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

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

*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.

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.

Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, 2017 The Graduate Center, City University of New York

#### Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, David Seff

*Dissertations, Theses, and Capstone Projects*

For any positive real number $\theta > 1$, and any natural number $n$, it is obvious that sequence $\theta^{1/n}$ goes to 1. Nathanson and O'Bryant studied the details of this convergence and discovered some truly amazing properties. One critical discovery is that for almost all $n$, $\displaystyle\floor{\frac{1}{\fp{\theta^{1/n}}}}$ is equal to $\displaystyle\floor{\frac{n}{\log\theta}-\frac{1}{2}}$, the exceptions, when $n > \log_2 \theta$, being termed atypical $n$ (the set of which for fixed $\theta$ being named $\mcA_\theta$), and that for $\log\theta$ rational, the number of atypical $n ...

Algorithmic Factorization Of Polynomials Over Number Fields, 2017 Rose-Hulman Institute of Technology

#### Algorithmic Factorization Of Polynomials Over Number Fields, Christian Schulz

*Mathematical Sciences Technical Reports (MSTR)*

The problem of exact polynomial factorization, in other words expressing a polynomial as a product of irreducible polynomials over some field, has applications in algebraic number theory. Although some algorithms for factorization over algebraic number fields are known, few are taught such general algorithms, as their use is mainly as part of the code of various computer algebra systems. This thesis provides a summary of one such algorithm, which the author has also fully implemented at https://github.com/Whirligig231/number-field-factorization, along with an analysis of the runtime of this algorithm. Let k be the product of the degrees of ...

From Simplest Recursion To The Recursion Of Generalizations Of Cross Polytope Numbers, 2017 Kennesaw State University

#### From Simplest Recursion To The Recursion Of Generalizations Of Cross Polytope Numbers, Yutong Yang

*KSU Journey Honors College Capstones and Theses*

My research project involves investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on "Generalizations of cross-polytope numbers". It will include the proofs of the combinatorics results in Dr. Edwards and Dr. Griffiths' recently published paper. $E(n,m)$ and $O(n,m)$, the even terms and odd terms for Dr. Edward's original combinatorial expression, are two distinct combinatorial expressions that are in fact equal. But there is no obvious ...

Roman Domination In Complementary Prisms, 2017 East Tennessee State University

#### Roman Domination In Complementary Prisms, Alawi I. Alhashim

*Electronic Theses and Dissertations*

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number ...

On The Reality Of Mathematics, 2017 Southeastern University - Lakeland

#### On The Reality Of Mathematics, Brendan Ortmann

*Selected Student Publications*

Mathematics is an integral cornerstone of science and society at large, and its implications and derivations should be considered. That mathematics is frequently abstracted from reality is a notion not countered, but one must also think upon its physical basis as well. By segmenting mathematics into its different, abstract philosophies and real-world applications, this paper seeks to peer into the space that mathematics seems to fill; that is, to understand *how* and *why* it works. Under mathematical theory, Platonism, Nominalism, and Fictionalism are analyzed for their validity and their shortcomings, in addition to the evaluation of infinities and infinitesimals, to ...

On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, 2017 The University of Western Ontario

#### On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi

*Electronic Thesis and Dissertation Repository*

The objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via Poincare series. In addition, it provides a proof of that vector-valued Poincare series on an irreducible bounded symmetric domain span the space of vector-valued automorphic forms.

Applications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, 2017 Yongsei University

#### Applications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, Jongsil Lee, James Mclaughlin, Jaebum Sohn

*Mathematics Faculty Publications*

In this paper we show that various continued fractions for the quotient of general Ramanujan functions G(aq, b, λq)/G(a, b, λ) may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer-Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine’s continued fraction for a ratio of 2φ1 functions, or other similar continued fraction expansions of ratios of 2φ1 functions. Further, by employing essentially the same methods, a ...

Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, 2017 West Chester University of Pennsylvania

#### Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, James Mclaughlin

*Mathematics Faculty Publications*

The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of 2ψ2 series ∞ ∑n=−∞ (a, c;q)n (b,d;q)n z n . Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say χ(q), and a root ...

On P-Adic Fields And P-Groups, 2017 University of Kentucky

#### On P-Adic Fields And P-Groups, Luis A. Sordo Vieira

*Theses and Dissertations--Mathematics*

The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to ...

Combinatorics Of Compositions, 2017 Georgia Southern University

#### Combinatorics Of Compositions, Meghann M. Gibson

*Electronic Theses and Dissertations*

Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.

P-Union And P-Intersection Of Neutrosophic Cubic Sets, 2017 University of New Mexico

#### P-Union And P-Intersection Of Neutrosophic Cubic Sets, Florentin Smarandache, Young Bae Jun, Chang Su Kim

*Mathematics and Statistics Faculty and Staff Publications*

Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.

Numbers In Base B That Generate Primes With Help The Luhn Function Of Order Ω, 2017 University of New Mexico

#### Numbers In Base B That Generate Primes With Help The Luhn Function Of Order Ω, Florentin Smarandache, Octavian Cira

*Mathematics and Statistics Faculty and Staff Publications*

We put the problem to determine the sets of integers in base b ≥ 2 that generate primes with using a function.

A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, 2017 University of New Mexico

#### A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mohsin Khan

*Mathematics and Statistics Faculty and Staff Publications*

In this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated.

Scaling Of Spectra Of Cantor-Type Measures And Some Number Theoretic Considerations, 2017 University of Central Florida

#### Scaling Of Spectra Of Cantor-Type Measures And Some Number Theoretic Considerations, Isabelle Kraus

*Honors Undergraduate Theses*

We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number *m* generates a complete or incomplete Fourier basis for a Cantor-type measure with scale *g*.

Mathematics Education From A Mathematicians Point Of View, 2016 University of Tennessee, Knoxville

#### Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson

*Masters Theses*

This study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.

On Sums Of Binary Hermitian Forms, 2016 The Graduate Center, City University of New York

#### On Sums Of Binary Hermitian Forms, Cihan Karabulut

*Dissertations, Theses, and Capstone Projects*

In one of his papers, Zagier defined a family of functions as sums of powers of quadratic polynomials. He showed that these functions have many surprising properties and are related to modular forms of integral weight and half integral weight, certain values of Dedekind zeta functions, Diophantine approximation, continued fractions, and Dedekind sums. He used the theory of periods of modular forms to explain the behavior of these functions. We study a similar family of functions, defining them using binary Hermitian forms. We show that this family of functions also have similar properties.