Titlebook: Computer Algebra in Scientific Computing; 8th International Wo Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhts Conference proceedings 20

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Circulant Digraphs and Monomial Ideals,hape. Its description provides the graph’s diameter and average distance on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural tool. We obtain some properties of the ideals we are concerned.

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Algebraic Topological Analysis of Time-Sequence of Digital Images,rays of pixels. Our answer is based on an algebraic-topological coding, called AT–model, for a . (.=2,3) digital binary-valued image . consisting simply in taking . together with an algebraic object depending on it. Considering AT–models for all the 2D digital images in a time sequence, it is possib

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,Hilbert Stratification and Parametric Gröbner Bases, a tool to check that the specialization of a “generic” Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called . of the as

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Systems, Stability, and Statecraftt the Cayley-Dixon construction does not contain any extraneous factors. The approach demonstrates that the resultant of a composed system can be effectively calculated by considering only the resultant of the outer system.

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Systems, Stability, and Statecraftgramming techniques, so as to achieve high practical performance. The algorithms are integrated in the public-domain C++ software library ., and their efficiency is illustrated by 9 experiments against existing implementations. Our code is faster in most cases; sometimes it is even faster than numerical approaches.

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The Fundamental Duality of System Theory,l, we provide formulae to compute the diameter and the average distance. Finally, we present a new and attractive family (parametrized with the diameter .>2) of circulant digraphs of degree three associated to an irreducible monomial ideal.

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