Mathematics Commons^™

Game Between The Third Party Payment Service Provider And Bank In Mobile Payment Market, Hui Jiang, Junhai Ma, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

With the innovation and integration of the Internet and the financial industry, the third-party payment market has developed greatly and has great potential. This paper discusses the duopoly game between third-party payment service providers and banks, which are the main participants in the mobile payment market. By constructing Nash game model, the conditions of equilibrium point, stability and bifurcation are analyzed. The effects of adjusting parameters and cooperation coefficient on business volume and profit are discussed. The conclusions are as follows: excessive investment will lead to unpredictable fluctuations in the market and fall into chaos; By strengthening cooperation, all participants …

Negative Order Kdv Equation With No Solitary Traveling Waves, Miguel Rodriguez, Jing Li, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.

Existence Results For Nonlinear Schrodinger Equations Involving The Fractional (P, Q)-Laplacian And Critical Nonlinearities, Huilin Lv, Shenzhou Zheng, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p, q)-Laplacian with Rabinowitz potentials defined in R-n,

(-Delta)(p)(s1) u + (-Delta)(q)(s2) q u+ V(epsilon x)(vertical bar u vertical bar(p-2)u+vertical bar u vertical bar(q-2)u) =lambda f(u) + sigma vertical bar u vertical bar q*(-2)(s2)u.

We prove existence by confining different ranges of the parameter lambda under the subcritical or critical nonlinearities caused by sigma = 0 or 1, respectively. In particular, a delicate calculation for the critical growth is provided so as to avoid the failure of a global Palais-Smale condition …

Chromatic Quasisymmetric Class Functions For Combinatorial Hopf Monoids, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study the chromatic quasisymmetric class function of a linearized combinatorial Hopf monoid. Given a linearized combinatorial Hopf monoid H, and an H-structure h on a set N, there are proper colorings of h, generalizing graph colorings and poset partitions. We show that the automorphism group of h acts on the set of proper colorings. The chromatic quasisymmetric class function enumerates the fixed points of this action, weighting each coloring with a monomial. For the Hopf monoid of graphs this invariant generalizes Stanley's chromatic symmetric function and specializes to the orbital chromatic polynomial of Cameron and Kayibi.

We also introduce …

A Multilayer Network Model Of The Coevolution Of The Spread Of A Disease And Competing Opinions, Kaiyan Peng, Zheng Lu, Vanessa Lin, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi, Mason A. Porter

School of Mathematical & Statistical Sciences Faculty Publications

During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — pro-physical-distancing and anti-physical-distancing — that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing …

Smooth Loops And Loop Bundles, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

A loop is a rather general algebraic structure that has an identity element and division, but is not necessarily associative. Smooth loops are a direct generalization of Lie groups. A key example of a non-Lie smooth loop is the loop of unit octonions. In this paper, we study properties of smooth loops and their associated tangent algebras, including a loop analog of the Maurer-Cartan equation. Then, given a manifold, we introduce a loop bundle as an associated bundle to a particular principal bundle. Given a connection on the principal bundle, we define the torsion of a loop bundle structure and …

Polynomial Embeddings Of Unilateral Weighted Shifts In 2-Variable Weighted Shifts, Raul E. Curto, Sang H. Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

Given a bounded sequence omega of positive numbers, and its associated unilateral weighted shift W-omega, acting on the Hilbert space l(2) (Z+), we consider natural representations of W-omega as a 2-variable weighted shift, acting on the Hilbert space l(2)(Z(+)(2)). Alternatively, we seek to examine the various ways in which the sequence omega can give rise to a 2-variable weight diagram, corresponding to a 2-variable weighted shift. Our best (and more general) embedding arises from looking at two polynomials p and q nonnegative on a closed interval I subset of R+ and the double-indexed moment sequence {integral p(r)(k) q(r)(l) d sigma(r)}(k,l …

Combined Amplification And Sound Therapy For Individuals With Tinnitus And Coexisting Hearing Loss: A Retrospective Cohort Study, Purushothaman Ganesan, Hansapani Rodrigo, Jason Schmiedge, Rob Reiter, Simham Swapna, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

BACKGROUND: The heterogeneity of tinnitus perception and its impact necessitates a tailor-made management approach in everyone. The current study examined the effects of residual inhibition in combined amplification and sound therapy in individuals with tinnitus and coexisting hearing loss.

METHODS: A retrospective analysis was performed on patients with tinnitus and coexisting hearing loss between 2016 and 2019. A total of 72 patients provided with combined amplification and sound therapy were divided into 3 groups based on residual inhibition: (i) complete residual inhibition, (ii) partial residual inhibition, and (iii) negative residual inhibition. Tinnitus severity was measured using the Tinnitus …

A Statistical Comparison Of Covid-19 In The United States Across Political Affiliations And Census Regions, Margarito Torres

Theses and Dissertations

In mid-January 2020, the United States reported their first cases of the coronavirus disease (COVID-19) from a passenger returning from Wuhan, China. Initially, the situation wasn’t very alarming as in China and European countries, but the situation began to worsen in March 2020 when the number of cases began to multiply. Then, in a matter of a few months, the United States became the number one country in terms of total cases and total deaths from COVID-19. We have been closely observing the United States and the world since July 2020. Our study aims to compare the political affiliations and …

Behavior Of Entanglement Entropy Near Periodic Orbits In A Hamiltonian Dynamical System, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Entanglement entropy growth is studied under a form of dynamics that is based on iteration. This approach allows the investigation of the role of decoherence in producing increases of entropy. This has important consequences as far as the study of decoherence is concerned. It is indicated that results are generally independent of Hilbert space partitioning. It is seen that a deep relationship between classical dynamical entropy and the growth of entanglement entropy exists in this kind of model. The former acts to bound the latter and in the asymptotic region, they tend to a common limit.

Evaluation Of The United States Covid-19 Vaccine Allocation Strategy, Md Rafiul Islam, Tamer Oraby, Audrey Mccombs, Mohammad Mihrab Chowdhury, Mohammad Al-Mamun, Michael G. Tyshenko, Claus Kadelkai

School of Mathematical & Statistical Sciences Faculty Publications

Background: Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested).

Methods and findings: We developed a compartmental disease model that incorporates key elements of the …

Covering By Homothets And Illuminating Convex Bodies, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number α and a convex body B, gα⁡(B) is the infimum of α-powers of finitely many homothety coefficients less than 1 such that there is a covering of B by translative homothets with these coefficients. hα⁡(B) is the minimal number of directions such that the boundary of B can be illuminated by this number of directions except for a subset whose Hausdorff dimension is less than α. In this paper, we prove that gα⁡(B)≤hα⁡(B), find upper and lower bounds for both numbers, …

Optimal Quantization For Mixed Distributions, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixed distributions are an exciting new area for optimal quantization. In this paper, we have determined the optimal sets of n -means, the n th quantization errors, and the quantization dimensions of different mixed distributions. Besides, we have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more …

Exploratory Data Mining Techniques (Decision Tree Models) For Examining The Impact Of Internet-Based Cognitive Behavioral Therapy For Tinnitus: Machine Learning Approach, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Background: There is huge variability in the way that individuals with tinnitus respond to interventions. These experiential variations, together with a range of associated etiologies, contribute to tinnitus being a highly heterogeneous condition. Despite this heterogeneity, a “one size fits all” approach is taken when making management recommendations. Although there are various management approaches, not all are equally effective. Psychological approaches such as cognitive behavioral therapy have the most evidence base. Managing tinnitus is challenging due to the significant variations in tinnitus experiences and treatment successes. Tailored interventions based on individual tinnitus profiles may improve outcomes. Predictive models of treatment …

High Precision Numerical Computation Of Principal Points For Univariate Distributions, Santanu Chakraborty, Mrinal Kanti Roychowdhury, Josef A. Sifuentes

School of Mathematical & Statistical Sciences Faculty Publications

Principal points were first introduced in 1990: for a positive integer n, n principal points of a random variable are the n points that minimize the mean squared distance between the random variable and the nearest of the n points. In this paper, we give a high precision numerical method for calculating the n principal points and the n th quantization errors for all positive integers n. For some absolutely continuous univariate distributions, we calculate the n principal points for different n using Newton’s method. Additionally, we also provide the corresponding values of mean squared distances.

Fundamental Solutions For The Dirac Equation In Curved Spacetime And Generalized Euler-Poisson-Darboux Equation, Karen Yagdjian, Anahit Galstian

School of Mathematical & Statistical Sciences Faculty Publications

We present the fundamental solutions for the spin-1/2 fields propagating in spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.

Isometric Flows Of G 2-Structures, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

We survey recent progress in the study of flows of isometric G 2-structures on seven-dimensional manifolds, that is, flows that preserve the metric, while modifying the G 2-structure. In particular, heat flows of isometric G 2-structures have been recently studied from several different perspectives, in particular in terms of 3-forms, octonions, vector fields, and geometric structures. We will give an overview of each approach, the results obtained, and compare the different perspectives.

Mitigating The Externality Of Diseases Of Poverty Through Health Aid, Kamal Jnawali, Michael G. Tyshenko, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Externality exists in healthcare when an individual benefits from others being healthy as it reduces the probability of getting sick from illness. Healthy workers are considered to be the more productive labourers leading to a country’s positive economic growth over time. Several research studies have modelled disease transmission and its economic impact on a single country in isolation. We developed a two-country diseaseeconomy model that explores disease transmission and crossborder infection of disease for its impacts. The model includes aspects of a worsening and rapid transmission of disease juxtaposed by positive impacts to the economy from tourism. We found that …

The Chromatic Quasisymmetric Class Function Of A Digraph, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the former is a generalization of a quasisymmetric function introduced by Grinberg. We prove representation-theoretic analogues of classical and recent results, including F-positivity, and combinatorial reciprocity theorems. We deduce results for orbital quasisymmetric functions, and study a generalization of the notion of strongly flawless sequences.

A Deep Learning Improved Numerical Method For The Simulation Of Rogue Waves Of Nonlinear Schrödinger Equation, Rui-Qi Wang, Liming Ling, Delu Zeng, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable for simulating rogue wave or breather solutions of the focusing nonlinear Schrödinger equation (NLSE) and other application problems with MI involved. Due to MI, the small perturbation on the boundary can lead to large and non-negligible errors for the simulation of initial-boundary problems. To deal with this challenging problem, we propose a method to modify the boundary problem through a deep learning algorithm so that the long time simulation for the rogue wave or breather solutions to the NLSE can be performed with a superior numerical errors. …

The Robust Inverse Scattering Method For Focusing Ablowitz–Ladik Equation On The Non-Vanishing Background, Yiren Chen, Bao-Feng Feng, Liming Ling

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we consider the robust inverse scattering method for the Ablowitz–Ladik (AL) equation on the non-vanishing background, which can be used to deal with arbitrary-order poles on the branch points and spectral singularities in a unified way. The Darboux matrix is constructed with the aid of loop group method and considered within the framework of robust inverse scattering transform. Various soliton solutions are constructed without using the limit technique. These solutions include general soliton, breathers, as well as high order rogue wave solutions.

Controlled Branching Processes With Continuous Time, Miguel Gonzalez, Manuel Molina, Ines Del Puerto, Nikolay Yanev, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Analytical Properties For The Fifth Order Camassa-Holm (Foch) Model, Mingxuan Zhu, Lu Cao, Zaihong Jiang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

This paper devotes to present analysiswork on the fifth order Camassa-Holm (FOCH) modelwhich recently proposed by Liu and Qiao. Firstly, we establish the local and global existence of the solution to the FOCH model. Secondly, we study the property of the infinite propagation speed. Finally, we discuss the long time behavior of the support of momentum density with a compactly supported initial data.

Globally Conservative Solutions For The Modified Camassa–Holm (Moch) Equation, Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa–Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to the standard ordinary differential equation theory with the aid of the conservation law, we give the global solutions of the semi-linear system. Finally, returning to the original variables, we obtain the globally conservative solutions to the MOCH equation.

Integrable Equation With No Solitary Traveling Waves, Miguel Rodriguez

Theses and Dissertations

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.

Empirical Bayes Estimates For The Reproduction Number Of Epidemics, Elijah Lee Hight

Theses and Dissertations

Epidemic outbreaks can be modelled as a branching process in which the total progeny or outbreak size, follows a Borel-Tanner (BT) distribution. Following a procedure described by Liang (2009), we construct empirical Bayes estimates for when the initial number of infected is a specified value r. Following the construction, we then simulate data and perform a numerical study, assuming BT distribution for the parameter θ, the reproduction number, with an initial outbreak size of three. Simulation results indicate that the empirical estimator suffers from “jumpiness.” We then proceed to monotonize the empirical estimate via a method outlined by Houwelingen (1979). …

Sexual Dimorphism In The Functional Development Of The Cochlear Amplifier In Humans, Sri Mishra, Samantha Zambrano, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Objectives:

Otoacoustic emissions, a byproduct of active cochlear mechanisms, exhibit a higher magnitude in females than in males. The relatively higher levels of androgen exposure in the male fetus are thought to cause this difference. Postnatally, the onset of puberty is also associated with the androgen surge in males. In this study, we investigated sexual dimorphism in age-related changes in stimulus-frequency otoacoustic emissions for children.

Design:

In a retrospective design, stimulus-frequency otoacoustic emissions were analyzed from a cross-sectional sample of 170 normal-hearing children (4 to 12 years) and 67 young adults. Wideband acoustic immittance and efferent inhibition measures were analyzed …

An Introduction To Generalized Entropy And Some Quantum Applications, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The concept of generalized entropy is introduced and some of its properties are studied. Irreversible time evolution can be generated by a non-Hermitian superoperator on the states of the system. The case when irreversibility comes about from embedding the system in a thermal reservoir is looked at. The time evolution is found compatible both with equilibrium thermodynamics and entropy production near the final state. Some examples are presented as well as a longer introduction as to how this might play a role in the black hole information loss paradox.

Non-Archimedean Models Of Morphogenesis, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing pattern consists of several domains (clusters), each of them supporting a different pattern but with the same parameter values. This type of patterns are typically produced by reaction-diffusion equations on large networks.

Positive Solutions For The Fractional Schrödinger Equations With Logarithmic And Critical Non-Linearities, Haining Fan, Zhaosheng Feng, Xingjie Yan

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non-linearities on an unbounded domain, and show that such an equation with positive or sign-changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik–Schnirelmann category, we investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential.