In this article, we present inverse and implicit function theorems forH -differentiable functions and semismooth functions, thereby generalizing the classical inverse and implicit function theorems to certain classes of nonsmooth functions. The classical inverse function theorem [47] asserts that a continuously differentiable function f : R → R is locally invertible at a point with a continuous...

We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in Ô(n/ log n) time, where the Ô notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs in Ô(n/ log n) time. Our algorithm generalizes the divide-and-conquer strategy of Chan’s algorithm. Moreover, we propose a general framewo...

Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, if every row (respectively column) of B, is g-majorized by the corresponding row (respectively column) of A. In this paper all kinds of g-majorization are studied on Mn,m, and the possible structure of their linear preservers will be found. Also all linear operators T : Mn,m ---> Mn...

background: matrix metalloproteinases comprise a family of enzyme degrade components of extra cellular matrix. there are single nucleotide polymorphisms in the promoter regions of several genes with ability to influence cancer susceptibility. the aim of this study was to analyze association between mmp 3 promoter polymorphisms and colorectal cancer occurrence and progression. materials and meth...

this paper analyzes an m/m/2 queueing system with two heterogeneous servers. both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. the vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. the system is analyzed in the steady st...

In response to a question posed by João P. Silva, I demonstrate that an arbitrary 2n×2n real orthogonal antisymmetric matrix can be parameterized by n(n−1) continuous angular parameters. An algorithm is provided for constructing the general form for such a matrix. This algorithm is based on observation that Sp(n,R) ∩ O(2n) ∼= U(n) and employs the parameterization of the coset space SO(2n)/U(n)....

Abstract. Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix P can be approximated by − 1 4 log detP. When the Markov process is assumed to be continuous in time, i.e. P = expQt it is easy to simulate this evolutionary process for a given br...

All the conventional criterions to verify if a matrix is positive definite, Hurwitz or an M-matrix, such as Sylvester condition and Hurwitz theorem, require us to compute n determinants. This paper develops a new and simple criterion, based on a new type of Gaussian elimination process. In contrast to the traditional criterions, the new criterion only computes one determinate. Thus, the computi...

This paper analyzes an M/M/2 queueing system with two heterogeneous servers. Both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady st...