‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

Given a group G and an endomorphism ? of G, two elements x,y?G are said to be ?-conjugate if x=gy?(g)?1 for some g?G. The number equivalence classes this relation is the Reidemeister R(?) ?. set {R(?)|??Aut(G)} called spectrum G. We investigate numbers spectra on direct products finitely many groups determine what information can derived from individual factors.

Lipid-associated ferritin from homogenates of guinea pig liver is released from its conjugate(s) by incubation with the non-ionic detergents Triton X-100 and Nonidet P-40 but not by incubation with the anionic detergent deoxycholate. The amount of lipid-associated ferritin released from its conjugate(s) depends on the concentration of the non-ionic detergents. At a final non-ionic detergent con...

Motivated by the recent applications of the conjugate residual method to nonsymmetric linear systems by Sogabe, Sugihara and Zhang [An extension of the conjugate residual method to nonsymmetric linear systems. J. Comput. Appl. Math., Vol. 266, 2009, pp. 103–113], this paper describes two conjugate direction methods, BiCR and BiCG, and attempts to extend their applications to compute the station...

A theorem proved by C. C. Hsiung in a recent paper [l]1 may be stated as follows : In a linear space Sn of n ( ̂ 3) dimensions let Nx be a conjugate net and w be a fixed hyperplane ; then the points M, M of intersection of the fixed hyperplane w and the two tangents at a point x of the net Nx describe two conjugate nets Nm, Nm in the hyperplane ir, respectively, and one of the two nets Nm, N¡¡ i...

We prove that differentials of lattice coordinate functions x must be algebraic independent to their involutive conjugate, else no correct continuum limit exists. PACS: 02.40.Gh, 11.15.Ha

Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product C∗-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via K-theory and C∗-algebras. For example, it is shown that two Cantor minimal systems are approximately τ -conjugate if and o...

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the ...

The aim of this paper is to give a uniied framework for deriving projection methods for solving systems of linear equations. We shall show that all these methods follow from a unique minimization problem. The particular cases of the methods of steepest descent, Richardson and conjugate gradients will be treated in details. Projection acceleration procedures for accelerating the convergence of a...