For every pattern P , consisting of a finite set of points in the plane, S′ P (n) is defined as the largest number of similar copies of P among sets of n points in the plane without 3 points on a line. A general construction, based on iterated Minkovski sums, is used to obtain new lower bounds for S′ P (n) when P is an arbitrary pattern. Improved bounds are obtained when P is a triangle or a re...

For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

A sum graph G is a graph with a mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph the integers of S that are the sum of two other integers of S form a set of integers that label a collection of isolated vertices associated with the graph G. A grap...

The sum of (nonlinear) maximal monotone operators is reconsidered from the Yosida approximation and graph-convergence point of view. This leads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maximal monotone. In the case of subdiierentials of convex lower semicontinuous proper functions, the variational sum is eq...

It is well known that the general subset sum problem is NP-complete. However, almost all subset sum problems with density less than 0.9408 . . . can be solved in polynomial time with an oracle that can find the shortest vector in a special lattice. In this paper, we give a similar result for the multiple subset sum problem which has k subset sum problems with the same solution. A modified latti...

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Recently Feng Qi has presented a sharp inequality between the sum of squares and the exponential of the sum of a nonnegative sequence. His result has been extended to more general power sums by Huan-Nan Shi, and, independently, by Yu Miao, Li-Min Liu, and Feng Qi. In this note we generalize those inequalitites by introducing weights and permitting more general functions. Inequalities in the opp...

Abstract. A parity checking-styled Weil sum algorithm is presented for a general class of the univariate polynomials which fully characterize a system of n polynomials in n variables over F2. The previously known proof methods of explicit Weil sum evaluation of Dembowski-Ostrom polynomials are extended to general case. The algorithm computes the absolute values of the Weil sums of the generic c...