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An Overview of Plithogenic Set and Symbolic Plithogenic Algebraic Structures

2023-04-01 Mathematics
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Release : 2023-04-01
Genre : Mathematics
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Book Synopsis An Overview of Plithogenic Set and Symbolic Plithogenic Algebraic Structures by : Florentin Smarandache

Download or read book An Overview of Plithogenic Set and Symbolic Plithogenic Algebraic Structures written by Florentin Smarandache. This book was released on 2023-04-01. Available in PDF, EPUB and Kindle. Book excerpt: This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)

2023-01-01 Mathematics
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Release : 2023-01-01
Genre : Mathematics
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Book Synopsis Introduction to the Symbolic Plithogenic Algebraic Structures (revisited) by : Florentin Smarandache

Download or read book Introduction to the Symbolic Plithogenic Algebraic Structures (revisited) written by Florentin Smarandache. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.

On the Symbolic 2-Plithogenic Rings

2023-01-01 Mathematics
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Release : 2023-01-01
Genre : Mathematics
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Book Synopsis On the Symbolic 2-Plithogenic Rings by : Hamiyet Merkepçi

Download or read book On the Symbolic 2-Plithogenic Rings written by Hamiyet Merkepçi. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to study for the first time the algebraic properties of symbolic 2-plithogenic rings generated from the fusion of symbolic plithogenic sets with algebraic rings, where we study some of the elementary properties and substructures of symbolic 2-plithogenic rings such as AH-ideals, AH-homomorphisms, and AHS-isomorphisms. Also, the idempotency and nilpotency of symbolic 2-plithogenic elements in terms of theorems have been discussed. Besides, many examples to clarify the validity of our work have been covered.

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

2023-01-01 Mathematics
Download On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices PDF Online Free

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Release : 2023-01-01
Genre : Mathematics
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Book Synopsis On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices by : Hamiyet Merkepçi

Download or read book On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices written by Hamiyet Merkepçi. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work.

An Introduction to The Symbolic 3-Plithogenic Vector Spaces

2023-01-01 Mathematics
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Release : 2023-01-01
Genre : Mathematics
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Book Synopsis An Introduction to The Symbolic 3-Plithogenic Vector Spaces by : Rozina Ali

Download or read book An Introduction to The Symbolic 3-Plithogenic Vector Spaces written by Rozina Ali. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to define and study for the first time the concept of symbolic 3-plithogenic vector spaces based on symbolic 3-plithogenic sets and classical vector spaces.Also, many related substructures will be defined and handled such as AH-functions, AH-spaces, and symbolic 3-plithogenic basis.

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