Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library In this paper, we in...

given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

Some partition theorems similar to the Rogers-Ramanujan theorems are proved. We shall prove the following partition theorems, namely THEOREM 1. The number of partitions of k, k = a 1 + a 2 + a 3 + · · · with a 1 > a 2 ≥ a 3 > a 4 ≥ · · ·

A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian e...

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic ...

We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal...

It is now well-known that when an infinitely long hyperelastic membrane tube free from any imperfections is inflated, a transcritical-type bifurcation may take place that corresponds to the sudden formation of a localized bulge. When the membrane tube is subjected to localized wall-thinning, the bifurcation curve would “unfold” into the turning-point type with the lower branch corresponding to ...

The complete list of CSC and SFB393 preprints is available via Abstract The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamilto-nian eigenproblems by considering a suitable transformation. Structure-induced shift-and-invert techniques are employed to steer the algo...