Galoitica: Journal of Mathematical Structures and Applications

This paper is dedicated to find Legendre polynomials by using novel linear algebraic methods based on matrices based on Liouville-Sturm theorem, where we find the matrix of the differential operator for Legendre polynomials, with their eigenvalues and their eigenvectors. Also, we illustrate many examples to clarify the validity of our work.

This paper is dedicated to find the values of the integrals in the spherical region of  depending on the generative Kernel method by finding the integral formula that we use in the orthogonal and regular operations to find Ortho-normal polynomials on the sphere with radius r. Also, we illustrate many examples to clarify the validity of our work.

The objective of this paper to study some algebraic properties of ternary rings in which all of their proper right ideals are prime. Also, we characterize the relation between this class of ternary rings and the rings that all of their right ideals are weakly prime.

In this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.

Recent time a problem is addressed while dealing the data with multi-valued attributes and its dynamicity. The problem is that these types of data set contain lots of opposite, non-opposite and uncertainty unconsciously. One of the suitable examples is handling soil data sets and its pattern for water storage and plant growth.  The precise representation of these types of data sets and its multi-veracity is one of the crucial tasks for the data science researchers. To achieve this goal, algebra of Intuitionistic Plithogenic set and its graph is utilized in this paper. The proposed method is explained using the example of Soil pollution.