Maximal Binary Matrices and Sum of Two Squares

The Sum of Two Squares

The sum of two maximal monotone operator is of type FPV

In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.

Computation of Maximal Determinants of Binary Circulant Matrices

We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here “binary matrix” means a matrix whose elements are drawn from {0, 1} or {−1, 1}. We describe efficient parallel algorithms for the search, using Duval’s algorithm for generation of Lyndon words and the well-known representation of the determinant of a circulant in terms of roots of unity....

Maximal Covering by Two Isothetic Unit Squares

Let P be the point set in two dimensional plane. In this paper, we consider the problem of locating two isothetic unit squares such that together they cover maximum number of points of P . In case of overlapping, the points in their common zone are counted once. To solve the problem, we propose an algorithm that runs in O(n log n) time using O(n log n) space.

Probabilistic lower bounds on maximal determinants of binary matrices

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of the distance d to the nearest (smaller) Hadamard matrix, defined by d = n − h, where h is the order of a Hadamard matrix and h is maximal subject to h ≤ n. The lower bounds on R(n) ...