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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.

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 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 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.

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.

Nidus Idearum. Scilogs, XIII: Structure / NeutroStructure / AntiStructure

2024-01-01 Mathematics
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Release : 2024-01-01
Genre : Mathematics
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Book Synopsis Nidus Idearum. Scilogs, XIII: Structure / NeutroStructure / AntiStructure by : Florentin Smarandache

Download or read book Nidus Idearum. Scilogs, XIII: Structure / NeutroStructure / AntiStructure written by Florentin Smarandache. This book was released on 2024-01-01. Available in PDF, EPUB and Kindle. Book excerpt: In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies. Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de Oliveira, Alexey Platonov, Andrei Pogany, Shakti Prasad, Ranulfo Paiva Barbosa (Sobrinho), Dmitri Rabounski, Ackbar Rezaei, Constantin Sandu, A. Saraswathi, Usman Shahzad, Gocho V. Sharlanov, Stefan Spaarmann, Michael Voskoglou, Vinay Kumar Yadav, Tomasz Witczak, William H. Woodall, Mircea Zărnescu, Mohamed Bisher Zeina (in order of reference in the book).

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