We show that in a knapsack feasibility problem an integral vector p, which is short, and near parallel to the constraint vector gives a branching direction with small integer width. We use this result to analyze two computationally efficient reformulation techniques on low density knapsack problems. Both reformulations have a constraint matrix with columns reduced in the sense of Lenstra, Lenst...

Algebraic immunity of Boolean function f is defined as the minimal degree of a nonzero g such that fg = 0 or (f + 1)g = 0. Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity n 2 is determined by the binary expansion of n. Based on the foregoing, all n-variable symmetric Boolean functions with max...

Abstract Consider the probability that a binomial random variable Bi ( n , m ? ) with integer expectation is at most its expectation. Chvatal conjectured for any given this smallest when closest to 2 3 . We show holds large.

Dumont and Foata introduced in 1976 a three-variable symmetric refinement of Genocchi numbers, which satisfies a simple recurrence relation. A six-variable generalization with many similar properties was later considered by Dumont. They generalize a lot of known integer sequences, and their ordinary generating function can be expanded as a Jacobi continued fraction. We give here a new combinato...

Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. ...

We prove an analogue of Fekete's subadditivity lemma for functions several real variables which are subadditive in each variable taken singularly. This extends both the classical case one variable, and a similar result integer variables. While doing so, we that with property mentioned above bounded every closed subset their domain. The arguments expand on those Chapter 6 E. Hille's 1948 textbook.

In this paper, we determine the trivial factors of L-functions of both finite and infinite symmetric products of Kloosterman sheaves. Let Fq be a finite field of characteristic p with q elements, let l be a prime number distinct from p, and let ψ : Fq → Q ∗ l be a nontrivial additive character. Fix an algebraic closure F of Fq. For any integer k, let Fqk be the extension of Fq in F with degree ...

In this paper, theoretical aspects to demonstrate the accuracy of the Interval Test (the I test and the direction vector I test) to be applied for resolving the problem stated above is presented. Also, it is proved from the proposed theoretical aspects that under a specific direction vector 1 ( , , ) d θ = = = ... there are integer-valued solutions for one-dimensional arrays with subscripts for...