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Tôhoku Mathematical Journal
The ''Tohoku Mathematical Journal'' is a mathematical research journal published by Tohoku University in Japan. It was founded in August 1911 by Tsuruichi Hayashi. History Due to World War II the publication of the journal stopped in 1943 with volume 49. Publication was resumed in 1949 with the volume numbering starting again at 1. In order to distinguish between the identical numbered volumes, volumes in the first publishing period are referred to as the ''first series'' whereas the later volumes are called ''second series''. Before volume 51 of the second series the journal was called ''Tôhoku Mathematical Journal'', with a circumflex over the second letter of ''Tohoku''. Selected papers *. The first publication of the Sprague–Grundy theorem, the basis for much of combinatorial game theory, later independently rediscovered by P. M. Grundy. *. This paper describes Weiszfeld's algorithm for finding the geometric median. *. This paper, often referred to as " The Tohoku pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patrick Michael Grundy
Patrick Michael Grundy (16 November 1917, Yarmouth, Isle of Wight – 4 November 1959) was an English mathematician and statistician. He was one of the eponymous co-discoverers of the Sprague–Grundy function and its application to the analysis of a wide class of combinatorial games. Biography Grundy received his secondary education from Malvern College, to which he had obtained a Major Scholarship in 1931, and from which he graduated in 1935. While there, he demonstrated his aptitude for mathematics by winning three prizes in that subject. After leaving school he entered Clare College, Cambridge, on a Foundation Scholarship, where he read for the Mathematical Tripos from 1936 to 1939, earning first class honours in Part II and a distinction in Part III. The work for which he is best known appeared in his first paper, ''Mathematics and Games'', first published in the Cambridge University Mathematical Society's magazine, ''Eureka'' in 1939, and reprinted by the same magaz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publications Established In 1911
To publish is to make content available to the general public.Berne Convention, article 3(3) URL last accessed 2010-05-10.Universal Copyright Convention, Geneva text (1952), article VI . URL last accessed 2010-05-10. While specific use of the term may vary among countries, it is usually applied to text, images, or other audio-visual content, including paper ( |
Mathematics Journals
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sasakian Manifold
In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold (M,\theta) equipped with a special kind of Riemannian metric g, called a ''Sasakian'' metric. Definition A Sasakian metric is defined using the construction of the ''Riemannian cone''. Given a Riemannian manifold (M,g), its Riemannian cone is the product :(M\times ^)\, of M with a half-line ^, equipped with the ''cone metric'' : t^2 g + dt^2,\, where t is the parameter in ^. A manifold M equipped with a 1-form \theta is contact if and only if the 2-form :t^2\,d\theta + 2t\, dt \cdot \theta\, on its cone is symplectic (this is one of the possible definitions of a contact structure). A contact Riemannian manifold is Sasakian, if its Riemannian cone with the cone metric is a Kähler manifold with Kähler form :t^2\,d\theta + 2t\,dt \cdot \theta. Examples As an example consider :S^\hookrightarrow ^=^ where the right hand side is a natural Kähler manifold and read as the cone ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Category
In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototypical example of an abelian category is the category of abelian groups, Ab. The theory originated in an effort to unify several cohomology theories by Alexander Grothendieck and independently in the slightly earlier work of David Buchsbaum. Abelian categories are very ''stable'' categories; for example they are regular and they satisfy the snake lemma. The class of abelian categories is closed under several categorical constructions, for example, the category of chain complexes of an abelian category, or the category of functors from a small category to an abelian category are abelian as well. These stability properties make them inevitable in homological algebra and beyond; the theory has major applications in algebraic geometry, cohomology and pure category theory. Abelian categories are na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the ''L''1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, = 3 and = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sprague–Grundy Theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim. It can therefore be represented as a natural number, the size of the heap in its equivalent game of nim, as an ordinal number in the infinite generalization, or alternatively as a nimber, the value of that one-heap game in an algebraic system whose addition operation combines multiple heaps to form a single equivalent heap in nim. The Grundy value or nim-value of any impartial game is the unique nimber that the game is equivalent to. In the case of a game whose positions are indexed by the natural numbers (like nim itself, which is indexed by its heap sizes), the sequence of nimbers for successive positions of the game is called the nim-sequence of the game. The Sprague–Grundy theorem and its proof encapsulate the main results of a theory discovered independently by R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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