Galoitica: Journal of Mathematical Structures and Applications

This paper introduces the concepts fuzzy pre-Hilbert spaces and fuzzy co-pre-Hilbert spaces and proves some theorems in this subject. Also, it illustrates many examples to clarify the validity of the new concepts.

The goal of this paper is to study the notions of completely semi prime ideal with respect to an element x (x-C.S.P.I) of a near ring and the completely semi prime ideal near ring with respect to an element x (x-C.S.P.I ), where the direct images and endomorphisms will be represented and discussed.

The concept of intuitionistic topological space was introduced by Coker. The aim of this paper is to discuss the relation between bi-topological spaces and double-topological spaces and give a notion of pairwise compact for double topological spaces.

The problem of the existence and construction of a resolution of singularities is one of the central questions of algebraic geometry. In this paper, we study this problem in connecting with the quotients for . It is known that the action of  on its Lie algebra is corresponding to the action of  on . As a result of this action, it will be an invariant ring, which determines the quotients for . This paper is devoted to studying the singularity of these quotients. We write this singularity as a matrix with interesting features such as, for example, its quadratic is a zero matrix and its rank is less than or equal to 1. Therefore, in this paper, we reduce the studying of the singularity of the quotients of , which is a hard problem, to the studying of a matrix of invariants which is an easy problem.

This paper presents an algorithm for generating random numbers that follow literal neutrosophic distributions using algebraic isomorphisms. The algorithm was applied to three distributions: literal neutrosophic uniform distribution, literal neutrosophic exponential distribution, and literal neutrosophic normal distribution. We also proposed a development of the Kolmogorov-Smirnov test to analyze goodness-of-fit for literal neutrosophic data. To evaluate the effectiveness of the proposed method, a simulation study was conducted, and the power results showed that increasing the sample size improved the test power. Our research contributes to the development of statistical methods for analyzing literal neutrosophic data, which has applications in a wide range of fields.