Physical Sciences and Mathematics Commons^™

Using Alternating Minimization And Convexified Carleman Weighted Objective Functional For A Time-Domain Inverse Scattering Problem, Nguyen T. Thanh

College of Science & Mathematics Departmental Research

This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of the scattering data. It is formulated as a coefficient identification problem for a wave equation. Using the Laplace transform, the inverse problem is converted into an overdetermined nonlinear system of partial differential equations. To solve this system, a Carleman weighted objective functional, which is proved to be strictly convex in an arbitrary set in a Hilbert space, is constructed. An alternating minimization algorithm is used to minimize the Carleman weighted objective functional. Numerical results are …

Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.

Internal Yoneda Ext Groups, Central H-Spaces, And Banded Types, Jarl Gunnar Taxerås Flaten

Electronic Thesis and Dissertation Repository

We develop topics in synthetic homotopy theory using the language of homotopy type theory, and study their semantic counterparts in an ∞-topos. Specifically, we study Grothendieck categories and Yoneda Ext groups in this setting, as well as a novel class of central H-spaces along with their associated bands. The former are fundamental notions from homological algebra that support important computations in traditional homotopy theory. We develop these tools with the goal of supporting similar computations in our setting. In contrast, our results about central H-spaces and bands are new, even when interpreted into the ∞-topos of spaces.

In Chapter …

Exploring The Genotypic And Phenotypic Differences Distinguishing Lactobacillus Jensenii And Lactobacillus Mulieris, Adriana Ene, Swarnali Banerjee, Alan J. Wolfe, Catherine Putonti

Mathematics and Statistics: Faculty Publications and Other Works

Lactobacillus crispatus, Lactobacillus gasseri, Lactobacillus iners, and Lactobacillus jensenii are dominant species of the urogenital microbiota. Prior studies suggest that these Lactobacillus species play a significant role in the urobiome of healthy females. In our prior genomic analysis of all publicly available L. jensenii and Lactobacillus mulieris genomes at the time (n = 43), we identified genes unique to these two closely related species. This motivated our further exploration here into their genotypic differences as well as into their phenotypic differences. First, we expanded genome sequence representatives of both species to 61 strains, including publicly available …

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

Waste Treatment Facility Location For Hotel Chains, Dolores R. Santos-Peñate, Rafael R. Suárez-Vega, Carmen Florido De La Nuez

ITSA 2022 Gran Canaria - 9th Biennial Conference: Corporate Entrepreneurship and Global Tourism Strategies After Covid 19

Tourism generates huge amounts of waste. About half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. We consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. An optimization model is applied to locate the facilities and allocate the waste and products, and several scenarios are analysed. The study shows that, …

Classification Of Finite Topological Quandles And Shelves Via Posets, Hitakshi Lahrani

USF Tampa Graduate Theses and Dissertations

The objective of this dissertation is to investigate finite topological quandles and topological shelves. Precisely, we give a classification of both finite topological quandles and topological shelves using the theory of posets. For quandles with more than one orbit, we prove the following Theorem.

Proposition 0.0.1. Let X be a finite quandle with n orbits X₁, ... , X_n. Then any right continuous poset on X is n-partite with vertex sets X₁, ... , X_n.

For connected quandles, we prove the following Theorem.

Theorem 0.0.2. There is no T …

Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams *, Benjamin F. Akers

Faculty Publications

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse …

A Generalized Two-Component Camassa-Holm System With Complex Nonlinear Terms And Waltzing Peakons, Xiaolin Pan, Shouming Zhou, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we deal with the Cauchy problem for a generalized two-component Camassa-Holm system with waltzing peakons and complex higher-order nonlinear terms. By the classical Friedrichs regularization method and the transport equation theory, the local well-posedness of solutions for the generalized coupled Camassa-Holm system in nonhomogeneous Besov spaces and the critical Besov space B5/22,1×B5/22,1 was obtained. Besides the propagation behaviors of compactly supported solutions, the global existence and precise blow-up mechanism for the strong solutions of this system are determined. In addition to wave breaking, the another one of the most essential property of this equation is the existence …

Random Variables With Overlapping Number And Weyl Algebras Ii, Ruma Dutta, Gabriela Popa, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

On Maximum Likelihood Estimators For A Jump-Type Affine Diffusion Two-Factor Model, Jiaming Yin Mr.

Major Papers

We consider a jump-type two-factor affine diffusion model driven by a subordinator in the context of continuous time observations. We study the asymptotic properties of the maximum likelihood estimator (MLE) for the drift parameters. In particular, we prove the strong consistency and the asymptotic normality of MLE in the subcritical case. We also present some numerical illustrations to confirm the theoretical results. The main difficulty of this major paper consists in proving the ergodicity of the model in the subcritical case and deriving the limiting behavior of the process.

Hierarchical Wilson–Cowan Models And Connection Matrices, Wilson A. Zuniga-Galindo, Brian A. Zambrano-Luna

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This work aims to study the interplay between the Wilson–Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson–Cowan equations provide a dynamical description of neural interaction. We formulate Wilson–Cowan equations on locally compact Abelian groups. We show that the Cauchy problem is well posed. We then select a type of group that allows us to incorporate the experimental information provided by the connection matrices. We argue that the classical Wilson–Cowan model is incompatible with the small-world property. A necessary condition to have this property is that the Wilson–Cowan equations be formulated on a compact group. We …

Local And 2-Local Derivations On Small Dimensional Zinbiel Algebras, Bakhtiyor Yusupov, Sabohat Rozimova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we investigate local and 2-local derivations on small dimensional Zinbiel algebras. We give a description of derivations and local derivations on all three and four-dimensional Zinbiel algebras. Moreover, similar problem concerning 2-local derivations on all three and four-dimensional Zinbiel algebras are investigated.

Weighted M-Subharmonic Measure And (M, 𝜓)-Regularity Of Compacts, Kobiljon Kuldoshev, Nurbek Narzillaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

It is known that, the m−subharmonic measure of a set E ⊂ D,  related to a domain D ⊂ ℂⁿ, is defined by m−subharmonic functions in D. In this article we define a generalization of the m−subharmonic measures and prove some of their properties.

Periodic, Nonperiodic, And Chaotic Solutions For A Class Of Difference Equations With Negative Feedback, Benjamin B. Kennedy

Math Faculty Publications

We study the scalar difference equation x(k + 1) = x(k) + (f(x(k - N))) / N,

where f is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation x'(t) = f(x(t - 1)).

We examine explicit families of such equations for which we can find, for infinitely many values of N and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our …

Some Thoughts On The 3 × 3 Magic Square Of Squares Problem, Desmond Weisenberg

Rose-Hulman Undergraduate Mathematics Journal

A magic square is a square grid of numbers where each row, column, and long diagonal has the same sum (called the magic sum). An open problem popularized by Martin Gardner asks whether there exists a 3×3 magic square of distinct positive square numbers. In this paper, we expand on existing results about the prime factors of elements of such a square, and then provide a full list of the ways a prime factor could appear in one. We also suggest a separate possible computational approach based on the prime signature of the center entry of the square.

Nontrivial Invariant Subspaces Of Linear Operator Pencils, Jaewoong Kim, Jasang Yoon

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair T=(T1,T2) and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of T and the linear pencil of the original pair T of bounded operators with dense ranges.

Understanding The Beauty Of Mathematics By Composing Claude Debussy's Syrinx Into Mathematical Equations, Mackenzi Mehlberg

Honors Projects

Mesmerizing melodies and narrative storytelling are exemplified in Claude Debussy's Syrinx. As a well-known piece of solo flute literature, it is considered beautiful. Conversely, mathematics is seen as logical, and by implication not beautiful. Using Fourier Analysis, Syrinx can be represented in a different context: a series of mathematical equations. These mathematical equations can then be played as a different interpretation of Syrinx. With this interpretation, we see that mathematics is beautiful.

A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs, Luis B. Morales, Dursun A. Bulotuglu

Faculty Publications

We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, s_max=4t+i, where i ∈ {0,2}, t ∈ Z^≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most (N+4t+i)/4 points. Using this equivalence, we formulate the search for two-symbol E(s²)-optimal and minimax-optimal SSDs with s_max ∈ {2,4,6} as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E(s²)-optimal and minimax-optimal SSDs achieving the sharpest known E(s²) lower bound with …

Computation Offloading Design For Deep Neural Network Inference On Iot Devices, Asmika Boosarapu

Theses and Dissertations

In recent times, advances in the technologies of Internet-of-Things (IoT) and Deep Neural Networks (DNN) have significantly increased the accuracy and speed of a variety of smart applications. However, one of the barriers to deploying DNN to IoT is the computational limitations of IoT devices as compared with the computationally expensive task of DNN inference. Computation offloading is an approach that addresses this problem by offloading DNN computation tasks to cloud servers. In this thesis we propose a collaborative computation offloading solution, in which some of the work is done on the IoT device, and the remainder of the work …

Survival Times And Investment Analysis With Dynamic Learning, Zhenzhen Li

Dissertations and Theses

The central statistical problem of survival analysis is to determine and characterize the conditional distribution of a survival time given a history of some observed health markers.

This dissertation contributes to the modeling of such conditional distributions in a setup where the health markers evolve randomly over time in a manner that can be represented by an Ito stochastic process, that is, a stochastic process that can be written as a sum of a time integral of some stochastic process and an Ito integral of some stochastic process, with both integrands subject to certain restrictions.

The random survival time is …

Contextualizing The Mathematical Knowledge For Teaching Framework For Teachers Of Emergent Bilinguals, Luis M. Fernandez, Mayra Ortiz Galarza

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We are amid a rapid demographic shift, with Emergent Bilinguals (EBs) being the fastest growing K-12 student population. This has created an ambitious goal for teacher education programs as they must prepare mathematics pre-service teachers (PSTs) to assess the needs of EBs. As a response, this study conducted a qualitative analysis of 16 PSTs to propose a contextualized version of the Mathematical Knowledge for Teaching (MKT) framework as an emerging knowledge base of teaching that can be used to further guide the planning and enactment of teacher education programs in the mathematics education of EBs, specifically.

A Pebbling Game On Powers Of Paths, Garth Isaak, Matthew Prudente, Joseph M. Marcinik Iii

Communications on Number Theory and Combinatorial Theory

Two Player Graph Pebbling is an extension of graph pebbling. Players Mover and Defender use pebbling moves, the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex, to win. If a specified vertex has a pebble on it, then Mover wins. If a specified vertex is pebble-free and there are no more valid pebbling moves, then Defender wins. The Two-Player Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement of m pebbles and for any specified vertex, Mover can win. We specify the …

Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya

Mathematics and Statistics Faculty Research & Creative Works

In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.

Vallée-Poussin Theorem For Equations With Caputo Fractional Derivative, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the functional differential equation (^CD_a^α+x)(t) + ^mΣ_i=0 (T_ix(ⁱ))(t) = f(t); t 2 [a; b]; with Caputo fractional derivative ^CD_a^α+ is studied. The operators Ti act from the space of continuous to the space of essentially bounded functions. They can be operators with deviations (delayed and advanced), integral operators and their various linear combinations and superpositions. Such equations could appear in various applications and in the study of systems of, for example, two fractional differential equations, when one of the components can be …

Production Functions Of Ncaa Men And Women Water Polo Matches, Joey Gullikson, Lewis R. Gale, John Mayberry, Lara Killick, John Kim

College of the Pacific Faculty Articles

Previous research has adapted the use of economic production functions to estimate the scoring production of teams in professional sports. Most of these studies have focused on professional male team sports, most notably, US baseball, basketball, and association football. This study adds to the literature by utilizing a new and distinctive data set of shooting statistics from 88 men’s and 38 women’s NCAA water polo contests to estimate production functions for United States’ collegiate water polo games and identify the most important variables for predicting margin of victory in such competitions. The results show that shots on goal, average shot …

(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …

(R1986) Neutrosophic Soft Contra E-Continuous Maps, Contra E-Irresolute Maps And Application Using Distance Measure, P. Revathi, K. Chitirakala, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, δ-continuous maps, δ- semi continuous maps, δ-pre continuous maps and e∗ continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance …

Modeling And A Domain Decomposition Method With Finite Element Discretization For Coupled Dual-Porosity Flow And Navier–Stokes Flow, Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We First Propose and Analyze a Steady State Dual-Porosity-Navier–Stokes Model, Which Describes Both Dual-Porosity Flow and Free Flow (Governed by Navier–Stokes Equation) Coupled through Four Interface Conditions, Including the Beavers–Joseph Interface Condition. Then We Propose a Domain Decomposition Method for Efficiently Solving Such a Large Complex System. Robin Boundary Conditions Are Used to Decouple the Dual-Porosity Equations from the Navier–Stokes Equations in the Coupled System. based on the Two Decoupled Sub-Problems, a Parallel Robin-Robin Domain Decomposition Method is Constructed and Then Discretized by Finite Elements. We Analyze the Convergence of the Domain Decomposition Method with the Finite …