We determine the shape of all sum-free sets in {1,2,…,n}2 size close to maximum 35n2, solving a problem Elsholtz and Rackham. show that such asymptotic lie completely stripe 45n−o(n)≤x+y≤85n+o(n). also for any positive integer p subset A⊆{1,2,…,n}2 which forbids triple (x,y,z) satisfying px+py=z.

Given a sequence Q of n numbers positive and negative the maximum subsequence of Q is the contiguous subsequence that has the maximum sum among all contiguous subsequences of Q Given a two dimensional array A of n n numbers positive and negative the maximum subarray of A is the contiguous subarray that has the maximum sum among all contiguous subarrays of A We present two O log n time parallel ...

If connecting properties of a multiquark hadron with those exhibited by its constituents, QCD sum rules inferred along the routes traditional wisdom necessarily involve contributions not related at all to and thus presenting information about multiquarks. Realizing this deficiency, we propose increase, for example tetraquarks, predictive power sum-rule formalism disposal unwanted from very begi...

Recently, researchers showed that dirty paper coding (DPC) is the optimal transmission strategy for multiple-input multiple-output broadcast channels (MIMO-BC). In this paper, we study how to determine the maximum weighted sum of DPC rates through solving the maximum weighted sum rate problem of the dual MIMO multiple access channel (MIMO-MAC) with a sum power constraint. We first simplify the ...

his research is designed to develop and investigate newly defined problems: the Maximum Convex Sum (MCS), and its generalisation, the K-Maximum Convex Sum (K-MCS), in a two-dimensional (2D) array based on dynamic programming. The study centres on the concept of finding the most useful informative array portion as defined by different parameters involved in data, which is generically expressed i...

The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant linear-time solution too. The problem is a classic exercise in the mathematics of program construction, illustrating important principles such as calculatio...

a r t i c l e i n f o a b s t r a c t Given a real number sequence A = (a 1 , a 2 ,. .. ,a n), an average lower bound L, and an average upper bound U , the Average-Constrained Maximum-Sum Segment problem is to locate a segment A(i, j) = (a i , a i+1 ,. .. ,a j) that maximizes ik j a k subject to L (ik j a k)/(j − i + 1) U. In this paper, we give an O (n)-time algorithm for the case where the av...