It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of degree m− 1 in 2m variables when m > 4; Generally, for any nonnegative integer k, there exists a positive...

this paper presents a genetic algorithm (ga) for solving a generalized model of single-item resource-constrained aggregate production planning (app) with linear cost functions. app belongs to a class of pro-duction planning problems in which there is a single production variable representing the total production of all products. we linearize a linear mixed-integer model of app subject to hiring...

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...

We prove a representation theorem of projections of sets of integer points by an integer matrix W . Our result can be seen as a polyhedral analogue of several classical and recent results related to the Frobenius problem. Our result is motivated by a large class of non-linear integer optimization problems in variable dimension. Concretely, we aim to optimize f(Wx) over a set F = P ∩ Z, where f ...

It is known that the well-posedness of time-fractional reaction–diffusion models with Mittag-Leffler kernel usually requires non-physical constraints on initial data. In this paper, we propose a variable-order equation and prove aforementioned could be eliminated by imposing integer limit variable fractional order at time, which mathematically demonstrates physically-relevance modifications.

We study mixed integer nonlinear programs (MINLP) that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is “turned off”, forces some of the decision variables to assume a fixed value, and, when it is “turned on”, forces them to belong to a convex set. Most of the integer variables in known...

Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixed-integer programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance is achieved by introducing an integer v...

We introduce a real-life problem faced by the blood bank of the Austrian Red Cross for Eastern Austria: how to cost-effectively organize the periodic delivery of blood products to Austrian hospitals. We present various solution approaches, based on integer programming and variable neighborhood search, and empirically evaluate their performance. Moreover, we study the potential value of switchin...

The m-ary method for computing x E partitions the bits of the integer E into words of constant length, and then performs as many multiplications as there are nonzero words. Variable length partitioning strategies have been suggested to reduce the number of nonzero words, and thus, the total numb e r o f m ultiplications. Algorithms for exponentiation using such partitioning strategies are terme...