This paper considers the nonlinear left coprime factorization (NLCF) of a nonlinear system. In order to study the balanced realization of such NLCF first a dual system notion is introduced. The important energy functions for the original NLCF and their relation with the dual NLCF are studied and relations between these functions are established. These developments can be used for studying a rel...

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...

The LU factorization is an important numerical algorithm for solving system of linear equations in science and engineering and is characteristic of many dense linear algebra computations. It has even become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected in the TOP500 website. In this context, the challen...

We used QCD factorization for the hadronic matrix elements to show that the existing data, in particular the branching ratios BR ( ?J/?K) and BR ( ?J/??), can be accounted for this approach. We analyzed the decay within the framework of QCD factorization. We have complete calculation of the relevant hard-scattering kernels for twist-2 and twist-3. We calculated this decays in a special scale ...

In this paper we solve two problems in linear systems theory: the computation of the inner–outer and spectral factorizations of a continuous–time system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the trans...

Structured dialogue models are currently the only tools for easily building spoken dialogue systems. This approach, however, requires the dialogue designer to completely specify all dialogue behavior between the user and system, including how information is grounded between the user and the system. In this paper, we advocate factoring out the grounding behavior from structured dialogue models b...

The method of obtaining the set of noncanonical hypercomplex number systems by conversion of infinite hypercomplex number system to finite hypercomplex number system depending on multiplication rules and factorization method is described. Systems obtained by this method starting from the 3dimension are noncanonical. The obtained systems of even dimension can be re-factorized. As a result of it ...

the triple factorization of a group $g$ has been studied recently showing that $g=aba$ for some proper subgroups $a$ and $b$ of $g$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. in this paper we study two infinite classes of non-abelian finite groups $d_{2n}$ and $psl(2,2^{n})$...

This thesis investigates relations over a category C relative to an (E;M)-factorization system of C. In order to establish the 2-categoryRel(C) of relations over C in the rst part we discuss su cient conditions for the associativity of horizontal composition of relations, and we investigate special classes of morphisms in Rel(C). Attention is particularly devoted to the notion of mapping as de ...