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https://en.wikipedia.org/wiki/Moser%27s%20trick
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In differential geometry, a branch of mathematics, the Moser's trick (or Moser's argument) is a method to relate two differential forms and on a smooth manifold by a diffeomorphism such that , provided that one can find a family of vector fields satisfying a certain ODE.
More generally, the argument holds for a family and produce an entire isotopy such that .
It was originally given by Jürgen Moser in 1965 to check when two volume forms are equivalent, but its main applications are in symplectic geometry. It is the standard argument for the modern proof of Darboux's theorem, as well as for the proof of Darboux-Weinstein theorem and other normal form results.
General statement
Let be a family of differential forms on . If the ODE admits a solution , then there exists a family of diffeomorphisms of such that and .
In particular, there is a diffeomorphism such that .
Proof
The trick consists in viewing as the flows of a time-dependent vector field, i.e. of a smooth family of vector fields on . Using the definition of flow, i.e. for every , one obtains from the chain rule that By hypothesis, one can always find such that , hence their flows satisfies .
Application to volume forms
Let be two volume forms on a compact -dimensional manifold . Then there exists a diffeomorphism of such that if and only if .
Proof
One implication holds by the invariance of the integral by diffeomorphisms: .
For the converse, we apply Moser's trick to the family of volume forms . Since , the de Rham cohomology class vanishes, as a consequence of Poincaré duality and the de Rham theorem. Then for some , hence . By Moser's trick, it is enough to solve the following ODE, where we used the Cartan's magic formula, and the fact that is a top-degree form:However, since is a volume form, i.e. , given one can always find such that .
Application to symplectic structures
In the context of symplectic geometry, the Moser's trick is often presented in the following form.Let be a family of symplectic forms on such that , for . Then there exists a family of diffeomorphisms of such that and .
Proof
In order to apply Moser's trick, we need to solve the following ODE
where we used the hypothesis, the Cartan's magic formula, and the fact that is closed. However, since is non-degenerate, i.e. , given one can always find such that .
Corollary
Given two symplectic structures and on such that for some point , there are two neighbourhoods and of and a diffeomorphism such that and .This follows by noticing that, by Poincaré lemma, the difference is locally for some ; then, shrinking further the neighbourhoods, the result above applied to the family of symplectic structures yields the diffeomorphism .
Darboux theorem for symplectic structures
The Darboux's theorem for symplectic structures states that any point in a given symplectic manifold admits a local coordinate chart such thatWhile the original proof by Darboux required a
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https://en.wikipedia.org/wiki/Jeong%20Ho-yeon%20%28footballer%29
|
Jeong Ho-yeon (; born 28 September 2000) is a South Korean footballer who plays as a midfielder for Gwangju FC in the K League 1.
Career statistics
Honours
South Korea U23
Asian Games: 2022
References
External links
2000 births
Living people
South Korean men's footballers
Men's association football midfielders
K League 2 players
K League 1 players
Gwangju FC players
Footballers at the 2022 Asian Games
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https://en.wikipedia.org/wiki/Immigration%20statistics%20in%20France
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Statistics about the immigration to France are based on variables whose compilation is governed by law. They are mainly produced from the census. Statistics on residence permits, asylum applications and thematic surveys of population samples are also used. The data produced varies from one organization to another, due to differences in definitions.
The type and quality of statistics compiled from the census have evolved over time, in line with changes in the status of foreigners, the possibilities of acquiring citizenship and the nomenclature of population categories. Within the scientific community, in connection with the fight against discrimination, there is a debate on the recording of variables revealing the origins of individuals.
Statistics on immigration in France have a political dimension. Political discourse and public action rely on the interpretation or manipulation of figures to shape immigration policy.
Categories of people in the French statistics system
In 1991, the French High Council for Integration defined the category of "immigrant" as distinct from "foreigner". An immigrant is a person born outside France who was of foreign nationality at birth. French descendants born abroad are neither immigrants nor foreigners. Foreigners born in France, generally children who will acquire French nationality, are not immigrants either, as they have not crossed a border. French immigrants are therefore included in both French citizen and immigration statistics.
Immigrants, on the other hand, are born abroad, whatever their nationality or nationalities at birth. This is a broader definition for people changing their place of residence. For its statistics, the United Nations defines an immigrant as a person whose daily resting place reaches, or is expected to reach, at least one year in the territory of a state other than that of his or her last habitual residence. The duration of residence may therefore be shorter than the duration of the residence permit.
Data sources
France does not have a population register. Data on illegal immigrants, i.e. those without a residence permit, are estimated on the basis of the number of people receiving state medical aid. Data on legal immigrants comes from several sources.
Censuses
The French National Institute for Statistics and Economic Studies (INSEE) is responsible for France's population census, a major source of data.
Since 2004, INSEE no longer carries out a general population census every eight or nine years, but instead conducts annual sample censuses, registering immigrants who have lived in France for more than a year. This is the only source covering also nationals of European Union countries. The loss of completeness is largely compensated for by the tighter annual frequency. In addition, questions on country of birth and current and previous nationalities make it possible to track changes in net migration between people born abroad (immigrants), those born in France and French-desc
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https://en.wikipedia.org/wiki/Math%20house
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Isfahan Mathematics House (Persian:خانه ریاضیات اصفهان) is a non-formal education institute in Iran, focusing primarily on statistics, biology, physics, maths, AI, computer programming courses. Established 1998 mainly priority of the Isfahan mathematics house is to offer students training.
References
External links
https://mathhouse.org/
Isfahan
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https://en.wikipedia.org/wiki/Cho%20Hyun-taek
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Cho Hyun-taek (; born 2 August 2001) is a South Korean footballer who plays as a Full-back for Ulsan Hyundai in the K League 1.
Career statistics
References
External links
2001 births
Living people
South Korean men's footballers
Men's association football defenders
K League 2 players
K League 1 players
Bucheon FC 1995 players
Ulsan Hyundai FC players
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https://en.wikipedia.org/wiki/Markov%20operator
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In probability theory and ergodic theory, a Markov operator is an operator on a certain function space that conserves the mass (the so-called Markov property). If the underlying measurable space is topologically sufficiently rich enough, then the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup.
The definition of Markov operators is not entirely consistent in the literature. Markov operators are named after the Russian mathematician Andrey Markov.
Definitions
Markov operator
Let be a measurable space and a set of real, measurable functions .
A linear operator on is a Markov operator if the following is true
maps bounded, measurable function on bounded, measurable functions.
Let be the constant function , then holds. (conservation of mass / Markov property)
If then . (conservation of positivity)
Alternative definitions
Some authors define the operators on the Lp spaces as and replace the first condition (bounded, measurable functions on such) with the property
Markov semigroup
Let be a family of Markov operators defined on the set of bounded, measurables function on . Then is a Markov semigroup when the following is true
.
for all .
There exist a σ-finite measure on that is invariant under , that means for all bounded, positive and measurable functions and every the following holds
.
Dual semigroup
Each Markov semigroup induces a dual semigroup through
If is invariant under then .
Infinitesimal generator of the semigroup
Let be a family of bounded, linear Markov operators on the Hilbert space , where is an invariant measure. The infinitesimale generator of the Markov semigroup is defined as
and the domain is the -space of all such functions where this limit exists and is in again.
The carré du champ operator measuers how far is from being a derivation.
Kernel representation of a Markov operator
A Markov operator has a kernel representation
with respect to some probability kernel , if the underlying measurable space has the following sufficient topological properties:
Each probability measure can be decomposed as , where is the projection onto the first component and is a probability kernel.
There exist a countable family that generates the σ-algebra .
If one defines now a σ-finite measure on then it is possible to prove that ever Markov operator admits such a kernel representation with respect to .
Literature
References
Probability theory
Ergodic theory
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https://en.wikipedia.org/wiki/Kramkov%27s%20optional%20decomposition%20theorem
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In probability theory, Kramkov's optional decomposition theorem (or just optional decomposition theorem) is a mathematical theorem on the decomposition of a positive supermartingale with respect to a family of equivalent martingale measures into the form
where is an adapted (or optional) process.
The theorem is of particular interest for financial mathematics, where the interpretation is: is the wealth process of a trader, is the gain/loss and the consumption process.
The theorem was proven in 1994 by Russian mathematician Dmitry Kramkov. The theorem is named after the Doob-Meyer decomposition but unlike there, the process is no longer predictable but only adapted (which, under the condition of the statement, is the same as dealing with an optional process).
Kramkov's optional decomposition theorem
Let be a filtered probability space with the filtration satisfying the usual conditions.
A -dimensional process is locally bounded if there exist a sequence of stopping times such that almost surely if and for and .
Statement
Let be -dimensional càdlàg (or RCLL) process that is locally bounded. Let be the space of equivalent local martingale measures for and without loss of generality let us assume .
Let be a positive stochastic process then is a -supermartingale for each if and only if there exist an -integrable and predictable process and an adapted increasing process such that
Commentary
The statement is still true under change of measure to an equivalent measure.
References
Probability theorems
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https://en.wikipedia.org/wiki/Statistics%20of%20the%20Hebrew%20Bible
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Statistics of the Hebrew Bible is the counting of verses, words, and letters in the Bible which has been known since the days of the Talmud (around the 3rd century). Later in the Masora period (between the 5th and 10th centuries), counting words and letters was one of the basic acts that were done to create a uniform version of the Bible and to safeguard it from disruptions. In the Babylonian Talmud, it is said that the families of the dead "scribes" in the Bible were named after a male working in counting the letters and words in the Torah. In Judaism, some regard the practice of counting letters and words as a mitzvah and a virtue.
According to the current version, the Hebrew Bible has approximately 22,864 verses, 306,757 Hebrew words, and 1,202,972 Hebrew letters. Out of these, there are 5,845 verses, 79,980 Hebrew words, and 304,805 letters in five Torah pentagrams. Various statistics of the Hebrew Bible have been published in Jewish literature over the generations.
References
Statistics
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https://en.wikipedia.org/wiki/Orthogonal%20circles
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In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle).
A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles, for instance in inversive geometry, then an orthogonal pair of lines or line and circle are orthogonal generalized circles.
In the conformal disk model of the hyperbolic plane, every geodesic is an arc of a generalized circle orthogonal to the circle of ideal points bounding the disk.
See also
Radical axis
Power center (geometry)
Apollonian circles
Bipolar coordinates
References
Circles
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https://en.wikipedia.org/wiki/Doignon%27s%20theorem
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Doignon's theorem in geometry is an analogue of Helly's theorem for the integer lattice. It states that, if a family of convex sets in Euclidean space have the property that the intersection of every contains an integer point, then the intersection of all of the sets contains an integer point. Therefore, integer linear programs form an LP-type problem of combinatorial and can be solved by certain generalizations of linear programming algorithms in an amount of time that is linear in the number of constraints of the problem and fixed-parameter tractable in its The same theorem applies more generally to any lattice, not just the integer
The theorem can be classified as belonging to convex geometry, discrete geometry, and the geometry of numbers. It is named after Belgian mathematician and mathematical psychologist Jean-Paul Doignon, who published it in 1973. Doignon credits Francis Buekenhout with posing the question answered by this It is also called the Doignon–Bell–Scarf theorem, crediting mathematical economists David E. Bell and Herbert Scarf, who both rediscovered it and pointed out its applications to integer
The result is tight: there exist systems of half-spaces for which every have an integer point in their intersection, but for which the whole system has no integer intersection. Such a system can be obtained, for instance, by choosing halfspaces that contain all but one vertex of the unit cube. Another way of phrasing the result is that the Helly number of convex subsets of the integers is More generally, the Helly number of any discrete set of Euclidean points equals the maximum number of points that can be chosen to form the vertices of a convex polytope that contains no other point from the Generalizing both Helly's theorem and Doignon's theorem, the Helly number of the Cartesian product
References
Theorems in convex geometry
Theorems in discrete geometry
Geometry of numbers
Lattice points
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https://en.wikipedia.org/wiki/Sophie%20Germain%27s%20identity
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In mathematics, Sophie Germain's identity is a polynomial factorization named after Sophie Germain stating that
Beyond its use in elementary algebra, it can also be used in number theory to factorize integers of the special form , and it frequently forms the basis of problems in mathematics competitions.
History
Although the identity has been attributed to Sophie Germain, it does not appear in her works. Instead, in her works one can find the related identity
Modifying this equation by multiplying by gives
a difference of two squares, from which Germain's identity follows. The inaccurate attribution of this identity to Germain was made by Leonard Eugene Dickson in his History of the Theory of Numbers, which also stated (equally inaccurately) that it could be found in a letter from Leonhard Euler to Christian Goldbach.
The identity can be proven simply by multiplying the two terms of the factorization together, and verifying that their product equals the right hand side of the equality. A proof without words is also possible based on multiple applications of the Pythagorean theorem.
Applications to integer factorization
One consequence of Germain's identity is that the numbers of the form
cannot be prime for . (For , the result is the prime number 5.) They are obviously not prime if is even, and if is odd they have a factorization given by the identity with and . These numbers (starting with ) form the integer sequence
Many of the appearances of Sophie Germain's identity in mathematics competitions come from this corollary of it.
Another special case of the identity with and
can be used to produce the factorization
where is the fourth cyclotomic polynomial. As with the cyclotomic polynomials more generally, is an irreducible polynomial, so this factorization of infinitely many of its values cannot be extended to a factorization of as a polynomial, making this an example of an aurifeuillean factorization.
Generalization
Germain's identity has been generalized to the functional equation
which by Sophie Germain's identity is satisfied by the square function.
References
Elementary algebra
Mathematical identities
Factorization
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https://en.wikipedia.org/wiki/It%C3%B4%E2%80%93Nisio%20theorem
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The Itô-Nisio theorem is a theorem from probability theory that characterizes convergence in Banach spaces. The theorem shows the equivalence of the different types of convergence for sums of independent and symmetric random variables in Banach spaces. The Itô-Nisio theorem leads to a generalization of Wiener's construction of the Brownian motion. The symmetry of the distribution in the theorem is needed in infinite spaces.
The theorem was proven by Japanese mathematicians Kiyoshi Itô and in 1968.
Statement
Let be a real separable Banach space with the norm induced topology, we use the Borel σ-algebra and denote the dual space as . Let be the dual pairing and is the imaginary unit. Let
be independent and symmetric -valued random variables defined on the same probability space
be the probability measure of
some -valued random variable.
The following is equivalent
converges almost surely.
converges in probability.
converges to in the Lévy–Prokhorov metric.
is uniformly tight.
in probability for every .
There exist a probability measure on such that for every
Remarks:
Since is separable point (i.e. convergence in the Lévy–Prokhorov metric) is the same as convergence in distribution . If we remove the symmetric distribution condition:
in a finite-dimensional setting equivalence is true for all except point (i.e. the uniform tighness of ),
in an infinite-dimensional setting is true but does not always hold.
Literature
References
Probability theorems
Banach spaces
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https://en.wikipedia.org/wiki/Weber%27s%20theorem
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Weber's theorem may refer to:
Kronecker–Weber theorem
Weber's theorem (Algebraic curves)
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https://en.wikipedia.org/wiki/Lee%20Sang-min%20%28footballer%2C%20born%201999%29
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Lee Sang-min (; born 30 August 1999) is a South Korean footballer who plays as a defender for Seongnam FC in the K League 1.
Career statistics
References
External links
1999 births
Living people
South Korean men's footballers
Men's association football defenders
K League 2 players
Chungnam Asan FC players
Seongnam FC players
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https://en.wikipedia.org/wiki/Hardy%20distribution
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In probability theory and statistics, the Hardy distribution is a discrete probability distribution that expresses the probability of the hole score for a given golf player. It is based on Hardy's (Hardy, 1945) basic assumption that there are three types of shots:
good ,
bad and
ordinary ,
where the probability of a good hit equals , the probability of a bad hit equals and the probability of an ordinary hit equals . Hardy further assigned
a value of 2 to a good stroke,
a value of 0 to a bad stroke and
a value of 1 to a regular or ordinary stroke.
Once the sum of the values is greater than or equal to the value of the par of the hole, the number of strokes in question is equal to the score achieved on that hole. A birdie on a par three could then have come about in three ways: , and , respectively, with probabilities , and .
Definitions
Probability mass function
A discrete random variable is said to have a Hardy distribution, with parameters , and if it has a probability mass function given by:
if m is odd
and
if m is even
with
and
where
is the par of the hole ()
is the golf hole score () if is even
is the golf hole score () if is odd
is the probability of a good shot ()
is the probability of a bad shot () and ()
The moment generating function is given by:
if m is odd
and
if m is even
with
and
Each raw moment and each central moment can be easily determined with the moment generating function, but the formulas involved are too large to present here.
Hardy distribution for a par three, four and five
For a par three:
For a par four:
Note the resemblance with . For a par five:
Note the resemblance with the formulas for and .
History
When trying to make a probability distribution in golf that describes the frequency distribution of the number of strokes on a hole, the simplest setup is to assume that there are only two types of strokes:
A good stroke with a probability of
A bad stroke with a probability of .
while
a good shot then gets the value 1 and
a bad shot gets the value 0.
Once the sum of the shot values equals the par of the hole, that is the number of strokes needed for the hole.
It is clear that with this setup, a birdie is not possible. After all, the smallest number of strokes one can get is the par of the hole. Hardy (1945) probably realized that too and then came up with the idea not to assume that there were just two types of strokes: good and bad , but three types:
good with probability
bad with probability
ordinary with probability .
In fact, Hardy called a good shot a supershot and a bad shot a subshot. Minton later called Hardy's supershot an excellent shot and Hardy's subshot a bad shot . In this article, Minton's excellent shot is called a good shot . Hardy came up with the idea of three types of shots in 1945, but the actual derivation of the probability distribution of the hole score was not given until 2012 by van der Ven
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https://en.wikipedia.org/wiki/2005%E2%80%9306%20Qatari%20Second%20Division
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Statistics of Qatari Second Division for the 2005–06 season.
Overview
It was contested by 6 teams, and Umm Salal won the championship and promotion to the Qatar Stars League.
League standings
References
2005–06 in Asian association football leagues
2005–06 in Qatari football
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https://en.wikipedia.org/wiki/Netz
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Netz is a surname. Notable people with the name include:
Luca Netz (born 2003), German professional footballer
Reviel Netz (born 1968), Israeli scholar of the history of pre-modern mathematics
Wolf-Rüdiger Netz (born 1950), former football player from East Germany
See also
Natz (disambiguation)
Netzer (disambiguation)
Notz
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https://en.wikipedia.org/wiki/Carl%20D.%20Murray
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Carl Desmond Murray (born September 1955) is an Irish academic who is Emeritus Professor of Mathematics and Astronomy at Queen Mary University of London (formerly Queen Mary College). He is a planetary scientist and a world expert on the rings of Saturn. With Stanley Dermott he is the author of a benchmark textbook in the field of Solar System Dynamics.
Education and career
Carl Murray was born September 1955 in Belfast, Northern Ireland, the son of physician Frank Murray. He grew up there and in Newcastle, County Down. He obtained a B.Sc. in Applied Mathematics with Astrophysics from Queen Mary College in London in 1977, achieving First Class Honours. He earned a Ph.D. from the same institution in January 1980, with the thesis "Aspects of the Dynamical Evolution of Small Particles in the Solar System" under Iwan P. Williams.
His career has been spent on the staff at Queen Mary College (later known as Queen Mary University of London). He has been a Courtesy Professor in the Department of Astronomy at the University of Florida since 1995.
Murray's interests span all facets of solar system dynamics, encompassing everything from the evolution of minute dust particles to the stability of celestial bodies like planets. Since being selected in 1990, he has been a key member of the Cassini Imaging Team, serving as the sole representative from the United Kingdom. He has studied the intricate dynamics of Saturn's rings, especially the complex and mysterious F-ring, along with gravitational interactions between the rings and neighboring moons.
In 2007 a team of astronomers from the European Space Agency led by Murray discovered a new moon (the 60th) of Saturn using the Casini Space Probe.
He has also served as:
(2014-2021) Science Editor for Monthly Notices of the Royal Astronomical Society
(1998-2004) Associate Editor of Celestial Mechanics and Dynamical Astronomy
(1991–2010) Associate/Consulting Editor of Icarus
Books
Planetary Ring Systems: Properties, Structure, and Evolution, with Matthew S. Tiscareno, Mar 22, 2018
Solar System Dynamics, with Stanley F. Dermott, Feb 26, 2010
Atlas of the Planar, Circular, Restricted Three-Body Problem, with Othon C. Winter, Sep 1, 1994
Expansion of the Planetary Disturbing Function of Eighth Ord, with David Harper, Mar 1, 1993
Awards and honors
Fellow of the Royal Astronomical Society (since 1980)
Member of the International Astronomical Union (since 1985)
Member of the American Astronomical Society (since 1990)
Member of the American Geophysical Union (since 2013)
Asteroid (5598) Carlmurray is named in his honour.
References
External links
Carl Murray's homepage
Research papers of Carl D. Murray
1955 births
living people
Alumni of the University of London
Academics of Queen Mary University of London
Planetary scientists
20th-century British astronomers
21st-century British astronomers
Fellows of the Royal Society
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https://en.wikipedia.org/wiki/Ein%20Shibli
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Ein Shibli () is a Palestinian village in the Nablus Governorate in northern West Bank, located 15.6 kilometers east of Nablus. According to the Palestinian Central Bureau of Statistics (PCBS), the village's population was estimated to be 313 inhabitants in 2017. Ein Shibli has a total area of approximately 567 dunums of which 296 are arable land and 32 dunums are registered as residential.
History
One account suggests that the name of the village originates from a notorious bandit named Shibli who resided near a water spring in the village and would rob travelers, leading to the village being named after him.
Ein Shibli was founded in 1948, and its inhabitants originally migrated from Jaffa and Al Hamma.
Under the Oslo II Interim Agreement signed on 28 September 1995, Ein Shibli was divided into two areas, namely Area B and Area C. Area B encompasses approximately 385 dunums, which accounts for 68% of the village's total area. In this area, the Palestinian National Authority (PNA) exercises full control over civil matters, while Israel retains ultimate responsibility for security. On the other hand, Area C, constituting 182 dunums or 32% of the total area, remains under Israel's complete control in terms of security and administrative affairs. In Area C, Palestinian construction and land management are restricted unless authorized or permitted by the Israeli Civil Administration. The majority of Ein Shibli's population resides in Area B.
Economy
The economy in Ein Shibli depends mainly on its agricultural sector, which employed 50% of the village's workforce in 2013, according to the village's council.
The results of a 2013 field survey conducted by Applied Research Institute - Jerusalem (ARIJ) indicated that the agriculture sector accounted for 50% of the labor force, while the Israeli labor market employed 30% of the workforce. The employees sector represented 10% of the labor force, followed by the trade sector at 5%, and the services sector also at 5%.
In 2013, the unemployment rate in Ein Shibli was 70%.
Education
According to the PCBS, in 2007, Ein Shibli had an illiteracy rate of approximately 18.2% among its population, with 65% of the illiterate individuals being female. Out of the total population, 17.7% possessed basic reading and writing skills without formal education, 21.4% had completed elementary education, 23.2% had received preparatory education, 13.6% had completed secondary education, and 5% had attained higher education
The village has one public school, Ein Shibli co-educational Elementary School, which operates under the Palestinian Ministry of Higher Education. As of 2012, there was no kindergarten available in the village, according to the Directorate of Education in Nablus. As of 2013, there was no secondary level education provided in the village and thus students from Ein Shibli enrolled at Al Aqrabaniya Secondary School in the nearby village of Al Aqrabaniya, located 4 km away.
Infrastructure
Electricit
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https://en.wikipedia.org/wiki/Al%20Aqrabaniya
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Al Aqrabaniya () is a Palestinian village in the Nablus Governorate in northern West Bank, located 12.1 kilometers east of Nablus. According to the Palestinian Central Bureau of Statistics (PCBS), the village's population was 939 inhabitants in 2017. It is bordered by Furush Beit Dajan to the east, Beit Dajan and Deir al-Hatab to the south, Al-Badhan to the west, and An-Nassariya and Beit Hasan to the north. The total area of the village consists of approximately 13,574 dunums.
History
Al Aqrabaniya was named after "al-aqraban" which is the name given to the male scorpion, of which there are many in the area. The village residents originally came from villages including Kafr Qallil and Salim.
Under the Oslo II Interim Agreement signed on 28 September 1995, Al Aqrabaniya was divided into two areas, namely Area B and Area C. Area B encompasses approximately 13,299 dunums, which accounts for 98% of the village's total area. In this area, the Palestinian National Authority (PNA) exercises full control over civil matters, while Israel retains ultimate responsibility for security. On the other hand, Area C, constituting 275 dunums or 2% of the total area, remains under Israel's complete control in terms of security and administrative affairs. In Area C, Palestinian construction and land management are restricted unless authorized or permitted by the Israeli Civil Administration. The majority of Al Aqrabaniya's population resides in Area B.
Economy
The economy in Al Aqrabaniya depends mainly on its agricultural sector, which employed 86.5% of the village's workforce in 2013, according to the village's council.
The results of a 2013 field survey conducted by Applied Research Institute - Jerusalem (ARIJ) indicated that the agriculture sector accounted for 86.5% of the labor force, while the Israeli labor market employed 1.5% of the workforce. The public employees sector represented 10% of the labor force, followed by the trade and services sectors both at 1%.
In 2013, the unemployment rate in Al Aqrabaniya was 30%.
Education
According to the PCBS, in 2007, Al Aqrabaniya had an illiteracy rate of approximately 11.8% among its population, with 69.8% of the illiterate individuals being female. Out of the total population, 20.8% could only read and write with no formal education, 31.4% had elementary education, 20.3% had preparatory education, 10.5% had secondary education, and 5.1% had completed higher education.
There is one public school in the village, which followed by UNRWA, which is run by the Palestinian Ministry of Higher Education. The village does not have a kindergarten.
Infrastructure
Healthcare
Al Aqrabaniya does not have any health facilities. Patients are transferred to the governmental An-Nassariya health center or to a health center run by UNRWA in An-Nassariya, 1 km away from the village.
Electricity and telecommunication services
Al Aqrabaniya has been connected to a public electricity network since 1994 and is served by the
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https://en.wikipedia.org/wiki/Lexell%27s%20theorem
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In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle, called Lexell's circle or Lexell's locus, passing through two points antipodal to the two base vertices.
The theorem is named for Anders Johan Lexell, who presented a paper about it (published 1784) including both a trigonometric proof and a geometric one. Lexell's colleague Leonhard Euler wrote another pair of proofs in 1778 (published 1797), and a variety of proofs have been written since by Adrien-Marie Legendre (1800), Jakob Steiner (1827), Carl Friedrich Gauss (1841), Paul Serret (1855), and Joseph-Émile Barbier (1864), among others.
The theorem is the analog of propositions 37 and 39 in Book I of Euclid's Elements, which prove that every planar triangle with the same area on a fixed base has its apex on a straight line parallel to the base. An analogous theorem can also be proven for hyperbolic triangles, for which the apex lies on a hypercycle.
Statement
Given a fixed base an arc of a great circle on a sphere, and two apex points and on the same side of great circle Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc where and are the points antipodal to and respectively.
As one analog of the planar formula for the area of a triangle, the spherical excess of spherical triangle can be computed in terms of the base (the angular length of arc and "height" (the angular distance between the parallel small circles
In the limit for triangles much smaller than the radius of the sphere, this reduces to the planar formula.
The small circles and each intersect the great circle at an angle of
Proofs
There are several ways to prove Lexell's theorem, each illuminating a different aspect of the relationships involved.
Isosceles triangles
The main idea in Lexell's geometric proof – also adopted by Eugène Catalan (1843), Robert Allardice (1883), Jacques Hadamard (1901), Antoine Gob (1922), and Hiroshi Maehara (1999) – is to split the triangle into three isosceles triangles with common apex at the circumcenter and then chase angles to find the spherical excess of triangle In the figure, points and are on the far side of the sphere so that we can clearly see their antipodal points and all of Lexell's circle
Let the base angles of the isosceles triangles (shaded red in the figure), (blue), and (purple) be respectively and (In some cases is outside then one of the quantities will be negative.) We can compute the internal angles of (orange) in terms of these angles: (the supplement of and likewise and finally
By Girard's theorem the spherical excess of is
If base is fixed, for any third vertex falling on the same arc of Lexell's circle, the point and therefore the quantity will not change, so the excess of which depends only on will likewise be constant. And vic
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https://en.wikipedia.org/wiki/Ellingston%20Special
|
The Ellingston Special was a variable-geometry aircraft, designed by Cornwallis "Con" Ellingston of Great Falls, Montana in the late 1930s.
Background
Ellingston, together with Earle Hansen, constructed the aircraft, with Hansen making the maiden flight on April 23, 1938. It was a single-seat low-wing monoplane, fitted with a retractable undercarriage, and was powered by a LeBlond 90-7D radial engine, fitted with a two-bladed tractor propeller. The primary structure was constructed from 4130 chromoly steel tubing.
The aircraft's most notable feature was its telescopic wings, which could vary in span between and , with it being possible to vary the wingspan while in flight. The maximum speed of the aircraft varied from with the wings retracted, to with the wings extended.
An article in the December 1939 issue of Popular Aviation magazine stated that Ellingston was working on a twin-engined transport aircraft, which would also incorporate variable span, construction of which was scheduled to begin that Winter.
Specifications (Special)
References
See also
1930s United States experimental aircraft
Single-engined tractor aircraft
Low-wing aircraft
Variable-geometry-wing aircraft
Aircraft first flown in 1938
|
https://en.wikipedia.org/wiki/2023%E2%80%9324%20PFC%20Levski%20Sofia%20season
|
The 2023–24 season is Levski Sofia's 103rd season in the First League. This article shows player statistics and all matches (official and friendly) that the club will play during the season.
Transfers
In
Out
Loans out
Squad
Updated on 14 August 2023.
Performance overview
Fixtures
Friendlies
Summer
First League
Preliminary stage
League table
Results summary
Results by round
Matches
The league fixtures were announced on 14 June 2023.
Bulgarian Cup
UEFA Europa Conference League
Second qualifying round
Third qualifying round
Play-off round
Squad statistics
Appearances and goals
|-
|colspan="14"|Players from the reserve team:
|-
|colspan="14"|Players away on loan:
|-
|colspan="14"|Players who left during the season:
|}
Goalscorers
Clean sheets
Disciplinary record
Includes all competitive matches.
References
General
Official club website
Specific
Notes
PFC Levski Sofia seasons
Levski Sofia
Levski Sofia
|
https://en.wikipedia.org/wiki/Nikhil%20Ranjan%20Sen
|
Nikhil Ranjan Sen (23 May 1894 – 13 January 1963) was an Indian-Bengali scientist who was a pioneer in the field of general relativity and called the father of applied mathematics in India. He received his PhD from Humboldt University of Berlin under the supervision of Max von Laue, thus becoming the first Indian to get a doctorate in relativity. Sen also worked on cosmogony, fluid dynamics, potential theory and probability, and founded the first fluid dynamics laboratory in India. He pioneered the study of ballistics and missiles in India and was also an advocate for science education in the Bengali language. His Bengali-language book titled “Soura Jagat” (The Solar System) was published by Visva-Bharati in 1949.
Early life and education
Nikhil Ranjan Sen was born on 23 May 1894 in Dhaka, the youngest of their four sons and four daughters of Kalimohan Sen and his wife Vidhumukhi Devi. He attended Dhaka Collegiate School, where his classmate was the famous scientist Meghnad Saha. He then went to complete his school education at Rajshahi Collegiate School. In 1909, he obtained a scholarship with his third position in order of merit for the entrance examination of Calcutta University. After passing the intermediate examination in 1911, he studied honors mathematics in Presidency College in Calcutta, where he had Saha and Satyendranath Bose as classmates. Bose, Saha, and Sen got the three highest spots in the 1913 honors examination in Calcutta University. They went on to become postgraduate students in Presidency College. Sen topped the 1916 Mixed Mathematics examination, a year after Bose and Saha topped the same exam.
Career and research
Sen, Saha, and Bose joined the postgraduate department of mathematics in University of Calcutta at almost the same time in 1917. During this period, his papers on Newtonian potential, solid geometry, elasticity, and hydrodynamics were published in Philosophical Magazine and in the Bulletin of Calcutta Mathematical Society.
In 1921, his thesis “Potentials of Uniform” was approved by G.T. Walker, D.N. Mallik, and Asutosh Mukherjee to be worthy of being awarded the doctorate (D.Sc.) degre from the university. With an extra allowance of five hundred taka per month, he went to Germany for research work at the universities of Berlin, Munich, and Paris. His work with Professor Arnold Sommerfeld in Munich from 1921 to 1922 was published in the Physikalische Zeitschrift. In the summer of 1922, he went to Berlin and studied under Max von Laue in the newly established Institute for Physics. Under von Laue, Sen received a Ph.D. from the University of Berlin for a general relativity dissertation on the boundary conditions for the gravitational field equations on surfaces of discontinuity. In his dissertation, Sen found that Einstein's equations imply that gravitational forces hold together the parts of a particle, then he calculated the equilibrium of a charged particle with a defnite spherical boundary. Sen also worked
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https://en.wikipedia.org/wiki/Ogawa%20integral
|
In stochastic calculus, the Ogawa integral (also named non-causal stochastic integral) is a stochastic integral for non-adapted processes as integrands. The corresponding calculus is called non-causal calculus in order to distinguish it from the anticipating calculus of the Skorokhod integral. The term causality refers to the adaptation to the natural filtration of the integrator.
The integral was introduced by the Japanese mathematician Shigeyoshi Ogawa in 1979.
Ogawa-Integral
Let
be a probability space,
be a one-dimensional standard Wiener process with ,
and be the natural filtration of the Wiener process,
the Borel σ-algebra,
be the Wiener integral,
be the Lebesgue measure.
Further let be the set of real-valued processes that are -measurable and almost surely in , i.e.
Ogawa integral
Let be a complete orthonormal basis of the Hilbert space.
A process is called -integrable if the random series
converges in probability and the corresponding sum is called the Ogawa integral with respect to the basis .
If is -integrable for any complete orthonormal basis of and the corresponding integrals share the same value then is called universal Ogawa integrable (or u-integrable).
More generally, the Ogawa integral can be defined for any -process (such as the fractional Brownian motion) as integrators
as long as the integrals
are well-defined.
Remarks
The convergence of the series depends not only on the orthonormal basis but also on the ordering of that basis.
There exist various equivalent definitions for the Ogawa integral which can be found in (). One way makes use of the Itô–Nisio theorem.
Regularity of the orthonormal basis
An important concept for the Ogawa integral is the regularity of an orthonormal basis. An orthonormal basis is call regular if
holds.
The following results on regularity are known:
Every semimartingale (causal or not) is -integrable if and only if is regular.
It was proven that there exist a non-regular basis for .
Further topics
There exist a non-causal Itô formula, a non-causal integration by parts formula and a non-causal Girsanov theorem.
The Ogawa integral for multidimensional Wiener processes was studied in ().
Relationship to other integrals
Stratonovich integral: let be a continuous -adapted semimartingale that is universal Ogawa integrable with respect to the Wiener process, then the Stratonovich integral exist and coincides with the Ogawa integral.
Skorokhod integral: the relationship between the Ogawa integral and the Skorokhod integral was studied in ().
Literature
References
Definitions of mathematical integration
Stochastic calculus
|
https://en.wikipedia.org/wiki/Antoinette%20d%27Aubeterre
|
Antoinette d'Aubeterre (1532–1580) was a French noble woman, who received a good classical education, learning mathematics from François Viète. François was her legal advisor, personal secretary, and tutor to Antoinette and her husband Jean V de Parthenay's daughter Catherine de Parthenay. Catherine married at about the age of 14 to Charles de Quelennec. Catherine was kidnapped by her husband in the middle of a scandal and Antoinette intervened to free her daughter.
Early life
Antoinette d'Aubeterre, the daughter of François II Bouchard, Seigneur d'Aubeterre and Isabelle de Saint-Seine was born in 1532.
Huguenot
Antoinette d'Aubeterre hired François Viète, a jurist, as her legal adviser to help her navigate legal issues that arose between the Calvinists (Huguenots) and the Catholics. He was born a Catholic, and did not personally engage in religious disputes. From 1564 to 1571, he worked as her personal secretary.
Marriage and children
Antoinette d'Aubeterre and Jean V of Parthenay were married on 3 May 1553. Their daughter, Catherine de Parthenay, was born on 22 March 1554 at Château du Parc-Soubise.
The couple had a clear division of labor. Jean V concerned himself with business and political affairs that often took him away from home. Antoinette managed the financial and other private affairs that concerned her family and their relationships in their community.
François Viète, who had been Antoinette's former mathematics tutor, was hired to be her daughter Catherine's tutor. Viète taught Catherine geography, current discoveries, cosmographic knowledge, and mathematics, from 1564 to 1568. While he worked for Antoinette d'Aubeterre, he worked on trigonometric functions that were published in two of his books (1579). Viète co-founded modern algebra. He also published manuscripts of memoirs and geneaology of the Parthenays. Antoinette was his patron.
Catherine married Charles de Quelennec in 1568 (when she was about 14). They had a difficult marriage and her husband imprisoned his wife at a castle in Brittany.
Intervention when Catherine was sequestered
On 6 September 1570, as Catherine was about to be kidnapped, she wrote a letter to her mother Antoinette. In it, she said she was being taken against her will and could not provide the care she wanted to provide for her ill mother. She stated she was the same as she "was on the eve of my wedding and that I have always been since my birth". Catherine snuck letters out of the castle. They were written in invisible ink of citrus juice and in Greek and Latin to her mother Antoinette d'Aubeterre and her former tutor. Antoinette contacted the Duke of Anjou (future King Henri III (1574–1589)) and his mother Catherine de Medici for guidance. They took Quelennec's side, but they would not have her detained. Antoinette then wrote to King Charles IX and the case went before the Grand Council on 11 September 1571, after which it was referred to boards of doctors and judges. Quelennec died the night
|
https://en.wikipedia.org/wiki/Fresh%20variable
|
In formal reasoning, in particular in mathematical logic, computer algebra, and automated theorem proving, a fresh variable is a variable that did not occur in the context considered so far.
The concept is often used without explanation.
Example
For example, in term rewriting, before applying a rule to a given term , each variable in should be replaced by a fresh one to avoid clashes with variables occurring in .
Given the rule
and the term
,
attempting to find a matching substitution of the rule's left-hand side, , within will fail, since cannot match .
However, if the rule is replaced by a fresh copy
before, matching will succeed with the answer substitution .
Notes
References
Rewriting systems
Automated theorem proving
Computer algebra
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https://en.wikipedia.org/wiki/Babbage%20Building
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The Babbage Building is a teaching building at the University of Plymouth.
Background
The Babbage Building is the main building for the university's School of Engineering, Computing and Mathematics and the School of Art, Design and Architecture.
It is named after Charles Babbage, a mathematician, philosopher, inventor and mechanical engineer who originated the concept of a digital programmable computer.
After renovations in 2021–2023, the building contains a number of fabrication and computing laboratories.
History
The building was originally constructed in the 1979 as an engineering block for the university.
2021 - 2023 Renovation
In 2019, a design competition was held for a renovation of the Babbage Building.
Permission was granted for the renovations in December 2020, and works began in 2021. The main contractor for the renovations is BAM, and the new building was designed by Feilden Clegg Bradley Studios.
In 2021, as part of the university's campus masterplan, the Babbage Building was closed for £30 million worth of renovation works. For the renovations to be able to take place, the university had to temporarily relocate classes and infrastructure to other places across the campus. The university's data center was mostly moved to the cloud as a result of the works.
The building was completely emptied, internal walls taken down, and the outer walls taken off, with only the concrete structure remaining. The renovated building has larger windows, blue cladding, and a rooftop garden. Babbage is also set to be expanded towards the rear and right side of the building.
As part of the works, the nearby Brunel building will be demolished and turned into a park when all of its functions have been moved into the babbage building.
The newly renovated building will contain 108,000 sq ft (10,000 sq m) of teaching and learning space, and will be focused on using low carbon technologies to reduce the university's carbon footprint.
The building is due to reopen in September 2023.
References
Buildings and structures in Plymouth, Devon
Buildings at the University of Plymouth
|
https://en.wikipedia.org/wiki/Type%20and%20cotype%20of%20a%20Banach%20space
|
In functional analysis, the type and cotype of a Banach space are a classification of Banach spaces through probability theory and a measure, how far a Banach space from a Hilbert space is.
The starting point is the Pythagorean identity for orthogonal vectors in Hilbert spaces
This identity no longer holds in general Banach spaces, however one can introduce a notion of orthogonality probabilistically with the help of Rademacher random variables, for this reason one also speaks of Rademacher type and Rademacher cotype.
The notion of type and cotype was introduced by French mathematician Jean-Pierre Kahane.
Definition
Let
be a Banach space,
be a sequence of independent Rademacher random variables, i.e. and for and .
Type
is of type for if there exist a finite constant such that
for all finite sequences . The sharpest constant is called type constant and denoted as .
Cotype
is of cotype for if there exist a finite constant such that
respectively
for all finite sequences . The sharpest constant is called cotype constant and denoted as .
Remarks
By taking the -th resp. -th root one gets the equation for the Bochner norm.
Properties
Every Banach space is of type (follows from the triangle inequality).
A Banach space is of type and cotype if and only if the space is also isomorphic to a Hilbert space.
If a Banach space:
is of type then it is also type .
is of cotype then it is also of cotype .
is of type for , then its dual space is of cotype with (conjugate index). Further it holds that
Examples
The spaces for are of type and cotype , this means is of type , is of type and so on.
The spaces for are of type and cotype .
The space is of type and cotype .
Literature
References
Functional analysis
Banach spaces
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https://en.wikipedia.org/wiki/1940%E2%80%9341%20Liverpool%20F.C.%20season
|
The 1940–41 season saw Liverpool compete in the wartime North Regional League and the League War Cup. Some matches were also part of the Lancashire Senior Cup.
Statistics
Appearances and Goals
|}
Competitions
North Region War League and Lancashire Senior Cup
Football League War Cup
References
LFC History.net – 1940–41 season
11v11
Soccer At War 1939-45 by Jack Rollin ISBN 9780755314317
Liverpool F.C. seasons
Liverpool
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https://en.wikipedia.org/wiki/Zhu%20algebra
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In the theory of vertex algebras, the Zhu algebra and the closely related C2-algebra are two associative algebras canonically constructed from a given vertex operator algebra. Many important representation theoretic properties of the vertex algebra are logically related to properties of its Zhu algebra or C2-algebra.
Definitions
Let be a graded vertex operator algebra with and let be the vertex operator associated to Define to be the subspace spanned by elements of the form for An element is homogeneous with if There are two binary operations on defined byfor homogeneous elements and extended linearly to all of . Define to be the span of all elements .
The algebra with the binary operation induced by is an associative algebra called the Zhu algebra of of .
The algebra with multiplication is called the C2-algebra of .
Main properties
The multiplication of the C2-algebra is commutative and the additional binary operation is a Poisson bracket on which gives the C2-algebra the structure of a Poisson algebra.
(Zhu's C2-cofiniteness condition) If is finite dimensional then is said to be C2-cofinite. There are two main representation theoretic properties related to C2-cofiniteness. A vertex operator algebra is rational if the category of admissible modules is semisimple and there are only finitely many irreducibles. It has been conjectured that rationality is equivalent to C2-cofiniteness and a stronger condition regularity. Various weaker versions of this conjecture are known, including that regularity implies C2-cofiniteness and that for C2-cofinite the conditions of rationality and regularity are equivalent. This conjecture is a vertex algebras analogue of Cartan's criterion for semisimplicity in the theory of Lie algebras because it relates a structural property of the algebra to the semisimplicity of its representation category.
The grading on induces a filtration where so that There is a surjective morphism of Poisson algebras .
Associated variety
Because the C2-algebra is a commutative algebra it may be studied using the language of algebraic geometry. The associated scheme and associated variety of are defined to be which are an affine scheme an affine algebraic variety respectively. Moreover, since acts as a derivation on there is an action of on the associated scheme making a conical Poisson scheme and a conical Poisson variety. In this language, C2-cofiniteness is equivalent to the property that is a point.
Example: If is the affine W-algebra associated to affine Lie algebra at level and nilpotent element then is the Slodowy slice through .
References
Algebra
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https://en.wikipedia.org/wiki/Lovre%20Rogi%C4%87
|
Lovre Rogić (born 27 August 1995) is a Croatian professional footballer who plays as a goalkeeper for Bosnian Premier League club Sarajevo. Rogić has previously played for Šibenik.
Career statistics
Club
References
1995 births
Living people
Croatian sportspeople
Croatian men's footballers
Men's association football goalkeepers
HNK Šibenik players
FK Sarajevo players
First Football League (Croatia) players
Premier League of Bosnia and Herzegovina players
Expatriate men's footballers in Bosnia and Herzegovina
Croatian expatriate sportspeople in Bosnia and Herzegovina
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https://en.wikipedia.org/wiki/Johan%20Gielis%20%28mathematician%29
|
Johan Gielis (born July 8, 1962) is a Belgian engineer, scientist, mathematician, and entrepreneur. Gielis is known for his contributions to the field of mathematics, specifically in the area of modeling and geometrical methods. He is best known for developing the concept of the superformula, which is a generalization of the traditional Pythagorean theorem and the equation of the circle, that can generate a wide variety of complex shapes found in nature.
Career
Gielis obtained a degree in horticultural engineering. Later, he changed direction from botany and plant biotechnology to geometry and mathematics. In 2013, Gielis co founded the Antenna Company, in Eindhoven. The company applies the superfomula to develop efficient antennas to transmit data via various frequencies. The company made antenna system for ultra-fast WiFi 6 devices. Antenna systems focus on 2-7 gigaHertz, in line with the IEEE 802.11ax standard and beyond. Other products focus on Internet of Things and mmWave antenna systems.
Superformula
Gielis proposed the superformula in 2003. The superfomula is a generalization of the superellipse. He suggested that it allows for the creation of shapes that can mimic natural forms such as flowers, shells, and other intricate structures. The mathematical equation combines elements of trigonometry and algebra to generate complex and visually appealing patterns. It also allowed for a generalization of minimal surfaces based on a more general notion of the energy functional and allowed for a generalized definition of the Laplacian, and the use of Fourier projection methods to solve boundary value problems.
r - distance from the center, Φ - Angle to the x-axis, m - symmetry, n1, n2, n3: - Form, a, b: - expansion (semi-axes)
Gielis patented the synthesis of patterns generated by the superformula. The superformula was used in No Man's Sky, an action-adventure survival game developed and published by Hello Games. The formula was also used in the Jewels of the Sea.
Publications
Books
Modeling in Mathematics Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics 2017
Inventing the Circle
The geometrical beauty of plants
Universal Natural Shapes
Journals
A generic geometric transformation that unifies a wide range of natural and abstract shapes
Diatom frustule morphogenesis and function: a multidisciplinary survey
Somatic embryogenesis from mature Bambusa balcooa Roxburgh as basis for mass production of elite forestry bamboos
Tissue culture strategies for genetic improvement of bamboo
Computer implemented tool box systems and methods
Superquadrics with rational and irrational symmetry
Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant
A general leaf area geometric formula exists for plants—Evidence from the simplified Gielis equation
References
External links
Genicap, Johan Gieli's homepage
P. Bou
|
https://en.wikipedia.org/wiki/Results%20of%20the%202022%20Danish%20general%20election%20in%20Denmark
|
This is a list of the results in the 2022 Danish general election in Denmark. The results are as found on the official website dedicated to the results made by Statistics Denmark.
Denmark
Vote share by electoral division
Vote share by constituency
Vote share by nomination district
Vote share by region
Vote share by Municipality
References
2022
Denmark
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https://en.wikipedia.org/wiki/Susan%20Hilsenbeck
|
Susan Galloway Hilsenbeck is an American biostatistician whose research interests include biomarkers and the applications of biostatistics in cancer research. She is a professor in the Baylor College of Medicine, where she directs the Quantitative Sciences Share Resource in the Dan L. Duncan Comprehensive Cancer Center.
Hilsenbeck earned her Ph.D. in 1990, at the University of Miami. Her dissertation, Acquisition and use of information on data quality in large population-based tumor registries, was supervised by Charles Kurucz. She was elected as a Fellow of the American Statistical Association in 2011.
Her hobbies include scuba diving and quilting. Her quilts have been featured in the books Amish Quilts, The Adventure Continues (2013) and Quarantine Quilts: Creativity in the Midst of Chaos (2021).
References
External links
Hilsenbeck's quilting blog
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
Biostatisticians
Baylor College of Medicine faculty
Fellows of the American Statistical Association
American quilters
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https://en.wikipedia.org/wiki/Chambolle-Pock%20algorithm
|
In mathematics, the Chambolle-Pock algorithm is an algorithm used to solve convex optimization problems. It was introduced by Antonin Chambolle and Thomas Pock in 2011 and has since become a widely used method in various fields, including image processing, computer vision, and signal processing.
The Chambolle-Pock algorithm is specifically designed to efficiently solve convex optimization problems that involve the minimization of a non-smooth cost function composed of a data fidelity term and a regularization term. This is a typical configuration that commonly arises in ill-posed imaging inverse problems such as image reconstruction, denoising and inpainting.
The algorithm is based on a primal-dual formulation, which allows for simultaneous updates of primal and dual variables. By employing the proximal operator, the Chambolle-Pock algorithm efficiently handles non-smooth and non-convex regularization terms, such as the total variation, specific in imaging framework.
Problem statement
Let be two real vector spaces equipped with an inner product and a norm . From up to now, a function is called simple if its proximal operator has a closed-form representation or can be accurately computed, for , where is referred to
Consider the following constrained primal problem:
where is a bounded linear operator, are convex, lower semicontinuous and simple.
The minimization problem has its dual corresponding problem as
where and are the dual map of and , respectively.
Assume that the primal and the dual problems have at least a solution , that means they satisfies
where and are the subgradient of the convex functions and , respectively.
The Chambolle-Pock algorithm solves the so-called saddle-point problem
which is a primal-dual formulation of the nonlinear primal and dual problems stated before.
Algorithm
The Chambolle-Pock algorithm primarily involves iteratively alternating between ascending in the dual variable and descending in the primal variable using a gradient-like approach, with step sizes and respectively, in order to simultaneously solve the primal and the dual problem. Furthermore, an over-relaxation technique is employed for the primal variable with the parameter .
stopping criterion.
end do
Chambolle and Pock proved that the algorithm converges if and , sequentially and with as rate of convergence for the primal-dual gap. This has been extended by S. Banert et al. to hold whenever and .
The semi-implicit Arrow-Hurwicz method coincides with the particular choice of in the Chambolle-Pock algorithm.
Acceleration
There are special cases in which the rate of convergence has a theoretical speed up. In fact, if , respectively , is uniformly convex then , respectively , has a Lipschitz continuous gradient. Then, the rate of convergence can be improved to , providing a slightly changes in the Chambolle-Pock algorithm. It leads to an accelerated version of the method and it consists in c
|
https://en.wikipedia.org/wiki/Pavel%20Povinec
|
Pavel P. Povinec (born 1942) is Professor of Physics at Faculty of Mathematics, Physics and Informatics of the Comenius University in Bratislava (Slovakia). Head of the Centre for Nuclear and Accelerator Technologies (CENTA)
Education and career
He was educated at the Faculty of Natural Sciences of the Comenius University in Bratislava, where in 1965 he obtained a master degree in physics (specialization Nuclear physics), a PhD in 1974 for development of gas proportional counters, and in 1984 he became full Professor of Physics. In 1980 he became Vice-Dean at the newly established Faculty of Mathematics and Physics of the Comenius University, where in 1981 he became Head of the Department of Nuclear Physics. In 1993 he moved to International Atomic Energy Agency’s (IAEA) Marine Environment Laboratories in Monaco, where he became Head of Radiometrics Laboratory
In 2005, after retiring from IAEA, he returned to his home, Comenius University, to continue his research on investigations of rare nuclear processes and environmental radioactivity. After successful applications for EU Structural funds, he established in 2013 the CENTA with a tandem accelerator of ions and ion beam analysis (IBA) lines, which was fully equipped in 2022 with accelerator mass spectrometry (AMS) line.
P. Povinec is distinguished for his contributions to the development of ultrasensitive techniques for radioactivity research (gas proportional counters, low-level gamma spectrometry, mass spectrometry), with applications in nuclear physics (rare nuclear processes and decays), in astrophysics (search for dark matter particles, radioactivity of meteorites), environmental physics (radioactivity of the atmosphere, impacts of nuclear power plants on the environment (including Chernobyl and Fukushima accidents), climate change studies), isotope oceanography (isotope tracing of processes in the marine environment, assessment of impacts of radioactive dumping sites and nuclear bomb test sites on the marine environment), and radiocarbon dating (archeological objects, food products, etc.). He was leading more than 20 international projects (IAEA, EC, STA Japan, FAO, UNESCO), and he has also been responsible for Slovak participation in international experiments (SuperNEMO, LEGEND, and CRESST). According to SCOPUS he published about 400 papers with more than 10,000 citations (Hirsch index h = 50).
He was a member of the EU, IAEA, Japan, and South Korea pannels on the assessment of the Fukushima accident. He has also been active in the organization of international conferences, and recently he established a new series of conferences on environmental radioactivity (ENVIRA). He participated in an organization of about 50 international conferences, and delivered about 40 invited lectures. He has been a member of editorial boards of several scientific journals (Scientific Reports/Nature, Radiocarbon, Journal of Environmental Radioactivity, Journal of Radioanalytical and Nuclear Chemistry, e
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https://en.wikipedia.org/wiki/Glenn%20McConnell%20%28footballer%29
|
Glenn McConnell (born 26 April 2005) is an Irish professional footballer currently playing as a forward for Cambridge United.
Career statistics
Club
.
Notes
References
2005 births
Living people
Men's association football forwards
Cambridge United F.C. players
St Albans City F.C. players
Republic of Ireland men's association footballers
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https://en.wikipedia.org/wiki/Dawn%20C.%20Porter
|
Dawn Cheree Porter is an American expert on business statistics, business analytics, and econometrics, known for her textbooks on these subjects. She is professor of clinical data sciences and operations management in the USC Marshall School of Business, where she directs the master's degree program in business analytics and holds the Fubon Teaching Chair in Business Administration.
Education and career
Porter majored in mathematics at Cornell University, and then went to the New York University Stern School of Business for a master's degree and Ph.D. in statistics.
She worked as an assistant professor at Georgetown University from 2001 to 2006, before moving to the University of Southern California, as assistant professor of clinical data sciences in the USC Marshall School of Business. She was promoted to associate professor in 2011 and full professor in 2017. She has directed the master's program in business analytics under different names since 2013. At USC, she holds the Fubon Teaching Chair in Business Administration. She was recognized by a Marshall Teaching Excellence Award in 2023.
Books
Porter is a coauthor or major contributor to textbooks including:
Basic Econometrics (with Damodar N. Gujarati, 5th ed., McGraw-Hill, 2009)
Essentials of Econometrics (with Damodar N. Gujarati, McGraw-Hill, 2009)
Essentials of Business Statistics (with Richard O'Connell, J. Burdeane Orris, and Bruce Bowerman, 2nd ed., McGraw-Hill, 2007)
Business Statistics and Analytics in Practice (with Bruce L. Bowerman, Richard O'Connell, Richard T. O'Connell, Emily S. Murphree, and Steven C. Huchendorf, 9th ed., McGraw-Hill, 2018)
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
American economists
American women economists
Econometricians
Cornell University alumni
New York University Stern School of Business alumni
University of Southern California faculty
|
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Liverpool%20F.C.%20season
|
The 1941–42 season saw Liverpool compete in the wartime North Regional League. Some matches were also part of the League War Cup and the Lancashire Senior Cup.
Statistics
Appearances and Goals
|}
Competitions
North Region War League, League War Cup and Lancashire Senior Cup
References
LFC History.net – 1941–42 season
11v11
Soccer At War 1939-45 by Jack Rollin ISBN 9780755314317
Liverpool F.C. seasons
Liverpool
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https://en.wikipedia.org/wiki/Ruan%20Ribeiro
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Ruan Ribeiro Rodrigues (born 15 August 2003), known as Ruan Ribeiro, is a Brazilian footballer who plays as a forward for Valmiera, on loan from Palmeiras.
Career statistics
References
Valmiera FC players
Latvian Higher League players
Expatriate men's footballers in Latvia
2003 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
Sociedade Esportiva Palmeiras players
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https://en.wikipedia.org/wiki/Ludvig%20Sylow
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Peter Ludvig Meidell Sylow () (12 December 1832 – 7 September 1918) was a Norwegian mathematician who proved foundational results in group theory.
Sylow processed and further developed the innovative works of mathematicians Niels Henrik Abel and Évariste Galois in algebra. Sylow theorems and p-groups, known as Sylow subgroups, are fundamental in finite groups. By profession, Sylow was a teacher at the Frederiksborg Latin School for 40 years from 1858 to 1898, and then a professor at the University of Oslo for 20 years from 1898 to 1918. Despite the isolation in Frederiksborg, Sylow was an active member of the mathematical world. He wrote a total of approximately 25 mathematical and biographical works, corresponded with many of the leading mathematicians of the time, and was an able co-editor of Acta Mathematica from the journal's start in 1882. He was also elected into the Norwegian Academy of Science and Letters in 1868, a corresponding member of the Academy of Sciences in Göttingen and the University of Copenhagen awarded him an honorary doctorate in 1894.
Early life
Ludvig Sylow was born in Kristiania (now Oslo) on 12 December 1832 to later minister and customs treasurer Thomas Edvard von Westen Sylow (1792–1875) and Magdalene Cecilie Cathrine Mejdell (1806–98). His father had been an officer and a captain in the cavalry, and later he served as the head of the Ministry of the Army between 1848 and 1854.
Initially, his father was aware of his son's talent in Mathematics, so he encouraged him to work independently. From home, Sylow learned a sense of duty and hard work, but was also taught to be modest and although this was done with the best of intentions, it would become an obstacle for him later in life since it meant that he was happy to spend many years in a more lowly position than he should have had.
Career as a mathematician
Education and first steps in mathematics
Sylow attended Christiania Cathedral School, graduating in 1850 after taking the examen artium. He then became a student at the University of Oslo where he began his studies of natural sciences. In 1853, the University of Oslo awarded him the Crown Prince's gold medal (Kronprinsens gullmedalje) for a Mathematics subject about Gnomonics. In 1856 he took the high school mathematics teacher's examination (Realkankidat, Norwish to Real candidate) with excellent grades.
He completed his graduation in 1856, but since no university post was available, he taught for two years at Hartvig Nissen School, an independent girls' school in the Uranienborg district of Christiania, which had been founded by Hartvig Nissen and Ole Jacob Broch. His years there came during Broch's most energetic university period, and it was Broch who introduced Sylow to Carl Gustav Jacob Jacobi's fundamental work on elliptic functions, among other things.
In 1858, Sylow moved to the town of Fredrikshald (now called Halden) in Ostfold county, where he taught at Frederiksborg Latin School as the Head Teache
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https://en.wikipedia.org/wiki/Census%20of%20Ireland
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The census of Ireland is held on a quinquennial basis by the Central Statistics Office to determine the population of the Republic of Ireland. The most recent census was held in 2022.
Dates of census
Sunday, 18 April 1926
Sunday, 26 April 1936
Sunday, 12 May 1946
Sunday, 8 April 1951
Sunday, 8 April 1956
Sunday, 9 April 1961
Sunday, 17 April 1966
Sunday, 18 April 1971
Sunday, 1 April 1979
Sunday, 5 April 1981
Sunday, 13 April 1986
Sunday, 21 April 1991
Sunday, 28 April 1996
Sunday, 28 April 2002
Sunday, 23 April 2006
Sunday, 10 April 2011
Sunday, 24 April 2016
Sunday, 3 April 2022
Political geography
Under Article 16 of the Constitution of Ireland, revisions of Dáil constituencies by the Oireachtas are required at a minimum every 12 years. However, they must also have due regard to changes in the population. Under the Electoral Reform Act 2022, the Electoral Commission is required to conduct a review of constituency boundaries after every census. From 1997 up to the establishment of the Electoral Commission in 2023, this function was carried out by a Constituency Commission created for this function.
Urban geography
From 1971 to 2006, census towns were "defined as a cluster of 50 or more occupied dwellings where, within a radius of 800 metres, there was a nucleus of 30 occupied dwellings". From 2016, a new census settlement was defined "as a minimum of 50 occupied dwellings, with a maximum distance between any dwelling and the building closest to it of 100 metres, accompanied by evidence of an urban centre". For the 2022 census, the CSO developed a new urban geography term the Built Up Area (BUA) to define urban areas.
References
External links
Census page on the CSO website
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https://en.wikipedia.org/wiki/Craig%20S.%20Kaplan
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Craig S. Kaplan is a Canadian computer scientist, mathematician, and mathematical artist. He is an editor of the Journal of Mathematics and the Arts (formerly chief editor), and an organizer of the Bridges Conference on mathematics and art. He is an associate professor of computer science at the University of Waterloo, Canada.
Kaplan's work primarily focuses on applications of geometry and computer science to visual art and design. He was part of the team that proved that the tile discovered by hobbyist David Smith is a solution to the einstein problem, a single shape which aperiodically tiles the plane but cannot do so periodically.
Education
Kaplan received BMath from the University of Waterloo in 1996. He further went on to receive MSc and PhD in computer science from University of Washington in 1998 and 2002, respectively.
Work
Kaplan's research work focuses on the application of computer graphics and mathematics in art and design. He is an expert on computational applications of tiling theory.
Exotic geometries in protein assembly
In 2019, Kaplan helped to apply the concepts of Archimedean solids to protein assembly, and together with an experimental team at RIKEN demonstrated that these exotic geometries lead to ultra-stable macromolecular cages. These new systems could have applications in targeted drug delivery systems or the design of new materials at the nanoscale.
Einstein problem
In 2023, Kaplan was part of the team that solved the einstein problem, a major open problem in tiling theory and Euclidean geometry. The problem is to find an "aperiodic monotile", a single geometric shape which can tesselate the plane aperiodically (without translational symmetry) but which cannot do so periodically. The discovery is under professional review and, upon confirmation, will be credited as solving a longstanding mathematical problem.
In 2022, hobbyist David Smith discovered a shape constructed by gluing together eight kites (each a sixth of a hexagon) which seemed from Smith's experiments to tile the plane but would no do so periodically. He contacted Kaplan for help analyzing the shape, which the two named the "hat". After Kaplan's computational tools also found the tiling to continue indefinitely, Kaplan and Smith recruited two other mathematicians, Joseph Samuel Myers and Chaim Goodman-Strauss to help prove they had found an aperiodic monotile. Smith also found a second tile, dubbed the "turtle", which seemed to have the same properties. In March 2023, the team of four announced their proof that the tiles discovered by David Smith, as well as an infinite family of other tiles interpolating the two, are aperiodic monotiles.
Both the hat and turtle tiles require some reflected copies to tile the plane. After the initial preprint, Smith noticed that a tile related to the hat tile could tile the plane either periodically or aperiodically, with the aperiodic tiling not requiring reflections. A suitable manipulation of the edge prevent
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https://en.wikipedia.org/wiki/Carl-Erik%20Sj%C3%B6stedt
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Carl-Erik Sjöstedt (born 1900, died 1979) was a Swedish mathematician, teacher, and philosopher. Sjöstedt focused much of his work on the teaching of mathematics in the Swedish curriculum, especially in the fields of geometry and logic. Sjöstedt was a follower of the Swedish philosopher Adolf Phalén, and a supporter of Uppsala philosophy. He also was a speaker and author in the constructed language Interlingue, founding a national association for the language in 1928.
Education
Sjöstedt was born on 31 July 1900 to foreman Karl August Sjöstedt and Matilda Åström in Eskilstuna parish, Södermanland County, Sweden. He began his education in the city, graduating in 1919. Sjöstedt would complete the rest of his education at Uppsala University, gaining a Bachelor of Arts () in 1921, a licentiate in 1927, and becoming a Doctor of Philosophy in 1930. His thesis for the latter was defended in 1929 and was on the subject of geometry.
During his research, Sjöstedt met philosopher Adolf Phalén, who would remain a friend of Sjöstedt's and influence his philosophical theories; Sjöstedt presented Phalén with a dissertation on the epistemology of geometry, which would be factored into a memorial to him in 1937. During the 1930s, Phalén, along with a group of other philosophers including Sjöstedt held private meetings to discuss the place of philosophy as a subject within the education system of Sweden. After Phalén's death, Sjöstedt collected much of Phalén's unfinished and unpublished work, mainly concerning the history of the theory of knowledge, and published it under the title Mindre Arbeten (Minor Works).
Throughout his life, like Phalén, Sjöstedt was a proponent of (Uppsala philosophy), countering opposing philosophies such as those of Hans Larsson.
Career
Sjöstedt worked as a teacher for much of his career, teaching at various private school until 1931, before lecturing in mathematics at the (then the Högre allmänna läroverket i Östersund; Higher General Education Agency in Östersund). In 1939, Sjöstedt acted as headmaster at the (form of Swedish secondary school, similar to a gymnasium) in Borås, Västergötland. After this, Sjöstedt was (counsel of pedagogy) of the (former Swedish Board of Education) from 1940 until 1962.
Sjöstedt was an opponent of the 1950s movement to introduce somprehensive schools, calling the movement "an educational utopia of colossal proportions"; his opposition was successful, as the 1962 Education Act replaced Sweden's previous schooling system which he had supported. Sjöstedt later lead an inquiry into the role of vocational schools, supporting them as a default, as opposed to Upper Secondary Schools, but later resigned from the position.
Works
Sjöstedt wrote several textbooks about geometry, publishing courses for high schools in 1936 and 1938, as well as a series of other textbooks through the 1950s. Sjöstedt also wrote for the Swedish journal Natur & Kultur from 1947. Aside from these, Sjöstedt also published
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https://en.wikipedia.org/wiki/Complete%20orthogonal%20decomposition
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In linear algebra, the complete orthogonal decompositon is a matrix decomposition. It is similar to the singular value decomposition, but typically somewhat cheaper to compute and in particular much cheaper and easier to update when the original matrix is slightly altered.
Specifically, the complete orthogonal decomposition factorizes an arbitrary complex matrix into a product of three matrices, , where and are unitary matrices and is a triangular matrix. For a matrix of rank , the triangular matrix can be chosen such that only its top-left block is nonzero, making the decomposition rank-revealing.
For a matrix of size , assuming , the complete ortogonal decomposition requires floating point operations and auxiliary memory to compute, similar to other rank-revealing decompositions. Crucially however, if a row/column is added or removed or the matrix is perturbed by a rank-one matrix, its decomposition can be updated in operations.
Because of its form, , the decomposition is also known as UTV decomposition. Depending on whether a left-triangular or right-triangular matrix is used in place of , it is also referred to as ULV decomposition or URV decomposition, respectively.
Construction
The UTV decomposition is usually computed by means of a pair of QR decompositions: one QR decomposition is applied to the matrix from the left, which yields , another applied from the right, which yields , which "sandwiches" triangular matrix in the middle.
Let be a matrix of rank . One first performs a QR decomposition with column pivoting:
,
where is a permutation matrix, is a unitary matrix, is a upper triangular matrix and is a matrix. One then performs another QR decomposition on the adjoint of :
,
where is a unitary matrix and is an lower (left) triangular matrix. Setting yields the complete orthogonal (UTV) decomposition:
.
Since any diagonal matrix is by construction triangular, the singular value decomposition, , where , is a special case of the UTV decomposition. Computing the SVD is slightly more expensive than the UTV decomposition, but has a stronger rank-revealing property.
See also
Rank-revealing QR decomposition
Schur decomposition
Online machine learning
References
Matrix decompositions
Numerical linear algebra
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https://en.wikipedia.org/wiki/Carlos%20Benjamin%20de%20Lyra
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Carlos Benjamin de Lyra (Pernambuco, 23 November 1927 – São Paulo, 21 July 1974) was a prominent Brazilian mathematician, a pioneer in algebraic topology in Brazil and professor at the University of São Paulo.
Born in Recife, Pernambuco, he came from a family of sugarcane plantation owners and his dad was the owner of the Diário de Pernambuco, a newspaper that was known nationwide. Lyra was an important mathematician in his area, his course Introdução à Topologia Algébrica was taught in the first Colóquio Brasileiro de Matemática and would become the first text in this field written in Brazilian Portuguese.
After the death of his father, his mother married a Wall Street stockbroker and, together, the couple moved to New York City with Lyra and his younger brother. When he was 15, in the suburbs of the city where he lived, he met Richard Courant. The founder of the presently named Courant Institute of Mathematical Sciences was responsible for inspiring de Lyra to study mathematics.
Lyra made a substantial career for himself throughout his life. Beginning as associate professor at the University of São Paulo alongside Elza Gomide, he helped to organize and administrate a course in the 1° Colóquio Brasileiro de Matemática, he became a doctor in Mathematics with his thesis Sobre os espaços de mesmo tipo de homotopia que o dos poliedros, he was one of the founders of the Sociedade Brasileira de Matemática, he was involved in the creation of the Instituto de Matemática e Estatística at the University of São Paulo (IME-USP), taught as a professor in a variety of courses, and participated in the restructuring of the undergraduate and postgraduate courses in Mathematics at the University of São Paulo.
On the 21st of July 1974, Carlos Benjamin de Lyra died due to a brain tumour. His thesis H-equivalencia de grupos topológicos, was revised and published by his friend Peter Hilton. In his honor, the library at the IME-USP bears his name, along with a road in the Chácara São João neighbourhood, in the capital of São Paulo.
Early life
Early years and education
Carlos Benjamin de Lyra was born in the city of Recife in Pernambuco on the 23rd of November 1927. His parents were Carlos de Lyra Filho, a sugarcane plantation owner and owner of the Pernambuco Daily newspaper which received a lot of national attention, and Elizabeth Lau de Lyra, a German woman that came to Brazil with her family. The marriage between them was arranged due to how close the two families were in business and faith. Carlos de Lyra Filho came from an earlier marriage, where he had five sons, where after the death of his first wife he remarried with Elizabeth, where they had two children: Carlos and George.
Carlos Benjamin de Lyra's father died when he was 9 years old. Widowed, his mother married Paul Nortz, a stockbroker at Wall Street. Together, the family, including the children, moved to New York City.
Lyra did not go to school during his early years, he was instead home schoole
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https://en.wikipedia.org/wiki/2004%E2%80%9305%20PFC%20CSKA%20Sofia%20season
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The 2004–05 season was PFC CSKA Sofia's 57th consecutive season in A Group.
Below is a list of player statistics and all matches (official and friendly) that the club played during the 2004–05 season.
Squad
Source:
Competitions
A Group
Table
Results summary
Results by round
Fixtures and results
Bulgarian Cup
UEFA Cup
Second qualifying round
First round
References
External links
CSKA Official Site
CSKA Fan Page with up-to-date information
Bulgarian A Professional Football Group Site
PFC CSKA Sofia seasons
Cska Sofia
Bulgarian football championship-winning seasons
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https://en.wikipedia.org/wiki/Kato%27s%20inequality
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In functional analysis, a subfield of mathematics, Kato's inequality is a distributional inequality for the Laplace operator or certain elliptic operators. It was proven in 1972 by the Japanese mathematician Tosio Kato.
The original inequality is for some degenerate elliptic operators. This article treats the special (but important) case for the Laplace operator.
Inequality for the Laplace operator
Let be a bounded and open set, and such that . Then the following holds
in ,
where
is the space of locally integrable functions – i.e., functions that are integrable on every compact subset of their domains of definition.
Remarks
Sometimes the inequality is stated in the form
in
where and is the indicator function.
If is continuous in then
in .
Literature
References
functional analysis
Inequalities
Differential operators
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https://en.wikipedia.org/wiki/2023%E2%80%9324%20PFC%20Ludogorets%20Razgrad%20season
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The 2023–24 season is Ludogorets Razgrad's thirteenth consecutive season in the First League, of which they are defending champions. This article shows player statistics and all matches (official and friendly) that the club has played during the season.
Players
First-team squad
Out on loan
Reserve team
Other players under contract
Transfers
In
Out
Pre-season and friendlies
Competitions
First League
Regular stage
League table
Results summary
Results by round
Results
The league fixtures were unveiled on 14 June 2023.
Bulgarian Cup
Bulgarian Supercup
UEFA Champions League
Qualifying rounds
UEFA Europa League
Qualifying rounds
UEFA Europa Conference League
Group stage
Squad statistics
Appearances and goals
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|colspan="18"|Players from the reserve team:
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|colspan="18"|Players away on loan:
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|colspan="18"|Players that left during the season:
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Goalscorers
Clean sheets
Disciplinary record
References
Notes
External links
PFC Ludogorets Razgrad seasons
Ludogorets Razgrad
Ludogorets Razgrad
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https://en.wikipedia.org/wiki/List%20of%20Hartlepool%20United%20F.C.%20records%20and%20statistics
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Hartlepool United Football Club is a professional association football club based in Hartlepool, County Durham, England. The club will compete in the National League from the 2023–24 season, following relegation from EFL League Two the previous season.
They were founded in 1908 as Hartlepools United Football Athletic Company. West Hartlepool won the FA Amateur Cup in 1905 and after the club was dissolved in 1910 its assets and liabilities were subsequently taken over by Hartlepools United, who were then playing in the North Eastern League. Hartlepools United were elected into the Football League in 1921 and would spend the next 37 years in the Third Division North, at which point they were placed into the Fourth Division. In 1968, the s and the United of the club's name were removed due to the merger of West Hartlepool with the town of Hartlepool and the village of Hart - forming the new borough of Hartlepool. The club won promotion in 1967–68 for the first time, though were relegated out of the Third Division the following season. In 1977, the United was added back to the team's name. They won another promotion in 1990–91, though were relegated in 1993–94. They won further promotions out of the fourth tier in 2002–03 and 2006–07, having been relegated again in 2005–06 after losing the 2005 League One play-off final to Sheffield Wednesday in the previous season. Hartlepool were relegated again in 2012–13 and ended their 96-year run in the Football League with relegation into the National League in 2016–17. Hartlepool achieved promotion back to the Football League in 2020–21, beating Torquay United in the 2021 National League play-off final. However, Hartlepool returned to the National League after two seasons following relegation in 2022–23.
This list encompasses the major honours won by Hartlepool United, and records set by the club, its players and its managers. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Hartlepool players on the international stage. Attendance records are also included.
All figures are correct as of the match played on 28 October 2023.
Honours and achievements
Hartlepool United's honours include the following:
League
Third Division North / League One (level 3)
Runners-up: 1956–57
Play-off runners-up: 2005
Fourth Division / League Two (level 4)
Runners-up: 2002–03, 2006–07
Promoted: 1967–68, 1990–91
National League (level 5)
Play-off winners: 2021
Cup
FA Amateur Cup
Winners: 1904–05
Durham Challenge Cup
Winners: 1908–09, 1909–10, 1956–57, 1957–58, 2004–05
Runners-up: 1997–98
Reserves & Youth
Division One East League
Champions: 2003–04, 2007–08
Runners-up: 2016–17
FL Youth Alliance
Champions: 2002–03
Dallas Cup U19
Winners: 2003–04
Third place: 2004–05
Best performances
As of the end of the 2022–23 season
Best FA Cup performance: Fourth round, 1954–55, 1977–78, 1988–89, 1992–
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https://en.wikipedia.org/wiki/Jink%C5%8Dki
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Jinkōki (, じんこうき, , Permanent Mathematics) is a three-volume work on Japanese mathematics, first edited and published by Yoshida Mitsuyoshi in 1627. Over his lifetime, Mitsuyoshi revised Jinkōki several times. The edition released in the eleventh year of the Kan'ei era (1641) became particularly widespread. The last version personally published by Mitsuyoshi was the Idai (), which came out in the eighteenth year of the Kan'ei (1634). Subsequent to that, various editions of Jinkōki were released, one of which includes Shinpen Jinkōki ().
The Jinkouki is partly based on the works of Yuan dynasty mathematicians in China.
The Jinkouki is also one of the most popular and influential Japanese mathematics books in history, having influenced many later Japanese mathematicians such as Seki Takakazu and Kaibara Ekken.
Etymology
In Chinese, the characters 塵劫記 () literally mean "dust tribulation record", where 劫 can mean a calamity or kalpa (a unit of time in Buddhism). In Buddhism, one aeon or kalpa (劫) is related to the age of the universe. Then in Chinese, the phrase 塵劫 / 尘劫 means an infinite, boundless kalpa. Thus in the Jinkouki, the 塵劫 is translated as "permanence". Later on 尘劫 has also been taken to refer to the calamities and tribulations of the mortal world (尘世).
The name 尘劫记 is derived from the 尘点劫 of the Buddhist Lotus Sutra (法华经 in the Chinese translation).
Contents
The book contained instructions for dividing and multiplying with a soroban and mathematical problems relevant to merchants and craftsmen. The book also contained several interesting mathematical problems, and was the first Japanese book to use printing in colour. As a result, the Jinkōki became the most popular Japanese mathematics book ever and one of the most widely read books of the Edo period. Mitsuyoshi made reference to everyday problems, such as buying and selling rice.
The book was originally published in three volumes, the first of which mainly describes multiplication and division using the soroban. The second and third volumes include an assortment of practical and recreational problems. The included problems are not arranged according to any specific order.
The book includes ideas that aimed to keep readers from boredom by adopting a wide variety of problems such as calculations of areas of rice fields, problems related to the construction of rivers and riverbanks, geometric progression, and the Josephus problem. The Shinpen Jinkōki was the most widespread version among the copies of Jinkōki, and widely used as a textbook for use of the soroban throughout the Edo period.
In addition to fundamental knowledge such as numerical notation, units, and multiplication tables, it also included slightly more specialised topics, such as methods to find square roots and cube roots, practical calculations of area, currency conversion, and interest calculation. The content covers almost all arithmetic needed in daily life at that time, and it is a characteristic of the book
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https://en.wikipedia.org/wiki/Aubrey%20E.%20Landry
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Aubrey Edward Landry (1880–1972) was a Canadian-American mathematician. He was the dissertation director of many of the earliest women to earn doctorates in mathematics in the United States, including the first African American woman, Euphemia Haynes.
Early life and education
He was born in Westmorland, New Brunswick, to Elizabeth R. "Eliza" McSweeney Landry and Tilman T. Landry, and was the oldest of nine children. He received an AB degree (bachelor's) from Harvard University in 1900, a PhD at The Johns Hopkins University in 1907 with the dissertation: "A Geometrical Application of Binary Syzygies" under Frank Morley.
Career and mentorship of women
Landry's dissertation director was Frank Morley, himself also a frequent advisor to women doctoral candidates (see inset quote below). Landry spent his career at Catholic University of America, where he began as a teaching fellow following his grad
uation from Harvard. He joined the permanent faculty after receiving his doctorate at Johns Hopkins. He directed 28 dissertations until his retirement in 1952, out of which 18 went to women. Lenore Blum writes,
All but two of these women were Roman Catholic sisters, a historical phenomenon nationwide because Catholic men's universities were sometimes open by special arrangement to nuns.
Notable women mentored
This list is incomplete, as Landry directed the dissertations of at least 18 women. Some of these come from the Mathematics Genealogy Project, and others from Pioneering Women in American Mathematics.
Mary Nicholas Arnoldy, Ph.D. 1937, Dissertation: "The Reality of the Double Tangents of the Rational Symmetric Quartic Curve."
Leonarda Burke, Ph.D. 1931, Dissertation: "On a case of the triangles in-and-circumscribed to a rational quartic curve with a line of symmetry."
Mary Charlotte Fowler, Ph.D. 1937, Dissertation: "The discriminant of the sextic of double point parameters of the plane rational quartic curve."
Catharine Francis Galvin, Ph.D. 1938, Dissertation: "Two Geometrical Representations of the Symmetric Correspondence C(N,N) with Their Interrelations."
Mary de Lellis Gough, Ph.D. 1931, first known Irish woman to earn a doctorate in mathematics. Dissertation: "On the Condition for the Existence of Triangles In-and-Circumscribed to Certain Types of Rational Quartic Curve and Having a Common Side."
Euphemia Haynes, Ph.D. 1943, Dissertation: "Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences."
Mary Laetitia Hill, Ph.D. 1935, Dissertation: "The Number and Reality of Quadrilaterals In-and-Circumscribed to a Rational Unicuspidal Quartic with Real Tangents from the Cusp."
Mary Gervase Kelley, Ph.D. 1917, Dissertation: "On the Cardioids Fulfilling Certain Assigned Conditions."
Marie Cecilia Mangold, Ph.D. 1929, Dissertation: "The Loci Described by the Vertices of Singly Infinite Systems of Triangles Circumscribed about a Fixed Conic."
Charles Mary Morrison, Ph.D. 1931, Diss
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https://en.wikipedia.org/wiki/Projection%20filters
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Projection filters are a set of algorithms based on stochastic analysis and information geometry, or the differential geometric approach to statistics, used to find approximate solutions for filtering problems for nonlinear state-space systems.
The filtering problem consists of estimating the unobserved signal of a random dynamical system from partial noisy observations of the signal. The objective is computing the probability distribution of the signal conditional on the history of the noise-perturbed observations. This distribution allows for calculations of all statistics of the signal given the history of observations. If this distribution has a density, the density satisfies specific stochastic partial differential equations (SPDEs) called Kushner-Stratonovich equation, or Zakai equation.
It is known that the nonlinear filter density evolves in an infinite dimensional function space.
One can choose a finite dimensional family of probability densities, for example Gaussian densities, Gaussian mixtures, or exponential families, on which the infinite-dimensional filter density can be approximated. The basic idea of the projection filter is to use a geometric structure in the chosen spaces of densities to project the infinite dimensional SPDE of the optimal filter onto the chosen finite dimensional family, obtaining a finite dimensional stochastic differential equation (SDE) for the parameter of the density in the finite dimensional family that approximates the full filter evolution. To do this, the chosen finite dimensional family is equipped with a manifold structure as in information geometry.
The projection filter was tested against the optimal filter for the cubic sensor problem. The projection filter could track effectively bimodal densities of the optimal filter that would have been difficult to approximate with standard algorithms like the extended Kalman filter.
Projection filters are ideal for in-line estimation, as they are quick to implement and run efficiently in time, providing a finite dimensional SDE for the parameter that can be implemented efficiently.
Projection filters are also flexible, as they allow fine tuning the precision of the approximation by choosing richer approximating families, and some exponential families make the correction step in the projection filtering algorithm exact. Some formulations coincide with heuristic based assumed density filters or with Galerkin methods. Projection filters can also approximate the full infinite-dimensional filter in an optimal way, beyond the optimal approximation of the SPDE coefficients alone, according to precise criteria such as mean square minimization. Projection filters have been studied by the Swedish Defense Research Agency and have also been successfully applied to a variety of fields including navigation, ocean dynamics, quantum optics and quantum systems, estimation of fiber diameters, estimation of chaotic time series, change point detection and other areas.
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https://en.wikipedia.org/wiki/Beatriz%20Haddad%20Maia%20career%20statistics
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This is a list of the main career statistics of professional Brazilian tennis player Beatriz Haddad Maia.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 WTA Elite Trophy.
Doubles
Current through the 2023 Wimbledon Championships.
Significant finals
Grand Slam tournaments
Doubles: 1 (runner-up)
WTA 1000 tournaments
Singles: 1 (runner-up)
Doubles: 3 (1 title, 2 runner-ups)
WTA Elite Trophy
Singles: 1 (title)
Doubles: 1 (title)
WTA Tour finals
Singles: 5 (3 titles, 2 runner-ups)
Doubles: 9 (6 titles, 3 runner-ups)
WTA Challenger finals
Singles: 2 (1 title, 1 runner-up)
Doubles: 1 (title)
ITF Circuit finals
Singles: 25 (17 titles, 8 runner–ups)
Doubles: 15 (9 titles, 6 runner–ups)
Junior career
Grand Slam tournament finals
Girls' doubles: 2 runner–ups
WTA Tour career earnings
Current through the 2022 Tallinn Open.
Career Grand Slam statistics
Seedings
The tournaments won by Haddad Maia are in boldface, and advanced into finals by Haddad Maia are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner-ups are in italics.
Head-to-head records
No. 1 wins
Record against top 10 players
She has a record against players who were, at the time the match was played, ranked in the top 10.
Double bagel matches
Longest winning streak
12 matches (2022)
Notes
References
Haddad Maia, Beatriz
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https://en.wikipedia.org/wiki/T.%20B.%20Dinesh
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T. B. Dinesh is an Indian computer scientist and media activist. He started his research with generating software based on algebraic specification and later focused on web 2.0, web accessibility, web annotation, hypermedia and mesh networking. In 1999, he co-founded the Pagelets project, and in 2002, he founded [Janastu.org Janastu] in Bangalore, a non-profit where he serves as technical director, and a company called Servelots, both serving non-profits with free and open-source software and developing ways for re-narration of the web with web accessibility for the print-impaired. He has studied and built community-based digital tools such as SWeeT Web, Alipi, Pantoto, CoLRN and Papad.
Life and career
Dinesh was born in Tumkur. He studied electronics and communication engineering. Dinesh studied mathematics and computer science at University of Iowa for his postgraduate program, and finished his Doctor of Philosophy in computer science in 1992, researching on generating software based on algebraic expression. He later continued his post-doctoral research at Centrum voor Wiskunde en Informatica where he had earlier worked for a doctoral project. He then worked at the Stanford Research Institute, where he co-founded the Pagelets project in 1999 along with Susan Uskudarli and Lambert Meertens. He moved to Bangalore in 2002 and built a participatory information resource creation and management system called Pantoto and founded Janastu in 2002.
References
Indian computer scientists
Year of birth missing (living people)
Living people
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https://en.wikipedia.org/wiki/Cisoidal
|
Cisoidal may refer to:
Cisoidal (mathematics), a term used in mathematics related to
Cisoidal (chemistry), a term used in chemistry concerning the spatial arrangement of atoms within molecules
See also
Cisoid (disambiguation)
Cissoid
Cosinusoidal
Sinusoidal
Transoidal
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https://en.wikipedia.org/wiki/David%20DeMets
|
David L. DeMets (born 27 November 1944) is an American biostatistician.
DeMets earned a doctorate in biostatistics from the University of Minnesota in 1970, and completed his postdoctoral research at the National Institutes of Health in 1972, then joined the University of Wisconsin–Madison faculty in 1972. He was later named Max Halperin Professor of Biostatistics, and awarded emeritus status upon retirement in 2017.
DeMets was elected a fellow of the American Statistical Association in 1986, a fellow of the American Association for the Advancement of Science in 1998, and a member of the Institute of Medicine in 2013.
References
University of Wisconsin–Madison faculty
Living people
University of Minnesota alumni
American statisticians
Members of the National Academy of Medicine
Fellows of the American Statistical Association
Biostatisticians
Fellows of the American Association for the Advancement of Science
1944 births
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https://en.wikipedia.org/wiki/Dong-Yun%20Kim
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Dong-Yun Kim is a biostatistician whose research involves clinical trials, change detection, and statistical genetics. She works as a mathematical statistician in the Office of Biostatistics Research of the National Heart, Lung, and Blood Institute, and is the 2023 president of the Caucus for Women in Statistics.
Education and career
Kim earned her Ph.D. from the University of Michigan in 2003. Her dissertation, Sequential Test and Change Point Problems with Staggered Entry, was supervised by Michael Woodroofe.
She joined Illinois State University as an assistant professor of mathematics in 2003, and moved to Virginia Tech as an assistant professor of statistics in 2007. She took her present position in the National Institutes of Health, as a mathematical statistician in the Office of Biostatistics Research of the National Heart, Lung, and Blood Institute, in 2013.
Professional service
Kim was elected as president of the Caucus for Women in Statistics for the 2023 term. She also serves on the board of directors of the Korean International Statistical Society.
Recognition
Kim was a 2022 recipient of an achievement award from Korean Women Scientists and Engineers, recognizing her "commitment to developing
collaboration and communication between Korean women scientists in
South Korea and Korean-American women scientists in the US".
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
University of Michigan alumni
Illinois State University faculty
Virginia Tech faculty
National Institutes of Health faculty
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https://en.wikipedia.org/wiki/Judith%20Goldberg
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Judith D. Goldberg is an American biostatistician and a professor in the New York University Grossman School of Medicine. Her research interests include the statistics of medical tests used for screening and medical diagnosis, clinical trials, and observational studies.
Education and career
Goldberg studied biostatistics at the Harvard School of Public Health, earning a master's degree in 1967 and completing her doctorate (Sc.D.) in 1972. After three years as a research statistician for the HIP Health Insurance Plan of New York, she became an assistant professor of biostatistics at the Mount Sinai School of Medicine from 1975 to 1983.
From 1983 to 1995, she worked at Lederle Laboratories, in the pharmaceutical division of American Cyanamid, as executive director of statistics and data management. After American Cyanamid was purchased, broken up, and reorganized in the mid-1990s, she became vice president for biostatistics and data management for Bristol Myers Squibb from 1995 to 1999.
In 1999 she returned to academia, as founding director of the Division of Biostatistics in NYU Langone Health, and as a professor in the Departments of Population Health and Environmental Medicine. She continued as director of biostatistics until stepping down in 2013.
Recognition
Goldberg was elected as a Fellow of the American Statistical Association in 1991, and as a Fellow of the American Association for the Advancement of Science in 1992.
She was the 2015 recipient of the Janet L. Norwood Award for Outstanding Achievement by a Woman in the Statistical Sciences, given annually by the School of Public Health of the University of Alabama at Birmingham.
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
Biostatisticians
Harvard T.H. Chan School of Public Health alumni
Icahn School of Medicine at Mount Sinai faculty
New York University Grossman School of Medicine faculty
Fellows of the American Statistical Association
Fellows of the American Association for the Advancement of Science
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https://en.wikipedia.org/wiki/Kim%20Hyun-Min
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Kim Hyun-Min () is a professor in the department of mathematics at Pusan National University among other positions at the university. He has served as vice president of the Korean Mathematical Society; vice president of the Youngnam Mathematical Society; director of the Big Data-based Finance, Fisheries, and Manufacturing Innovation Industrial Mathematics Center; and the sixth president of the National Institute for Mathematical Sciences.
Education
Kim majored in mathematics in the College of Natural Sciences at Pusan National University for his bachelor's and master's. He earned a second master's degree and a doctorate in mathematics specializing in numerical analysis and calculation at the Victoria University of Manchester.
Career
His first position was as a post-doc in the department of mathematics at KAIST. Following that, he taught at Pusan National University and held positions at Kyungpook National University, Samsung Heavy Industries College of Engineering, and the Korean Society for Industrial and Applied Mathematics.
Research
Kim's research is focused on developing algorithms for solving various types of nonlinear matrix equations.
Scientific society
Member of Society for Industrial and Applied Mathematics
Member of Korean Mathematical Society
Member of Korea Society of Industrial Applied Mathematics
Member of Youngnam Mathematical Society
Selected publications
References
External links
National Research Foundation of Korea
Living people
South Korean scientists
Seoul National University alumni
Institute for Basic Science
Academic staff of KAIST
National Institute for Mathematical Sciences
1966 births
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https://en.wikipedia.org/wiki/2003%E2%80%9304%20PFC%20CSKA%20Sofia%20season
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The 2003–04 season was PFC CSKA Sofia's 57th consecutive season in A Group.
Below is a list of player statistics and all matches (official and friendly) that the club played during the 2003–04 season.
Squad
Source:
Competitions
A Group
Table
Results summary
Results by round
Fixtures and results
Bulgarian Cup
UEFA Champions League
Second qualifying round
Third qualifying round
UEFA Cup
First round
References
External links
CSKA Official Site
CSKA Fan Page with up-to-date information
Bulgarian A Professional Football Group Site
PFC CSKA Sofia seasons
Cska Sofia
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https://en.wikipedia.org/wiki/Fungai%20Ndemera
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Fungai Ndemera is a United Kingdom based Zimbabwean entrepreneur, speaker, Angel investor, mentor as well as STEM (Science, technology, engineering, and mathematics) ambassador.
Fungai Ndemera was born in Mhondoro, Zimbabwe. She then grew up in Rimuka, Kadoma before moving to Harare from where she relocated to the United Kingdom to work as nurse . She started her career as a businesswoman in 2001 when she co-founded The Flame Lily Healthcare whilst working as a nurse. She then founded of Independent Care Solutions in 2011 and in 2016 she established CheckUp Health Software Solutions, an NHS approved primary healthcare AI-driven platform for remote monitoring of patients with clinicians and healthcare professionals.
In 2021 she was awarded a project grant by Innovate UK for CheckUp Health. During the Covid-19 pandemic, Fungai developed remote monitoring modules for the CheckUp Health application through a grant from Innovate UK’s Sustainable Innovation Fund then she ran a study through which the platform was reported to have saved the NHS an estimated £4 million.
Fungai Ndemera contributed to the book The Voice in the Shadow which highlights the journeys of 51 prominent Black women in the UK who have made an impact in the tech industry. She also authored The all dots digital transformation model and co-authored Cultivating Your IT Factor in 2015.
In 2023 Fungai Ndemera was shortlisted for the 100 Most Impactful and Influential person in Africa at African Business Chamber.
Awards and recognition
African Enterprise Awards 2014 - African Personality Of The Year (nomination)
Zimbabwe Achievers Awards 2018 - Female Entrepreneur of the year
The Great British Entrepreneur Spirit Award 2020
UK Business Tech Awards Finalist 2023
Black British Business Awards finalist 2023
Black Owned Birmingham 2023 - Award of Excellence in Tech (nominee)
References
People from Kadoma, Zimbabwe
Zimbabwean businesspeople
Year of birth missing (living people)
Living people
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https://en.wikipedia.org/wiki/Soddy%20circles%20of%20a%20triangle
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In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the plane. Their centers are the Soddy centers of the triangle. They are all named for Frederick Soddy, who rediscovered Descartes' theorem on the radii of mutually tangent quadruples of circles.
Any triangle has three externally tangent circles centered at its vertices. Two more circles, its Soddy circles, are tangent to the three circles centered at the vertices; their centers are called Soddy centers. The line through the Soddy centers is the Soddy line of the triangle. These circles are related to many other notable features of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two.
Construction
Let be the three vertices of a circle, and let be the lengths of the opposite sides, and be the semiperimeter. Then the three Soddy circles centered at have radii , respectively.
By Descartes' theorem, two more circles, sometimes also called Soddy circles, are tangent to these three circles. The centers of these two tangent circles are the Soddy
centers of the triangle.
Related features
Each of the three circles centered at the vertices crosses two sides of the triangle at right angles, at one of the three intouch points of the triangle, where its incircle is tangent to the side. The two circles tangent to these three circles are separated by the incircle, one interior to it and one exterior. The Soddy centers lie at the common intersections of three hyperbolas, each having two triangle vertices as foci and passing through the third vertex.
The inner Soddy center is an equal detour point: the polyline connecting any two triangle vertices through the inner Soddy point is longer than the line segment connecting those vertices directly, by an amount that does not depend on which two vertices are chosen. By Descartes' theorem, the inner Soddy circle's curvature is , where is the triangle's area, is its circumradius, and is its inradius. The outer Soddy circle has curvature . When this curvature is positive, the outer Soddy center is another equal detour point; otherwise the equal detour point is unique. When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and two vertices of the starting triangle all have the same perimeter. Triangles whose outer circle degenerates to a straight line with curvature zero have been called "Soddyian triangles".
Excentric circles
As well as the three externally tangent circles formed from a triangle, three more triples of tangent circles also have their centers at the triangle vertices, but with one of the circles surrounding the other two. Their triples of radii are or where a negative radius indicates that the circle is tangent to the other two in its interior. Their points of tangency lie on the lines through the sides of the t
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https://en.wikipedia.org/wiki/Elizabeth%20Ryan%20career%20statistics
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This is a list of the main career statistics of professional American tennis player Elizabeth Ryan.
Grand Slam finals
Singles: 5 (5 runner-ups)
Included:
(*) Denotes All-Comers Final
Women's doubles: 21 (17 titles, 4 runner-ups)
Included:
Mixed doubles: 14 (9 titles, 5 runner-ups)
Included:
World Championship finals
Singles: 1 (1 runner up)
Career finals
Notes:Ryans career began in 1905 with her first singles title coming in 1912. During a 19-year run within that career she won an incredible 659 titles in singles, doubles and mixed doubles. Her final singles title came in 1934.
Singles (299) titles (244) runners up (55)
(*) Denotes All-Comers final (w.o.) denotes walkover. NY denotes (New Year)
Career splits
Notes
References
Tennis career statistics
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https://en.wikipedia.org/wiki/Jamie%20Mullins
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Jamie Mullins (born 29 September 2004) is an Irish footballer who plays for the academy of Brighton & Hove Albion.
Career statistics
Career
Mullins was a product of St Kevin’s Boys before playing for Bohemians U19s. He signed for the Bohemians first-team in 2021. Mullins scored on his debut for Bohemians FC against Longford Town FC in July 2021, aged just 16 years-old, making him the youngest ever goalscorer for the club in the League of Ireland. He also made his UEFA Conference League debut for the club against Stjarnan at the Aviva Stadium in July 2021.
Mullins signed for the youth academy of Brighton & Hove Albion from Bohemians in January 2023 for an undisclosed fee, signing a two and-a-half year contract, until 2025. The first-team pathway granted to Evan Ferguson, who also made the switch from Bohemians to Brighton, was said to be a factor in the decision to move.
References
Living people
2004 births
Men's association football midfielders
Republic of Ireland men's youth international footballers
Republic of Ireland men's association footballers
Bohemian F.C. players
League of Ireland players
Expatriate men's footballers in England
Republic of Ireland expatriate men's association footballers
Irish expatriate sportspeople in England
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https://en.wikipedia.org/wiki/Giorgos%20Pontikou
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Giorgos Pontikou (; born 8 January 2003) is a Cypriot footballer who plays as a left midfielder for Apollon Limassol in the Cypriot First Division.
Career statistics
References
2003 births
Living people
Men's association football midfielders
Cypriot men's footballers
Cypriot First Division players
Apollon Limassol FC players
Doxa Katokopias FC players
Cyprus men's under-21 international footballers
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https://en.wikipedia.org/wiki/Paul%20Couderc
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Paul Couderc (15 July 1899 – 5 February 1981) was a French academic who held mathematics professorships at lycées in Chartres (1926–1929) and Paris (1930–1944).
Biography
Couderc completed his education at lycées in Nevers and Dijon, followed by a doctorate in mathematical sciences from the École Normale Supérieure in Paris. In 1926, he married Blanch Jurus.
Throughout his career, Couderc authored approximately fifteen works in the field of astronomy. He provided an interpretation for the phenomena of light echoes around Nova Persei (1901), specifically their perceived superluminal expansion. This geometrical explanation later found application in the study of supernovae, quasars, and γ-ray bursts.
Awards and recognition
Kalinga Prize for the Popularization of Science (1966)
References
1899 births
1981 deaths
French mathematicians
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https://en.wikipedia.org/wiki/Isbell%27s%20zigzag%20theorem
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Isbell's zigzag theorem, a theorem of abstract algebra characterizing the notion of a dominion, was introduced by American mathematician John R. Isbell in 1966. Dominion is a concept in semigroup theory, within the study of the properties of epimorphisms. For example, let is a subsemigroup of containing , the inclusion map is an epimorphism if and only if , furthermore, a map is an epimorphism if and only if . The categories of rings and semigroups are examples of categories with non-surjective epimorphism, and the Zig-zag theorem gives necessary and sufficient conditions for determining whether or not a given morphism is epi. Proofs of this theorem are topological in nature, beginning with for semigroups, and continuing by , completing Isbell's original proof. The pure algebraic proofs were given by and .
Statement
Zig-zag
Zig-zag: If is a submonoid of a monoid (or a subsemigroup of a semigroup) , then a system of equalities;
in which and , is called a zig-zag of length in over with value . By the spine of the zig-zag we mean the ordered -tuple .
Dominion
Dominion: Let is a submonoid of a monoid (or a subsemigroup of a semigroup) . The dominion is the set of all elements such that, for all homomorphisms coinciding on , .
We call a subsemigroup of a semigroup closed
if , and dense if .
Isbell's zigzag theorem
Isbell's zigzag theorem:
If is a submonoid of a monoid then if and only if either or there exists a zig-zag in over with value that is, there is a sequence of factorizations of of the form
This statement also holds for semigroups.
For monoids, this theorem can be written more concisely:
Let be a monoid, let be a submonoid of , and let . Then if and only if in the tensor product .
Application
Let be a commutative subsemigroup of a semigroup . Then is commutative.
Every epimorphism from a finite commutative semigroup to another semigroup is surjective.
Inverse semigroups are absolutely closed.
Example of non-surjective epimorphism in the category of rings: The inclusion is an epimorphism in the category of all rings and ring homomorphisms by proving that any pair of ring homomorphisms which agree on are fact equal.
We show that: Let to be ring homomorphisms, and , . When for all , then for all .
as required.
See also
Epimorphisms
References
Citations
Bibliography
Further reading
Footnote
External links
Semigroup theory
Theorems in group theory
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https://en.wikipedia.org/wiki/Jennifer%20Taback
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Jennifer Taback is an American mathematician whose research focuses on geometric group theory and combinatorial group theory. She is the Isaac Henry Wing Professor of Mathematics and Chair of the Mathematics Department at Bowdoin College in Maine.
Education and career
After earning a bachelor's degree in mathematics at Yale University in 1993, Taback went to the University of Chicago for graduate study in mathematics, earning a master's degree in 1994 and completing her Ph.D. in 1998. Her 1998 doctoral dissertation, Quasi-Isometric Rigity for , was supervised by Benson Farb.
After a postdoctoral stay at the University of California, Berkeley as Charles B. Morrey assistant professor, she became an assistant professor of mathematics at the University at Albany in 1999, moving to her present position at Bowdoin in 2004. She was tenured as an associate professor in 2007, and promoted to full professor in 2012.
She was given the Isaac Henry Wing Professorship in 2021; the professorship was endowed in 1906 by a former Bowdoin student.
References
External links
Home page
Year of birth missing (living people)
Living people
American mathematicians
American women mathematicians
Yale University alumni
University of Chicago alumni
University at Albany, SUNY faculty
Bowdoin College faculty
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https://en.wikipedia.org/wiki/List%20of%20striking%20US%20workers%20by%20year
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Throughout the history of labor in the United States, many workers have gone on strike. The Bureau of Labor Statistics, and the predecessor organizations it cites, have kept track of the number of striking workers per year since 1881.
For data from 1881 to 1905 the Commissioner of Labor, then within the Department of Interior conducted four periodic surveys covering that period. The data is considered likely un-comprehensive but still used the same definition of strikes as later periods. For this era, all strikes with more than six workers or less than one day were excluded. No concrete data was collected for the amount of strikes from 1906 to 1913 federally.
Data from 1915 to 1926 is more comprehensive. In 1915, the Bureau of Labor Statistics had formed a more systemized set of data collection. Data on the number of workers involved remained a rough estimate but more consistent. The data however also included strikes with fewer than six workers involved, likely leading to slightly higher worker estimates.
Data from 1927 to 1981 is more detailed then the previous periods. In 1927, monthly and yearly strike reports by the department were implemented. Any strikes with fewer than six workers or lasting less than a day were excluded from data leading to marginally smaller estimates then the previous period. For strike numbers this change could pose issues, however for total worker estimates it is considered to only have small effects. Within this period, with the passing of the Taft-Hartley Act in 1947, the program was revamped under the work stoppage program, however the criteria remained largely identical.
Data from 1981 to present remains an underestimate of workers striking each year in comparison to all other periods. In February 1982, the BLS had to stop counting strikes with fewer than 1,000 workers, as budget cuts to its Division of Industrial Relations made it infeasible to count them any more.
See also
List of US strikes by size
US Strike wave of 1919
US Strike wave of 1945–1946
Notes
References
Further reading
Brenner, Aaron, et al. eds. The Encyclopedia of Strikes in American History (Routledge, 2009) Library
Strikes in the United States
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https://en.wikipedia.org/wiki/Yadollah%20Ordokhani
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Yadollah Ordokhani is an Iranian mathematician and Professor of Mathematics at Alzahra University.
He is among the most-cited Iranian researchers and is known for his works on fractional wavelet, optimal control problem, numerical analysis, integral equations and time-delay systems.
He is a former head of Iran's National Elites Foundation-Tehran Branch and a former Deputy Head of Research at Alzahra University.
Books
Y. Ordokhani, A. Gilani, M. Shahrezaee. Engineering mathematics part 1: Fourier analysis and partial differential equations, Tafresh: Tafresh University
References
External links
Living people
Academic staff of Al-Zahra University
21st-century Iranian mathematicians
Amirkabir University of Technology alumni
Tarbiat Modares University alumni
Arak University alumni
People from Tafresh
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Vugar%20Aliyev%20Amir
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Aliyev Vugar Amir () is an Azeri doctor of physics and mathematics.
Life
Vugar Aliyev was born January 2, 1955, in the Georgian SSR. In 1976 he graduated from the Baku State University. In 1982 he defended his dissertation for his degree in physical and mathematical sciences on the topic "Photoelectric effects in TlGaSe2 single crystals". In 1997 he defended his doctoral degree in Physical and Mathematical Sciences
Awards
Honorary Diploma of the Federation of Cosmonautics of the USSR (1983)
Laureate of the National Prize named after G.Z. Tagiev in the field of charity (1997).
Laureate of the Academician Y. Mammadaliyev Prize in the field of enlightenment (1998).
Laureate of the National Independent Award "Humay" in the field of literary translation (2001).
Laureate of the Machabeli Prize of the Writers' Union of Georgia (2010).
Laureate of the Golden Pen media award (2011).
Diploma of scientific discovery (No. 340) and the P. L. Kapitsa Gold Medal (2007).
Archimedes Gold Medal for inventions (2022).
Nikola Tesla Gold Medal for Innovative Technologies (2022).
References
External links
List of publications on GoogleScholar
Azerbaijani physicists
1955 births
Living people
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https://en.wikipedia.org/wiki/Takao%20Hayashi
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Takao Hayashi (born 1949) is a Japanese mathematics educator, historian of mathematics specializing in Indian mathematics. Hayashi was born in Niigata, Japan. He obtained Bachelor of Science degree form Tohoku University, Sendai, Japan in 1974, Master of Arts degree from Tohuku University, Sendai, Japan in 1976 and a postgraduate degree from Kyoto University, Japan in 1979. He secured the Doctor of Philosophy degree from Brown University, USA in 1985 under the guidance of David Pingree.
He was a researcher at Mehta Research Institute for Mathematics and Mathematical Physics, Allahabad, India during 1982–1983, a lecturer at Kyoto Women's College during 1985–1987. He joined Doshisha University, Kyoto as a lecturer in history of science in 1986 and was promoted as professor in 1995. He has also worked in various universities in Japan in different capacities.
Publications
Hayashi has a large number of research publications relation to the history of Indian mathematics. He has also contributed chapters to several encyclopedic publications. The books he has published include:
The Babkhshali Manuscript: An Ancient Indian Mathematical Treatise, Egbert Forsten Publishing, 1995
(jointly with S. R. Sarma, Takanori Kusuba and Michio Yano), Gaṇitasārakaumudī: The Moonlight of the Essence of Mathematics by Thakkura Pherū, Manohar Publishers and Distributors, 2009
Kuṭṭā̄kāraśiromaṇi of Devarāja: Sanskrit Text with English Translation, Indian National Science Academy, 2012
Gaṇitamañjarī of Gaṇeśa, Indian National Science Academy, 2013
(jointly with Clemency Montelle, K. Ramasubramanian) Bhāskara-prabhā, Springer Singapore, 2018
Awards/Prizes
The awards and prizes conferred on Hayashi include:
The Salomon Reinach Foundation Prize, Institut de France (2001)
Kuwabara Prize, the History of Mathematics Society of Japan (2005)
Publication Prize, Mathematical Society of Japan (2005)
References
1949 births
Living people
Historians of astronomy
Historians of mathematics
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https://en.wikipedia.org/wiki/Projected%20normal%20distribution
|
In directional statistics, the projected normal distribution (also known as offset normal distribution or angular normal distribution) is a probability distribution over directions that describes the radial projection of a random variable with n-variate normal distribution over the unit (n-1)-sphere.
Definition and properties
Given a random variable that follows a multivariate normal distribution , the projected normal distribution represents the distribution of the random variable obtained projecting over the unit sphere. In the general case, the projected normal distribution can be asymmetric and multimodal. In case is orthogonal to an eigenvector of , the distribution is symmetric.
Density function
The density of the projected normal distribution can be constructed from the density of its generator n-variate normal distribution by re-parametrising to n-dimensional spherical coordinates and then integrating over the radial coordinate.
In spherical coordinates with radial component and angles , a point can be written as , with . The joint density becomes
and the density of can then be obtained as
Circular distribution
Parametrising the position on the unit circle in polar coordinates as , the density function can be written with respect to the parameters and of the initial normal distribution as
where and are the density and cumulative distribution of a standard normal distribution, , and is the indicator function.
In the circular case, if the mean vector is parallel to the eigenvector associated to the largest eigenvalue of the covariance, the distribution is symmetric and has a mode at and either a mode or an antimode at , where is the polar angle of . If the mean is parallel to the eigenvector associated to the smallest eigenvalue instead, the distribution is also symmetric but has either a mode or an antimode at and an antimode at .
Spherical distribution
Parametrising the position on the unit sphere in spherical coordinates as where are the azimuth and inclination angles respectively, the density function becomes
where , , , and have the same meaning as the circular case.
See also
Directional statistics
Multivariate normal distribution
References
Sources
Normal distribution
Continuous distributions
Directional statistics
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https://en.wikipedia.org/wiki/1942%E2%80%9343%20Liverpool%20F.C.%20season
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The 1942–43 season saw Liverpool compete in the wartime North Regional League. Some matches were also part of the League War Cup and the Lancashire Senior Cup.
Statistics
Appearances and Goals
|}
Competitions
North Region War League, War League Cup and Lancashire Senior Cup
Lancashire Senior Cup Final
References
LFC History.net – 1942–43 season
11v11
Soccer At War 1939-45 by Jack Rollin ISBN 9780755314317
Liverpool F.C. seasons
English football clubs 1942–43 season
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https://en.wikipedia.org/wiki/Ranjan%20Roy
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Ranjan Roy (1948 - 2020) was an India born American mathematician and a distinguished college teacher of mathematics. He secured BS from Indian Institute of Technology Kharagpur and MS in mathematics from Indian Institute of Technology Kanpur. He developed his career and spent most of his working years at Beloit College, Beloit, Wisconsin joining the college in the year 1982. He became the Ralph C. Huffer Professor of Mathematics and Astronomy at the college and at the time of his death was the chair of the Mathematics and Computer Science Department.
Early years
After receiving his PhD, Roy taught at the University of Kentucky for a short time and then returned to India where he was first at I.I.T. Delhi and then at Himachal Pradesh University in Shimla. Soon he got a fellowship at the Institute for Advanced Study in Shimla. After spending two years at the institute, he joined the Mathematics Institute at Punjab University as a Reader. Soon he returned to the US at SUNY Plattsburgh. In 1982, he joined Beloit College and spent the rest of his career there.
Publications
Roy has published many papers on differential equations, fluid mechanics, special functions, Fuchsian groups, and the history of mathematics. He authored three advanced mathematics books: "Sources in the development of mathematics" (2011), "Elliptic and modular functions from Gauss to Dedekind to Hecke" (2017) and "Series and Products in the Development of Mathematics" (2021) all published by Cambridge University Press. He is a coauthor of the well-known book "Special Functions" (with G. E. Andrews and R. Askey), published by Cambridge University Press in 1999.
Awards
Roy had earned several recognitions for distinguished mathematics teaching including the following:
In 2003, he was one of three professors to receive the Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics, the Mathematical Association of America's (MAA) highest national teaching honor.
The MAA Carl B. Allendoerfer Award
The MAA Wisconsin Section teaching award
References
Beloit College people
Beloit College faculty
American academics of Indian descent
20th-century American mathematicians
1948 births
2020 deaths
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https://en.wikipedia.org/wiki/Avadhesh%20Narayan%20Singh
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Avadhesh Narayan Singh (Benares, 1901 – July 10, 1954) was an Indian mathematician and historian of mathematics.
Singh received a master's degree from Banaras Hindu University in his hometown (Varanasi was then called Banaras or Benares) in 1924, where he was a student of Ganesh Prasad, and received his DSc in mathematics from the University of Calcutta in 1929 for his dissertation titled "Derivation and Non-Differentiable functions". After securing DSc, Singh went to Lucknow University, where he became a Reader in 1940 and a professor in 1943. There he opened a Hindu Mathematics section and revived the nearly defunct Banaras Mathematical Society under the name of Bharata Ganita Parisad. In the 1930s he wrote a history of Indian mathematics with Bibhutibhushan Datta, which became a standard work. As a mathematician, he dealt with non-differentiable functions (an example of an everywhere non-differentiable function is the Weierstrass function).
Publications
Singh published about a dozen papers related to the history of Indian mathematics, three dozen papers related to the non-differentiability of functions. He also published following two books:
"The Theory and Construction of Non-Differentiable Functions", Lucknow University Studies No. I, 1935. (accessed on 2 August 2023).
Volume 3 of the "History of Hindu Mathematics" was edited by Kripa Shankar Shukla and published in several papers in Indian Journal of History of Science (Vol. 5, 1980 to Vol. 28, 1993). These edited papers are available in Studies in Indian Mathematics and Astronomy (Selected Articles of Kripa Shankar Shukla).
References
Historians of mathematics
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https://en.wikipedia.org/wiki/Kripa%20Shankar%20Shukla
|
Kripa Shankar Shukla (10 July 1918 - 22 September 2007) was a historian of Indian mathematics. He was awarded the DLitt degree by Lucknow University 1n 1955 for his thesis on “Astronomy in the Seventh Century India: Bhāskara I and His Works” which was completed under the guidance of A. N. Singh. He retired in 1979.
Shukla published several important source works in Indian mathematics and astronomy with translation/notes/explanation. He also authored a large number of research papers bringing out many previously unknown facts in the historical development of mathematics in India. He continued his active research even after retirement from his official position in Lucknow University. Shukla supervised the research work of several research scholars
including that of Yukio Ohashi (1955 - 2019) from Japan whose dissertation was titled "A History of Astronomical Instruments in India".
Publications
Source works brought out by K. S. Shula
The important source works brought out by Shukla include the following:
Sūrya-siddhānta with the commentary of Parameśvara (1957)
Pāṭīgaṇita of Śrīdharācārya (1959)
Mahābhāskarīya of Bhāskara I (1960)
Laghubhāskarīya of Bhāskara I (1963)
Dhīkoṭida-karaṇa of Śrīpati (1969)
Bījagaṇitāvataṃsa of Nārāyaṇa Paṇḍita (1970)
Āryabhaṭīya of Āryabhaṭa (1976)
Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara (1976)
Karaṇaratna of Devācārya (1979)
Vaṭeśvarasiddhānta and Gola of Vaṭeśvara (2 Vols) (1985–86)
Laghumānasa of Mañjula (1990)
Gaṇitapañcaviṃśī (published posthumously) (2017)
Research papers
Aditya Kolachana, K. Mahesh and K. Ramasubramanian have brought out a 754-page volume containing a collection of selected articles by Shukla under the title "Studies in Indian Mathematics and Astronomy" in 2019.
Awards and accolades
The awards and prizes conferred on Shukla include the following:
Awarded Banerji Research Prize of the Lucknow University.
Elected Fellow of the National Academy of Sciences, India in 1984
Selected as a Corresponding Member of the International Academy of History of Science, Paris, in 1988.
References
Historians of mathematics
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https://en.wikipedia.org/wiki/Camila%20Giorgi%20career%20statistics
|
This is a list of the main career statistics of professional Italian tennis player Camila Giorgi.
Performance timelines
Only main-draw results in WTA Tour and Grand Slam tournaments, Fed Cup/Billie Jean King Cup, and Olympic Games are included in win–loss records.
Singles
Current through the 2023 Wimbledon Championships.
Doubles
Current after the 2022 season.
Significant finals
WTA 1000 tournaments
Singles: 1 (title)
WTA Tour finals
Singles: 10 (4 titles, 6 runner-ups)
ITF Circuit finals
Singles: 7 (5 titles, 2 runner–ups)
Fed Cup/Billie Jean King Cup participation
Giorgi debuted for the Italy Fed Cup team in 2014.
Singles (7–7)
Doubles (0–1)
WTA Tour career earnings
current as of 23 May 2022
Head-to-head records
Record against top 10 players
She has a 17–27 () record against players who were, at the time the match was played, ranked in the top 10.
Double-bagel matches
Notes
References
Giorgi, Camila
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https://en.wikipedia.org/wiki/Ekaterina%20Alexandrova%20career%20statistics
|
This is a list of the main career statistics of professional Russian tennis player Ekaterina Alexandrova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 Guadalajara Open.
Doubles
Current after the 2023 Italian Open.
WTA career finals
Singles: 7 (4 titles, 3 runner-ups)
Doubles: 1 (title)
WTA 125 finals
Singles: 3 (3 titles)
Doubles: 1 (runner-up)
ITF Circuit finals
Singles: 15 (7 titles, 8 runner–ups)
Team competition
Billie Jean King Cup participation
Singles (2–1)
WTA Tour career earnings
Current after the 2022 Korea Open.
Head-to-head records
Record against top 10 players
She has a 11–23 () record against players who were, at the time the match was played, ranked in the top 10.
Awards
National
The Russian Cup in the nominations:
Olympians-2020;
Team of the Year: 2021.
Notes
References
Alexandrova, Ekaterina
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https://en.wikipedia.org/wiki/Arthur%20Getis
|
Arthur Getis (1934–2022) was an American geographer known for his significant contributions to spatial statistics and geographic information science (GIScience). With a career spanning over four decades, Getis authored more than one hundred peer-reviewed papers and book chapters, greatly influencing GIScience and geography as a whole. The Getis-Ord family of statistics, one of the most commonly used in spatial analysis, is based on his and J. Keith Ord's work and is still widely used in the creation of hot spot maps.
Education and field
Arthur Getis earned his Ph.D. in geography at the University of Washington. Here, he worked as a doctoral student under William Garrison, a prominent geographer and leader of the quantitative revolution in geography. His doctoral dissertation focused on individual behaviors and how they manifest as collective spatial patterns. This experience would set him on a path to researching spatial statistics as they apply to fields such as retail, public health, and crime clustering, among others.
Ph.D., Geography, University of Washington, 1961
M.S., Geography, Pennsylvania State University
B.S., Geography, Pennsylvania State University
Career
Arthur Getis held many academic positions during his four decades-long career. After graduating from the University of Washington, Getis took a position at Rutgers University Livingston College in 1963, where he did groundbreaking research in the discipline of spatial analysis. Getis Left Rutgers in 1977 for a position in the geography department at the University of Illinois Urbana-Champaign, where he served as department head. In 1990, Getis left University of Illinois Urbana-Champaign to work at the University of California, Santa Barbara, where he headed a new joint Ph.D. program. In addition to these academic positions, he also held visiting professorships at the University of Bristol and the University of Cambridge.
During his career, Getis focused his research on spatial descriptive statistics, where he focused on topics like spatial autocorrelation, k-function analysis, and their applications to real-world problems. Working with Keith Ord, he created the innovative and highly influential Getis-Ord family of statistics.
Getis collaborated with numerous geographers throughout his career to advance GIScience, Geographic Information Systems (GIS), and geography as a whole. With Luc Anselin, Getis worked to explore the then-new technology of GIS. As the concept of computer cartography was only introduced in 1959 by Waldo Tobler, and the term "geographic information systems" introduced in the 1960s by Roger Tomlinson, this research was extremely influential in laying the foundation for GIS, and modern cartography. Getis worked with geographer Michael Goodchild to establish GIScience foundations in academia, advancing the discipline.
Getis worked with Manfred M. Fischer to found the Journal of Geographical Systems in 1994. This journal focuses on both theoretical and applie
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https://en.wikipedia.org/wiki/Angela%20Mihai
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Loredana Angela Mihai is an applied mathematician and numerical analyst. Originally from Romania, she works in the UK as professor of applied mathematics at Cardiff University, and director of research and innovation for the Cardiff University School of Mathematics. She specialises in mathematical modeling of the mechanical properties of soft materials, such as biological tissue.
Education and career
Mihai is from Romania, where she was an undergraduate student. She completed a DPhil in numerical analysis at Durham University in 2005. Her dissertation, A class of alternate strip-based domain decomposition methods for elliptic partial differential equations, was supervised by Alan W. Craig.
After postdoctoral research at the University of Strathclyde, University of Cambridge, and University of Oxford, she joined the Cardiff University academic staff as a lecturer in 2011.
Professional service
In 2023, Mihai was elected vice-president of the United Kingdom and Republic of Ireland Section of the Society for Industrial and Applied Mathematics.
References
External links
Year of birth missing (living people)
Living people
Romanian emigrants to the United Kingdom
British mathematicians
British women mathematicians
Alumni of Durham University
Academics of Cardiff University
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https://en.wikipedia.org/wiki/Galia%20Dafni
|
Galia Devora Dafni is a mathematician specializing in harmonic analysis and function spaces. Educated in the US, she works in Canada as a professor of mathematics and statistics at Concordia University. She is also affiliated with the Centre de Recherches Mathématiques, where she is deputy director for publications and communication.
Education
Dafni lived in Texas as a teenager. After beginning her undergraduate studies at the University of Texas at Austin, Dafni transferred to Pennsylvania State University, where she earned a bachelor's degree in 1988 in mathematics and computer science, "with highest distinction and with honors in mathematics". She went to Princeton University for graduate study in mathematics, earning a master's degree in 1990 and completing her Ph.D. in 1993. Her doctoral dissertation, Hardy Spaces on Strongly Pseudoconvex Domains in and Domains of Finite Type in , was supervised by Elias M. Stein.
Career
After another year as an instructor at Princeton, Dafni continues through three postdoctoral positions: as Charles B. Morrey Jr. Assistant Professor of Mathematics at the University of California, Berkeley from 1994 to 1996, as Ralph Boas Assistant Professor of Mathematics at Northwestern University from 1996 to 1998, and as a postdoctoral fellow and research assistant professor at Concordia University from 1998 to 2000. Her move to Montreal and Concordia was motivated in part by a two-body problem with her husband, who also worked in Montreal.
Finally, in 2000, she obtained a regular-rank assistant professorship at Concordia, supported by a 5-year NSERC University Faculty Award, through a program to support women in STEM. She obtained tenure there as an associate professor in 2005, and since became a full professor.
Personal life
Dafni is married to Henri Darmon, a mathematician at another Montreal university, McGill University. They met in the early 1990s at Princeton, where Darmon was a postdoctoral researcher.
References
External links
Home page
Year of birth missing (living people)
Living people
American mathematicians
American women mathematicians
Canadian mathematicians
Canadian women mathematicians
Functional analysts
Pennsylvania State University alumni
Princeton University alumni
Academic staff of Concordia University
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https://en.wikipedia.org/wiki/Mensur%20Dogan
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Mensur Dogan (born 22 February 1971) is a Bosnian professional football manager who is the current director of the youth academy of Bosnian Premier League club Sarajevo.
Managerial statistics
Honours
Manager
Olimpik
Second League of FBiH: 2004–05 (Center)
References
External links
Mensur Dogan at LinkedIn
1971 births
Living people
People from Jajce
Bosniaks of Bosnia and Herzegovina
Bosnia and Herzegovina football managers
FK Olimpik managers
FK Radnik Hadžići managers
FK Sarajevo managers
Premier League of Bosnia and Herzegovina managers
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https://en.wikipedia.org/wiki/Hand%27s%20paradox
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In statistics, Hand's paradox arises from ambiguity when comparing two treatments. It shows that a comparison of the effects of the treatments applied to two independent groups can contradict a comparison of the effects of both treatments applied to a single group.
Paradox
Comparisons of two treatments often involve comparing the responses of a random sample of patients receiving one treatment with an independent random sample receiving the other. One commonly used measure of the difference is then the probability that a randomly chosen member of one group will have a higher score than a randomly chosen member of the other group. However, in many situations, interest really lies in which of the two treatments will give a randomly chosen patient the greater probability of doing better. These two measures, a comparison between two randomly chosen patients, one from each group, and a comparison of treatment effects on a randomly chosen patient, can lead to different conclusions.
This has been called Hand's paradox, and appears to have first been described by Hand (1992).
Examples
Example 1
Label the two treatments A and B and suppose that:
Patient 1 would have response values 2 and 3 to A and B respectively.
Patient 2 would have response values 4 and 5 to A and B respectively.
Patient 3 would have response values 6 and 1 to A and B respectively.
Then the probability that the response to A of a randomly chosen patient is greater than the response to B of a randomly chosen patient is 6/9 = 2/3. But the probability that a randomly chosen patient will have a greater response to A than B is 1/3. Thus a simple comparison of two independent groups may suggest that patients have a higher probability of doing better under A, whereas in fact patients have a higher probability of doing better under B.
Example 2
Suppose we have two random variables, and , corresponding to the effects of two treatments. If we assume that and are independent, then , suggesting that A is more likely to benefit a patient than B. In contrast, the joint distribution which minimises leads to . This means that it is possible that in up to 62% of cases treatment B is better than treatment A.
References
Statistical paradoxes
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https://en.wikipedia.org/wiki/Liudmila%20Samsonova%20career%20statistics
|
This is a list of the main career statistics of professional Russian tennis player Liudmila Samsonova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 China Open.
Doubles
Current through the 2023 Wimbledon Championships.
Significant finals
WTA 1000 tournaments
Singles: 2 (2 runner-ups)
Doubles: 1 (title)
WTA Tour finals
Singles: 7 (4 titles, 3 runner-ups)
Doubles: 1 (title)
ITF Circuit finals
Singles: 11 (4 titles, 7 runner–ups)
Doubles: 3 (2 titles, 1 runner–up)
Billie Jean King Cup participation
Singles (2–0)
Doubles (3–0)
WTA Tour career earnings
Current through the 2022 Washington Open.
Career Grand Slam statistics
Seedings
The tournaments won by Samsonova are in boldface, and advanced into finals by Samsonova are in italics.
Head-to-head records
Record against top 10 players
She has a record against players who were, at the time the match was played, ranked in the top 10.
Double-bagel matches
Longest winning streak
13-match win streak (2022)
Awards
International
Billie Jean King Cup Finals:
Most Valuable Player: 2021.
Rookie of the Year: 2021.
National
The Russian Cup in the nomination:
Team of the Year: 2021.
Notes
References
Samsonova, Liudmila
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https://en.wikipedia.org/wiki/Hideyuki%20Matsumura
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was a Japanese mathematician particularly known for his text books in commutative algebra.
References
External links
The Oberwolfach Photo Collection has fotos of him.
1930 births
1995 deaths
20th-century Japanese mathematicians
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https://en.wikipedia.org/wiki/Perfect%20ideal
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In commutative algebra, a perfect ideal is a proper ideal in a Noetherian ring such that its grade equals the projective dimension of the associated quotient ring.
A perfect ideal is unmixed.
For a regular local ring a prime ideal is perfect if and only if is Cohen-Macaulay.
The notion of perfect ideal was introduced in 1913 by Francis Sowerby Macaulay in connection to what nowadays is called a Cohen-Macaulay ring, but for which Macaulay did not have a name for yet. As Eisenbud and Gray point out, Macaulay's original definition of perfect ideal coincides with the modern definition when is a homogeneous ideal in polynomial ring, but may differ otherwise. Macaulay used Hilbert functions to define his version of perfect ideals.
References
Ideals (ring theory)
Commutative algebra
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https://en.wikipedia.org/wiki/Grade%20%28ring%20theory%29
|
In commutative and homological algebra, the grade of a finitely generated module over a Noetherian ring is a cohomological invariant defined by vanishing of Ext-modules
For an ideal the grade is defined via the quotient ring viewed as a module over
The grade is used to define perfect ideals. In general we have the inequality
where the projective dimension is another cohomological invariant.
The grade is tightly related to the depth, since
References
Ring theory
Homological algebra
Commutative algebra
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https://en.wikipedia.org/wiki/Saralees%20Nadarajah
|
Saralees Nadarajah is a British statistician specialising in distribution theory, extreme value theory, nonparametric statistics, and their applications.
Early life and education
Nadarajah was born in Sri Lanka and grew up in Zimbabwe. He obtained his B.Sc. in mathematics from the University of Zimbabwe in Harare.
Nadarajah earned his M.Sc. and Ph.D. degrees in statistics from the University of Sheffield in the UK, in 1991 and 1994 respectively.
Career
Nadarajah is a reader at the Department of Mathematics, University of Manchester. He was previously affiliated with the Department of Statistics, University of Nebraska–Lincoln and the University of South Florida.
Nadarajah is the founder of Educate Africa project which he started in 2017.
Research
Nadarajah specializes in statistical fields including extreme value and distribution theory, nonparametric statistics, information theory, and reliability. His expertise also extends to sampling theory, statistical software development, and time series analysis. Nadarajah-Haghighi (UNH) class of distribution is named after him.
Awards and recognition
Jacob Wolfowitz Prize (2007)
University of Manchester Education Award (2021)
Selected publications
Extreme value distributions: theory and applications (2000)
Multivariate t-distributions and their applications (2004)
Handbook of beta distribution and its applications (2004)
A generalized normal distribution (2005)
The beta exponential distribution (2006)
Lindley distribution and its application (2008)
On the inefficiency of Bitcoin (2017)
References
External links
Educate Africa project homepage
1965 births
Alumni of the University of Sheffield
Academics of the University of Manchester
Living people
British statisticians
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https://en.wikipedia.org/wiki/Du%C5%A1an%20Kapr%C3%A1lik
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Dušan Kaprálik (21 February 1948 – 8 August 2023) was a Slovak actor.
Dušan Kaprálik was born on in Martin 21 February 1948. In his youth, he was interested in mathematics and physics, but eventually decided to pursue an acting career. He studied at the Academy of Performing Arts in Bratislava.
Following his graduation, he acted at regional theatres in Trnava, Nitra and his hometown of Martin. In 1973 he joined the New Scene theatre in Bratislava, where he remained until his retirement for health reasons in 2021. He taught acting at the Bratislava Conservatory.
In addition to stage acting, he acted in several movies, including The Teacher (2016) and Old-Timers (2019).
Personal life and death
Kaprálik was married to Helena Romančíková, the daughter of the actor Elo Romančík. They had two children together. She died at the age of 33 following a sudden illness. Kaprálik later married Silvia Kapráliková, a fencer, with whom he had additional two children.
Dušan Kaprálik died on 8 August 2023, at the age of 75 at a retirement home in the Dúbravka borough of Bratislava.
References
1948 births
2023 deaths
20th-century Slovak male actors
21st-century Slovak male actors
Academy of Performing Arts in Bratislava alumni
Slovak television actors
Slovak film actors
Slovak stage actors
People from Martin, Slovakia
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https://en.wikipedia.org/wiki/The%20Great%20Brain%20Robbery%20%28disambiguation%29
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The Great Brain Robbery is a board game.
The Great Brain Robbery may also refer to:
Math Blaster Mystery: The Great Brain Robbery, a 1998 video game about mathematics
"The Great Brain Robbery" (Justice League Unlimited episode)
The Great Brain Robbery (album), a 2000 album by The Crocketts
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https://en.wikipedia.org/wiki/1943%E2%80%9344%20Liverpool%20F.C.%20season
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The 1943–44 season saw Liverpool compete in the wartime North Regional League. Some matches were also part of the League War Cup and the Lancashire Senior Cup.
Statistics
Appearances and Goals
|}
Competitions
North Region War League, War League Cup and Lancashire Senior Cup
Lancashire Senior Cup Final
References
LFC History.net – 1943–44 season
11v11
Soccer At War 1939-45 by Jack Rollin ISBN 9780755314317
Liverpool F.C. seasons
English football clubs 1943–44 season
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https://en.wikipedia.org/wiki/Kent%20Edunjobi
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Hassan Kehinde Daniel popularly known as Kent Edunjobi is a Nigerian songwriter and music producer.
Early life and career
Kehinde studied Computer Science and Statistics at the University of Nigeria, Nsukka. Kehinde started his music career as member of the Apex Choir of the Celestial Church of Christ where he is now the music director. He started working for Kunle Afolayan Productions in 2016 and has been composing soundtracks for the production company since.
In 2023, he came into limelight after composing the soundtrack for won Aníkúlápó. In the same year, he released Ebenezer with the Apex Choir and it had 1 million views on YouTube within its first month.
Discography
Awards
Best Soundtrack at Africa Movie Academy Awards for Citation.
Best Soundtrack at 2023 Africa Magic Viewers' Choice Awards for Aníkúlápó.
References
Nigerian male musicians
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https://en.wikipedia.org/wiki/Doron%20Levy
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Doron Levy is a mathematician, scientist, magician, and academic. He is a Professor and chair at the Department of Mathematics at the University of Maryland, College Park. He is also the Director of the Brin Mathematics Research Center.
Levy's research encompasses the field of numerical analysis, applied nonlinear PDEs, and biology and medical applications, particularly focusing on analyzing cancer dynamics, immunology, and cell motility. He has written more than 100 peer-reviewed articles. He is the recipient of the National Science Foundation Career Award.
Levy is a Fellow of the John Simon Guggenheim Memorial Foundation He is an Editorial Board Member of the Bulletin of Mathematical Biology, Discrete and Continuous Dynamics Systems Series B, Le Matematiche, Acta Applicandae Mathematicae, Frontiers in Systems Biology, Cancer Research, Applied Mathematics Modelling, PLoS One, and Differential Equations and Dynamical Systems. He is the Editor-in-Chief at ImmunoInformatics.
Education
Levy earned his Baccalaureate degree in Mathematics and Physics in 1991 and completed a master's degree in Applied Mathematics in 1994 from Tel Aviv University. His Master's thesis was titled "From Semi-Discrete to Fully-Discrete: The Stability of Runge-Kutta Schemes by the Energy Method". In 1997, he received a Ph.D. in Applied Mathematics under the guidance of Eitan Tadmor, with a thesis on "Topics in Approximate Methods for Non-Linear Partial Differential Equations." Afterward, he held several post-doctorate fellowships at Laboratoire d'Analyse Numerique (University of Paris 6), École normale supérieure (Paris), University of California, Berkeley, and the Lawrence Berkeley National Laboratory.
Career
Following his post-doctoral fellowship at Berkeley in 2000, Levy joined the Department of Mathematics at Stanford University as an assistant professor. In 2007, he was appointed as associate professor of mathematics and a member of the Center for Scientific Computation and Mathematical Modeling at the University of Maryland, College Park. In 2014, he became a Pauli Fellow at the Wolfgang Pauli Institute of the University of Vienna in Austria. Since 2011, he has been a professor at the Department of Mathematics & Center for Scientific Computation and Mathematical Modeling of the University of Maryland, College Park.
Levy served as a Member of the Board of Governors of the Institute for Mathematics and Its Applications (IMA) at the University of Minnesota in 2018 for one year, and a Member of the Board of Directors of the Society for Mathematical Biology from 2018 to 2022. Since 2022, he has been serving as the Founding Director of the Brin Mathematics Research Center at the University of Maryland, College Park.
As of 2020, Levy has been a chair at the Department of Mathematics and the Director of the Center for Scientific Computation and Mathematical Modeling of the University of Maryland, College Park.
Research
Levy's research is focused on mathematical equation
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https://en.wikipedia.org/wiki/2023%20Rugby%20World%20Cup%20statistics
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This article documents the statistics of the 2023 Rugby World Cup that was held in France from 8 September to 28 October.
Team statistics
The following table shows the team's results in major statistical categories.
Last updated: 30 October 2023
Try scorers
8 tries
Will Jordan
6 tries
Damian Penaud
5 tries
Henry Arundell
Bundee Aki
Leicester Fainga'anuku
Damian McKenzie
Darcy Graham
Louis Rees-Zammit
4 tries
Theo Dan
Louis Bielle-Biarrey
Aaron Smith
Cobus Reinach
3 tries
Mateo Carreras
Santiago Carreras
Peato Mauvaka
Tadhg Beirne
Hugo Keenan
Johnny Sexton
Amato Fakatava
Cam Roigard
Ardie Savea
Mark Telea
Sama Malolo
Makazole Mapimpi
Solomone Kata
Baltazar Amaya
2 tries
Emiliano Boffelli
Tomás Cubelli
Juan Martín González
Nicolás Sánchez
Ben Donaldson
Mark Nawaqanitawase
Ben Earl
Joe Marchant
Marcus Smith
Mesake Doge
Waisea Nayacalevu
Josua Tuisova
Cyril Baille
Jonathan Danty
Melvyn Jaminet
Yoram Moefana
Charles Ollivon
Jamison Gibson-Park
Mack Hansen
Rob Herring
James Lowe
Peter O'Mahony
Lorenzo Cannone
Ange Capuozzo
Monty Ioane
Manuel Zuliani
Michael Leitch
Jone Naikabula
Beauden Barrett
Dane Coles
Shannon Frizell
Anton Lienert-Brown
Dalton Papalii
Raffaele Storti
Nigel Ah Wong
Duncan Paia'aua
Rory Darge
Ali Price
Kurt-Lee Arendse
Deon Fourie
Cheslin Kolbe
Willie le Roux
Grant Williams
Ben Tameifuna
Nicolás Freitas
Jac Morgan
George North
1 try
Martín Bogado
Rodrigo Bruni
Santiago Chocobares
Agustín Creevy
Rodrigo Isgro
Ignacio Ruiz
Joel Sclavi
Richie Arnold
Angus Bell
Marika Koroibete
Fraser McReight
Jordan Petaia
Dave Porecki
Suliasi Vunivalu
Tomás Dussaillant
Alfonso Escobar
Rodrigo Fernández
Danny Care
Ollie Chessum
Courtney Lawes
Lewis Ludlam
Bevan Rodd
Freddie Steward
Manu Tuilagi
Jack Willis
Vilimoni Botitu
Vinaya Habosi
Viliame Mata
Peni Ravai
Lekima Tagitagivalu
Baptiste Couilloud
Antoine Dupont
Thibaud Flament
Antoine Hastoy
Matthieu Jalibert
Thomas Ramos
Beka Gigashvili
Luka Ivanishvili
Vano Karkadze
Davit Niniashvili
Merab Sharikadze
Akaki Tabutsadze
Tengizi Zamtaradze
Caelan Doris
Iain Henderson
Joe McCarthy
Garry Ringrose
Dan Sheehan
Juan Ignacio Brex
Hame Faiva
Paolo Garbisi
Michele Lamaro
Dino Lamb
Paolo Odogwu
Lorenzo Pani
Warner Dearns
Kazuki Himeno
Lappies Labuschagné
Ryōto Nakamura
Naoto Saitō
J. C. Greyling
Jordie Barrett
Caleb Clarke
Ethan de Groot
David Havili
Rieko Ioane
Richie Mo'unga
Fletcher Newell
Brodie Retallick
Tamaiti Williams
Pedro Bettencourt
Rafael Simões
Cristi Boboc
Gabriel Rupanu
Marius Simionescu
Florin Surugiu
Seilala Lam
Christian Leali'ifano
Fritz Lee
Jonathan Taumateine
Ewan Ashman
Matt Fagerson
Chris Harris
Ben Healy
George Horne
Blair Kinghorn
Johnny Matthews
Ollie Smith
Kyle Steyn
George Turner
Duhan van der Merwe
Hamish Watson
Damian de Allende
Pieter-Steph du Toit
Eben Etzebeth
Jesse Kriel
Canan Moodie
Kw
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https://en.wikipedia.org/wiki/Bodhisattva%20Sen
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Bodhisattva Sen is an Indian-American statistician.
Sen earned his bachelor and master of statistics from the Indian Statistical Institute in 2002 and 2004, respectively. He then completed a doctorate in statistics at the University of Michigan in the United States. Sen's doctoral dissertation, A Study of Bootstrap And Likelihood Based Methods In Non-standard Problems, was published in 2008 and jointly advised by Michael Woodroofe and Moulinath Banerjee.
Sen joined the Columbia University Department of Statistics as an assistant professor in 2008. Sen was successively promoted to an associate professorship in 2013, and a full professorship in 2020. In 2022, he was elected a fellow of the Institute of Mathematical Statistics for "important contributions to nonparametric inference under shape constraints, optimal transport and its applications to Statistics, and the bootstrap".
References
Indian Statistical Institute alumni
University of Michigan alumni
Indian statisticians
Indian expatriate academics in the United States
Columbia University faculty
Fellows of the Institute of Mathematical Statistics
Living people
Year of birth missing (living people)
21st-century Indian mathematicians
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https://en.wikipedia.org/wiki/Moulinath%20Banerjee
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Moulinath (Mouli) Banerjee (born 1974) is an Indian statistician at the University of Michigan.
Education and career
Banerjee completed his bachelor's and master's in statistics at the Indian Statistical Institute in 1995 and 1997, respectively, then authored a doctoral dissertation, Likelihood Ratio Inference in Regular and Nonregular Problems in 2000, advised by Jon A. Wellner of the University of Washington. Banerjee remained in Washington as a lecturer until joining the University of Michigan faculty in 2001.
Research
Banerjee's research interests comprise non-standard statistical models, shape-constrained methods, empirical process theory, distributed computing, and meta-learning. Apart from his statistical pursuits, he takes an avid interest in classical music, fine dining, literature, and philosophy, and together with a co-author has published a new translation of the Rubaiyat of Omar Khayyam from the original Persian.
Honors and awards
In 2017, Banerjee was elected a fellow of the Institute of Mathematical Statistics (IMS). The following year, the American Statistical Association elected him to an equivalent honor. Banerjee will deliver one of the prestigious IMS Medallion Lectures in 2024 and is serving as Editor of IMS's primary review journal, Statistical Science, from 2023 to 2025.
References
1974 births
Indian expatriates in the United States
University of Washington alumni
University of Michigan faculty
Living people
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
Indian statisticians
Indian expatriate academics
Indian Statistical Institute alumni
21st-century Indian mathematicians
Mathematical statisticians
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https://en.wikipedia.org/wiki/Hsin-Cheng%20Huang
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Hsin-Cheng Huang () is a Taiwanese statistician.
Huang earned his bachelor's degree in mathematics from National Taiwan University in 1989, followed by a master's degree and doctorate in statistics at Iowa State University. He completed his doctoral dissertation, Spatial Modeling Using Graphical Markov Models and Wavelets, in 1997, advised by Noel Cressie. He subsequently worked for the Academia Sinica's Institute of Statistical Science. In Taiwan, Huang has also held an adjunct appointment at National Central University, and a joint appointment at National Yang Ming Chiao Tung University. In 2016, Huang was elected a fellow of the American Statistical Association.
References
Taiwanese statisticians
Year of birth missing (living people)
Living people
20th-century Taiwanese mathematicians
21st-century Taiwanese mathematicians
Taiwanese expatriates in the United States
Iowa State University alumni
National Taiwan University alumni
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