A Remark on З-Permutability of Finite Groups

Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result： If the cyclic subgroups of prime order or order 4 iif p = 2） of every member of З are З-permutable subgroups in G, then G is supersolvable. In this paper, we give an elementary proof of this theorem and generalize it in terms of formation.     

On the Characterization of the Core of a π-Prefrattini Subgroup of a Finite Soluble Group

Siberian Mathematical Journal - Let π be a set of primes and let H be a π-prefrattini subgroup of a finite soluble group G. We prove that there exist elements x, y, z ∈ G such that...     

A Remark on Finite Horizon Markov Decision processes

本文是利用压缩算子求解的折扣有限水平Markov决策过程逼近非折扣情形的一点注记。这里涉及的状态集与活动集均为可数集。     

Separability of the subgroups of residually nilpotent groups in the class of finite π-groups

Siberian Mathematical Journal - Given a nonempty set π of primes, call a nilpotent group π-bounded whenever it has a central series whose every factor F is such that: In every quotient...     

A Remark on the Intrinsic Rigidity of Compact Minimal Submanifolds in A Sphere

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Strongly Modular Subgroup in Finite Group

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A Remark on the Fixed point Theorem of the Expansion Mappings

Let X be a Complete metric space with distance function d, anp T a mapping from X into X. T is said to be a first type of the expansion mapping, if it satisfies the following condition     

A Remark on the Completeness of Systems of Exponentials with Weight in L2(ℝ)

We establish new conditions for the completeness of systems of exponentials with weight in L ²(), which complement and generalize the results obtained earlier by the authors.     

A Note on the Graph of Class One

1 Introduction Let G be a simple graph. An edge colouring ∏ of G is a map ∏: E(G)→{1,2,…} such that no two adjacent edges have the same image. The chromatic index X' (G) of G is the minimum cardinality of all possible images of colouring of G. By Vizing's theorem if △ is the maximum degree of G.     

A Remark on the Convergence of the Douglas–Rachford Iteration in a Non-convex Setting

Using a known construction of a Lyapunov function, it is shown that the Douglas–Rachford iteration with respect to a sphere and a line in a Hilbert space converges to the intersection point in a fashion which is stronger than uniform convergence on compact sets.     

A Remark on the Self-similar Solution of Semi-linear Schrodinger Equation

In this paper we consider the Cauchy problem to the following semi-linear Schrdinger equation     

A Remark on Steinness

In this paper, the authors prove that if Mn is a complete noncompact Kahler manifold with a pole p, and its holomorphic bisectional curvature is asymptotically non-negative to p, then it is a Stein manifold.     

A Remark on the Boundedness of Calderón-Zygmund Operators in Non-homogeneous Spaces

Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.     

A Remark on the Dimension of the Bergman Space of Some Hartogs Domains

Let D be a Hartogs domain of the form \(D=\{(z,w)\in\mathbb{C}\times\mathbb{C}^{N}: \|w\| where u is a subharmonic function on ?. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite-dimensional.     

A Remark on the Weak Topology and the Degree

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A Note on the π—regularity of Rings

LetRbeassociativewithanidentity.RingRiscalledaπ-regularringifandonlyifforeveryelementainR,thereexistsomen1,c∈Rsuchthatan=ancan.RingRiscalledaunitπ-regularringifandonlyifforanyelementainR,thereissomem1suchthatam=amuamforaunitu∈R.Manyringsareunitπ-regularrings,suchassemicommutativeπ-regularrings,finitesemicommutativerings,stronglyπ-regularringsandunit-regularrings.Risstronglyπ-regularifforeverya∈Rthereexistn1andc∈Rsuchthatan=an 1c.Ifthein-dexnaboveisoneforalla∈R,thenRiscalledabel…     

A Remark on the Hörmander Inequality

A sufficient condition is given in order to ensure the Hörmander inequality for a (formally) self-adjoint transversally elliptic pseudodifferential operator P in the case of the symplectic form changing rank on the characteristic manifold.     

Interpolation Sequences for the Class of Functions of Finite η-Type Analytic in the Unit Disk

We establish conditions for the existence of a solution of the interpolation problem f( _n ) = b _n in the class of functions f analytic in the unit disk and such that

A Remark on a Theorem of Szegö

Let be a polynomial with complex coefficients and define, for , where ||P|| is the euclidean norm of the polynomial P. By a theorem of Szegö where is the Mahler measure of F. Recently, J. Dégot proved an effective version of this result. In this paper we sharpen Dégot's result, under the additional hypotheses that F is a square-free polynomial with integer coefficients and without reciprocal factors.