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Algebraic Geometry Commons™

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2020

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Articles 31 - 39 of 39

Full-Text Articles in Algebraic Geometry

Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi Jan 2020

Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.

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The Neutrosophic Triplet Of ����-Algebras, Florentin Smarandache, Akbar Rezaei Jan 2020

The Neutrosophic Triplet Of ����-Algebras, Florentin Smarandache, Akbar Rezaei

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, the concepts of a Neutro-����-algebra and Anti-����-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-����-algebra is an alternative of the class of ����-algebras.

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A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim Jan 2020

A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CI-algebras are not BE-algebras.

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On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei Jan 2020

On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.

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New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal Jan 2020

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

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Phylogenetic Networks And Functions That Relate Them, Drew Scalzo Jan 2020

Phylogenetic Networks And Functions That Relate Them, Drew Scalzo

Williams Honors College, Honors Research Projects

Phylogenetic Networks are defined to be simple connected graphs with exactly n labeled nodes of degree one, called leaves, and where all other unlabeled nodes have a degree of at least three. These structures assist us with analyzing ancestral history, and its close relative - phylogenetic trees - garner the same visualization, but without the graph being forced to be connected. In this paper, we examine the various characteristics of Phylogenetic Networks and functions that take these networks as inputs, and convert them to more complex or simpler structures. Furthermore, we look at the nature of functions as they relate …

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Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick Jan 2020

Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick

Senior Honors Theses

Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …

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Heat Kernel Voting With Geometric Invariants, Alexander Harr Jan 2020

Heat Kernel Voting With Geometric Invariants, Alexander Harr

All Graduate Theses, Dissertations, and Other Capstone Projects

Here we provide a method for comparing geometric objects. Two objects of interest are embedded into an infinite dimensional Hilbert space using their Laplacian eigenvalues and eigenfunctions, truncated to a finite dimensional Euclidean space, where correspondences between the objects are searched for and voted on. To simplify correspondence finding, we propose using several geometric invariants to reduce the necessary computations. This method improves on voting methods by identifying isometric regions including shapes of genus greater than 0 and dimension greater than 3, as well as almost retaining isometry.

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Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin Jan 2020

Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin

UNF Graduate Theses and Dissertations

We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …

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