A New Type Of Group Action Through The Applications Of Fuzzy Sets And Neutrosophic Sets,
2015
University of New Mexico
A New Type Of Group Action Through The Applications Of Fuzzy Sets And Neutrosophic Sets, Florentin Smarandache, Mumtaz Ali
Branch Mathematics and Statistics Faculty and Staff Publications
Fuzzy sets are the most significant tools to handle uncertain data while neutrosophic sets are the generalizations of fuzzy sets in the sense to handle uncertain, incomplete, inconsistent, indeterminate, false data. In this paper, we introduced fuzzy subspaces and neutrosophic subspaces (generalization of fuzzy subspaces) by applying group actions.Further, we define fuzzy transitivity and neutrosophic transitivty in this paper. Fuzzy orbits and neutrosophic orbits are introduced as well. We also studied some basic properties of fuzzy subspaces as well as neutrosophic subspaces.
Neutrosophic Axiomatic System,
2015
University of New Mexico
Neutrosophic Axiomatic System, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we introduce for the first time the notions of Neutrosophic Axiom, Neutrosophic Axiomatic System, Neutrosophic Deducibility and Neutrosophic Inference, Neutrosophic Proof, Neutrosophic Tautologies, Neutrosophic Quantifiers, Neutrosophic Propositional Logic, Neutrosophic Axiomatic Space, Degree of Contradiction (Dissimilarity) of Two Neutrosophic Axioms, and Neutrosophic Model. A class of neutrosophic implications is also introduced. A comparison between these innovatory neutrosophic notions and their corresponding classical notions is made. Then, three concrete examples of neutrosophic axiomatic systems, describing the same neutrosophic geometrical model, are presented at the end of the paper.
Infinite Quaternion Pseudo Rings Using [0, N),
2015
University of New Mexico
Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place the fundamental theorem of algebra, “a nth degree polynomial has n and only n roots”, n is untrue in case of polynomial in polynomial quaternion rings in general. Further the very concept of derivative and integrals of these polynomials are untrue. Finally interval pseudo quaternion rings also behave in an erratic way. Not …
Mod Functions: A New Approach To Function Theory,
2015
University of New Mexico
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers,
2015
University of New Mexico
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m …
Mod Planes: A New Dimension To Modulo Theory,
2015
University of New Mexico
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …
Mod Pseudo Linear Algebras,
2015
University of New Mexico
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD …
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate,
2015
University of New Mexico
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
255 Compiled And Solved Problems In Geometry And Trigonometry,
2015
University of New Mexico
255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Readup Buildup. Thync - Instant Α-Readings,
2015
University of New Mexico
Readup Buildup. Thync - Instant Α-Readings, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Polynomials With Prescribed Bad Primes,
2014
University of Minnesota - Morris
Polynomials With Prescribed Bad Primes, David P. Roberts
Mathematics Publications
We tabulate polynomials in ℚ[t] with a given factorization partition, bad reduction entirely within a given set of primes, and satisfying auxiliary conditions associated to 0, 1, and ∞. We explain how these polynomials are of particular interest because of their role in the construction of nonsolvable number fields of arbitrarily large degree and bounded ramification.
Deconstructing The Welch Equation Using P-Adic Methods,
2014
Rose-Hulman Institute of Technology
Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh
Mathematical Sciences Technical Reports (MSTR)
The Welch map x -> gx-1+c is similar to the discrete exponential map x -> gx, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: gx-1+c = x (mod pe) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo pe, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …
Deconstructing The Welch Equation Using P-Adic Methods,
2014
Rose-Hulman Institute of Technology
Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh
Rose-Hulman Undergraduate Research Publications
The Welch map x -> gx-1+c is similar to the discrete exponential map x -> gx, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: gx-1+c = x (mod pe) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo pe, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …
The Tame-Wild Principle For Discriminant Relations For Number Fields,
2014
Arizona State University
The Tame-Wild Principle For Discriminant Relations For Number Fields, John W. Jones, David P. Roberts
Mathematics Publications
Consider tuples ( K1 , … , Kr ) of separable algebras over a common local or global number field F1, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki ∕ F . We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.
Polynomial Factoring Algorithms And Their Computational Complexity,
2014
University of Connecticut - Storrs
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Honors Scholar Theses
Finite fields, and the polynomial rings over them, have many neat algebraic properties and identities that are very convenient to work with. In this paper we will start by exploring said properties with the goal in mind of being able to use said properties to efficiently irreducibly factorize polynomials over these fields, an important action in the fields of discrete mathematics and computer science. Necessarily, we must also introduce the concept of an algorithm’s speed as well as particularly speeds of basic modular and integral arithmetic opera- tions. Outlining these concepts will have laid the groundwork for us to introduce …
Computing Local Constants For Cm Elliptic Curves,
2014
College of Saint Benedict/Saint John's University
Computing Local Constants For Cm Elliptic Curves, Sunil Chetty, Lung Li
Mathematics Faculty Publications
Let E/k be an elliptic curve with CM by O. We determine a formula for (a generalization of) the arithmetic local constant of Mazur-Rubin at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to describe extensions F/Q over which the O-rank of E grows.
A Frobenius Question Related To Actions On Curves In Characteristic P,
2014
Gettysburg College
A Frobenius Question Related To Actions On Curves In Characteristic P, Darren B. Glass
Math Faculty Publications
We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases.
Finding Zeros Of Rational Quadratic Forms,
2014
Claremont McKenna College
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
CMC Senior Theses
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.
Multi-Criteria Decision Making Based On Dsmt-Ahp,
2014
University of New Mexico
Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we present an extension of the multicriteria decision making based on the Analytic Hierarchy Process (AHP) which incorporates uncertain knowledge matrices for generating basic belief assignments (bba’s). The combination of priority vectors corresponding to bba’s related to each (sub)- criterion is performed using the Proportional Conflict Redistribution rule no. 5 proposed in Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. The method presented here, called DSmT-AHP, is illustrated on very simple examples.
There And Back Again: Elliptic Curves, Modular Forms, And L-Functions,
2014
Harvey Mudd College
There And Back Again: Elliptic Curves, Modular Forms, And L-Functions, Allison F. Arnold-Roksandich
HMC Senior Theses
L-functions form a connection between elliptic curves and modular forms. The goals of this thesis will be to discuss this connection, and to see similar connections for arithmetic functions.
