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https://en.wikipedia.org/wiki/Aurel%20Wintner | Aurel Friedrich Wintner (8 April 1903 – 15 January 1958) was a mathematician noted for his research in mathematical analysis, number theory, differential equations and probability theory. He was one of the founders of probabilistic number theory. He received his Ph.D. from the University of Leipzig in 1928 under the guidance of Leon Lichtenstein. He taught at Johns Hopkins University.
He was a nephew of the astronomer Samuel Oppenheim, and the son-in-law of mathematician Otto Hölder.
Works
Spektraltheorie der unendlichen Matrizen, 1929
The Analytical Foundations of Celestial Mechanics, 1941 (reprinted in 2014 by Dover)
Eratosthenian Averages, 1943
The Theory of Measure in Arithmetical Semi-Groups, 1944
An Arithmetical Approach to Ordinary Fourier Series, 1945
The Fourier Transforms of Probability Distributions, 1947
References
External links
Spektraltheorie Der Unendlichen Matrizen at the Internet Archive
1903 births
1958 deaths
20th-century Hungarian mathematicians
Mathematicians from Budapest
Leipzig University alumni
Johns Hopkins University faculty |
https://en.wikipedia.org/wiki/1930%E2%80%9331%20Galatasaray%20S.K.%20season | The 1930–31 season was Galatasaray SK's 27th in existence and the club's 20th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
Istanbul Football League
Standings
Results summary
Results by round
Matches
Kick-off listed in local time (EEST)
Friendly Matches
İstanbul Shield Final Match
References
Futbol vol.2, Galatasaray. Tercüman Spor Ansiklopedisi.(1981) (page 602)
Erdoğan Arıpınar; Tevfik Ünsi Artun, Cem Atabeyoğlu, Nurhan Aydın, Ergun Hiçyılmaz, Haluk San, Orhan Vedat Sevinçli, Vala Somalı (June 1992). Türk Futbol Tarihi (1904-1991) vol.1, Page(47), Türkiye Futbol Federasyonu Yayınları.
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(111, 114, 116).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(159-160, 177-178). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1930–31 season
1930s in Istanbul |
https://en.wikipedia.org/wiki/Inclination%20%28disambiguation%29 | Inclination is the angle between a reference plane and the orbital plane.
Inclination may also refer to:
Science
Slope, tilt, steepness, or angle from horizontal of a line (in mathematics and geometry)
Axial tilt, also known as equatorial inclination
Grade (slope), the tilt of a topographic feature (hillside, etc.) or constructed element (road, etc.)
Depression angle, part of a spherical coordinate system
Literature
Inclination (ethics), an examination of desire in the context of moral worthiness
"Inclination" (novella), a science fiction novella by William Shunn |
https://en.wikipedia.org/wiki/Sociedade%20Brasileira%20de%20Matem%C3%A1tica%20Aplicada%20e%20Computacional | The Sociedade Brasileira de Matemática Aplicada e Computacional (Brazilian Society for Applied and Computational Mathematics, SBMAC) was created on November 1, 1978 at the First National Symposium on Numerical Analysis, held on the premises of the Institute of Exact Sciences, Federal University of Minas Gerais, in Belo Horizonte, Minas Gerais.
At that time was also appointed the Organizing Committee in charge of dealing with administrative procedures for the installation and operation of the company, as well as the preparation of preliminary design of the Statute.
The Brazilian Society of Applied and Computational Mathematics is organized for the following purposes:
To develop the applications of mathematics in science, technology and industry,
Encourage the development and implementation of effective methods and mathematical techniques to be applied for the benefit of science and Technology,
encourage the training of human resources in mathematics with emphasis on content and efficient use of available computational resources, and
Promote the exchange of ideas and information between the areas of mathematical applications.
See also
Universidade Federal de Minas Gerais
References
O Documento article
External links
Site da SBMAC
Mathematical societies |
https://en.wikipedia.org/wiki/Olimp%C3%ADada%20Brasileira%20de%20Matem%C3%A1tica%20das%20Escolas%20P%C3%BAblicas | The Brazilian Mathematical Olympiad of Public Schools () (OBMEP) is an annual Mathematics contest created in 2005 by the Brazilian Ministério da Ciência e Tecnologia (MCT) and Ministério da Educação (MEC), in collaboration with Instituto Nacional de Matemática Pura e Aplicada (IMPA) and Sociedade Brasileira de Matemática (SBM), to stimulate the mathematics education in Brazil. It is open to public school students from fifth grade to high school. In 2014 more than 18 million students were enrolled for its first round.
References
External links
Official site
See also
Olimpíada Brasileira de Matemática
Brazilian education awards
Mathematics competitions |
https://en.wikipedia.org/wiki/1987%20Cricket%20World%20Cup%20statistics | This is a list of statistics for the 1987 Cricket World Cup.
Team statistics
Highest team totals
The following table lists the ten highest team scores during this tournament.
Batting statistics
Most runs
The top ten highest run scorers (total runs) in the tournament are included in this table.
Highest scores
This table contains the top ten highest scores of the tournament made by a batsman in a single innings.
Highest partnerships
The following tables are lists of the highest partnerships for the tournament.
Bowling statistics
Most wickets
The following table contains the ten leading wicket-takers of the tournament.
Best bowling figures
This table lists the top ten players with the best bowling figures in the tournament.
Fielding statistics
Most dismissals
This is a list of the wicketkeepers who have made the most dismissals in the tournament.
Most catches
This is a list of the outfielders who have taken the most catches in the tournament.
References
External links
Cricket World Cup 1987 Stats from Cricinfo
1987 Cricket World Cup
Cricket World Cup statistics |
https://en.wikipedia.org/wiki/Iblin%2C%20Syria | Iblin (), also spelled Ibleen, is a village in the Arihah District in the Idlib Governorate in Syria. It is located in the Zawiya Mountain. According to the Syria Central Bureau of Statistics (CBS), Iblin had a population of 2,949 in the 2004 census.
Syrian Civil War
During the Syrian Civil War, the village became occupied by Tahrir al-Sham (HTS), a Jihadist opposition faction. After the Syrian Army's 'Dawn of Idlib 2' campaign in 2020, the village became situated near the frontline of fighting in the area.
On 10 June 2021, 4 civilians and 9 Tahrir al-Sham fighters were killed in a Syrian army rocket attack on the village. The spokesperson of the military wing of HTS, Abu Khaled al-Shamy and the media coordinator in the HTS military media department, Abu Mosa’ab were both killed.
References
Populated places in Ariha District
Villages in Idlib Governorate |
https://en.wikipedia.org/wiki/FC%20U%20Craiova%201948%20in%20European%20football | FC U Craiova 1948 is a Romanian football club which currently plays in Liga I.
Total statistics
Statistics by country
Statistics by competition
Notes for the abbreviations in the tables below:
1R: First round
2R: Second round
PR: Preliminary round
QR: Qualifying round
UEFA Champions League / European Cup
UEFA Cup Winners' Cup / European Cup Winners' Cup
UEFA Europa League / UEFA Cup
UEFA Intertoto Cup
References
Romanian football clubs in international competitions
European |
https://en.wikipedia.org/wiki/Jason%20Becker%20%28ice%20hockey%29 | Jason Becker (born May 26, 1974) is a Canadian former ice hockey defenceman who is an assistant coach for the Prince George Cougars in the WHL.
Career statistics
Awards and honours
References
External links
1974 births
Canadian ice hockey defencemen
Fresno Falcons players
Cardiff Devils players
Kamloops Blazers players
Living people
Reading Royals players
Red Deer Rebels players
Saskatchewan Huskies ice hockey players
Saskatoon Blades players
Ice hockey people from Saskatoon
Swift Current Broncos players
Canadian expatriate ice hockey players in Germany
Canadian expatriate ice hockey players in the United States
Canadian expatriate ice hockey players in Wales |
https://en.wikipedia.org/wiki/FC%20Politehnica%20Timi%C8%99oara%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
UEFA Champions League / European Cup
UEFA Cup Winners' Cup / European Cup Winners' Cup
UEFA Europa League / UEFA Cup
External links
Official website
FC Politehnica Timișoara
Romanian football clubs in international competitions |
https://en.wikipedia.org/wiki/Robbins%20problem | The Robbins problem may mean either of:
the Robbins conjecture that all Robbins algebras are Boolean algebras.
Robbins' problem of optimal stopping in probability theory. |
https://en.wikipedia.org/wiki/1908%E2%80%9309%20Galatasaray%20S.K.%20season | The 1908–09 season was Galatasaray SK's 5th in existence and the club's 3rd consecutive season in the IFL. Galatasaray won the league for the first time.
Squad statistics
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Istanbul Football League and Union Club Cup Match
Istanbul Football League
Istanbul Football League
Friendly Matches
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
Yüce, Mehmet.
1908-1909 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(30). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1908–09 season
1900s in Istanbul |
https://en.wikipedia.org/wiki/1906%E2%80%9307%20Galatasaray%20S.K.%20season | The 1906–07 season was Galatasaray SK's 3rd in existence and the club's 1st in the Istanbul Football League.
Squad statistics
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Friendly Matches
References
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(53). Arset Matbaacılık Kol.Şti.
Dağlaroğlu, Rüştü.Fenerbahçe Spor Kulübü Tarihi 1907-1957 - The History of Fenerbahçe SK 1907-1957
Galatasaray. Tercüman Spor Ansiklopedisi Vol. 2 Page (552). Tercüman Yayıncılık ve Matbaacılık AŞ
1906-1907 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(29). (June 1992) Türkiye Futbol Federasyonu Yayınları. Original Source: "The Levant Herald Newspaper"
Şenol, Mehmet. A letter dated November 12, 1906, from Emin Bülent Serdaroğlu to Ali Sami Yen. Galatasaray Magazine, March 2011, page 66-69.
Şenol, Mehmet. A letter dated December 9, 1906, from Asım Tevfik Sonumut to Ali Sami Yen. Galatasaray Magazine, June–July 2011, page 84.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1906–07 season
1900s in Istanbul |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Galatasaray%20S.K.%20season | The 1938–39 season was Galatasaray SK's 35th in existence and the club's 27th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
Istanbul Football Super League
Classification
Matches
Kick-off listed in local time (EEST)
Milli Küme Şampiyonası
Classification
Matches
Kick-off listed in local time (EEST)
Friendly Matches
Stadium Cup
Galatasaray SK won the cup on goal difference over Fenerbahçe SK.
Tan Cup
Galatasaray SK won 2 cups beating Fenerbahçe SK twice.
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
Futbol vol.2, Galatasaray. Tercüman Spor Ansiklopedisi.(1981) (page 586, 595). Tercüman Gazetecilik ve Matbaacılık AŞ.
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(120–123, 183). Arset Matbaacılık Kol.Şti.
Atabeyoğlu, Cem. 1453–1991 Türk Spor Tarihi Ansiklopedisi. page(149–151).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
1938 Milli Küme Maçları. Türk Futbol Tarihi vol.1. page(80–81). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Yeni Sabah Newspaper Archives, April–May 1939
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1938–39 season
1930s in Istanbul |
https://en.wikipedia.org/wiki/%C5%9Aleszy%C5%84ski%E2%80%93Pringsheim%20theorem | In mathematics, the Śleszyński–Pringsheim theorem is a statement about convergence of certain continued fractions. It was discovered by Ivan Śleszyński and Alfred Pringsheim in the late 19th century.
It states that if , , for are real numbers and for all , then
converges absolutely to a number satisfying , meaning that the series
where are the convergents of the continued fraction, converges absolutely.
See also
Convergence problem
Notes and references
Continued fractions
Theorems in real analysis |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20Galatasaray%20S.K.%20season | The 1979–80 season was Galatasaray's 76th in existence and the club's 22nd consecutive season in the Turkish First Football League. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
2nd leg Galatasaray SK – Bursa SK squad has not been added
Players in / out
In
Out
1. Lig
Standings
Matches
Kick-off listed in local time (EET)
Turkiye Kupasi
5th stage
6th stage
Quarter-final
Semi-final
Final
UEFA Cup
First round
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
1979–1980 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(121). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1979–80 season
1970s in Istanbul
1980s in Istanbul |
https://en.wikipedia.org/wiki/Philip%20Batchelor | Philip Batchelor (30 December 1967 in St Austell, Cornwall, UK – 30 August 2011 near Annecy, France), was a Swiss-British academic in the fields of mathematics and medical imaging.
Life
Batchelor was born in St Austell, Cornwall and grew up in Vouvry, a village in Switzerland. He graduated from ETH Zurich with a Masters in Theoretical Physics in 1992 and continued studying in Zurich for a PhD in Mathematics, which he obtained in 1997. In 1998, Batchelor joined United Medical and Dental School, which later became part of King's College London (KCL), to work on the application of mathematical principles to magnetic resonance imaging (MRI) at Guy's Hospital. He rapidly made an impact by employing concepts from differential geometry to study folding and curvature in the developing human brain. In 2005 he moved to the Centre for Medical Image Computing at University College London, and was appointed a Senior Lecturer in the Imaging Sciences Division at KCL in 2006.
He gained a reputation for an ability to get to the heart of the issue and to draw in knowledge from other areas. A good example of this came during his work on diffusion tensor imaging (DTI). In trying to quantify the shapes of fibre tracts seen in DTI, he found measures that focussed on shape, not brain size. Furthermore, these measures were inspired from such varied fields as torsion and polymer structure analysis and even the orbits of asteroids. In 2002, the choice of which diffusion gradient directions to acquire in diffusion tensor imaging was the subject of debate in the literature, with various empirical approaches having been proposed. At its core, this was a problem that combined the geometry related to the equal distribution of points on a hemisphere (the diffusion directions) and the diffusion-attenuated signal in MRI. Batchelor showed why direction schemes based on icosahedral shapes are optimal, and provided proof that the noise propagation in these icosahedral direction schemes was closely related to the best that could ever be done by acquiring an infinite number of directions.
There was also the issue of how to manipulate the tensor data from DTI. In one of his most highly cited papers, Batchelor provided a rigorous framework that showed how to measure the geodesic distance between tensors (always maintaining an ellipsoid shape), how to average them, how to perform interpolation and rotation and he devised a metric called the geodesic anisotropy – an alternative to the commonly used fractional anisotropy measure.
Another key insight came from considering the key problem of how to correct non-rigid liver motion in MRI. Batchelor had the insight that this highly non-linear process could nonetheless be expressed concisely and in a general form using matrices. This has opened the field of non-rigid motion correction in MRI (e.g.).
Batchelor was a committed teacher and was always willing to patiently assist his colleagues and students with tutorials in mathematics. He rec |
https://en.wikipedia.org/wiki/Zs%C3%B3fi%20Szemerey | Zsófi Szemerey (born 2 June 1994) is a Hungarian handball goalkeeper who plays for Mosonmagyaróvári KC SE.
References
External links
Profile on Győri ETO KC official website
Career statistics at Worldhandball
1994 births
Living people
People from Kazincbarcika
Hungarian female handball players
Győri Audi ETO KC players
Sportspeople from Borsod-Abaúj-Zemplén County |
https://en.wikipedia.org/wiki/FC%20Arge%C8%99%20Pite%C8%99ti%20in%20European%20football | FC Argeș Pitești is a football club from Romania which currently plays in Liga I.
Statistics by competition
Statistics by country
Statistics by competition
Notes for the abbreviations in the tables below:
1R: First round
2R: Second round
3R: Third round
1QR: First qualifying round
2QR: Second qualifying round
UEFA Champions League / European Cup
UEFA Europa League / UEFA Cup
Inter-Cities Fairs Cup
External links
Official website
Romanian football clubs in international competitions
FC Argeș Pitești |
https://en.wikipedia.org/wiki/Sauer%E2%80%93Shelah%20lemma | In combinatorial mathematics and extremal set theory, the Sauer–Shelah lemma states that every family of sets with small VC dimension consists of a small number of sets. It is named after Norbert Sauer and Saharon Shelah, who published it independently of each other in 1972. The same result was also published slightly earlier and again independently, by Vladimir Vapnik and Alexey Chervonenkis, after whom the VC dimension is named. In his paper containing the lemma, Shelah gives credit also to Micha Perles, and for this reason the lemma has also been called the Perles–Sauer–Shelah lemma.
Buzaglo et al. call this lemma "one of the most fundamental results on VC-dimension", and it has applications in many areas. Sauer's motivation was in the combinatorics of set systems, while Shelah's was in model theory and that of Vapnik and Chervonenkis was in statistics. It has also been applied in discrete geometry and graph theory.
Definitions and statement
If is a family of sets and is a set, then is said to be shattered by if every subset of (including the empty set and itself) can be obtained as the intersection of with some set in the family. The VC dimension of is the largest cardinality of a set shattered by .
In terms of these definitions, the Sauer–Shelah lemma states that if is a family of sets, the union of has elements, and
then shatters a set of size . Equivalently, if the VC dimension of is then can consist of at most sets, as expressed using big O notation.
The bound of the lemma is tight: Let the family be composed of all subsets of with size less than . Then the size of is exactly but it does not shatter any set of size .
The number of shattered sets
A strengthening of the Sauer–Shelah lemma, due to , states that every finite set family shatters at least sets. This immediately implies the Sauer–Shelah lemma, because only of the subsets of an -item universe have cardinality less than . Thus, when there are not enough small sets to be shattered, so one of the shattered sets must have cardinality at least .
For a restricted type of shattered set, called an order-shattered set, the number of shattered sets always equals the cardinality of the set family.
Proof
Pajor's variant of the Sauer–Shelah lemma may be proved by mathematical induction; the proof has variously been credited to Noga Alon or to Ron Aharoni and Ron Holzman.
Base Every family of only one set shatters the empty set.
Step Assume the lemma is true for all families of size less than and let be a family of two or more sets. Let be an element that belongs to some but not all of the sets in . Split into two subfamilies, of the sets that contain and the sets that do not contain . By the induction assumption, these two subfamilies shatter two collections of sets whose sizes add to at least . None of these shattered sets contain , since a set that contains cannot be shattered by a family in which all sets contain or all sets do not contain . Some |
https://en.wikipedia.org/wiki/Inflation%20in%20India | Inflation rate in India was 5.5% as of May 2019, as per the Indian Ministry of Statistics and Programme Implementation. This represents a modest reduction from the previous annual figure of 9.6% for June 2011. Inflation rates in India are usually quoted as changes in the Wholesale Price Index (WPI), for all commodities.
Many developing countries use changes in the consumer price index (CPI) as their central measure of inflation. In India, CPI (combined) is declared as the new standard for measuring inflation (April 2014). CPI numbers are typically measured monthly, and with a significant lag, making them unsuitable for policy use. India uses changes in the CPI to measure its rate of inflation.
The WPI measures the price of a representative basket of wholesale goods. In India, this basket is composed of three groups: Primary Articles (22.62% of total weight), Fuel and Power (13.15%) and Manufactured Products (64.23%). Food Articles from the Primary Articles Group account for 15.26% of the total weight. The most important components of the Manufactured Products Group are, Food products (19.12%); Chemicals and Chemical products (12%); Basic Metals, Alloys and Metal Products (10.8%); Machinery and Machine Tools (8.9%); Textiles (7.3%) and Transport, Equipment and Parts (5.2%).
WPI numbers were typically measured weekly by the Ministry of Commerce and Industry. This makes it more timely than the lagging and infrequent CPI statistic. However, since 2009 it has been measured monthly instead of weekly.
Issues
The challenges in developing economy are many, especially when in context of the monetary policy with the Central Bank, the inflation and price stability phenomenon. There has been a universal argument these days when monetary policy is determined to be a key element in depicting and controlling inflation. The Central Bank works on the objective to control and have a stable price for commodities. A good environment of price stability happens to create saving mobilisation and a sustained economic growth.
The former Governor of RBI C. Rangarajan points out that there is a long-term trade-off between output and inflation. He adds on that short-term trade-off happens to only introduce uncertainty about the price level in future. There is an agreement that the central banks have aimed to introduce the target of price stability while an argument supports it for what that means in practice.
Optimal inflation rate
It arises as the basic theme in deciding an adequate monetary policy. There are two debatable proportions for an effective inflation, whether it should be in the range of 1–3 per cent as the inflation rate that persists in the industrialized economy or should it be in the range of 6–7 per cent. While deciding on the elaborate inflation rate certain problems occur regarding its measurement.
The measurement bias has often calculated an inflation rate that is comparatively more than actual. Secondly, there often arises a problem when the qu |
https://en.wikipedia.org/wiki/Almgren%20regularity%20theorem | In geometric measure theory, a field of mathematics, the Almgren regularity theorem, proved by , states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long. Within the proof many new ideas are introduced, such as monotonicity of a frequency function and the use of a center manifold to perform a more intricate blow-up procedure.
A streamlined and more accessible proof of Almgren's regularity theorem, following the same ideas as Almgren, was given by Camillo De Lellis and Emanuele Spadaro in a series of three papers.
References
Theorems in measure theory
Theorems in geometry |
https://en.wikipedia.org/wiki/MINLOG | MINLOG is a proof assistant developed at the University of Munich by the team of Helmut Schwichtenberg.
MINLOG is based on first order natural deduction calculus. It is intended to reason about computable functionals, using minimal rather than classical or intuitionistic logic. The primary motivation behind MINLOG is to exploit the proofs-as-programs paradigm for program development and program verification. Proofs are, in fact, treated as first-class objects, which can be normalized. If a formula is existential, then its proof can be used for reading off an instance of it or changed appropriately for program development by proof transformation. To this end, MINLOG is equipped with tools to extract functional programs directly from proof terms. This also applies to non-constructive proofs, using a refined A-translation. The system is supported by automatic proof search and normalization by evaluation as an efficient term rewriting device.
External links
MINLOG homepage
Proof assistants |
https://en.wikipedia.org/wiki/1904%E2%80%9305%20Galatasaray%20S.K.%20season | The 1904–05 season was Galatasaray SK's first. Galatasaray SK did not join the IFL.
Squad statistics
Friendly Matches
Kick-off listed in local time (EEST)
References
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1904–05 season
1900s in Istanbul |
https://en.wikipedia.org/wiki/1905%E2%80%9306%20Galatasaray%20S.K.%20season | The 1905–06 season was Galatasaray SK's 2nd in existence. Galatasaray SK did not join the IFL.
Squad statistics
Friendly Matches
Kick-off listed in local time (EEST)
Kick-off listed in local time (EEST)
References
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(53). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1905–06 season
1900s in Istanbul |
https://en.wikipedia.org/wiki/Juan%20Pedro%20Pina | Juan Pedro Pina Martínez (born 29 June 1985 in Murcia) is a Spanish professional footballer who plays for Orihuela CF as a right back.
Career statistics
References
External links
1985 births
Living people
Spanish men's footballers
Footballers from Murcia
Men's association football defenders
La Liga players
Segunda División players
Segunda División B players
Tercera División players
Real Murcia Imperial players
Real Murcia CF players
CD Alcoyano footballers
UCAM Murcia CF players
Lorca FC players
Recreativo de Huelva players
Orihuela CF players
Cypriot First Division players
Doxa Katokopias FC players
Spanish expatriate men's footballers
Expatriate men's footballers in Cyprus
Spanish expatriate sportspeople in Cyprus |
https://en.wikipedia.org/wiki/Radical%20extension | In mathematics and more specifically in field theory, a radical extension of a field K is an extension of K that is obtained by adjoining a sequence of nth roots of elements.
Definition
A simple radical extension is a simple extension F/K generated by a single element satisfying for an element b of K. In characteristic p, we also take an extension by a root of an Artin–Schreier polynomial to be a simple radical extension. A radical series is a tower where each extension is a simple radical extension.
Properties
If E is a radical extension of F and F is a radical extension of K then E is a radical extension of K.
If E and F are radical extensions of K in an extension field C of K, then the compositum EF (the smallest subfield of C that contains both E and F) is a radical extension of K.
If E is a radical extension of F and E > K > F then E is a radical extension of K.
Solvability by radicals
Radical extensions occur naturally when solving polynomial equations in radicals. In fact a solution in radicals is the expression of the solution as an element of a radical series: a polynomial f over a field K is said to be solvable by radicals if there is a splitting field of f over K contained in a radical extension of K.
The Abel–Ruffini theorem states that such a solution by radicals does not exist, in general, for equations of degree at least five. Évariste Galois showed that an equation is solvable in radicals if and only if its Galois group is solvable. The proof is based on the fundamental theorem of Galois theory and the following theorem.
The proof is related to Lagrange resolvents. Let be a primitive nth root of unity (belonging to K). If the extension is generated by with as a minimal polynomial, the mapping induces a K-automorphism of the extension that generates the Galois group, showing the "only if" implication. Conversely, if is a K-automorphism generating the Galois group, and is a generator of the extension, let
The relation implies that the product of the conjugates of (that is the images of by the K-automorphisms) belongs to K, and is equal to the product of by the product of the nth roots of unit. As the product of the nth roots of units is , this implies that and thus that the extension is a radical extension.
It follows from this theorem that a Galois extension may be extended to a radical extension if and only if its Galois group is solvable (but there are non-radical Galois extensions whose Galois group is solvable, for example ). This is, in modern terminology, the criterion of solvability by radicals that was provided by Galois. The proof uses the fact that the Galois closure of a simple radical extension of degree n is the extension of it by a primitive nth root of unity, and that the Galois group of the nth roots of unity is cyclic.
References
Galois theory
Equations |
https://en.wikipedia.org/wiki/STEM%20Academy | STEM Academy or S.T.E.M. Academy, a school for science, technology, engineering and mathematics, may refer to:
Bluford Drew Jemison STEM Academy West, a Middle/High School at Walbrook High School in Baltimore, Maryland
Downingtown STEM Academy, a magnet high school in Downingtown, Pennsylvania
Knox County STEM Academy, a magnet high school in Knoxville, Tennessee
STEM Academy at A. L. Brown High School in Kannapolis, North Carolina
STEM Academy at Cypress Creek High School (Harris County, Texas)
STEM Academy at Franklin High School (Elk Grove, California)
STEM Academy at University High School (Orange City) in Orange City, Florida
STEM Academy at Ponitz Career Technology Center in Dayton, Ohio
STEM Academy at Robert E. Lee High School (San Antonio, Texas)
STEM Academy at Comstock Public School District in Kalamazoo, Michigan
Tesla STEM High School, a magnet school in Redmond, Washington
STEM Magnet Academy at Chicago Public Schools in Chicago, Illinois
S.T.E.M. Academy at Liverpool High School in Liverpool, New York
S.T.E.M. Academy at Stony Point High School in Round Rock, Texas
STEMS Academy at Springfield High School (Springfield, Ohio)
Phoenix STEM Academy at Dalton L. McMichael High School in Mayodan, North Carolina
A-STEM Academy at Pemberton Township High School in Pemberton, New Jersey
T-STEM Academy at Humble High School in Humble, Texas
STEM Academy at Great Mills High School in Great Mills, Maryland |
https://en.wikipedia.org/wiki/Estevam%20Soares | Estevam Eduardo Lemos Soares (born 10 June 1956, in Cafelândia, São Paulo), known as Estevam Soares, is a Brazilian football manager.
Managerial statistics
Honours
Manager
Inter de Limeira
Campeonato Paulista Série A2: 1995
América-RN
Campeonato Potiguar: 1997
CSA
Campeonato Alagoano: 1999
References
1956 births
Living people
Brazilian men's footballers
Men's association football defenders
Brazilian football managers
Expatriate football managers in Lebanon
Expatriate football managers in Saudi Arabia
Campeonato Brasileiro Série A managers
Campeonato Brasileiro Série B managers
Campeonato Brasileiro Série C managers
Campeonato Brasileiro Série D managers
Guarani FC players
Esporte Clube XV de Novembro (Jaú) players
São Paulo FC players
Associação Portuguesa de Desportos players
Esporte Clube Bahia players
Sport Club do Recife players
Esporte Clube Vitória players
Associação Atlética Ponte Preta players
Sampaio Corrêa Futebol Clube players
Fluminense de Feira Futebol Clube players
Associação Atlética Internacional (Limeira) managers
ABC Futebol Clube managers
União Recreativa dos Trabalhadores managers
Guarani FC managers
América Futebol Clube (RN) managers
Centro Sportivo Alagoano managers
Associação Atlética Ponte Preta managers
Clube Náutico Capibaribe managers
Clube de Regatas Brasil managers
Sociedade Esportiva do Gama managers
Sociedade Esportiva Palmeiras managers
Al-Ittihad Club (Jeddah) managers
Associação Desportiva São Caetano managers
Coritiba Foot Ball Club managers
Grêmio Barueri Futebol managers
Associação Portuguesa de Desportos managers
Botafogo de Futebol e Regatas managers
Ceará Sporting Club managers
São Bernardo Futebol Clube managers
Oeste Futebol Clube managers
Esporte Clube XV de Novembro (Piracicaba) managers
Clube Atlético Sorocaba managers
Rio Claro Futebol Clube managers
Tupi Football Club managers
Clube Atlético Bragantino managers
Itumbiara Esporte Clube managers
Central Sport Club managers
Associação Atlética de Altos managers
Sociedade Imperatriz de Desportos managers
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20properties%20of%20points | In mathematics, the following appear:
Algebraic point
Associated point
Base point
Closed point
Divisor point
Embedded point
Extreme point
Fermat point
Fixed point
Focal point
Geometric point
Hyperbolic equilibrium point
Ideal point
Inflection point
Integral point
Isolated point
Generic point
Heegner point
Lattice hole, Lattice point
Lebesgue point
Midpoint
Napoleon points
Non-singular point
Normal point
Parshin point
Periodic point
Pinch point
Point (geometry)
Point source
Rational point
Recurrent point
Regular point, Regular singular point
Saddle point
Semistable point
Separable point
Simple point
Singular point of a curve
Singular point of an algebraic variety
Smooth point
Special point
Stable point
Torsion point
Vertex (curve)
Weierstrass point
Calculus
Critical point (aka stationary point), any value v in the domain of a differentiable function of any real or complex variable, such that the derivative of v is 0 or undefined
Geometry
Antipodal point, the point diametrically opposite to another point on a sphere, such that a line drawn between them passes through the centre of the sphere and forms a true diameter
Conjugate point, any point that can almost be joined to another by a 1-parameter family of geodesics (e.g., the antipodes of a sphere, which are linkable by any meridian
Vertex (geometry), a point that describes a corner or intersection of a geometric shape
Apex (geometry), the vertex that is in some sense the highest of the figure to which it belongs
Topology
Adherent point, a point x in topological space X such that every open set containing x contains at least one point of a subset A
Condensation point, any point p of a subset S of a topological space, such that every open neighbourhood of p contains uncountably many points of S
Limit point, a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be approximated by points of S, since every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself
Accumulation point (or cluster point), a point of a sequence (xn)n ∈ N for which there are, for every neighbourhood V of x, infinitely many natural numbers n such that xn ∈ V
See also
:Category:Triangle centers, special points associated with triangles
Points |
https://en.wikipedia.org/wiki/Divisor%20%28disambiguation%29 | A divisor is the second operand of a division.
A divisor may also refer to
Divisor (number theory), an integer that divides evenly another integer
Divisor (ring theory), a generalization of the preceding concept
Divisor (algebraic geometry), a generalization of codimension one subvarieties of algebraic varieties |
https://en.wikipedia.org/wiki/1909%E2%80%9310%20Galatasaray%20S.K.%20season | The 1909–10 season was Galatasaray SK's 6th in existence and the club's 4th consecutive season in the IFL. Galatasaray won the league for the second time.
Squad statistics
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Friendly Matches
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
1909-1910 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(31). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1909–10 season
1900s in Istanbul
1910s in Istanbul |
https://en.wikipedia.org/wiki/1992%20Cricket%20World%20Cup%20statistics | This is a list of statistics for the 1992 Cricket World Cup.
Team statistics
Highest team totals
The following table lists the ten highest team scores during this tournament.
Batting statistics
Most runs
The top ten highest run scorers (total runs) in the tournament are included in this table.
Highest scores
This table contains the top ten highest scores of the tournament made by a batsman in a single innings.
Highest partnerships
The following tables are lists of the highest partnerships for the tournament.
Bowling statistics
Most wickets
The following table contains the ten leading wicket-takers of the tournament.
Best bowling figures
This table lists the top ten players with the best bowling figures in the tournament.
Fielding statistics
Most dismissals
This is a list of the wicketkeepers who have made the most dismissals in the tournament.
References
External links
Cricket World Cup 1992 stats from Cricinfo
Knockout stage
Cricket World Cup statistics |
https://en.wikipedia.org/wiki/1910%E2%80%9311%20Galatasaray%20S.K.%20season | The 1910–11 season was Galatasaray SK's 7th in existence and the club's 5th consecutive season in the IFL. Galatasaray won the league for the third time.
Squad statistics
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Friendly Matches
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
1910-1911 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(31). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(60).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Şenol, Mehmet. First trip to Europe. Galatasaray Magazine, August 2011, page 70-73.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1910–11 season
1910s in Istanbul |
https://en.wikipedia.org/wiki/LEGO%20%28proof%20assistant%29 | LEGO is a proof assistant developed by Randy Pollack at the University of Edinburgh. It implements several type theories: the Edinburgh Logical Framework (LF), the Calculus of Constructions (CoC), the Generalized Calculus of Constructions (GCC) and the Unified Theory of Dependent Types (UTT).
References
External links
Proof assistants
Dependently typed languages |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20Galatasaray%20S.K.%20season | The 1980–81 season was Galatasaray's 77th in existence and the 23rd consecutive season in the Turkish First Football League. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
2nd leg Galatasaray SK – Bursa SK squad has not been added
Players in / out
In
Out
1. Lig
Standings
Matches
Kick-off listed in local time (EET)
Turkiye Kupasi
Kick-off listed in local time (EET)
5th Round
6th Round
Quarter-final
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1980–81 season
1980s in Istanbul |
https://en.wikipedia.org/wiki/Twisted%20geometries | Twisted geometries are discrete geometries that play a role in loop quantum gravity and spin foam models,
where they appear in the semiclassical limit of spin networks. A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph.
Intrinsic and extrinsic curvatures are defined in a manner similar to Regge calculus, but with the generalisation of including a certain type of metric discontinuities: the face shared by two adjacent polyhedra has a unique area, but its shape can be different.
This is a consequence of the quantum geometry of spin networks: ordinary Regge calculus is "too rigid" to account for all the geometric degrees of freedom described by the semiclassical limit of a spin network.
The name twisted geometry captures the relation between these additional degrees of freedom and the off-shell presence of torsion in the theory, but also the fact that this classical description can be derived from Twistor theory, by assigning a pair of twistors to each link of the graph, and suitably constraining their helicities and incidence relations.
References
Loop quantum gravity
Physics beyond the Standard Model |
https://en.wikipedia.org/wiki/Skip%20Garibaldi | Skip Garibaldi is an American mathematician doing research on algebraic groups and especially exceptional groups.
Biography
Garibaldi dropped out of high school to attend Purdue University, where he earned B.S. degrees in mathematics and in computer science. He then obtained a Ph.D. in mathematics from the University of California, San Diego in 1998. His doctoral thesis was on triality and algebraic groups. After holding positions at ETH Zurich and the University of California, Los Angeles, (with Jared Hersh serving as his long-time Reader and typist) he joined the faculty at Emory University in 2002, and was eventually promoted to Winship Distinguished Research Professor. In 2013 he became associate director of IPAM at UCLA.
On winning the lottery
Garibaldi plays the lottery and has given some math-based tips on how to increase bettors' chances of winning lotto games, particularly the Powerball and Mega Millions. For instance, he advises against betting on the same numbers (as lotto winner Richard Lustig once advocated) in favor of randomly selected numbers, explaining that the latter decrease the probability of splitting the jackpot with another bettor using the former, and that the odds of winning using either method are ultimately the same.
Scientific contributions
Garibaldi's most-cited work is the book "Cohomological invariants in Galois cohomology" written with Alexander Merkurjev and Jean-Pierre Serre, which gives the foundations of the theory of cohomological invariants of algebraic groups. His long work "Cohomological invariants: exceptional groups and Spin groups" built on this theme.
He received press coverage for his paper "There is no Theory of Everything inside E8" with Jacques Distler proposing a disproof of Garrett Lisi's "An Exceptionally Simple Theory of Everything".
He is also known for his less-technical articles on the lottery which led to TV appearances and policy changes in Florida and Georgia. He contributed to a story in Slate magazine by Chris Wilson about arranging stars on the US flag that was reported on CBS News Sunday Morning.
Recognition
In 2011 he received the Lester R. Ford Award from the Mathematical Association of America.
He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to group theory and service to the mathematical community, particularly in support of promoting mathematics to a wide audience".
References
External links
Personal Webpage
Living people
Year of birth missing (living people)
20th-century American mathematicians
21st-century American mathematicians
Group theorists
Emory University faculty
Algebraists
Fellows of the American Mathematical Society
Purdue University alumni
University of California, San Diego alumni |
https://en.wikipedia.org/wiki/Gorenstein%E2%80%93Harada%20theorem | In mathematical finite group theory, the Gorenstein–Harada theorem, proved by in a 464-page paper, classifies the simple finite groups of sectional 2-rank at most 4. It is part of the classification of finite simple groups.
Finite simple groups of section 2 that rank at least 5, have Sylow 2-subgroups with a self-centralizing normal subgroup of rank at least 3, which implies that they have to be of either component type or of characteristic 2 type. Therefore, the Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two sub-cases.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Koichiro%20Harada | is a Japanese mathematician working on finite group theory.
The Institute for Advanced Study was Harada's first position in the United States in 1968.
He graduated from University of Tokyo in 1972.
Rutgers University was the scene from 1969 to 73 of his collaboration with Daniel Gorenstein on the classification challenge in finite groups. In 1971 he first taught at Ohio State University, and in 1973 he was a visitor at Cambridge University where the Harada-Norton group was discovered.
The Gorenstein–Harada theorem classifies finite simple groups of sectional 2-rank at most 4.
In 1996 Ohio State held a Special Research Quarter on the Monster group and Lie algebras with Proceedings edited by Joseph Ferrar and Harada.
In 2000 Mathematical Society of Japan awarded Harada the Algebra Prize.
After the classification of finite simple groups was announced, Harada proposed the following challenges to group theorists:
Find natural mathematical objects realizing all simple groups as their automorphism groups.
Prove that there are only finitely many sporadic simple groups.
Find the reason why the 26 sporadic simple groups exist.
Find a generalization of the Glauberman Z* theorem.
Find an arithmetic to give the Schur multipliers of finite simple groups.
Complete the theory of modular representations.
Classify the 2-groups that can be the Sylow 2-subgroups of finite simple groups.
Look for a completely new proof of the classification.
Classify finite simple groups having a strongly p-embedded subgroup.
Solve problems around the restricted Burnside problem.
Publications
1974: (with Daniel Gorenstein) Finite simple groups whose 2-subgroups are generated by at least 4 elements, Memoirs of the American Mathematical Society.
1975: On the simple group F of order 214 · 36 · 56 · 7 · 11 · 19. Proc. Group Theory Conference in Park City, Utah, pp. 119–276.
1989: Some elliptic curves arising from the Leech lattice, Journal of Algebra 125: 289–310.
1999: Monster. Iwanami Publishing, (in Japanese; book on the Monster group).
2010: "Moonshine" of Finite Groups, European Mathematical Society
References
20th-century Japanese mathematicians
21st-century Japanese mathematicians
Living people
1941 births |
https://en.wikipedia.org/wiki/G%C3%B6del%27s%20speed-up%20theorem | In mathematics, Gödel's speed-up theorem, proved by , shows that there are theorems whose proofs can be drastically shortened by working in more powerful axiomatic systems.
Kurt Gödel showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is unimaginably long. For example, the statement:
"This statement cannot be proved in Peano arithmetic in fewer than a googolplex symbols"
is provable in Peano arithmetic (PA) but the shortest proof has at least a googolplex symbols, by an argument similar to the proof of Gödel's first incompleteness theorem: If PA is consistent, then it cannot prove the statement in fewer than a googolplex symbols, because the existence of such a proof would itself be a theorem of PA, a contradiction. But simply enumerating all strings of length up to a googolplex and checking that each such string is not a proof (in PA) of the statement, yields a proof of the statement (which is necessarily longer than a googolplex symbols).
The statement has a short proof in a more powerful system: in fact the proof given in the previous paragraph is a proof in the system of Peano arithmetic plus the statement "Peano arithmetic is consistent" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic).
In this argument, Peano arithmetic can be replaced by any more powerful consistent system, and a googolplex can be replaced by any number that can be described concisely in the system.
Harvey Friedman found some explicit natural examples of this phenomenon, giving some explicit statements in Peano arithmetic and other formal systems whose shortest proofs are ridiculously long . For example, the statement
"there is an integer n such that if there is a sequence of rooted trees T1, T2, ..., Tn such that Tk has at most k+10 vertices, then some tree can be homeomorphically embedded in a later one"
is provable in Peano arithmetic, but the shortest proof has length at least A(1000), where A(0)=1 and A(n+1)=2A(n). The statement is a special case of Kruskal's theorem and has a short proof in second order arithmetic.
If one takes Peano arithmetic together with the negation of the statement above, one obtains an inconsistent theory whose shortest known contradiction is equivalently long.
See also
Blum's speedup theorem
List of long proofs
References
Proof theory
Theorems in the foundations of mathematics
Speed-up theorem |
https://en.wikipedia.org/wiki/1928%E2%80%9329%20Galatasaray%20S.K.%20season | The 1928–29 season was Galatasaray SK's 25th in existence and the club's 18th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1928–29 season
In:
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
Gazi Büstü
Gazi Büstü Tournament was a football tournament between Fenerbahçe SK and Galatasaray SK to promote Tayyare Cemiyeti. The winner of this tournament was awarded with an Atatürk bust which was very important. This statue was the first and last thing that was in the name of Atatürk when he was alive.
Kick-off listed in local time (EEST)
Match officials
Assistant referees:
Unknown
Unknown
Match rules
90 minutes
Match officials
Assistant referees:
Unknown
Unknown
Match rules
90 minutes
Friendly matches
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) page (561)
1928-1929 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(47). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (119) Yapı Kredi Yayınları
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(104, 107, 108, 109).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(176). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1928–29 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/Veeravalli%20S.%20Varadarajan | Veeravalli Seshadri Varadarajan (18 May 1937 – 25 April 2019) was an Indian mathematician at the University of California, Los Angeles, who worked in many areas of mathematics, including probability, Lie groups and their representations, quantum mechanics, differential equations, and supersymmetry.
Biography
Varadarajan's father, Seshadri, was an Inspector of Schools in the Department of Education. He was transferred to Madras where the medium of instruction was generally English. After Varadarajan completed his high school studies, he joined Intermediate for two years at Loyola College, Madras where he was taught mathematics by K.A. Adivarahan, a very strict disciplinarian who made a strong impression on him. Varadarajan received his undergraduate degree in 1957 from Presidency College, Madras and his doctorate in 1960 from the Indian Statistical Institute in Calcutta, under the supervision of C. R. Rao. He was one of the "famous four" at the Indian Statistical Institute during 1956-1963 (the others being
R. Ranga Rao, K. R. Parthasarathy, and S. R. Srinivasa Varadhan). In 1960, after his doctorate, Varadarajan went to Princeton University as a post-doctoral fellow and in the Fall of 1960 he went to the University of Washington, Seattle where he spent the academic year, followed by a year at the Courant Institute at NYU, after which he returned to the Indian Statistical Institute in 1962. He joined the Department of Mathematics at UCLA in 1965. Varadarajan was a member of the Institute for Advanced Study during the periods September 1968 until December 1968 and January 1976 until June 1976. In March 2019, it was announced by UCLA that Varadarajan and his wife had donated $1 million to the Department of Mathematics at UCLA to establish the Ramanujan Visiting Professorship.
Contributions
Varadarajan's early work, including his doctoral thesis, was in the area of probability theory. He then moved into representation theory where he has done some of his best known work. He has also done work in mathematical physics, in particular quantum theory and p-adic themes in physics. In the 1980s, he wrote a series of papers with Donald Babbitt on the theory of differential equations with irregular singularities. His latest work has been in supersymmetry.
He introduced Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with Bertram Kostant, K. R. Parthasarathy and R. Ranga Rao in 1967, the Trombi–Varadarajan theorem in 1972 and the Enright–Varadarajan modules in 1975.
Recognition
He was awarded the Onsager Medal in 1998 for his work. He was recognized along with 23 Indian and Indian American members "who have made outstanding contributions to the creation, exposition advancement, communication, and utilization of mathematics" by the Fellows of the American Mathematical Society program on 1 November 2012.
Bibliography
Varadarajan, Veeravalli S (1984). Geometry of quantum theory, Springer-Verlag. 1st Edition 1968.
;
;
Varadarajan, Ve |
https://en.wikipedia.org/wiki/Leopold%20Hofmann%20%28footballer%29 | Leopold Hofmann (31 October 1905 – 9 January 1976) was an Austrian football midfielder who played for Austria in the 1934 FIFA World Cup. He also played for First Vienna FC.
Statistics
International
International goals
As of match played 24 October 1937. Austria score listed first, score column indicates score after each Hofmann goal.
References
External links
FIFA profile
1905 births
1976 deaths
Austrian men's footballers
Austria men's international footballers
Men's association football midfielders
First Vienna FC players
1934 FIFA World Cup players
Footballers from Vienna
Austrian football managers
First Vienna FC managers |
https://en.wikipedia.org/wiki/Harish-Chandra%27s%20function | In mathematics, Harish-Chandra's function may refer to:
Harish-Chandra's c-function
Harish-Chandra's σ function
Harish-Chandra's Ξ function |
https://en.wikipedia.org/wiki/FxStat%20Group | FxStat Group or FxStat, is an online social networking service in financial services headquartered in United Kingdom, London and the name FxStat comes from a combination of Forex and Statistics. FxStat was founded in April 2010 and focusing on the foreign exchange market, Stock market, and Commodity market. The focus was initially on social networking only, but later expanded to trading statement track record assessment, following successful traders portfolio, copying top performing traders, reading news, and sharing trades through a single platform to FxStat Group, Facebook, and Twitter.
In 2011, FxStat Group mixed social networking service and Trade (financial instrument) nowadays called Social trading that allows a real-time copy trading the top performing Trader (finance) automatically with full control and transparency.
The site is available in 12 languages, including English, French, German, Spanish, Arabic, Chinese, Russian, Farsi, Italian, Portuguese, Dutch, and Urdu .
History
FxStat Group (BVI) was founded in April 2010 by Sarmad Daneshmand and Bander Alweshaigri as a track record assessment and performance page provider for the traders under the name FX Stat (an abbreviation for Forex Statistics ). In 2013, expanded to Jordan and currently has offices in UK (London), Saudi Arabia (Riyadh), Jordan (Amman).
FX STAT Ltd UK is regulated and authorized by The Financial Conduct Authority (FCA).
Products and services
Social trading platforms
In April 2011, FxStat launched its first social trading platform Tradebook, a paid service offering automatic real-time trading through signal providers. where started being used by FXCC, Cysec regulated broker Cyprus Securities and Exchange Commission
Users can set their account to follow other member's trades and automatically execute them, becoming signal followers. In order to get FxStat's approval as signal providers, traders' accounts have to be proven real accounts and with a positive trading results history. These experienced investors are chosen by their followers using the analytics and performance comparison features. Users are still able to set their own trading rules while following a provider, like trading on a fixed lot, maximum open trades or maximum open orders, stop loss or maximum floating loss.
Later that year, in October 2011, FxStat launched Managed book platform. Managed book allows investors finding the best market leaders signal providers to copy automatically in real-time without paying per transaction commission. Instead, paying a success fee based on high water mark. where Managed book started being used by Varengold Bank FX in Germany.
FxStat covers over 1,000 brokers worldwide. In July 2011, broker FXOpen announced the integration of FxStat Tradebook in its platform.
See also
References
External links
Financial services companies established in 2010
Foreign exchange companies
British social networking websites
British companies established in 2010 |
https://en.wikipedia.org/wiki/FC%20UTA%20Arad%20in%20European%20football | Fotbal Club UTA Arad is a Romanian professional football club based in Arad, Arad County.
Total statistics
Statistics by country
Statistics by competition
UEFA Champions League / European Cup
UEFA Europa League / UEFA Cup
Balkans Cup
References
Romanian football clubs in international competitions
FC UTA Arad |
https://en.wikipedia.org/wiki/1913%E2%80%9314%20Galatasaray%20S.K.%20season | The 1913–14 season was Galatasaray SK's 10th in existence and the club's 6th consecutive season in the IFL.
Squad statistics
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Friendly Matches
Hilâl-i Ahmer Kupası
Galatasaray B Team won the cup.
References
Futbol vol.2, Galatasaray. Tercüman Spor Ansiklopedisi.(1981) (page 555-556)
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(66-67).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1913–14 season
1910s in Istanbul |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Roda%20JC%20Kerkrade%20season | The 2011-12 season will be the 39th season for Roda JC competing in the Dutch Eredivisie. This article will show statistics and list details of all matches played by the club during the season.
Club
Team kit
Diadora will be supplying the team kits for another season. Accon-avm is the shirt sponsor for the second season on a row.
Coaching staff
Statistics
Appearances and goals
Last updated on 23 October 2011.
|-
|colspan="14"|Players no longer at the club:
|}
Top scorers
Cards
Accounts for all competitions. Last updated on 23 October 2011.
Starting formations
Accounts for all competitions. Last updated on 23 October 2011.
Starting XI
These are the most used starting players (Eredivisie only) in the most used formation throughout the complete season. Last updated on 23 October 2011.
Transfers
In
Out
Loans in
Loans out
Competitions
Pre-season
Eredivisie
League table
Results summary
Matches
KNVB Cup
References
2011-12
Roda JC Kerkrade |
https://en.wikipedia.org/wiki/FC%20Bra%C8%99ov%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
UEFA Europa League / UEFA Cup
Romanian football clubs in international competitions |
https://en.wikipedia.org/wiki/CSM%20Ceahl%C4%83ul%20Piatra%20Neam%C8%9B%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
UEFA Intertoto Cup
Romanian football clubs in international competitions |
https://en.wikipedia.org/wiki/Blackwell%E2%80%93Tapia%20prize | The Blackwell–Tapia Prize is a mathematics award that recognizes active mathematical scientists who have (1) contributed and continue to contribute significantly to research in their fields of expertise, and (2) served as role models for mathematical scientists and students from underrepresented minority groups or contributed in other significant ways to addressing the problem of the underrepresentation of minorities in mathematics It is presented every other year at the Blackwell-Tapia Conference, which promotes mathematical excellence by minority researchers and is sponsored by the National Science Foundation. The prize is named for David Blackwell and Richard Tapia.
Recipients
The following mathematicians have been honored with the Blackwell–Tapia Prize:
See also
List of mathematics awards
References
Mathematics awards |
https://en.wikipedia.org/wiki/FC%20Sportul%20Studen%C8%9Besc%20Bucure%C8%99ti%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
UEFA Europa League / UEFA Cup
Romanian football clubs in international competitions
FC Sportul Studențesc București |
https://en.wikipedia.org/wiki/1914%E2%80%9315%20Galatasaray%20S.K.%20season | The 1914–15 season was Galatasaray SK's 11th in existence and the club's 7th consecutive season in the IFL.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Final Match
Kick-off listed in local time (EEST)
Friendly Matches
Kick-off listed in local time (EEST)
References
Futbol vol.2, Galatasaray. Tercüman Spor Ansiklopedisi.(1981) (page 555-556)
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1914–15 season
1910s in Istanbul |
https://en.wikipedia.org/wiki/FC%20Unirea%20Urziceni%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
Romanian football clubs in international competitions
FC Unirea Urziceni |
https://en.wikipedia.org/wiki/1927%E2%80%9328%20Galatasaray%20S.K.%20season | The 1927–28 season was Galatasaray SK's 24th in existence. The Istanbul Football League was aborted due to 1928 Summer Olympics, which were held in Amsterdam.
Squad statistics
İstanbul Ligi
Only two matches were played.
Kick-off listed in local time (EET)
Amatör Futbol Şampiyonası
Friendly Matches
Kick-off listed in local time (EEST)
Turkish Football Republic Cup
References
Futbol vol.2, Galatasaray. Tercüman Spor Ansiklopedisi.(1981) (page 561)
1927-1928 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(47). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(101-102, 104, 148).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(176). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1927–28 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/1929%E2%80%9330%20Galatasaray%20S.K.%20season | The 1929–30 season was Galatasaray SK's 26th in existence and the club's 19th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1929–1930 season
In:
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
İstanbul Shield
Kick-off listed in local time (EEST)
Friendly Matches
References
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(587).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(176-177). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1929–30 season
1920s in Istanbul
1930s in Istanbul |
https://en.wikipedia.org/wiki/1915%E2%80%9316%20Galatasaray%20S.K.%20season | The 1915–16 season was Galatasaray SK's 12th in existence and the club's 8th consecutive season in the IFL.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Fukaraperver Hanımlar Cemiyeti Kupası
Kick-off listed in local time (EEST)
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) (page 556)
1915-1916 İstanbul Cuma Ligi. Türk Futbol Tarihi vol.1. page(41). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (115) Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1915–16 season
1910s in Istanbul |
https://en.wikipedia.org/wiki/AS%20Progresul%20Bucure%C8%99ti%20in%20European%20football |
Total statistics
Statistics by country
Statistics by competition
UEFA Cup Winners' Cup / European Cup Winners' Cup
UEFA Europa League / UEFA Cup
UEFA Intertoto Cup
FC Progresul București
Romanian football clubs in international competitions |
https://en.wikipedia.org/wiki/FC%20Farul%20Constan%C8%9Ba%20in%20European%20football | FC Farul Constanța, now FCV Farul Constanța after the merger with FC Viitorul Constanța, is a Romanian football club which currently plays in Liga I.
Total statistics
Statistics by country
Statistics by competition
Notes for the abbreviations in the table below:
1R: First round
2R: Second round
3R: Third round
R16: Round of 16
1QR: First qualifying round
2QR: Second qualifying round
3QR: Third qualifying round
PO: Play-off round
Romanian football clubs in international competitions
FCV Farul Constanța |
https://en.wikipedia.org/wiki/Marcia%20Linn | Marcia C. Linn (née Cyrog) is a professor of development and cognition. Linn, specializes in education in mathematics, science, and technology in the Graduate School of Education at the University of California, Berkeley. Since 1970, Linn has made contributions to the understanding of the use of computers and technology to support learning and teaching in mathematics and science.
Family
Linn was born in Milwaukee, Wisconsin to Frances and George Cyrog. Frances became the principal of Sorenson School in Whittier, California. George was a supervisor in the postal service as well as a rockhound who founded the Whittier Gem and Mineral Society. Marcia's lifelong interest in science learning stems from growing up as the oldest child in a family enthusiastic about learning. Her father, George, believed everyone could learn about all aspects of science and engineering and implemented this in his hobby of collecting rocks and minerals. Her mother, Frances, developed a philosophy for individualized reading instruction starting when she taught elementary school and continuing as she became an elementary school principal.
Education
Linn received a B.A. in psychology and statistics (1965), an M. A. in educational psychology (1967), and a Ph.D. in Educational Psychology (1970) from Stanford University working under the mentorship of Lee Cronbach. Her research addresses how technology-enhanced curricula, visualizations, and assessments can deepen student understanding of science.
In 1967-68, Linn worked with Jean Piaget and other researchers at the Institute Jean Jacques Rousseau in Geneva, Switzerland. In Geneva, listening to researchers probe students' ideas motivated her to listen closely to the ideas that students bring to a learning situation. Linn spent time in schools interviewing students and learning to conduct interviews using the Piagetian clinical method. In Geneva, and when she returned to California, Linn conducted many interviews in which she asked students to explore scientific problems. She learned that student ideas about scientific topics are diverse and often well connected. These interviews formed the basis for her perspective on knowledge integration.
Academic career
Linn was a Research Psychologist at the Lawrence Hall of Science (1970–1987) and led the ACCEL program, a National Science Foundation-funded research project that investigated the cognitive consequences of computer environments for learning. She won an Apple Wheels for the Mind grant in 1985 for The Computer as Lab Partner, a project to bring Apple computers equipped with sensing probes into schools. With Robert Tinker, she developed the first Microcomputer-based Labs and probeware for middle school science.
In 1983 she was Fulbright Professor at the Weizmann Institute of Science in Rehovot, Israel. In 1983 she won one of two grants awarded by the National Institute of Education to study the emerging role of technology in education. This project, Assessing the Cognitive |
https://en.wikipedia.org/wiki/Cochran%27s%20C%20test | In statistics, Cochran's C test, named after William G. Cochran, is a one-sided upper limit variance outlier test. The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or standard deviations) with which the single estimate is supposed to be comparable. The C test is discussed in many text books and has been recommended by IUPAC and ISO. Cochran's C test should not be confused with Cochran's Q test, which applies to the analysis of two-way randomized block designs.
The C test assumes a balanced design, i.e. the considered full data set should consist of individual data series that all have equal size. The C test further assumes that each individual data series is normally distributed. Although primarily an outlier test, the C test is also in use as a simple alternative for regular homoscedasticity tests such as Bartlett's test, Levene's test and the Brown–Forsythe test to check a statistical data set for homogeneity of variances. An even simpler way to check homoscedasticity is provided by Hartley's Fmax test, but Hartley's Fmax test has the disadvantage that it only accounts for the minimum and the maximum of the variance range, while the C test accounts for all variances within the range.
Description
The C test detects one exceptionally large variance value at a time. The corresponding data series is then omitted from the full data set. According to ISO standard 5725 the C test may be iterated until no further exceptionally large variance values are detected, but such practice may lead to excessive rejections if the underlying data series are not normally distributed.
The C test evaluates the ratio:
where:
Cj = Cochran's C statistic for data series j
Sj = standard deviation of data series j
N = number of data series that remain in the data set; N is decreased in steps of 1 upon each iteration of the C test
Si = standard deviation of data series i (1 ≤ i ≤ N)
The C test tests the null hypothesis (H0) against the alternative hypothesis (Ha):
H0: All variances are equal.
Ha: At least one variance value is significantly larger than the other variance values.
Critical values
The sample variance of data series j is considered an outlier at significance level α if Cj exceeds the upper limit critical value CUL. CUL depends on the desired significance level α, the number of considered data series N, and the number of data points (n) per data series. Selections of values for CUL have been tabulated at significance levels α = 0.01, α = 0.025, and α = 0.05. CUL can also be calculated from:
Here:
CUL = upper limit critical value for one-sided test on a balanced design
α = significance level, e.g., 0.05
n = number of data points per data series
Fc = critical value of Fisher's F ratio; Fc can be obtained from tables of the F distribution or using computer software for this function.
Generalization
The C test can be generalized to include unbalanced d |
https://en.wikipedia.org/wiki/Zaal%20Samadashvili | Zaal Samadashvili () (born 3 October 1953) is a Georgian writer.
The biography
Zaal Samadashvili graduated from Tbilisi State University, where he studied mathematics.
He says: 'I wish each of us was not only proud of living in Tbilisi but I wish all of us had a desire and an opportunity to do as much as possible for the Capital. So that every single person could awake and deepen the responsibility towards the house, the street and the square where they live at present, where his ancestors had lived and where his descendants will live in future.'
Author of several full-length film scripts, he has published five collected stories. He is the chairman of the Tbilisi City Assembly.
Samadashvili initiated the Gala literary prize, which is awarded under the aegis of the Tbilisi City Assembly.
Job Description
1977 Hydro-Electric Research Institute Laboratory Assistant
1978–1980 Geological Expedition Caucasus Mineral Raw Materials Institute-Engineer
Technical University of Georgia, Department of Automation and Telemechanics junior member of research staff
1983–1989 Film studio "Georgian Film's Creative Union of Writers Probationer
1989–1994 Newspaper "Mamuli" Deputy Editor. Literary magazine "XX Saukune – Editor. Georgian Technical University Humanitarian Faculty lecturer
2005–2007 Tbilisi Public School No. 53 – Principal
2006 Tbilisi City Assembly – Member
2008 to date Tbilisi City Assembly – Chairman
Works
Books
As hoarse song on the guitar (1994) –
As an old Italian films (1999) –
The fire in smoked glass (2001) –
Gypsies (2003) –
Plekhanov News (2004) –
How to love one another (2004) –
Sandro Kandelaki's Boot (2006) –
Stories for Boys (2010) -
Movie
Temo, 'Georgian television films', director Levan Zakareishvili, 1986
References
External links
Zaal Samadashvili
Samadašvili, Zaal
Zaal Samadašvili
Samadashvili Zaal
Writers from Tbilisi
1953 births
Living people
Screenwriters from Georgia (country)
Translators from Georgia (country)
Recipients of the Presidential Order of Excellence |
https://en.wikipedia.org/wiki/Johann%20Heinrich%20Jakob%20M%C3%BCller | Johann Heinrich Jakob Müller (30 April 1809, Kassel, Kingdom of Westphalia – 3 October 1875, Freiburg im Breisgau) was a German physicist.
Biography
From 1829 he studied mathematics and physics at the University of Bonn, where one of his instructors was Julius Plücker, then continued his education at the University of Giessen as a student of Justus von Liebig. In 1834 he became a teacher at the Darmstadt gymnasium, and in 1837 returned to Giessen as an instructor at the Realschule. In 1844 he was appointed professor of physics and technology at the University of Freiburg, a position he maintained up until his death in 1875.
He conducted research on optics, galvanism and magnetism, as well as studies of light and heat radiation. Beginning in 1846 he performed analysis of Fraunhofer lines.
Works
His principal work, "Lehrbuch der Physik und Meteorologie" (2 volumes, Braunschweig, 1842; 7th edition, 1868–69), was originally a version of Claude Pouillet's "Éléments de physique expérimentale et de météorologie"; and he published a supplement to it, "Lehrbuch der kosmischen Physik" (1856; 3rd edition, 1872). Later on, Leopold Pfaundler published an enlarged 9th edition, titled "Müller-Pouillet's Lehrbuch der physik und meteorologie" (1886–98, 3 volumes).
Among his other works are:
Grundriss der Physik und Meteorologie (1846; 10th edition, 1869–70; with two supplements); later translated in English and published as "Principles of Physics and Meteorology" (Hippolyte Bailliere, London 1847; Lea and Blanchard, Philadelphia 1848).
Grundzüge der Krystallographie (1845; 2nd edition, 1869).
Anfangsgründe der geometrischen Disciplin für Gymnasien, &c. (3rd edition, 1869).
References
1809 births
1875 deaths
Scientists from Kassel
People from the Kingdom of Westphalia
19th-century German physicists
Academic staff of the University of Freiburg |
https://en.wikipedia.org/wiki/1916%E2%80%9317%20Galatasaray%20S.K.%20season | The 1916–17 season was Galatasaray SK's 12th in existence and the club's 8th consecutive season in the IFL.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Friendly Matches
Kick-off listed in local time (EEST)
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2. (1981) (page 556)
1916-1917 İstanbul Cuma Ligi. Türk Futbol Tarihi vol.1. page(42). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1916–17 season
1910s in Istanbul |
https://en.wikipedia.org/wiki/Dependency%20network | The dependency network approach provides a system level analysis of the activity and topology of directed networks. The approach extracts causal topological relations between the network's nodes (when the network structure is analyzed), and provides an important step towards inference of causal activity relations between the network nodes (when analyzing the network activity). This methodology has originally been introduced for the study of financial data, it has been extended and applied to other systems, such as the immune system, and semantic networks.
In the case of network activity, the analysis is based on partial correlations, which are becoming ever more widely used to investigate complex systems. In simple words, the partial (or residual) correlation is a measure of the effect (or contribution) of a given node, say j, on the correlations between another pair of nodes, say i and k. Using this concept, the dependency of one node on another node is calculated for the entire network. This results in a directed weighted adjacency matrix of a fully connected network. Once the adjacency matrix has been constructed, different algorithms can be used to construct the network, such as a threshold network, Minimal Spanning Tree (MST), Planar Maximally Filtered Graph (PMFG), and others.
Importance
The partial correlation based dependency network is a class of correlation network, capable of uncovering hidden relationships between its nodes.
This original methodology was first presented at the end of 2010, published in PLoS ONE. They quantitatively uncovered hidden information about the underlying structure of the U.S. stock market, information that was not present in the standard correlation networks. One of the main results of this work is that for the investigated time period (2001–2003), the structure of the network is dominated by companies belonging to the financial sector, which are the hubs in the dependency network. Thus, they were able for the first time to quantitatively show the dependency relationships between the different economic sectors. Following this work, the dependency network methodology has been applied to the study of the immune system, and semantic networks. As such, this methodology is applicable to any complex system.
Overview
To be more specific, the partial correlations of the pair, given j is the correlations between them after proper subtraction of the correlations between i and j and between k and j. Defined this way, the difference between the correlations and the partial correlations provides a measure of the influence of node j on the correlation. Therefore, we define the influence of node j on node i, or the dependency of node i on node j − D(i,j), to be the sum of the influence of node j on the correlations of node i with all other nodes.
In the case of network topology, the analysis is based on the effect of node deletion on the shortest paths between the network nodes. More specifically, we define the influ |
https://en.wikipedia.org/wiki/Victoria%20Bucure%C8%99ti%20in%20European%20football | Victoria București competed in UEFA football competitions. Their best performance was reaching the quarterfinals of the 1988–89 UEFA Cup where they lost to Dynamo Dresden.
All time statistics
By competition
By season
By country
References
Romanian football clubs in international competitions
Victoria București |
https://en.wikipedia.org/wiki/1924%E2%80%9325%20Galatasaray%20S.K.%20season | The 1924–25 season was Galatasaray SK's 21st in existence and the club's 15th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
İstanbul Football League
Semifinals
Final
Friendly matches
Kick-off listed in local time (EEST)
Match officials
Assistant referees:
Unknown
Unknown
Match rules
90 minutes
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) (page 560)
1924-1925 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(46). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (117) Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1924–25 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/1925%E2%80%9326%20Galatasaray%20S.K.%20season | The 1925–26 season was Galatasaray SK's 22nd in existence and the club's 16th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Finals
Friendly Matches
Kick-off listed in local time (EEST)
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) (page 560)
1925-1926 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(46). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (117) Yapı Kredi Yayınları
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(174-175). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1925–26 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/1926%E2%80%9327%20Galatasaray%20S.K.%20season | The 1926–27 season was Galatasaray SK's 23rd in existence and the club's 17th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1926–27 season
In:
Competitions
İstanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
Friendly matches
Kick-off listed in local time (EEST)
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) page (561)
1926–1927 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(46–47). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (118) Yapı Kredi Yayınları
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(174–175). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1926–27 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/Regularity%20theorem | In mathematics, regularity theorem may refer to:
Almgren regularity theorem
Elliptic regularity
Harish-Chandra's regularity theorem
Regularity theorem for Lebesgue measure |
https://en.wikipedia.org/wiki/Jean-Pierre%20Carniaux |
Biography
Carniaux studied Mathematics at the University of Paris, from which he graduated in 1972. He then studied at Massachusetts Institute of Technology and received a B.A. in Art and Design (1974) and a Master of Architecture (1976).
He joined Ricardo Bofill Taller de Arquitectura (RBTA) in 1976. In 1986 he was in charge of opening the firm's office in New York City, which he led until 1990. He was Senior Partner at RBTA until 2020.
Work
Jean-Pierre Carniaux’s design work has included the design of the National Theater of Catalonia, the Antigone new district in Montpellier (240,000 m2), the Shiseido representative building in Ginza, Lazona Kawasaki Plaza, as well as the design of perfume bottles for Christian Dior. He has participated in the projects of the New Terminal 1 at Barcelona Airport and .
Selected projects as Senior Partner at Bofill Arquitectura
W Barcelona, 2009, Barcelona, Spain
Shangri.la hotel , 2008, Beijing, China
Supershine Upper East side, 2008, Beijing, China
La Place de l’Europe, 2007, Luxembourg
La Porte, 2004, Luxembourg
Corso II, 2004, Prague, Czech Republic
Cartier headquarters, 2003, Paris, France
Competition for Qingdao Sail Base (Olympic Games 2008), 2003, Qingdao, China
Crystal Karlín, 2002, Prague, Czech Republic
Logistic Park office complex, 2002, Barcelona, Spain
Nexus II, 2002, Barcelona, Spain
Platinum Tower, 2002, Beirut, Lebanon
Colombo’s Resort, 2001, Porto Santo Island, Portugal
Shiseido New Ginza Building, 2001, Tokyo, Japan
Kawasaki Project, 2001, Tokyo, Japan
Funchalcentrum, 2001, Funchal, Madeira, Portugal
Compave Building, 2001, Lisbon, Portugal
Axa Headquarters, 2000, Paris, France
Corso, 2000, Prague, Czech Republic
Savona Sea Port, 2000, Savona, Italy
Corso Karlin, 2000, Prague, Czech Republic
Nova Karlin District, 1999, Prague, Czech Republic
Aoyama Palacio, 1999, Tokyo, Japan
The New Port Mouth of Barcelona, 1999, Barcelona, Spain
Crystal Palace, 1998, Prague, Czech Republic
Manzanares Park, 1998, Madrid, Spain
National Theatre of Catalonia, 1997, Barcelona, Spain
Plateau Kirchberg, 1996, Luxembourg
Piscine Olympique de Montpellier, 1996, Montpellier, France
Reinhold Tower, 1993, Madrid, Spain
Villa Olímpica Housing Complex, 1991, Barcelona, Spain
Kobe Sea Port, 1991, Kobe, Japan
Hotel Mercure, 1991, Montpellier, France
L’Aire des Volcans, 1991, Clermont-Ferrand, France
Le Capitole & Le Parnasse, 1990, Montpellier, France
Port Juvenal, 1989, Montpellier, France
Vieux Port De Montreal, 1989, Montréal, Canada
Arsenal Music Center, 1988, Metz, France
Domaine Chateau Lafite-Rothschild, 1988, Bordeaux, France
Hotel de La Région Languedoc-Roussillon, 1988, Montpellier, France
Central Park North, 1987, New York City, US
Les Echelles de La Ville, 1986, Montpellier, France
Port Imperial, 1985, New Jersey, US
Corner Condominium, 1985, New York City, US
Jefferson Tower, 1985, New York City, US
La Place du Nombre D’Or, 1984, Montpellier, France
Les Es |
https://en.wikipedia.org/wiki/Spherically%20complete%20field | In mathematics, a field K with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls (in the sense of the metric induced by the absolute value) is nonempty:
The definition can be adapted also to a field K with a valuation v taking values in an arbitrary ordered abelian group: (K,v) is spherically complete if every collection of balls that is totally ordered by inclusion has a nonempty intersection.
Spherically complete fields are important in nonarchimedean functional analysis, since many results analogous to theorems of classical functional analysis require the base field to be spherically complete.
Examples
Any locally compact field is spherically complete. This includes, in particular, the fields Qp of p-adic numbers, and any of their finite extensions.
Every spherically complete field is complete. On the other hand, Cp, the completion of the algebraic closure of Qp, is not spherically complete.
Any field of Hahn series is spherically complete.
References
Algebra
Functional analysis |
https://en.wikipedia.org/wiki/Hartogs%E2%80%93Rosenthal%20theorem | In mathematics, the Hartogs–Rosenthal theorem is a classical result in complex analysis on the uniform approximation of continuous functions on compact subsets of the complex plane by rational functions. The theorem was proved in 1931 by the German mathematicians Friedrich Hartogs and Arthur Rosenthal and has been widely applied, particularly in operator theory.
Statement
The Hartogs–Rosenthal theorem states that if K is a compact subset of the complex plane with Lebesgue measure zero, then any continuous complex-valued function on K can be uniformly approximated by rational functions.
Proof
By the Stone–Weierstrass theorem any complex-valued continuous function on K can be uniformly approximated by a polynomial in and .
So it suffices to show that can be uniformly approximated by a rational function on K.
Let g(z) be a smooth function of compact support on C equal to 1 on K and set
By the generalized Cauchy integral formula
since K has measure zero.
Restricting z to K and taking Riemann approximating sums for the integral on the right hand side yields the required uniform approximation of by a rational function.
See also
Runge's theorem
Mergelyan's theorem
Notes
References
Rational functions
Theorems in approximation theory
Theorems in complex analysis |
https://en.wikipedia.org/wiki/1921%E2%80%9322%20Galatasaray%20S.K.%20season | The 1921–22 season was Galatasaray SK's 18th in existence and the club's 12th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Friendly Matches
Galatasaray Cup
Galatasaray won the cup.
References
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Association football clubs 1921–22 season
1920s in Istanbul
Galatasaray Sports Club 1921–22 season
1921 in Turkish sport
1922 in Turkish sport |
https://en.wikipedia.org/wiki/1920%E2%80%9321%20Galatasaray%20S.K.%20season | The 1920–21 season was Galatasaray SK's 17th in existence and the club's 11th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
İstanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
Friendly matches
Galatasaray Cup
Galatasaray won the cup.
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) page (557, 594)
1920-1921 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(42). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1920–21 season
1920s in Istanbul
Galatasaray Sports Club 1920–21 season |
https://en.wikipedia.org/wiki/1922%E2%80%9323%20Galatasaray%20S.K.%20season | The 1922–23 season was Galatasaray SK's 19th in existence and the club's 13th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
Friendly matches
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) page (557)
1926-1927 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(43-44). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Tuncay, Bülent (2002). Galatasaray Tarihi. Page (116) Yapı Kredi Yayınları
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(75).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1922–23 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/Maass%E2%80%93Selberg%20relations | In mathematics, the Maass–Selberg relations are some relations describing the inner products of truncated real analytic Eisenstein series, that in some sense say that distinct Eisenstein series are orthogonal. Hans Maass introduced the Maass–Selberg relations for the case of real analytic Eisenstein series on the upper half plane. Atle Selberg extended the relations to symmetric spaces of rank 1. Harish-Chandra generalized the Maass–Selberg relations to Eisenstein series of higher rank semisimple group (and named the relations after Maass and Selberg) and found some analogous relations between Eisenstein integrals, that he also called Maass–Selberg relations.
Informally, the Maass–Selberg relations say that the inner product of two distinct Eisenstein series is zero. However the integral defining the inner product does not converge, so the Eisenstein series first have to be truncated. The Maass–Selberg relations then say that the inner product of two truncated Eisenstein series is given by a finite sum of elementary factors that depend on the truncation chosen, whose finite part tends to zero as the truncation is removed.
Notes
References
Modular forms
Representation theory |
https://en.wikipedia.org/wiki/William%20P.%20Byers | William Paul Byers (born 1943) is a Canadian mathematician and philosopher; professor emeritus in mathematics and statistics at Concordia University in Montreal, Quebec, Canada.
He completed a BSc ('64), and an MSc ('65) from McGill University, and obtained his PhD ('69) from the University of California, Berkeley. His dissertation, Anosov Flows, was supervised by Stephen Smale.
His area of interests include dynamical systems and the philosophy of mathematics.
Books
Byers is the author of three books on mathematics:
How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics (Princeton University Press, 2007)
The Blind Spot: Science and the Crisis of Uncertainty (Princeton University Press, 2011)
Deep Thinking: What Mathematics Can Teach Us About the Mind (World Scientific, 2015)
See also
List of people from Montreal
References
External links
1943 births
Canadian philosophers
Philosophers of mathematics
Canadian non-fiction writers
Living people
Academic staff of Concordia University
University of California, Berkeley alumni
20th-century Canadian philosophers |
https://en.wikipedia.org/wiki/Classical%20Mechanics%20%28Kibble%20and%20Berkshire%29 | Classical Mechanics is a well-established textbook written by Thomas Walter Bannerman Kibble and Frank Berkshire of the Imperial College Mathematics Department. The book provides a thorough coverage of the fundamental principles and techniques of classical mechanics, a long-standing subject which is at the base of all of physics.
Publication history
The English language editions were published as follows:
The first edition was published by Kibble, as Kibble, T. W. B. Classical Mechanics. London: McGraw–Hill, 1966. 296 p.
The second ed., also just by Kibble, was in 1973 .
The 4th, jointly with F H Berkshire, was is 1996
The 5th, jointly with F H Berkshire, in 2004
The book has been translated into several languages:
French, by Michel Le Ray and Françoise Guérin as Mécanique classique
Modern Greek, by Δ. Σαρδελής και Π. Δίτσας, επιμέλεια Γ. Ι. Παπαδόπουλος. Σαρδελής, Δ. Δίτσας, Π as Κλασσική μηχανική
German
Turkish, by Kemal Çolakoğlu as Klasik mekanik
Spanish, as Mecánica clásica
Portuguese as Mecanica classica
Reception
The various editions are held in 1789 libraries.
In comparison, the various (2011) editions of Herbert Goldstein's Classical Mechanics are held in 1772. libraries
The original edition was reviewed in Current Science.
The fourth edition was reviewed by C. Isenberg in 1997 in the European Journal of Physics, and the fifth edition was reviewed in Contemporary Physics.
Contents (5th edition)
Preface
Useful Constants and Units
Chapter 1: Introduction
Chapter 2: Linear motion
Chapter 3: Energy and Angular momentum
Chapter 4: Central Conservative Forces
Chapter 5: Rotating Frames
Chapter 6: Potential Theory
Chapter 7: The Two-Body Problem
Chapter 8: Many-Body Systems
Chapter 9: Rigid Bodies
Chapter 10: Lagrangian mechanics
Chapter 11: Small oscillations and Normal modes
Chapter 12: Hamiltonian mechanics
Chapter 13: Dynamical systems and their geometry
Chapter 14: Order and Chaos in Hamiltonian systems
Appendix A: Vectors
Appendix B: Conics
Appendix C: Phase plane Analysis near Critical Points
Appendix D: Discrete Dynamical Systems – Maps
Answers to Problems
Bibliography
Index
See also
Newtonian mechanics
Classical Mechanics (Goldstein book)
List of textbooks on classical and quantum mechanics
References
External links
2004 non-fiction books
Classical mechanics
Mathematical physics
Physics textbooks
Theoretical physics |
https://en.wikipedia.org/wiki/%CE%9E%20function | In mathematics, the Ξ function (named for the Greek letter Ξ or Xi) may refer to:
Riemann Xi function, a variant of the Riemann zeta function with a simpler functional equation
Harish-Chandra's Ξ function, a special spherical function on a semisimple Lie group |
https://en.wikipedia.org/wiki/Hierarchical%20matrix | In numerical mathematics, hierarchical matrices (H-matrices)
are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension can be represented efficiently in units of storage by storing only its non-zero entries, a non-sparse matrix would require units of storage, and using this type of matrices for large problems would therefore be prohibitively expensive in terms of storage and computing time. Hierarchical matrices provide an approximation requiring only units of storage, where is a parameter controlling the accuracy of the approximation. In typical applications, e.g., when discretizing integral equations,
preconditioning the resulting systems of linear equations,
or solving elliptic partial differential equations, a rank proportional to with a small constant is sufficient to ensure an accuracy of . Compared to many other data-sparse representations of non-sparse matrices, hierarchical matrices offer a major advantage: the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in operations, where
Basic idea
Hierarchical matrices rely on local low-rank approximations:
let be index sets, and let denote the matrix we have to approximate.
In many applications (see above), we can find subsets such that
can be approximated by a rank- matrix. This approximation can be represented in factorized form with factors
.
While the standard representation of the matrix requires units of storage,
the factorized representation requires only units. If is not too large, the storage requirements are reduced significantly.
In order to approximate the entire matrix , it is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation in order to improve efficiency.
Low-rank matrices are closely related to degenerate expansions used in panel clustering and the fast multipole method
to approximate integral operators. In this sense, hierarchical matrices can be considered the algebraic counterparts of these techniques.
Application to integral operators
Hierarchical matrices are successfully used to treat integral equations, e.g., the single and double layer potential operators
appearing in the boundary element method. A typical operator has the form
The Galerkin method leads to matrix entries of the form
where and are families of finite element basis functions.
If the kernel function is sufficiently smooth, we can approximate it by polynomial interpolation to obtain
where is the family of interpolation points and
is the corresponding family of Lagrange polynomials.
Replacing by yields an approximation
with the coefficients
If we choose and use the same interpolation points for all , we obtain
.
Obviously, any other approximation separating the variables and , e.g., the multipole expansion,
would also allow us to split the doubl |
https://en.wikipedia.org/wiki/An%20Essay%20towards%20solving%20a%20Problem%20in%20the%20Doctrine%20of%20Chances | An Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by Thomas Bayes, published in 1763, two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title comes from the contemporary use of the phrase "doctrine of chances" to mean the theory of probability, which had been introduced via the title of a book by Abraham de Moivre. Contemporary reprints of the Essay carry a more specific and significant title: A Method of Calculating the Exact Probability of All Conclusions founded on Induction.
The essay includes theorems of conditional probability which form the basis of what is now called Bayes's Theorem, together with a detailed treatment of the problem of setting a prior probability.
Bayes supposed a sequence of independent experiments, each having as its outcome either success or failure, the probability of success being some number p between 0 and 1. But then he supposed p to be an uncertain quantity, whose probability of being in any interval between 0 and 1 is the length of the interval. In modern terms, p would be considered a random variable uniformly distributed between 0 and 1. Conditionally on the value of p, the trials resulting in success or failure are independent, but unconditionally (or "marginally") they are not. That is because if a large number of successes are observed, then p is more likely to be large, so that success on the next trial is more probable. The question Bayes addressed was: what is the conditional probability distribution of p, given the numbers of successes and failures so far observed. The answer is that its probability density function is
(and ƒ(p) = 0 for p < 0 or p > 1) where k is the number of successes so far observed, and n is the number of trials so far observed. This is what today is called the Beta distribution with parameters k + 1 and n − k + 1.
Outline
Bayes's preliminary results in conditional probability (especially Propositions 3, 4 and 5) imply the truth of the theorem that is named for him. He states:"If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right is P/b.".
Symbolically, this implies (see Stigler 1982):
which leads to Bayes's Theorem for conditional probabilities:
However, it does not appear that Bayes emphasized or focused on this finding. Rather, he focused on the finding the solution to a much broader inferential problem:
"Given the number of times in which an unknown event has happened and failed [... Find] the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named."
The essay includes an example of a man trying to guess the ratio of "blanks" and "prizes" |
https://en.wikipedia.org/wiki/Quaternionic%20discrete%20series%20representation | In mathematics, a quaternionic discrete series representation is a discrete series representation of a semisimple Lie group G associated with a quaternionic structure on the symmetric space of G. They were introduced by .
Quaternionic discrete series representations exist when the maximal compact subgroup of the group G has a normal subgroup isomorphic to SU(2). Every complex simple Lie group has a real form with quaternionic discrete series representations. In particular the classical groups SU(2,n), SO(4,n), and Sp(1,n) have quaternionic discrete series representations.
Quaternionic representations are analogous to holomorphic discrete series representations, which exist when the symmetric space of the group has a complex structure. The groups SU(2,n) have both holomorphic and quaternionic discrete series representations.
See also
Quaternionic symmetric space
References
External links
Representation theory |
https://en.wikipedia.org/wiki/Ismar%20Gor%C4%8Di%C4%87 | Ismar Gorčić (born 22 May 1983) is a Bosnian former professional tennis player. He is currently a tennis coach.
Career statistics
Singles titles (0)
Doubles titles (9)
References
Sources
1983 births
Living people
Bosnia and Herzegovina male tennis players |
https://en.wikipedia.org/wiki/2011%20Dhivehi%20League | Statistics of Dhivehi League in the 2011 season.
Clubs
All Youth Linkage FC
Club Eagles
Club Valencia
Club Vyansa
Maziya S&RC
New Radiant SC
VB Sports Club
Victory Sports Club
Standings
Format: In Round 1 and Round 2, all eight teams played against each other. Top six teams after Round 2 play against each other in Round 3. Teams with most total points after Round 3 are crowned the Dhivehi League champions and qualify for the AFC Cup. The top four teams qualify for the President's Cup. Bottom two teams after Round 2 play against top two teams of Second Division in Dhivehi League Qualification for places in next year's Dhivehi League.
Promotion/relegation playoff
References
Dhiraagu Dhivehi League Standings (2011)
Dhivehi League Qualification Standings (2011)
President's Cup Standings (2011)
External links
Football Association of Maldives
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/Holomorphic%20discrete%20series%20representation | In mathematics, a holomorphic discrete series representation is a discrete series representation of a semisimple Lie group that can be represented in a natural way as a Hilbert space of holomorphic functions. The simple Lie groups with holomorphic discrete series are those whose symmetric space is Hermitian. Holomorphic discrete series representations are the easiest discrete series representations to study because they have highest or lowest weights, which makes their behavior similar to that of finite-dimensional representations of compact Lie groups.
found the first examples of holomorphic discrete series representations, and classified them for all semisimple Lie groups.
and described the characters of holomorphic discrete series representations.
See also
Quaternionic discrete series representation
References
External links
Representation theory of Lie groups |
https://en.wikipedia.org/wiki/1923%E2%80%9324%20Galatasaray%20S.K.%20season | The 1923–24 season was Galatasaray SK's 20th in existence and the club's 14th consecutive season in the Istanbul Football League.
Squad statistics
Competitions
İstanbul Football League
Semifinals
Final
Group matches
Kick-off listed in local time (EEST)
Knockout phase
Kick-off listed in local time (EEST)
Friendly matches
References
Futbol, Galatasaray. Tercüman Spor Ansiklopedisi vol.2 (1981) page (559-560)
1923-1924 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(45). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(88, 93).(1991) An Grafik Basın Sanayi ve Ticaret AŞ.
Tekil, Süleyman. Dünden bugüne Galatasaray(1983). Page(173-174). Arset Matbaacılık Kol.Şti.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1923–24 season
1920s in Istanbul |
https://en.wikipedia.org/wiki/Khalil%20Allawi | Khalil Mohammed Allawi (born 6 September 1958) is an Iraqi football defender who played for Iraq in the 1986 FIFA World Cup. He also played for Al-Rasheed Club.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
External links
1958 births
Iraqi men's footballers
Iraq men's international footballers
Men's association football defenders
Al-Karkh SC players
1986 FIFA World Cup players
Living people
Olympic footballers for Iraq
Footballers at the 1984 Summer Olympics
Asian Games medalists in football
Footballers at the 1982 Asian Games
Al-Shorta SC players
Asian Games gold medalists for Iraq
Medalists at the 1982 Asian Games |
https://en.wikipedia.org/wiki/Karim%20Allawi | Karim Mohammed Allawi (born 1 April 1960) is an Iraqi football midfielder who played for Iraq in the 1986 FIFA World Cup. He also played for Al-Rasheed Club.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
External links
FIFA profile (archived 12 November 2012)
1960 births
Iraqi men's footballers
Iraq men's international footballers
Men's association football midfielders
Al-Karkh SC players
Abahani Limited Dhaka players
1986 FIFA World Cup players
Living people
Olympic footballers for Iraq
Footballers at the 1984 Summer Olympics
Footballers at the 1988 Summer Olympics
Asian Games medalists in football
Footballers at the 1982 Asian Games
Footballers at the 1986 Asian Games
Asian Games gold medalists for Iraq
Medalists at the 1982 Asian Games |
https://en.wikipedia.org/wiki/Ismail%20Mohammed%20Sharif | Ismail Mohammed Sharif (born 19 January 1962) is an Iraqi football midfielder who played for Iraq in the 1986 FIFA World Cup. He also played for Al-Shorta SC and Al-Shabab.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
External links
FIFA profile
1962 births
Iraqi men's footballers
Iraq men's international footballers
Men's association football midfielders
1986 FIFA World Cup players
Al-Shorta SC players
Living people
Olympic footballers for Iraq
Footballers at the 1988 Summer Olympics |
https://en.wikipedia.org/wiki/Mathematical%20manuscripts%20of%20Karl%20Marx | The mathematical manuscripts of Karl Marx are a manuscript collection of Karl Marx's mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles.
The notes that Marx took have been collected into four independent treatises: On the Concept of the Derived Function, On the Differential, On the History of Differential Calculus, and Taylor's Theorem, MacLaurin's Theorem, and Lagrange's Theory of Derived Functions, along with several notes, additional drafts, and supplements to these four treatises. These treatises attempt to construct a rigorous foundation for calculus and use historical materialism to analyze the history of mathematics.
Marx's contributions to mathematics did not have any impact on the historical development of calculus, and he was unaware of many more recent developments in the field at the time, such as the work of Cauchy. However, his work in some ways anticipated, but did not influence, some later developments in 20th century mathematics. These manuscripts, which are from around 1873–1883, were not published in any language until 1968 when they were published in the Soviet Union alongside a Russian translation. Since their publication, Marx's independent contributions to mathematics have been analyzed in terms of both his own historical and economic theories, and in light of their potential applications of nonstandard analysis.
Contents
Marx left over 1000 manuscript pages of mathematical notes on his attempts at discovering the foundations of calculus. The majority of these manuscript pages have been collected into four papers, along with drafts and supplementary notes in the published editions of his collected works. In these works, Marx attempted to draw analogies between his theories of the history of economics and the development of calculus by constructing differential calculus in terms of mathematical symbols altered by an upheaval that would reveal their meaning.
On the Concept of the Derived Function
Marx wrote On the Concept of the Derived Function in 1881, just two years before his death. In this work, he demonstrates the mechanical steps needed to calculate a derivative for several basic functions from first principles. Despite the fact that Marx's principle sources primarily relied on geometric arguments for the definition of the derivative, Marx's explanations rely much more strongly on algebraic explanations than geometric ones, suggesting he likely preferred to think of things algebraically. Fahey et al. state that although "We might be alarmed to find a student writing 0/0 ... [Marx] was well aware of what he was doing when he wrote '0/0'." However, Marx was evidently disturbed by the implications of this, stating that "The closely held belief of some rationalising mathematicians that dy and dx are quantitatively actually only infinitely small, only approaching 0/0, is a chimera".
On the Differential
In On the Differential, Marx tries to construct the |
https://en.wikipedia.org/wiki/Teach%20to%20One | Teach to One, previously known as School of One (SO1), is a middle school mathematics program of the New York City Department of Education . It began in 2009 and is currently operating in six schools in Manhattan, The Bronx, and Brooklyn. Its innovative program integrates the use of technology in the development and implementation of personalized curriculum and learning as well as the use of technology in the learning environment.
Educational approach
The program is based on each student's individual learning requirements, also called learner-based-learning or student-centred learning. The approach is to provide students with their own Personal Learning Environment. In traditional learning environments, teachers lead students through the curriculum such that each student is expected to learn the same material at the same time. At Teach to One, each student is provided a blended learning environment geared towards their individual learning needs. These are identified by State assessments and test results and are then used to create a student's “playlist,” or Individual Learning Plan. Each student receives a daily schedule based on their own learning needs and strengths, with each schedule and instruction plan adjusted to suit their ability. Teachers can acquire real-time data on each student's achievement and adjust their live instruction to suit, usually daily. Teach to One focuses on learning progression, but depending on pre-identified skills of the students, each student might begin the same lesson at a different point. Each student participates in multiple instructional methods, including teacher-led instruction, small group collaboration, individual tutoring, independent learning, work with online tutors, or any combination thereof.
The classrooms at Teach to One are centered around an open space with multiple learning stations. These stations provide the lessons selected by the curriculum software as well as connecting students with a teacher, software, and online tutors. This allows the student to work independently or in collaboration with other online students, either individually or in groups. The student-teacher ratio is 10, significantly lower than in most programs.
Technology
Teach to One uses digital technology to develop individualized, daily-adjusted student curricula which the students access via an online portal. A computer-based Machine Learning algorithm collects data to generate a daily lesson plan or "playlist" for each student based on what is determined to best meet their learning needs. It functions as an adaptive scheduler to ensure each student is learning in his or her educational "sweet spot." As it collects data, the algorithm generates a daily lesson plan and schedule for each student and teacher by analyzing factors including each student's academic history and profile, assessment of previous work sessions, as well as the school's available resources, space, and staffing. Teachers can review and s |
https://en.wikipedia.org/wiki/Hidden%20algebra | Hidden algebra provides a formal semantics for use in the field of software engineering, especially for concurrent distributed object systems. It supports correctness proofs.
Hidden algebra was studied by Joseph Goguen. It handles features of large software-based systems, including concurrency, distribution, nondeterminism, and local states. It also handled object-oriented features like classes, subclasses (inheritance), attributes, and methods. Hidden algebra generalizes process algebra and transition system approaches.
References
External links
Hidden Algebra Tutorial
Abstract algebra
Universal algebra
Logical calculi
Concurrent computing
Distributed computing |
https://en.wikipedia.org/wiki/Matic%20Maru%C5%A1ko | Matic Maruško (born 30 November 1990) is a Slovenian football midfielder who plays for Mura.
Career statistics
Honours
Mura
Slovenian PrvaLiga: 2020–21
Slovenian Second League: 2017–18
Slovenian Cup: 2019–20
References
External links
NZS profile
1990 births
Living people
Sportspeople from Murska Sobota
Slovenian men's footballers
Slovenia men's under-21 international footballers
Men's association football midfielders
Slovenian Second League players
Slovenian PrvaLiga players
Slovak First Football League players
2. Liga (Slovakia) players
Kazakhstan Premier League players
ND Mura 05 players
NK Nafta Lendava players
FC Spartak Trnava players
FC Kaisar players
FC Akzhayik players
NŠ Mura players
Slovenian expatriate men's footballers
Slovenian expatriate sportspeople in Slovakia
Expatriate men's footballers in Slovakia
Expatriate men's footballers in Kazakhstan
Slovenian expatriate sportspeople in Austria
Expatriate men's footballers in Austria |
https://en.wikipedia.org/wiki/Gyula%20Forr%C3%B3 | Gyula Forró (born 6 June 1988) is a Hungarian football player who currently plays for Dorogi FC.
Career statistics
References
Player profile at HLSZ
1988 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
MTK Budapest FC players
Soroksár SC players
FC Dabas footballers
BKV Előre SC footballers
Kecskeméti TE players
Újpest FC players
Puskás Akadémia FC players
Nyíregyháza Spartacus FC players
Dorogi FC footballers
Győri ETO FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Hungary men's international footballers |
https://en.wikipedia.org/wiki/Edward%20Linfoot | Edward Hubert Linfoot (8 June 1905 – 14 October 1982) was a British mathematician, primarily known for his work on optics, but also noted for his work in pure mathematics.
Early life and career
Edward Linfoot was born in Sheffield, England, in 1905. He was the eldest child of George Edward Linfoot, a violinist and mathematician, and George's wife Laura, née Clayton. After attending King Edward VII School he won a scholarship to Balliol College at the University of Oxford.
During his time at Oxford he met the number theorist G. H. Hardy, and after graduating in 1926, Linfoot completed a D.Phil under the supervision of Hardy with a thesis entitled Applications of the Theory of Functions of a Complex Variable.
After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol. During the 1930s Linfoot's interests slowly made the transition from pure mathematics to the application of mathematics to the study of optics, but not before proving an important result in number theory with Hans Heilbronn, that there are at most ten imaginary quadratic number fields with class number 1.
Shift to optics
The exact reasons that Linfoot chose to switch his research from pure mathematics to optics are complex and there is probably no single most important reason. John Bell has highlighted the role played by Linfoot's political awareness, in particular his relationship with Heilbronn who had been forced to flee Nazi Germany. Suspecting a second world war was imminent, and knowing his delicate constitution would not make it through military physical examinations, Linfoot decided to contribute to the future war with scientific advancements in the field of optics. Other contributing factors to this change in focus were his lifelong fondness for astronomy and, by Linfoot's own testimony, a feeling that he had reached the limits of his pure mathematical creativity.
This shift was facilitated by C. R. Burch of the H. H. Wills Physics Laboratory in Bristol who led the University's optics group. Burch was a physical thinker but recognised the benefits of strong mathematical ability in understanding physics, and so encouraged Linfoot in his transition. Linfoot availed himself of the laboratory's facilities to first construct his own telescope and later to apply the theory of aspheric lenses to create a new microscope which he exhibited at the 1939 Annual Exhibition of the Physical Society.
It was also during this time, in 1935, that Linfoot married fellow mathematician Joyce Dancer, with whom he had three children, Roger in 1941, Margaret in 1945 and Sebastian in 1947.
During World War II Linfoot put his skills to use for the Ministry of Aircraft Production, producing optical systems for air reconnaissance.
Cambridge astronomer
Following the war, Linfoot was awarded an ScD by the University of Oxford for his work in mathematics. |
https://en.wikipedia.org/wiki/Nonlinear%20Oscillations | Nonlinear Oscillations is a quarterly peer-reviewed mathematical journal that was established in 1998. It is published by Springer Science+Business Media on behalf of the Institute of Mathematics, National Academy of Sciences of Ukraine. It covers research in the qualitative theory of differential or functional differential equations. This includes the qualitative analysis of differential equations with the help of symbolic calculus systems and applications of the theory of ordinary and functional differential equations in various fields of mathematical biology, electronics, and medicine.
Nonlinear Oscillations is a translation of the Ukrainian journal Neliniyni Kolyvannya (). The editor-in-chief is Anatoly M. Samoilenko (Institute of Mathematics of the National Academy of Sciences of Ukraine).
External links
Mathematics journals
Quarterly journals
English-language journals
Springer Science+Business Media academic journals
Academic journals established in 1998 |
https://en.wikipedia.org/wiki/List%20of%20small%20polyhedra%20by%20vertex%20count | In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded by alternating faces and edges. The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids, Archimedean solids, Catalan solids, and Johnson solids, as well as dihedral symmetry families including the pyramids, bipyramids, prisms, antiprisms, and trapezohedrons.
Polyhedra by vertex count
Notes: Polyhedra with different names that are topologically identical are listed together. Except in the cases of four and five vertices, the lists below are by no means exhaustive of all possible polyhedra with the given number of vertices, but rather just include particularly simple/common/well-known/named examples. The "Counting Polyhedra" link below gives the exact number of distinct polyhedra with n vertices for small values of n.
References
External links
Counting Polyhedra |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Galatasaray%20S.K.%20season | The 1932–33 season was Galatasaray SK's 29th in existence and the club's 21st consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1932–33 season
In:
Out:
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
İstanbul Shield
Kick-off listed in local time (EEST)
Friendly Matches
References
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(127).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(63-64, 140, 179). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 587. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1932–33 season
1930s in Istanbul |
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