In this paper, we investigate a Transportation problem which is a special kind of linear programming in which profits; supply and demands are considered as Intuitionistic triangular fuzzy numbers. The crisp values of these Intuitionistic triangular fuzzy numbers are obtained by defuzzifying them and the problem is formulated into linear programming problem. The solution of the formulated proble...

A model is defined that interpolates between integer dimension and integer q-state Potts models. Phase transitions in these models are studied, and in particular the critical value qc where the phase transition changes from second into first order is determined for several dimensions. For (d, qc) the values (2.0;4.05), (2.5;2.68), (3.0;2.21), (3.5;2.15) and (4.0;2.07) are obtained. ∗e-mail: bar...

Let M(P (z1, . . . , zn)) denote Mahler’s measure of the polynomial P (z1, . . . , zn). Measures of polynomials in n variables arise naturally as limiting values of measures of polynomials in fewer variables. We describe several methods for searching for polynomials in two variables with integer coefficients having small measure, demonstrate effective methods for computing these measures, and i...

Let A be an m × n integral matrix of rank n. We say that A is bimodular if the maximum of the absolute values of the n×n minors is at most 2. We give a polynomial time algorithm that finds an integer solution for system Ax ≤ b. A polynomial time algorithm for integer program max{cx : Ax ≤ b} is constructed proceeding on some assumptions.

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k = 1 and k = 2, every optimal solution is integral. In contrast to this, for every k ≥ 3 there exist instances where every optimal solution takes non-integral values.

Consider the m-th roots of unity in C, where m > 0 is an integer. We address the following question: For what values of n can one find n such m-th roots of unity (with repetitions allowed) adding up to zero? We prove that the answer is exactly the set of linear combinations with non-negative integer coefficients of the prime factors of m.

For a positive integer k, the Erdös-Selfridge function is the least integer g(k) > k + 1 such that all prime factors of (g(k) k ) exceed k. This paper describes a rapid method of tabulating g(k) using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of g(k). A table of values of g(...

A classical result of Pólya states that 2 is the slowest growing transcendental entire function taking integer values on the non-negative integers. Langley generalised this result to show that 2 is the slowest growing transcendental function in the closed right halfplane Ω = {z ∈ C : <(z) ≥ 0} taking integer values on the non-negative integers. Let E be a subset of the Gaussian integers in the ...

We consider the problem of estimating optima of covering integer linear programs with 0-1 variables under the following conditions: we do not know exact values of elements in the constraint matrix A but we know what elements of A are zero and what are nonzero, and also know minimal and maximal values of nonzero elements. We find bounds for variation of the optima of such programs in the worst a...

This paper proposes a class of surrogate constraint heuristics for obtaining approximate, 'near optimal solutions to integer programming problems. These heuris· tics are based on a simple framework that illuminates the character of several carlier heuristic proposals and provides a variety of new alternatives. The paper also pro· poses additional heuristics that can be used either to supplement...