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https://en.wikipedia.org/wiki/1980%20in%20Japanese%20football | Japanese football in 1980
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1981%20in%20Japanese%20football | Japanese football in 1981
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1982%20in%20Japanese%20football | Japanese football in 1982
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1983%20in%20Japanese%20football | Japanese football in 1983
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1984%20in%20Japanese%20football | Japanese football in 1984
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1989%20in%20Japanese%20football | Japanese football in 1989
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1990%20in%20Japanese%20football |
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1991%20in%20Japanese%20football | Japanese football in 1991
Japan Soccer League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
Japan Soccer League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1993%20in%20Japanese%20football | Japanese football in 1993
J.League
Japan Football League
Division 1
Division 2
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1994%20in%20Japanese%20football | Japanese football in 1994
J.League
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1995%20in%20Japanese%20football | Japanese football in 1995
J.League
Japan Football League
Japanese Regional Leagues
Emperor's Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1996%20in%20Japanese%20football | Japanese football in 1996
J.League
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (men)
Results
Players statistics
National team (women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1997%20in%20Japanese%20football | Japanese football in 1997
J.League
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1998%20in%20Japanese%20football | The following describes Japanese football in 1998.
J.League
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/1999%20in%20Japanese%20football | Japanese football in 1999
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2000%20in%20Japanese%20football | Japanese football in 2000
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2001%20in%20Japanese%20football | Japanese football in 2001
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2002%20in%20Japanese%20football | Japanese football in 2002
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2003%20in%20Japanese%20football | Japanese football in 2003
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2008%20in%20Japanese%20football | Japanese football in 2008
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2009%20in%20Japanese%20football | Japanese football in 2009
J.League Division 1
J.League Division 2
Japan Football League
Japanese Regional Leagues
Emperor's Cup
J.League Cup
National team (Men)
Results
Players statistics
National team (Women)
Results
Players statistics
External links
Seasons in Japanese football |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20Wycombe%20Wanderers%20F.C.%20season | The 2009–10 Football League One was Wycombe Wanderers F.C.'s sixteenth season of League football. This article shows statistics of the club's players in the season, and also lists all matches that the club has played during the season.
Match results
Legend
Football League One
FA Cup
League Cup
Football League Trophy
Squad statistics
Appearances for competitive matches only
See also
2009–10 in English football
Wycombe Wanderers F.C.
References
External links
Wycombe Wanderers official website
Wycombe Wanderers 2009–10 season players stats at Soccerbase
Wycombe Wanderers F.C. seasons
Wycombe Wanderers |
https://en.wikipedia.org/wiki/Wolfhart%20Zimmermann | Wolfhart Zimmermann (17 February 1928 – 18 September 2016) was a German theoretical physicist. Zimmermann attained a doctorate in 1950 at Freiburg im Breisgau in topology ("Eine Kohomologietheorie topologischer Räume").
Biography
Zimmermann was born in Freiburg im Breisgau. In the 1950s he lived in Göttingen and was one of the pioneers of the mathematical quantum field theory. He developed the LSZ theory with Kurt Symanzik and Harry Lehmann. From 1962 to 1974 he was a professor at the New York University. From 1974 to 1996 he was a director at the Max Planck Institute for physics in Munich, later becoming the "Director Emeritus".
Since 1977 he was an honorary professor ("Honorarprofessor") at TU Munich. He took a year-long sabbatical stay at the Institute for Advanced Study in Princeton (1957/8 and 1960/1), at the Courant Institute of Mathematical Sciences of New York University, at the University of Chicago and at IHES in Paris. In addition to his work on the LSZ formalism he is also known for the development of Bogolyubov - Parasiuk renormalization schema (also BPHZ Renormalization schema named after Klaus Hepp and Zimmermann). Along with Kenneth G. Wilson he was one of the pioneers in applications of operator product expansion in quantum field theory. With Reinhard Oehme of the Enrico Fermi Institute in Chicago (with whom he already collaborated in Göttingen in the 1950s), he worked on the reduction of coupling parameters with group renormalization methods and introduced superconvergence relations for the propagator (gauge field propagator) into Yang–Mills theory, to establish connections between the borders of high energy (e.g. asymptotic freedom) and low energy (confinement).
In 1991 he received the Max Planck medal.
References
Sources
Peter Breitenlohner (Ed.) "Quantum Field Theory- Proceedings on the Ringberg Workshop, Tegernsee 1998, On the Occasion of Wolfhart Zimmermann´s 70. Birthday", Lecture Notes in Physics 558, Springer, 1998.
Zimmermann "Local operator products and renormalization in Quantum Field Theory", Brandeis Summer Institute in Theoretical Physics Lectures 1970, pp. 399–589
External links
Quantum field theory/BPHZ - Physics wiki - TheTangentBundle
1928 births
2016 deaths
20th-century German physicists
New York University faculty
Scientists from Freiburg im Breisgau
Winners of the Max Planck Medal |
https://en.wikipedia.org/wiki/Polat%20Keser | Polat Keser (born 4 December 1985 in Marl) is a German–born Turkish football goalkeeper who plays for Ceyhanspor.
Career
Statistics
References
External links
Polat Keser Interview
1985 births
Living people
Turkish men's footballers
VfL Bochum players
VfL Bochum II players
Antalyaspor footballers
Men's association football goalkeepers
Süper Lig players
Turkey men's youth international footballers
People from Marl, North Rhine-Westphalia
Footballers from Münster (region)
TSV Marl-Hüls players |
https://en.wikipedia.org/wiki/Linear%20bottleneck%20assignment%20problem | In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem (LBAP) is similar to the linear assignment problem.
In plain words the problem is stated as follows:
There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task in such a way that the maximum cost among the individual assignments is minimized.
The term "bottleneck" is explained by a common type of application of the problem, where the cost is the duration of the task performed by an agent. In this setting the "maximum cost" is "maximum duration", which is the bottleneck for the schedule of the overall job, to be minimized.
Formal definition
The formal definition of the bottleneck assignment problem is
Given two sets, A and T, together with a weight function C : A × T → R. Find a bijection f : A → T such that the cost function:
is minimized.
Usually the weight function is viewed as a square real-valued matrix C, so that the cost function is written down as:
Mathematical programming formulation
subject to:
Asymptotics
Let denote the optimal objective function value for the problem with n agents and n tasks. If the costs are sampled from the uniform distribution on (0,1), then
and
References
Combinatorial optimization |
https://en.wikipedia.org/wiki/Quadratic%20bottleneck%20assignment%20problem | In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research, from the category of the facilities location problems.
It is related to the quadratic assignment problem in the same way as the linear bottleneck assignment problem is related to the linear assignment problem, the "sum" is replaced with "max" in the objective function.
The problem models the following real-life problem:
There are a set of n facilities and a set of n locations. For each pair of locations, a distance is specified and for each pair of facilities a weight or flow is specified (e.g., the amount of supplies transported between the two facilities). The problem is to assign all facilities to different locations with the goal of minimizing the maximum of the distances multiplied by the corresponding flows.
Computational complexity
The problem is NP-hard, as it can be used to formulate the Hamiltonian cycle problem by using flows in the pattern of a cycle and distances that are short for graph edges and long for non-edges.
Special cases
Bottleneck traveling salesman problem
Graph bandwidth problem
References
NP-hard problems
Combinatorial optimization |
https://en.wikipedia.org/wiki/Rainer%20Burkard | Rainer Ernst Burkard (born 28 January 1943, Graz, Austria ) is an Austrian mathematician. His research interests include discrete optimization, graph theory, applied discrete mathematics, and applied number theory.
He earned his Ph.D. from the University of Vienna in 1967 and received his habilitation from the University of Graz in 1971. From 1973–1981 Rainer Burkard was full professor of Applied Mathematics at the University of Cologne (Germany).
Since 1981 Rainer Burkard is full professor with the Graz University of Technology.
Positions held
1984-1986 Vice President of GMÖOR
1986-1988 President of the Austrian Society of Operations Research
1995-1997 EURO Vice President of IFORS
1993-1996 Dean of the Faculty of Science, Graz University of Technology
1994-1998 Member of the Council of the European Consortium of Mathematics in Industry
1991-2000 Member of the Senate of the Christian Doppler Research Society
2001-2002 Vice President of EURO
Awards
Prize of the Austrian Mathematical Society in 1972
The Scientific Prize of the Society of Mathematics, Economics and Operations Research in 1991
The EURO Gold Medal 1997
Since 1998 Honorary Member of the Hungarian Academy of Sciences
Since 2011 Honorary Member of the Austrian Society of Operations Research
Books
Methoden der ganzzahligen Optimierung, Springer Wien, 1972
with Ulrich Derigs: Assignment and Matching Problems: Solution Methods with FORTRAN- Programs. Lecture Notes in Economics and Mathematical Systems, Band 184, Berlin-New York: Springer 1980.
Graph Algorithms in Computer Science. HyperCOSTOC Computer Science, Vol. 36, Hofbauer Publ., Wiener Neustadt, 1989.
With Mauro Dell' Amico and Silvano Martello: Assignment Problems, SIAM, Philadelphia, 2009.
References
Austrian mathematicians
University of Graz alumni
University of Vienna alumni
Living people
1943 births |
https://en.wikipedia.org/wiki/Rob%20J.%20Hyndman | Robin John Hyndman (born 2 May 1967) is an Australian statistician known for his work on forecasting and time series. He is Professor of Statistics at Monash University and was Editor-in-Chief of the International Journal of Forecasting from 2005–2018. In 2007 he won the Moran Medal from the Australian Academy of Science for his contributions to statistical research. In 2021 he won the Pitman Medal from the Statistical Society of Australia.
Hyndman is co-creator and proponent of the scale-independent forecast error measurement metric mean absolute scaled error (MASE). Common metrics of forecast error, such as mean absolute error, geometric mean absolute error, and mean squared error, have shortcomings related to dependence on scale of data and/or handling zeros and negative values within the data. Hyndman's MASE metric resolves these and can be used under any forecast generation method. It allows for comparison between models due to its scale-free property.
Hyndman studied statistics and mathematics at the University of Melbourne, where he earned a Bachelor of Science with first class honours and a PhD. He was elected Fellow of the Academy of the Social Sciences in Australia in 2020, and Fellow of the Australian Academy of Science in 2021.
Major books
Makridakis, S., Wheelwright, S., and Hyndman, R.J. (1998) Forecasting: methods and applications, Wiley.
Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer.
Hyndman, R.J., and Athanasopoulos, G. (2014) Forecasting: principles and practice, OTexts. (self-published)
Hyndman, R.J. (2015) Unbelievable, CreateSpace. (self-published)
References
External links
Professor Rob J Hyndman Personal website
1967 births
Living people
Australian statisticians
Academic staff of Monash University
University of Melbourne alumni
People from Beechworth
Fellows of the Academy of the Social Sciences in Australia
Fellows of the Australian Academy of Science |
https://en.wikipedia.org/wiki/Wirtinger%27s%20representation%20and%20projection%20theorem | In mathematics, Wirtinger's representation and projection theorem is a theorem proved by Wilhelm Wirtinger in 1932 in connection with some problems of approximation theory. This theorem gives the representation formula for the holomorphic subspace of the simple, unweighted holomorphic Hilbert space of functions square-integrable over the surface of the unit disc of the complex plane, along with a form of the orthogonal projection from to .
Wirtinger's paper contains the following theorem presented also in Joseph L. Walsh's well-known monograph
(p. 150) with a different proof. If is of the class on , i.e.
where is the area element, then the unique function of the holomorphic subclass , such that is least, is given by
The last formula gives a form for the orthogonal projection from to . Besides, replacement of by makes it Wirtinger's representation for all . This is an analog of the well-known Cauchy integral formula with the square of the Cauchy kernel. Later, after the 1950s, a degree of the Cauchy kernel was called reproducing kernel, and the notation became common for the class .
In 1948 Mkhitar Djrbashian extended Wirtinger's representation and projection to the wider, weighted Hilbert spaces of functions holomorphic in , which satisfy the condition
and also to some Hilbert spaces of entire functions. The extensions of these results to some weighted spaces of functions holomorphic in and similar spaces of entire functions, the unions of which respectively coincide with all functions holomorphic in and the whole set of entire functions can be seen in.
See also
References
Theorems in complex analysis
Theorems in functional analysis
Theorems in approximation theory |
https://en.wikipedia.org/wiki/Cem%20Sultan%20%28footballer%29 | Cem Sultan (born 27 February 1991) is a Turkish footballer who plays as a striker for the Circassian club Nart SK in the Amateur league.
References
External links
Statistics at TFF.org
1991 births
Living people
Footballers from Istanbul
Men's association football forwards
Galatasaray S.K. footballers
Kayserispor footballers
Manisaspor footballers
Süper Lig players
Turkey men's under-21 international footballers
Turkey men's youth international footballers
TFF First League players
Turkish men's footballers |
https://en.wikipedia.org/wiki/List%20of%20Seattle%20Sounders%20FC%20records%20and%20statistics | Seattle Sounders FC is an American professional soccer club based in Seattle, Washington that competes in Major League Soccer (MLS). Sounders FC was established on November 13, 2007, as an MLS expansion team, making it the 15th team in the league. Fans chose the Sounders name through an online poll in 2008, making the Seattle Sounders FC the third Seattle soccer club to share the name.
The list encompasses the major honors won by Seattle Sounders FC, records set by the club, their managers and their players.
Honors
Seattle Sounders' first trophy was the 2009 U.S. Open Cup, which they won against D.C. United. The club also won the Heritage Cup for the first time the following year against the San Jose Earthquakes.
National competitions
MLS Cup
Winners (2): 2016, 2019
Runners-up (2): 2017, 2020
Supporters' Shield
Winners (1): 2014
Runners-up (1): 2011
U.S. Open Cup
Winners (4): 2009, 2010, 2011, 2014
Runners-up (1): 2012
Continental competitions
CONCACAF Champions League
Winners (1): 2022
Leagues Cup
Runners-up (1): 2021
Friendly trophies and other awards
Cascadia Cup: 5
2011, 2015, 2018, 2019, 2021
Heritage Cup: 8
2010, 2011, 2013, 2016, 2017, 2018, 2019, 2021
Community Shield: 2
2011, 2012
Desert Diamond Cup: 1
2013
MLS Fair Play Award: 1
2017
CCL Fair Play Award: 1
2022
Player records
Goals scored
Competitive, professional matches only.
Assists
MLS Competitive, professional matches only.
Appearances
All statistics are correct .
Youngest first-team player: Danny Leyva, 16 years old (vs. Montreal Impact, Major League Soccer, June 5, 2019)
Oldest
All statistics are correct .
Oldest first-team player: Kasey Keller, 41 years, 11 months, 8 days (vs. Real Salt Lake, Major League Soccer, November 3, 2011)
Goalscorers
In a season
All statistics are correct .
Most MLS goals in a season: 17, Obafemi Martins (2014)
Most all competition goals in a season: 19, Obafemi Martins (2014)
Most by a rookie in a season: 12, Jordan Morris (2016)
In a single match
All statistics are correct .
Most goals in a single match:
4, Jordan Morris (vs. Sporting Kansas City: Children's Mercy Park; March 25, 2023)
Hat-tricks
All statistics are correct .
Sorted by number of goals:
4, Jordan Morris (vs. Sporting Kansas City: Children's Mercy Park; March 25, 2023)
3, Blaise Nkufo (vs. Columbus Crew; Columbus Crew Stadium; September 18, 2010)
3, Lamar Neagle (vs. Columbus Crew; CenturyLink Field; August 27, 2011)
3, David Estrada (vs. Toronto FC: CenturyLink Field; March 17, 2012)
3, Fredy Montero (vs. Chivas USA: Home Depot Center; August 25, 2012)
3, Clint Dempsey (vs. Portland Timbers: Providence Park; April 5, 2014)
3, Clint Dempsey (vs. Orlando City SC: Camping World Stadium; August 7, 2016)
3, Jordan Morris (vs. FC Dallas: CenturyLink Field; October 19, 2019, 2019 MLS Cup Playoffs)
Assists
In a single match
All statistics are correct .
Most assists in a single match:
4, Léo Chú (vs. Sporting Kansas City: Children's Mercy Park; March |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20Exeter%20City%20F.C.%20season | The 2009–10 Football League One was Exeter City F.C.'s first season back in the third tier of English football since 1994. This article shows statistics of the club's players in the season, and also lists all matches that the club has played during the season.
Match results
Legend
Football League One
League Cup
FA Cup
Football League Trophy
Squad statistics
Appearances for competitive matches only
See also
2009–10 in English football
Exeter City F.C.
External links
Exeter City official website
Exeter City 2009–10 season players stats at Soccerbase
Exeter City
Exeter City F.C. seasons |
https://en.wikipedia.org/wiki/Symmetry-preserving%20filter | In mathematics, Symmetry-preserving observers, also known as invariant filters, are estimation techniques whose structure and design take advantage of the natural symmetries (or invariances) of the considered nonlinear model. As such, the main benefit is an expected much larger domain of convergence than standard filtering methods, e.g. Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF).
Motivation
Most physical systems possess natural symmetries (or invariance), i.e. there exist transformations (e.g. rotations, translations, scalings) that leave the system unchanged. From mathematical and engineering viewpoints, it makes sense that a filter well-designed for the system being considered should preserve the same invariance properties.
Definition
Consider a Lie group, and
(local) transformation groups , where .
The nonlinear system
is said to be invariant if it is left unchanged by the action of , i.e.
where .
The system is then an invariant filter if
, i.e. that it can be witten , where the correction term is equal to when
, i.e. it is left unchanged by the transformation group.
General equation and main result
It has been proved that every invariant observer reads
where
is an invariant output error, which is different from the usual output error
is an invariant frame
is an invariant vector
is a freely chosen gain matrix.
Given the system and the associated transformation group being considered, there exists a constructive method to determine , based on the moving frame method.
To analyze the error convergence, an invariant state error is defined, which is different from the standard output error , since the standard output error usually does not preserve the symmetries of the system. One of the main benefits of symmetry-preserving filters is that the error system is "autonomous", but for the free known invariant vector , i.e. . This important property allows the estimator to have a very large domain of convergence, and to be easy to tune.
To choose the gain matrix , there are two possibilities:
a deterministic approach, that leads to the construction of truly nonlinear symmetry-preserving filters (similar to Luenberger-like observers)
a stochastic approach, that leads to Invariant Extended Kalman Filters (similar to Kalman-like observers).
Applications
There has been numerous applications that use such invariant observers to estimate the state of the considered system. The application areas include
attitude and heading reference systems with or without position/velocity sensor (e.g. GPS)
ground vehicle localization systems
chemical reactors
oceanography
References
Nonlinear filters
Signal estimation |
https://en.wikipedia.org/wiki/Cartan%27s%20lemma%20%28potential%20theory%29 | In potential theory, a branch of mathematics, Cartan's lemma, named after Henri Cartan, is a bound on the measure and complexity of the set on which a logarithmic Newtonian potential is small.
Statement of the lemma
The following statement can be found in Levin's book.
Let μ be a finite positive Borel measure on the complex plane C with μ(C) = n. Let u(z) be the logarithmic potential of μ:
Given H ∈ (0, 1), there exist discs of radii ri such that
and
for all z outside the union of these discs.
Notes
Complex analysis |
https://en.wikipedia.org/wiki/Pierre%20Galin | Pierre Galin (16 December 1786–31 August 1821) was a French music educator, and developer of what became the Galin-Paris-Chevé system.
Life and career
Galin studied mathematics and commerce, and became a mathematics teacher in Bordeaux, at a school for children with speech and hearing difficulties. He studied music on his own, but had difficulty understanding his textbooks until he discovered the principles of movable do solfège. He advised separate study of pitch and rhythm, and devised a numbered musical notation similar to that of Rousseau, although he recommended students learn staff notation as well.
After success teaching with his ideas in Bordeaux, he moved to Paris where he led a group of enthusiastic students, especially Aimé Paris. Paris ended up plagiarizing his ideas in print, and later claimed never to have known him. Galin became sick, though he continued teaching up to his death. He is buried in Père Lachaise Cemetery.
System
He never published an explanation of his teaching system, although his Exposition d’une nouvelle méthode pour l’enseignement de la musique or Explanation of a New Way of Teaching Music (1818), addressed to the teacher, sets out many of his ideas. In addition to his new notation, he advocated the use of méloplaste ("song-shaper"), a staff with no clef but only a keynote indicated, from which he pointed tunes with a stick for the students to sing. For rhythm, he advocated a chronomerist, a table of note values all clearly related to a single unit, which makes clear the accentual patterns.
Works
Exposition d’une nouvelle méthode pour l’enseignement de la musique / Explanation of a New Way of Teaching Music (3 eds.: 1818, 1835, 1862)
Notes
References
Kenneth Simpson. Some Great Music Educators. Borough Green: Novello, 1976. Pages 20–22.
External links
1786 births
1822 deaths
French music educators
Burials at Père Lachaise Cemetery |
https://en.wikipedia.org/wiki/Chunking%20%28division%29 | In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. It has a counterpart in the grid method for multiplication as well.
In general, chunking is more flexible than the traditional method in that the calculation of quotient is less dependent on the place values. As a result, it is often considered to be a more intuitive, but a less systematic approach to divisionswhere the efficiency is highly dependent upon one's numeracy skills.
To calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away "chunks" of the large number, where each "chunk" is an easy multiple (for example 100×, 10×, 5× 2×, etc.) of the small number, until the large number has been reduced to zeroor the remainder is less than the small number itself. At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself.
For example, to calculate 132 8, one might successively subtract 80, 40 and 8 to leave 4:
132
80 (10 × 8)
--
52
40 ( 5 × 8)
--
12
8 ( 1 × 8)
--
4
--------
132 = 16 × 8 + 4
Because 10 + 5 + 1 = 16, 132 8 is 16 with 4 remaining.
In the UK, this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the National Numeracy Strategy in its "numeracy hour" brought in a new emphasis on more free-form oral and mental strategies for calculations, rather than the rote learning of standard methods.
Compared to the short division and long division methods that are traditionally taught, chunking may seem strange, unsystematic, and arbitrary. However, it is argued that chunking, rather than moving straight to short division, gives a better introduction to division, in part because the focus is always holistic, focusing throughout on the whole calculation and its meaning, rather than just rules for generating successive digits. The more freeform nature of chunking also means that it requires more genuine understandingrather than just the ability to follow a ritualised procedureto be successful.
An alternative way of performing chunking involves the use of the standard long division tableauexcept that the partial quotients are stacked up on the top of each other above the long division sign, and that all numbers are spelled out in full. By allowing one to subtract more chunks than what one currently has, it is also possible to expand chunking into a fully bidirectional method as well.
References
Further reading |
https://en.wikipedia.org/wiki/Cartan%27s%20lemma | In mathematics, Cartan's lemma refers to a number of results named after either Élie Cartan or his son Henri Cartan:
In exterior algebra: Suppose that v1, ..., vp are linearly independent elements of a vector space V and w1, ..., wp are such that
in ΛV. Then there are scalars hij = hji such that
In several complex variables: Let and and define rectangles in the complex plane C by
so that . Let K2, ..., Kn be simply connected domains in C and let
so that again . Suppose that F(z) is a complex analytic matrix-valued function on a rectangle K in Cn such that F(z) is an invertible matrix for each z in K. Then there exist analytic functions in and in such that
in K.
In potential theory, a result that estimates the Hausdorff measure of the set on which a logarithmic Newtonian potential is small. See Cartan's lemma (potential theory).
References
Lemmas |
https://en.wikipedia.org/wiki/Depth%20of%20noncommutative%20subrings | In ring theory and Frobenius algebra extensions, areas of mathematics, there is a notion of depth two subring or depth of a Frobenius extension. The notion of depth two is important in a certain noncommutative Galois theory, which generates Hopf algebroids in place of the more classical Galois groups, whereas the notion of depth greater than two measures the defect, or distance, from being depth two in a tower of iterated endomorphism rings above the subring. A more recent definition of depth of any unital subring in any associative ring is proposed (see below) in a paper studying the depth of a subgroup of a finite group as group algebras over a commutative ring.
Definition and first examples
A unital subring has (or is) right depth two if there is a split epimorphism of natural A-B-bimodules from for some positive integer n; by switching to natural B-A-bimodules, there is a corresponding definition of left depth two. Here we use the usual notation (n times) as well as the common notion, p is a split epimorphism if there is a homomorphism q in the reverse direction such that pq = identity on the image of p. (Sometimes the subring B in A is referred to as the ring extension A over B; the theory works as well for a ring homomorphism B into A, which induces right and left B-modules structures on A.) Equivalently, the condition for left or right depth two may be given in terms of a split monomorphism of bimodules where the domains and codomains above are reversed.
For example, let A be the group algebra of a finite group G (over any commutative base ring k; see the articles on group theory and group ring for the elementary definitions). Let B be the group (sub)algebra of a normal subgroup H of index n in G with coset representatives . Define a split A-B epimorphism p: by . It is split by the mapping defined by where for g in the coset (and extended linearly to a mapping A into B, a B-B-module homomorphism since H is normal in G): the splitting condition pq = the identity on is satisfied. Thus B is right depth two in A.
As another example (perhaps more elementary than the first; see ring theory or module theory for some of the elementary notions), let A be an algebra over a commutative ring B, where B is taken to be in the center of A. Assume A is a finite projective B-module, so there are B-linear mapping and elements (i = 1,...,n) called a projective base for the B-module A if it satisfies for all a in A. It follows that B is left depth two in A by defining
with splitting map as the reader may verify. A similar argument naturally shows that B is right depth two in A.
Depth in relation to Hopf algebras
For a Frobenius algebra extension A | B (such as A and B group algebras of a subgroup pair of finite index) the two one-sided conditions of depth two are equivalent, and a notion of depth n > 2 makes sense via the right endomorphism ring extension iterated to generate a tower of rings (a technical procedure beyond the scope |
https://en.wikipedia.org/wiki/Cohen%20structure%20theorem | In mathematics, the Cohen structure theorem, introduced by , describes the structure of complete Noetherian local rings.
Some consequences of Cohen's structure theorem include three conjectures of Krull:
Any complete regular equicharacteristic Noetherian local ring is a ring of formal power series over a field. (Equicharacteristic means that the local ring and its residue field have the same characteristic, and is equivalent to the local ring containing a field.)
Any complete regular Noetherian local ring that is not equicharacteristic but is unramified is uniquely determined by its residue field and its dimension.
Any complete Noetherian local ring is the image of a complete regular Noetherian local ring.
Statement
The most commonly used case of Cohen's theorem is when the complete Noetherian local ring contains some field. In this case Cohen's structure theorem states that the ring is of the form k[[x1,...,xn]]/(I) for some ideal I, where k is its residue class field.
In the unequal characteristic case when the complete Noetherian local ring does not contain a field, Cohen's structure theorem states that the local ring is a quotient of a formal power series ring in a finite number of variables over a Cohen ring with the same residue field as the local ring. A Cohen ring is a field or a complete characteristic zero discrete valuation ring whose maximal ideal is generated by a prime number p (equal to the characteristic of the residue field).
In both cases, the hardest part of Cohen's proof is to show that the complete Noetherian local ring contains a coefficient ring (or coefficient field), meaning a complete discrete valuation ring (or field) with the same residue field as the local ring.
All this material is developed carefully in the Stacks Project .
References
Cohen's paper was written when "local ring" meant what is now called a "Noetherian local ring".
Commutative algebra
Theorems in ring theory |
https://en.wikipedia.org/wiki/Al-Zaazu%27 | Al-Zaazu' () is a village in northern Syria, administratively part of Raqqa Governorate, located north of Raqqa. According to the Syria Central Bureau of Statistics (CBS), al-Zaazu' had a population of 779 in the 2004 census.
References
Populated places in Tell Abyad District
Villages in Syria |
https://en.wikipedia.org/wiki/Palm%E2%80%93Khintchine%20theorem | In probability theory, the Palm–Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of renewal processes, not necessarily Poissonian, when combined ("superimposed") will have Poissonian properties.
It is used to generalise the behaviour of users or clients in queuing theory. It is also used in dependability and reliability modelling of computing and telecommunications.
Theorem
According to Heyman and Sobel (2003), the theorem states that the superposition of a large number of independent equilibrium renewal processes, each with a finite intensity, behaves asymptotically like a Poisson process:
Let be independent renewal processes and be the superposition of these processes. Denote by the time between the first and the second renewal epochs in process . Define the th counting process, and .
If the following assumptions hold
1) For all sufficiently large :
2) Given , for every and sufficiently large : for all
then the superposition of the counting processes approaches a Poisson process as .
See also
Law of large numbers
References
Queueing theory
Network performance
Point processes
Probability theorems |
https://en.wikipedia.org/wiki/B%C3%B6hm%20tree | In the study of denotational semantics of the lambda calculus, Böhm trees, Lévy-Longo trees, and Berarducci trees are (potentially infinite) tree-like mathematical objects that capture the "meaning" of a term up to some set of "meaningless" terms.
Motivation
A simple way to read the meaning of a computation is to consider it as a mechanical procedure consisting of a finite number of steps that, when completed, yields a result. In particular, considering the lambda calculus as a rewriting system, each beta reduction step is a rewrite step, and once there are no further beta reductions the term is in normal form. We could thus, naively following Church's suggestion, say the meaning of a term is its normal form, and that terms without a normal form are meaningless. For example the meanings of I = λx.x and I I are both I. This works for any strongly normalizing subset of the lambda calculus, such as a typed lambda calculus.
This naive assignment of meaning is however inadequate for the full lambda calculus. The term Ω =(λx.x x)(λx.x x) does not have a normal form, and similarly the term X=λx.xΩ does not have a normal form. But the application Ω (K I), where K denotes the standard lambda term λx.λy.x, reduces only to itself, whereas the application X (K I) reduces with normal order reduction to I, hence has a meaning. We thus see that not all non-normalizing terms are equivalent. We would like to say that Ω is less meaningful than X because applying X to a term can produce a result but applying Ω cannot.
In the infinitary lambda calculus, the term N N, where N = λx.I(xx), reduces to both to I (I (...)) and Ω. Hence there are also issues with confluence of normalization.
Sets of meaningless terms
We define a set of meaningless terms as follows:
Root-activeness: Every root-active term is in . A term is root-active if for all there exists a redex such that .
Closure under β-reduction: For all , if then .
Closure under substitution: For all and substitutions , .
Overlap: For all , .
Indiscernibility: For all , if can be obtained from by replacing a set of pairwise disjoint subterms in with other terms of , then if and only if .
Closure under β-expansion. For all , if , then . Some definitions leave this out, but it is useful.
There are infinitely many sets of meaningless terms, but the ones most common in the literature are:
The set of terms without head normal form
The set of terms without weak head normal form
The set of root-active terms, i.e. the terms without top normal form or root normal form. Since root-activeness is assumed, this is the smallest set of meaningless terms.
Note that Ω is root-active and therefore for every set of meaningless terms .
λ⊥-terms
The set of λ-terms with ⊥ (abbreviated λ⊥-terms) is defined coinductively by the grammar . This corresponds to the standard infinitary lambda calculus plus terms containing . Beta-reduction on this set is defined in the standard way. Given a set of meaningles |
https://en.wikipedia.org/wiki/Riemannian | Riemannian most often refers to Bernhard Riemann:
Riemannian geometry
Riemannian manifold
Pseudo-Riemannian manifold
Sub-Riemannian manifold
Riemannian submanifold
Riemannian metric
Riemannian circle
Riemannian submersion
Riemannian Penrose inequality
Riemannian holonomy
Riemann curvature tensor
Riemannian connection
Riemannian connection on a surface
Riemannian symmetric space
Riemannian volume form
Riemannian bundle metric
List of topics named after Bernhard Riemann
but may also refer to Hugo Riemann:
Neo-Riemannian theory (music) |
https://en.wikipedia.org/wiki/Tam%C3%A1s%20Horv%C3%A1th%20%28footballer%2C%20born%201991%29 | Tamás Horváth (born 29 April 1991, in Kaposvár) is a Hungarian football player who currently plays for Kaposvári Rákóczi FC.
Club statistics
Updated to games played as of 28 April 2013.
References
Player profile at HLSZ
1991 births
Living people
Footballers from Kaposvár
Hungarian men's footballers
Men's association football midfielders
Kaposvári Rákóczi FC players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/South%20Africans%20in%20the%20United%20Arab%20Emirates | There is a large population of South Africans in the United Arab Emirates. While the UAE National Bureau of Statistics does not publish any demographic data in relation to nationality, estimates reveal the number of South African immigrants in the country to be about 100,000 as of 2014. Time Out magazine estimated that 50,000 South Africans resided in Dubai alone . The influx of South Africans has been so large as to lead South African newspaper Independent Online to unofficially dub the United Arab Emirates "South Africa's 10th province".
Demographic characteristics
Half of the South Africans in the UAE hold higher educational qualifications, and only 15% work in entry-level positions. They are motivated to emigrate from South Africa to escape the country's high crime levels and gain international experience. Additional attractions include the high quality of health care, low cost of cars compared to South Africa, and attractive salaries; conversely, South African employees are attractive to UAE firms because they are accustomed to lower salaries than their European peers. Some also describe "reverse discrimination" as a motivation for their departure from South Africa. They tend to be white, male, under 35, and English- rather than Afrikaans-speaking. Roughly 15% intend to remain in the UAE for 10 years or longer. However, most do not to see the UAE as a long-term home, and stay in the country for shorter times than other expatriates in traditional emigration destinations such as London. Nevertheless, there are worries that South African migration to the UAE could become a permanent "brain drain" for the country.
Organisations
Scholars International Academy has offered courses in Afrikaans to South African children in Dubai since 2007. There is also an Afrikaans-speaking church, and a South African Women's Association.
References
External links
Gulfnews: South Africans in Dubai celebrate Freedom Day
United Arab Emirates
Ethnic groups in the United Arab Emirates
Emirati people of South African descent |
https://en.wikipedia.org/wiki/Circle%20packing%20in%20a%20square | Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack unit circles into the smallest possible square. Equivalently, the problem is to arrange points in a unit square aiming to get the greatest minimal separation, , between points. To convert between these two formulations of the problem, the square side for unit circles will be .
Solutions
Solutions (not necessarily optimal) have been computed for every . Solutions up to are shown below.
The obvious square packing is optimal for 1, 4, 9, 16, 25, and 36 circles (the six smallest square numbers), but ceases to be optimal for larger squares from 49 onwards.
Circle packing in a rectangle
Dense packings of circles in non-square rectangles have also been the subject of investigations.
See also
Square packing in a circle
References
Circle packing |
https://en.wikipedia.org/wiki/Harish-Chandra%20module | In mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module, named after the Indian mathematician and physicist Harish-Chandra, is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions. When the associated representation is a -module, then its Harish-Chandra module is a representation with desirable factorization properties.
Definition
Let G be a Lie group and K a compact subgroup of G. If is a representation of G, then the Harish-Chandra module of is the subspace X of V consisting of the K-finite smooth vectors in V. This means that X includes exactly those vectors v such that the map via
is smooth, and the subspace
is finite-dimensional.
Notes
In 1973, Lepowsky showed that any irreducible -module X is isomorphic to the Harish-Chandra module of an irreducible representation of G on a Hilbert space. Such representations are admissible, meaning that they decompose in a manner analogous to the prime factorization of integers. (Of course, the decomposition may have infinitely many distinct factors!) Further, a result of Harish-Chandra indicates that if G is a reductive Lie group with maximal compact subgroup K, and X is an irreducible
-module with a positive definite Hermitian form satisfying
and
for all and , then X is the Harish-Chandra module of a unique irreducible unitary representation of G.
References
See also
(g,K)-module
Admissible representation
Unitary representation
Representation theory of Lie groups |
https://en.wikipedia.org/wiki/DrGeo | GNU Dr. Geo, and later Dr. Geo II, is interactive geometry software that allows its users to design & manipulate interactive geometric sketches. It is free software (source code, translations, icons and installer are released under GNU GPL license), created by Hilaire Fernandes, it is part of the GNU project.
It runs over a Morphic graphic system (which means that it runs on Linux, Mac OS, Windows, Android). Dr. Geo was developed in C++ and Dr. Geo II is a complete rewrite using Pharo that happened in 2005.
Objects
Dr. Geo manipulates different kinds of objects such as points, lines, circles, block of code.
Points
Dr. Geo has several kinds of points: a free point, which can be moved with the mouse (but may be attached to a curve) and a point given by its coordinates.
Points can also be created as the intersection of 2 curves or as the midpoint of a segment.
Lines
Dr. Geo is equipped with the classic line, ray, segment and vector.
Other curvilinear objects include circles (defined by 2 points, a center and segment or a radius), arcs (defined by three points or center and angle), polygons (regular or not, defined by end points), and loci.
Transformations
Besides the parallel and perpendicular line through a point, Dr. Geo can apply to a point or a line one of these transformations:
reflexion
symmetry
translation
rotation
homothety
Macro-construction
Dr. Geo comes with macro-construction: a way to teach Dr. Geo new constructions. It allows to add new objects to Dr. Geo: new transformations like circle inversion, tedious constructions involving a lot of intermediate objects or constructions involving script (also named macro-script).
When some objects, called final depend on other objects, called initial, it is possible to create a complex construction deducing the final objects from the user-given initial objects. This is a macro-construction, a graph of interdependent objects.
Programming
Access to user programming is at the essence of Dr. Geo: from the software, the user can directly read, study, modify and redistribute modified version of Dr. Geo. Additionally, scripting embedded in sketch is proposed.
Dr. Geo source code is Pharo. It is also the language used for user programming: to extend Dr. Geo with arbitrary computing operations (Pharo script) and to define a geometric sketch entirely with programming instructions (Pharo sketch).
Dr. Geo is shipped with its source code and the developer tools. Therefore its code can be edited and recompiled from Dr. Geo while it is functioning. This design, inherited from Pharo, makes easy to test new ideas and new designs.
Pharo script
A script is a first class object defined along Dr. Geo code. It comes with zero, one or several arguments, from types selected when defining the script. When an instance of a script is plugged in a canvas, the user first selects its arguments in the canvas with mouse clicks, then the position in the canvas of the script output. The script is update |
https://en.wikipedia.org/wiki/Axiomatic%20geometry | Axiomatic geometry may refer to:
Foundations of geometry: the study of the axioms of geometry.
Synthetic geometry: the coordinate-free study of geometry. |
https://en.wikipedia.org/wiki/Torsionless%20module | In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI. Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f:
This notion was introduced by Hyman Bass.
Properties and examples
A module is torsionless if and only if the canonical map into its double dual,
is injective. If this map is bijective then the module is called reflexive. For this reason, torsionless modules are also known as semi-reflexive.
A unital free module is torsionless. More generally, a direct sum of torsionless modules is torsionless.
A free module is reflexive if it is finitely generated, but for some rings there are also infinitely generated free modules that are reflexive. For instance, the direct sum of countably many copies of the integers is a reflexive module over the integers, see for instance.
A submodule of a torsionless module is torsionless. In particular, any projective module over R is torsionless; any left ideal of R is a torsionless left module, and similarly for the right ideals.
Any torsionless module over a domain is a torsion-free module, but the converse is not true, as Q is a torsion-free Z-module which is not torsionless.
If R is a commutative ring which is an integral domain and M is a finitely generated torsion-free module then M can be embedded into Rn and hence M is torsionless.
Suppose that N is a right R-module, then its dual N∗ has a structure of a left R-module. It turns out that any left R-module arising in this way is torsionless (similarly, any right R-module that is a dual of a left R-module is torsionless).
Over a Dedekind domain, a finitely generated module is reflexive if and only if it is torsion-free.
Let R be a Noetherian ring and M a reflexive finitely generated module over R. Then is a reflexive module over S whenever S is flat over R.
Relation with semihereditary rings
Stephen Chase proved the following characterization of semihereditary rings in connection with torsionless modules:
For any ring R, the following conditions are equivalent:
R is left semihereditary.
All torsionless right R-modules are flat.
The ring R is left coherent and satisfies any of the four conditions that are known to be equivalent:
All right ideals of R are flat.
All left ideals of R are flat.
Submodules of all right flat R-modules are flat.
Submodules of all left flat R-modules are flat.
(The mixture of left/right adjectives in the statement is not a mistake.)
See also
Prüfer domain
reflexive sheaf
Note
References
Chapter VII of
Module theory |
https://en.wikipedia.org/wiki/Klaus%20Hepp | Klaus Hepp (born 11 December 1936) is a German-born Swiss theoretical physicist working mainly in quantum field theory. Hepp studied mathematics and physics at Westfälischen Wilhelms-Universität in Münster and at the Eidgenössischen Technischen Hochschule (ETH) in Zurich, where, in 1962, with Res Jost as thesis first advisor and Markus Fierz as thesis second advisor, he received a doctorate for the thesis ("Kovariante analytische Funktionen“) and at ETH in 1963 attained the rank of Privatdozent. From 1966 until his retirement in 2002 he was professor of theoretical physics there. From 1964 to 1966 he was at the Institute for Advanced Study in Princeton. Hepp was also Loeb Lecturer at Harvard and was at the IHÉS near Paris.
Hepp worked on relativistic quantum field theory, quantum statistical mechanics, and theoretical laser physics. In quantum field theory he gave a complete proof of the Bogoliubov–Parasyuk renormalization theorem (Hepp and Wolfhart Zimmermann, called in their honor the BPHZ theorem). Since a research stay 1975/6 at MIT he also worked in neuroscience (for example, reciprocal effect between movement sensors, visual sense and eye movements with V. Henn in Zurich).
In 2004 he received the Max Planck Medal.
Selected works
“Renormalisaton Theory“, in de Witt, Stora „Statistical Mechanics and Quantum Field Theory“, Gordon and Breach, New York 1971
“Progress in Quantum Field Theory“, Erice Lectures 1972
“Theorie de la Renormalisation“, Springer 1970
“On the quantum mechanical N-body problem“, Helvetica physica Acta, Bd.42, 1969, S.425
“On the connection between Wightman and LSZ quantum field theory“, in Chretien, Deser „Axiomatic Quantum Field Theory“, New York 1966
"Quantum mechanics in the brain" (with Christof Koch) in Nature 440(611), 2006
See also
Gell-Mann and Low theorem
Mean-field particle methods
Superradiant phase transition
Wightman axioms
References
External links
Hepp Biographie an der ETH
DPG zur Verleihung der Max Planck Medaille
1936 births
Living people
Swiss physicists
Theoretical physicists
Academic staff of ETH Zurich
Winners of the Max Planck Medal |
https://en.wikipedia.org/wiki/Characteristic%20set | Characteristic set may refer to
The characteristic set of an algebraic matroid
The characteristic set of a linear matroid
Wu's method of characteristic set |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20Doncaster%20Rovers%20F.C.%20season | The 2009–10 Football League Championship was Doncaster Rovers F.C.'s second season in the Championship. This article shows statistics of the club's players in the season, and also lists all matches that the club has played during the 2009–10 season.
Match results
Legend
Football League Championship
League Cup
FA Cup
Squad statistics
Appearances for competitive matches only
External links
Doncaster Rovers official website
Doncaster Rovers 2009–10 season players stats at Soccerbase
2009–10
2009–10 Football League Championship by team |
https://en.wikipedia.org/wiki/Process%20graph | In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling.
Description
With a process graph, the vertices of the graph are of two types, operation (O) and material (M). These vertex types form two disjunctive sets. The edges of the graph link the O and M vertices. An edge from an operation vertex (O) connects to a material vertex (M) if M is the output of O, such as a 'document' (material) that is output by a 'write-up' (operation). An edge from M to O indicates that M is an element of the input set of O, e.g. a document may be part of the input to a 'review' operation.
Applications
Process-graph is in use in different fields of application in Process Network Synthesis (PNS) . An example for an application is Process Network Synthesis. The method is in scientific use to find optimum process chains in chemical formulas, energy technology networks and other optimisation problems like evacuation routes in buildings or transportation routes.
Process graphs are also used in understanding the control flow of multi-threaded processes. If there are n concurrent threads running, a process graph models the execution of n concurrent threads and their trajectories through an n dimensional Cartesian plane. The origin of the graph corresponds to the initial state where none of the threads have completed an instruction. Each directed edge corresponds to the execution of an instruction and transition to other. Valid edges can either go up or right because programs cannot run backward for the edges to left or down. Since two threads can't complete the same instruction at the same time, diagonal edges are not allowed.
References
External links
P-Graph wiki
Process Network Synthesis Problem Definition
Application-specific graphs |
https://en.wikipedia.org/wiki/Wiener%20algebra | In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by , is the space of absolutely convergent Fourier series. Here denotes the circle group.
Banach algebra structure
The norm of a function is given by
where
is the th Fourier coefficient of . The Wiener algebra is closed under pointwise multiplication of functions. Indeed,
therefore
Thus the Wiener algebra is a commutative unitary Banach algebra. Also, is isomorphic to the Banach algebra , with the isomorphism given by the Fourier transform.
Properties
The sum of an absolutely convergent Fourier series is continuous, so
where is the ring of continuous functions on the unit circle.
On the other hand an integration by parts, together with the Cauchy–Schwarz inequality and Parseval's formula, shows that
More generally,
for (see ).
Wiener's 1/f theorem
proved that if has absolutely convergent Fourier series and is never zero, then its reciprocal also has an absolutely convergent Fourier series. Many other proofs have appeared since then, including an elementary one by .
used the theory of Banach algebras that he developed to show that the maximal ideals of are of the form
which is equivalent to Wiener's theorem.
See also
Wiener–Lévy theorem
Notes
References
Banach algebras
Fourier series |
https://en.wikipedia.org/wiki/Partial%20permutation | In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S
is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation.
Representation
It is common to consider the case when the set S is simply the set {1, 2, ..., n} of the first n integers. In this case, a partial permutation may be represented by a string of n symbols, some of which are distinct numbers in the range from 1 to and the remaining ones of which are a special "hole" symbol ◊. In this formulation, the domain U of the partial permutation consists of the positions in the string that do not contain a hole, and each such position is mapped to the number in that position. For instance, the string "1 ◊ 2" would represent the partial permutation that maps 1 to itself and maps 3 to 2.
The seven partial permutations on two items are
◊◊, ◊1, ◊2, 1◊, 2◊, 12, 21.
Combinatorial enumeration
The number of partial permutations on n items, for n = 0, 1, 2, ..., is given by the integer sequence
1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114, 234662231, ...
where the nth item in the sequence is given by the summation formula
in which the ith term counts the number of partial permutations with support of size i, that is, the number of partial permutations with i non-hole entries.
Alternatively, it can be computed by a recurrence relation
This is determined as follows:
partial permutations where the final elements of each set are omitted:
partial permutations where the final elements of each set map to each other.
partial permutations where the final element of the first set is included, but does not map to the final element of the second set
partial permutations where the final element of the second set is included, but does not map to the final element of the first set
, the partial permutations included in both counts 3 and 4, those permutations where the final elements of both sets are included, but do not map to each other.
Restricted partial permutations
Some authors restrict partial permutations so that either the domain
or the range of the bijection is forced to consist of the first k items in the set of n items being permuted, for some k. In the former case, a partial permutation of length k from an n-set is just a sequence of k terms from the n-set without repetition. (In elementary combinatorics, these objects are sometimes confusingly called "k-permutations" of the n-set.)
References
Combinatorics
Functions and mappings |
https://en.wikipedia.org/wiki/Pancho%20Gonzales%20career%20statistics | This is a list of the main career statistics of former tennis player Pancho Gonzales whose career ran from 1947 until 1974.
As an amateur player, Gonzales won at least 17 singles titles, including two Grand Slam tournaments. As a professional player, he won at least 85 singles titles, including 12 Pro Slam tournaments; at the same time he was banned from competing in the Grand Slam events from 1950 to 1967 due to being a professional player. During this professional period, he won seven times the World Pro Tour. The Open era arrived very late for Gonzales, by which time he was in his forties. Even at this advanced age he was able to win at least 11 singles titles. Overall Gonzales won at least 113 titles in his career in a span of 25 years.
Major titles
Performance timeline
Gonzales started playing professional tennis in 1950 and was unable to compete in 73 Grand Slam tournaments until the start of the Open Era at the 1968 French Open. (NH = not held).
Grand Slam and Pro Slam finals
Singles
Grand Slam finals (2–0)
Pro Slam finals (13–6)
Career titles
Amateur eraSingles (1948–1949) : 17 titlesProfessional eraSingles (1950–1967) : 85 titlesNotes: All tournaments with a final pro set are basically 4-men tournaments.
1 : 4-men tournaments
2 : T.O.C. = Tournament of Champions.
Open eraSingles (1968–1972) : 10Professional toursSingles (1950–1961) : 10 tours'''
References
Sources
Michel Sutter, Vainqueurs Winners 1946–2003, Paris 2003.
World Tennis Magazines.
Joe McCauley, The History of Professional Tennis'', London 2001.
Gonzales, Pancho |
https://en.wikipedia.org/wiki/Association%20of%20Road%20Racing%20Statisticians | The Association of Road Racing Statisticians is an independent, non-profit organization that collects, analyzes, and publishes statistics regarding road running races. The primary purpose of the ARRS is to maintain a valid list of world road records for standard race distances and to establish valid criteria for road record-keeping. The official publication of the ARRS is the Analytical Distance Runner. This newsletter contains recent race results and analysis and is distributed to subscribers via e-mail. The ARRS is the only organized group that maintains records on indoor marathons.
History
Ken Young (November 9, 1941 - February 3, 2018) of Petrolia, California was a retired professor of atmospheric physics and former American record-holder in the indoor marathon who currently holds two of the top 10 marks in the event. Ted Haydon, a former track coach for the University of Chicago Track Club and the United States in the 1968 Olympic Games, reportedly staged an indoor marathon for Young so that he could make an attempt at a world record in the indoor marathon. Young also earned a PhD in geophysical sciences with a minor in statistics, and taught at the University of Arizona. Young was the founder and director of the National Running Data Center (NRDC), self-described as "an independent, non-profit organization devoted to the collection, analysis, publication and dissemination of long-distance running information." This group pioneered and developed road racing records in the United States.
After the United States Congress passed the Amateur Sports Act of 1978, The Athletics Congress (TAC), now known as USA Track & Field, replaced the Amateur Athletic Union as the national governing body for the sport of athletics. Although the records maintained by Young and the NRDC were initially "unofficial", The Athletics Congress recognized them as its official records at their annual meeting in late 1979. In 1986, the official record-keeping for TAC would be assumed by TACStats, later known as the Road Information Center.
References
External links
Association of Road Racing Statisticians - Official website
Association of Road Racing Statisticians - Facebook
Press release outlining formation of the Association of Road Racing Statisticians (September 13, 2003)
See also
Association of Track and Field Statisticians
Athletics organizations
Statistical societies |
https://en.wikipedia.org/wiki/Ryosuke%20Amo | is a former Japanese football player.
Club statistics
References
External links
sonysendaifc.com
1983 births
Living people
Chuo University alumni
Association football people from Tokushima Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokushima Vortis players
Sony Sendai FC players
Kamatamare Sanuki players
FC Osaka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Shota%20Arai%20%28footballer%2C%20born%201985%29 | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Urawa Red Diamonds players
Ehime FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ryota%20Arimitsu | is a Japanese former professional footballer who played as a forward.
Club statistics
References
External links
library.footballjapan.jp
1981 births
Living people
People from Iizuka, Fukuoka
Association football people from Fukuoka Prefecture
Japanese men's footballers
Japanese expatriate men's footballers
J1 League players
J2 League players
Japan Football League players
Avispa Fukuoka players
V-Varen Nagasaki players
Men's association football forwards |
https://en.wikipedia.org/wiki/Toshiki%20Chino | is a Japanese former football player.
Club statistics
References
External links
library.footballjapan.jp
1985 births
Living people
Association football people from Yamanashi Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Ventforet Kofu players
Blaublitz Akita players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuki%20Fuji | is a Japanese football player for Suzuka Unlimited FC.
Club career statistics
Updated to 23 February 2017.
References
External links
Twitter Account
Instagram Account
1981 births
Living people
Kokushikan University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokushima Vortis players
Giravanz Kitakyushu players
FC Gifu players
Suzuka Point Getters players
Men's association football defenders |
https://en.wikipedia.org/wiki/Yuji%20Goto | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Gifu Prefecture
Japanese men's footballers
J1 League players
Japan Football League players
Yokohama F. Marinos players
FC Gifu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuki%20Hamano | is a former Japanese football player.
Club statistics
References
External links
1978 births
Living people
Momoyama Gakuin University alumni
Association football people from Kagoshima Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Kataller Toyama players
Men's association football defenders |
https://en.wikipedia.org/wiki/Satoshi%20Hashida | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Doshisha University alumni
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kyoto Sanga FC players
Kataller Toyama players
Thespakusatsu Gunma players
Universiade medalists in football
FISU World University Games gold medalists for Japan
Men's association football goalkeepers
Association football people from Kyoto |
https://en.wikipedia.org/wiki/Takehiro%20Hayashi | is a former Japanese football player.
Club statistics
References
External links
1976 births
Living people
Rissho University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Japan Football League (1992–1998) players
Japan Football League players
Tokushima Vortis players
Men's association football forwards |
https://en.wikipedia.org/wiki/Hideaki%20Ikematsu | is a former Japanese football player.
Club statistics
References
External links
sports.geocities.jp
1986 births
Living people
Association football people from Osaka Prefecture
People from Yao, Osaka
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kyoto Sanga FC players
Fagiano Okayama players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yasuki%20Ishidate | is a former Japanese football player.
Club statistics
References
External links
jsgoal.jp
1984 births
Living people
Tokoha University alumni
Association football people from Aichi Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kashiwa Reysol players
Tochigi SC players
Tochigi City FC players
Zweigen Kanazawa players
Men's association football forwards |
https://en.wikipedia.org/wiki/Shohei%20Kamada | is a Japanese former football player.
Club statistics
References
External links
j-league
1980 births
Living people
University of Tsukuba alumni
Association football people from Nagano Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokushima Vortis players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Sho%20Kamogawa | is a former Japanese football player.
Club statistics
References
External links
library.footballjapan.jp
1983 births
Living people
Juntendo University alumni
Association football people from Ōita Prefecture
Japanese men's footballers
J1 League players
Japan Football League players
Nagoya Grampus players
Fagiano Okayama players
Verspah Oita players
Men's association football forwards |
https://en.wikipedia.org/wiki/Tatsuya%20Kamohara | is a former Japanese football player.
Club statistics
References
External links
FC Machida Zelvia
1983 births
Living people
Kokushikan University alumni
Association football people from Saga Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Sagan Tosu players
FC Ryukyu players
FC Machida Zelvia players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Takafumi%20Kanazawa | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Osaka University of Commerce alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J2 League players
Ventforet Kofu players
Mito HollyHock players
Iwate Grulla Morioka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Koichi%20Kawai | is a former Japanese football player. His brother is Kenta Kawai.
Club statistics
References
External links
1979 births
Living people
Chukyo University alumni
Association football people from Ehime Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Ehime FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Shota%20Koide | is a former Japanese football player.
Club statistics
Updated to 20 February 2017.
References
External links
Profile at Nara Club
1981 births
Living people
Fukuoka University alumni
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Sagan Tosu players
Gainare Tottori players
Iwate Grulla Morioka players
Nara Club players
Expatriate men's footballers in Thailand
Men's association football midfielders
Association football people from Fukuoka (city) |
https://en.wikipedia.org/wiki/Manabu%20Kubota | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Tokyo Gakugei University alumni
Association football people from Shimane Prefecture
Japanese men's footballers
J2 League players
Yokohama FC players
Giravanz Kitakyushu players
Men's association football forwards |
https://en.wikipedia.org/wiki/Takeshi%20Kuwahara | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Japanese men's footballers
J2 League players
Hokkaido Consadole Sapporo players
Mito HollyHock players
Thespakusatsu Gunma players
Fukushima United FC players
Men's association football midfielders
Association football people from Fukuoka (city) |
https://en.wikipedia.org/wiki/Atsushi%20Matsuura%20%28footballer%2C%20born%201981%29 | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Hannan University alumni
Association football people from Aichi Prefecture
Japanese men's footballers
J2 League players
Tokushima Vortis players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Go%20Nakamura | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Gifu Prefecture
Japanese men's footballers
J1 League players
J2 League players
Júbilo Iwata players
Ehime FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hiroshi%20Narazaki | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Fukuoka University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J2 League players
Sagan Tosu players
Men's association football forwards |
https://en.wikipedia.org/wiki/Yuji%20Oe | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Reilac Shiga FC players
Vissel Kobe players
FC Machida Zelvia players
Men's association football forwards
Association football people from Kyoto |
https://en.wikipedia.org/wiki/Ryunosuke%20Okamoto | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Association football people from Okayama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Gamba Osaka players
Tokushima Vortis players
Kamatamare Sanuki players
FC Osaka players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hirokazu%20Otsubo | is a former Japanese football player who is currently a football referee.
Club statistics
References
External links
spcom.co.jp
1979 births
Living people
Fukuyama University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokushima Vortis players
Sagawa Shiga FC players
Ehime FC players
SP Kyoto FC players
Men's association football forwards
Japanese football referees |
https://en.wikipedia.org/wiki/Yuji%20Rokutan | is a Japanese football player. He currently plays for Yokohama FC.
Club career statistics
Updated to 18 February 2019.
International career
On 7 May 2015, Japan's coach Vahid Halilhodžić called him for a two-days training camp. Rokutan received his first call up to the senior Japan team in August 2015 for 2018 FIFA World Cup qualifiers against Cambodia and Afghanistan.
Honours
Yokohama F. Marinos
Emperor's Cup: 2013
References
External links
Profile at Shimizu S-Pulse
1987 births
Living people
Association football people from Kagoshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
Avispa Fukuoka players
Yokohama F. Marinos players
Vegalta Sendai players
Shimizu S-Pulse players
Yokohama FC players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Masaki%20Saito%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokyo Verdy players
SC Sagamihara players
Zweigen Kanazawa players
Men's association football forwards |
https://en.wikipedia.org/wiki/Shogo%20Sakurai | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Japanese men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Iwate Grulla Morioka players
SP Kyoto FC players
Ococias Kyoto AC players
Men's association football forwards
Association football people from Kyoto |
https://en.wikipedia.org/wiki/Ryuji%20Shimoshi | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Ehime Prefecture
Japanese men's footballers
J2 League players
Sagan Tosu players
Men's association football forwards |
https://en.wikipedia.org/wiki/Yuki%20Takabayashi | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
University of Tsukuba alumni
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Shimizu S-Pulse players
Sagan Tosu players
Montedio Yamagata players
Blaublitz Akita players
Men's association football midfielders
Association football people from Shizuoka (city) |
https://en.wikipedia.org/wiki/Ryota%20Takahashi | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Tokushima Prefecture
Japanese men's footballers
J1 League players
Japan Football League players
Nagoya Grampus players
FC Kariya players
Zweigen Kanazawa players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Shuta%20Takahashi | is a former Japanese football player.
Club statistics
References
External links
1983 births
Living people
Waseda University alumni
Association football people from Tokyo
Japanese men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Tokyo Musashino United FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Fundamental%20group%20scheme | In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete valuation ring). It is a generalisation of the étale fundamental group. Although its existence was conjectured by Alexander Grothendieck, the first proof if its existence is due, for schemes defined over fields, to Madhav Nori. A proof of its existence for schemes defined over Dedekind schemes is due to Marco Antei, Michel Emsalem and Carlo Gasbarri.
History
The (topological) fundamental group associated with a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. Although it is still being studied for the classification of algebraic varieties even in algebraic geometry, for many applications the fundamental group has been found to be inadequate for the classification of objects, such as schemes, that are more than just topological spaces. The same topological space may have indeed several distinct scheme structures, yet its topological fundamental group will always be the same. Therefore, it became necessary to create a new object that would take into account the existence of a structural sheaf together with a topological space. This led to the creation of the étale fundamental group, the projective limit of all finite groups acting on étale coverings of the given scheme . Nevertheless, in positive characteristic the latter has obvious limitations, since it does not take into account the existence of group schemes that are not étale (e.g., when the characteristic is ) and that act on torsors over , a natural generalization of the coverings. It was from this idea that Grothendieck hoped for the creation of a new true fundamental group (un vrai groupe fondamental, in French), the existence of which he conjectured, back in the early 1960s in his celebrated SGA 1, Chapitre X. More than a decade had to pass before a first result on the existence of the fundamental group scheme came to light. As mentioned in the introduction this result was due to Madhav Nori who in 1976 published his first construction of this new object for schemes defined over fields. As for the name he decided to abandon the true fundamental group name and he called it, as we know it nowadays, the fundamental group scheme. It is also often denoted as , where stands for Nori, in order to distinguish it from the previous fundamental groups and to its modern generalizations. The demonstration of the existence of defined on regular schemes of dimension 1 had to wait about forty more years. There are various generalizations such as the -fundamental group scheme and the quasi finite fundamental group scheme .
Definition and construction
The original definition and the first construction have been suggested by Nori for schemes over fields. Then they have been adapted to a wider range of schemes. So far the only complete theories exist for schemes d |
https://en.wikipedia.org/wiki/Wendel%27s%20theorem | In geometric probability theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an -dimensional hypersphere all lie on the same "half" of the hypersphere. In other words, one seeks the probability that there is some half-space with the origin on its boundary that contains all N points. Wendel's theorem says that the probability is
The statement is equivalent to being the probability that the origin is not contained in the convex hull of the N points and holds for any probability distribution on that is symmetric around the origin. In particular this includes all distribution which are rotationally invariant around the origin.
This is essentially a probabilistic restatement of Schläfli's theorem that hyperplanes in general position in divides it into regions.
References
Probability theorems
Theorems in geometry |
https://en.wikipedia.org/wiki/Lester%20S.%20Hill | Lester S. Hill (1891–1961) was an American mathematician and educator who was interested in applications of mathematics to communications. He received a bachelor's degree (1911) and a master's degree (1913) from Columbia College and a Ph.D. from Yale University (1926). He taught at the University of Montana, Princeton University, the University of Maine, Yale University, and Hunter College. Among his notable contributions was the Hill cipher. He also developed methods for detecting errors in telegraphed code numbers and wrote two books.
References
Rosen, Kenneth (2005). Elementary Number Theory and its Applications, fifth edition, Addison-Wesley, p. 292.
1891 births
Columbia College (New York) alumni
Yale University alumni
University of Montana faculty
Princeton University faculty
University of Maine faculty
Yale University faculty
Hunter College faculty
1961 deaths
20th-century American mathematicians
Mathematicians from New York (state) |
https://en.wikipedia.org/wiki/Reeb%20stability%20theorem | In mathematics, Reeb stability theorem, named after Georges Reeb, asserts that if one leaf of a codimension-one foliation is closed and has finite fundamental group, then all the leaves are closed and have finite fundamental group.
Reeb local stability theorem
Theorem: Let be a , codimension foliation of a manifold and a compact leaf with finite holonomy group. There exists a neighborhood of , saturated in (also called invariant), in which all the leaves are compact with finite holonomy groups. Further, we can define a retraction such that, for every leaf , is a covering map with a finite number of sheets and, for each , is homeomorphic to a disk of dimension k and is transverse to . The neighborhood can be taken to be arbitrarily small.
The last statement means in particular that, in a neighborhood of the point corresponding to a compact leaf
with finite holonomy, the space of leaves is Hausdorff.
Under certain conditions the Reeb local stability theorem may replace the Poincaré–Bendixson theorem in higher dimensions. This is the case of codimension one, singular foliations , with , and some center-type singularity in .
The Reeb local stability theorem also has a version for a noncompact codimension-1 leaf.
Reeb global stability theorem
An important problem in foliation theory is the study of the influence exerted by a compact leaf upon the global structure of a foliation. For certain classes of foliations, this influence is considerable.
Theorem: Let be a , codimension one foliation of a closed manifold . If contains a compact leaf with finite fundamental group, then all the leaves of are compact, with finite fundamental group. If is transversely orientable, then every leaf of is diffeomorphic to ; is the total space of a fibration over , with fibre , and is the fibre foliation, .
This theorem holds true even when is a foliation of a manifold with boundary, which is, a priori, tangent
on certain components of the boundary and transverse on other components. In this case it implies Reeb sphere theorem.
Reeb Global Stability Theorem is false for foliations of codimension greater than one. However, for some special kinds of foliations one has the following global stability results:
In the presence of a certain transverse geometric structure:
Theorem: Let be a complete conformal foliation of codimension of a connected manifold . If has a compact leaf with finite holonomy group, then all the leaves of are compact with finite holonomy group.
For holomorphic foliations in complex Kähler manifold:
Theorem: Let be a holomorphic foliation of codimension in a compact complex Kähler manifold. If has a compact leaf with finite holonomy group then every leaf of is compact with finite holonomy group.
References
C. Camacho, A. Lins Neto: Geometric theory of foliations, Boston, Birkhauser, 1985
I. Tamura, Topology of foliations: an introduction, Transl. of Math. Monographs, AMS, v.97, 2006, 193 p.
Notes
Foli |
https://en.wikipedia.org/wiki/Kim%20Lennhammer | Kim Lennhammer (born July 31, 1990) is a professional ice hockey defenseman who currently plays for Djurgårdens IF in the Elitserien.
Career statistics
References
External links
1990 births
Living people
Swedish ice hockey defencemen
Almtuna IS players
Djurgårdens IF Hockey players
Ice hockey people from Stockholm |
https://en.wikipedia.org/wiki/Kerala%20School%20of%20Mathematics%2C%20Kozhikode | The Kerala School of Mathematics (KSoM) in Kozhikode, India is a research institute in Theoretical sciences with a focus on Mathematics. The institute is a joint venture of the Department of Atomic Energy (DAE) and the Kerala State Council for Science, Technology and Environment (KSCSTE). Kerala School of Mathematics is a center of advanced research and learning in Mathematics and is a meeting ground for leading Mathematicians from around the world.
Kerala School of Mathematics has a doctoral program to which students are admitted on an yearly basis. The institute also has an Integrated MSc-PhD program with an option for students to exit the program with an MSc degree at the end of two years.
History
Mathematics in Kerala, during the times of Madhava of Sangamagrama, majorly flourished in the Muziris region of Thrikkandiyur, Thirur, Alattiyur, and Tirunavaya in the Malabar region of Kerala. Kerala school of astronomy and mathematics flourished between the 14th and 16th centuries. Commemorating the rich heritage of Mathematics in the region, Kerala School of Mathematics was hence chosen to be set up in the scenic mountains of the Western Ghats in the city of Kozhikode.
The nascent plan to set up Kerala School of Mathematics started forming shape in around 2004. The then DAE chairman Anil Kakodkar and the then executive vice president of KSCSTE, M. S. Valiathan were instrumental in setting up the institute with the guidance of M. S. Raghunathan, Rajeeva Karandikar and Alladi Sitaram. The foundation stone of KSoM was laid by the then Chief Minister A.K. Antony in 2004. The institute was later inaugurated in 2008 by the then Chief Minister V. S. Achuthanandan and finally set up in 2009 with Parameswaran A. J. as the founding director.
External links
Official Website
References
Arts and Science colleges in Kerala
Universities and colleges in Kozhikode
Science and technology in Kozhikode
Educational institutions established in 2009
Research institutes in Kerala
Mathematical institutes
2009 establishments in Kerala
Mathematics education in India |
https://en.wikipedia.org/wiki/Stefan%20S%C3%B6der | Stefan Söder (born 11 February 1990 in Stockholm, Sweden) is a professional Swedish ice hockey player. He is currently a forward for Djurgårdens IF in Hockeyallsvenskan.
Career statistics
References
External links
1990 births
Djurgårdens IF Hockey players
Swedish ice hockey forwards
Living people
Ice hockey people from Stockholm |
https://en.wikipedia.org/wiki/Arvid%20Str%C3%B6mberg | Arvid Strömberg (born 30 June 1991 in Stockholm, Sweden) is a professional Swedish ice hockey player. He is currently a forward for Djurgårdens IF in Elitserien.
Career statistics
References
External links
1991 births
Djurgårdens IF Hockey players
Swedish ice hockey forwards
Living people
Ice hockey people from Stockholm |
https://en.wikipedia.org/wiki/Jean%20Fontaine | Jean Fontaine (2 December 1936 – 1 May 2021) was a French writer, theologian, and missionary.
Biography
In 1953, Fontaine earned a bachelor's degree in mathematics. On 15 September 1955, he left for Algeria as part of the White Fathers. From 1956 to 1957, he studied theology at Saint-Joseph de Thibar in Tunisia before becoming a teacher in Algeria. He then took three years of theology courses in Carthage and Arabic studied in Manouba from 1962 to 1964. From 1964 to 1965, he completed his Arabic studies at the Pontifical Institute of Arab and Islamic Studies in Rome. In 1968, he obtained a licentiate in Arabic from Tunis University. From 1968 to 1977, he was a librarian at the and directed the journal Ibla from 1977 to 1999. He earned a doctorate from the University of Provence in 1977.
Jean Fontaine died from COVID-19 on 1 May 2021, at the age of 84 in Tunis, Tunisia.
Publications
Vingt ans de littérature tunisienne 1956-1975 (1977)
Mort-résurrection : une lecture de Tawfiq al-Hakim (1978)
Aspects de la littérature tunisienne 1976-1983 (1985)
Histoire de la littérature tunisienne par les textes, t. I : Des origines à la fin du XIIe siècle (1988)
Études de la littérature tunisienne 1984-1987 (1989)
La littérature tunisienne contemporaine (1990)
Écrivaines tunisiennes (1990)
Regards sur la littérature tunisienne (1991)
Romans arabes modernes (1992)
Histoire de la littérature tunisienne par les textes, t. II : Du XIIIe siècle à l'indépendance (1994)
La crise religieuse des écrivains syro-libanais chrétiens de 1825 à 1940 (1996)
Bibliographie de la littérature tunisienne contemporaine en arabe 1954-1996 (1997)
Propos de littérature tunisienne 1881-1993 (1998)
La blessure de l'âne (1998)
Recherches de littérature arabe moderne (1998)
Itinéraire dans le pays de l'autre (1998)
Histoire de la littérature tunisienne par les textes, t. III : De l'indépendance à nos jours (1999)
Le roman tunisien de langue arabe. 1956-2001 (2002)
Kalimât muhâjira (2002)
Le roman tunisien de langue française (2004)
Points de suspension… (2008)
Le roman tunisien a 100 ans (1906-2006) (2009)
Traduction de Noureddine Alaoui. Une musette de mirages (2010)
Bréviaire des prisonniers étrangers en Tunisie (2012)
Du côté des salafistes en Tunisie (2016)
References
1936 births
2021 deaths
French theologians
French writers
Tunis University alumni
University of Provence alumni
People from Nord (French department)
Deaths from the COVID-19 pandemic in Tunisia
Tunisian theologians |
https://en.wikipedia.org/wiki/Centre%20for%20Mathematical%20Sciences%20%28Kerala%29 | Centre for Mathematical Sciences (CMS), with campuses at Thiruvananthapuram and Pala in Kerala, India, is a research level institution devoted to mathematics and other related disciplines like statistics, theoretical physics, computer and information sciences.
The Centre was incorporated in 1977 as a non-profit scientific research and training centre under the Travancore-Cochin Literary, Scientific and Charitable Societies Registration Act XII of 1955. The driving force behind the establishment of the Centre was Prof. Aleyamma George, who had been Professor and Head of the Department of Statistics of University of Kerala. Since 2006, the Centre is a Department of Science and Technology (India) (DST), Government of India, New Delhi Centre for Mathematical Sciences and is fully financed by DST, New Delhi.
The Centre is headed by a Chairman, a position currently held by Dr. A Sukumaran Nair, a former Vice-Chancellor of Mahatma Gandhi University, Kottayam, and a Director a position now held by Dr. A.M. Mathai, Emeritus Professor of Mathematics and Statistics, McGill University, Canada. The activities of the Thiruvananthapuram Campus are coordinated by Dr. K. S. S. Nambooripad.
The Centre has started doing good work in its early years itself. At present, several research teams are operating in the Centre like Astrophysics Research Group, Fractional Calculus Research Group, Special Functions Research Group, Statistical Distribution Theory Research Group, Geometrical Probability Research Group, Stochastic Process Research Group, and Discrete Mathematics in Chemistry Research Group.
History
Centre for Mathematical Sciences was established in 1977 in Trivandrum, Kerala, India. In 2002, the Pala Campus of the Centre was established in a one-floor finished building donated by the Diocese of Palai in Kerala, India. In 2006, Hill Area Campus of the Centre was established. The office, the library and most of the facilities are at the Pala Campus. Starting from 1985, Professor Dr. A.M. Mathai of McGill University, Canada is the Director of the Centre. In 2006-2007 the Department of Science and Technology (India) (DST) gave a development grant to the Centre. Starting from December 2006, the Centre is being developed as a DST Centre for Mathematical Sciences. DST has similar centres at three other locations in India.
From 1977 to 2006, the activities at the Centre were carried out by a group of researchers in Kerala, mostly retired professors, through voluntary service. Starting from 2007, DST created full-time salaried positions of three Assistant Professors, one Full Professor and one Liaison Officer. They are at Pala Campus. DST approved up to 15 junior research fellows (JRF) and one senior research fellow (SRF). They are the current PhD students at the Pala Campus. They would receive their PhD degrees from Mahatma Gandhi University, Kottayam, Kerala.
Publications
Publications Series (books, proceedings, collections of research papers, lecture n |
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