Some Remarks on the Article “On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory”

Ukrainian Mathematical Journal -     

本刊英文版Vol.26(2010),No.3论文摘要(英文)

<正>A Decomposition Theorem for G-GroupsⅠ.LIZASOAIN Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups(G-groups).In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations.Moreover,we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.     

本刊英文版Vol.28(2012),No.3论文摘要(英文)

<正>Closed 3-stop Center and Periphery in Graphs Linda EROH Ralucca GERA Steven J.WINTERS A delivery person must leave the central location of the business,deliver packages at a number of addresses,and then return.Naturally,he/she wishes to reduce costs by finding the most efficient route.This motivates the following: Given a set of k distinct vertices S = {x_1,x_2,…,x_k} in a simple graph G,the closed k-stop-distance of set S is defined to be     

本刊英文版Vol.27(2011),No.3论文摘要(英文)

<正>Group Connectivity and Group Colorings of Graphs—A Survey Hong-Jian LAI Xiangwen LI Yehong SHAO Mingquan ZHAN Abstract In 1950s,Tutte introduced the theory of nowhere-zero flows as a tool to investigate the coloring problem of maps,together with his most fascinating conjectures on nowhere-zero flows.These have been extended by Jaeger et al.in 1992 to group connectivity,the nonhomogeneous form of nowhere-zero flows.Let G be a 2-edge-connected undirected graph,A be an (additive) abelian group and A* = A - {0}.The graph G is A-connected if G has an orientation D(G) such that for every map b:V(G)(?) A satisfying∑_(v∈V(G)) b(v) = 0,there is a function f:E(G)(?) A* such that for each vertex v∈V(G),the total amount of f-values on the edges directed out from v minus the total amount of f-values on the edges directed into v is equal to     

Correction to the paper “on the curvature of a generalization of a contact metric manifolds”

We considered in Example 3.1 of the paper [1] an S-structure on R^2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.     

Erratum to: “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”

Mathematical Notes - An embedding theorem of weighted spaces of functions of positive smoothness defined on irregular domains of n-dimensional Euclidean space in weighted Lebesgue spaces is...     

The Stability in W s,p (Γ) Spaces of L 2-Projections on Some Convex Sets

ABSTRACT

For a polygonal open bounded subset of ?², of boundary Γ, we study stability estimates for the projection operator from L ¹(Γ) on a convex set K _h of continuous piecewise affine functions satisfying bound constraints. We establish stability estimates in L ^p (Γ) and in W ^s,p (Γ) for 1 ≤ p ≤ ∞ and 0 < s ≤ 1. This kind of result plays a crucial role in error estimates for the numerical approximation of optimal control problems of partial differential equations with bilateral control constraints.     

Another Approach to Hölder Estimates for the ∂¯-Operator on Polycylinders - Some Comments to P.W. Darko's Paper

P.W. Darko [Hölder estimates for the ?¯-operator on polycylinders. Complex Variables, 48(10), 929-934.] uses Hölder estimates for the ?¯-operator in order to solve some problems for holomorphic functions in several complex variables such as the corona problem. The present short note proves a generalized version of these estimates.     

Corrigendum to “Some problems of Wielandt revisited” [J. Algebra 302 (1) (2006) 167–185]

An error in the proof of Theorem 2 in [W. Knapp, Some problems of Wielandt revisited, J. Algebra 302 (1) (2006) 167–185] (concerning the action of semisimple groups) is corrected.