Notes on orthogonal polynomials for exponential weights (Root-distances. Weighted Lebesgue function)

We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for exponential weights, where the weights are not necessarily symmetric. Supported by the Hungarian National Science Foundation Grants (OTKA) T37299 and T047132.     

On the linear combination of <Emphasis Type="Italic">q</Emphasis>-additive functions at prime places

Necessary and sufficient conditions are given for linear combinations of q-ary additive functions to belong to some function classes when the summation is extended to the set of primes. Supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA T46993.     

On the relationships of seven numerical sequences

We analyze the relationships of four classical and three recently defined classes of numerical sequences. This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # T042462 and TS44782.     

On circle groups of nilpotent rings of charateristic 2

We prove that every nilpotent group of class 2 and exponent 4 is the circle group of a nilpotent ring of index 3 and characteristic 2.Dedicated to Professor László Fuchs on his 70th birthdayResearch supported by the Hungarian National Foundation for Scientific Research grant No. T 014279     

Generalized hessian forC 1,1 functions in infinite dimensional normed spaces

The subject of this paper is the systematic study of second order notions concerning differentiable functions with Lipschitz derivative. The results and notions are motivated by recent papers of Cominetti, Correa and Hiriart-Urruty. The first goal of this paper is the comparison of several known second order directional derivatives. The second goal is the introduction of a generalized Hessian which is a set of certain symmetric bilinear forms. The relation of this generalized Hessian to other existing second order derivatives is also described. The research was supported by a grant from the National Science Foundation NSF-66-2270, which is gratefully acknowledged. Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T-016846 and by the Humboldt Foundation.     

Higher order Lipschitz classes of functions and absolutely convergent Fourier series

We introduce the higher order Lipschitz classes Λ _r (α) and λ _r (α) of periodic functions by means of the rth order difference operator, where r = 1, 2, ..., and 0 < α ≦ r. We study the smoothness property of a function f with absolutely convergent Fourier series and give best possible sufficient conditions in terms of its Fourier coefficients in order that f belongs to one of the above classes. This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.     

A converse result for approximation by a weighted Szász-Mirakyan operator

We prove that the weighted error of approximation by the Szász-Mirakyan-type operator introduced in [1] is equivalent to the modulus of smoothness of the function. This result is analogous to previous results for Bernstein-type operators obtained by Ditzian-Ivanov and Szabados. Research supported by Hungarian Scientific Research Fund (OTKA), Grant No. T-049196.     

Enlargements and generalized topologies

The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is replaced by a generalized topology. Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786.     

Groups with super-exponential subgroup growth

We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation.     

On a convex body with odd hadwiger number

We construct a convex body K ⊃ ℝ³ such that the maximum number of mutually nonoverlapping translates of K which touch K is 15. The work is in part supported by grant no. T043556 of the Hungarian National Science Foundation (OTKA).     

Regular and determinant forms for representing the cauchy index of a rational function

We consider regular and determinant forms for representing the index of an arbitrary rational function based on a proposed generalization of the Routh method. We propose forms for representing the index relative to the negative real axis, the positive real axis and the entire axis, as well as the greatest common divisor of polynomials both in terms of the elements of the Routh method and in terms of the determinant of the corresponding Hurwitz matrix. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

EP Theorem for Dual Linear Complementarity Problems

The linear complementarity problem (LCP) belongs to the class of -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix. The research of Tibor Illés and Marianna Nagy has been supported by the Hungarian National Research Fund OTKA T 049789 and by the Hungarian Science and Technology Foundation TéT SLO-4/2005. Tamàs Terlaky has been supported by an NSERC Discovery grant, MITACS and the Canada Research Chair program.     

Singular spaces of matrices and their application in combinatorics

We study linear spaces of n×n matrices in which every matrix is singular. Examples are given to illustrate that a characterization of such subspaces would solve various open problems in combinatorics and in computational algebra. Several important special cases of the problem are solved, although often in disguise. Research supported by Hungarian National Research fund No. 1812.     

Über endliche galoissche schiefkörpererweiterungen ohne endliche galoisgruppen

We define a generalized Brauer-Severi variety to be the projective Variety whose closed points correspond to rank m right ideals in a central simple algebra. We show that these varieties are forms of the Grassmann variety and their function fields are generic partial splitting fields for the associated algebras. The subgroup of the Brauer group split by the function field is calculated. Following Schofield and van den Bergh, we calculate the index of a simple ailgebra extended by the function field of a generalized Brauer-Severi variety associated with any other central simple algebra.     

On generalized neighbourhood systems

It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following the paper [3], we discuss some questions related to this construction. Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786.     

On the (un)decidability of a near-unanimity term

We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present partial results towards proving the decidability of the general problem. While working on this paper, the author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant nos. T 37877 and K 60148.     

A new algorithm for the assignment problem

We propose a new algorithm for the classical assignment problem. The algorithm resembles in some ways the Hungarian method but differs substantially in other respects. The average computational complexity of an efficient implementation of the algorithm seems to be considerably better than the one of the Hungarian method. In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin. The factor of improvement increases with the problem dimensionN and reaches an order of magnitude forN equal to several hundreds.Work supported by Grant NSF ENG-7906332.     

On a Class of Hungarian Semigroups and the Factorization Theorem of Khinchin

Let G be a connected reductive Lie group and K be a maximal compact subgroup of G. We prove that the semigroup of all K-biinvariant probability measures on G is a strongly stable Hungarian semigroup. Combining with the result [see Rusza and Szekely⁽⁹⁾], we get that the factorization theorem of Khinchin holds for the aforementioned semigroup. We also prove that certain subsemigroups of K-biinvariant measures on G are Hungarian semigroups when G is a connected Lie group such that Ad G is almost algebraic and K is a maximal compact subgroup of G. We also prove a p-adic analogue of these results.     

Type monotonic allocation schemes for a class of market games

We consider an extension of glove markets, called T-markets, characterize a family of weighted allocation rules, and define related cooperative games. For the class of T-market games we introduce a new solution concept called the type monotonic allocation scheme. It turns out that the nucleolus and the τ-value generate the same type monotonic allocation scheme with nice extra properties. Initial research for this paper was supported by the Hungarian Scientific Research Fund grant OTKA T030945. The authors thank Ruud Hendrickx for his valuable comments. Research of T. Solymosi was also supported in part by OTKA grant T046194.