Sufficient regularity conditions for common transversals

A well-known condition sufficient for the existence of a transversal of a family of sets is generalized to common transversals of two families, in both the finite and the infinite cases.     

Necessary and sufficient conditions for hyperplane transversals

We prove that a finite family ={B ₁,B ₂, ...,B _n } of connected compact sets in ^d has a hyperplane transversal if and only if for somek there exists a set of pointsP={p ₁,p ₂, ...,p _n } (i.e., ak-dimensional labeling of the family) which spans ^k and everyk+2 sets of are met by ak-flat consistent with the order type ofP. This is a common generalization of theorems of Hadwiger, Katchalski, Goodman-Pollack and Wenger.Supported in part by NSF grant DMS-8501947 and CCR-8901484, NSA grant MDA904-89-H-2030, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a National Science Foundation Science and Technology Center, under NSF grant STC88-09648.Supported by the National Science and Engineering Research Council of Canada and DIMACS.     

On the equivalence of some conditions for weighted Hardy spaces

Let G ∈ H _σ ^p (ℂ₊), where H _σ ^p (ℂ₊) is the class of functions analytic in the half plane ℂ₊ = {z: Re z > 0} and such that

On the conditions for the existence of fractal domain integrals

It is shown that noise transformation processes in some systems with delay may be described in terms of two sorts of fractal domain integrals. The convergence conditions of these integrals are analyzed. The structure of multifractals associated with the integrals for different contraction coefficients is considered.Translated from Teoreticheskaya i Mate-maticheskaya Fizika, Vol. 107, No. 1, pp. 3–11, April, 1996.Translated by A. M. Semikhatov.     

On the equivalence of two variational problems

We consider the following problems where is a convex function, is an open bounded subset of is a closed convex subset of such that and and are suitable obstacles. We give conditions on the function {\it g} under which the two problems are equivalent. Received March 24, 1999/ Accepted January 14, 2000 / Published online June 28, 2000     

On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

On the existence for viscoelastodynamic problems with unilateral boundary conditions

This note deals with a damped wave equation and the evolution of a Kelvin–Voigt viscoelastic material, both problems being subject to unilateral boundary conditions. The functional properties of all the traces are precisely identified through Fourier analysis, which implies the existence of a solution satisfying almost everywhere the unilateral boundary conditions. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On certain conditions for the existence of solutions of equilibrium problems

The main purpose of this paper is the study of sufficient and/or necessary conditions for existence of solutions of equilibrium problems. We discuss some of the assumptions of the problem, under which the introduced conditions are sufficient and/or necessary, and also analyze the effect of these assumptions on the connection between the solution sets of the equilibrium problem and of a related convex feasibility problem.     

On the equivalence of ball conditions for simplicial finite elements in Rd

We prove that the inscribed and circumscribed ball conditions, commonly used in finite element analysis, are equivalent in any dimension.     

Necessary and sufficient conditions for transversals of countable set systems

This paper proves a conjecture of C. St. J. A. Nash-Williams giving necessary and sufficient conditions for an arbitrary countable system of sets to have a transversal.     

On the existence of a metric for path-spaces of order two

Proceedings - Mathematical Sciences -     

On the existence of graphs of diameter two and defect two

In the context of the degree/diameter problem, the ‘defect’ of a graph represents the difference between the corresponding Moore bound and its order. Thus, a graph with maximum degree d and diameter two has defect two if its order is n=d²−1. Only four extremal graphs of this type, referred to as (d,2,2)-graphs, are known at present: two of degree d=3 and one of degree d=4 and 5, respectively. In this paper we prove, by using algebraic and spectral techniques, that for all values of the degree d within a certain range, (d,2,2)-graphs do not exist.The enumeration of (d,2,2)-graphs is equivalent to the search of binary symmetric matrices A fulfilling that AJ_n=dJ_n and A²+A+(1−d)I_n=J_n+B, where J_n denotes the all-one matrix and B is the adjacency matrix of a union of graph cycles. In order to get the factorization of the characteristic polynomial of A in Q[x], we consider the polynomials F_i,d(x)=f_i(x²+x+1−d), where f_i(x) denotes the minimal polynomial of the Gauss period , being ζ_i a primitive ith root of unity. We formulate a conjecture on the irreducibility of F_i,d(x) in Q[x] and we show that its proof would imply the nonexistence of (d,2,2)-graphs for any degree d>5.     

On the number of isomorphism classes of transversals

In this paper we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of normalized right transversals of H in G is four.     

Some conditions for the existence of f-factors

Let m, l, n be three odd integers such that m > l > n. It is proved that if a graph G has an m-factor and an n-factor, then it also has an l-factor. In addition, we obtain sufficient conditions for the existence of an f-factor, in terms of vertex-deleted subgraphs.