## Prospects for Applied Mathematics and Data Analysis

##### Journal DOI

https://doi.org/10.54216/PAMDA

2836-4449ISSN (Online)

#### Studying the isotherm of the complementary Schaefer Ignaczak thermodynamical process of the first plane state of elastic strains for the unbounded micropolar body-Fourier Schaefer-Ignaczak formulas

##### Kheder Manhal Al-Saleh , Mountajab Al-Hasan , Monir Makhlouf

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.

Vol. 3 Issue. 1 PP. 08-20, (2023)

#### Double Indeterminacy - Neutrosophic study of an Approximation Techniques Used to Find Random Variables

##### Maissam Jdid , Florentin Smarandache

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