Related papers: On the absolute matrix summability factors
In the present paper we show that the functor of idempotent probability measures satisfies all of conditions with an additional claim of uniform metrizability of functors.
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
We give a sufficient condition for the strong symmetric version of Strassen's additivity conjecture: the Waring rank of a sum of forms in independent variables is the sum of their ranks, and every Waring decomposition of the sum is a sum of…
We give a criterion for a group homomorphism on a valued abelian group to be surjective and to preserve spherical completeness. We apply this to give a criterion for the existence of integration on a valued differential field. Further, we…
We give concrete, "infinitesimal" conditions for a proper geodesically complete CAT(0) space to have semistable fundamental group at infinity.
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.
In this work, the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix. The necessary and sufficient condition there is also shown to be sufficient for the symmetric nonnegative inverse…
We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…
We give necessary conditions for perfection of some families of odd numbers with special multiplicative forms. Extending earlier work of Steuerwald, Kanold, McDaniel et al.
We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.
A real square matrix is algebraically positive if there exists a real polynomial $f$ such that $f(A)$ is a positive matrix. In this paper, we give a sufficient condition for a sign pattern matrix to allow algebraic positivity, and give some…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
Given a matrix with partitions of its rows and columns and entries from a field, we give the necessary and sufficient conditions that it has a non--singular submatrix with certain number of rows from each row partition and certain number of…
It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…
We announce three results in the theory of Jacobi matrices and Schr\"odinger operators. First, we give necessary and sufficient conditions for a measure to be the spectral measure of a Schr\"odinger operator $-\f{d^2}{dx^2} +V(x)$ on $L^2…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
In this paper, we have generalized a main theorem dealing with weighted mean summability method for absolute matrix summability method which plays a vital role in summability theory and applications to the other sciences by using…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
We prove that symmetry in the presence of gravity implies a version of the completeness hypothesis. For a broad class of theories, we demonstrate that the existence of finitely many charged particles logically necessitates the existence of…