A string x is an outfix of a string y if there is a string w such that x1wx2 = y and x = x1x2. A set X of strings is outfix-free if no string in X is an outfix of any other string in X . Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines outfix-freeness of regular languages. Note that outfix-free regular languages are always finite. We consider two...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

We present an algorithm for the generation of prime implicates in equational logic, that is, of the most general consequences of formulæ containing equations and disequations between first-order terms. This algorithm is defined by a calculus that is proved to be correct and complete. We then focus on the case where the considered clause set is ground, i.e., contains no variables, and devise a s...

In this paper, we present a novel Field Programmable Gate Array (FPGA) implementation of advanced encryption standard (AES128) algorithm based on the design of high performance S-Box built using reduced residue of prime numbers. The objective is to present an efficient hardware realization of AES-128 using very high speed integrated circuit hardware description language (VHDL). The novel S-Box ...

Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$‎. ‎Recently people have been using prime graphs to study simple groups‎. ‎Naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? In this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$Gcong S_p$ if and only‎ ‎if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$‎, ‎whe...

We investigate the behaviour of linear cellular automata with state space ZN and only finitely many states. After some general comments about linear cellular automata over ZN , the general case is reduced to that of N being the power of a prime. For a prime power modulus, it is proved under fairly general conditions that the period length for “most” orbits increase by a factor of p when the mod...

In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18]. Let G be a finite group. The functor Ordset(G) yielding a subset of N is defined by the term (Def. 1) the set of all ord(a) where a is an element of G. One can ch...