In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems where fuzzy coefficient matrix is a positive matrix. This paper mainly discusses a new decomposition of a nonsingular fuzzy matrix, a symmetric matrix times to a triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy s...

First, we give a new example of silting-discrete algebras. Second, one explores when the algebra triangular matrices over finite dimensional is τ-tilting finite. In particular, classify algebras which matrix are Finally, investigate silting-discrete.

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

Let T be a right exact functor from an abelian category ℬ into another $${\mathscr A}$$ . Then there exists p the product A} \times {\mathscr B}$$ to comma ( $$\left( {T \downarrow A}} \right)$$ ). In this paper, we study property of extension closure some classes objects in ), exactness and detailed description orthogonal given class $${\rm{P}}\left( {{\cal X},{\cal Y}} Moreover, characterize ...

It has been known for at least thirty years that certain nilpotent groups cannot be Kähler groups, i.e., fundamental groups of compact Kähler manifolds. The best known examples are lattices in the three-dimensional real or complex Heisenberg groups. It is also known that lattices in certain other standard nilpotent Lie groups, e.g., the full group of upper triangular matrices and the free k-ste...

Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of...

The aim of the present paper is to carry on the research of Czédli in determining the maximum number of rectangular islands on a rectangular grid. We estimate the maximum of the number of triangular islands on a triangular grid.

For a function f : {0, 1} → R and an invertible linear transformation L ∈ GLn(2), we consider the function Lf : {0, 1} → R defined by Lf(x) = f(Lx). We raise two conjectures: First, we conjecture that if f is Boolean and monotone then I(Lf) ≥ I(f), where I(f) is the total influence of f . Second, we conjecture that if both f and L(f) are monotone, then f = L(f) (up to a permutation of the coord...

Abstract. Let B+ ⊂ GLn(R) denote the subgroup of upper triangular n × nmatrices with positive entries on the main diagonal. A matrix M ∈ B+ is called totally positive if the determinants of all its minors not containing a row or column lying completely under the main diagonal are positive. We give a simple determinantal equation for the boundary of all positive upper triangular matrices in B+.

This note employs recurrence techniques to obtain entry-wise optimal inequalities for inverses of triangular matrices whose entries satisfy some monotonicity constraints. The derived bounds are easily computable.