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https://en.wikipedia.org/wiki/C-minimal%20theory | In model theory, a branch of mathematical logic, a C-minimal theory is a theory that is "minimal" with respect to a ternary relation C with certain properties. Algebraically closed fields with a (Krull) valuation are perhaps the most important example.
This notion was defined in analogy to the o-minimal theories, which are "minimal" (in the same sense) with respect to a linear order.
Definition
A C-relation is a ternary relation C(x;y,z) that satisfies the following axioms.
A C-minimal structure is a structure M, in a signature containing the symbol C, such that C satisfies the above axioms and every set of elements of M that is definable with parameters in M is a Boolean combination of instances of C, i.e. of formulas of the form C(x;b,c), where b and c are elements of M.
A theory is called C-minimal if all of its models are C-minimal. A structure is called strongly C-minimal if its theory is C-minimal. One can construct C-minimal structures which are not strongly C-minimal.
Example
For a prime number p and a p-adic number a, let |a|p denote its p-adic absolute value. Then the relation defined by is a C-relation, and the theory of Qp with addition and this relation is C-minimal. The theory of Qp as a field, however, is not C-minimal.
References
Model theory |
https://en.wikipedia.org/wiki/Topological%20game | In mathematics, a topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have transfinite lengths, and extensions to continuum time have been put forth. The conditions for a player to win can involve notions like topological closure and convergence.
It turns out that some fundamental topological constructions have a natural counterpart in topological games; examples of these are the Baire property, Baire spaces, completeness and convergence properties, separation properties, covering and base properties, continuous images, Suslin sets, and singular spaces. At the same time, some topological properties that arise naturally in topological games can be generalized beyond a game-theoretic context: by virtue of this duality, topological games have been widely used to describe new properties of topological spaces, and to put known properties under a different light. There are also close links with selection principles.
The term topological game was first introduced by Claude Berge,
who defined the basic ideas and formalism in analogy with topological groups. A different meaning for topological game, the concept of “topological properties defined by games”, was introduced in the paper of Rastislav Telgársky,
and later "spaces defined by topological games";
this approach is based on analogies with matrix games, differential games and statistical games, and defines and studies topological games within topology. After more than 35 years, the term “topological game” became widespread, and appeared in several hundreds of publications. The survey paper of Telgársky
emphasizes the origin of topological games from the Banach–Mazur game.
There are two other meanings of topological games, but these are used less frequently.
The term topological game introduced by Leon Petrosjan in the study of antagonistic pursuit–evasion games. The trajectories in these topological games are continuous in time.
The games of Nash (the Hex games), the Milnor games (Y games), the Shapley games (projective plane games), and Gale's games (Bridg-It games) were called topological games by David Gale in his invited address [1979/80]. The number of moves in these games is always finite. The discovery or rediscovery of these topological games goes back to years 1948–49.
Basic setup for a topological game
Many frameworks can be defined for infinite positional games of perfect information.
The typical setup is a game between two players, I and II, who alternately pick subsets of a topological space X. In the nth round, player I plays a subset In of X, and player II responds with a subset Jn. There is a round for every natural number n, and after all rounds are played, player I wins if the sequence
I0, J0, I1, J1,...
satisfies some property, and otherwise player II wins |
https://en.wikipedia.org/wiki/Rule%20of%20nines | Rule of nines or rule of nine may refer to:
Rule of nine (linguistics), an orthographic rule of the Ukrainian language.
Rule of nines (mathematics), a test for divisibility by 9 involving summing the decimal digits of a number
Wallace rule of nines, used to determine the percentage of total body surface area affected when assessing burn injuries
See also
Rule No. 9 |
https://en.wikipedia.org/wiki/Beit%20Fajjar | Beit Fajjar () is a Palestinian town located eight kilometers south of Bethlehem in the Bethlehem Governorate, in the central West Bank. According to the Palestinian Central Bureau of Statistics, the town had a population of over 13,520 in 2017.
History
A tomb, dating from about the time of Constantine the Great, or the 4th century C.E, have been excavated here.
Beit Fajjar is believed to have been a camping area for the Islamic Caliph, Umar ibn al-Khattab.
Ottoman era
According to the people of Beit Fajjar, they came from Bethlehem, and settled at Beit Fajjar in 1784.
Edward Robinson noted the village on his travels in the area in 1838, as a Muslim village in the Hebron district. According to Kark and Oren-Nordheim, Beit Fajjar was mostly farmland until the 19th century, when it gradually transformed into an urban settlement. The residents were descendants to a semi-nomadic family from the Hauran. The lands formerly belonged to the village of Buraikut.
Victor Guérin visited the village in 1863, and described it as a village on the top of a hill, with about 400 people. The villagers still buried their dead in rock-cut tombs, below the village. An Ottoman village list of about 1870 indicated 27 houses and a population of 81, though the population count included only men.
In the 1883, the PEF's Survey of Western Palestine, Beit Fejjar was described as a "small stone village standing very high on a ridge. It is supplied by the fine springs and spring wells of Wady el Arrub".
In 1896 the population of Bet faddscar was estimated to be about 624 persons.
British Mandate era
The site's high altitude was the highest point in the area and later the town expanded into other hills. During British rule in Palestine in the 1920s-1940s, Beit Fajjar was used as an observation point for the Bethlehem-Hebron area.
In the 1922 census of Palestine conducted by the British Mandate authorities, Bait Fajjar (alternative spelling) had a population 766, all Muslims. In the 1931 census the population of Beit Fajjar was counted together with Umm Salamuna, Marah Ma'alla and Marah Rabah. The total population was 1043, still all Muslims, in 258 houses.
In the 1945 statistics the population of Beit Fajjar was 1,480, all Muslims, who owned 17,292 dunams of land according to an official land and population survey. 2,572 dunams were plantations and irrigable land, 2,633 for cereals, while 87 dunams were built-up (urban) land.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Beit Fajjar came under Jordanian rule.
In 1961, the population was 2,182.
After 1967
Since the Six-Day War in 1967, Beit Fajjar has been under Israeli occupation. The population in the 1967 census conducted by the Israeli authorities was 2,474.
The former head of Beit Fajjar's local council, Saber Mohammed Abdul Latif, testified to United Nations representatives that after his arrest on November 1, 1969, how Beit Fajjar had been |
https://en.wikipedia.org/wiki/Supermodule | In mathematics, a supermodule is a Z2-graded module over a superring or superalgebra. Supermodules arise in super linear algebra which is a mathematical framework for studying the concept supersymmetry in theoretical physics.
Supermodules over a commutative superalgebra can be viewed as generalizations of super vector spaces over a (purely even) field K. Supermodules often play a more prominent role in super linear algebra than do super vector spaces. These reason is that it is often necessary or useful to extend the field of scalars to include odd variables. In doing so one moves from fields to commutative superalgebras and from vector spaces to modules.
In this article, all superalgebras are assumed be associative and unital unless stated otherwise.
Formal definition
Let A be a fixed superalgebra. A right supermodule over A is a right module E over A with a direct sum decomposition (as an abelian group)
such that multiplication by elements of A satisfies
for all i and j in Z2. The subgroups Ei are then right A0-modules.
The elements of Ei are said to be homogeneous. The parity of a homogeneous element x, denoted by |x|, is 0 or 1 according to whether it is in E0 or E1. Elements of parity 0 are said to be even and those of parity 1 to be odd. If a is a homogeneous scalar and x is a homogeneous element of E then |x·a| is homogeneous and |x·a| = |x| + |a|.
Likewise, left supermodules and superbimodules are defined as left modules or bimodules over A whose scalar multiplications respect the gradings in the obvious manner. If A is supercommutative, then every left or right supermodule over A may be regarded as a superbimodule by setting
for homogeneous elements a ∈ A and x ∈ E, and extending by linearity. If A is purely even this reduces to the ordinary definition.
Homomorphisms
A homomorphism between supermodules is a module homomorphism that preserves the grading.
Let E and F be right supermodules over A. A map
is a supermodule homomorphism if
for all a∈A and all x,y∈E. The set of all module homomorphisms from E to F is denoted by Hom(E, F).
In many cases, it is necessary or convenient to consider a larger class of morphisms between supermodules. Let A be a supercommutative algebra. Then all supermodules over A be regarded as superbimodules in a natural fashion. For supermodules E and F, let Hom(E, F) denote the space of all right A-linear maps (i.e. all module homomorphisms from E to F considered as ungraded right A-modules). There is a natural grading on Hom(E, F) where the even homomorphisms are those that preserve the grading
and the odd homomorphisms are those that reverse the grading
If φ ∈ Hom(E, F) and a ∈ A are homogeneous then
That is, the even homomorphisms are both right and left linear whereas the odd homomorphism are right linear but left antilinear (with respect to the grading automorphism).
The set Hom(E, F) can be given the structure of a bimodule over A by setting
With the above grading Hom(E, F) becomes a sup |
https://en.wikipedia.org/wiki/APMonitor | Advanced process monitor (APMonitor) is a modeling language for differential algebraic (DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
Programming language integration
Julia, MATLAB, Python are mathematical programming languages that have APMonitor integration through web-service APIs. The GEKKO Optimization Suite is a recent extension of APMonitor with complete Python integration. The interfaces are built-in optimization toolboxes or modules to both load and process solutions of optimization problems. APMonitor is an object-oriented modeling language and optimization suite that relies on programming languages to load, run, and retrieve solutions. APMonitor models and data are compiled at run-time and translated into objects that are solved by an optimization engine such as APOPT or IPOPT. The optimization engine is not specified by APMonitor, allowing several different optimization engines to be switched out. The simulation or optimization mode is also configurable to reconfigure the model for dynamic simulation, nonlinear model predictive control, moving horizon estimation or general problems in mathematical optimization.
As a first step in solving the problem, a mathematical model is expressed in terms of variables and equations such as the Hock & Schittkowski Benchmark Problem #71 used to test the performance of nonlinear programming solvers. This particular optimization problem has an objective function and subject to the inequality constraint and equality constraint . The four variables must be between a lower bound of 1 and an upper bound of 5. The initial guess values are . This mathematical model is translated into the APMonitor modeling language in the following text file.
! file saved as hs71.apm
Variables
x1 = 1, >=1, <=5
x2 = 5, >=1, <=5
x3 = 5, >=1, <=5
x4 = 1, >=1, <=5
End Variables
Equations
minimize x1*x4*(x1+x2+x3) + x3
x1*x2*x3*x4 > 25
x1^2 + x2^2 + x3^2 + x4^2 = 40
End Equations
The problem is then solved in Python by first installing the APMonitor package with pip install APMonitor or from the following Python code.
# Install APMonitor
import pip
pip.main(['install','APMonitor'])
Installing a Python is only required once for any module. Once the APMonitor package is installed, it is imported and the apm_solve function solves the optimization problem. The solution is returned |
https://en.wikipedia.org/wiki/Taught%20Course%20Centre | The Taught Course Centre or TCC is a collaboration between the mathematics departments at five UK universities aimed at providing a broader range of lecture courses for postgraduate students.
Members
The five collaborating universities are:
University of Bath
University of Bristol
Imperial College London
University of Oxford
University of Warwick
Lectures are given at all five universities and, using Access Grid technology, students at each of the other four institutes may participate with each lecture.
The TCC was set up in 2007 with funding from the EPSRC. Twenty six courses were made available to students in the first year of the collaboration, with topics from diverse areas of mathematics including number theory, partial differential equations, random matrix theory, and group theory. One of the aims of the project was to encourage contact between postgraduate mathematics students at the five universities and set up future collaborative work.
Configuration
In normal operation, the TCC uses access grid technology for video conferencing using the proprietary IOCOM software suite. The lectures take place in the virtual venue named Maths TCC. These lectures may be recorded upon request if permission from participants is obtained in advance.
TCC lectures normally transmit video streams using H.261 and audio as G.711 for compatibility with the freely available AG3 software.
Each Access Grid session is paired with a Jabber/XMPP session on the Access Grid Support Centre (AGSC) Virtual Venue Server. The XMPP session allows instant messaging with other participants allowing fault diagnosis or communication without interrupting a session.
Oxford
The Oxford TCC is equipped with a Smart Board and Sympodium that can be viewed locally and transmitted to all participants of the meeting.
Events
January 21, 2008
TCC Number Theory Event Day was held at Bristol and students were given a chance to talk about their research to their peers and share ideas.
May 21, 2013
Graduate TCC Conference in Number Theory was a successful continuation of the aforementioned event.
External links
The TCC website
The Graduate TCC Conference in Number Theory website
College and university associations and consortia in the United Kingdom
Taught Course Centre
Engineering and Physical Sciences Research Council
Grid computing projects
Mathematics education in the United Kingdom
Organisations associated with the University of Oxford |
https://en.wikipedia.org/wiki/Cunningham%20number | In mathematics, specifically in number theory, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham.
Definition
Cunningham numbers are a simple type of binomial number – they are of the form
where b and n are integers and b is not a perfect power. They are denoted C±(b, n).
Primality
Establishing whether or not a given Cunningham number is prime has been the main focus of research around this type of number. Two particularly famous families of Cunningham numbers in this respect are the Fermat numbers, which are those of the form C+(2, 2m), and the Mersenne numbers, which are of the form C−(2, n).
Cunningham worked on gathering together all known data on which of these numbers were prime. In 1925 he published tables which summarised his findings with H. J. Woodall, and much computation has been done in the intervening time to fill these tables.
See also
Cunningham project
References
External links
Cunningham Number at MathWorld
The Cunningham Project, a collaborative effort to factor Cunningham numbers
Number theory |
https://en.wikipedia.org/wiki/Leslie%20Fox%20Prize%20for%20Numerical%20Analysis | The Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications (IMA) is a biennial prize established in 1985 by the IMA in honour of mathematician Leslie Fox (1918-1992). The prize honours "young numerical analysts worldwide" (any person who is less than 31 years old), and applicants submit papers for review. A committee reviews the papers, invites shortlisted candidates to give lectures at the Leslie Fox Prize meeting, and then awards First Prize and Second Prizes based on "mathematical and algorithmic brilliance in tandem with presentational skills."
Prize winners list
Source: Institute of Mathematics and its Applications
1985 - Lloyd N. Trefethen (inaugural prize winner)
1986 - J. W. Demmel and N. I. M. Gould
1988 - Nicholas J. Higham
1989 - 3 first prizes: Martin Buhmann ("Multivariable cardinal interpolation with radial basis functions"), Bart De Moor ("The restrictricted singular value decomposition: properties and applications"), Andrew M. Stuart ("Linear instability implies spurious periodic solutions")
1991 - Christopher Budd and J. F. B. M. Kraaijevanger
1993 - Yuying Li
1995 - Adrian Hill
1997 - Wim Sweldens, ("The Lifting Scheme: A Construction of Second Generation Wavelets")
1999 - Niles Pierce and Reha Tütüncü
2001 - Anna-Karin Tornberg
2003 - Jared Tanner
2005 - Roland Opfer and Paul Tupper
2007 - Yoichiro Mori and Ioana Dumitriu
2009 - Brian Sutton
2011 - Yuji Nakatsukasa
2013 - Michael Neilan
2015 - Iain Smears and Alex Townsend
2017 - Nicole Spillane
2019 - Yunan Yang
2021 - Lindon Roberts
2023 - Alice Cortinovis and Melanie Weber
Second Prize awardees
Source: Institute of Mathematics and its Applications
1985 - Nicholas Higham (Manchester), S.P.J. Matthews (Dundee), P.K. Sweby (Reading), Y. Yuan (Cambridge)
1986 - J.L. Barlow (Penn State), J. Scott (Oxford), A.J. Wathen (Bristol)
1988 - T. Hagstrom (SUNY, Stony Brook), P.T. Harker (Univ of Pennsylvania), I.R.H. Jackson (Cambridge), T. Tang (Leeds)
1989 - M. Ainsworth (Durham), R.H. Chan (Hong Kong), Alan Edelman (MIT), Desmond Higham (Toronto)
1991 - J. Levesley (Coventry), P.D. Loach (Bristol), B.F. Smith (Argonne), H. Zha (Stanford)
1993 - A. Edelman (Berkeley), D.J. Higham (Dundee), Z. Jia (Bielefeld), P. Lin (Oxford), R. Mathias (Minnesota)
1995 - X-W. Chang (McGill), L. Jay (Minnesota), Y. Liu (Cambridge), K-C. Toh (Cornell), D. Wang (Purdue)
1997 - T.A. Driscoll (Boulder), Valeria Simoncini (Pavia), Eric de Sturler (Zurich), R.H. Tütüncü (Carnegie-Mellon), Antonella Zanna (Cambridge), T. Zhang (Stanford)
1999 - Aurelian Bejancu (Cambridge), Vincent Heuveline (Heidelberg), Paul Houston (Oxford), Ross Lippert (Sandia National Laboratories)
2001 - Tilo Arens (Brunel University), Begona Cano (University of Valladolid), Eric Darve (Stanford University), Jing-Rebecca Li (Courant Institute NYU), Dominik Schötzau (University of Minnesota), Divakar Viswanath (University of Chicago)
2003 - Melvin Leok (California |
https://en.wikipedia.org/wiki/Preordered%20class | In mathematics, a preordered class is a class equipped with a preorder.
Definition
When dealing with a class C, it is possible to define a class relation on C as a subclass of the power class C C . Then, it is convenient to use the language of relations on a set.
A preordered class is a class with a preorder on it. Partially ordered class and totally ordered class are defined in a similar way. These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set. However, it is difficult to work with them as in the small case because many constructions common in a set theory are no longer possible in this framework.
Equivalently, a preordered class is a thin category, that is, a category with at most one morphism from an object to another.
Examples
In any category C, when D is a class of morphisms of C containing identities and closed under composition, the relation 'there exists a D-morphism from X to Y is a preorder on the class of objects of C.
The class Ord' of all ordinals is a totally ordered class with the classical ordering of ordinals.
References
Nicola Gambino and Peter Schuster, Spatiality for formal topologies
Order theory
Set theory |
https://en.wikipedia.org/wiki/Roman%20Catholic%20Archdiocese%20of%20Gda%C5%84sk | The Archdiocese of Gdańsk () is a Latin Church ecclesiastical jurisdiction or archdiocese of the Catholic Church in Poland. The diocese's episcopal see is Gdańsk.
According to the church statistics Sunday mass attendance was 38.1% in 2013 making it lower than the Polish average of weekly mass attendance (39.1%).
Its Archcathedral Basilica of The Holy Trinity, Blessed Virgin Mary and St Bernard in Gdańsk is listed as a Historic Monument of Poland.
History
After World War I and restoration of independent Poland, the city of Gdańsk (Danzig) was not restored to Poland from Germany, but rather turned into a free city according to the Treaty of Versailles. The Catholic congregation west of the Vistula belonged to the Diocese of Chełmno, which was restored to Poland and east of the Vistula to the Diocese of Warmia, which remained part of Weimar Germany in the interbellum. Germans within the administration of the Diocese of Chełmno were replaced by Polish priests and the Polish language was implemented as binding. While about 130,000 people in Danzig were Catholic, only about 10 percent of them were Polish-speaking and the first attempts to reorganize the ecclesiastical allocation were made in spring 1919, when members of the German congregation asked for an affiliation to the Diocese of Warmia.
While these attempts were supported by the German government, the Polish government tried to preserve the current situation. Pope Pius XI decided to establish an Apostolic Administrator of the Free City of Danzig on 24 April 1922, which was directly subordinated to the Pope. In 1925 a concordat between Poland and the Holy See was signed and the Apostolic Administrator was now supposed to be subordinated to the Nuncio of Warsaw, which caused protests among the local populace. Thus the Pope established the exempt Diocese of Danzig on 30 December 1925 and appointed Edward O'Rourke as the first Bishop on 2 January 1926.
The Diocese was promoted as Metropolitan Archdiocese of Gdańsk on 25 March 1992. On 17 November 1993, the Archbishop issued the instructions on the status of Kashubian as a language of liturgy.
Reports of sex abuse
In 2019, three protestors toppled a statue of Rev. Henryk Jankowski following revelations that he sexually Barbara Borowiecka when she was a girl. Jankowski, who also had a criminal investigation involving the sexual abuse of a boy dropped against him in 2004, had been defrocked in 2005. However, he died in 2010 without ever being convicted of sex abuse. It has also been acknowledged that Lech Walsea's personal chaplain Rev. Franciszek Cybula had been accused of committing acts of sex abuse while serving in the as well. On 13 August 2020, Pope Francis removed Gdańsk Archbishop Sławoj Leszek Głódź, who was among those who covered up abuse committed by Jankowski and Cybula. Glodz had also presided over Cybula's funeral. Despite the fact that Glodz had just turned 75, the required age for Catholic Bishops to offer their resignation, |
https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%E2%80%93Riesel%20test | In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N = k ⋅ 2n − 1 (Riesel numbers) with odd k < 2n. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form. For numbers of the form N = k ⋅ 2n + 1 (Proth numbers), either application of Proth's theorem (a Las Vegas algorithm) or one of the deterministic proofs described in Brillhart–Lehmer–Selfridge 1975 (see Pocklington primality test) are used.
The algorithm
The algorithm is very similar to the Lucas–Lehmer test, but with a variable starting point depending on the value of k.
Define a sequence ui for all i > 0 by:
Then N = k ⋅ 2n − 1, with k < 2n is prime if and only if it divides un−2.
Finding the starting value
The starting value u0 is determined as follows.
If k ≡ 1 or 5 (mod 6): if 1 (mod 6) and n is even, or 5 (mod 6) and n is odd, then 3 divides N, and there is no need to test. Otherwise, N ≡ 7 (mod 24) and the Lucas V(4,1) sequence may be used: we take , which is the kth term of that sequence. This is a generalization of the ordinary Lucas–Lehmer test, and reduces to it when k = 1.
Otherwise, we are in the case where k is a multiple of 3, and it is more difficult to select the right value of u0. It is known that if k = 3 and n ≡ 0 or 3 (mod 4), we can take u0 = 5778.
An alternative method for finding the starting value u0 is given in Rödseth 1994. The selection method is much easier than that used by Riesel for the 3 divides k case. First find a P value that satisfies the following equalities of Jacobi symbols:
.
In practice, only a few P values need be checked before one is found (5, 8, 9, or 11 work in about 85% of trials).
To find the starting value u0 from the P value we can use a Lucas(P,1) sequence, as shown in as well as page 124 of. The latter explains that when 3 ∤ k, P=4 may be used as above, and no further search is necessary.
The starting value u0 will be the Lucas sequence term Vk(P,1) taken mod N. This process of selection takes very little time compared to the main test.
How the test works
The Lucas–Lehmer–Riesel test is a particular case of group-order primality testing; we demonstrate that some number is prime by showing that some group has the order that it would have were that number prime, and we do this by finding an element of that group of precisely the right order.
For Lucas-style tests on a number N, we work in the multiplicative group of a quadratic extension of the integers modulo N; if N is prime, the order of this multiplicative group is N2 − 1, it has a subgroup of order N + 1, and we try to find a generator for that subgroup.
We start off by trying to find a non-iterative expression for the . Following the model of the Lucas–Lehmer test, put , and by induction we have .
So we can consider ourselves as looking at the 2ith term of the sequence . If a satisfies a quadratic equation, this is a L |
https://en.wikipedia.org/wiki/BCMP%20network | In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form equilibrium distribution exists. It is named after the authors of the paper where the network was first described: Baskett, Chandy, Muntz, and Palacios. The theorem is a significant extension to a Jackson network allowing virtually arbitrary customer routing and service time distributions, subject to particular service disciplines.
The paper is well known, and the theorem was described in 1990 as "one of the seminal achievements in queueing theory in the last 20 years" by J. Michael Harrison and Ruth J. Williams.
Definition of a BCMP network
A network of m interconnected queues is known as a BCMP network if each of the queues is of one of the following four types:
FCFS discipline where all customers have the same negative exponential service time distribution. The service rate can be state dependent, so write for the service rate when the queue length is j.
Processor sharing queues
Infinite-server queues
LCFS with pre-emptive resume (work is not lost)
In the final three cases, service time distributions must have rational Laplace transforms. This means the Laplace transform must be of the form
Also, the following conditions must be met.
external arrivals to node i (if any) form a Poisson process,
a customer completing service at queue i will either move to some new queue j with (fixed) probability or leave the system with probability , which is non-zero for some subset of the queues.
Theorem
For a BCMP network of m queues which is open, closed or mixed in which each queue is of type 1, 2, 3 or 4, the equilibrium state probabilities are given by
where C is a normalizing constant chosen to make the equilibrium state probabilities sum to 1 and represents the equilibrium distribution for queue i.
Proof
The original proof of the theorem was given by checking the independent balance equations were satisfied.
Peter G. Harrison offered an alternative proof by considering reversed processes.
References
Queueing theory |
https://en.wikipedia.org/wiki/Bartell%20mechanism | The Bartell mechanism is a pseudorotational mechanism similar to the Berry mechanism. It occurs only in molecules with a pentagonal bipyramidal molecular geometry, such as IF7. This mechanism was first predicted by H. B. Bartell. The mechanism exchanges the axial atoms with one pair of the equatorial atoms with an energy requirement of about 2.7 kcal/mol. Similarly to the Berry mechanism in square planar molecules, the symmetry of the intermediary phase of the vibrational mode is "chimeric" of other mechanisms; it displays characteristics of the Berry mechanism, a "lever" mechanism seen in pseudorotation of disphenoidal molecules, and a "turnstile" mechanism (which can be seen in trigonal bipyramidal molecules under certain conditions).
References
See also
Pseudorotation
Bailar twist
Berry mechanism
Ray–Dutt twist
Fluxional molecule
Molecular geometry
Reaction mechanisms |
https://en.wikipedia.org/wiki/Enveloping%20von%20Neumann%20algebra | In operator algebras, the enveloping von Neumann algebra of a C*-algebra is a von Neumann algebra that contains all the operator-algebraic information about the given C*-algebra. This may also be called the universal enveloping von Neumann algebra, since it is given by a universal property; and (as always with von Neumann algebras) the term W*-algebra may be used in place of von Neumann algebra.
Definition
Let A be a C*-algebra and πU be its universal representation, acting on Hilbert space HU. The image of πU, πU(A), is a C*-subalgebra of bounded operators on HU. The enveloping von Neumann algebra of A is the closure of πU(A) in the weak operator topology. It is sometimes denoted by A′′.
Properties
The universal representation πU and A′′ satisfies the following universal property: for any representation π, there is a unique *-homomorphism
that is continuous in the weak operator topology and the restriction of Φ to πU(A) is π.
As a particular case, one can consider the continuous functional calculus, whose unique extension gives a canonical Borel functional calculus.
By the Sherman–Takeda theorem, the double dual of a C*-algebra A, A**, can be identified with A′′, as Banach spaces.
Every representation of A uniquely determines a central projection (i.e. a projection in the center of the algebra) in A′′; it is called the central cover of that projection.
See also
Universal enveloping algebra
C*-algebras |
https://en.wikipedia.org/wiki/Brian%20Conrey | John Brian Conrey (23 June 1955) is an American mathematician and the executive director of the American Institute of Mathematics. His research interests are in number theory, specifically analysis of L-functions and the Riemann zeta function.
Education
Conrey received his B.S. from Santa Clara University in 1976 and received his Ph.D. at the University of Michigan in 1980 under the supervision of Hugh Lowell Montgomery.
Career
Conrey is the founding executive director of the American Institute of Mathematics, a position he has held since 1997. Since 2005, he has been part-time professor at the University of Bristol, England.
He is on the editorial board of the Journal of Number Theory.
Research
With Bui and Young, Conrey proved in 2011 that more than 41 percent of the zeros of the Riemann zeta function are on the critical line.
With Jonathan Keating, Nina Snaith, and others, Conrey researched correlations of eigenvalues of random unitary matrices and Riemann zeta zeros.
Awards and honors
The American Mathematical Society jointly awarded him the eighth annual Levi L. Conant Prize for expository writing in 2008 for The Riemann Hypothesis. In 2015 he was elected as a Fellow of the American Mathematical Society.
References
External links
20th-century American mathematicians
21st-century American mathematicians
Number theorists
Academics of the University of Bristol
Living people
Santa Clara University alumni
University of Michigan alumni
Fellows of the American Mathematical Society
1955 births
Albuquerque Academy Alumni |
https://en.wikipedia.org/wiki/Igor%20%C4%8Cagalj | Igor Čagalj (born 6 October 1982) is a retired Bosnian-born Croatian football defender who last played for NK Ravnice.
Statistics
Club
Honours
Gorica
Druga HNL: 2017-18
References
External links
1982 births
Living people
Sportspeople from Doboj
Men's association football defenders
Croatian men's footballers
Croatia men's youth international footballers
HNK Segesta players
NK Hrvatski Dragovoljac players
NK Inter Zaprešić players
HNK Šibenik players
HNK Rijeka players
NK Istra 1961 players
HNK Gorica players
NK Vinogradar players
First Football League (Croatia) players
Croatian Football League players
Slovenian PrvaLiga players
Second Football League (Croatia) players
Croatian expatriate men's footballers
Expatriate men's footballers in Slovenia
Croatian expatriate sportspeople in Slovenia |
https://en.wikipedia.org/wiki/Computation%20of%20cyclic%20redundancy%20checks | Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive or operations replace subtractions. Division of this type is efficiently realised in hardware by a modified shift register, and in software by a series of equivalent algorithms, starting with simple code close to the mathematics and becoming faster (and arguably more obfuscated) through byte-wise parallelism and space–time tradeoffs.
Various CRC standards extend the polynomial division algorithm by specifying an initial shift register value, a final Exclusive-Or step and, most critically, a bit ordering (endianness). As a result, the code seen in practice deviates confusingly from "pure" division, and the register may shift left or right.
Example
As an example of implementing polynomial division in hardware, suppose that we are trying to compute an 8-bit CRC of an 8-bit message made of the ASCII character "W", which is binary 010101112, decimal 8710, or hexadecimal 5716. For illustration, we will use the CRC-8-ATM (HEC) polynomial . Writing the first bit transmitted (the coefficient of the highest power of ) on the left, this corresponds to the 9-bit string "100000111".
The byte value 5716 can be transmitted in two different orders, depending on the bit ordering convention used. Each one generates a different message polynomial . Msbit-first, this is = 01010111, while lsbit-first, it is = 11101010. These can then be multiplied by to produce two 16-bit message polynomials .
Computing the remainder then consists of subtracting multiples of the generator polynomial . This is just like decimal long division, but even simpler because the only possible multiples at each step are 0 and 1, and the subtractions borrow "from infinity" instead of reducing the upper digits. Because we do not care about the quotient, there is no need to record it.
Observe that after each subtraction, the bits are divided into three groups: at the beginning, a group which is all zero; at the end, a group which is unchanged from the original; and a blue shaded group in the middle which is "interesting". The "interesting" group is 8 bits long, matching the degree of the polynomial. Every step, the appropriate multiple of the polynomial is subtracted to make the zero group one bit longer, and the unchanged group becomes one bit shorter, until only the final remainder is left.
In the msbit-first example, the remainder polynomial is . Converting to a hexadecimal number using the convention that the highest power of x is the msbit; this is A216. In the lsbit-first, the remainder is . Converting to hexadecimal using the convention that the highest power of x is the lsbit, this is 1916.
Implementation
Writing out the full message at each step, as done in the example above, is very tedious |
https://en.wikipedia.org/wiki/Information%20Security%20Group | Founded in 1990, the Information Security Group (ISG) is an academic department focusing on Information and Cyber Security within the Engineering, Physical Sciences and Mathematics School (EPMS) at Royal Holloway, University of London. It has around 25 established academic posts, 7 visiting Professors or Fellows and over 90 research students. The Founder Director of the ISG was Professor Fred Piper, and the current director is Professor Chris Mitchell. Previous directors include Professors Peter Komisarczuk, Keith Martin, Keith Mayes and Peter Wild.
In 1998 the ISG was awarded a Queen's Anniversary Prize in recognition of its work in the field of information security. It has also been awarded the status of Academic Centre of Excellence in Cyber Security Research (ACE-CSR) and hosts a Centre for Doctoral Training in cyber security.
In 1992, the ISG introduced an MSc in information security, being the first university in the world to offer a postgraduate course in the subject. In 2014 this course received full certification from GCHQ. In 2017 it won the award for the Best Cyber Security Education Programme at SC Awards Europe 2017 and in 2021 it was awarded gold status by the National Cyber Security Centre (NCSC).
Research topics addressed by the ISG include: the design and evaluation of cryptographic algorithms, protocols and key management; provable security; smart cards; RFID; electronic commerce; security management; mobile telecommunications security; authentication and identity management; cyber-physical systems; embedded security; Internet of Things (IoT); and human related aspects of cyber security. The current director of Research is Professor Stephen Wolthusen.
The ISG includes the Smart Card and IoT Security Centre (previously named Smart Card Centre, SCC) that was founded in October 2002 by Royal Holloway, Vodafone and Giesecke & Devrient, for training and research in the field of Smart cards, applications and related technologies: its research topics include RFID, Near Field Communication (NFC), mobile devices, IoT, and general embedded/implementation system security. In 2008, the SCC was commissioned to perform a counter expertise review of the OV-chipkaart by the Dutch Ministry of Transport, Public Works and Water Management. The SCC has received support from a number of industrial partners, such as Orange Labs (UK), the UK Cards Association, Transport for London and ITSO. The current director of the Smart Card and IoT Security Centre is Dr. Konstantinos Markantonakis.
The ISG also includes a Systems Security Research Lab (S2Lab), which was created in 2014, to investigate how to protect systems from software related threats, such as malware and botnets. The research in the lab covers many different Computer Science-related topics, such as operating systems, computer architecture, program analysis, and machine learning. The current Lab Leader is Dr. Lorenzo Cavallaro.
Current and former associated academics include Whitfield |
https://en.wikipedia.org/wiki/Luigi%20Poletti%20%28architect%29 | Luigi Poletti (28 October 1792 – 2 August 1869) was an Italian architect, active in a neoclassical style.
Biography
He was born in Modena. He initially obtained a doctorate in Mathematics and Philosophy in Bologna. He returns to Modena and becomes engineer of the Garfagnana, and professor of Mechanics and Hydraulics at the University. He then received a stipend to study in Rome. There he studied under Raffaele Stern.
In 1823, the ancient Basilica of San Paolo fuori le Mura, one of the seven pilgrimage churches of Rome, was destroyed by fire. When plans for a new church were announced, a great hue arose from the neoclassic adherents of the past, such as Carlo Fea, who advocated for the church to be rebuilt as an exact replica of the past. Initially Pasquale Belli was hired, but soon after was replaced by Poletti who promised a closer replica. But he proposed to build a church as if the original builders had returned and, in their spirit, availed themselves of all the erudition compiled in the interim, revisiting the design and correcting its errors.
Poletti also added a choir to the Pantheon in 1840 and built the theaters in Fano (1845–1863), Rimini (1843–1857) and Terni (1840–1848). He rebuilt the church of San Venanzio in Camerino, which had fallen in the earthquake of 1792. After the damage from an earthquake in 1832, he rebuilt (1836–40) the Basilica of Santa Maria degli Angeli in Assisi. He built the Cathedral of Montalto delle Marche on the foundations that had been started under Pope Sixtus V. He designed the church of San Filippo in the town of Nocera (disambiguate?). He completed the chapel and altar of Santissima Maria (called dell'acqua) in San Francesco in Rimini. He built a similar chapel in Fossombrone. He designed the lighthouse and arsenal in the port of Ripa Grande. He designed the Palazzo Ceccopieri in Via di Monte Catino. He designed a number of funereal monuments in and around Rome including one dedicated to Vincenzo Casciani (1832) in the Costa Chapel, Santa Maria del Popolo and to the papal architect Cavalierie Pietro Bosio in the Campo Santo.
He also reconstructed Sant'Andrea degli Scozzesi in Rome (1869). His pupils included Virginio Vespignani. He also helped design the Column of the Immaculate Conception, Rome. He died in Milan.
References
Sources
www.italycyberguide.com
External links
Ashton Rollins Willard, History of modern Italian art, Longmans, Green & Co., London, New York [etc.], 1902 (on line from Internet Archive)
1792 births
1869 deaths
19th-century Italian architects
Architects from Modena
Italian neoclassical architects |
https://en.wikipedia.org/wiki/List%20of%20Persepolis%20F.C.%20statistics%20and%20records | Persepolis Football Club is an Iranian professional association football club based in Tehran. The club was formed in 1963, and played its first competitive match against Rah Ahan F.C. Persepolis currently plays in the Persian Gulf Pro League. Persepolis is the only club, never to have been relegated from the league. They have also been involved in Asian football, winning the Asian Cup Winners' Cup.
This list encompasses the major honours won by Persepolis and records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records the highest transfer fees paid and received by the club.
This page details Persepolis Football Club records.
Statistics
Statistics in IPL
Seasons in IPL: 20 (all)
Best position in IPL: First (2001-02), (2007-08), (2016-17), (2017-18), (2018-19), (2019-20), (2020-21), (2022-23)
Worst position in IPL: 12 (2011-12)
Most goals scored in a season: 56 (Azadegan League 1998-99),55 (IPL 2007-08)
Most goals scored in a match: 8 against Pegah F.C. (IPL 2003-04)
Most goals conceded in a match: 4 against Esteghlal Ahvaz F.C. (IPL 2007-08), TractorSazi (2011-12)
Statistics in AFC Champions League
Most goals scored in a match: 6 against Al-Shabab (UAE)
Most goals conceded in a match: 5 against Al-Gharafa (2009) (21 April 2009)
Player records
Appearances
Most Appearances:341 Ali Parvin
Most League Appearances: Afshin Peyrovani (209)
Most Goalkeeper Appearances: Vahid Ghelich (185)
Youngest first-team player : Mehdi Mahdavikia (17 years and 206 days old)
Youngest first-team player in a league match : Mehdi Mahdavikia (17 years and 206 days old)
Oldest first-team player : Ali Parvin (41 years and ? days old)
Player who has won most league titles: Kamal Kamyabinia (6 titles), Afshin Peyrovani, Behrouz Rahbarifard, Esmaeil Halali, Jalal Hosseini and Božidar Radošević (5 Titles)
Goalscorers
All-time top scorer: Farshad Pious with 153 goals
First Goalscorer : Nazem Ganjapour
First Goalscorer in Tehran derby: Nazem Ganjapour
Most Goalscorer in Tehran derby: 7 (Safar Iranpak)
Most goals in a season : 26 (Ali Alipour', 2017–18)
Most League goals in a season : 20 (Farshad Pious, 1994–95)
Most goals in a single match at home : 4 goals (Ali Daei, 2003–04)
Most goals in an AFC Champions League match : 3 Emon Zayed (Al-Shabab), Mehdi Taremi (Al Wahda )
Fastest recorded goal : 00:07 Gholamreza Rezaei vs Fajr Sepasi (2012-13 Pro League)
Latest recorded goal : 90+10:24 Vahid Amiri vs Machine Sazi (2019-20 Hazfi Cup)
Youngest goalscorer : Mehdi Mahdavikia against Polyacryl Esfahan F.C. (17 years and 300 days old)
Players statistics
Most appearances
Top goalscorers
Most goals scored in official competi |
https://en.wikipedia.org/wiki/Saint-Pierre%2C%20Quebec | Saint-Pierre () is a village municipality in Joliette Regional County Municipality in the Lanaudière region of Quebec, Canada.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Saint-Pierre had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
Population:
Population in 2016: 276 (2011 to 2016 population change: -9.5%)
Population in 2011: 305 (2006 to 2011 population change: 0.3%)
Population in 2006: 304
Population in 2001: 293
Population in 1996: 357
Population in 1991: 358
Mother tongue:
English as first language: 0%
French as first language: 100%
English and French as first language: 0%
Other as first language: 0%
Education
The Sir Wilfrid Laurier School Board operates anglophone public schools, including:
Joliette Elementary School in Saint-Charles-Borromée
Joliette High School in Joliette
See also
List of village municipalities in Quebec
References
Incorporated places in Lanaudière
Villages in Quebec |
https://en.wikipedia.org/wiki/Wired%20logic%20connection | A wired logic connection is a logic gate that implements boolean algebra (logic) using only passive components such as diodes and resistors. A wired logic connection can create an AND or an OR gate. Limitations include the inability to create a NOT gate, the lack of amplification to provide level restoration, and its constant ohmic heating for most logic (particularly more than CMOS) which indirectly limits density of components and speed.
Wired logic works by exploiting the high impedance of open collector outputs (and its variants: open emitter, open drain, or open source) by just adding a pull-up or pull-down resistor to a voltage source, or can be applied to push-pull outputs by using diode logic (with the disadvantage of incurring a diode drop voltage loss).
Active-high wired AND connection
See also:
The wired AND connection is a form of AND gate. When using open collector or similar outputs (which can be identified by the ⎐ symbol in schematics), wired AND only requires a pull up resistor on the shared output wire. In this example, 5V is considered HIGH (true), and 0V is LOW (false). This gate can be easily extended with more inputs.
When all inputs are HIGH, they all present high impedance, and the pull-up resistor pulls output voltage HIGH, but if any input is LOW, they pull the output LOW:
When driving a load, the HIGH output is reduced by the pull-up's voltage drop, though the LOW output is almost 0V. But if diode logic is used, each input requires a diode, and the LOW output voltage will additionally be raised by the diode's forward voltage. Care should be taken to ensure the output still lies within valid voltage levels.
Active-high wired OR connection
See also:
The wired OR connection electrically performs the Boolean logic operation of an OR gate using open emitter or similar inputs (which can be identified by the ⎏ symbol in schematics) connected to a shared output with a pull-down resistor. This gate can also be easily extended with more inputs.
When all inputs are LOW, they all present high impedance, and the pull-down resistor pulls the output voltage LOW, but if any input is HIGH, they pull the output HIGH:
When driving a load, the LOW output is raised by the pull-down's voltage drop, though the HIGH output is almost the supply voltage (5V). But if diode logic is used, each input requires a diode, and the HIGH output voltage will additionally be lowered by the diode's forward voltage.
Reversing active level
An active-high wired AND can be treated as active-low wired OR (and an active-high wired OR can be treated as active-low wired AND), by using active-low logic (or negative logic) and applying De Morgan's laws.
Compatibility of wired AND OR using diodes
Diode logic uses a diode for each input in addition to a shared pull-up resistor (for wired AND) or a pull-down resistor (for wired OR). However, each stage of diode logic reduces output voltage levels. So without amplification, the output voltage may not be |
https://en.wikipedia.org/wiki/Vague%20topology | In mathematics, particularly in the area of functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally compact Hausdorff spaces.
Let be a locally compact Hausdorff space. Let be the space of complex Radon measures on and denote the dual of the Banach space of complex continuous functions on vanishing at infinity equipped with the uniform norm. By the Riesz representation theorem is isometric to The isometry maps a measure to a linear functional
The vague topology is the weak-* topology on The corresponding topology on induced by the isometry from is also called the vague topology on Thus in particular, a sequence of measures converges vaguely to a measure whenever for all test functions
It is also not uncommon to define the vague topology by duality with continuous functions having compact support that is, a sequence of measures converges vaguely to a measure whenever the above convergence holds for all test functions This construction gives rise to a different topology. In particular, the topology defined by duality with can be metrizable whereas the topology defined by duality with is not.
One application of this is to probability theory: for example, the central limit theorem is essentially a statement that if are the probability measures for certain sums of independent random variables, then converge weakly (and then vaguely) to a normal distribution, that is, the measure is "approximately normal" for large
See also
References
.
G. B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed, John Wiley & Sons, Inc., 1999.
Real analysis
Measure theory
Topology of function spaces |
https://en.wikipedia.org/wiki/Australian%20Institute%20of%20Health%20and%20Welfare | The Australian Institute of Health and Welfare (AIHW) is Australia's national agency for information and statistics on Australia's health and welfare. Statistics and data developed by the AIHW are used extensively to inform discussion and policy decisions on health, community services and housing assistance. Under Australia's constitution, health and welfare services are primarily delivered by the states and territories, who are also mainly responsible for the collection of statistics on these services. A fundamental aim of the institute is to promote consistency among national, state and territory statistics, in order to produce comprehensive national data of the highest standard.
The AIHW is an Australian Government statutory agency established under the Australian Institute of Health and Welfare Act 1987. The Act contains very strong confidentiality protections for all data held, and requires the AIHW to publish two key biennial reports in alternate years: Australia's health and Australia's welfare. Numerous other reports are produced each year, all of which are available free of charge on the AIHW website.
In 2016, the Australian Institute of Health and Welfare and the National Hospital Performance Authority merged.
References
Medical and health organisations based in Australia |
https://en.wikipedia.org/wiki/Venkatesan%20Guruswami | Venkatesan Guruswami (born 1976) is a senior scientist at the Simons Institute for the Theory of Computing and Professor of EECS and Mathematics at the University of California, Berkeley. He did his high schooling at Padma Seshadri Bala Bhavan in Chennai, India. He completed his undergraduate in Computer Science from IIT Madras and his doctorate from Massachusetts Institute of Technology under the supervision of Madhu Sudan in 2001. After receiving his PhD, he spent a year at UC Berkeley as a Miller Fellow, and then was a member of the faculty at the University of Washington from 2002 to 2009. His primary area of research is computer science, and in particular on error-correcting codes. During 2007–2008, he visited the Institute for Advanced Study as a Member of School of Mathematics. He also visited SCS at Carnegie Mellon University during 2008–09 as a visiting faculty. From July 2009 through December 2020 he was a faculty member in the Computer Science Department in the School of Computer Science at Carnegie Mellon University.
Recognition
Guruswami was awarded the 2002 ACM Doctoral Dissertation Award for his dissertation List Decoding of Error-Correcting Codes, which introduced an algorithm that allowed for the correction of errors beyond half the minimum distance of the code. It applies to Reed–Solomon codes and more generally to algebraic geometry codes. This algorithm produces a list of codewords (it is a list-decoding algorithm) and is based on interpolation and factorization of polynomials over and its extensions.
He was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Mathematical Aspects of Computer Science."
Guraswami was one of two winners of the 2012 Presburger Award, given by the European Association for Theoretical Computer Science for outstanding contributions by a young theoretical computer scientist.
He was elected as an ACM Fellow in 2017, as an IEEE Fellow in 2019, and to the 2023 class of Fellows of the American Mathematical Society, "for contributions to the theory of computing and error-correcting codes, and for service to the profession".
Selected publications
See also
Guruswami–Sudan list decoding algorithm
References
External links
Venkatesan Guruswami's Homepage
1976 births
Living people
Scientists from Chennai
Indian computer scientists
Theoretical computer scientists
IIT Madras alumni
Massachusetts Institute of Technology alumni
Carnegie Mellon University faculty
University of California, Berkeley faculty
Padma Seshadri Bala Bhavan schools alumni
Fellows of the Association for Computing Machinery
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20of%20Bolivia | The Instituto Nacional de Estadística de Bolivia or National Institute of Statistics of Bolivia is a branch of the Government of Bolivia which specifically collects factual data in the country of Bolivia in South America. The Institute compiles statistics ranging from the area of its provinces and municipalities to population structure, and demographics and education. It also provides information on transport services and industry and salary details and electricity rates.
References
Government of Bolivia |
https://en.wikipedia.org/wiki/Hyperdeterminant | In algebra, the hyperdeterminant is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an n × n square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor. Many other properties of determinants generalize in some way to hyperdeterminants, but unlike a determinant, the hyperdeterminant does not have a simple geometric interpretation in terms of volumes.
There are at least three definitions of hyperdeterminant. The first was discovered by Arthur Cayley in 1843 presented to the Cambridge Philosophical Society. It is in two parts and Cayley's first hyperdeterminant is covered in the second part. It is usually denoted by det0. The second Cayley hyperdeterminant originated in 1845 and is often denoted "Det". This definition is a discriminant for a singular point on a scalar valued multilinear map.
Cayley's first hyperdeterminant is defined only for hypercubes having an even number of dimensions (although variations exist in odd dimensions). Cayley's second hyperdeterminant is defined for a restricted range of hypermatrix formats (including the hypercubes of any dimensions). The third hyperdeterminant, most recently defined by Glynn, occurs only for fields of prime characteristic p. It is denoted by detp and acts on all hypercubes over such a field.
Only the first and third hyperdeterminants are "multiplicative," except for the second hyperdeterminant in the case of "boundary" formats. The first and third hyperdeterminants also have closed formulae as polynomials and therefore their degrees are known, whereas the second one does not appear to have a closed formula or degree in all cases that are known.
The notation for determinants can be extended to hyperdeterminants without change or ambiguity. Hence the hyperdeterminant of a hypermatrix A may be written using the vertical bar notation as |A| or as det(A).
A standard modern textbook on Cayley's second hyperdeterminant Det (as well as many other results) is "Discriminants, Resultants and Multidimensional Determinants" by Gel'fand, Kapranov and Zelevinsky. Their notation and terminology is followed in the next section.
Cayley's second hyperdeterminant Det
In the special case of a 2 × 2 × 2 hypermatrix the hyperdeterminant is known as Cayley's hyperdeterminant after the British mathematician Arthur Cayley who discovered it. The quartic expression for the Cayley's hyperdeterminant of hypermatrix A with components aijk, ∊ } is given by
Det(A) = a0002a1112 + a0012a1102 + a0102a1012 + a1002a0112
− 2a000a001a110a111 − 2a000a010a101a111 − 2a000a011a100a111 − 2a001a010a101a110 − 2a001a011a110a100 − 2a010a011a101a100 + 4a000a011a101a110 + 4a001a010a100a111.
This expression acts as a discriminant in the sense that it is zero if and only if there is a non-zero solution in six unknowns xi, yi, zi |
https://en.wikipedia.org/wiki/David%20Williams%20%28mathematician%29 | David Williams FRS is a Welsh mathematician who works in probability theory.
Early life and education
David Williams was born at Gorseinon, near Swansea, Wales. He was educated at Gowerton Grammar School, winning a mathematics scholarship to Jesus College, Oxford, and went on to obtain a DPhil under the supervision of David George Kendall and Gerd Edzard Harry Reuter, with a thesis titled Random time substitution in Markov chains.
Career
Williams held posts at the Stanford University (1962–63), University of Durham, University of Cambridge (1966–69), and at Swansea University (1969–85), where he was promoted to a personal chair in 1972.
In 1985, he was elected to the Professorship of Mathematical Statistics, University of Cambridge, where he remained until 1992, serving as Director of the Statistical Laboratory between 1987 and 1991. Following this, he held the Chair of Mathematical Sciences jointly with the Mathematics and Statistics Groups at the University of Bath.
In 1999, he returned to Swansea University, where he currently holds a Research Professorship.
Williams's research interests encompass Brownian motion, diffusions, Markov processes, martingales and Wiener–Hopf theory. Recognition for his work includes being elected Fellow of the Royal Society in 1984, where he was cited for his achievements on the construction problem for Markov chains and on path decompositions for Brownian motion, and being awarded the London Mathematical Society's Pólya Prize in 1994.
One of his main discoveries is the decomposition of Brownian paths with respect to their maximum.
He is the author of Probability With Martingales and Weighing the Odds, and co-author (with L. C. G. Rogers) of both volumes of Diffusions, Markov Processes and Martingales.
Books
Diffusions, Markov processes, and martingales, Wiley 1979; 2nd. edn. with L. C. G. Rogers: Diffusions, Markov processes, and martingales, Volume One: Foundations, Wiley 1995; reprinting of 2nd edn. Cambridge University Press 2000
with L. C. G. Rogers: Diffusions, Markov processes, and martingales, Volume Two: Itō calculus, Wiley 1988; 2nd edn. Cambridge University Press 2000
Probability with martingales, Cambridge Mathematical Textbooks, Cambridge University Press 1991
Weighing the Odds: a course in probability and statistics, Cambridge University Press 2001
ed. with J. C. R. Hunt, O. M. Phillips: Turbulence and stochastic processes. Kolmogorov´s ideas 50 years on, London, Royal Society 1991
Notes
References
External links
20th-century British mathematicians
21st-century British mathematicians
Alumni of Jesus College, Oxford
Fellows of the Royal Society
Living people
People from Swansea
Probability theorists
Welsh mathematicians
Year of birth missing (living people)
People educated at Gowerton Grammar School
Stanford University Department of Mathematics faculty
Academics of Durham University
Academics of Swansea University
Professors of the University of Cambridge
Academics of the University of Ba |
https://en.wikipedia.org/wiki/David%20Rees%20%28mathematician%29 | David Rees FRS (29 May 1918 – 16 August 2013) was a British professor of pure mathematics at the University of Exeter, having been head of the Mathematics / Mathematical Sciences Department at Exeter from 1958 to 1983. During the Second World War, Rees was active on Enigma research in Hut 6 at Bletchley Park.
Early life
Rees was born in Abergavenny to David Rees (1881–), a corn merchant, and his wife Florence Gertrude (Gertie) née Powell (1884–1970), the 4th out of 5 children. Despite periods of ill health and absence, he successfully completed his early education at King Henry VIII Grammar School.
Education and career
Rees won a scholarship to Sidney Sussex College, Cambridge, supervised by Gordon Welchman and graduating in summer 1939. On completion of his education, he initially worked on semigroup theory; the Rees factor semigroup is named after him. He also characterised completely simple and completely 0-simple semigroups, in what is nowadays known as Rees's theorem. The matrix-based semigroups used in this characterisation are called Rees matrix semigroups.
Later in 1939, Welchman drafted Rees into Hut 6, Bletchley Park, for the war effort. He was credited with the first decode using the Herivel tip. He was subsequently seconded to the Enigma Research Section, where the Abwehr Enigma was broken, and later to the Newmanry, where the Colossus computer was built.
After the war, Rees was appointed an assistant lecturer at Manchester University in 1945 and a full lecturer at University of Cambridge in 1948. In 1949, he was a Fellow of Downing College.
At the behest of Douglas Northcott he switched his research focus to commutative algebra. In 1954, in a joint paper with Northcott, Rees introduced the Northcott–Rees theory of reductions and integral closures, which has subsequently been influential in commutative algebra.
In 1956 he introduced the Rees decomposition of a commutative algebra.
In 1958, Rees and his family moved to Exeter, where he had been appointed to the Chair of Pure Mathematics. In 1959, he was awarded a DSc by the University of Cambridge.
According to Craig Steven Wright, Rees was the third part of the Satoshi team that created Bitcoin.
Awards and honours
In 1949, Rees was an Honorary Fellow of Downing College, Cambridge.
In 1968, he was elected a Fellow of the Royal Society (FRS).
In 1993, he was also awarded an Honorary DSc by the University of Exeter. The same year, he was awarded the Pólya Prize by the London Mathematical Society. In August 1998 a conference on commutative algebra was held at Exeter in honour of David Rees' 80th Year.
Personal life
In 1952, Rees married Joan S. Cushen, who became a Senior Lecturer in Mathematics at Exeter, with four children:
(Susan) Mary Rees FRS, Professor of Mathematics at the University of Liverpool, b. 1953
Rebecca Rees, b. 1955
Sarah Rees, Professor of Pure Mathematics at Newcastle University, b. 1957
Deborah Rees, b. 1960
External links
Obituary by R.Y. Sharp, |
https://en.wikipedia.org/wiki/Contour%20set | In mathematics, contour sets generalize and formalize the everyday notions of
everything superior to something
everything superior or equivalent to something
everything inferior to something
everything inferior or equivalent to something.
Formal definitions
Given a relation on pairs of elements of set
and an element of
The upper contour set of is the set of all that are related to :
The lower contour set of is the set of all such that is related to them:
The strict upper contour set of is the set of all that are related to without being in this way related to any of them:
The strict lower contour set of is the set of all such that is related to them without any of them being in this way related to :
The formal expressions of the last two may be simplified if we have defined
so that is related to but is not related to , in which case the strict upper contour set of is
and the strict lower contour set of is
Contour sets of a function
In the case of a function considered in terms of relation , reference to the contour sets of the function is implicitly to the contour sets of the implied relation
Examples
Arithmetic
Consider a real number , and the relation . Then
the upper contour set of would be the set of numbers that were greater than or equal to ,
the strict upper contour set of would be the set of numbers that were greater than ,
the lower contour set of would be the set of numbers that were less than or equal to , and
the strict lower contour set of would be the set of numbers that were less than .
Consider, more generally, the relation
Then
the upper contour set of would be the set of all such that ,
the strict upper contour set of would be the set of all such that ,
the lower contour set of would be the set of all such that , and
the strict lower contour set of would be the set of all such that .
It would be technically possible to define contour sets in terms of the relation
though such definitions would tend to confound ready understanding.
In the case of a real-valued function (whose arguments might or might not be themselves real numbers), reference to the contour sets of the function is implicitly to the contour sets of the relation
Note that the arguments to might be vectors, and that the notation used might instead be
Economics
In economics, the set could be interpreted as a set of goods and services or of possible outcomes, the relation as strict preference, and the relationship as weak preference. Then
the upper contour set, or better set, of would be the set of all goods, services, or outcomes that were at least as desired as ,
the strict upper contour set of would be the set of all goods, services, or outcomes that were more desired than ,
the lower contour set, or worse set, of would be the set of all goods, services, or outcomes that were no more desired than , and
the strict lower contour set of would be the set of all goods, services, or outcomes th |
https://en.wikipedia.org/wiki/Pentagonal%20pyramidal%20molecular%20geometry | In chemistry, pentagonal pyramidal molecular geometry describes the shape of compounds where in six atoms or groups of atoms or ligands are arranged around a central atom, at the vertices of a pentagonal pyramid. It is one of the few molecular geometries with uneven bond angles.
Examples
References
Pentagonal pyramid, Wolfram MathWorld
Molecular geometry |
https://en.wikipedia.org/wiki/Hubert%20Kennedy | Hubert Collings Kennedy (born 1931) is an American author and mathematician.
Kennedy was born in Florida and studied mathematics at several universities. From 1961 he was professor of mathematics, with research interest in the history of mathematics, at Providence College (Rhode Island), He spent three sabbatical years doing research in Italy and Germany. He published a definitive biography of Giuseppe Peano who conceived modern mathematical notation.
Kennedy came out as gay on the cover of the magazine The Cowl, and, along with Eric Gordon, was part of the first Gay Pride parade in Providence, Rhode Island, which was held on June 26, 1976.
In 1986 Kennedy moved to San Francisco, where he continued his historical research, now on the beginnings of the gay movement in Germany. He has over 200 publications in several languages, from an analysis of the mathematical manuscripts of Karl Marx and a revelation of Marx's homophobia, to theoretical genetics and a proof of the impossibility of an organism that requires more than two sexes in order to reproduce. In addition, Kennedy has written biographies of the Italian mathematician Giuseppe Peano and the German homosexual emancipationist/theorist Karl Heinrich Ulrichs, and has edited the collected writings of Ulrichs. His translations of the boy-love novels of the German anarchist writer John Henry Mackay and his investigations of the writings of Mackay have helped establish Mackay's place in the gay canon.
Kennedy married his longtime companion Don Endy in 2014.
Bibliography
John Henry Mackay (Sagitta), Anarchist der Liebe, biography (2007).
Karl Heinrich Ulrichs, Pioneer of the Modern Gay Movement (2002).
PEANO: Life and Works of Giuseppe Peano.
Collection of articles on life and mathematics of Peano (1960s to 1980s).
Sex & Math in the Harvard Yard: The Memoirs of James Mills Peirce, novel.
Homosexuality and Male Bonding in Pre-Nazi Germany: The Youth Movement, the Gay Movement and Male Bonding Before Hitler’s Rise: Original Transcripts from "Der Eigene", the First Gay Journal in the World (1991).
Life’s Little Loafer, short story.
From My Life (2009), autobiography by Kennedy.
A Touch of Royalty: Gay Author James Barr, essay.
Eight Mathematical Biographies, collections of short biographies.
The Ideal Gay Man: The Story of "Der Kreis" (1999).
Negation of the Negation: Karl Marx and Differential Calculus.
In Memoriam: Five Gay Obituaries on Glenn Hogan, Mario Mieli, Roger Austen, Peter Schult, and Robert Turner.
John Henry Mackay, Die letzte Pflicht & Albert Schnells Untergang (2007).
References
External links
Hubert Kennedy in German National Bibliothek
Hubert Kennedy
1931 births
Living people
20th-century American mathematicians
American non-fiction writers
American gay writers
Gay academics
LGBT mathematicians |
https://en.wikipedia.org/wiki/Edna%20Kramer | Edna Ernestine Kramer Lassar (May 11, 1902 – July 9, 1984), born Edna Ernestine Kramer, was an American mathematician and author of mathematics books.
Kramer was born in Manhattan to Jewish immigrants. She earned her B.A. summa cum laude in mathematics from Hunter College in 1922. While teaching at local high schools, she earned her M.A. in 1925 and Ph.D. in 1930 in mathematics (with a minor in physics) from Columbia University with Edward Kasner as her advisor.
She wrote The Nature and Growth of Modern Mathematics, A First Course in Educational Statistics, Mathematics Takes Wings: An Aviation Supplement to Secondary Mathematics, and The Main Stream of Mathematics.
Kramer married the French teacher Benedict Taxier Lassar on July 2, 1935. Kramer-Lassar died at the age of 82 in Manhattan of Parkinson's disease.
Works
The Main Stream of Mathematics (1951)
The Nature and Growth of Modern Mathematics (1970)
References
External links
Biography from Agnes Scott College
MacTutor biography
Biography on p. 335-337 of the Supplementary Material at AMS
1902 births
1984 deaths
Hunter College alumni
Columbia Graduate School of Arts and Sciences alumni
People from Manhattan
20th-century American mathematicians
American women mathematicians
Neurological disease deaths in New York (state)
Deaths from Parkinson's disease
20th-century women mathematicians
Mathematicians from New York (state)
20th-century American women |
https://en.wikipedia.org/wiki/Hansraj%20Gupta | Hansraj Gupta (9 October 1902 – 23 November 1988) was an Indian mathematician specialising in number theory, in particular the study of the partition function.
Biography
Gupta was born 9 October 1902 in Rawalpindi, then part of British India. His father was Gulraj Gupta, an executive engineer with the Bombay, Baroda and Central India Railway. He studied at the Panjab University in Lahore, where he graduated with a M.A. in 1925. In 1928 he became a lecturer at the Government College in Hoshiarpur. He received his Ph.D. from the Panjab University in 1936. By then he had already published several papers on partitions.
Gupta was elected a fellow of the Indian National Science Academy (INSA) in 1950. He became head of the Panjab University's new department of mathematics in 1954. He served as president of the Indian Mathematical Society (IMS) for the term 1963–4. He retired as director of the Centre of Advanced Study in Mathematics in 1966, by which time he was already travelling North America as a visiting professor: at the University of Colorado at Boulder (1962), the University of Arizona (1966), and the University of Alberta (1969). He represented the INSA at the 1974 International Congress of Mathematicians in Vancouver. He continued actively researching and publishing mathematics for many years after retirement.
Gupta died 23 November 1988. Since 1990 the annual IMS conference has included a lecture in his honour, the Hansraj Gupta Memorial Award Lecture.
Selected publications
References
External links
IMS biography
1902 births
1988 deaths
Indian number theorists
Presidents of the Indian Mathematical Society
20th-century Indian mathematicians
People from Rawalpindi
Scientists from Punjab, India |
https://en.wikipedia.org/wiki/CCNF | CCNF may also mean Canonical conjunctive normal form in Boolean algebra.
G2/mitotic-specific cyclin-F is a protein that in humans is encoded by the CCNF gene.
Function
This gene encodes a member of the cyclin family. Cyclins are important regulators of cell cycle transitions through their ability to bind and activate cyclin-dependent protein kinases. This member also belongs to the F-box protein family which is characterized by an approximately 40 amino acid motif, the F-box. The F-box proteins constitute one of the four subunits of the ubiquitin protein ligase complex called SCFs (SKP1-cullin-F-box), which are part of the ubiquitin-proteosome system (UPS). The F-box proteins are divided into 3 classes: Fbws containing WD-40 domains, Fbls containing leucine-rich repeats, and Fbxs containing either different protein-protein interaction modules or no recognizable motifs. The protein encoded by this gene belongs to the Fbxs class and it was one of the first proteins in which the F-box motif was identified.
Discovery and gene/protein characteristics
CCNF gene was first discovered in 1994 by the Elledge laboratory while experimenting with Saccharomyces cerevisiae. At the same time, the Frischauf laboratory also identified cyclin F as a new cyclin during their search for new candidate genes for polycystic kidney. CCNF gene has 17 exons and is located at position 16p13.3 on the human chromosome. Its protein, cyclin F, is made up of 786 amino acids and has a predicted molecular weight of 87 kDa. Cyclin F is the main member of the F-box protein family, which has about 40 amino acid motif, forming the F-box.
Cyclin F most closely resembles cyclin A in terms of sequence and expression patterns. Moreover, it has additional shared features of cyclins, such as pEST region, protein quantity, localization, cell cycle-regulated mRNA, and ability to influence cell cycle and progression. Cyclin F differs from other cyclins by its ability to monitor and regulate cell cycle without the need for cyclin-dependent kinases (CDKs). Instead, the Pagano laboratory found that cyclin F is the substrate receptor of an SCF ubiquitin ligase that ubiquitinates and directly interacts with downstream targets, such as CP110 and RRM2, through its hydrophobic patch.
Expression patterns
Cyclin F mRNA is expressed in all human tissues, but at different quantities. It is found most abundantly in the nucleus, and the quantity levels vary during the different stages of cell cycle. Its expression pattern closely resembles the one from cyclin A. Cyclin F levels begin to rise during S phase and reaches its peak during G2.
Role
Cyclin F interacts with other proteins that are important for centrosomal duplication, gene transcription, and DNA synthesis, stability and repair.
RRM2
RRM2 is a ribonucleotide reductase (RNR), an enzyme responsible for the conversion of ribonucleotides into dNTPs. dNTPs are essential for DNA synthesis during DNA replication and repair. Cyclin F interacts |
https://en.wikipedia.org/wiki/Sports%20information%20director | A sports information director is a type of public relations worker who provides statistics, team and player notes and other information about a college or university's sports teams to the news media and general public. Abbreviated "SID," sports information directors often have varying titles, such as media relations director, director of athletics communications, and communications director.
SIDs are generally responsible for a number of external publicity efforts by an athletics department. This ranges from updating and maintaining the content on the school's athletics website and social media accounts to statistics management to historical records keeping. SIDs also are often responsible for the production of official publications, most notably media guides, game notes and game programs. Media guides are used both as a resource for the news media and as a recruiting piece for the individual teams.
The College Sports Information Directors of America (CoSIDA) provides an organizational structure for SIDs at all collegiate levels in the United States and Canada. The organization has named Academic All-Americans since 1952. CoSIDA also provides career resources for potential SIDs such as job postings and résumé exchanges.
Some schools offer academic programming aimed at training future sports information directors. Duquesne University, for example, offers a major and a minor in "Sports Information and Media."
References
External links
College Sports Information Directors of America (CoSIDA) official website
Sports occupations and roles |
https://en.wikipedia.org/wiki/Lau%20Nim%20Yat | Lau Nim Yat (, born 4 December 1989) is a former Hong Kong professional footballer who played as a full back.
Honours
Hong Kong
2009 East Asian Games: Gold medal
Career statistics
Club
As of 11 September 2009
International
Hong Kong U-23
As of 19 June 2011
Hong Kong
As of 16 October 2012
References
External links
Lau Nim Yat at HKFA
1989 births
Living people
Men's association football defenders
Hong Kong First Division League players
Hong Kong Premier League players
Hong Kong men's footballers
Eastern Sports Club footballers
Hong Kong Pegasus FC players
South China AA players
Hong Kong Rangers FC players
Hong Kong men's international footballers |
https://en.wikipedia.org/wiki/Aqraba%2C%20Nablus | Aqraba () is a Palestinian town in the Nablus Governorate, located eighteen kilometers southeast of Nablus in the northern West Bank. According to the Palestinian Central Bureau of Statistics (PCBS), Aqraba had a population of approximately 10,024 inhabitants in 2017.
According to Applied Research Institute–Jerusalem since 1967, Israel has confiscated 1,425 dunums of Aqraba and Yanun's land for use for settlements, Israeli Military bases and for the Wall Zone. According to Kerem Navot, 3,265 dunams of mostly cultivated land were seized per military order T12/72 and transferred to the settlement of Gittit.
Nearby hamlets surround the village and are considered to be natural extensions of Aqraba; they are the khirbets of al-Arama, al-Kroom, Abu ar-Reisa, ar-Rujman, Firas ad-Din and Tell al-Khashaba. The total population of these hamlets was estimated to be 500 in 2008. The prominent families of Aqraba are Al Dayriyeh, Bani Jaber, Al-Mayadima, Bani Jame', and Bani Fadel.
Aqrabah has been the site of price tag attacks by Israeli settlers.
Etymology
The origin of the name is Semitic - Canaanite or Aramaic. In Arabic 'aqraba' means "scorpion".
History and archaeology
Pottery sherds from Iron Age II, Hellenistic, Roman, Byzantine, Umayyad and Crusader/Ayyubid period, as well as rock-hewn cisterns have been found in Aqraba. In 1874 surveyors found near the village rock-cut kokhim tombs.
During the Second Temple period it was an important town (see Mishna, Ma'aser Sheni 5:2), named by Josephus (37–c. 100) as Akrabbatá, the capital of a district called Akrabbatène (Wars 3:3, 5). Eusebius calls the town 'Akrabbeim and the district Akrabbatinés. Safrai suggested that the Bar Kokhba revolt devastated Akrabbatène's Jewish population, and Samaritans thereafter assumed control of the area.
Byzantine period
Aqraba was inhabited by Christians during the Byzantine period. A Syriac document notes that the village contained two Byzantine-era monasteries, called after saints Titus and Stephan. Local tradition concurs with a number of British scholars who believe the mosque was originally a Byzantine-era church.
Early Muslim period
The inhabitants of Aqraba became Muslim during the early Muslim period (630s–1099). Shihab al-Din Ahmad al-Aqrabani, a follower of the noted Muslim jurist al-Shafi'i, lived and was buried there in 180 AH/796–797 CE.
Crusader/Ayyubid to Mamuk period
Several medieval buildings and other remains were described in the 1930s and 1940s and revisited in the 1990s, such as a fortified courtyard building northwest of the mosque, known as al-Hisn ("the castle") dominating the village from its highest point and now part of a private building; an open cistern or pool (Arabic:birka) in the centre of the village, well preserved but now used as an orchard; and a domed building said to be Mamluk, probably a mosque which is in use as the village school The mosque's mihrab was flanked by marble columns topped by capitals, both from the Crusader period |
https://en.wikipedia.org/wiki/Cristian%20Dumitru%20Popescu | Cristian Dumitru Popescu (born 1964) is a Romanian-American mathematician at the University of California, San Diego. His research interests are in algebraic number theory, and in particular, in special values of L-functions.
Education and career
The son of historian Dumitru Micu Popescu and biologist Rodica Jerișteanu,
Popescu was born in 1964 in Novaci, Gorj County. After completing his undergraduate studies at the Faculty of Mathematics of the University of Bucharest, he obtained his Ph.D. from the Ohio State University in 1996, with thesis "On a refined Stark conjecture for function fields" written under the direction of Karl Rubin. He became a professor at Johns Hopkins University, after which he moved to his current position as a professor at UC San Diego.
Research contributions
Popescu formulated and proved function field versions of the Gras conjectures and Rubin's integral refinement of the abelian Stark conjectures. He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's conjecture. Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension. Popescu and Cornelius Greither formulated equivariant versions of Iwasawa's main conjecture over function fields and number fields, proving unconditionally the function field version and conditionally the number field version. These conjectures have important implications for the Brumer–Stark conjecture, the Coates-Sinnott conjecture and Gross' conjecture on special values of L-functions.
Recognition
Popescu was awarded the Simion Stoilow Prize by the Romanian Academy in 2002. In 2015-2016, he was a Simons Fellow at Harvard University. He was elected to the 2021 class of fellows of the American Mathematical Society "for contributions to number theory and arithmetic geometry". He is an honorary member of the Institute of Mathematics of the Romanian Academy.
References
External links
Home page
1964 births
People from Gorj County
Living people
20th-century Romanian mathematicians
20th-century American mathematicians
21st-century Romanian mathematicians
21st-century American mathematicians
Romanian emigrants to the United States
University of Bucharest alumni
Ohio State University alumni
Johns Hopkins University faculty
University of California, San Diego faculty
Number theorists
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/List%20of%20unsolved%20problems%20in%20statistics | There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox.
Inference and testing
How to detect and correct for systematic errors, especially in sciences where random errors are large (a situation Tukey termed uncomfortable science).
The Graybill–Deal estimator is often used to estimate the common mean of two normal populations with unknown and possibly unequal variances. Though this estimator is generally unbiased, its admissibility remains to be shown.
Meta-analysis: Though independent p-values can be combined using Fisher's method, techniques are still being developed to handle the case of dependent p-values.
Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the difference of two means when the variances are unknown and possibly unequal. That is, there is no exact test (meaning that, if the means are in fact equal, one that rejects the null hypothesis with probability exactly α) that is also the most powerful for all values of the variances (which are thus nuisance parameters). Though there are many approximate solutions (such as Welch's t-test), the problem continues to attract attention as one of the classic problems in statistics.
Multiple comparisons: There are various ways to adjust p-values to compensate for the simultaneous or sequential testing of hypotheses. Of particular interest is how to simultaneously control the overall error rate, preserve statistical power, and incorporate the dependence between tests into the adjustment. These issues are especially relevant when the number of simultaneous tests can be very large, as is increasingly the case in the analysis of data from DNA microarrays.
Bayesian statistics: A list of open problems in Bayesian statistics has been proposed.
Experimental design
As the theory of Latin squares is a cornerstone in the design of experiments, solving the problems in Latin squares could have immediate applicability to experimental design.
Problems of a more philosophical nature
Sampling of species problem: How is a probability updated when there is unanticipated new data?
Doomsday argument: How valid is the probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far?
Exchange paradox: Issues arise within the subjectivistic interpretation of probability theory; more specifically within Bayesian decision theory. This is still an open problem among the subjectivists as no consensus has been reached yet. Examples include:
The two envelopes problem
The necktie paradox
Sunrise problem: What is the probability |
https://en.wikipedia.org/wiki/Florence%20Nightingale%20David | Florence Nightingale David, also known as F. N. David (23 August 1909 – 23 July 1993) was an English statistician. She was head of the Statistics Department at the University of California, Riverside between 1970 – 77 and her research interests included the history of probability and statistical ideas.
Early life and education
David was born on 23 August 1909 in Ivington, near Leominster, England. Her parents were Florence Maude and William Richard David who were both Elementary School head teachers. David was named after Florence Nightingale, who was a friend of her parents.
David was tutored privately by a local parson, beginning at age five. By that age she already knew some arithmetic, so she began with algebra. Since David already knew English, the parson taught her Latin and Greek. At the age of ten, she entered to formal schooling at Colyton Grammar School. She studied mainly mathematics for three years, with the aim of becoming an actuary, but at that time the actuarial firms only accepted men. She earned a degree in Mathematics from Bedford College for Women in 1931.
David received a scholarship and continued her studies with Karl Pearson at University College, London, as his research assistant. In this function she produced tables for the correlation coefficient. When Pearson retired, his son Egon, and Ronald Fisher, took over Karl's duties. After Karl Pearson died in 1934, David returned to the Biometrics laboratory to work with Jerzy Neyman, submitting her four most recently published papers as her doctoral (PhD) thesis, and earned a doctorate in 1938.
Career
Working for Karl Pearson, F. N. David computed solutions to complicated multiple integrals, and the distribution of the correlation coefficients. As a result, her first book was released in 1938, called Tables of the Correlation Coefficient. All the calculations were done on a hand-cranked mechanical calculator known as a Brunsviga.
During World War II, David worked as an Experimental Officer in the Ordnance Board for the Ministry of Supply, a Senior Statistician for the Research and Experiments Department for the Ministry of Home Security; a Member of the Land Mines Committee of the Scientific Advisory Council, and as a Scientific Advisor on Mines to the Military Experimental Establishment. In late 1939 when war had started but England had not yet been attacked, she created statistical models to predict the possible consequences of bombs exploding in high density populations such as the big cities of England and especially London. From these models, she determined estimates of harm to humans and other damage. This included the possible numbers living and dead, the reactions to fires and damaged buildings as well as damages to communications, utilities such as telephones, water, gas, electricity and sewers. As a result, when the Germans bombed London in 1940 and 1941, vital services were kept going and her models were updated and modified with the evidence from the real |
https://en.wikipedia.org/wiki/St%20David%27s%20School%2C%20Middlesbrough | St David's School was a Roman Catholic Technology College in Acklam, Middlesbrough, North Yorkshire, England, specialising in Mathematics, Science, Technology (cooking, textiles, electronics & wood work) and ICT. The school was awarded Technology College status in July 2002 and this was renewed for a further four years in 2007. It was also one of very few schools to offer a construction course.
The school opened in 1970 as St. George's then it was renamed in 1984 after the amalgamation with St Paul's School, which in turn had been an earlier amalgamation of St Thomas's and St Michael's schools. The last headmaster of St. Davids was Mr Peter Coady who replaced Mr Phillip Tucker. School subjects included Applied business, Art, Design, Technology, rama, EAL (English as an Additional Language), English, Geography, History, ICT, Key Skills, Maths, Media Studies, Modern Languages, Music, PE, RE, Science, SEN (Special Education needs).
The school combined with Newlands School FCJ, also in Middlesbrough, in 2009 to form the biggest Roman Catholic School in North East England. The combined school is called Trinity Catholic College. In September 2011 the St David's site was closed down and all pupils transferred to the Newlands site, which is the site of the combined school.
External links
St. David's School website
Defunct Catholic schools in the Diocese of Middlesbrough
Defunct schools in Middlesbrough
Educational institutions disestablished in 2009
2009 disestablishments in England |
https://en.wikipedia.org/wiki/Plim | plim may be:
An acronym for:
"Probability limit" (plim) – see Convergence in probability
"Phosphorescence Lifetime Imaging Microscopy" (PLIM) - An imaging technique similar to Fluorescence-lifetime imaging microscopy but based on phosphorescence rather than fluorescence.
"Physical Layer Information Module" (PLIM) in Router and Switches
"Plant Life Management" (PLIM) in nuclear power
"Programmable Logic In-the-Middle" (PLIM) - A technique in computing where dataflows originated from a CPU are routed through a block of FPGA for analysis and manipulation. |
https://en.wikipedia.org/wiki/Distributed%20lag | In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable.
The starting point for a distributed lag model is an assumed structure of the form
or the form
where yt is the value at time period t of the dependent variable y, a is the intercept term to be estimated, and wi is called the lag weight (also to be estimated) placed on the value i periods previously of the explanatory variable x. In the first equation, the dependent variable is assumed to be affected by values of the independent variable arbitrarily far in the past, so the number of lag weights is infinite and the model is called an infinite distributed lag model. In the alternative, second, equation, there are only a finite number of lag weights, indicating an assumption that there is a maximum lag beyond which values of the independent variable do not affect the dependent variable; a model based on this assumption is called a finite distributed lag model.
In an infinite distributed lag model, an infinite number of lag weights need to be estimated; clearly this can be done only if some structure is assumed for the relation between the various lag weights, with the entire infinitude of them expressible in terms of a finite number of assumed underlying parameters. In a finite distributed lag model, the parameters could be directly estimated by ordinary least squares (assuming the number of data points sufficiently exceeds the number of lag weights); nevertheless, such estimation may give very imprecise results due to extreme multicollinearity among the various lagged values of the independent variable, so again it may be necessary to assume some structure for the relation between the various lag weights.
The concept of distributed lag models easily generalizes to the context of more than one right-side explanatory variable.
Unstructured estimation
The simplest way to estimate parameters associated with distributed lags is by ordinary least squares, assuming a fixed maximum lag , assuming independently and identically distributed errors, and imposing no structure on the relationship of the coefficients of the lagged explanators with each other. However, multicollinearity among the lagged explanators often arises, leading to high variance of the coefficient estimates.
Structured estimation
Structured distributed lag models come in two types: finite and infinite. Infinite distributed lags allow the value of the independent variable at a particular time to influence the dependent variable infinitely far into the future, or to put it another way, they allow the current value of the dependent variable to be influenced by values of the independent variable that occurred infinitely long ago; but beyond some lag length the effects taper off toward z |
https://en.wikipedia.org/wiki/Bird%20Cove | Bird Cove is a town in the Canadian province of Newfoundland and Labrador.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Bird Cove had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of cities and towns in Newfoundland and Labrador
Newfoundland and Labrador Route 430
References
Towns in Newfoundland and Labrador |
https://en.wikipedia.org/wiki/Brent%27s%20Cove | Brent's Cove is a town in the Canadian province of Newfoundland and Labrador.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Brent's Cove had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of cities and towns in Newfoundland and Labrador
References
Towns in Newfoundland and Labrador |
https://en.wikipedia.org/wiki/Brighton%2C%20Newfoundland%20and%20Labrador | Brighton is a town in the Canadian province of Newfoundland and Labrador.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Brighton had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of cities and towns in Newfoundland and Labrador
References
Towns in Newfoundland and Labrador |
https://en.wikipedia.org/wiki/Bryant%27s%20Cove | Bryant's Cove is a town in the Canadian province of Newfoundland and Labrador.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Bryant's Cove had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of cities and towns in Newfoundland and Labrador
References
Towns in Newfoundland and Labrador |
https://en.wikipedia.org/wiki/Northern%20Arm | Northern Arm is a town in the Canadian province of Newfoundland and Labrador. The town had a population of 371 in the Canada 2021 Census.
In the 2021 Census of Population conducted by Statistics Canada, Northern Arm had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of cities and towns in Newfoundland and Labrador
References
Towns in Newfoundland and Labrador |
https://en.wikipedia.org/wiki/Regular%20p-group | In mathematical finite group theory, the concept of regular p-group captures some of the more important properties of abelian p-groups, but is general enough to include most "small" p-groups. Regular p-groups were introduced by .
Definition
A finite p-group G is said to be regular if any of the following equivalent , conditions are satisfied:
For every a, b in G, there is a c in the derived subgroup of the subgroup H of G generated by a and b, such that ap · bp = (ab)p · cp.
For every a, b in G, there are elements ci in the derived subgroup of the subgroup generated by a and b, such that ap · bp = (ab)p · c1p ⋯ ckp.
For every a, b in G and every positive integer n, there are elements ci in the derived subgroup of the subgroup generated by a and b such that aq · bq = (ab)q · c1q ⋯ ckq, where q = pn.
Examples
Many familiar p-groups are regular:
Every abelian p-group is regular.
Every p-group of nilpotency class strictly less than p is regular. This follows from the Hall–Petresco identity.
Every p-group of order at most pp is regular.
Every finite group of exponent p is regular.
However, many familiar p-groups are not regular:
Every nonabelian 2-group is irregular.
The Sylow p-subgroup of the symmetric group on p2 points is irregular and of order pp+1.
Properties
A p-group is regular if and only if every subgroup generated by two elements is regular.
Every subgroup and quotient group of a regular group is regular, but the direct product of regular groups need not be regular.
A 2-group is regular if and only if it is abelian. A 3-group with two generators is regular if and only if its derived subgroup is cyclic. Every p-group of odd order with cyclic derived subgroup is regular.
The subgroup of a p-group G generated by the elements of order dividing pk is denoted Ωk(G) and regular groups are well-behaved in that Ωk(G) is precisely the set of elements of order dividing pk. The subgroup generated by all pk-th powers of elements in G is denoted ℧k(G). In a regular group, the index [G:℧k(G)] is equal to the order of Ωk(G). In fact, commutators and powers interact in particularly simple ways . For example, given normal subgroups M and N of a regular p-group G and nonnegative integers m and n, one has [℧m(M),℧n(N)] = ℧m+n([M,N]).
Philip Hall's criteria of regularity of a p-group G: G is regular, if one of the following hold:
[G:℧1(G)] < pp
[:℧1()| < pp−1
|Ω1(G)| < pp−1
Generalizations
Powerful p-group
power closed p-group
References
Properties of groups
Finite groups
P-groups |
https://en.wikipedia.org/wiki/List%20of%20Huddersfield%20Town%20A.F.C.%20records%20and%20statistics | These are a list of player and club records for Huddersfield Town Association Football Club.
Club records
Victories
Record league victory: 10–1 v Blackpool, Division One, 13 December 1930
Record FA Cup victory: 11–0 v Heckmondwike, preliminary round, 18 September 1909
Record League Cup victory: 5–1 v Mansfield Town, first round, second leg, 13 September 1983
Defeats
Record league defeat: 1–10 v Manchester City, Division Two, 7 November 1987
Record FA Cup defeat: 0–6 v Sunderland, third round, 7 January 1950
Record League Cup defeat: 0–5 v Arsenal, second round, first leg, 21 September 1993
Attendances
Record attendance at Leeds Road: 67,037 v Arsenal, FA Cup Sixth Round, 27 February 1932
Record attendance at John Smith's Stadium: 24,169 v Manchester United, Premier League, 21 October 2017
Sequences
Longest unbeaten league run: 43 – 1 January 2011 to 28 November 2011.
Longest unbeaten league run (in a single season): 25 – 1 January 2011 to 7 May 2011.
Longest unbeaten home league run: 28 – 5 May 1982 to 17 September 1983.
Longest unbeaten away league run: 22 – 1 January 2011 to 29 October 2011.
Longest run of league wins: 11 – 5 April 1920 to 9 September 1920.
Longest run of home league wins: 11 – 28 December 1925 to 30 August 1926.
Longest run of away league wins: 6 – 12 March 2011 to 30 April 2011.
Longest run of league defeats: 8 – 1 December 2018 to 2 January 2019.
Longest run of home league defeats: 7 – 1 December 2018 to 9 February 2019 and 2 March 2019 to 26 April 2019.
Longest run of away league defeats: 9 – 13 April 1912 to 16 November 1912, 14 November 1914 to 13 March 1915, 4 September 1946 to 7 December 1946 and 12 March 1988 to 3 October 1988.
Longest run of league draws: 6 – 3 March 1987 to 3 April 1987.
Longest run of home league draws: 6 – 3 May 1977 to 17 September 1977.
Longest run of away league draws: 6 – 28 August 1926 to 23 October 1926.
Longest run of league matches without a win: 22 – 27 November 1971 to 29 April 1972.
Longest run of matches without a win: 19 – 26 August 2000 to 25 November 2000.
Longest league scoring run: 27 – 12 March 2005 to 12 November 2005.
Longest league home scoring run: 21 – 26 December 2004 to 10 October 2005.
Longest league away scoring run: 24 – 20 January 1962 to 12 April 1963.
Longest league non-scoring run: 7 – 22 January 1972 to 21 March 1972.
Longest run of matches without conceding a goal: 8 – 13 March 1965 to 19 April 1965.
Longest run of wins at the start of a season: 4 – 1924–25 season.
Longest run of defeats at the start of a season: 6 – 1992–93 season.
Seasonal records
Most wins in a season: 28 – 1919–20 season.
Most home wins in a season: 16 – 1919–20 season, 1933–34 season, 1979–80 season and 2003–04 season.
Most away wins in a season: 13 – 2010–11 season.
Fewest wins in a season: 3 – 2018–19 season.
Fewest home wins in a season: 2 – 2018–19 season.
Fewest away wins in a season: 0 – 1936–37 season.
Most defeats in a season: 28 – 1987–88 season and 2018–19 season.
Most hom |
https://en.wikipedia.org/wiki/Abdelillah%20Bagui | Abdelilah Bagui (; born 17 February 1978) is a Moroccan former footballer.
Bagui played for FC Spartak Moscow and FC Rostov in the Russian Premier League.
Career statistics
International
Statistics accurate as of match played 12 January 2008
References
External links
Profile at kawkabi.com
1978 births
Living people
Moroccan men's footballers
Morocco men's international footballers
Footballers from Fez, Morocco
Maghreb de Fès players
FC Spartak Moscow players
Raja CA players
FC Rostov players
KAC Marrakech players
Chabab Rif Al Hoceima players
Olympic Safi players
Kénitra AC players
Botola players
Russian Premier League players
2002 African Cup of Nations players
2008 Africa Cup of Nations players
Moroccan expatriate men's footballers
Expatriate men's footballers in Russia
Moroccan expatriate sportspeople in Russia
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/List%20of%20Eintracht%20Frankfurt%20records%20and%20statistics | This article details various records of German football club Eintracht Frankfurt under the categories listed below.
Player records
Appearances
Record appearances: Charly Körbel, 728, 1972–1991
Record league appearances: Charly Körbel, 602, 1972–1991
Record DFB-Pokal appearances: Charly Körbel, 70
Record European football appearances: Charly Körbel, 53
Most capped player: Makoto Hasebe, 114, Japan
Most capped German player: Andreas Möller, 85
Most caps gained while at Eintracht: Jürgen Grabowski, 44
First capped player: Fritz Becker (at Eintracht predecessor FC Frankfurter Kickers) (for Germany v Switzerland, 3–5, 5 April 1908)
All-time appearances
Goalscorers
All-time record goalscorer: Karl Ehmer, 225 goals, 1927–1938
Most Bundesliga goals: Bernd Hölzenbein, 160 goals, 1967–1981
Most Bundesliga goals in one season: André Silva, 28 goals, 2020–21
Most DFB-Pokal goals: Bernd Hölzenbein, 23 goals
Most European goals: Bernd Hölzenbein, 24 goals
All-time goalscorers
Club records
Scores
Record Bundesliga win: 9–1 vs. Rot-Weiss Essen, Waldstadion (H), 5 October 1974
Record DFB-Pokal win:
8–0 vs. Karlsruher SC, Wildparkstadion (A), 12 April 1959
8–0 vs. Rödelheimer FC 02, venue unknown (A), 19 December 1959
10–2 vs. Hertha Zehlendorf, Waldstadion (H), 15 October 1976
Record European win: 9–0 vs. Widzew Łódź, Waldstadion (H), 30 September 1992
Record Bundesliga defeat: 0–7, vs. Karlsruher SC, Waldstadion (H), 19 October 1964
Firsts
First match: (as FFC Victoria) vs. 1. Bockenheimer FC 1899, Friendly, 4–1, venue unknown (H), 19 March 1899
First match: (as Eintracht Frankfurt) vs. SV Wiesbaden, Friendly, 2–2, venue unknown (H), 2 May 1920
First DFB-Pokal match: vs. SC Opel Rüsselsheim, 1–3, venue unknown (H), 11 May 1935
First Bundesliga match: vs. 1. FC Kaiserslautern, 0-0, Waldstadion (H), 24 August 1963
First match at Waldstadion: vs. Boca Juniors, Friendly, lost 0–2, 27 May 1925
First European match: vs. Young Boys, won 4–1, European Cup, Wankdorfstadion (A), 4 November 1959
Attendances
Record home attendance: 81,000 vs. FK Pirmasens, won 3–2, Waldstadion (H), 23 May 1959
Record European attendance: 127,621 vs. Real Madrid, lost 3–7, Hampden Park, (N), 18 May 1960
Record season average attendance: 50,041 2022–23
Transfers
Bought
Sold
Bundesliga records
Club records
Wins and losses
Lowest number of losses in a season closing half: 0 by Eintracht Frankfurt (1976–77) same as Bayern Munich (1986–87, 2012–13 and 2019–20) and Borussia Dortmund (2011–12)
Lowest number of losses in a season at home (34 games): 0 by Eintracht Frankfurt (1971–72 and 1973–74) same as 1860 Munich (1965–66), Bayern Munich (1970–71 to 1973–74, 1980–81, 1983–84, 1996–97, 1998–99, 2001–02, 2007–08 and 2016–17), MSV Duisburg (1970–71), Schalke 04 (1970–71), 1. FC Köln (1972–73 and 1987–88), Hertha BSC (1974–75 and 1977–78), Eintracht Braunschweig (1975–76), Hamburger SV (1981–82, 1982–83 and 1995–96), 1. FC Kaiserslautern (1981–82 and 1994–95), Werder Bremen |
https://en.wikipedia.org/wiki/History%20of%20quaternions | In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.
Hamilton's discovery
In 1843, Hamilton knew that the complex numbers could be viewed as points in a plane and that they could be added and multiplied together using certain geometric operations. Hamilton sought to find a way to do the same for points in space. Points in space can be represented by their coordinates, which are triples of numbers and have an obvious addition, but Hamilton had difficulty defining the appropriate multiplication.
According to a letter Hamilton wrote later to his son Archibald:
Every morning in the early part of October 1843, on my coming down to breakfast, your brother William Edwin and yourself used to ask me: "Well, Papa, can you multiply triples?" Whereto I was always obliged to reply, with a sad shake of the head, "No, I can only add and subtract them."
On October 16, 1843, Hamilton and his wife took a walk along the Royal Canal in Dublin. While they walked across Brougham Bridge (now Broom Bridge), a solution suddenly occurred to him. While he could not "multiply triples", he saw a way to do so for quadruples. By using three of the numbers in the quadruple as the points of a coordinate in space, Hamilton could represent points in space by his new system of numbers. He then carved the basic rules for multiplication into the bridge:
Hamilton called a quadruple with these rules of multiplication a quaternion, and he devoted the remainder of his life to studying and teaching them. From 1844 to 1850 Philosophical Magazine communicated Hamilton's exposition of quaternions. In 1853 he issued Lectures on Quaternions, a comprehensive treatise that also described biquaternions. The facility of the algebra in expressing geometric relationships led to broad acceptance of the method, several compositions by other authors, and stimulation of applied algebra generally. As mathematical terminology has grown since that time, and usage of some terms has changed, the traditional expressions are referred to classical Hamiltonian quaternions.
Precursors
Hamilton's innovation consisted of expressing quaternions as an algebra over . The formulae for the multiplication of quaternions are implicit in the four squares formula devised by Leonhard Euler in 1748; Olinde Rodrigues applied this formula to representing rotations in 1840.
Response
The special claims of quaternions as the algebra of four-dimensional space were challenged by James Cockle with his exhibits in 1848 and 1849 of tessarines and coquaternions as alternatives. Nevertheless, the |
https://en.wikipedia.org/wiki/Mogensen%E2%80%93Scott%20encoding | In computer science, Scott encoding is a way to represent (recursive) data types in the lambda calculus. Church encoding performs a similar function. The data and operators form a mathematical structure which is embedded in the lambda calculus.
Whereas Church encoding starts with representations of the basic data types, and builds up from it, Scott encoding starts from the simplest method to compose algebraic data types.
Mogensen–Scott encoding extends and slightly modifies Scott encoding by applying the encoding to Metaprogramming. This encoding allows the representation of lambda calculus terms, as data, to be operated on by a meta program.
History
Scott encoding appears first in a set of unpublished lecture notes by Dana Scott
whose first citation occurs in the book Combinatorial Logic, Volume II. Michel Parigot gave a logical interpretation of and strongly normalizing recursor for Scott-encoded numerals, referring to them as the "Stack type" representation of numbers.
Torben Mogensen later extended Scott encoding for the encoding of Lambda terms as data.
Discussion
Lambda calculus allows data to be stored as parameters to a function that does not yet have all the parameters required for application. For example,
May be thought of as a record or struct where the fields have been initialized with the values . These values may then be accessed by applying the term to a function f. This reduces to,
c may represent a constructor for an algebraic data type in functional languages such as Haskell. Now suppose there are N constructors, each with arguments;
Each constructor selects a different function from the function parameters . This provides branching in the process flow, based on the constructor. Each constructor may have a different arity (number of parameters). If the constructors have no parameters then the set of constructors acts like an enum; a type with a fixed number of values. If the constructors have parameters, recursive data structures may be constructed.
Definition
Let D be a datatype with N constructors, , such that constructor has arity .
Scott encoding
The Scott encoding of constructor of the data type D is
Mogensen–Scott encoding
Mogensen extends Scott encoding to encode any untyped lambda term as data. This allows a lambda term to be represented as data, within a Lambda calculus meta program. The meta function mse converts a lambda term into the corresponding data representation of the lambda term;
The "lambda term" is represented as a tagged union with three cases:
Constructor a - a variable (arity 1, not recursive)
Constructor b - function application (arity 2, recursive in both arguments),
Constructor c - lambda-abstraction (arity 1, recursive).
For example,
Comparison to the Church encoding
The Scott encoding coincides with the Church encoding for booleans. Church encoding of pairs may be generalized to arbitrary data types by encoding of D above as
compare this to the Mogense |
https://en.wikipedia.org/wiki/Shift%20space | In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms. The most widely studied shift spaces are the subshifts of finite type and the sofic shifts.
In the classical framework a shift space is any subset of , where is a finite set, which is closed for the Tychonov topology and invariant by translations. More generally one can define a shift space as the closed and translation-invariant subsets of , where is any non-empty set and is any monoid.
Definition
Let be a monoid, and given , denote the operation of with by the product . Let denote the identity of . Consider a non-empty set (an alphabet) with the discrete topology, and define as the set of all patterns over indexed by . For and a subset , we denote the restriction of to the indices of as .
On , we consider the prodiscrete topology, which makes a Hausdorff and totally disconnected topological space. In the case of being finite, it follows that is compact. However, if is not finite, then is not even locally compact.
This topology will be metrizable if and only if is countable, and, in any case, the base of this topology consists of a collection of open/closed sets (called cylinders), defined as follows: given a finite set of indices , and for each , let . The cylinder given by and is the set
When , we denote the cylinder fixing the symbol at the entry indexed by simply as .
In other words, a cylinder is the set of all set of all infinite patterns of which contain the finite pattern .
Given , the g-shift map on is denoted by and defined as
.
A shift space over the alphabet is a set that is closed under the topology of and invariant under translations, i.e., for all . We consider in the shift space the induced topology from , which has as basic open sets the cylinders .
For each , define , and . An equivalent way to define a shift space is to take a set of forbidden patterns and define a shift space as the set
Intuitively, a shift space is the set of all infinite patterns that do not contain any forbidden finite pattern of .
Language of shift space
Given a shift space and a finite set of indices , let , where stands for the empty word, and for let
be the set of all finite configurations of that appear in some sequence of , i.e.,
Note that, since is a shift space, if is a translation of , i.e., for some , then if and only if there exists such that if . In other words, and contain the same configurations modulo translation. We will call the set
the language of . In the general context stated here, the language of a shift space has not the same mean of that in Formal Language Theory, but in the classical framework which considers the alphabet being finite, and being or with the usual addition, the language of a shift space is a form |
https://en.wikipedia.org/wiki/List%20of%20bridges%20in%20Paris | There are many bridges in the city of Paris, principally over the River Seine, but also over the Canal de l'Ourcq.
Statistics
In 2006, Paris had:
148 bridges over the Boulevard Périphérique
58 bridges used to carry Parisian streets over each other
49 passerelles piétonnières (pedestrian bridges)
37 bridges over the Seine
33 bridges used by the SNCF
10 bridges used by the Régie Autonome des Transports Parisiens (RATP)
Seine
Paris has 37 bridges across the Seine, of which 5 are pedestrian only and 2 are rail bridges. Three link Île Saint-Louis to the rest of Paris, 8 do the same for Île de la Cité and one links the 2 islands to each other. A list follows, from upstream to downstream :
Pont amont (carrying the Boulevard Périphérique, situated at the river's entry to the city)
Pont National
Pont de Tolbiac
Passerelle Simone-de-Beauvoir (pedestrian), inaugurated 13 July 2006
Pont de Bercy (made up of a railway bridge carrying the Line 6 of the Paris Métro and another stage for road traffic) ;
Pont Charles-de-Gaulle (1996)
Viaduc d'Austerlitz (railway bridge used for Line 5 of the métro), directly followed on the Rive Droite by the ,
Pont d'Austerlitz
Pont de Sully (crosses the eastern corner of Île Saint-Louis)
Pont de la Tournelle (between the Rive Gauche and the Île Saint-Louis)
Pont Marie (between Île Saint-Louis and the rive droite)
Pont Louis-Philippe (between Île Saint-Louis and the rive droite)
Pont Saint-Louis (pedestrian zone, between Île de la Cité and the Île Saint-Louis)
Pont de l'Archevêché (between the rive gauche and Île de la Cité)
Pont au Double (between the rive gauche and Île de la Cité)
Pont d'Arcole (between Île de la Cité and the rive droite)
Petit Pont (between the rive gauche and Île de la Cité)
Pont Notre-Dame (between the Île de la Cité and the rive droite)
Pont Saint-Michel (between the Rive Gauche and the Île de la Cité)
Pont au Change (between the Île de la Cité and the Rive Droite)
Pont Neuf (crossing the west corner of the Île de la Cité, Paris's oldest bridge, built between 1578 and 1607)
Passerelle des Arts (pedestrian)
Pont du Carrousel
Pont Royal
Passerelle Léopold-Sédar-Senghor (1999) (pedestrian, formerly the Passerelle de Solférino, renamed in 2006)
Pont de la Concorde
Pont Alexandre III
Pont des Invalides
Pont de l'Alma
Passerelle Debilly (pedestrian)
Pont d'Iéna
Pont de Bir-Hakeim (crossing the Île aux Cygnes, comprising one stage with a railway bridge carrying Line 6 of the Paris Métro and another for road traffic)
Pont Rouelle (rail viaduct for line C of the RER crossing the Île aux Cygnes)
Pont de Grenelle (crossing the Île aux Cygnes)
Pont Mirabeau
Pont du Garigliano
Pont aval (used by the boulevard périphérique, at the river's exit from the city)
Parisian canals
The are crossed by a number of bridges – the majority of which are passerelles piétonnes (footbridges) – and many of the road bridges can be raised or turned (temporarily interrupting road t |
https://en.wikipedia.org/wiki/Indians%20in%20Spain | Indians in Spain form one of the smaller populations of the Indian diaspora. According to the statistics of India's Ministry of External Affairs, they number only 35,000, or 0.07% of the population of Spain. 2009 statistics of Spain's Instituto Nacional de Estadística showed 35,686 Indian citizens in Spain; this figure does not include persons of Indian origin holding other citizenships. Most Indians originally migrated to Spain from Africa, while others came from India and even Japan and Southeast Asia. The overwhelming majority of Indians in Spain live in the Barcelona area (over 26,000 as of 2019). According to data from 2021, Indians in Spain number more than 57,000 (0.12% of the total population).
Migration history
Sindhi traders and shopkeepers thrived in the free ports of the Spanish Canary Islands of Las Palmas and Tenerife following the imposition of import and foreign exchange restrictions in Spain after World War II. They conducted a brisk trade with the North African continent from Las Palmas. When Ceuta and Melilla, parts of Spanish Morocco, were also declared as free ports, Indian businessmen set up trading houses and retail shops catering to the tourist trade.
The next wave of Indians to go to Spain were descendants of Indian labourers from former Spanish colony of Equatorial Guinea. By the mid-seventies, there were over 200 Indian trading houses in Ceuta and Melilla. With the liberalisation in import policies introduced in the eighties, business activity shifted to the port cities of Malaga and Barcelona. Madrid also attracted many Indian businessmen.
Religion
Sindhis and Sikhs form the majority of the Indian community. Spain has recognised three entities of Hinduism. The community celebrates various Indian festivals. Rath Yatras are also taken out by members of the Hare Rama Hare Krishna movement with the enthusiastic support of the Indian community. There are temples in Valencia, Ceuta, and Canary Islands.
Business
The Indian community in Spain enjoys a good reputation. Indians are considered hard working, non-political and peaceful. The Indian community has integrated well with Spanish society. There are many Indian restaurants in the island of Mallorca.
The majority of Indian people living in Spain have their own business such as stores, restaurants, call centres, grocery stores, clothes store, construction firm, telecommunication shops, bar, dance and Bhangra groups etc.
Currently, the largest Hindu community in Spain is in the Canary Islands, especially on the island of Tenerife.
Several electronics and camera stores owned by Indians in the Canary Islands have been accused of being a fraud. In 2016 the Danish TV program "Svindlerjagt" (Eng: Swindler Hunt), went to Gran Canaria to expose several electronics stores which scammed Danish customers.
Spanish people of Indian descent
Sagar Prakash Khatnani, born in Tenerife, is a prolific writer of novels.
Robert Masih Nahar, member of the Spanish senate
Ma Anand Ya |
https://en.wikipedia.org/wiki/Charles%20Seife | Charles Seife is an American author, journalist, and professor at New York University. He has written extensively on scientific and mathematical topics.
Career
Seife holds a mathematics degree from Princeton University (1993), an M.S. in mathematics from Yale University and a M.S. in journalism from Columbia University.
Seife wrote for Science magazine and New Scientist before joining the Department of Journalism at New York University where he became a professor.
Books
His first and best-known published book is Zero: The Biography of a Dangerous Idea.
Another well-known book from Seife is Proofiness: How You're Being Fooled By the Numbers. Here, Seife focuses on how much propaganda uses numbers worded in such a way that they confuse people and can be misinterpreted.
Other books by Seife are:
Alpha & Omega: The Search for the Beginning and End of the Universe, Penguin Putnam, 2003.
Decoding the Universe, Penguin, 2007.
Sun in a Bottle: The Strange History of Fusion and the Science of Wishful Thinking, Viking, 2008.
Virtual Unreality: Just Because the Internet Told You, How Do You Know It's True?, Penguin Putnam, 2014.
Other writing
His freelance work has appeared in The Philadelphia Inquirer, The Washington Post, The New York Times, Scientific American, and The Economist, among others.
Throughout his career, Seife has written many book reviews, especially of books which focus on mathematics.
Professional associations
He is a member of PEN, the National Association of Science Writers, and the D.C. Science Writers Association.
Awards
2001 PEN/Martha Albrand Award for First Nonfiction for Zero: The Biography of a Dangerous Idea
References
External links
Article on edge.org
DC Science Writers Association website
Homepage
Leonard Lopate interview with Charles Seife
American science writers
Mathematics writers
Mathematics popularizers
Year of birth missing (living people)
Living people
Princeton University alumni
Yale University alumni
Columbia University Graduate School of Journalism alumni
New York University faculty
American journalism academics |
https://en.wikipedia.org/wiki/Borel%20determinacy%20theorem | In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. A Gale-Stewart game is a possibly infinite two-player game, where both players have perfect information and no randomness is involved.
The theorem is a far reaching generalization of Zermelo's Theorem about the determinacy of finite games. It was proved by Donald A. Martin in 1975, and is applied in descriptive set theory to show that Borel sets in Polish spaces have regularity properties such as the perfect set property and the property of Baire.
The theorem is also known for its metamathematical properties. In 1971, before the theorem was proved, Harvey Friedman showed that any proof of the theorem in Zermelo–Fraenkel set theory must make repeated use of the axiom of replacement. Later results showed that stronger determinacy theorems cannot be proven in Zermelo–Fraenkel set theory, although they are relatively consistent with it, if certain large cardinals are consistent.
Background
Gale–Stewart games
A Gale–Stewart game is a two-player game of perfect information. The game is defined using a set A, and is denoted GA. The two players alternate turns, and each player is aware of all moves before making the next one. On each turn, each player chooses a single element of A to play. The same element may be chosen more than once without restriction. The game can be visualized through the following diagram, in which the moves are made from left to right, with the moves of player I above and the moves of player II below.
The play continues without end, so that a single play of the game determines an infinite sequence of elements of A. The set of all such sequences is denoted Aω. The players are aware, from the beginning of the game, of a fixed payoff set (a.k.a. winning set) that will determine who wins. The payoff set is a subset of Aω. If the infinite sequence created by a play of the game is in the payoff set, then player I wins. Otherwise, player II wins; there are no ties.
This definition initially does not seem to include traditional perfect information games such as chess, since the set of moves available in such games changes every turn. However, this sort of case can be handled by declaring that a player who makes an illegal move loses immediately, so that the Gale-Stewart notion of a game does in fact generalize the concept of a game defined by a game tree.
Winning strategies
A winning strategy for a player is a function that tells the player what move to make from any position in the game, such that if the player follows the function they will surely win. More specifically, a winning strategy for player I is a function f that takes as input sequences of elements of A of even length and returns an element of A, such that player I will win every play of the form
A winning strategy for player II is a function g |
https://en.wikipedia.org/wiki/Goldstine%20theorem | In functional analysis, a branch of mathematics, the Goldstine theorem, named after Herman Goldstine, is stated as follows:
Goldstine theorem. Let be a Banach space, then the image of the closed unit ball under the canonical embedding into the closed unit ball of the bidual space is a weak*-dense subset.
The conclusion of the theorem is not true for the norm topology, which can be seen by considering the Banach space of real sequences that converge to zero, c0 space and its bi-dual space Lp space
Proof
Lemma
For all and there exists an such that for all
Proof of lemma
By the surjectivity of
it is possible to find with for
Now let
Every element of satisfies and so it suffices to show that the intersection is nonempty.
Assume for contradiction that it is empty. Then and by the Hahn–Banach theorem there exists a linear form such that and Then and therefore
which is a contradiction.
Proof of theorem
Fix and Examine the set
Let be the embedding defined by where is the evaluation at map. Sets of the form form a base for the weak* topology, so density follows once it is shown for all such The lemma above says that for any there exists a such that and in particular Since we have We can scale to get The goal is to show that for a sufficiently small we have
Directly checking, one has
Note that one can choose sufficiently large so that for Note as well that If one chooses so that then
Hence one gets as desired.
See also
References
Banach spaces
Theorems in functional analysis
de:Schwach-*-Topologie#Eigenschaften |
https://en.wikipedia.org/wiki/Jans%20Bay | Jans Bay is a northern hamlet in the Canadian province of Saskatchewan.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Jans Bay had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of communities in Northern Saskatchewan
List of communities in Saskatchewan
References
Division No. 18, Saskatchewan
Northern hamlets in Saskatchewan |
https://en.wikipedia.org/wiki/Jalal%20Rafkhaei | Seyed Jalal Rafkhaei (, born 24 April 1984) is an Iranian football player.
Club career statistics
He is a Malavan youth system product and played with the senior team for five years then transferred to Zob Ahan and after one season he returned to his hometown club. He became top scorer of 2012–13 season with 19 goals.
Last Update: 4 June 2019
Assist Goals
International career
In 2008, he was called for the Iran national football team by the Iran's coach Ali Daei. Rafkhaei debuted for Iran versus Palestine on August 7, 2008.
International goals
Scores and results list Iran's goal tally first.
Honours
Country
WAFF Championship
Winner (1): 2008
Individual
Iran Pro League Top Goalscorer (19 goals): 2012–13
Iran Pro League Golden Boot (1): 2012–13
References
Iran Premier League Stats
External links
1984 births
Living people
Footballers from Bandar-e Anzali
Iranian men's footballers
Malavan F.C. players
Zob Ahan Esfahan F.C. players
Machine Sazi F.C. players
F.C. Rayka Babol players
Aluminium Arak F.C. players
Persian Gulf Pro League players
Azadegan League players
Men's association football forwards |
https://en.wikipedia.org/wiki/Babak%20Pourgholami | Babak Pourgholami is an Iranian football player who plays for Aluminium in Azadegan League.
Club career
Club career statistics
Last updated: 30 April 2013
Assist Goals
External links
Persian League Profile
Iranian men's footballers
1981 births
Living people
Footballers from Bandar-e Anzali
Persian Gulf Pro League players
Fajr Sepasi Shiraz F.C. players
Malavan F.C. players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Internet%20in%20Botswana | The Internet in Botswana is used by about 28.4% of the population. This is slightly lower than the figure of 28.6% for Africa as a whole in 2015.
Statistics
Internet top-level domain: .bw
Internet users:
323,368 users, 15% of the population (2013).
241,272 users, 148th in the world; 11.5% of the population, 166th in the world (2012);
120,000 users, 154th in the world (2009);
80,000 users (2007).
Internet broadband:
16,407 fixed broadband subscriptions, 134th in the world; 0.8% of the population, 143rd in the world;
348,124 wireless broadband subscriptions, 102nd in the world; 16.6% of the population, 76th in the world.
The average internet subscription costs $60.72, 108th in the world.
Internet hosts:
1,806 hosts (2012);
6,374 hosts (2008).
Internet IPv4 addresses: 100,096 addresses allocated, less than 0.05% of the world total, 47.7 addresses per 1000 people (2012).
Internet Service Providers:
53 ISPs (2020);
11 ISPs (2001);
2 ISPs (1999).
ADSL
Botswana Telecom rolled out ADSL in early 2006. Current residential ADSL offerings include speeds from 512 kbit/s to 4096 kbit/s with prices from 292 to 863 BWP (~32 to ~97 US$).
ADSL has been introduced in the following areas:
Gaborone, Tlokweng, Mogoditshane, Molepolole, Phakalane, Francistown, Lobatse, Palapye, Maun, Kasane, Selibe-Phikwe, Letlhakane, Jwaneng, and Orapa.
Internet censorship and surveillance
There are no government restrictions on access to the Internet or credible reports the government monitors e-mail or Internet chat rooms.
The constitution and law provide for freedom of speech and press and the government generally respects these rights. The constitution and law prohibit arbitrary interference with privacy, family, home, correspondence, or browsing pornographic websites, and the government generally respects these prohibitions in practice.
See also
Botswana
Botswana Internet Exchange
Botswana Communications Regulatory Authority
Media of Botswana
Telecommunications in Botswana
References
External links
Botswana Communications Regulatory Authority (BOCRA).
"Botswana", Africa south of the Sahara: Selected Internet resources, Stanford University Libraries.
"Computer and Internet Use Among Families: A Case of Botswana", Rama Srivastava and Ishaan Srivastava, BVICAM’S International Journal of Information Technology (New Delhi, 2008). |
https://en.wikipedia.org/wiki/Ch%C3%A9pica | Chépica is a Chilean town and commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Chépica spans an area of and has 13,857 inhabitants (7,100 men and 6,757 women). Of these, 6,949 (50.1%) lived in urban areas and 6,908 (49.9%) in rural areas. The population fell by 1.7% (244 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Chépica is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2021-24 alcalde is Fabián Soto.
References
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Nancagua | Nancagua () is a Chilean city and commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Nancagua spans an area of and has 15,634 inhabitants (7,959 men and 7,675 women). Of these, 9,264 (59.3%) lived in urban areas and 6,370 (40.7%) in rural areas. The population grew by 8.5% (1,220 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Nancagua is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2021-2024 alcalde is Mario Bustamante.
References
External links
Municipality of Nancagua
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Palmilla | Palmilla is a Chilean city and commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, the commune of Palmilla spans an area of and has 11,200 inhabitants (5,825 men and 5,375 women). Of these, 2,088 (18.6%) lived in urban areas and 9,112 (81.4%) in rural areas. The population grew by 3.1% (336 persons) between the 1992 and 2002 censuses.
The urban area of Palmilla forms a conurbation with the city of Santa Cruz, to the south, totaling 20,691 inhabitants.
Administration
As a commune, Palmilla is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2021-2024 alcaldesa is Gloria Paredes.
References
External links
Municipality of Palmilla
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Peralillo | Peralillo is a Chilean town and commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Peralillo spans an area of and has 9,729 inhabitants (5,007 men and 4,722 women). Of these, 5,882 (60.5%) lived in urban areas and 3,847 (39.5%) in rural areas. The population grew by 6.4% (585 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Peralillo is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2021-2024 mayor is Claudio Cumsille.
References
External links
Municipality of Peralillo
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Placilla | Placilla is a Chilean town and commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Placilla spans an area of and has 8,078 inhabitants (4,134 men and 3,944 women). Of these, 2,114 (26.2%) lived in urban areas and 5,964 (73.8%) in rural areas. The population grew by 3.6% (279 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Placilla is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2012–2016 mayor was José Joaquín Latorre Muñoz (PDC); Latorre, however, died as a consequence of a car crash on 22 July 2013. Latorre had previously held the mayoral office between 1992 and 2008. He was succeeded by Tulio Contreras Álvarez, a member of the local council, who has been reelected until 2024. He died in 2022, during his third term as mayor of Placilla, and was succeeded by Marcelo González, also a Christian Democrat.
References
External links
Municipality of Placilla
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Pumanque | Pumanque is a Chilean commune in Colchagua Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Pumanque spans an area of and has 3,442 inhabitants (1,793 men and 1,649 women), making the commune an entirely rural area. The population fell by 8.8% (331 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Pumanque is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2021-2024 mayor is Gonzalo Baraona Bezanilla.
References
External links
Municipality of Pumanque
Communes of Chile
Populated places in Colchagua Province |
https://en.wikipedia.org/wiki/Mehdi%20Kamrani | Mehdi Kamrani (, born June 1, 1982, in Ray, Iran) is an Iranian professional basketball player.
Career statistics
|-
|style="text-align:left;"|2014–15
|style="text-align:left;"|Jiangsu Monkey King
|35||34||37.1||.463||.339||.745||3.5||5.2||2.8||0.1||16.4
|-
|style="text-align:left;"|2015–16
|style="text-align:left;"|Beikong Fly Dragons
|34||34||39.4||.447||.380||.675||4.6||6.5||2.8||0.1||19.3
|}
Honours
National team
Asian Championship
Gold medal: 2007, 2009, 2013
Asian Games
Bronze medal: 2006, 2010
Islamic Solidarity Games
Bronze medal: 2005
Asian Indoor Games
Gold medal: 2009
Club
Asian Championship
Gold medal: 2008 (Saba Battery), 2009, 2010 (Mahram)
West Asian Championship
Gold medal: 2009, 2010, 2012 (Mahram)
Iranian Basketball Super League
Champions: 2004 (Saba Battery), 2008, 2009, 2010, 2011, 2012 (Mahram)
References
External links
Kamrani profile at FIBA
Kamarni at Basketball.Asia-Basket.com
Kamrani on Instagram
Kamrani on Facebook
1982 births
Living people
Asian Games silver medalists for Iran
Asian Games bronze medalists for Iran
Asian Games medalists in basketball
Basketball players at the 2006 Asian Games
Basketball players at the 2008 Summer Olympics
Basketball players at the 2010 Asian Games
Basketball players at the 2014 Asian Games
Beijing Royal Fighters players
Iranian expatriate basketball people in China
Iranian men's basketball players
Nanjing Tongxi Monkey Kings players
Jilin Northeast Tigers players
Mahram Tehran BC players
Medalists at the 2006 Asian Games
Medalists at the 2010 Asian Games
Medalists at the 2014 Asian Games
Olympic basketball players for Iran
Sportspeople from Tehran
Point guards
2014 FIBA Basketball World Cup players
2010 FIBA World Championship players
Islamic Solidarity Games competitors for Iran |
https://en.wikipedia.org/wiki/Internet%20in%20Estonia | Internet in Estonia has one of the highest penetration rates in the world. In the first quarter of 2010, 75% out of 1.34 million people in the country used the Internet according to Statistics Estonia. In 2017, according to the World Bank came 13th in the world by the percentage of population using the Internet, with 88.1% people using it.
Facts and figures
Top-level domain: .ee
Internet users:
1.0 million users, 119th in the world; 79.0% of the population, 34th in the world (2012);
971,700 users, 102nd in the world (2009).
Fixed broadband: 327,243 subscriptions, 78th in the world; 25.7% of the population, 31st in the world (2012).
Wireless broadband: 924,699 subscriptions, 74th in the world; 72.5% of the population, 12th in the world (2012).
Internet hosts: 865,494 hosts, 49th in the world (2012).
IPv4: 1.3 million addresses allocated, less than 0.05% of the world total, 945.8 addresses per 1000 people (2012).
History
In 1965 the first school computer in the USSR, Ural-1, was set up in the town of Nõo. Mass usage of computing networks first came with FidoNet, the first Estonian node of which appeared in 1989. The first Internet connections in the country were introduced in 1992 at academic facilities in Tallinn and Tartu. The national domain (.ee) was registered in the middle of 1992. By virtue of its geographical location, the country played important role in transporting Internet culture to neighbouring Russia. One of the first backbone links for Russia was built in 1991 by Relcom through Estonia to Finland. In 1996 Estonian president Lennart Meri started the four-year state program "Tiigrihüpe" to computerize and internetize all of the country's schools.
The first public Wi-Fi area was launched in 2001 and a system of mobile data networks that enable widespread wireless broadband access has developed. In 2011, the country had over 2,440 free, certified Wi-Fi areas meant for public use, including at cafes, hotels, hospitals, schools, and gas stations. A countrywide wireless internet service based on CDMA technology has been deployed. Three mobile operators offer mobile 3G and 3.5G services, and as of May 2013, 4G services covered over 95 percent of the territory.
Computerization and digital connection for people are encouraged and supported by the state. The country has a digital ID card system, and in 2005 local elections were held with the official possibility to vote online – the first case of its kind in the world.
In 2008, the North Atlantic Treaty Organization (NATO) established a joint cyberdefense center in Estonia to improve cyberdefense interoperability and provide security support for all NATO members.
In 2009, the Estonian Internet Foundation was established to manage Estonia's top level domain, ".ee". As a multi-stakeholder organization it represents the Estonian Internet community internationally with respect to various Internet governance issues.
In 2013 there were over 200 operators offering electronic communi |
https://en.wikipedia.org/wiki/Chaplygin%20problem | In mathematics, particularly in the fields of nonlinear dynamics and the calculus of variations, the Chaplygin problem is an isoperimetric problem with a differential constraint. Specifically, the problem is to determine what flight path an airplane in a constant wind field should take in order to encircle the maximum possible area in a given amount of time. The airplane is assumed to be constrained to move in a plane, moving at a constant airspeed v, for time T, and the wind is assumed to move in a constant direction with speed w.
The solution of the problem is that the airplane should travel in an ellipse whose major axis is perpendicular to w, with eccentricity w/v.
References
See also
Isoperimetric inequality : zero wind speed case
Calculus of variations |
https://en.wikipedia.org/wiki/SVD | SVD may stand for:
Geography
Argyle International Airport (IATA airport code SVD) on Saint Vincent island
Mathematics
Singular value decomposition of a matrix in mathematics
Media
Svenska Dagbladet (SvD), a Swedish newspaper
Medicine
Spontaneous vaginal delivery, a type of birth
Swine vesicular disease
Small vessel disease, of blood vessels
Popular culture
Sander van Doorn (b. 1979), Dutch DJ
Religion
Society of the Divine Word (Societas Verbi Divini), a Roman Catholic religious order
Science and technology
Saturation vapor density
Semi-virtual diskette, emulating a floppy drive
Simultaneous voice and data, in telecommunications
Weapons
SVD (rifle) (Russian: Snayperskaya Vintovka Dragunova), a Soviet marksman rifle. |
https://en.wikipedia.org/wiki/Differential%20geometry%20of%20surfaces | In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.
Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space.
Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves. An important role in their study has been played by Lie groups (in the spirit of the Erlangen program), namely the symmetry groups of the Euclidean plane, the sphere and the hyperbolic plane. These Lie groups can be used to describe surfaces of constant Gaussian curvature; they also provide an essential ingredient in the modern approach to intrinsic differential geometry through connections. On the other hand, extrinsic properties relying on an embedding of a surface in Euclidean space have also been extensively studied. This is well illustrated by the non-linear Euler–Lagrange equations in the calculus of variations: although Euler developed the one variable equations to understand geodesics, defined independently of an embedding, one of Lagrange's main applications of the two variable equations was to minimal surfaces, a concept that can only be defined in terms of an embedding.
History
The volumes of certain quadric surfaces of revolution were calculated by Archimedes. The development of calculus in the seventeenth century provided a more systematic way of computing them. Curvature of general surfaces was first studied by Euler. In 1760 he proved a formula for the curvature of a plane section of a surface and in 1771 he considered surfaces represented in a parametric form. Monge laid down the foundations of their theory in his classical memoir L'application de l'analyse à la géometrie which appeared in 1795. The defining contribution to the theory of surfaces was made by Gauss in two remarkable papers written in 1825 and 1827. This marked a new departure from tradition because for the first time Gauss considered the intrinsic geometry of a surface, the properties which are determined only by the geodesic distances between points on the surface independently of the particular way in which the surface is located in the ambient Euclidean space. The crowning result, the Theorema Egregium of Gauss, established that the Gaussian curvature is an intrinsic invariant, i.e. invariant under local isometries. This point of view was extended to higher-dimensional spaces by Riemann and led to what is known today as Riemannia |
https://en.wikipedia.org/wiki/Foundations%20of%20statistics | Statistics concerns the collection, organization, analysis, interpretation, and presentation of data, used to solve practical problems and draw conclusions. When analyzing data, the approaches used can lead to different conclusions on the same data. For example, weather forecasts often vary among different forecasting agencies that use different algorithms and techniques. Conclusions drawn from statistical analysis often involve uncertainty as they represent the probability of an event occurring. For instance, a weather forecast indicating a 90% probability of rain means it will likely rain, while a 5% probability means it is unlikely to rain. The actual outcome, whether it rains or not, can only be determined after the event.
Statistics is also fundamental to disciplines of science that involve predicting or classifying events based on a large set of data. It is an integral part of machine learning, bioinformatics, genomics, economics, and more.
Statistics focuses on the quantitative characteristics of numerous repeatable phenomena. This is because certain conclusions in some fields are difficult to express with certainty, unlike mathematical formulas or theorems. For instance, it is commonly believed that taller parents are more likely to have taller children. However, it's important to note that individual parent-child pairings can deviate from these expectations, with the child potentially exceeding or falling short of the anticipated height based on their parents' stature. Randomness plays a role in height variations, influenced by factors like genetics, living environment, diet, habits, and other variables. Nevertheless, taller parents are generally more likely to have taller children. Height can vary to a degree, exhibiting randomness, but the overall stability of average height suggests the presence of a statistical rule. Therefore, statistics also encompasses the study of identifying statistical laws.
The foundations of statistics involve the epistemological debate, describing how inductive inference from data should be conducted. Statistical inference addresses various issues, including Bayesian inference versus frequentist inference; the distinction between Fisher's "significance testing" and Neyman-Pearson "hypothesis testing"; and whether the likelihood principle should be followed.
Some of these issues have been subject to unresolved debate for up to two centuries.
Bandyopadhyay & Forster describe four statistical paradigms: classical statistics (or error statistics), Bayesian statistics, likelihood-based statistics, and the use of the Akaike Information Criterion as a statistical basis. More recently, Judea Pearl reintroduced a formal mathematics for attributing causality in statistical systems that addresses fundamental limitations of both bayesian and Neyman-Pearson methods.
Leonard J. Savage's text, Foundations of Statistics, states:
Fisher's "significance testing" vs. Neyman–Pearson "hypothesis testing"
During the second |
https://en.wikipedia.org/wiki/Cribbage%20statistics | In cribbage, the probability and maximum and minimum score of each type of hand can be computed.
Distinct hands
There are 12,994,800 possible hands in Cribbage: 52 choose 4 for the hand, and any one of the 48 left as the starter card.
Another, and perhaps more intuitive way of looking at it, is to say that there are 52 choose 5 different 5-card hands, and any one of those 5 could be the turn-up, or starter card. Therefore, the calculation becomes:
1,009,008 (approximately 7.8%) of these score zero points, or 1,022,208 if the hand is the crib, as the starter must be the same suit as the crib's four cards for a flush.
Not accounting for suit, there are 14,715 unique hands.
Maximum scores
The highest score for one hand is 29: 555J in hand with the starter 5 of the same suit as the Jack (8 points for four J-5 combinations, 8 points for four 5-5-5 combinations, 12 points for pairs of 5s and one for the nob). There is also the “Dealer’s 30”, (28 for 5-5-5-5 in the hand and a Jack as the starter. The dealer would take 2 for cutting the Jack…to make 30.)
The second highest score is 28 (hand and starter together comprise any ten-point card plus all four 5s, apart from the 29-point hand above).
The third highest score is 24 (A7777, 33339, 36666, 44447, 44556, 44566, 45566, 67788 or 77889); 24 is the maximum score for any card combination without a 2 or a ten-card, except for the above examples with four 5s.
The maximum score for any hand containing a 2 is 20; either 22229 or 26778 if the latter is a four-card flush.
The highest score as a dealer from the hand and crib is 53. The starter must be a 5, the hand must be J555, with the Jack suit matching the starter (score 29), and the crib must be 4466 (score 24), or vice versa.
The highest number of points possible (excluding pegging points) in one round is 77. The dealer must score 53, the opponent must then have the other 4466 making another 24 point hand for a total of 77.
The highest number of points from a hand that has a potential to be a "19 hand" is 15. It is a crib hand of one suit, 46J and another ten card, with a 5 of that suit cut up. The points are 15 for 6, a run for 9, nobs for 10, and a flush for 15. Any of the following cards in an unlike suit yields a "19 hand"; 2,3,7,8,and an unpaired ten card.
The most points that can be pegged by playing one card is 15, by completing a double pair royal on the last card and making the count 15: 12 for double pair royal (four-of-a-kind), 2 for the 15, and 1 for the last card. This can happen in two ways in a two-player game. The non-dealer must have two ten-value cards and two 2s, and the dealer must have one ten-value card and 722, in which case the play must go: 10-10-10-go; 7-2-2-2-2. For example:
Alternatively, the players can each have two deuces, with one also holding A-4 and the other two aces. Then play might go 4-A-A-A-2-2-2-2.
The maximum number of points that can be scored in a single deal by the dealer in a two player game is |
https://en.wikipedia.org/wiki/1525%20in%20art | Events from the year 1525 in art.
Events
Albrecht Dürer publishes his work on geometry, The Four Books on Measurement ("Underweysung der Messung mit dem Zirckel und Richtscheyt" or "Instructions for Measuring with Compass and Ruler") at Nuremberg
Lucas Horenbout is named royal "pictor maker" to King Henry VIII of England, and will introduce the techniques of portrait miniatures to England
Jan Cornelisz Vermeyen is named Court Painter to Archduchess Margaret of Austria
Works
Painting
Lucas Cranach the Elder
Cardinal Albert of Brandenburg before Christ on the Cross (approximate date)
Venus and Cupid
Antonio da Correggio – Venus with Mercury and Cupid or The School of Love (approximate date)
Michelangelo – Head of Bearded Man Shouting
Pontormo – Youth in a Pink Cloak Jan Provoost – Last Judgment (Groeningemuseum)
Nicola da Urbino – Panel with the Adoration of the Magi Bernard van Orley – The Last Judgment (triptych, commissioned for Antwerp)
Bartolomeo Veneto – Flora (approximate date)
Pseudo Jan Wellens de Cock – The Crucifixion (triptych, approximate date)
Sculpture
Conrad Meit – Judith with the head of Holofernes (alabaster)
Armor
Kolman Helmschmid – Portions of a Costume Armor (Metropolitan Museum of Art)
Birthsdate unknownCesare Baglioni, Italian painter specializing in quadratura (died 1590)
Pieter Balten, Flemish Renaissance painter (died 1584)
Ferrando Bertelli, Italian engraver of the Renaissance period (died unknown)
René Boyvin, French engraver who lived in Angers (died 1598)
Pieter Bruegel the Elder, Netherlandish Renaissance painter and printmaker known for his landscapes and peasant scenes (died 1569)
Ascanio Condivi, Italian painter and writer, primarily remembered as the biographer of Michelangelo (died 1574)
Cristofano dell'Altissimo, Italian painter primarily working in Florence (died 1605)
Guillaume Le Bé, French engraver (died 1598)
Giulio Mazzoni, Italian painter and stuccoist (died 1618)
Francesco Terzi, Italian painter of primarily religious themes (died 1600)
Giovanni Maria Verdizotti, Venetian artist and poet (died 1600)
Juan Valverde de Amusco, Italian anatomist and engraver (died 1587)
Francisco Venegas, Spanish painter active in Portugal (died 1594)
Alessandro Vittoria, Italian Mannerist sculptor of the Venetian school (died 1608)
Song Xu, Chinese landscape painter (died unknown)
1525/1530: Hans Collaert, Flemish engraver (died 1580)
Deaths
January 24 - Franciabigio, Italian painter of the Florentine Renaissance (born 1482)
June - Girolamo di Benvenuto, Italian painter, son of Benvenuto di Giovanni (born 1470)
June 10 - Tosa Mitsunobu, Japanese painter and founder of the Tosa school of painting (born 1434)
August 4 - Andrea della Robbia, Italian Renaissance sculptor, especially in ceramics (born 1435)date unknownBernardino Bergognone - Italian Renaissance painter of the Milanese school (born 1455)
Boccaccio Boccaccino, Italian painter of the Emilian school (born 1467)
Vittore Carpaccio, Italian pain |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20Norwich%20City%20F.C.%20season | The 2007–08 season was Norwich City's third consecutive year in the Football League Championship. This article shows statistics and lists all matches that Norwich City played in the season.
Season summary
Norwich had a busy summer with Peter Grant bringing in 9 players, which included goalkeeper David Marshall and former players Jamie Cureton and Darel Russell making returns to Carrow Road. 10 players departed Norwich, most notably Dickson Etuhu and Robert Earnshaw, while Darren Huckerby caused controversy by criticizing the club for selling their best players.
Norwich started off with a goalless draw away at Preston and a 2–1 win over Southampton, but after this Norwich endured a horrendous run of form, winning 1 league game in 8. After a 1–0 away defeat to QPR, Grant and City parted company by mutual consent.
Jim Duffy took over as caretaker boss, but lost his 3 games in charge.
On 30 October, Glenn Roeder was appointed as Grant's successor with the team bottom of the table. His first game was the East Anglian Derby against Ipswich, a 2–2 draw with Norwich coming back from 2–0 down. Norwich lost their next 2 games, including a dreadful 3–0 defeat away at Plymouth Argyle, and were 8 points away from safety. After that defeat Roeder brought in Matty Pattison, Mo Camara and Ched Evans on loan to add to the loan signing of Martin Taylor, who had been signed before the game against Ipswich (Pattison's loan move was made permanent in January). Norwich's form improved greatly, with only one defeat in eleven league games. After a 3–1 win over Barnsley on 12 January Norwich were in 18th position, four points clear of the relegation zone. Roeder began an overhaul of the squad during the January transfer window, selling Chris Brown to Preston and releasing David Strihavka, Julien Brellier and Ian Murray, all of whom had been signed by Grant and who had not figured in the first team since the defeat at Plymouth.
Results
Pre-season friendlies
League
August
September
October
November
December
January
February
March
April
May
FA Cup
League Cup
Transfers
Transfers in
Loans in
Transfers out
Loans out
Players
First team squad
Squad at end of season
Left club during season
Board and staff members
Board members
Coaching staff
Final league table
Notes
References
Norwich City F.C. seasons
Norwich City |
https://en.wikipedia.org/wiki/Martin%20Badoian | Martin J. Badoian (August 23, 1928October 27, 2018) was a teacher of mathematics at Canton High School in Canton, Massachusetts, who taught for 60 years at the school. Badoian was a co-founder and vice-president of the American Regions Mathematics League.
Badoian attended Brown University, graduating in 1952, where he excelled in athletics. He was a tri-captain athlete at Brown University in golf, basketball, and baseball. He won awards at the state and New England level for his achievements in athletics.
Badoian founded and was the coach of the Canton High math team. He was recognized as the driving force behind their success. The team, from the late 1970s to the late 1990s, had taken 19 of 21 annual New England championships and 14 of 21 state championships. News articles sometimes compared them to the Boston Celtics because of their dominance over other teams. Apart from coaching his high school team, Badoian was the director of New England Math Meet, the New England Mathematics League and the Greater Boston Mathematics League.
Awards
Massachusetts Teacher of the Year Award 1977
Edyth May Sliffe Award 1989 and 1991
Two-time winner of The Alfred Kalfus Founder's Award in 1987 and 1990 (Award for dedication to ARML)
Presidential Award for Excellence in Mathematics and Science Teaching (State & National Winner)
Tandy Scholar (National Winner)
References
External links
Schoolteachers from Massachusetts
2018 deaths
1928 births
Brown University alumni |
https://en.wikipedia.org/wiki/Clone%20%28algebra%29 | In universal algebra, a clone is a set C of finitary operations on a set A such that
C contains all the projections , defined by ,
C is closed under (finitary multiple) composition (or "superposition"): if f, g1, …, gm are members of C such that f is m-ary, and gj is n-ary for all j, then the n-ary operation is in C.
The question whether clones should contain nullary operations or not is not treated uniformly in the literature. The classical approach as evidenced by the standard monographs on clone theory considers clones only containing at least unary operations. However, with only minor modifications (related to the empty invariant relation) most of the usual theory can be lifted to clones allowing nullary operations. The more general concept includes all clones without nullary operations as subclones of the clone of all at least unary operations and is in accordance with the custom to allow nullary terms and nullary term operations in universal algebra. Typically, publications studying clones as abstract clones, e.g. in the category theoretic setting of Lawvere's algebraic theories, will include nullary operations.
Given an algebra in a signature σ, the set of operations on its carrier definable by a σ-term (the term functions) is a clone. Conversely, every clone can be realized as the clone of term functions in a suitable algebra by simply taking the clone itself as source for the signature σ so that the algebra has the whole clone as its fundamental operations.
If A and B are algebras with the same carrier such that every basic function of A is a term function in B and vice versa, then A and B have the same clone. For this reason, modern universal algebra often treats clones as a representation of algebras which abstracts from their signature.
There is only one clone on the one-element set (there are two if nullary operations are considered). The lattice of clones on a two-element set is countable, and has been completely described by Emil Post (see Post's lattice, which traditionally does not show clones with nullary operations). Clones on larger sets do not admit a simple classification; there are continuum-many clones on a finite set of size at least three, and 22κ (even just maximal, i.e. precomplete) clones on an infinite set of cardinality κ.
Abstract clones
Philip Hall introduced the concept of abstract clone. An abstract clone is different from a concrete clone in that the set A is not given.
Formally, an abstract clone comprises
a set Cn for each natural number n,
elements k,n in Cn for all k ≤ n, and
a family of functions ∗:Cm × (Cn)m → Cn for all m and n
such that
c * (1,n, …, n,n) = c
k,m * (c1, …, cm) = ck
c * (d1 * (e1, …, en), …, dm * (e1, …, en)) = (c * (d1, …, dm)) * (e1, …, en).
Any concrete clone determines an abstract clone in the obvious manner.
Any algebraic theory determines an abstract clone where Cn is the set of terms in n variables, k,n are variables, and ∗ is substitution. Two theories determine |
https://en.wikipedia.org/wiki/Post%27s%20lattice | In logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published a complete description of the lattice in 1941. The relative simplicity of Post's lattice is in stark contrast to the lattice of clones on a three-element (or larger) set, which has the cardinality of the continuum, and a complicated inner structure. A modern exposition of Post's result can be found in Lau (2006).
Basic concepts
A Boolean function, or logical connective, is an n-ary operation for some , where 2 denotes the two-element set {0, 1}. Particular Boolean functions are the projections
and given an m-ary function f, and n-ary functions g1, ..., gm, we can construct another n-ary function
called their composition. A set of functions closed under composition, and containing all projections, is called a clone.
Let B be a set of connectives. The functions which can be defined by a formula using propositional variables and connectives from B form a clone [B], indeed it is the smallest clone which includes B. We call [B] the clone generated by B, and say that B is the basis of [B]. For example, [¬, ∧] are all Boolean functions, and [0, 1, ∧, ∨] are the monotone functions.
We use the operations ¬, Np, (negation), ∧, Kpq, (conjunction or meet), ∨, Apq, (disjunction or join), →, Cpq, (implication), ↔, Epq, (biconditional), +, Jpq (exclusive disjunction or Boolean ring addition), ↛, Lpq, (nonimplication), ?: (the ternary conditional operator) and the constant unary functions 0 and 1. Moreover, we need the threshold functions
For example, th1n is the large disjunction of all the variables xi, and thnn is the large conjunction. Of particular importance is the majority function
We denote elements of 2n (i.e., truth-assignments) as vectors: . The set 2n carries a natural product Boolean algebra structure. That is, ordering, meets, joins, and other operations on n-ary truth assignments are defined pointwise:
Naming of clones
Intersection of an arbitrary number of clones is again a clone. It is convenient to denote intersection of clones by simple juxtaposition, i.e., the clone is denoted by C1C2...Ck. Some special clones are introduced below:
M is the set of monotone functions: for every .
D is the set of self-dual functions: .
A is the set of affine functions: the functions satisfying
for every i ≤ n, a, b ∈ 2n, and c, d ∈ 2. Equivalently, the functions expressible as for some a0, a.
U is the set of essentially unary functions, i.e., functions which depend on at most one input variable: there exists an i = 1, ..., n such that whenever .
Λ is the set of conjunctive functions: . The clone Λ consists of the conjunctions for all subsets I of {1, ..., n} (including the empty conjunction, i.e., the constant 1), and the constant 0.
V is the set of disjunctive functions: . Equivalently, V consists of the disjunctions for all subsets I of {1, ..., n} (including the e |
https://en.wikipedia.org/wiki/Variational%20vector%20field | In the mathematical fields of the calculus of variations and differential geometry, the variational vector field is a certain type of vector field defined on the tangent bundle of a differentiable manifold which gives rise to variations along a vector field in the manifold itself.
Specifically, let X be a vector field on M. Then X generates a one-parameter group of local diffeomorphisms FlXt, the flow along X. The differential of FlXt gives, for each t, a mapping
where TM denotes the tangent bundle of M. This is a one-parameter group of local diffeomorphisms of the tangent bundle. The variational vector field of X, denoted by T(X) is the tangent to the flow of d FlXt.
References
Calculus of variations |
https://en.wikipedia.org/wiki/Frequentist%20inference | Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist-inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded.
History of frequentist statistics
The primary formulation of frequentism stems from the presumption that statistics could be perceived to have been a probabilistic frequency. This view was primarily developed by Ronald Fisher and the team of Jerzy Neyman and Egon Pearson. Ronald Fisher contributed to frequentist statistics by developing the frequentist concept of "significance testing", which is the study of the significance of a measure of a statistic when compared to the hypothesis. Neyman-Pearson extended Fisher's ideas to multiple hypotheses by conjecturing that the ratio of probabilities of hypotheses when maximizing the difference between the two hypotheses leads to a maximization of exceeding a given p-value, and also provides the basis of type I and type II errors. For more, see the foundations of statistics page.
Definition
For statistical inference, the statistic about which we want to make inferences is , where the random vector is a function of an unknown parameter, . The parameter is further partitioned into (), where is the parameter of interest, and is the nuisance parameter. For concreteness, might be the population mean, , and the nuisance parameter the standard deviation of the population mean, .
Thus, statistical inference is concerned with the expectation of random vector , .
To construct areas of uncertainty in frequentist inference, a pivot is used which defines the area around that can be used to provide an interval to estimate uncertainty. The pivot is a probability such that for a pivot, , which is a function, that is strictly increasing in , where is a random vector. This allows that, for some 0 < < 1, we can define , which is the probability that the pivot function is less than some well-defined value. This implies , where is a upper limit for . Note that is a range of outcomes that define a one-sided limit for , and that is a two-sided limit for , when we want to estimate a range of outcomes where may occur. This rigorously defines the confidence interval, which is the range of outcomes about which we can make statistical inferences.
Fisherian reduction and Neyman-Pearson operational criteria
Two complementary concepts in frequentist inference are the Fisherian reduction and the Neyman-Pearson operational criteria. Together these concepts illustrate a way of constructing frequentist intervals that define the limits for . The Fisherian reduction is a method of determining the interval within which the true value of may lie, while the Neyman-Pearson operational cr |
https://en.wikipedia.org/wiki/Phil%20Martin%20%28boxer%29 | Phil Martin (aka Philip Martin Adelagan) (5 April 1950 – 27 May 1994) was an English professional light-heavyweight boxer. He fought during the 1970s with career statistics of won 14 (KO 6) and lost 6 (KO 4).
Early life
Martin was born in Moss Side, Manchester, England, on 5 April 1950.
Boxing career
He had a record of 14 wins and six defeat. The highlight of his career was beating former British Light Heavyweight Champion Gypsy Johnny Frankham over 10 rounds at Belle Vue, Greater Manchester, in November 1975. His professional career ended when he retired after the Ennio Cometti fight in 1978.
Martin went on to become a successful boxing trainer, after meeting with Chet Alexander who convinced him to return to a career in boxing. Before this Martin had become involved in left-wing political activism, which he was frustrated with, and he moved enthusiastically back into the sport, in the role of a trainer, working at the Alexander Foundation on Princess Road in Moss Side, Manchester. After taking classes in training at the Alexander Foundation, he set up his own gym in a disused building in Princess Road, Moss Side (in an area that had seen rioting in 1981), which he named the 'Champs Camp Gym', where he guided numerous boxers, such as Tony Ekubia, Frank Grant, Maurice Core, Ossie Maddix, Ensley Bingham and Steve Walker, to British European and Commonwealth title contests.
Death
Martin died on 27 May 1994 from the effects of cancer at the age of 44. The Champ Camp Gym was renamed the Phil Martin Centre in his honour.
Professional record
References
1950 births
1994 deaths
English male boxers
Light-heavyweight boxers
People from Moss Side |
https://en.wikipedia.org/wiki/CaRMetal | CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in Java. CaRMetal is free, under GNU GPL license. It keeps an amount of functionality of C.a.R. but uses a different graphical interface which purportedly eliminates some intermediate dialogs and provides direct access to numerous effects. Constructions are done using a main palette, which contains some useful construction shortcuts in addition to the standard compass and ruler tools. These include perpendicular bisector, circle through three points, circumcircular arc through three points, and conic section through five points. Also interesting are the loci, functions, parametric curves, and implicit plots. Element thickness, color, label, and other attributes (including the so-called magnetic property) can be set using a separate panel.
CaRMetal also supports a configurable restricted construction palette and has assignment capabilities, which use an apparently unique feature called Monkey. CaRMetal has a scripting language (JavaScript) which allows the user to build rather complex figures like fractals. CaRMetal has several locales including French, English, Spanish, German, Italian, Dutch, Portuguese and Arabic.
Didactic interest
Anticipation
When one chooses a tool like the parallel to a line through a point, or a circle, the intended object appears in yellow color and follows the mouse movements. This allows the user to make conjectures even before the construction is finished. This constant interaction between the pupil and the object of experimentation is in phase with modern theories about didactics and, in this view, CaRMetal is intended to be used by students.
Amodality
The windows which show the history, the tools palette, the properties of the selected object are around the figure and never above it. These windows are not modal windows in the sense that they never hide the construction. For example, whenever the user wants to change the color of a polygon, he sees the new color immediately.
Transformations
When a transformation (for example a macro) has been defined, such that it transforms points into points, this transformation can also be applied to curves. Once again, this allows the learning subject to see the properties of the transformation at a glance, even before the transformation has actually been applied.
Assignments
The workbooks (see below) can be exported as HTML files, with a restricted tools palette (for example, leaving only the intersection and circle tools lets the pupil make compass-only construction). To create an assignment, the teacher chooses the initial objects, the objects to be created by the pupil, and writes a text explaining what is to be done. Since 2010, when the pupil has finished the construction and wants to test it, random variations are tested (with a tool called Monkey) and a quality note is attributed to the pupil (actually, a percentage of the good construct |
https://en.wikipedia.org/wiki/97.5th%20percentile%20point | In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96, meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean. Because of the central limit theorem, this number is used in the construction of approximate 95% confidence intervals. Its ubiquity is due to the arbitrary but common convention of using confidence intervals with 95% probability in science and frequentist statistics, though other probabilities (90%, 99%, etc.) are sometimes used. This convention seems particularly common in medical statistics, but is also common in other areas of application, such as earth sciences, social sciences and business research.
There is no single accepted name for this number; it is also commonly referred to as the "standard normal deviate", "normal score" or "Z score" for the 97.5 percentile point, the .975 point, or just its approximate value, 1.96.
If X has a standard normal distribution, i.e. X ~ N(0,1),
and as the normal distribution is symmetric,
One notation for this number is z.975. From the probability density function of the standard normal distribution, the exact value of z.975 is determined by
History
The use of this number in applied statistics can be traced to the influence of Ronald Fisher's classic textbook, Statistical Methods for Research Workers, first published in 1925:
In Table 1 of the same work, he gave the more precise value 1.959964.
In 1970, the value truncated to 20 decimal places was calculated to be
1.95996 39845 40054 23552...
The commonly used approximate value of 1.96 is therefore accurate to better than one part in 50,000, which is more than adequate for applied work.
Some people even use the value of 2 in the place of 1.96, reporting a 95.4% confidence interval as a 95% confidence interval. This is not recommended but is occasionally seen.
Software functions
The inverse of the standard normal CDF can be used to compute the value. The following is a table of function calls that return 1.96 in some commonly used applications:
See also
Margin of error
Probit
Reference range
Standard error (statistics)
68–95–99.7 rule
References
Further reading
Estimation theory
Normal distribution
Mathematical constants |
https://en.wikipedia.org/wiki/A.%20P.%20Balachandran | Aiyalam Parameswaran Balachandran (born 25 January 1938) is an Indian theoretical physicist known for his extensive contributions to the role of classical topology in quantum physics. He is currently an emeritus professor in the Department of Physics, Syracuse University, where he was previously the Joel Dorman Steele Professor of Physics between 1999 and 2012. He has also been a fellow of the American Physical Society since 1988 and was awarded a prize by the U.S. Chapter of the Indian Physics Association in recognition of his outstanding scientific contributions.
In 1990, Syracuse University honored him with a Chancellor's Citation for Exceptional Academic Achievement.
Early life and education
Balachandran was born on 25 January 1938 in Salem, Tamil Nadu, India. His father, Aiyalam Sundaram Parameswaran, was a chartered accountant in Pierce Leslie and Company in Cochin. Balachandran had a gifted poet, Vyloppilli Sreedhara Menon, as his teacher. Balachandran completed his first two college years in Guruvayurappan College, Kozhikode, specialising in physics, chemistry and mathematics and passing the 'Intermediate Examination' with all-State distinction in 1953. He joined BSc (Hons) in Physics in the Madras Christian College, Tambaram, Chennai. Balachandran graduated from MCC in 1958.
Research
Balachandran received his PhD degree under Professor Alladi Ramakrishnan at the University of Madras. Then he joined Theoretisch Physics, University at Wien as a postdoctoral fellow under Professor Walter Thirring, subsequently at the Enrico Fermi Institute as a postdoc. In 1964, he joined the Syracuse University faculty. Balachandran's key scientific works to date include the revival of the Skyrme model which successfully describes baryons as topological solitons of meson fields and mathematical concepts such as homotopy groups and fibre bundles to problems in quantum physics. In recent, Balachandran's research has been focused on the formulation of quantum field theories on noncommutative spacetimes and investigating the emergent significance of Hopf algebras in quantum physics as generalisations of symmetry groups.
Books
A. P. Balachandran, S. G. Jo, G. Marmo, Group Theory and Hopf Algebras: Lectures for Physicists, World Scientific Publishing Co. Pte. Ltd., 2010. .
A. P. Balachandran, G. Marmo, B. S. Skagerstam, A. Stern, Classical Topology and Quantum States, World Scientific Publishing Co. Pte. Ltd., Singapore, 1991. -- (pbk.)
A. P. Balachandran, G. Marmo, B. S. Skagerstam, A. Stern, Gauge Symmetries and Fibre Bundles : Applications to Particle Dynamics, Springer Verlag, 1983. .
A. P. Balachandran (editor), A. P. Balachandran, E. Ercolessi, G. Morandi, A.M. Srivastava, Hubbard Model and Anyon Superconductivity, World Scientific Publishing Co. 1990. .
A. P. Balachandran, S. Kurkcuoglu, S. Vaidya, Lectures on Fuzzy and Fuzzy Susy Physics, World Scientific Publishing Co. 2007. .
A. P. Balachandran, G.C. Trahern, Lectures on Group Theory for Physic |
https://en.wikipedia.org/wiki/Parovicenko%20space | In mathematics, a Parovicenko space is a topological space similar to the space of non-isolated points of the Stone–Čech compactification of the integers.
Definition
A Parovicenko space is a topological space X satisfying the following conditions:
X is compact Hausdorff
X has no isolated points
X has weight c, the cardinality of the continuum (this is the smallest cardinality of a base for the topology).
Every two disjoint open Fσ subsets of X have disjoint closures
Every non-empty Gδ of X has non-empty interior.
Properties
The space βN\N is a Parovicenko space, where βN is the Stone–Čech compactification of the natural numbers N. proved that the continuum hypothesis implies that every Parovicenko space is isomorphic to βN\N. showed that if the continuum hypothesis is false then there are other examples of Parovicenko spaces.
References
General topology |
https://en.wikipedia.org/wiki/Professor%20Kageyama%27s%20Maths%20Training%3A%20The%20Hundred%20Cell%20Calculation%20Method | Professor Kageyama's Maths Training: The Hundred Cell Calculation Method is a puzzle video game published by Nintendo and developed by Jupiter for the Nintendo DS handheld video game console. It was first released in Japan, then later in Europe and Australasia. It was released in North America as Personal Trainer: Math on January 12, 2009 and also in South Korea in 2009. The game is part of both the Touch! Generations and Personal Trainer series. The game received mixed reviews, with common criticisms cited for the game's difficulty in recognizing some numbers and for not being very entertaining to play. At GameRankings, it holds an average review score of 65%.
Gameplay
Maths Training, designed to be played daily, uses a method called "The Hundred Cell Calculation Method" that focuses on repetition of basic arithmetic. This method was developed by Professor Kageyama who works at the Centre for Research and Educational Development at Ritsumeikan University, Kyoto. Utilizing a 10 x 10 grid of blank squares lined with rows of numbers along the top and side of the grid, the player has to match up each top number with each side number and add or subtract or multiply them. They then fill in the appropriate square with the appropriate answer.
The game is played by holding the Nintendo DS vertically like a book, and it supports both right- and left-handed users, allowing them to view the exercises on the message screen while they note down their answers with the stylus on the Touch Screen. The user can play against up to 15 other Nintendo DS users by using the DS Download Play option or with multiple game cards.
See also
List of Nintendo DS games
Personal Trainer: Cooking
Personal Trainer: Walking
Notes
References
External links
Official website for Japan
2007 video games
Brain training video games
Mathematical education video games
Jupiter (company) games
Nintendo DS games
Nintendo DS-only games
Nintendo games
Shogakukan
Touch! Generations
Video games developed in Japan
Multiplayer and single-player video games |
https://en.wikipedia.org/wiki/List%20of%20forcing%20notions | In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M. The poset P used will determine what statements hold in the new universe (the 'extension'); to force a statement of interest thus requires construction of a suitable P. This article lists some of the posets P that have been used in this construction.
Notation
P is a poset with order <
V is the universe of all sets
M is a countable transitive model of set theory
G is a generic subset of P over M.
Definitions
P satisfies the countable chain condition if every antichain in P is at most countable. This implies that V and V[G] have the same cardinals (and the same cofinalities).
A subset D of P is called dense if for every there is some with .
A filter on P is a nonempty subset F of P such that if and then , and if and then there is some with and .
A subset G of P is called generic over M if it is a filter that meets every dense subset of P in M.
Amoeba forcing
Amoeba forcing is forcing with the amoeba order, and adds a measure 1 set of random reals.
Cohen forcing
In Cohen forcing (named after Paul Cohen) P is the set of functions from a finite subset of ω2 × ω to {0,1}
and if .
This poset satisfies the countable chain condition. Forcing with this poset adds ω2 distinct reals to the model; this was the poset used by Cohen in his original proof of the independence of the continuum hypothesis.
More generally, one can replace ω2 by any cardinal κ so construct a model where the continuum has size at least κ. Here, there is no restriction. If κ has cofinality ω, the reals end up bigger than κ.
Grigorieff forcing
Grigorieff forcing (after Serge Grigorieff) destroys a free ultrafilter on ω.
Hechler forcing
Hechler forcing (after Stephen Herman Hechler) is used to show that Martin's axiom implies that every family of less than c functions from ω to ω is eventually dominated by some such function.
P is the set of pairs where s is a finite sequence of natural numbers (considered as functions from a finite ordinal to ω) and E is a finite subset of some fixed set G of functions from ω to ω. The element (s, E) is stronger than if t is contained in s, F is contained in E, and if k is in the domain of s but not of t then for all h in F.
Jockusch–Soare forcing
Forcing with classes was invented by Robert Soare and Carl Jockusch to prove, among other results, the low basis theorem. Here P is the set of nonempty subsets of (meaning the sets of paths through infinite, computable subtrees of ), ordered by inclusion.
Iterated forcing
Iterated forcing with finite supports was introduced by Solovay and Tennenbaum to show the consistency of Suslin's hypothesis. Easton introduced another type of iterated forcing to determine the possible values of the continuum function at regular cardinals. Iterated forcing with countable support was investigated by Laver in his proof of the consistency of Borel's conjecture |
https://en.wikipedia.org/wiki/Crime%20in%20China | Despite a reportedly low crime rate in China, crime still occurs in various forms. The Chinese government does not release exact unified statistics on crime rates and the rate of criminal offending due to such information being considered politically sensitive. Scarce official statistics released are the subject of much academic debate due to allegations of statistical fabrication, under-reporting and corruption. The illegal drug trade in China is a significant driver of violent crime, including murder. There is an increase in drug trafficking or drug addiction, that is why it is contributing to the increase in homicides.
History
A distinguishing feature of the Qin empire was its treatment of criminals: harsh but careful and fair. Succeeding dynasties moderated the law in various ways. In Ming times, commercialization and urbanization meant that scams abounded. Fences who disposed of stolen goods thrived.
The People's Republic of China was established in 1949 and, from 1949 to 1956, underwent the process of transferring the means of production to common ownership. During this time, the new government worked to decrease the influence of criminal gangs and reduce the prevalence of narcotics and gambling. Efforts to crack down on criminal activity by the government led to a decrease in crime.
Between 1949 and 1956, larceny, arson, rape, murder, and robbery were major nonpolitical offenses. The majority of economic crimes were committed by business people who engaged in tax evasion, theft of public property, and bribery.
Government officials also engaged in illegal economic activity, which included improperly taking public property and accepting bribes. Between 1957 and 1965, rural areas experienced little reported crime. Crime rates increased later. The year 1981 represented a peak in reported crime. This may have been correlated to the economic reform in the late 1970s, which allowed some elements of a market economy and gave rise to an increase in economic activity. Below is a comparison of reported cases of crime from 1977 to 1988 (excluding economic crimes):
Crime by youth increased rapidly in the 1980s. Crime by youths consisted 60.2% of total crime in 1983, 63.3% in 1984, 71.4% in 1985, 72.4% in 1986, and 74.3% in 1987. The number of fleeing criminals increased over the years. Economic crimes have increased in recent years. From 1982 to 1988, the total number of economic crimes were 218,000.
In 1989, a total of 76,758 cases of economic offenses were registered, which included bribery, smuggling, and tax evasion. The changes in economic policy had an influence on the characteristics of criminality. Since the Second Plenary Session of the Eleventh Central Committee of the Chinese Communist Party, crime has increased and diversified.
Crime by type
Murder
In 2011, the reported murder rate in China was 1.0 per 100,000 people, with 13,410 murders. The murder rate in 2018 was 0.5. The reported murder rates have been criticized for under-re |
https://en.wikipedia.org/wiki/List%20of%20Toronto%20FC%20records%20and%20statistics | This page details Toronto FC records from their inaugural season in 2007 as a member of Major League Soccer. It includes player records, attendances and competition information. All records listed are from competitive matches only, unless otherwise stated.
Honours
Source:
Other honours
MLS Cup
Runners-up (2): 2016, 2019
Supporters' Shield
Runners-up: 2020
CONCACAF Champions League
Runners-up: 2018
Semi-finals: 2011–12
Campeones Cup
Runners-up: 2018
Canadian Championship
Runners-up (5): 2008, 2014, 2019, 2021, 2022
Eastern Conference (Regular Season)
Runners-up: 2020
Third place: 2016
Carolina Challenge Cup
Runners-up (2): 2007, 2009
Third place: 2010
Walt Disney World Pro Soccer Classic
Runners-up (2): 2010, 2012
Texas Pro Soccer Festival
Third place: 2008
Individual records
Appearances
Youngest player – Jahkeele Marshall-Rutty, 16 years 4 months 8 days (at Philadelphia Union, MLS, October 24, 2020)
Youngest starter – Fuad Ibrahim, 16 years 11 months 3 days (v. San Jose Earthquakes, MLS, July 19, 2008)
Oldest player – Rick Titus, 39 years 5 months 27 days (v. Chivas USA, MLS, September 6, 2008)
Most consecutive appearances – Chad Barrett, 39 (August 3, 2008 – August 4, 2009)
Bold indicates player still active with club.
Goalscorers
Most goals in a season (all competitions) – Sebastian Giovinco, 23 (2015) (22 in MLS)
Most goals in a game – Dwayne De Rosario, 3 (at Montreal Impact, Canadian Championship, June 18, 2009); Sebastian Giovinco, 3 (at New York City FC, MLS, July 12, 2015; v. Orlando City SC, MLS, August 5, 2015; v. D.C. United, MLS, July 23, 2016; v. New England Revolution, MLS, August 6, 2016 and at New York City FC, MLS Playoffs, November 6, 2016); Justin Morrow, 3 (v. New York Red Bulls, MLS, September 30, 2017); Jozy Altidore, 3 (v. Vancouver Whitecaps FC, Canadian Championship, August 14, 2018) and Ayo Akinola, 3 (v. Montreal Impact, MLS is Back Tournament, July 16, 2020)
Fastest goal – Tsubasa Endoh, 29 seconds (v. Atlanta United FC, MLS, June 26, 2019)
Youngest scorer – Fuad Ibrahim, 16 years 10 months 27 days (at Chicago Fire, MLS, July 12, 2008)
Oldest scorer – Benoît Cheyrou, 36 years 0 months 20 days (at Ottawa Fury, Canadian Championship, May 23, 2017)
Most consecutive MLS games with a goal – 5, Dwayne De Rosario (April 10 – May 1, 2010) and Danny Koevermans (June 20 – July 4, 2012)
Bold indicates player still active with club.
Debut goals
Jarrod Smith (at LA Galaxy, MLS, April 13, 2008)
Julius James (v. LA Galaxy, MLS, May 31, 2008)
Fuad Ibrahim (at Chicago Fire, MLS, July 12, 2008)
Ali Gerba (at Columbus Crew, MLS, July 25, 2009)
Peri Marošević (at Portland Timbers, MLS, July 30, 2011)
Luis Silva (v. LA Galaxy, CONCACAF Champions League, March 7, 2012)
Justin Braun (v. FC Dallas, MLS, April 6, 2013)
Jermain Defoe (at Seattle Sounders FC, MLS, March 15, 2014)
Jozy Altidore (at Vancouver Whitecaps FC, MLS, March 7, 2015)
Robbie Findley (at Vancouver Whitecaps FC, M |
https://en.wikipedia.org/wiki/Ellis%E2%80%93Numakura%20lemma | In mathematics, the Ellis–Numakura lemma states that if S is a non-empty semigroup with a topology such that S is compact and the product is semi-continuous, then S has an idempotent element p, (that is, with pp = p). The lemma is named after Robert Ellis and Katsui Numakura.
Applications
Applying this lemma to the Stone–Čech compactification βN of the natural numbers shows that there are idempotent elements in βN. The product on βN is not continuous, but is only semi-continuous (right or left, depending on the preferred construction, but never both).
Proof
By compactness and Zorn's Lemma, there is a minimal non-empty compact sub semigroup of S, so replacing S by this sub semi group we can assume S is minimal.
Choose p in S. The set Sp is a non-empty compact subsemigroup, so by minimality it is S and in particular contains p, so the set of elements q with qp = p is non-empty.
The set of all elements q with qp = p is a compact semigroup, and is nonempty by the previous step, so by minimality it is the whole of S and therefore contains p. So pp = p.
References
External links
T. Tao lecture-5
Ergodic theory
General topology
Theorems in topology |
https://en.wikipedia.org/wiki/Gerald%20Eckert | Gerald Eckert (born 27 December 1960) is a German composer, cellist, and painter. He currently lives in Eckernförde.
Biography
Eckert, born in Nuremberg, studied mathematics at the University of Erlangen, violoncello and conducting at the conservatory of Nürnberg. Then he studied of composition with Nicolaus A. Huber and Walter Zimmermann and electroacoustic composition at the Folkwang-Hochschule Essen. Composition courses with James Dillon, Brian Ferneyhough and Jonathan Harvey.
1995 he received a scholarship of the Fondation Royaumont/France. 1996/97 work as visiting scholar at the CCRMA of the Stanford University/US. 1998 he was guest professor at Darmstadt and at Akiyoshidai/Japan. 1999 he received a scholarship of the Heinrich-Strobel-Fondation, 2000/02 he was lecturer at the TU Darmstadt.
2000 he realized a dance project with Dyane Neiman. 2006 he was composer in residence at the festival for contemporary music at Zurich/Switzerland. 2008 he realized together with the academy of the arts Berlin a project for choir, dancers, ensemble, video and electronics.
He received various prizes and awards: Gulbenkian Prize '93, NDR-Prize '94, Kranichsteiner Musikpreis '96, nomination for the ICMC '96 Hong-Kong and '03 Singapore, composition award of the "Biennale Hannover" '97, "S. Martirano Competition" USA 2003, 1st prize of Bourges 2003, nomination for the world-music-days '95 and '04, 1st prize of Stuttgart 2005, a scholarship for Venice 2006 and for Los Angeles 2010.
As cello player various recordings on different broadcasting stations of works by John Cage, Morton Feldman, Hans Zender, a.o.
Since 1989 work on paintings. Exhibitions and installations.
External links
1960 births
Living people
Musicians from Nuremberg
German classical cellists |
https://en.wikipedia.org/wiki/Statistical%20Society%20of%20Canada | The Statistical Society of Canada (abbreviated as SSC; ) is a professional organization whose mission is to promote the use and development of statistics and probability.
Its objectives are
to make the general public aware of the value of statistical thought, the importance of this science and the contribution of statisticians to Canadian society;
to ensure that decisions that could have a major impact on Canadian society are based on relevant data, interpreted properly using statistics;
to promote the pursuit of excellence in training and statistical practice in Canada;
to encourage improvements in statistical methodology;
to maintain a sense of belonging within the profession, and to promote dialogue among theoreticians and practitioners of statistics.
Each year the SSC awards the CRM-SSC Prize, in collaboration with the Centre de Recherches Mathématiques, to an exceptional young Canadian statistician.
Publisher of
The Canadian Journal of Statistics
Arms
See also
President of the Statistical Society of Canada
References
External links
Official website
Statistical societies
Higher education in Canada
Professional associations based in Canada
Learned societies of Canada |
https://en.wikipedia.org/wiki/Euclidean%20plane | In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted . It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement.
A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane.
The set of the pairs of real numbers (the real coordinate plane), equipped with the dot product, is often called the Euclidean plane, since every Euclidean plane is isomorphic to it.
History
Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics.
Later, the plane was described in a so-called Cartesian coordinate system, a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
The idea of this system was developed in 1637 in writings by Descartes and independently by Pierre de Fermat, although Fermat also worked in three dimensions, and did not publish the discovery. Both authors used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work.
Later, the plane was thought of as a field, where any two points could be multiplied and, except for 0, divided. This was known as the complex plane. The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named after Jean-Robert Argand (1768–1822), although they were first described by Danish-Norwegian land surveyor and mathematician Caspar Wessel (1745–1818). Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane.
In geometry
Coordinate systems
In mathematics, analytic geometry (also called Cartesian geometry) describes every point in two-dimensional space by means of two coordinates. Two perpendicular coordinate axes are given which cross each other a |
https://en.wikipedia.org/wiki/Numerical%20range | In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex matrix A is the set
where denotes the conjugate transpose of the vector . The numerical range includes, in particular, the diagonal entries of the matrix (obtained by choosing x equal to the unit vectors along the coordinate axes) and the eigenvalues of the matrix (obtained by choosing x equal to the eigenvectors).
In engineering, numerical ranges are used as a rough estimate of eigenvalues of A. Recently, generalizations of the numerical range are used to study quantum computing.
A related concept is the numerical radius, which is the largest absolute value of the numbers in the numerical range, i.e.
Properties
The numerical range is the range of the Rayleigh quotient.
(Hausdorff–Toeplitz theorem) The numerical range is convex and compact.
for all square matrix and complex numbers and . Here is the identity matrix.
is a subset of the closed right half-plane if and only if is positive semidefinite.
The numerical range is the only function on the set of square matrices that satisfies (2), (3) and (4).
(Sub-additive) , where the sum on the right-hand side denotes a sumset.
contains all the eigenvalues of .
The numerical range of a matrix is a filled ellipse.
is a real line segment if and only if is a Hermitian matrix with its smallest and the largest eigenvalues being and .
If is a normal matrix then is the convex hull of its eigenvalues.
If is a sharp point on the boundary of , then is a normal eigenvalue of .
is a norm on the space of matrices.
, where denotes the operator norm.
Generalisations
C-numerical range
Higher-rank numerical range
Joint numerical range
Product numerical range
Polynomial numerical hull
See also
Spectral theory
Rayleigh quotient
Workshop on Numerical Ranges and Numerical Radii
Bibliography
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"Functional Characterizations of the Field of Values and the Convex Hull of the Spectrum", Charles R. Johnson, Proceedings of the American Mathematical Society, 61(2):201-204, Dec 1976.
Matrix theory
Spectral theory
Operator theory
Linear algebra |
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