基于非适应性组合群测的多路存取信道模型的构作

在多路存取信道中当前用户的信息传输是计算机通信网络的一个重要内容,基于组合群测理论构作了多路存取信道模型,介绍了它在多路存取信道中当前用户信息传输方面的应用.     

Lattice valued intuitionistic fuzzy sets

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets. The research supported by Serbian Ministry of Science and Technology, Grant No. 1227.     

Multiplicative character sums with the sum of g-ary Digits Function

We establish upper bounds for multiplicative character sums with the function σ_g (n) which computes the sum of the digits of n in a fixed base g ≥ 2. Our results may be viewed as analogues of some previously known results for exponential sums with sum of g-ary digits function. 2000 Mathematics Subject Classification Primary—11A63, 11B50, 11L40     

Note on generalized open sets

Characterizations of γ-open sets and locally γ-regular sets are given. We generalize some already established results and answer an open question by giving a characterization to γ-quasi-open sets.      

The further unified theory for modifications of g-closed sets

We introduce a new set called mng-closedwhich is defined on a set with two families of sets satisfying some minimal conditions. This set enables us to unify modifications of g-closed sets due to Levine [19].      

An asymptotic formula for the minimal capacity among sets of equal area

We give an asymptotic formula for

Abstract version of the Cauchy-Kowalewski problem

We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem. Partially supported by grants RFBR 02-01-00400     

Ordered sets with interval representation and (m,n)-Ferrers relation

Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that we call “d-weak orders”, “d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation.     

Convergence of tail sum for records

Suppose is the sequence of lower records from a distribution F, where F is continuous with . We derive conditions under which logarithm of the tail sum of records, ∑ _j=n ^∞ R _n ^(L) (F), properly centered and scaled, converge weakly. We also prove two results on Π-varying and regularly varying functions, which are of independent interest.     

Blow-up of optimal sets in the irrigation problem

We consider the minimization problem for an average distance functional in the plane, among all compact connected sets of prescribed length. For a minimizing set, the blow-up sequence in the neighborhood of any point is investigated. We show existence of the blow up limits and we characterize them, using the results to get some partial regularity statements.     

On Λ-generalized closed sets in topological spaces

We introduce new classes of sets called Λ _g -closed sets and Λ _g -open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ _g -closed sets and Λ _g -open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively. Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday     

Direct solution of an optimal layout problem for isotropic heat conductors with a volume fraction constraint

This paper considers the problem of the optimal layout of two isotropic heat conductors on a plane subject to a constraint on the overall volume fraction of the better conductor. The problem is solved initially using the traditionalG _m -closure technique. Later, the utility of the direct relaxation technique introduced in Ref. 1 is illustrated as we apply it to verify the original results.This paper is dedicated with gratitude by the author to his advisor K. A. Lurie. The author wishes to acknowledge discussions with D. Clomenil.     

G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates

In Ref. 1, we considered theG-closure of some initially given arbitrary setU of the positive-definite, symmetrical plane tensorsD of the 2nd rank, connected with the differential operator ·D · in two dimensions. Here, theG-closure procedure is applied to the 4th-order operator ··D ·· in a plane, arising in the theory of plates and containing self-adjoint tensorsD of the 4th rank. The paper generalizes some results obtained earlier in Refs. 2 and 3. The complete solution of the general problem of regularization, which presupposes the arbitrary character of the initially given setU, is not yet obtained.     

Tchebotaröv’s extremal problem

Central European Journal of Mathematics - We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric...     

The Dirichlet problem for Baire-one functions

Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.     

On weighted approximations in D[0, 1] with applications to self-normalized partial sum processes

Let X,X ₁,X ₂,… be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in D[0, 1] for the partial sum processes {S _[nt], 0 ≦ t ≦ 1} where S _n = Σ _j=1 ⁿ X _j , under the assumption that X belongs to the domain of attraction of the normal law. The conclusions then are used to establish similar results for the sequence of self-normalized partial sum processes {S _[nt]=V _n , 0 ≦ t ≦ 1}, where V _n ² = Σ _j=1 ⁿ X _j ² . L _p approximations of self-normalized partial sum processes are also discussed.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

A geometric Cauchy problem for timelike minimal surfaces

We investigate two-dimensional timelike surfaces in a Lorentz manifold (X,g). It is shown that orientable surfaces with two spacelike boundary components (homeomorphic toS ¹) are necessarily of topological type [0,1] x S¹. We treat the initial value problem of a string (known from physics) as a purely geometric problem: Find a minimal surface which is specified by an initial curve and by a distribution of timelike tangent planes along . We prove the local existence and uniqueness of and also obtain global existence for special types (X,g). Global existence does not generally hold; we give a counter-example, which can be interpreted as a string collapsing into a black hole.     

On a sum involving Fourier coefficients of cusp forms

We improve the existing upper bound for the quantity |∑ _n⩽x a(n ²)|, where a(n ²) is the n ²th Hecke eigenvalue of a normalized holomorphic cusp form (Hecke eigenform) of the full modular group SL(2, ℤ), whenever the weight of the original holomorphic cusp form (Hecke eigenform) lies in a certain range. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 565–583, October–December, 2006.     

Polynomial recognition of equal unions in hypergraphs with few vertices of large degree

A family of nonempty sets has the equal union property if there exist two nonempty disjoint subfamilies having equal unions. If every point belongs to the unions, then we say the family has the full equal union property. Recognition of both properties is NP-complete even when restricted to families for which the degree of every point is at most three. In this paper we show that both recognition problems can be solved in polynomial time for families in which there is a bound on the number of points whose degree exceeds two.