (IME). Then it was taken to Salvador, Bahia, in order to be exhibited in the II Bienal da Sociedade Brasileira de Matemática. A presentation in Rio de Janeiro, at the IV World Congress of Science Centers, in conjunction with the USP's Science Station, showed the organizers the potential of the collection for the general public, especially students of all levels. The project began to aim at the popularization of mathematics, giving preference to interactive objects that could be approached by means of direct challenges to the visitor. As a way to expand the field of access, Matemateca participated in an upload drive to Wikimedia Commons of some digital images belonging to the collection, under the free Creative Commons Attribution-Share Alike 4.0 International license.
Collection
Matemateca's collection is divided in approximately forty different themes that include equations and functions among other mathematical and statistical concepts. The visitors, be them USP students, family members, teachers or students from other schools and colleges are granted full permission to handle all the exposed content, thus allowing and encouraging an interactive experiential learning. Some items can be seen below.
Chladni figures
Plates made of metal, in various formats, covered with sawdust, which, when suffering interference from the musical notes emitted by the playing of a violin bow, spreads and forms geometric figures.
Chaotic Water Wheel
Made by undergraduate students, in a course taught by two professors from the Mathematics Department of IME and a professor from the FA
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https://en.wikipedia.org/wiki/Vassilios%20Lakon
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Vassilios Lakon ( or , 1831–1900) was an astronomer, mathematician, experimental physicist, philologist, author, and professor. He was a pioneer in 19th-century Greek geometry. He did research in the fields of physics and mathematics. His professors were world-renowned physicist Dimitrios Stroumpos and astronomer Georgios Konstantinos Vouris. He also studied in France with Joseph Bertrand. He was exposed to the works of Joseph Liouville, Augustin-Louis Cauchy, Bernard Lamy, and Jacques Charles François Sturm. Lakon's math textbooks were used in high schools across Greece during the second half of the 19th century.
Lakon was born on the island of Kea. He was from a prominent family. He was the first student to receive a doctorate degree in Mathematics from the University of Athens in 1850. He continued his post-doctoral studies in France. He returned to Greece. He introduced modern French mathematical concepts to Greek education. He was involved in high school and higher education. He spent the rest of his life teaching and writing science books. He participated in the scientific debates of the time. His axiomatic foundation expanded Euclid's Elements. He presented the idea of motion relative to geometry and discussed the rotation and placement of geometric figures on a plane and in space. He also contributed to the fields of electromagnetism and astronomy. His first son was the famous Greek poet . His other son was a botanist.
Biography
He was born in Kea in 1831. His father's name was Ioannis. His brother was a poet and legal writer Dimitrios I. Lakon. Vassilios married Aspasia and had two sons. His oldest son was the famous Greek poet Kostas Karthaios (Κώστας Καρθαίος). He was initially born (Cleandros Lakon) Κλέανδρος Λάκων. Vassilio's second son was Giorgios Lakon. He was a famous botanist. Vassilios obtained his early education on the island of Kea. He attended high school ( Hellenic School or Gymnasium) in Athens. He was accepted at the University of Athens. His professors in Athens were world-renowned physicist Dimitrios Stroumpos and astronomer Georgios Konstantinos Vouris. He was the first student to receive a doctoral degree in Mathematics from the University of Athens in 1850. He graduated with honors and was awarded 100 drachmas. He decided to follow the path of his professor Dimitrios Stroumpos. He continued his post-doctoral studies in Paris from (1850-1854) at the Sorbonne.
Europe and France were undergoing a modern scientific revolution. Greece and Italy were under the restrictive educational systems of Korydalism. England, France, and Germany were undergoing the age of enlightenment in science. Francis Bacon embraced science while Italy imposed the inquisition on Galileo. The Greek community did the same to Methodios Anthrakites during the Methodios affair.
Lakon and his contemporaries embraced European education and promoted new ideas. Lakon studied in France with Joseph Bertr
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https://en.wikipedia.org/wiki/Fernando%20Illescas
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Fernando Illescas Mariñelarena (born 1 June 1999) is a Mexican professional footballer who plays as an attacking midfielder.
Career statistics
Club
References
External links
Living people
1999 births
Mexican men's footballers
Men's association football midfielders
Celaya F.C. footballers
Club Necaxa footballers
Liga de Expansión MX players
Liga MX players
Mazatlán F.C. footballers
Footballers from Chihuahua
Sportspeople from Chihuahua City
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https://en.wikipedia.org/wiki/Gabriel%20L%C3%B3pez%20%28footballer%2C%20born%202003%29
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Gabriel López Reza (born 10 February 2003) is a Mexican professional footballer who plays as an forward for Liga MX club Mazatlán.
Career statistics
Club
Notes
References
External links
Living people
2003 births
Men's association football forwards
Liga MX players
Mazatlán F.C. footballers
Footballers from Michoacán
Mexican men's footballers
People from Parácuaro
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https://en.wikipedia.org/wiki/Titanium%20compounds
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The +4 oxidation state dominates titanium chemistry, but compounds in the +3 oxidation state are also numerous. Commonly, titanium adopts an octahedral coordination geometry in its complexes, but tetrahedral TiCl4 is a notable exception. Because of its high oxidation state, titanium(IV) compounds exhibit a high degree of covalent bonding.
Oxides, sulfides, and alkoxides
The most important oxide is TiO2, which exists in three important polymorphs; anatase, brookite, and rutile. All three are white diamagnetic solids, although mineral samples can appear dark (see rutile). They adopt polymeric structures in which Ti is surrounded by six oxide ligands that link to other Ti centers.
The term titanates usually refers to titanium(IV) compounds, as represented by barium titanate (BaTiO3). With a perovskite structure, this material exhibits piezoelectric properties and is used as a transducer in the interconversion of sound and electricity. Many minerals are titanates, such as ilmenite (FeTiO3). Star sapphires and rubies get their asterism (star-forming shine) from the presence of titanium dioxide impurities.
A variety of reduced oxides (suboxides) of titanium are known, mainly reduced stoichiometries of titanium dioxide obtained by atmospheric plasma spraying. Ti3O5, described as a Ti(IV)-Ti(III) species, is a purple semiconductor produced by reduction of TiO2 with hydrogen at high temperatures, and is used industrially when surfaces need to be vapor-coated with titanium dioxide: it evaporates as pure TiO, whereas TiO2 evaporates as a mixture of oxides and deposits coatings with variable refractive index. Also known is Ti2O3, with the corundum structure, and TiO, with the rock salt structure, although often nonstoichiometric.
The alkoxides of titanium(IV), prepared by treating TiCl4 with alcohols, are colorless compounds that convert to the dioxide on reaction with water. They are industrially useful for depositing solid TiO2 via the sol-gel process. Titanium isopropoxide is used in the synthesis of chiral organic compounds via the Sharpless epoxidation.
Titanium forms a variety of sulfides, but only TiS2 has attracted significant interest. It adopts a layered structure and was used as a cathode in the development of lithium batteries. Because Ti(IV) is a "hard cation", the sulfides of titanium are unstable and tend to hydrolyze to the oxide with release of hydrogen sulfide.
Nitrides and carbides
Titanium nitride (TiN) is a refractory solid exhibiting extreme hardness, thermal/electrical conductivity, and a high melting point. TiN has a hardness equivalent to sapphire and carborundum (9.0 on the Mohs scale), and is often used to coat cutting tools, such as drill bits. It is also used as a gold-colored decorative finish and as a barrier layer in semiconductor fabrication. Titanium carbide (TiC), which is also very hard, is found in cutting tools and coatings.
Halides
Titanium tetrachloride (titanium(IV) chloride, TiCl4) is a colorless volatile li
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https://en.wikipedia.org/wiki/Abraham%20Flores
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Abraham Flores Cruz (born 14 July 2002) is a Mexican professional footballer who plays as a centre-back for Liga MX club Tijuana.
Career statistics
Club
Honours
Mexico U17
CONCACAF U-17 Championship: 2019
FIFA U-17 World Cup runner-up: 2019
References
External links
Living people
2002 births
Mexican men's footballers
Mexico men's youth international footballers
Men's association football defenders
Club Tijuana footballers
Liga MX players
Footballers from Tijuana
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https://en.wikipedia.org/wiki/Alan%20Ruiz%20%28footballer%2C%20born%202001%29
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Alan Fabrizio Ruiz Preza (born 3 January 2001) is a Mexican professional footballer who plays as a midfielder for Liga Premier club Racing Porto Palmeiras.
Career statistics
Club
References
External links
Living people
2001 births
Mexican men's footballers
Men's association football midfielders
C.D. Veracruz footballers
Club Tijuana footballers
Liga MX players
Footballers from Veracruz
Sportspeople from Veracruz (city)
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https://en.wikipedia.org/wiki/Gerhard%20Larcher
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Gerhard Larcher is an Austrian mathematician and professor of financial mathematics at the Johannes Kepler University (JKU) in Linz, Austria. He is the head of the Institute of Financial Mathematics.
Career
Gerhard Larcher studied mathematics at the University of Salzburg from 1978 to 1982 and received his doctorate with the highest distinction sub auspiciis Praesidentis under Harald Niederreiter in 1985; he completed his postdoc in mathematics four years later.
From 1983 to 2000, Larcher worked at the University of Salzburg as an assistant professor and lecturer and from 1996 as an associate professor of mathematics. During this time he headed the Institute of Mathematics for two years. Since 1999 he was speaker and leader of the FWF-Research Center (FSP) Number-Theoretic Algorithms and their Applications.
In 2000, Larcher was appointed as a full professor of financial mathematics at the Johannes Kepler University (JKU) in Linz, Austria. Three years later, he founded the asset management company Art In Finance in Vienna, which developed and implemented alternative investment strategies. After years of strong profits, the option strategies of Art In Finance sustained massive losses in the course of the financial crisis in 2008. The strategies were then adapted accordingly and successfully reintroduced. At the start of 2017, he withdrew from the company and the asset management business. From 2003 to 2005, he was the department head of financial mathematics at the Johann Radon Institute for Computational and Applied Mathematics at the Austrian Academy of Sciences.
Since 2014 he has been the speaker of the Austrian special research area Quasi-Monte Carlo Methods: Theory and Applications at the Austrian Science Fund. In addition to his work at the Johannes Kepler University, Larcher runs seminars and workshops in the field of quantitative finance.
He is the author of the monograph Quantitative Finance: Strategien, Investments, Analysen published by Springer-Gabler Verlag, of the trilogy The Art of Quantitative Finance. Strategies, Investmens, Research by Springer and Die Black-Scholes-Theorie, In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis also published by Springer.
In 2019, he founded the Linz School of Quantitative Finance (LSQF), a work group at the JKU Linz that deals with finance consulting and the creation of highly specialized finance software. Among other things, the LSQF team developed the Fynup Ratio, a new method for measuring the quality of investment funds based on machine learning techniques.
His work and research focuses on the development and analysis of trading strategies, the valuation of derivative finance products, Monte Carlo and quasi-Monte Carlo methods and number theory.
Awards
Science Award of Rotary Austria (1987)
Christian Doppler Prize for Natural Sciences (1988)
The Kardinal Innitzer Prize for the Advancement of Natural Sciences (1994)
Prize of the Austrian Mathematical Society (1996)
Edmund and
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https://en.wikipedia.org/wiki/Alam%20Galindo
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Alam Fernando Galindo Gajón (born 21 May 2001) is a Mexican professional footballer who plays as a midfielder for Liga MX club Tijuana.
Career statistics
Club
References
External links
Living people
2001 births
Mexican men's footballers
Men's association football midfielders
Club Tijuana footballers
Liga MX players
Footballers from Tijuana
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https://en.wikipedia.org/wiki/List%20of%20Newcastle%20Breakers%20FC%20records%20and%20statistics
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Newcastle Breakers Football Club was an Australian semi-professional association football club based in Newcastle. The club was formed in 1991 was admitted into the National Soccer League in the 1991–92 season. The club had never qualified for the Finals series in the National Soccer League in all eight seasons of existence until they became defunct in 2000.
The list encompasses the records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. Attendance records in Newcastle are also included.
The club's record appearance maker is Andy Roberts, who made 169 appearances between 1978 and 1984. Warren Spink was Newcastle Breakers' record goalscorer, scoring 28 goals in total.
Player records
Appearances
Most league appearances: Andy Roberts, 164
Most NSL Cup appearances: Glenn Sprod, 10
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in a season: John Buonavoglia, 16 goals (in the 1999–2000 season)
Top goalscorers
Warren Spink was the all-time top goalscorer for Newcastle Breakers.
Competitive matches only. Numbers in brackets indicate appearances made.
Club records
Matches
Firsts
First National Soccer League match: Newcastle Breakers 0–2 Adelaide City, National Soccer League, 6 October 1991
First NSL Cup match: Newcastle Breakers 0–3 Marconi Fairfield, First round, 20 November 1991
Record wins
Record NSL win: 6–0 against Heidelberg United, National Soccer League, 26 December 1993
Record NSL Cup win: 7–1 against Northern NSW Lions, First round, 12 September 1996
Record defeats
Record NSL defeat: 0–6 against Melbourne Croatia, National Soccer League, 8 December 1991
Record NSL Cup defeat: 0–3 against Marconi Fairfield, First round, 20 November 1991
Record consecutive results
Record consecutive wins: 4
from 26 November 1999 to 17 December 1999
from 6 February 2000 to 25 February 2000
Record consecutive defeats: 10, from 12 March 1996 to 28 April 1996
Record consecutive draws: 4, from 26 December 1991 to 12 January 1992
Record consecutive matches without a defeat: 10, from 19 November 1999 to 21 January 2000
Record consecutive matches without a win: 17, from 12 October 1997 to 30 January 1998
Goals
Most NSL goals scored in a season: 44 in 34 matches, National Soccer League, 1999–2000
Fewest NSL goals scored in a season: 28 in 26 matches, National Soccer League, 1991–92
Most NSL goals conceded in a season: 77 in 33 matches, National Soccer League, 1995–96
Fewest NSL goals conceded in a season: 29 in 26 matches, National Soccer League, 1992–93
Points
Most points in a season: 51 in 34 matches, National Soccer League, 1999–2000
Fewest points in a season: 22 in 26 matches, National Soccer League, 1991–92
Attendances
Highest attendance at Newcastle: 7,674, against Adelaide Force, National Socce
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https://en.wikipedia.org/wiki/Algebraic%20decision%20diagram
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An algebraic decision diagram (ADD) or a multi-terminal binary decision diagram (MTBDD), is a data structure that is used to symbolically represent a Boolean function whose codomain is an arbitrary finite set S. An ADD is an extension of a reduced ordered binary decision diagram, or commonly named binary decision diagram (BDD) in the literature, which terminal nodes are not restricted to the Boolean values 0 (FALSE) and 1 (TRUE). The terminal nodes may take any value from a set of constants S.
Definition
An ADD represents a Boolean function from to a finite set of constants S, or carrier of the algebraic structure. An ADD is a rooted, directed, acyclic graph, which has several nodes, like a BDD. However, an ADD can have more than two terminal nodes which are elements of the set S, unlike a BDD.
An ADD can also be seen as a Boolean function, or a vectorial Boolean function, by extending the codomain of the function, such that with and for some integer n. Therefore, the theorems of the Boolean algebra applies to ADD, notably the Boole's expansion theorem.
Each node of is labeled by a Boolean variable and has two outgoing edges: a 1-edge which represents the evaluation of the variable to the value TRUE, and a 0-edge for its evaluation to FALSE.
An ADD employs the same reduction rules as a BDD (or Reduced Ordered BDD):
merge any isomorphic subgraphs, and
eliminate any node whose two children are isomorphic.
ADDs are canonical according to a particular variable ordering.
Matrix partitionning
An ADD can be represented by a matrix according to its cofactors.
Applications
ADDs were first implemented for sparse matrix multiplication and shortest path algorithms (Bellman-Ford, Repeated Squaring, and Floyd-Warshall procedures).
See also
Binary decision diagram
Zero-suppressed decision diagram
References
Diagrams
Graph data structures
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https://en.wikipedia.org/wiki/Pablo%20Bennevendo
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Pablo Bennevendo Peña (born 3 January 2000) is a Mexican professional footballer who plays as a full-back for Liga MX club UNAM.
Career statistics
Club
References
External links
Living people
2000 births
Men's association football defenders
Club Universidad Nacional footballers
Liga de Expansión MX players
Liga MX players
Footballers from Mexico City
Mexican men's footballers
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https://en.wikipedia.org/wiki/Santiago%20Trigos
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Santiago Trigos Nava (born 22 January 2002) is a Mexican professional footballer who plays as a defensive midfielder for Liga MX club UNAM.
Career statistics
Club
References
External links
Living people
2002 births
Mexican men's footballers
Men's association football midfielders
Club Universidad Nacional footballers
Liga de Expansión MX players
Liga MX players
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Jos%C3%A9%20Navarro%20%28footballer%2C%20born%202003%29
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José Navarro Hernández (born 20 February 2003) is a Mexican professional footballer who plays as a forward for Liga MX club UNAM.
Career statistics
Club
References
External links
Living people
2003 births
Mexican men's footballers
Men's association football forwards
Club Universidad Nacional footballers
Liga MX players
Footballers from Mexico City
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