A mapping $f:V^n longrightarrow W$, where $V$ is a commutative semigroup, $W$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings i...

The final coder in Burrows-Wheeler compression is usually either an adaptive Huffman coder (for speed) or a complex of arithmetic coders for better compression. This article describes the use of conventional pre-defined variable length codes or universal codes and shows that they too can give excellent compression. The paper also describes a “sticky Move-to-Front” modification which gives a use...

In this paper we propose a new hybrid heuristic for solving 0-1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to ...

Jeroslow and Lowe gave an exact geometric characterization of subsets of R that are projections of mixed-integer linear sets, a.k.a MILP-representable sets. We give an alternate algebraic characterization by showing that a set is MILP-representable if and only if the set can be described as the intersection of finitely many affine Chvátal inequalities. These inequalities are a modification of a...

Let P be a polytope satisfying that each row of the defining matrix has at most one positive entry. Determining whether there is an integer point in P is known to be an NP-complete problem. By introducing an integer labeling rule on an augmented set and applying a triangulation of the Euclidean space, we develop in this paper a variable dimension method for computing an integer point in P. The ...

this paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. the objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. a 0-1 mixed intege...

Bhargava defined p-orderings of subsets of Dedekind domains and with them studied polynomials which take integer values on those subsets. In analogy with this construction for subsets of Z(p) and p-local integer-valued polynomials in one variable, we define projective p-orderings of subsets of Z(p). With such a projective p-ordering for Z(p) we construct a basis for the module of homogeneous, p...

In this paper a new PID controller is presented. Its peculiarity consists in the non integer order of the derivative and integral, being this order variable in the range [0,1], and providing two further parameters to the controller. The key element is a Multi-layer Perceptron that evaluate a non integer order integration. The neural network approach allows to overcome some problems related to p...