Neutrosophic Hough Transform, 2017 University of New Mexico

#### Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

*Mathematics and Statistics Faculty and Staff Publications*

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its ...

Neutrosophic Commutative N-Ideals In Bck-Algebras, 2017 University of New Mexico

#### Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun

*Mathematics and Statistics Faculty and Staff Publications*

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.

Generating Pythagorean Triples: A Gnomonic Exploration, 2017 Colorado State University-Pueblo

#### Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett

*Number Theory*

No abstract provided.

The Pell Equation In India, 2017 SUNY Oneonta

#### The Pell Equation In India, Toke Knudsen, Keith Jones

*Number Theory*

No abstract provided.

Asymptotic Counting Formulas For Markoff-Hurwitz Tuples, 2017 The Graduate Center, City University of New York

#### Asymptotic Counting Formulas For Markoff-Hurwitz Tuples, Ryan Ronan

*Dissertations, Theses, and Capstone Projects*

The Markoff equation is a Diophantine equation in 3 variables first studied in Markoff's celebrated work on indefinite binary quadratic forms. We study the growth of solutions to an n variable generalization of the Markoff equation, which we refer to as the Markoff-Hurwitz equation. We prove explicit asymptotic formulas counting solutions to this generalized equation with and without a congruence restriction. After normalizing and linearizing the equation, we show that all but finitely many solutions appear in the orbit of a certain semigroup of maps acting on finitely many root solutions. We then pass to an accelerated subsemigroup of ...

Some Results In Combinatorial Number Theory, 2017 The Graduate Center, City University of New York

#### Some Results In Combinatorial Number Theory, Karl Levy

*Dissertations, Theses, and Capstone Projects*

The first chapter establishes results concerning equidistributed sequences of numbers. For a given $d\in\mathbb{N}$, $s(d)$ is the largest $N\in\mathbb{N}$ for which there is an $N$-regular sequence with $d$ irregularities. We compute lower bounds for $s(d)$ for $d\leq 10000$ and then demonstrate lower and upper bounds $\left\lfloor\sqrt{4d+895}+1\right\rfloor\leq s(d)< 24801d^{3} + 942d^{2} + 3$ for all $d\geq 1$. In the second chapter we ask if $Q(x)\in\mathbb{R}[x]$ is a degree $d$ polynomial such that for $x\in[x_k]=\{x_1,\cdots,x_k\}$ we have $|Q(x)|\leq 1$, then how big can its lead coefficient be? We prove that there is a unique polynomial, which we call $L_{d,[x_k]}(x)$, with maximum lead coefficient under these constraints and construct an algorithm that generates $L_{d,[x_k]}(x)$.

On A Frobenius Problem For Polynomials, 2017 Gettysburg College

#### On A Frobenius Problem For Polynomials, Ricardo Conceição, R. Gondim, M. Rodriguez

*Math Faculty Publications*

We extend the famous diophantine Frobenius problem to a ring of polynomials over a field~*k*. Similar to the classical problem we show that the *n* = 2 case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over ℤ to *k*[*t*] and give an algorithm to solve the Frobenius problem for polynomials over a field *k* of sufficiently large size.

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, 2017 Utah State University

#### Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

*All Graduate Plan B and other Reports*

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log_{2}(α)^{3} + 16.5log_{2}(α)^{2} + 6log ...

Transfinite Ordinal Arithmetic, 2017 Governors State University

#### Transfinite Ordinal Arithmetic, James Roger Clark

*All Student Theses*

Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion ...

A Math Poem, 2017 Essex Street Academy

Dynamical Systems And Zeta Functions Of Function Fields, 2017 University of Massachusetts Amherst

#### Dynamical Systems And Zeta Functions Of Function Fields, Daniel Nichols

*Doctoral Dissertations*

This doctoral dissertation concerns two problems in number theory. First, we examine a family of discrete dynamical systems in F_2[t] analogous to the 3x + 1 system on the positive integers. We prove a statistical result about the large-scale dynamics of these systems that is stronger than the analogous theorem in Z. We also investigate mx + 1 systems in rings of functions over a family of algebraic curves over F_2 and prove a similar result there.

Second, we describe some interesting properties of zeta functions of algebraic curves. Generally L-functions vanish only to the order required by their root number ...

Primes, Divisibility, And Factoring, 2017 Central Washington University

#### Primes, Divisibility, And Factoring, Dominic Klyve

*Number Theory*

No abstract provided.

Babylonian Numeration, 2017 Central Washington University

Construction Of The Figurate Numbers, 2017 New Mexico State University

#### Construction Of The Figurate Numbers, Jerry Lodder

*Number Theory*

No abstract provided.

Pascal's Triangle And Mathematical Induction, 2017 New Mexico State University

#### Pascal's Triangle And Mathematical Induction, Jerry Lodder

*Number Theory*

No abstract provided.

Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, 2017 Colorado State University-Pueblo

#### Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett

*Number Theory*

No abstract provided.

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, 2017 Colorado State University-Pueblo

#### Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

*Number Theory*

No abstract provided.

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, 2017 University of New Mexico

#### Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.

Counting Rational Points, Integral Points, Fields, And Hypersurfaces, 2017 The Graduate Center, City University of New York

#### Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther

*Dissertations, Theses, and Capstone Projects*

This thesis comes in four parts, which can be read independently of each other.

In the first chapter, we prove a generalization of Poonen's finite field Bertini theorem, and use this to show that the obvious obstruction to embedding a curve in some smooth surface is the only obstruction over perfect fields, extending a result of Altman and Kleiman. We also prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.

In the second chapter, for a fixed base curve over a finite field of characteristic at least 5 ...

Neutrosophy, A Sentiment Analysis Model, 2017 University of New Mexico

#### Neutrosophy, A Sentiment Analysis Model, Florentin Smarandache, Mirela Teodorescu, Daniela Gifu

*Mathematics and Statistics Faculty and Staff Publications*

This paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis. The aim of this pilot study is to find a procedure to diminish the uncertainties from public discourse induced, especially, by humans (politicians, journalists, etc.). We consider that Neutrosophy Theory is a sentiment analysis specific case regarding processing of the three states: positive, negative, and neutral. The study is intended to identify a method to answer to uncertainties solving in order to support politician's staff, NLP specialists, artificial intelligence researchers and generally the electors.