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Yuri Ershov
Yury Leonidovich Yershov (, born 1 May 194 is a Soviet and Russian mathematician. Yury Yershov was born in 1940 in Novosibirsk. In 1958 he entered the Tomsk State University and in 1963 graduated from the Mathematical Department of the Novosibirsk State University. In 1964 he successfully defended his PhD thesis "Decidable and Undecidable Theories" (advisor Anatoly Maltsev). In 1966 he successfully defended his DrSc thesis "Elementary Theory of Fields" (Элементарные теория полей). Apart from being a mathematician, Yershov was a member of the Communist Party and had different distinguished administrative duties in Novosibirsk State University. Yershov has been accused of antisemitic practices, and his visit to the U.S. in 1980 drew public protests by a number of U.S. mathematicians. Yershov himself denied the validity of these accusations. Yury Yershov is a member of the Russian Academy of Sciences, professor emeritus of Novosibirsk State University and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novosibirsk
Novosibirsk is the largest city and administrative centre of Novosibirsk Oblast and the Siberian Federal District in Russia. As of the 2021 Russian census, 2021 census, it had a population of 1,633,595, making it the most populous city in Siberia and the list of cities and towns in Russia by population, third-most populous city in Russia after Moscow and Saint Petersburg. Additionally, it is the largest city in the Asian part of Russia and the most populous city in the country that does not have the status of a Federal subjects of Russia, federal subject. Novosibirsk is located in southwestern Siberia, on the banks of the Ob River. Novosibirsk was founded in 1893 on the Ob River crossing point of the future Trans-Siberian Railway, where the Novosibirsk Rail Bridge was constructed. Originally named Novonikolayevsk ("New Nicholas") in honor of Nicholas II of Russia, Emperor Nicholas II, the city rapidly grew into a major transport, commercial, and industrial hub. Novosibirsk was r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra I Logika
''Algebra i Logika'' (English: ''Algebra and Logic'') is a peer-reviewed Russian mathematical journal founded in 1962 by Anatoly Ivanovich Malcev, published by the Siberian Fund for Algebra and Logic at Novosibirsk State University. An English translation of the journal is published by Springer-Verlag as ''Algebra and Logic'' since 1968. It published papers presented at the meetings of the "Algebra and Logic" seminar at the Novosibirsk State University. The journal is edited by academician Yury Yershov. The journal is reviewed cover-to-cover in ''Mathematical Reviews'' and ''Zentralblatt MATH''. Abstracting and Indexing ''Algebra i Logika'' is indexed and abstracted in the following databases: According to the ''Journal Citation Reports'', the journal had a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demidov Prize
The Demidov Prize () is a national scientific prize in Russia awarded annually to the members of the Russian Academy of Sciences. Originally awarded from 1832 to 1866 in the Russian Empire, it was revived by the government of Russia's Sverdlovsk Oblast in 1993. In its original incarnation it was one of the first annual scientific awards, and its traditions influenced other awards of this kind including the Nobel Prize. History In 1831 Count Pavel Nikolaievich Demidov, representative of the famous Demidov family, established a scientific prize in his name. The Saint Petersburg Academy of Sciences (now the Russian Academy of Sciences) was chosen as the awarding institution. In 1832 the president of the Petersburg Academy of Sciences, Sergei Uvarov, awarded the first prizes. From 1832 to 1866 the Academy awarded 55 full prizes (5,000 rubles) and 220 part prizes. Among the winners were many prominent Russian scientists: the founder of field surgery and inventor of the plaster im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributive Lattice
In mathematics, a distributive lattice is a lattice (order), lattice in which the operations of join and meet distributivity, distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union (set theory), union and intersection (set theory), intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to order isomorphism, isomorphism—given as such a lattice of sets. Definition As in the case of arbitrary lattices, one can choose to consider a distributive lattice ''L'' either as a structure of order theory or of universal algebra. Both views and their mutual correspondence are discussed in the article on lattice (order), lattices. In the present situation, the algebraic description appears to be more convenient. A lattice (''L'',∨,∧) is distributive if the following additional identity holds for all ''x'', ''y'', and ''z'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relatively Complemented
In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element ''a'' has a complement, i.e. an element ''b'' satisfying ''a'' ∨ ''b'' = 1 and ''a'' ∧ ''b'' = 0. Complements need not be unique. A relatively complemented lattice is a lattice such that every interval 'c'', ''d'' viewed as a bounded lattice in its own right, is a complemented lattice. An orthocomplementation on a complemented lattice is an involution that is order-reversing and maps each element to a complement. An orthocomplemented lattice satisfying a weak form of the modular law is called an orthomodular lattice. In bounded distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra. Definition and basic properties A complemented lattice is a bounded lattice (with least el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group \mathrm_n defined over a finite set of n symbols consists of the permutations that can be performed on the n symbols. Since there are n! (n factorial) such permutation operations, the order (number of elements) of the symmetric group \mathrm_n is n!. Although symmetric groups can be defined on infinite sets, this article focuses on the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Number
In number theory, given a prime number , the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and extending to the left rather than to the right. For example, comparing the expansion of the rational number \tfrac15 in base vs. the -adic expansion, \begin \tfrac15 &= 0.01210121\ldots \ (\text 3) &&= 0\cdot 3^0 + 0\cdot 3^ + 1\cdot 3^ + 2\cdot 3^ + \cdots \\ mu\tfrac15 &= \dots 121012102 \ \ (\text) &&= \cdots + 2\cdot 3^3 + 1 \cdot 3^2 + 0\cdot3^1 + 2 \cdot 3^0. \end Formally, given a prime number , a -adic number can be defined as a series s=\sum_^\infty a_i p^i = a_k p^k + a_ p^ + a_ p^ + \cdots where is an integer (possibly negative), and each a_i is an integer such that 0\le a_i < p. A -adic integer is a -adic number such that < ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Theory
In mathematical logic, an elementary theory is a theory that involves axioms using only finitary first-order logic, without reference to set theory or using any axioms that have consistency strength equal to set theory. Saying that a theory is elementary is a weaker condition than saying it is algebraic. Examples Examples of elementary theories include: * The theory of groups ** The theory of finite groups ** The theory of abelian groups * The theory of fields ** The theory of finite fields ** The theory of real closed fields * Axiomization of Euclidean geometry Related *Elementary definition * Elementary theory of the reals References * Mac Lane and Moerdijk Moerdijk () is a municipality and a town in the South of the Netherlands, in the province of North Brabant. History The municipality of Moerdijk was founded in 1997 following the merger of the municipalities of Fijnaart en Heijningen, Klunde ..., ''Sheaves in Geometry and Logic: A First Introduction to Topos T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality consists. Major themes that are dealt with in philosophy of mathematics include: *''Reality'': The question is whether mathematics is a pure product of human mind or whether it has some reality by itself. *''Logic and rigor'' *''Relationship with physical reality'' *''Relationship with science'' *''Relationship with applications'' *''Mathematical truth'' *''Nature as human activity'' (science, the arts, art, game, or all together) Major themes Reality Logic and rigor Mathematical reasoning requires Mathematical rigor, rigor. This means that the definitions must be absolutely unambiguous and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
