The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) “reflects” factorization systems. In particular, a generalization of the well-known Cassidy-HébertKelly factorization theorem is given. The problem of relat...

These notes were written to accompany a talk given in the Algebraic Topology and Category Theory Proseminar in Fall 2008 at the University of Chicago. We first introduce orthogonal factorization systems, give a few examples, and prove some basic theorems. Next, we turn to weak factorization systems, which play an important role in the theory of model categories, a connection which we make expli...

Channel-factorization aided detector (CFAD) is one of the important low-complexity detectors used in multiple input, multiple output (MIMO) receivers. Through channel factorization, this method transforms the original MIMO system into an equivalent system with a betterconditioned channel where detection is performed with a low-complexity detector; the estimate is then transferred back to the or...

using qcd factorization for the hadronic matrix elements, we show that existing data, inparticular the branching ratios br ( b →j/ψk) and br ( b →j/ψπ), can be accounted for in this approach.we analyze the decay b j /k( ) within the framework of qcd factorization. the calculation of therelevant hard-scattering kernels for twist-2 and twist-3 is completed. we calculate this decay in a special...

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 $PSL(2,2^{n})$...

Spectral factorization methods are used for the estimation of minimum phase time series from a given power spectrum. We present an efficient technique for spectral factorization, based on Newton’s method. We show how to apply the method to the factorization of both auto and cross-spectra, and present a simple example of 2-D deconvolution in the helical coordinate system.

We study lax epimorphisms in 2-categories, with special attention to Cat and V-Cat. show that any 2-category convenient colimits has an orthogonal LaxEpi-factorization system, we give a concrete description of this factorization Cat.

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...