source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/1989%E2%80%9390%20Ekstraklasa | Statistics of Ekstraklasa for the 1989–90 season.
Overview
It was contested by 16 teams, and Lech Poznań won the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1989–90 in Polish football
Pol |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20Ekstraklasa | Statistics of Ekstraklasa for the 1990–91 season.
Overview
The league was contested by 16 teams, and Zagłębie Lubin won the championship.
League table
Results
Relegation playoffs
The matches were played on 28 June and 1 July 1991.
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1990–91 in Polish football
Pol |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20Ekstraklasa | Statistics of the Ekstraklasa for the 1991–92 season.
Overview
It was contested by 18 teams, and Lech Poznań won the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1991–92 in Polish football
Pol |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20Ekstraklasa | Statistics of the Ekstraklasa for the 1993–94 season.
Overview
18 teams competed in the league. The title was won by Legia Warsaw.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1993–94 in Polish football
Pol |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20Ekstraklasa | Statistics of the Ekstraklasa for the 1994–95 season.
Overview
18 teams competed in the 1994–95 season with Legia Warsaw winning the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1994–95 in Polish football
Pol |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20Ekstraklasa | Statistics of Ekstraklasa for the 1995–96 season.
Overview
18 teams competed in the 1995–96 season with Widzew Łódź winning the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1995–96 in Polish football
Pol |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20Ekstraklasa | Statistics of Ekstraklasa for the 1996–97 season.
Overview
18 teams and played in the league and the title was won by Widzew Łódź.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1996–97 in Polish football
Pol |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20Ekstraklasa | Statistics of the Ekstraklasa for the 1997–98 season.
Overview
18 teams competed in the 1997–98 season. ŁKS Łódź won the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
1997–98 in Polish football
Pol |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20Ekstraklasa | Statistics of Ekstraklasa for the 1998–99 season.
Overview
A total of 16 teams competed in the 1998–99 season. Wisła Kraków won the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
Poland
1998–99 in Polish football |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20Ekstraklasa | Statistics of Ekstraklasa for the 1999–2000 season.
Overview
A total of 16 teams competed in the 1999–2000 season. Polonia Warsaw won the championship.
League table
Results
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
Poland
1999–2000 in Polish football |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Ekstraklasa | Statistics of Ekstraklasa for the 2000–01 season.
Overview
16 teams competed in the 2000–01 season. Wisła Kraków won the championship.
League table
Results
Relegation playoffs
The matches were played on 20 and 24 June 2001.
Top goalscorers
References
External links
Poland – List of final tables at RSSSF
Ekstraklasa seasons
Poland
1 |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20Ekstraklasa | Statistics of Ekstraklasa for the 2001–02 season.
Overview
16 teams competed in the 2001–02 season. Legia Warsaw won the championship.
First phase
Group A
Results
Group B
Results
Final phase
Championship group
Results
Relegation group
Results
Relegation playoffs
The matches were played on 8 and 12 May 2002.
Top goalscorers
References
Ekstraklasa seasons
Poland
1 |
https://en.wikipedia.org/wiki/Skorokhod%20integral | In mathematics, the Skorokhod integral (also named Hitsuda-Skorokhod integral), often denoted , is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod and japanese mathematician Masuyuki Hitsuda. Part of its importance is that it unifies several concepts:
is an extension of the Itô integral to non-adapted processes;
is the adjoint of the Malliavin derivative, which is fundamental to the stochastic calculus of variations (Malliavin calculus);
is an infinite-dimensional generalization of the divergence operator from classical vector calculus.
The integral was introduced by Hitsuda in 1972 and by Skorokhod in 1975.
Definition
Preliminaries: the Malliavin derivative
Consider a fixed probability space and a Hilbert space ; denotes expectation with respect to
Intuitively speaking, the Malliavin derivative of a random variable in is defined by expanding it in terms of Gaussian random variables that are parametrized by the elements of and differentiating the expansion formally; the Skorokhod integral is the adjoint operation to the Malliavin derivative.
Consider a family of -valued random variables , indexed by the elements of the Hilbert space . Assume further that each is a Gaussian (normal) random variable, that the map taking to is a linear map, and that the mean and covariance structure is given by
for all and in . It can be shown that, given , there always exists a probability space and a family of random variables with the above properties. The Malliavin derivative is essentially defined by formally setting the derivative of the random variable to be , and then extending this definition to "smooth enough" random variables. For a random variable of the form
where is smooth, the Malliavin derivative is defined using the earlier "formal definition" and the chain rule:
In other words, whereas was a real-valued random variable, its derivative is an -valued random variable, an element of the space . Of course, this procedure only defines for "smooth" random variables, but an approximation procedure can be employed to define for in a large subspace of ; the domain of is the closure of the smooth random variables in the seminorm :
This space is denoted by and is called the Watanabe–Sobolev space.
The Skorokhod integral
For simplicity, consider now just the case . The Skorokhod integral is defined to be the -adjoint of the Malliavin derivative . Just as was not defined on the whole of , is not defined on the whole of : the domain of consists of those processes in for which there exists a constant such that, for all in ,
The Skorokhod integral of a process in is a real-valued random variable in ; if lies in the domain of , then is defined by the relation that, for all ,
Just as the Malliavin derivative was first defined on simple, smooth random variables, the Skorokhod integral has a simple expression for "s |
https://en.wikipedia.org/wiki/Adri%C3%A1n%20Szekeres | Adrián Szekeres (born 21 April 1989 in Budapest) is a retired Hungarian football player.
Club statistics
Honours
FIFA U-20 World Cup:
Third place: 2009
References
External links
UEFA
Hungarian Football Federation
1989 births
Living people
Footballers from Budapest
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football defenders
Újpest FC players
MTK Budapest FC players
Fehérvár FC players
Puskás Akadémia FC players
Dunaújváros PASE players
Gyirmót FC Győr players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Radius%20of%20curvature | In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.
Definition
In the case of a space curve, the radius of curvature is the length of the curvature vector.
In the case of a plane curve, then is the absolute value of
where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature.
Formula
In two dimensions
If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2)
where and denotes the absolute value of .
If the curve is given parametrically by functions and , then the radius of curvature is
where and
Heuristically, this result can be interpreted as
where
In dimensions
If is a parametrized curve in then the radius of curvature at each point of the curve, , is given by
As a special case, if is a function from to , then the radius of curvature of its graph, , is
Derivation
Let be as above, and fix . We want to find the radius of a parametrized circle which matches in its zeroth, first, and second derivatives at . Clearly the radius will not depend on the position , only on the velocity and acceleration . There are only three independent scalars that can be obtained from two vectors and , namely , , and . Thus the radius of curvature must be a function of the three scalars , and .
The general equation for a parametrized circle in is
where is the center of the circle (irrelevant since it disappears in the derivatives), are perpendicular vectors of length (that is, and ), and is an arbitrary function which is twice differentiable at .
The relevant derivatives of work out to be
If we now equate these derivatives of to the corresponding derivatives of at we obtain
These three equations in three unknowns (, and ) can be solved for , giving the formula for the radius of curvature:
or, omitting the parameter for readability,
Examples
Semicircles and circles
For a semi-circle of radius in the upper half-plane with
For a semi-circle of radius in the lower half-plane
The circle of radius has a radius of curvature equal to .
Ellipses
In an ellipse with major axis and minor axis , the vertices on the major axis have the smallest radius of curvature of any points, and the vertices on the minor axis have the largest radius of curvature of any points, .
The radius of curvature of an ellipse, as a function of parameter , is
where
The radius of curvature of an ellipse, as a function of , is
where the eccentricity of the ellipse, , is given by
Applications
For the use in differential geometry, see Cesàro equation.
For the radius of curvature of the Earth (approximated by an oblate ellip |
https://en.wikipedia.org/wiki/Second%20moment%20method | In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.
The method is often quantitative, in that one can often deduce a lower bound on the probability that the random variable is larger than some constant times its expectation. The method involves comparing the second moment of random variables to the square of the first moment.
First moment method
The first moment method is a simple application of Markov's inequality for integer-valued variables. For a non-negative, integer-valued random variable , we may want to prove that with high probability. To obtain an upper bound for , and thus a lower bound for , we first note that since takes only integer values, . Since is non-negative we can now apply Markov's inequality to obtain . Combining these we have ; the first moment method is simply the use of this inequality.
Second moment method
In the other direction, being "large" does not directly imply that is small. However, we can often use the second moment to derive such a conclusion, using Cauchy–Schwarz inequality.
The method can also be used on distributional limits of random variables. Furthermore, the estimate of the previous theorem can be refined by means of the so-called Paley–Zygmund inequality. Suppose that is a sequence of non-negative real-valued random variables which converge in law to a random variable . If there are finite positive constants , such that
hold for every , then it follows from the Paley–Zygmund inequality that for every and in
Consequently, the same inequality is satisfied by .
Example application of method
Setup of problem
The Bernoulli bond percolation subgraph of a graph at parameter is a random subgraph obtained from by deleting every edge of with probability , independently. The infinite complete binary tree is an infinite tree where one vertex (called the root) has two neighbors and every other vertex has three neighbors. The second moment method can be used to show that at every parameter with positive probability the connected component of the root in the percolation subgraph of is infinite.
Application of method
Let be the percolation component of the root, and let be the set of vertices of that are at distance from the root. Let be the number of vertices in . To prove that is infinite with positive probability, it is enough to show that with positive probability. By the reverse Fatou lemma, it suffices to show that . The Cauchy–Schwarz inequality gives
Therefore, it is sufficient to show that
that is, that the second moment is bounded from above by a constant times the first moment squared (and both are nonzero). In many applications of the second moment method, one is not able to calculate the moments precisely, |
https://en.wikipedia.org/wiki/Bence%20Iszlai | Bence Iszlai (born 29 May 1990) is a Hungarian football player.
Club statistics
Updated to games played as of 15 May 2021.
External links
1990 births
Sportspeople from Veszprém
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
FC Veszprém footballers
Szombathelyi Haladás footballers
Mezőkövesdi SE footballers
Diósgyőri VTK players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Footballers from Veszprém County |
https://en.wikipedia.org/wiki/Attila%20Busai | Attila Busai (born 21 January 1989) is a Hungarian football player who plays for BKV Előre SC.
Club statistics
Updated to games played as of 28 July 2018.
Honours
Ferencvárosi
Nemzeti Bajnokság I: 2015–16, runner-up 2014–15
Magyar Kupa: 2014–15, 2015–16, 2016–17
Szuperkupa: 2015, 2016
Ligakupa: 2014–15
References
External links
Attila Busai – UEFA competition record (archive)
1989 births
Living people
Footballers from Budapest
Hungarian men's footballers
Hungarian expatriate men's footballers
Men's association football midfielders
MTK Budapest FC players
FC Wil players
Ferencvárosi TC footballers
Szolnoki MÁV FC footballers
Diósgyőri VTK players
Nyíregyháza Spartacus FC players
NEROCA FC players
Nyköpings BIS players
BKV Előre SC footballers
Nemzeti Bajnokság I players
I-League players
Hungarian expatriate sportspeople in Switzerland
Hungarian expatriate sportspeople in India
Hungarian expatriate sportspeople in Sweden
Expatriate men's footballers in Switzerland
Expatriate men's footballers in India
Expatriate men's footballers in Sweden |
https://en.wikipedia.org/wiki/Minimax%20%28disambiguation%29 | Minimax is a strategy in decision theory and related disciplines.
Minimax, minmax, or min-max can also refer to:
Mathematics
Minimax estimator, an estimator which maximal risk is minimal between all possible estimators
Minimax approximation algorithm, algorithms to approximate a function
The Courant minimax principle, a characterization of the eigenvalues of a real symmetric matrix
Minimax theorem, one of a number of theorems relating to the max-min inequality
The Min-max theorem, a characterization of eigenvalues of compact Hermitian operators on Hilbert spaces
Minimax Condorcet method, one of the Condorcet compliant electoral systems.
God's number, the minimum number of moves required to solve a puzzle at its maximum complexity
Yao's principle, regarding the expected cost of algorithms
The fundamental max–min inequality of real analysis
Saddle point, also known as the minimax point
Other
Minimax (TV channel), a television channel available in Central and Eastern Europe (not to be confused with the Pakistani television channel)
Disney XD (Spanish TV channel), formerly known as Minimax
Teletoon+, a Polish television channel formerly known as Minimax
Min-maxing, a role-playing or wargame strategy
'mini-maxing', a strategy in the board game Hex
Mini-MAX, a family of ultralight aircraft
Minimax Limited, a manufacturer of fire extinguishers
miniMAX Discount, defunct Romanian supermarket chain
Minimax, a cooking approach promoted by celebrity chef Graham Kerr in the 1980s and 1990s
Frosted Mini-Wheats, a cereal made by Kellogg's known as Mini Max in the UK
Mini-Max, a character in Disney's Big Hero 6: The Series |
https://en.wikipedia.org/wiki/Andr%C3%A1s%20G%C3%A1l | András Gál (born 20 May 1989, in Budapest) is a Hungarian football player who plays for Austrian club SV Petzenkirchen.
Club statistics
Updated to games played as of 2 June 2013.
External links
http://www.UEFA.com
Hungarian Football Federation
András Gál at ÖFB
1989 births
Living people
Footballers from Budapest
Hungarian men's footballers
Hungarian expatriate men's footballers
Men's association football defenders
MTK Budapest FC players
BFC Siófok players
Nemzeti Bajnokság I players
Hungarian expatriate sportspeople in Austria
Expatriate men's footballers in Austria |
https://en.wikipedia.org/wiki/Nan%20Laird | Nan McKenzie Laird (born September 18, 1943) is the Harvey V. Fineberg Professor of Public Health, Emerita in Biostatistics at the Harvard T.H. Chan School of Public Health. She served as Chair of the Department from 1990 to 1999. She was the Henry Pickering Walcott Professor of Biostatistics from 1991 to 1999. Laird is a Fellow of the American Statistical Association, as well as the Institute of Mathematical Statistics. She is a member of the International Statistical Institute.
Education
Laird began her undergraduate studies at Rice University in 1961, first majoring in mathematics, before switching to French. She left Rice in her junior year in college and moved to New York City. Later, she resumed studies at University of Georgia in computer science before eventually switching to statistics and earned her BA in 1969. Laird worked between 1969 and 1971 as a computer programmer on the Apollo program at MIT's Draper Laboratory before starting her graduate studies at Harvard University in statistics in 1971. She received her PhD from Harvard in 1975 under Arthur Dempster and was hired as a faculty member directly after graduation. She remained at Harvard until her retirement, when she became an emeritus professor.
Career and research
Laird is well known for many seminal papers in biostatistics applications and methods, including the expectation–maximization algorithm.
Selected publications
Laird NM and Ware, JH. (1982) "Random effects models for longitudinal data: an overview of recent results". Biometrics,; 38:963-974.
Honors and awards
Her honors include the third International Prize in Statistics in 2021, the 25th Annual Distinguished Statistician Lecture from the University of Connecticut, the American Statistical Association and Pfizer in 2016, the 25th Annual Lowell Reed Lecturer, from the American Public Health Association in 2011, the Samuel S. Wilks Award, from the American Statistical Association in 2011, the Myra Samuels Lecturer award from Purdue University in 2004, the Janet L. Norwood Award in 2003 from the American Statistical Association, the Florence Nightingale David Award in 2001 from the Committee of Presidents of Statistical Societies, and several other fellowships.
References
1943 births
Living people
American statisticians
20th-century American mathematicians
Women statisticians
Fellows of the Institute of Mathematical Statistics
Rice University alumni
University of Georgia alumni
Harvard University alumni
Harvard University faculty
Fellows of the American Statistical Association
Elected Members of the International Statistical Institute
20th-century women mathematicians
Fellows of the American Association for the Advancement of Science
People from Gainesville, Florida
Massachusetts Institute of Technology people |
https://en.wikipedia.org/wiki/Richard%20Shore | Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on , the partial order of the Turing degrees.
Shore settled the Rogers homogeneity conjecture by showing that there are Turing degrees and such that and , the structures of the degrees above and respectively, are not isomorphic.
In joint work with Theodore Slaman, Shore showed that the Turing jump is definable in .
Career
He was, in 1983, an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk The Degrees of Unsolvability: the Ordering of Functions by Relative Computability. In 2009, he was the Gödel Lecturer (Reverse mathematics: the playground of logic). He was an editor from 1984 to 1993 of the Journal of Symbolic Logic and from 1993 to 2000 of the Bulletin of Symbolic Logic. In 2012, he became a fellow of the American Mathematical Society.
References
External links
Cornell Math - Richard A. Shore.
Living people
American logicians
Cornell University faculty
Fellows of the American Mathematical Society
20th-century American mathematicians
21st-century American mathematicians
1946 births |
https://en.wikipedia.org/wiki/Small%20triambic%20icosahedron | In geometry, the small triambic icosahedron is a star polyhedron composed of 20 intersecting non-regular hexagon faces. It has 60 edges and 32 vertices, and Euler characteristic of −8. It is an isohedron, meaning that all of its faces are symmetric to each other. Branko Grünbaum has conjectured that it is the only Euclidean isohedron with convex faces of six or more sides, but the small hexagonal hexecontahedron is another example.
Geometry
The faces are equilateral hexagons, with alternating angles of and . The dihedral angle equals .
Related shapes
The external surface of the small triambic icosahedron (removing the parts of each hexagonal face that are surrounded by other faces, but interpreting the resulting disconnected plane figures as still being faces) coincides with one of the stellations of the icosahedron. If instead, after removing the surrounded parts of each face, each resulting triple of coplanar triangles is considered to be three separate faces, then the result is one form of the triakis icosahedron, formed by adding a triangular pyramid to each face of an icosahedron.
The dual polyhedron of the small triambic icosahedron is the small ditrigonal icosidodecahedron. As this is a uniform polyhedron, the small triambic icosahedron is a uniform dual. Other uniform duals whose exterior surfaces are stellations of the icosahedron are the medial triambic icosahedron and the great triambic icosahedron.
References
Further reading
(p. 46, Model W26, triakis icosahedron)
(pp. 42–46, dual to uniform polyhedron W70)
H.S.M. Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, , 3.6 6.2 Stellating the Platonic solids, pp.96-104
External links
Polyhedral stellation
Dual uniform polyhedra |
https://en.wikipedia.org/wiki/Viktor%20Hrachov | Viktor Oleksandrovych Hrachov (, born 17 September 1956 in Dzerzhynsk) is a retired Ukrainian football player and currently a manager.
Career statistics
Club
Honours
Soviet Cup winner: 1980, 1983
UEFA Cup Winners' Cup 1983–84 top scorer
IFA Shield: 1985
International career
Hrachov played his only game for USSR on 15 May 1984 in a friendly against Finland.
References
Profile
1956 births
Living people
People from Toretsk
Soviet men's footballers
Soviet Union men's international footballers
Ukrainian men's footballers
Soviet expatriate men's footballers
Ukrainian expatriate men's footballers
Expatriate men's footballers in Hungary
Soviet Top League players
Ukrainian Premier League players
Nemzeti Bajnokság I players
FC Oryol players
FK Köpetdag Aşgabat players
FC Torpedo Moscow players
FC Shakhtar Donetsk players
FC Spartak Moscow players
Budapesti VSC footballers
Debreceni VSC players
Ukrainian football managers
Ukrainian Premier League managers
FC Shakhtar-2 Donetsk managers
FC Shakhtar-3 Donetsk managers
SC Tavriya Simferopol managers
Ukrainian expatriate sportspeople in Hungary
Soviet expatriate sportspeople in Hungary
Men's association football forwards
Footballers from Donetsk Oblast |
https://en.wikipedia.org/wiki/An-Nassariya | an-Nassariya () is a Palestinian town in the Nablus Governorate in the North central West Bank, located 14 kilometers East of Nablus. According to the Palestinian Central Bureau of Statistics (PCBS), the village had a population of 1,889 inhabitants in 2017. The healthcare facilities for the surrounding villages are based in an-Nassariya, and the facilities are designated as MOH level 2.
References
External links
Survey of Western Palestine, Map 12: IAA, Wikimedia commons
An Nassariya Village profile, Applied Research Institute–Jerusalem, ARIJ
an-Nassariya, aerial photo, ARIJ
Nablus Governorate
Villages in the West Bank
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Dahiyat%20Sabah%20al-Kheir | Dahiyat Sabah al-Kheir () is a Palestinian village in the Jenin Governorate in the northern West Bank, located 4 kilometers north of Jenin. According to the Palestinian Central Bureau of Statistics, the town had a population of 1,457 inhabitants in mid-year 2006.
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Dahiyat Sabah al-Kheir came under Jordanian rule.
Since the Six-Day War in 1967, Dahiya Sabah al-Kheir has been under Israeli occupation.
References
External links
Survey of Western Palestine, Map 8: IAA, Wikimedia commons
Jenin Governorate
Villages in the West Bank
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Symmetric%20inverse%20semigroup |
In abstract algebra, the set of all partial bijections on a set X ( one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is or . In general is not commutative.
Details about the origin of the symmetric inverse semigroup are available in the discussion on the origins of the inverse semigroup.
Finite symmetric inverse semigroups
When X is a finite set {1, ..., n}, the inverse semigroup of one-to-one partial transformations is denoted by Cn and its elements are called charts or partial symmetries. The notion of chart generalizes the notion of permutation. A (famous) example of (sets of) charts are the hypomorphic mapping sets from the reconstruction conjecture in graph theory.
The cycle notation of classical, group-based permutations generalizes to symmetric inverse semigroups by the addition of a notion called a path, which (unlike a cycle) ends when it reaches the "undefined" element; the notation thus extended is called path notation.
See also
Symmetric group
Notes
References
Semigroup theory
Algebraic structures |
https://en.wikipedia.org/wiki/Al-Jarushiya | al-Jarushiya () is a Palestinian village in the Tulkarm Governorate in the western West Bank, located 6 kilometers North of Tulkarm. According to the Palestinian Central Bureau of Statistics, al Jarushiya had a population of 1,183 inhabitants in 2017. 8.4% of the population of al-Jarushiya were refugees in 1997. The healthcare facilities for the surrounding villages are based in al-Jarushiya, the facilities are designated as MOH level 2.
History
In 1961, under Jordanian rule, the population of Jarushiya was 245.
Post 1967
After the Six-Day War in 1967, Al-Jarushiya came under Israeli occupation.
Footnotes
Bibliography
External links
Welcome To al-Jaroushiyya
Survey of Western Palestine, Map 11: IAA, Wikimedia commons
Villages in the West Bank
Tulkarm Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Al-Ras%2C%20Tulkarm | al-Ras () is a Palestinian village in the Tulkarm Governorate in the eastern West Bank, located 7 kilometers South-east of Tulkarm. According to the Palestinian Central Bureau of Statistics, al-Ras had a population of 650 inhabitants in 2017. In 1997, refugees made up 11.1% of the population of al-Ras. The healthcare facilities for al-Ras are based in Kafr Sur, where the facilities are designated as MOH level 2.
History
Ceramics from the Byzantine era have been found here.
Seven ruins are shown on the plan north of this village within about a mile. They are ancient watch towers, like those of Azzun. One of them, known as Gasr Bint esh-Sheikh, dates from the late Hellenistic and early Roman periods.
Ottoman era
Al-Ras was incorporated into the Ottoman Empire in 1517 with all of Palestine, and in 1596 it appeared in the tax registers as being in the Nahiya of Bani Sa'b of the Liwa of Nablus. It had a population of 25 households, all Muslim. The villagers paid a fixed tax-rate of 33,3% on various agricultural products, including wheat, barley, summer crops, olive trees, goats and/or beehives in addition to occasional revenues and a fixed tax for people of Nablus area; a total of 6,600 akçe. All the revenues went to a waqf.
In 1838, Robinson noted er-Ras as a village in Beni Sa'ab district, west of Nablus.
In 1870/1871 (1288 AH), an Ottoman census listed the village with 23 Household in the nahiya (sub-district) of Bani Sa'b.
In 1882 the PEF's Survey of Western Palestine (SWP) described Er Ras as: "a small hamlet on a high knoll, supplied by cisterns, with olives below on the north."
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Ras had a population of 92 Muslims, increasing in the 1931 census to 119 Muslims, living in 26 houses.
In the 1945 statistics the population of Er Ras was 160 Muslims, with 5,646 dunams of land according to an official land and population survey. Of this, 1,029 dunams were plantations and irrigable land, 2,027 were used for cereals, while 3 dunams were built-up (urban) land.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Al-Ras came under Jordanian rule.
In 1961, the population of Al-Ras was 269.
Post 1967
Since the Six-Day War in 1967, Al-Ras has been under Israeli occupation.
References
Bibliography
External links
Welcome To al-Ras
Survey of Western Palestine, Map 11: IAA, Wikimedia commons
Villages in the West Bank
Tulkarm Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Shufa%2C%20Tulkarm | Shufa () is a Palestinian village in the Tulkarm Governorate in the eastern West Bank, located 6 kilometers South-east of Tulkarm. According to the Palestinian Central Bureau of Statistics, Shufa had a population of approximately 1,253 inhabitants in mid-year 2006 and 1,350 by 2017. 5.4% of the population of Shufa were refugees in 1997. The healthcare facilities for Shufa are at Kafr al-Labad or Saffarin where the facilities are designated as MOH level 2.
History
Ceramics from the Byzantine era have been found here.
Ottoman era
Shufa, like all of Palestine was incorporated into the Ottoman Empire in 1517. In the 1596 tax registers, it was named Sufa, part of the nahiya ("subdistrict") of Jabal Sami, part of the larger Sanjak of Nablus. It had a population of 8 households, all Muslims. The inhabitants paid a fixed tax rate of 33,3% on agricultural products, including wheat, barley, summer crops, olive trees, goats and beehives, in addition to occasional revenues and a press for olive oil or grape syrup, and a fixed tax for people of Nablus area; a total of 3,202 akçe.
In 1838, it was noted as a village, Shaufeh in the Wady esh-Sha'ir district, west of Nablus.
In the 1860s, the Ottoman authorities granted the village an agricultural plot of land called Ghabat Shufa in the former confines of the Forest of Arsur (Ar. Al-Ghaba) in the coastal plain, west of the village.
In 1870 Victor Guérin noted the village on a hilltop, and taking it as equal importance as Saffarin.
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of Wadi al-Sha'ir.
In 1882 the PEF's Survey of Western Palestine (SWP) described Shufeh as: "A small stone village, in a strong position on a ridge, with steep slopes north and south. It is supplied by a well in the village, and has a few olives below it. A good view is obtained from it over the plain, and the country north and south, as well as to the range north of Sebustieh."
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Shufeh had a population of 207 Muslims, increasing in the 1931 census to 259 Muslims, living in 47 houses.
In the 1945 statistics the population of Shufa was 370 Muslims, with 11,690 dunams of land according to an official land and population survey. Of this, 4,315 dunams were used for cereals, while 6 dunams were built-up (urban) land.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Shufa came under Jordanian rule.
In 1961, the population was 503.
Post 1967
Since the Six-Day War in 1967, Shufa has been under Israeli occupation.
See also
Peasants' revolt in Palestine
Omer Goldman
List of violent incidents in the Israeli–Palestinian conflict, January–June 2015
Footnotes
Bibliography
External links
Welcome To Shufa
Survey of Western Palestine, Map 11: IAA, Wikimedia commons
Villages in the West Bank
Tulkarm Governorate
Municipalities of the State |
https://en.wikipedia.org/wiki/Zeita%2C%20Tulkarm | Zeita () is a Palestinian town in the Tulkarm Governorate in the western West Bank, located 11 kilometers North-east of Tulkarm. According to the Palestinian Central Bureau of Statistics, Zeita had a population of 3,078 inhabitants in 2017. 21.5% of the population of Zeita were refugees in 1997. The healthcare facilities for Zeita are designated as MOH level 2.
History
Zeita is an ancient village where marble Corinthian capitals have been reused in a local Maqam.
Pottery remains have been found here from the Byzantine, early Muslim and the Middle Ages.
The place was mentioned as a Samaritan settlement in Baba Rabba's revolt during the 4th century CE. A Samaritan elder and leader named haCohen Levi lived there. According to Levy-Rubin, it was inhabited by Samaritans from the 4th to the 9th centuries.
In 1265, Zeita was among the villages and estates sultan Baibars allocated to his amirs after he had expelled the Crusaders. Half of Zaita was given to emir Jamal al-Din Aidughdi al-'Azizi, a quarter to emir Shams al-Din Ildikuz al-Karaki, and a quarter to emir Saif al-Din Qilij al-Baghdadi.
Ottoman era
The village was incorporated into the Ottoman Empire with the rest of Palestine in 1517. In the 1596 Ottoman tax records, it appeared under the name of Zaita, located in the Nahiya Qaqun, in the Nablus Sanjak. It had a population of 91 Muslim and 7 Christian households. They paid a fixed tax-rate of 33.3% on agricultural products, including wheat, barley, summer crops, olive trees, goats and beehives, in addition to occasional revenues and a press for olive oil or grape syrup and a jizya tax on people in the Nablus area; a total of 3,440 akçe. Pottery remains from the Ottoman era have also been found here.
Zeita appears on sheet 45 Jacotin's map drawn-up during Napoleon's invasion in 1799, though its position is not accurate.
During the 1834 Peasants' revolt in Palestine, Ibrahim Pasha of Egypt pursued rebels to Zeita. Ninety rebels were slain here, while the rest fled to nearby Deir al-Ghusun. At Deir al-Ghusun, many of the inhabitants and rebels heeded a call by Husayn Abd al-Hadi to flee once the Egyptian troops arrived. In response, rebel commander Qasim had several of the defectors among his ranks killed. Ibrahim Pasha's troops stormed the hill and the rebels (mostly members of the Qasim, Jarrar, Jayyusi and Barqawi families) were routed, suffering 300 fatalities. In 1838 it was noted as a village, Zeita, in the western Esh-Sha'rawiyeh administrative region, north of Nablus.
In 1870 Victor Guérin found here a village with 600 inhabitants. He further noted: "Here I found, just as at Jett, an ancient capital hollowed out to make a mortar, and used for the same purpose. A very good well, constructed of cut stone, seems ancient."
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of al-Sha'rawiyya al-Gharbiyya.
In 1882, the PEF's Survey of Western Palestine (SWP) described it as: "a good |
https://en.wikipedia.org/wiki/Nur%20Shams | Nur Shams () is a Palestinian refugee camp in the Tulkarm Governorate in the northwestern West Bank, located three kilometers east of Tulkarm. According to the Palestinian Central Bureau of Statistics, Nur Shams had a population of 6,479 inhabitants in 2007 and 6,423 by 2017. 95.1% of the population of Nur Shams were refugees in 1997. The UNRWA-run healthcare facility for Nur Shams camp was re-built in 1996 with contributions from the Government of Germany.
Historian Benny Morris describes it as having been "a lonely and exclusively Arab area" in early 1936.
During the Mandate period, a British detention camp was situated at Nur Shams.
Nur Shams camp was established in 1952 on 226 dunums. The camp was transferred to Palestinian Authority control in November 1998, after the signing of the Wye River Memorandum and the first phase of further Israeli redeployment.
The two schools in the camp are in poor condition and are listed on UNRWA's priority list for replacement pending securing of funds to carry out the project. A four story Boys' school was constructed in 2004 and has 1035 pupils, the girls' school was constructed in 2001 and has 975 pupils.
In 2023, the IDF entered the camp.
See also
Palestinian refugee camps
References
External links
Welcome To Nur Shams R.C.
Populated places established in 1952
Palestinian refugee camps in the West Bank
Tulkarm Governorate
1952 establishments in Jordan |
https://en.wikipedia.org/wiki/Azzun%20Atma | 'Azzun 'Atma () is a Palestinian village in the Qalqilya Governorate in the western West Bank, located 5 kilometers South-east of Qalqilya. According to the Palestinian Central Bureau of Statistics, 'Azzun 'Atma had a population of 2,068 inhabitants in 2017. 3.9% of the population of 'Azzun 'Atma were refugees in 1997. The healthcare facilities for 'Azzun 'Atma are designated as MOH level 2.
Location
‘Azzun ‘Atma is located 8.82 km south of Qalqiliya. It is bordered by Mas-ha and Sha'arei Tikva to the east, Az Zawiya to the south, Oranit to the west, and Beit ‘Amin and ‘Izbat Salman to the north.
History
Potsherds from the Iron Age II, Persian, Hellenistic, Byzantine, Byzantine/Umayyad, Crusader/Ayyubid and Mamluk eras have been found.
Old stones have been reused in homes, and the mosque is possibly an old church.
Ottoman era
The place appeared in 1596 Ottoman tax registers as 'Azzun, being in the Nahiya of Jabal Qubal of the Liwa of Nablus. It had a population of 29 households and 2 bachelors, all Muslim. The villagers paid a fixed tax rate of 33,3%, on wheat, barley, summer crops, olives, goats and beehives; a total of 4,200 akçe.
Potsherds from the early Ottoman era have also been found here.
When the French explorer Victor Guérin visited the place in 1870 it was described it as a large Arab village, then deserted. Many small, square houses were still partly standing, and near the mosque he noticed old columns and large stone from older buildings. Old fig trees and beautiful mimosa were scattered through the ruins. In the PEF's Survey of Western Palestine (1882), it is also described as a "ruined village".
Jordanian Era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Azzun Atma came under Jordanian rule.
Post-1967
Since the Six-Day War in 1967, Azzun Atma has been under Israeli occupation.
After the 1995 accords, about 3.8% of village land was classified as Area B, the remaining 96.2% as Area C. Israel has confiscated 2,689 dunams of village land in order to construct three Israeli settlements of Sha'are Tikva, Oranit and Zamarot (Zamarot becoming part of Oranit), in addition to land for the Israeli West Bank barrier, which almost entirely surrounds Azzun Atma, and which also isolate the village from much of its remaining land behind the wall.
See also
Sanniriya
References
Bibliography
External links
Survey of Western Palestine, Map 14: IAA, Wikimedia commons
‘Azzun ‘Atma Village (Fact Sheet), Applied Research Institute–Jerusalem, ARIJ
‘Azzun ‘Atma Village Profile, ARIJ
‘Azzun ‘Atma, aerial photo, ARIJ
Development Priorities and Needs in ‘Azzun ‘Atma, ARIJ
Azzun- Atma: A village encircled by the Wall 17, May, 2004, POICA
Israeli Occupation Forces Expands its Siege on Residents of Azzun Atma – Qalqiliya Governorate 16, May, 2006, POICA
New Stage for completing the Segregation wall around 'Azzun 'Atma village in Qalqilyia, 02, October, 2006, POICA
Azzun Atme village engulfed by two walls 05, Nov |
https://en.wikipedia.org/wiki/Reflecting%20cardinal | In set theory, a mathematical discipline, a reflecting cardinal is a cardinal number κ for which there is a normal ideal I on κ such that for every X∈I+, the set of α∈κ for which X reflects at α is in I+. (A stationary subset S of κ is said to reflect at α<κ if S∩α is stationary in α.)
Reflecting cardinals were introduced by .
Every weakly compact cardinal is a reflecting cardinal, and is also a limit of reflecting cardinals.
The consistency strength of an inaccessible reflecting cardinal is strictly greater than a greatly Mahlo cardinal, where a cardinal κ is called greatly Mahlo if it is κ+-Mahlo . An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.
See also
List of large cardinal properties
References
Large cardinals |
https://en.wikipedia.org/wiki/Nabi%20Ilyas | Nabi Ilyas () is a Palestinian village in the Qalqilya Governorate in the western West Bank, located two kilometers east of Qalqilya. According to the Palestinian Central Bureau of Statistics, an Nabi Ilyas had a population of 1,399 inhabitants in 2017. 25.6% of the population of an Nabi Ilyas were refugees in 1997.
The health care facilities for an Nabi Ilyas are in Qalqilya designated as MoH level 4 there are also two clinics one run by the UNRWA and one run by the Palestinian Ministry of Health.
Location
An Nabi Ilyas is located 5.06 km east of Qalqiliya. It is bordered by ‘Izbat at Tabib and ‘Isla to the east, Ras at Tira and ‘Izbat al Ashqar to the south, ‘Arab Abu Farda to the west, and Jayyus to the north.
History
The village is situated on an ancient site. Cisterns, and graves cut into rock have been found here, together with ceramics from the Byzantine era.
Ottoman era
Nabi Ilyas was incorporated into the Ottoman Empire in 1517 with all of Palestine, and in 1596 it appeared in the tax registers under the name of Ilyas, as being in the Nahiya of Bani Sa'b of the Liwa of Nablus. It was noted as hali, empty, but a fixed tax rate of 33,3% was paid on agricultural products; a total of 1,200 akçe.
In 1882 the PEF's Survey of Western Palestine described Neby Elyas (under "Archæology") as: "Walls and wells, with a ruined kubbeh."
British Mandate era
In the 1945 statistics, during the British Mandate of Palestine, the population was counted under Azzun.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Nabi Ilyas came under Jordanian rule.
In 1961, the population of Nabi Ilyas was 223.
1967-present
Since the Six-Day War in 1967, Nabi Ilyas has been under Israeli occupation.
After the 1995 accords, 2.7% of Nabi Ilyas land has been defined as Area B land, while the remaining 97.3% is Area C.
Israel confiscated 1,943 dunums of village land (43.8% of the total village lands) for the Israeli settlement of Alfei Menashe, in addition to confiscating land from other neighbouring Palestinian villages. The Separation Wall would further separate the village from much of its land.
By 2009 Israeli consumers were using Nabi Ilyas for bargain hunting. Jewish shoppers, who were kept out of the main Palestinian cities by Israeli security regulations, were drawn by the cheap prices for groceries, furniture and dental treatment that are on offer in Nabi Ilyas.
Footnotes
Bibliography
External links
An Nabi Elyas, Welcome to Palestine
Survey of Western Palestine, Map 11: IAA, Wikimedia commons
An Nabi Elyas Village (Fact Sheet), Applied Research Institute–Jerusalem, ARIJ
An Nabi Elyas Village Profile, ARIJ
An Nabi Elyas, aerial photo, ARIJ
Development Priorities and Needs in An Nabi Elyas, ARIJ
Villages in the West Bank
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Acz%C3%A9l | Aczél is a Hungarian surname meaning "steel". Notable people with the surname include:
Amir Aczel (1950–2015), Israeli-born American mathematics writer of Hungarian origin; author of books on mathematicians and the history of mathematics
György Aczél (1917–1991), Hungarian communist politician
János Aczél (royal secretary) (died 1523), Hungarian poet
János Aczél (mathematician) (1924–2020), Hungarian-Canadian mathematician
József Aczél (1900–1945), Hungarian footballer
Peter Aczel (born 1941), British mathematician
Steve Aczel (born 1954), Hungarian/Australian boxer of the 1980s, '90s and 2000s
Zoltán Aczél (born 1967), Hungarian footballer
See also
Aczel's anti-foundation axiom
Hungarian-language surnames |
https://en.wikipedia.org/wiki/Az-Za%27ayyem | az-Za'ayyem () is a Palestinian village in the Jerusalem Governorate, located 3 kilometers east of Jerusalem in the central West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 6,270 in 2017. The healthcare facilities for az-Za'ayyem according to the Ministry of Health are obtained in East Jerusalem.
History
1967, aftermath
After the 1967 Six-Day War, az-Za'ayyem has been under Israeli occupation.
After the 1995 accords, 3.8% (or 236 dunams) of the land was classified as Area B, the remaining 96.2% (or 5,896 dunams) as Area C.
Israel has confiscated land from az-Za'ayyem in order to construct two Israeli settlements:
406 dunams for Ma’ale Adumim,
138 dunams for Mishor Adumim (industrial zone).
az-Za'ayyem lies close to Highway 1 to Jerusalem and the az-Za'ayyem check point in the separation barrier.
References
External links
Az Za'ayyem Village (Fact Sheet), Applied Research Institute–Jerusalem ARIJ
Az Za'ayyem Village Profile, ARIJ
Aerial photo, ARIJ
Locality Development Priorities and Needs in Az Za'ayyem, ARIJ
Villages in the West Bank
Jerusalem Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/J%C3%B3nsson%20function | In mathematical set theory, an ω-Jónsson function for a set x of ordinals is a function with the property that, for any subset y of x with the same cardinality as x, the restriction of to is surjective on . Here denotes the set of strictly increasing sequences of members of , or equivalently the family of subsets of with order type , using a standard notation for the family of subsets with a given order type. Jónsson functions are named for Bjarni Jónsson.
showed that for every ordinal λ there is an ω-Jónsson function for λ.
Kunen's proof of Kunen's inconsistency theorem uses a Jónsson function for cardinals λ such that 2λ = λℵ0, and Kunen observed that for this special case there is a simpler proof of the existence of Jónsson functions. gave a simple proof for the general case.
The existence of Jónsson functions shows that for any cardinal there is an algebra with an infinitary operation that has no proper subalgebras of the same cardinality. In particular if infinitary operations are allowed then an analogue of Jónsson algebras exists in any cardinality, so there are no infinitary analogues of Jónsson cardinals.
References
Set theory
Functions and mappings |
https://en.wikipedia.org/wiki/Fieller%27s%20theorem | In statistics, Fieller's theorem allows the calculation of a confidence interval for the ratio of two means.
Approximate confidence interval
Variables a and b may be measured in different units, so there is no way to directly combine the standard errors as they may also be in different units. The most complete discussion of this is given by Fieller (1954).
Fieller showed that if a and b are (possibly correlated) means of two samples with expectations and , and variances and and covariance , and if are all known, then a (1 − α) confidence interval (mL, mU) for is given by
where
Here is an unbiased estimator of based on r degrees of freedom, and is the -level deviate from the Student's t-distribution based on r degrees of freedom.
Three features of this formula are important in this context:
a) The expression inside the square root has to be positive, or else the resulting interval will be imaginary.
b) When g is very close to 1, the confidence interval is infinite.
c) When g is greater than 1, the overall divisor outside the square brackets is negative and the confidence interval is exclusive.
Other methods
One problem is that, when g is not small, the confidence interval can blow up when using Fieller's theorem. Andy Grieve has provided a Bayesian solution where the CIs are still sensible, albeit wide. Bootstrapping provides another alternative that does not require the assumption of normality.
History
Edgar C. Fieller (1907–1960) first started working on this problem while in Karl Pearson's group at University College London, where he was employed for five years after graduating in Mathematics from King's College, Cambridge. He then worked for the Boots Pure Drug Company as a statistician and operational researcher before becoming deputy head of operational research at RAF Fighter Command during the Second World War, after which he was appointed the first head of the Statistics Section at the National Physical Laboratory.
See also
Gaussian ratio distribution
Notes
Further reading
Fieller, EC. (1940) "The biological standardisation of insulin". Journal of the Royal Statistical Society (Supplement). 1:1–54.
Motulsky, Harvey (1995) Intuitive Biostatistics. Oxford University Press.
Senn, Steven (2007) Statistical Issues in Drug Development. Second Edition. Wiley.
Theorems in statistics
Statistical approximations
Normal distribution |
https://en.wikipedia.org/wiki/Al-Burj%2C%20Hebron | Al-Burj () is a Palestinian village located southwest of Hebron, in the Hebron Governorate of State of Palestine, in the southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 3,205 in 2017. The primary health care facilities for the village are designated by the Ministry of Health as level 2.
History
Ceramics from the Byzantine era have been found here.
Ottoman era
In 1838, Edward Robinson noted el-Burj as a place "in ruins or deserted," part of the area between the mountains and Gaza, but subject to the government of el-Khulil. Robinson further noted: "The ruins here consists of the remains of a square fortress, about two hundred feet on a side, situated directly upon the surface the projecting hill [..] On the eastern and southern sides a trench has been hewn out in the rock, which sees to have extended quite around the fortress. The walls are mostly broken down [..] the general appearance of the ruin is decidedly that of a Saracenic structure; and I am disposed to regard it as one of the line of strong Saracenic or Turkish fortresses, which appears once to have been drawn along the southern frontier of Palestine. Of these we had now listed four, viz. at Kurmul, Semua, Dhoheriyeh, and this at el-Burj".
In 1863 Victor Guérin called the place Khirbet el-Bordj and noted a maqam, shaped like a tower and dedicated to a Sheikh Mahmoud. He also noted "several caves, some of which are used today as refuge for the shepherds, when they come to graze their herds on this mountain."
In 1883, the PEF's Survey of Palestine described the place, which they called Burj el Beiyarah: "Remains of a fort 200 feet side, with a fosse on the east and south, hewn in rock. Foundations only remain of small masonry, with the joints packed with smaller stones. Round it are caves in the rocks."
British Mandate era
At the time of the 1931 census of Palestine the population of al Burj was counted under Dura.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, al-Burj came under Jordanian rule.
On 25 February 1953, five Arab shepherds were killed and mutilated by Israel in the so called The Har-Zion Affair at al-Burj, including a 16-year-old.
In 1961, the population of Burj was 712.
1967, aftermath
After the Six-Day War in 1967, al-Burj has been under Israeli occupation.
References
Bibliography
External links
Welcome To al-Burj
Survey of Western Palestine, Map 20: IAA, Wikimedia commons
Al Burj Village (Fact Sheet), Applied Research Institute–Jerusalem (ARIJ)
Al Burj Village Profile, ARIJ
Al Burj Village Area Photo, ARIJ
The priorities and needs for development in Al Burj village based on the community and local authorities’ assessment, ARIJ
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Moore%20matrix | In linear algebra, a Moore matrix, introduced by , is a matrix defined over a finite field. When it is a square matrix its determinant is called a Moore determinant (this is unrelated to the Moore determinant of a quaternionic Hermitian matrix). The Moore matrix has successive powers of the Frobenius automorphism applied to its columns (beginning with the zeroth power of the Frobenius automorphism in the first column), so it is an m × n matrix
or
for all indices i and j. (Some authors use the transpose of the above matrix.)
The Moore determinant of a square Moore matrix (so m = n) can be expressed as:
where c runs over a complete set of direction vectors, made specific by having the last non-zero entry equal to 1, i.e.,
In particular the Moore determinant vanishes if and only if the elements in the left hand column are linearly dependent over the finite field of order q. So it is analogous to the Wronskian of several functions.
Dickson used the Moore determinant in finding the modular invariants of the general linear group over a finite field.
See also
Alternant matrix
Vandermonde matrix
Vandermonde determinant
List of matrices
References
Chapter 1.
Matrices
Determinants |
https://en.wikipedia.org/wiki/Iv%C3%A1n%20Furios | Iván Alejandro Furios (born 20 May 1979) is an Argentine football defender who plays for Olimpo in the Argentine Torneo Federal A.
External links
Argentine Primera statistics
1979 births
Living people
Footballers from Entre Ríos Province
Men's association football defenders
Argentine men's footballers
Argentine expatriate men's footballers
Boca Juniors footballers
Chacarita Juniors footballers
Club Alianza Lima footballers
José Gálvez FBC footballers
Instituto Atlético Central Córdoba footballers
Club Atlético Aldosivi footballers
Neuchâtel Xamax FCS players
Club Olimpo footballers
Club Atlético Patronato footballers
Peruvian Primera División players
Swiss Super League players
Expatriate men's footballers in Peru
Expatriate men's footballers in Switzerland |
https://en.wikipedia.org/wiki/Cocker%27s%20Decimal%20Arithmetick | Cocker's Decimal Arithmetick is a grammar school mathematics textbook written by Edward Cocker (1631–1676) and published posthumously by John Hawkins in 1684. Decimal Arithmetick along with companion volume, Cocker's Arithmetick published in 1677, were used in schools in the United Kingdom for more than 150 years.
The concept of decimal fractions and the advantages of using them in calculations were well known, but a wide variety of different notations were in use. After surveying various notations, Decimal Arithmetick recommends the decimal point notation introduced by John Napier:
A decimal fraction being written ... by having a point or prick prefixed before it ... being written according to the first direction, I conceive they may be most fit for calculation.
Decimal Arithmetick gives instructions for calculations involving decimals, methods of extracting roots, and an overview of the concept of logarithms. There are many worked examples, some of which involve solid geometry or the calculation of interest.
References
1678 books
Mathematics textbooks
Mathematics education in the United Kingdom |
https://en.wikipedia.org/wiki/Gevrey | Gevrey may refer to:
Gevrey-Chambertin
Maurice Gevrey, mathematician
Gevrey class in mathematics |
https://en.wikipedia.org/wiki/Charles%20R.%20Doering | Charles Rogers Doering was a professor of mathematics at the University of Michigan, Ann Arbor. He is notable for his research that is generally focused on the analysis of stochastic dynamical systems arising in biology, chemistry and physics, to systems of nonlinear partial differential equations. Recently he had been focusing on fundamental questions in fluid dynamics as part of the $1M Clay Institute millennium challenge concerning the regularity of solutions to the equations of fluid dynamics. With J. D. Gibbon, he notably co-authored the book Applied Analysis of the Navier-Stokes Equations, published by Cambridge University Press. He died on May 15, 2021.
Education
He received his BS from Antioch College, 1977; his MS from the University of Cincinnati, 1978; and his PhD from The University of Texas at Austin under Cécile DeWitt-Morette, 1985, in the area of applying stochastic differential equations to statistical mechanics and field theory. His masters thesis was entitled: Generation of solutions to the Einstein equations. His PhD thesis was entitled, Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics.
Career
In 1986–87, he was a Director's Postdoctoral Fellow 1986–87, Center for Nonlinear Studies, Los Alamos National Laboratory; in 1987–96, he rose to Professor of Physics, 1987–96, Clarkson University; in 1994–96, he was Deputy Director of Los Alamos' Center for Nonlinear Studies. He joined the faculty of the University of Michigan in 1996, where he eventually became the Nicholas D. Kazarinoff Collegiate Professor of Complex Systems, Mathematics and Physics and the Director of the Center for the Study of Complex Systems. He was very active in the Geophysical Fluid Dynamics Program at the Woods Hole Oceanographic Institute.
Honors
Doering received a number of honours including the Presidential Young Investigator Award, 1989–94; Fulbright Scholarship, 2001; 1995; Fellow of the American Physical Society, 2001; the Humboldt Research Award, 2003. He was named Fellow of the Society for Industrial and Applied Mathematics in 2011, a Simons Foundation Fellow in Theoretical Physics in 2014, a Guggenheim Fellowship in Applied Mathematics in 2016, and a Simons Foundation Fellow in Mathematics in 2021.
See also
Quantum Aspects of Life
References
External links
Doering at the scientific commons
Doering's math genealogy
Doering's homepage
1956 births
2021 deaths
Antioch College alumni
University of Texas at Austin College of Natural Sciences alumni
University of Michigan faculty
Fluid dynamicists
Probability theorists
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Physical Society
Fellows of the Society for Industrial and Applied Mathematics |
https://en.wikipedia.org/wiki/Multivariate%20adaptive%20regression%20spline | In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.
The term "MARS" is trademarked and licensed to Salford Systems. In order to avoid trademark infringements, many open-source implementations of MARS are called "Earth".
The basics
This section introduces MARS using a few examples. We start with a set of data: a matrix of input variables x, and a vector of the observed responses y, with a response for each row in x. For example, the data could be:
Here there is only one independent variable, so the x matrix is just a single column. Given these measurements, we would like to build a model which predicts the expected y for a given x.
A linear model for the above data is
The hat on the indicates that is estimated from the data. The figure on the right shows a plot of this function:
a line giving the predicted versus x, with the original values of y shown as red dots.
The data at the extremes of x indicates that the relationship between y and x may be non-linear (look at the red dots relative to the regression line at low and high values of x). We thus turn to MARS to automatically build a model taking into account non-linearities. MARS software constructs a model from the given x and y as follows
The figure on the right shows a plot of this function: the predicted versus x, with the original values of y once again shown as red dots. The predicted response is now a better fit to the original y values.
MARS has automatically produced a kink in the predicted y to take into account non-linearity. The kink is produced by hinge functions. The hinge functions are the expressions starting with (where is if , else ). Hinge functions are described in more detail below.
In this simple example, we can easily see from the plot that y has a non-linear relationship with x (and might perhaps guess that y varies with the square of x). However, in general there will be multiple independent variables, and the relationship between y and these variables will be unclear and not easily visible by plotting. We can use MARS to discover that non-linear relationship.
An example MARS expression with multiple variables is
This expression models air pollution (the ozone level) as a function of the temperature and a few other variables. Note that the last term in the formula (on the last line) incorporates an interaction between and .
The figure on the right plots the predicted as and vary, with the other variables fixed at their median values. The figure shows that wind does not affect the ozone level unless visibility is low. We see that MARS can build quite flexible regression surfaces by combining hinge functions.
To obtain the above expression, the MARS model building procedure automa |
https://en.wikipedia.org/wiki/Unique%20sink%20orientation | In mathematics, a unique sink orientation is an orientation of the edges of a polytope such that, in every face of the polytope (including the whole polytope as one of the faces), there is exactly one vertex for which all adjoining edges are oriented inward (i.e. towards that vertex). If a polytope is given together with a linear objective function, and edges are oriented from vertices with smaller objective function values to vertices with larger objective values, the result is a unique sink orientation. Thus, unique sink orientations can be used to model linear programs as well as certain nonlinear programs such as the smallest circle problem.
In hypercubes
The problem of finding the sink in a unique sink orientation of a hypercube was formulated as an abstraction of linear complementarity problems by and it was termed "unique sink orientation" in 2001 .
It is possible for an algorithm to determine the unique sink of a -dimensional hypercube in time for , substantially smaller than the time required to examine all vertices. When the orientation has the additional property that the orientation forms a directed acyclic graph, which happens when unique sink orientations are used to model LP-type problems, it is possible to find the sink using a randomized algorithm in expected time exponential in the square root of d .
In simple polytopes
A simple d-dimensional polytope is a polytope in which every vertex has exactly d incident edges. In a unique-sink orientation of a simple polytope, every subset of k incoming edges at a vertex v determines a k-dimensional face for which v is the unique sink. Therefore, the number of faces of all dimensions of the polytope (including the polytope itself, but not the empty set) can be computed by the sum of the number of subsets of incoming edges,
where G(P) is the graph of the polytope, and din(v) is the in-degree (number of incoming edges) of a vertex v in the given orientation .
More generally, for any orientation of a simple polytope, the same sum counts the number of incident pairs of a face of the polytope and a sink of the face. And in an acyclic orientation, every face must have at least one sink. Therefore, an acyclic orientation is a unique sink orientation if and only if there is no other acyclic orientation with a smaller sum. Additionally, a k-regular subgraph of the given graph forms a face of the polytope if and only if its vertices form a lower set for at least one acyclic unique sink orientation. In this way, the face lattice of the polytope is uniquely determined from the graph . Based on this structure, the face lattices of simple polytopes can be reconstructed from their graphs in polynomial time using linear programming .
References
.
.
.
.
.
.
.
Graph theory objects
Polyhedral combinatorics |
https://en.wikipedia.org/wiki/Tom%20Whiteside | Derek Thomas Whiteside FBA (23 July 1932 – 22 April 2008) was a British historian of mathematics.
Biography
In 1954 Whiteside graduated from Bristol University with a B.A. having studied French, Latin, mathematics and philosophy. He had spent part of 1952 studying at the Sorbonne. In 1956 he began graduate study with Richard Braithwaite who referred him to Michael Hoskin (1930–2021). In 1959 he submitted the manuscript "Mathematical patterns of thought in the late seventeenth century" to Hoskin who submitted it to Archive for History of Exact Sciences for publication.
Hoskin and Whiteside were joined by Adolf Prag (1906–2004) to edit the eight volume Mathematical Papers of Isaac Newton (1967 to 1981). Reviewing first volume of the work, Christoph Scriba wrote,
"...must be praised the extraordinary care and conscientiousness of the editor who collected, organized, transcribed and edited the wealth of material in a superb way." According to Carl Boyer, "Historians of science in general, and Newtonian scholars in particular, owe a heavy debt of gratitude to Dr Whiteside for the altogether exemplary manner in which he is making available to us the ample evidence concerning the making of one of the world's three greatest mathematicians." Boyer also notes that "Rene Descartes and two Hollanders, Hudde and van Schooten, are cited more frequently than are Barrow and Wallis", discounting the notion that Isaac Barrow was Newton's teacher. Rosalind Tanner described the beginning of volume one: "the Preface, Editorial Note, General Introduction, and brief Forward to Volume 1, providing in turn the story of the undertaking, the how and why of the presentation, the history of the Newton manuscripts, and the scope of this Volume 1, and each in its way a notable achievement." Tanner also reviewed volume 2 and its concern with Gerhard Kinckhuysen's Dutch textbook on algebra, partially translated into Latin by Nicholas Mercator, and worked on by Newton until the project was abandoned in 1676.
In 1969 Whiteside became Assistant Director of Research in the Department of History and Philosophy of Science at Cambridge University. He also was Senior Research Fellow at Churchill College. He was elected Fellow of the British Academy in 1975 and promoted to Reader at Cambridge the following year. In 1987 he moved to the department of Pure Mathematics, but his health began to fail. In 1992 Cambridge organized a festschrift in his honour: The Investigation of Difficult Things.
Tom and Ruth Whiteside had two children, Simon and Philippa, to whom volume 8 of Mathematical Papers of Isaac Newton was dedicated.
Whiteside retired in 1999 and died on 22 April 2008.
Isaac Newton
Whiteside wrote a 19-page non-technical account, Newton the Mathematician. In this essay he describes Newton's mathematical development starting in secondary school. Whiteside says that the most important influence on Newton's mathematical development was Book II of René Descartes's La Géométrie. Boo |
https://en.wikipedia.org/wiki/Ad-Duwwara | ad-Duwwara () is a Palestinian village located four kilometers east of Hebron.The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 1,685 in mid-year 2006. The primary health care facilities for the village are located at Beit Einun, which are designated by the Ministry of Health as level 2.
Footnotes
External links
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Mate%20Brajkovi%C4%87 | Mate Brajković (born 18 June 1981 in Sombor) is a Croatian retired football player. The striker last played for NK Turbina.
Career statistics
References
External links
soccerterminal
Living people
1981 births
Sportspeople from Sombor
Footballers from West Bačka District
Croats of Vojvodina
Men's association football forwards
Croatian men's footballers
Croatia men's under-21 international footballers
HNK Rijeka players
NK Zadar players
FC Admira Wacker Mödling players
NK Kamen Ingrad players
Flamurtari FC players
NK Crikvenica players
NK Pomorac 1921 players
NK Krk players
Croatian Football League players
Austrian Football Bundesliga players
Kategoria Superiore players
First Football League (Croatia) players
Croatian expatriate men's footballers
Expatriate men's footballers in Austria
Croatian expatriate sportspeople in Austria
Expatriate men's footballers in Albania
Croatian expatriate sportspeople in Albania |
https://en.wikipedia.org/wiki/List%20of%20Carlton%20Football%20Club%20coaches | The following is a list of coaches who have coached the Carlton Football Club at a game of Australian rules football in the Australian Football League (AFL), formerly the VFL.
Statistics are correct to the end of Round 21 2023
Key:
G = Games
W = Won
L = Lost
D = Drew
W% = Win percentage
References
Carlton Football Club coaches
Carlton Football Club coaches |
https://en.wikipedia.org/wiki/Lee%20Jong-min%20%28footballer%2C%20born%201983%29 | Lee Jong-Min (born 1 September 1983) is a retired South Korean footballer.
Club career statistics
Honors
Club
Suwon Samsung Bluewings
K League (1) : 2004
FA Cup (1) : 2002
Asian Club Championship (1) : 2002
Asian Super Cup (1) : 2002
Ulsan Hyundai
K League (1) : 2005
League Cup (1) : 2007
Korean Super Cup (1) : 2006
A3 Champions Cup (1) : 2006
FC Seoul
K League (1) : 2010
League Cup (1) : 2010
References
External links
Lee Jong-min – National Team stats at KFA
1983 births
Living people
Men's association football midfielders
South Korean men's footballers
South Korea men's international footballers
Suwon Samsung Bluewings players
Ulsan Hyundai FC players
FC Seoul players
Gimcheon Sangmu FC players
Gwangju FC players
Busan IPark players
K League 1 players
K League 2 players
Footballers at the 2006 Asian Games
Asian Games competitors for South Korea
Sportspeople from Jeju Province |
https://en.wikipedia.org/wiki/Al-Heila | al-Heila () is a Palestinian village located eight kilometers south of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 1,277 in 2007. The primary health care facilities for the village are designated by the Ministry of Health as level 1.
Footnotes
External links
Welcome To al-Heila
Survey of Western Palestine, Map 21: IAA, Wikimedia commons
Al Heila Village (Fact Sheet), Applied Research Institute–Jerusalem, ARIJ
Al Heila Village Profile, ARIJ
Al Heila Village Area Photo, ARIJ
The priorities and needs for development in Al Heila village based on the community and local authorities’ assessment, ARIJ
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Parametrix | In mathematics, and specifically the field of partial differential equations (PDEs), a parametrix is an approximation to a fundamental solution of a PDE, and is essentially an approximate inverse to a differential operator.
A parametrix for a differential operator is often easier to construct than a fundamental solution, and for many purposes is almost as good. It is sometimes possible to construct a fundamental solution from a parametrix by iteratively improving it.
Overview and informal definition
It is useful to review what a fundamental solution for a differential operator with constant coefficients is: it is a distribution on ℝn such that
in the weak sense, where is the Dirac delta distribution.
In a similar way, a parametrix for a variable coefficient differential operator is a distribution such that
where is some function with compact support.
The parametrix is a useful concept in the study of elliptic differential operators and, more generally, of hypoelliptic pseudodifferential operators with variable coefficient, since for such operators over appropriate domains a parametrix can be shown to exist, can be somewhat easily constructed and be a smooth function away from the origin.
Having found the analytic expression of the parametrix, it is possible to compute the solution of the associated fairly general elliptic partial differential equation by solving an associated Fredholm integral equation: also, the structure itself of the parametrix reveals properties of the solution of the problem without even calculating it, like its smoothness and other qualitative properties.
Parametrices for pseudodifferential operators
More generally, if is any pseudodifferential operator of order , then another pseudodifferential operator of order is called a parametrix for if the operators
are both pseudodifferential operators of negative order. The operators and will admit continuous extensions to maps between the Sobolev spaces and .
On a compact manifold, the differences above are compact operators. In this case the original operator defines a Fredholm operator between the Sobolev spaces.
Hadamard parametrix construction
An explicit construction of a parametrix for second order partial differential operators based on power series developments was discovered by Jacques Hadamard. It can be applied to the Laplace operator, the wave equation and the heat equation.
In the case of the heat equation or the wave equation, where there is a distinguished time parameter ,
Hadamard's method consists in taking the fundamental solution of the constant coefficient differential operator obtained freezing the coefficients at a fixed point and seeking a general solution as a product of this solution, as the point varies, by a formal power series in . The constant term is 1 and the higher coefficients are functions determined recursively as integrals in a single variable.
In general, the power series will not converge but w |
https://en.wikipedia.org/wiki/Cone%20algorithm | In computational geometry, the cone algorithm is an algorithm for identifying the particles that are near the surface of an object composed of discrete particles. Its applications include computational surface science and computational nano science. The cone algorithm was first described in a publication about nanogold in 2005.
The cone algorithm works well with clusters in condensed phases, including solid and liquid phases. It can handle the situations when one configuration includes multiple clusters or when holes exist inside clusters. It can also be applied to a cluster iteratively to identify multiple sub-surface layers.
References
Yanting Wang, S. Teitel, and Christoph Dellago (2005), Melting of Icosahedral Gold Nanoclusters from Molecular Dynamics Simulations. Journal of Chemical Physics vol. 122, pp 214722–214738.
External links
Cone Algorithm — Generic surface particle identification algorithm, Yanting Wang.
Molecular modelling software
Geometric algorithms |
https://en.wikipedia.org/wiki/Chiuza | Chiuza () is a commune in Bistrița-Năsăud County, Transylvania, Romania. It is composed of four villages: Chiuza, Mireș (Diófás), Piatra (Kőfarka) and Săsarm (Szészárma).
According to statistics from 1760–1762, Piatra village had 58 families, three priests and a church.
References
Communes in Bistrița-Năsăud County
Localities in Transylvania |
https://en.wikipedia.org/wiki/Hutchinson%20operator | In mathematics, in the study of fractals, a Hutchinson operator is the collective action of a set of contractions, called an iterated function system. The iteration of the operator converges to a unique attractor, which is the often self-similar fixed set of the operator.
Definition
Let be an iterated function system, or a set of contractions from a compact set to itself. The operator is defined over subsets as
A key question is to describe the attractors of this operator, which are compact sets. One way of generating such a set is to start with an initial compact set (which can be a single point, called a seed) and iterate as follows
and taking the limit, the iteration converges to the attractor
Properties
Hutchinson showed in 1981 the existence and uniqueness of the attractor . The proof follows by showing that the Hutchinson operator is contractive on the set of compact subsets of in the Hausdorff distance.
The collection of functions together with composition form a monoid. With N functions, then one may visualize the monoid as a full N-ary tree or a Cayley tree.
References
Fractals |
https://en.wikipedia.org/wiki/Trimmed%20estimator | In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.
Given an estimator, the x% trimmed version is obtained by discarding the x% lowest or highest observations or on both end: it is a statistic on the middle of the data. For instance, the 5% trimmed mean is obtained by taking the mean of the 5% to 95% range. In some cases a trimmed estimator discards a fixed number of points (such as maximum and minimum) instead of a percentage.
Examples
The median is the most trimmed statistic (nominally 50%), as it discards all but the most central data, and equals the fully trimmed mean – or indeed fully trimmed mid-range, or (for odd-size data sets) the fully trimmed maximum or minimum. Likewise, no degree of trimming has any effect on the median – a trimmed median is the median – because trimming always excludes an equal number of the lowest and highest values.
Quantiles can be thought of as trimmed maxima or minima: for instance, the 5th percentile is the 5% trimmed minimum.
Trimmed estimators used to estimate a location parameter include:
Trimmed mean
Modified mean, discarding the minimum and maximum values
Interquartile mean, the 25% trimmed mean
Midhinge, the 25% trimmed mid-range
Trimmed estimators used to estimate a scale parameter include:
Interquartile range, the 25% trimmed range
Interdecile range, the 10% trimmed range
Trimmed estimators involving only linear combinations of points are examples of L-estimators.
Applications
Estimation
Most often, trimmed estimators are used for parameter estimation of the same parameter as the untrimmed estimator. In some cases the estimator can be used directly, while in other cases it must be adjusted to yield an unbiased consistent estimator.
For example, when estimating a location parameter for a symmetric distribution, a trimmed estimator will be unbiased (assuming the original estimator was unbiased), as it removes the same amount above and below. However, if the distribution has skew, trimmed estimators will generally be biased and require adjustment. For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.
When estimating a scale parameter, using a trimmed estimator as a robust measures of scale, such as to estimate the population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation.
For example, dividing the IQR by (using the error funct |
https://en.wikipedia.org/wiki/Modulus%20%28algebraic%20number%20theory%29 | In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.
Definition
Let K be a global field with ring of integers R. A modulus is a formal product
where p runs over all places of K, finite or infinite, the exponents ν(p) are zero except for finitely many p. If K is a number field, ν(p) = 0 or 1 for real places and ν(p) = 0 for complex places. If K is a function field, ν(p) = 0 for all infinite places.
In the function field case, a modulus is the same thing as an effective divisor, and in the number field case, a modulus can be considered as special form of Arakelov divisor.
The notion of congruence can be extended to the setting of moduli. If a and b are elements of K×, the definition of a ≡∗b (mod pν) depends on what type of prime p is:
if it is finite, then
where ordp is the normalized valuation associated to p;
if it is a real place (of a number field) and ν = 1, then
under the real embedding associated to p.
if it is any other infinite place, there is no condition.
Then, given a modulus m, a ≡∗b (mod m) if a ≡∗b (mod pν(p)) for all p such that ν(p) > 0.
Ray class group
The ray modulo m is
A modulus m can be split into two parts, mf and m∞, the product over the finite and infinite places, respectively. Let Im to be one of the following:
if K is a number field, the subgroup of the group of fractional ideals generated by ideals coprime to mf;
if K is a function field of an algebraic curve over k, the group of divisors, rational over k, with support away from m.
In both case, there is a group homomorphism i : Km,1 → Im obtained by sending a to the principal ideal (resp. divisor) (a).
The ray class group modulo m is the quotient Cm = Im / i(Km,1). A coset of i(Km,1) is called a ray class modulo m.
Erich Hecke's original definition of Hecke characters may be interpreted in terms of characters of the ray class group with respect to some modulus m.
Properties
When K is a number field, the following properties hold.
When m = 1, the ray class group is just the ideal class group.
The ray class group is finite. Its order is the ray class number.
The ray class number is divisible by the class number of K.
Notes
References
Algebraic number theory |
https://en.wikipedia.org/wiki/Kuseis | Kuseise () is a Palestinian village located seven kilometers west of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 2,276 in mid-year 2006. The primary health care facilities for the village are designated by the Ministry of Health as level 1.
Footnotes
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Kim%20Ho-jun | Kim Ho-Jun (; born 21 June 1984) is a South Korean football player who plays for Bucheon FC 1995.
His debut was a match against Daejeon Citizen in 2005.
Club career statistics
External links
1985 births
Living people
Men's association football goalkeepers
South Korean men's footballers
FC Seoul players
Jeju United FC players
Gimcheon Sangmu FC players
Gangwon FC players
K League 1 players |
https://en.wikipedia.org/wiki/Khursa | Khursa () is a Palestinian village located seven kilometers south-west of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 3,481 in 2017. The primary health care facilities for the village are designated by the Ministry of Health as level 2.
Etymology
According to Palmer, the name Khirbet Kurza means "the ruin of kurza", a pine cone.
History
In 1883, the PEF's Survey of Western Palestine found here "walls, caves, a well, and a vault, probably a cistern. There were several cisterns and a sacred place to the west. Some of the ruins appear to be modern, some ancient."
Footnotes
Bibliography
External links
Survey of Western Palestine, Map 21: IAA, Wikimedia commons
Kurza Village (fact sheet), Applied Research Institute–Jerusalem, ARIJ
Kurza Village profile, ARIJ
Kurza Village aerial photo, ARIJ
The priorities and needs for development in Kurza village based on the community and local authorities’ assessment, ARIJ
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/As-Sura | as-Sura is a Palestinian village located fifteen kilometers south-west of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 3,941 in 2017. The primary health care facilities for the village are obtained at Imreish where they are designated by the Ministry of Health as level 1.
Footnotes
External links
Survey of Western Palestine, Map 21: IAA, Wikimedia commons
As Sura Village (fact sheet), Applied Research Institute–Jerusalem, ARIJ
As Sura village profile, ARIJ
As Sura aerial photo, ARIJ
The priorities and needs for development in As Sura village based on the community and local authorities' assessment, ARIJ
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20Real%20Madrid%20CF%20season | The 1999–2000 season was Real Madrid C.F.'s 69th season in La Liga. This article lists all matches that the club played in the 1999–2000 season, and also shows statistics of the club's players.
Summary
John Toshack was sacked by Real Madrid in November 1999 as a consequence of league's bad form following a 3–2 defeat against Rayo Vallecano that left them in eighth position and re-hired Vicente del Bosque who previously managed the club in 1994 and 1996 as a caretaker only.
This season marked the start of the del Bosque era of trophy winning at the club, having taken over from Toshack early in the campaign. The squad was also largely different from the previous squad, with the arrival of Steve McManaman (Liverpool) and Nicolas Anelka (Arsenal) from the English Premier League respectively, as well as local talents Míchel Salgado, and Iván Helguera, to support the budding young talent of Raúl, Iker Casillas, Fernando Morientes and Guti, as well as veterans such as Fernando Hierro and Roberto Carlos.
Players
Squad
Transfers
In
Total spending: €95,700,000
Out
Total income: €0 million
Competitions
Overall
Friendlies
La Liga
Results summary
League table
Results by round
Matches
Copa del Rey
Champions League
First Group stage
Second Group stage
Knockout stage
Final
FIFA Club World Championship
Group stage
Third-place play-off
Squad statistics
Players statistics
Goal scorers
See also
1999–2000 La Liga
1999–2000 Copa del Rey
1999–2000 UEFA Champions League
2000 UEFA Champions League Final
2000 FIFA Club World Championship
References
External links
Realmadrid.com Official Site
Real Madrid Team Page
Real Madrid (Spain) profile
uefa.com - UEFA Champions League
Web Oficial de la Liga de Fútbol Profesional
FIFA
Spanish football clubs 1999–2000 season
1999–2000
1999–2000 |
https://en.wikipedia.org/wiki/Hureiz | Hureiz () is a Palestinian village located seven kilometers south-east of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 997 in mid-year 2006. The primary health care facilities for the village are at Zif designated by the Ministry of Health as level 1 and at Yatta, level 3.
Footnotes
External links
Hureiz aerial photo, Applied Research Institute - Jerusalem (ARIJ)
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Zif%2C%20Hebron | Zif () is a Palestinian village located south of Hebron. The village is in the Hebron Governorate in the southern West Bank. According to the Palestinian Central Bureau of Statistics, Zif had a population of 1,061 in 2017. The primary health care facilities in the village itself are designated by the Ministry of Health as level 1 and at nearby Yatta as level 3.
History
Iron Age
Zif is identified with the biblical town of Ziph. It appears several times in the Hebrew Bible as a town in the vicinity of Hebron that belongs to Tribe of Judah (). The nearby "Wilderness of Ziph" is mentioned as a place where David hides himself from Saul (). Later, the town of Ziph is said to be fortified by Rehoboam (). Its name was found on a number of royal Judahite LMLK seals along with those of Hebron, Socoh and MMST.
Iron Age remains were found in the nearby tell.
Classical Era
Zif existed as a village in the Roman era. It had a Jewish population until at least the 4th century, but it became Christian during the Byzantine period.
The remains of a Byzantine-era Christian communal church have been discovered at Zif. Pot sherds from the Byzantine era have also been found here.
Ottoman Era
In 1838 Edward Robinson was the first to identify the village Zif and its adjacent Tell Zif with the biblical town of Ziph.
In 1863 Victor Guérin visited and described the ruins.
In 1874 surveyors from the PEF Survey of Palestine visited, and noted about Tell ez Zif: "A large mound, partly natural; on the north side a quarry; on the south are tombs. One of these has a single chamber, with a broad bench running round; on the back wall are three kokim with arched roofs, the arches pointed on the left side wall; at the back is another similar koka. A second tomb was a chamber, 8 feet to the back, 9 feet wide, with three recesses, one on each side, one at the back; they are merely shelves, 8 feet by 5 feet, raised some 2 feet. This tomb has a porch in front, supported by two square rock-cut piers.
Zif Today
Zif has been under Israeli occupation since 1967.
In September 2002, a bomb filled with screws and nails, planted by Jewish settlers, exploded in the village's school, wounding five children. A second bomb was found by the school's principal and was detonated by Israeli bomb experts.
References
Bibliography
(p. 315)
(p. 408)
External links
Zif Village | قرية زيف on Facebook
Zif Village (Fact Sheet), Applied Research Institute–Jerusalem, ARIJ
Zif Village Profile, ARIJ
Zif aerial photo, ARIJ
The priorities and needs for development in Zif village based on the community and local authorities’ assessment, ARIJ
Survey of Western Palestine, Map 21: IAA, Wikimedia commons
Villages in the West Bank
Hebron Governorate
Ancient Jewish settlements of Judaea
Municipalities of the State of Palestine
Biblical archaeology |
https://en.wikipedia.org/wiki/Qila%2C%20Hebron | Qila () is a Palestinian village located north-west of Hebron. The village is in the Hebron Governorate Southern West Bank. According to the Palestinian Central Bureau of Statistics, the village had a population of 918 in mid-year 2006. The primary health care facilities for the village are at Qila designated by the Ministry of Health as level 1 and at Beit Ula, Kharas or Nuba where the healthcare is at level 2.
History
Many scholars identify Qila with the biblical Keilah, mentioned in 1 Samuel.
Footnotes
Bibliography
(p. 86)
(pp. 314, 357)
(Check pp. 341–343; pp. 350-351)
External links
Welcome To Qila
Survey of Western Palestine, Map 21: IAA, Wikimedia commons
Villages in the West Bank
Hebron Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Generator%20set | Generator set may refer to:
Diesel generator
Engine-generator
Generating set (mathematics) |
https://en.wikipedia.org/wiki/Ulrike%20Tillmann | Ulrike Luise Tillmann FRS is a mathematician specializing in algebraic topology, who has made important contributions to the study of the moduli space of algebraic curves. She is the president of the London Mathematical Society in the period 2021–2022.
She is titular Professor of Mathematics at the University of Oxford and a Fellow of Merton College, Oxford. In 2021 she was appointed Director of the Isaac Newton Institute at the University of Cambridge, and N.M. Rothschild & Sons Professor of Mathematical Sciences at Cambridge, but continued to hold a part-time position at Oxford.
Education
Tillmann completed her Abitur at Gymnasium Georgianum in Vreden. She received a BA from Brandeis University in 1985, followed by a MA from Stanford University in 1987. She read for a PhD under the supervision of Ralph Cohen at Stanford University, where she was awarded her doctorate in 1990. She was awarded Habilitation in 1996 from the University of Bonn.
Awards and honours
In 2004 she was awarded the Whitehead Prize of the London Mathematical Society.
She was elected a Fellow of the Royal Society in 2008 and a Fellow of the American Mathematical Society in 2013. She has served on the council of the Royal Society and in 2018 was its vice-president. In 2017, she became a member of the German Academy of Sciences Leopoldina.
Tillmann was awarded the Bessel Prize by the Alexander von Humboldt Foundation in 2008 and was the Emmy Noether Lecturer of the German Mathematical Society in 2009.
She was elected as president-designate of the London Mathematical Society in June 2020 and took over the presidency from Jonathan Keating in November 2021. She was elected to the European Academy of Sciences (EURASC) in 2021. In October 2021 she became the director of the Isaac Newton Institute, taking a post which lasts for five years.
Personal life
Tillmann's parents are Ewald and Marie-Luise Tillmann. In 1995 she married Jonathan Morris with whom she has had three daughters.
Publications
References
External links
Living people
People from Rhede
Women mathematicians
Fellows of the Royal Society
Female Fellows of the Royal Society
Fellows of the American Mathematical Society
Members of the German National Academy of Sciences Leopoldina
Topologists
20th-century German mathematicians
Whitehead Prize winners
Brandeis University alumni
Stanford University alumni
Academics of the University of Oxford
Fellows of Merton College, Oxford
21st-century German mathematicians
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Mary%20Rees | Susan Mary Rees, FRS (born 31 July 1953) is a British mathematician and an emeritus professor of mathematics at the University of Liverpool since 2018, specialising in research in complex dynamical systems.
Career
Rees was born in Cambridge. After obtaining her BA in 1974 and MSc in 1975 at St Hugh's College, Oxford, she did research in mathematics under the direction of Bill Parry at the University of Warwick, obtaining a PhD in 1978. Her first postdoctoral position was at the Institute for Advanced Study from 1978 to 1979. Later she worked at Institut des hautes études scientifiques and the University of Minnesota. Following this she worked at the University of Liverpool until her retirement. She became professor of mathematics in 2002 and retired in 2018, becoming an emeritus professor.
She was awarded a Whitehead Prize of the London Mathematical Society in 1988. The citation notes that, in particular,Her most spectacular theorem has been to show that in the space of rational maps of the Riemann sphere of degree d ≥ 2 those maps that are ergodic with respect to Lebesgue measure and leave invariant an absolutely continuous probability measure form a set of positive measure.
She also spoke at the ICM at Kyoto in 1990. In recent years, much of Rees' work has focused on the dynamics of quadratic rational maps; i.e. rational maps of the Riemann sphere of degree two, including an extensive monograph. In 2004, she also presented an alternative proof of the Ending Laminations Conjecture of Thurston, which had been proved by Brock, Canary and Minsky shortly before.
FRS
She was elected to a Fellowship of the Royal Society in 2002.
Family
Her father David Rees was also a distinguished mathematician, who worked on Enigma in Hut 6 at Bletchley Park. Her sister Sarah Rees is also a mathematician.
Works
Mary Rees (2010) "Multiple equivalent matings with the aeroplane polynomial". Ergodic Theory and Dynamical Systems, pp. 20
Mary Rees (2008) "William Parry FRS 1934–2006". Biographical Memoirs of the Royal Society, 54, pp. 229–243
Mary Rees (2004) "Teichmuller distance is not $C^{2+\varepsilon }$". Proc London Math, 88, pp. 114–134
Mary Rees (2003) "Views of Parameter Space: Topographer and Resident". Asterisque, 288, pp. 1–418
Mary Rees (2002) "Teichmuller distance for analytically finite surfaces is $C^{2}$." Proc. London Math. Soc. 85 (2002) 686 – 716.,85, pp. 686–716
References
Female Fellows of the Royal Society
Living people
1953 births
Whitehead Prize winners
20th-century British mathematicians
21st-century British mathematicians
British women mathematicians
People from Cambridge
Academics of the University of Liverpool
Alumni of St Hugh's College, Oxford
Alumni of the University of Warwick
Fellows of the Royal Society
Dynamical systems theorists
20th-century women mathematicians
21st-century women mathematicians |
https://en.wikipedia.org/wiki/P-Laplacian | In mathematics, the p-Laplacian, or the p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where is allowed to range over . It is written as
Where the is defined as
In the special case when , this operator reduces to the usual Laplacian. In general solutions of equations involving the p-Laplacian do not have second order derivatives in classical sense, thus solutions to these equations have to be understood as weak solutions. For example, we say that a function u belonging to the Sobolev space is a weak solution of
if for every test function we have
where denotes the standard scalar product.
Energy formulation
The weak solution of the p-Laplace equation with Dirichlet boundary conditions
in a domain is the minimizer of the energy functional
among all functions in the Sobolev space satisfying the boundary conditions in the trace sense. In the particular case and is a ball of radius 1, the weak solution of the problem above can be explicitly computed and is given by
where is a suitable constant depending on the dimension and on only. Observe that for the solution is not twice differentiable in classical sense.
Notes
Sources
Further reading
.
Notes on the p-Laplace equation by Peter Lindqvist
Juan Manfredi, Strong comparison Principle for p-harmonic functions
Elliptic partial differential equations |
https://en.wikipedia.org/wiki/Janez%20Pate | Janez "Jani" Pate (born 6 October 1965) is a Slovenian football manager and former player.
Career statistics
International goals
References
External links
PrvaLiga profile
Living people
1965 births
Footballers from Ljubljana
Yugoslav men's footballers
Slovenian men's footballers
Men's association football midfielders
Slovenia men's international footballers
NK Olimpija Ljubljana (1945–2005) players
S.F.K. Pierikos (football) players
Alki Larnaca FC players
NK Primorje players
NK Triglav Kranj players
NK Olimpija Ljubljana (2005) players
Cypriot First Division players
Slovenian PrvaLiga players
Football League (Greece) players
Slovenian expatriate men's footballers
Expatriate men's footballers in Greece
Slovenian expatriate sportspeople in Greece
Expatriate men's footballers in Cyprus
Slovenian expatriate sportspeople in Cyprus
Expatriate men's footballers in Austria
Slovenian expatriate sportspeople in Austria
Slovenian football managers
NK Olimpija Ljubljana (2005) managers |
https://en.wikipedia.org/wiki/Arnold%20Buffum%20Chace | Arnold Buffum Chace (November 10, 1845 – February 28, 1932) was an American textile businessman, mathematics scholar, and eleventh chancellor of Brown University in Providence, Rhode Island.
Family
Arnold was born November 10, 1845, in Cumberland, Rhode Island. His paternal grandfather Oliver Chace was founder of the Valley Falls textile company, which later became Berkshire Hathaway. His parents Samuel Buffington Chace and Elizabeth Buffum Chace were Quakers and prominent anti-slavery activists. His maternal grandfather, Arnold Buffum, was president of the New England Anti-Slavery Society. His sister Lillie became an author and social reformer.
Arnold married Eliza Chace Greene, daughter of Christopher A. and Sarah A. Greene, on October 24, 1871. Their three children were: Malcolm Greene Chace, Edward Gould Chace, cotton manufacturer, and Margaret Chace, wife of Russell S. Rowland, M.D. of Detroit, MI.
Academics
Arnold Buffum Chace received his bachelor's degree from Brown University in 1866 and a Doctor of Science from Brown in 1892. He also studied for one year at the École de Médecine in Paris. Chace taught physics and mathematics for one term at Brown (1868–69), before having to interrupt his career to handle the family textile business. He remained involved in leadership at Brown for most of his life. In 1876, he was elected trustee; in 1882 he became treasurer; and in 1907 he was elected Chancellor.
Chace's lifelong passion was mathematics. He wrote many articles on mathematical subjects, including one called "A Certain Class of Cubic Surfaces Treated by Quaternions" in the Journal of Mathematics. He attended the International Mathematical Congress at Cambridge, England in 1912. Chace published his work on the Egyptian Rhind Papyrus in 1927 and 1929, at age 87.
Business and banking
His academic career was interrupted in 1869, when he became responsible for his family's cotton mill on the death of a family member. In 1871, he became a director of Westminster Bank, and in 1894 he became its president. He was also a director of the National Bank of North America. During this time, he managed to attend mathematics classes at Harvard once a week.
Death and burial
Chace died in Providence, Rhode Island, on February 28, 1932 and is buried at Swan Point Cemetery.
References
External links
1845 births
1932 deaths
Brown University faculty
Harvard University alumni
Brown University alumni
Burials at Swan Point Cemetery |
https://en.wikipedia.org/wiki/Puerto%20Rico%20Islanders%20records%20and%20statistics | Puerto Rico Islanders is a Puerto Rican professional soccer team.
This article contains historical and current statistics and records pertaining to the club.
All stats are accurate as of match played February 26, 2009.
Recent seasons
Color:
Statistics in USSF Division 2 Professional League
Seasons in USSF Division 2: 1
First game in USSF Division 2: PRI 3 - NSC Minnesota Stars 1 (April 21, 2010)
Longest consecutive wins in League matches: 2 (April 21, 2010 - April 24, 2010)
Longest unbeaten run in League matches:
Longest unbeaten run at home in league matches:
Longest unbeaten run in away league matches:
Longest winning run in the League (home):
Longest winning run in the League (away):
Most goals scored in a match: PRI 4 - Miami FC 2 (June 2, 2010)
Most goals conceded in a match: Rochester Rhinos 3 - PRI 0 (June 26, 2010)
Largest attendance in a league playoff game:
Statistics in USL First Division
Seasons in USL First Division: 6
First game in USL First Division: Toronto Lynx 1 - PRI 0 (April 17, 2004)
Best position in USL First Division: 1 (2008)
Worst position in USL First Division: 9, Eastern (2004)
Longest consecutive wins in USL First Division:
Longest unbeaten run in League matches: 12 (6 wins, 6 ties) (Aug 3 - Sep 21, 2008)
Longest unbeaten run at home in league matches: 10 (7 wins, 3 ties) (Jun 3 - Sep 16, 2007)
Longest unbeaten run in away league matches: 10 (7 wins, 3 ties) (Jul 6 - Sep 12)
Longest winning run in the League (home): 5 (July 22 - Sep 16, 2007)
Longest winning run in the League (away):5 (Jul 6 - 27, 2008)
Most goals scored in a season: 46 (2005)
Most goals scored in a match: PRI 4 - Rochester Rhinos 0 (2008-08-08)
Most goals conceded in a match: Portland Timbers 5 - PRI 0 (2004)
Most wins in a league season: 15 (2008)
Most draws in a league season: 10 (2007)
Most defeats in a league season: 17 (2004)
Fewest wins in a league season: 5 (2004)
Fewest draws in a league season: 6 (2004)
Fewest defeats in a league season: 6 (2008)
Largest attendance in a league playoff game: 12,098 (2007)
Statistics in CFU Club Championship
First game in CFUCC: PRI 3 - Hoppers FC 1 (12/9/2006)
Most goals scored in a match: PRI 10 - Sap FC 0 (11/6/2007)
Most goals conceded in a match: PRI 2 - Harbor View FC 2 (11/4/2007)
Statistics in CONCACAF Champions League
First game in the CCL: PRI 1 - LD Alajuelense 1 (8/27/2008)
Longest unbeaten run in the CCL matches: 4 (Aug 27 - Sep 23, 2008)
Most goals scored in a match: PRI 4 - Los Angeles Galaxy 1 (7/28/2010)
Largest attendance in the CCL: 12,993 (8/4/2010)
Historical goals
1st Goal: Mauricio Salles (April 29, 2004), PRI 1 - 2 Syracuse Salty Dogs
Goalscorer records
All-time goalscorer
Appearance records
All-Time Appearance Leaders
Minutes records
All-Time Minutes Leaders
References
Statistics
Puerto Rican football club records and statistics |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Mera | José Mera (Full name: José Hermes Mera Vergara) (born 11 March 1979) is a retired Colombian football defender.
Statistics (Official games/Colombian Ligue and Colombian Cup)
(Updated 14 November 2010)
References
External links
1979 births
Living people
Deportes Quindío footballers
Independiente Medellín footballers
Deportivo Cali footballers
Club Libertad footballers
Deportivo Pereira footballers
Deportivo Pasto footballers
Caracas FC players
Millonarios F.C. players
Categoría Primera A players
Paraguayan Primera División players
Colombian men's footballers
Colombia men's international footballers
Colombian expatriate men's footballers
Expatriate men's footballers in Paraguay
Expatriate men's footballers in Venezuela
2003 FIFA Confederations Cup players
2003 CONCACAF Gold Cup players
Men's association football defenders
Footballers from Cauca Department |
https://en.wikipedia.org/wiki/Hadamard%20%28disambiguation%29 | Hadamard may refer to:
Zélie Hadamard (1849–1901), French actress
Jacques Hadamard (1865–1963), a French mathematician, whose name is associated with the following topics in mathematics:
Differential geometry
Hadamard space, a geodesically complete metric space of non-positive curvature
Cartan-Hadamard theorem, a result on the topology of non-positively curved manifolds
Differential equations and dynamical systems
Hadamard's method of descent, a method of solving partial differential equations by reducing dimensions
Hadamard parametrix construction, a method of solving second order partial differential equations
Hadamard's dynamical system, a type of chaotic dynamical system
Complex analysis and convexity
Hadamard three-lines theorem: a bound on the maximum modulus complex analytic functions defined on a strip in the complex plane;
Hadamard three-circle theorem, a bound on the maximum modulus of complex analytic functions defined on an annulus in the complex plane; closely related to the three-lines theorem;
Hadamard factorization theorem, a specific factorization of an entire function of finite order, involving its zeros and the exponential of a polynomial
Ostrowski–Hadamard gap theorem, a result on the analytic continuation of lacunary power series
Hermite–Hadamard inequality, bounding the integral of convex functions.
Transform calculus
Hadamard transform, an example of a generalized class of Fourier transforms
Fast Walsh–Hadamard transform, an efficient algorithm to compute the Hadamard transform
Theory of matrices
Hadamard matrix, a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal
Hadamard code, a system used for signal error detection and correction based on Hadamard matrices
Hadamard's inequality, a bound on the determinants of matrices.
Hadamard product, a name for element-wise multiplication of matrices/
Quantum computing
Hadamard gate, a standard quantum gate that generalizes a coin flip. |
https://en.wikipedia.org/wiki/Fourier%20transform%20on%20finite%20groups | In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups.
Definitions
The Fourier transform of a function at a representation of is
For each representation of , is a matrix, where is the degree of .
The inverse Fourier transform at an element of is given by
Properties
Transform of a convolution
The convolution of two functions is defined as
The Fourier transform of a convolution at any representation of is given by
Plancherel formula
For functions , the Plancherel formula states
where are the irreducible representations of .
Fourier transform for finite abelian groups
If the group G is a finite abelian group, the situation simplifies considerably:
all irreducible representations are of degree 1 and hence equal to the irreducible characters of the group. Thus the matrix-valued Fourier transform becomes scalar-valued in this case.
The set of irreducible G-representations has a natural group structure in its own right, which can be identified with the group of group homomorphisms from G to . This group is known as the Pontryagin dual of G.
The Fourier transform of a function is the function given by
The inverse Fourier transform is then given by
For , a choice of a primitive n-th root of unity yields an isomorphism
given by . In the literature, the common choice is , which explains the formula given in the article about the discrete Fourier transform. However, such an isomorphism is not canonical, similarly to the situation that a finite-dimensional vector space is isomorphic to its dual, but giving an isomorphism requires choosing a basis.
A property that is often useful in probability is that the Fourier transform of the uniform distribution is simply , where 0 is the group identity and is the Kronecker delta.
Fourier Transform can also be done on cosets of a group.
Relationship with representation theory
There is a direct relationship between the Fourier transform on finite groups and the representation theory of finite groups. The set of complex-valued functions on a finite group, , together with the operations of pointwise addition and convolution, form a ring that is naturally identified with the group ring of over the complex numbers, . Modules of this ring are the same thing as representations. Maschke's theorem implies that is a semisimple ring, so by the Artin–Wedderburn theorem it decomposes as a direct product of matrix rings. The Fourier transform on finite groups explicitly exhibits this decomposition, with a matrix ring of dimension for each irreducible representation.
More specifically, the Peter-Weyl theorem (for finite groups) states that there is an isomorphism
given by
The left hand side is the group algebra of G. The direct sum is over a complete set of inequivalent irreducible G-representations .
The Fourier transform for a finite group is just this isomorphism. The product formula mentioned ab |
https://en.wikipedia.org/wiki/Shi%20Yuzhu | Shi Yuzhu () is a Chinese entrepreneur and software engineer.
Early life and education
Shi was born in 1962 in Huaiyuan County, Anhui, China. After he graduated from the Department of Mathematics at Zhejiang University, he did his postgraduate study in the Department of Software Engineering at Shenzhen University.
Business career
Chairman of the Board and Chief Executive Officer of Giant Interactive Group, one of China's most successful online game companies. In October, licensed flagship game ZT Online to Astrum Nival of Russia. Founded the company in 2005. Took it public in the United States in November 2007. Got a bachelor's degree in mathematics from Zhejiang University, and created a huge following for his Zhuhai Giant Hi-Tech Group in 1991, based on the popularity of a single videogame. Zhuhai Giant collapsed under the weight of massive debt incurred for a 70-story skyscraper that was never built. His recent return to games through an online services provider he founded, ZTgame, has given new life to his entrepreneurial reputation. Shi also has more than 3% stakes in Minsheng Bank, of which he's a director, and Huaxia Bank. Diversifying into Chinese rice wine market.
Giant Interactive Group
Giant Interactive Group is an online game developer and operator in China. The Company focuses on massively multiplayer online (MMO) games that are played through networked game servers, in which a number of players are able to simultaneously connect and interact. The Company’s three MMO games include ZT Online, ZT Online PTP, a pay-to-play game based on the ZT Online free-to-play game, and Giant Online. ZT Online, ZT Online PTP, ZT Online Green, ZT Online Classic Edition and Giant Online together had 1,572,000 quarterly peak concurrent users and 474,000 quarterly average concurrent users during the year ended December 31, 2009. In addition, it launched two free-to-play games, ZT Online Green and My Sweetie, and introduced King of Kings III, or K III, XT Online and The Golden Land in 2009. In December 2009, and January 2010, the Company acquired two licenses to operate Elsword and Allods Online, two three dimensional-MMO games, in mainland China.
Wealth
In 2010's, Forbes World's Billionaires List, Shi was ranked no. 616 in the world.
In terms of Asia, Shi is ranking at number 49 in the richest people in China, according to the Forbes 2015 rich list. His estimated worth is 3.15 billion US dollars.
References
External links
Shi Yuzhu's biography at Sina Finance
Hurun Report 2007 - No.15 Shi Yuzhu
2007 China IT Rich List: No.2 Shi Yuzhu
China's Famous Private Entrepreneur - Shi Yuzhu
Forbes Mainland China Rich List 2007
1962 births
Living people
Chinese billionaires
Engineers from Anhui
Businesspeople from Anhui
Zhejiang University alumni
Shenzhen University alumni
People from Huaiyuan County
Chinese technology company founders |
https://en.wikipedia.org/wiki/Moon%20Ki-han | Moon Ki-han (; born March 17, 1989) is a South Korean footballer who currently plays as midfielder for Dangjin Citizen FC.
Club career statistics
Statistics accurate as of 25 December 2016
References
External links
Moon Ki-han – National Team stats at KFA
1989 births
Living people
Men's association football midfielders
South Korean men's footballers
FC Seoul players
Asan Mugunghwa FC players
Daegu FC players
Bucheon FC 1995 players
K League 1 players
K League 2 players
Footballers from Busan
South Korea men's under-20 international footballers
South Korea men's under-23 international footballers |
https://en.wikipedia.org/wiki/Minimum%20weight | The minimum weight is a concept used in various branches of mathematics and computer science related to measurement.
Minimum Hamming weight, a concept in coding theory
Minimum weight spanning tree
Minimum-weight triangulation, a topic in computational geometry and computer science |
https://en.wikipedia.org/wiki/Guy%20Nason | Guy Philip Nason (born 28 August 1966) is a British statistician, and professor of Statistics at Imperial College London.
Nason received his BSc from the University of Bath in 1988, a diploma in Mathematical Statistics from the University of Cambridge in 1989, and a PhD in Statistics from the University of Bath in 1992. He served as a Council member of the Royal Statistical Society (2004–08), and was Vice-President (Academic Affairs) 2016–2020. He is a member of the EPSRC Strategic Advisory Team for Mathematics. He was an EPSRC Advanced Research Fellow during 2000–5 and was awarded the Guy Medal in bronze by the Royal Statistical Society (RSS) in 2001. He took over the post as head of mathematics at Bristol from Stephen Wiggins in 2008.
Nason is best known for his work in the area of time series analysis, especially wavelet approaches.
He has served as the Secretary of the RSS Research Section (2002–04), associate editor for the Journal of the RSS, Series B, Computational Statistics and Statistica Sinica and is currently an associate editor for Biometrika.
References
External links
Professor Nason's homepage at Bristol
University of Bristol, Department of Mathematics homepage
1966 births
Living people
British statisticians
20th-century English mathematicians
21st-century English mathematicians
Academics of the University of Bristol
Alumni of the University of Bath
Alumni of Jesus College, Cambridge |
https://en.wikipedia.org/wiki/Hans-Egon%20Richert | Hans-Egon Richert (June 2, 1924 – November 25, 1993) was a German mathematician who worked primarily in analytic number theory. He is the author (with Heini Halberstam) of a definitive book on sieve theory.
Life and education
Hans-Egon Richert was born in 1924 in Hamburg, Germany. He attended the University of Hamburg and received his Ph.D under Max Deuring in 1950. He held a temporary chair at the University of Göttingen and then a newly created chair at the University of Marburg. In 1972 he moved to the University of Ulm, where he remained until his retirement in 1991. He died on November 25, 1993 in Blaustein, near Ulm, Germany.
Work
Richert worked primarily in analytic number theory, and beginning around 1965 started a collaboration with Heini Halberstam and shifted his focus to sieve theory. For many years he was a chairman of the Analytic Number Theory meetings at the Mathematical Research Institute of Oberwolfach.
Analytic number theory
Richert made contributions to additive number theory, Dirichlet series, Riesz summability, the multiplicative analog of the Erdős–Fuchs theorem, estimates of the number of non-isomorphic abelian groups, and bounds for exponential sums. He proved the exponent 15/46 for the Dirichlet divisor problem, a record that stood for many years.
Sieve methods
One of Richert's notable results was the Jurkat–Richert theorem, joint work with Wolfgang B. Jurkat that improved the Selberg sieve and is used in the proof of Chen's theorem.
Richert also produced a "readable form" of Chen's theorem (it is covered in the last chapter of Sieve Methods).
Halberstam & Richert's book Sieve Methods was the first exhaustive account of the subject.
In reviewing the book in 1976, Hugh Montgomery wrote "In the past, researchers have generally derived the sieve bounds required for an application, but now workers will find that usually an appeal to an appropriate theorem of Sieve methods will suffice," and "For years to come, Sieve methods will be vital to those seeking to work in the subject, and also to those seeking to make applications."
Notes
External links
1924 births
1993 deaths
20th-century German mathematicians
Number theorists
University of Hamburg alumni
Academic staff of the University of Marburg
Academic staff of the University of Ulm |
https://en.wikipedia.org/wiki/Besov%20space | In mathematics, the Besov space (named after Oleg Vladimirovich Besov) is a complete quasinormed space which is a Banach space when . These spaces, as well as the similarly defined Triebel–Lizorkin spaces, serve to generalize more elementary function spaces such as Sobolev spaces and are effective at measuring regularity properties of functions.
Definition
Several equivalent definitions exist. One of them is given below.
Let
and define the modulus of continuity by
Let be a non-negative integer and define: with . The Besov space contains all functions such that
Norm
The Besov space is equipped with the norm
The Besov spaces coincide with the more classical Sobolev spaces .
If and is not an integer, then , where denotes the Sobolev–Slobodeckij space.
References
DeVore, R. and Lorentz, G. "Constructive Approximation", 1993.
DeVore, R., Kyriazis, G. and Wang, P. "Multiscale characterizations of Besov spaces on bounded domains", Journal of Approximation Theory 93, 273-292 (1998).
Leoni, Giovanni (2017). A First Course in Sobolev Spaces: Second Edition. Graduate Studies in Mathematics. 181. American Mathematical Society. pp. 734.
Banach spaces
Function spaces |
https://en.wikipedia.org/wiki/Hermite%20number | In mathematics, Hermite numbers are values of Hermite polynomials at zero argument. Typically they are defined for physicists' Hermite polynomials.
Formal definition
The numbers Hn = Hn(0), where Hn(x) is a Hermite polynomial of order n, may be called Hermite numbers.
The first Hermite numbers are:
Recursion relations
Are obtained from recursion relations of Hermitian polynomials for x = 0:
Since H0 = 1 and H1 = 0 one can construct a closed formula for Hn:
where (n - 1)!! = 1 × 3 × ... × (n - 1).
Usage
From the generating function of Hermitian polynomials it follows that
Reference gives a formal power series:
where formally the n-th power of H, Hn, is the n-th Hermite number, Hn. (See Umbral calculus.)
Notes
Integer sequences |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Fuchs%20theorem | In mathematics, in the area of additive number theory, the Erdős–Fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of elements of a given additive basis, stating that the average order of this number cannot be too close to being a linear function.
The theorem is named after Paul Erdős and Wolfgang Heinrich Johannes Fuchs, who published it in 1956.
Statement
Let be an infinite subset of the natural numbers and its representation function, which denotes the number of ways that a natural number can be expressed as the sum of elements of (taking order into account). We then consider the accumulated representation function
which counts (also taking order into account) the number of solutions to , where . The theorem then states that, for any given , the relation
cannot be satisfied; that is, there is no satisfying the above estimate.
Theorems of Erdős–Fuchs type
The Erdős–Fuchs theorem has an interesting history of precedents and generalizations. In 1915, it was already known by G. H. Hardy that in the case of the sequence of perfect squares one has
This estimate is a little better than that described by Erdős–Fuchs, but at the cost of a slight loss of precision, P. Erdős and W. H. J. Fuchs achieved complete generality in their result (at least for the case ). Another reason this result is so celebrated may be due to the fact that, in 1941, P. Erdős and P. Turán conjectured that, subject to the same hypotheses as in the theorem stated, the relation
could not hold. This fact remained unproven until 1956, when Erdős and Fuchs obtained their theorem, which is even stronger than the previously conjectured estimate.
Improved versions for h = 2
This theorem has been extended in a number of different directions. In 1980, A. Sárközy considered two sequences which are "near" in some sense. He proved the following:
Theorem (Sárközy, 1980). If and are two infinite subsets of natural numbers with , then cannot hold for any constant .
In 1990, H. L. Montgomery and R. C. Vaughan were able to remove the log from the right-hand side of Erdős–Fuchs original statement, showing that
cannot hold. In 2004, Gábor Horváth extended both these results, proving the following:
Theorem (Horváth, 2004). If and are infinite subsets of natural numbers with and , then cannot hold for any constant .
General case (h ≥ 2)
The natural generalization to Erdős–Fuchs theorem, namely for , is known to hold with same strength as the Montgomery–Vaughan's version. In fact, M. Tang showed in 2009 that, in the same conditions as in the original statement of Erdős–Fuchs, for every the relation
cannot hold. In another direction, in 2002, Gábor Horváth gave a precise generalization of Sárközy's 1980 result, showing that
Theorem (Horváth, 2002) If () are (at least two) infinite subsets of natural numbers and the following estimates are valid:
<li>
<li> (for )
then the relation:
cannot hold for any constant .
Non-lin |
https://en.wikipedia.org/wiki/Daniel%20Goldberg%20%28politician%29 | Daniel Goldberg (born 24 August 1965, Saint-Denis, France) is a French Socialist politician. A mathematics teacher, he was elected deputy in 2007 to represent La Courneuve.
Biography
Goldberg was born on the August 24th 1965. He studied at the University of Paris 13 and earned a PhD at Pierre and Marie Curie University (Paris VI).
He was a member of the regional council of the Île-de-France from 2004 to 2007.
References
External links
Official blog
1965 births
Living people
People from Saint-Denis, Seine-Saint-Denis
Politicians from Île-de-France
Socialist Party (France) politicians
Deputies of the 13th National Assembly of the French Fifth Republic
Deputies of the 14th National Assembly of the French Fifth Republic
Sorbonne Paris North University alumni
Paris 8 University Vincennes-Saint-Denis alumni |
https://en.wikipedia.org/wiki/MathPath | MathPath is a mathematics enrichment summer program for students ages 11–14 (middle-school age in the US). It is four weeks long, and moves to a different location each year. MathPath is visited by mathematicians such as John H. Conway and Francis Su.
It was probably the original, and is still one of the few, international residential high-end summer camps exclusively for mathematics and exclusively for students of middle school age.
History
MathPath was founded in 2002 by George Rubin Thomas, who had previously founded Mathcamp for high school students and has since founded Epsiloncamp for children age 7–11 (in 2011, originally aged 8–11) and Delta Camp for children 6 and 7 (in 2014 and 2015, now merged with Epsilon Camp). His goal was to inspire and advance the most mathematically gifted middle school age students, through a summer camp.
Subjects
At MathPath, students learn about many math topics that are rarely taught in American schools, or taught in much depth, such as non-Euclidean geometry, advanced Euclidean geometry, number theory, combinatorics, induction, spherical trigonometry, mathematical origami, and the mathematics of card shuffling. They also learn some history of math and work on mathematical writing. Topics vary somewhat each year, depending on instructor interest. As well, students have the opportunity to prepare for contests such as MATHCOUNTS, AMC, or AIME.
Staff
Some staff are regular annual participants. Usually they come for 2–4 weeks, but a few come for only one week. Notable regular staff include the late John Horton Conway, Sam Vandervelde, and Glen Van Brummelen.
Visiting staff are participants for one year or occasional years. Usually they attend for one week or a day or two to give a few lectures. Often, they are faculty at the host institution or nearby institutions. Notable visiting mathematicians have included Gene Abrams and Robin Hartshorne.
Admissions
MathPath is selective. The primary criterion for admission is the applicant's work on the yearly Qualifying Test, though academic and nonacademic references are also required.
Locations
2002 – Black Hills State University, Spearfish, SD
2003 – Black Hills State University, Spearfish, SD
2004 – Roger Williams University, Bristol, RI
2005 – Colorado College, Colorado Springs, CO
2006 – University of California, Santa Cruz, CA
2007 – Colorado College, Colorado Springs, CO
2008 – The University of Vermont at Burlington
2009 – Colorado College, Colorado Springs, CO
2010 – Macalester College, St. Paul, MN
2011 – Colorado College, Colorado Springs, CO
2012 – Mount Holyoke College, South Hadley, MA
2013 – Macalester College, St. Paul, MN
2014 – Mount Holyoke College, South Hadley, MA
2015 - Lewis & Clark College, Portland, OR
2016 - Macalester College, St. Paul, MN
2017 - Mount Holyoke College, South Hadley, MA
2018 - Lewis & Clark College, Portland, OR
2019 - Grand Valley State University, Allendale, MI
2020 and 2021 - Held online due |
https://en.wikipedia.org/wiki/Pfeffer%20integral | In mathematics, the Pfeffer integral is an integration technique created by Washek Pfeffer as an attempt to extend the Henstock–Kurzweil integral to a multidimensional domain. This was to be done in such a way that the fundamental theorem of calculus would apply analogously to the theorem in one dimension, with as few preconditions on the function under consideration as possible. The integral also permits analogues of the chain rule and other theorems of the integral calculus for higher dimensions.
Definition
The construction is based on the Henstock or gauge integral, however Pfeffer proved that the integral, at least in the one dimensional case, is less general than the Henstock integral. It relies on what Pfeffer refers to as a set of bounded variation, this is equivalent to a Caccioppoli set. The Riemann sums of the Pfeffer integral are taken over partitions made up of such sets, rather than intervals as in the Riemann or Henstock integrals. A gauge is used, exactly as in the Henstock integral, except that the gauge function may be zero on a negligible set.
Properties
Pfeffer defined a notion of generalized absolute continuity , close to but not equal to the definition of a function being , and proved that a function is Pfeffer integrable if it is the derivative of an function. He also proved a chain rule for the Pfeffer integral. In one dimension his work as well as similarities between the Pfeffer integral and the McShane integral indicate that the integral is more general than the Lebesgue integral and yet less general than the Henstock–Kurzweil integral.
Bibliography
Definitions of mathematical integration |
https://en.wikipedia.org/wiki/Victor%20Shestakov | Victor Ivanovich Shestakov (Russian: ) (1907–1987) was a Russian/Soviet logician and theoretician of electrical engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits. He graduated from Moscow State University (1934) and worked there in the General Physics Department almost until his death.
Shestakov proposed a theory of electric switches based on Boolean logic earlier than Claude Shannon (according to certification of Soviet logicians and mathematicians Sofya Yanovskaya, M. G. Gaaze-Rapoport, Roland Dobrushin, Oleg Lupanov, Yu. A. Gastev, Yu. T. Medvedev, and Vladimir Andreevich Uspensky), though Shestakov and Shannon defended Theses the same year (1938) and the first publication of Shestakov's result took place only in 1941 (in Russian).
In the early 20th century, relay circuits began to be more widely used in automatics, defense of electric and communications systems. Every relay circuit schema for practical use was a distinct invention, because the general principle of simulation of these systems was not known. Shestakov's credit (and independently later Claude Shannon's) is the general theory of logical simulation, inspired by the rapidly increasing complexity of technical demands. Logical simulation requires solid mathematical foundations. Namely these foundations were originally established by Shestakov.
Shestakov set forth an algebraic logic model of electrical two-pole switches (later three- and four-pole switches) with series and parallel connections of schematic elements (resistors, capacitors, magnets, inductive coils, etc.). Resistance of these elements could take arbitrary values on the real-number line, and upon the two-element set {0, ∞} this degenerates into the bivalent Boolean algebra of logic.
Shestakov may be considered as a forerunner of combinatorial logic and its application (and, hence, Boolean algebra of logic as well) in electric engineering, the 'language' of which is broad enough to simulate non-electrical objects of any conceivable physical nature. He was a pioneer of study of merged continual algebraic logic (parametrical) and topological (structural) models.
See also
List of pioneers in computer science
Boolean differential calculus
References
Shestakov, V. I. Algebra of Two Poles Schemata (Algebra of A-Schemata). In: Automatics and Telemechanics, 1941, N 2, p. 15 – 24 (Russian)
Shestakov, V. I. Algebra of Two Poles Schemata (Algebra of A-Schemata).In: Journal of Technical Physics, 1941, Vol. 11, N 6. p. 532 – 549 (Russian)
Bazhanov, V. A., Volgin, L. I. V. I. Shestakov and C. Shannon: the Fate of One Brilliant Idea. In: Scientific and Technical Kaleidoscope, 2001, N2, pp. 43 – 48. (Russian)
Bazhanov, V. A. V. I. Shestakov and C. Shannon: Different Fates of One Brilliant Idea Architects. In: Problems of History of Science and Technology, 2005, N 2, pp. 112– 121. (Russian)
Bazhanov, V. A. History of Logic in Russia and the US |
https://en.wikipedia.org/wiki/Ceiling%20%28disambiguation%29 | A ceiling is the upper surface of a room.
Ceiling may also refer to:
Ceiling function in mathematics
Glass ceiling, a barrier to advancement of a qualified person
Ceiling (aeronautics), the maximum density altitude an aircraft can reach under a set of conditions
Price ceiling, an imposed limit on the price of a product
Ceiling (cloud), the height above ground at which (accumulated) cloud layers cover more than 50% of the sky
Ceilings (album), an album by Dentist
"The Ceiling" (short story), a 2001 short story by American writer Kevin Brockmeier
The Ceiling (album), a 2019 album by Jaws
Katto, also known as The Ceiling, a short film that competed in the Short Film Palme d'Or group at the 2017 Cannes Film Festival
See also
Ceiling effect (disambiguation) |
https://en.wikipedia.org/wiki/Paulin%20Voavy | Paulin Voavy (born 10 November 1987) is a Malagasy professional footballer who plays for Réunion Premier League side Saint-Pauloise FC and the Madagascar national team.
Career statistics
Scores and results list Madagascar's goal tally first, score column indicates score after each Voavy goal.
Honours
Évian TGFC
Championnat National: 2009–10
CS Constantine
best team player of the season 2015-2016.
Misr El Maqasa
Egyptian Premier League runner-up: 2017
Madagascar
Indian Ocean Island Games silver medal: 2007
Madagascar U20
COSAFA U-20 Challenge Cup: 2005
Individual
COSAFA Cup top scorer: 2007
Indian Ocean Island Games Top scorer: 2007
AFCON Qualifiers Best XI: 2019 Matchday 1
Knight Order of Madagascar: 2019
Record
top scorer of the madagascar team all time
References
External links
francefootball.fr (archived 27 September 2008)
lfp.fr (archived 11 June 2008)
1987 births
Living people
People from Melaky
Malagasy men's footballers
Men's association football midfielders
Men's association football forwards
Madagascar men's international footballers
2019 Africa Cup of Nations players
Ligue 2 players
Algerian Ligue Professionnelle 1 players
Egyptian Premier League players
US Boulogne players
AS Cannes players
Misr Lel Makkasa SC players
Thonon Evian Grand Genève FC players
CS Constantine players
Ghazl El Mahalla SC players
Malagasy expatriate men's footballers
Malagasy expatriate sportspeople in France
Expatriate men's footballers in France
Expatriate men's footballers in Réunion
Malagasy expatriate sportspeople in Algeria
Expatriate men's footballers in Algeria
Malagasy expatriate sportspeople in Egypt
Expatriate men's footballers in Egypt
Recipients of orders, decorations, and medals of Madagascar |
https://en.wikipedia.org/wiki/Compact%20stencil | In mathematics, especially in the areas of numerical analysis called numerical partial differential equations, a compact stencil is a type of stencil that uses only nine nodes for its discretization method in two dimensions. It uses only the center node and the adjacent nodes. For any structured grid utilizing a compact stencil in 1, 2, or 3 dimensions the maximum number of nodes is 3, 9, or 27 respectively. Compact stencils may be compared to non-compact stencils. Compact stencils are currently implemented in many partial differential equation solvers, including several in the topics of CFD, FEA, and other mathematical solvers relating to PDE's.
Two Point Stencil Example
The two point stencil for the first derivative of a function is given by:
.
This is obtained from the Taylor series expansion of the first derivative of the function given by:
.
Replacing with , we have:
.
Addition of the above two equations together results in the cancellation of the terms in odd powers of :
.
.
.
Three Point Stencil Example
For example, the three point stencil for the second derivative of a function is given by:
.
This is obtained from the Taylor series expansion of the first derivative of the function given by:
.
Replacing with , we have:
.
Subtraction of the above two equations results in the cancellation of the terms in even powers of :
.
.
.
See also
Stencil (numerical analysis)
Non-compact stencil
Five-point stencil
References
Numerical differential equations |
https://en.wikipedia.org/wiki/Non-compact%20stencil | In numerical mathematics, a non-compact stencil is a type of discretization method, where any node surrounding the node of interest may be used in the calculation. Its computational time grows with an increase of layers of nodes used. Non-compact stencils may be compared to Compact stencils.
See also
Nine-point stencil
Five-point stencil
References
Numerical differential equations |
https://en.wikipedia.org/wiki/Stencil%20%28numerical%20analysis%29 | In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine. Stencils are the basis for many algorithms to numerically solve partial differential equations (PDE). Two examples of stencils are the five-point stencil and the Crank–Nicolson method stencil.
Stencils are classified into two categories: compact and non-compact, the difference being the layers from the point of interest that are also used for calculation.
In the notation used for one-dimensional stencils n-1, n, n+1 indicate the time steps where timestep n and n-1 have known solutions and time step n+1 is to be calculated. The spatial location of finite volumes used in the calculation are indicated by j-1, j and j+1.
Etymology
Graphical representations of node arrangements and their coefficients arose early in the study of PDEs. Authors continue to use varying terms for these such as "relaxation patterns", "operating instructions", "lozenges", or "point patterns". The term "stencil" was coined for such patterns to reflect the concept of laying out a stencil in the usual sense over a computational grid to reveal just the numbers needed at a particular step.
Calculation of coefficients
The finite difference coefficients for a given stencil are fixed by the choice of node points. The coefficients may be calculated by taking the derivative of the Lagrange polynomial interpolating between the node points, by computing the Taylor expansion around each node point and solving a linear system, or by enforcing that the stencil is exact for monomials up to the degree of the stencil. For equi-spaced nodes, they may be calculated efficiently as the Padé approximant of , where is the order of the stencil and is the ratio of the distance between the leftmost derivative and the left function entries divided by the grid spacing.
See also
Compact stencil
Non-compact stencil
Five-point stencil
References
W. F. Spotz. High-Order Compact Finite Difference Schemes for Computational Mechanics. PhD thesis, University of Texas at Austin, Austin, TX, 1995.
Communications in Numerical Methods in Engineering, Copyright © 2008 John Wiley & Sons, Ltd.
Numerical differential equations |
https://en.wikipedia.org/wiki/Bingham%20distribution | In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the n-sphere. It is a generalization of the Watson distribution and a special case of the Kent and Fisher–Bingham distributions.
The Bingham distribution is widely used in paleomagnetic data analysis, and has been used in the field of computer vision.
Its probability density function is given by
which may also be written
where x is an axis (i.e., a unit vector), M is an orthogonal orientation matrix, Z is a diagonal concentration matrix, and
is a confluent hypergeometric function of matrix argument. The matrices M and Z are the result of diagonalizing the positive-definite covariance matrix of the Gaussian distribution that underlies the Bingham distribution.
See also
Directional statistics
von Mises–Fisher distribution
Kent distribution
References
Directional statistics
Continuous distributions |
https://en.wikipedia.org/wiki/Erwin%20Plein%20Nemmers%20Prize%20in%20Economics | The Erwin Plein Nemmers Prize in Economics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Frederic Esser Nemmers Prize in Mathematics. Both are part a $14 million donation from the Nemmers brothers, who envisioned creating an award that would be as prestigious as the Nobel prize. Nine out of the past 15 Nemmers economics prize winners have gone on to win a Nobel Prize : Peter Diamond, Thomas J. Sargent, Robert Aumann, Daniel McFadden, Edward C. Prescott, Lars Peter Hansen, Jean Tirole, Paul R. Milgrom and, most recently, Claudia Goldin.
Those who already have won a Nobel Prize are ineligible to receive a Nemmers prize. The Nemmers prizes are given in recognition of major contributions to new knowledge or the development of significant new modes of analysis in the respective disciplines. As of 2023, the prize carries a $300,000 stipend, among the largest monetary awards in the United States for outstanding achievements in economics.
Awardees
2022: Ariel Pakes, "for his fundamental contributions to the development of the field of empirical industrial organization."
2020: Claudia Goldin, "for her groundbreaking insights into the history of the American economy, the evolution of gender roles and the interplay of technology, human capital and labor markets." (Nobel 2023)
2018: David Kreps, "for his work in game theory, decision theory and finance."
2016: Richard Blundell, "for his important contributions to labor economics, public finance and applied econometrics."
2014: Jean Tirole, "based on his various contributions to economic theory and its application to finance, industrial organization and behavioral economics." (Nobel 2014)
2012: Daron Acemoglu
2010: Elhanan Helpman
2008: Paul R. Milgrom (Nobel 2020)
2006: Lars Peter Hansen (Nobel 2013)
2004: Ariel Rubinstein
2002: Edward C. Prescott (Nobel 2004)
2000: Daniel McFadden (Nobel 2000)
1998: Robert Aumann (Nobel 2005)
1996: Thomas J. Sargent (Nobel 2011)
1994: Peter Diamond (Nobel 2010)
See also
List of economics awards
References
"Nemmers awards in economics, math announced, Northwestern University NewsCenter, April 22, 2008.
Northwestern University's web page describing the origin of the Prize and biographical notes on Nemmers
Economics awards
Northwestern University
1994 establishments in Illinois |
https://en.wikipedia.org/wiki/Koreans%20in%20Chile | Koreans in Chile (Spanish: Coreanos en Chile) (Korean: 칠레 한국인) formed Latin America's sixth-largest Korean diaspora community , according to the statistics of South Korea's Ministry of Foreign Affairs and Trade.
Migration history
The earliest Korean migrants to Chile were soldiers of the North Korean army captured by United Nations forces, who declined repatriation after the signing of the Korean Armistice Agreement and came to Chile under the auspices of the Red Cross. They were resettled in the city of Temuco.
Immigration from South Korea to Chile would not begin until 1970, when five families came to work in the floriculture sector. Three more families came by way of Bolivia in 1975 and another ten in 1976. By 1978, the year of the founding of the Asociación Coreana de Chile, there were between twenty and thirty Korean families residing in Chile. In 1978, twenty Korean families founded a school, the Colegio Coreano, with the assistances of the Presbyterian Church to offer weekend courses in Korean language, culture and history to Korean children in Chile.
Most of the families immigrating in those days actually had Argentina as their final destination, and intended to reside in Chile only as long as it took them to obtain an Argentine visa, but as Argentina required prospective immigrants to have at least US$30,000 in capital, many found themselves unable to qualify; they instead settled in Chile, where the requirement was merely one-sixth that amount. Many settled in the Barrio Patronato, a traditionally immigrant-dominated neighbourhood then filled largely with Arabs. They started out in the textile manufacturing sector, but along with Chile's shift away from an import substitution-oriented economic model, they turned to opening shops and importing clothing and other products from their homeland instead.
Between 1997 and 2005, the Korean population of Chile grew by one-quarter, from 1,470 to 1,858 individuals, surpassing in size the community of Koreans in Peru. Afterwards, the population continued to grow, to 2,510 by 2011. South Korean governments showed a total of 48 ethnic Koreans with Chilean nationality, 2,366 with permanent residency, seven international students, and 119 with other types of visas.
Inter-ethnic relations
Koreans in Chile are respected by Chileans of other backgrounds for their work ethic, but are perceived as a very closed community, especially with regards to interracial marriage. The Korean shops of Patronato are well known for their low prices and diverse products but some Chileans and competitors feel some envy towards the commercial success of Koreans in their country. At the same time, however, Chileans have respect for the rapid economic development undertaken by South Korea. On the other hand, Koreans in Chile often perceive Chileans as superficial in their friendships, lazy, irresponsible, and somewhat racist.
Religion
Among the Korean community in Chile, Protestantism is the majority religion; Patronato |
https://en.wikipedia.org/wiki/Institute%20for%20Experimental%20Mathematics | The Institute for Experimental Mathematics (IEM) was founded, with the support of the Volkswagen
Foundation, as a central scientific facility of the former University of Essen, now University of Duisburg-Essen in 1989. With the addition of the Alfried Krupp von Bohlen und Halbach Foundation Chair on 1 January 1999, the Institute was expanded in the area of Computer Networking Technology. A.J. Han Vinck is currently the Institute's managing director.
The primary objective of the Institute is to foster interactions between the fields of mathematics, computer science and the engineering sciences. Mathematicians, computer experts and telecommunications engineers are engaged in trans-disciplinary collaboration under one roof. The main areas of research are discrete mathematics, number theory, digital communication, and computer networking technology.
Staff members
Prof. Dr. Massimo Bertolini
Prof. Dr. Dr. h.c. Gerhard Frey
Prof. Dr. Wolfgang Lempken
Prof. Dr.-Ing. Erwin P. Rathgeb
Prof. Dr. Trung van Tran
Prof. Dr. ir. Han Vinck
Prof. Dr. Helmut Völklein
External staff members
Prof. Dr. Gebhard Böckle, Universität Duisburg-Essen
Prof. Dr. Hélène Esnault, Universität Duisburg-Essen
Prof. Dr. Eckart Viehweg, Universität Duisburg-Essen
Prof. Dr. Dr. h.c. Kees Schouhamer Immink, Turing Machines, Netherlands
Prof. Dr. Gabor Wiese
External links
IEM Home page
University of Duisburg-Essen
Mathematical institutes |
https://en.wikipedia.org/wiki/Ernest%20Michael | Ernest A. Michael (August 26, 1925 – April 29, 2013) was a prominent American mathematician known for his work in the field of general topology, most notably for his pioneering research on set-valued mappings. He is credited with developing the theory of continuous selections. The Michael selection theorem is named for him, which he proved in . Michael is also known in topology for the Michael line, a paracompact space whose product with the topological space of the irrational numbers is not normal. He wrote over 100 papers, mostly in the area of general topology.
Michael was born in Zürich, Switzerland, August 26, 1925, to Ashkenazi Jewish parents, Jacob and Erna Michael. He lived in Berlin, Germany, until 1932. Anticipating the burgeoning threat of Nazism, his family moved to The Hague, Netherlands, and then to New York in 1939. Michael attended Horace Mann High School, graduating at age 15. His undergraduate career at Cornell University was interrupted when he enlisted in the United States Navy (1944–46), where he served aboard the USS Kwajalein. He returned to Cornell, where he received his B.A. in 1947. He earned his M.A. from Harvard University in 1948, and Ph.D. from The University of Chicago in 1951, writing his dissertation titled Locally Multiplicatively-Convex Topological Algebras under the supervision of Irving Segal.
Michael was a member of the Department of Mathematics at the University of Washington (assistant professor 1952–56, associate professor 1956–60, professor 1960) for over 40 years, from 1952 until his retirement in 1993. He was also a visiting scholar at the Institute for Advanced Study (1951–52, 1956–57, 1960–61, 1968–69), ETH Zurich (1973–74) and University of Stuttgart (1978–79).
In 2012 he became an inaugural fellow of the American Mathematical Society.
Michael died in 2013 at the age of 87.
Selected works
References
20th-century American mathematicians
21st-century American mathematicians
American people of German-Jewish descent
Institute for Advanced Study visiting scholars
Mathematical analysts
Topologists
University of Chicago alumni
Fellows of the American Mathematical Society
1925 births
2013 deaths
Harvard University alumni
Cornell University alumni
Horace Mann School alumni
Mathematicians from New York (state) |
https://en.wikipedia.org/wiki/Mohammad%20Salsali | Mohammad Salsali (, born August 28, 1983, in Esfahan, Iran) is an Iranian football player.
Club career
Club career statistics
Last Update 10 May 2013
Assist Goals
Honours
Aboomoslem
Hazfi Cup
Runners-up (1): 2004–05
Zob Ahan
AFC Champions League
Runners-up (1): 2010
Iran Pro League
Runners-up (2): 2008–09, 2009–10
Hazfi Cup (1): 2008–09
External links
Persian League Profile
Iranian men's footballers
Men's association football defenders
Zob Ahan Esfahan F.C. players
Persian Gulf Pro League players
Azadegan League players
Footballers from Isfahan
1983 births
Living people |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.