The non-commutative analytic Toeplitz algebra is the wot-closed algebra generated by the left regular representation of the free semigroup on n generators. The structure theory of contractions in these algebras is examined. Each is shown to have an H∞ functional calculus. The isometries defined by words are shown to factor only as the words do over the unit ball of the algebra. This turns out t...

This paper presents the design and implementation of a memory scalable parallel symbolic factorization algorithm for general sparse unsymmetric matrices. Our parallel algorithm uses a graph partitioning approach, applied to the graph of |A|+ |A| , to partition the matrix in such a way that is good for sparsity preservation as well as for parallel factorization. The partitioning yields a so-call...

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discus...

In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category K is introduced, as a pair (comonad, monad) over K. The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories. Dedica...

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...

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

We have recently developed a new program analysis strat egy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis In this paper we show how fractal symbolic analysis can be used to convert between left looking and right looking versions of three kernels of central importance in compu tational science Cholesky factorization LU factorization...

In view of possible photoproduction studies in ultraperipheral heavy-ion collisions at the LHC, we briefly review the present theoretical understanding of photons and hard photoproduction processes at HERA, discussing the production of jets, light and heavy hadrons, quarkonia, and prompt photons. We address in particular the extraction of the strong coupling constant from photon structure funct...