In this paper, a novel architecture for a finite field integer multiplier based on a superset of the triple moduli set {2-1,2,2+1} is presented. The superset is constructed by adding extra moduli of the form 2±1 (for any non-zero integer n) to extend its range. The multiplier uses index transform approach whereby multiplication is carried out by index addition, and is organized into submodules ...

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

Let f be a binary word and let Fd(f) be the set of words of length d which do not contain f as a factor (alias words that avoid the pattern f). A word is called even/odd if it contains an even/odd number of 1s. The parity index of f (of dimension d) is introduced as the difference between the number of even words and the number of odd words in Fd(f). A word f is called prime if every nontrivial...

The concept of topological gyrogroups is a generalization group. In this work, ones prove that gyrogroup G metrizable iff has an {\omega}{\omega}-base and Frechet-Urysohn. Moreover, in gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn having are all weakly three-space properties with H closed L-subgyrogroup