Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2021

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 961 - 990 of 1314

Full-Text Articles in Mathematics

Regularized Estimations In Some Statistical Problems, Feng Yu Jan 2021

Regularized Estimations In Some Statistical Problems, Feng Yu

Electronic Theses and Dissertations, 2020-2023

In this dissertation, we consider estimations with regularization in three statistical problems relating to linear time system, stochastic block model and matrix variate regression. In the first part of the dissertation, we specifically investigate Mixture Multilayer Stochastic Block Model, where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. The Mixture Multilayer Stochastic Block Model was introduced by Bing-yi Jing [2020] and a clustering methodology, TWIST, is …

Go to article

A Mathematical Model For Predicting Animal Population Persistence On Fragmented Landscapes, Allyson Jones Jan 2021

A Mathematical Model For Predicting Animal Population Persistence On Fragmented Landscapes, Allyson Jones

Electronic Theses and Dissertations, 2020-2023

The effects of roads, buildings, and cities on animal populations are widespread and, often times, disastrous. These structures fragment animals' homes, inhibiting their ability to obtain essential resources and to reproduce. The question arises then: Under what circumstances can an animal population persist in a fragmented landscape? To attempt to answer this question, we present a spatially explicit reaction-diffusion model with varying growth and diffusion rates that incorporates animal behavior at points where habitats are fragmented for four different habitats. The outcome of extinction or persistence of the animal population is determined by examining the effects of changing parameters on …

Go to article

On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank Jan 2021

On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank

Faculty Journal Articles

We determine the ranks of string C-group representations of the groups PSp(4,q)=Ω(5,q), and comment on those of higher-dimensional symplectic and orthogonal groups.

Go to article

Three Imprimitive Character Sums, Brad Isaacson Jan 2021

Three Imprimitive Character Sums, Brad Isaacson

Publications and Research

We express three imprimitive character sums in terms of generalized Bernoulli numbers. These sums are generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko and Ramanujan in the context of modular forms and theta function identities. As a corollary, we obtain a formula for cotangent power sums considered by Apostol.

Go to article

A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals, Nathan D. Potter, Hannah Adera Rooney, Melody Locher, Debra Kinsey Jan 2021

A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals, Nathan D. Potter, Hannah Adera Rooney, Melody Locher, Debra Kinsey

Journal of Mathematics and Science: Collaborative Explorations

How does the mathematics specialist provide a profound and lasting impact on instruction? We believe that a productive partnership between the principal and specialist, which we will call the principal-specialist relationship, is at the crux of the matter. When the principal-specialist relationship is built upon a foundation of a shared vision, clear roles, communication, and trust, both the teachers and students in the school benefit. We will explore the impact of the principal-specialist relationship on teacher success during the era of distance learning as necessitated by the COVID-19 pandemic. In order to explore how these ideas come alive in the …

Go to article

A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$, Huan Q. Bui Jan 2021

A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$, Huan Q. Bui

Honors Theses

In this thesis, we consider a class of function on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean norm, positive homogeneous functions appear naturally in the study of convolution powers of complex-valued functions on $\mathbb{Z}^d$. As the spherical measure is a Radon measure on the unit sphere which is invariant under the symmetry group of the Euclidean norm, to each positive homogeneous function $P$, we construct a Radon measure $\sigma_P$ on $S=\{\eta \in \mathbb{R}^d:P(\eta)=1\}$ which is invariant under the symmetry group of $P$. With this measure, we prove …

Go to article

Optimal Claim Settlement Strategies Under Constraint Of Cap On Claim Loss, Hong Mao, Krzysztof Ostaszewski Jan 2021

Optimal Claim Settlement Strategies Under Constraint Of Cap On Claim Loss, Hong Mao, Krzysztof Ostaszewski

Faculty Publications – Mathematics

In this paper, we examine the question of how to devise an optimal insurance claim settlement scheme under the constraint of a cap on the amount of the claim payment. We establish objective functions to maximize the net benefit due to exaggerated claims while at the same time maximizing the total expected wealth of the insured. Then, we establish a dual objective function to minimize the total expected loss, including the perspective of the insurer. Finally, we illustrate applications of our work and provide numerical analysis of it along with an example.

Go to article

Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups, Qidong He Jan 2021

Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups, Qidong He

Honors Theses

Given a compact exceptional group $G$ and $m,s\in\mathbb{N}$, let $N(G,m)$ be the number of conjugacy classes of elements of order $m$ in $G$, and $N(G,m,s)$ the number of such classes whose elements have $s$ distinct eigenvalues. In string theory, the problem of enumerating certain classes of vacua in the string landscape can be rephrased in terms of the study of these quantities. We develop unified combinatorial algorithms based on Burnside's Lemma that can be used to compute both quantities for each of the five compact exceptional groups. Thus, we provide a combinatorial, alternative method to that of Djoković and extend …

Go to article

Some Properties Of Extending Hypermodules, C11-Hypermodules And T-Extending Hyperrings, Chokchai Wongyai Jan 2021

Some Properties Of Extending Hypermodules, C11-Hypermodules And T-Extending Hyperrings, Chokchai Wongyai

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this research, extending hypermodules, C11-hypermodules and t-extending hyperrings are defined and studied. We characterize extending hypermodules, C11-hypermodules and t-extending hyperrings in many ways under some conditions of hypermodules and hyperrings. Moreover, some properties concerning subhypermodules of extending hypermodules and C11-hypermodules are investigated. Especially, we study C11-hypermodules in the case that they can be decomposed as a direct sum of two subhypermodules.

Go to article

S-Magic Labelings Of Some Complete Tripartite Graphs, Sararat Numai Jan 2021

S-Magic Labelings Of Some Complete Tripartite Graphs, Sararat Numai

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Go to article

Use Of Lymesim 2.0 To Assess The Potential For Single And Integrated Management Methods To Control Blacklegged Ticks (Ixodes Scapularis; Acari: Ixodidae) And Transmission Of Lyme Disease Spirochetes, Shravani Chitineni, Elizabeth R. Gleim, Holly D. Gaff Jan 2021

Use Of Lymesim 2.0 To Assess The Potential For Single And Integrated Management Methods To Control Blacklegged Ticks (Ixodes Scapularis; Acari: Ixodidae) And Transmission Of Lyme Disease Spirochetes, Shravani Chitineni, Elizabeth R. Gleim, Holly D. Gaff

Undergraduate Honors Theses

Annual Lyme disease cases continue to rise in the U.S. making it the most reported vector-borne illness in the country. The pathogen (Borrelia burgdorferi) and primary vector (Ixodes scapularis; blacklegged tick) dynamics of Lyme disease are complicated by the multitude of vertebrate hosts and varying environmental factors, making models an ideal tool for exploring disease dynamics in a time- and cost-effective way. In the current study, LYMESIM 2.0, a mechanistic model, was used to explore the effectiveness of three commonly used tick control methods: habitat-targeted acaricide (spraying), rodent-targeted acaricide (bait boxes), and white-tailed deer targeted acaricide (4-poster …

Go to article

Steepest Descent, Elastic Energy, And Stability In Infinite Dimensional Hilbert Manifolds, Scott W. Rexford Jan 2021

Steepest Descent, Elastic Energy, And Stability In Infinite Dimensional Hilbert Manifolds, Scott W. Rexford

Graduate Research Theses & Dissertations

Consider constant-speed planar curves $\gamma =(x,y):[0,1]\to\mathbb{R}^2$ subject to $\gamma (0)=(0,0)$ and a prescribed value of $x(1)$, but with $y(1)$ unconstrained. We analyze the existence and the stability of critical curves of the elastic energy. Elastic curves are here thought of as points in an infinite-dimensional Sobolev manifold where the intrinsic gradient of the elastic energy vanishes. The admissible curves subject to constraints are members of a Riemannian submanifold using the ambient metric. A curve is stable with respect to the negative gradient flow if it is global or local minimum, and unstable otherwise. We analyze the stability of the classical …

Go to article

Isolation Intervals Of The Real Roots Of The Parametric Cubic Equation, Emil Prodanov Jan 2021

Isolation Intervals Of The Real Roots Of The Parametric Cubic Equation, Emil Prodanov

Articles

The isolation intervals of the real roots of the real symbolic monic cubic polynomial $p(x) = x^3 + a x^2 + b x + c$ are found in terms of simple functions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$, $\pm \sqrt{-b}$, when $b$ is negative), and the roots of some auxiliary quadratic equations whose coefficients are also simple functions of the coefficients of the cubic. All possible cases are presented with clear and very detailed diagrams. It is very easy to identify which of these diagrams is the relevant one for any given cubic equation and …

Go to article

Portfolio Selection Problem Based On Exponential Loss Function Under Independent Binomial Model In Set50, Krerkkiat Charoenying Jan 2021

Portfolio Selection Problem Based On Exponential Loss Function Under Independent Binomial Model In Set50, Krerkkiat Charoenying

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we investigate the portfolio allocation problem in the Stock Exchange of Thailand by considering the stocks of the 48 biggest companies in terms of market capitalization, with the requirement that an investor wants to invest under these 48 assets only and their risk is measured by the exponential loss function. The stocks under consideration must be independent and the prices of the stocks at the maturity time are assumed to follow the well-known binomial model. The Pearson correlation test is used for selecting stocks with independence property. In this study, we are interested in an investor investing …

Go to article

Comparison Of Software Packages For Detecting Differentially Expressed Genes From Single-Sample Rna-Seq Data, Rong Zhou Jan 2021

Comparison Of Software Packages For Detecting Differentially Expressed Genes From Single-Sample Rna-Seq Data, Rong Zhou

Electronic Theses and Dissertations

RNA-sequencing (RNA-seq) has rapidly become the tool in many genome-wide transcriptomic studies. It provides a way to understand the RNA environment of cells in different physiological or pathological states to determine how cells respond to these changes. RNA-seq provides quantitative information about the abundance of different RNA species present in a given sample. If the difference or change observed in the read counts or expression level between two experimental conditions is statistically significant, the gene is declared as differentially expressed. A large number of methods for detecting differentially expressed genes (DEGs) with RNA-seq have been developed, such as the methods …

Go to article

Elementary College Geometry (2021 Ed.), Henry Africk Jan 2021

Elementary College Geometry (2021 Ed.), Henry Africk

Open Educational Resources

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem proving or formal methods of reasoning. However the topics …

Go to article

The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov Jan 2021

The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov

Articles

The isolation intervals of the real roots of the symbolic monic cubic polynomial x 3 ` ax2 ` bx ` c are determined, in terms of the coefficients of the polynomial, by solving the Siebeck–Marden–Northshield triangle — the equilateral triangle that projects onto the three real roots of the cubic polynomial and whose inscribed circle projects onto an interval with endpoints equal to stationary points of the polynomial.

Go to article

On Newton's Rule Of Signs, Emil Prodanov Jan 2021

On Newton's Rule Of Signs, Emil Prodanov

Articles

Analysing the cubic sectors of a real polynomial of degree n, a minor modification of Newton’s Rule of signs is proposed with which stricter upper limits on the number of real roots can be found. A new necessary condition for reality of the roots of a polynomial is also proposed. Relationship between the quadratic elements of the polynomial is established through its roots and those of its derivatives. Some aspects of polynomial discriminants are also discussed.

Go to article

Fostering Mathematical Creativity Among Middle School Mathematics Teachers, Ceire H. Monahan Jan 2021

Fostering Mathematical Creativity Among Middle School Mathematics Teachers, Ceire H. Monahan

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand in-service teachers’ experiences with and ideas about mathematical creativity after participating in a targeted professional development program. The professional development program encouraged participants to think creatively and foster students’ creativity. In this study I present the results from the main unit of analysis, 12 participants in a professional development program, along with a deep analysis of three exemplar teachers from each of the identified groups, adherence to traditional teaching practices (traditional), appreciation for teaching for creativity (creative but hesitant), and teaching for creativity (creative). The findings of this study highlight the combination …

Go to article

Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching, Jessica Tybursky Nuzzi Jan 2021

Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching, Jessica Tybursky Nuzzi

Theses, Dissertations and Culminating Projects

Reform standards in mathematics education have called for classrooms that are student-centered and that incorporate problem solving and reasoning for meaningful learning. After decades of reform efforts involving multiple stakeholders, research indicates that most classrooms remain teacher-centered and procedurally focused, due to the complexity of concerns and competing intentions that teachers face in their work. Coteaching, a commitment between two teachers to coplan, coenact, and coreflect on lessons, can serve as an ongoing, sustained, focused, integrated, reflective professional development structure that supports teachers towards growth. The theoretical constructs used to describe possible growth towards reform orientations in teaching secondary mathematics …

Go to article

Combinatorial Models For Representations Of Simple And Affine Lie Algebras, Adam Lee Schultze Jan 2021

Combinatorial Models For Representations Of Simple And Affine Lie Algebras, Adam Lee Schultze

Legacy Theses & Dissertations (2009 - 2024)

Part I: Koskta-Foulkes polynomials are Lusztig's q-analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polynomials can be written with all non-negative coefficients. A statistic on semistandard Young tableaux with partition content, called \textit{charge}, was used to give a combinatorial formula exhibiting this fact in type $A$. Defining a charge statistic beyond type $A$ has been a long-standing problem. In the first part of this thesis, we take a completely new approach based on the definition of Kostka-Foulkes polynomials as an alternating sum over Kostant partitions, which can be thought of …

Go to article

Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges, David Vakil '92 Jan 2021

Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges, David Vakil '92

Doctoral Dissertations

To guide practitioners of rapidly evolving developmental math reform in community colleges, this study surveyed California community college math faculty who taught accelerated developmental courses or corequisite support courses. The survey was conducted during the early implementation phase of both course types, during spring and fall 2018 terms. This study measured faculty’s self-reported provision of forms of non-academic support, frequency of implementation, and reasons faculty believed the support would help students succeed. The literature review guided grouping non-academic support into five forms: nurturing, helping students’ motivation, providing a growth mindset theory of intelligence, helping provide social integration, and helping to …

Go to article

Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana Jan 2021

Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana

Turkish Journal of Mathematics

The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result in the setting of discrete valued structures. The first problem asks for the shapes of Lagrange-type interpolation polynomials which constitute a basis for integer-valued polynomials and satisfy the Lucas property; the result so obtained extends a 2001 result of Boulanger and Chabert. For the second problem, we show that the Carlitz polynomials, which form a basis for integer-valued polynomials in a function field, satisfy the …

Go to article

Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk Jan 2021

Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk

Turkish Journal of Mathematics

In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.

Go to article

A Short Note On Generic Initial Ideals, Beki̇r Daniş Jan 2021

A Short Note On Generic Initial Ideals, Beki̇r Daniş

Turkish Journal of Mathematics

The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a …

Go to article

On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan Jan 2021

On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan

Turkish Journal of Mathematics

The theoretical development of fractional calculus includes the formulation of different definitions, the extension of properties from standard calculus, and the application of fractional operators to special functions. In two recent papers, incomplete versions of classical fractional operators were formulated in connection with special functions. Here, we develop the theory of incomplete fractional calculus more deeply, investigating further properties of these operators and answering some fundamental questions about how they work. By considering appropriate function spaces, we discover that incomplete fractional calculus may be used to analyse a wider class of functions than classical fractional calculus can consider. By using …

Go to article

Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca Jan 2021

Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca

Turkish Journal of Mathematics

The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to Poisson distribution series. Several corollaries and consequences of the main results are also considered.

Go to article

Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna Jan 2021

Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna

Turkish Journal of Mathematics

In this paper, we investigate the matrix-valued$\ q-$Sturm--Liouville problems. We establish an existence and uniqueness result. Later, we introduce the corresponding maximal and minimal operators for this system. Moreover, we give a criterion under which these operators are self-adjoint. Finally, we characterize extensions (maximal dissipative, maximal accumulative, and self-adjoint) of the minimal symmetric operator.

Go to article

Statistically Multiplicative Convergence On Locally Solid Riesz Algebras, Abdullah Aydin, Mi̇kai̇l Et Jan 2021

Statistically Multiplicative Convergence On Locally Solid Riesz Algebras, Abdullah Aydin, Mi̇kai̇l Et

Turkish Journal of Mathematics

In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to algebra multiplication and solid topology. We study this concept and the notion of $st_m$-bounded sequences, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime $f$-algebras.

Go to article

Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou Jan 2021

Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou

Turkish Journal of Mathematics

In this paper, some characterizations for boundedness, essential norm and compactness of generalized Stevic-Sharma type operators from Hardy spaces into $n$th weighted type spaces are given.

Go to article

First Prev Next Last