## Prospects for Applied Mathematics and Data Analysis

##### Journal DOI

https://doi.org/10.54216/PAMDA

2836-4449ISSN (Online)

#### Study on the Expectation of Geometric Distribution

When we want to know the truth of the emergence of a scientific principle, we find in many cases that it is no more than a process of interpretation, description and analysis of existing natural phenomena of various kinds, this is done by identifying the components on which these phenomena depend and the qualities and characteristics that each organism enjoys, which enables us to form a clear strategic vision that helps us in developing pre-solutions to what we expect from the problems resulting from any emergency or exceptional circumstance Most studies in the fields of science need two types of study: 1-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Study the real data obtained through observation and description, and&nbsp; then record and tabulate the case information we are studying. 2-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the study of phenomena to predict what the phenomenon will become in the near and even distant future, The statistical analysis puts us in the merits of the current and future situation of the system under study, and statistical analysis is the applied aspect of probability science, through the probability distributions that are used in different fields of science, the probability of the values of the variable can be calculated by applying a mathematical equation called the probability density function and by using distinctive values for these distributions such as expectation, variance and standard deviation&nbsp;&nbsp; From analyzing the data to reach the desired results, after reviewing a number of references, it drew my attention that the expectation of the geometric distribution is calculated using a relationship that varies from one return to another, knowing that these references start from the basic definition of the expectation or from the moment-generating function,&nbsp; and logically the results must be the same, so I prepared this research, through which I explained the reason for&nbsp; the difference, which in turn may have an impact on the results of studies for the systems which works according to this distribution (the importance of this effect depends on the meaning of the expectation for the studied system)

Vol. 1 Issue. 1 PP. 52-56, (2023)

#### A Study of a Neutrosophic Differential Equation by Using the One-Dimensional Geometric AH-Isometry

##### Ahmed Salamah , Malath F Alaswad , Rasha Dallah

In this paper, the definition of a Neutrosophic Differential Equation by Using the One-Dimensional Geometric AH-Isometry. The main objective is define a Neutrosophic identical linear differential equation and Neutrosophic non-homogeneous linear differential equation and find solutions for this equation.

Vol. 1 Issue. 1 PP. 57-62, (2023)

#### A Study of Neutrosophic Property Functions

##### Ahmed Salamah , Malath F. Alaswad , Rasha Dallah

This paper is dedicated to neutrosophic property functions its generalizations, especially neutrosophic Gamma function, neutrosophic Beta function, neutrosophic Zeta function. Also, this work gives the interested reader a background in the study of neutrosophic polynomial orthogonality.

Vol. 1 Issue. 1 PP. 08-22, (2023)

#### Application of Integral Operator Generated by Touchard Polynomials to Certain Subclasses of Harmonic Functions

##### Khalifa AlShaqsi

Let SH denote the class of functions f = h + g which are harmonic univalent and sense-preserving in the unite disk U = {z : |z| &lt; 1} where h(z) = z +P&infin; k=2 akzk, g(z) =&infin;Pk=1 bkzk (|b1| &lt; 1). In this paper we establish connections between various subclasses of harmonic univalent functions by applying certain integral operator involving the Touchard Polynomials.