The notion of a Markov chain is ubiquitous in linear algebra and probability books. In linear algebra a Markov chain is a sequence {xk} of vectors defined recursively by a specified vector x0, a square matrix P and the recursion xk = Pxk−1 for k = 1, 2, . . .. That is, xk = P x0. Natural probabilistic restrictions are imposed on x0 and P . It is assumed that x0 is a probability vector; that is,...

BACKGROUND Adult device circumcision may potentially reach more men in Sub-Saharan Africa, with fewer human resource and capacity needs than surgical procedures. Despite these advantages, little is known about device acceptability, including pain and maintaining the device in situ. METHODS Healthy, HIV-negative men, between 18 and 49 years, in a Maputo clinic, were consecutively asked to part...

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

We give more properties and applications to the class of somewhat nearly continuous functions introduced by Piotrowski. Among applications, we show that Baire property is preserved under quasiopen injection images spaces are countable fiber complete preimages. The later statement generalizes results given Noll, Mirmostafaee

The goal of this research is to establish control theoretic methods enhance cyber security networked motion systems by utilizing somewhat homomorphic encryption. proposed approach will encrypt the entire schemes including: sensor signals, model parameters, feedback gains, and performs computation in ciphertext space generate commands servo without a hole. paper discuss implementation encrypted ...

In this paper we port Brakerski’s fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and...