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Grothendieck Inequality
In mathematics, the Grothendieck inequality states that there is a universal constant K_G with the following property. If ''M''''ij'' is an ''n'' × ''n'' (real or complex) matrix with : \Big, \sum_ M_ s_i t_j \Big, \le 1 for all (real or complex) numbers ''s''''i'', ''t''''j'' of absolute value at most 1, then : \Big, \sum_ M_ \langle S_i, T_j \rangle \Big, \le K_G for all vectors ''S''''i'', ''T''''j'' in the unit ball ''B''(''H'') of a (real or complex) Hilbert space ''H'', the constant K_G being independent of ''n''. For a fixed Hilbert space of dimension ''d'', the smallest constant that satisfies this property for all ''n'' × ''n'' matrices is called a Grothendieck constant and denoted K_G(d). In fact, there are two Grothendieck constants, K_G^(d) and K_G^(d), depending on whether one works with real or complex numbers, respectively. The Grothendieck inequality and Grothendieck constants are named after Alexander Grothendieck, who proved the existen ... [...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] |
Symposium On Foundations Of Computer Science
The IEEE Annual Symposium on Foundations of Computer Science (FOCS) is an academic conference in the field of theoretical computer science. FOCS is sponsored by the IEEE Computer Society. As writes, FOCS and its annual Association for Computing Machinery counterpart STOC (the Symposium on Theory of Computing) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at FOCS and STOC as one of several defining characteristics of theoretical computer scientists. Awards The Knuth Prize for outstanding contributions to theoretical computer science is presented alternately at FOCS and STOC. Works of the highest quality presented at the conference are awarded the Best Paper Award. In addition, the Machtey Award is presented to the best student- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency Matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information about the degree of each vertex. Definition For a simple graph with vertex set , the adjacency matrix is a square matrix such that its element is one when there is an edge from vertex to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphon
GraphOn GO-Global is a multi-user remote access application for Windows. Overview GO-Global allows multiple users to concurrently run Microsoft Windows applications installed on a Windows server or server farm from network-connected locations and devices. GO-Global redirects the user interface of Windows applications running on the Windows server to the display or browser on the user's device. Applications look and feel like they are running on the user's device. Supported end-user devices include Windows, Mac and Linux personal computers, iOS and Android mobile devices, and Chromebooks. GO-Global is used by Independent Software Vendors (ISVs), Hosted Service Providers (HSPs), and Managed Service Providers (MSPs) to publish Windows applications without modification of existing code for the use of local and remote users. Architecture GO-Global enables multi-user remote access to Windows applications without the use of Microsoft Remote Desktop Services (RDS) or the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurable Function
In mathematics and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in direct analogy to the definition that a continuous function between topological spaces preserves the topological structure: the preimage of any open set is open. In real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable. Formal definition Let (X,\Sigma) and (Y,\Tau) be measurable spaces, meaning that X and Y are sets equipped with respective \sigma-algebras \Sigma and \Tau. A function f:X\to Y is said to be measurable if for every E\in \Tau the pre-image of E under f is in \Sigma; that is, for all E \in \Tau f^(E) := \ \in \Sigma. That is, \sigma (f)\subseteq\Sigma, where \sigma (f) is the σ-algebra gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Journal Of Mathematics
'' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem (Magnes Press). Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section F), the journal publishes articles on all areas of mathematics. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.70, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... was 0.754. External links * Mathematics journals Publications established in 1963 English-language journals Bimonthly journals Hebrew University of Jerusalem {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Physics A
The ''Journal of Physics A: Mathematical and Theoretical'' is a peer-reviewed scientific journal published by IOP Publishing. It is part of the ''Journal of Physics'' series and covers theoretical physics focusing on sophisticated mathematical and computational techniques. It was established in 1968 from the division of the earlier title, ''Proceedings of the Physical Society''. The journal is divided into six sections covering: statistical physics; chaotic and complex systems; mathematical physics; quantum mechanics and quantum information theory; classical and quantum field theory; fluid and plasma theory. The editor in chief is Joseph A Minahan (Uppsala Universitet, Sweden). According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 2.132. Indexing The journal is indexed in: * Scopus * Inspec * Chemical Abstracts * GeoRef * INIS Atomindex * Astrophysics Data System * PASCAL * ''Referativny Zhurnal'' * Zentralblatt MATH * Science Citation Index ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications In Mathematical Physics
''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, statistical mechanics and quantum field theory, and in operator algebras, quantum information and relativity. History Rudolf Haag conceived this journal with Res Jost, and Haag became the Founding Chief Editor. The first issue of ''Communications in Mathematical Physics'' appeared in 1965. Haag guided the journal for the next eight years. Then Klaus Hepp succeeded him for three years, followed by James Glimm, for another three years. Arthur Jaffe began as chief editor in 1979 and served for 21 years. Michael Aizenman became the fifth chief editor in the year 2000 and served in this role until 2012. The current editor-in-chief is Horng-Tzer Yau. Archives Articles from 1965 to 1997 are available in electronic form free of charge, via Pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the ''SIAM Journal on Matrix Analysis and Applications'', to replace the ''SIAM Journal on Algebraic and Discrete Methods''. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.57. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor of 0.755. Although its official ISO abbreviation is ''SIAM J. Discrete Math.'', its publisher and contributors frequently use the shorter abbreviation ''SIDMA''. References External links * Combinatorics journals Publications established in 1988 English-language journals Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost (Max Planck Institute for the Physics of Complex Systems). History In 1893, the ''Physical Review'' was established at Cornell University. It was taken over by the American Physical Society (formed in 1899) in 1913. In 1970, ''Physical Review'' was subdivided into ''Physical Review A'', ''B'', ''C'', and ''D''. At that time section ''A'' was subtitled ''Physical Review A: General Physics''. In 1990 a process was started to split this journal into two, resulting in the creation of ''Physical Review E'' in 1993. Hence, in 1993, ''Physical Review A'' changed its statement of scope to ''Atomic, Molecular and Optical Physics.'' In January 2007, the section of ''Physical Review E'' that published papers on classical optics was merged into ''Physical Review ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
