Search results for "Group Theory"

On finite products of totally permutable groups

1996

In this paper the structure of finite groups which are the product of two totally permutable subgroups is studied. In fact we can obtain the -residual, where is a formation, -projectors and -normalisers, where is a saturated formation, of the group from the corresponding subgroups of the factor subgroups.

Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains

2016

We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…

Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems

2021

In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

1986

Etude de deux systemes differents avec de l'hydroxy-4 benzoate de phenyle comme unite mesogene. Les separateurs sont formes de 6 unites methylene et le squelette est de l'acide poly(meth)acrylique

Nonlocal (Pair Site) Reactivity from Second-Order Static Density Response Function:  Gas- and Solution-Phase Reactivity of the Acetaldehyde Enolate a…

1999

A nonlocal (pair site) reactivity scheme is developed and tested. The theory is cast in terms of the first-order Fukui response function f(r,r‘), previously proposed by Fuentealba and Parr [J. Chem. Phys. 1991, 94, 5559]. A change of variables is introduced by using the softness s(r) and t(r) = [∂s(r)/∂N]υ(r) (the variation of softness with respect to the changes in the total number of electrons N at constant external potential υ(r)) that leads to a simple expression for the variation of the Fukui function at site k, namely = − for an electrophilic attack. The first term describes a local contribution, proportional to the variation of the electrostatic potential that can be induced, for exa…

Does glycosyl transfer involve an oxacarbenium intermediate? Computational simulation of the lifetime of the methoxymethyl cation in water

2011

2D free-energy surfaces for transfer of the methoxymethyl cation between two water molecules are constructed from molecular dynamics (MD) simulations in which these atoms are treated quantum-mechanically within a box of 1030 classical solvent water molecules at 300 K. This provides a simple model for glycosyl transfer in water. The AM1/TIP3P surfaces with 2D-spline corrections at either MPWB1K/6-31+G(d,p) or MP2/6-31+G(d,p) contain a shallow free-energy well corresponding to an oxacarbenium ion intermediate in a DN*AN mechanism. MD analysis at three temperatures leads to a classical estimate of the lifetime of the methoxymethyl cation in water; when quantum corrections for vibrational zero-…

Form factors of the isovector scalar current and the ηπ scattering phase shifts

2015

33 pages.- 14 figures.- v2: Some clarifications and corrections of typos

Injectors with a central socle in a finite solvable group

2013

Abstract In response to an Open Question of Doerk and Hawkes (1992) [2, IX §4, p. 628] , we shall describe three constructions for the Z π -injectors of a finite solvable group, where Z π is the Fitting class formed by the finite solvable groups whose π -socle is central (and π is a set of prime numbers).

Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations

2014

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/395368 Open Access We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.

Second-Order Calculus on RCD Spaces

2020

In this conclusive chapter we introduce the class of those metric measure spaces that satisfy the Riemannian curvature-dimension condition, briefly called RCD spaces, and we develop a thorough second-order differential calculus over these structures.