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 ( ...

We consider the LU factorization of unsymmetric sparse matrices using a threephase approach (analysis, factorization and triangular solution). Usually the analysis phase first determines a set of potentially good pivot and then orders this set of pivots to decrease the fill-in in the factors. In this paper, we present a preprocessing algorithm that simultaneously achieves the objectives of sele...

Let O be an order of an algebraic number field. It was shown by Ge that given a factorization of an O-ideal a into a product of O-ideals it is possible to compute in polynomial time an overorder O′ of O and a gcdfree refinement of the input factorization; i.e., a factorization of aO′ into a power product of O′-ideals such that the bases of that power product are all invertible and pairwise copr...

In path factorization, H. Wang [1] gives the necessary and sufficient conditions for the existence of P_k-factorization of a complete bipartite graph for k, an even integer. Further, Beiling Du [2] extended the work of H. Wang, and studied the P_2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers. P_3-factorization ...

Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the stratification of factorization manifolds. Furthermore, ...