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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.

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

2023-01-01 Mathematics
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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 an 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.

Introduction to Symbolic 2-Plithogenic Probability Theory

2023-01-01 Mathematics
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Release : 2023-01-01
Genre : Mathematics
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Book Synopsis Introduction to Symbolic 2-Plithogenic Probability Theory by : Mohamed Bisher Zeina

Download or read book Introduction to Symbolic 2-Plithogenic Probability Theory written by Mohamed Bisher Zeina. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On Clean and Nil-clean 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 Clean and Nil-clean Symbolic 2-Plithogenic Rings by : P. Prabakaran

Download or read book On Clean and Nil-clean Symbolic 2-Plithogenic Rings written by P. Prabakaran. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR.

Introduction to Prehomogeneous Vector Spaces

2002 Vector spaces
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Release : 2002
Genre : Vector spaces
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Book Rating : 406/5 ( reviews)

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Book Synopsis Introduction to Prehomogeneous Vector Spaces by : Tatsuo Kimura

Download or read book Introduction to Prehomogeneous Vector Spaces written by Tatsuo Kimura. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces. This book is written for students, and is appropriate for second-year graduate level and above. However, because it is self-contained, coverin.

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