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In this paper we investigate the properties of multimodular functions. In doing so we give elementary proofs for properties already established by Hajek and we generalize some of his results. In particular, we extend the relation between convexity and multimodularity to some convex subsets of Zm. We also obtain general optimization results for average costs related lo a sequence of multimodular functions rather than to a single function. Under this general context, we show that the expected average cost problem is optimized by using regular sequences. We finally illustrate the usefulness of this theory in admission control into a D/D/1 queue with fixed batch arrivals, with no state information. We show that the regular policy minimizes the average queue length for the case of an infinite queue, but not for the case of a finite queue. When further adding a constraint on the losses, it is shown that a regular policy is also optimal for the finite queue case. [ABSTRACT FROM AUTHOR]

The theorems of continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established through making use of the functions of bounded Φ-variation were introduced by Musiclak and Orlicz in paper [2]. The results are essential generalization of continuous dependence of bounded variation solutions on parameters for Kurzweil equations in paper [6]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation on a time scale ; here is a quotient of odd positive integers with and real-valued positive functions defined on . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. [Copyright &y& Elsevier]

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by [n/2]. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class. [Copyright &y& Elsevier]

This article claims to have established several existence theorems of positive solutions for nonlinear m-point boundary value problem for several dynamic equations on time scales. These equations include (φ(u&Delta))&nabla + α(t) f (t, u(t)) = 0, t ... (0,T), φ(uΔ(0)) = Σ i=1m-2 αiφ(uΔ(...i, u(T) = Σi=1m-2biu(...i, where φ : R &rar; R is an increasing homoemorphism and homomorphism and φ(0) = 0. It provides example calcalations using these equations.

We present a new Bregman-function-based algorithm which is a modification of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. The principal advantage of the presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we eliminate the assumption of pseudomonotonicity which was, until now, standard in proving convergence for paramonotone operators. Thus we obtain a convergence result which is new even for exact generalized proximal point methods. Finally, we present some new results on the theory of Bregman functions. For example, we show that the standard assumption of convergence consistency is a consequence of the other properties of Bregman functions, and is therefore superfluous. [ABSTRACT FROM AUTHOR]

A Lagrangian or an affine Hamiltonian is called totally singular if it is defined by affine functions in highest velocities or momenta respectively. A natural duality relation between these Lagrangians and affine Hamiltonians is considered. The energy of a second order affine Hamiltonian is related with a dual corresponding Lagrangian of order one. Relations between the curves that are solutions of Euler and Hamilton equations of dual objects are also studied using semi-sprays. In order to generate examples of second order, a natural lifting procedure is considered. [ABSTRACT FROM AUTHOR]

The article analyzes the boundary asymptotic behavior of solutions for weighted p(x)-Laplacian equations that take infinite value on a bounded domain. It was found that the boundary asymptotic of solutions of the Laplacian function is continuous and positive. The p(x)-Laplacian possesses more complicated inhomogeneous nonlinearities, thus, some special techniques are needed. Its main difficulty arises from the lack of compactness. The uniqueness and asymptotic behavior of solutions for problem is a nonnegative function which is allowed to vanish on the boundary.