Pk -factorization of a complete bipartite graph for k, an even integer was studied by H. Wang [1]. Further, Beiling Du [2] extended the work of H.Wang, and studied the P2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers[3,4,5]. P3-factorization of complete bipartite graph was studied by K.Ushio [3]. P5-factorizatio...

A palindrome is a symmetric string, phrase, number, or other sequence of units sequence that reads the same forward and backward. We present an algorithm for maximal palindromic factorization of a finite string by adapting an Gusfield algorithm [15] for detecting all occurrences of maximal palindromes in a string in linear time to the length of the given string then using the breadth first sear...

A functorial treatment of factorization structures is presented, under extensive use of well-pointed endofunctors. Actually, so-called weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reeective subcategories and factorization systems. The second part of the paper presents two important factorization structures...

I provide the details of the factorization of the Mersenne number 21061 − 1 by the Special Number Field Sieve. Although this factorization is easier than the completed factorization of RSA-768, it represents a new milestone for factorization using publicly available software.

in this paper‎, ‎an efficient dropping criterion has been used to compute the iul factorization obtained from backward factored approximate inverse (bfapinv) and ilu factorization obtained from forward factored approximate inverse (ffapinv) algorithms‎. ‎we use different drop tolerance parameters to compute the preconditioners‎. ‎to study the effect of such a dropping on the quality of the ilu ...

We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...