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https://en.wikipedia.org/wiki/Vladimir%20Markovic | Vladimir Marković is a Professor of Mathematics at University of Oxford. He was previously the John D. MacArthur Professor at the California Institute of Technology (2013–2020) and Sadleirian Professor of Pure Mathematics at the University of Cambridge (2013–2014).
Education
Marković was educated at the University of Belgrade where he was awarded a Bachelor of Science degree in 1995 and a PhD in 1998.
Career and research
Previously, Marković has held positions at the University of Warwick, Stony Brook University and the University of Minnesota. Marković is editor of Proceedings of the London Mathematical Society.
Marković's research interests are in low-dimensional geometry, topology and dynamics and functional and geometric analysis.
Awards and honours
Marković was elected a Fellow of the Royal Society (FRS) in 2014. His nomination reads:
Marković was also awarded the Clay Research Award in 2012, Whitehead Prize and Philip Leverhulme Prize in 2004.
In Fall of 2015 Marković worked as an Institute for Advanced Study member. In 2016 he received a Simons Investigator Award.
References
External links
Caltech: Markovic Elected to Great Britain's Royal Society
Living people
Serbian mathematicians
20th-century American mathematicians
Fellows of the Royal Society
Royal Society Wolfson Research Merit Award holders
Whitehead Prize winners
Clay Research Award recipients
1973 births
Topologists
Simons Investigator
University of Belgrade alumni
Sadleirian Professors of Pure Mathematics
California Institute of Technology faculty
Stony Brook University faculty
Academics of the University of Warwick
University of Minnesota faculty
21st-century American mathematicians |
https://en.wikipedia.org/wiki/Roscio%20Municipality | The Roscio Municipality is one of the 11 municipalities (municipios) that makes up the Venezuelan state of Bolívar and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 21,750. The town of Guasipati is the shire town of the Roscio Municipality.
Demographics
The Roscio Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 23,957 (up from 19,777 in 2000). This amounts to 1.6% of the state's population. The municipality's population density is .
Government
The mayor of the Roscio Municipality is Manuel de Jesús González Marrero, re-elected on October 31, 2004, with 51% of the vote. The municipality is divided into one (two if you count the Capital Roscio section) parishes; Salom.
See also
Guasipati
Bolívar
Municipalities of Venezuela
References
Municipalities of Bolívar (state) |
https://en.wikipedia.org/wiki/Sifontes%20Municipality | The Sifontes Municipality is one of the 11 municipalities (municipios) that makes up the Venezuelan state of Bolívar and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 50,082. The town of Tumeremo was the shire town of the Sifontes Municipality.
Demographics
The Sifontes Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 40,042 (up from 34,277 in 2000). This amounts to 2.6% of the state's population. The municipality's population density is .
Government
The mayor of the Sifontes Municipality is Carlos Chancellor, elected on December 8, 2013, with 50,23% of the vote. He replaced Marlene Vargas shortly after the elections. The municipality is divided into two (three if the Capital Tumeremo section is counted) parishes; Dalla Costa and San Isidro.
History
Its first settlers were Guayan Indians and Kamaracotos, coming from the savanna of the Divina Pastora and Tupuquen located to the left margin of the river Yuruari. They fed on hunting, fishing and agriculture. Tumeremo was founded on January 26, 1788 under the name of "Mission of Our Lady of Bethlehem of Tumeremo" by the Capuchin monks of Catalonia, among them: Fray Mariano de Perafita, Fray Bonaventura de Carrocera and Fray Tomas de Santa Eugenia. Tumeremo means "Painted Snake", in the dialect of the first Indians who inhabited these lands.
During the Campaign of Guayana, General Manuel Piar fights against the realists to seize the missions of the kingdom of Spain. After releasing Tumeremo, the Spanish survivors were imprisoned and sentenced to death. From there, the city was a strategic site and barracks for the patriot soldiers commanded by Simón Bolívar. From 1830 many indigenous and other populations began to emerge around Tumeremo.
In 1894 a group of British settlers who came from the British Guyana tried to take part of the present municipal territory, before which General Domingo Antonio Sifontes founded in March 2nd of the same year the population of El Dorado in which it established a military position, for Then expel the invaders from the area; Since then General Sifontes became a local hero in recognition of the defense of Venezuelan sovereignty. The name of the municipality takes its name in honor to the general Antonio Domingo Sifontes, but the jurisdiction abbreviated its name li
In 2013, 60% of all malaria cases in Venezuela occurred in Sifontes.
Fauna, flora and vegetation
The municipality of Sifontes lies in the Guianan Highlands moist forests ecoregion, and the major habitat type is tropical and subtropical moist broadleaf forests.
Common birds include the Orange-winged Parrot (Amazona amazonica), Painted Parakeet (Pyrrhura picta), White Bellbird (Procnias alba), Helmeted Pygmy-Tyrant (Lophotriccus galeatus), Fiery-shouldered Parakeet (Pyrrhura egregia), Blue-headed Parrot (Pionus menstruus). At least 58 species of du |
https://en.wikipedia.org/wiki/Idles%20%28disambiguation%29 | Idles are a British rock band.
Idles may also refer to:
Idlès, a town and commune in Algeria
The Teen Idles or Idles, an American hardcore punk band
See also
Ideles, in abstract algebra
Idless, a hamlet in England
Idle (disambiguation)
Idols (disambiguation) |
https://en.wikipedia.org/wiki/Prouhet%E2%80%93Tarry%E2%80%93Escott%20problem | In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.
That is, the two multisets should satisfy the equations
for each integer i from 1 to a given k. It has been shown that n must be strictly greater than k. Solutions with are called ideal solutions. Ideal solutions are known for and for . No ideal solution is known for or for .
This problem was named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Edward B. Escott, who studied it in the early 1910s. The problem originates from letters of Christian Goldbach and Leonhard Euler (1750/1751).
Examples
Ideal solutions
An ideal solution for n = 6 is given by the two sets { 0, 5, 6, 16, 17, 22 }
and { 1, 2, 10, 12, 20, 21 }, because:
01 + 51 + 61 + 161 + 171 + 221 = 11 + 21 + 101 + 121 + 201 + 211
02 + 52 + 62 + 162 + 172 + 222 = 12 + 22 + 102 + 122 + 202 + 212
03 + 53 + 63 + 163 + 173 + 223 = 13 + 23 + 103 + 123 + 203 + 213
04 + 54 + 64 + 164 + 174 + 224 = 14 + 24 + 104 + 124 + 204 + 214
05 + 55 + 65 + 165 + 175 + 225 = 15 + 25 + 105 + 125 + 205 + 215.
For n = 12, an ideal solution is given by A = {±22, ±61, ±86, ±127, ±140, ±151} and B = {±35, ±47, ±94, ±121, ±146, ±148}.
Other solutions
Prouhet used the Thue–Morse sequence to construct a solution with for any . Namely, partition the numbers from 0 to into a) the numbers each with an even number of ones in its binary expansion and b) the numbers each with an odd number of ones in its binary expansion; then the two sets of the partition give a solution to the problem. For instance, for and , Prouhet's solution is:
01 + 31 + 51 + 61 + 91 + 101 + 121 + 151 = 11 + 21 + 41 + 71 + 81 + 111 + 131 + 141
02 + 32 + 52 + 62 + 92 + 102 + 122 + 152 = 12 + 22 + 42 + 72 + 82 + 112 + 132 + 142
03 + 33 + 53 + 63 + 93 + 103 + 123 + 153 = 13 + 23 + 43 + 73 + 83 + 113 + 133 + 143.
Generalizations
A higher dimensional version of the Prouhet–Tarry–Escott problem has been introduced and studied by Andreas Alpers and Robert Tijdeman in 2007: Given parameters , find two different multi-sets , of points from such that
for all with This problem is related to discrete tomography and also leads to special Prouhet-Tarry-Escott solutions over the Gaussian integers (though solutions to the Alpers-Tijdeman problem do not exhaust the Gaussian integer solutions to Prouhet-Tarry-Escott).
A solution for and is given, for instance, by:
and
.
No solutions for with are known.
See also
Euler's sum of powers conjecture
Beal's conjecture
Jacobi–Madden equation
Lander, Parkin, and Selfridge conjecture
Taxicab number
Pythagorean quadruple
Sums of powers, a list of related conjectures and theorems
Discrete tomography
Notes
References
Chap.11.
.
External links
Diophantine equations
Mathematical problems |
https://en.wikipedia.org/wiki/Idempotent%20measure | In mathematics, an idempotent measure on a metric group is a probability measure that equals its convolution with itself; in other words, an idempotent measure is an idempotent element in the topological semigroup of probability measures on the given metric group.
Explicitly, given a metric group X and two probability measures μ and ν on X, the convolution μ ∗ ν of μ and ν is the measure given by
for any Borel subset A of X. (The equality of the two integrals follows from Fubini's theorem.) With respect to the topology of weak convergence of measures, the operation of convolution makes the space of probability measures on X into a topological semigroup. Thus, μ is said to be an idempotent measure if μ ∗ μ = μ.
It can be shown that the only idempotent probability measures on a complete, separable metric group are the normalized Haar measures of compact subgroups.
References
(See chapter 3, section 3.)
Group theory
Measures (measure theory)
Metric geometry |
https://en.wikipedia.org/wiki/Perfect%20measure | In mathematics — specifically, in measure theory — a perfect measure (or, more accurately, a perfect measure space) is one that is "well-behaved" in some sense. Intuitively, a perfect measure μ is one for which, if we consider the pushforward measure on the real line R, then every measurable set is "μ-approximately a Borel set". The notion of perfectness is closely related to tightness of measures: indeed, in metric spaces, tight measures are always perfect.
Definition
A measure space (X, Σ, μ) is said to be perfect if, for every Σ-measurable function f : X → R and every A ⊆ R with f−1(A) ∈ Σ, there exist Borel subsets A1 and A2 of R such that
Results concerning perfect measures
If X is any metric space and μ is an inner regular (or tight) measure on X, then (X, BX, μ) is a perfect measure space, where BX denotes the Borel σ-algebra on X.
References
Measures (measure theory) |
https://en.wikipedia.org/wiki/Tell%2C%20Nablus | Tell (), pronounced Till, is a Palestinian town in the Nablus Governorate in northern West Bank, located five kilometers southwest of Nablus. According to the Palestinian Central Bureau of Statistics (PCBS), the town had a population of 5,162 inhabitants in 2017. Most of the town's laborers work in agriculture, with figs and olives being the major source of income.
Mohammad Shtayyeh, a Palestinian economist and politician, was born in Tell.
History
Ceramics from the Byzantine era have been found here.
Ottoman era
In 1517, the village was included in the Ottoman empire with the rest of Palestine, and it appeared in the 1596 tax-records as Till, located in the Nahiya of Jabal Qubal of the Liwa of Nablus. The population was 46 households, all Muslim. They paid a fixed tax rate of 33.3% on agricultural products, such as wheat, barley, summer crops, olive trees, goats and beehives, in addition to occasional revenues, a press for olive oil or grape syrup, and a fixed tax for people of Nablus area; a total of 5,100 akçe.
In 1838, Till was located in the District of Jurat 'Amra, south of Nablus.
In 1863, Victor Guérin found it to have a population of one thousand inhabitants. It was divided into several districts, each administered by a different sheikh. He further noted: "Some houses are large and fairly well built. Around the village grow, in pens, beautiful plantations of fig and pomegranate trees."
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of Jamma'in al-Thani, subordinate to Nablus.
In 1882, the PEF's Survey of Western Palestine described Till as: "A village of moderate size on low ground, with a high mound behind it on the south; it has a well and a few trees, and on the west a pool in winter; the hills to the north are bare and white, but terraced to the very top."
British mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Tel had a population of 567 Muslims, increasing in the 1931 census to 803 Muslims, in 209 houses.
In the 1945 statistics the population was 1,060 Muslims, while the total land area was 13,766 dunams, according to an official land and population survey.
Of this, 1,056 dunams were for plantations and irrigable land, 7,023 for cereals, while 55 dunams were classified as built-up areas.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Tell came under Jordanian rule.
The Jordanian census of 1961 found 1,539 inhabitants.
1967, aftermath
Since the Six-Day War in 1967, Tell has been held under Israeli military occupation.
References
Bibliography
External links
Welcome to Tall
Survey of Western Palestine, Map 11: IAA, Wikimedia commons
Tell, aerial photo, Applied Research Institute–Jerusalem (ARIJ)
Nablus Governorate
Villages in the West Bank
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Fast%20Library%20for%20Number%20Theory | The Fast Library for Number Theory (FLINT) is a C library for number theory applications. The two major areas of functionality currently implemented in FLINT are polynomial arithmetic over the integers and a quadratic sieve. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is released under the GNU General Public License. It is developed by William Hart of the University of Kaiserslautern (formerly University of Warwick) and David Harvey of University of New South Wales (formerly Harvard University) to address the speed limitations of the PARI and NTL libraries.
Design Philosophy
Asymptotically Fast Algorithms
Implementations Fast as or Faster than Alternatives
Written in Pure C
Reliance on GMP
Extensively Tested
Extensively Profiled
Support for Parallel Computation
Functionality
Polynomial Arithmetic over the Integers
Quadratic Sieve
References
Notes
FLINT 1.0.9: Fast Library for Number Theory by William Hart and David Harvey
Video of the talk Parallel Computation in Number Theory (30 January 2007) by William Hart
Video of the talk FLINT and Fast Polynomial Arithmetic (13 June 2007) By David Harvey
Video of the talk A short talk on short division (1 October 2007) by William Hart
Video of the talk Algebraic Number Theory with FLINT (11 November 2007) by William Hart
Computational number theory
Free software programmed in C
Integer factorization algorithms
Numerical software |
https://en.wikipedia.org/wiki/Quaternion%20Society | The Quaternion Society was a scientific society, self-described as an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics". At its peak it consisted of about 60 mathematicians spread throughout the academic world that were experimenting with quaternions and other hypercomplex number systems. The group's guiding light was Alexander Macfarlane who served as its secretary initially, and became president in 1909. The association published a Bibliography in 1904 and a Bulletin (annual report) from 1900 to 1913.
The Bulletin became a review journal for topics in vector analysis and abstract algebra such as the theory of equipollence. The mathematical work reviewed pertained largely to matrices and linear algebra as the methods were in rapid development at the time.
Genesis
In 1895, Professor P. Molenbroek of The Hague, Holland, and Shinkichi Kimura studying at Yale put out a call for scholars to form the society in widely circulated journals: Nature, Science, and the Bulletin of the American Mathematical Society. Giuseppe Peano also announced the society formation in his Rivista di Matematica.
The call to form an Association was encouraged by Macfarlane in 1896:
The logical harmony and unification of the whole of mathematical analysis ought to be kept in view. The algebra of space ought to include the algebra of the plane as a special case, just as the algebra of the plane includes the algebra of the line…When vector analysis is developed and presented...we may expect to see many zealous cultivators, many fruitful applications, and, finally, universal diffusion ... May the movement initiated by Messrs. Molenbroek and Kimura hasten the realization of this happy result.
In 1897 the British Association met in Toronto where vector products were discussed:
Professor Henrici proposed a new notation to denote the different products of vectors, which consists in using square brackets for vector products and round brackets for scalar products. He likewise advocated adoption of Heaviside’s term "ort" for vector, the tensor of which is the number 1. Prof. A. Macfarlane read a communication on the solution of the cubic equation in which he explained how the two binomials in Cardano’s formula may be treated as complex quantities, either circular or hyperbolic, all the roots of the cubic can then be deduced by a general method.
A system of national secretaries was announced in the AMS Bulletin in 1899: Alexander McAulay for Australasia, Victor Schlegel for Germany, Joly for Great Britain and Ireland, Giuseppe Peano for Italy, Kimura for Japan, Aleksandr Kotelnikov for Russia, F. Kraft for Switzerland, and Arthur Stafford Hathaway for the USA. For France the national secretary was Paul Genty, an engineer with the division of Ponts et Chaussees, and a quaternion collaborator with Charles-Ange Laisant, author of Methode des Quaterniones (1881).
Victor Schlegel reported on the new institution in the Monatshefte für M |
https://en.wikipedia.org/wiki/San%20Fernando%20Airport%20%28Argentina%29 | San Fernando Airport () is located southwest of the center of San Fernando, a northwest suburb of Buenos Aires in Argentina. The airport is operated by Aeropuertos Argentina 2000.
Statistics
See also
Transport in Argentina
List of airports in Argentina
References
External links
SkyVector - San Fernando Airport
Airports in Buenos Aires Province |
https://en.wikipedia.org/wiki/Filipinos%20in%20the%20Netherlands | Filipinos in the Netherlands comprise migrants from the Philippines to the Netherlands and their descendants living there. According to Dutch government statistics, 16,719 persons of first or second-generation Philippine background lived in the Netherlands in 2011. Though Filipinos live throughout the country, Amsterdam and Rotterdam are homes to the largest Filipino communities.
Migration history and motivations
The first Filipina to marry and settle came in 1947 to work in a hospital. In the 1960s, a larger number of Filipinos arrived to work in hospitals in Leiden and Utrecht, as well as a clothing factory in Achterhoek. Since then, most Filipinos went to the Netherlands as contract workers, higher-education students, or medical workers. Partly because of the large number of Filipinos living in the Netherlands, in 2009 KLM increased the number of direct flights to Ninoy Aquino International Airport (in Manila) to seven per week, and seven per week amongst other Filipino airports.
Every day, roughly 300–500 Filipino seamen pass through Dutch ports. One-third of the au pairs in the Netherlands (1,500) are Filipinas. In addition, about 500 Filipinos work on oil rigs in the North Sea. More than 80 Filipino students attend Dutch universities pursuing Masters or Doctorate degrees.
Community organisations
The first Filipino organisation in the Netherlands, Philippine Nurses Association of the Academisch Ziekenhuis in Leiden, was created in 1965. After this, other organisations such as the Dutch-Philippine Association and Dutch-Philippine Club were formed. In 1999 there were more than 20 such organisations in the Netherlands.
There are two major Philippine publications in the Netherlands, the Philippine Digest and the Munting Nayon.
Notable people
Paul Mulders, footballer
Jason de Jong, footballer
Jose Maria Sison, Filipino Communist politician in exile in the Netherlands; called a "person supporting terrorism" by the U.S. and the European Union
Laidback Luke, Filipino-Dutch DJ and producer
See also
Netherlands–Philippines relations
References
External links
Federation of Filipino Organizations in the Netherlands
Asian diaspora in the Netherlands
N
Ethnic groups in the Netherlands
Filipino expatriates in the Netherlands |
https://en.wikipedia.org/wiki/Chevalley%E2%80%93Shephard%E2%80%93Todd%20theorem | In mathematics, the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by pseudoreflections. In the case of subgroups of the complex general linear group the theorem was first proved by who gave a case-by-case proof. soon afterwards gave a uniform proof. It has been extended to finite linear groups over an arbitrary field in the non-modular case by Jean-Pierre Serre.
Statement of the theorem
Let V be a finite-dimensional vector space over a field K and let G be a finite subgroup of the general linear group GL(V). An element s of GL(V) is called a pseudoreflection if it fixes a codimension 1 subspace of V and is not the identity transformation I, or equivalently, if the kernel Ker (s − I) has codimension one in V. Assume that the order of G is relatively prime to the characteristic of K (the so-called non-modular case). Then the following properties are equivalent:
(A) The group G is generated by pseudoreflections.
(B) The algebra of invariants K[V]G is a (free) polynomial algebra.
(B) The algebra of invariants K[V]G is a regular ring.
(C) The algebra K[V] is a free module over K[V]G.
(C) The algebra K[V] is a projective module over K[V]G.
In the case when the field K is the field C of complex numbers, the first condition is usually stated as "G is a complex reflection group". Shephard and Todd derived a full classification of such groups.
Examples
Let V be one-dimensional. Then any finite group faithfully acting on V is a subgroup of the multiplicative group of the field K, and hence a cyclic group. It follows that G consists of roots of unity of order dividing n, where n is its order, so G is generated by pseudoreflections. In this case, K[V] = K[x] is the polynomial ring in one variable and the algebra of invariants of G is the subalgebra generated by xn, hence it is a polynomial algebra.
Let V = Kn be the standard n-dimensional vector space and G be the symmetric group Sn acting by permutations of the elements of the standard basis. The symmetric group is generated by transpositions (ij), which act by reflections on V. On the other hand, by the main theorem of symmetric functions, the algebra of invariants is the polynomial algebra generated by the elementary symmetric functions e1, ... en.
Let V = K2 and G be the cyclic group of order 2 acting by ±I. In this case, G is not generated by pseudoreflections, since the nonidentity element s of G acts without fixed points, so that dim Ker (s − I) = 0. On the other hand, the algebra of invariants is the subalgebra of K[V] = K[x, y] generated by the homogeneous elements x2, xy, and y2 of degree 2. This subalgebra is not a polynomial algebra because of the relation x2y2 = (xy)2.
Generalizations
gave an extension of the Chevalley–Shephard–Todd theorem to positive characteristic.
There has been much work on the question o |
https://en.wikipedia.org/wiki/Special%20cases%20of%20Apollonius%27%20problem | In Euclidean geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of zero or infinite radius. The nine types of such limiting cases of Apollonius' problem are to construct the circles tangent to:
three points (denoted PPP, generally 1 solution)
three lines (denoted LLL, generally 4 solutions)
one line and two points (denoted LPP, generally 2 solutions)
two lines and a point (denoted LLP, generally 2 solutions)
one circle and two points (denoted CPP, generally 2 solutions)
one circle, one line, and a point (denoted CLP, generally 4 solutions)
two circles and a point (denoted CCP, generally 4 solutions)
one circle and two lines (denoted CLL, generally 8 solutions)
two circles and a line (denoted CCL, generally 8 solutions)
In a different type of limiting case, the three given geometrical elements may have a special arrangement, such as constructing a circle tangent to two parallel lines and one circle.
Historical introduction
Like most branches of mathematics, Euclidean geometry is concerned with proofs of general truths from a minimum of postulates. For example, a simple proof would show that at least two angles of an isosceles triangle are equal. One important type of proof in Euclidean geometry is to show that a geometrical object can be constructed with a compass and an unmarked straightedge; an object can be constructed if and only if (iff) (something about no higher than square roots are taken). Therefore, it is important to determine whether an object can be constructed with compass and straightedge and, if so, how it may be constructed.
Euclid developed numerous constructions with compass and straightedge. Examples include: regular polygons such as the pentagon and hexagon, a line parallel to another that passes through a given point, etc. Many rose windows in Gothic Cathedrals, as well as some Celtic knots, can be designed using only Euclidean constructions. However, some geometrical constructions are not possible with those tools, including the heptagon and trisecting an angle.
Apollonius contributed many constructions, namely, finding the circles that are tangent to three geometrical elements simultaneously, where the "elements" may be a point, line or circle.
Rules of Euclidean constructions
In Euclidean constructions, five operations are allowed:
Draw a line through two points
Draw a circle through a point with a given center
Find the intersection point of two lines
Find the intersection points of two circles
Find the intersection points of a line and a circle
The initial elements in a geometric construction are called the "givens", such as a given point, a given line or a given circle.
Example 1: Perpendicular bisector
To construct the perpendicular bisector of the line segment between two points requires two circles, each ce |
https://en.wikipedia.org/wiki/Jan%20Kjell%20Larsen | Jan Kjell Larsen (born 24 June 1983) is a Norwegian former football goalkeeper.
Career statistics
References
Player profile on official club website
National caps
1983 births
Living people
Sportspeople from Haugesund
Footballers from Rogaland
People from Karmøy
Men's association football goalkeepers
Norwegian men's footballers
Norway men's under-21 international footballers
FK Haugesund players
Molde FK players
Stabæk Fotball players
Norwegian First Division players
Eliteserien players |
https://en.wikipedia.org/wiki/Bejuma%20Municipality | The Bejuma Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 48,538. The town of Bejuma is the shire town of the Bejuma Municipality.
Demographics
The Bejuma Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 45,306 (up from 39,945 in 2000). This amounts to 2% of the state's population. The municipality's population density is .
Government
The mayor of the Bejuma Municipality is Lorenzo Remedios, re-elected on November 23, 2008, with 46% of the vote. The municipality is divided into three parishes; Bejuma, Canoabo, and Simón Bolívar.
Vegetation and natural resources
The municipality of Bejuma lies in the Cordillera La Costa Montane Forests ecoregion, and the major habitat type is tropical and subtropical moist broadleaf forests.
See also
Bejuma
Carabobo
Municipalities of Venezuela
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Libertador%20Municipality%2C%20Carabobo | The Libertador Municipality is one of the 14 municipalities (municipios) that makes up Carabobo State of Venezuela and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 166,166. The town of Tocuyito is the shire town of the Libertador Municipality. The municipality is one of a number in Venezuela named "Libertador Municipality", in honour of Venezuelan independence hero Simón Bolívar.
Demographics
The Libertador Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 175,255 (up from 149,721 in 2000). This amounts to 7.9% of the state's population The municipality's population density is .
Government
The mayor of the Libertador Municipality is Carmen Alvarez, elected on November 23, 2008, with 49% of the vote She replaced Argenis Isaias Loreto Puerta shortly after the elections. The municipality is divided into two parishes; Tocuyito and Independencia.
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Samir%20Aliyev | Samir Aliyev (, born 14 April 1979) is a retired Azerbaijani footballer. Aliyev made 34 appearances for the Azerbaijan national football team, scoring four goals.
National team statistics
International goals
Honours
FC Kapaz
Azerbaijan Premier League: 1998–99
Personal
Azerbaijan Player of the Year: 2002
References
External links
affa.az
1979 births
Living people
People from Tashir
Azerbaijani men's footballers
Azerbaijan men's international footballers
Azerbaijani expatriate men's footballers
Azerbaijani football managers
Men's association football forwards
FC Elista players
Khazar Lankaran FK players
FC Volyn Lutsk players
Ukrainian Premier League players
Expatriate men's footballers in Ukraine
Azerbaijani expatriate sportspeople in Ukraine
MOIK Baku players
Neftçi PFK players
Expatriate men's footballers in Russia |
https://en.wikipedia.org/wiki/Diego%20Ibarra%20Municipality | The Diego Ibarra Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 104,536. The town of Mariara is the shire town of the Diego Ibarra Municipality.
Demographics
The Diego Ibarra Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 110,131 (up from 96,983 in 2000). This amounts to 4.9% of the state's population. The municipality's population density is .
Government
The mayor of the Diego Ibarra Municipality is Roger Martinez, elected on November 23, 2008, with 50% of the vote. He replaced Rafael Ruiz Manrique shortly after the elections. The municipality is divided into two parishes; Aguas Calientes and Mariara.
See also
Municipalities of Venezuela
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/L%C3%BCroth%27s%20theorem | In mathematics, Lüroth's theorem asserts that every field that lies between a field K and the rational function field K(X) must be generated as an extension of K by a single element of K(X). This result is named after Jacob Lüroth, who proved it in 1876.
Statement
Let be a field and be an intermediate field between and , for some indeterminate X. Then there exists a rational function such that . In other words, every
intermediate extension between and is a simple extension.
Proofs
The proof of Lüroth's theorem can be derived easily from the theory of rational curves, using the geometric genus.
This method is non-elementary, but several short proofs using only the basics of field theory have long been known, mainly using the concept of transcendence degree.
Many of these simple proofs use Gauss's lemma on primitive polynomials as a main step.
References
Algebraic varieties
Birational geometry
Field (mathematics)
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Guacara%20Municipality | The Guacara Municipality is one of the fourteen municipalities (municipios) that make up the Venezuelan state of Carabobo. according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 176,218. The town of Guacara is the shire town of the Guacara Municipality.
Demographics
The Guacara Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 171,123 (up from 145,132 in 2000). This amounts to 7.7% of the state's population. The municipality's population density is .
Government
The mayor of the Guacara Municipality is Jhoan Castañeda. He replaced Jose Manuel Flores Salazar shortly after the elections. The municipality is divided into three parishes; Ciudad Alianza, Guacara, and Yagua.
See also
Guacara
Carabobo
Municipalities of Venezuela
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Juan%20Jos%C3%A9%20Mora%20Municipality | The Juan José Mora Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 69,236. The town of Morón is the shire town of the Juan José Mora Municipality.
Demographics
The Juan José Mora Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 65,239 (up from 57,701 in 2000). This amounts to 2.9% of the state's population. The municipality's population density is .
Government
The mayor of the Juan José Mora Municipality is Matson Caldera, elected on November 23, 2008, with 52% of the vote. He replaced José Gregorio Frías shortly after the elections. The municipality is divided into two parishes; Morón and Urama.
See also
Morón
Carabobo
Municipalities of Venezuela
References
External links
juanjosemora-carabobo.gob.ve
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Los%20Guayos%20Municipality | The Los Guayos Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 149,646. The town of Los Guayos is the shire town of the Los Guayos Municipality.
History
On February 20, 1694, Don Francisco Berroterán, governor of the Province of Venezuela, declared Los Guayos "Town of Indians". The area was belonged to the Guayos tribe. On June 6, 1710, the priest Mariano de Martí made "Los Guayos" a parish. In 1751, inhabitants of Los Guayos joined the national uprising led by Francisco de León against the Compañía Guipuzcoana. In 1812, Francisco de Miranda left a troop in the town of Los Guayos to defend the road against the Spanish troops while he followed his campaign in the Valencia region. The troop engaged in a battle with the Spanish troops and was about to win the battle when one of its officers turned to the enemy. The troop then dispersed itself.
Geography
The town of Los Guayos is part of the Los Guayos municipality. It has now almost merged with other towns in the area. The Caracas-Valencia motorway lies immediately to the North-Northeast of Los Guayos. The Los Guayos river runs from the northeast to the southeast part of the town.
Sites of Interest
The Colonial church of San Antonio de Padua or Church of Los Guayos: This is one of the oldest churches in Venezuela. Its first building dates back to 1650, when it was the church for the tibes of the area. The bell tower, with two adjacent areas, dates back to 1779.
Demographics
The Los Guayos Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 157,787 (up from 133,237 in 2000). This amounts to 7.1% of the state's population. The municipality's population density is .
Government
The mayor of the Los Guayos Municipality is Anibal Jose Dose Rumbos, re-elected on November 23, 2008 with 52% of the vote. The municipality is divided into one parish (Los Guayos).
See also
Los Guayos
Carabobo
Municipalities of Venezuela
References
External links
losguayos-carabobo.gov.ve
Municipalities of Carabobo
nl:Los Guayos
pt:Los Guayos
sv:Los Guayos |
https://en.wikipedia.org/wiki/Montalb%C3%A1n%20Municipality | The Montalbán Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 24,908. The town of Montalbán is the shire town of the Montalbán Municipality.
Demographics
The Montalbán Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 23,712 (up from 20,559 in 2000). This amounts to 1.1% of the state's population. The municipality's population density is .
Government
The mayor of the Montalbán Municipality is Luis Sánchez, elected on November 23, 2008, with 44% of the vote. He replaced Tulio Salvatierra Salazar shortly after the elections. The municipality is divided into one parish (Montalbán).
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Miranda%20Municipality%2C%20Carabobo | Miranda is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 29,092. The town of Miranda is the shire town of the Miranda Municipality.
Name
The municipality is one of several in Venezuela named Miranda Municipality for independence hero Francisco de Miranda.
Demographics
The Miranda Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 27,609 (up from 23,869 in 2000). This amounts to 1.2% of the state's population. The municipality's population density is .
Government
The mayor of the Miranda Municipality is Eduardo A. Sequera. He replaced Fernando Jimenez shortly after the last municipal elections. The municipality is divided into one parish (Miranda).
References
External links
miranda-carabobo.gob.ve
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Naguanagua%20Municipality | The Naguanagua () municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 157,437. The town of Naguanagua is the shire town of the Naguanagua Municipality. It forms part of the greater Valencia Metropolitan Area in Venezuela. It is in the valley of the Cabriales River at the base of Cerro El Café and the El Trigal Mountain. Valencia and Naguanagua form a continuous urban area. The highway that runs from the centre of Valencia towards Puerto Cabello passes through this community; Bolivar Avenue in Valencia becomes University Avenue in Naguanagua on the northern side of a traffic roundabout, or redoma.
Demographics
The Naguanagua County, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 143,315 (up from 134,728 in 2000). This amounts to 6.4% of the state's population. The municipality's population density is .
Government
The mayor of the Naguanagua County is Alejandro Feo la Cruz, elected on November 23, 2008 with 45% of the vote. He replaced Julio Castillo shortly after the elections. The municipality is divided into one parish (Naguanagua).
History
Naguanagua was founded as a parish district between Valencia and Puerto Cabello. The name of the district/municipio (similar to a county) is Naguanagua, and the main city in the district is Naguanagua. The map at top right shows the municipio in red and the other municipios of Carabobo in gray. Naguanagua was founded as a curacy on 14 May 1782 by the Bishop of Caracas Don Mariano Martí. The name Naguanagua means "Abundance of Waters".
Tourism and places of interest
Downtown Naguanagua features the Parochial Church of Naguanagua, the Parochial House and Bolívar Square. Near the Carabobo Hospital is the Spaniards Road (Camino de Los Españoles), Colonial Way at the San Esteban National Park (Parque Nacional San Esteban), where one can to go down to San Esteban town near to Puerto Cabello. Also, you can visit La Entrada, a village near Naguanagua where there is the Atanasio Girardot Monument.
Between the Sport Square are the "Don Bosco Field" (Campo Don Bosco) in the downtown, the "Simón Bolívar Bicentennial Sport Complex" in La Granja, the "Patinodrome of Capremco" and the "University City Sport Complex" in the Campus Bárbula. Naguanagua has the largest shopping centres Carabobo State including Sambil Centre in Ciudad Jardín Mañongo, La Granja Shopping Centre, Cristal Naguanagua Centre in Las Quintas III Stage and Vía Veneto Shopping Center in Ciudad Jardín Mañongo.
Other places include the offices of El Carabobeño newspaper on University Avenue, Los Guayabitos Park, the Botanical Garden of Naguanagua (Salvador Feo La Cruz Avenue), Paseo La Granja Park (Venezuela Avenue), Liberty Park or the Peace Park (Liberty Corner, 10th Street Avenue of Las Quintas, La |
https://en.wikipedia.org/wiki/San%20Diego%20Municipality%2C%20Carabobo | The San Diego Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 93,257. The town of San Diego is the municipal seat of the San Diego Municipality.
Geography
The San Diego river, coming from the Northern mountains, crosses the city in its way to the Valencia Lake.
Places of interest
San Diego's church is a well-preserved colonial church.
The area around the San Diego church, around the Bolívar Square, also keep the traditional architecture.
Economy
The city was the centre of an agricultural region. It has grown very rapidly in recent years. Many of the areas previously used for agriculture have been taken over by further urbanizations. Now the service industry has overtaken agriculture as the area's main source of income.
Demographics
The San Diego Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 74,941 (up from 60,330 in 2000). This amounts to 3.4% of the state's population. The municipality's population density is .
Government
In San Diego there is the mayor's office of the Municipality of San Diego located in C.C. San Diego popularly known as Fin de Siglo. First Mayor of San Diego José Gregorio Ruiz. (1995-2004) (2 periods) main parties that supported him: AD, SEGUIMOS.
The current mayor is León Jurado (ConEnzo), democratically elected with 49.05% [3] The previous mayor, Vicencio Scarano (2004-2014), was dismissed from his position for failing to comply with a ruling of the Supreme Court of Justice, in the who was asked to lift the barricades made during the demonstrations in the municipality in 2014. Elections were held on May 25, 2014 to restore him (with his wife Rosa De Scarano as the winner with 88%).
Education
Universidad José Antonio Paez (University)
Universidad Arturo Michelena (University)
Instituto Tecnológico de Seguridad Industrial (College)
Colegio Universitario Monseñor de Talavera (College)
Unidad Educativa Monseñor Luis Eduardo Henríquez.
Unidad Educativa Colegio Joseph Lancaster.
Unidad Educativa Colegio Las Californias.
Unidad Educativa Hipolito Cisneros.
Unidad Educativa Colegio Patria Bolivariana.
Unidad Educativa Olga Bayone.
References
External links
sandiego-carabobo.gob.ve
Official page of the Mayor of San Diego
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/San%20Joaqu%C3%ADn%20Municipality%2C%20Carabobo | The San Joaquín Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 64,124. The town of San Joaquín is the municipal seat of the San Joaquín Municipality.
Location
It borders Aragua State to the north, the Lake Valencia to the south, the Diego Ibarra Municipality to the east, and the Guacara Municipality to the west.
Demographics
The San Joaquín Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 60,953 (up from 48,946 in 2000). This amounts to 2.7% of the state's population. The municipality's population density is .
Government
The mayor of the San Joaquín Municipality is Luis Aguiar, elected on November 23, 2008, with 55% of the vote. He replaced César Emilio Hernández Meza shortly after the elections. The municipality is divided into one parish (San Joaquín).
Tradition
The municipality is well known for its local biscuits, the "panelas of San Joaquín".
See also
San Joaquín
Carabobo
Municipalities of Venezuela
References
Municipalities of Carabobo |
https://en.wikipedia.org/wiki/Valencia%20Municipality%2C%20Carabobo | The Valencia Municipality is one of the 14 municipalities (municipios) that makes up the Venezuelan state of Carabobo and, according to the 2011 census by the National Institute of Statistics of Venezuela, the municipality has a population of 829,856. The city of Valencia is the shire town of the Valencia Municipality.
History
The city of Valencia has been an active participant of Venezuela's history. Valencia was founded by Captain Alonso Díaz Moreno on March 25, 1555 — as the locals are proud of reminding visitors, eight years before Caracas. It was the first Spanish settlement in central Venezuela and its official name was Nuestra Señora de la Asunción de Nueva Valencia del Rey. The infamous conquistador Lope de Aguirre besieged the city in 1561. In 1677 it was raided by French pirates, who burnt down its City Hall, thus destroying many very important documents about the early settlement of Venezuela. The German scientist Alexander von Humboldt visited the city on his trip through the Americas. He reported that at the time of his visit the city had around 6000 to 7000 inhabitants. On June 24, 1821, the Battle of Carabobo was fought on the outskirts of the city, sealing the Independence of Venezuela from imperial Spanish rule.
Media
The main newspaper servicing Valencia is "The Carabobian" or "Diario El Carabobeño" . In May 2007, many universities in Venezuela, including within Valencia, held demonstrations protesting the non-renewal of the broadcast license of Venezuelan Television station, Radio Caracas Televisión (RCTV). RCTV has been at odds with Venezuelan president Hugo Chávez.
Sites of interest
Art centers
Ateneo de Valencia
Teatro Municipal de Valencia
Museums
Casa Páez
Casa de los Celis, settlement of the Museum of Art and History and the Lisandro Alvarado Foundation.
Museum of History and Anthropology
Iturriza Palace, or Quinta Isabela, Museum of the city (Museo de la Ciudad).
Parks and points of interest
Negra Hipólita Park or Fernand Peñalver Park
Metropolitan Park (Parque Metropolitano)
Valencia's Aquarium (Acuario de Valencia) (ranks as largest aquarium in Latin America)
Plaza Monumental de Valencia, second largest bullring in the world.
Demographics
The Valencia Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, has a population of 830,420 (up from 756,605 in 2000). This amounts to 37.3% of the state's population. The municipality's population density is .
Government
The mayor of the Valencia Municipality is Edgardo Parra, elected on November 23, 2008 with 38% of the vote. He replaced Francisco Cabrera Santos shortly after the elections. The municipality is divided into nine parishes:
Candelaria
Catedral
El Socorro
Miguel Peña Parish
Rafael Urdaneta
San Blas
San José
Santa Rosa
Negro Primero
Transportation
The city is well connected with the rest of the country by a network of highways and roads well maintained by INVIAL.
A modern metro syst |
https://en.wikipedia.org/wiki/Interval%20chromatic%20number%20of%20an%20ordered%20graph | In mathematics, the interval chromatic number X<(H) of an ordered graph H is the minimum number of intervals the (linearly ordered) vertex set of H can be partitioned into so that no two vertices belonging to the same interval are adjacent in H.
Difference with chromatic number
It is interesting about interval chromatic number that it is easily computable. Indeed, by a simple greedy algorithm one can efficiently find an optimal partition of the vertex set of H into X<(H) independent intervals. This is in sharp contrast with the fact that even the approximation of the usual chromatic number of graph is an NP hard task.
Let K(H) is the chromatic number of any ordered graph H. Then for any ordered graph H,
X<(H) ≥ K(H).
One thing to be noted, for a particular graph H and its isomorphic graphs the chromatic number is same, but the interval chromatic number may differ. Actually it depends upon the ordering of the vertex set.
References
Graph coloring |
https://en.wikipedia.org/wiki/Rationalisation%20%28mathematics%29 | In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.
If the denominator is a monomial in some radical, say with , rationalisation consists of multiplying the numerator and the denominator by and replacing by (this is allowed, as, by definition, a th root of is a number that has as its th power). If , one writes with (Euclidean division), and then one proceeds as above by multiplying by
If the denominator is linear in some square root, say rationalisation consists of multiplying the numerator and the denominator by and expanding the product in the denominator.
This technique may be extended to any algebraic denominator, by multiplying the numerator and the denominator by all algebraic conjugates of the denominator, and expanding the new denominator into the norm of the old denominator. However, except in special cases, the resulting fractions may have huge numerators and denominators, and, therefore, the technique is generally used only in the above elementary cases.
Rationalisation of a monomial square root and cube root
For the fundamental technique, the numerator and denominator must be multiplied by the same factor.
Example 1:
To rationalise this kind of expression, bring in the factor :
The square root disappears from the denominator, because by definition of a square root:
which is the result of the rationalisation.
Example 2:
To rationalise this radical, bring in the factor :
The cube root disappears from the denominator, because it is cubed; so
which is the result of the rationalisation.
Dealing with more square roots
For a denominator that is:
Rationalisation can be achieved by multiplying by the conjugate:
and applying the difference of two squares identity, which here will yield −1. To get this result, the entire fraction should be multiplied by
This technique works much more generally. It can easily be adapted to remove one square root at a time, i.e. to rationalise
by multiplication by
Example:
The fraction must be multiplied by a quotient containing .
Now, we can proceed to remove the square roots in the denominator:
Example 2:
This process also works with complex numbers with
The fraction must be multiplied by a quotient containing .
Generalizations
Rationalisation can be extended to all algebraic numbers and algebraic functions (as an application of norm forms). For example, to rationalise a cube root, two linear factors involving cube roots of unity should be used, or equivalently a quadratic factor.
References
This material is carried in classic algebra texts. For example:
George Chrystal, Introduction to Algebra: For the Use of Secondary Schools and Technical Colleges is a nineteenth-century text, first edition 1889, in print (); a trinomial example with square roots is on p. 256, while a general theory of rationalising factors for surds is on pp. 189–199.
Elementary algebra
Fract |
https://en.wikipedia.org/wiki/Liberia%20Institute%20of%20Statistics%20and%20Geo-Information%20Services | The Liberia Institute of Statistics and Geo-Information Services (LISGIS) is an agency of the Liberian government. It organized a census in March 2008, 24 years after the last one.
References
External links
Official website
Government of Liberia
National statistical services |
https://en.wikipedia.org/wiki/NESSUS%20Probabilistic%20Analysis%20Software | NESSUS is a general-purpose, probabilistic analysis program that simulates variations and uncertainties in loads, geometry, material behavior and other user-defined inputs to compute probability of failure and probabilistic sensitivity measures of engineered systems. Because NESSUS uses highly efficient and accurate probabilistic analysis methods, probabilistic solutions can be obtained even for extremely large and complex models. The system performance can be hierarchically decomposed into multiple smaller models and/or analytical equations. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety critical and one-of-a-kind systems, and to maintain a level of quality while reducing manufacturing costs for larger quantity products.
NESSUS is interfaced to all major commercial finite element programs and includes capabilities for analyzing computationally intensive real-world problems. It has been successfully applied to a diverse range of problems in aerospace, gas turbine engines, biomechanics, pipelines, defense, weaponry and infrastructure.
Project history
NESSUS was originally developed by a team led by Southwest Research Institute (SwRI) as part of a 10-year NASA project to develop a probabilistic design tool for the Space Shuttle main engine.
In 1999, SwRI was contracted by Los Alamos National Laboratory (LANL) to adapt NESSUS for application to extremely large and complex weapon reliability problems in support of its Stockpile Stewardship program.
In 2002, SwRI was contracted by the NASA Glenn Research Center to further enhance NESSUS for application to large-scale, aero-propulsion system problems.
The end result of these two large programs was a completely redesigned software tool — NESSUS Version 8.2 — that includes
a graphical user interface, three-dimensional probability contouring and results visualization, capabilities for performing advanced design of experiments and sensitivity analysis, a probabilistic input database, and interfaces to many new third-party codes such as ABAQUS, ANSYS, LS-DYNA, MSC.NASTRAN and ParaDyn.
Applications
NESSUS can compute the probabilistic response or reliability of virtually any engineered system where mathematical models can be developed to describe the performance of the system. NESSUS has been applied to a diverse range of problems including aerospace structures, automotive structures, biomechanics, gas turbine engines, geomechanics, nuclear waste packaging, offshore structures, pipelines and rotordynamics.
Recent specific applications of NESSUS include:
Aircraft Control Lever Fatigue
Automotive Crankshaft High-Cycle Fatigue
Cervical Spine Impact Injury
Tunnel Vulnerability Assessment
Orthopaedic Implant Cement Loosening
Stochastic Crashworthiness in Head-on Impact
Nuclear Weapon System Verification and Validation
Pipeline Reliability Assessment
Space Shuttle Main Engine Flow Line
See also
Fast |
https://en.wikipedia.org/wiki/Lefschetz%20duality | In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by , at the same time introducing relative homology, for application to the Lefschetz fixed-point theorem. There are now numerous formulations of Lefschetz duality or Poincaré–Lefschetz duality, or Alexander–Lefschetz duality.
Formulations
Let M be an orientable compact manifold of dimension n, with boundary , and let be the fundamental class of the manifold M. Then cap product with z (or its dual class in cohomology) induces a pairing of the (co)homology groups of M and the relative (co)homology of the pair . Furthermore, this gives rise to isomorphisms of with , and of with for all .
Here can in fact be empty, so Poincaré duality appears as a special case of Lefschetz duality.
There is a version for triples. Let decompose into subspaces A and B, themselves compact orientable manifolds with common boundary Z, which is the intersection of A and B. Then, for each , there is an isomorphism
Notes
References
Duality theories
Manifolds |
https://en.wikipedia.org/wiki/Daniel%20Sobralense | Daniel Lopes da Silva (born 10 February 1983), known as Daniel Sobralense, is a Brazilian footballer who plays for Campinense as an attacking midfielder.
Career statistics
Honours
Club
Fortaleza
Campeonato Cearense: 2004, 2007, 2016
Parnahyba
Campeonato Piauiense: 2006
Kalmar FF
Allsvenskan: 2008
Svenska Supercupen: 2009
IFK Göteborg
Svenska Cupen: 2012–13
Paysandu
Campeonato Paraense: 2017
References
External links
(archive)
1983 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Allsvenskan players
Guarany Sporting Club players
Fortaleza Esporte Clube players
Parnahyba Sport Club players
Associação Desportiva Recreativa e Cultural Icasa players
Clube Náutico Capibaribe players
Kalmar FF players
IFK Göteborg players
Örebro SK players
Paysandu Sport Club players
Santa Cruz Futebol Clube players
Campinense Clube players
Men's association football midfielders
Expatriate men's footballers in Sweden
Brazilian expatriate sportspeople in Sweden
People from Sobral, Ceará
Footballers from Ceará |
https://en.wikipedia.org/wiki/Aurelio%20Baldor | Aurelio Ángel Baldor de la Vega (October 22, 1906, Havana, Cuba – April 2, 1978, Miami) was a Cuban mathematician, educator and lawyer. Baldor is the author of a secondary school algebra textbook, titled Álgebra, used throughout the Spanish-speaking world and published for the first time in 1941.
He was the youngest child of Daniel and Gertrudis Baldor. He was the founder and director of the Baldor School in the exclusive Vedado section of Havana. In its heyday, the school had 3,500 students and used 23 buses to provide transportation to its students. In 1959, with the arrival of Fidel Castro's communist regime, Aurelio Baldor and his family began experiencing some problems. Raúl Castro had intended to arrest Baldor, but Camilo Cienfuegos—one of Fidel Castro's own top commanders—prevented the arrest, as he highly admired and respected Baldor for his accomplishments as an educator.
After the death of Camilo Cienfuegos approximately one month later in an airplane which disappeared over the sea, Baldor and his family left Cuba and were exiled in Mexico for a short time, and then they migrated to New Orleans, Louisiana. Afterward, they moved on to New York (Brooklyn) and New Jersey, where Baldor continued teaching at Saint Peter's College in Jersey City. He also taught daily classes in mathematics at the now defunct Stevens Academy, in Hoboken, New Jersey.
He spent much time writing mathematical theorems and exercises. Once a tall and imposing man weighing 100 kg (220 lbs), Baldor slowly began losing weight as his health declined. He died from pulmonary emphysema in Miami, FL, on April 2, 1978. His seven children, grandchildren and great-grandchildren still reside in Miami. Other family include Francisco Baldor, Maria Cristina Baldor and Aurelio Baldor's second cousin Teresita Baldor.
Baldor's algebra textbook Álgebra (With Graphics and 6,523 exercises and answers) published by Compañía Cultural Editora y Distribuidora de Textos Americanos, S. A. continues being used to this day in secondary schools throughout Latin America.
References
Cuban emigrants to the United States
Saint Peter's University faculty
1906 births
20th-century Cuban mathematicians
1978 deaths |
https://en.wikipedia.org/wiki/Abacus%20school | Abacus school is a term applied to any Italian school or tutorial after the 13th century, whose commerce-directed curriculum placed special emphasis on mathematics, such as algebra, among other subjects. These schools sprang up after the publication of Fibonacci's Book of the Abacus and his introduction of the Hindu–Arabic numeral system. In Fibonacci's viewpoint, this system, originating in India around 400 BCE, and later adopted by the Arabs, was simpler and more practical than using the existing Roman numeric tradition. Italian merchants and traders quickly adopted the structure as a means of producing accountants, clerks, and so on, and subsequently abacus schools for students were established. These were done in many ways: communes could appeal to patrons to support the institution and find masters; religious institutions could finance and oversee the curriculum; independent masters could teach pupils. Unless they were selected for teaching occupations that were salaried, most masters taught students who could pay as this was their main source of income.
The words abacus or abaco refers to calculations, especially the subject of direct calculations, and does not imply the use of an abacus.
Significance
Abacus schools were significant for a couple of reasons:
Firstly, because mathematics was associated with many professions, including trade, there was an increasing need to do away with the old Roman numeral system which produced too many errors. The number of Roman characters a merchant needed to memorize to carry out financial transactions as opposed to Hindu-numerals made the switch practical. Commercialists were first introduced to this new system through Leonardo Fibonacci, who came from a business family and had studied Arabic math. Being convinced of its uses, abacus schools were therefore created and dominated by wealthy merchants, with some exceptions. Sons could now be trained by the best and brightest teachers to take over their family business and the fortunate poor had more access to a variety of vocations. Morality also played a role in determining the school attendance of commoners.
Secondly, reading, writing, and some elementary math as job requirements for general occupations meant that literacy levels rose with the number of ordinary students attending institutions or being tutored at home. Sailors, for example, who wished to climb the social ladder had to present literacy and arithmetic skills on their résumé. Aspiring abbaco masters themselves need have studied only elementary, or secondary abbaco in order to teach others.
School system
Italian abacus school systems differed more in their establishment than in their curriculum during the Middle Ages. For example, institutions and appointed educators were set up in a number of ways, either through commune patronage or independent masters' personal funds. Some abbaco teachers tutored privately in homes. All instructors, however, were contractually bound to their agreem |
https://en.wikipedia.org/wiki/List%20of%20Aberdeen%20F.C.%20records%20and%20statistics | Aberdeen Football Club are a Scottish professional association football club based in Aberdeen. They have played at their home ground, Pittodrie, since the club's formation in 1903. Aberdeen joined the Scottish Football League in 1904, and the Scottish Premier League in 1998 as well as the Scottish Professional Football League in 2013.
The club's record appearance maker is Willie Miller, who made 796 appearances between 1972 and 1990. Joe Harper is the club's record goalscorer, scoring 199 goals in major competitions during his two spells at Aberdeen.
This list encompasses the major honours won by Aberdeen, records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Aberdeen players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at Pittodrie are also included in the list.
Honours
Aberdeen's first trophy was the Southern League Cup in 1946, which was won after a 3-2 win against Rangers. Their first national trophy win was the Scottish Cup in 1947. Aberdeen's first Scottish League Cup victory came in 1955.
In 1983, Aberdeen won two European trophies, the European Cup Winners' Cup and the European Super Cup. The 1980s was Aberdeen's most successful in terms of trophies won, with three league championships, four Scottish Cups and two Scottish League Cups added to the two European trophies. Aberdeen's most recent trophy win was in 2014, when they defeated Inverness Caledonian Thistle in the Scottish League Cup final.
National
League
Scottish Top Tier: (4)
Scottish First Division – 1954–55
Scottish Premier Division – 1979–80, 1983–84, 1984–85
Runners-up (17): 1910–11, 1936–37, 1955–56, 1970–71, 1971–72, 1977–78, 1980–81, 1981–82, 1988–89, 1989–90, 1990–91, 1992–93, 1993–94, 2014–15, 2015–16, 2016–17, 2017–18
Scottish Cup
Winners: (7)
1946–47, 1969–70, 1981–82, 1982–83, 1983–84, 1985–86, 1989–90
Runners-up (9): 1936–37, 1952–53, 1953–54, 1958–59, 1966–67, 1977–78, 1992–93, 1999–00, 2016–17
Scottish League Cup
Winners: (6)
1955–56, 1976–77, 1985–86, 1989–90, 1995–96, 2013–14
Runners-up (9): 1946–47, 1978–79, 1979–80, 1987–88, 1988–89, 1992–93, 1999–00, 2016–17, 2018–19
European
UEFA Cup Winners' Cup: 1
1982–83
Semi-final: 1983–84
UEFA Super Cup: 1
1983
Regional
Aberdeenshire Cup (36): 1903–04, 1904–05, 1906–07, 1907–08, 1908–09, 1909–10, 1911–12, 1912–13, 1913–14, 1914–15, 1919–20, 1920–21, 1921–22, 1922–23, 1923–24, 1924–25, 1925–26, 1926–27, 1927–28, 1928–29, 1929–30, 1930–31, 1931–32, 1932–33, 1933–34, 1980–81, 1981–82, 1982–83, 1987–88, 1989–90, 1990–91, 1992–93, 1997–98, 2002–03, 2003–04, 2004–05
Aberdeenshire and District League (7): 1919–20, 1920–21, 1925–26, 1926–27, 1927–28, 1928–29, 1947–48
Dewar Shield (17): 1906–07, 1908–09, 1912–13, 1914–15, 1926–27, 1928–29, 1930–31, 1931–32, 1932– |
https://en.wikipedia.org/wiki/2005%20Djurg%C3%A5rdens%20IF%20season | Djurgården will in the 2005 season compete in the Allsvenskan, Svenska Cupen and UEFA Cup
Squad information
Squad
Player statistics
Appearances for competitive matches only.
|}
Goals
Total
Allsvenskan
Svenska Cupen
Royal League
Competitions
Overall
Allsvenskan
League table
Results summary
Matches
Svenska Cupen
2nd round
3rd round
4th round
Quarter-finals
Semi-finals
Final
UEFA Cup
UEFA Cup 1st round
2004–05 Royal League
1st group stage
2005–06 Royal League
Group stage
The tournament continued in the 2006 season.
Friendlies
Djurgårdens IF Fotboll seasons
Djurgarden
Swedish football championship-winning seasons |
https://en.wikipedia.org/wiki/History%20of%20group%20theory | The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early researchers in the field of group theory.
Early 19th century
The earliest study of groups as such probably goes back to the work of Lagrange in the late 18th century. However, this work was somewhat isolated, and 1846 publications of Augustin Louis Cauchy and Galois are more commonly referred to as the beginning of group theory. The theory did not develop in a vacuum, and so three important threads in its pre-history are developed here.
Development of permutation groups
One foundational root of group theory was the quest of solutions of polynomial equations of degree higher than 4.
An early source occurs in the problem of forming an equation of degree m having as its roots m of the roots of a given equation of degree . For simple cases, the problem goes back to Johann van Waveren Hudde (1659). Nicholas Saunderson (1740) noted that the determination of the quadratic factors of a biquadratic expression necessarily leads to a sextic equation, and Thomas Le Seur (1703–1770) (1748) and Edward Waring (1762 to 1782) still further elaborated the idea. Waring proved the fundamental theorem of symmetric polynomials, and specially considered the relation between the roots of a quartic equation and its resolvent cubic.
Lagrange's goal (1770, 1771) was to understand why equations of third and fourth degree admit formulas for solutions, and a key object was the group of permutations of the roots. On this was built the theory of substitutions. He discovered that the roots of all Lagrange resolvents (résolvantes, réduites) which he examined are rational functions of the roots of the respective equations. To study the properties of these functions, he invented a Calcul des Combinaisons. The contemporary work of Alexandre-Théophile Vandermonde (1770) developed the theory of symmetric functions and solution of cyclotomic polynomials. Leopold Kronecker has been quoted as saying that a new boom in algebra began with Vandermonde's first paper. Similarly Cauchy gave credit to both Lagrange and Vandermonde for studying symmetric functions and permutations of variables.
Paolo Ruffini (1799) attempted a proof of the impossibility of solving the quintic and higher equations. Ruffini was the first person to explore ideas in the theory of permutation groups such as the order of an element of a group, conjugacy, and the cycle decomposition of elements of permutation groups. Ruffini distinguished what are now called intransitive and transitive, and imprimitive and primitive groups, and (1801) uses the group of an equation under the name l'assieme delle permutazioni. He also published a letter from Pietro Abbati to himself, in which the group idea is prominent |
https://en.wikipedia.org/wiki/Nahia%20%28given%20name%29 |
Etymology
Nahia is a Basque female name meaning "aspiration" / "wish" / "desire".
Pronunciation
Nahia
Usage
The Basque Statistics Office cited it as the 5th most popular given name for baby girls born in the Basque Country between 2010 and 2012.
Outside the Basque Country, specially in Spain, the name of Naia is a more frequent given name and while, in Spanish they are pronounced similarly, they have different etymologies; Naia has instead a Greek mythological origin.
Other forms
Variants of Nahia are:
Nahikari
Gure
Since it is pronounced similarly, Naia is sometimes considered as a variant of Nahia when one prefers to consider its origin as Greek rather than Basque.
Notes
Given names |
https://en.wikipedia.org/wiki/Microsoft%20Math%20Solver | Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool. Until 2015, it ran on Microsoft Windows. Since then, it has been developed for the web platform and mobile devices.
Microsoft Math was originally released as a bundled part of Microsoft Student. It was then available as a standalone paid version starting with version 3.0. For version 4.0, it was released as a free downloadable product and was called Microsoft Mathematics 4.0. It is no longer in active development and has been removed from the Microsoft website. A related freeware add-in, called "Microsoft Mathematics Add-In for Word and OneNote," is also available from Microsoft and offers comparable functionality (Word 2007 or higher is required).
Microsoft Math received the 2008 Award of Excellence from Tech & Learning Magazine.
Features
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Versions
Microsoft Math 1.0: Part of Microsoft Student 2006
Microsoft Math 2.0: Part of Microsoft Student 2007
Microsoft Math 3.0: Standalone commercial product that requires product activation; includes calculus support, digital ink recognition features and a special display mode for video projectors
Encarta Calculator: Lite version of Microsoft Math 3.0; part of Microsoft Student 2008
Microsoft Mathematics 4.0 (removed): The first freeware version, released in 32-bit and 64-bit editions in January 2011; features a ribbon GUI
Microsoft Math for Windows Phone (removed): A branded mobile application for Windows Phone released in 2015 specifically for South African and Tanzanian students; also known as Nokia Mobile-Mathematics or Nokia Momaths
Microsoft Math in Bing app – Math helper as a feature within the Bing mobile app on iOS and Android platforms, released in August 2018
Microsoft Math Solver – Mobile app for iOS (first released in November 2019) and Android (first released in December 2019), as well as a Microsoft Edge extension. Recognizes handwritten math. Provides a detailed step-by-step explanation, interactive graphs, relevant online video lectures, and practice problems. A web version is available on .
System requirements
The system requirements for Microsoft Mathematics 4.0 are:
See also
Grapher
Maple (software)
Symbolab
Wolfram Mathematica
WolframAlpha
References
External links
Download details: Microsoft Mathematics Add-In for Word and OneNote
Educational math software
Science education software
Mathematical software
Math Solver
Nokia services
Freeware |
https://en.wikipedia.org/wiki/Cheeger%20constant | In Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h(M) defined in terms of the minimal area of a hypersurface that divides M into two disjoint pieces. In 1970, Jeff Cheeger proved an inequality that related the first nontrivial eigenvalue of the Laplace–Beltrami operator on M to h(M). This proved to be a very influential idea in Riemannian geometry and global analysis and inspired an analogous theory for graphs.
Definition
Let M be an n-dimensional closed Riemannian manifold. Let V(A) denote the volume of an n-dimensional submanifold A and S(E) denote the n−1-dimensional volume of a submanifold E (commonly called "area" in this context). The Cheeger isoperimetric constant of M is defined to be
where the infimum is taken over all smooth n−1-dimensional submanifolds E of M which divide it into two disjoint submanifolds A and B. The isoperimetric constant may be defined more generally for noncompact Riemannian manifolds of finite volume.
Cheeger's inequality
The Cheeger constant h(M) and the smallest positive eigenvalue of the Laplacian on M, are related by the following fundamental inequality proved by Jeff Cheeger:
This inequality is optimal in the following sense: for any h > 0, natural number k and ε > 0, there exists a two-dimensional Riemannian manifold M with the isoperimetric constant h(M) = h and such that the kth eigenvalue of the Laplacian is within ε from the Cheeger bound.
Buser's inequality
Peter Buser proved an upper bound for in terms of the isoperimetric constant h(M). Let M be an n-dimensional closed Riemannian manifold whose Ricci curvature is bounded below by −(n−1)a2, where a ≥ 0. Then
See also
Cheeger constant (graph theory)
Isoperimetric problem
Spectral gap
References
Riemannian geometry |
https://en.wikipedia.org/wiki/Goat%20grazing%20problem | The goat grazing problem is either of two related problems in recreational mathematics involving a tethered goat grazing a circular area: the interior grazing problem and the exterior grazing problem. The former involves grazing the interior of a circular area, and the latter, grazing an exterior of a circular area. For the exterior problem, the constraint that the rope can not enter the circular area dictates that the grazing area forms an involute. If the goat were instead tethered to a post on the edge of a circular path of pavement that did not obstruct the goat (rather than a fence or a silo), the interior and exterior problem would be complements of a simple circular area.
The original problem was the exterior grazing problem and appeared in the 1748 edition of the English annual journal The Ladies' Diary: or, the Woman's Almanack, designated as Question attributed to Upnorensis (an unknown historical figure), stated thus:
Observing a horse tied to feed in a gentlemen’s park, with one end of a rope to his fore foot, and the other end to one of the circular iron rails, enclosing a pond, the circumference of which rails being 160 yards, equal to the length of the rope, what quantity of ground at most, could the horse feed?
The related problem involving area in the interior of a circle without reference to barnyard animals first appeared in 1894 in the first edition of the renown journal American Mathematical Monthly. Attributed to Charles E. Myers, it was stated as:
A circle containing one acre is cut by another whose center is on the circumference of the given circle, and the area common to both is one-half acre. Find the radius of the cutting circle.
The solutions in both cases are non-trivial but yield to straightforward application of trigonometry, analytical geometry or integral calculus. Both problems are intrinsically transcendental – they do not have closed-form analytical solutions in the Euclidean plane. The numerical answers must be obtained by an iterative approximation procedure. The goat problems do not yield any new mathematical insights; rather they are primarily exercises in how to artfully deconstruct problems in order to facilitate solution.
Three-dimensional analogues and planar boundary/area problems on other shapes, including the obvious rectangular barn and/or field, have been proposed and solved. A generalized solution for any smooth convex curve like an ellipse, and even unclosed curves, has been formulated.
Exterior grazing problem
The question about the grazable area outside a circle is considered. This concerns a situation where the animal is tethered to a silo. The complication here is that the grazing area overlaps around the silo (i.e., in general, the tether is longer than one half the circumference of the silo): the goat can only eat the grass once, he can't eat it twice. The answer to the problem as proposed was given in the 1749 issue of the magazine by a Mr. Heath, and stated as 76,257.86 sq.yds. whic |
https://en.wikipedia.org/wiki/2002%20Djurg%C3%A5rdens%20IF%20season | In the 2002 season, Djurgårdens IF competed in the Allsvenskan, the Svenska Cupen, and the UEFA Cup.
Squad information
Squad
Player statistics
Appearances for competitive matches only
|}
Topscorers
Total
Allsvenskan
Svenska Cupen
UEFA Cup
Competitions
Overall
Allsvenskan
League table
Matches
Svenska Cupen
UEFA Cup
|}
Friendlies
References
Djurgarden
Djurgårdens IF Fotboll seasons
Swedish football championship-winning seasons |
https://en.wikipedia.org/wiki/Vica | José Luis Mauro (born 10 March 1961 in Araraquara), commonly known as Vica, is a Brazilian football manager and former player who played as a central defender.
Club career statistics
Honours
Player
Fluminense
Campeonato Carioca: 1984, 1985
Campeonato Brasileiro Série A: 1984
Coritiba
Campeonato Paranaense: 1989
Manager
Rio Branco-PR
Campeonato Paranaense Série Prata: 1995
Goiás
Copa Centro-Oeste: 2000
ASA
Campeonato Alagoano: 2009, 2011
Copa Alagoas: 2015
Santa Cruz
Campeonato Brasileiro Série C: 2013
External links
1961 births
Living people
Sportspeople from Araraquara
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série A players
Associação Ferroviária de Esportes players
Joinville Esporte Clube players
Fluminense FC players
Coritiba Foot Ball Club players
Comercial Futebol Clube (Ribeirão Preto) players
Club Athletico Paranaense players
Paraná Clube players
São José Esporte Clube players
Itumbiara Esporte Clube players
Rio Branco Sport Club players
Brazilian football managers
Campeonato Brasileiro Série B managers
Campeonato Brasileiro Série C managers
Rio Branco Sport Club managers
Itumbiara Esporte Clube managers
Associação Atlética Anapolina managers
Associação Desportiva São Caetano managers
Nacional Futebol Clube managers
Atlético Clube Goianiense managers
América Futebol Clube (SP) managers
Goiás Esporte Clube managers
Esporte Clube Santo André managers
Associação Atlética Internacional (Limeira) managers
Clube Recreativo e Atlético Catalano managers
Anápolis Futebol Clube managers
Rio Preto Esporte Clube managers
Londrina Esporte Clube managers
Grêmio Esportivo Catanduvense managers
Associação Atlética Caldense managers
Nacional Fast Clube managers
Agremiação Sportiva Arapiraquense managers
Fortaleza Esporte Clube managers
Treze Futebol Clube managers
Santa Cruz Futebol Clube managers
Paysandu Sport Club managers
Ríver Atlético Clube managers
Esporte Clube XV de Novembro (Piracicaba) managers
Botafogo Futebol Clube (SP) managers
Associação Portuguesa de Desportos managers
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Crispin%20Nash-Williams | Crispin St John Alvah Nash-Williams FRSE (19 December 1932 – 20 January 2001) was a British mathematician. His research interest was in the field of discrete mathematics, especially graph theory.
Biography
Nash-Williams was born on 19 December 1932 in Cardiff, Wales. His father, Victor Erle Nash-Williams ( Williams), was an archaeologist at University College Cardiff, and his mother had studied classics at Oxford. As a small boy, Nash-Williams attended Christ Church Cathedral School in Oxford, which was then headed by Wilfrid Oldaker. A biographer has said that Oldaker was a formative influence on Nash-Williams.
After studying mathematics at the University of Cambridge, earning the title of Senior Wrangler in 1953, he remained at Cambridge for his graduate studies, under the supervision of Shaun Wylie and David Rees. He then continued his education for a year at Princeton University, with Norman Steenrod; all three of Wylie, Rees, and Steenrod are listed as the supervisors of his Ph.D. dissertation. He finished his dissertation in 1958, but before doing so he returned to Britain as an assistant lecturer at the University of Aberdeen.
He remained in Aberdeen for ten years, during which time he was twice promoted. In 1967 he moved to the University of Waterloo and became one of the three faculty members in the newly formed Department of Combinatorics and Optimization there. In 1972, he returned to Aberdeen as Professor of Pure Mathematics, but stayed only briefly, moving to the University of Reading in 1975. There he succeeded Richard Rado, who had earlier been one of his dissertation examiners.
He retired in 1996 and died on 20 January 2001, aged 68, in Ascot, Berkshire, where his brother was rector.
Awards and honours
He was elected to the Royal Society of Edinburgh in 1969. In 1994, the University of Waterloo gave him an honorary doctorate for his contributions to combinatorics. A conference in his honor was held on his retirement in 1996, the proceedings of which were published as a festschrift. The 18th British Combinatorial Conference, held in Sussex in July 2001, was dedicated to his memory.
Contributions
He is known for the Nash-Williams theorem.
Hilton writes that "Themes running through his papers are Hamiltonian cycles, Eulerian graphs, spanning trees, the marriage problem, detachments, reconstruction, and infinite graphs."
In his first papers Nash-Williams considered the knight's tour and random walk problems on infinite graphs; the latter paper included an important recurrence criterion for general Markov chains, and was also the first to apply electrical network techniques of Rayleigh to random walks. His dissertation, which he finished in 1958, concerned generalizations of Euler tours to infinite graphs.
Welsh writes that his subsequent work defining and characterizing the arboricity of graphs (discovered in parallel and independently by W. T. Tutte) has "had a huge impact," in part because of its implications in matroid |
https://en.wikipedia.org/wiki/Quincunx%20matrix | In mathematics, the matrix
is sometimes called the quincunx matrix. It is a 2×2 Hadamard matrix, and its rows form the basis of a diagonal square lattice consisting of the integer points whose coordinates both have the same parity; this lattice is a two-dimensional analogue of the three-dimensional body-centered cubic lattice.
See also
Quincunx
Notes
Matrices |
https://en.wikipedia.org/wiki/School%20of%20Mathematics%20and%20Naval%20Construction | The Central School of Mathematics and Naval Construction was a short-lived shipbuilding college at Portsmouth Dockyard on the south coast of England. It was founded in 1848 but only lasted five years, until 1853. The first Principal was Joseph Woolley, who in 1864 would found the Royal School of Naval Architecture and Marine Engineering in South Kensington that became part of the Royal Naval College, Greenwich in 1873.
Building
The school was sited in the dockyard at Portsea, Portsmouth in the building formerly used by the School of Naval Architecture (1816–1832), facing the Commissioner’s house and Old Naval Academy. It is long by wide and high, to a design by Edward/Edmund Hall. Construction began in 1815 and was completed in 1817. The building has since seen use as a residence, Port Admirals Office, Tactical School, War College, NATO and Naval HQ and C in C Western Fleet Offices.
Education
The School of Mathematics and Naval Construction was intended as a finishing school for a select number of shipwright apprentices, to prepare them as officers in the dockyards. They were sent to the school for the final three years of their seven-year apprenticeship, to be taught mathematics by Wooley and shipbuilding by the master shipwright of the dockyard. Unusually, they were also taught chemistry in a laboratory created at the back of the school for the use of W.J. Hay, the chemical assistant of the dockyard.
Alumni
Sir Edward James Reed - Chief Constructor of the Royal Navy from 1863 until 1870
Sir Nathaniel Barnaby - Reed's successor and brother-in-law
Frederick Kynaston Barnes - Naval Architect
References
Journal of the Statistical Society of London, Volume 16 (1853) p 210
Further reading
H. W.Dickinson, 'Joseph Woolley - Pioneer of British Naval Education; 1848 - 1873', Education Research and Perspectives (2007) 34(1) pages 1–26
External links
1848 establishments in England
Marine engineering organizations
History of the Royal Navy
Education in Portsmouth
Former training establishments of the Royal Navy |
https://en.wikipedia.org/wiki/Aricagua%20Municipality | The Aricagua Municipality is one of the 23 municipalities (municipios) that make up the Venezuelan state of Mérida and, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, the municipality had a population of 4,564. The town of Aricagua is the shire town of the Aricagua Municipality.
Demographics
The Aricagua Municipality, according to a 2007 population estimate by the National Institute of Statistics of Venezuela, had a population of 4,564 (up from 4,514 in 2000). This amounted to 0.5% of the state's population. The municipality's population density is .
Government
The mayor of the Aricagua Municipality is Nelson Jesus Márquez Rojas, re-elected on October 31, 2004, with 59% of the vote. The municipality is divided into two parishes; Capital Aricagua and San Antonio.
References
External links
aricagua-merida.gob.ve]
Municipalities of Mérida (state) |
https://en.wikipedia.org/wiki/Pariah%20group | In group theory, the term pariah was introduced by Robert Griess in to refer to the six sporadic simple groups which are not subquotients of the monster group.
The twenty groups which are subquotients, including the monster group itself, he dubbed the happy family.
For example, the orders of J4 and the Lyons Group Ly are divisible by 37. Since 37 does not divide the order of the monster, these cannot be subquotients of it; thus J4 and Ly are pariahs. Three other sporadic groups were also shown to be pariahs by Griess in 1982, and the Janko Group J1 was shown to be the final pariah by Robert A. Wilson in 1986. The complete list is shown below.
References
Robert A. Wilson (1986). Is J1 a subgroup of the monster?, Bull. London Math. Soc. 18, no. 4 (1986), 349-350
Sporadic groups |
https://en.wikipedia.org/wiki/Charles%20Castonguay | Charles Castonguay (born 1940) is a retired associate professor of Mathematics and Statistics at the University of Ottawa.
Biography
A native English speaker, Castonguay was sent by his parents to a French Catholic primary school. He took his first English courses in high school. Enrolled in the Canadian Armed Forces to pursue university-level studies, he obtained a masters of mathematics from the University of Ottawa. During the three years of his military service, he was posted to National Defence headquarters in Ottawa as counsellor in mathematics and also taught young officers at the Collège militaire royal de Saint-Jean.
After his service, he began teaching mathematics and statistics at the University of Ottawa and registered at McGill University to study the philosophy of mathematics and epistemology. The subject of his doctoral thesis was "meaning" and "existence" in mathematics. He obtained his Ph.D. in 1971. The thesis was published in 1972 and 1973.
In 1970, he attended a meeting of the Parti Québécois in the Laurier riding. René Lévesque was the speaker at this meeting, designed to inform English speakers of the party's Sovereignty-Association project. After that experience, he campaigned for the party until the election of 1976.
Partly to understand himself as a francized English speaker, he took great interest in the analysis of the linguistic behaviours of populations and language policies. He became a specialist on the subject of language shifts and completed several studies on behalf of the Office québécois de la langue française.
On January 25, 2001, he took an active part in a symposium held by the commission of the Estates-General on the Situation and Future of the French Language in Quebec (Les enjeux démographiques et l'intégration des immigrants). Thereafter, he co-authored a book criticizing its final report.
Since 2000, he contributes to the Dossier linguistique in the newspaper L'aut'journal. He participated in the foundation of the Institut de recherche sur le français en Amérique in 2008.
Works
In English
Thesis
Meaning and Existence in Mathematics, New York: Springer-Verlag, 1972, 159 pages (also New York: Springer, 1973)
Articles
"Nation Building and Anglicization in Canada's Capital Region", in Inroads Journal, Issue 11, 2002, pp. 71–86
"French is on the ropes. Why won’t Ottawa admit it ?", in Policy Options, volume 20, issue 8, 1999, pp. 39–50
"Getting the facts straight on French : Reflections following the 1996 Census", in Inroads Journal, Issue 8, 1999, pages 57 to 77
"The Fading Canadian Duality", in Language in Canada (ed. John R. Edwards), pp. 36–60, Cambridge: Cambridge University Press, 1998, 520 pages
"Assimilation Trends among Official-Language Minorities. 1971-1991", in Towards the Twenty-First Century: Emerging Socio-Demographic Trends and Policy Issues in Canada, pp. 201–205, Federation of Canadian Demographers, Ottawa, 1996
"The Anglicization of Canada, 1971-1981", in Language Problems |
https://en.wikipedia.org/wiki/George%20P.%20Fletcher | George P. Fletcher (born March 5, 1939) is the Cardozo Professor of Jurisprudence at Columbia University School of Law.
Fletcher attended Cornell University from 1956 to 1959, studying mathematics and Russian. He received a B.A. in 1960 from University of California, Berkeley and his J.D. in 1964 from the University of Chicago. He studied at the University of Freiburg from 1964 to 1965 and received a Masters in Comparative Law in 1965 from the University of Chicago. He taught at the law schools of the University of Florida, University of Washington, and Boston College and then UCLA, from 1969 to 1983. Since then he has taught at Columbia Law School in New York where he was made Charles Keller Beekman Professor of Law in 1989 and Cardozo Professor of Jurisprudence in 1994. He has been a visiting professor at the Hebrew University of Jerusalem, the Free University of Brussels, the University of Frankfurt, Germany, and Yale Law School.
An internationally recognized scholar of criminal law, torts, comparative law, and legal philosophy, Fletcher is one of the most cited experts in the United States on criminal law. The 2003 Propter Honoris Respectum issue of the Notre Dame Law Review was dedicated to the study of his work, and symposia on his scholarship have been hosted by the Cardozo Law Review and Criminal Justice Ethics.
Fletcher's most widely-taught book Rethinking Criminal Law is a "well known time-honored classic of criminal law jurisprudence and the most cited scholarly book on criminal law second only to Glanville Williams Criminal Law: The General Part." The book was cited both by the majority opinion by Justice O'Connor and the dissenting opinion of Justice Brennan in the U.S. Supreme Court case, Tison v. Arizona, 481 U.S. 137 (1987). Fletcher was honored on the twenty-fifth anniversary of its publication with a "Symposium: Twenty-Five Years of George Fletcher's Rethinking Criminal Law."
In 2013, Oxford University Press published Fletcher's Essays on Criminal Law, edited by Russell L. Christopher and with contributions by an international panel of leading scholars including Kyron Huigens, Douglas Husak, John Gardner, Larry Alexander and Kimberly Ferzan, Heidi Hurd, Susan Estrich, Peter Westen, Alon Harel, Joshua Dressler, Victoria Nourse, Judge John T. Noonan, Jr., Alan Wertheimer, and Stephen Schulhofer.
In 1989, the American Bar Association awarded the Silver Gavel for outstanding lawbook of the year to Fletcher's study of the trial of the "subway vigilante," Bernard Goetz, "A Crime of Self-Defense." The bar noted the book probed the complex question of self-defense and its legal and moral implications for contemporary urban life.
Fletcher has been active in several high-profile legal disputes. He was an expert witness in the Agent Orange case, presenting evidence for the court that the use of herbicides and defoliants violated international law as they were considered chemical weapons. However, the court ruled that the use of he |
https://en.wikipedia.org/wiki/2003%20Djurg%C3%A5rdens%20IF%20season |
Squad information
Squad
Player statistics
Appearances for competitive matches only
|}
Topscorers
Total
Allsvenskan
Svenska Cupen
Champions League
Competitions
Overall
Allsvenskan
League table
Matches
Svenska Cupen
Champions League
2nd qualifying round
Friendlies
Notes
References
Djurgarden
Djurgårdens IF Fotboll seasons
Swedish football championship-winning seasons |
https://en.wikipedia.org/wiki/Shape%20analysis%20%28digital%20geometry%29 | This article describes shape analysis to analyze and process geometric shapes.
Description
Shape analysis is the (mostly) automatic analysis of geometric shapes, for example using a computer to detect similarly shaped objects in a database or parts that fit together. For a computer to automatically analyze and process geometric shapes, the objects have to be represented in a digital form. Most commonly a boundary representation is used to describe the object with its boundary (usually the outer shell, see also 3D model). However, other volume based representations (e.g. constructive solid geometry) or point based representations (point clouds) can be used to represent shape.
Once the objects are given, either by modeling (computer-aided design), by scanning (3D scanner) or by extracting shape from 2D or 3D images, they have to be simplified before a comparison can be achieved. The simplified representation is often called a shape descriptor (or fingerprint, signature). These simplified representations try to carry most of the important information, while being easier to handle, to store and to compare than the shapes directly.
A complete shape descriptor is a representation that can be used to completely reconstruct the original object (for example the medial axis transform).
Application fields
Shape analysis is used in many application fields:
archeology for example, to find similar objects or missing parts
architecture for example, to identify objects that spatially fit into a specific space
medical imaging to understand shape changes related to illness or aid surgical planning
virtual environments or on the 3D model market to identify objects for copyright purposes
security applications such as face recognition
entertainment industry (movies, games) to construct and process geometric models or animations
computer-aided design and computer-aided manufacturing to process and to compare designs of mechanical parts or design objects.
Shape descriptors
Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis operating on point clouds).
Another class of shape descriptors (called intrinsic shape descriptors) is invariant with respect to isometry. These descriptors do not change with different isometric embeddings of the shape. Their advantage is that they can be applied nicely to deformable objects (e.g. a person in different body postures) as these deformations do not involve much stretching but are in fact near-isometric. Such descriptors are commonly based on geodesic distances measures along the surface of an object or on other isometry invariant characteristics such as the Laplace–Beltrami spectrum (see also s |
https://en.wikipedia.org/wiki/Indians%20in%20Thailand | Thai Indians are Thai people with full or partial Indian ancestry. But these ancestral ties are usually left out of statistics. About 65,000 Indian Thais have full Thai citizenship, but around 400,000 persons of Indian origin settled in Thailand mainly in the urban cities.
Migration history
Since ancient time, there have been various exchanges between the Indians and Thailand. Modern Indian communities have been around since the 1860s of the British Raj era. Most of the Indians arrived in the last century, notably from Tamil Nadu and other areas of Southern India. Some others came from Northern India such as Delhi, Punjab, Rajasthan and some from Gujarat. Buddhism and Hinduism originally arrived in Thailand from India and spread over the centuries.
Some Thai Muslims, especially in the Southern part of Thailand, have Indian ancestry.
The historical number of the Indian population in Thailand can be seen in British consular statistics; however, these figures often lumped Indians together with Sinhalese and Malays. According to 1912 statistics, there were 30 Indians registered in the Chiengmai (Chiang Mai) consular district, 41 Indians and Malays in the Puket (Phuket) consular district, 40 Indians and Malays in the Senggora (Songkhla) consular district, and 423 Indians, Sinhalese, and Malays in the Bangkok consular district. These figures were also believed to be a gross undercount of the true population; for example, the Bangkok consular district had registered only 517 British subjects, but other estimates claimed the number was 20 times higher.
Notable people
Aloke Lohia - Billionaire Businessman
Ammar Siamwalla - One of Thailand's most prominent economists
Lek Nana - Businessman and Politician
Napakpapha Nakprasitte - Thai actress and Model
Savika Chaiyadej - Thai soap actress
Nishita Shah - Businesswoman
Ratana Pestonji - Thai film director, producer, screenwriter and cinematographer
Santi Thakral - Member of the Privy Council of King Bhumibol Adulyadej of Thailand
Vidya Dhar Shukla - Chief Hindu priest of Thailand
See also
Demographics of Thailand
Religion in Thailand
Phahurat
Hinduism in Southeast Asia
Sikhism in Thailand
Nepalis in Thailand
Pakistanis in Thailand
Mariamman Temple, Bangkok
References
External links
India Thailand Trade
Thai Indian Update
Thaindian.com
Thai Sikh Organization
Masala Magazine for Indians In Thailand
Indians
India–Thailand relations |
https://en.wikipedia.org/wiki/Uniformly%20hyperfinite%20algebra | In mathematics, particularly in the theory of C*-algebras, a uniformly hyperfinite, or UHF, algebra is a C*-algebra that can be written as the closure, in the norm topology, of an increasing union of finite-dimensional full matrix algebras.
Definition
A UHF C*-algebra is the direct limit of an inductive system {An, φn} where each An is a finite-dimensional full matrix algebra and each φn : An → An+1 is a unital embedding. Suppressing the connecting maps, one can write
Classification
If
then rkn = kn + 1 for some integer r and
where Ir is the identity in the r × r matrices. The sequence ...kn|kn + 1|kn + 2... determines a formal product
where each p is prime and tp = sup {m | pm divides kn for some n}, possibly zero or infinite. The formal product δ(A) is said to be the supernatural number corresponding to A. Glimm showed that the supernatural number is a complete invariant of UHF C*-algebras. In particular, there are uncountably many isomorphism classes of UHF C*-algebras.
If δ(A) is finite, then A is the full matrix algebra Mδ(A). A UHF algebra is said to be of infinite type if each tp in δ(A) is 0 or ∞.
In the language of K-theory, each supernatural number
specifies an additive subgroup of Q that is the rational numbers of the type n/m where m formally divides δ(A). This group is the K0 group of A.
CAR algebra
One example of a UHF C*-algebra is the CAR algebra. It is defined as follows: let H be a separable complex Hilbert space H with orthonormal basis fn and L(H) the bounded operators on H, consider a linear map
with the property that
The CAR algebra is the C*-algebra generated by
The embedding
can be identified with the multiplicity 2 embedding
Therefore, the CAR algebra has supernatural number 2∞. This identification also yields that its K0 group is the dyadic rationals.
References
C*-algebras |
https://en.wikipedia.org/wiki/Vector%20spherical%20harmonics | In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH are complex-valued functions expressed in the spherical coordinate basis vectors.
Definition
Several conventions have been used to define the VSH.
We follow that of Barrera et al.. Given a scalar spherical harmonic , we define three VSH:
with being the unit vector along the radial direction in spherical coordinates and the vector along the radial direction with the same norm as the radius, i.e., . The radial factors are included to guarantee that the dimensions of the VSH are the same as those of the ordinary spherical harmonics and that the VSH do not depend on the radial spherical coordinate.
The interest of these new vector fields is to separate the radial dependence from the angular one when using spherical coordinates, so that a vector field admits a multipole expansion
The labels on the components reflect that is the radial component of the vector field, while and are transverse components (with respect to the radius vector ).
Main properties
Symmetry
Like the scalar spherical harmonics, the VSH satisfy
which cuts the number of independent functions roughly in half. The star indicates complex conjugation.
Orthogonality
The VSH are orthogonal in the usual three-dimensional way at each point :
They are also orthogonal in Hilbert space:
An additional result at a single point (not reported in Barrera et al, 1985) is, for all ,
Vector multipole moments
The orthogonality relations allow one to compute the spherical multipole moments of a vector field as
The gradient of a scalar field
Given the multipole expansion of a scalar field
we can express its gradient in terms of the VSH as
Divergence
For any multipole field we have
By superposition we obtain the divergence of any vector field:
We see that the component on is always solenoidal.
Curl
For any multipole field we have
By superposition we obtain the curl of any vector field:
Laplacian
The action of the Laplace operator separates as follows:
where and
Also note that this action becomes symmetric, i.e. the off-diagonal coefficients are equal to , for properly normalized VSH.
Examples
First vector spherical harmonics
Expressions for negative values of are obtained by applying the symmetry relations.
Applications
Electrodynamics
The VSH are especially useful in the study of multipole radiation fields. For instance, a magnetic multipole is due to an oscillating current with angular frequency and complex amplitude
and the corresponding electric and magnetic fields, can be written as
Substituting into Maxwell equations, Gauss's law is automatically satisfied
while Faraday's law decouples as
Gauss' law for the magnetic field implies
and Ampère–Maxwell's equation gives
In this way, the partial differential equations have been transformed into a set of ordinary differential equations.
Alternative defi |
https://en.wikipedia.org/wiki/Monroe%20D.%20Donsker | Monroe David Donsker (October 17, 1924 – June 8, 1991) was an American mathematician and a professor of mathematics at New York University (NYU). His research interest was probability theory.
Education and career
Donsker was born in Burlington, Iowa. He received a Ph.D. in mathematics at the University of Minnesota in 1948 under the supervision of Robert Horton Cameron. He became a professor at NYU's Courant Institute of Mathematical Sciences in 1962, about a year before his frequent co-author S.R.S. Varadhan started working there. Before joining NYU, Donsker taught at Cornell University and the University of Minnesota. His doctoral students include Glen E. Baxter.
Donsker also served as chair of the Fulbright Foreign Scholarship Board, a U.S. government panel responsible for student exchange programs, after being appointed by presidents Ford and Carter.
In probability theory, Donsker is known for his proof of the Donsker invariance principle which shows the convergence in distribution of a rescaled random walk to the Wiener process.
Personal life
Donsker was married to Mary Davis (1923 – 2013), who was a watercolor artist with a degree in economics from University of Minnesota.
See also
Donsker's theorem
References
External links
1924 births
1991 deaths
University of Minnesota College of Liberal Arts alumni
20th-century American mathematicians
Probability theorists
People from Burlington, Iowa
Educators from Minnesota
Mathematical statisticians
Courant Institute of Mathematical Sciences faculty
Cornell University faculty
University of Minnesota faculty
New York University faculty |
https://en.wikipedia.org/wiki/Wadi%20as-Salqa | Wadi as-Salqa ( is a Palestinian agricultural town in the Deir al-Balah Governorate, located south of Deir al-Balah. According to the Palestinian Central Bureau of Statistics (PCBS), the municipality had a population of 6,715 in 2017.
Over half of the inhabitants are below the age of 18. Since the economic sanctions on the Gaza Strip following Hamas' victory in the Palestinian National Authority's legislative elections in 2006, about 85% of Wadi as-Salqa's population lived under the poverty line.
References
Towns in the Gaza Strip
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Germ%C3%A1n%20Castillo | Germán Pablo Castillo (born 19 October 1977 in El Trébol) is an Argentine footballer who plays for Cerro Porteño in Paraguay.
External links
Argentine Primera statistics
Interview at Radio-mundial.com
1977 births
Living people
Argentine men's footballers
People from San Martín Department, Santa Fe
Men's association football midfielders
Argentine Primera División players
Paraguayan Primera División players
Ecuadorian Serie A players
Club de Gimnasia y Esgrima La Plata footballers
Unión de Santa Fe footballers
Club Atlético Lanús footballers
C.D. Cuenca footballers
Club Atlético Huracán footballers
Cerro Porteño players
Expatriate men's footballers in Paraguay
Expatriate men's footballers in Ecuador
Footballers from Santa Fe Province |
https://en.wikipedia.org/wiki/Shinji%20Tsujio | is a Japanese football player for SC Sagamihara.
Career
Tsujio was a member of F.C. Tokyo's youth program, and after graduating from Chuo University he joined S-Pulse in 2008.
Club statistics
Updated to 23 February 2019.
References
External links
Profile at Zweigen Kanazawa
1985 births
Living people
Chuo University alumni
Sportspeople from Sakai, Osaka
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shimizu S-Pulse players
Sanfrecce Hiroshima players
Oita Trinita players
Zweigen Kanazawa players
SC Sagamihara players
Footballers at the 2006 Asian Games
Men's association football defenders
Asian Games competitors for Japan |
https://en.wikipedia.org/wiki/Genki%20Omae | is a Japanese professional footballer who plays as a forward for Nankatsu SC. Omae has made several appearances for Japan’s under 19 national team.
Career statistics
Club
.
1Includes Emperor's Cup and DFB-Pokal.
2Includes J. League Cup.
References
External links
Profile at Omiya Ardija
Profile at Nankatsu SC
1989 births
Living people
Men's association football forwards
Association football people from Kanagawa Prefecture
Japanese men's footballers
Japan men's youth international footballers
J1 League players
J2 League players
Bundesliga players
2. Bundesliga players
Shimizu S-Pulse players
Omiya Ardija players
Fortuna Düsseldorf players
Thespakusatsu Gunma players
Kyoto Sanga FC players
Nankatsu SC players
Japanese expatriate men's footballers
Japanese expatriate sportspeople in Germany
Expatriate men's footballers in Germany |
https://en.wikipedia.org/wiki/Prepotential | Prepotential may refer to:
In medicine, the tendency for the action potential of cardiac cell membranes to drift towards threshold following repolarization
In mathematics, the vector superfield in supersymmetric gauge theory |
https://en.wikipedia.org/wiki/2004%20Djurg%C3%A5rdens%20IF%20season |
Squad information
Squad
Player statistics
Appearances for competitive matches only
|}
Topscorers
Total
Allsvenskan
Svenska Cupen
Europe
Competitions
Overall
Allsvenskan
League table
Matches
Svenska Cupen
Champions League
2nd qualifying round
Djurgården won 2 – 0 on aggregate.
3rd qualifying round
Juventus won 6 – 3 on aggregate.
UEFA Cup
UEFA Cup 1st round
Utrecht won 4 – 3 on aggregate.
Royal League
1st group stage
The tournament continued in the 2005 season.
Friendlies
Djurgarden
Djurgårdens IF Fotboll seasons |
https://en.wikipedia.org/wiki/Ross%20Haven | Ross Haven is a summer village in Alberta, Canada. It is located on the northern shore of Lac Ste. Anne, south of Highway 43.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of Ross Haven had a population of 126 living in 60 of its 212 total private dwellings, a change of from its 2016 population of 160. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of Ross Haven had a population of 160 living in 64 of its 215 total private dwellings, a change from its 2011 population of 137. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1962 establishments in Alberta
Lac Ste. Anne County
Summer villages in Alberta |
https://en.wikipedia.org/wiki/Birch%20Cove | Birch Cove is a summer village in Alberta, Canada. It is located between Highway 33 and Lac la Nonne, northwest of Edmonton.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of Birch Cove had a population of 67 living in 27 of its 61 total private dwellings, a change of from its 2016 population of 45. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of Birch Cove had a population of 45 living in 20 of its 74 total private dwellings, which represents no change from its 2011 population of 45. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1988 establishments in Alberta
Lac Ste. Anne County
Summer villages in Alberta |
https://en.wikipedia.org/wiki/Poplar%20Bay | Poplar Bay is a summer village in Alberta, Canada. It is located on the western shore of Pigeon Lake.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of Poplar Bay had a population of 113 living in 59 of its 182 total private dwellings, a change of from its 2016 population of 103. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of Poplar Bay had a population of 103 living in 46 of its 179 total private dwellings, a change from its 2011 population of 80. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1967 establishments in Alberta
Summer villages in Alberta |
https://en.wikipedia.org/wiki/South%20View%2C%20Alberta | South View is a summer village in Alberta, Canada. It is located on the northern shore of Isle Lake, opposite from Silver Sands.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of South View had a population of 72 living in 35 of its 86 total private dwellings, a change of from its 2016 population of 67. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of South View had a population of 67 living in 30 of its 88 total private dwellings, a change from its 2011 population of 35. With a land area of , it had a population density of in 2016.
The Summer Village of South View's 2012 municipal census counted a population of 76.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1970 establishments in Alberta
Lac Ste. Anne County
Summer villages in Alberta |
https://en.wikipedia.org/wiki/Sunbreaker%20Cove | Sunbreaker Cove is a summer village in Alberta, Canada. It is located on the northern shore of Sylvan Lake.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of Sunbreaker Cove had a population of 131 living in 64 of its 236 total private dwellings, a change of from its 2016 population of 81. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of Sunbreaker Cove had a population of 81 living in 41 of its 240 total private dwellings, a change from its 2011 population of 69. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1990 establishments in Alberta
Summer villages in Alberta |
https://en.wikipedia.org/wiki/Val%20Quentin | Val Quentin is a summer village in Alberta, Canada. It is located on the southern shore of Lac Ste. Anne.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of Val Quentin had a population of 158 living in 74 of its 160 total private dwellings, a change of from its 2016 population of 252. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of Val Quentin had a population of 252 living in 128 of its 224 total private dwellings, a change from its 2011 population of 157. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1966 establishments in Alberta
Lac Ste. Anne County
Summer villages in Alberta |
https://en.wikipedia.org/wiki/West%20Cove | West Cove is a summer village in Alberta, Canada. It is located on the southern shore of Lac Ste. Anne.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of West Cove had a population of 222 living in 108 of its 238 total private dwellings, a change of from its 2016 population of 149. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of West Cove had a population of 149 living in 78 of its 214 total private dwellings, a change from its 2011 population of 121. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1963 establishments in Alberta
Lac Ste. Anne County
Summer villages in Alberta |
https://en.wikipedia.org/wiki/South%20Baptiste | South Baptiste is a summer village in Alberta, Canada. It is located on the southern shore of Baptiste Lake, west of Athabasca.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of South Baptiste had a population of 70 living in 33 of its 76 total private dwellings, a change of from its 2016 population of 66. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of South Baptiste had a population of 66 living in 30 of its 77 total private dwellings, a change from its 2011 population of 52. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1983 establishments in Alberta
Summer villages in Alberta |
https://en.wikipedia.org/wiki/West%20Baptiste | West Baptiste is a summer village in Alberta, Canada. It is located on the western shore of Baptiste Lake, west of Athabasca.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, the Summer Village of West Baptiste had a population of 46 living in 25 of its 64 total private dwellings, a change of from its 2016 population of 38. With a land area of , it had a population density of in 2021.
In the 2016 Census of Population conducted by Statistics Canada, the Summer Village of West Baptiste had a population of 38 living in 19 of its 47 total private dwellings, a change from its 2011 population of 52. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of summer villages in Alberta
List of resort villages in Saskatchewan
References
External links
1983 establishments in Alberta
Summer villages in Alberta |
https://en.wikipedia.org/wiki/List%20of%20Olympic%20records%20in%20speed%20skating | This is the current list of Olympic records in speed skating.
Men's records
♦ denotes a performance that is also a current world record. Statistics are correct as of 11 February 2022.
Women's records
Note
See also
List of world records in speed skating
List of Olympic records in short track speed skating
References
Speed skating
Records
Speed skating records
Speed skating-related lists |
https://en.wikipedia.org/wiki/Dual%20impedance | Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance is its reciprocal, or algebraic inverse . For this reason, the dual impedance is also called the inverse impedance. Another way of stating this is that the dual of is the admittance .
The dual of a network is the network whose impedances are the duals of the original impedances. In the case of a black-box network with multiple ports, the impedance looking into each port must be the dual of the impedance of the corresponding port of the dual network.
This is consistent with the general notion duality of electric circuits, where the voltage and current are interchanged, etc., since yields
Scaled and normalised duals
In physical units, the dual is taken with respect to some nominal or characteristic impedance. To do this, Z and Z' are scaled to the nominal impedance Z0 so that
Z0 is usually taken to be a purely real number R0, so Z' is changed by a real factor of R02. In other words, the dual circuit is qualitatively the same circuit, but all the component values are scaled by R02. The scaling factor R02 has the dimensions of Ω2, so the constant 1 in the unitless expression would actually be assigned the dimensions Ω2 in a dimensional analysis.
Duals of basic circuit elements
Graphical method
There is a graphical method of obtaining the dual of a network which is often easier to use than the mathematical expression for the impedance. Starting with a circuit diagram of the network in question, Z, the following steps are drawn on the diagram to produce Z' superimposed on top of Z. Typically, Z' will be drawn in a different colour to help distinguish it from the original, or, if using computer-aided design, Z' can be drawn on a different layer.
A generator is connected to each port of the original network. The purpose of this step is to prevent the ports from being "lost" in the inversion process. This happens because a port left open circuit will transform into a short circuit and disappear.
A dot is drawn at the centre of each mesh of the network Z. These dots will become the circuit nodes of Z'.
A conductor is drawn, which encloses the network Z. This conductor also becomes a node of Z'.
For each circuit element of Z, its dual is drawn between the nodes in the centre of the meshes on either side of Z. Where Z is on the edge of the network, one of these nodes will be the enclosing conductor from the previous step.
This completes the drawing of Z'. This method also demonstrates that the dual of a mesh transforms into a node, and the dual of a node transforms into a mesh. Two examples are given below.
Example: star network
It is clear that the dual of a star network of inductors is a delta network of capacitors. This dual circuit is not the same thing as a star-delta (Y-Δ) transformation. A Y-Δ transform results in an equivalent circuit, not a dual circuit.
Example: Cauer network
Filters designed using Cauer's |
https://en.wikipedia.org/wiki/EqWorld | EqWorld is a free online mathematics reference site that lists information about mathematical equations.
It covers ordinary differential, partial differential, integral, functional, and other mathematical equations. It also outlines some methods for solving equations, and lists many resources for solving equations, and has an equation archive which users can add to.
References
Science, 2005, Vol 308, Issue 5727, p. 1387.
Physics Today, July 2005, p. 35.
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, Chapman & Hall/CRC Press 1998. xxvi+787 pp. .
External links
EqWorld home page
Mathematics websites
Equations
Multilingual websites |
https://en.wikipedia.org/wiki/Wilson%20Morelo | Wilson David Morelo López (born 21 May 1987), is a Colombian football striker who plays for Categoría Primera A club Independiente Santa Fe.
Career statistics
Source:
Notes
Honours
Club
Santa Fe
Categoría Primera A (1): 2014–II
Superliga Colombiana (1): 2015
Copa Sudamericana (1): 2015
Individual
Copa Sudamericana top goalscorer (1): 2015
References
External links
1987 births
Living people
Colombian men's footballers
Colombian expatriate men's footballers
Envigado F.C. players
Millonarios F.C. players
América de Cali footballers
Atlético Huila footballers
Deportes Tolima footballers
La Equidad footballers
C.F. Monterrey players
Everton de Viña del Mar footballers
Club Atlético Colón footballers
Independiente Santa Fe footballers
Copa Sudamericana-winning players
Argentine Primera División players
Chilean Primera División players
Categoría Primera A players
Liga MX players
Expatriate men's footballers in Argentina
Expatriate men's footballers in Chile
Expatriate men's footballers in Mexico
Colombian expatriate sportspeople in Argentina
Colombian expatriate sportspeople in Chile
Colombian expatriate sportspeople in Mexico
Men's association football forwards
People from Montería
Sportspeople from Córdoba Department |
https://en.wikipedia.org/wiki/S-finite%20measure | In measure theory, a branch of mathematics that studies generalized notions of volumes, an s-finite measure is a special type of measure. An s-finite measure is more general than a finite measure, but allows one to generalize certain proofs for finite measures.
The s-finite measures should not be confused with the σ-finite (sigma-finite) measures.
Definition
Let be a measurable space and a measure on this measurable space. The measure is called an s-finite measure, if it can be written as a countable sum of finite measures (),
Example
The Lebesgue measure is an s-finite measure. For this, set
and define the measures by
for all measurable sets . These measures are finite, since for all measurable sets , and by construction satisfy
Therefore the Lebesgue measure is s-finite.
Properties
Relation to σ-finite measures
Every σ-finite measure is s-finite, but not every s-finite measure is also σ-finite.
To show that every σ-finite measure is s-finite, let be σ-finite. Then there are measurable disjoint sets with and
Then the measures
are finite and their sum is . This approach is just like in the example above.
An example for an s-finite measure that is not σ-finite can be constructed on the set with the σ-algebra . For all , let be the counting measure on this measurable space and define
The measure is by construction s-finite (since the counting measure is finite on a set with one element). But is not σ-finite, since
So cannot be σ-finite.
Equivalence to probability measures
For every s-finite measure , there exists an equivalent probability measure , meaning that . One possible equivalent probability measure is given by
References
Measures (measure theory) |
https://en.wikipedia.org/wiki/1976%20North%20American%20Soccer%20League%20season | Statistics of North American Soccer League in season 1976. This was the 9th season of the NASL.
Overview
The league's twenty teams were divided into two conferences (Atlantic or Pacific), playing a total of 240 matches. Each team's 24 matches were divided between a round-robin with other teams in the same conference and six matches against different teams in the other conference. Points were awarded for wins (six) and each goal (up to three) regardless of results; ties in regulation were decided by 15 minutes of sudden death overtime followed by a penalty shootout from . The playoffs were expanded from eight to twelve teams with automatic berths for the top two teams in each of the four divisions and two wild card slots per conference for the remaining best finishing teams.
The Toronto Metros-Croatia defeated the Minnesota Kicks in the Soccer Bowl on August 28 to win the championship. The match was hosted at the Kingdome in Seattle, the new home of the Seattle Sounders. The Tampa Bay Rowdies finished the regular season with the best record, giving them consecutive titles in three different domestic NASL competitions. Though not in a calendar year, within 12 months they won the Soccer Bowl in August 1975, the NASL indoor cup in March 1976, and the regular season shield or premiership in August 1976. Since NASL teams at that time did not participate in the U.S. Open Cup, this would be the closest one would ever come to achieving any sort of a North American treble.
Changes from the previous season
New teams
None
Teams folding
None
Teams moving
Baltimore Comets to San Diego Jaws
Denver Dynamos to Minnesota Kicks
Name changes
None
Regular season
Pld = Played, W = Wins, L = Losses, GF = Goals For, GA = Goals Against, GD = Goal Differential, BP = Bonus Points, Pts= total points
6 points for a win,
1 point for a shootout win,
0 points for a loss,
1 point for each regulation goal scored up to three per game.
-Premiers (most points). -Other playoff teams.
Atlantic Conference
Pacific Conference
NASL All-Stars
Playoffs
All playoff games in all rounds including Soccer Bowl '76 were single game elimination match ups.
Bracket
First round
Conference semifinals
Conference Championships
Soccer Bowl '76
1976 NASL Champions: Toronto Metros-Croatia
Post season awards
Most Valuable Player: Pelé, New York
Coach of the year: Eddie Firmani, Tampa Bay
Rookie of the year: Steve Pecher, Dallas
North American Player of the Year: Arnie Mausser, Tampa Bay
References
External links
Complete Results and Standings
North American Soccer League (1968–1984) seasons
1976
1976 in Canadian soccer |
https://en.wikipedia.org/wiki/1977%20North%20American%20Soccer%20League%20season | Statistics of North American Soccer League in season 1977. This was the 10th season of the NASL.
Overview
The league was made up of 18 teams. The schedule was expanded to 26 games and the playoffs to 12 teams. Team rosters consisted of 17 players, 6 of which had to be U.S. or Canadian citizens. The NASL began using its own variation of the penalty shoot-out procedure for tied matches. Matches tied at the end of regulation would now go to a golden goal overtime period and, if still tied, on to a shoot-out. Instead of penalty kicks however, the shoot-out attempt started 35 yards from the goal and allowed the player 5 seconds to attempt a shot. The player could make as many moves as he wanted in a breakaway situation within the time frame. NASL procedure also called for the box score or score-line to show an additional "goal" given to the winning side of a shoot-out. This "victory goal" however was not credited in the "Goals For" column of the league table. The Cosmos defeated the Seattle Sounders in the final on August 28 to win the championship.
Changes from the previous season
New teams
None
Teams folding
Boston Minutemen
Philadelphia Atoms
Teams moving
Miami Toros - Fort Lauderdale Strikers
San Antonio Thunder - Team Hawaii
San Diego Jaws - Las Vegas Quicksilvers
Name changes
Hartford Bicentennials to Connecticut Bicentennials
Cosmos drop "New York" from name
Regular season
W = Wins, L = Losses, GF = Goals For, GA = Goals Against, BP = Bonus Points, Pts= point system
6 points for a win, 0 points for a loss, 1 point for each regulation goal scored up to three per game.
-Premiers (most points). -Other playoff teams.
Atlantic Conference
Pacific Conference
NASL All-Stars
Playoffs
The first round and the Soccer Bowl were single game match ups, while the conference semifinals and championships were all two-game series.
Bracket
First round
Division Championships
*Minnesota Kicks hosted Game 1 (instead of Game 2) due to a scheduling conflict with the Twins baseball club.
Conference Championships
#Seattle Sounders hosted Game 2 (instead of Game 1) due to a scheduling conflict with the Mariners baseball club.
Soccer Bowl '77
1977 NASL Champions: Cosmos
Post season awards
Most Valuable Player: Franz Beckenbauer, Cosmos
Coach of the year: Ron Newman, Fort Lauderdale
Rookie of the year: Jim McAlister, Seattle
References
External links
The Year in American Soccer – 1977
Chris Page's NASL Archive
Complete Results and Standings
North American Soccer League (1968–1984) seasons
1977
1977 in Canadian soccer |
https://en.wikipedia.org/wiki/Leonid%20Vaserstein | Leonid Nisonovich Vaserstein () is a Russian-American mathematician, currently Professor of Mathematics at Penn State University. His research is focused on algebra and dynamical systems. He is well known for providing a simple proof of the Quillen–Suslin theorem, a result in commutative algebra, first conjectured by Jean-Pierre Serre in 1955, and then proved by Daniel Quillen and Andrei Suslin in 1976.
Leonid Vaserstein got his Master's degree and doctorate in Moscow State University, where he was until 1978. He then moved to Europe and United States.
Alternate forms of the last name: Vaseršteĭn, Vasershtein, Wasserstein.
The Wasserstein metric was named after him by R.L. Dobrushin in 1970.
Biography
Leonid Vaserstein grew up in the Soviet Union. In secondary school he won the second prize in the All-Russian High School Mathematical Olympiad. Vaserstein got his undergraduate, masters (1966), and doctoral degrees (1969) in mathematics from Moscow State University, where he worked as a lecturer concurrently with his doctoral research. After his doctoral graduation he worked for the Moscow State University-associated "Informelectro" Institute, a Federal State Unitary Enterprise focused on ways to develop industries in Russia with emphases on electrical engineering, energy efficiency, and environmental technologies like greenhouse gas mitigation. He started as a senior researcher for Informelectro and continued working there until 1978, eventually becoming head of his department. In 1978 and 1979 he made his way to the United States of America by way of Europe, taking a series of visiting professor positions at the University of Bielefeld, Institut des Hautes Études Scientifiques, University of Chicago, and Cornell University. In 1979, Vaserstein took a full-time position as a professor in the Department of Mathematics at Penn State University.
Vaserstein's research interests extend across the areas of topology, algebra, and number theory, and the applications of these areas, including classical groups over rings, algebraic K-theory, systems with local interactions, and optimization and planning. Additionally, Vaserstein maintains the Penn State University Math Department's website on Algebra and Number Theory.
Selected publications
See also
List of Russian mathematicians
References
External links
A web page about Leonid N. Vaserstein's publications
Leonid N. Vaserstein home page
Living people
Moscow State University alumni
Russian mathematicians
Pennsylvania State University faculty
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Bridged%20T%20delay%20equaliser | The bridged-T delay equaliser is an electrical all-pass filter circuit utilising bridged-T topology whose purpose is to insert an (ideally) constant delay at all frequencies in the signal path. It is a class of image filter.
Applications
The network is used when it is required that two or more signals are matched to each other on some form of timing criterion. Delay is added to all other signals so that the total delay is matched to the signal which already has the longest delay. In television broadcasting, for instance, it is desirable that the timing of the television waveform synchronisation pulses from different sources are aligned as they reach studio control rooms or network switching centres. This ensures that cuts between sources do not result in disruption at the receivers. Another application occurs when stereophonic sound is connected by landline, for instance from an outside broadcast to the studio centre. It is important that delay is equalised between the two stereo channels as a difference will destroy the stereo image. When the landlines are long and the two channels arrive by substantially different routes it can require many filter sections to fully equalise the delay.
Operation
The operation is best explained in terms of the phase shift the network introduces. At low frequencies L is low impedance and C' is high impedance and consequently the signal passes through the network with no shift in phase. As the frequency increases, the phase shift gradually increases, until at some frequency, ω0, the shunt branch of the circuit, L'C', goes in to resonance and causes the centre-tap of L to be short-circuited to ground. Transformer action between the two halves of L, which had been steadily becoming more significant as the frequency increased, now becomes dominant. The winding of the coil is such that the secondary winding produces an inverted voltage to the primary. That is, at resonance the phase shift is now 180°. As the frequency continues to increase, the phase delay also continues to increase and the input and output start to come back into phase as a whole cycle delay is approached. At high frequencies L and L' approach open-circuit and C approaches short-circuit and the phase delay tends to level out at 360°.
The relationship between phase shift (φ) and time delay (TD) with angular frequency (ω) is given by the simple relation,
It is required that TD is constant at all frequencies over the band of operation. φ must, therefore, be kept linearly proportional to ω. With a suitable choice of parameters, the network phase shift can be made linear up to about 180° phase shift.
The network is terminated in a characteristic impedance (not shown in the circuit diagram), ideally a resistance R, which is the input impedance to the successive circuit or transmission line.
Design
The four component values of the network provide four degrees of freedom in the design. It is required from image theory (see Zobel netw |
https://en.wikipedia.org/wiki/Gomboc | Gomboc may refer to:
Mathematics
Gömböc, a convex three-dimensional body that has one stable and one unstable point of equilibrium
People
Andreja Gomboc (born 1969), Slovenian astrophysicist
Adrian Gomboc (born 1995), Slovenian judoka
Ron Gomboc (born 1947), Slovenian-born Australian sculptor
Slovene-language surnames |
https://en.wikipedia.org/wiki/Lie%20sphere%20geometry | Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. The main idea which leads to Lie sphere geometry is that lines (or planes) should be regarded as circles (or spheres) of infinite radius and that points in the plane (or space) should be regarded as circles (or spheres) of zero radius.
The space of circles in the plane (or spheres in space), including points and lines (or planes) turns out to be a manifold known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry can be difficult to visualize because Lie transformations do not preserve points in general: points can be transformed into circles (or spheres).
To handle this, curves in the plane and surfaces in space are studied using their contact lifts, which are determined by their tangent spaces. This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface. It also allows for a natural treatment of Dupin cyclides and a conceptual solution of the problem of Apollonius.
Lie sphere geometry can be defined in any dimension, but the case of the plane and 3-dimensional space are the most important. In the latter case, Lie noticed a remarkable similarity between the Lie quadric of spheres in 3-dimensions, and the space of lines in 3-dimensional projective space, which is also a quadric hypersurface in a 5-dimensional projective space, called the Plücker or Klein quadric. This similarity led Lie to his famous "line-sphere correspondence" between the space of lines and the space of spheres in 3-dimensional space.
Basic concepts
The key observation that leads to Lie sphere geometry is that theorems of Euclidean geometry in the plane (resp. in space) which only depend on the concepts of circles (resp. spheres) and their tangential contact have a more natural formulation in a more general context in which circles, lines and points (resp. spheres, planes and points) are treated on an equal footing. This is achieved in three steps. First an ideal point at infinity is added to Euclidean space so that lines (or planes) can be regarded as circles (or spheres) passing through the point at infinity (i.e., having infinite radius). This extension is known as inversive geometry with automorphisms known as "Mobius transformations". Second, points are regarded as circles (or spheres) of zero radius. Finally, for technical reasons, the circles (or spheres), including the lines (or planes) are given orientations.
These objects, i.e., the points, oriented circles and oriented lines in the plane, or the points, oriented spheres and oriented planes in space, are sometimes called cycles or Lie cycles. It turns out that they form a quadric hypersurface in a projective space of dimension 4 or 5, which is kn |
https://en.wikipedia.org/wiki/Pushforward%20%28homology%29 | In algebraic topology, the pushforward of a continuous function : between two topological spaces is a homomorphism between the homology groups for .
Homology is a functor which converts a topological space into a sequence of homology groups . (Often, the collection of all such groups is referred to using the notation ; this collection has the structure of a graded ring.) In any category, a functor must induce a corresponding morphism. The pushforward is the morphism corresponding to the homology functor.
Definition for singular and simplicial homology
We build the pushforward homomorphism as follows (for singular or simplicial homology):
First we have an induced homomorphism between the singular or simplicial chain complex and defined by composing each singular n-simplex : with to obtain a singular n-simplex of , : . Then we extend linearly via .
The maps : satisfy where is the boundary operator between chain groups, so defines a chain map.
We have that takes cycles to cycles, since implies . Also takes boundaries to boundaries since .
Hence induces a homomorphism between the homology groups for .
Properties and homotopy invariance
Two basic properties of the push-forward are:
for the composition of maps .
where : refers to identity function of and refers to the identity isomorphism of homology groups.
A main result about the push-forward is the homotopy invariance: if two maps are homotopic, then they induce the same homomorphism .
This immediately implies that the homology groups of homotopy equivalent spaces are isomorphic:
The maps induced by a homotopy equivalence are isomorphisms for all .
References
Allen Hatcher, Algebraic topology. Cambridge University Press, and
Topology
Homology theory |
https://en.wikipedia.org/wiki/PSPP | PSPP is a free software application for analysis of sampled data, intended as a free alternative for IBM SPSS Statistics. It has a graphical user interface and conventional command-line interface. It is written in C and uses GNU Scientific Library for its mathematical routines. The name has "no official acronymic expansion".
Features
This software provides a comprehensive set of capabilities including frequencies, cross-tabs comparison of means (t-tests and one-way ANOVA), linear regression, logistic regression, reliability (Cronbach's alpha, not failure or Weibull), and re-ordering data, non-parametric tests, factor analysis, cluster analysis, principal components analysis, chi-square analysis and more.
At the user's choice, statistical output and graphics are available in ASCII, PDF, PostScript, SVG or HTML formats. A range of statistical graphs can be produced, such as histograms, pie-charts, scree plots, and np-charts.
PSPP can import Gnumeric and OpenDocument spreadsheets, Postgres databases, comma-separated values and ASCII files. It can export files in the SPSS 'portable' and 'system' file formats and to ASCII files. Some of the libraries used by PSPP can be accessed programmatically; PSPP-Perl provides an interface to the libraries used by PSPP.
Origins
The PSPP project (originally called "Fiasco") was born at the end of the 1990s as a free software replacement for SPSS, which is a data management and analysis tool, at the time produced by SPSS Inc. The nature of SPSS's proprietary licensing and the presence of digital restrictions management motivated the author to write an alternative which later became functionally identical, but with permission for everyone to copy, modify and share.
Third Party Reviews
In the book "SPSS For Dummies", the author discusses PSPP under the heading of "Ten Useful Things You Can Find on the Internet". Another review of free to use statistical software also finds that the statistical results from PSPP match statistical results for SAS, for frequencies, means, correlation and regression.
Research about PSPP
One study found that students who used PSPP became more positive about learning statistics while using PSPP.
Examples of Research Performed using PSPP
Among the studies done using PSPP are one about posttraumatic stress in adolescents, another about nutrition software, and another about internet addiction.
See also
Free statistical software
Comparison of statistical packages
External Resources
PSPP for Beginners
References
External links
PSPP on Free Software Directory
Source code at Savannah
Third-party resources
Review by UK SPSS user group (as of version 0.1.22)
Using PSPP to import SPSS data into R
PSPP review in Slovene (English translation via Google)
User review from communication research info
Yet another user review
Free educational software
Free software programmed in C
Free statistical software
GNU Project software
Science software that uses GTK |
https://en.wikipedia.org/wiki/William%20Hunter%20%28statistician%29 | William Gordon Hunter, or Bill Hunter, was a statistician at the University of Wisconsin–Madison. He was co-author of the classic book Statistics for Experimenters, and co-founder of the Center for Quality and Productivity Improvement with George E. P. Box.
Hunter was born March 27, 1937, in Buffalo, New York. In 1959 he received a bachelor's degree from Princeton and in 1960 a master's from the University of Illinois in chemical engineering. He then became the first doctoral student at the new department of statistics at the University of Wisconsin–Madison founded by George Box.
He contributed to the book Statistics for Experimenters by Box, William Hunter, and Stuart Hunter (no relation to William Hunter). He founded the Statistics Division of the American Society for Quality and the Center for Quality and Productivity Improvement in Madison, Wisconsin. The Statistics Division of the American Society for Quality gives an annual award called the William G. Hunter Award.
According to Box, "[Hunter] wanted to make a difference in the lives of less fortunate people, and he and his family spent extended periods of time helping third world countries." Hunter taught in Singapore for a year and half and Nigeria for a year, both in the 1970s. In the early 1980s, before China allowed in many foreign experts, he spent a summer lecturing there. He helped build Singapore's quality movement.
Hunter was a leader in the effort to adopt the Deming system of Profound Knowledge and related ideas in the public sector. He contributed to Deming's Out of the Crisis, relating how the city of Madison applied Deming's ideas to a public sector organization.
He was a fellow of the American Statistical Association, the American Association for the Advancement of Science, and the American Society for Quality Control. From 1963 to 1983 he was an associate editor of Technometrics. He was the chairman of the Section on Physical and Engineering Sciences of the American Statistical Association and also served on that organization's board of directors. He served on boards for the National Research Council of the National Academy of Sciences and the National Academy of Engineering.
Hunter died of cancer on December 29, 1986, at the age of 49.
References
External links
Web site by his son
Assessment of his life by George Box
Statistics for Experimenters
Obituary (starting on page 5)
Hunter Award presented by the Statistics Division of the American Society for Quality
1937 births
1986 deaths
Scientists from Buffalo, New York
University of Wisconsin–Madison faculty
Princeton University alumni
University of Illinois alumni
University of Wisconsin–Madison College of Letters and Science alumni
American statisticians
Mathematicians from New York (state) |
https://en.wikipedia.org/wiki/Jeong%20Han%20Kim | Jeong Han Kim (; born July 20, 1962) is a South Korean mathematician.
He studied physics and mathematical physics at Yonsei University, and earned his Ph.D. in mathematics at Rutgers University. He was a researcher at AT&T Bell Labs and at Microsoft Research, and was Underwood Chair Professor of Mathematics at Yonsei University. He is currently a Professor of the School of Computational Sciences at the Korea Institute for Advanced Study.
His main research fields are combinatorics and computational mathematics. His best known contribution to the field is his proof that the Ramsey number R(3,t) has asymptotic order of magnitude t2/log t. He received the Fulkerson Prize in 1997 for his contributions to Ramsey theory.
In 2008, he became president of the National Institute for Mathematical Sciences of South Korea and was also awarded the Kyung-Ahm Prize. He was discharged of the position in 2011 after being accused of having allegedly misappropriated research funds. However, he was found not guilty by prosecution's investigation.
References
External links
Faculty page of Jeong Han Kim at Korea Institute for Advanced Study
Fulkerson Prize Winners at Mathematical Programming Society
Categories
1962 births
Living people
20th-century South Korean mathematicians
21st-century South Korean mathematicians
Graph theorists
Rutgers University alumni
Yonsei University alumni
National Institute for Mathematical Sciences |
https://en.wikipedia.org/wiki/Redescending%20M-estimator | In statistics, redescending M-estimators are Ψ-type M-estimators which have ψ functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ψ functions can be chosen to redescend smoothly to zero, so that they usually satisfy ψ(x) = 0 for all x with |x| > r, where r is referred to as the minimum rejection point.
Due to these properties of the ψ function, these kinds of estimators are very efficient, have a high breakdown point and, unlike other outlier rejection techniques, they do not suffer from a masking effect. They are efficient because they completely reject gross outliers, and do not completely ignore moderately large outliers (like median).
Advantages
Redescending M-estimators have high breakdown points (close to 0.5), and their Ψ function can be chosen to redescend smoothly to 0. This means that moderately large outliers are not ignored completely, and greatly improves the efficiency of the redescending M-estimator.
The redescending M-estimators are slightly more efficient than the Huber estimator for several symmetric, wider tailed distributions, but about 20% more efficient than the Huber estimator for the Cauchy distribution. This is because they completely reject gross outliers, while the Huber estimator effectively treats these the same as moderate outliers.
As other M-estimators, but unlike other outlier rejection techniques, they do not suffer from masking effects.
Disadvantages
The M-estimating equation for a redescending estimator may not have a unique solution. Consequently, the initial point for an iterative solution must be chosen with care, e.g., by use of another estimator.
Choosing redescending Ψ functions
When choosing a redescending Ψ function, care must be taken such that it does not descend too steeply, which may have a very bad influence on the denominator in the expression for the asymptotic variance
where F is the mixture model distribution.
This effect is particularly harmful when a large negative value of ψ′(x) combines with a large positive value of ψ2(x), and there is a cluster of outliers near x.
Examples
1. Hampel's three-part M estimators have Ψ functions which are odd functions and defined for any x by:
This function is plotted in the following figure for a = 1.645, b = 3 and r = 6.5.
2. Tukey's biweight or bisquare M estimators have Ψ functions for any positive k, which defined by:
This function is plotted in the following figure for k = 5.
3. Andrew's sine wave M estimator has the following Ψ function:
This function is plotted in the following figure.
References
Redescending M-estimators, Shevlyakov, G, Morgenthaler, S and Shurygin, A. M., J Stat Plann Inference 138:2906–2917, 2008.
Robust Estimation and Testing, Robert G. Staudte and Simon J. Sheather, Wiley 1990.
Robust Statistics,Huber, P., New York: Wiley, 1981.
See also
M-estimator
Robust statistics
Robust statistics
M-estimators |
https://en.wikipedia.org/wiki/Dedekind%E2%80%93MacNeille%20completion | In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille whose 1937 paper first defined and constructed it, and after Richard Dedekind because its construction generalizes the Dedekind cuts used by Dedekind to construct the real numbers from the rational numbers. It is also called the completion by cuts or normal completion.
Order embeddings and lattice completions
A partially ordered set (poset) consists of a set of elements together with a binary relation on pairs of elements that is reflexive ( for every x), transitive (if and then ), and antisymmetric (if both and hold, then ). The usual numeric orderings on the integers or real numbers satisfy these properties; however, unlike the orderings on the numbers, a partial order may have two elements that are incomparable: neither nor holds. Another familiar example of a partial ordering is the inclusion ordering ⊆ on pairs of sets.
If is a partially ordered set, a completion of means a complete lattice with an order-embedding of into . The notion of a complete lattice means that every subset of elements of has an infimum and supremum; this generalizes the analogous properties of the real numbers. The notion of an order-embedding enforces the requirements that distinct elements of must be mapped to distinct elements of , and that each pair of elements in has the same ordering in as they do in . The extended real number line (real numbers together with +∞ and −∞) is a completion in this sense of the rational numbers: the set of rational numbers {3, 3.1, 3.14, 3.141, 3.1415, 3.14159, ...} does not have a rational least upper bound, but in the real numbers it has the least upper bound .
A given partially ordered set may have several different completions. For instance, one completion of any partially ordered set is the set of its downwardly closed subsets ordered by inclusion. is embedded in this (complete) lattice by mapping each element to the lower set of elements that are less than or equal to . The result is a distributive lattice and is used in Birkhoff's representation theorem. However, it may have many more elements than are needed to form a completion of . Among all possible lattice completions, the Dedekind–MacNeille completion is the smallest complete lattice with embedded in it.
Definition
For each subset of a partially ordered set , let denote the set of upper bounds of ; that is, an element of belongs to whenever is greater than or equal to every element in . Symmetrically, let denote the set of lower bounds of , the elements that are less than or equal to every element in . Then the Dedekind–MacNeille completion of consists of all subsets for which
;
it is ordered by inclusion: in the completion if and only if as sets.
An element of embeds into the completion as its principal ideal, the set of elements less tha |
https://en.wikipedia.org/wiki/Barycentric-sum%20problem | Combinatorial number theory deals with number theoretic problems which involve combinatorial ideas in their formulations or solutions. Paul Erdős is the main founder of this branch of number theory. Typical topics include covering system, zero-sum problems, various restricted sumsets, and arithmetic progressions in a set of integers. Algebraic or analytic methods are powerful in this field.
In combinatorial number theory, the barycentric-sum problems are questions that can be answered using combinatorial techniques. The context of barycentric-sum problems are the barycentric sequences.
Example
Let be the cyclic group of integers modulo n. Let S be a sequence of elements of , where the repetition of elements is allowed. Let be the length of S. A sequence with is barycentric or has a
barycentric-sum if it contains one element such that .
Informally, if contains one element , which is the ”average” of its terms. A barycentric sequence of length is called a t-barycentric sequence. Moreover, when S is a set, the term barycentric set is used instead of barycentric sequence. For example, the set {0,1,2,3,4} is 5-barycentric with barycenter 2, however the set {0,2,3,4,5} is not 5-barycentric. The barycentric-sum problem consist in finding the smallest integer t such that any sequence of length t contains a k-barycentric sequence for some given k. The study of the existence of such t related with k and the study of barycentric constants are part of the barycentric-sum problems. It has been introduced by Ordaz, inspired in a theorem of Hamidoune: every sequence of length in contains a k-barycentric sequence. Notice that a k-barycentric sequence in , with k a multiple of n, is a sequence with zero-sum. The zero-sum problem on sequences started in 1961 with the Erdős, Ginzburg and Ziv theorem: every sequence of length in an abelian group of order n, contains an n-subsequence with zero-sum.
Barycentric-sum problems have been defined in general for finite abelian groups. However, most of the main results obtained up to now are in .
The barycentric constants introduced by Ordaz are: k-barycentric Olson constant, k-barycentric Davenport constant, barycentric Davenport constant, generalized barycentric Davenport constant, constrained barycentric Davenport constant. This constants are related to the Davenport constant i.e. the smallest integer t such that any t-sequence contains a subsequence with zero-sum. Moreover, related to the classical Ramsey numbers, the barycentric Ramsey numbers are introduced. An overview of the results computed manually or automatically are presented. The implemented algorithms are written in C.
References
External links
Divulgacions Matemáticas (Spanish)
Combinatorics |
https://en.wikipedia.org/wiki/DAP%20%28software%29 | Dap is a statistics and graphics program based on the C programming language that performs data management, analysis, and C-style graphical visualization tasks without requiring complex syntax. Its name is an acronym for Data Analysis and Presentation.
Dap was written to be a free replacement for SAS, but users are assumed to have a basic familiarity with the C programming language in order to permit greater flexibility.
It has been designed to be used on large data sets and is primarily used in statistical consulting practices.
However, even with its clear benefits, Dap hasn't been updated since 2014 and hasn't seen widespread use when compared to other statistical analysis programs.
Features
Dap is a command line driven program. Below are various features that DAP can perform.
DAP can compute means and percentiles, correlation, & ANOVA from data sets. This includes Unbalanced as well as Crossed, Nested ANOVA. It can also be used to create scatterplots, line graphs and histograms of data. This can include split plots, treatment combinations, as well as latin squares.
DAP can perform linear regression and can utilize regressions to build linear models. In addition to linear regression, DAP can also perform logistic regression analysis as well. There's a variety of other analysis that DAP can do as well including building loglinear models as well as Logit models for linear-by-linear association.
In terms of models, DAP can create mixed balanced and unbalanced models as well as random unbalanced models.
It has been designed so as to cope with very large data sets; even when the size of the data exceeds the size of the computer's memory due to the fact that the program processes files one line at a time rather than reading entire files into memory.
Applications
Industry Uses
Statistical Consulting Practices
Low-level Statistical Analysis
References
Sources
See also
Comparison of statistical packages
gretl
PSPP
External links
administrative page
GNU Project software
Free software programmed in C
Free statistical software |
https://en.wikipedia.org/wiki/Lev%20Bulat | Lev Petrovich Bulat (; 1947–2016) was a Russian physicist.
Bulat was born on April 11, 1947, in Chernovtsy, Ukraine. In 1988 he received a D.Sc in Physics and Mathematics, from Leningrad Polytechnical Institute, with the thesis: "Transport Phenomena in Semiconductors under Large Temperature Gradients".
He was an expert in transport properties of semiconductors, physics of nanostructures, thermoelectric phenomena, direct energy conversion, thermoelectric cooling. He was a Professor of electrical and electronic engineering in Saint Petersburg State University of Low Temperatures and Food Engineering, Russia.
He died suddenly on June 12, 2016, age 69, less than two weeks after attending an international conference.
Awards and Grants
2009. A diploma of the International Thermoelectric Academy, Kiev, Ukraine
2009. A grant of EERSS Program. Singapore.
2008. A grant of the Russian Federal Agency on Sciences and Innovation
2007. A grant of EERSS Program. Singapore.
2006. The Certificate of Honor, the Ministry of Education and Sciences, Russian Federation.
1996–2009. Eleven grants of the Russian Foundation for Basic Research.
2005. A grant of SSHN (France).
2004, 2007. Two grants of CONACYT (Mexico).
2003–2004. A grant of the Ministry of Education, Russian Federation .
1997? A grant of KOSEF (Korea)
1997. A grant of the McArthour Foundation (USA).
1997–2000. A holder of a personal grant of the Russian Academy of Science as an outstanding scientist.
1997. Two grants of the Material Research Society (USA).
1993–1994. Three grants of the International Science Foundation, USA.
SOCIETIES AND ORGANIZATIONS
2004. The Board of the International Thermoelectric Academy
2003. The Board of the International Academy of Refrigeration
2002. Active Member of the International Thermoelectric Academy https://web.archive.org/web/20021204093057/http://www.ite.cv.ua/ita/index.html
1999. Honorary Member of the International Biographical Center's Advisory Council, Cambridge, England. http://www.melrosepress.co.uk/index.html
1998. A member of the Euroscience Society (France). https://web.archive.org/web/20080115202436/http://www.euroscience.org/index.html
1997. A member of the Branch on Thermoelectric Energy Conversion of the Science Council for the Problem "Direct Energy Conversion", the Russian Academy of Sciences.
1997. Active Member of the International Academy of Refrigeration. http://www.maxiar.spb.ru/conf.shtml
1996. Head of the Section for Alternative Methods of Refrigeration of the International Academy of Refrigeration. https://web.archive.org/web/20071013151654/http://zts.com/iar
1996. The Board of the Russian Thermoelectric Society.
1991. The Materials Research Society, USA. http://www.mrs.org/
1990. The International Thermoelectric Society. http://www.its.org/
1989. The Branch on Thermoelectric Materials Research of the Science Council on the Problem "Solid State Physics", the Ukrainian Academy of Sciences.
1982. The Branch on Th |
https://en.wikipedia.org/wiki/Stein%27s%20unbiased%20risk%20estimate | In statistics, Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of "a nearly arbitrary, nonlinear biased estimator." In other words, it provides an indication of the accuracy of a given estimator. This is important since the true mean-squared error of an estimator is a function of the unknown parameter to be estimated, and thus cannot be determined exactly.
The technique is named after its discoverer, Charles Stein.
Formal statement
Let be an unknown parameter and let be a measurement vector whose components are independent and distributed normally with mean and variance . Suppose is an estimator of from , and can be written , where is weakly differentiable. Then, Stein's unbiased risk estimate is given by
where is the th component of the function , and is the Euclidean norm.
The importance of SURE is that it is an unbiased estimate of the mean-squared error (or squared error risk) of , i.e.
with
Thus, minimizing SURE can act as a surrogate for minimizing the MSE. Note that there is no dependence on the unknown parameter in the expression for SURE above. Thus, it can be manipulated (e.g., to determine optimal estimation settings) without knowledge of .
Proof
We wish to show that
We start by expanding the MSE as
Now we use integration by parts to rewrite the last term:
Substituting this into the expression for the MSE, we arrive at
Applications
A standard application of SURE is to choose a parametric form for an estimator, and then optimize the values of the parameters to minimize the risk estimate. This technique has been applied in several settings. For example, a variant of the James–Stein estimator can be derived by finding the optimal shrinkage estimator. The technique has also been used by Donoho and Johnstone to determine the optimal shrinkage factor in a wavelet denoising setting.
References
Point estimation performance |
https://en.wikipedia.org/wiki/Representation%20ring | In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable.
Formal definition
Given a group G and a field F, the elements of its representation ring RF(G) are the formal differences of isomorphism classes of finite dimensional linear F-representations of G. For the ring structure, addition is given by the direct sum of representations, and multiplication by their tensor product over F. When F is omitted from the notation, as in R(G), then F is implicitly taken to be the field of complex numbers.
Succinctly, the representation ring of G is the Grothendieck ring of the category of finite-dimensional representations of G.
Examples
For the complex representations of the cyclic group of order n, the representation ring RC(Cn) is isomorphic to Z[X]/(Xn − 1), where X corresponds to the complex representation sending a generator of the group to a primitive nth root of unity.
More generally, the complex representation ring of a finite abelian group may be identified with the group ring of the character group.
For the rational representations of the cyclic group of order 3, the representation ring RQ(C3) is isomorphic to Z[X]/(X2 − X − 2), where X corresponds to the irreducible rational representation of dimension 2.
For the modular representations of the cyclic group of order 3 over a field F of characteristic 3, the representation ring RF(C3) is isomorphic to Z[X,Y]/(X2 − Y − 1, XY − 2Y,Y2 − 3Y).
The continuous representation ring R(S1) for the circle group is isomorphic to Z[X, X −1]. The ring of real representations is the subring of R(G) of elements fixed by the involution on R(G) given by X ↦ X −1.
The ring RC(S3) for the symmetric group on three points is isomorphic to Z[X,Y]/(XY − Y,X2 − 1,Y2 − X − Y − 1), where X is the 1-dimensional alternating representation and Y the 2-dimensional irreducible representation of S3.
Characters
Any representation defines a character χ:G → C. Such a function is constant on conjugacy classes of G, a so-called class function; denote the ring of class functions by C(G). If G is finite, the homomorphism R(G) → C(G) is injective, so that R(G) can be identified with a subring of C(G). For fields F whose characteristic divides the order of the group G, the homomorphism from RF(G) → C(G) defined by Brauer characters is no longer injective.
For a compact connected group R(G) is isomorphic to the subring of R(T) (where T is a maximal torus) consisting of tho |
https://en.wikipedia.org/wiki/Ferran%20Lavi%C3%B1a | Ferran Laviña is a Spanish former professional basketball player.
Trophies
With Joventut Badalona
Copa del Rey: (1) 2008
ULEB Cup: (1) 2008
Euroleague statistics
|-
| style="text-align:left;"| 2006–07
| style="text-align:left;"| DKV Joventut
| 20 || 6 || 14.3 || .343 || .222 || .889 || 1.8 || .5 || .6 || .1 || 3.9 || 3.3
|-
| style="text-align:left;"| 2008–09
| style="text-align:left;"| DKV Joventut
| 10 || 4 || 18.9 || .452 || .300 || .733 || 1.9 || 1.1 || .3 || .1 || 5.5 || 3.9
|-
| style="text-align:left;"| Career
| style="text-align:left;"|
| 30 || 10 || 15.8 || .384 || .255 || .833 || 1.8 || .7 || .5 || .1 || 4.4 || 3.5
References
External links
ACB Profile
Euroleague.net Profile
1977 births
Living people
Baloncesto Fuenlabrada players
Bàsquet Manresa players
CB L'Hospitalet players
Gijón Baloncesto players
Joventut Badalona players
Liga ACB players
Small forwards
Spanish men's basketball players |
https://en.wikipedia.org/wiki/Josip%20Kri%C5%BEan | Josip Križan (December 31, 1841 in Kokoriči – July 16, 1921 in Varaždin, Croatia) was a Slovenian mathematician, physicist, philosopher and astronomer.
He studied mathematics, physics and philosophy in Graz and between 1867 and 1869 obtained a doctorate to become a professor.
Sources
Slovenian Wikipedia
20th-century Slovenian mathematicians
Slovenian physicists
20th-century Slovenian philosophers
Slovenian astronomers
1841 births
1921 deaths
People from the Municipality of Križevci
19th-century Slovenian philosophers |
https://en.wikipedia.org/wiki/Nonlinear%20partial%20differential%20equation | In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem.
The distinction between a linear and a nonlinear partial differential equation is usually made in terms of the properties of the operator that defines the PDE itself.
Methods for studying nonlinear partial differential equations
Existence and uniqueness of solutions
A fundamental question for any PDE is the existence and uniqueness of a solution for given boundary conditions. For nonlinear equations these questions are in general very hard: for example, the hardest part of Yau's solution of the Calabi conjecture was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes equations is one of the seven Millennium Prize problems in mathematics.
Singularities
The basic questions about singularities (their formation, propagation, and removal, and regularity of solutions) are the same as for linear PDE, but as usual much harder to study. In the linear case one can just use spaces of distributions, but nonlinear PDEs are not usually defined on arbitrary distributions, so one replaces spaces of distributions by refinements such as Sobolev spaces.
An example of singularity formation is given by the Ricci flow: Richard S. Hamilton showed that while short time solutions exist, singularities will usually form after a finite time. Grigori Perelman's solution of the Poincaré conjecture depended on a deep study of these singularities, where he showed how to continue the solution past the singularities.
Linear approximation
The solutions in a neighborhood of a known solution can sometimes be studied by linearizing the PDE around the solution. This corresponds to studying the tangent space of a point of the moduli space of all solutions.
Moduli space of solutions
Ideally one would like to describe the (moduli) space of all solutions explicitly, and
for some very special PDEs this is possible. (In general this is a hopeless problem: it is unlikely that there is any useful description of all solutions of the Navier–Stokes equation for example, as this would involve describing all possible fluid motions.) If the equation has a very large symmetry group, then one is usually only interested in the moduli space of solutions modulo the symmetry group, and this is sometimes a finite-dimensional compact manifold, possibly with singularities; for example, this happens in the case of the Seiberg–Witten equations. A slightly more complicated case is the self dual Yang–Mills equations, when the |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20Atlanta%20Flames%20season | The 1974–75 Atlanta Flames season was the third season for the franchise.
Regular season
Final standings
Record vs. opponents
Schedule and results
Player statistics
Skaters
Note: GP = Games played; G = Goals; A = Assists; Pts = Points; PIM = Penalty minutes
†Denotes player spent time with another team before joining Atlanta. Stats reflect time with the Flames only.
‡Traded mid-season
Goaltending
Note: GP = Games played; TOI = Time on ice (minutes); W = Wins; L = Losses; OT = Overtime/shootout losses; GA = Goals against; SO = Shutouts; GAA = Goals against average
Transactions
The Flames were involved in the following transactions during the 1974–75 season.
Trades
Free agents
Expansion Draft
Draft picks
References
Flames on Hockey Database
Atlanta
Atlanta
Atlanta Flames seasons |
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