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Graph Algebra
In mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by McNulty and Shallon, and has seen many uses in the field of universal algebra since then. Definition Let be a directed graph, and an element not in . The graph algebra associated with has underlying set V \cup \, and is equipped with a multiplication defined by the rules * if x,y \in V and (x,y) \in E, * if x,y \in V \cup \ and (x,y)\notin E. Applications This notion has made it possible to use the methods of graph theory in universal algebra and several other areas of discrete mathematics and computer science. Graph algebras have been used, for example, in constructions concerning dualities, equational theories, flatness, groupoid rings, topologies, varieties, finite-state machines, tree languages and tree automata, etc. See also * Group algebra (other) * Incidence algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Finite-state Machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of ''State (computer science), states'' at any given time. The FSM can change from one state to another in response to some Input (computer science), inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—Deterministic finite automaton, deterministic finite-state machines and Nondeterministic finite automaton, non-deterministic finite-state machines. For any non-deterministic finite-state machine, an equivalent deterministic one can be constructed. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over concerns about competing with the '' American Journal of Mathematics''. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Marcel Dekker
Marcel Dekker was a journal and encyclopedia publishing company with editorial boards found in New York City. Dekker encyclopedias are now published by CRC Press, part of the Taylor and Francis publishing group. History Initially a textbook publisher, the company added journal publishing in the 1970s, and encyclopedia publishing in the early 1980s. Serving mathematics, it published a series of ''Lecture Notes in Pure and Applied Mathematics''. The company was purchased by Taylor and Francis in 2003. At that time, it published 78 journals and 300 new books annually. The imprint closed in 2005. As of 2008, they have a total of 26 encyclopedias available. These encyclopedias deal with scientific issues such as agricult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algebra Universalis
''Algebra Universalis'' is an international scientific journal focused on universal algebra and lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bou .... The journal, founded in 1971 by George Grätzer, is currently published by Springer-Verlag. Honorary editors in chief of the journal included Alfred Tarski and Bjarni Jónsson. External links ''Algebra Universalis'' on Springer.com''Algebra Universalis'' homepage, including instructions to authors * Universal algebra Algebra journals Academic journals established in 1971 Springer Science+Business Media academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Journal Of Algebra
''Journal of Algebra'' (ISSN 0021-8693) is an international mathematical research journal in algebra. An imprint of Academic Press, it is published by Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, .... ''Journal of Algebra'' was founded by Graham Higman, who was its editor from 1964 to 1984. From 1985 until 2000, Walter Feit served as its editor-in-chief. In 2004, ''Journal of Algebra'' announced (vol. 276, no. 1 and 2) the creation of a new section on computational algebra, with a separate editorial board. The first issue completely devoted to computational algebra was vol. 292, no. 1 (October 2005). The Editor-in-Chief of the ''Journal of Algebra'' is Michel Broué, Université Paris Diderot, and Gerhard Hiß, Rheinisch-Westfälische Technische Hochschule Aachen ( R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact facto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Path Algebra
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation of a quiver assigns a vector space to each vertex of the quiver and a linear map to each arrow . In category theory, a quiver can be understood to be the underlying structure of a category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from (the category of categories) to (the category of multidigraphs). Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. Definition A quiver consists of: * The set of vertices of * The set of edges of * Two functions: giving the ''start'' or ''source'' of the edge, and another function, giving the ''target'' of the edge. This definition is identical to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Incidence Algebra
In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative ring with unity. Subalgebra#Subalgebras_for_algebras_over_a_ring_or_field, Subalgebras called reduced incidence algebras give a natural construction of various types of generating functions used in combinatorics and number theory. Definition A locally finite poset is one in which every Partially ordered set#Intervals, closed interval :[''a, b''] = is finite set, finite. The members of the incidence algebra are the function (mathematics), functions ''f'' assigning to each empty set, nonempty interval [''a, b''] a scalar ''f''(''a'', ''b''), which is taken from the ''ring (mathematics), ring of scalars'', a commutative ring with unity. On this underlying set one defines addition and scalar multiplication pointwise, and "multiplication" in the incidence algebra is a convolution defined by :(f*g)(a, b)=\sum_f(a, x)g(x, b). A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Group Algebra (other) .
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In mathematics, the group algebra can mean either *A group ring of a group over some ring. *A group algebra of a locally compact group In functional analysis and related areas of mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that representations of the algebra are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
