Prospects for Applied Mathematics and Data Analysis

In this paper, we will describe a natural procedure formula that will lead us to find a solution for a class of polynomials with degree  associate with the equation .

Nonlinear programming is an important and essential part of operations research and is more comprehensive than linear programming, its applications have spread in all branches of science, engineering, physics, chemistry, management, economic and military fields, etc.  Nonlinear programming can also be used in  forecasting, estimation, applied statistics and determining the costs resulting from the production, purchase and storage of goods, the mathematical model is a nonlinear model if any of the vehicles of the target or constraints are nonlinear statements and may be nonlinear statements In both, after neutrosophic science has achieved a  great development in most fields of science, it was necessary  to reformulate  nonlinear models according to its concepts, we present in this research a study of neutrosophic nonlinear dependencies and neutrosophic nonlinear models as a prelude to future research through which we study some methods of solving neutrosophic nonlinear models. 

The importance of results of this paper consist in supplying new analytical method for solving the Ignaczak tensorial equations, governing the thermodynamical plane state of small elastic strains of the homogeneous, isotropic, micropolar elastic solid of 5 material constants of Eringen-Nowacki type, which shortly called  2D (E-N:5) (Iron plates, copper plates, aluminum plates, .. etc.).  The paper covers the mathematical model of the first plane state of small elastic strains of micropolar homogeneous and isotropic solid, of five material constants, subjected to temperature field, mathematically proposed by Eringen and Nowacki, and shortly called 2D (E-N:5).  In paper, for the 2D (E-N:5) considerable body, we generalize the Schaefer vector method to: I) The Traditional Description of the 2D (E-N:5) considerable body, II) The Ignaczak Description of the 2D (E-N:5) considerable body. Subsequently, these results have important applications in material resistance, plate theory, industry ….etc.    

We present this research to all researchers and scholars who have realized the existence of indeterminacy in all data, through the results they obtain and the values that are not accurate enough and that may cause loss to the systems and facilities under study, and we will present through it the emergence, foundations and development of Neutrosophic theories and their applications for more than two decades (1995- 2023) since it was defined and studied, along with its applications, in order to be able to present new studies and research that keep pace with the great scientific development that our contemporary world is witnessing, through the use of research that has been published by the professionals and found on the attached open links.

This articles presents a new concept in mathematics according to a neutrosophic logic, which is the first of its kind in applied mathematics, which is the concept of the movement of a neutrosophic point in the neutrosophic plane and determining the path of this point, after determining Cartesian and polar neutrosophic coordinates of this point and also defining the neutrosophic local, velocity and acceleration vectors of these point. We have also determined the relationsships between the motion of a neutrosophic point and its equivalent in the classical plane, through an AH-isometry that connects the neutrosophic and classical plane. We conducted the previous study on three different examples, each example differs from the other in the form of a path and type of movement of the studied point.