Published in Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
Published in Serbian Journal of Experimental and Clinical Research
The rheumatoid arthritis is chronic disease with progressive course and deteriorations of joints as well as other organs. The pathogenesis of rheumatoid arthritis is characterized with chronic synovitis and inflammation. The main roles in development of rheumatoid arthritis have auto-reactive T cells and inflammatory cytokines, especially tumor nec...
Published in Mathematical Morphology - Theory and Applications
When fitting archaeological artifacts, one would like to have a representation that simplifies fragments while preserving their complementarity. In this paper, we propose to employ the scale-spaces of mathematical morphology to hierarchically simplify potentially fitting fracture surfaces. We study the masking effect when morphological operations a...
Published in Special Matrices
Symmetric matrix classes of bandwidth 2r + 1 was studied in 1972 through binomial coefficients. In this paper, non-symmetric matrix classes with the binomial coefficients are considered where r + s + 1 is the bandwidth, r is the lower bandwidth and s is the upper bandwidth. Main results for inverse, determinants and norm-infinity of inverse are pre...
Published in Special Matrices
Given a real number a ≥ 1, let Kn(a) be the set of all n × n unit lower triangular matrices with each element in the interval [−a, a]. Denoting by λn(·) the smallest eigenvalue of a given matrix, let cn(a) = min {λ n(YYT) : Y ∈ Kn(a)}. Then cn(a)\sqrt {{c_n}\left( a \right)} is the smallest singular value in Kn(a). We find all minimizing matrices. ...
Published in Special Matrices
We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, 23 (2018) 61], to handle the problem of when a linear combination matrix X=∑i=1mciXiX = \sum\nolimits_{i = 1}^m {{c_i}{X_i}} is a matrix such that its spectrum is a subset of a particular set, where ci, i = 1, 2, ..., m, are nonzero scalars and Xi, i = ...
Published in Special Matrices
By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general symmetric M-matrices with no restrictions, this means that we do not have to assume the diagonally dominance hypothesis. We express the group inverse of a symmetric M–matrix in terms of the weight of spanning rooted forests. In fact, we give a combinato...
Published in Special Matrices
Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A. A longstanding open question concerns the smallest possible number of nonzero entries in an n × n spectrally arbitra...
Published in Special Matrices
It is well-known that the finite difference discretization of the Laplacian eigenvalue problem −Δu = λu leads to a matrix eigenvalue problem (EVP) Ax =λx where the matrix A is Toeplitz-plus-Hankel. Analytical solutions to tridiagonal matrices with various boundary conditions are given in a recent work of Strang and MacNamara. We generalize the resu...
Published in Special Matrices
The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.
