Now showing items 1-10 of 54
On a class of nonlocal wave equations from applications
(American Institute of Physics Inc., 2016-06)
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods ...
Evaluation of Hessenberg Determinants via Generating Function Approach
(University of Nis, 2017)
In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ...
Formulæ related to the q-Dixon formula with applications to Fibonomial sums
(Kluwer Academic Publishers, 2015-06)
The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...
A class of non-symmetric band determinants with the Gaussian q-binomialcoefficients
(Taylor and Francis Ltd., 2017)
A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper ...
The generalized Lilbert matrix
We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the ...
Evaluation of sums containing triple aerated generalized Fibonomial coefficients
(De Gruyter Open Ltd, 2017-04)
We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ...
Closed form evaluation of sums containing squares of Fibonomial coefficients
(De Gruyter Open Ltd, 2016-06)
We give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms ...
Some Gaussian binomial sum formulæ with applications
(Indian National Science Academy, 2016-09)
We introduce and compute some Gaussian q-binomial sums formul ae. In order to prove these sums, our approach is to use q-analysis, in particular a formula of Rothe, and computer algebra. We present some applications of our ...
Closed Form Evaluation Of Melham's Reciprocal Sums
(Univ Miskolc Inst Math, 2017)
Recently Melham  gives closed formul ae for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we ...
Two Variants of the Reciprocal Super Catalan Matrix
(Kyungpook National University, 2016-06)
In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.