Search results for "Computational Mathematic"
showing 10 items of 987 documents
Identities of *-superalgebras and almost polynomial growth
2015
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
Estimating the length of minimal spanning trees in compression of files
1984
Compression of a formatted file by a minimal spanning tree (MST) is studied. Here the records of the file are considered as the nodes of a weighted undirected graph. Each record pair is connected in the graph and the corresponding arc is weighted by the sum of field lengths of those fields which differ in the two records. The actual compression is made by constructing an MST of the graph and by storing it in an economic way to preserve the information of the file. The length of the MST is a useful measure in the estimation of the power of the compression. In the paper we study upper bounds of this length, especially in the case where the field lengths of the different fields may vary. The u…
Transformations by diagonal matrices in a normed space
1962
INTERVAL-BASED TRACING OF STRANGE ATTRACTORS
2006
The method described here relies on interval arithmetic and graph theory to compute guaranteed coverings of strange attractors like Hénon attractor. It copes with infinite intervals, using either a geometric method or a new directed projective interval arithmetic.
Some local properties defining $\mathcal T_0$-groups and related classes of groups
2016
We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.
Quantum computing thanks to Bianchi groups
2018
It has been shown that the concept of a magic state (in universal quantum computing: uqc) and that of a minimal informationally complete positive operator valued measure: MIC-POVMs (in quantum measurements) are in good agreement when such a magic state is selected in the set of non-stabilizer eigenstates of permutation gates with the Pauli group acting on it [1]. Further work observed that most found low-dimensional MICs may be built from subgroups of the modular group PS L(2, Z) [2] and that this can be understood from the picture of the trefoil knot and related 3-manifolds [3]. Here one concentrates on Bianchi groups PS L(2, O10) (with O10 the integer ring over the imaginary quadratic fie…
About Graph Mappings
2019
Summary In this articles adjacency-preserving mappings from a graph to another are formalized in the Mizar system [7], [2]. The generality of the approach seems to be largely unpreceeded in the literature to the best of the author’s knowledge. However, the most important property defined in the article is that of two graphs being isomorphic, which has been extensively studied. Another graph decorator is introduced as well.
About Graph Unions and Intersections
2020
Summary In this article the union and intersection of a set of graphs are formalized in the Mizar system [5], based on the formalization of graphs in [7].
A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying ϕ-Contractive Condition
2013
The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings, satisfyingϕ-contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results.
On Different Type Solutions of Boundary Value Problems
2016
We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].