Journal of Mathematical Extension
Volume:14 Issue: 4, Autumn 2020

RSA is a well-known public-key cryptosystem. It is the most commonly used and currently most important public-key algorithm which can be used for both encryption and signing. RSA cryptosystem involves exponentiation modulo an integer number n that is the product of two large primes p and q. The security of the system is based on the difficulty of factoring large integers in terms of its key size and the length of the modulus n in bits which is said to be the key size. In this paper, we present a method that increases the speed of RSA cryptosystem. Also an efficient implementation of arithmetic and modular operations are used to increase its speed. The security is also enhanced by using a variable key size space. There exist numerous implementations (hardware or software) of RSA cryptosystem, but most of them are restricted in key size. An important improvement achieved in this paper is that the system is designed flexibly in terms of key size according to user security.

One approximation to apply superiority and preference information in Data Envelopment Analysis (DEA) is to use value efficiency approach. The purpose of calculating value efficiency approach is to calculate increase in outputs and reduce in inputs to achieve value function frontier that passes most preferred solution (MPS) point. Note that value function is an unknown function and we can use linear approximation for the approximation of this function and the new frontier will replace the real frontier. In this paper, directional distance function is used to calculate value efficiency. Thus, different values of value efficiency are achieved by selecting various directions. In the following, the above models are used to assess the value efficiency of bank branches by applying the comments of managers and we will see that without the application of weight restrictions, we can apply the comments of managers for a proper assessment.

We employ the concept of average 2-degree of the vertices and, more generally, the number of walks between two vertices to introduce new upper and lower bounds for the spectral radius and the smallest eigenvalue of a graph. We, further, show how these bounds are better than previous bounds in some cases.

In this paper, firstly, we introduce a new extension of F-Suzuki-contraction mappings namely generalized $F_p$-Suzuki contraction. Moreover, we prove a fixed point theorem for such contraction mappings even without considering the completeness condition of space. In the following, we respond the open question of Rhoades(see Rhoades \cite{23}, p.242) regarding existence of a contractive definition which is strong enough to generate a fixed point but dose not force the mapping to be continuous at the fixed point.  Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value problem of a nonlinear fractional differential equation for our results.

Amenability and pseudo-amenability of $ \ell^{1}(S,\omega) $ ischaracterized, where $S$ is a left (right) zero semigroup or it is arectangular band semigroup. The equivalence conditions toamenability of $\ell^{1}(S,\omega)$ are provided, where  $ S $ is aband semigroup. The equivalence properties of amenability of$\ell^{1}(S, \omega)^{**}$ are described, where $S$ is an inversesemigroup. For a locally compact group $G$, pseudo-amenability of $\ell^{1}(G,\omega) $ is also discussed.

This paper investigates how the extensions of a double fuzzy topological space affect its regular fuzzy closed sets. While some type of extensions leave all the regular fuzzy closed sets intact, there are regular fuzzy closed sets which remain so under all its extensions.

Let $RG$ be the gruop ring of the group $G$ over ring $R$and $\u(RG)$ be its unit group.In this paper, we obtain the structure of unit group of $\f_{2^n}D_{14}$.

In spite of widespread use as well as theoretical properties of the multivariate scale mixture normal distributions, practical studies show a lack of stability and robustness against asymmetric features such as asymmetry and heavy tails. In this paper, we develop a new multivariate model by assuming the Birnbaum-Saunders distribution for the mixing variable in the scale mix- tures restricted skew-normal distribution. An analytically simple and efficient EM-type algorithm is adopted for iteratively computing maximum likelihood estimate of model parameters. To account standard errors, the observed in- formation matrix is derived analytically by offering an information-based ap-proach. Results obtained from real and simulated datasets are reported toillustrate the practical utility of the proposed methodology.

Let $S$ be a ternary semigroup‎. ‎In this article we introduce our notation and prove some elementary properties of a pair ideal $(I,J)$ of a ternary semigroup $S$ and give some characterizations of the minimality of pair left (right) and middle ideal in ternary semigroup.‎

The purpose of this work is to apply function sequences to Darbo's theorem with the integral type transformation by changing the roles of function sequences with function classes used in fixed point theory and to examine the existence of fixed points. Also, an interesting example will be shown.

We introduce the notion of statistical limit of continuous fuzzy number valued functions at infinity and compare its relationship with ordinary limit. We obtain ordinary limit from statistical limit at infinity in terms of a slowly oscillating-like condition. We also establish a Tauberian theorem for statistical summability by weighted means of continuous fuzzy number valued functions.

The purpose of this paper is to establish some Hermite-Hadamard type inequalities for h-convex functions utilizing generalized fractional integrals. We also obtain some generalized trapezoidand midpoint type inequalities for the mapping whose first derivatives absolutely value are h-convex.The results proved in this paper generalize the several inequalities obtained earlier works.