Mathematics Commons^™

General Rogue Wave Solutions To The Sasa-Satsuma Equation, Chengfa Wu, Guangxiong Zhang, Changyan Shi, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

General rogue wave solutions to the Sasa-Satsuma equation are constructed by the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented in three different forms. The first form is expressed in terms of recursively defined differential operators while the second form shares a similar solution structure except that the differential operators are no longer recursively defined. Instead of using differential operators, the third form is expressed by Schur polynomials.

Solution Of The Reconstruction-Of-The-Measure Problem For Canonical Invariant Subspaces, Raul E. Curto, Sang H. Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts W(α,β), when the initial data are given as the Berger measure of the restriction of W(α,β) to a canonical invariant subspace, together with the marginal measures for the 0–th row and 0–th column in the weight diagram for W(α,β). We prove that the natural necessary conditions are indeed sufficient. When the initial data correspond to a soluble problem, we give a concrete formula for the Berger measure of W(α,β). Our strategy is to build on previous results for back-step extensions and onestep extensions. A key new theorem allows us …

On Three-Dimensional Rotating Viscoelastic Jets In The Giesekus Model, Daniel N. Riahi, Saulo Orizaga

School of Mathematical & Statistical Sciences Faculty Publications

We investigate three-dimensional nonlinear rotating viscoelastic curved jets in the presence of gravity force. Applying the Giesekus model for the viscoelastic stress parts of the jet flow system and using perturbation methods with a consistent scaling, a relatively simple system of equations with realistic three-dimensional centerlines is developed. We determine numerically the relevant solution quantities of the model in terms of the radius, speed, tensile force, stretching rate, strain rate and the jet centerline versus arc length and for different parameter values associated with gravity, viscosity, rotation, surface tension and viscoelasticity. Considering the jet flow system in full 3-dimensions and …

Justice And The Mathematics Classroom: Realizing The Goals Of The Amte Standards For Preparing Teachers Of Mathematics, Shandy Hauk, Marilyn Strutchens, Dorothy Y. White, Jennifer Bay-Williams, Jenq Jong Tsay, Billy Jackson

School of Mathematical & Statistical Sciences Faculty Publications

This chapter is an introduction to justice in the post-secondary context of mathematics courses for prospective teachers. The chapter is a research-to-practice report (i.e., it describes an aspect of instruction and discusses how it is informed by, connects to, or is illustrative of findings from research). While the reader might be any type of mathematics teacher educator, the focus here is supporting those who teach mathematics content courses for elementary school teacher candidates. In addition to having an effect on discipline-specific knowledge, college mathematics classes contribute to the ways candidates communicate in/with/through mathematics in working with children. The chapter includes …

Non-Archimedean Statistical Field Theory, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The advantage of the approach presented here is that all the perturbation calculations can be carried out in the standard way using functional derivatives, but in a mathematically rigorous way.

Canonical Sequences Of Optimal Quantization For Condensation Measures, Doğan Çömez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure on R with compact support. Let D(μ) denote the quantization dimension of a measure μ if it exists. In this paper, we study self-similar measures ν satisfying D(ν)>κ, D(ν)κ, the D(P)-dimensional lower and upper quantization coefficients are finite, positive and unequal; and for D(ν)≤κ, the D(P)-dimensional lower quantization coefficient is infinity.

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure …

Quantization For A Probability Distribution Generated By An Infinite Iterated Function System, Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on R. For such a probability measure P , an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ …

Networks Of Necessity: Simulating Covid-19 Mitigation Strategies For Disabled People And Their Caregivers, Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Abstract

A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of …

Evolution Of Eigenvalues Of A Geometric Operator Under Ricci Flow On A Riemannian Manifold, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The behavior of the eigenvalues of a geometric operator closely related to the Laplacian under Ricci flow is investigated. These depend on a coupling parameter in the operator as well as an evolution parameter which gives a flow on a compact manifold of finite dimension. The main objective is to study the monotonicity properties of the eigenvalues.

Political Corruption And Corporate Risk-Taking, Hinh Khieu, Nam H. Nguyen, Hieu V. Phan, Jon A. Fulkerson

School of Mathematical & Statistical Sciences Faculty Publications

We use variation in corruption convictions across judicial districts in the US to examine the relationship between political corruption and risk-taking of public firms. Firms headquartered in regions with high levels of political corruption have lower total risk and lower idiosyncratic risk on average. Further analysis shows that corruption tends to encourage firms to pursue risk-decreasing investments, lower the riskiness of their operations, and decrease asset liquidity. While managerial ownership is intended to align the interests of managers and shareholders, the presence of corruption appears to encourage undiversified managers to decrease risk-taking. Our evidence is consistent with agency theory and …

Quantization For Infinite Affine Transformations, Dogan Comez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of affine transformations {S-ij} on R-2 with associated probabilities {p(ij)} such that p(ij) > 0 for all i, j is an element of N and Sigma(infinity)(i,j=1) p(ij) = 1. For such a probability measure P, the optimal sets of n-means and the nth quantization error are calculated for every natural number n. It is shown that the distribution of such a probability measure is the …

An Integrable Semidiscretization Of The Modified Camassa-Holm Equation With Linear Dispersion Term, Han-Han Sheng, Guo-Fu Yu, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, we are with integrable discretization of a modified Camassa-Holm (mCH) equation with linear dispersion term. The key of the construction is the semidiscrete analog for a set of bilinear equations of the mCH equation. First, we show that these bilinear equations and their determinant solutions either in Gram-type or Casorati-type can be reduced from the discrete Kadomtsev-Petviashvili (KP) equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semidiscrete bilinear equations and their general soliton solution in Gram-type or Casorati-type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, …

Heat And Mass Transfer Of A Molten Polymer Conveying Nanoparticles In A Wire Coating Process With Temperature-Dependent Fluid Properties: Optimization Using Response Surface Method, Mahanthesh Basavarajappa, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Heat and mass transfer rates play a significant role in achieving a high-efficiency, low-cost wire coating process. Therefore, the flow analysis of molten polymer (polyvinyl chloride) carrying nanoparticles inside a pressure-type die is presented. The third-grade liquid model is used for the constitutive equation of the polyvinyl chloride (PVC), while the non-homogeneous biphasic model is used for nanoparticles. The properties of PVC are temperature-dependent. The melt flow is governed by the modified Navier-Stokes equation for the third-grade fluid, energy conservation, and nanoparticles' continuity equation. The finite difference method-based routine is applied to solve the nonlinear differential equations that include …

Multiple Periodic Vibrations Of Auxetic Honeycomb Sandwich Plate With 1:2 Internal Resonance, Shaotao Zhu, Jing Li, Zhijun Qiao, Ji Zhou

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we focus on the multiple periodic vibration behaviors of an auxetic honeycomb sandwich plate subjected to in-plane and transverse excitations. Nonlinear equation of motion for the plate is derived based on the third-order shear deformation theory and von Kármán type nonlinear geometric assumptions. The Melnikov method is extended to detect the bifurcation and multiple periodic vibrations of the plate under 1:2 internal resonance. The effects of transverse excitation on nonlinear vibration behaviors are discussed in detail. Evolution laws and waveforms of multiple periodic vibrations are obtained to analyze the energy transfer process between the first two order …

Number Of Bounded Distance Equivalence Classes In Hulls Of Repetitive Delone Sets, Dirk Frettlöh, Alexey Garber, Lorenzo Sadun

School of Mathematical & Statistical Sciences Faculty Publications

Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.

Integrable Semi-Discretization Of A Modified Short Wave Equation, Yujuan Zhang, Ruyun Ma, Na Xiong, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we are concerned with one of the integrable equations proposed by Hone et al. (2018). We firstly show that it can be derived from the Tzitzeica equation through hodograph or reciprocal transformations and it is linked to the short wave limits of the DP and Novikov equations, respectively, through Miura transformations. Based on the semi-discrete analogue of CKP-Toda hierarchy, we construct the integrable semi-discretization of what we call the modified short wave equation and provide its multi-soliton solution.

Optimal Quantization For Mixed Distributions Generated By Two Uniform Distributions, Ashley Gomez, Olga Lopez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, for mixed distributions generated by two uniform distributions we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. Some conjectures and open problems are also given.

Multi-Breather Solutions To The Sasa-Satsuma Equation, Chengfa Wu, Bo Wei, Changyan Shi, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

General breather solution to the Sasa-Satsuma (SS) equation is systematically investigated in this paper. We firstly transform the SS equation into a set of three Hirota bilinear equations under proper plane wave background. Starting from a specially arranged tau-function of the Kadomtsev-Petviashvili hierarchy and a set of eleven bilinear equations satisfied, we implement a series steps of reduction procedure, i.e., C-type reduction, dimension reduction and complex conjugate reduction, and reduce these eleven equations to three bilinear equations for the SS equation. Meanwhile, general breather solution to the SS equation is found in determinant of even order. The one- and two-breather …

Inverse Scattering Transform For The Complex Coupled Short-Pulse Equation, Aikaterini Gkogkou, Bao-Feng Feng, A. David Trubatch

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we develop the Riemann–Hilbert approach to the inverse scattering transform (IST) for the complex coupled short-pulse equation on the line with zero boundary conditions at space infinity, which is a generalization of recent work on the scalar real short-pulse equation (SPE) and complex short-pulse equation (cSPE). As a byproduct of the IST, soliton solutions are also obtained. As is often the case, the zoology of soliton solutions for the coupled system is richer than in the scalar case, and it includes both fundamental solitons (the natural, vector generalization of the scalar case), and fundamental breathers (a superposition …

Euclidean Quantum Field Formulation Of P-Adic Open String Amplitudes, A. R. Fuquen-Tibatá, H. García-Compeán, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.

The Reduced Order Method For Solving The Linear Complementarity Problem With An M-Matrix, Xi-Ming Fang, Heng-Jun Zhao, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, by seeking the zero and the positive entry positions of the solution, we provide a direct method, called the reduced order method, for solving the linear complementarity problem with an M-matrix. By this method, the linear complementarity problem is transformed into a low order linear complementarity problem with some low order linear equations and the solution is constructed by the solution of the low order linear complementarity problem and the solutions of these low order linear equations in the transformations. In order to show the accuracy and the effectiveness of the method, the corresponding numerical experiments …

Affect Graphing: Leveraging Graphical Representations In The Study Of Students’ Affect In Mathematics, V. Rani Satyam, Younggon Bae, John P. Smith Iii, Mariana Levin

School of Mathematical & Statistical Sciences Faculty Publications

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students’ expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during mathematical experiences. We analyze three studies that used graphing to represent, stimulate recall, and reflect on affect. In each, students were asked to draw their perception of an affective construct, such as confidence or intensity of emotion, against time. The studies differed in participant populations, target affect, timescales …

Graphs, Local Zeta Functions, Log-Coulomb Gases, And Phase Transitions At Finite Temperature, Wilson A. Zuniga-Galindo, Brian A. Zambrano-Luna, E. León-Cardenal

School of Mathematical & Statistical Sciences Faculty Publications

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e., R, C, and Qp being the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the sites of the particles are connected by an edge of the network. The partition functions of such gases turn out to be a particular class of multivariate local zeta functions attached to the network and a positive test function, which is determined by the confining potential. The methods and results of the theory of local …

Using A Stochastic Continuous-Time Markov Chain Model To Examine Alternative Timing And Duration Of The Covid-19 Lockdown In Kuwait: What Can Be Done Now?, Mustafa Al-Zoughool, Tamer Oraby, Harri Vainio, Janvier Gasana, Joseph C. Longenecker, Walid Al Ali, Mohammad Alseaidan, Susie Elsaadany, Michael G. Tyshenko

School of Mathematical & Statistical Sciences Faculty Publications

Background

Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations.

Methods

The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and …

Optimal Measures For P-Frame Energies On Spheres, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

School of Mathematical & Statistical Sciences Faculty Publications

We provide new answers about the distribution of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the pp-frame energies, i.e., energies with the kernel given by the absolute value of the inner product raised to a positive power pp. Application of linear programming methods in the setting of projective spaces allows for describing the minimizing measures in full in several cases: we show optimality of tight designs and of the 600-cell for several ranges of pp in different dimensions. Our methods apply to a much broader class of potential functions, namely, those …

P-Adic Analysis: A Quick Introduction, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

These notes aim to provide a fast introduction to p-adic analysis assuming basic knowledge in algebra and analysis. The text corresponds to the lecture notes for a Mini-Course in the L. Santal´o Research Summer School 2019. Palacio de la Magdalena, Santander, Spain, June 24-28, 2019.

Global Existence And Blow-Up Phenomena For A Periodic Modified Camassa–Holm Equation (Moch), Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study global existence and blow-up for a periodic modified Camassa–Holm equation in nonhomogeneous Sobolev spaces. Also, we provide a key blow-up criteria to investigate norm inflation and ill-posedness problem for the equation in the critical Sobolev space.

On Rotationally Driven Nonlinear Inclined Polymeric Jet With Gravity Effect, Daniel N. Riahi, Saulo Orizaga

School of Mathematical & Statistical Sciences Faculty Publications

We consider rotationally driven nonlinear polymeric fiber jet, whose centerline is in an inclined plane, in the presence of gravity force. An empirical viscosity model is used for the polymeric fluid flow to investigate properties of the rotating inclined polymeric fiber jet. The aim of the study is to understand properties of such inclined fiber jet shape, which can be due to orientation change of an orifice in a rotating spinneret that generates such jet. Perturbation, asymptotic, scaling and numerical techniques are used to determine the nonlinear steady solutions for the jet quantities for different values of the parameters due …

Global In Time Self-Interacting Dirac Fields In The De Sitter Space, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

In this paper the semilinear equation of the spin-12 fields in the de Sitter space is investigated. We prove the existence of the global in time small data solution in the expanding de Sitter universe. Then, under the Lochak–Majorana condition, we prove the existence of the global in time solution with large data. The sufficient conditions for the solutions to blow up in finite time are given for large data in the expanding and contracting de Sitter spacetimes. The influence of the Hubble constant on the lifespan is estimated.

Online List Coloring For Signed Graphs, Melissa Tupper, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We generalize the notion of online list coloring to signed graphs. We define the online list chromatic number of a signed graph, and prove a generalization of Brooks’ Theorem. We also give necessary and sufficient conditions for a signed graph to be degree paintable, or degree choosable. Finally, we classify the 2-list-colorable and 2-list-paintable signed graphs.