in this paper we investigate a new notion of bases in hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in hilbert spaces. we also introducea new denition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. next we dene the fusionbiorthogonal sequence, bessel fusion basis, hilbe...

Abstract: This is the first of two articles devoted to a exposition of the generatingfunction method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp’s character method. An alternative approach to the construction of tensor-product generating functions ...

We present a new method that addresses the various deficiencies of the state-ofthe-art non-linear invariant generation methods for hybrid systems. Present approaches for non-linear invariant generation are limited to linear systems, or they relay on non scalable methods which have high complexity. Moreover, for hybrid systems with discrete transitions, differential rules, and local conditions t...

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

labeling theory is one of the most famous theories in criminology domain. the pivots of this theory consist of the role of power owners in definition of crime and determination of offender, effects of labeling and solutions for prevention of entering label. with study the pivots of labeling theory in islamic sources, we observe that however there is no similarity between religious bases and bas...

In this paper we present algorithms to compute finite state automata which, given any rational language, recognize the languages of normal words and n-chains. We also show how these automata can be used to compute the Hilbert series and Poincaré series for any algebra with a rational set of leading words of its minimal Gröbner basis.

The determination of a set of geometric entities that satisfy a series of geometric relations (constraints) constitutes the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem. This problem appears in diierent forms in Assembly Planning, Constraint Driven Design, Computer Vision, etc. Its solution is related to the existence of roots to systems of polynomial equations. Previ...

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Faugère’s F4 is a well-known Gröbner bases algorithm to solve this problem. However, a serious drawback exists in the Gröbner bases based algebraic attacks, namely, any information won’t be got if we couldn’t work out the Gröbner bases of the polynomial equations system. In this paper, we in-dept...

We provide a polynomial time algorithm for computing the universal Gröbner basis of any polynomial ideal having a finite set of common zeros in fixed number of variables. One ingredient of our algorithm is an effective construction of the state polyhedron of any member of the Hilbert scheme Hilbn of n-long d-variate ideals, enabled by introducing the Hilbert zonotope Hn and showing that it simu...