# Mathematics Commons™

## All Articles in Mathematics

6,882 full-text articles. Page 1 of 160.

2015 East Tennessee State University

#### The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant

##### Electronic Theses and Dissertations

In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.

2015 East Tennessee State University

#### Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

##### Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial ...

Augmented Happy Functions Of Higher Powers, 2015 The Citadel, Charleston, SC

#### Augmented Happy Functions Of Higher Powers, Marcus Harbol, Breeanne B. Swart

##### Journal of the South Carolina Academy of Science

No abstract provided.

Combinatorial Properties Of Generalized M-Matrices, 2015 National Institute of Tecnology- Meghalya

#### Combinatorial Properties Of Generalized M-Matrices, Manideepa Saha, Sriparna Bandopadhyay

##### Electronic Journal of Linear Algebra

An M_∨-matrix has the form A = sI − B with s ≥ ρ(B) and B^k is entrywise nonnegative for all sufficiently large integers k. In this paper, the existence of a preferred basis for a singular M_∨- matrix A = sI − B with index(B) ≤ 1 is proven. Some equivalent conditions for the equality of the height and level characteristics of A are studied. The well structured property of the reduced graph of A is discussed. Also the possibility of the existence of preferred basis for another generalization of M-matrices, known as GM-matrices, is studied.

Mathematics In Contemporary Society Chapter 1, 2015 Queensborough Community College

#### Mathematics In Contemporary Society Chapter 1, Patrick J. Wallach

##### Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook will be posted in weekly installments.

On The Inverse Of A Class Of Bipartite Graphs With Unique Perfect Matchings, 2015 IIT Guwahati

#### On The Inverse Of A Class Of Bipartite Graphs With Unique Perfect Matchings, Swarup Kumar Panda, Dr. Sukanta Pati

##### Electronic Journal of Linear Algebra

Let G be a simple, undirected graph and Gw be the weighted graph obtained from G by giving weights to its edges using a positive weight function w. A weighted graph Gw is said to be nonsingular if its adjacency matrix A(Gw) is nonsingular. In [9], Godsil has given a class $\mathcal{G }$of connected, unweighted, bipartite, nonsingular graphs G with a unique perfect matching, such that A(G)−1 is signature similar to a nonnegative matrix, that is, there exists a diagonal matrix D with diagonal entries ±1 such that DA(G)−1D is nonnegative. The graph associated ...

A Nonlinear Filter For Markov Chains And Its Effect On Diffusion Maps, 2015 Yale University

#### A Nonlinear Filter For Markov Chains And Its Effect On Diffusion Maps, Stefan Steinerberger

##### Yale Day of Data

Diffusion maps are a modern mathematical tool that helps to find structure in large data sets - we present a new filtering technique that is based on the assumption that errors in the data are intrinsically random to isolate and filter errors and thus boost the efficiency of diffusion maps. Applications include data sets from medicine (the Cleveland Heart Disease Data set and the Wisconsin Breast Cancer Data set) and engineering (the Ionosphere data set).

A Combinatorial Determinant Dual To The Group Determinant, 2015 Indian Institute of Technology - Bombay

#### A Combinatorial Determinant Dual To The Group Determinant, Murali K. Srinivasan, Ashish Mishra

##### Electronic Journal of Linear Algebra

We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We give the following combinatorial example of a commuting algebra determinant. Let $\Bq(n)$ denote the set of all subspaces of an $n$-dimensional vector space over $\Fq$. The {\em type} of an ordered pair $(U,V)$ of subspaces, where $U,V\in \Bq(n)$, is the ordered triple $(\mbox{dim }U, \mbox{dim }V, \mbox{dim }U\cap V)$ of nonnegative integers. Assume that there are independent indeterminates corresponding to each type. Let \$X_q(n ...

Wave Packet Transform Over Finite Fields, 2015 Faculty of Mathematics, University of Vienna

#### Wave Packet Transform Over Finite Fields, Arash Ghaani Farashahi

##### Electronic Journal of Linear Algebra

In this article we introduce the notion of finite wave packet groups over finite fields as the finite group of dilations, translations, and modulations. Then we will present a unified theoretical linear algebra approach to the theory of wave packet transform (WPT) over finite fields. It is shown that each vector defined over a finite field can be represented as a coherent sum of finite wave packet group elements as well.

An Example Of Lagrangian For A Non-Holonomic System, 2015 University of North Georgia

#### An Example Of Lagrangian For A Non-Holonomic System, Piotr W. Hebda, Beata A. Hebda

##### Faculty Publications

An adjustable two-mass-point Chaplygin Sleigh is used as an example of a non-holonomic system. Newtonian equations of motion based the assumption of zero virtual work done by constraints are calculated. A Lagrangian that reproduces these equations as its unmodified Euler-Lagrange equations is then explicitly given. The Lagrangian uses variables that are present in the Chaplygin Sleigh equations of motion, as well as some additional variables. Some of the Euler-Lagrange equations of that Lagrangian are non-differential. These non-differential equations automatically and completely reduce out all of these additional variables, so that only the variables that appear in the original equations of ...

Sentential Logic, 2015 CSU, San Bernardino

#### Sentential Logic, Tony Roy

##### Books

Excerpted from chapters 1 - 7 of Symbolic Logic

Contents

Preface i

Contents v

Named Deﬁnitions ix

Quick Reference Guides xvii

I The Elements: Four Notions of Validity 1

1 Logical Validity and Soundness 4

1.1 Consistent Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 The Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Some Consequences . . . . . . . . . . . . . . . . . . . . . . . . . 22

2 Formal Languages 29

2.1 Sentential Languages . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.2 Quantiﬁcational Languages . . . . . . . . . . . . . . . . . . . . . . 44

3 Axiomatic Deduction 45

3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2 Sentential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3 Quantiﬁcational . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4 Semantics 59

4.1 Sentential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Quantiﬁcational . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 Translation 76

CONTENTS vi

5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5 ...

Symbolic Logic, 2015 CSU, San Bernardino

#### Symbolic Logic, Tony Roy

##### Books

Contents

Preface i

Contents v

Named Deﬁnitions ix

Quick Reference Guides xvii

I The Elements: Four Notions of Validity 1

1 Logical Validity and Soundness 4

1.1 Consistent Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 The Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 Some Consequences . . . . . . . . . . . . . . . . . . . . . . . . . 22

2 Formal Languages 30

2.1 Sentential Languages . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Quantiﬁcational Languages . . . . . . . . . . . . . . . . . . . . . . 46

3 Axiomatic Deduction 67

3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2 Sentential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3 Quantiﬁcational . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4 Semantics 96

4.1 Sentential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.2 Quantiﬁcational . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5 Translation 137

5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.2 Sentential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.3 Quantiﬁcational . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6 Natural Deduction ...

Art, Math, And Physics; All About For, 2015 Fresno Pacific University

#### Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls Dr.

##### The STEAM Journal

Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.

Ambiguity In Speaking Chemistry And Other Stem Content: Educational Implications, 2015 Ivy Tech Community College

#### Ambiguity In Speaking Chemistry And Other Stem Content: Educational Implications, Mick D. Isaacson, Michelle Michaels

##### Journal of Science Education for Students with Disabilities

Ambiguity in speech is a possible barrier to the acquisition of knowledge for students who have print disabilities (such as blindness, visual impairments, and some specific learning disabilities) and rely on auditory input for learning. Chemistry appears to have considerable potential for being spoken ambiguously and may be a barrier to accessing knowledge and to learning. Educators in chemistry may be unaware of, or have limited awareness of, potential ambiguity in speaking chemistry and may speak chemistry ambiguously to their students. One purpose of this paper is to increase awareness of potential ambiguity in speaking chemistry and other STEM fields ...

Geometric Constructions From An Algebraic Perspective, 2015 California State University-San Bernardino

#### Geometric Constructions From An Algebraic Perspective, Betzabe Bojorquez

##### Electronic Theses, Projects, and Dissertations

Many topics that mathematicians study at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular lines, bisected angles, regular polygons, and other basic geometric figures, we are actually constructing what in geometry is simply stated and accepted, because it will be proven using abstract algebra. Also we will look at many classic problems in Geometry that are not possible ...

Hilbert Spaces And Fourier Series, 2015 California State University - San Bernardino

#### Hilbert Spaces And Fourier Series, Terri Joan Harris Mrs.

##### Electronic Theses, Projects, and Dissertations

I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.

Problems In The Theory Of Extremal Graphs And Hypergraphs, 2015 University of Montana - Missoula

#### Problems In The Theory Of Extremal Graphs And Hypergraphs, Cory T. Palmer

##### University Grant Program Reports

Objective: Investigate the tree packing conjecture from graph theory and extremal numbers for hypergraphs.

Precalculus, 2015 NYC College of Technology

#### Precalculus, Thomas Tradler, Holly Carley

##### Open Educational Resources

From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to ...

On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", 2015 University of Maine - Main

#### On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", Joseph Jp Arsenault Jr

##### Electronic Theses and Dissertations

We provide an analytic read-through of Richard Dedekind's 1901 article “Über die Permutationen des Körpers aller algebraischen Zahlen," describing the principal results concerning infinite Galois theory from both Dedekind's point of view and a modern perspective, noting an apparently uncorrected error in the supplement to the article in the Collected Works. As there is no published English-language translation of the article, we provide an annotated original translation.

A Study Of Green’S Relations On Algebraic Semigroups, 2015 The University of Western Ontario

#### A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara

##### Electronic Thesis and Dissertation Repository

The purpose of this work is to enhance the understanding regular algebraic semigroups by considering the structural influence of Green's relations. There will be three chief topics of discussion.

• Green's relations and the Adherence order on reductive monoids
• Renner’s conjecture on regular irreducible semigroups with zero
• a Green’s relation inspired construction of regular algebraic semigroups

Primarily, we will explore the combinatorial and geometric nature of reductive monoids with zero. Such monoids have a decomposition in terms of a Borel subgroup, called the Bruhat decomposition, which produces a finite monoid, R, the Renner monoid. We will explore ...