Abstract We give an upper-bound for the X -rank of points with respect to a non-degenerate irreducible variety in case that sub-generic generate hypersurface.

in this paper the family of elliptic curves over q given by the equation ep :y2 = (x - p)3 + x3 + (x + p)3 where p is a prime number, is studied. itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(ep(q)) = 0 or rank(ep(q)) = 1 orrank(ep(q))≥2 are given.

The inertia of a Hermitian matrix is defined to be a triplet composed by the numbers of the positive, negative and zero eigenvalues of the matrix counted with multiplicities, respectively. In this paper, we give various closed-form formulas for the maximal and minimal values for the rank and inertia of the Hermitian expression A + X, where A is a given Hermitian matrix and X is a variable Hermi...

The rank of a matrix and the inertia of a square matrix are two of the most generic concepts in matrix theory for describing the dimension of the row/column vector space and the sign distribution of the eigenvalues of the matrix. Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which decision variables are matrices running over certain matrix ...

Abstract. In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and sufficient conditions for having a measure theoretical eigenvalue. These conditions are established from the combinatorial information of the Bratteli-Vers...