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Studying a mathematical model of parallel computation by algebraic topology methods
Journal of Applied and Industrial Mathematics, 2009Under study is one of the mathematical models of parallel computational processes, i.e., an asynchronous transition system. Some methods are proposed for calculating the homology groups and the Poincare polynomial of a finite asynchronous transition system.
A. A. Khusainov +2 more
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Mathematical knowledge management in algebraic topology
ACM Communications in Computer Algebra, 2012The work presented in this thesis tries to particularize Mathematical Knowledge Management to Algebraic Topology. Mathematical Knowledge Management is a branch of Computer Science whose main goal consists in developing integral assistants for Mathematics including computation, deduction and powerful user interfaces able to make the daily work of ...
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2020
Advancing from eight imaginary worlds of octonion algebra, for the first time we introduce dodecanion algebra, a mathematical universe made of twelve imaginary worlds one inside another. The difference between eight and twelve imaginary worlds is that the Fano plane that sets the products of imaginary vectors is replaced by a triplet of manifolds that ...
Pushpendra Singh +7 more
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Advancing from eight imaginary worlds of octonion algebra, for the first time we introduce dodecanion algebra, a mathematical universe made of twelve imaginary worlds one inside another. The difference between eight and twelve imaginary worlds is that the Fano plane that sets the products of imaginary vectors is replaced by a triplet of manifolds that ...
Pushpendra Singh +7 more
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Operator Algebras, Mathematical Physics, and Low Dimensional Topology
1993This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.
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Physics Bulletin, 1976
Paul Roman Oxford: Pergamon 1975 Vol 1 pp xlviii + 378 Vol 2 pp lxi + 381–666 price each £10.55 (cased), £7.40 (paperback) The books begin with a somewhat terse review of the theory of sets and maps, and then proceed to a more leisurely coverage of the topics mentioned in the titles.
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Paul Roman Oxford: Pergamon 1975 Vol 1 pp xlviii + 378 Vol 2 pp lxi + 381–666 price each £10.55 (cased), £7.40 (paperback) The books begin with a somewhat terse review of the theory of sets and maps, and then proceed to a more leisurely coverage of the topics mentioned in the titles.
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1995
Offers an extensive investigation of the theory of closure operators in different areas of mathematics, including (but not limited to) algebra, topology, combinatorics, etc. The closure operators are used to describe relevant concepts and properties as epimorphisms, injectivity, compactness, (dis)connectedness, torsion theories, factoriaztion systems ...
DIKRANJAN, Dikran, THOLEN W.
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Offers an extensive investigation of the theory of closure operators in different areas of mathematics, including (but not limited to) algebra, topology, combinatorics, etc. The closure operators are used to describe relevant concepts and properties as epimorphisms, injectivity, compactness, (dis)connectedness, torsion theories, factoriaztion systems ...
DIKRANJAN, Dikran, THOLEN W.
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Exploring the Applications of Algebraic Topology in Modern Mathematics and Data Analysis
Algebraic topology is a vibrant and intricate branch of mathematics that intertwines the abstract structures of algebra with the intuitive notions of topology. At its core, algebraic topology investigates topological spaces and their properties through algebraic invariants, enabling mathematicians to classify and understand spaces in a profound way ...openaire +1 more source
(Hodge Conjecture). Description: Let X be a smooth projective complexalgebraic variety. Its cohomology admits a Hodge decomposition:H2k(X, C) = Mp+q=2kHp,q(X).Conjecture: Every class inHk,k(X) ∩ H2k(X, Q)is a rational linear combination of classes of algebraic cycles.2Problem 1.2 (Jacobian Conjecture). Description: Let F = (F1, . . . , Fn) : Cn → Cn be
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The Role of Algebraic Topology in Mathematics
Journal of the London Mathematical Society, 1966openaire +2 more sources
BUILDING MATHEMATICAL MATURITY THROUGH ALGEBRAIC TOPOLOGY CHALLENGING PATHS
A central educational goal of higher-level mathematics undergraduate courses is to foster the development of competences that enable students to use mathematical abstraction and formalism and, at the same time, to develop mathematical creativity. Does it mean mathematical maturity? Research in university mathematics education suggests that to grasp theopenaire +1 more source