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Belardo F.,Messina University | De Filippis V.,Messina University | Simic S.K.,Mathematical Institute SANU
Match | Year: 2011

Recently, in the book [A Combinatorial Approach to Matrix Theory and Its Applications, CRC Press (2009)] the authors proposed a combinatorial approach to matrix theory by means of graph theory. In fact, if A is a square matrix over any field, then it is possible to associate to A a weighted digraph G a, called Coates digraph. Through Ga (hence by graph theory) it is possible to express and prove results given for the matrix theory. In this paper we express the permanental polynomial of any matrix A in terms of permanental polynomials of some digraphs related to Ga. Source


Cvetkovic D.,Mathematical Institute SANU | Rowlinson P.,University of Stirling | Stanic Z.,University of Belgrade | Yoon M.-G.,Gangneung - Wonju National University
Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques | Year: 2011

The eigenvalues of a graph are the eigenvalues of its adjacency matrix. An eigenvalue of a graph is called main if the corresponding eigenspace contains a vector for which the sum of coordinates is different from 0. Connected graphs in which all eigenvalues are mutually distinct and main have recently attracted attention in control theory. Source


Dragovic V.,University of Texas at Dallas | Dragovic V.,Mathematical Institute SANU | Kukic K.,University of Belgrade
Journal of Geometric Mechanics | Year: 2014

We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable each. Our classification is based on the study of structures of zeros of a polynomial component P of a discriminant. This classification is related to the classification of pencils of conics in a delicate way. We establish a relationship between our classification and the classification of integrable quad-equations which has been suggested recently by Adler, Bobenko, and Suris. ©American Institute of Mathematical Sciences. Source


Fuji H.,Nagoya University | Gukov S.,California Institute of Technology | Gukov S.,Max Planck Institute For Mathematik | Stosic M.,University of Lisbon | And 4 more authors.
Journal of High Energy Physics | Year: 2013

We study singularities of algebraic curves associated with 3d N = 2 theories that have at least one global flavor symmetry. Of particular interest is a class of theories T K labeled by knots, whose partition functions package Poincaré polynomials of the S r -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d N = 2 theories T K and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in S r -colored HOMFLY homologies. © 2013 SISSA. Source


Hedrih K.,Mathematical Institute SANU | Hedrih K.,University of Nis | Nikoli-Stanojevi V.,State University of Novi Pazar | Nikoli-Stanojevi V.,University of Kragujevac
Mathematical Problems in Engineering | Year: 2010

A theoretical model of multistep gear transmission dynamics is presented. This model is based on the assumption that the connection between the teeth of the gears is with properties within the range from ideal clasic to viscoelastic so that a new model of connection between the teeth was expressed by means of derivative of fractional order. For this model a two-step gear transmision with three degrees of freedom of motion has been used. The obtained solutions are in the analytic form of the expansion according to time. As boundary cases this model gives results for the case of ideally elastic connection of the gear teeth and for the case of viscoelastic connection of the gear teeth, as well. Eigen fractional modes are obtained and a vizualization is done. © 2010 K. S. Hedrih and V. Nikoliá-Stanojeviá. Source

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