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 r and s be reduced rings with identities whose idempotents are central, and let m be an(r, s)-bimodule such that annr (m)=0. in this paper, we determine first the structure of automorphisms ofthe triangular ring, =sr mt0, and then, for all automorphisms α ,β of t we determine the structureof (α,β)-derivations of t.

The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics...

The problem we are dealing with is the following: find two sequences an and bn such that the average of the first bn triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the an-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the seque...

a facility layout problem is concerned with determining the best position of departments, cells, or machines on the plant. an efficient layout contributes to the overall efficiency of operations. it’s been proved that, when system characteristics change, it can cause a significant increase in material handling cost. consequently, the efficiency of the current layout decreases or is lost and it ...

we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.

there are some problems with estimating the time required for the manufacturing process of products, especially when there is a variable serving time, like control stage. these problems will cause overestimation of process time. layout constraints, reworking constraints and inflexible product schedule in multi product lines need a precise planning to reduce volume in particular situation of lin...