Prospects for Applied Mathematics and Data Analysis

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.

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-       Study the real data obtained through observation and description, and  then record and tabulate the case information we are studying. 2-       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   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,  and logically the results must be the same, so I prepared this research, through which I explained the reason for  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)

In this paper, we devoted to study the language monadic predicate logic system plus identity (LMPLS+I) as extension of the language of propositional logic system (LPLS). I.e., ( (LMPLS+I), which it contains all the hereditary traits (or features) of   , furthermore that, we will add some new data information between relationship of object, subject and predicate. This is the task of monadic predicate logic system addressed.  As mentioned in pervious papers, the main task of system of logic is classifying between valid and invalid arguments, moreover, the central role the system of logic how distinguishes between the conclusions which follow from their premises of the arguments and   those do not follow from their premises. As a matter of fact, when we encounter some proofs that seem perceptually (or intuitively) sound, but we are -unable to prove their validity due to the inability language of propositional logic system (LPLS). Hence, it was necessary to uses the monadic predicate logic system (LMPLS+I) to overcome this problem. In this article, we study syntax, semantics and inference on language monadic predicate logic system plus identity (LMPLS+I) and investigation characteristics of arguments such valid \ invalid and types of formulas and relations between formulas like consistency and inconsistency sets.

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

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.