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https://en.wikipedia.org/wiki/Sofiane%20Djebarat | Sofiane Djebarat (born 7 May 1983 in Toudja, Béjaïa Province) is an Algerian professional football player who currently plays as a defender for Algerian Ligue 2 club Olympique de Médéa.
Statistics
References
External links
1983 births
Living people
People from Toudja
Algerian men's footballers
Olympique de Médéa players
Algerian Ligue 2 players
AS Khroub players
MC Oran players
JSM Béjaïa players
MO Béjaïa players
Men's association football defenders
21st-century Algerian people |
https://en.wikipedia.org/wiki/Dyadic%20cubes | In mathematics, the dyadic cubes are a collection of cubes in Rn of different sizes or scales such that the set of cubes of each scale partition Rn and each cube in one scale may be written as a union of cubes of a smaller scale. These are frequently used in mathematics (particularly harmonic analysis) as a way of discretizing objects in order to make computations or analysis easier. For example, to study an arbitrary subset of A of Euclidean space, one may instead replace it by a union of dyadic cubes of a particular size that cover the set. One can consider this set as a pixelized version of the original set, and as smaller cubes are used one gets a clearer image of the set A. Most notable appearances of dyadic cubes include the Whitney extension theorem and the Calderón–Zygmund lemma.
Dyadic cubes in Euclidean space
In Euclidean space, dyadic cubes may be constructed as follows: for each integer k let Δk be the set of cubes in Rn of sidelength 2−k and corners in the set
and let Δ be the union of all the Δk.
The most important features of these cubes are the following:
For each integer k, Δk partitions Rn.
All cubes in Δk have the same sidelength, namely 2−k.
If the interiors of two cubes Q and R in Δ have nonempty intersection, then either Q is contained in R or R is contained in Q.
Each Q in Δk may be written as a union of 2n cubes in Δk+1 with disjoint interiors.
We use the word "partition" somewhat loosely: for although their union is all of Rn, the cubes in Δk can overlap at their boundaries. These overlaps, however, have zero Lebesgue measure, and so in most applications this slightly weaker form of partition is no hindrance.
It may also seem odd that larger k corresponds to smaller cubes. One can think of k as the degree of magnification. In practice, however, letting Δk be the set of cubes of sidelength 2k or 2−k is a matter of preference or convenience.
The one-third trick
One disadvantage to dyadic cubes in Euclidean space is that they rely too much on the specific position of the cubes. For example, for the dyadic cubes Δ described above, it is not possible to contain an arbitrary ball inside some Q in Δ (consider, for example, the unit ball centered at zero). Alternatively, there may be such a cube that contains the ball, but the sizes of the ball and cube are very different. Because of this caveat, it is sometimes useful to work with two or more collections of dyadic cubes simultaneously.
Definition
The following is known as the one-third trick:
Let Δk be the dyadic cubes of scale k as above. Define
This is the set of dyadic cubes in Δk translated by the vector α. For each such α, let Δα be the union of the Δkα over k.
There is a universal constant C > 0 such that for any ball B with radius r < 1/3, there is α in {0,1/3}n and a cube Q in Δα containing B whose diameter is no more than Cr.
More generally, if B is a ball with any radius r > 0, there is α in {0, 1/3, 4/3, 42/3, ...}n and a cube Q in Δα containing B who |
https://en.wikipedia.org/wiki/Doubling%20space | In mathematics, a metric space with metric is said to be doubling if there is some doubling constant such that for any and , it is possible to cover the ball with the union of at most balls of radius . The base-2 logarithm of is called the doubling dimension of . Euclidean spaces equipped with the usual Euclidean metric are examples of doubling spaces where the doubling constant depends on the dimension . For example, in one dimension, ; and in two dimensions, . In general, Euclidean space has doubling dimension .
Assouad's embedding theorem
An important question in metric space geometry is to characterize those metric spaces that can be embedded in some Euclidean space by a bi-Lipschitz function. This means that one can essentially think of the metric space as a subset of Euclidean space. Not all metric spaces may be embedded in Euclidean space. Doubling metric spaces, on the other hand, would seem like they have more of a chance, since the doubling condition says, in a way, that the metric space is not infinite dimensional. However, this is still not the case in general. The Heisenberg group with its Carnot-Caratheodory metric is an example of a doubling metric space which cannot be embedded in any Euclidean space.
Assouad's Theorem states that, for a M-doubling metric space X, if we give it the metric d(x, y)ε for some 0 < ε < 1, then there is a L-bi-Lipschitz map f:X → ℝd, where d and L depend on M and ε.
Doubling Measures
Definition
A nontrivial measure on a metric space X is said to be doubling if the measure of any ball is finite and approximately the measure of its double, or more precisely, if there is a constant C > 0 such that
for all x in X and r > 0. In this case, we say μ is C-doubling. In fact, it can be proved that, necessarily, C 2.
A metric measure space that supports a doubling measure is necessarily a doubling metric space, where the doubling constant depends on the constant C. Conversely, every complete doubling metric space supports a doubling measure.
Examples
A simple example of a doubling measure is Lebesgue measure on a Euclidean space. One can, however, have doubling measures on Euclidean space that are singular with respect to Lebesgue measure. One example on the real line is the weak limit of the following sequence of measures:
One can construct another singular doubling measure μ on the interval [0, 1] as follows: for each k ≥ 0, partition the unit interval [0,1] into 3k intervals of length 3−k. Let Δ be the collection of all such intervals in [0,1] obtained for each k (these are the triadic intervals), and for each such interval I, let m(I) denote its "middle third" interval. Fix 0 < δ < 1 and let μ be the measure such that μ([0, 1]) = 1 and for each triadic interval I, μ(m(I)) = δμ(I). Then this gives a doubling measure on [0, 1] singular to Lebesgue measure.
Applications
The definition of a doubling measure may seem arbitrary, or purely of geometric interest. However, many results from c |
https://en.wikipedia.org/wiki/Iterated%20local%20search | Iterated Local Search (ILS) is a term in applied mathematics and computer science
defining a modification of local search or hill climbing methods for solving discrete optimization problems.
Local search methods can get stuck in a local minimum, where no improving neighbors are available.
A simple modification consists of iterating calls to the local search routine, each time starting from a different initial configuration. This is called repeated local search, and implies that the knowledge obtained during the previous local search phases is not used. Learning implies that the previous history, for example the memory about the previously found local minima, is mined to produce better and better starting points for local search.
The implicit assumption is that of a clustered distribution of local minima: when minimizing a function, determining good local minima is easier when starting from a local minimum with a low value than when starting from a random point. The only caveat is to avoid confinement in a given attraction basin, so that the kick to transform a local minimizer into the starting point for the next run has to be appropriately strong, but not too strong to avoid reverting to memory-less random restarts.
Iterated Local Search is based on building a sequence of locally optimal solutions by:
perturbing the current local minimum;
applying local search after starting from the modified solution.
The perturbation strength has to be sufficient to lead the trajectory to a different attraction basin leading to a different local optimum.
Perturbation Algorithm
Finding the perturbation algorithm for ILS is not an easy task. The main aim is not to get stuck at the same local minimum and in order to ensure this property, the undo operation is forbidden. Despite this, a good permutation has to consider a lot of values, since there exist two kind of bad permutations:
too weak: fall back to the same local minimum
too strong: random restart
Benchmark Perturbation
The procedure consists in fixing a number of values for the perturbation such that these values are significant for the instance: on average probability and not rare. After that, on runtime it will be possible to check the benchmark plot in order to get an average idea on the instances passed.
Adaptive Perturbation
Since there is no function a priori that tells which one is the most suitable value for a given perturbation, the best criterion is to get it adaptive. For instance Battiti and Protasi proposed a reactive search algorithm for MAX-SAT which fits perfectly into the ILS framework. They perform a "directed" perturbation scheme which is implemented by a tabu search algorithm and after each perturbation they apply a standard local descent algorithm. Another way of adapting the perturbation is to change deterministically its strength during the search.
Optimizing Perturbation
Another procedure is to optimize a sub-part of the problem while keeping the not-undo property ac |
https://en.wikipedia.org/wiki/Minimal%20axioms%20for%20Boolean%20algebra | In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra:
where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke).
It is one of 25 candidate axioms for this property identified by Stephen Wolfram, by enumerating the Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models with four or fewer variables, and was first proven equivalent by William McCune, Branden Fitelson, and Larry Wos. MathWorld, a site associated with Wolfram, has named the axiom the "Wolfram axiom". McCune et al. also found a longer single axiom for Boolean algebra based on disjunction and negation.
In 1933, Edward Vermilye Huntington identified the axiom
as being equivalent to Boolean algebra, when combined with the commutativity of the OR operation, , and the assumption of associativity, . Herbert Robbins conjectured that Huntington's axiom could be replaced by
which requires one fewer use of the logical negation operator . Neither Robbins nor Huntington could prove this conjecture; nor could Alfred Tarski, who took considerable interest in it later. The conjecture was eventually proved in 1996 with the aid of theorem-proving software. This proof established that the Robbins axiom, together with associativity and commutativity, form a 3-basis for Boolean algebra. The existence of a 2-basis was established in 1967 by Carew Arthur Meredith:
The following year, Meredith found a 2-basis in terms of the Sheffer stroke:
In 1973, Padmanabhan and Quackenbush demonstrated a method that, in principle, would yield a 1-basis for Boolean algebra. Applying this method in a straightforward manner yielded "axioms of enormous length", thereby prompting the question of how shorter axioms might be found. This search yielded the 1-basis in terms of the Sheffer stroke given above, as well as the 1-basis
which is written in terms of OR and NOT.
References
Boolean algebra
History of logic
NAND gate
Propositional calculus |
https://en.wikipedia.org/wiki/List%20of%20Miller%20Research%20Fellows | List of Miller Research Fellows:
This list is incomplete: Only those in mathematics are included so far. There are Miller Fellows in all basic sciences, for example also in Astronomy, Physics, and Chemistry. There is a complete list at the Miller Institute web page.
Mathematics
References
Mathematics Genealogy Project
The Miller Institute web page
Miller Research Fellows
University of California, Berkeley people
!Miller Research
Miller |
https://en.wikipedia.org/wiki/Kig%20%28software%29 | KIG is free and open-source interactive geometry software, which is part of the KDE Education Project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.
Import and export
Kig can import files made by DrGeo and Cabri Geometry as well as its own file format, which is XML-encoded. Kig can export figures in LaTeX format and as SVG (vector graphics) files.
Objects
Kig can handle any classical object of the dynamic geometry, but also:
The center of curvature and osculating circle of a curve;
The dilation, generic affinity, inversion, projective application, homography and harmonic homology;
The hyperbola with given asymptotes;
The Bézier curves (2nd and 3rd degree);
The polar line of a point and pole of a line with respect to a conic section;
The asymptotes of a hyperbola;
The cubic curve through 9 points;
The cubic curve with a double point through 6 points;
The cubic curve with a cusp through 4 points.
Scripting language
Inside the figure
Another object is available inside Kig, it is a Python language script. It can accept Kig objects as variables, and always return one object.
For example, if there is already a numeric object inside the figure, for example 3, the following Python object can yield its square (9):
def square(arg1):
return DoubleObject(arg1.value() ** 2)
The variables are always called arg1, arg2 etc. in the order they are clicked upon. Here there is only one variable arg1 and its numerical value is obtained with arg1.value().
If no one wants to implement the square of a complex number (represented by a point in the Argand diagram), the object which has to be selected at the creation of the script must necessarily be a point, and the script is
def csquare(arg1):
x = arg1.coordinate().x
y = arg1.coordinate().y
z = x * x - y * y
y = 2 * x * y
x = z
return Point(Coordinate(x, y))
The abscissa of the point representing the square of the complex number is as can be seen by expanding , Coordinate(x,y) creates a Python list made of the two coordinates of the new point. And Point creates the point which coordinates are precisely given by this list.
But a Python object inside a figure can only create one object and for more complex figures one has to build the figure with a script:
Figure created by a script
Kig comes up with a little program (written in Python) called pykig.py which can
load a Python script, e.g. MyScript.py
build a Kig figure, described by this script
open Kig and display the figure.
For example, here is how a Sierpinski triangle can be made (as an IFS) with pykig:
from random import *
kigdocument.hideobjects()
A = Point(0, 2)
A.show()
B = Point(-2, -1)
B.show()
C = Point(2, -1)
C.show()
M = Point(.1, .1)
for i in range(1, 1000):
d = randrange(3)
if d == 0:
s = Segment(A, M)
M = s.midpoint()
if d == 1:
s = Segment(B, M)
M = s.midpoint()
if d == 2:
s = Segme |
https://en.wikipedia.org/wiki/KIG | KIG may refer to either one of these things:
Kig (software), a geometry software
Kent International Gateway, a proposed rail-freight interchange in Kent, England
ISO 639:kig or Kimaghama, a language spoken on Yos Sudarso Island in Papua province, Indonesia
Animegao kigurumi, a type of cosplay
See also
Keig, a village in Aberdeenshire, Scotland |
https://en.wikipedia.org/wiki/2011%20Copa%20Centroamericana%20squads | Below are the rosters for the 2011 Copa Centroamericana in Panama, from January 14–23. Every national team's roster consists of 21 players with three goalkeepers included. Statistics of players are accurate as of before the start of the tournament.
Group A
Belize
Head coach: José de la Paz Herrera
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El Salvador
Head coach: José Luis Rugamas
Nicaragua
Head coach: Enrique Llena
Panama
Head coach: Julio Dely Valdés
Group B
Costa Rica
Head coach: Ricardo La Volpe
Guatemala
Head coach: Ever Almeida
Juan Jose Paredes Guzman GK 27/11/1984 C.S.D. Comunicaciones (Guatemala)
Riqui Nelson Murga Juarez MF 15/07/1980 Deportivo Marquense (Guatemala)
Fredy Omar Iboy Aguilar DF 18/04/1983 Deportivo Mictlan (Guatemala)
Honduras
Head coach: Juan de Dios Castillo
References
Copa Centroamericana squads
squads |
https://en.wikipedia.org/wiki/Leonardo%20%28footballer%2C%20born%20June%201992%29 | Leonardo Ramos dos Santos, known as Leonardo (born June 9, 1992, in Ourinhos) is a Brazilian former professional football player who most recently played for Hapoel Bnei Lod.
Career statistics
References
External links
1992 births
Living people
People from Ourinhos
Brazilian men's footballers
Men's association football forwards
Brazilian expatriate men's footballers
Expatriate men's footballers in Belarus
Expatriate men's footballers in Georgia (country)
Expatriate men's footballers in Russia
Expatriate men's footballers in Israel
Brazilian expatriate sportspeople in Belarus
Brazilian expatriate sportspeople in Georgia (country)
Brazilian expatriate sportspeople in Russia
Brazilian expatriate sportspeople in Israel
Liga Leumit players
FC Dinamo Minsk players
FC Dila Gori players
FC SKA-Khabarovsk players
FC Samtredia players
Hapoel Bnei Lod F.C. players
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Tourism%20in%20Tarn | The Tarn department is situated in the southwest of France.
Statistics
In 2009, there were:
Nightly rentals: 8.6 million
Beds available: 23,100
Business hotels represented 305,000 tourists for a total of 470,200 nights
Campsites represented 54,000 tourists for a total of 254,000 nights
152,353 nightly rentals booked from the 2 main centers (Tarn Reservation Tourisme and Gîtes de France)
Historical and cultural attractions
Steeped in history, from the Cathar era to the Industrial Revolution, the Tarn department has a rich heritage of fortified villages, castles, churches and museums.
While the south-western houses are mostly stone-built, cities from the northwest of the department are often made of the local red brick, typical of the region.
Albi and its Cathedral, dedicated to Saint-Cecilia. A unique red-brick fortified cathedral, renowned worldwide for its ornamented stone roodscreen. Together with the Berbie palace, a former bishops’ estate now home to the Toulouse-Lautrec Museum, it is the core of the Vieil-Alby, the ancient centre of the city, with its half-timbered and corbelled houses, that has been designated a UNESCO World Heritage Site in July 2010.
The peninsula of Ambialet, with a view on the Tarn River from the Priory.
Cagnac-les-Mines, its Mining Museum and the amusement park Cap découverte, located in a former open-sky mine.
Castres and its houses on the Agoût River, the Goya Museum and Jean Jaures Museum.
Carmaux and its Glass Museum, in an old chapel transformed into a workshop, with demonstrations on site.
Graulhet with its Pont Vieux (the “Old Bridge”), built in 1244 and classified a “Monument Historique”, and the medieval district of Panessac (16th-and-17th-century timbered and corbelled housing). L'Hostellerie du Lyon d'Or, built in the 15th century and also listed a “Monument Historique”, was reportedly cherished by Henry de Navarre, the future King Henry IV, for gourmet moments.
Gaillac is also a red-brick city, famous for its wine. You can also visit the St Michel Abbey.
Lavaur and the St Alain Cathedral.
The department is also known for its heritage of remarkably well-preserved bastides (fortified villages built in the 13th century to protect the population from the Wars of Religion). Famous bastides include:
Cordes-sur-Ciel the very first bastide, built in 1222.
Castelnau-de-Montmiral
Lautrec
Labastide-de-Lévis
Lisle-sur-Tarn
Puycelci
Rabastens
Réalmont
Other renowned villages in the Tarn:
Vabre and Brassac, with ruins of the Wars of Religion
Ferrières and its Protestantism Museum.
Lacaune, with its casino, a remainder from its past as a spa town.
Mazamet, an industrial city, specialized in wool pulling, and Hautpoul, a medieval village nearby.
Sports and natural attractions
Sports
Many outdoor activities such as hiking, skiing, canoeing and canyoneering can also be ways to discover the department and its landscapes.
Tourists can also go swimming, fishing or sailing in the various lakes, |
https://en.wikipedia.org/wiki/Norman%20Robinson%20%28priest%29 | Norman Robinson (18 February 1905 – 27 April 1973) was an Anglican priest. He was educated at Ulverston Grammar School and Liverpool University and began his working life as a teacher of Mathematics at Quarry Bank School, Liverpool Ordained in 1935, he held curacies at Mossley Hill and Southport before a spell at Lancaster Priory. After incumbencies at Newbarns, Hawcoat, Penrith and West Derby he was appointed Provost of Blackburn in 1961. He retired in 1972 and died a year later.
Notes
1905 births
People educated at Ulverston Grammar School
Alumni of the University of Liverpool
Provosts and Deans of Blackburn
1973 deaths |
https://en.wikipedia.org/wiki/Dieter%20Versen | Dieter Versen (born 22 June 1945) is a German former professional footballer who played as a defender.
Career statistics
Notes
References
External links
NASL career stats at NASLjerseys.com
1945 births
Living people
Footballers from Bochum
German men's footballers
Bundesliga players
VfL Bochum players
San Jose Earthquakes (1974–1988) players
North American Soccer League (1968–1984) players
German expatriate men's footballers
Expatriate men's soccer players in the United States
Men's association football defenders
West German men's footballers |
https://en.wikipedia.org/wiki/Hans-G%C3%BCnter%20Etterich | Hans-Günter Etterich (born 16 August 1951) is a German former professional footballer who played as a midfielder.
Career statistics
References
External links
Günter Etterich at NASLjerseys.com
1951 births
Living people
Footballers from Bochum
German men's footballers
Men's association football midfielders
Bundesliga players
2. Bundesliga players
North American Soccer League (1968–1984) players
VfL Bochum players
SC Westfalia Herne players
San Jose Earthquakes (1974–1988) players
Wuppertaler SV players
FSV Frankfurt players
SC Paderborn 07 players
German expatriate men's footballers
German expatriate sportspeople in the United States
Expatriate men's soccer players in the United States |
https://en.wikipedia.org/wiki/Harry%20Fechner | Harry Fechner (born 4 May 1950) is a German former professional footballer who played as a defender. He is the father of fellow professional footballer Gino Fechner.
Career statistics
References
External links
1950 births
Living people
German men's footballers
Bundesliga players
2. Bundesliga players
VfL Bochum players
VfL Bochum II players
1. FC Saarbrücken players
Men's association football defenders |
https://en.wikipedia.org/wiki/Holger%20Aden | Holger Aden (born 25 August 1965) is a German retired professional footballer who played as a forward.
Career statistics
References
External links
1965 births
Living people
Footballers from Hamburg
German men's footballers
Men's association football forwards
Bundesliga players
2. Bundesliga players
SC Concordia von 1907 players
FC Eintracht Norderstedt 03 players
Altonaer FC von 1893 players
Bayer 04 Leverkusen players
Eintracht Braunschweig players
VfL Bochum players
SV 19 Straelen players |
https://en.wikipedia.org/wiki/Hans%20Walitza | Hans Walitza (born 26 November 1945) is a German retired professional football player and manager who played as a forward.
Career statistics
1 1966–67, 1969–70 and 1970–71 include the Regionalliga promotion playoffs. 1975–76 and 1977–78 include the 2. Bundesliga/Bundesliga promotion/relegation playoffs.
References
External links
1945 births
Living people
Sportspeople from Mülheim
Footballers from Düsseldorf (region)
German men's footballers
West German men's footballers
Men's association football forwards
Bundesliga players
2. Bundesliga players
VfL Bochum players
1. FC Nürnberg players |
https://en.wikipedia.org/wiki/Hans-J%C3%BCrgen%20K%C3%B6per | Hans-Jürgen Köper (born 29 August 1951) is a German football manager and former player who played as a midfielder.
Career statistics
References
External links
1951 births
Living people
German men's footballers
Men's association football midfielders
Bundesliga players
VfL Bochum players
Footballers from Bochum
West German men's footballers |
https://en.wikipedia.org/wiki/Werner%20Balte | Werner Balte (17 February 1948 – 17 March 2007) was a German footballer who played as a midfielder.
Career
Balte won the German Goal of the Month for June 1971.
Career statistics
References
External links
1948 births
2007 deaths
German men's footballers
Footballers from Bochum
Men's association football midfielders
Bundesliga players
VfL Bochum players
West German men's footballers |
https://en.wikipedia.org/wiki/Alexander%20Shin | Alexander Andreyevich Shin (; born November 21, 1985) is a Kazakhstani professional ice hockey player.
Career statistics
International
External links
1985 births
Barys Nur-Sultan players
Competitors at the 2013 Winter Universiade
Living people
Kazakhstani ice hockey left wingers
Kazzinc-Torpedo players
Saryarka Karagandy players
Ice hockey people from Oskemen
Universiade medalists in ice hockey
Universiade silver medalists for Kazakhstan |
https://en.wikipedia.org/wiki/Denis%20Kartsev | Denis Kartsev is a Russian professional ice hockey winger who currently plays for HC Sibir Novosibirsk of the Kontinental Hockey League (KHL).
Career statistics
References
External links
Living people
HC Sibir Novosibirsk players
1976 births
Russian ice hockey centres |
https://en.wikipedia.org/wiki/Vertex%20of%20a%20representation | In mathematical finite group theory, the vertex of a representation of a finite group is a subgroup associated to it, that has a special representation called a source. Vertices and sources were introduced by .
References
Representation theory
Finite groups |
https://en.wikipedia.org/wiki/Alexei%20Troschinsky | Alexei Borisovich Troschinsky (; born October 9, 1973) is a Kazakhstani former professional ice hockey defenceman.
Career statistics
Regular season and playoffs
International
External links
1973 births
Living people
Barys Nur-Sultan players
Atlant Moscow Oblast players
Ice hockey players at the 1998 Winter Olympics
Kazakhstani ice hockey defencemen
Kazzinc-Torpedo players
Olympic ice hockey players for Kazakhstan
Ice hockey people from Oskemen
Soviet ice hockey defencemen
Torpedo Nizhny Novgorod players
Kazakhstani expatriate sportspeople in Russia
Kazakhstani expatriate ice hockey people
Expatriate ice hockey players in Russia |
https://en.wikipedia.org/wiki/Genetic%20algebra | In mathematical genetics, a genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. Some variations of these algebras are called train algebras, special train algebras, gametic algebras, Bernstein algebras, copular algebras, zygotic algebras, and baric algebras (also called weighted algebra). The study of these algebras was started by .
In applications to genetics, these algebras often have a basis corresponding to the genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. The laws of inheritance are then encoded as algebraic properties of the algebra.
For surveys of genetic algebras see , and .
Baric algebras
Baric algebras (or weighted algebras) were introduced by . A baric algebra over a field K is a possibly non-associative algebra over K together with a homomorphism w, called the weight, from the algebra to K.
Bernstein algebras
A Bernstein algebra, based on the work of on the Hardy–Weinberg law in genetics, is a (possibly non-associative) baric algebra B over a field K with a weight homomorphism w from B to K satisfying . Every such algebra has idempotents e of the form with . The Peirce decomposition of B corresponding to e is
where and . Although these subspaces depend on e, their dimensions are invariant and constitute the type of B. An exceptional Bernstein algebra is one with .
Copular algebras
Copular algebras were introduced by
Evolution algebras
An evolution algebra over a field is an algebra with a basis on which multiplication is defined by the product of distinct basis terms being zero and the square of each basis element being a linear form in basis elements. A real evolution algebra is one defined over the reals: it is non-negative if the structure constants in the linear form are all non-negative. An evolution algebra is necessarily commutative and flexible but not necessarily associative or power-associative.
Gametic algebras
A gametic algebra is a finite-dimensional real algebra for which all structure constants lie between 0 and 1.
Genetic algebras
Genetic algebras were introduced by who showed that special train algebras are genetic algebras and genetic algebras are train algebras.
Special train algebras
Special train algebras were introduced by as special cases of baric algebras.
A special train algebra is a baric algebra in which the kernel N of the weight function is nilpotent and the principal powers of N are ideals.
showed that special train algebras are train algebras.
Train algebras
Train algebras were introduced by as special cases of baric algebras.
Let be elements of the field K with . The formal polynomial
is a train polynomial. The baric algebra B with weight w is a train algebra if
for all elements , with defined as principal powers, .
Zygotic algebras
Zygotic algebras were introduced by
References
.
Further reading
Population g |
https://en.wikipedia.org/wiki/Ivor%20Etherington | Ivor Malcolm Haddon Etherington FRSE (8 February 1908 -1 January 1994) was a mathematician who worked initially on general relativity, and later on genetics and introduced genetic algebras.
Life
He was born in Lewisham in London the son of Annie Margaret and her husband Bruce Etherington, both of whom were Baptist missionaries normally based in Ceylon. His father had died in Ceylon, leaving his mother and two older siblings to return to Britain alone. His mother remarried in 1913 to Edwin Duncombe de Russet, a Baptist minister, but Ivor retained his original name. In 1921 the growing family moved out of London to Thorpe Bay on the Essex coast, where his father then founded the Thorpe Bay School for Boys. In 1922 Ivor was sent back to London to be educated at Mill Hill School. He was later educated at the University of Oxford and continued as a postgraduate at the University of Edinburgh where he received his doctorate. He later became a professor of mathematics at the same university.
He was elected a Fellow of the Royal Society of Edinburgh in 1934. His proposers were Sir Edmund Whittaker, Herbert Westren Turnbull, Edward Thomas Copson and David Gibb. He won the Society's Keith Medal for 1955-57.
On his retirement in 1974, he moved with his wife to Easdale on the Scottish west coast, where the family had always had a holiday home.
He died on 1 January 1994.
Family
He married Elizabeth (Betty) Goulding in 1934. They had two daughters, Donia and Judy. When Betty died in 1982, Donia came to care for her father.
During World War II he and his wife aided 32 German refugees, giving many shelter in their own home.
See also
Etherington's reciprocity theorem
Wedderburn–Etherington number
References
20th-century British mathematicians
1908 births
1994 deaths
Academics of the University of Edinburgh
Fellows of the Royal Society of Edinburgh
People educated at Mill Hill School |
https://en.wikipedia.org/wiki/Horst%20Christopeit | Horst Christopeit (born 15 August 1939) is a German former professional footballer who played as a goalkeeper.
Career statistics
References
External links
1939 births
Living people
German men's footballers
VfL Bochum players
SC Preußen Münster players
Men's association football goalkeepers
West German men's footballers |
https://en.wikipedia.org/wiki/Gerd%20Wiesemes | Gerd Wiesemes (born 29 January 1943) is a retired German football defender.
Career
Statistics
1 1964–65 and 1974–75 include the Verbandsliga Westfalen promotion playoffs. 1969–70 and 1970–71 include the Regionalliga promotion playoffs.
References
External links
1943 births
Living people
Footballers from Bochum
German men's footballers
Bundesliga players
VfL Bochum players
SC Westfalia Herne players
Men's association football defenders
West German men's footballers |
https://en.wikipedia.org/wiki/Heinz-J%C3%BCrgen%20Blome | Heinz-Jürgen Blome (14 December 1946 – 7 November 2012) was a German association football defender.
Career
Statistics
1 1969–70 and 1970–71 include the Regionalliga promotion playoffs.
References
External links
1946 births
2012 deaths
German men's footballers
Bundesliga players
VfL Bochum players
Men's association football defenders
West German men's footballers |
https://en.wikipedia.org/wiki/Werner%20Jablonski | Werner Jablonski (born 26 June 1938) is a German retired professional footballer who played as a defender or midfielder.
Career statistics
1 1964–65 includes the Verbandsliga Westfalen promotion playoffs. 1969–70 and 1970–71 include the Regionalliga promotion playoffs.
References
External links
1938 births
Living people
German men's footballers
Men's association football midfielders
Bundesliga players
VfL Bochum players
West German men's footballers |
https://en.wikipedia.org/wiki/Nikolai%20Pronin | Nikolai Pronin (born April 13, 1979) is a Russian professional ice hockey winger who currently plays for HC CSKA Moscow of the Kontinental Hockey League (KHL).
Career statistics
References
External links
1979 births
Living people
Russian ice hockey left wingers
Atlant Moscow Oblast players
Avtomobilist Yekaterinburg players
Charlotte Checkers (1993–2010) players
HC CSKA Moscow players
Metallurg Magnitogorsk players
Rubin Tyumen players
Thunder Bay Thunder Cats (UHL) players
Toledo Storm players
Zvezda Chekhov players |
https://en.wikipedia.org/wiki/Gleb%20Klimenko | Gleb Viktorovich Klimenko (; born July 28, 1983) is a Russian former professional ice hockey winger. He played in the Kontinental Hockey League (KHL) from 2008 to 2017.
Career statistics
Regular season and playoffs
References
External links
1983 births
Living people
Ak Bars Kazan players
Amur Khabarovsk players
Atlant Moscow Oblast players
Avtomobilist Yekaterinburg players
GKS Tychy (ice hockey) players
HC Neftekhimik Nizhnekamsk players
HC Spartak Moscow players
HC Vityaz players
Metallurg Magnitogorsk players
Russian ice hockey left wingers
Severstal Cherepovets players
SKA Saint Petersburg players |
https://en.wikipedia.org/wiki/Peirce%20decomposition | In ring theory, a Peirce decomposition is a decomposition of an algebra as a sum of eigenspaces of commuting idempotent elements.
The Peirce decomposition for associative algebras was introduced by . A similar but more complicated Peirce decomposition for Jordan algebras was introduced by .
Peirce decomposition for associative algebras
If e is an idempotent (e2 = e) in an associative algebra A, then the two-sided Peirce decomposition writes A as the direct sum of eAe, eA(1 − e), (1 − e)Ae, and (1 − e)A(1 − e). There are also left and right Peirce decompositions, where the left decomposition writes A as the direct sum of eA and (1 − e)A, and the right one writes A as the direct sum of Ae and A(1 − e).
More generally, if e1, ..., en are mutually orthogonal idempotents with sum 1, then A is the direct sum of the spaces eiAej for 1 ≤ i, j ≤ n.
Blocks
An idempotent of a ring is called central if it commutes with all elements of the ring.
Two idempotents e, f are called orthogonal if ef = fe = 0.
An idempotent is called primitive if it is nonzero and cannot be written as the sum of two orthogonal nonzero idempotents.
An idempotent e is called a block or centrally primitive if it is nonzero and central and cannot be written as the sum of two orthogonal nonzero central idempotents. In this case the ideal eR is also sometimes called a block.
If the identity 1 of a ring R can be written as the sum
1 = e1 + ... + en
of orthogonal nonzero centrally primitive idempotents, then these idempotents are unique up to order and are called the blocks or the ring R. In this case the ring R can be written as a direct sum
R = e1R + ... + enR
of indecomposable rings, which are sometimes also called the blocks of R.
References
External links
Peirce decomposition on http://www.tricki.org/
Algebras |
https://en.wikipedia.org/wiki/Erd%C5%91s%20distinct%20distances%20problem | In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015.
The conjecture
In what follows let denote the minimal number of distinct distances between points in the plane, or equivalently the smallest possible cardinality of their distance set. In his 1946 paper, Erdős proved the estimates
for some constant . The lower bound was given by an easy argument. The upper bound is given by a square grid. For such a grid, there are numbers below n which are sums of two squares, expressed in big O notation; see Landau–Ramanujan constant. Erdős conjectured that the upper bound was closer to the true value of g(n), and specifically that (using big Omega notation) holds for every .
Partial results
Paul Erdős' 1946 lower bound of was successively improved to:
by Leo Moser in 1952,
by Fan Chung in 1984,
by Fan Chung, Endre Szemerédi, and William T. Trotter in 1992,
by László A. Székely in 1993,
by József Solymosi and Csaba D. Tóth in 2001,
by Gábor Tardos in 2003,
by Nets Katz and Gábor Tardos in 2004,
by Larry Guth and Nets Katz in 2015.
Higher dimensions
Erdős also considered the higher-dimensional variant of the problem: for let denote the minimal possible number of distinct distances among points in -dimensional Euclidean space. He proved that and and conjectured that the upper bound is in fact sharp, i.e., . József Solymosi and Van H. Vu obtained the lower bound in 2008.
See also
Falconer's conjecture
Erdős unit distance problem
References
External links
William Gasarch's page on the problem
Conjectures
Paul Erdős
Discrete geometry |
https://en.wikipedia.org/wiki/Complex%20group | In mathematics, complex group may refer to:
An archaic name for the symplectic group
Complex reflection group
A complex algebraic group
A complex Lie group |
https://en.wikipedia.org/wiki/Y-DNA%20haplogroups%20in%20populations%20of%20East%20and%20Southeast%20Asia | The tables below provide statistics on the human Y-chromosome DNA haplogroups most commonly found among ethnolinguistic groups and populations from East and South-East Asia.
ST means Sino-Tibetan languages.
Main table
Austronesian and Tai-Kadai
The following is a table of Y-chromosome DNA haplogroup frequencies of Austro-Tai peoples (i.e., Tai-Kadai peoples and Austronesian peoples).
Tibeto-Burman branch of Sino-Tibetan
The following table of Y-chromosome DNA haplogroup frequencies of Tibeto-Burman-speaking peoples of western and southwestern China is from Wen, et al. (2004).
See also
Y-DNA haplogroups by group
Y-DNA haplogroups in populations of South Asia
Y-DNA haplogroups in populations of Central and North Asia
Y-DNA haplogroups in populations of Oceania
Y-DNA haplogroups in populations of the Near East
Y-DNA haplogroups in populations of North Africa
Y-DNA haplogroups in populations of Europe
Y-DNA haplogroups in populations of the Caucasus
Y-DNA haplogroups in populations of Sub-Saharan Africa
Y-DNA haplogroups in indigenous peoples of the Americas
Far East
East Asian languages
Classification schemes for Southeast Asian languages
Ethnic groups in Asia
Ethnic groups of Southeast Asia
Notes
References
External links
Y-DNA Ethnographic and Genographic Atlas and Open-Source Data Compilation
Asia East And Southeast |
https://en.wikipedia.org/wiki/List%20of%20Oxford%20United%20F.C.%20records%20and%20statistics | Oxford United is an English professional association football club based in Oxford, Oxfordshire. They play in League One, the third level of the English football league system, as of the 2019–20 season. The club was formed in 1893 as Headington United, before changing its name (to Oxford United) in 1960, and has played home matches at two stadiums throughout its history, the Manor Ground until 2001, and the Kassam Stadium since. In 1986 they won their only major trophy, the League Cup. The club joined the Oxfordshire Senior League in 1921, before joining the Spartan League in 1947. Two years later the club moved to the Southern League, before being elected to the Football League in 1962. Oxford spent three years in the First Division between August 1985 and May 1988. At the end of the 2005–06 season, after 44 years in the League, United were relegated to the Football Conference. They returned to the League after winning the Conference National Play-off Final in 2010.
The record for most games played for the club is held by Ron Atkinson, who made 560 appearances between 1959 and 1971. John Shuker holds the record for the most appearances since they joined the Football League. Graham Atkinson is the club's record goalscorer, scoring 107 goals including 97 in the league. Jim Magilton holds the record for the most international caps gained as an Oxford player, having made 18 appearances for Northern Ireland. The highest transfer fee ever paid by the club is the £470,000 paid to Aberdeen for Dean Windass in 1998, though it has been reported that the undisclosed fee paid for Marvin Johnson in 2016 exceeded this amount, and the highest fee received is the estimated £3,000,000 paid by Leeds United for Kemar Roofe in 2016. The highest attendance recorded at the Manor Ground was 22,750 for the visit of Preston North End in the FA Cup, while the highest attendance at the Kassam is 12,243 against Leyton Orient.
Honours and achievements
Oxford United's only major honour in English football is the League Cup, which the club won in the 1985–86 season, defeating Queen's Park Rangers in the final 3–0. The club has also won the Third Division championship twice and the Second Division championship once. The latter Third Division, Second Division and League Cup victories all occurred within the space of two years. United also achieved promotion from the Fourth Division after the 1964–65 season. Oxford's highest top-flight finish is eighteenth, which was achieved twice in two years, starting in 1986. The most recent promotion occurred after the 2009–10 season, when they beat York City 3–1 in the Conference National play-off final.
Oxford's best performance in the FA Cup involved reaching the quarter-finals against Preston North End in the 1963–64 season. In doing so, they became the first team to reach that stage from the Fourth Division. Before the club were admitted to the Football League in 1962, they won the Southern Football League championship on three o |
https://en.wikipedia.org/wiki/Justi%20Baumgardt | Justi Michelle Baumgardt-Yamada (; born July 22, 1975) is a retired American soccer midfielder who was a member of the United States women's national soccer team.
International career statistics
References
External links
W-League player profile
WUSA player profile
Crossfire Premier youth soccer coaching profile
1975 births
Living people
Parade High School All-Americans (girls' soccer)
Portland Pilots women's soccer players
Sportspeople from Renton, Washington
Soccer players from King County, Washington
New York Power players
Washington Freedom players
American women's soccer players
United States women's international soccer players
Women's association football midfielders
California Storm players
Seattle Sounders Women players
USL W-League (1995–2015) players
Women's United Soccer Association players
Women's Premier Soccer League players |
https://en.wikipedia.org/wiki/Jenny%20Benson | Jennifer Lee Spiehs (; born January 25, 1978) is a retired American soccer midfielder/defender who was a member of the United States women's national soccer team.
International career statistics
References
External links
W-League player profile
WUSA player profile
WUSA Festival player profile
Nebraska Cornhuskers player profile
1978 births
Living people
USL W-League (1995–2015) players
American women's soccer players
United States women's international soccer players
Philadelphia Charge players
Nebraska Cornhuskers women's soccer players
Women's United Soccer Association players
Women's association football midfielders
Women's association football defenders
FC Energy Voronezh players
American expatriate sportspeople in Russia
Expatriate women's footballers in Russia
American expatriate women's soccer players
New Jersey Wildcats players
Denver Diamonds players |
https://en.wikipedia.org/wiki/Tam%C3%A1s%20Sz%C5%91nyi | Tamás Szőnyi (born July 23, 1957, Budapest) is a Hungarian mathematician, doing research in discrete mathematics, particularly finite geometry and algebraic coding theory. He is full professor at the department of computer science of the Eötvös Loránd University, Budapest, vice director of the Institute of Mathematics, and vice chairman of the mathematical committee of the Hungarian Academy of Sciences. In 2001, he received the Doctor of Science title from the Hungarian Academy of Sciences. Szőnyi created a successful school in finite geometry. He has done influential work on blocking sets
and the polynomial method.
Notes
External links
Homepage of Tamás Szőnyi
page of the finite geometry research group
members of the mathematical committee of the HAS
1957 births
Living people
20th-century Hungarian mathematicians
21st-century Hungarian mathematicians
Combinatorialists |
https://en.wikipedia.org/wiki/Dusm%C3%A1ta%20Tak%C3%A1cs | Dusmáta Takács (born 15 November 1986 in Dunaújváros) is a former Hungarian handballer.
Achievements
Magyar Kupa:
Bronze Medallist: 2009
References
External links
Dusmáta Takács career statistics on Worldhandball.com
1986 births
Living people
Hungarian female handball players
Sportspeople from Dunaújváros
21st-century Hungarian women |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Gallai%20theorem | The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph. A sequence obeying these conditions is called "graphic". The theorem was published in 1960 by Paul Erdős and Tibor Gallai, after whom it is named.
Statement
A sequence of non-negative integers can be represented as the degree sequence of a finite simple graph on n vertices if and only if is even and
holds for every in .
Proofs
It is not difficult to show that the conditions of the Erdős–Gallai theorem are necessary for a sequence of numbers to be graphic. The requirement that the sum of the degrees be even is the handshaking lemma, already used by Euler in his 1736 paper on the bridges of Königsberg. The inequality between the sum of the largest degrees and the sum of the remaining degrees can be established by double counting: the left side gives the numbers of edge-vertex adjacencies among the highest-degree vertices, each such adjacency must either be on an edge with one or two high-degree endpoints, the term on the right gives the maximum possible number of edge-vertex adjacencies in which both endpoints have high degree, and the remaining term on the right upper bounds the number of edges that have exactly one high degree endpoint. Thus, the more difficult part of the proof is to show that, for any sequence of numbers obeying these conditions, there exists a graph for which it is the degree sequence.
The original proof of was long and involved. cites a shorter proof by Claude Berge, based on ideas of network flow. Choudum instead provides a proof by mathematical induction on the sum of the degrees: he lets be the first index of a number in the sequence for which (or the penultimate number if all are equal), uses a case analysis to show that the sequence formed by subtracting one from and from the last number in the sequence (and removing the last number if this subtraction causes it to become zero) is again graphic, and forms a graph representing the original sequence by adding an edge between the two positions from which one was subtracted.
consider a sequence of "subrealizations", graphs whose degrees are upper bounded by the given degree sequence. They show that, if G is a subrealization, and i is the smallest index of a vertex in G whose degree is not equal to di, then G may be modified in a way that produces another subrealization, increasing the degree of vertex i without changing the degrees of the earlier vertices in the sequence. Repeated steps of this kind must eventually reach a realization of the given sequence, proving the theorem.
Relation to integer partitions
describe close connections between the Erdős–Gallai theorem and the theory of integer partitions.
Let ; then the sorted integer sequences sum |
https://en.wikipedia.org/wiki/Amin%20Shokrollahi | Amin Shokrollahi (born 1964) is a German-Iranian mathematician who has worked on a variety of topics including coding theory and algebraic complexity theory. He is best known for his work on iterative decoding of graph based codes for which he received the IEEE Information Theory Paper Award of 2002 (together with Michael Luby, Michael Mitzenmacher, and Daniel Spielman, as well as Tom Richardson and Ruediger Urbanke). He is one of the inventors of a modern class of practical erasure codes known as tornado codes,
and the principal developer of raptor codes,
which belong to a class of rateless erasure codes known as Fountain codes. In connection with the work on these codes, he received the IEEE Eric E. Sumner Award in 2007 together with Michael Luby "for bridging mathematics, Internet design and mobile broadcasting as well as successful standardization" and the IEEE Richard W. Hamming Medal in 2012 together with Michael Luby "for the conception, development, and analysis of practical rateless codes". He also received the 2007 joint Communication Society and Information Theory Society best paper award as well as the 2017 Mustafa Prize for his work on raptor codes.
He is the principal inventor of Chordal Codes, a new class of codes specifically designed for communication on electrical wires between chips. In 2011 he founded the company Kandou Bus dedicated to commercialization of the concept of Chordal Codes. The first implementation, transmitting data on 8 correlated wires and implemented in a 40 nm process, received the Jan Van Vessem Award for best European Paper at the International Solid-State Circuits Conference (ISSCC) 2014.
References
External links
Amin Shokrollahi on LinkedIn
20th-century Iranian mathematicians
21st-century Iranian mathematicians
Living people
Academic staff of the École Polytechnique Fédérale de Lausanne
1964 births
Coding theorists
Information theorists |
https://en.wikipedia.org/wiki/Quasisymmetric%20map | In mathematics, a quasisymmetric homeomorphism between metric spaces is a map that generalizes bi-Lipschitz maps. While bi-Lipschitz maps shrink or expand the diameter of a set by no more than a multiplicative factor, quasisymmetric maps satisfy the weaker geometric property that they preserve the relative sizes of sets: if two sets A and B have diameters t and are no more than distance t apart, then the ratio of their sizes changes by no more than a multiplicative constant. These maps are also related to quasiconformal maps, since in many circumstances they are in fact equivalent.
Definition
Let (X, dX) and (Y, dY) be two metric spaces. A homeomorphism f:X → Y is said to be η-quasisymmetric if there is an increasing function η : [0, ∞) → [0, ∞) such that for any triple x, y, z of distinct points in X, we have
Basic properties
Inverses are quasisymmetric If f : X → Y is an invertible η-quasisymmetric map as above, then its inverse map is -quasisymmetric, where
Quasisymmetric maps preserve relative sizes of sets If and are subsets of and is a subset of , then
Examples
Weakly quasisymmetric maps
A map f:X→Y is said to be H-weakly-quasisymmetric for some if for all triples of distinct points in , then
Not all weakly quasisymmetric maps are quasisymmetric. However, if is connected and and are doubling, then all weakly quasisymmetric maps are quasisymmetric. The appeal of this result is that proving weak-quasisymmetry is much easier than proving quasisymmetry directly, and in many natural settings the two notions are equivalent.
δ-monotone maps
A monotone map f:H → H on a Hilbert space H is δ-monotone if for all x and y in H,
To grasp what this condition means geometrically, suppose f(0) = 0 and consider the above estimate when y = 0. Then it implies that the angle between the vector x and its image f(x) stays between 0 and arccos δ < π/2.
These maps are quasisymmetric, although they are a much narrower subclass of quasisymmetric maps. For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ℝ.
Doubling measures
The real line
Quasisymmetric homeomorphisms of the real line to itself can be characterized in terms of their derivatives. An increasing homeomorphism f:ℝ → ℝ is quasisymmetric if and only if there is a constant C > 0 and a doubling measure μ on the real line such that
Euclidean space
An analogous result holds in Euclidean space. Suppose C = 0 and we rewrite the above equation for f as
Writing it this way, we can attempt to define a map using this same integral, but instead integrate (what is now a vector valued integrand) over ℝn: if μ is a doubling measure on ℝn and
then the map
is quasisymmetric (in fact, it is δ-monotone for some δ depending on the measure μ).
Quasisymmetry and quasiconformality in Euclidean space
Let |
https://en.wikipedia.org/wiki/Ring%20of%20mixed%20characteristic | In commutative algebra, a ring of mixed characteristic is a commutative ring having characteristic zero and having an ideal such that has positive characteristic.
Examples
The integers have characteristic zero, but for any prime number , is a finite field with elements and hence has characteristic .
The ring of integers of any number field is of mixed characteristic
Fix a prime p and localize the integers at the prime ideal (p). The resulting ring Z(p) has characteristic zero. It has a unique maximal ideal pZ(p), and the quotient Z(p)/pZ(p) is a finite field with p elements. In contrast to the previous example, the only possible characteristics for rings of the form are zero (when I is the zero ideal) and powers of p (when I is any other non-unit ideal); it is not possible to have a quotient of any other characteristic.
If is a non-zero prime ideal of the ring of integers of a number field , then the localization of at is likewise of mixed characteristic.
The p-adic integers Zp for any prime p are a ring of characteristic zero. However, they have an ideal generated by the image of the prime number p under the canonical map . The quotient Zp/pZp is again the finite field of p elements. Zp is an example of a complete discrete valuation ring of mixed characteristic.
The integers, the ring of integers of any number field, and any localization or completion of one of these rings is a characteristic zero Dedekind domain.
References
Commutative algebra |
https://en.wikipedia.org/wiki/Juan%20Luis%20V%C3%A1zquez%20Su%C3%A1rez | Juan Luis Vázquez Suárez is Professor of Applied Mathematics at Universidad Autónoma de Madrid (UAM), Spain.
Education
He was born in Oviedo on July 26, 1946. In the years 1964/69 he studied Telecommunication Engineering at the Superior Technical School of Ingenieros de Telecomunicación (ETSIT) in Madrid. In 1973 he graduated in Mathematics at the Universidad Complutense de Madrid, where he also obtained the Ph. D. degree in 1979 with a thesis directed by Haïm Brezis.
Contributions
Outstanding researcher in concrete areas of the mathematics such as nonlinear partial differential equations and their applications. He is author of numerous research articles in scientific journals like Archive for Rational Mechanics and Analysis, Communications on Pure and Applied Mathematics, Journal de mathématiques pures et appliquées, Advances in Mathematics among others. He was president of Spanish Society for Applied Mathematics (SEMA) in the period 1996/98. Organizer of international events like the International Conference on Free Boundaries FB1993 (Toledo, Spain) or the Summer Schools at the Universidad Internacional Menéndez Pelayo, UIMP.
Awards and honors
He obtained the Spanish National Prize of Research in Mathematics (Premio Nacional de Investigación Julio Rey Pastor) in 2003, and that year he was included in the Thomson Reuters list of Highly Cited Scientists.
He was invited as main speaker at the International Congress of Mathematicians held in Madrid in 2006 (ICM2006) with the plenary conference entitled "Nonlinear diffusion, from analysis to physics and geometry."
In 2012 he became a fellow of the American Mathematical Society.
Books
The Porous Medium Equation. Mathematical Theory. Oxford University Press, , , 2006, Clarendon Press, 648 pages, 234x156 mm. Series: Oxford Mathematical Monographs.
Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type. Oxford University Press, , , August 2006, 248 pages, 234x156 mm, Oxford Lecture Series.
A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach. PNLDE 56 (Progress in Non-Linear Differential Equations and Their Applications), Birkhäuser Verlag, 2003, 391 pages. (with V.A. Galaktionov.)
Recent Trends in Partial Differential Equations. American Mathematical Society, , 2006, 123 pages, Series: Contemporary Mathematics number 409; (with X. Cabré and José A. Carrillo)
References
External links
Official Web Page
Departamento de Matemáticas UAM
1946 births
Living people
21st-century Spanish mathematicians
People from Oviedo
Fellows of the American Mathematical Society
20th-century Spanish mathematicians
Academic staff of the Autonomous University of Madrid |
https://en.wikipedia.org/wiki/Gordon%20Kaufman | Gordon Kaufman may refer to:
Gordon D. Kaufman (1925–2011), theologian
Gordon M. Kaufman, professor of statistics
See also
Gordon Kaufmann, American architect |
https://en.wikipedia.org/wiki/Sanford%20L.%20Segal | Sanford Leonard Segal ( – ) was a mathematician and historian of science and mathematics at the University of Rochester. Mathematically he specialized in analytic number theory, and complex analysis. He wrote the textbook Nine Introductions in Complex Analysis (1981), and the tome Mathematicians Under the Nazis (2003), a historical recount from that period. He also taught courses in women's studies, and nuclear arms. He was on the Committee of Actuarial Studies at the University of Rochester.
Life
In 1937 he was born into a conservative Jewish family.
In 1958, he received his B.A. degree from Wesleyan University with Honors in Mathematics and High Honors in Classical Civilization studies.
In 1959 he spent a year as a Fulbright student in Mainz, Germany.
In 1963, he earned his Ph.D. in Mathematics at University of Colorado under the supervision of Sarvadaman D. S. Chowla with the dissertation entitled The Error Term in the Formula for the Average Value of the Euler Phi Function.
Career
After his Ph.D., he worked at the University of Rochester for 44 years until his retirement in 2008. In 1965 he received a grant from the Fulbright Program as a research fellow in Vienna, Austria. And in 1977, he received a grant from the National Institute for Pure and Applied Mathematics to teach in Rio de Janeiro.
In 1981 he published Nine Introductions in Complex Analysis with North Holland Press (a revised edition was published in 2011 by Elsevier, which had taken over North Holland Press). He later received a grant from The Alexander von Humboldt Foundation to research history of science in Nazi Germany. Princeton University Press later published the book Mathematicians Under the Nazis in 2003, which addresses the experience of mathematics academics in Nazi Germany. The book involved a lot of direct research and interviews with survivors and translations from German.
He translated from French the book History of Mathematics: Highways and Byways in 2009. In addition, Segal published more than 45 papers on mathematics, mathematics education, and the history of science.
He was a member of the Religious Society of Friends. He was also a member of Sigma Xi and of Phi Beta Kappa.
He married Rima Maxwell and had three children, Adam, Joshua, and Zoë.
He died on May 7, 2010.
Academic publications
References
Number theorists
Wesleyan University alumni
20th-century American mathematicians
21st-century American mathematicians
University of Rochester faculty
1937 births
2010 deaths |
https://en.wikipedia.org/wiki/Kantor%E2%80%93Koecher%E2%80%93Tits%20construction | In algebra, the Kantor–Koecher–Tits construction is a method of constructing a Lie algebra from a Jordan algebra, introduced by , , and .
If J is a Jordan algebra, the Kantor–Koecher–Tits construction puts a Lie algebra structure on J + J + Inner(J), the sum of 2 copies of J and the Lie algebra of inner derivations of J.
When applied to a 27-dimensional exceptional Jordan algebra it gives a Lie algebra of type E7 of dimension 133.
The Kantor–Koecher–Tits construction was used by to classify the finite-dimensional simple Jordan superalgebras.
References
Lie algebras
Non-associative algebras |
https://en.wikipedia.org/wiki/Max%20Koecher | Max Koecher (; 20 January 1924 in Weimar – 7 February 1990, Lengerich) was a German mathematician.
Biography
Koecher studied mathematics and physics at the Georg-August-Universität in Göttingen.
In 1951, he received his doctorate under Max Deuring with his work on Dirichlet series with functional equation where he introduced Koecher–Maass series. He qualified in 1954 at the Westfälische Wilhelms University in Münster. From 1962 to 1970, Koecher was department chair at the University of Munich. He retired in 1989.
His main research area was the theory of Jordan algebras, where he introduced the Kantor–Koecher–Tits construction and the Koecher–Vinberg theorem. He discovered the Koecher boundedness principle in the theory of Siegel modular forms.
References
External links
Max Koecher on Wikimedia Commons
20th-century German mathematicians
1990 deaths
1924 births |
https://en.wikipedia.org/wiki/Wallis%27%20integrals | In mathematics, and more precisely in analysis, the Wallis integrals constitute a family of integrals introduced by John Wallis.
Definition, basic properties
The Wallis integrals are the terms of the sequence defined by
or equivalently,
The first few terms of this sequence are:
The sequence is decreasing and has positive terms. In fact, for all
because it is an integral of a non-negative continuous function which is not identically zero;
again because the last integral is of a non-negative continuous function.
Since the sequence is decreasing and bounded below by 0, it converges to a non-negative limit. Indeed, the limit is zero (see below).
Recurrence relation
By means of integration by parts, a reduction formula can be obtained. Using the identity , we have for all ,
Integrating the second integral by parts, with:
, whose anti-derivative is
, whose derivative is
we have:
Substituting this result into equation (1) gives
and thus
for all
This is a recurrence relation giving in terms of . This, together with the values of and give us two sets of formulae for the terms in the sequence , depending on whether is odd or even:
Another relation to evaluate the Wallis' integrals
Wallis's integrals can be evaluated by using Euler integrals:
Euler integral of the first kind: the Beta function:
for
Euler integral of the second kind: the Gamma function:
for .
If we make the following substitution inside the Beta function:
we obtain:
so this gives us the following relation to evaluate the Wallis integrals:
So, for odd , writing , we have:
whereas for even , writing and knowing that , we get :
Equivalence
From the recurrence formula above , we can deduce that
(equivalence of two sequences).
Indeed, for all :
(since the sequence is decreasing)
(since )
(by equation ).
By the sandwich theorem, we conclude that , and hence .
By examining , one obtains the following equivalence:
(and consequently ).
Deducing Stirling's formula
Suppose that we have the following equivalence (known as Stirling's formula):
for some constant that we wish to determine. From above, we have
(equation (3))
Expanding and using the formula above for the factorials, we get
From (3) and (4), we obtain by transitivity:
Solving for gives In other words,
Deducing the Double Factorial Ratio
Similarly, from above, we have:
Expanding and using the formula above for double factorials, we get:
Simplifying, we obtain:
or
Evaluating the Gaussian Integral
The Gaussian integral can be evaluated through the use of Wallis' integrals.
We first prove the following inequalities:
In fact, letting ,
the first inequality (in which ) is
equivalent to ;
whereas the second inequality reduces to
,
which becomes .
These 2 latter inequalities follow from the convexity of the
exponential function
(or from an analysis of the function ).
Letting and
making use of the basic properties of improper integrals
(the convergence of the integra |
https://en.wikipedia.org/wiki/Koecher%E2%80%93Maass%20series | In mathematics, a Koecher–Maass series is a type of Dirichlet series that can be expressed as a Mellin transform of a Siegel modular form, generalizing Hecke's method of associating a Dirichlet series to a modular form using Mellin transforms. They were introduced by and .
References
Automorphic forms |
https://en.wikipedia.org/wiki/Isaiah%20Kantor | Isaiah Kantor (or Issai Kantor, or Isai Lʹvovich Kantor) (1936–2006) was a mathematician who introduced the Kantor–Koecher–Tits construction, and the Kantor double, a Jordan superalgebra constructed from a Poisson algebra.
References
Russian mathematicians
2006 deaths
1936 births |
https://en.wikipedia.org/wiki/Kantor%20double | In mathematics, the Kantor double is a Jordan superalgebra structure on the sum of two copies of a Poisson algebra. It is named after Isaiah Kantor, who introduced it in .
References
Non-associative algebras |
https://en.wikipedia.org/wiki/Murray%20Gerstenhaber | Murray Gerstenhaber (born June 5, 1927) is an American mathematician and professor of mathematics at the University of Pennsylvania, best known for his contributions to theoretical physics with his discovery of Gerstenhaber algebra. He is also a lawyer and a lecturer in law at the University of Pennsylvania Law School.
Early life and education
Gerstenhaber was born in Brooklyn, New York, to Pauline (née Rosenzweig; who was born in Romania; died in 1978) and Joseph Gerstenhaber (who was born in 1892 in Romania; died in 1975). His father was trained as a jeweler, "but being unable to find work in this line he [took] employment in a factory making airplane precision instruments”. As to his mother, in 2015 he noted: "For someone born into a minority family without means, I have been exceedingly lucky. The problems faced by talented but disadvantaged children today are preventing many who could be important contributors to the sciences, arts, and society in general, from achieving their potential. They don’t all have mothers like mine, who fought to find a path to education for her child. We have to seek them out but are not doing enough to find them, bring them out of isolation, and give them the opportunities I was so fortunate to have enjoyed."
He was a child prodigy who was profiled in Leta Hollingworth's book Children Above 180 IQ (1942). In this book, Gerstenhaber was dubbed "Child L," and his prodigious abilities and personality traits were described in great detail. At age 9 years 5 months, a Stanford-Binet test showed him to have a mental age of between 17 and 18 and an IQ between 195 and 198. A second revised Stanford-Binet given a year later found him to have a mental age of 19 years 11 months and an IQ of 199+.
He attended the now-defunct Speyer School, a school for rapid learners in New York City. Many years later, his daughter-in-law co-founded Speyer Legacy School, naming the new school after the original. After graduating from Speyer School, Gerstenhaber entered the Bronx High School of Science in 1940. From 1945 to 1947 he served in the infantry in the United States Army as a corporal assigned to the Office of Military Government for Germany.
Gerstenhaber finished his B.S. in mathematics at Yale University (1948). At Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University (along with Murray Gell-Mann and Henry O. Pollak) that won the second prize in 1947; each of them received a monetary prize of $30 ($ in current dollar terms). His 1948 participation in the competition earned him a Top 10 ranking.
He earned an M.A. and a Ph.D. (1951) in mathematics from the University of Chicago, under the instruction of Abraham Adrian Albert. Gerstenhaber's dissertation was entitled "Rings of Derivations."
Gerstenhaber earned a J.D. from the University of Pennsylvania Law School in 1973, and was admitted to the Pennsylvania bar in 1974.
Career
Gerstenhaber was an assistant |
https://en.wikipedia.org/wiki/Ambalamedu%20High%20School | Ambalamedu High School (AHS) was a school in Kerala, India. AHS provided co-curricular activities including Nature Club, Maths Club, Science Club, School band, Youth Festival, Scouts, Guides and NCC.
Formation
The school was inaugurated on 18 May 1970, the first SSLC batch in 1973 had four students. It maintained a continuous 100% pass in the SSLC board examinations. It was run by the Cochin Division of the Fertilizers and Chemicals Travancore Ltd (FACT). The school enjoyed an all-pass status till 2004, the last year of its run under FACT before it was leased out to a private management.
Tenure under TocH Residential Public School
Ambalamedu High School was handed over to TocH Residential Public School (Prabhat Residential Public School) in 2004. The private firm ran the school for five years and handed in back to FACT in 2009. A trust formed under a society in FACT managed the school for another two years for the sake of the students who were in class nine and ten. It closed down in 2011.
Closure
The school was closed down at the end of 2011, as the company refused to run it any longer. The school today exists only in the realm of memory. Mr. V Gopalakrishna Pillai was the last headmaster of the school.
Notable alumni
former NASA scientist Rajeev Nambiar,
student scientist Manu S. Madhav, who was part of NASA's Mars Redrover project,
Dr Hafeez Rahman, chairman of Sunrise Hospitals,
CA.Dr. Binoy J. Kattadiyil, Economist; managing director, IPA, Insolvency & Bankruptcy Board of India,
actor Krishnakumar.
Ananthu M
External links
School alumni website
A Facebook page to confess about the sins the students have committed during their school days
References
Schools in Ernakulam district
Defunct schools in India |
https://en.wikipedia.org/wiki/Hirokazu%20Usami | is a Japanese football player who currently plays for Fukushima United FC.
Career statistics
Updated to 23 February 2018.
References
External links
Profile at Fukushima United FC
1987 births
Living people
Kansai University alumni
Association football people from Osaka Prefecture
People from Moriguchi, Osaka
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Tochigi SC players
Shonan Bellmare players
Montedio Yamagata players
Fukushima United FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Tatsuya%20Onodera | is a Japanese football player. He currently plays for Giravanz Kitakyushu.
Career statistics
Updated to 23 February 2020.
References
External links
Profile at Giravanz Kitakyushu
1987 births
Living people
Takushoku University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Tochigi SC players
V-Varen Nagasaki players
Giravanz Kitakyushu players
Tegevajaro Miyazaki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Picard%E2%80%93Vessiot%20theory | In differential algebra, Picard–Vessiot theory is the study of the differential field extension generated by the solutions of a linear differential equation, using the differential Galois group of the field extension. A major goal is to describe when the differential equation can be solved by quadratures in terms of properties of the differential Galois group. The theory was initiated by Émile Picard and Ernest Vessiot from about 1883 to 1904.
and give detailed accounts of Picard–Vessiot theory.
History
The history of Picard–Vessiot theory is discussed by .
Picard–Vessiot theory was developed by Picard between 1883 and 1898 and by Vessiot from 1892 to 1904 (summarized in and ). The main result of their theory says very roughly that a linear differential equation can be solved by quadratures if and only if its differential Galois group is connected and solvable. Unfortunately it is hard to tell exactly what they proved as the concept of being "solvable by quadratures" is not defined precisely or used consistently in their papers. gave precise definitions of the necessary concepts and proved a rigorous version of this theorem.
extended Picard–Vessiot theory to partial differential fields (with several commuting derivations).
described an algorithm for deciding whether second order homogeneous linear equations can be solved by quadratures, known as Kovacic's algorithm.
Picard–Vessiot extensions and rings
An extension F ⊆ K of differential fields is called a Picard–Vessiot extension if all constants are in F and K can be generated by adjoining the solutions of a homogeneous linear ordinary differential polynomial.
A Picard–Vessiot ring R over the differential field F is a differential ring over F that is simple (no differential ideals other than 0 and R) and generated as a k-algebra by the coefficients of A and 1/det(A), where A is an invertible matrix over F such that B = /A has coefficients in F. (So A is a fundamental matrix for the differential equation = By.)
Liouvillian extensions
An extension F ⊆ K of differential fields is called Liouvillian if all constants are in F, and K can be generated by adjoining a finite number of integrals, exponential of integrals, and algebraic functions. Here, an integral of an element a is defined to be any solution of = a, and an exponential of an integral of a is defined to be any solution of = ay.
A Picard–Vessiot extension is Liouvillian if and only if the identity component of its differential Galois group is solvable (, ). More precisely, extensions by algebraic functions correspond to finite differential Galois groups, extensions by integrals correspond to subquotients of the differential Galois group that are 1-dimensional and unipotent, and extensions by exponentials of integrals correspond to subquotients of the differential Galois group that are 1-dimensional and reductive (tori).
Sources
External links
Differential algebra |
https://en.wikipedia.org/wiki/Oxford%20University%20Invariant%20Society | The Oxford University Invariant Society, or 'The Invariants', is a university society open to members of the University of Oxford, dedicated to promotion of interest in mathematics. The society regularly hosts talks from professional mathematicians on topics both technical and more popular, from the mathematics of juggling to the history of mathematics. Many prominent British mathematicians were members of the society during their time at Oxford.
History
The Society was founded in 1936 by J. H. C. Whitehead together with two of his students at Balliol College, Graham Higman and Jack de Wet. The name of the society was chosen at random by Higman from the titles of the books on Whitehead's shelf; in this case, Oswald Veblen's Invariants of Quadratic Differential Forms. The opening lecture was given by G. H. Hardy in Hilary Term 1936, with the title 'Round Numbers'.
Though many members joined the armed forces during the war, meetings continued, including lectures by Douglas Hartree and Max Newman, as well as debates - 'Is Mathematics an end in itself?' - and mathematical films.
The society has hosted hundreds of prominent mathematicians, including lectures by Benoit Mandelbrot, Sir Roger Penrose, and Simon Singh.
Since 1961, the Society has published a magazine entitled The Invariant.
References
External links
Official website
Archive of old termcards and committee lists
1936 establishments in England
Clubs and societies of the University of Oxford
Mathematics education in the United Kingdom
Student organizations established in 1936 |
https://en.wikipedia.org/wiki/Pekka%20Saarenheimo | Pekka Saarenheimo (born May 6, 1982) is a Finnish professional ice hockey centre who currently plays for Södertälje SK of the Elitserien.
Career statistics
References
External links
Living people
Södertälje SK players
1982 births
Lahti Pelicans players
Finnish ice hockey centres
Oulun Kärpät players
Lukko players
Tingsryds AIF players
Mikkelin Jukurit players
Ice hockey people from North Ostrobothnia |
https://en.wikipedia.org/wiki/Daiki%20Umei | is a Japanese football player for SC Sagamihara.
Club Statistics
Updated to 23 February 2017.
References
External links
Profile at SC Sagamihara
1989 births
Living people
People from Fukui (city)
Association football people from Fukui Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Yokohama F. Marinos players
Thespakusatsu Gunma players
Oita Trinita players
Zweigen Kanazawa players
Fukushima United FC players
SC Sagamihara players
Men's association football defenders |
https://en.wikipedia.org/wiki/Shingo%20Arizono | is a former Japanese football player who last played for Ococias Kyoto AC.
Club statistics
Updated to 19 January 2019.
Honours
Blaublitz Akita
J3 League (1): 2017
References
External links
Profile at Thespakusatsu Gunma
Profile at Blaublitz Akita
Profile at Giravanz Kitakyushu
1985 births
Living people
Japan University of Economics alumni
Association football people from Kagoshima Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Thespakusatsu Gunma players
FC Machida Zelvia players
Blaublitz Akita players
Giravanz Kitakyushu players
Nara Club players
Men's association football defenders |
https://en.wikipedia.org/wiki/Jigu%20Suanjing | Jigu suanjing (, Continuation of Ancient Mathematics) was the work of early Tang dynasty calendarist and mathematician Wang Xiaotong, written some time before the year 626, when he presented his work to the Emperor. Jigu Suanjing was included as one of the requisite texts for Imperial examination; the amount of time required for the study of Jigu Suanjing was three years, the same as for The Nine Chapters on the Mathematical Art and Haidao Suanjing.
The book began with presentations to the Emperor, followed by a pursuit problem similar to the one in Jiu Zhang Suan shu, followed by thirteen three-dimensional geometry problems based mostly on engineering construction of astronomic observation tower, dike, barn, excavation of a canal bed etc., and six problems in right angled triangle plane geometry. Apart from the first problem which was solved by arithmetic, the problems deal with the solution of cubic equations, the first known Chinese work to deal with complete cubic equations, as such, it played important roles in the development for solution of high order polynomial equations in the history of Chinese mathematics. Before his time, The Nine Chapters on the Mathematical Art developed algorithm of solving simple cubic equation numerically, often referred to as the "finding the root method".
Wang Xiaotong used an algebraic method to solve three-dimensional geometry problems, and his work is a major advance in Algebra in the history of Chinese mathematics.
Each problem in Jigu Suanjing follows the same format, the question part begins with "suppose we have such and such,... question:...how many are there?"; followed by "answer:", with concrete numbers; then followed by "The algorithm says:...", in which Wang Xiaotong detailed the reasoning and procedure for the construction of equations, with a terse description of the method of solution. The emphasis of the book is on how to solve engineering problems by construction of mathematical equations from geometric properties of the relevant problem.
In Jigu Suanjin, Wang established and solved 25 cubic equations, 23 of them from problem 2 to problem 18 have the form
The remaining two problems 19, and 20 each has a double quadratic equation:
Problem 3, two cubic equations:
；
Problem 4 two cubic equations:
Problem 5
Problem 7:
Problem 8:
Problem 15:
。
Problem 17:
Problem 20:"Suppose the long side of a right angle triangle equals to sixteen and a half, the square of the product of the short side and the hypothenuse equals to one hundred sixty four and 14 parts of 25, question, what is the length of the short side ?"
Answer: "the length of the short side is eight and four fifth."
Algorithm:"Let the square of the square of product as 'shi' (the constant term), and let the square of the long side of right angle triangle be the 'fa' (the coefficient of the y term). Solve by 'finding the root method', then find the square root again."
The algorithm is about set |
https://en.wikipedia.org/wiki/Peter%20Nemenyi | Peter Björn Nemenyi (April 14, 1927 – May 20, 2002) was an American mathematician, who worked in statistics and probability theory. He taught mathematics at a number of American colleges and universities, including Hunter College, Tougaloo College, Oberlin College, University of North Carolina at Chapel Hill, Virginia State College and the University of Wisconsin–Madison. Several statistical tests, for example the Nemenyi test, bear his name. He was also a prominent civil-rights activist. He was the son of Paul Nemenyi an eminent fluid and engineering mechanics expert of the twentieth century. His mother was Aranka Heller, poet and scholar, daughter of Bernat Heller, a renowned 'Aggadist, Islamic scholar and folklorist.
Life
Peter Nemenyi was born in Berlin, to which his parents had fled after anti-Jewish laws had been enacted in Hungary. His parents separated, and he was brought up in a socialist boarding school operated by the ISK, a German socialist party founded by Leonard Nelson.
After the rise of Nazism, the party was banned in Germany and its property was seized. The school frequently relocated to different European countries, as Nazi strength grew. During the Second World War the adults in the party were interned on the Isle of Man and Nemenyi lived in a number of foster homes and youth homes.
After the war, Peter moved to the United States to live with his father in Hanford, Washington.
He was drafted almost immediately and served near Trieste.
After military service, he attended Black Mountain College under the G.I. Bill.
He received his Ph.D. from Princeton University with a thesis on Distribution-Free Multiple Comparisons advised by John Wilder Tukey. Several statistical tests, most notably the Nemenyi test bear his name.
Peter Nemenyi is also known as a civil-rights activist in the Deep South. He also worked for the revolutionary government in Nicaragua, which affected his health.
He was an active member of the Congress of Racial Equality in New York, working in Mississippi in 1962, in Jackson, and 1964-5 in Laurel.
Nemenyi's father, Paul Nemenyi, was probably the father of 1972 World Chess Champion Bobby Fischer. Peter Nemenyi was aware of this, and made efforts to care for the young Fischer after Paul Nemenyi died in 1952.
Publications
Peter Nemenyi: Distribution-free multiple comparisons, Doctoral Thesis, Princeton University, 1963.
Peter Nemenyi and Sylvia K. Dixon: Statistics from Scratch. Holden-Day Series in Probability and Statistics, 1977.
References
1927 births
2002 deaths
Academics from Berlin
Jewish emigrants from Nazi Germany to the United States
American statisticians
American people of Hungarian-Jewish descent
Black Mountain College alumni
University of Wisconsin–Madison faculty
20th-century chess players |
https://en.wikipedia.org/wiki/Kain%20Massin | Kain Massin is an Australian writer of speculative fiction.
Biography
Massin is based in Adelaide, South Australia where he is a high school maths and science teacher. He is also a member of the Blackwood Writers Group. Massin's first work was published in 1998 with his short story "Escape from Stalingrad" which was featured in fourth edition of Harbinger. "Escape from Stalingrad" was nominated for the 1999 Aurealis Award for best horror short story but lost to Sean Williams and Simon Brown's "Atrax". In 2008 Massin's first novel was published by ABC Books, entitled God for the Killing, after he won the 2008 ABC Fiction Award which has a A$10,000 prize and a publication deal for the novel.
Awards and nominations
Bibliography
Anthologies
As editor
Tales from the Black Wood (2006, co-editor)
Novels
God for the Killing (2008)
Short stories
"Escape from Stalingrad" (1998) in Harbinger #4
"Wrong Dreaming" (2000) in On Spec Fall 2000 (ed. Jena Snyder)
"A Guide for the Grave-Robber" (2000) in Altair #5 (ed. Robert N. Stephenson, Jim Deed, Andrew Collings)
References
General
Specific
External links
Official site
21st-century Australian novelists
Australian male novelists
Australian male short story writers
Living people
Year of birth missing (living people)
21st-century Australian short story writers
21st-century Australian male writers |
https://en.wikipedia.org/wiki/Skolem%E2%80%93Mahler%E2%80%93Lech%20theorem | In additive and algebraic number theory, the Skolem–Mahler–Lech theorem states that if a sequence of numbers satisfies a linear difference equation, then with finitely many exceptions the positions at which the sequence is zero form a regularly repeating pattern. This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler (who proved it for sequences of algebraic numbers), and Christer Lech (who proved it for sequences whose elements belong to any field of characteristic 0). Its known proofs use p-adic analysis and are non-constructive.
Theorem statement
Let be a sequence of complex numbers satisfying for all , where are complex number constants (i.e., a constant-recursive sequence of order ). Then the set of zeros is equal to the union of a finite set and finitely many arithmetic progressions.
If we have (excluding sequences such as 1, 0, 0, 0, ...), then the set of zeros in fact equal to the union of a finite set and finitely many full arithmetic progressions, where an infinite arithmetic progression is full if there exist integers a and b such that the progression consists of all positive integers equal to b modulo a.
Example
Consider the sequence
that alternates between zeros and the Fibonacci numbers.
This sequence can be generated by the linear recurrence relation
(a modified form of the Fibonacci recurrence), starting from the base cases F(1) = F(2) = F(4) = 0 and F(3) = 1. For this sequence,
F(i) = 0 if and only if i is either one or even. Thus, the positions at which the sequence is zero can be partitioned into a finite set (the singleton set {1}) and a full arithmetic progression (the positive even numbers).
In this example, only one arithmetic progression was needed, but other recurrence sequences may have zeros at positions forming multiple arithmetic progressions.
Related results
The Skolem problem is the problem of determining whether a given recurrence sequence has a zero. There exist an algorithm to test whether there are infinitely many zeros, and if so to find the decomposition of these zeros into periodic sets guaranteed to exist by the Skolem–Mahler–Lech theorem. However, it is unknown whether there exists an algorithm to determine whether a recurrence sequence has any non-periodic zeros.
References
, cited in Lech 1953.
, cited in Lech 1953.
.
.
.
External links
Theorems in number theory
Algebraic number theory
Additive number theory
Recurrence relations |
https://en.wikipedia.org/wiki/Matt%20Tee | Matt Tee graduated from the University of Leeds (Mathematics 1996). He was previously the Permanent Secretary for Government Communications in the Cabinet Office. After several roles in public sector communications, Tee served as the Director of Business Development at Dr Foster. He then served as the interim Director General of Communications in the Department of Health for 2006–7, before being appointed Chief Executive of NHS Direct in July 2007. Tee became Permanent Secretary for Government Communications in the Cabinet Office. In November 2010 it was announced that Tee would leave his post heading Government Communications in March 2011 following a review of the Central Office of Information. He was the first Chief Executive of the Independent Press Standards Organisation (IPSO), serving from September 2014 until March 2020.
References
Living people
Permanent Secretaries of the Cabinet Office
Civil servants in the Ministry of Health (United Kingdom)
Alumni of the University of Leeds
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Tube%20domain | In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary part is unconstrained; likewise, a tube is the set of complex vectors whose real part is in some given collection of real vectors, and whose imaginary part is unconstrained.
Tube domains are domains of the Laplace transform of a function of several real variables (see multidimensional Laplace transform). Hardy spaces on tubes can be defined in a manner in which a version of the Paley–Wiener theorem from one variable continues to hold, and characterizes the elements of Hardy spaces as the Laplace transforms of functions with appropriate integrability properties. Tubes over convex sets are domains of holomorphy. The Hardy spaces on tubes over convex cones have an especially rich structure, so that precise results are known concerning the boundary values of Hp functions. In mathematical physics, the future tube is the tube domain associated to the interior of the past null cone in Minkowski space, and has applications in relativity theory and quantum gravity. Certain tubes over cones support a Bergman metric in terms of which they become bounded symmetric domains. One of these is the Siegel half-space which is fundamental in arithmetic.
Definition
Let Rn denote real coordinate space of dimension n and Cn denote complex coordinate space. Then any element of Cn can be decomposed into real and imaginary parts:
Let A be an open subset of Rn. The tube over A, denoted TA, is the subset of Cn consisting of all elements whose real parts lie in A:
Tubes as domains of holomorphy
Suppose that A is a connected open set. Then any complex-valued function that is holomorphic in a tube TA can be extended uniquely to a holomorphic function on the convex hull of the tube , which is also a tube, and in fact
Since any convex open set is a domain of holomorphy (holomorphically convex), a convex tube is also a domain of holomorphy. So the holomorphic envelope of any tube is equal to its convex hull.
Hardy spaces
Let A be an open set in Rn. The Hardy space H p(TA) is the set of all holomorphic functions F in TA such that
for all x in A.
In the special case of p = 2, functions in H2(TA) can be characterized as follows. Let ƒ be a complex-valued function on Rn satisfying
The Fourier–Laplace transform of ƒ is defined by
Then F is well-defined and belongs to H2(TA). Conversely, every element of H2(TA) has this form.
A corollary of this characterization is that H2(TA) contains a nonzero function if and only if A contains no straight line.
Tubes over cones
Let A be an open convex cone in Rn. This means that A is an open convex set such that, whenever x lies in A, so does the entire ray from the origin to x. Symbolically,
If A is a cone, then the elements of H2(TA) ha |
https://en.wikipedia.org/wiki/Tomoya%20Ugajin | is a Japanese footballer who plays for FC Gifu.
Club statistics
Updated to 20 December 2022.
1Includes Emperor's Cup.
2Includes J. League Cup.
3Includes Japanese Super Cup, J. League Championship and FIFA Club World Cup.
National team statistics
Honours
Club
Urawa Red Diamonds
AFC Champions League: 2017
J.League Cup: 2016
Emperor's Cup: 2018, 2021
References
External links
Tomoya Ugajin at Urawa Red Diamonds official site
Tomoya Ugajin at Yahoo! Japan sports
1988 births
Living people
Ryutsu Keizai University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
Urawa Red Diamonds players
J3 League players
FC Gifu players
Japan men's international footballers
Men's association football defenders
Men's association football midfielders |
https://en.wikipedia.org/wiki/Edinburgh%20Institution | Edinburgh Institution may refer to:
Edinburgh Institution F.P., a former Edinburgh rugby union club
Stewart's Melville College, formerly Edinburgh Institution for Languages and Mathematics
Royal Scottish Academy, formerly Royal Institution for the Encouragement of the Fine Arts |
https://en.wikipedia.org/wiki/Nearly%20K%C3%A4hler%20manifold | In mathematics, a nearly Kähler manifold is an almost Hermitian manifold , with almost complex structure ,
such that the (2,1)-tensor is skew-symmetric. So,
for every vector field on .
In particular, a Kähler manifold is nearly Kähler. The converse is not true.
For example, the nearly Kähler six-sphere is an example of a nearly Kähler manifold that is not Kähler. The familiar almost complex structure on the six-sphere is not induced by a complex atlas on .
Usually, non Kählerian nearly Kähler manifolds are called "strict nearly Kähler manifolds".
Nearly Kähler manifolds, also known as almost Tachibana manifolds, were studied by Shun-ichi Tachibana in 1959 and then by Alfred Gray from 1970 on.
For example, it was proved that any 6-dimensional strict nearly Kähler manifold is an Einstein manifold and has vanishing first Chern class
(in particular, this implies spin).
In the 1980s, strict nearly Kähler manifolds obtained a lot of consideration because of their relation to Killing
spinors: Thomas Friedrich and Ralf Grunewald showed that a 6-dimensional Riemannian manifold admits
a Riemannian Killing spinor if and only if it is nearly Kähler. This was later given a more fundamental explanation by Christian Bär, who pointed out that
these are exactly the 6-manifolds for which the corresponding 7-dimensional Riemannian cone has holonomy G2.
The only compact simply connected 6-manifolds known to admit strict nearly Kähler metrics are , and . Each of these admits such a unique nearly Kähler metric that is also homogeneous, and these examples are in fact the only compact homogeneous strictly nearly Kähler 6-manifolds.
However, Foscolo and Haskins recently showed that and also admit strict nearly Kähler metrics that are not homogeneous.
Bär's observation about the holonomy of Riemannian cones might seem to indicate that the nearly-Kähler condition is
most natural and interesting in dimension 6. This actually borne out by a theorem of Nagy, who proved that any strict, complete nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces over quaternion-Kähler manifolds, and 6-dimensional nearly Kähler manifolds.
Nearly Kähler manifolds are also an interesting class of manifolds admitting a metric connection with
parallel totally antisymmetric torsion.
Nearly Kähler manifolds should not be confused with almost Kähler manifolds.
An almost Kähler manifold is an almost Hermitian manifold with a closed Kähler form:
. The Kähler form or fundamental 2-form is defined by
where is the metric on . The nearly Kähler condition and the almost Kähler condition are essentially exclusive: an almost Hermitian manifold is both nearly Kähler and almost Kahler if and only if it is Kähler.
References
Topology
Differential geometry
Manifolds |
https://en.wikipedia.org/wiki/Thomas%20J%C3%B6rg | Thomas Jörg (born December 2, 1981) is a German professional ice hockey forward who currently plays for Augsburger Panther of the Deutsche Eishockey Liga (DEL).
Career statistics
References
External links
1981 births
Living people
Augsburger Panther players
DEG Metro Stars players
ERC Ingolstadt players
German ice hockey forwards
People from Immenstadt
Sportspeople from Swabia (Bavaria)
Ice hockey people from Bavaria |
https://en.wikipedia.org/wiki/Radiodrome | In geometry, a radiodrome is the pursuit curve followed by a point that is pursuing another linearly-moving point. The term is derived from the Greek words and . The classic (and best-known) form of a radiodrome is known as the "dog curve"; this is the path a dog follows when it swims across a stream with a current after something it has spotted on the other side. Because the dog drifts with the current, it will have to change its heading; it will also have to swim further than if it had taken the optimal heading. This case was described by Pierre Bouguer in 1732.
A radiodrome may alternatively be described as the path a dog follows when chasing a hare, assuming that the hare runs in a straight line at a constant velocity.
Mathematical analysis
Introduce a coordinate system with origin at the position of the dog at time
zero and with y-axis in the direction the hare is running with the constant
speed . The position of the hare at time zero is with and at time it is
The dog runs with the constant speed towards the instantaneous position of the hare.
The differential equation corresponding to the movement of the dog, , is consequently
It is possible to obtain a closed-form analytic expression for the motion of the dog.
From () and (), it follows that
Multiplying both sides with and taking the derivative with respect to , using that
one gets
or
From this relation, it follows that
where is the constant of integration determined by the initial value of ' at time zero, , i.e.,
From () and (), it follows after some computation that
Furthermore, since , it follows from () and () that
If, now, , relation () integrates to
where is the constant of integration. Since again , it's
The equations (), () and (), then, together imply
If , relation () gives, instead,
Using once again, it follows that
The equations (), () and (), then, together imply that
If , it follows from () that
If , one has from () and () that , which means that the hare will never be caught, whenever the chase starts.
See also
Mice problem
References
.
Plane curves
Differential equations
Analytic geometry
Pursuit–evasion |
https://en.wikipedia.org/wiki/Thomas%20Elrington%20%28bishop%29 | Thomas Elrington (18 December 1760 – 12 July 1835) was an Irish academic and bishop. He was Donegall Lecturer in Mathematics (1790-1795) at Trinity College Dublin (TCD). While at TCD he also served as Erasmus Smith's Professor of Mathematics (1795–1799) and as Erasmus Smith's Professor of Natural and Experimental Philosophy (1799–1807). Later, he was Provost of Trinity College Dublin (1811-1820), then Bishop of Limerick, Ardfert and Aghadoe (1820-1822), and finally Bishop of Ferns and Leighlin till his death in Liverpool in 1835.
Life
The only child of Richard and Catherine Elrington of Dublin, he was born near that city on 18 December 1760. He entered Trinity College Dublin, on 1 May 1775 as a pensioner, under the tutorship of the Rev. Dr. Drought, and was elected a Scholar in 1778. He graduated B.A. in 1780, M.A. in 1785, and B.D. and D.D. in 1795.
In 1781 he was elected a fellow of his college. He was Donegall Lecturer of Mathematics (1790-1795), and in 1794 he was the first to hold the office of Donnellan Divinity Lecturer. In 1795 he was appointed Archbishop King's Lecturer in Divinity, succeeded to a senior fellowship, and also became the third Erasmus Smith's Professor of Mathematics (1795–1799). In 1799 he exchanged the Erasmus Smith's professorship of mathematics for the Erasmus Smith's Professor of Natural and Experimental Philosophy.
In 1789, he published the mathematical treatise Euclidis Elementorum Sex Libri Priores, Cum Notis (Dublin University Press), whose 10th edition appeared in 1833.
On resigning his fellowship in 1806 Elrinton was presented by his college to the rectory of Ardtrea, in the diocese of Armagh, which he held until December 1811. He resigned, having been appointed to the provostship of Trinity College. During his tenure in this office, he was the acting manager of almost every public board, and a supporter of charitable institutions.
Elrington was advanced on 25 September 1820 to the bishopric of Limerick, and on 21 December 1822, he was translated to Leighlin and Ferns. While on his way to attend Parliament duties in London he died of paralysis at Liverpool on 12 July 1835. He was buried under the chapel of Trinity College Dublin, in which there was a monument with a Latin inscription to his memory. Another monument was erected by his clergy in the cathedral church of Ferns. Elrington was an active member of the Royal Irish Academy, and of other literary and scientific societies. The Elrington theological essay prize was instituted in Trinity College in 1837.
A portrait of the bishop was painted in 1820 for his brother, Major Elrington, by Thomas Foster; engraved by William Ward, it was published in 1836 by Graves & Co. There was a marble bust in the library of Trinity College.
Elrington was a highly intelligent man, but contemporaries found him inflexible, rigid and narrow-minded. Students, while praising him for his learning, found him personally obnoxious.
Works
His works are:
'Refutation of the Arg |
https://en.wikipedia.org/wiki/Topology%20%28chemistry%29 | In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for explaining how the atoms ethereal wave functions must fit together. Molecular topology is a part of mathematical chemistry dealing with the algebraic description of chemical compounds so allowing a unique and easy characterization of them.
Topology is insensitive to the details of a scalar field, and can often be determined using simplified calculations. Scalar fields such as electron density, Madelung field, covalent field and the electrostatic potential can be used to model topology.
Each scalar field has its own distinctive topology and each provides different information about the nature of chemical bonding and structure. The analysis of these topologies, when combined with simple electrostatic theory and a few empirical observations, leads to a quantitative model of localized chemical bonding. In the process, the analysis provides insights into the nature of chemical bonding.
Applied topology explains how large molecules reach their final shapes and how biological molecules achieve their activity.
Circuit topology is a topological property of folded linear polymers. It describes the arrangement of intra-chain contacts. Contacts can be established by intra-chain interactions, the so called hard contacts (h-contacts), or via chain entanglement or soft contacts (s-contacts). This notion has been applied to structural analysis of biomolecules such as proteins, RNAs, and genome.
Topological indices
It is possible to set up equations correlating direct quantitative structure activity relationships with experimental properties, usually referred to as topological indices (TIs). Topological indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.
See also
Circuit topology
Theoretical chemistry
Molecular geometry
Molecular graph
References
Francl, Michelle; Stretching topology Nature Chemistry 1, 334–335 (2009)
Rouvray, D. H.; A rationale for the topological approach to chemistry; Journal of Molecular Structure: THEOCHEM Volume 336, Issues 2–3, 30 June 1995, pages 101–114
Molecular geometry
Supramolecular chemistry
Topology
Cheminformatics
Mathematical chemistry |
https://en.wikipedia.org/wiki/Denise%20Lievesley | Denise Anne Lievesley is a British social statistician. She has formerly been Chief Executive of the English Information Centre for Health and Social Care, Director of Statistics at UNESCO, in which capacity she founded the UNESCO Institute for Statistics, and Director (1991–1997) of what is now the UK Data Archive (known as the ESRC Data Archive and as the Data Archive during her tenure).
While Director of the Data Archive, Lievesley held the position of Professor of Research Methods at the University of Essex. She has served as a United Nations Special Adviser on Statistics, stationed in Addis Ababa.
She served as president of the Royal Statistical Society from 1999 to 2001, and has been President of the International Statistical Institute (2007–2009) and the International Association for Official Statistics (1995–1997). She was appointed Commander of the Order of the British Empire (CBE) in the 2014 Birthday Honours for services to social science.
From 2015 to 2020 she was Principal of Green Templeton College, Oxford.
She is an Honorary Fellow of St Edmund's College, Cambridge.
References
British statisticians
Living people
Academics of the University of Essex
Academics of King's College London
Presidents of the International Statistical Institute
Presidents of the Royal Statistical Society
Place of birth missing (living people)
Year of birth missing (living people)
Commanders of the Order of the British Empire
Fellows of the Academy of Social Sciences
Fellows of the American Statistical Association
Women statisticians
Principals of Green Templeton College, Oxford
Women academic administrators |
https://en.wikipedia.org/wiki/Bochner%E2%80%93Martinelli%20formula | In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by and .
History
Bochner–Martinelli kernel
For , in the Bochner–Martinelli kernel is a differential form in of bidegree defined by
(where the term is omitted).
Suppose that is a continuously differentiable function on the closure of a domain in n with piecewise smooth boundary . Then the Bochner–Martinelli formula states that if is in the domain then
In particular if is holomorphic the second term vanishes, so
See also
Bergman–Weil formula
Notes
References
.
.
.
.
.
.
, (ebook).
. The first paper where the now called Bochner-Martinelli formula is introduced and proved.
. Available at the SEALS Portal . In this paper Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula.
. The notes form a course, published by the Accademia Nazionale dei Lincei, held by Martinelli during his stay at the Accademia as "Professore Linceo".
. In this article, Martinelli gives another form to the Martinelli–Bochner formula.
Theorems in complex analysis
Several complex variables |
https://en.wikipedia.org/wiki/Antti%20M%C3%A4kil%C3%A4 | Antti Mäkilä is a Finnish retired ice hockey forward.
Career statistics
References
External links
1989 births
Living people
Porin Ässät (men's ice hockey) players
Finnish ice hockey forwards
KooKoo players
Lempäälän Kisa players
Oulun Kärpät players
Ice hockey people from Pori |
https://en.wikipedia.org/wiki/Tapio%20Sammalkangas | Tapio Sammalkangas (born March 16, 1980) is a Finnish former professional ice hockey defenceman.
Career statistics
External links
Living people
Porin Ässät (men's ice hockey) players
Ilves players
Tappara players
Fresno Falcons players
AaB Ishockey players
1980 births
Finnish ice hockey defencemen
Ice hockey people from Tampere |
https://en.wikipedia.org/wiki/Mikko%20Kurvinen | Mikko Kurvinen (born March 11, 1979) is a Finnish professional ice hockey defenceman. He currently plays for HIFK of the Finnish Liiga.
Career statistics
References
External links
1979 births
Living people
Finnish ice hockey defencemen
FoPS players
HIFK (ice hockey) players
Kiekko-Vantaa players
Modo Hockey players
Mora IK players |
https://en.wikipedia.org/wiki/Tommi%20Kovanen | Tommi Kovanen (born July 15, 1975) is a Finnish former professional ice hockey defenceman.
Career statistics
References
External links
1975 births
Living people
People from Pieksämäki
SHC Fassa players
Finnish ice hockey defencemen
HC Fribourg-Gottéron players
HIFK (ice hockey) players
Jokerit players
JYP Jyväskylä players
KalPa players
KooKoo players
Lukko players
Mikkelin Jukurit players
Lahti Pelicans players
Tappara players
Ice hockey people from South Savo |
https://en.wikipedia.org/wiki/Miikka%20M%C3%A4nnikk%C3%B6 | Miikka Männikkö (born March 27, 1979) is a Finnish professional ice hockey forward who currently plays for Tappara of the SM-liiga.
Career statistics
References
External links
1979 births
Living people
Finnish expatriate ice hockey people in Austria
Finnish ice hockey right wingers
Espoo Blues players
Graz 99ers players
HPK players
Ice hockey people from Tampere
Ilves players
JYP Jyväskylä players
KOOVEE players
Lahti Pelicans players
Lempäälän Kisa players
Mikkelin Jukurit players
Nyköpings Hockey players
Tappara players
Vaasan Sport players
Växjö Lakers players
Finnish expatriate ice hockey people in Sweden |
https://en.wikipedia.org/wiki/Jukka%20Laamanen | Jukka Laamanen (born October 4, 1976) is a Finnish professional ice hockey player who currently plays for HPK in the SM-liiga.
Career statistics
References
External links
Living people
1976 births
Finnish ice hockey defencemen
Porin Ässät (men's ice hockey) players
HPK players
Mikkelin Jukurit players
Oulun Kärpät players
SaPKo players
Tappara players
Ice hockey people from Savonlinna |
https://en.wikipedia.org/wiki/Formally%20%C3%A9tale%20morphism | In commutative algebra and algebraic geometry, a morphism is called formally étale if it has a lifting property that is analogous to being a local diffeomorphism.
Formally étale homomorphisms of rings
Let A be a topological ring, and let B be a topological A-algebra. Then B is formally étale if for all discrete A-algebras C, all nilpotent ideals J of C, and all continuous A-homomorphisms , there exists a unique continuous A-algebra map such that , where is the canonical projection.
Formally étale is equivalent to formally smooth plus formally unramified.
Formally étale morphisms of schemes
Since the structure sheaf of a scheme naturally carries only the discrete topology, the notion of formally étale for schemes is analogous to formally étale for the discrete topology for rings. That is, a morphism of schemes is formally étale if for every affine Y-scheme Z, every nilpotent sheaf of ideals J on Z with be the closed immersion determined by J, and every Y-morphism , there exists a unique Y-morphism such that .
It is equivalent to let Z be any Y-scheme and let J be a locally nilpotent sheaf of ideals on Z.
Properties
Open immersions are formally étale.
The property of being formally étale is preserved under composites, base change, and fibered products.
If and are morphisms of schemes, g is formally unramified, and gf is formally étale, then f is formally étale. In particular, if g is formally étale, then f is formally étale if and only if gf is.
The property of being formally étale is local on the source and target.
The property of being formally étale can be checked on stalks. One can show that a morphism of rings is formally étale if and only if for every prime Q of B, the induced map is formally étale. Consequently, f is formally étale if and only if for every prime Q of B, the map is formally étale, where .
Examples
Localizations are formally étale.
Finite separable field extensions are formally étale. More generally, any (commutative) flat separable A-algebra B is formally étale.
See also
Formally unramified
Formally smooth
Étale morphism
Notes
References
Morphisms of schemes |
https://en.wikipedia.org/wiki/Hollis%20Chair | Hollis Chair may refer to:
Hollis Chair of Divinity, a chair established at Harvard College
Hollis Chair of Mathematics and Natural Philosophy, a chair established at Harvard College |
https://en.wikipedia.org/wiki/1991%20S%C3%A3o%20Paulo%20FC%20season | The 1991 season was São Paulo's 62nd season since club's existence.
Statistics
Scorers
Transfers
July
Overall
{|class="wikitable"
|-
|Games played || 69 (23 Campeonato Brasileiro, 34 Campeonato Paulista, 12 Friendly match)
|-
|Games won || 37 (12 Campeonato Brasileiro, 21 Campeonato Paulista, 4 Friendly match)
|-
|Games drawn || 24 (7 Campeonato Brasileiro, 12 Campeonato Paulista, 5 Friendly match)
|-
|Games lost || 8 (4 Campeonato Brasileiro, 1 Campeonato Paulista, 3 Friendly match)
|-
|Goals scored || 109
|-
|Goals conceded || 55
|-
|Goal difference || +54
|-
|Best result || 5–0 (A) v Catanduvense - Campeonato Paulista - 1991.09.185–0 (H) v São José - Campeonato Paulista - 1991.10.12
|-
|Worst result || 1–4 (H) v Internacional - Campeonato Paulista - 1991.10.09
|-
|Top scorer || Raí (28)
|-
Friendlies
Troféo Naranja
Troféo Ciutat de Barcelona
Official competitions
Campeonato Brasileiro
League table
Matches
Semifinals
Finals
Final standings
Record
Campeonato Paulista
League table
Matches
Second stage
Matches
Finals
Record
External links
official website
Sao Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Truncus%20%28mathematics%29 | In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points (x,y) satisfying an equation of the form
where a, b, and c are given constants. The two asymptotes of a truncus are parallel to the coordinate axes. The basic truncus y = 1 / x2 has asymptotes at x = 0 and y = 0, and every other truncus can be obtained from this one through a combination of translations and dilations.
For the general truncus form above, the constant a dilates the graph by a factor of a from the x-axis; that is, the graph is stretched vertically when a > 1 and compressed vertically when 0 < a < 1. When a < 0 the graph is reflected in the x-axis as well as being stretched vertically. The constant b translates the graph horizontally left b units when b > 0, or right when b < 0. The constant c translates the graph vertically up c units when c > 0 or down when c < 0.
The asymptotes of a truncus are found at x = -b (for the vertical asymptote) and y = c (for the horizontal asymptote).
This function is more commonly known as a reciprocal squared function, particularly the basic example .
See also
Rational functions
Multiplicative inverse
References
Curves |
https://en.wikipedia.org/wiki/Distortion%20problem | In functional analysis, a branch of mathematics, the distortion problem is to determine by how much one can distort the unit sphere in a given Banach space using an equivalent norm. Specifically, a Banach space X is called λ-distortable if there exists an equivalent norm |x| on X such that, for all infinite-dimensional subspaces Y in X,
(see distortion (mathematics)). Note that every Banach space is trivially 1-distortable. A Banach space is called distortable if it is λ-distortable for some λ > 1 and it is called arbitrarily distortable if it is λ-distortable for any λ. Distortability first emerged as an important property of Banach spaces in the 1960s, where it was studied by and .
James proved that c0 and ℓ1 are not distortable. Milman showed that if X is a Banach space that does not contain an isomorphic copy of c0 or ℓp for some (see sequence space), then some infinite-dimensional subspace of X is distortable. So the distortion problem is now primarily of interest on the spaces ℓp, all of which are separable and uniform convex, for .
In separable and uniform convex spaces, distortability is easily seen to be equivalent to the ostensibly more general question of whether or not every real-valued Lipschitz function ƒ defined on the sphere in X stabilizes on the sphere of an infinite dimensional subspace, i.e., whether there is a real number a ∈ R so that for every δ > 0 there is an infinite dimensional subspace Y of X, so that |a − ƒ(y)| < δ, for all y ∈ Y, with ||y|| = 1. But it follows from the result of that on ℓ1 there are Lipschitz functions which do not stabilize, although this space is not distortable by . In a separable Hilbert space, the distortion problem is equivalent to the question of whether there exist subsets of the unit sphere separated by a positive distance and yet intersect every infinite-dimensional closed subspace. Unlike many properties of Banach spaces, the distortion problem seems to be as difficult on Hilbert spaces as on other Banach spaces. On a separable Hilbert space, and for the other ℓp-spaces, 1 < p < ∞, the distortion problem was solved affirmatively by , who showed that ℓ2 is arbitrarily distortable, using the first known arbitrarily distortable space constructed by
.
See also
Tsirelson space
Banach space
References
.
.
.
.
.
.
Functional analysis |
https://en.wikipedia.org/wiki/Scott%20King%20%28ice%20hockey%2C%20born%201977%29 | Scott King (born January 21, 1977) is a Canadian former professional ice hockey player who last played for Lausitzer Füchse in the DEL2 league.
Career statistics
Awards and honours
ECHL Most Valuable Player (2000–01)
ECHL Leading Scorer (2000–01)
Participated in 2009 Spengler Cup (with Adler Mannheim)
External links
1977 births
Living people
Adler Mannheim players
Augsburger Panther players
Boston University Terriers men's ice hockey players
Charlotte Checkers (1993–2010) players
EC Bad Tölz players
Fredericton Canadiens players
Hannover Scorpions players
Iserlohn Roosters players
Kelowna Rockets players
Krefeld Pinguine players
Lausitzer Füchse players
Milwaukee Admirals players
Mississippi Sea Wolves players
New Orleans Brass players
Nürnberg Ice Tigers players
Ice hockey people from Saskatoon
Springfield Falcons players
Canadian expatriate ice hockey players in Germany
Canadian ice hockey centres |
https://en.wikipedia.org/wiki/Vampyrius | {
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Vampyrius vampyrus is a medium-sized species of flying frogs endemic to Vietnam. It is found in southern Vietnam, and is not known to be found in other places globally. It Is in the kingdom Animalia, phylum Chordata, and class Amphibia. Along with this, it is in the order Anura, family Rhacophoridae, and it is the only member of the genus Vampyrus. It is also known as the vampire tree frog or the vampire flying frog because of the presence of a pair of fang-like hooks in the mouth of the tadpoles.
It is found in montane evergreen forests at 1470–2004 m. The frog is adapted to arboreal living with webbings of feet that allow it to glide between trees. These webbed feet give the name "flying" to the common name vampire flying frog, as the frog glides between trees it appears to be flying.
Rhacophorus vampyrus and Vampyrius vampyrus are used interchangeably between academic articles.
Taxonomy
The first specimen was discovered in 2008 by Jodi Rowley of the Australian Museum at Sydney, Australia, and her student Le Thi Thuy Duong from Ho Chi Minh City University of Science. After collecting more specimens in 2009 and 2010, her team described the new species as Rhacophorus vampyrus in the journal Zootaxa in 2010. In 2012, the species was classified as Rhacophorus calcaneus due to the morphology of adult frogs; however, in 2014 the species was reclassified as R. vampyrus through phylogenic research. In 2021, a phylogenetic study found the species to fall far outside Rhacophorus, and instead be the sister genus to Gracixalus; for this reason, it was reclassified into the new genus Vampyrius. This classification is accepted by Amphibian Species of the World, but has not been followed by AmphibiaWeb. This disagreement among scientists contributes to why this article uses Rhacophor |
https://en.wikipedia.org/wiki/System%20of%20Integrated%20Environmental%20and%20Economic%20Accounting | System of Environmental-Economic Accounting (SEEA) is a framework to compile statistics linking environmental statistics to economic statistics. SEEA is described as a satellite system to the United Nations System of National Accounts (SNA). This means that the definitions, guidelines and practical approaches of the SNA are applied to the SEEA. This system enables environmental statistics to be compared to economic statistics as the system boundaries are the same after some processing of the input statistics. By analysing statistics on the economy and the environment at the same time it is possible to show different patterns of sustainability for production and consumption. It can also show the economic consequences of maintaining a certain environmental standard.
Scope
The SEEA is a satellite system of the SNA that consists of several sets of accounts. In broad terms, the area can be described as enabling any user of statistics to compare environmental issues to general economics, knowing that the comparisons are based on the same entities, for example, pollution levels caused by a producing industry can be linked to the specific economics of that industry.
The different areas of SEEA can be briefly described as follows:
Flows of materials and energy
By this is meant flows of materials and energy through the economy, e.g., fuels, natural resources and chemicals, together with their emissions, may it be air emissions, water pollution or waste to which these flows give rise. Data on emissions, above all to the air, have been published for many countries, in particular, European countries following SEEA. The main difference between traditional emissions statistics and emissions in environmental accounts are related to the system boundaries. For example, the inventories produced for the reporting of air emissions to the United Nations Framework Convention on Climate Change (UNFCCC) are based on the geographic borders of a country while the air emission accounts following SEEA use the boundary of a specific economy (this is the "residence principle" of the national accounts). This difference is mainly shown in transport emissions as all emissions caused by an economy are included in SEEA. For example, emissions from trucks, ships or airplanes are allocated to their country of origin, even if the emissions occur outside of the borders of this country. Moreover, in the UNFCCC inventories, "transport" is a specific sector of its own and it is not possible to know the share of households and of different industries in the transport emissions.
Other statistics that have been developed with relation to flows of material are economy-wide material flow accounts and still being developed are energy flow- and water flow accounts.
Environmental economic statistics
Economic variables that are already included in the national accounts but are of obvious environmental interest, such as investments and expenditure in the area of environmental protection, env |
https://en.wikipedia.org/wiki/Bergman%E2%80%93Weil%20formula | In mathematics, the Bergman–Weil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by and .
Weil domains
A Weil domain is an analytic polyhedron with a domain U in Cn defined by inequalities fj(z) < 1
for functions fj that are holomorphic on some neighborhood of the closure of U, such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2n − 1, and the intersections of k faces have codimension at least k.
See also
Andreotti–Norguet formula
Bochner–Martinelli formula
References
.
.
Theorems in complex analysis
Several complex variables |
https://en.wikipedia.org/wiki/1992%20S%C3%A3o%20Paulo%20FC%20season | The 1992 season was São Paulo's 63rd season since club's existence.
Statistics
Scorers
Managers performance
Overall
{|class="wikitable"
|-
|Games played || 84 (25 Campeonato Brasileiro, 14 Copa Libertadores, 34 Campeonato Paulista, 4 Supercopa Sudamericana, 1 Intercontinental Cup, 6 Friendly match)
|-
|Games won || 45 (10 Campeonato Brasileiro, 8 Copa Libertadores, 21 Campeonato Paulista, 1 Supercopa Sudamericana, 1 Intercontinental Cup, 4 Friendly match)
|-
|Games drawn || 21 (7 Campeonato Brasileiro, 3 Copa Libertadores, 9 Campeonato Paulista, 1 Supercopa Sudamericana, 0 Intercontinental Cup, 1 Friendly match)
|-
|Games lost || 18 (8 Campeonato Brasileiro, 3 Copa Libertadores, 4 Campeonato Paulista, 2 Supercopa Sudamericana, 0 Intercontinental Cup, 1 Friendly match)
|-
|Goals scored || 133
|-
|Goals conceded || 73
|-
|Goal difference || +60
|-
|Best result || 6–0 (H) v Noroeste - Campeonato Paulista - 1992.10.15
|-
|Worst result || 0–4 (H) v Palmeiras - Campeonato Brasileiro - 1992.03.08
|-
|Top scorer || Raí (31)
|-
Friendlies
Trofeo Teresa Herrera
Trofeo Ramón de Carranza
Trofeo Ciudad de Barcelona
Trofeo Villa de Madrid
Official competitions
Campeonato Brasileiro
League table
Matches
Second stage
Matches
Record
Copa Libertadores
First stage
Eightfinals
Quarterfinals
Semifinals
Finals
Record
Campeonato Paulista
League table
Matches
Second phase
Matches
Finals
Record
Supercopa Sudamericana
Record
Intercontinental Cup
Record
External links
official website
Sao Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Energy%20distance | Energy distance is a statistical distance between probability distributions. If X and Y are independent random vectors in Rd with cumulative distribution functions (cdf) F and G respectively, then the energy distance between the distributions F and G is defined to be the square root of
where (X, X', Y, Y') are independent, the cdf of X and X' is F, the cdf of Y and Y' is G, is the expected value, and || . || denotes the length of a vector. Energy distance satisfies all axioms of a metric thus energy distance characterizes the equality of distributions: D(F,G) = 0 if and only if F = G.
Energy distance for statistical applications was introduced in 1985 by Gábor J. Székely, who proved that for real-valued random variables is exactly twice Harald Cramér's distance:
For a simple proof of this equivalence, see Székely (2002).
In higher dimensions, however, the two distances are different because the energy distance is rotation invariant while Cramér's distance is not. (Notice that Cramér's distance is not the same as the distribution-free Cramér–von Mises criterion.)
Generalization to metric spaces
One can generalize the notion of energy distance to probability distributions on metric spaces. Let be a metric space with its Borel sigma algebra . Let denote the collection of all probability measures on the measurable space . If μ and ν are probability measures in , then the energy-distance of μ and ν can be defined as the square root of
This is not necessarily non-negative, however. If is a strongly negative definite kernel, then is a metric, and conversely. This condition is expressed by saying that has negative type. Negative type is not sufficient for to be a metric; the latter condition is expressed by saying that has strong negative type. In this situation, the energy distance is zero if and only if X and Y are identically distributed. An example of a metric of negative type but not of strong negative type is the plane with the taxicab metric. All Euclidean spaces and even separable Hilbert spaces have strong negative type.
In the literature on kernel methods for machine learning, these generalized notions of energy distance are studied under the name of maximum mean discrepancy. Equivalence of distance based and kernel methods for hypothesis testing is covered by several authors.
Energy statistics
A related statistical concept, the notion of E-statistic or energy-statistic was introduced by Gábor J. Székely in the 1980s when he was giving colloquium lectures in Budapest, Hungary and at MIT, Yale, and Columbia. This concept is based on the notion of Newton’s potential energy. The idea is to consider statistical observations as heavenly bodies governed by a statistical potential energy which is zero only when an underlying statistical null hypothesis is true. Energy statistics are functions of distances between statistical observations.
Energy distance and E-statistic were considered as N-distances and N-statistic in Z |
https://en.wikipedia.org/wiki/Brian%20Casey%20%28ice%20hockey%29 | Brian Casey (born January 10, 1973) is a Canadian former professional ice hockey defenceman who last played for AaB Ishockey in the Metal Ligaen in Denmark.
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https://en.wikipedia.org/wiki/Martin%20G%C3%A1lik | Martin Gálik is a Slovak professional ice hockey player who played with HC Slovan Bratislava in the Slovak Extraliga.
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https://en.wikipedia.org/wiki/Vladim%C3%ADr%20G%C3%BDna | Vladimír Gýna (born 27 September 1975) is a Czech professional ice hockey player who played with HC Slovan Bratislava in the Slovak Extraliga.
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https://en.wikipedia.org/wiki/Jan%20Hor%C3%A1%C4%8Dek | Jan Horáček (born 22 May, 1979) is a Czech former professional ice hockey player who last played with HC Vlasim in the Czech Republic.
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https://en.wikipedia.org/wiki/Dalibor%20Kusovsky | Dalibor Kusovsky is a Slovak professional ice hockey player who played with HC Slovan Bratislava in the Slovak Extraliga.
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https://en.wikipedia.org/wiki/R%C3%B3bert%20Li%C5%A1%C4%8D%C3%A1k | Róbert Liščák (born 4 April 1978) is a Slovak professional ice hockey player who played with HC Slovan Bratislava in the Slovak Extraliga.
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