In the work interval colorings [1] of complete bipartite graphs and trees are investigated. The obtained results were announced in [2]. Non defined concepts can be found in [3, 4]. Let G = (V (G), E(G)) be an undirected graph without multiple edges and loops. The degree of a vertex x in G is denoted by dG(x), the greatest degree of vertices – by ∆(G), the chromatic index of G – by χ(G). Interva...

A hidden positive row diagonally dominant (hprdd) matrix is a square matrix A for which there exist square matrices C and B so that AC = B and each diagonal entry of B and C is greater than the sum of the absolute values of the off-diagonal entries in its row. A linear program with 5n2 − 4n variables and 2n2 constraints is defined that takes as input an n × n matrix A and produces C and B satis...

Let G be a simple undirected graph on n vertices and let S(G) be the class of real symmetric n× n matrices whose nonzero off-diagonal entries correspond exactly to the edges of G. Given 2n − 1 real numbers λ1 ≥ μ1 ≥ λ2 ≥ μ2 ≥ · · · ≥ λn−1 ≥ μn−1 ≥ λn, and a vertex v of G, the question is addressed of whether or not there exists A ∈ S(G) with eigenvalues λ1, . . . , λn such that A(v) has eigenva...

The paper discusses a new technique for the removal of blur in a X-ray caused by uniform linear motion. This method assumes that the linear motion corresponds to an integral number of pixels and is aligned with the horizontal (or vertical) sampling. The proposed approach can be summarized as follows: Given is a gray value vector g, the row of the digitized degraded X-ray . The unknown to be rec...

In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regres...

In this paper we describe the use of the theory of generalized polar decompositions [H. Munthe-Kaas, G. R. W. Quispel, and A. Zanna, Found. Comput. Math., 1 (2001), pp. 297–324] to approximate a matrix exponential. The algorithms presented have the property that, if Z ∈ g, a Lie algebra of matrices, then the approximation for exp(Z) resides in G, the matrix Lie group of g. This property is very...

We evaluate and compare the storage efficiency of different sparse matrix storage formats as index structure for text collection and their corresponding sparse matrixvector multiplication algorithm to perform query processing in information retrieval (IR) application. We show the results of our implementations for several sparse matrix algorithms such as Coordinate Storage (COO), Compressed Spa...

Exercise 7. Let A be an n × n matrix such that the sum of every row is 0 and the sum of every column is 0. Let Aij be the (n − 1) × (n − 1) matrix obtained by removing row i and column j from A. Prove: det(Aij) = (−1) det(A11). (Note that this result applies in particular to the Laplacian L: the determinant of the reduced Laplacian, obtained by removing the i-th row and the i-th column from L, ...

We give simple necessary and sufficient conditions for the existence of a zero-one matrix with given row and column sums and at most one structural zero in each row and column. © 2006 Elsevier B.V. All rights reserved.

An alternating sign matrix [1] is a generalization of a permutation matrix. It consists of a matrix whose entries are 1, −1, and 0, and it satisfies the condition that in every row and column, the 1’s and −1’s alternate (possibly with 0’s in between) and the sum of the entries in every row or column is equal to 1 (so the permutation matrices are one type of these, in which there are no −1’s). F...