source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/Makhonine%20Mak-10 | The Makhonine Mak-10, was a variable-geometry research aircraft, built to investigate variable area / telescopic wings during 1931 in France.
Design and development
In the early 1930s several designers became interested in the possibility of changing the configuration of wings between take off and fast flight. Two routes were explored, the first primarily involving camber and hence lift coefficient reduction and the other a decrease of wing area by span reduction at high speed. The Schmeidler variable wing and that of the Gloster built Antoni-Breda Ba.15 were examples of the first group and the Makhonine Mak-10 of the second.
Details of the Mak-10 are sparse but its novel feature was a telescopic wing which increased the span for take-off by or 60% of its high speed configuration. The outer panels retracted into the central ones, their inner ends supported on bearings rolling along one or more spars. The ends of the centre section were reinforced with cuffs. The wing apart, it was a conventional cantilever low wing monoplane, with twin open cockpits, the rear one sometimes faired in, and faired, fixed landing gear. It was powered by a , three bank, W-configuration, twelve cylinder Lorraine 12Eb engine.
The first flight of the Mak-10 was on 11 August 1931. During four years of development the Mak-10 was re-engined with a Gnome-Rhône 14K Mistral Major fourteen cylinder, two row radial engine which gave it a top speed of and the new designation Mak-101.
44 years later, the Akaflieg Stuttgart FS-29 experimental high performance sailplane also used telescopic wings to optimise both low speed thermalling and high speed penetration performance without the added induced drag of camber and area changing flaps.
Variants
Mak-10 W-configuration, twelve cylinder Lorraine 12Eb engine.
Mak-101 Gnome-Rhône 14K Mistral Major fourteen cylinder radial engine.
Specifications (Mak-10)
See also
References
Bibliography
External links
Photo of the Makhonine Mak-10
Film of wing deployment, take off and flight
Mak-010
1930s French experimental aircraft
Single-engined tractor aircraft
Low-wing aircraft
Variable-geometry-wing aircraft
Aircraft first flown in 1931 |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20PFC%20Levski%20Sofia%20season | The 2010–11 season is Levski Sofia's 89th season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the 2010–11 season.
Transfers
Summer transfers
In:
Out:
See List of Bulgarian football transfers summer 2010
Winter transfers
In:
Out:
See List of Bulgarian football transfers winter 2010–11.
Squad
As of August 29, 2010
Statistics
Goalscorers
Assists
Cards
Pre-season and friendlies
Summer
Winter
Competitions
A Group
Table
Results summary
Results by round
Fixtures and results
Bulgarian Cup
UEFA Europa League
Second qualifying round
Third qualifying round
Play-off round
Group stage
References
PFC Levski Sofia seasons
Levski Sofia |
https://en.wikipedia.org/wiki/Manoel%20%28footballer%2C%20born%201991%29 | Manoel Segundo Jardim Júnior (born 12 August 1991 in São Bernardo do Campo) is a Brazilian footballer.
Career
Plays in the Associação Esportiva Jataiense.
Career statistics
(Correct )
Contract
Goiás.
See also
Football in Brazil
List of football clubs in Brazil
References
External links
ogol
soccerway
1991 births
Living people
Brazilian men's footballers
Goiás Esporte Clube players
Men's association football forwards
Footballers from São Bernardo do Campo
21st-century Brazilian people |
https://en.wikipedia.org/wiki/Geovane%20%28footballer%2C%20born%201989%29 | Geovane Batista de Faria, known simply Geovane (born 20 February 1989 in Pedregulho, São Paulo), is a footballer who plays as a midfielder. He currently plays for CSA.
Career statistics
Honours
CSA
Campeonato Alagoano: 2021
Contract
Goiás.
Cruzeiro Esporte Clube.
References
External links
1989 births
Living people
Brazilian men's footballers
Goiás Esporte Clube players
Cruzeiro Esporte Clube players
Vila Nova Futebol Clube players
Agremiação Sportiva Arapiraquense players
Associação Atlética Aparecidense players
Cuiabá Esporte Clube players
Centro Sportivo Alagoano players
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Men's association football midfielders
People from Pedregulho
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Guilherme%20%28footballer%2C%20born%20August%201990%29 | Guilherme Mascarenhas Santana, known as just Guilherme born in the Brasília is a midfielder.
Career
Plays in the Goiás.
Career statistics
(Correct )
Contract
Goiás.
See also
Football in Brazil
List of football clubs in Brazil
References
External links
ogol
soccerway
1990 births
Living people
Brazilian men's footballers
Goiás Esporte Clube players
Men's association football midfielders
Footballers from Brasília |
https://en.wikipedia.org/wiki/Anderson%20Bill | Anderson Martins Pedro, the Anderson Bill, also known as King William, born in the Criciúma is a centre back who plays in the Veranópolis.
Career
Plays in the Grêmio Prudente.
Career statistics
(Correct )
Contract
Grêmio Prudente.
References
External links
ogol
soccerway
WebSoccerClub
1981 births
Living people
Brazilian men's footballers
Sociedade Esportiva e Recreativa Caxias do Sul players
Men's association football central defenders |
https://en.wikipedia.org/wiki/Dade%20isometry | In mathematical finite group theory, the Dade isometry is an isometry from class function on a subgroup H with support on a subset K of H to class functions on a group G . It was introduced by as a generalization and simplification of an isometry used by in their proof of the odd order theorem, and was used by in his revision of the character theory of the odd order theorem.
Definitions
Suppose that H is a subgroup of a finite group G, K is an invariant subset of H such that if two elements in K are conjugate in G, then they are conjugate in H, and π a set of primes containing all prime divisors of the orders of elements of K. The Dade lifting is a linear map f → fσ from class functions f of H with support on K to class functions fσ of G, which is defined as follows: fσ(x) is f(k) if there is an element k ∈ K conjugate to the π-part of x, and 0 otherwise.
The Dade lifting is an isometry if for each k ∈ K, the centralizer CG(k) is the semidirect product of a normal Hall π' subgroup I(K) with CH(k).
Tamely embedded subsets in the Feit–Thompson proof
The Feit–Thompson proof of the odd-order theorem uses "tamely embedded subsets" and an isometry from class functions with support on a tamely embedded subset. If K1 is a tamely embedded subset, then the subset K consisting of K1 without the identity element 1 satisfies the conditions above, and in this case the isometry used by Feit and Thompson is the Dade isometry.
References
Finite groups
Representation theory |
https://en.wikipedia.org/wiki/Arthur%20Henrique%20%28footballer%2C%20born%201987%29 | Arthur Henrique Ricciardi Oyama (born 14 January 1987 in São Paulo), also known simply as Arthur or Arthur Henrique, is a Brazilian footballer who plays as a left back.
Career statistics
(Correct )
Honours
Santo André
Campeonato Paulista Série A2: 2008
References
External links
ogol
soccerway
1987 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Primeira Liga players
First Professional Football League (Bulgaria) players
Maltese Premier League players
Esporte Clube Santo André players
Grêmio Barueri Futebol players
C.D. Nacional players
Botev Plovdiv players
K.S.C. Lokeren Oost-Vlaanderen players
Floriana F.C. players
Gżira United F.C. players
Sliema Wanderers F.C. players
Brazilian expatriate sportspeople in Portugal
Brazilian expatriate sportspeople in Bulgaria
Brazilian expatriate sportspeople in Belgium
Brazilian expatriate sportspeople in Malta
Expatriate men's footballers in Portugal
Expatriate men's footballers in Bulgaria
Expatriate men's footballers in Belgium
Expatriate men's footballers in Malta
Men's association football fullbacks
Footballers from São Paulo |
https://en.wikipedia.org/wiki/Eisenbud%E2%80%93Levine%E2%80%93Khimshiashvili%20signature%20formula | In mathematics, and especially differential topology and singularity theory, the Eisenbud–Levine–Khimshiashvili signature formula gives a way of computing the Poincaré–Hopf index of a real, analytic vector field at an algebraically isolated singularity. It is named after David Eisenbud, Harold I. Levine, and George Khimshiashvili. Intuitively, the index of a vector field near a zero is the number of times the vector field wraps around the sphere. Because analytic vector fields have a rich algebraic structure, the techniques of commutative algebra can be brought to bear to compute their index. The signature formula expresses the index of an analytic vector field in terms of the signature of a certain quadratic form.
Nomenclature
Consider the n-dimensional space Rn. Assume that Rn has some fixed coordinate system, and write x for a point in Rn, where
Let X be a vector field on Rn. For there exist functions such that one may express X as
To say that X is an analytic vector field means that each of the functions is an analytic function. One says that X is singular at a point p in Rn (or that p is a singular point of X) if , i.e. X vanishes at p. In terms of the functions it means that for all . A singular point p of X is called isolated (or that p is an isolated singularity of X) if and there exists an open neighbourhood , containing p, such that for all q in U, different from p. An isolated singularity of X is called algebraically isolated if, when considered over the complex domain, it remains isolated.
Since the Poincaré–Hopf index at a point is a purely local invariant (cf. Poincaré–Hopf theorem), one may restrict one's study to that of germs. Assume that each of the ƒk from above are function germs, i.e. In turn, one may call X a vector field germ.
Construction
Let An,0 denote the ring of analytic function germs . Assume that X is a vector field germ of the form
with an algebraically isolated singularity at 0. Where, as mentioned above, each of the ƒk are function germs . Denote by IX the ideal generated by the ƒk, i.e. Then one considers the local algebra, BX, given by the quotient
The Eisenbud–Levine–Khimshiashvili signature formula states that the index of the vector field X at 0 is given by the signature of a certain non-degenerate bilinear form (to be defined below) on the local algebra BX.
The dimension of is finite if and only if the complexification of X has an isolated singularity at 0 in Cn; i.e. X has an algebraically isolated singularity at 0 in Rn. In this case, BX will be a finite-dimensional, real algebra.
Definition of the bilinear form
Using the analytic components of X, one defines another analytic germ given by
for all . Let denote the determinant of the Jacobian matrix of F with respect to the basis Finally, let denote the equivalence class of JF, modulo IX. Using ∗ to denote multiplication in BX one is able to define a non-degenerate bilinear form β as follows:
where is any linear function |
https://en.wikipedia.org/wiki/Exceptional%20character | In mathematical finite group theory, an exceptional character of a group is a character related in a certain way to a character of a subgroup. They were introduced by , based on ideas due to Brauer in .
Definition
Suppose that H is a subgroup of a finite group G, and C1, ..., Cr are some conjugacy classes of H, and
φ1, ..., φs are some irreducible characters of H.
Suppose also that they satisfy the following conditions:
s ≥ 2
φi = φj outside the classes C1, ..., Cr
φi vanishes on any element of H that is conjugate in G but not in H to an element of one of the classes C1, ..., Cr
If elements of two classes are conjugate in G then they are conjugate in H
The centralizer in G of any element of one of the classes C1,...,Cr is contained in H
Then G has s irreducible characters s1,...,ss, called exceptional characters, such that the induced characters φi* are given by
φi* = εsi + a(s1 + ... + ss) + Δ
where ε is 1 or −1, a is an integer with a ≥ 0, a + ε ≥ 0, and Δ is a character of G not containing any character si.
Construction
The conditions on H and C1,...,Cr imply that induction is an isometry from generalized characters of H with support on C1,...,Cr to generalized characters of G. In particular if i≠j then (φi − φj)* has norm 2, so is the difference of two characters of G, which are the exceptional characters corresponding to φi and φj.
See also
Dade isometry
Coherent set of characters
References
Finite groups
Representation theory |
https://en.wikipedia.org/wiki/Ioan%20Filip | Ioan Constantin Filip (born 20 May 1989) is a Romanian professional footballer who plays as a defensive midfielder for Liga I club Universitatea Cluj.
Club statistics
Updated to games played as of 9 October 2023.
Honours
Club
Luceafărul-Lotus Băile Felix
Liga III: 2007–08
Oțelul Galați
Liga I: 2010–11
Supercupa României: 2011
Viitorul Constanța
Liga I: 2016–17
Universitatea Cluj
Cupa României runner-up: 2022–23
References
External links
1989 births
Living people
Footballers from Bihor County
Romanian men's footballers
Men's association football midfielders
FC Bihor Oradea (1958) players
CS Luceafărul Oradea players
ASC Oțelul Galați players
FC Petrolul Ploiești players
FC Viitorul Constanța players
Debreceni VSC players
FC Dinamo București players
FC Universitatea Cluj players
CS Gaz Metan Mediaș players
Liga I players
Liga II players
Liga III players
Nemzeti Bajnokság I players
Romanian expatriate men's footballers
Expatriate men's footballers in Hungary
Romanian expatriate sportspeople in Hungary
Men's association football defenders |
https://en.wikipedia.org/wiki/Renan%20%28footballer%2C%20born%20April%201990%29 | Marcos Renan Oliveira Santana, (born 7 April 1990) also called Renan (ヘナン), is a football midfielder for Fukushima United FC.
Club statistics
Updated to 23 February 2017.
References
External links
ogol
Profile at Fukushima United FC
1990 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
J3 League players
Hokkaido Consadole Sapporo players
Fukushima United FC players
Grêmio Barueri Futebol players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Juan%20Lima | Juan Gomes de Lima, the Juan Lima born in the São Paulo, is a forward who plays in the Grêmio Prudente.
Career
Plays in the Grêmio Prudente.
Career statistics
(Correct )
Contract
Grêmio Prudente.
References
External links
ogol
soccerway
1991 births
Living people
Brazilian men's footballers
Men's association football forwards
Grêmio Barueri Futebol players
Footballers from São Paulo |
https://en.wikipedia.org/wiki/Douglas%20Camilo | Douglas Camilo da Silva, known as Douglas Camilo born in the Barretos, is a midfielder who plays in the Inter de Bebedouro.
Career
Plays in the Inter de Bebedouro.
Career statistics
(Correct )
Contract
Inter de Bebedouro.
See also
Football in Brazil
List of football clubs in Brazil
References
External links
ogol
soccerway
1990 births
Living people
Brazilian men's footballers
Footballers from São Paulo (state)
Men's association football midfielders
Grêmio Barueri Futebol players
Associação Atlética Internacional (Bebedouro) players
People from Barretos |
https://en.wikipedia.org/wiki/Ara%C3%BAjo%20%28footballer%2C%20born%201984%29 | Adolpho Araújo Netto (born March 2, 1984), known as Araújo, is a Brazilian former footballer who played as a forward and last played for Taboão da Serra.
Career
Career statistics
(Correct )
Contract
Grêmio Prudente.
References
External links
soccerway
Adolpho Araújo Netto at ZeroZero
1984 births
Living people
Brazilian men's footballers
Grêmio Barueri Futebol players
Marília Atlético Clube players
Men's association football forwards
Footballers from São Paulo |
https://en.wikipedia.org/wiki/List%20of%20Club%20Necaxa%20records%20and%20statistics | These are some of Necaxa football club records from 1923–present
Most appearances
Necaxa's Season lead scorers in the Amateur Football League or Liga Mayor de D.F (1923–1937)
Necaxa's Season Career Scorers in the Liga De Ascenso
Necaxa's Season lead scorers in the First Division League
Necaxa's Top three Single Season lead scorers in the First Division League
Single Season play began in 1996
Necaxa's Single Season Assist leaders in the First Division League
Necaxa's top ten leading strikers
Club Necaxa's Goal Keeping records
Club Necaxa Managerial statistics
Amateur era 1920–1943
no football played in 1930–1931 season
"Professional Mexican" football begins 1943 in Mexico(Early Capitalism)
Athletico Espanol
"Professional Mexican" football begins 1997 in Mexico(Advanced Capitalism)
Club Records
Most Goals in National Championship: 9–0 vs Atlante (27-Oct-1934)
Most Goals in a Single season : 5–0 vs Pachuca (27-Sept-2005)
Most Goals in an International Tournament: 6–0 vs Morelia (26-Feb-2002)
Best Position in Table: 1º (Season 1992–1993)
Worst Position in Table: 18º (2009)
Longest undefeated streak: 29 games (Fall 2009 + Spring 2010)
Individual Necaxa Footballer Awards
CONCACAF Footballer of the Year
The following players have won the CONCACAF Footballer of the Year award while playing for Club Necaxa:
Adolfo Ríos (1996–97)
Adolfo Ríos (1998)
CONCACAF Youth Footballer of the Year
Luis Pérez (1999)
Bicentennial Golden Footballer of the Year 2010
Pablo Quatrocchi (2010)
Coaching History
Player/Coach/Captain
Necaxa footballers(free-agency economic model)
Footnotes
Club Necaxa |
https://en.wikipedia.org/wiki/List%20of%20Reading%20F.C.%20records%20and%20statistics | Reading Football Club hold the record for the number of successive league wins at the start of a season, with a total of 13 wins at the start of the 1985–86 Third Division campaign and also the record for the number of points gained in a professional league season with 106 points in the 2005–06 Football League Championship campaign. Reading finished champions of their division on both of these occasions.
The club's largest win was a 10–0 victory over Gibraltar on 10 July 2019 in a pre-season friendly. Their biggest league win was a 10–2 victory over Crystal Palace on 4 September 1946 in the Third Division South. Reading's heaviest loss was an 18–0 defeat against Preston North End in the FA Cup 1st round on 27 January 1894.
The player with the most league appearances is Martin Hicks with a total of 500 from 1978 to 1991. The most capped player is Kevin Doyle, who earned 26 for Ireland while at the club. The most league goals in total and in a season is Ronnie Blackman with 158 from 1947 to 1954 and 39 in 1951–52 respectively. The player with the most league goals in a game is Arthur Bacon with six against Stoke City in 1930–31. The first Reading-based player to play in the World Cup is Bobby Convey at the 2006 World Cup with the United States. The record time for a goalkeeper not conceding a goal is Steve Death at 1,103 minutes in 1978–79, which is a former English league record.
Reading's highest attendance at Elm Park was in 1927, when 33,042 spectators watched Reading beat Brentford 1–0. The highest attendance at the Madejski Stadium is 24,160 for the Premier League game with Tottenham Hotspur on 16 September 2012.
The highest transfer fee received for a Reading player is the £8 million received from Crystal Palace for Michael Olise in July 2021, beating the £7 million fee that 1899 Hoffenheim paid for Gylfi Sigurðsson in August 2010. The most expensive player Reading have ever bought is George Pușcaș, for an estimated £8,000,000 from Internazionale on 7 August 2019.
Honours
League competitions
English 2nd tier
Winners (2): 2006, 2012
Runners Up (1): 1995
English 3rd tier
Winners (3): 1926, 1986, 1994
Runners Up (5): 1932, 1935, 1949, 1952, 2002
English 4th tier
Winners (1): 1979
Highest league finish
Premier League 2007, 8th Place
Cup competitions
FA Cup
Semi-final: 1927, 2015
Quarter-final: 1901, 2010, 2011, 2016
EFL Cup
Quarter-final: 1996, 1998
Full Members Cup
Winners (1): 1988
London War Cup
Winners (1): 1941
Football League Third Division South Cup
Winners (1): 1938
Youth and reserve competitions
Premier League Cup
Winners (1): 2014
Runners Up (1): 2017
Berks & Bucks Senior Cup
Winners (3): 1879, 1892, 1995
Runners-Up (4): 1941, 1997, 1998, 2000
Managerial
LMA Manager of the Year
Steve Coppell 2005–06, 2006–07
LMA Championship Manager of the Year
Brian McDermott 2011–12
Player records
Appearances
Most appearances: Martin Hicks (603; 1978–1991)
Most league appearances: Martin Hicks (500; 1978–1991)
Goals
Most go |
https://en.wikipedia.org/wiki/Ricardo%20Xavier | Ricardo Gomes Xavier (born July 22, 1978 in Bonito, Mato Grosso do Sul) is a Brazilian football forward.
Career
Played for Náutico.
Career statistics
(Correct )
Contract
Guarani.
References
External links
Ricardo Xavier at oGol
1978 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Criciúma Esporte Clube players
União São João Esporte Clube players
Guarani FC players
Clube Náutico Capibaribe players
FC Spartak Vladikavkaz players
Associação Desportiva São Caetano players
Expatriate men's footballers in Russia
Footballers from Mato Grosso do Sul
Clube Atlético Sorocaba players
Men's association football forwards |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Kert%C3%A9sz | János Kertész is a Hungarian physicist. He is one of the pioneers of econophysics, complex networks and application of fractal geometry in physical problems.
He is the director of the Institute of Physics in Budapest University of Technology and Economics, Budapest, Hungary.
References
External links
Personal Homepage
21st-century Hungarian physicists
Living people
Academic staff of Central European University
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Guilherme%20Mattis | Guilherme Cruz de Mattis (born 12 September 1990 in São Paulo), known as Guilherme Mattis, is a centre back who plays for São Bernardo.
Career
Plays in the Guarani.
Career statistics
(Correct )
Contract
Guarani.
References
External links
Guilherme Mattis at Ogol
1990 births
Living people
Footballers from São Paulo
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Guarani FC players
Clube Atlético Bragantino players
Fluminense FC players
Esporte Clube Vitória players
Santa Cruz Futebol Clube players
Clube de Regatas Brasil players
Esporte Clube São Bento players
São Bernardo Futebol Clube players |
https://en.wikipedia.org/wiki/Standard%20Borel%20space | In mathematics, a standard Borel space is the Borel space associated to a Polish space. Discounting Borel spaces of discrete Polish spaces, there is, up to isomorphism of measurable spaces, only one standard Borel space.
Formal definition
A measurable space is said to be "standard Borel" if there exists a metric on that makes it a complete separable metric space in such a way that is then the Borel σ-algebra.
Standard Borel spaces have several useful properties that do not hold for general measurable spaces.
Properties
If and are standard Borel then any bijective measurable mapping is an isomorphism (that is, the inverse mapping is also measurable). This follows from Souslin's theorem, as a set that is both analytic and coanalytic is necessarily Borel.
If and are standard Borel spaces and then is measurable if and only if the graph of is Borel.
The product and direct union of a countable family of standard Borel spaces are standard.
Every complete probability measure on a standard Borel space turns it into a standard probability space.
Kuratowski's theorem
Theorem. Let be a Polish space, that is, a topological space such that there is a metric on that defines the topology of and that makes a complete separable metric space. Then as a Borel space is Borel isomorphic to one of
(1) (2) or (3) a finite discrete space. (This result is reminiscent of Maharam's theorem.)
It follows that a standard Borel space is characterized up to isomorphism by its cardinality, and that any uncountable standard Borel space has the cardinality of the continuum.
Borel isomorphisms on standard Borel spaces are analogous to homeomorphisms on topological spaces: both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous, instead of both being only Borel measurable.
See also
References
Descriptive set theory
General topology
Measure theory
Space (mathematics) |
https://en.wikipedia.org/wiki/NERD%20%28sabermetrics%29 | In baseball statistics, NERD is a quantitative measure of expected aesthetic value. NERD was originally created by Carson Cistulli and is part of his project of exploring the "art" of sabermetric research. The original NERD formula only took into account the pitcher's expected performance while a later model factors in the entire team's performance.
History
The premise for NERD was developed in Cistulli's piece "Why We Watch" in which he establishes the five reasons that baseball continues to captivate the American imagination from game to game: "Pitching Matchups," "Statistically Notable (or Otherwise Compelling) Players," "Rookies (and Debuts)," "Seasonal Context," and "Quality of Broadcast". Fellow sabermatrician Rob Neyer, who had collaborated with Cistulli on this piece, wrote "the only thing missing [...] is a points system that would let us put a number on each game" and on June 2, 2010, Cistulli unveiled the Pitcher NERD formula.
Pitcher NERD
Pitcher NERD tries to determine which pitchers will be the most aesthetically appealing to watch for a baseball fan and is both a historical and a predictive statistic. The formula uses a player's standard deviations from the mean (a weighted z-score) of the DIPS statistic xFIP (expected Fielding Independent Pitching), swinging strike percentage, overall strike percentage, and the differential between the pitcher's ERA and xFIP to determine a quantitative value for each pitcher.
The factor of 4.69 is added to make the number fit on a 0 to 10 scale. While there has been some disagreement on the calculation of Cistulli's luck component, the general consensus among sports writers seems to be that a player with a below-average ERA and an above-average xFIP has been "unlucky".
Team NERD
Following the model of his Pitching NERD, Team NERD tries to give a quantitative value to the aesthetic value of each of the 30 baseball teams. For factors it accounts for "Age," "Park-Adjusted weighted Runs Above Average (wRAA)," "Park-Adjusted Home Run per Fly Ball (HR/FB)," "Team Speed," "Bullpen Strength," "Team Defense," "Luck" (Base Runs – Actual Runs Scored), and "Payroll".
In an interview, Cistulli admitted that there is a disconnect between the Tampa Bay Rays high tNERD rating and low attendance saying that he is considered adding a "park-adjustment" to his formula which would reflect either the stadium itself or "attendance relative to the stadium's capacity" but overall reception of this statistic has been positive and Fangraphs started reporting Team NERD in Cistulli's "One Night Only" columns beginning August 23, 2010.
Notes
References
Baseball statistics |
https://en.wikipedia.org/wiki/Gerg%C5%91%20Nagy%20%28footballer%29 | Gergő Nagy (born 7 January 1993) is a Hungarian football player who plays for Mezőkövesd.
Club career
In June 2022, Nagy signed with Mezőkövesd.
Club statistics
Updated to games played as of 15 May 2022.
Honours
Honvéd
Nemzeti Bajnokság I: 2016–17
Hungarian Cup: 2019-20
References
External links
MLSZ
HLSZ
1993 births
People from Gyula
Footballers from Békés County
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Budapest Honvéd FC players
Budapest Honvéd FC II players
Mezőkövesdi SE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players |
https://en.wikipedia.org/wiki/Modular%20invariant%20theory | In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by .
Dickson invariant
When G is the finite general linear group GLn(Fq) over the finite field Fq of order a prime power q acting on the ring Fq[X1, ...,Xn] in the natural way, found a complete set of invariants as follows. Write [e1, ..., en] for the determinant of the matrix whose entries are X, where e1, ..., en are non-negative integers. For example, the Moore determinant [0,1,2] of order 3 is
Then under the action of an element g of GLn(Fq) these determinants are all multiplied by det(g), so they are all invariants of SLn(Fq) and the ratios [e1, ...,en] / [0, 1, ..., n − 1] are invariants of GLn(Fq), called Dickson invariants. Dickson proved that the full ring of invariants Fq[X1, ...,Xn]GLn(Fq) is a polynomial algebra over the n Dickson invariants [0, 1, ..., i − 1, i + 1, ..., n] / [0, 1, ..., n − 1] for i = 0, 1, ..., n − 1.
gave a shorter proof of Dickson's theorem.
The matrices [e1, ..., en] are divisible by all non-zero linear forms in the variables Xi with coefficients in the finite field Fq. In particular the Moore determinant [0, 1, ..., n − 1] is a product of such linear forms, taken over 1 + q + q2 + ... + qn – 1 representatives of (n – 1)-dimensional projective space over the field. This factorization is similar to the factorization of the Vandermonde determinant into linear factors.
See also
Sanderson's theorem
References
Invariant theory |
https://en.wikipedia.org/wiki/Charles%20Royal%20Johnson | Charles Royal Johnson (born January 28, 1948) is an American mathematician specializing in linear algebra. He is a Class of 1961 professor of mathematics at College of William and Mary. The books Matrix Analysis and Topics in Matrix Analysis, co-written by him with Roger Horn, are standard texts in advanced linear algebra.
Career
Charles R. Johnson received a B.A. with distinction in Mathematics and Economics from Northwestern University in 1969. In 1972, he received a Ph.D. in Mathematics and Economics from the California Institute of Technology, where he was advised by Olga Taussky Todd; his dissertation was entitled "Matrices whose Hermitian Part is Positive Definite". Johnson held various professorships over ten years at the University of Maryland, College Park starting in 1974. He was a professor at Clemson University from 1984 to 1987. In 1987, he became a professor of mathematics at the College of William and Mary, where he remains today.
Books
(1st edition 1985)
(1st edition 1991)
as editor
References
External links
Charles Royal Johnson Curriculum Vitae
20th-century American mathematicians
21st-century American mathematicians
College of William & Mary faculty
Northwestern University alumni
California Institute of Technology alumni
1948 births
Living people
Linear algebraists |
https://en.wikipedia.org/wiki/Advisory%20Committee%20on%20Mathematics%20Education | The Advisory Committee on Mathematics Education (ACME) is a British policy council for the Royal Society based in London, England. Founded in 2002 by the Royal Society and the Joint Mathematical Council, ACME analyzes mathematics education practices and provides advice on education policy. ACME is funded by the Gatsby Charitable Foundation (2002-2015) and the Department for Education.
Members
The committee chair is appointed for a three-year term. As of 2018, the membership is composed of:
Frank Kelly (Chair)
Martin Bridson
Paul Glaister
Paul Golby
Jeremy Hodgen
Mary McAlinden
Lynne McClure
Emma McCoy
Jil Matheson
David Spiegelhalter
Sally Bridgeland
References
2002 establishments in the United Kingdom
Mathematics education in the United Kingdom |
https://en.wikipedia.org/wiki/PhysMath%20Central | PhysMath Central was an imprint of Springer Science+Business Media, publishing online open-access scientific journals in physics and mathematics and operated by BioMed Central. It was active from 2007 until 2011.
Journals published were:
PMC Physics A
PMC Physics B
PMC Biophysics
PMC Physics A and B were discontinued in 2011 in favor of EPJ Open, the open-access component of the European Physical Journal. PMC Biophysics was relaunched as BMC Biophysics within the BioMed Central journal family.
References
External links
Springer Science+Business Media imprints
Online-only journals
Physics journals |
https://en.wikipedia.org/wiki/Char%20Chinar | {
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
74.86664414405824,
34.10316995155632
]
}
}
]
}
Char Chinar, also sometimes called Char Chinari, Ropa Lank, or Rupa Lank, is an island in Dal Lake, Srinagar, Jammu and Kashmir. Dal Lake includes 3 islands, 2 of which are marked with beautiful Chinar trees. The island located on the Lakut Dal (small Dal) is known as Roph Lank (Silver Island), is marked with the presence of majestic Chinar trees at the four corners, thus known as Char-Chinari (Four Chinars). The second Chinar Island, known as Sone Lank (Gold Island), is located on the Bod Dal (Big Dal) and overlooks the holy shrine of Hazratbal.
History
Murad Baksh, brother of the Mughal emperor Aurangzeb, constructed the Roph Lank.
Chinar
Chinar trees characteristically grow in Western Himalayas. Their botanical name is Platanus orientalis. They have been an important part of Kashmiri tradition, in that, a Chinar tree is found in almost every village in Kashmir. These trees have survived for ages, because Chinar is basically a long-living tree. It spreads wide across a region of cool climate with sufficient water. The tree has several properties - leaves and bark are used as medicine, the wood, known as lace wood, has been used for delicate furniture and the twigs and roots are used for making dyes.
Decline and restoration
Chinar all over Jammu and Kashmir have been affected due to various reasons such as indiscriminate tree felling and floods. It is common to find locals and media houses reporting that the four chinar at Char Chinar no longer are as majestic as they once were. Three of the four trees have shown signs of drying up. Some locals blame construction on the island, whereas others blame recent floods and climate change.
The floriculture department of Jammu and Kashmir is making efforts to restore the island to its former glory and have also planted more Chinar trees on the island.
Gallery
References
External links
Photo of Char Chinar (Rupa Lank)
Photo of Char Chinar (YongKianOn)
Kashmir Beauty-Chinar
Islands of Jammu and Kashmir
Srinagar
Lake islands of India
Islands of India
Uninhabited islands of India
Char Chinar Dal lake, Srinagar Kashmir |
https://en.wikipedia.org/wiki/Pr%C3%BCfer%20manifold | In mathematics, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by and named after Heinz Prüfer.
Construction
The Prüfer manifold can be constructed as follows . Take an uncountable number of copies Xa of the plane, one for each real number a, and take a copy H of the upper half plane (of pairs (x, y) with y > 0). Then glue the open upper half of each plane Xa to the upper half plane H by identifying (x,y)∈Xa for y > 0 with the point in H. The resulting quotient space Q is the Prüfer manifold. The images in Q of the points (0,0) of the spaces Xa under identification form an uncountable discrete subset.
See also
Long line (topology)
References
Topological spaces
Surfaces |
https://en.wikipedia.org/wiki/B-theorem | The B-theorem is a mathematical finite group theory result formerly known as the B-conjecture.
The theorem states that if is the centralizer of an involution of a finite group, then every component of is the image of a component of .
References
Theorems about finite groups
Conjectures that have been proved |
https://en.wikipedia.org/wiki/Balance%20theorem | In mathematical group theory, the balance theorem states that if G is a group with no core then G either has disconnected Sylow 2-subgroups or it is of characteristic 2 type or it is of component type .
The significance of this theorem is that it splits the classification of finite simple groups into three major subcases.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Johan%20Alfarizi | Johan Ahmat Farizi (born 25 May 1990 in Malang, East Java) is an Indonesian professional footballer who plays as a left-back for and captains Liga 1 club Arema.
Career statistics
International
Honours
Club
Arema
Indonesia Super League: 2009–10
East Java Governor Cup: 2013
Indonesian Inter Island Cup: 2014/15
Indonesia President's Cup: 2017, 2019, 2022
International
Indonesia U-23
Islamic Solidarity Games Silver medal: 2013
Individual
Liga 1 Team of the Season: 2021–22
References
External links
Johan Farizi at Liga Indonesia
Living people
1990 births
Footballers from Malang
Footballers from East Java
Indonesian men's footballers
Arema F.C. players
Liga 1 (Indonesia) players
Indonesian Premier League players
Persija Jakarta players
Men's association football defenders
Men's association football wingers
Indonesia men's youth international footballers
Indonesia men's international footballers |
https://en.wikipedia.org/wiki/Pordata | Pordata is the Contemporary Portugal Database equipped with official and certified statistics about Portugal and Europe. The information is divided in several themes like population, education, health, between others. This database is available for everybody, free of charge, and complete with exempt and accurate information. All of its information is provided by official entities, such as the Portuguese National Institute of Statistics and Eurostat. The number of sources being used so far goes up to a total of 60. All of the available data is presented in a yearly fashion, and whenever possible dating back to 1960.
Pordata was organized by the Francisco Manuel dos Santos Foundation, created in 2009 by Alexandre Soares dos Santos and his family. FFMS, is presided by Prof. António Barreto and set its main objective in promoting study, knowledge, information and public debate.
When released to the public on February 23, 2010 under the direction of Prof. Maria João Valente Rosa, Pordata included only contents about Portugal, nationally. On November 3, the Foundation, launches an extension of its database to the new Pordata Europe. It now includes not only data about Portugal, but also about the European Union, Schengen Area, United States and Japan.
About Pordata
Created by the Francisco Manuel dos Santos Foundation (FFMS) on February 23, 2010, Contemporary Portugal Database Pordata is a public service, free of charge of unlimited use.
Pordata allows the user a fast access to the numbers of the Portuguese reality, spread out across different themes as diverse as population, justice, education, health, environment, among several others. All presented in a chronologic evolution starting, whenever possible in 1960. About 40 official sources in Pordata Portugal, and more than 20 in Pordata Europe are responsible for the rigorous and exempt treatment of the published numbers.
With more than 70.000 series available, Pordata allows the analysis of different themes in the same search enviorement. Here, the user is able to use a vast set of both visualization tools (such as graphs and tables) and editing ones (%, variations, etc.).
Directed by Professor Maria João Valente Rosa, the project Pordata is the result of a sequence of studies coordinated and put to motion by António Barreto in the Social Sciences Institute of Lisbon University dating back to the late 90s. FFMS believes that side by side with the rapid development of information and communication technologies, the general interest in statistics as suffered a significant growth in the last few years, putting it in a vital position inside the process of analyzing and knowing nowadays societies.
According to Maria João Valente Rosa, Pordata “is trying to answer the needs of credible information, so many times disperse and with complex access, to a public as wider as possible”. Furthermore: “This is a project destined to everybody, a real public service, thought out to a vast number of users tha |
https://en.wikipedia.org/wiki/Richard%20Balam | Richard Balam (fl. 1653), was an English mathematician.
Balam was the author of Algebra, or the Doctrine of composing, inferring, and resolving an Equation (1653). It is a possible source of developments in John Wallis, Mathesis Universalis (1657), relating to geometric progressions treated as an axiomatic theory.
References
17th-century English mathematicians
17th-century English writers
17th-century English male writers |
https://en.wikipedia.org/wiki/Divisibility%20sequence | In mathematics, a divisibility sequence is an integer sequence indexed by positive integers n such that
for all m, n. That is, whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term. The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined.
A strong divisibility sequence is an integer sequence such that for all positive integers m, n,
Every strong divisibility sequence is a divisibility sequence: if and only if . Therefore, by the strong divisibility property, and therefore .
Examples
Any constant sequence is a strong divisibility sequence.
Every sequence of the form for some nonzero integer k, is a divisibility sequence.
The numbers of the form (Mersenne numbers) form a strong divisibility sequence.
The repunit numbers in any base form a strong divisibility sequence.
More generally, any sequence of the form for integers is a divisibility sequence. In fact, if and are coprime, then this is a strong divisibility sequence.
The Fibonacci numbers form a strong divisibility sequence.
More generally, any Lucas sequence of the first kind is a divisibility sequence. Moreover, it is a strong divisibility sequence when .
Elliptic divisibility sequences are another class of such sequences.
References
Sequences and series
Integer sequences
Arithmetic functions |
https://en.wikipedia.org/wiki/Group%20of%20symplectic%20type | In mathematical finite group theory, a p-group of symplectic type is a p-group such that all characteristic abelian subgroups are cyclic.
According to , the p-groups of symplectic type were classified by P. Hall in unpublished lecture notes, who showed that they are all a central product of an extraspecial group with a group that is cyclic, dihedral, quasidihedral, or quaternion. gives a proof of this result.
The width n of a group G of symplectic type is the largest integer n such that the group contains an extraspecial subgroup H of order p1+2n such that G = H.CG(H), or 0 if G contains no such subgroup.
Groups of symplectic type appear in centralizers of involutions of groups of GF(2)-type.
References
Finite groups |
https://en.wikipedia.org/wiki/Group%20of%20GF%282%29-type | In mathematical finite group theory, a group of GF(2)-type is a group with an involution centralizer whose generalized Fitting subgroup is a group of symplectic type .
As the name suggests, many of the groups of Lie type over the field with 2 elements are groups of GF(2)-type. Also 16 of the 26 sporadic groups are of GF(2)-type, suggesting that in some sense sporadic groups are somehow related to special properties of the field with 2 elements.
showed roughly that groups of GF(2)-type can be subdivided into 8 types. The groups of each of these 8 types were classified by various authors. They consist mainly of groups of Lie type with all roots of the same length over the field with 2 elements, but also include many exceptional cases, including the majority of the sporadic simple groups.
gave a survey of this work.
gives a table of simple groups containing a large extraspecial 2-group.
References
Correction:
Finite groups |
https://en.wikipedia.org/wiki/Nicole%20Tomczak-Jaegermann | Nicole Tomczak-Jaegermann FRSC (8 June 1945 – 17 June 2022) was a Polish-Canadian mathematician, a professor of mathematics at the University of Alberta, and the holder of the Canada Research Chair in Geometric Analysis.
Contributions
Her research is in geometric functional analysis, and is unusual in combining asymptotic analysis with the theory of Banach spaces and infinite-dimensional convex bodies. It formed a key component of Fields medalist Timothy Gowers' solution to Stefan Banach's homogeneous space problem, posed in 1932. Her 1989 monograph on Banach–Mazur distances is also highly cited.
Education and career
Tomczak-Jaegermann earned her M.S. in 1968 from the University of Warsaw, and her Ph.D. from the same university in 1974, under the supervision of Aleksander Pełczyński. She remained on the faculty at the University of Warsaw from 1975 until 1983, when she moved to Alberta.
Recognition
In 1996, Tomczak-Jaegermann was elected to the Royal Society of Canada, and in 1999 she won the Krieger–Nelson Prize for an outstanding female Canadian mathematician. In 1998 she was an Invited Speaker of the International Congress of Mathematicians in Berlin. She was the winner of the 2006 CRM-Fields-PIMS prize for exceptional research in mathematics.
Death
Tomczak-Jaegermann died on 17 June 2022 at the age 77 in Edmonton, Alberta, Canada.
References
External links
Home page at the University of Alberta
1945 births
2022 deaths
People from Paris
Functional analysts
Polish mathematicians
Polish women mathematicians
20th-century Polish mathematicians
21st-century Polish mathematicians
Canadian women mathematicians
Canadian mathematicians
Canadian people of Polish descent
Canada Research Chairs
University of Warsaw alumni
Texas A&M University faculty
Academic staff of the University of Alberta
Fellows of the Royal Society of Canada |
https://en.wikipedia.org/wiki/Son%20Jeong-ryun | Son Jeong-Ryun (born September 18, 1991) is a Japanese-born North Korean football player.
Club statistics
References
1991 births
Living people
Association football people from Yamaguchi Prefecture
North Korean men's footballers
Zainichi Korean men's footballers
J1 League players
J2 League players
Japan Football League players
Avispa Fukuoka players
Renofa Yamaguchi FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Mironenko%20reflecting%20function | In applied mathematics, the reflecting function of a differential system connects the past state of the system with the future state of the system by the formula The concept of the reflecting function was introduced by Uladzimir Ivanavich Mironenka.
Definition
For the differential system with the general solution in Cauchy form, the Reflecting Function of the system is defined by the formula
Application
If a vector-function is -periodic with respect to , then is the in-period transformation (Poincaré map) of the differential system Therefore the knowledge of the Reflecting Function give us the opportunity to find out the initial dates of periodic solutions of the differential system and investigate the stability of those solutions.
For the Reflecting Function of the system the basic relation
is holding.
Therefore we have an opportunity sometimes to find Poincaré map of the non-integrable in quadrature systems even in elementary functions.
Literature
Мироненко В. И. Отражающая функция и периодические решения дифференциальных уравнений. — Минск, Университетское, 1986. — 76 с.
Мироненко В. И. Отражающая функция и исследование многомерных дифференциальных систем. — Гомель: Мин. образов. РБ, ГГУ им. Ф. Скорины, 2004. — 196 с.
External links
The Reflecting Function Site
How to construct equivalent differential systems
Differential equations |
https://en.wikipedia.org/wiki/Encyclopedic%20Dictionary%20of%20Mathematics | The Encyclopedic Dictionary of Mathematics is a translation of the Japanese . The editor of the first and second editions was Shokichi Iyanaga; the editor of the third edition was Kiyosi Itô; the fourth edition was edited by the Mathematical Society of Japan.
Editions
; paperback version of the 1987 edition
References
Mathematics books
Dictionary
MIT Press books |
https://en.wikipedia.org/wiki/Double%20origin%20topology | In mathematics, more specifically general topology, the double origin topology is an example of a topology given to the plane R2 with an extra point, say 0*, added. In this case, the double origin topology gives a topology on the set , where ∐ denotes the disjoint union.
Construction
Given a point x belonging to X, such that and , the neighbourhoods of x are those given by the standard metric topology on We define a countably infinite basis of neighbourhoods about the point 0 and about the additional point 0*. For the point 0, the basis, indexed by n, is defined to be:
In a similar way, the basis of neighbourhoods of 0* is defined to be:
Properties
The space }, along with the double origin topology is an example of a Hausdorff space, although it is not completely Hausdorff. In terms of compactness, the space }, along with the double origin topology fails to be either compact, paracompact or locally compact, however, X is second countable. Finally, it is an example of an arc connected space.
References
General topology |
https://en.wikipedia.org/wiki/Alexei%20Borodin | Alexei Mikhailovich Borodin (; born June 30, 1975) is a professor of mathematics at the Massachusetts Institute of Technology.
Research
His research concerns asymptotic representation theory, relations with random matrices and integrable systems, and the difference equation formulation of monodromy.
Education and career
Borodin was born in Donetsk, the son of Donetsk State University mathematics professor Mikhail Borodin.
He competed for Ukraine in the 1992 International Mathematical Olympiad, earning a silver medal there.
In the same year, he began studying mathematics at Moscow State University, and (because of the collapse of the Soviet Union) was forced to choose between Ukrainian and Russian citizenship, deciding at that time to be Russian. He graduated from Moscow State in 1997 and received M.S.E. in computers and information science and Ph.D. in mathematics from the University of Pennsylvania.
He was a Clay Research Fellow and a researcher at the Institute for Advanced Study in Princeton, New Jersey.
Next, he taught at the California Institute of Technology from 2003 to 2010, before moving to MIT. In 2016–2017 he was a Fellow at the Radcliffe Institute at Harvard University.
Awards and honors
In 2008, Borodin won the European Mathematical Society Prize, one of ten prizes awarded every four years for excellence by a young mathematics researcher.
In 2010, he was one of four Caltech faculty invited to present their work at the International Congress of Mathematicians. In 2015 he won the Loève Prize and the Henri Poincaré Prize. In 2018 he became a Fellow of the American Academy of Arts and Sciences, and in 2019 he was awarded the Fermat Prize.
References
1975 births
Living people
20th-century Russian mathematicians
21st-century Russian mathematicians
Probability theorists
Moscow State University alumni
University of Pennsylvania alumni
California Institute of Technology faculty
International Mathematical Olympiad participants
Institute for Advanced Study faculty
Radcliffe fellows
University of Pennsylvania School of Engineering and Applied Science alumni |
https://en.wikipedia.org/wiki/Robert%20J.%20T.%20Bell | Robert J. T. Bell RSE FRSE (15 January 1876 – 8 September 1963) was a Scottish mathematician. He held the positions of Professor of Pure and Applied Mathematics and Dean of the Faculty of Arts and Science, at the University of Otago in Dunedin, New Zealand.
Early life and career
Robert John Tainsh Bell was born to the Rev. George Bell and Margaret Walker Scott in Falkirk, Stirlingshire, Scotland, on 15 January 1876. The family moving to Hamilton, South Lanarkshire, Bell was educated at Hamilton Academy from which he matriculated at the University of Glasgow, having won a high placement in the university’s Open Bursary Competition. Bell graduated in 1898 as M.A. (with First Class Honours) in Mathematics and Natural Philosophy.
Appointed a William Ewing Fellow, Bell continued at the university as a tutorial assistant and in 1901 was promoted to junior assistant.
In 1902 he married Agnes Thomson.
Later career
In 1911 Bell was appointed Lecturer in Mathematics and awarded a D.Sc. by the university for his treatise on the geometry of three dimensions, published in book form in 1910 as An Elementary Treatise on Co-ordinate Geometry of Three Dimensions. An instant success, this textbook was to be translated into other languages, including Japanese and three of the languages of the Indian sub-continent. The textbook ran to a third edition (1944) and, from 1938, chapters 1–9 were issued separately as Co-ordinate Solid Geometry. It has since been reprinted (BiblioBazaar, 2009.)
In March 1899 Bell had become a member of Edinburgh Mathematical Society and from 1911–1920 he served as editor of the Society’s journal, the Proceedings, during which time he also contributed papers such as Note on the axes of a normal section of the enveloping cylinder of a conchoid, presented to the Society’s meeting of 9 January 1914.
On 6 March 1916, Bell was elected to the Royal Society of Edinburgh, his proposers being George Alexander Gibson, Professor of Mathematics, Glasgow; the physicist Andrew Gray, Professor of Natural Philosophy, Glasgow; Robert Alexander Houstoun, and Diarmid Noel Paton, Regius Professor of Physiology, Glasgow (and eldest son of the artist Sir Joseph Noel Paton.)
In 1920 Bell was appointed Professor of Pure and Applied Mathematics at the University of Otago, Dunedin, New Zealand. At Otago he joined another former pupil of Hamilton Academy and near contemporary, the physicist Robert Jack who had also gone on to graduate from Glasgow M.A. with Honours in Mathematics and Natural Philosophy and who had also been awarded a D.Sc. from Glasgow. Robert Jack had arrived at Otago six years before Bell, in 1914, taking up the appointment as Professor of Physics. Like Robert Jack, Robert Bell went on to serve also as Chairman of the university’s Professorial Board and Dean of the Faculty of Arts and Science. (Bell also held the positions as a representative member on the Academic Board of the University of New Zealand and on the University of New Zealand |
https://en.wikipedia.org/wiki/Educational%20data%20mining | Educational data mining (EDM) is a research field concerned with the application of data mining, machine learning and statistics to information generated from educational settings (e.g., universities and intelligent tutoring systems). At a high level, the field seeks to develop and improve methods for exploring this data, which often has multiple levels of meaningful hierarchy, in order to discover new insights about how people learn in the context of such settings. In doing so, EDM has contributed to theories of learning investigated by researchers in educational psychology and the learning sciences. The field is closely tied to that of learning analytics, and the two have been compared and contrasted.
Definition
Educational data mining refers to techniques, tools, and research designed for automatically extracting meaning from large repositories of data generated by or related to people's learning activities in educational settings. Quite often, this data is extensive, fine-grained, and precise. For example, several learning management systems (LMSs) track information such as when each student accessed each learning object, how many times they accessed it, and how many minutes the learning object was displayed on the user's computer screen. As another example, intelligent tutoring systems record data every time a learner submits a solution to a problem. They may collect the time of the submission, whether or not the solution matches the expected solution, the amount of time that has passed since the last submission, the order in which solution components were entered into the interface, etc. The precision of this data is such that even a fairly short session with a computer-based learning environment (e.g. 30 minutes) may produce a large amount of process data for analysis.
In other cases, the data is less fine-grained. For example, a student's university transcript may contain a temporally ordered list of courses taken by the student, the grade that the student earned in each course, and when the student selected or changed his or her academic major. EDM leverages both types of data to discover meaningful information about different types of learners and how they learn, the structure of domain knowledge, and the effect of instructional strategies embedded within various learning environments. These analyses provide new information that would be difficult to discern by looking at the raw data. For example, analyzing data from an LMS may reveal a relationship between the learning objects that a student accessed during the course and their final course grade. Similarly, analyzing student transcript data may reveal a relationship between a student's grade in a particular course and their decision to change their academic major. Such information provides insight into the design of learning environments, which allows students, teachers, school administrators, and educational policy makers to make informed decisions about how to interact with, prov |
https://en.wikipedia.org/wiki/Vladik%20Kreinovich | Vladik Kreinovich is a professor of computer science at the University of Texas at El Paso.
He was educated at Leningrad State University and received a doctorate in mathematics from the Sobolev Institute of Mathematics, affiliated with Novosibirsk State University in Novosibirsk.
His research spans several areas of computer science, computational statistics and computational mathematics generally, including interval arithmetic, fuzzy mathematics, probability theory, and probability bounds analysis. His research addresses computability issues, algorithm development, verification, and validated numerics for applications in uncertainty processing, data processing, intelligent control, geophysics and other engineering fields. In 2015, the Society For Design and Process Science gave him its Zadeh Award.
Books
Vladik Kreinovich (ed.), Uncertainty Modeling, Springer Verlag, Cham, Switzerland, 2017.
Christian Servin and Vladik Kreinovich, Propagation of Interval and Probabilistic Uncertainty in Cyberinfrastructure-related Data Processing and Data Fusion, Springer Verlag, Berlin, Heidelberg, 2015.
Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, and Gang Xiang, Computing Statistics under Interval and Fuzzy Uncertainty, Springer Verlag, Berlin, Heidelberg, 2012.
Vladik Kreinovich, Anatoly Lakeyev, Jiri Rohn, and Patrick Kahl, Computational complexity and feasibility of data processing and interval computations, Kluwer, Dordrecht, 1998.
R. Baker Kearfott and Vladik Kreinovich (eds.). Applications of Interval Computations Kluwer, Dordrecht, 1996.
Selected publications
V. Kreinovich, "Solving equations (and systems of equations) under uncertainty: how different practical problems lead to different mathematical and computational formulations", Granular Computing, 2016, Vol. 1, No. 3, pp. 171–179.
V. Kreinovich and S. Shary, "Interval methods for data fitting under uncertainty: a probabilistic treatment", Reliable Computing, 2016, Vol. 23, pp. 105–141.
L. Thompson, A. Velasco, V. Kreinovich, "Construction of ShearWave models by applying multi-objective optimization to multiple geophysical data sets", In: G. O. Tost and O. Vasilieva (eds.), Analysis, Modelling, Optimization, and Numerical Techniques, Springer Verlag, Berlin, Heidelberg, 2015, pp. 309–326.
A. Jalal-Kamali, M. S. Hossain, and V. Kreinovich, "How to Understand Connections Based on Big Data: From Cliques to Flexible Granules", In: S.-M. Chen et al. (eds.), Information Granularity, Big Data, and Computational Intelligence, Springer, Cham, 2015, pp. 63–87.
V. Kreinovich, "Interval computations and interval-related statistical techniques", In: F. Pavese et al. (eds.), Advanced Mathematical and Computational Tools in Metrology and Testing, World Scientific, Singapore, 2015, pp. 38–49.
V. Kreinovich, "Decision Making under Interval Uncertainty (and beyond)", In: P. Guo and W. Pedrycz (eds.), Human-Centric Decision-Making Models for Social Sciences, Springer Verlag, 2014, pp. 163–193.
M. Beer, S |
https://en.wikipedia.org/wiki/Uniqueness%20case | In mathematical finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem.
The uniqueness case covers groups G of characteristic 2 type with e(G) ≥ 3 that have an almost strongly p-embedded maximal 2-local subgroup for all primes p whose 2-local p-rank is sufficiently large (usually at least 3).
proved that there are no finite simple groups in the uniqueness case.
References
Finite groups |
https://en.wikipedia.org/wiki/Chicago%20Bulls%20accomplishments%20and%20records | This page details the all-time statistics, records, and other achievements pertaining to the Chicago Bulls.
Individual awards
NBA Most Valuable Player
Michael Jordan – 1988, 1991, 1992, 1996, 1998
Derrick Rose – 2011
NBA Defensive Player of the Year
Michael Jordan – 1988
Joakim Noah – 2014
NBA Rookie of the Year
Michael Jordan – 1985
Elton Brand – 2000 (Co-Rookie of the Year)
Derrick Rose – 2009
NBA Sixth Man of the Year
Toni Kukoč – 1996
Ben Gordon – 2005
NBA Most Improved Player Award
Jimmy Butler – 2015
NBA Finals MVP
Michael Jordan – 1991–1993, 1996–1998
Best NBA Player ESPY Award
Michael Jordan – 1993, 1997–1999
NBA Sportsmanship Award
Luol Deng – 2007
J. Walter Kennedy Citizenship Award
Joakim Noah – 2015
NBA Coach of the Year
Johnny "Red" Kerr – 1967
Dick Motta – 1971
Phil Jackson – 1996
Tom Thibodeau – 2011
NBA Executive of the Year
Jerry Krause – 1988, 1996
Gar Forman – 2011 (Co-Executive of the Year)
NBA Scoring Champion
Michael Jordan – 1987–1993, 1996–1998
All-NBA First Team
Michael Jordan – 1987–1993, 1996–1998
Scottie Pippen – 1994–1996
Derrick Rose – 2011
Joakim Noah – 2014
All-NBA Second Team
Bob Love – 1971, 1972
Norm Van Lier – 1974
Michael Jordan – 1985
Scottie Pippen – 1992, 1997
Pau Gasol – 2015
DeMar DeRozan – 2022
All-NBA Third Team
Scottie Pippen – 1993, 1998
Jimmy Butler – 2017
NBA All-Defensive First Team
Jerry Sloan – 1969, 1972, 1974, 1975
Norm Van Lier – 1974, 1976, 1977
Michael Jordan – 1988–1993, 1996–1998
Scottie Pippen – 1992–1998
Dennis Rodman – 1996
Joakim Noah – 2013, 2014
Alex Caruso – 2023
NBA All-Defensive Second Team
Jerry Sloan – 1970, 1971
Norm Van Lier – 1972, 1973, 1975, 1978
Bob Love – 1972, 1974, 1975
Artis Gilmore – 1978
Scottie Pippen – 1991
Horace Grant – 1993, 1994
Kirk Hinrich – 2007
Ben Wallace – 2007
Joakim Noah – 2011
Luol Deng – 2012
Jimmy Butler – 2014, 2016
NBA All-Rookie First Team
Erwin Mueller – 1967
Clifford Ray – 1972
Scott May – 1977
Reggie Theus – 1979
David Greenwood – 1980
Quintin Dailey – 1983
Michael Jordan – 1985
Charles Oakley – 1986
Elton Brand – 2000
Kirk Hinrich – 2004
Luol Deng – 2005
Ben Gordon – 2005
Derrick Rose – 2009
Taj Gibson – 2010
Nikola Mirotić – 2015
Lauri Markkanen – 2018
NBA All-Rookie Second Team
Stacey King – 1990
Toni Kukoč – 1994
Ron Artest – 2000
Marcus Fizer – 2001
Jay Williams – 2003
Tyrus Thomas – 2007
Coby White – 2020
Patrick Williams – 2021
Ayo Dosunmu – 2022
Hold the record for the fewest points per game in a season after 1954–55 (81.9 in 1998–99)
Hold the record for the fewest points in a game after 1954–55 (49, April 10, 1999)
Hold the record for largest margin of victory in an NBA Finals game (42; defeated the Utah Jazz 96–54)
Hold the record for fewest points allowed in an NBA Finals game (54 against the Utah Jazz)
Share lowest free throw percentage by two teams in one game (.410 with the Los Angeles Lakers, February 7, 1968)
Share record for m |
https://en.wikipedia.org/wiki/Rudolf%20Kruse | Rudolf Kruse (born 12 September 1952 in Rotenburg/Wümme) is a German computer scientist and mathematician.
Education and professional career
Rudolf Kruse obtained his diploma (Mathematics) degree in 1979 from the TU Braunschweig, Germany, and a PhD in Mathematics in 1980 as well as the venia legendi in Mathematics in 1984 from the same university. Following a short stay at the Fraunhofer Society, in 1986 he joined the University of Braunschweig as a professor of computer science. From 1996–2017 he was a full professor at the Department of Computer Science of the Otto-von-Guericke Universität Magdeburg where he has been leading the computational intelligence research group. Since October 2017 he has been an emeritus professor.
Research activities
He has carried out research and projects in statistics, artificial intelligence, expert systems, Fuzzy control, fuzzy data analysis, Computational Intelligence, and information mining. His research group was very successful in various industrial applications.
Rudolf Kruse has coauthored 40 books as well as more than 450 refereed technical papers in various scientific areas. He is associate editor of several scientific journals. He is a fellow of the International Fuzzy Systems Association (IFSA), fellow of the European Coordinating Committee for Artificial Intelligence (ECCAI) and fellow of the Institute of Electrical and Electronics Engineers (IEEE).
References
External links
Web pages of the Computational Intelligence group
Personal Homepage R. Kruse
Scientific Publications (DBLP)
Living people
1952 births
Fellows of the European Association for Artificial Intelligence |
https://en.wikipedia.org/wiki/Northwest%20Italy | Northwest Italy ( or just ) is one of the five official statistical regions of Italy used by the National Institute of Statistics (ISTAT), a first level NUTS region and a European Parliament constituency. Northwest encompasses four of the country's 20 regions:
Aosta Valley
Liguria
Lombardy
Piedmont
Geography
It borders to the west with France via the Western Alps, to the north with Switzerland via the Central Alps, to the east with the regions of Trentino-Alto Adige, Veneto and Emilia-Romagna belonging to Northeast Italy and to the south with the Ligurian Sea and the extreme offshoot of Tuscany in Central Italy. Northwest Italy includes a large part of the Po Valley and is crossed by the Po river, the longest in Italy.
Demography
In 2022, the population resident in north-western Italy amounts to 15,817,057 inhabitants.
Regions
Most populous municipalities
Below is the list of the population residing in 2022 in municipalities with more than inhabitants:
Economy
The Gross domestic product (GDP) of the region was 580.3 billion euros in 2018, accounting for 32.9% of Italy's economic output. GDP per capita adjusted for purchasing power was 35,900 euros or 119% of the EU27 average in the same year.
See also
National Institute of Statistics (Italy)
NUTS statistical regions of Italy
Italian NUTS level 1 regions:
Northeast Italy
South Italy
Insular Italy
Northern Italy
Central Italy
Southern Italy
References
Geography of Italy
NUTS 1 statistical regions of the European Union |
https://en.wikipedia.org/wiki/Classical%20involution%20theorem | In mathematical finite group theory, the classical involution theorem of classifies simple groups with a classical involution and satisfying some other conditions, showing that they are mostly groups of Lie type over a field of odd characteristic. extended the classical involution theorem to groups of finite Morley rank.
A classical involution t of a finite group G is an involution whose centralizer has a subnormal subgroup containing t with quaternion Sylow 2-subgroups.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Gilman%E2%80%93Griess%20theorem | In finite group theory, a mathematical discipline, the Gilman–Griess theorem, proved by , classifies the finite simple groups of characteristic 2 type with e(G) ≥ 4 that have a "standard component", which covers one of the three cases of the trichotomy theorem.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Infinite%20expression | In mathematics, an infinite expression is an expression in which some operators take an infinite number of arguments, or in which the nesting of the operators continues to an infinite depth. A generic concept for infinite expression can lead to ill-defined or self-inconsistent constructions (much like a set of all sets), but there are several instances of infinite expressions that are well-defined.
Examples
Examples of well-defined infinite expressions are
infinite sums, such as
infinite products, such as
infinite nested radicals, such as
infinite power towers, such as
infinite continued fractions, such as
where the left hand side uses Gauss' Kettenbruch notation.
In infinitary logic, one can use infinite conjunctions and infinite disjunctions.
Even for well-defined infinite expressions, the value of the infinite expression may be ambiguous or not well-defined; for instance, there are multiple summation rules available for assigning values to series, and the same series may have different values according to different summation rules if the series is not absolutely convergent.
From the hyperreal viewpoint
From the point of view of the hyperreal numbers, such an infinite expression is obtained in every case from the sequence of finite expressions, by evaluating the sequence at a hypernatural value of the index n, and applying the standard part, so that .
See also
Iterated binary operation
Infinite word
Decimal expansion
Power series
Infinite compositions of analytic functions
Omega language
References
Abstract algebra
Mathematical analysis |
https://en.wikipedia.org/wiki/Statistical%20Yearbook%20of%20Switzerland | The Statistical Yearbook of Switzerland (German/French) published by the Federal Statistical Office has been the standard reference book for Swiss statistics since 1891. It summarises the most important statistical findings on Switzerland's population, society, government, economy and environment. It serves not only as a reference book, but also provides in a series of overview articles a comprehensive picture of the social and economic situation of Switzerland.
History
The desirability of having a statistical yearbook was expressed for the first time on 29 June 1887. The Federal Council agreed to consider implementing this proposal, but before publishing the Yearbook it wanted to wait until the results of the 1888 census were available so they could be included in it (which subsequently proved to be only partially possible).
Two years later, on 22 July 1889, the Director of the Statistical Bureau, Dr. Guillaume, presented a yearbook proposal divided into six theses to the Conference of Swiss statisticians in Aarau, which was adopted after a short discussion. The first thesis described the purpose of the publication: the Yearbook was supposed to inform the general public about the main results of Swiss statistics in easy-to-understand tables and comparable time series. Guillaume indicated that he had modelled the Statistical Yearbook of Switzerland on the Statistical Yearbook of Finland (a thin bilingual booklet) and the Statistical Yearbook of the German Reich (a more comprehensive volume with coloured maps).
On 18 October 1890, Guillaume presented an outline of the Yearbook's chapters as well as a draft chapter to the Conference of Swiss statisticians for consultation.
The first Statistical Yearbook of Switzerland, weighing in at 270 pages, was published on 8 April 1891. Apparently the response was mostly positive and the first edition seemed to live up to the expectations that might be made upon such a publication.
Development over 100 years
The concept adopted in the early days of the Statistical Yearbook, which aimed to make information available not just to specialists but to the public at large, corresponds to modern principles of statistical dissemination. This explains a certain similarity in the way information has been presented for more than 100 years: for example, the first edition already contained a visualisation of statistics in a series of thematic maps; and the 1897 edition was a graphic volume. By 1892, the "text" element also featured more prominently in the Yearbook.
But not all editions of the Yearbook were modern in the sense described above: for several decades, volumes consisting purely of tables were published; text and graphs were dispensed with, not least for cost considerations. It was only for the 96th edition in 1989 that clear steps were taken to make the Yearbook more easily comprehensible and user-friendly again. As Federal Councillor Cotti put it in the foreword, the new design aimed "to bring statistic |
https://en.wikipedia.org/wiki/Kolmogorov%20equations | In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov processes. In particular, they describe how the probability that a continuous-time Markov process is in a certain state changes over time.
Diffusion processes vs. jump processes
Writing in 1931, Andrei Kolmogorov started from the theory of discrete time Markov processes, which are described by the Chapman–Kolmogorov equation, and sought to derive a theory of continuous time Markov processes by extending this equation. He found that there are two kinds of continuous time Markov processes, depending on the assumed behavior over small intervals of time:
If you assume that "in a small time interval there is an overwhelming probability that the state will remain unchanged; however, if it changes, the change may be radical", then you are led to what are called jump processes.
The other case leads to processes such as those "represented by diffusion and by Brownian motion; there it is certain that some change will occur in any time interval, however small; only, here it is certain that the changes during small time intervals will be also small".
For each of these two kinds of processes, Kolmogorov derived a forward and a backward system of equations (four in all).
History
The equations are named after Andrei Kolmogorov since they were highlighted in his 1931 foundational work.
William Feller, in 1949, used the names "forward equation" and "backward equation" for his more general version of the Kolmogorov's pair,
in both jump and diffusion processes. Much later, in 1956, he referred to the equations for the jump process as "Kolmogorov forward equations" and "Kolmogorov backward equations".
Other authors, such as Motoo Kimura, referred to the diffusion (Fokker–Planck) equation as Kolmogorov forward equation, a name that has persisted.
The modern view
In the context of a continuous-time Markov process with jumps, see Kolmogorov equations (Markov jump process). In particular, in natural sciences the forward equation is also known as master equation.
In the context of a diffusion process, for the backward Kolmogorov equations see Kolmogorov backward equations (diffusion). The forward Kolmogorov equation is also known as Fokker–Planck equation.
An example from biology
One example from biology is given below:
This equation is applied to model population growth with birth. Where is the population index, with reference the initial population, is the birth rate, and finally , i.e. the probability of achieving a certain population size.
The analytical solution is:
This is a formula for the probability in terms of the preceding ones, i.e. .
References
Markov processes
Stochastic models
Mathematical and theoretical biology
Population models |
https://en.wikipedia.org/wiki/Spherical%20sector | In geometry, a spherical sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of the sector of a circle.
Volume
If the radius of the sphere is denoted by and the height of the cap by , the volume of the spherical sector is
This may also be written as
where is half the cone angle, i.e., is the angle between the rim of the cap and the direction to the middle of the cap as seen from the sphere center.
The volume of the sector is related to the area of the cap by:
Area
The curved surface area of the spherical sector (on the surface of the sphere, excluding the cone surface) is
It is also
where is the solid angle of the spherical sector in steradians, the SI unit of solid angle. One steradian is defined as the solid angle subtended by a cap area of .
Derivation
The volume can be calculated by integrating the differential volume element
over the volume of the spherical sector,
where the integrals have been separated, because the integrand can be separated into a product of functions each with one dummy variable.
The area can be similarly calculated by integrating the differential spherical area element
over the spherical sector, giving
where is inclination (or elevation) and is azimuth (right). Notice is a constant. Again, the integrals can be separated.
See also
Circular sector — the analogous 2D figure.
Spherical cap
Spherical segment
Spherical wedge
References
Spherical geometry |
https://en.wikipedia.org/wiki/Hall%27s%20theorem | In mathematics, Hall's theorem may refer to:
Hall's marriage theorem
One of several theorems about Hall subgroups |
https://en.wikipedia.org/wiki/Exterior%20dimension | In geometry, exterior dimension is a type of dimension that can be used to characterize the scaling behavior of "fat fractals".
A fat fractal is defined to be a subset of Euclidean space such that, for every point of the set and every sufficiently small number ,
the ball of radius centered at contains both a nonzero Lebesgue measure of points belonging to the fractal, and a nonzero Lebesgue measure of points that do not belong to the fractal. For such a set, the Hausdorff dimension is the same as that of the ambient space.
The Hausdorff dimension of a set can be computed by "fattening" (taking its Minkowski sum with a ball of radius ), and examining how the volume of the resulting fattened set scales with , in the limit as tends to zero. The exterior dimension is computed in the same way but looking at the volume of the difference set obtained by subtracting the original set from the fattened set.
In the paper introducing exterior dimension, it was claimed that it would be applicable to networks of blood vessels. However, inconsistent behavior of these vessels in different parts of the body, the relatively low number of levels of branching, and the slow convergence of methods based on exterior dimension cast into doubt the practical applicability of this parameter.
References
Fractals
Dimension |
https://en.wikipedia.org/wiki/Wallace%20%28footballer%2C%20born%201987%29 | Wallace Reis da Silva, known simply as Wallace (born 26 December 1987), is a Brazilian professional footballer who plays as a centre-back for Brusque, on loan from Vitória.
Career
Career statistics
(Correct )
FIFA Club World Cup
Honours
Vitória
Campeonato Baiano: 2008, 2009, 2010
Corinthians
Campeonato Brasileiro Série A: 2011
Copa Libertadores: 2012
FIFA Club World Cup: 2012
Flamengo
Copa do Brasil: 2013
Campeonato Carioca: 2014
References
External links
ogol
Wallace Reis at Soccerway
1987 births
Living people
Brazilian men's footballers
Esporte Clube Vitória players
Sport Club Corinthians Paulista players
Copa Libertadores-winning players
CR Flamengo footballers
Grêmio Foot-Ball Porto Alegrense players
Gaziantepspor footballers
Göztepe S.K. footballers
Campeonato Brasileiro Série A players
Süper Lig players
Brazilian expatriate men's footballers
Expatriate men's footballers in Turkey
Brazilian expatriate sportspeople in Turkey
Men's association football central defenders
Footballers from Bahia |
https://en.wikipedia.org/wiki/List%20of%20Miami%20Marlins%20owners%20and%20executives |
General managers
Statistics current through 2009 season
Owners
''Statistics updated March 3, 2019
References
Miami
Owners and executives |
https://en.wikipedia.org/wiki/Mark%20Kisin | Mark Kisin is a mathematician known for work in algebraic number theory and arithmetic geometry. In particular, he is known for his contributions to the study of p-adic representations and p-adic cohomology.
Born in Vilnius, Lithuania and raised from the age of five in Melbourne, Australia, he won a silver medal at the International Mathematical Olympiad in 1989 and received his B.Sc. from Monash University in 1991. He received his Ph.D. from Princeton University in 1998 under the direction of Nick Katz. From 1998 to 2001 he was a Research Fellow at the University of Sydney, after which he spent three years at the University of Münster.
After six years at the University of Chicago, Kisin took the post in 2009 of professor of mathematics at Harvard University.
He was elected a Fellow of the Royal Society in 2008. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Number Theory". In 2012 he became a fellow of the American Mathematical Society. He was elected to the American Academy of Arts and Sciences in 2022.
References
External links
1971 births
Living people
Scientists from Vilnius
20th-century American mathematicians
21st-century American mathematicians
Australian mathematicians
Harvard University Department of Mathematics faculty
Harvard University faculty
Fellows of the Royal Society
Fellows of the American Mathematical Society
International Mathematical Olympiad participants
Academic staff of Monash University
Princeton University alumni
Academic staff of the University of Sydney
Academic staff of the University of Münster
Arithmetic geometers |
https://en.wikipedia.org/wiki/List%20of%20captains%20of%20Dynamo%20Kyiv | List of captains of the Ukrainian football club Dynamo Kyiv.
External links
Statistics of Dynamo Kyiv
FC Dynamo Kyiv |
https://en.wikipedia.org/wiki/James%20Discovers%20Math | James Discovers Math is an educational video game that was developed in 1995 by Broderbund in association with Australian developer Brains.
Summary
The video game teaches vital skills in mathematics and is aimed at children aged 3–6 (preschool through first grade).
Because the game was partially developed in Australia, the characters speak with Australian accents, and several Australian brands, such as Qantas, make an appearance. The main character is James, a 6-year-old boy who is based on an actual Australian boy named James. The highlight of the game is a story called "James Makes a Salad", in which James destroys several fruits that his mother has just bought. This is based on something that the real James had done.
References
1995 video games
Broderbund games
Children's educational video games
Mathematical education video games
Video games developed in Australia |
https://en.wikipedia.org/wiki/Home%20prime | In number theory, the home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP(n) is designated HPn(m). For instance, HP(10) = 773, as 10 factors as 2×5 yielding HP10(1) = 25, 25 factors as 5×5 yielding HP10(2) = HP25(1) = 55, 55 = 5×11 implies HP10(3) = HP25(2) = HP55(1) = 511, and 511 = 7×73 gives HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773, a prime number. Some sources use the alternative notation HPn for the homeprime, leaving out parentheses. Investigations into home primes make up a minor side issue in number theory. Its questions have served as test fields for the implementation of efficient algorithms for factoring composite numbers, but the subject is really one in recreational mathematics.
The outstanding computational problem is whether HP(49) = HP(77) can be calculated in practice. As each iteration is greater than the previous up until a prime is reached, factorizations generally grow more difficult so long as an end is not reached. the pursuit of HP(49) concerns the factorization of a 251-digit composite factor of HP49(119) after a break was achieved on 3 December 2014 with the calculation of HP49(117). This followed the factorization of HP49(110) on 8 September 2012 and of HP49(104) on 11 January 2011, and prior calculations extending for the larger part of a decade that made extensive use of computational resources. Details of the history of this search, as well as the sequences leading to home primes for all other numbers through 100, are maintained at Patrick De Geest's worldofnumbers website. A wiki primarily associated with the Great Internet Mersenne Prime Search maintains the complete known data through 1000 in base 10 and also has lists for the bases 2 through 9.
The primes in HP(n) are
2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, ...
Aside from the computational problems that have had so much time devoted to them, it appears absolute proof of existence of a home prime for any specific number might entail its effective computation. In purely heuristic terms, the existence has probability 1 for all numbers, but such heuristics make assumptions about numbers drawn from a wide variety of processes that, though they are likely correct, fall short of the standard of proof usually required of mathematical claims.
Properties
HP(n) = n for n prime.
Early history and additional terminology
While it is unlikely that the idea was not conceived of numerous times in the past, the first reference in print appears to be an article written in 1990 in a small and now-defunct publication called Recreational and Educational Computation. The same person who authored that article, Jeffrey Heleen, revisited the subject in the |
https://en.wikipedia.org/wiki/Essentially%20finite%20vector%20bundle | In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav V. Nori, as the main tool in the construction of the fundamental group scheme. Even if the definition is not intuitive there is a nice characterization that makes essentially finite vector bundles quite natural objects to study in algebraic geometry. The following notion of finite vector bundle is due to André Weil and will be needed to define essentially finite vector bundles:
Finite vector bundles
Let be a scheme and a vector bundle on . For an integral polynomial with nonnegative coefficients define
Then is called finite if there are two distinct polynomials for which is isomorphic to .
Definition
The following two definitions coincide whenever is a reduced, connected and proper scheme over a perfect field.
According to Borne and Vistoli
A vector bundle is essentially finite if it is the kernel of a morphism where are finite vector bundles.
The original definition of Nori
A vector bundle is essentially finite if it is a subquotient of a finite vector bundle in the category of Nori-semistable vector bundles.
Properties
Let be a reduced and connected scheme over a perfect field endowed with a section . Then a vector bundle over is essentially finite if and only if there exists a finite -group scheme and a -torsor such that becomes trivial over (i.e. , where ).
When is a reduced, connected and proper scheme over a perfect field with a point then the category of essentially finite vector bundles provided with the usual tensor product , the trivial object and the fiber functor is a Tannakian category.
The -affine group scheme naturally associated to the Tannakian category is called the fundamental group scheme.
Notes
Scheme theory
Topological methods of algebraic geometry |
https://en.wikipedia.org/wiki/Ale%C3%ADlson | Aleílson Sousa Rabelo (born December 3, 1985) is a Brazilian association footballer. He was an attacking midfielder for Paragominas football club.
Career statistics
(Correct )
Honours
Águia de Marabá
Campeonato Paraense: 2008
Olaria
Torneio Moisés Mathias de Andrade: 2010
External links
ogol
soccerway
Aleílson at Footballzz
1985 births
Living people
Brazilian men's footballers
CR Flamengo footballers
Red Bull Bragantino II players
Águia de Marabá Futebol Clube players
Men's association football forwards
People from Marabá
Footballers from Pará |
https://en.wikipedia.org/wiki/1999%20S%C3%A3o%20Paulo%20FC%20season | The 1999 season was São Paulo's 70th season since club's existence.
Statistics
Scorers
Overall
{|class="wikitable"
|-
|Games played || 70 (8 Torneio Rio-São Paulo, 17 Campeonato Paulista, 4 Copa do Brasil, 6 Copa Mercosur, 26 Campeonato Brasileiro, 2 Copa Libertadores seletive, 5 Friendly match)
|-
|Games won || 41 (5 Torneio Rio-São Paulo, 12 Campeonato Paulista, 2 Copa do Brasil, 3 Copa Mercosur, 13 Campeonato Brasileiro, 1 Copa Libertadores seletive, 5 Friendly match)
|-
|Games drawn || 7 (1 Torneio Rio-São Paulo, 4 Campeonato Paulista, 1 Copa do Brasil, 1 Copa Mercosur, 1 Campeonato Brasileiro, 0 Copa Libertadores seletive, 0 Friendly match)
|-
|Games lost || 20 (2 Torneio Rio-São Paulo, 2 Campeonato Paulista, 1 Copa do Brasil, 2 Copa Mercosur, 12 Campeonato Brasileiro, 1 Copa Libertadores seletive, 0 Friendly match)
|-
|Goals scored || 148
|-
|Goals conceded || 88
|-
|Goal difference || +60
|-
|Best result || 5–0 (H) v Bayer Leverkusen - Friendly match - 1999.01.205–0 (A) v Cruz Azul - Friendly match - 1999.07.22
|-
|Worst result || 1–5 (A) v Boca Juniors - Copa Mercosur - 1999.08.01
|-
|Top scorer ||
|-
Friendlies
Euro-America Cup
La Soccer Cup
Trofeo Ciudad de Pachuca
Official competitions
Torneio Rio-São Paulo
Record
Campeonato Paulista
Record
Copa do Brasil
Record
Campeonato Brasileiro
Amended result by justice
Round 3
Round 16
Sandro Hiroshi played in irregular condition
Record
Copa Mercosur
Record
Copa Libertadores selective tournament
Record
External links
official website
São Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Kolmogorov%20equations%20%28continuous-time%20Markov%20chains%29 | In mathematics and statistics, in the context of Markov processes, the Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, are a pair of systems of differential equations that describe the time evolution of the process's distribution. This article, as opposed to the article titled Kolmogorov equations, focuses on the scenario where we have a continuous-time Markov chain (so the state space is countable). In this case, we can treat the Kolmogorov equations as a way to describe the probability , where (the state space) and are the final and initial times, respectively.
The equations
For the case of a countable state space we put in place of .
The Kolmogorov forward equations read
,
where is the transition rate matrix (also known as the generator matrix),
while the Kolmogorov backward equations are
The functions are continuous and differentiable in both time arguments. They represent the
probability that the system that was in state at time jumps to state at some later time . The continuous quantities satisfy
Background
The original derivation of the equations by Kolmogorov starts with the Chapman–Kolmogorov equation (Kolmogorov called it fundamental equation) for time-continuous and differentiable Markov processes on a finite, discrete state space. In this formulation, it is assumed that the probabilities are continuous and differentiable functions of . Also, adequate limit properties for the derivatives are assumed. Feller derives the equations under slightly different conditions, starting with the concept of purely discontinuous Markov process and then formulating them for more general state spaces. Feller proves the existence of solutions of probabilistic character to the Kolmogorov forward equations and Kolmogorov backward equations under natural conditions.
Relation with the generating function
Still in the discrete state case, letting and assuming that the system initially is found in state
, the Kolmogorov forward equations describe an initial-value problem for finding the probabilities of the process, given the quantities . We write where , then
For the case of a pure death process with constant rates the only nonzero coefficients are . Letting
the system of equations can in this case be recast as a partial differential equation for with initial condition . After some manipulations, the system of equations reads,
History
A brief historical note can be found at Kolmogorov equations.
See also
Kolmogorov equations
Master equation (in physics and chemistry), a synonym of "Kolmogorov equations" for many continuous-time Markov chains appearing in physics and chemistry.
References
Markov processes |
https://en.wikipedia.org/wiki/Grothendieck%20category | In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these categories was further developed in Pierre Gabriel's seminal thesis in 1962.
To every algebraic variety one can associate a Grothendieck category , consisting of the quasi-coherent sheaves on . This category encodes all the relevant geometric information about , and can be recovered from (the Gabriel–Rosenberg reconstruction theorem). This example gives rise to one approach to noncommutative algebraic geometry: the study of "non-commutative varieties" is then nothing but the study of (certain) Grothendieck categories.
Definition
By definition, a Grothendieck category is an AB5 category with a generator. Spelled out, this means that
is an abelian category;
every (possibly infinite) family of objects in has a coproduct (also known as direct sum) in ;
direct limits of short exact sequences are exact; this means that if a direct system of short exact sequences in is given, then the induced sequence of direct limits is a short exact sequence as well. (Direct limits are always right-exact; the important point here is that we require them to be left-exact as well.)
possesses a generator, i.e. there is an object in such that is a faithful functor from to the category of sets. (In our situation, this is equivalent to saying that every object of admits an epimorphism , where denotes a direct sum of copies of , one for each element of the (possibly infinite) set .)
The name "Grothendieck category" neither appeared in Grothendieck's Tôhoku paper nor in Gabriel's thesis; it came into use in the second half of the 1960s in the work of several authors, including Jan-Erik Roos, Bo Stenström, Ulrich Oberst, and Bodo Pareigis. (Some authors use a different definition in that they don't require the existence of a generator.)
Examples
The prototypical example of a Grothendieck category is the category of abelian groups; the abelian group of integers can serve as a generator.
More generally, given any ring (associative, with , but not necessarily commutative), the category of all right (or alternatively: left) modules over is a Grothendieck category; itself can serve as a generator.
Given a topological space , the category of all sheaves of abelian groups on is a Grothendieck category. (More generally: the category of all sheaves of right -modules on is a Grothendieck category for any ring .)
Given a ringed space , the category of sheaves of OX-modules is a Grothendieck category.
Given an (affine or projective) algebraic variety (or more generally: any scheme), the category of quasi-coherent sheaves on is a Grothendieck category.
Given a small site (C, J) (i.e. a small category C together with a Grothendieck topology J), the category of all sheaves of abelian groups |
https://en.wikipedia.org/wiki/AB5%20category | In mathematics, in his "Tôhoku paper" introduced a sequence of axioms of various kinds of categories enriched over the symmetric monoidal category of abelian groups. Abelian categories are sometimes called AB2 categories, according to the axiom (AB2). AB3 categories are abelian categories possessing arbitrary coproducts (hence, by the existence of quotients in abelian categories, also all colimits). AB5 categories are the AB3 categories in which filtered colimits of exact sequences are exact. Grothendieck categories are the AB5 categories with a generator.
References
Category theory
Homological algebra |
https://en.wikipedia.org/wiki/John%20Stembridge | John Stembridge is a Professor of Mathematics at University of Michigan. He received his Ph.D. from Massachusetts Institute of Technology in 1985 under the direction of Richard P. Stanley. His dissertation was called Combinatorial Decompositions of Characters of SL(n,C).
He is one of the participants in the Atlas of Lie Groups and Representations.
Research
His research interests are in combinatorics, with particular emphasis on the following areas:
Topics related to algebra, especially representation theory
Coxeter groups and root systems
Enumerative combinatorics
Symmetric functions
Hypergeometric series and q-series
Computational problems and algorithms in algebra
He was awarded a Guggenheim Fellowship in 2000 for work in Combinatorial aspects of root systems and Weyl characters..
He has written Maple packages that can be used for computing symmetric functions, posets, root systems, and finite Coxeter groups.
References
Living people
Year of birth missing (living people)
20th-century American mathematicians
21st-century American mathematicians
Massachusetts Institute of Technology School of Science alumni
University of Michigan faculty |
https://en.wikipedia.org/wiki/Paraproduct | In mathematics, a paraproduct is a non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on. According to Svante Janson and Jaak Peetre, in an article from 1988, "the name 'paraproduct' denotes an idea rather than a unique definition; several versions exist and can be used for the same purposes." The concept emerged in J.-M. Bony’s theory
of paradifferential operators.
This said, for a given operator to be defined as a paraproduct, it is normally required to satisfy the following properties:
It should "reconstruct the product" in the sense that for any pair of functions in its domain,
For any appropriate functions and with , it is the case that .
It should satisfy some form of the Leibniz rule.
A paraproduct may also be required to satisfy some form of Hölder's inequality.
Notes
Further references
Árpád Bényi, Diego Maldonado, and Virginia Naibo, "What is a Paraproduct?", Notices of the American Mathematical Society, Vol. 57, No. 7 (Aug., 2010), pp. 858–860.
Bilinear maps |
https://en.wikipedia.org/wiki/Factorization%20of%20polynomials%20over%20finite%20fields | In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.
All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.
As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.
Background
Finite field
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory.
A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power , there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus in GF(p) means the same as .
Irreducible polynomials
Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F.
Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element |
https://en.wikipedia.org/wiki/Korean%20Christians%20in%20Hong%20Kong | According to the Census and Statistics Department of Hong Kong, there were approximately 5 thousand Koreans in 2006, of which 94.4% were usual residents while mobile residents occupied 5.6%. Korean formed one minority group in Hong Kong, constituting 1.4% out of the whole ethnic minority’s population. There were around 2000 Korean immigrant individuals who were Christians.
Korean Christian development
Christian churches in Korea have been increased drastically since 1980 and the world's largest church (Yoido Full Gospel Church) also locates there. Korea comes after the US as the second largest Christian missionary country in the world. There have been more than 17,000 Christian evangelists from Korea sent abroad.
According to an International Bulletin of Missionary Research survey conducted in 2008, Korean churches send out over a thousand of new foreign missionaries every year which presents one of the rapid growing national missionary movements around the world. Korean missionaries served 26 countries around the world in 1979. The number of countries of service rose gradually in years. In 1990 there were 87 countries receiving Korean missionary service which was more than tripled comparing to a decade before. This number almost doubled again in 2006 in which Korean missionary were serving in 168 countries worldwide.
The report showed that the greatest proportion of 47.3% of Korean missionaries served in Asia. It is because Asia is the most populous but least evangelized continent. Thomas Wang, who is the honorary chairman of the Chinese Coordination Centre of World Evangelism (世界華人福音事工聯絡中心), described Korea as the largest missionary country in Asia. Korean Christians consider China as the largest missionary service country. 70% of those who dedicate their life to missionary are willing to serve in China. As China is the main target of Korean missionary work, academic research or any other resources specifically focusing on Korean Christian development in Hong Kong is very rare.
Migration history
The settlement of Koreans in Hong Kong, parts of them Christian, can be traced back to 1948. In the 1960s, economic and trade relations between Korea and Hong Kong were close, therefore Koreans started to settle down and reside in Hong Kong.
Living conditions
Koreans in Hong Kong mostly work in the field of Wholesale, Retail and Import / Export Trades, Restaurants and Hotels, Transport, Storage and Communications, Financing, Insurance, Real Estate and Business Services. Over 80% of the males are "managers and administrators" and "professionals/associate professionals". About 50% of Koreans reside on Hong Kong Island, and 30% of them work in Central and Western District.
Korean Christians form their own community in Hong Kong, all well blended into social, cultural, economic lives and church. There are about 14 Korean Christian churches, mostly located in Hong Kong Island and Kowloon. Apart from churches, Korean Christians also organized |
https://en.wikipedia.org/wiki/Roberto%20Paliska | Roberto Paliska (born 14 December 1963 in Rijeka) is a Croatian former football player.
Although born in Rijeka, he is originally from Labin.
Statistics
Player
References
External links
Profile at Playerhistory.
hrepka.com
Foreign players in Greece at RSSSF.
Profile at Strukljeva.net
1963 births
Living people
People from Labin
Sportspeople from Istria County
Footballers from Rijeka
Men's association football defenders
Yugoslav men's footballers
Croatian men's footballers
HNK Rijeka players
S.F.K. Pierikos (football) players
WSG Tirol players
FC Kärnten players
FC St. Veit players
Yugoslav First League players
Super League Greece players
2. Liga (Austria) players
Croatian Football League players
Austrian Regionalliga players
Croatian expatriate men's footballers
Expatriate men's footballers in Greece
Croatian expatriate sportspeople in Greece
Expatriate men's footballers in Austria
Croatian expatriate sportspeople in Austria |
https://en.wikipedia.org/wiki/Polyvector%20field | A Polyvector field within Mathematics topology is concerned with the properties of a geometric object. A multivector field, polyvector field of degree k , or k-vector field, on a manifold , is a generalization of the notion of a vector field on a manifold.
Whereas a vector field is a global section of tangent bundle, which assigns to each point on the manifold a tangent vector , a multivector field is a section of the kth exterior power of the tangent bundle, , and to each point it assigns a k-vector in . Just as the smooth sections of the tangent bundle (vector fields) make up a vector space, the space of smooth k-vector fields over M make up a vector space .
Furthermore, since the tangent bundle is dual to the cotangent bundle, multivector fields of degree k are dual to k-forms, and both are subsumed in the general concept of a tensor field, which is a section of some tensor bundle, often consisting of exterior powers of the tangent and cotangent bundles. A (k,0)-tensor field is a differential k-form, a (0,1)-tensor field is a vector field, and a (0,k)-tensor field is k-vector field. While differential forms are widely studied as such in differential geometry and differential topology, multivector fields are often encountered as tensor fields of type (0,k), except in the context of the geometric algebra (see also Clifford algebra).
See also
Multivector
Blade (geometry)
References
Differential topology |
https://en.wikipedia.org/wiki/Roderick%20Melnik | Roderick Melnik is a Canadian-Australian mathematician and scientist, internationally known for his research in applied mathematics, numerical analysis, and mathematical modeling for scientific and engineering applications.
Biography
Melnik is a Tier I Canada Research Chair in Mathematical Modeling and Professor at Wilfrid Laurier University in Waterloo, Canada. His other affiliations include the University of Waterloo and University of Guelph.
Education and career
He earned his Ph.D. at Kiev State University in the late 1980s. According to the Mathematics Genealogy Project, his scientific ancestors include A. Tikhonov and other outstanding mathematicians and scientists.
Before moving to Canada as a Tier I Canada Research Chair, Melnik gained a worldwide reputation in mathematical modelling and applied mathematics, while working in Europe, Australia, and the United States.
Awards and honors
Melnik is a recipient of many fellowships and awards, including the Andersen fellowship at Syddansk Universitet in Denmark, the Isaac Newton Institute visiting fellowship at the University of Cambridge in England, the Ikerbasque Fellowship in Spain, the fellowship of the Institute of Advanced Studies at the University of Bologna in Italy, and others. He is a life member of the Canadian Applied and Industrial Mathematics Society. Melnik is the director of the Laboratory of Mathematical Modeling for New Technologies (M2NeT Lab) in Waterloo, Ontario, Canada.
Research
In his early works Melnik studied fully coupled hyperbolic-elliptic models applied in dynamic piezoelectricity theory. Such models, originally proposed by W. Voigt in 1910, have found many applications, and Melnik was the first to rigorously prove well-posedness of a large class of such models in the dynamic case. The piezoelectric effect itself, captured by such models, was discovered in 1880 by Pierre and Jacques Curie. Mathematical models describing this effect in time-dependent situations are based on initial-boundary value problems for coupled systems of partial differential equations. The mathematical and computational analysis of such coupled systems has been in the focus of many Melnik's works. In the 1990s he extended his scientific interests to applications of mathematics in semiconductor and other advanced technologies, including smart and bio-inspired materials technologies, where in collaboration with A. Roberts and their students he pioneered computationally efficient low-dimensional reductions of complex time-dependent nonlinear mathematical models. His other important contributions at that time included fundamental problems in control theory and dynamic system evolution, as well as a range of problems in industrial & applied mathematics and numerical analysis.
Melnik is an expert in computational and applied mathematics with a number of important results in the coupled field theory as applied in physics, biology, and engineering. He is a leading computational analyst, we |
https://en.wikipedia.org/wiki/Sufficient%20dimension%20reduction | In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency.
Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector , regression analysis aims to study the distribution of , the conditional distribution of given . A dimension reduction is a function that maps to a subset of , k < p, thereby reducing the dimension of . For example, may be one or more linear combinations of .
A dimension reduction is said to be sufficient if the distribution of is the same as that of . In other words, no information about the regression is lost in reducing the dimension of if the reduction is sufficient.
Graphical motivation
In a regression setting, it is often useful to summarize the distribution of graphically. For instance, one may consider a scatter plot of versus one or more of the predictors. A scatter plot that contains all available regression information is called a sufficient summary plot.
When is high-dimensional, particularly when , it becomes increasingly challenging to construct and visually interpret sufficiency summary plots without reducing the data. Even three-dimensional scatter plots must be viewed via a computer program, and the third dimension can only be visualized by rotating the coordinate axes. However, if there exists a sufficient dimension reduction with small enough dimension, a sufficient summary plot of versus may be constructed and visually interpreted with relative ease.
Hence sufficient dimension reduction allows for graphical intuition about the distribution of , which might not have otherwise been available for high-dimensional data.
Most graphical methodology focuses primarily on dimension reduction involving linear combinations of . The rest of this article deals only with such reductions.
Dimension reduction subspace
Suppose is a sufficient dimension reduction, where is a matrix with rank . Then the regression information for can be inferred by studying the distribution of , and the plot of versus is a sufficient summary plot.
Without loss of generality, only the space spanned by the columns of need be considered. Let be a basis for the column space of , and let the space spanned by be denoted by . It follows from the definition of a sufficient dimension reduction that
where denotes the appropriate distribution function. Another way to express this property is
or is conditionally independent of , given . Then the subspace is defined to be a dimension reduction subspace (DRS).
Structural dimensionality
For a regression , the structural dimension, , is the smallest number of distinct linear combinations of necessary to preserve the conditional distribution of . In other words, the smallest dimension reduction that is still sufficient maps to a subset of . The corresponding DRS will be d-dimensional. |
https://en.wikipedia.org/wiki/Y%C5%8Dsuke%20Mikami | is a Japanese footballer who plays as a midfielder for J2 League club Blaublitz Akita.
Club statistics
Updated to 3 December 2022.
Honours
Blaublitz Akita
J3 League (1): 2020
References
External links
Profile at Sapporo
Profile at Nagano Parceiro
Profile at Akita
Profile at Kataller Toyama
1992 births
Living people
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Hokkaido Consadole Sapporo players
Kataller Toyama players
AC Nagano Parceiro players
Men's association football forwards
Association football people from Sapporo |
https://en.wikipedia.org/wiki/Yuji%20Fujikawa | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Kanagawa University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Mito HollyHock players
Oita Trinita players
Matsumoto Yamaga FC players
YSCC Yokohama players
Men's association football defenders
Universiade bronze medalists for Japan
Universiade medalists in football
Medalists at the 2009 Summer Universiade |
https://en.wikipedia.org/wiki/Yuji%20Sakuda | is a Japanese football player currently playing for Zweigen Kanazawa.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Zweigen Kanazawa
1987 births
Living people
University of Tsukuba alumni
Association football people from Ishikawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Mito HollyHock players
Oita Trinita players
Montedio Yamagata players
Zweigen Kanazawa players
Men's association football defenders |
https://en.wikipedia.org/wiki/Sho%20Murata | is a Japanese football player. He is currently playing for Thespakusatsu Gunma.
Club statistics
Updated to 23 February 2017.
References
External links
Profile at Thespakusatsu Gunma
1987 births
Living people
Chuo University alumni
Association football people from Tokyo
Japanese men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Briobecca Urayasu players
Thespakusatsu Gunma players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Shota%20Otsuka | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
University of Tsukuba alumni
Association football people from Kumamoto Prefecture
Japanese men's footballers
J2 League players
Mito HollyHock players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Robert%20Small%20%28minister%29 | Robert Small FRSE (1732–1808) was a Scottish minister who served as Moderator of the General Assembly of the Church of Scotland in 1791. He was keenly interested in mathematics and astronomy and was a founder member of the Royal Society of Edinburgh, (elected Fellow on 17 November 1783) to whose Transactions he contributed a paper proving some theorems in geometry. He was Minister of the first charge (St Mary's) in the Parish of Dundee, and used his mathematical abilities to compile, in 1792, an exemplary Report on his Parish for the First Statistical Account of Scotland. In 1804 he published an explanation of Kepler's laws of planetary motion. He was very active in social improvements in his parish, organising (in conjunction with Robert Stewart, a surgeon) a subscription for Voluntary Dispensary, and Surgery, which eventually became Dundee Royal Infirmary.
Life
Small was born on 12 December 1732 in Carmyllie, Angus, the son of Rev. James Small (d.1771), the local minister, and his wife, Lillias Scott. As was normal with the clergy he was from a gentrified background.
Robert received his education at Dundee Grammar School. He then studied Divinity at the University of St Andrews graduating BD around 1750. He was elected by the Town Council of Dundee to be preacher in the Cross Church and catechist and took up post on 2 May 1759. He was called to be minister of the first charge of the Parish of Dundee, St Mary's, where he was ordained on 20 May 1761. He was appointed chaplain to the Royal Highlanders (83rd Foot) in 1778. He was awarded an honorary doctorate (DD) by his alma mater in the same year. In 1783 he was a co-founder of the Royal Society of Edinburgh.
He was called before the General Assembly to reply to charges that, when ordaining Elders, on 9 September 1798, in his Parish he asked unconventional, surprise questions, and did not require them to subscribe to the Westminster Confession of Faith. He was admonished and warned to be more careful in future. On Thursday 29 May 1800, the Assembly voted to enjoin Dr Small to be careful hereafter, to testify, by his whole conduct, that respect for the Standards of this Church, and for the fences wisely provided by our Ecclesiastical Constitution, against dangerous innovation, which corresponds to the declaration stated in his defences, as repeatedly made by him in the Kirk-session of Dundee, that he glorified in the Confession of Faith.
He was reputed to be an excellent classical scholar and an interesting preacher, well versed in natural philosophy and mathematics and was a patron of literature.
His brother, William was by profession a physician but seems to was more active in scientific and industrial concerns. He emigrated for a time to Virginia, where he was Professor of Mathematics at the College of William & Mary and tutored Thomas Jefferson, but returned to Britain, carrying a letter of introduction from Benjamin Franklin to the industrialist Matthew Boulton. In turn, Dr Small intr |
https://en.wikipedia.org/wiki/Hirofumi%20Watanabe | is a Japanese football player currently playing for Renofa Yamaguchi FC.
Career statistics
Updated to 4 December 2020.
References
External links
Profile at Vissel Kobe
1987 births
Living people
Senshu University alumni
Association football people from Yamagata Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kashiwa Reysol players
Tochigi SC players
Vegalta Sendai players
Vissel Kobe players
Renofa Yamaguchi FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Mirkan%20Ayd%C4%B1n | Mirkan Aydın (born 8 July 1987) is a German professional footballer who plays as a forward.
Career statistics
References
External links
1987 births
German people of Kurdish descent
German sportspeople of Turkish descent
People from Hattingen
Footballers from Arnsberg (region)
Living people
German men's footballers
Men's association football forwards
TSG Sprockhövel players
VfL Bochum II players
VfL Bochum players
Eskişehirspor footballers
Göztepe S.K. footballers
Dalkurd FF players
SC Preußen Münster players
Altınordu F.K. players
Hatayspor footballers
İstanbulspor footballers
Ankaraspor footballers
Regionalliga players
Oberliga (football) players
Bundesliga players
2. Bundesliga players
Süper Lig players
TFF First League players
Superettan players
3. Liga players
TFF Second League players
German expatriate men's footballers
German expatriate sportspeople in Turkey
Expatriate men's footballers in Turkey
German expatriate sportspeople in Sweden
Expatriate men's footballers in Sweden |
https://en.wikipedia.org/wiki/Takashi%20Kamoshida | is a Japanese football player. He currently plays for Fukushima United FC.
Career statistics
Updated to 23 February 2019.
References
External links
Profile at Fukushima United FC
1985 births
Living people
Kanagawa University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Tochigi SC players
Fukushima United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Makoto%20Sugimoto | is a Japanese football player who currently plays for Vonds Ichihara.
Career
On 11 January 2019, Sugimoto joined Vonds Ichihara.
Career statistics
Updated to 23 February 2017.
References
External links
Profile at Tochigi SC
1987 births
Living people
Takushoku University alumni
Association football people from Nagano Prefecture
Japanese men's footballers
J2 League players
J3 League players
Tochigi SC players
Vonds Ichihara players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hideyuki%20Akai | is a Japanese football player. He currently plays for SC Sagamihara.
Career statistics
Updated to 23 February 2016.
References
External links
Profile at SC Sagamihara
1985 births
Living people
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
J3 League players
Tochigi SC players
SC Sagamihara players
Men's association football defenders |
https://en.wikipedia.org/wiki/Nottingham%20group | In the mathematical field of infinite group theory, the Nottingham group is the group J(Fp) or N(Fp) consisting of formal power series t + a2t2+...
with coefficients in Fp. The group multiplication is given by formal composition also called substitution. That is, if
and if is another element, then
.
The group multiplication is not abelian. The group was studied by number theorists as the group of wild automorphisms of the local field Fp((t)) and by group theorists including D. and the name "Nottingham group" refers to his former domicile.
This group is a finitely generated pro-p-group, of finite width. For every finite group of order a power of p there is a closed subgroup of the Nottingham group isomorphic to that finite group.
References
Group theory
History of Nottingham
University of Nottingham |
https://en.wikipedia.org/wiki/Differential%20algebraic%20group | In mathematics, a differential algebraic group is a differential algebraic variety with a compatible group structure. Differential algebraic groups were introduced by .
References
Algebraic groups |
https://en.wikipedia.org/wiki/Ezechiel%20de%20Decker | Ezechiel de Decker (c. 1603-c. 1647) was a Dutch surveyor and teacher of mathematics.
Tables of logarithms
In 1625, De Decker entered a contract with Adriaan Vlacq for the publication of
several translations of books by John Napier, Edmund Gunter and Henry Briggs. A first book was published in 1626, with several translations
done by Vlacq. A second book was made of the logarithms of the first 10000 numbers
from Briggs' Arithmetica logarithmica published in 1624. The logarithms were shortened
to 10 places. In 1627, De Decker's "Tweede deel" was published and it contained
the logarithms of all numbers from 1 to 100000, to 10 places. Only very few copies of
this book are known and its publication was apparently stopped or delayed.
In 1628, Vlacq's Arithmetica logarithmica was published and contained exactly
the tables published in 1627.
Publications
Ezechiel de Decker: Eerste Deel van de Nieuwe Telkonst, 1626
Ezechiel de Decker: Nieuwe Telkonst, 1626
Ezechiel de Decker: Tweede Deel van de Nieuwe Tel-konst, 1627 (partial facsimile published in 1964)
References
1600s births
1640s deaths
Dutch surveyors |
https://en.wikipedia.org/wiki/Daniel%20Cruz%20%28footballer%2C%20born%201982%29 | Daniel Lopez Cruz (born 12 January 1982) is a Brazilian footballer who most recently played for Gabala as a defender. Previously he has played for Naval.
Career statistics
References
External links
Living people
1982 births
Brazilian men's footballers
Gabala SC players
Expatriate men's footballers in Poland
Expatriate men's footballers in Azerbaijan
Men's association football defenders
Footballers from Salvador, Bahia |
https://en.wikipedia.org/wiki/Binary%20expression%20tree | A binary expression tree is a specific kind of a binary tree used to represent expressions. Two common types of expressions that a binary expression tree can represent are algebraic and boolean. These trees can represent expressions that contain both unary and binary operators.
Like any binary tree, each node of a binary expression tree has zero, one, or two children. This restricted structure simplifies the processing of expression trees.
Construction of an expression tree
Example
The input in postfix notation is: a b + c d e + * *
Since the first two symbols are operands, one-node trees are created and pointers to them are pushed onto a stack. For convenience the stack will grow from left to right.
The next symbol is a '+'. It pops the two pointers to the trees, a new tree is formed, and a pointer to it is pushed onto the stack.
Next, c, d, and e are read. A one-node tree is created for each and a pointer to the corresponding tree is pushed onto the stack.
Continuing, a '+' is read, and it merges the last two trees.
Now, a '*' is read. The last two tree pointers are popped and a new tree is formed with a '*' as the root.
Finally, the last symbol is read. The two trees are merged and a pointer to the final tree remains on the stack.
Algebraic expressions
Algebraic expression trees represent expressions that contain numbers, variables, and unary and binary operators. Some of the common operators are × (multiplication), ÷ (division), + (addition), − (subtraction), ^ (exponentiation), and - (negation). The operators are contained in the internal nodes of the tree, with the numbers and variables in the leaf nodes. The nodes of binary operators have two child nodes, and the unary operators have one child node.
Boolean expressions
Boolean expressions are represented very similarly to algebraic expressions, the only difference being the specific values and operators used. Boolean expressions use true and false as constant values, and the operators include (AND), (OR), (NOT).
See also
Expression (mathematics)
Term (logic)
Context-free grammar
Parse tree
Abstract syntax tree
References
Binary trees
Computer algebra |
https://en.wikipedia.org/wiki/There%20Was%20a%20Father | is a 1942 Japanese film directed by Yasujirō Ozu.
Plot summary
Shuhei Horikawa (Chishū Ryū) works as a mathematics school-teacher in a middle school. A widower, he has a ten-year-old son named Ryohei (Haruhiko Tsuda), who studies in the same school. While taking his class out for an excursion one day, one of his pupils drowns after running off with a classmate on a secret boat trip. Shuhei blames himself for the accident, and quits his teaching job out of remorse.
Shuhei enrolls his son to a junior high school in Ueda, where Ryohei studies as a boarder, and goes to work in Tokyo to finance his son's education.
Years pass. The twenty-five-year-old Ryohei (Shūji Sano) has finished college and has himself become a school-teacher in Akita. Shuhei now works as a clerk in a Tokyo textile factory and the two meet occasionally. Ryohei has thoughts of quitting his teaching job to join his father at Tokyo, but Shuhei rebukes him for not doing what his duty decrees. Ryohei takes a ten-day vacation to join his father in Tokyo. Together with retired headmaster Makoto Hirata (Takeshi Sakamoto), Shuhei attends a get-together with his former pupils and the group reminisce about their school days. When Shuhei returns home, he suffers a heart attack and is admitted to the hospital. Asking Hirata's daughter Fumiko (Mitsuko Mito) to take care of his son, he dies soon after. The final scene shows Ryohei and his new wife Fumiko returning to Akita, with the urn containing his father's ashes resting on the luggage rack; the two have agreed to live together with Hirata and Fumiko's younger brother.
Cast
Chishū Ryū as Shuhei
Shūji Sano as Ryohei (as an adult)
Haruhiko Tsuda as Ryohei (as a child)
Shin Saburi as Yasutaro Kurokawa
Takeshi Sakamoto as Makoto Hirata
Mitsuko Mito as Fumi
Shinichi Himori as Minoru Uchida
Kōji Mitsui as alumnus
Production
Yasujirō Ozu wrote the first draft of There Was a Father before he went to China in 1937. On returning to Japan, he rewrote it, feeling that "it could still be improved".
Release
There Was a Father was released on April 1, 1942. In 2023, scenes depicting patriotic poetry and music that had been cut from its only existing prints by occupation censors were restored for presentation of the film at the Venice Film Festival.
Reception
There Was a Father placed second in the Kinema Junpo's annual critics' poll of Japan's Best Ten films. It currently has a 100% rating on Rotten Tomatoes. Trevor Johnston of Time Out praised Ryu's performance, arguing that the actor's "stoic underplaying offers a heartbreaking performance for the ages." Richard Brody of The New Yorker wrote, "In such chilling nuances as Shuhei’s silent grief, his rigid deference to authority, his joyful anticipation of Ryohei’s military service, and Ryohei’s serene lessons on the destructive power of TNT, Ozu reveals a society heading blindly toward the abyss and destroying its future in the name of the past."
Home media
There Was a Father was release |
https://en.wikipedia.org/wiki/Kazamaki%27s%20condition | In mathematics, Kazamaki's condition gives a sufficient criterion ensuring that the Doléans-Dade exponential of a local martingale is a true martingale. This is particularly important if Girsanov's theorem is to be applied to perform a change of measure. Kazamaki's condition is more general than Novikov's condition.
Statement of Kazamaki's condition
Let be a continuous local martingale with respect to a right-continuous filtration . If is a uniformly integrable submartingale, then the Doléans-Dade exponential Ɛ(M) of M is a uniformly integrable martingale.
References
Martingale theory |
https://en.wikipedia.org/wiki/Andreas%20Wittwer | Andreas Wittwer (born 5 October 1990) is a Swiss professional footballer who plays as a left back.
Career statistics
References
External links
Player profile at football.ch
1990 births
Footballers from Bern
Living people
Swiss men's footballers
Switzerland men's under-21 international footballers
Swiss Super League players
Swiss Challenge League players
FC Thun players
FC St. Gallen players
Grasshopper Club Zürich players
FC Winterthur players
Men's association football defenders |
https://en.wikipedia.org/wiki/Mathematical%20Notes | Mathematical Notes is a peer-reviewed mathematical journal published by Springer Science+Business Media on behalf of the Russian Academy of Sciences that covers all aspects of mathematics. It is an English language translation of the Russian-language journal Matematicheskie Zametki () and is published simultaneously with the Russian version.
The journal was established in 1967 as Mathematical Notes of the Academy of Sciences of the USSR and obtained its current title in 1991. The current editor-in-chief is Victor P. Maslov. According to the Journal Citation Reports, the journal has a 2011 impact factor of 0.295.
References
External links
Mathematics journals
Springer Science+Business Media academic journals
Monthly journals
English-language journals
Academic journals established in 1967
Russian Academy of Sciences academic journals
Russian-language journals |
https://en.wikipedia.org/wiki/Masahiro%20Nasukawa | is a Japanese football player who currently plays for Fujieda MYFC.
Career statistics
Updated to 24 February 2019.
1Includes Promotion Playoffs to J1.
References
External links
Profile at Oita Trinita
1986 births
Living people
Chukyo University alumni
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Tokyo Verdy players
Tochigi SC players
Tokushima Vortis players
Matsumoto Yamaga FC players
Oita Trinita players
Fujieda MYFC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Radha%20Laha | Radha Govind Laha (1 October 1930 – 14 July 1999) was an Indian-American probabilist, statistician, and mathematician, known for his work in probability theory, characteristic functions, and characterisation of distributions.
Biography
Early life
He was born in Calcutta, India and he was a student of C. R. Rao at Calcutta University, where in 1957 he earned a doctorate in analytical probability theory from the Indian Statistical Institute. His dissertation was entitled Some Characterization Problems in Probability Theory and Mathematical Statistics.
Laha's primary and secondary education was completed in Calcutta. In 1949 he graduated first in rank with a bachelor's degree in statistics from Presidency College, Calcutta. He earned his master's degree in statistics in 1951, and doctoral degree in analytical probability theory from Calcutta University in 1957. Prizes and awards during this period include the Saradprasad prize, the Duff scholarship, the S.S. Bose Gold Medal, a University of Calcutta Silver Medal, and Fulbright Fellowship in the US
Career
In 1952 Laha joined the staff of the Indian Statistical Institute, Theoretical Research and Training School, Calcutta, India, in pure and applied statistics. In 1958 he was a research associate at Catholic University of America in Washington, D.C. He returned to the Indian Statistical Institute for two years, and joined the faculty of Catholic University as a faculty member in 1962. During this period Laha established an international reputation, and he visited statistical institutes at University of Paris, France, ETH Zurich, Switzerland, and in the United States. He moved to Bowling Green State University in 1972, along with his colleagues Eugene Lukacs and Vijay Rohatgi, to start a new PhD program there. Laha retired from Bowling Green State University in 1996 and died in Perrysburg, Ohio on 14 July 1999 after a long illness.
Laha was the author of several classical texts on probability theory and statistics and numerous publications in journals. He was an honoured Fellow of the Institute of Mathematical Statistics and an elected member of the International Statistical Institute.
Laha was particularly interested in characterisations of the normal distribution. One of his well-known results is his disproof of a long-standing conjecture: that the ratio of two independent, identically distributed random variables is Cauchy distributed if and only if the variables have normal distributions. Laha became known for disproving this conjecture. Laha also proved several generalisations of the classical characterisation of normal sample distribution by the independence of sample mean and sample variance.
Philanthropist
Laha made a generous endowment from his estate to the American Mathematical Society and the Institute of Mathematical Statistics.
The AMS established the Radha G. Laha Gardens in 2001. A portion of the Laha Gardens outside the AMS headquarters in Providence, Rhode Island is identifie |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.