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2018

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Articles 1231 - 1260 of 1332

Full-Text Articles in Mathematics

A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi Jan 2018

A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi

Turkish Journal of Mathematics

Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …

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The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano Jan 2018

The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano

Turkish Journal of Mathematics

Let $R$ be a commutative ring, $I$ be a proper ideal of $R$, and $S(I)=\{a\in R : ra\in I \text{ for some } r\in R\sm I\}$ be the set of all elements of $R$ that are not prime to $I$. The total graph of $R$ with respect to $I$, denoted by $T(\Gamma_I(R))$, is the simple graph with all elements of $R$ as vertices, and for distinct $x,y\in R$, the vertices $x$ and $y$ are adjacent if and only if $x+y\in S(I)$. In this paper, we determine all isomorphic classes of commutative Artinian rings whose ideal-based total graph has genus at …

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Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu Jan 2018

Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu

Turkish Journal of Mathematics

In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

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On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk Jan 2018

On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk

Turkish Journal of Mathematics

Let $(\Omega ,\mathcal{A},\mu )$ be a finite positive measure space, $E$ a Banach space, and $1

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Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu Jan 2018

Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu

Turkish Journal of Mathematics

By means of the modified Abel lemma on summation by parts, we examine a class of terminating balanced $q$-series. Two transformation formulae are established that contain ten summation formulae as consequences.

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Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara Jan 2018

Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara

Turkish Journal of Mathematics

This paper is written to correct the proof of Lemma 2.1$(i)$ in \cite{K} and to add some decomposition results for the class of $PD$-modules defined in \cite{K}.

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A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao Jan 2018

A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao

Turkish Journal of Mathematics

Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_I(R)$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{(x,y,z)}(R)$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik's conjecture is true in the regular local rings case.

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On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer Jan 2018

On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer

Turkish Journal of Mathematics

Let $\Jt$ be the canonical para-complex structure on $\R^4$. In this paper we study $3$-dimensional centro-affine hypersurfaces with a $\Jt$-tangent centro-affine vector field (sometimes called $\Jt$-tangent centro-affine hypersurfaces) as well as $3$-dimensional $\Jt$-tangent affine hyperspheres with the property that at least one null-direction of the second fundamental form coincides with either $\DD^+$ or $\DD^-$. The main purpose of this paper is to give a full local classification of the above-mentioned hypersurfaces. In particular, we prove that every nondegenerate centro-affine hypersurface of dimension $3$ with a $\Jt$-tangent centro-affine vector field that has two null-directions $\DD^+$ and $\DD^-$ must be both an …

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On A Pseudodifferential Calculus With Modest Boundary Decay Condition, Binbin Huang Jan 2018

On A Pseudodifferential Calculus With Modest Boundary Decay Condition, Binbin Huang

Graduate Dissertations and Theses

A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.

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Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures, Gabriel Johnson Jan 2018

Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures, Gabriel Johnson

Honors Theses

We describe an application written to automate a calculation for the mathematical research of Dr. Spiroff of University of Mississippi & Dr. Enescu of Georgia State University. This work represents a way to overcome the barriers of the mathematical calculations in obtaining theoretical results.

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Clustered Networks Protect Cooperation Against Catastrophic Collapse, Gwen Spencer Jan 2018

Clustered Networks Protect Cooperation Against Catastrophic Collapse, Gwen Spencer

Mathematics Sciences: Faculty Publications

Assuming a society of conditional cooperators (or moody conditional cooperators), this computational study proposes a new perspective on the structural advantage of social network clustering. Previous work focused on how clustered structure might encourage initial outbreaks of cooperation or defend against invasion by a few defectors. Instead, we explore the ability of a societal structure to retain cooperative norms in the face of widespread disturbances. Such disturbances may abstractly describe hardships like famine and economic recession, or the random spatial placement of a substantial numbers of pure defectors (or round-1 defectors) among a spatially-structured population of players in a laboratory …

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The Fivethirtyeight R Package: ‘Tame Data’ Principles For Introductory Statistics And Data Science Courses, Albert Y. Kim, Chester Ismay, Jennifer Chunn Jan 2018

The Fivethirtyeight R Package: ‘Tame Data’ Principles For Introductory Statistics And Data Science Courses, Albert Y. Kim, Chester Ismay, Jennifer Chunn

Mathematics Sciences: Faculty Publications

As statistics and data science instructors, we often seek to use data in our courses that are rich, real, realistic, and relevant. To this end we created the fivethirtyeight R package of data and code behind the stories and interactives at the data journalism website FiveThirtyEight.com. After a discussion on the conflicting pedagogical goals of "minimizing prerequisites to research" (Cobb 2015) while at the same time presenting students with a realistic view of data as it exists "in the wild," we articulate how a desired balance between these two goals informed the design of the package. The details behind this …

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How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin Baumer Jan 2018

How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin Baumer

Mathematics Sciences: Faculty Publications

Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variability of team …

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The Dihedral Genus Of A Knot, Patricia Cahn, Alexandra Kjuchukova Jan 2018

The Dihedral Genus Of A Knot, Patricia Cahn, Alexandra Kjuchukova

Mathematics Sciences: Faculty Publications

Let K ⊂ S3 be a Fox p-colored knot and assume K bounds a locally flat surface S ⊂ B4 over which the given p-coloring extends. This coloring of S induces a dihedral branched cover X → S4 . Its branching set is a closed surface embedded in S4 locally flatly away from one singularity whose link is K. When S is homotopy ribbon and X a definite four-manifold, a condition relating the signature of X and the Murasugi signature of K guarantees that S in fact realizes the four-genus of K. We exhibit an infinite …

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Action Of The Symmetric Group On The Free Lanke: A Catalanke Theorem, Tamar Friedmann, Philip Hanlon, Richard P. Stanley, Michelle L. Wachs Jan 2018

Action Of The Symmetric Group On The Free Lanke: A Catalanke Theorem, Tamar Friedmann, Philip Hanlon, Richard P. Stanley, Michelle L. Wachs

Mathematics Sciences: Faculty Publications

We initiate a study of the representation of the symmetric group on the multilinear component of an n-ary generalization of the free Lie algebra, which we call a free LAnKe. Our central result is that the representation of the symmetric group S2n−1 on the multilinear component of the free LAnKe with S2n−1 generators is given by an irreducible representation whose dimension is the nth Catalan number. This leads to a more general result on eigenspaces of a certain linear operator. A decomposition, into irreducibles, of the representation of S3n−2 on the multilinear component the free LAnKe …

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Strong Comparison Principle For P-Harmonic Functions In Carnot-Caratheodory Spaces, Luca Capogna, Xiaodan Zhou Jan 2018

Strong Comparison Principle For P-Harmonic Functions In Carnot-Caratheodory Spaces, Luca Capogna, Xiaodan Zhou

Mathematics Sciences: Faculty Publications

We extend Bony’s propagation of support argument to C1 solutions of the nonhomogeneous subelliptic p-Laplacian associated to a system of smooth vector fields satisfying Hörmander’s finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf.

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Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest Jan 2018

Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest

Department of Mathematics Faculty Scholarship and Creative Works

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss …

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A Covariational Understanding Of Function: Putting A Horse Before The Cart, Teo Paoletti, Kevin C. Moore Jan 2018

A Covariational Understanding Of Function: Putting A Horse Before The Cart, Teo Paoletti, Kevin C. Moore

Department of Mathematics Faculty Scholarship and Creative Works

Supporting students developing understandings of function has been a notoriously elusive task in mathematics education. We present Thompson and Carlson’s (2017) description of a covariational meaning of function and provide an example of a student who maintains meanings compatible with this description. We use this student’s activity to illustrate nuances in a covariational meaning of function and to highlight how such meanings can be powerful for students. In doing so, we argue that a student who has develop meanings compatible with the covariational meaning of function presented by Thompson and Carlson has the foundational meanings needed to understand a formal …

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Interlace Polynomials Of Friendship Graphs, Christina Eubanks-Turner, Aihua Li Jan 2018

Interlace Polynomials Of Friendship Graphs, Christina Eubanks-Turner, Aihua Li

Department of Mathematics Faculty Scholarship and Creative Works

In this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the Friendship Theorem given by Erdös, Rényi and Sos. Explicit formulas, special values, and behaviour of coefficients of these polynomials are provided. We also give the interlace polynomials of other similar graphs, such as, the butterfly graph.

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A Mixed Finite Element Method For The Coupling Of Linear Elasticity And Stokes Flow, Maranda Bean Jan 2018

A Mixed Finite Element Method For The Coupling Of Linear Elasticity And Stokes Flow, Maranda Bean

Open Access Theses & Dissertations

The complex interaction between fluids and structures require the coupling the laws concerning structure mechanics and fluid dynamics and are of vital importance to many scientific and engineering fields. We propose a method for modeling the coupling of a linearly elastic solid and slow fluid flow modeled by Stokes equations. The model equations are expressed in terms of displacement, velocity and stress. With these primary variables, we use a single mixed finite element space based on the Hellinger-Reissner variational principle for linear elasticity to discretize the resulting system spatially. This results in more accurate approximations for stress than those obtained …

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Pbw Bases And Marginally Large Tableaux In Type D, Ben Salisbury, Adam Schultze, Peter Tingley Jan 2018

Pbw Bases And Marginally Large Tableaux In Type D, Ben Salisbury, Adam Schultze, Peter Tingley

Mathematics and Statistics: Faculty Publications and Other Works

We give an explicit description of the unique crystal isomorphism between two realizations of B(∞) in type D: that using marginally large tableaux and that using PBW monomials with respect to one particularly nice reduced expression of the longest word

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How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer Jan 2018

How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer

Mathematics and Statistics: Faculty Publications and Other Works

Statistical applications in sports have long centered on how to best separate signal (e.g., team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season and game-to-game variability of team …

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How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer Jan 2018

How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer

Mathematics and Statistics: Faculty Publications and Other Works

Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variability of team …

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Logic -> Proof -> Rest, Maxwell Taylor Jan 2018

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

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Sports Analytics With Computer Vision, Colby T. Jeffries Jan 2018

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

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Local And Global Dynamic Bifurcations Of Nonlinear Evolution Equations, Desheng Li, Zhi-Qiang Wang Jan 2018

Local And Global Dynamic Bifurcations Of Nonlinear Evolution Equations, Desheng Li, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form ut + Au = fλ(u) on a Banach space X, where A is a sectorial operator, and λ ∈ R is the bifurcation parameter. Suppose the equation has a trivial solution branch {(0, λ) : λ ∈ R}. Denote Φλ the local semiflow generated by the initial value problem of the equation. It is shown that if the crossing number n at a bifurcation value λ = λ0 is nonzero and moreover, S0 = {0} is an isolated invariant set of Φλ0 , then …

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Did They Learn Anything? - Learning Assessment In A General Business Analytics Course, Zsolt Ugray, Brynja Kohler Jan 2018

Did They Learn Anything? - Learning Assessment In A General Business Analytics Course, Zsolt Ugray, Brynja Kohler

Mathematics and Statistics Faculty Publications

There is a projected need for 2 to 4 million of business translators who are not only experts in their business disciplines but also conversant and familiar with the use and limitations of business analytics. Preparing business students to step into the business translator role requires a general introductory analytics course. This paper presents a multi-component learning assessment to evaluate the depth of learning from such a course. This learning assessment is novel in a sense that it uses four distinct tools, both quantitative and qualitative ones, to measure students’ improvements in a comprehensive manner.

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Introductory Statistics, Barbara Illowsky, Susan Dean Jan 2018

Introductory Statistics, Barbara Illowsky, Susan Dean

Open Access Textbooks

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.

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Comparing Two Thickened Cycles: A Generalization Of Spectral Inequalities, Hannah E. Pieper Jan 2018

Comparing Two Thickened Cycles: A Generalization Of Spectral Inequalities, Hannah E. Pieper

Honors Papers

Motivated by an effort to simplify the Watts-Strogatz model for small-world networks, we generalize a theorem concerning interlacing inequalities for the eigenvalues of the normalized Laplacians of two graphs differing by a single edge. Our generalization allows weighted edges and certain instances of self loops. These inequalities were first proved by Chen et. al in [2] but our argument generalizes the simplified argument given by Li in [8].

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A Computational Introduction To Elliptic And Hyperelliptic Curve Cryptography, Nicholas Wilcox Jan 2018

A Computational Introduction To Elliptic And Hyperelliptic Curve Cryptography, Nicholas Wilcox

Honors Papers

At its core, cryptography relies on problems that are simple to construct but difficult to solve unless certain information (the “key”) is known. Many of these problems come from number theory and group theory. One method of obtaining groups from which to build cryptosystems is to define algebraic curves over finite fields and then derive a group structure from the set of points on those curves. This thesis serves as an exposition of Elliptic Curve Cryptography (ECC), preceded by a discussion of some basic cryptographic concepts and followed by a glance into one generalization of ECC: cryptosystems based on hyperelliptic …

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