Prospects for Applied Mathematics and Data Analysis

The objective of this paper is to present and study elementary properties for concept a neutrosophic ring homomorphism and isomorphism which introduced by Florentine Smarandache in 2006. We will use a concept ring homomorphism and isomorphism in classical ring.

Solving polynomial equations involves finding their roots. In this respect, this idea dominates the minds of many mathematicians about how to find those roots. The Abel Ruffini theorem emphasizes that there is no general formula involving only the coefficients of a polynomial equation of degree five or higher that allows us to compute its solutions using radicals and its associate to the Galois Theory. The mathematical need for solving polynomial equations represents the motivation for the development of systems of numbers from Natural numbers to Complex numbers throughout the history of mathematics. Complex numbers play a central role in this context. The Fundamental Theorem of Algebra tell us that every nonconstant polynomial equation with complex coefficients has at least one complex root. While the Galois group associated with a polynomial captivates its symmetries and determines whether it is solvable by radicals. From a mathematical standpoint, it is customary to visualize polynomials in the form:P_n (x)=a_n x n+a_(n-1) x (n-1)+---+a_1 x 1+a_0, Where the set of coefficients {a_n, a_(n-1),---,a_0}ECand P_n (x)EC[x]. We have reconceptualized the polynomial generated by the formula (ax+y)^n=c in our previous work and computing radicals of more degree 5. In this article, we present a natural procedure formula that will lead us to find a solution for a class of polynomials nonlinear Complex numbers with degree 𝑛 associated with the equation:(ansquris K + (x+10y) nsquris)n = c as a particular class of Complex Polynomials.

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

The main interest in statistical analysis is to generate a series of random variables that follow the probability distribution in which the system under study operates. In almost all simulation tests, we need to generate random variables that follow a distribution, a distribution that adequately describes and represents the physical process involved in the experiment at That point. During the experiment, it may be necessary to simulate a real and perform the process of generating a random variable from a distribution many times depending on the complexity of the model to be simulated in order to obtain more accurate simulation results. In previous research, we presented a neutrosophical study of the process of generating random numbers and some techniques that can be used to convert these random numbers into variables. Randomness follows the probability distributions according to which the system to be simulated operates. These techniques were specific to probability distributions defined by a probability density function that is easy to deal with in terms of finding the cumulative distribution function and the inverse function of the cumulative distribution function or by calculating the values of this function at a certain value, and in reality, we encounter Many systems operate according to these distributions, which requires techniques other than the techniques presented. Therefore, in this research we will present a neutrosophical study of the approximation technique for generating random variables that follow probability distributions known as a complex probability density function. We will apply this study to find random variables that follow the distribution. Standard natural

This paper concerns the Ignaczak stress-temperature distribution [2] of the homogenous isotropic 2D micropolar thermodynamical in the first plane state of elastic strain, which discussed by Eringen [9] and Nowacki [8]. In [1] we provide this problem with new analytical method called Schaefer-Ignaczak method. In the paper, we do the following; We prove that the complementary Schaefer-Ignaczak process is an isothermal process for infinite 2D (E-N:5) [6,8], with no stresses and temperature at infinity, and then we find the related Fourier Schaefer-Ignaczak formulas [1] for the classical and complementary behavior of a two-dimensional infinite body (E-N:5), which is a micropolar body.