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https://en.wikipedia.org/wiki/C%2B-probability | {{DISPLAYTITLE:c+-probability}}
In statistics, a c+-probability is the probability that a contrast variable obtains a positive value.
Using a replication probability, the c+-probability is defined as follows: if we get a random draw from each group (or factor level) and calculate the sampled value of the contrast variable based on the random draws, then the c+-probability is the chance that the sampled values of the contrast variable are greater than 0 when the random drawing process is repeated infinite times. The c+-probability is a probabilistic index accounting for distributions of compared groups (or factor levels).
The c+-probability and SMCV are two characteristics of a contrast variable. There is a link between SMCV and c+-probability.
The SMCV and c+-probability provides a consistent interpretation to the strength of comparisons in contrast analysis. When only two groups are involved in a comparison, the c+-probability becomes d+-probability which is the probability that the difference of values from two groups is positive. To some extent, the d+-probability (especially in the independent situations) is equivalent to the well-established probabilistic index P(X > Y). Historically, the index P(X > Y) has been studied and applied in many areas.
The c+-probability and d+-probability have been used for data analysis in high-throughput experiments and biopharmaceutical research.
See also
Contrast (statistics)
Effect size
SSMD
SMCV
Contrast variable
ANOVA
References
Regression analysis
Biostatistics |
https://en.wikipedia.org/wiki/1930%20Baltic%20Cup | The 1930 Baltic Cup was the third playing of the Baltic Cup football tournament. It was held in Kaunas, Lithuania from 15–17 August 1930.
Results
Statistics
Goalscorers
See also
Balkan Cup
Nordic Football Championship
References
External links
http://www.eu-football.info/_tournament.php?id=BtC-3
1930
1930–31 in European football
1930 in Lithuanian football
1930 in Latvian football
1930 in Estonian football
1930 |
https://en.wikipedia.org/wiki/Divided%20%28disambiguation%29 | Divided refers to arithmetic division in mathematics.
Divided may also refer to:
Television
Divided (British game show), a 2009–2010 game show
Divided (American game show), a 2017–2018 U.S. version of the British show
Divided (Indian game show), a 2018 Tamil-language game show
"Divided" (Stargate Universe), an episode of Stargate Universe
"Divided" (Arrow), an episode of Arrow
Music
The Divided, a British metal band
Divided (EP), a 2010 EP by Benevolent
"Divided" (song), a 1999 song by Tara MacLean
"Divided", an instrumental by Linkin Park
Books
Divided (book), a 2018 non-fiction book by Tim Marshall
See also
Divided By (album), a 2011 album by Structures |
https://en.wikipedia.org/wiki/Josef%20Teichmann | Josef Teichmann (* 27 August 1972 in Lienz) is an Austrian mathematician and professor at ETH Zürich working on mathematical finance.
After studying mathematics at the University of Graz, he pursued his PhD at the University of Vienna. The title of his dissertation in 1999 under the supervision of Peter W. Michor was "The Theory of Infinite-Dimensional Lie Groups from the Point of View of Functional Analysis".
After working at the Vienna University of Technology, he obtained the Habilitation there in 2002. Since June 2009 he has been a professor at the Department of Mathematics at ETH Zürich.
In 2005 he was awarded the Prize of the Austrian Mathematical Society and in 2006 the Start-Preis of the FWF.
In 2014 he was awarded the Louis Bachelier Prize by the French Academy of Sciences.
External links
Teichmann's personal website
Portrait on the website of FWF
Living people
Austrian mathematicians
Academic staff of ETH Zurich
People from Lienz
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Triple%20helix | In the fields of geometry and biochemistry, a triple helix (: triple helices) is a set of three congruent geometrical helices with the same axis, differing by a translation along the axis. This means that each of the helices keeps the same distance from the central axis. As with a single helix, a triple helix may be characterized by its pitch, diameter, and handedness. Examples of triple helices include triplex DNA, triplex RNA, the collagen helix, and collagen-like proteins.
Structure
A triple helix is named such because it is made up of three separate helices. Each of these helices shares the same axis, but they do not take up the same space because each helix is translated angularly around the axis. Generally, the identity of a triple helix depends on the type of helices that make it up. For example: a triple helix made of three strands of collagen protein is a collagen triple helix, and a triple helix made of three strands of DNA is a DNA triple helix.
As with other types of helices, triple helices have handedness: right-handed or left-handed. A right-handed helix moves around its axis in a clockwise direction from beginning to end. A left-handed helix is the right-handed helix's mirror image, and it moves around the axis in a counterclockwise direction from beginning to end. The beginning and end of a helical molecule are defined based on certain markers in the molecule that do not change easily. For example: the beginning of a helical protein is its N terminus, and the beginning of a single strand of DNA is its 5' end.
The collagen triple helix is made of three collagen peptides, each of which forms its own left-handed polyproline helix. When the three chains combine, the triple helix adopts a right-handed orientation. The collagen peptide is composed of repeats of Gly-X-Y, with the second residue (X) usually being Pro and the third (Y) being hydroxyproline.
A DNA triple helix is made up of three separate DNA strands, each oriented with the sugar/phosphate backbone on the outside of the helix and the bases on the inside of the helix. The bases are the part of the molecule closest to the triple helix's axis, and the backbone is the part of the molecule farthest away from the axis. The third strand occupies the major groove of relatively normal duplex DNA. The bases in triplex DNA are arranged to match up according to a Hoogsteen base pairing scheme. Similarly, RNA triple helices are formed as a result of a single stranded RNA forming hydrogen bonds with an RNA duplex; the duplex consists of Watson-Crick base pairing while the third strand binds via Hoogsteen base pairing.
Stabilizing factors
The collagen triple helix has several characteristics that increase its stability. When proline is incorporated into the Y position of the Gly-X-Y sequence, it is post-translationally modified to hydroxyproline. The hydroxyproline can enter into favorable interactions with water, which stabilizes the triple helix because the Y residues |
https://en.wikipedia.org/wiki/Physical%20mathematics | The subject of physical mathematics is concerned with physically motivated mathematics and is considered by some as a subfield of mathematical physics.
Overview
According to Margaret Osler the simple machines of Hero of Alexandria and the ray tracing of Alhazen did not refer to causality or forces. Accordingly these early expressions of kinematics and optics do not rise to the level of mathematical physics as practiced by Galileo and Newton.
The details of physical units and their manipulation were addressed by Alexander Macfarlane in Physical Arithmetic in 1885. The science of kinematics created a need for mathematical representation of motion and has found expression with complex numbers, quaternions, and linear algebra.
At Cambridge University the Mathematical Tripos tested students on their knowledge of "mixed mathematics". "... [N]ew books which appeared in the mid-eighteenth century offered a systematic introduction to the fundamental operations of the fluxional calculus and showed how it could be applied to a wide range of mathematical and physical problems. ... The strongly problem-oriented presentation in the treatises ... made it much easier for university students to master the fluxional calculus and its applications [and] helped define a new field of mixed mathematical studies..."
An adventurous expression of physical mathematics is found in A Treatise on Electricity and Magnetism which used partial differential equations. The text aspired to describe phenomena in four dimensions but the foundation for this physical world, Minkowski space, trailed by forty years.
String theorist Greg Moore said this about physical mathematics in his vision talk at Strings 2014.
See also
Theoretical physics
Mathematical physics
References
Eric Zaslow, Physmatics,
Arthur Jaffe, Frank Quinn, "Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics", Bulletin of the American Mathematical Society 30: 178-207, 1994,
Michael Atiyah et al., "Responses to Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, by A. Jaffe and F. Quinn", Bull. Am. Math. Soc. 30: 178-207, 1994,
Michael Stöltzner, "Theoretical Mathematics: On the Philosophical Significance of the Jaffe-Quinn Debate", in: The Role of Mathematics in Physical Sciences, pages 197-222,
Kevin Hartnett (November 30, 2017) "Secret link discovered between pure math and physics", Quanta Magazine
Fields of mathematics
Mathematical physics |
https://en.wikipedia.org/wiki/Mersad%20Selimbegovi%C4%87 | Mersad Selimbegović (born 29 April 1982) is a Bosnian professional football coach and former player who last managed Jahn Regensburg.
Managerial statistics
References
External links
1982 births
Living people
People from Rogatica
Bosnia and Herzegovina men's footballers
Men's association football defenders
NK Žepče players
FK Željezničar Sarajevo players
3. Liga players
SSV Jahn Regensburg players
2. Bundesliga managers
SSV Jahn Regensburg managers
SSV Jahn Regensburg non-playing staff
Bosnia and Herzegovina expatriate men's footballers
Bosnia and Herzegovina expatriate football managers
Bosnia and Herzegovina expatriate sportspeople in Germany
Expatriate men's footballers in Germany
Expatriate football managers in Germany |
https://en.wikipedia.org/wiki/Equioscillation%20theorem | In mathematics, the equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev.
Statement
Let be a continuous function from to . Among all the polynomials of degree , the polynomial minimizes the uniform norm of the difference if and only if there are points such that where is either -1 or +1.
Variants
The equioscillation theorem is also valid when polynomials are replaced by rational functions: among all rational functions whose numerator has degree and denominator has degree , the rational function , with and being relatively prime polynomials of degree and , minimizes the uniform norm of the difference if and only if there are points such that where is either -1 or +1.
Algorithms
Several minimax approximation algorithms are available, the most common being the Remez algorithm.
References
External links
The Chebyshev Equioscillation Theorem by Robert Mayans
The de la Vallée-Poussin alternation theorem at the Encyclopedia of Mathematics
Approximation theory by Remco Bloemen
Theorems about polynomials
Numerical analysis
Theorems in analysis |
https://en.wikipedia.org/wiki/Moral%20statistics | Moral statistics most narrowly refers to numerical data generally considered to be indicative of social pathology in groups of people. Examples include statistics on crimes (against persons and property), illiteracy, suicide, illegitimacy, abortion, divorce, prostitution, and the economic situation sometimes called pauperism in the 19th century.
The gathering of anything that might be called social statistics is often dated from John Graunt’s (1662)
analysis of the London Bills of Mortality, which tabulated birth and death data collected by London parishes. The beginnings of the systematic collection of population statistics (now called demography) occurred in the mid-18th century, often attributed to Johann Peter Süssmilch in 1741. Data on moral variables began to be collected and disseminated by various state agencies (most notably in France and Britain) in the early 19th century, and were widely used in debates about social reform.
The first major work on this topic was the Essay on moral statistics of France by
André-Michel Guerry in 1833. In this book, Guerry presented thematic maps of the departments of France, shaded according to illiteracy, crimes against persons and against property, illegitimacy, donations to the poor and so forth, and used these to ask questions about how such moral variables were related.
In Britain this theme was taken up beginning in 1847 by Joseph Fletcher who published several articles on the topic Moral and educational statistics of England and Wales.
References
Further reading
Friendly M. (2007) "A.-M. Guerry's Moral Statistics of France: Challenges for Multivariable Spatial Analysis", Statistical Science, 22 (3), 368–399. Project Euclid
Social statistics |
https://en.wikipedia.org/wiki/TetGen | TetGen is a mesh generator developed by Hang Si which is designed to partition any 3D geometry into tetrahedrons by employing a form of Delaunay triangulation whose algorithm was developed by the author.
TetGen has since been incorporated into other software packages such as Mathematica and Gmsh.
Some improvements by speed in quality in Version 1.6 were introduced.
See also
Gmsh
Salome (software)
References
External links
Weierstrass Institute: Hang Si's personal homepage
Numerical analysis software for Linux
Cross-platform software
Mesh generators
Numerical analysis software for macOS
Numerical analysis software for Windows
Free mathematics software
Free software programmed in C++
Cross-platform free software |
https://en.wikipedia.org/wiki/LAE | LAE may refer to:
Local area emergency, by Specific Area Message Encoding
Least absolute errors, an alternate name for least absolute deviations in statistics
Loterías y Apuestas del Estado, Spanish lottery
Popular Unity (Greece) (, Laïkí Enótita), a left-wing political party in Greece
Lae, the capital of Morobe Province and the second-largest city in Papua New Guinea
Lae Atoll, atoll in the Marshall Islands
HMAS Lae, two Australian warships
LAE-32 (D-Lysergic acid ethylamide), a derivative of ergine
Lae language, also known as Aribwatsa, an extinct member of the Busu subgroup of Lower Markham languages in the area of Lae, Morobe Province, Papua New Guinea
Left atrial enlargement, enlargement of the left atrium (LA) of the heart and a form of cardiomegaly
See also |
https://en.wikipedia.org/wiki/L-packet | In the field of mathematics known as representation theory, an L-packet is a collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have the same Langlands parameter, and so have the same L-function and ε-factors. L-packets were introduced by Robert Langlands in , .
The classification of irreducible representations splits into two parts: first classify the L-packets, then classify the representations in each L-packet. The local Langlands conjectures state (roughly) that the L-packets of a reductive group G over a local field F are conjecturally parameterized by certain homomorphisms of the Langlands group of F to the L-group of G, and Arthur has given a conjectural description of the representations in a given L-packet.
The elements of an L-packet
For irreducible representations of connected complex reductive groups, Wallach proved that all the L-packets contain just one representation. The L-packets, and therefore the irreducible representations, correspond to quasicharacters of a Cartan subgroup, up to conjugacy under the Weyl group.
For general linear groups over local fields, the L-packets have just one representation in them (up to isomorphism).
An example of an L-packet is the set of discrete series representations with a given infinitesimal character and given central character. For example, the discrete series representations of SL2(R) are grouped into L-packets with two elements.
gave a conjectural parameterization of the elements of an L-packet in terms of the connected components of C/Z, where Z is the center of the L-group, and C is the centralizer in the L-group of Im(φ), and φ is the homomorphism of the Langlands group to the L-group corresponding to the L-packet. For example, in the general linear group, the centralizer of any subset is Zariski connected, so the L-packets for the general linear group all have 1 element. On the other hand, the centralizer of a subset of the projective general linear group can have more than 1 component, corresponding to the fact that L-packets for the special linear group can have more than 1 element.
References
Langlands program |
https://en.wikipedia.org/wiki/Shelling%20%28topology%29 | In mathematics, a shelling of a simplicial complex is a way of gluing it together from its maximal simplices (simplices that are not a face of another simplex) in a well-behaved way. A complex admitting a shelling is called shellable.
Definition
A d-dimensional simplicial complex is called pure if its maximal simplices all have dimension d. Let be a finite or countably infinite simplicial complex. An ordering of the maximal simplices of is a shelling if the complex
is pure and of dimension for all . That is, the "new" simplex meets the previous simplices along some union of top-dimensional simplices of the boundary of . If is the entire boundary of then is called spanning.
For not necessarily countable, one can define a shelling as a well-ordering of the maximal simplices of having analogous properties.
Properties
A shellable complex is homotopy equivalent to a wedge sum of spheres, one for each spanning simplex of corresponding dimension.
A shellable complex may admit many different shellings, but the number of spanning simplices and their dimensions do not depend on the choice of shelling. This follows from the previous property.
Examples
Every Coxeter complex, and more generally every building (in the sense of Tits), is shellable.
The boundary complex of a (convex) polytope is shellable. Note that here, shellability is generalized to the case of polyhedral complexes (that are not necessarily simplicial).
There is an unshellable triangulation of the tetrahedron.
Notes
References
Algebraic topology
Properties of topological spaces
Topology |
https://en.wikipedia.org/wiki/Honda%E2%80%93Tate%20theorem | In mathematics, the Honda–Tate theorem classifies abelian varieties over finite fields up to isogeny. It states that the isogeny classes of simple abelian varieties over a finite field of order q correspond to algebraic integers all of whose conjugates (given by eigenvalues of the Frobenius endomorphism on the first cohomology group or Tate module) have absolute value .
showed that the map taking an isogeny class to the eigenvalues of the Frobenius is injective, and showed that this map is surjective, and therefore a bijection.
References
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Leigh%20Academy%20Tonbridge | Leigh Academy Tonbridge, formerly Hayesbrook School, is a non-selective secondary school with academy status in Tonbridge, Kent, United Kingdom. It has specialisms in Sports and Mathematics.
Location
The school is located in Brook Street, Tonbridge. It is next to The Judd School and close to West Kent College.
History
In 1985, Andrew Skipjack was one of the winners of The Times fifth computer competition, winning an Atari 600XL and a copy of The Times Atlas of World History.
Academy and sponsorship
In December 2010, Hayesbrook was the first secondary school in West Kent to gain academy status.
In September 2012, The Hayesbrook Academy Trust took over Angley School in Cranbrook, Kent which was subsequently renamed the High Weald Academy.
In August 2013, The Hayesbrook Academy Trust changed its name to The Brook Learning Trust, which coincided with the sponsorship of The Swan Valley Community School in Swanscombe to gain academy status - changing its name to The Ebbsfleet Academy.
The school became the coeducational Leigh Academy Tonbridge in September 2023.
Houses
Hayesbrook has five houses (or teams, as the school calls them), all named after famous Athletes: Ali, Pelé, MacArthur, Redgrave, and Thompson.
Ofsted
The school was classed as "Excellent" by Ofsted in 2005, 2008 and 2009.
In 2013 the school was rated as "Good", with "Outstanding" behaviour and safety of pupils.
References
Secondary schools in Kent
Boys' schools in Kent
Schools in Tonbridge
Academies in Kent
Educational institutions established in 1964
1964 establishments in England |
https://en.wikipedia.org/wiki/Paul%20Walker%20%28Arctic%20explorer%29 | Paul Walker is an Arctic explorer and Polar Guide born in Shrewsbury, England. He achieved a B.Ed Honours degree in Outdoor Education and Mathematics and has organised more than 250 arctic expeditions to Spitsbergen (Svalbard), Baffin Island (Canada), Iceland and Greenland over 30+ years. In 2006 he led an 8 man team to make the first and only winter ascent of Gunnbjørnsfjeld, the highest mountain in the Arctic Circle.
Biography
Born in Shrewsbury, Shropshire Walker moved to Wetherby aged 8 and later graduated from Charlotte Mason College,
Ambleside with a B.Ed Honours degree in Outdoor Education and Mathematics. It was here he led his first Greenland expedition, a 2 month climbing trip to the Schweizerland Alps.
At 23, Walker became one of the UK's youngest Winter Mountain Leaders.
In 1993 he made the first ascent of the 28 pitch northeast ridge of Mont Forel in east Greenland. In 1996 he climbed a number of the main summits of the Crown Prince Frederick Range together with members of the Tangent British East Greenland Expedition.
In 1999 he led the first British guided ski crossing of the Greenland Icecap using kites. In 2001 he headed to Svalbard to lead the "Polestar" team to make the first British south-north ski traverse of Spitsbergen.
In 2004 Paul organized and led the US Navy Air Crash Recovery Expedition to the Kronborg Glacier, east Greenland. This expedition was commissioned by the US Navy to recover the human remains of US Navy personnel lost in an earlier air crash of a P-2V Neptune on January 12, 1962.
In 2006 he led an 8 man team to make the first winter ascent of Gunnbjørnsfjeld, the highest mountain in the Arctic Circle. During this expedition the team were attacked during the night at their base camp by a polar bear who ripped through several tents.
Paul has worked extensively as a Greenland location and logistics consultant for numerous TV documentaries, films and marketing projects. He has also worked with a range of celebrities organising their personal adventure holidays, expeditions and TV programme logistics including Ian Wright, Christie Turlington, Paul Rose, Steve Backshall and Google founders Larry Page & Sergei Bryn.
In 2018 he was logistics consultant for the record breaking longest vehicle polar journey in history, with the double south-north-south crossing of the Greenland icecap by three specially adapted 4x4 and 6x6 vehicles, supplied by Arctic Trucks of Reykjavik, Iceland.
He was logistics, safety and location consultant for the latest Disney+ and National Geographic TV channel 3 part expedition documentary series entitled "On The Edge", with Oscar award-winning climber Alex Honnold.
Personal life
After 30 years living in the Lake District, North West England, Paul moved to the small village of Kirknewton, near Wooler, in Northumberland in 2014. Paul has three children.
References
Growing old disgracefully in Greenland
https://web.archive.org/web/20120327213914/http://www.nicearticles.net/trave |
https://en.wikipedia.org/wiki/Dante%20Tessieri | Dante Tessieri was an Argentine scientist born in the late nineteenth century. He worked in the fields of physics, electricity and mathematics. Tessieri wrote a book, "La Relatividad General ante la prueba Suprema", disagreeing with Albert Einstein's general relativity theory. In the book, Dante Tessieri uses the alias "Galileo".
His Life
Not much of his life is known. He was born between 1850 and 1875 and died between 1920 and 1935. Tessieri wrote articles for magazines such as the "Revista de Obras Publicas (Magazine of Public Inventions). In 1904 he published an article on improving the efficiency of fans by adding electric motors.
Tessieri was head of the Freemasons in Argentina through which he associated with some of the most influential people in the country.
During Albert Einstein's visit to Buenos Aires in 1925, Tessieri attempted to publish a note challenging relativity in the newspaper La Nación, but was refused. He nevertheless managed to publicly challenge Einstein.
References
External Sources
"La Relatividad General ante la prueba Suprema", (Argentine National Congress Library )
20th-century Argentine physicists |
https://en.wikipedia.org/wiki/Ron%20Larson%20%28disambiguation%29 | Ron Larson (born 1941), is a mathematics professor at Penn State Erie, The Behrend College, Pennsylvania.
Ron Larson may also refer to:
Ron Larson (artist) art director, album cover designer and graphic artist
See also
Ronnie Larsen, playwright |
https://en.wikipedia.org/wiki/1985%20S%C3%A3o%20Paulo%20FC%20season | The 1985 season was São Paulo's 56th season since club's existence.
Statistics
Scorers
Overall
{|class="wikitable"
|-
|Games played || 71 (20 Campeonato Brasileiro, 42 Campeonato Paulista, 9 Friendly match)
|-
|Games won || 35 (7 Campeonato Brasileiro, 23 Campeonato Paulista, 5 Friendly match)
|-
|Games drawn || 21 (6 Campeonato Brasileiro, 12 Campeonato Paulista, 2 Friendly match)
|-
|Games lost || 16 (7 Campeonato Brasileiro, 7 Campeonato Paulista, 2 Friendly match)
|-
|Goals scored || 121
|-
|Goals conceded || 74
|-
|Goal difference || +47
|-
|Best result || 5–0 (H) v São Bento - Campeonato Paulista - 1985.07.31
|-
|Worst result || 2–4 (A) v Atlético Mineiro - Campeonato Brasileiro - 1985.02.10
|-
|Top scorer || Careca (35)
|-
Friendlies
Torneio Triangular LuIz Henrique Rosas
Official competitions
Campeonato Brasileiro
First round
Matches
Second round
Matches
Record
Campeonato Paulista
First phase
Second phase
Matches
Final standings
Semifinals
Finals
Record
External links
official website
Association football clubs 1985 season
1985
1985 in Brazilian football |
https://en.wikipedia.org/wiki/Ken%20Rosewall%20career%20statistics | This is a list of the main career statistics of Australian former tennis player Ken Rosewall whose playing career ran from 1951 until 1980. He played as an amateur from 1951 until the end of 1956 when he joined Jack Kramer's professional circuit. As a professional he was banned from playing the Grand Slam tournaments as well as other tournaments organized by the national associations of the International Lawn Tennis Federation (ILTF). In 1968, with the advent of the Open Era, the distinction between amateurs and professionals disappeared and Rosewall was again able to compete in most Grand Slam events until the end of his career in 1978. During his career he won eight Grand Slam, 15 Pro Slam and three Davis Cup titles.
Major finals
Grand Slam finals
Singles: 16 finals (8 titles, 8 runner-ups)
Pro Slam finals
Singles * : 15 titles, 4 runner-ups
* other events (important professional tournaments – 2 runners-up)
WCT year end championship
Singles: 2 titles
Performance timeline
Ken Rosewall joined professional tennis in 1957 and was unable to compete in 45 Grand Slam tournaments until the open era arrives in 1968. Summarizing Grand Slam and Pro Slam tournaments, Rosewall won 23 titles, he has a winning record of 242–46 which represents 84.02% spanning 28 years.
Ken Rosewall Singles finals:(251)
Singles titles 147, Runners-Up 104
Amateur era
Singles (1951–1956) : 26 titles
Professional era
Singles (1957–1968) : 64 titles
Notes:
1 : 4-men tournaments
2 : Players take turns challenging the winner of the last game. Rosewall was the one who won the most matches.
3 : 1 listed by the ATP Website
Open era
Singles (1968–1977) : 43 titles (including 39 listed by the ATP Website)
Notes:
1 : 4-men tournaments.
2 : 39 listed by the ATP website
Professional tours
Singles (1957–1967) : 7 tours
Team events
Davis Cup
Rosewall won 17 out of 19 Davis Cup singles matches and 2 out of 3 doubles. Rosewall was a member of the victorious Australian Davis Cup teams in 1953, 1955, 1956 and 1973, in all cases defeating USA in the final. He did not personally participate in the 1973 final.
Kramer Cup
In this pro "Davis Cup-format" team event, held just 3 years (1961–1963) and opposing the subcontinents Australia, Europe, North America and South America, Rosewall won 9 out of 10 singles matches and 4 out of 5 doubles. Australia won all three editions.
Head to head
Rosewall's win–loss record against top players is as follows.
Notes
Sources
Joe McCauley, The History of Professional Tennis, London 2001.
Michel Sutter, Vainqueurs Winners 1946–2003, Paris 2003.
Tony Trabert, Tennis de France.
Robert Geist, Der Grösste Meister Die denkwürdige Karriere des australischen Tennisspielers Kenneth Robert Rosewall, Vienna 1999.
Bud Collins, The Bud Collins History of Tennis, 2008.
External links
Rosewall, Ken
fr:Ken Rosewall |
https://en.wikipedia.org/wiki/World%20heavyweight%20boxing%20championship%20records%20and%20statistics | Below is a list of world heavyweight boxing championship records and statistics.
Championship recognition
As per International Boxing Hall Of Fame:
1884–1921
Champions were recognized by public acclamation. A champion in that era was a fighter who had a notable win over another fighter and kept winning afterward. It was a lineal championship. The only way to win the championship was to beat the current champion. Retirements or disputed results could lead to a championship being split among several men for periods of time. With only minor exceptions, the heavyweight division remained free from dual title-holders until the 1960s. For an early example, see the 1896 World Heavyweight Championship.
Sanctioning organizations: 1921–present
Gradually, the role of recognizing champions in the division evolved into a more formal affair, with public acclamation being supplemented (or in some cases, contradicted) by recognition by one or more athletic commissions, sanctioning organizations, or a combination of them. The International Boxing Hall of Fame (IBHOF) recognizes these organizations as major in boxing:
The New York State Athletic Commission (NYSAC). A governmental entity initially formed for the purpose of regulating boxing in the State of New York, thanks to New York's place as the epicenter of boxing from the 1930s through 1950s, the NYSAC expanded its reach to sanctioning championship bouts. This practice continued until, like the IBU, the NYSAC became a member of the WBC.
The National Boxing Association (NBA) was organized in 1921. In 1962, the organization was renamed the World Boxing Association (WBA).
The WBC was organized in 1963.
The IBF, which was founded in 1983 by the members of the United States Boxing Association after the USBA withdrew from membership in the WBA.
The WBO, founded in 1988. The IBHOF started recognizing WBO as a major organization no later than August 23, 1997.
There are also titles that are not considered major, but play a significant role in legitimizing the heavyweight champion:
The Ring began awarding championship belts in 1922, stopped giving belts to world champions in the 1990s, then reintroduced their title in 2002, and ignored the current ongoing world championship lineage. Under the original version of the policy, you could win the title by either defeating the reigning champion or winning a box-off between the magazine's No. 1 and No. 2 (occasionally No. 3) ranked contenders. A fighter could not be stripped of the title unless he lost or retired. Since May 2012, under the new policy, The Ring title can be awarded when the No. 1 and No. 2 contenders face each other or when either of them faces No. 3, No. 4 or No. 5 contender. In addition, the title can be taken away by losing the fight, not scheduling a fight for 18 months, not scheduling a fight with a top 5 contender for two years, or retiring.
Most opponents beaten in title fights
Keys:
Active title reign
Reign has ended
Note: Secondary |
https://en.wikipedia.org/wiki/Bass%20conjecture | In mathematics, especially algebraic geometry, the Bass conjecture says that certain algebraic K-groups are supposed to be finitely generated. The conjecture was proposed by Hyman Bass.
Statement of the conjecture
Any of the following equivalent statements is referred to as the Bass conjecture.
For any finitely generated Z-algebra A, the groups K'n(A) are finitely generated (K-theory of finitely generated A-modules, also known as G-theory of A) for all n ≥ 0.
For any finitely generated Z-algebra A, that is a regular ring, the groups Kn(A) are finitely generated (K-theory of finitely generated locally free A-modules).
For any scheme X of finite type over Spec(Z), K'n(X) is finitely generated.
For any regular scheme X of finite type over Z, Kn(X) is finitely generated.
The equivalence of these statements follows from the agreement of K- and K'-theory for regular rings and the localization sequence for K'-theory.
Known cases
Daniel Quillen showed that the Bass conjecture holds for all (regular, depending on the version of the conjecture) rings or schemes of dimension ≤ 1, i.e., algebraic curves over finite fields and the spectrum of the ring of integers in a number field.
The (non-regular) ring A = Z[x, y]/x2 has an infinitely generated K1(A).
Implications
The Bass conjecture is known to imply the Beilinson–Soulé vanishing conjecture.
References
, p. 53
Algebraic geometry
Algebraic K-theory
Unsolved problems in geometry |
https://en.wikipedia.org/wiki/II25%2C1 | {{DISPLAYTITLE:II25,1}}
In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice. It has several unusual properties, arising from Conway's discovery that it has a norm zero Weyl vector. In particular it is closely related to the Leech lattice Λ, and has the Conway group Co1 at the top of its automorphism group.
Construction
Write Rm,n for the m+n-dimensional vector space
Rm+n with the inner product of
(a1,...,am+n) and (b1,...,bm+n) given by
a1b1+...+ambm − am+1bm+1 − ... − am+nbm+n.
The lattice II25,1 is given by all vectors (a1,...,a26)
in R25,1 such that either all the ai are integers or they are all integers
plus 1/2, and their sum is even.
Reflection group
The lattice II25,1 is isomorphic to Λ⊕H where:
Λ is the Leech lattice,
H is the 2-dimensional even Lorentzian lattice, generated by 2 norm 0 vectors z and w with inner product –1,
and the two summands are orthogonal. So we can write vectors of II25,1 as (λ,m, n) = λ+mz+nw with λ in Λ and m,n integers, where (λ,m, n) has norm λ2 –2mn. To give explicitly the isomorphism, let , and , so that the subspace generated by and is the 2-dimensional even Lorentzian lattice. Then is isomorphic to and we recover one of the definitions of Λ.
Conway showed that the roots (norm 2 vectors) having inner product –1 with w=(0,0,1) are the simple roots of the reflection group. These are the vectors (λ,1,λ2/2–1) for λ in the Leech lattice. In other words, the simple roots can be identified with the points of the Leech lattice, and moreover this is an isometry from the set of simple roots to the Leech lattice.
The reflection group is a hyperbolic reflection group acting on 25-dimensional hyperbolic space.
The fundamental domain of the reflection group has 1+23+284 orbits of vertices as follows:
One vertex at infinity corresponding to the norm 0 Weyl vector.
23 orbits of vertices at infinity meeting a finite number of faces of the fundamental domain. These vertices correspond to the deep holes of the Leech lattice, and there are 23 orbits of these corresponding to the 23 Niemeier lattices other than the Leech lattice. The simple roots meeting one of these vertices form an affine Dynkin diagram of rank 24.
284 orbits of vertices in hyperbolic space. These correspond to the 284 orbits of shallow holes of the Leech lattice. The simple roots meeting any of these vertices form a spherical Dynkin diagram of rank 25.
Automorphism group
described the automorphism group Aut(II25,1) of II25,1 as follows.
First of all, Aut(II25,1) is the product of a group of order 2 generated by –1 by the index 2 subgroup Aut+(II25,1) of automorphisms preserving the direction of time.
The group Aut+(II25,1) has a normal subgroup Ref generated by its reflections, whose simple roots correspond to the Leech lattice vectors.
The group Aut+(II25,1)/Ref is isomorphic to the group of affine automorphisms of the Leech lattice Λ, and so has a normal subgroup of translations isomorphic to Λ=Z24, and the |
https://en.wikipedia.org/wiki/Haj%C3%B3s%20construction | In graph theory, a branch of mathematics, the Hajós construction is an operation on graphs named after that may be used to construct any critical graph or any graph whose chromatic number is at least some given threshold.
The construction
Let and be two undirected graphs, be an edge of , and be an edge of . Then the Hajós construction forms a new graph that combines the two graphs by identifying vertices and into a single vertex, removing the two edges and , and adding a new edge .
For example, let and each be a complete graph on four vertices; because of the symmetry of these graphs, the choice of which edge to select from each of them is unimportant. In this case, the result of applying the Hajós construction is the Moser spindle, a seven-vertex unit distance graph that requires four colors.
As another example, if and are cycle graphs of length and respectively, then the result of applying the Hajós construction is itself a cycle graph, of length .
Constructible graphs
A graph is said to be -constructible (or Hajós--constructible) when it formed in one of the following three ways:
The complete graph is -constructible.
Let and be any two -constructible graphs. Then the graph formed by applying the Hajós construction to and is -constructible.
Let be any -constructible graph, and let and be any two non-adjacent vertices in . Then the graph formed by combining and into a single vertex is also -constructible. Equivalently, this graph may be formed by adding edge to the graph and then contracting it.
Connection to coloring
It is straightforward to verify that every -constructible graph requires at least colors in any proper graph coloring. Indeed, this is clear for the complete graph , and the effect of identifying two nonadjacent vertices is to force them to have the same color as each other in any coloring, something that does not reduce the number of colors. In the Hajós construction itself, the new edge forces at least one of the two vertices and to have a different color than the combined vertex for and , so any proper coloring of the combined graph leads to a proper coloring of one of the two smaller graphs from which it was formed, which again causes it to require colors.
Hajós proved more strongly that a graph requires at least colors, in any proper coloring, if and only if it contains a -constructible graph as a subgraph. Equivalently, every -critical graph (a graph that requires colors but for which every proper subgraph requires fewer colors) is -constructible. Alternatively, every graph that requires colors may be formed by combining the Hajós construction, the operation of identifying any two nonadjacent vertices, and the operations of adding a vertex or edge to the given graph, starting from the complete graph .
A similar construction may be used for list coloring in place of coloring.
Constructibility of critical graphs
For , every -critical graph (that is, every odd cycle) can be generated |
https://en.wikipedia.org/wiki/Ted%20Bastin | Edward William "Ted" Bastin (8 January 1926 – 15 October 2011) was a physicist and mathematician who held doctorate degrees in mathematics from Queen Mary College, London University and physics from King's College, Cambridge, to which he won an Isaac Newton studentship. For a time, he was visiting fellow at Stanford University, California and a research fellow, King's College, Cambridge, England.
The boats stored at the River Cam boathouse, King's College, Cambridge, include "Ted", the lightweight wooden scull named after Ted Bastin, who won races in it for King's from 1950 to 1953.
Work
Bastin’s research specialties included the foundations of physics, especially the discrete and finite aspects of quantum mechanics and relativity. He believed that a view of physical space in which space is defined not as a continuum but as a finite set of points was capable of resolving the clash between the continuum aspect of the classic theory of relativity and the discrete aspect of quantum physics. He was strongly influenced by Eddington's view that the various dimensionless and cosmological constants such as the fine structure constant had a unique status or significance as constraints upon the possible values of the natural atomic and cosmological constants of which they are ratios, and hence on all possible measurements. Along with Frederick Parker-Rhodes, Clive W. Kilmister and John Amson, Ted Bastin is noted for the discovery of, and research on applications of, the so-called combinatorial hierarchy which defines this view of space. While at the Cambridge Language Research Unit (founded by Margaret Masterman) he and Parker-Rhodes used Maurice Wilkes' EDSAC to compute the combinatorial hierarchy. However, the theory gave rise to no testable predictions and was generally regarded as too speculative.
He was on firmer ground in his objection to the (then generally accepted) Copenhagen interpretation of quantum theory, and also to other conceptual difficulties, such as the nature and role of observation and measurement, which he regarded as contributing to logical muddle arising from confusing ontological and epistemological aspects of the theory. His assessment of the philosophical difficulties and obscurities in quantum theory that had to be overcome before any change in the basic structure could take place was penetrating; it was only his attempt to overcome the formal difficulties that failed.
He collaborated with David Bohm to organize the "Quantum Theory and Beyond" colloquium at Cambridge University in July 1968, chaired by O. R. Frisch. The colloquium was sponsored by the Royal Society, Carnegie Institution of Science, and Theoria Inc., and resulted in a book by the same name. Bastin worked with David Bohm on other theoretical physics projects as well, particularly by having discussions with the latter on his theory of hidden variables in quantum theory.
Bastin was a founding member, with H. Pierre Noyes, Clive W. Kilmister, John Amson and Fre |
https://en.wikipedia.org/wiki/List%20of%20West%20Coast%20Eagles%20records | This is a list of records and statistics achieved by the West Coast Eagles in the VFL/AFL from their debut in 1987.
All-time games table
End of 2019
Team records
Records listed only include matches played against other AFL teams in home and away or finals matches.
Key
Achieved during the 2018 season
Scoring records
Individual records
Records listed only include players who played at least one game for the club.
Key
Currently on the club's list.
Games records
Most games overall
G: games played
Goalkicking records
Most goals overall
G: Goals
B: Behinds
Most goals in a season
G: Goals
B: Behinds
Cummings won the Coleman Medal in 1999, Kennedy won the award in 2015 and 2016.
Most goals in a match
G: Goals
B: Behinds
Statistics
Kicks
Handballs
Disposals
Marks
Tackles
Hit-outs
Physical records
Height
Height refers to the player's highest maximum or lowest minimum playing height:
Weight
Weight refers to the player's highest maximum or lowest minimum playing weight:
Age
References
West Coast statistics – AFL Tables.
Records
West Coast Eagles records
Australian rules football-related lists |
https://en.wikipedia.org/wiki/Tallinna%20FC%20Olympic%20Olybet | Tallinna FC Olympic Olybet is an Estonian football club, playing in the town of Tallinn.
Current squad
''As of 29 October 2017.
Statistics
League and Cup
References
Football clubs in Tallinn
2000 establishments in Estonia |
https://en.wikipedia.org/wiki/Gergely%20D%C3%A9lczeg | Gergely Délczeg (born 9 August 1987) is a Hungarian former professional footballer.
Club statistics
Updated to games played as of 7 April 2014.
External links
Gergely Délczeg at HLSZ
Gergely Délczeg at MLSZ
1987 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football forwards
Rákospalotai EAC footballers
Zalaegerszegi TE players
BFC Siófok players
Budapest Honvéd FC players
Paksi FC players
Kisvárda FC players
Dorogi FC footballers
Szombathelyi Haladás footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Alexisz%20Nov%C3%A1k | Alexisz Novák (born 22 November 1987) is a Hungarian professional footballer who plays for BFC Siófok and was born in Budapest.
Club statistics
Updated to games played as of 9 March 2014.
External links
Profile at HLSZ
1987 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football defenders
MTK Budapest FC players
BKV Előre SC footballers
FC Felcsút players
Budaörsi SC footballers
Budapest Honvéd FC players
BFC Siófok players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20FC%20Universitatea%20Cluj%20season | The 2011–12 season was the 86th season of competitive football by Universitatea Cluj.
Players
Current squad
As of 10 June 2011.
Squad changes
In
Out
Player statistics
Appearances and goals
Last updated on 24 July 2011.
|}
Liga I
League table
Results by round
Points by opponent
Competitive
Liga I
Kickoff times are in EET.
Results
FC Universitatea Cluj seasons
Universitatea Cluj |
https://en.wikipedia.org/wiki/Kanakanahalli%20Ramachandra | Kanakanahalli Ramachandra (18 August 1933 – 17 January 2011) was an Indian mathematician working in both analytic number theory and algebraic number theory.
Early career
Ramachandra went to the Tata Institute of Fundamental Research (TIFR), Bombay, for his graduate studies in 1958. He obtained his PhD from University of Mumbai in 1965; his doctorate was guided by K. G. Ramanathan.
Later career
Between the years 1965 and 1995 he worked at the Tata Institute of Fundamental Research and after retirement joined the National Institute of Advanced Studies, Bangalore where he worked till 2011, the year he died. During the course of his lifetime, he published over 200 articles, of which over 170 have been catalogued by Mathematical Reviews.
His work was primarily in the area of prime number theory, working on the Riemann zeta function and allied functions. Apart from prime number theory, he made substantial contributions to the theory of transcendental number theory, in which he is known for his proof of the six exponentials theorem, achieved independently of Serge Lang. He also contributed to many other areas of number theory.
In 1978 he founded the Hardy–Ramanujan journal, and published it on behalf of the Hardy–Ramanujan society until his death.
Awards and distinctions
Elected President of the Calcutta Mathematical Society for the period; 2007–2010
Publications
References
External links
Kanakanahalli Ramachandra
People from Mandya
20th-century Indian mathematicians
21st-century Indian mathematicians
1933 births
2011 deaths
Scientists from Karnataka
Indian number theorists |
https://en.wikipedia.org/wiki/Ram%20Prakash%20Bambah | Ram Prakash Bambah (born 17 September 1925) is an Indian mathematician working in number theory and discrete geometry.
Education and career
Bambah earned a bachelor's degree from Government College University, Lahore, and a master's degree from the University of the Punjab, Lahore.
He then went to England for his doctoral studies, earning his Ph.D. in 1950 from St John's College, Cambridge under the supervision of Louis J. Mordell. Returning to India, he became a reader at Panjab University, Chandigarh, in 1952, and was promoted to professor there in 1957. Maintaining his position at Panjab University, he also held a position as professor at Ohio State University in the US from 1964 to 1969. He retired from Panjab University in 1993.
Bambah was president of the Indian Mathematical Society in 1969, and vice chancellor of Panjab University from 1985 to 1991.
Awards and honours
He was elected to the Indian National Science Academy in 1955.
In 1979 he was awarded the Srinivasa Ramanujan Medal, and in 1974 was elected to the Indian Academy of Sciences. In 1988 he received the Aryabhata Medal of the Indian National Science Academy and the Padma Bhushan award.
References
1925 births
Living people
20th-century Indian mathematicians
Indian number theorists
Geometers
Government College University, Lahore alumni
University of the Punjab alumni
Alumni of St John's College, Cambridge
Ohio State University faculty
Presidents of the Indian Mathematical Society
Recipients of the Padma Bhushan in science & engineering |
https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan%20Journal | The Hardy–Ramanujan Journal is a mathematics journal covering prime numbers, Diophantine equations, and transcendental numbers. It is named for G. H. Hardy and Srinivasa Ramanujan. Together with the Ramanujan Journal and the Journal of the Ramanujan Mathematical Society, it is one of three journals named after Ramanujan.
It was established in 1978 by R. Balasubramanian and K. Ramachandra and is published once a year on Ramanujan's birthday December 22. It is indexed in MathSciNet.
Both Balasubramanian and Ramachandra are respected mathematicians and accomplished a great deal in the field of mathematics. They both also focused their mathematical careers on number theory. Most importantly, they were both inspired by Srinivasa Ramanujan, which led them to the creation of the Hardy–Ramanujan Journal. Before Ramachandra's death, the two would publish a new journal almost every year on Ramanujan's birthday, December 22. However, after that time a decision was made to continue the journal by a new team of editors. These editors consisted of people who shared the same passion as Ramachandra and Balasubramanian and contributed to the journal in the past. The goal of the journal remains the same.
References
External links
Page scans of the Hardy–Ramanujan Journal
Mathematics journals
English-language journals
Academic journals established in 1978
Annual journals
Srinivasa Ramanujan |
https://en.wikipedia.org/wiki/1943%20Latvian%20Higher%20League | Statistics of Latvian Higher League in the 1943 season.
Overview
It was contested by 7 teams, and ASK won the championship.
League standings
References
RSSSF
Latvian Higher League seasons
1943 in Latvian football
Lat |
https://en.wikipedia.org/wiki/%C3%96mer%20Cerraho%C4%9Flu | Ömer Cerrahoğlu (born 3 May 1995) is a Romanian child prodigy in mathematics. At the age of , he won a gold medal at the 2009 International Mathematical Olympiad, making him the third-youngest gold medalist in IMO history, behind Terence Tao and Raúl Chávez Sarmiento.
Early life and education
He was born in Istanbul, Turkey to a Romanian mother and a Turkish father and when he was five years old, he moved with his family to Baia Mare, Romania. He graduated from the Massachusetts Institute of Technology (MIT) in June 2018, where he studied computer science.
Career
In 2017, he participated in the 78th William Lowell Putnam Mathematical Competition as a student of MIT and earned a Putnam Fellowship. Since his victory in 2009, he won three more silver medals at the 2010, 2011 and 2013 IMO's missing the gold by only 1, 2 and 1 points, respectively, and one more gold medal at the IMO 2012 in Argentina.
See also
List of child prodigies
List of International Mathematical Olympiad participants
References
External links
1995 births
Living people
International Mathematical Olympiad participants
Romanian people of Turkish descent
Romanian Muslims
Romanian expatriates in the United States
Putnam Fellows |
https://en.wikipedia.org/wiki/Braided%20vector%20space | In mathematics, a braided vector space is a vector space together with an additional structure map symbolizing interchanging of two vector tensor copies:
such that the Yang–Baxter equation is fulfilled. Hence drawing tensor diagrams with an overcrossing the corresponding composed morphism is unchanged when a Reidemeister move is applied to the tensor diagram and thus they present a representation of the braid group.
As first example, every vector space is braided via the trivial braiding (simply flipping). A superspace has a braiding with negative sign in braiding two odd vectors. More generally, a diagonal braiding means that for a -base we have
A good source for braided vector spaces entire braided monoidal categories with braidings between any objects , most importantly the modules over quasitriangular Hopf algebras and Yetter–Drinfeld modules over finite groups (such as above)
If additionally possesses an algebra structure inside the braided category ("braided algebra") one has a braided commutator (e.g. for a superspace the anticommutator):
Examples of such braided algebras (and even Hopf algebras) are the Nichols algebras, that are by definition generated by a given braided vectorspace. They appear as quantum Borel part of quantum groups and often (e.g. when finite or over an abelian group) possess an arithmetic root system, multiple Dynkin diagrams and a PBW-basis made up of braided commutators just like the ones in semisimple Lie algebras.
Hopf algebras
Quantum groups |
https://en.wikipedia.org/wiki/Benson%20Farb | Benson Stanley Farb (born October 25, 1967) is an American mathematician at the University of Chicago. His research fields include geometric group theory and low-dimensional topology.
Early life
A native of Norristown, Pennsylvania, Farb earned his bachelor's degree from Cornell University. In 1994, he obtained his doctorate from Princeton University, under supervision of William Thurston.
Career
Farb has advised over 40 students, including Pallavi Dani, Kathryn Mann, Dan Margalit, Karin Melnick and Andrew Putman.
In 2012 Farb became a fellow of the American Mathematical Society. In 2014 he was an invited speaker at the International Congress of Mathematicians in Seoul, speaking in the section on Topology. He was elected to the American Academy of Arts and Sciences in 2021.
Books
Personal life
Farb married Amie Wilkinson, professor of mathematics at the University of Chicago, on December 28, 1996. They are professors in the same department.
References
External links
1967 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Cornell University alumni
Princeton University alumni
University of Chicago faculty
Fellows of the American Mathematical Society
Fellows of the American Academy of Arts and Sciences
Topologists |
https://en.wikipedia.org/wiki/G%C3%A9raud%20S%C3%A9nizergues | Géraud Sénizergues (born 9 March 1957) is a French computer scientist at the University of Bordeaux.
He is known for his contributions to automata theory, combinatorial group theory and abstract rewriting systems.
He received his Ph.D. (Doctorat d'état en Informatique) from the Université Paris Diderot (Paris 7) in 1987 under the direction of Jean-Michel Autebert.
With Yuri Matiyasevich he obtained results about the Post correspondence problem. He won the 2002 Gödel Prize "for proving that equivalence of deterministic pushdown automata is decidable". In 2003 he was awarded with the Gay-Lussac Humboldt Prize.
References
External links
Homepage
Living people
French computer scientists
Academic staff of the University of Bordeaux
Gödel Prize laureates
1957 births |
https://en.wikipedia.org/wiki/Euphemia%20Haynes | Martha Euphemia Lofton Haynes (September 11, 1890 – July 25, 1980) was an American mathematician and educator. She was the first African American woman to earn a PhD in mathematics, which she earned from the Catholic University of America in 1943.
Life
Euphemia Lofton was the first child and only daughter of William S. Lofton, a dentist and financier, and Lavinia Day Lofton, a kindergarten teacher. She was the valedictorian of M Street High School in 1907 and then graduated from Normal School for Colored Girls, now known as University of the District of Columbia, with distinction and a degree in education in 1909. She went on to earn an undergraduate mathematics major (and psychology minor) from Smith College in 1914. In 1917 she married Harold Appo Haynes, a teacher. She gained a master's degree in education from the University of Chicago in 1930. In 1943 gained her PhD from The Catholic University of America with a dissertation, supervised by Aubrey E. Landry, entitled The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences.
Haynes "contributed quite grandly to the educational system of the District of Columbia." She taught in the public schools of Washington, D.C., for 47 years and in 1966 became the first woman to chair the DC Board of Education, on which she served through 1967. While on the DC Board of Education, she was an outspoken critic of the "track system", which she argued discriminated against African American students by assigning them to tracks that left them unprepared for college. This work contributed towards the filing of Hobson v. Hansen (1967) which led to the end of the track system in DC. She taught first grade at Garrison and Garfield Schools, and mathematics at Armstrong High School. She taught mathematics and served as chair of the Math Department at Dunbar High School. Haynes was a professor of mathematics at the University of the District of Columbia where she was chair of the Division of Mathematics and Business Education, a department she created dedicated to training African American teachers.
She retired in 1959 from the public school system, but went on to establish the mathematics department at the University of the District of Columbia. She also occasionally taught part-time at Howard University. Haynes was involved in many community activities. She served as first vice president of the Archdiocesan Council of Catholic Women, chair of the advisory board of Fides Neighborhood House, on the Committee of International Social Welfare, on the executive committee of the National Social Welfare Assembly, secretary and member of the executive committee of the DC Health and Welfare Council, on the local and national committees of the United Service Organization, a member of the National Conference of Christians and Jews, Catholic Interracial Council of Washington, the National Urban League, NAACP, League of Women Voters, and the American Association of |
https://en.wikipedia.org/wiki/1927%20LFF%20Lyga | The 1927 LFF Lyga was the 6th season of the LFF Lyga football competition in Lithuania. Statistics of the LFF Lyga for the 1927 season. LFLS Kaunas won the championship.
Kaunas Group
Klaipėda Group
North Division
South Division
Klaipėda Group Final
Sportverein Pagėgiai 2-1 Spielvereiningung Klaipėda
Šiauliai Group
Final
LFLS Kaunas 3-1 Sportverein Pagėgiai
References
RSSSF
LFF Lyga seasons
Lith
Lith
1927 in Lithuanian football |
https://en.wikipedia.org/wiki/1933%20LFF%20Lyga | Statistics of the LFF Lyga for the 1933 season.
Overview
It was contested by 7 teams, and Kovas Kaunas won the championship.
League standings
References
RSSSF
LFF Lyga seasons
Lith
Lith
1 |
https://en.wikipedia.org/wiki/Tr%E1%BA%A7n%20Minh%20Quang | Trần Minh Quang is a former Vietnamese goalkeeper. He is currently the first coach assistant of Bình Dương .
International statistics
Caps and goals by year
Honours
Club
Bình Dương F.C.
V-League: 2008
Vietnamese Super Cup: 2008
Individual
Vietnamese Silver Ball: 2002
References
1973 births
Living people
Vietnamese men's footballers
Vietnam men's international footballers
People from Bình Định province
SEA Games silver medalists for Vietnam
SEA Games medalists in football
Men's association football goalkeepers
Competitors at the 1999 SEA Games
Quy Nhon Binh Dinh FC players
Becamex Binh Duong FC players
V.League 1 players |
https://en.wikipedia.org/wiki/Roger%20Fletcher%20%28mathematician%29 | Roger Fletcher FRS FRSE (29 January 1939 – 15 July 2016) was a British mathematician and professor at University of Dundee.
He was a Fellow of the Society for Industrial and Applied Mathematics (SIAM) and was elected as a Fellow of the Royal Society in 2003.
In 2006, he won the Lagrange Prize from SIAM.
In 2008, he was awarded a Royal Medal of the Royal Society of Edinburgh.
See also
BFGS method
Davidon–Fletcher–Powell formula
Nonlinear conjugate gradient method
Bibliography
Practical methods of optimization, Wiley, 1987, ; Wiley, 2000,
References
1939 births
2016 deaths
British mathematicians
Fellows of the Royal Society of Edinburgh
Fellows of the Royal Society
Academics of the University of Dundee |
https://en.wikipedia.org/wiki/J%C3%B3zsef%20Windecker | József Windecker (born 2 December 1992 in Szeged, Hungary) is a Hungarian football player, currently playing for Paksi FC.
Club statistics
Updated to games played as of 15 May 2021.
External links
Profile
1992 births
Living people
Footballers from Szeged
Hungarian people of German descent
Hungarian men's footballers
Men's association football midfielders
Győri ETO FC players
BFC Siófok players
Paksi FC players
Újpest FC players
Levadiakos F.C. players
Nemzeti Bajnokság I players
Super League Greece players
Hungarian expatriates in Greece
Expatriate men's footballers in Greece |
https://en.wikipedia.org/wiki/Joseph%20Born%20Kadane | Joseph "Jay" Born Kadane (born January 10, 1941) is the Leonard J. Savage University Professor of Statistics, Emeritus in the Department of Statistics and Social and Decision Sciences at Carnegie Mellon University. Kadane is one of the early proponents of Bayesian statistics, particularly the subjective Bayesian philosophy.
Education and career
Kadane was born in Washington, DC and raised in Freeport on Long Island, Kadane, prepared at Phillips Exeter Academy, earned an A.B. in mathematics from Harvard College and a Ph.D. in statistics from Stanford in 1966, under the supervision of Professor Herman Chernoff. While in graduate school, Kadane worked for the Center for Naval Analyses (CNA). Upon finishing, he accepted a joint appointment at the Yale statistics department and the Cowles Foundation. In 1968, he left Yale and served as an analyst at CNA for three years. In 1971, he moved to Pittsburgh to join Morris H. DeGroot at Carnegie Mellon University. He became the second tenured professor in the Department of Statistics. Kadane served as department head from 1972-1981 and steered the department to a balance between theoretical and applied work, advocating that statisticians should engage in joint research in substantive areas rather than acting as consultants.
Research
Kadane's contributions span a wide range of fields: econometrics, law, medicine, political science, sociology, computer science (see maximum subarray problem), archaeology, and environmental science, among others. He has been elected as a Fellow of the American Academy of Arts and Sciences, a fellow of the American Association for the Advancement of Science, a fellow of the American Statistical Association, and a fellow of the Institute of Mathematical Statistics. Kadane authored over 250 peer-reviewed publications and has served the statistical community in many capacities, including as editor of the Journal of the American Statistical Association from 1983-85.
Bibliography
References
External links
http://www.stat.cmu.edu/people/faculty/jay-kadane
http://www.stat.cmu.edu/~kadane
1941 births
Living people
American statisticians
Bayesian statisticians
Harvard College alumni
Carnegie Mellon University faculty
Fellows of the American Statistical Association
Stanford University alumni
Fellows of the American Academy of Arts and Sciences
Phillips Exeter Academy alumni
People from Freeport, New York
Mathematical statisticians
Yale University faculty |
https://en.wikipedia.org/wiki/Michel%20Demazure | Michel Demazure (; born 2 March 1937) is a French mathematician. He made contributions in the fields of abstract algebra, algebraic geometry, and computer vision, and participated in the Nicolas Bourbaki collective. He has also been president of the French Mathematical Society and directed two French science museums.
Biography
In the 1960s, Demazure was a student of Alexandre Grothendieck, and, together with Grothendieck, he ran and edited the Séminaire de Géométrie Algébrique du Bois Marie on group schemes at the Institut des Hautes Études Scientifiques near Paris from 1962 to 1964. Demazure obtained his doctorate from the Université de Paris in 1965 under Grothendieck's supervision, with a dissertation entitled Schémas en groupes réductifs. He was maître de conférence at Strasbourg University (1964–1966), and then university professor at Paris-Sud in Orsay (1966–1976) and the École Polytechnique in Palaiseau (1976–1999). From approximately 1965 to 1985, he was also one of the core members of the Bourbaki group, a group of French mathematicians writing under the collective pseudonym Nicolas Bourbaki.
In 1988 Demazure was the president of the Société Mathématique de France.
From 1991 to 1998, he was the director of the Palais de la Découverte in Paris and, from 1998 to 2002, the chairman of the Cité des Sciences et de l'Industrie in La Villette, two major science museums in France; in taking these positions, he changed places with Jean Audouze, who was at La Villette from 1993 to 1996, and became director of the Palais de la Découverte on Demazure's departure. Demazure also chairs the regional advisory committee of research for Languedoc-Roussillon.
Research contributions
In SGA3, Demazure introduced the definition of a root datum, a generalization of root systems for reductive groups that is central to the notion of Langlands duality. A 1970 paper of Demazure on subgroups of the Cremona group has been later recognized as the beginning of the study of toric varieties.
The Demazure character formula and Demazure modules and Demazure conjecture are named after Demazure, who wrote about them in 1974. Demazure modules are submodules of a finite-dimensional representation of a semisimple Lie algebra, and the Demazure character formula is an extension of the Weyl character formula to these modules. Demazure's work in this area was marred by a dependence on a false lemma in an earlier paper (also by Demazure); the flaw was pointed out by Victor Kac, and subsequent research clarified the conditions under which the formula remains valid.
Later in his career, Demazure's research emphasis shifted from pure mathematics to more computational problems, involving the application of algebraic geometry to image reconstruction problems in computer vision. The Kruppa–Demazure theorem, stemming from this work, shows that if a scene consisting of five points is viewed from two cameras with unknown positions but known focal lengths then, in general, there will be |
https://en.wikipedia.org/wiki/Pyrrho%27s%20lemma | In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the coefficients (signs and sizes), as well as predictions, the R-squared, the t-statistics, prediction- and confidence-intervals. The argument for the coefficients was advanced by Herman Wold and Lars Juréen but named, extended to include the other statistics and explained more fully by Theo Dijkstra. Dijkstra named it after the sceptic philosopher Pyrrho and concludes his article by noting that this lemma provides "some ground for a wide-spread scepticism concerning products of extensive datamining". One can only prove that a model 'works' by testing it on data different from the data that gave it birth.
The result has been discussed in the context of econometrics.
References
Theorems in statistics
Regression analysis
Lemmas |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Applied%20Mathematics%20and%20Computer%20Science | The International Journal of Applied Mathematics and Computer Science is a peer-reviewed quarterly scientific journal published since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The editor-in-chief is Józef Korbicz. The journal covers various fields related to control theory, applied mathematics, scientific computing, and computer science.
Indexing and abstracting
The journal is abstracted and indexed, e.g., in:
The full list of indexing services is available on the journal's website.
According to the Journal Citation Reports, the journal has a 2021 impact factor of 2.157.
References
External links
Computer science journals
Mathematics journals
English-language journals
Open access journals
Academic journals established in 1991
Quarterly journals
Polish Academy of Sciences academic journals |
https://en.wikipedia.org/wiki/The%20Code%20%28British%20TV%20programme%29 | The Code is a mathematics-based documentary television programme for BBC Two presented by Marcus du Sautoy, beginning on 27 July 2011 and ended on 10 August 2011. Each episode covers a different branch of mathematics. As well as being a documentary, The Code is also included a series of online challenges forming a treasure hunt, with clues to finding the treasure being included in the episodes, online games and other challenges.
Episodes
Treasure hunt
The treasure hunt is a series of online mathematical challenges. The BBC planned to offer the challenges to 1000 participants selected from among people who applied to participate via Twitter or email. There are three stages to the treasure hunt: The Codebreakers, the Ultimate Challenge, and the Finale.
Stage 1: The Codebreakers
The first puzzles are "The Codebreakers". These consist of three wheels, one relating to each episode. Each Codebreaker has six different questions and challenges relating to it, the answers to which surround the wheel. Answers to these questions can be found by watching the episode for clues, completing a flash game, solving a puzzle on the programme's blog or reaching a milestone in a mass community challenge, which involves trying to find examples of all the prime numbers between 2 and 2011 in the real world. Once a clue is found, the challenger can enter it into the Codebreaker by moving the correct "hand" around the Codebreaker. Each time a hand is moved, the password given changes. Each possible outcome of the Codebreaker produces a different password to the ultimate challenge. Entering the correct solutions into each of the three Codebreakers will result in the challenger getting the three correct passwords. Once these are entered, the Ultimate Challenge is accessible.
Stage 2: The Ultimate Challenge
The Ultimate Challenge was made accessible after all three episodes had been broadcast, and could only be accessed if the challenger entered all three passwords correctly. Once it was accessed, the first three eligible people to solve the Ultimate Challenge went through to the Finale.
Stage 3: The Finale
The Finale took place at Bletchley Park during the weekend of 10 September 2011. The prize, a specially commissioned mathematical sculpture of the platonic solids , was won by Pete Ryland.
References
External links
2011 British television series debuts
2011 British television series endings
2010s British documentary television series
BBC television documentaries
Documentary television series about mathematics
English-language television shows |
https://en.wikipedia.org/wiki/Andr%C3%A1s%20Fejes | András Fejes (born 26 August 1988, in Székesfehérvár) is a Hungarian football player who currently plays for III. Kerületi TVE.
Club statistics
References
Profile at HLSZ
1988 births
Living people
Footballers from Székesfehérvár
Hungarian men's footballers
Men's association football defenders
Fehérvár FC players
FC Felcsút players
Puskás Akadémia FC players
BFC Siófok players
MTK Budapest FC players
Paksi FC players
Győri ETO FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20NK%20Osijek%20season | This article shows statistics of individual players for the Osijek football club. It also lists all matches that Osijek played in the 2011–12 season.
First-team squad
Competitions
Overall
Prva HNL
Classification
Results summary
Results by round
Matches
Pre-season
Prva HNL
† Varaždin was expelled so the match was awarded as a 3–0 forfeit win to Osijek
Croatian Cup
Player seasonal records
Competitive matches only. Updated to games played 12 May 2012.
Goalscorers
Source: Competitive matches
Disciplinary record
Includes all competitive matches. Players with 1 card or more included only.
Source: Prva-HNL.hr
Appearances and goals
Source: Prva-HNL.hr
References
Croatian football clubs 2011–12 season
2011 |
https://en.wikipedia.org/wiki/Total%20active%20reflection%20coefficient | The total active reflection coefficient (TARC) within mathematics and physics scattering theory, relates the total incident power to the total outgoing power in an N-port microwave component. The TARC is mainly used for multiple-input multiple-output (MIMO) antenna systems and array antennas, where the outgoing power is unwanted reflected power. The name shows the similarities with the active reflection coefficient, which is used for single elements.
The TARC is the square root of the sum of all outgoing powers at the ports, divided by the sum of all incident powers at the ports of an N-port antenna. Similarly to the active reflection coefficient, the TARC is a function of frequency, and it also depends on scan angle and tapering. With this definition we can characterize the multi-port antenna’s frequency bandwidth and radiation performance. When the antennas are made of lossless materials, TARC can be computed directly from the scattering matrix by
where is the antenna's scattering matrix, is the excitation vector, and represents the scattered vector. The TARC is a real number between zero and one, although it is typically presented in decibel scale. When the value of the TARC is equal to zero, all the delivered power is accepted by the antenna and when it is equal to one, all the delivered is coming back as outgoing power (thus the all power is reflected, but not necessarily in the same port).
The normalized total accepted power is given by . Since antennas in general have radiation efficiency , the normalized total radiated power is given by . If the directivity of the antenna array is known, the realized gain can therefore be computed by multiplication by . As with all reflection coefficients, a small reflection coefficient does not guarantee a high radiation efficiency since the small reflected signal could also be due to losses.
See also
Active reflection coefficient
Antenna (radio)
Antenna array
References
Scattering theory
Matrices
Antennas (radio) |
https://en.wikipedia.org/wiki/Alain%20Lascoux | Alain Lascoux (17 October 1944 – 20 October 2013) was a French mathematician at Université de Paris VII, University of Marne la Vallée and Nankai University. His research was primarily in algebraic combinatorics, particularly Hecke algebras and Young tableaux.
Lascoux earned his doctorate in 1977 from the University of Paris. He worked for twenty years with Marcel-Paul Schützenberger on properties of the symmetric group. They wrote many articles together and had a major impact on the development of algebraic combinatorics. They succeeded in giving a combinatorial understanding of various algebraic and geometric questions in representation theory. Thus they introduced many new objects related to both fields like Schubert polynomials and Grothendieck polynomials, as well as novel terminology like the plactic monoid and vexillary permutations. They were also the first to define the crystal graph structure on Young tableaux (though not under this name).
Lascoux was an invited speaker at the 1998 International Congress of Mathematicians in Berlin, Germany.
See also
LLT polynomial
References
External links
Website at Université de Marne-la-Vallée
1944 births
University of Paris alumni
2013 deaths
Combinatorialists
20th-century French mathematicians
21st-century French mathematicians |
https://en.wikipedia.org/wiki/Leonid%20Polterovich | Leonid Polterovich (; ; born 30 August 1963) is a Russian-Israeli mathematician at Tel Aviv University. His research field includes symplectic geometry and dynamical systems.
A native of Moscow, Polterovich earned his undergraduate degree at Moscow State University in 1984. He moved to Israel after the collapse of communism, earning his doctorate from Tel Aviv University in 1990. In 1996, he was awarded the EMS Prize, and in 1998 the Erdős Prize. In 1998, he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He was a member of the faculty of the University of Chicago.
References
External links
Website at Tel Aviv University
1963 births
Living people
Russian Jews
Mathematicians from Moscow
Israeli mathematicians
Israeli people of Russian-Jewish descent
Moscow State University alumni
Tel Aviv University alumni
University of Chicago faculty
Russian emigrants to Israel
Erdős Prize recipients |
https://en.wikipedia.org/wiki/Big%20O | Big O or The Big O may refer to:
Fiction
The Big O, a 1999 Japanese animated TV series
Mathematics and computing
Big Omega function (disambiguation), various arithmetic functions in number theory
Big O notation, asymptotic behavior in mathematics and computing
Time complexity in computer science, whose functions are commonly expressed in big O notation
People
Omar Gooding (born 1976), American actor, rapper, voice artist and comedian
Oliver Miller (born 1970), former professional basketball player
Takashi Nagasaki (born 1958), Japanese author
Barack Obama (born 1961), 44th President of the United States
Roy Orbison (1936–1988), American singer-songwriter
Glenn Ordway (born 1951), Boston-area sports radio host
Otis Redding (1941–1967), American soul singer-songwriter and record producer
Oscar Robertson (born 1938), former professional basketball player
Oscar Santana, American radio personality
Oprah Winfrey (born 1954), American television host, producer and philanthropist
Oscar McInerney (born 1994), Australian rules footballer
Structures and venues
Big O (Ferris wheel), the world's largest centerless Ferris wheel, in Japan
Big "O", a structure on Skinner Butte in Eugene, Oregon, United States, listed on the National Register of Historic Places
Olympic Stadium (Montreal), Quebec, Canada; the main venue of the 1976 Summer Olympics
Ontario Motor Speedway, California, USA; former superspeedway racecar track
Other uses
Omega (Ω), a Greek letter, whose name translates literally as "great O"
Big O Tires, a tire retailer in the United States and Canada
The Big O (album), by Roy Orbison
Big Orange Chorus, a barbershop men's chorus in Jacksonville, Florida
See also
Bigo (disambiguation) |
https://en.wikipedia.org/wiki/Demazure%20module | In mathematics, a Demazure module, introduced by , is a submodule of a finite-dimensional representation generated by an extremal weight space under the action of a Borel subalgebra. The Demazure character formula, introduced by , gives the characters of Demazure modules, and is a generalization of the Weyl character formula.
The dimension of a Demazure module is a polynomial in the highest weight, called a Demazure polynomial.
Demazure modules
Suppose that g is a complex semisimple Lie algebra, with a Borel subalgebra b containing a Cartan subalgebra h. An irreducible finite-dimensional representation V of g splits as a sum of eigenspaces of h, and the highest weight space is 1-dimensional and is an eigenspace of b. The Weyl group W acts on the weights of V, and the conjugates wλ of the highest weight vector λ under this action are the extremal weights, whose weight spaces are all 1-dimensional.
A Demazure module is the b-submodule of V generated by the weight space of an extremal vector wλ, so the Demazure submodules of V are parametrized by the Weyl group W.
There are two extreme cases: if w is trivial the Demazure module is just 1-dimensional, and if w is the element of maximal length of W then the Demazure module is the whole of the irreducible representation V.
Demazure modules can be defined in a similar way for highest weight representations of Kac–Moody algebras, except that one now has 2 cases as one can consider the submodules generated by either the Borel subalgebra b or its opposite subalgebra. In the finite-dimensional these are exchanged by the longest element of the Weyl group, but this is no longer the case in infinite dimensions as there is no longest element.
Demazure character formula
History
The Demazure character formula was introduced by .
Victor Kac pointed out that Demazure's proof has a serious gap, as it depends on , which is false; see for Kac's counterexample. gave a proof of Demazure's character formula using the work on the geometry of Schubert varieties by and . gave a proof for sufficiently large dominant highest weight modules using Lie algebra techniques. proved a refined version of the Demazure character formula that conjectured (and proved in many cases).
Statement
The Demazure character formula is
Here:
w is an element of the Weyl group, with reduced decomposition w = s1...sn as a product of reflections of simple roots.
λ is a lowest weight, and eλ the corresponding element of the group ring of the weight lattice.
Ch(F(wλ)) is the character of the Demazure module F(wλ).
P is the weight lattice, and Z[P] is its group ring.
is the sum of fundamental weights and the dot action is defined by .
Δα for α a root is the endomorphism of the Z-module Z[P] defined by
and Δj is Δα for α the root of sj
References
Representation theory |
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20Ku%C4%8Dera%20%28footballer%2C%20born%201984%29 | Tomáš Kučera (born 19 June 1984) is a Slovak football player, who played in Slovakia and the Czech Republic as a goalkeeper.
Career statistics
References
External links
Guardian Football
1984 births
Living people
Slovak men's footballers
Men's association football goalkeepers
Czech First League players
FK Dukla Prague players
MFK Karviná players |
https://en.wikipedia.org/wiki/Dinostratus%27%20theorem | In geometry, Dinostratus' theorem describes a property of Hippias' trisectrix, that allows for the squaring the circle if the trisectrix can be used in addition to straightedge and compass. The theorem is named after the Greek mathematician Dinostratus who proved it around 350 BC when he attempted to square the circle himself.
The theorem states that Hippias' trisectrix divides one of the sides of its associated square in a ratio of .
Arbitrary points on Hippias' trisectrix itself however cannot be constructed by circle and compass alone but only a dense subset. In particular it is not possible to construct the exact point where the trisectrix meets the edge of the square. For this reason Dinostratus' approach is not considered a "real" solution of the classical problem of squaring the circle.
References
Thomas Little Heath: A History of Greek Mathematics. Volume 1. From Thales to Euclid. Clarendon Press 1921 (Nachdruck Elibron Classics 2006), S. 225–230 ()
Horst Hischer: Klassische Probleme der Antike – Beispiele zur „Historischen Verankerung“. In: Blankenagel, Jürgen & Spiegel, Wolfgang (Hrsg.): Mathematikdidaktik aus Begeisterung für die Mathematik — Festschrift für Harald Scheid. Stuttgart/Düsseldorf/Leipzig: Klett 2000, S. 97–118 (German).
Pi
Euclidean plane geometry |
https://en.wikipedia.org/wiki/Takayuki%20Fukumura | is a Japanese footballer who plays for FC Ryukyu.
Career statistics
Updated to 2 January 2020.
References
External links
Profile at FC Gifu
Profile at Shimizu S-Pulse
1991 births
Living people
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Kyoto Sanga FC players
People from Hirakata
Shimizu S-Pulse players
FC Gifu players
Gainare Tottori players
Tokyo Verdy players
FC Ryukyu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Atsutaka%20Nakamura | is a Japanese footballer who plays for Montedio Yamagata.
Career statistics
Club
Updated to 23 February 2019.
1Includes Promotion Playoffs, Suruga Bank Championship, J. League Championship and FIFA Club World Cup.
Honours
Club
Kyoto Sanga
Emperor's Cup Runner-up : 2011
Kashima Antlers
J1 League (1): 2016
Emperor's Cup (1): 2016
J. League Cup (1): 2015
Japanese Super Cup (1): 2017
Suruga Bank Championship (1): 2013
AFC Champions League (1): 2018
References
External links
Profile at Kashima Antlers
1990 births
Living people
Sportspeople from Sakai, Osaka
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kyoto Sanga FC players
Kashima Antlers players
Montedio Yamagata players
Men's association football forwards |
https://en.wikipedia.org/wiki/List%20of%20Brisbane%20Roar%20FC%20records%20and%20statistics | Brisbane Roar Football Club is an Australian professional association football club based in Milton, Brisbane. The club was formed in 1957 as Hollandia-Inala before it was renamed to Brisbane Lions in 1977, and then Queensland Lions in 2005. Brisbane Roar became the first Queensland member admitted into the A-League Men in 2005.
The list encompasses the honours won by Brisbane Roar at national and friendly level, records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Brisbane Roar players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at Lang Park, the club's home ground since 2005 and Dolphin Stadium are also included.
Brisbane Roar have won five top-flight titles. The club's record appearance maker is Matt McKay, who made 303 appearances between 2005 and 2019. Besart Berisha is Brisbane Roar's record goalscorer, scoring 50 goals in total.
All figures are correct as of 6 January 2023
Honours and achievements
Domestic
National Soccer League (until 2004) and A-League Men Premiership
Winners (2): 2010–11, 2013–14
Runners-up (1): 2011–12
National Soccer League (until 2004) and A-League Men Championship
Winners (3): 2011, 2012, 2014
NSL Cup
Winners (1): 1981
Other
Pre-season
Surf City Cup
Winners (1): 2019
Player records
Appearances
Most league appearances: Matt McKay, 272
Most FFA Cup appearances: Jamie Young, 6
Most Asian appearances: Thomas Broich, 14
Youngest first-team player: Jordan Courtney-Perkins, 16 years, 274 days (against Sydney FC, A-League, 7 August 2019)
Oldest first-team player: Massimo Maccarone, 38 years, 226 days (against Melbourne City, A-League, 20 April 2018)
Most consecutive appearances: Erik Paartalu, 85 (from 8 August 2010 to 12 January 2013)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored. Players in bold are currently playing for Brisbane Roar
a. Includes the National Soccer League and A-League Men.
b. Includes the A-League Pre-Season Challenge Cup and Australia Cup
c. Includes goals and appearances (including those as a substitute) in the 2005 Australian Club World Championship Qualifying Tournament.
Goalscorers
Most goals in a season: Besart Berisha, 23 goals (in the 2011–12 season)
Most league goals in a season: Besart Berisha, 21 goals in the A-League, 2011–12)
Most goals in a match: 4 goals (against Adelaide United, A-League, 28 October 2011)
Youngest goalscorer: Tommy Oar, 17 years, 18 days (against Wellington Phoenix, A-League, 28 December 2008)
Oldest goalscorer: Massimo Maccarone, 38 years, 156 days (against Melbourne Victory, A-League, 9 February 2018)
Top goalscorers
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate appearances ma |
https://en.wikipedia.org/wiki/Annamalai%20Ramanathan | Annamalai Ramanathan (29 August 1946 – 12 March 1993) was an Indian mathematician in the field of algebraic geometry, who introduced the notion of Frobenius splitting of algebraic varieties jointly with Vikram Bhagvandas Mehta in . The notion of Frobenius splitting led to the solution of many classical problems, in particular a proof of the Demazure character formula and results on the equations defining Schubert varieties in general flag manifolds.
Research career
Ramanathan got his B.Sc in Mathematics at Ramakrishna Mission Vivekananda College, and was recruited to attend TIFR, where he got his Ph.D. in Mathematics in 1976. His thesis on moduli for principal bundles was published in 1996 in two papers in Proc. Indian Acad. Sci. three years after his death.
Ramanathan, was a Professor of Mathematics at the TIFR in Bombay, India. He has also been employed at University of Bonn, Johns Hopkins University and University of Illinois at Urbana-Champaign. Ramanathan made significant contributions to many areas of mathematics, including moduli of vector bundles, Gauge theory, algebraic geometry in positive characteristic and representation theory.
Awards
The Council of Scientific and Industrial Research awarded he and his collaborator Vikram Bhagvandas Mehta the Shanti Swarup Bhatnagar Prize for Science and Technology (the Indian Presidential award for achievement in the mathematical sciences) in 1991 for his work in algebraic geometry.
Personal life
Ramanathan was third of four children born to a Tamil family S. RM. CT. Annamalai and Lakshmi. Ramanathan was crippled
by adult onset polio in his late teens, and he used a crutch for the rest of his life.
During his tenure as a visiting professor at University of Illinois at Urbana-Champaign, Ramanathan died in Chicago, Friday, 12 March 1993, of complications
following treatment for a heart attack. He is survived by his wife RM. Vasantha and three daughters Lakshmi Valli Priya.
Sources
External links
Annamalai Ramanathan citation
References
20th-century Indian mathematicians
1993 deaths
1949 births
Tata Institute of Fundamental Research alumni
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
Polio survivors |
https://en.wikipedia.org/wiki/Vikram%20Bhagvandas%20Mehta | Vikram Bhagvandas Mehta (August 15, 1946 – June 4, 2014) was an Indian mathematician who worked on algebraic geometry and vector bundles. Together with Annamalai Ramanathan he introduced the notion of Frobenius split varieties, which led to the solution of several problems about Schubert varieties. He is also known to have worked, from the 2000s onward, on the fundamental group scheme. It was precisely in the year 2002 when he and Subramanian published a proof of a conjecture by Madhav V. Nori that brought back into the limelight the theory of an object that until then had met with little success.
Awards
The Council of Scientific and Industrial Research awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology in 1991 for his work in algebraic geometry.
References
External links
Vikram Bhagvandas Mehta citation
20th-century Indian mathematicians
Living people
1946 births
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/G%C3%A1bor%20J%C3%A1nv%C3%A1ri | Gábor Jánvári (born 25 April 1990) is a Hungarian football player.
Club statistics
Updated to games played as of 30 September 2018.
References
External links
Player profile at HLSZ
1990 births
Living people
People from Kisvárda
Hungarian men's footballers
Men's association football defenders
Kaposvári Rákóczi FC players
Kisvárda FC players
Nyíregyháza Spartacus FC players
Szombathelyi Haladás footballers
BFC Siófok players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Footballers from Szabolcs-Szatmár-Bereg County
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Frobenius%20splitting | In mathematics, a Frobenius splitting, introduced by , is a splitting of the injective morphism OX→F*OX from a structure sheaf OX of a characteristic p > 0 variety X to its image F*OX under the Frobenius endomorphism F*.
give a detailed discussion of Frobenius splittings.
A fundamental property of Frobenius-split projective schemes X is that the higher cohomology Hi(X,L) (i > 0) of ample line bundles L vanishes.
References
External links
Conference on Frobenius splitting in algebraic geometry, commutative algebra, and representation theory at Michigan, 2010.
Algebraic geometry |
https://en.wikipedia.org/wiki/Mehdi%20Nasiri | Mehdi Nasiri (, born 11 November 1987 in Isfahan, Iran) is an Iranian association footballer who currently plays for Giti Pasand Fc in Azadegan League.
Club career
Club career statistics
Last Update 24 November 2012
Assist Goals
Honours
Club
Sepahan
Iran Pro League (2): 2010–11, 2011–12
References
1987 births
Living people
Footballers from Isfahan
Sanaye Giti Pasand F.C. players
Iranian men's footballers
Sepahan S.C. footballers
Men's association football defenders |
https://en.wikipedia.org/wiki/Continuous%20geometry | In mathematics, continuous geometry is an analogue of complex projective geometry introduced by , where instead of the dimension of a subspace being in a discrete set , it can be an element of the unit interval . Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.
Definition
Menger and Birkhoff gave axioms for projective geometry in terms of the lattice of linear subspaces of projective space. Von Neumann's axioms for continuous geometry are a weakened form of these axioms.
A continuous geometry is a lattice L with the following properties
L is modular.
L is complete.
The lattice operations ∧, ∨ satisfy a certain continuity property,
, where A is a directed set and if then , and the same condition with ∧ and ∨ reversed.
Every element in L has a complement (not necessarily unique). A complement of an element a is an element b with , , where 0 and 1 are the minimal and maximal elements of L.
L is irreducible: this means that the only elements with unique complements are 0 and 1.
Examples
Finite-dimensional complex projective space, or rather its set of linear subspaces, is a continuous geometry, with dimensions taking values in the discrete set
The projections of a finite type II von Neumann algebra form a continuous geometry with dimensions taking values in the unit interval .
showed that any orthocomplemented complete modular lattice is a continuous geometry.
If V is a vector space over a field (or division ring) F, then there is a natural map from the lattice PG(V) of subspaces of V to the lattice of subspaces of that multiplies dimensions by 2. So we can take a direct limit of
This has a dimension function taking values all dyadic rationals between 0 and 1. Its completion is a continuous geometry containing elements of every dimension in . This geometry was constructed by , and is called the continuous geometry over F
Dimension
This section summarizes some of the results of . These results are similar to, and were motivated by, von Neumann's work on projections in von Neumann algebras.
Two elements a and b of L are called perspective, written , if they have a common complement. This is an equivalence relation on L; the proof that it is transitive is quite hard.
The equivalence classes A, B, ... of L have a total order on them defined by if there is some a in A and b in B with . (This need not hold for all a in A and b in B.)
The dimension function D from L to the unit interval is defined as follows.
If equivalence classes A and B contain elements a and b with then their sum is defined to be the equivalence class of . Otherwise the sum is not defined. For a positive integer n, the product nA is defined to be the sum of n copies of A, if this sum is defined.
For equivalence classes A and B with A not {0} the integer |
https://en.wikipedia.org/wiki/Series%20multisection | In mathematics, a multisection of a power series is a new power series composed of equally spaced terms extracted unaltered from the original series. Formally, if one is given a power series
then its multisection is a power series of the form
where p, q are integers, with 0 ≤ p < q. Series multisection represents one of the common transformations of generating functions.
Multisection of analytic functions
A multisection of the series of an analytic function
has a closed-form expression in terms of the function :
where is a primitive q-th root of unity. This expression is often called a root of unity filter. This solution was first discovered by Thomas Simpson. This expression is especially useful in that it can convert an infinite sum into a finite sum. It is used, for example, in a key step of a standard proof of Gauss's digamma theorem, which gives a closed-form solution to the digamma function evaluated at rational values p/q.
Examples
Bisection
In general, the bisections of a series are the even and odd parts of the series.
Geometric series
Consider the geometric series
By setting in the above series, its multisections are easily seen to be
Remembering that the sum of the multisections must equal the original series, we recover the familiar identity
Exponential function
The exponential function
by means of the above formula for analytic functions separates into
The bisections are trivially the hyperbolic functions:
Higher order multisections are found by noting that all such series must be real-valued along the real line. By taking the real part and using standard trigonometric identities, the formulas may be written in explicitly real form as
These can be seen as solutions to the linear differential equation with boundary conditions , using Kronecker delta notation. In particular, the trisections are
and the quadrisections are
Binomial series
Multisection of a binomial expansion
at x = 1 gives the following identity for the sum of binomial coefficients with step q:
References
Somos, Michael A Multisection of q-Series, 2006.
Algebra
Combinatorics
Mathematical analysis
Complex analysis
Mathematical series |
https://en.wikipedia.org/wiki/Tikhonov%27s%20theorem%20%28dynamical%20systems%29 | In applied mathematics, Tikhonov's theorem on dynamical systems is a result on stability of solutions of systems of differential equations. It has applications to chemical kinetics. The theorem is named after Andrey Nikolayevich Tikhonov.
Statement
Consider this system of differential equations:
Taking the limit as , this becomes the "degenerate system":
where the second equation is the solution of the algebraic equation
Note that there may be more than one such function .
Tikhonov's theorem states that as the solution of the system of two differential equations above approaches the solution of the degenerate system if is a stable root of the "adjoined system"
References
Differential equations
Perturbation theory
Theorems in dynamical systems |
https://en.wikipedia.org/wiki/Rank%20ring | In mathematics, a rank ring is a ring with a real-valued rank function behaving like the rank of an endomorphism. introduced rank rings in his work on continuous geometry, and showed that the ring associated to a continuous geometry is a rank ring.
Definition
defined a ring to be a rank ring if it is regular and has a real-valued rank function R with the following properties:
0 ≤ R(a) ≤ 1 for all a
R(a) = 0 if and only if a = 0
R(1) = 1
R(ab) ≤ R(a), R(ab) ≤ R(b)
If e2 = e, f 2 = f, ef = fe = 0 then R(e + f ) = R(e) + R(f ).
References
Ring theory |
https://en.wikipedia.org/wiki/Semyon%20Alesker | Semyon Alesker (; born 1972 in Moscow, Soviet Union) is an Israeli mathematician at Tel Aviv University. For his contributions in convex geometry and integral geometry, in particular his work on valuations, he won the EMS Prize in 2000, and the Erdős Prize in 2004.
References
External links
Website at Tel Aviv University
1972 births
Living people
Israeli mathematicians
Academic staff of Tel Aviv University
Erdős Prize recipients |
https://en.wikipedia.org/wiki/Rapha%C3%ABl%20Cerf | Raphaël Cerf is a French mathematician at Paris-Sud 11 University. For his contributions to probability theory, he won the Rollo Davidson Prize in 1999, and the EMS Prize in 2000. He was an Invited Speaker at the ICM in 2006 in Madrid.
Selected works
The Wulff Crystal in Ising and Percolation models. Springer, Lecture Notes in Mathematics 1878, École d’été de probabilités de Saint-Flour, no. 34, 2004
On Cramérs Theory in infinite dimensions. Société Mathématique de France, 2007
Large deviations for three dimensional supercritical percolation. Société Mathématique de France, 2000
References
External links
Website at Paris-Sud 11 University
1969 births
Living people
French mathematicians
Academic staff of the University of Paris |
https://en.wikipedia.org/wiki/Lucas%20Parodi | Lucas Parodi (born 30 November 1990) is an Argentine football midfielder who plays for Temperley.
External links
GOAL statistics
BDFA profile
1990 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Men's association football defenders
Club Atlético Belgrano footballers
C.D. Cobresal footballers
Chilean Primera División players
Argentine Primera División players
Expatriate men's footballers in Chile |
https://en.wikipedia.org/wiki/Christian%20Gro%C3%9F | Christian Groß (born 8 February 1989) is a German professional footballer who plays as a defensive midfielder or centre back for Bundesliga club Werder Bremen.
Career statistics
References
External links
1989 births
Living people
German men's footballers
Footballers from Bremen (city)
Men's association football midfielders
Germany men's youth international footballers
Bundesliga players
2. Bundesliga players
3. Liga players
Regionalliga players
Hamburger SV II players
Hamburger SV players
SV Babelsberg 03 players
Sportfreunde Lotte players
VfL Osnabrück players
SV Werder Bremen II players
SV Werder Bremen players |
https://en.wikipedia.org/wiki/Weinan%20E | Weinan E (; born September 1963) is a Chinese mathematician. He is known for his pathbreaking work in applied mathematics and machine learning. His academic contributions include novel mathematical and computational results in stochastic differential equations; design of efficient algorithms to compute multiscale and multiphysics problems, particularly those arising in fluid dynamics and chemistry; and pioneering work on the application of deep learning techniques to scientific computing. In addition, he has worked on multiscale modeling and the study of rare events.
He has also made contributions to homogenization theory, theoretical models of turbulence, stochastic partial differential equations, electronic structure analysis, multiscale methods, computational fluid dynamics, and weak KAM theory. He is currently a professor in the Department of Mathematics and Program in Applied and Computational Mathematics at Princeton University, and the Center for Machine Learning Research and the
School of Mathematical Sciences at Peking University. Since 2015, he has been the inaugural director of the Beijing Institute of Big Data Research. He was an invited Plenary Speaker of the International Congress of Mathematicians 2022 in St. Petersburg.
Biography
E Weinan was born in Jingjiang, China. He completed his undergraduate studies in the Department of Mathematics at University of Science and Technology of China in 1982, and his master's degree in Academy of Mathematics and Systems Science at Chinese Academy of Sciences in 1985. He obtained his Ph.D. degree under the advice of Björn Engquist in the Department of Mathematics at University of California, Los Angeles in 1989. He then became a visiting member in Courant Institute, New York University from 1989 to 1991, and a member in Institute for Advanced Study from 1991 to 1992. After spending two more years as a long term member in Institute for Advanced Study, he joined Courant Institute, New York University as an associate professor in 1994, and became a full professor in 1997. Since 1999, he has been holding a professorship in the Department of Mathematics and Program in Applied and Computational Mathematics at Princeton University. He currently holds a professorship at the Center for Machine Learning Research and the School of Mathematical Sciences at Peking University.
He has made contributions to homogenization theory, theoretical models of turbulence, stochastic partial differential equations, electronic structure analysis, multiscale methods, computational fluid dynamics, and weak KAM theory.
In the study of rare events, he and collaborators have developed the string method and transition path theory. In multiscale modeling, he and collaborators have developed the heterogeneous multiscale methods (HMM). He has also made significant contributions to the mathematical understanding of the microscopic foundation to the macroscopic theories for solids.
Awards
He received Presidential Early Career |
https://en.wikipedia.org/wiki/Utti%20Air%20Base | Utti Air Base () is a military airport located in Utti, Kouvola, Finland, east of Kouvola city centre. The helicopter battalion of the Utti Jaeger Regiment is based here.
Statistics
See also
List of the largest airports in the Nordic countries
References
External links
AIP Finland – Utti Airport
Airports in Finland
Kouvola
Finnish Air Force bases
Buildings and structures in Kymenlaakso |
https://en.wikipedia.org/wiki/Sherman%E2%80%93Takeda%20theorem | In mathematics, the Sherman–Takeda theorem states that if A is a C*-algebra then its double dual is a W*-algebra, and is isomorphic to the weak closure of A in the universal representation of A.
The theorem was announced by and proved by . The double dual of A is called the universal enveloping W*-algebra of A.
References
Banach algebras
C*-algebras
Functional analysis
Operator theory
Von Neumann algebras |
https://en.wikipedia.org/wiki/Hindley%E2%80%93Milner%20type%20system | A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis.
Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity. HM is preferably used for functional languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably with type class constraints like those in Haskell.
Introduction
As a type inference method, Hindley–Milner is able to deduce the types of variables, expressions and functions from programs written in an entirely untyped style. Being scope sensitive, it is not limited to deriving the types only from a small portion of source code, but rather from complete programs or modules. Being able to cope with parametric types, too, it is core to the type systems of many functional programming languages. It was first applied in this manner in the ML programming language.
The origin is the type inference algorithm for the simply typed lambda calculus that was devised by Haskell Curry and Robert Feys in 1958.
In 1969, J. Roger Hindley extended this work and proved that their algorithm always inferred the most general type.
In 1978, Robin Milner, independently of Hindley's work, provided an equivalent algorithm, Algorithm W.
In 1982, Luis Damas finally proved that Milner's algorithm is complete and extended it to support systems with polymorphic references.
Monomorphism vs. polymorphism
In the simply typed lambda calculus, types are either atomic type constants or function types of form . Such types are monomorphic. Typical examples are the types used in arithmetic values:
3 : Number
add 3 4 : Number
add : Number -> Number -> Number
Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function
id ≡ λ x . x
which simply returns whatever value it is applied to. Less trivial examples include parametric types like lists.
While polymorphism in general means that operations accept values of more than one type, the polymorphism used here is parametric. One finds the notation of type schemes in the literature, too, emphasizing the parametric nature of the polymorphism. Additionally, constants may be typed with (quantified) type variables. E.g.:
cons : forall a . a -> List a -> List a
nil : forall a . List a
id : forall a . |
https://en.wikipedia.org/wiki/Theorycraft | Theorycraft (or theorycrafting) is the mathematical analysis of game mechanics, usually in video games, to discover optimal strategies and tactics. Theorycraft involves analyzing statistics, hidden systems, or underlying game code in order to glean information that is not apparent during normal gameplay. Theorycraft is similar to analyses performed in sports or other games, such as baseball's sabermetrics. The term has been said to come from StarCraft players as a portmanteau of "game theory" and "StarCraft".
Theorycraft is prominent in multiplayer games, where players attempt to gain competitive advantage by analyzing game systems. As a result, theorycraft can lower barriers between players and game designers. Game designers must consider that players will have a comprehensive understanding of game systems; and players can influence design by exploiting game systems and discovering dominant or unintended strategies.
The way players theorycraft varies from game to game, but often games under the same genres (e.g. collectible card games, MMORPGs, turn-based strategy) will have similar theorycrafting methods. Communities develop standardized ways to communicate their findings, including use of specialized tools to measure and record game data, and terminology and simulations to represent certain data. Theorycrafts proven potent usually find inclusion in the metagame. Knowledge from theorycrafts are often communicated through blogs, community forums, or game guides.
The term theorycraft can be used in a pejorative sense. In this sense, "theorycraft" refers to naïve or impractical theorizing that would not succeed during actual gameplay.
See also
Econometrics
References
Game theory
Video game gameplay |
https://en.wikipedia.org/wiki/Levente%20Lantos | Levente Lantos (born 26 July 1980) is a Hungarian former football player.
Club statistics
Updated to games played as of 28 November 2014.
References
Profile at HLSZ
1980 births
Living people
Footballers from Pécs
Hungarian men's footballers
Men's association football midfielders
Pécsi MFC players
Komlói Bányász SK footballers
Kozármisleny SE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/1991%20Croatian%20census | The 1991 population census in Croatia was the last census of the population of Croatia taken before the Croatian War of Independence. It was conducted by the Croatian Bureau of Statistics during the final week of March 1991. For the 1991 census there were 106 municipalities of which five were part of Zagreb.
Population by ethnicity
TOTAL = 4,784,265
Croats = 3,736,356 (78.1%)
Serbs = 581,663 (12.2%)
Yugoslavs = 106,041 (2.2%)
ethnic Muslims = 43,469 (0.9%)
Slovenes = 22,376 (0.5%)
Hungarians = 22,355 (0.5%)
Italians = 21,303 (0.4%)
Czechs = 13,086 (0.3%)
Albanians = 12,032 (0.3%)
Montenegrins = 9,724 (0.2%)
Romani = 6,695 (0.1%)
Macedonians = 6,280 (0.1%)
Slovaks = 6,606 (0.1%)
Rusyns 3,253 (0.1%)
Germans = 2,635 (0.1%)
Ukrainians = 2,494
Romanians = 810
Russians = 706
Poles = 679
Jews = 600
Bulgarians = 458
Turks = 320
Greeks = 281
Austrians = 214
Vlachs and Morlachs = 22
others = 3,012
unspecified = 73,376
regional affiliation = 45,493
unknown = 62,926
By municipality
References
Croatia
Population
Demographic history of Croatia
Croatia |
https://en.wikipedia.org/wiki/Noncentral%20beta%20distribution | In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a noncentral generalization of the (central) beta distribution.
The noncentral beta distribution (Type I) is the distribution of the ratio
where is a noncentral chi-squared random variable with degrees of freedom m and noncentrality parameter , and is a central chi-squared random variable with degrees of freedom n, independent of .
In this case,
A Type II noncentral beta distribution is the distribution
of the ratio
where the noncentral chi-squared variable is in the denominator only. If follows
the type II distribution, then follows a type I distribution.
Cumulative distribution function
The Type I cumulative distribution function is usually represented as a Poisson mixture of central beta random variables:
where λ is the noncentrality parameter, P(.) is the Poisson(λ/2) probability mass function, \alpha=m/2 and \beta=n/2 are shape parameters, and is the incomplete beta function. That is,
The Type II cumulative distribution function in mixture form is
Algorithms for evaluating the noncentral beta distribution functions are given by Posten and Chattamvelli.
Probability density function
The (Type I) probability density function for the noncentral beta distribution is:
where is the beta function, and are the shape parameters, and is the noncentrality parameter. The density of Y is the same as that of 1-X with the degrees of freedom reversed.
Related distributions
Transformations
If , then follows a noncentral F-distribution with degrees of freedom, and non-centrality parameter .
If follows a noncentral F-distribution with numerator degrees of freedom and denominator degrees of freedom, then
follows a noncentral Beta distribution:
.
This is derived from making a straightforward transformation.
Special cases
When , the noncentral beta distribution is equivalent to the (central) beta distribution.
References
Citations
Sources
M. Abramowitz and I. Stegun, editors (1965) "Handbook of Mathematical Functions", Dover: New York, NY.
Christian Walck, "Hand-book on Statistical Distributions for experimentalists."
Continuous distributions
b |
https://en.wikipedia.org/wiki/Roland%20Giberti | Roland Giberti, born in Gémenos (Bouches-du-Rhône department, Provence-Alpes-Côte-d'Azur region)) in 1951, is a French politician belonging to the Nouveau Centre party.
Trained as a mathematics' teacher, he was elected mayor of Gémenos in 2001, after having served eighteen years (since 1983) as a member of the city council. He was elected representative in the general council (Conseil général) of the Bouches-du-Rhône department in 2004 for the canton of Aubagne-Est. He is also vice-president of the Urban Community of Marseille Provence Métropole.
Notes and references
French politicians
1951 births
Living people |
https://en.wikipedia.org/wiki/Lange%20%28Brazilian%20footballer%29 | Marcos Antonio Menezes Godoi (born December 18, 1966) is a former Brazilian football player.
Club statistics
References
External links
1966 births
Living people
Brazilian men's footballers
Japan Soccer League players
J1 League players
Cerezo Osaka players
Gamba Osaka players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/Gonzalo%20Espinoza | Gonzalo Alejandro Espinoza Toledo (born 9 April 1990), known as Gonzalo Espinoza, is a Chilean footballer who plays for Unión San Felipe as a midfielder.
Career statistics
International career
He got his first call up to the senior Chile squad for a friendly against the United States in January 2015 and made his international debut in the match.
Notes
References
External links
1990 births
Living people
People from Constitución, Chile
Footballers from Maule Region
Men's association football midfielders
Chilean men's footballers
Chile men's international footballers
Chilean expatriate men's footballers
Tercera División de Chile players
Chilean Primera División players
Argentine Primera División players
Süper Lig players
A.C. Barnechea footballers
Unión San Felipe footballers
Racing Club de Avellaneda footballers
Arsenal de Sarandí footballers
All Boys footballers
Club Universidad de Chile footballers
Club Atlético Patronato footballers
Kayserispor footballers
Unión Española footballers
Chilean expatriate sportspeople in Argentina
Chilean expatriate sportspeople in Turkey
Expatriate men's footballers in Argentina
Expatriate men's footballers in Turkey |
https://en.wikipedia.org/wiki/Ed%20Perkins | Edwin Arend Perkins, (born 31 August 1953) is a Canadian mathematician who has been Professor of Mathematics at the University of British Columbia since 1989 and Canada Research Chair in Probability since 2001. He was elected to the Royal Society of Canada in 1988 and to the Royal Society in 2007. He won the 2003 CRM-Fields-PIMS prize.
He obtained his PhD in 1979 under the supervision of Frank Bardsley Knight at the University of Illinois at Urbana–Champaign with a dissertation titled 'A Nonstandard Approach to Brownian Local Time'.
References
1953 births
Fellows of the Royal Society
Fellows of the Royal Society of Canada
Academic staff of the University of British Columbia
Canada Research Chairs
Living people
Probability theorists |
https://en.wikipedia.org/wiki/Askey%20scheme | In mathematics, the Askey scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in , the Askey scheme was first drawn by and by , and has since been extended by and to cover basic orthogonal polynomials.
Askey scheme for hypergeometric orthogonal polynomials
give the following version of the Askey scheme:
Wilson | Racah
Continuous dual Hahn | Continuous Hahn | Hahn | dual Hahn
Meixner–Pollaczek | Jacobi | Pseudo Jacobi | Meixner | Krawtchouk
Laguerre | Bessel | Charlier
Hermite
Here indicates a hypergeometric series representation with parameters
Askey scheme for basic hypergeometric orthogonal polynomials
give the following scheme for basic hypergeometric orthogonal polynomials:
43 Askey–Wilson | q-Racah
32 Continuous dual q-Hahn | Continuous q-Hahn | Big q-Jacobi | q-Hahn | dual q-Hahn
21 Al-Salam–Chihara | q-Meixner–Pollaczek | Continuous q-Jacobi | Big q-Laguerre | Little q-Jacobi | q-Meixner | Quantum q-Krawtchouk | q-Krawtchouk | Affine q-Krawtchouk | Dual q-Krawtchouk
20/11 Continuous big q-Hermite | Continuous q-Laguerre | Little q-Laguerre | q-Laguerre | q-Bessel | q-Charlier | Al-Salam–Carlitz I | Al-Salam–Carlitz II
10 Continuous q-Hermite | Stieltjes–Wigert | Discrete q-Hermite I | Discrete q-Hermite II
Completeness
While there are several approaches to constructing still more general families of orthogonal polynomials, it is usually not possible to extend the Askey scheme by reusing hypergeometric functions of the same form. For instance, one might naively hope to find new examples given by
above which corresponds to the Wilson polynomials. This was ruled out in under the assumption that the are degree 1 polynomials such that
for some polynomial .
References
Orthogonal polynomials
Hypergeometric functions
Q-analogs |
https://en.wikipedia.org/wiki/Jo%C3%A3o%20Filipe | João Filipe Rabelo da Costa Silva (born 11 June 1988), known as João Filipe, is a Brazilian footballer who plays a central defender or a defensive midfielder for Tombense.
Career
Career statistics
As of 21 September 2011
Honours
São Paulo
Copa Sudamericana: 2012
External links
Profile at IG Esporte's website
1988 births
Living people
Brazilian men's footballers
Men's association football defenders
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Figueirense FC players
Botafogo de Futebol e Regatas players
São Paulo FC players
Clube Náutico Capibaribe players
Avaí FC players
Fluminense FC players
Atlético Clube Goianiense players
Footballers from Rio de Janeiro (city) |
https://en.wikipedia.org/wiki/L-semi-inner%20product | In mathematics, there are two different notions of semi-inner-product. The first, and more common, is that of an inner product which is not required to be strictly positive. This article will deal with the second, called a L-semi-inner product or semi-inner product in the sense of Lumer, which is an inner product not required to be conjugate symmetric. It was formulated by Günter Lumer, for the purpose of extending Hilbert space type arguments to Banach spaces in functional analysis. Fundamental properties were later explored by Giles.
Definition
We mention again that the definition presented here is different from that of the "semi-inner product" in standard functional analysis textbooks, where a "semi-inner product" satisfies all the properties of inner products (including conjugate symmetry) except that it is not required to be strictly positive.
A semi-inner-product, L-semi-inner product, or a semi-inner product in the sense of Lumer for a linear vector space over the field of complex numbers is a function from to usually denoted by , such that for all
Nonnegative-definiteness:
Linearity in the 1st argument, meaning:
Additivity in the 1st argument:
Homogeneity in the 1st argument:
Conjugate homogeneity in the 2nd argument:
Cauchy-Schwarz inequality:
Difference from inner products
A semi-inner-product is different from inner products in that it is in general not conjugate symmetric, that is,
generally. This is equivalent to saying that
In other words, semi-inner-products are generally nonlinear about its second variable.
Semi-inner-products for normed spaces
If is a semi-inner-product for a linear vector space then defines a norm on .
Conversely, if is a normed vector space with the norm then there always exists a (not necessarily unique) semi-inner-product on that is consistent with the norm on in the sense that
Examples
The Euclidean space with the norm ()
has the consistent semi-inner-product:
where
In general, the space of -integrable functions on a measure space where with the norm
possesses the consistent semi-inner-product:
Applications
Following the idea of Lumer, semi-inner-products were widely applied to study bounded linear operators on Banach spaces.
In 2007, Der and Lee applied semi-inner-products to develop large margin classification in Banach spaces.
Recently, semi-inner-products have been used as the main tool in establishing the concept of reproducing kernel Banach spaces for machine learning.
Semi-inner-products can also be used to establish the theory of frames, Riesz bases for Banach spaces.
See also
References
Functional analysis |
https://en.wikipedia.org/wiki/South%20Sudan%20national%20football%20team%20results | This page details the match results and statistics of the South Sudan national football team.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
South Sudan's score is shown first in each case.
Notes
Record by opponent
References
South Sudan national football team results |
https://en.wikipedia.org/wiki/Favard%27s%20theorem | In mathematics, Favard's theorem, also called the Shohat–Favard theorem, states that a sequence of polynomials satisfying a suitable 3-term recurrence relation is a sequence of orthogonal polynomials. The theorem was introduced in the theory of orthogonal polynomials by and , though essentially the same theorem was used by Stieltjes in the theory of continued fractions many years before Favard's paper, and was rediscovered several times by other authors before Favard's work.
Statement
Suppose that y0 = 1, y1, ... is a sequence of polynomials where yn has degree n. If this is a sequence of orthogonal polynomials for some positive weight function then it satisfies a 3-term recurrence relation. Favard's theorem is roughly a converse of this, and states that if these polynomials satisfy a 3-term recurrence relation of the form
for some numbers cn and dn,
then the polynomials yn form an orthogonal sequence for some linear functional Λ with Λ(1)=1; in other words Λ(ymyn) = 0 if m ≠ n.
The linear functional Λ is unique, and is given by Λ(1) = 1, Λ(yn) = 0 if n > 0.
The functional Λ satisfies Λ(y) = dn Λ(y), which implies that Λ is positive definite if (and only if) the numbers cn are real and the numbers dn are positive.
See also
Jacobi operator
James Alexander Shohat
References
Reprinted by Dover 2011,
Orthogonal polynomials
Theorems in approximation theory |
https://en.wikipedia.org/wiki/Richard%20Johnsonbaugh | Richard F. Johnsonbaugh (born 1941) is an American mathematician and computer scientist. His interests include discrete mathematics and the history of mathematics. He is the author of several textbooks.
Johnsonbaugh earned a bachelor's degree in mathematics from Yale University, and then moved to the University of Oregon for graduate study. He completed his Ph.D. at Oregon in 1969. His dissertation, I. Classical Fundamental Groups and Covering Space Theory in the Setting of Cartan and Chevalley; II. Spaces and Algebras of Vector-Valued Differentiable Functions, was supervised by Bertram Yood. He also has a second master's degree in computer science from the University of Illinois at Chicago.
He is currently professor emeritus at De Paul University.
Books
Discrete Mathematics (MacMillan, 1984; 8th ed., Pearson, 2018)
Foundations of Mathematical Analysis (with W. E. Pfaffenberger, Marcel Dekker, 1981; Dover, 2010)
Applications Programming in ANSI C (with Martin Kalin, Prentice Hall, 1993; 3rd ed., 1996)
Object-oriented Programming in C++ (with Martin Kalin, Prentice Hall, 1995)
Algorithms (with Marcus Schaefer, Prentice Hall, 2003)
References
External links
Richard Johnsonbaugh's webpage at De Paul
20th-century American mathematicians
21st-century American mathematicians
American computer scientists
Living people
Yale University alumni
University of Oregon alumni
University of Illinois Chicago alumni
DePaul University faculty
1941 births
American textbook writers |
https://en.wikipedia.org/wiki/Bence%20Gyurj%C3%A1n | Bence Gyurján (born 21 February 1992) is a Hungarian football player who plays for Tiszakécske. His brother Márton is a footballer too.
Club statistics
Updated to games played as of 26 October 2014.
References
HLSZ
1992 births
Living people
Footballers from Nyíregyháza
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Szombathelyi Haladás footballers
Gyirmót FC Győr players
Békéscsaba 1912 Előre footballers
Nyíregyháza Spartacus FC players
Tiszakécske FC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/WPS%20records%20and%20statistics | Women's Professional Soccer (WPS) was an American professional women's soccer league that operated as the top division of women's soccer in the United States. The league was formed in 2008 and dissolved in 2012. Below are notable records and statistics for WPS teams, players, and seasons, all as of the end of the league's final season in 2011.
WPS champions and runners-up
Career leaders
All-time table
Average season attendances
Records
Longest winning streak to start a season: 3 wins
Los Angeles Sol (2009)
magicJack (2011)
Longest winning streak to end a season: 5, Western New York Flash (2011)
Longest unbeaten streak to start a season: 8, Western New York Flash (2011; 7W, 1T)
Longest unbeaten streak to end a season: 13, FC Gold Pride (2010; 9W, 4T)
Trivia
No team played in every playoff series.
If magicJack is considered to be the continuation of the Washington Freedom, that team qualified for every playoff series.
Two core groups of players have played together in all three seasons and qualified for the playoffs:
Freedom-magicJack, centered on Abby Wambach
Sol-Gold Pride-Flash, centered on Marta
The team to win the regular season in each of the league's first two seasons, which were also the league's attendance leaders, folded during the following offseason.
See also
Annual Women's Professional Soccer awards
List of Women's Professional Soccer stadiums
List of WPS drafts
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References
General
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https://en.wikipedia.org/wiki/Susanna%20S.%20Epp | Susanna Samuels Epp (born 1943) is an author, mathematician, and professor. Her interests include discrete mathematics, mathematical logic, cognitive psychology, and mathematics education, and she has written numerous articles, publications, and textbooks. She is currently professor emerita at DePaul University, where she chaired the Department of Mathematical Sciences and was Vincent de Paul Professor in Mathematics.
Education and career
Epp holds degrees in mathematics from Northwestern University and the University of Chicago, where she completed her doctorate in 1968 under the supervision of Irving Kaplansky. She taught at Boston University and at the University of Illinois at Chicago before becoming a professor at DePaul University.
Contributions
Initially researching commutative algebra, Epp became interested by cognitive psychology, especially in education of Mathematics, Logic, Proof, and the Language of mathematics. She wrote several articles about teaching logic and proof in American Mathematical Monthly, and the Mathematics Teacher, a Journal by the National Council of Teachers of Mathematics.
She is the author of several books including Discrete Mathematics with Applications (4th ed., Brooks/Cole, 2011), the third edition of which earned a Textbook Excellence Award from the Textbook and Academic Authors Association.
"By combining discussion of theory and practice, I have tried to show that mathematics has engaging and important applications as well as being interesting and beautiful in its own right" - Susanna S. Epp wrote in the Preface of the 4th Edition of Discrete Mathematics.
Recognition
In 2005, she received the Louise Hay Award from the Association for Women in Mathematics in recognition for her contributions to mathematics education.
Selected publications
Epp, S.S., Variables in Mathematics Education. In Tools for Teaching Logic. Blackburn, P., van Ditmarsch, H., et al., eds. Springer Publishing, 2011. (Reprinted in Best Writing on Mathematics 2012, M. Pitici, Ed. Princeton Univ. Press, Nov. 2012.)
Epp, S.S., V. Durand-Guerrier, et al. Argumentation and proof in the mathematics classroom. In Proof and Proving in Mathematics Education, G. Hanna & M. de Villiers Eds. Springer Publishing. (co-authors: V. Durand-Guerrier, P. Boero, N. Douek, D. Tanguay), 2012.
Epp, S.S., V. Durand-Guerrier, et al. Examining the role of logic in teaching proof. In Proof and Proving in Mathematics Education, G. Hanna & M. de Villiers Eds. Springer Publishing, 2012.
Epp, S.S., Proof Issues with Existential Quantification. In Proof and Proving in Mathematics Education: ICMI Study 19 Conference Proceedings, F. L. Lin et al. eds., National Taiwan Normal University, 2009.
Epp, S.S., The Use of Logic in Teaching Proof. In Resources for Teaching Discrete Mathematics. B. Hopkins, ed. Washington, DC: Mathematical Association of America, 2009, pp. 313–322.
Epp, S.S., The Role of Logic in Teaching Proof, American Mathematical Monthly (110) |
https://en.wikipedia.org/wiki/Continuous%20dual%20Hahn%20polynomials | In mathematics, the continuous dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by
give a detailed list of their properties.
Closely related polynomials include the dual Hahn polynomials Rn(x;γ,δ,N), the continuous Hahn polynomials pn(x,a,b, , ), and the Hahn polynomials. These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Qn(x;α,β, N;q), and so on.
Relation to other polynomials
Wilson polynomials are a generalization of continuous dual Hahn polynomials
References
Special hypergeometric functions
Orthogonal polynomials |
https://en.wikipedia.org/wiki/Continuous%20Hahn%20polynomials | In mathematics, the continuous Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by
give a detailed list of their properties.
Closely related polynomials include the dual Hahn polynomials Rn(x;γ,δ,N), the Hahn polynomials Qn(x;a,b,c), and the continuous dual Hahn polynomials Sn(x;a,b,c). These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Qn(x;α,β, N;q), and so on.
Orthogonality
The continuous Hahn polynomials pn(x;a,b,c,d) are orthogonal with respect to the weight function
In particular, they satisfy the orthogonality relation
for , , , , , .
Recurrence and difference relations
The sequence of continuous Hahn polynomials satisfies the recurrence relation
Rodrigues formula
The continuous Hahn polynomials are given by the Rodrigues-like formula
Generating functions
The continuous Hahn polynomials have the following generating function:
A second, distinct generating function is given by
Relation to other polynomials
The Wilson polynomials are a generalization of the continuous Hahn polynomials.
The Bateman polynomials Fn(x) are related to the special case a=b=c=d=1/2 of the continuous Hahn polynomials by
The Jacobi polynomials Pn(α,β)(x) can be obtained as a limiting case of the continuous Hahn polynomials:
References
Special hypergeometric functions
Orthogonal polynomials |
https://en.wikipedia.org/wiki/Dual%20Hahn%20polynomials | In mathematics, the dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined on a non-uniform lattice and are defined as
for and the parameters are restricted to .
Note that is the rising factorial, otherwise known as the Pochhammer symbol, and is the generalized hypergeometric functions
give a detailed list of their properties.
Orthogonality
The dual Hahn polynomials have the orthogonality condition
for . Where ,
and
Numerical instability
As the value of increases, the values that the discrete polynomials obtain also increases. As a result, to obtain numerical stability in calculating the polynomials you would use the renormalized dual Hahn polynomial as defined as
for .
Then the orthogonality condition becomes
for
Relation to other polynomials
The Hahn polynomials, , is defined on the uniform lattice , and the parameters are defined as . Then setting the Hahn polynomials become the Chebyshev polynomials. Note that the dual Hahn polynomials have a q-analog with an extra parameter q known as the dual q-Hahn polynomials.
Racah polynomials are a generalization of dual Hahn polynomials.
References
Special hypergeometric functions
Orthogonal polynomials |
https://en.wikipedia.org/wiki/Continuous%20q-Hahn%20polynomials | In mathematics, the continuous q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by
Gallery
References
Orthogonal polynomials
Q-analogs
Special hypergeometric functions |
https://en.wikipedia.org/wiki/David%20Jobin | David Jobin (born September 27, 1981) is a Swiss professional ice hockey player who played for the SC Bern in Switzerland's National League A (NLA).
Career statistics
Awards and honours
References
External links
1981 births
SC Bern players
EHC Biel players
Living people
Swiss ice hockey defencemen
Ice hockey people from Bern |
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