Applied Mathematics Commons^™

Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented …

Data Mining Based Hybridization Of Meta-Raps, Fatemah Al-Duoli, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

Though metaheuristics have been frequently employed to improve the performance of data mining algorithms, the opposite is not true. This paper discusses the process of employing a data mining algorithm to improve the performance of a metaheuristic algorithm. The targeted algorithms to be hybridized are the Meta-heuristic for Randomized Priority Search (Meta-RaPS) and an algorithm used to create an Inductive Decision Tree. This hybridization focuses on using a decision tree to perform on-line tuning of the parameters in Meta-RaPS. The process makes use of the information collected during the iterative construction and improvement phases Meta-RaPS performs. The data mining algorithm …

Experimental Validation Of Robotic Manifold Tracking In Gyre-Like Flows, Matthew Michini, M. Ani Hsieh, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper, we present a first attempt toward experimental validation of a multi-robot strategy for tracking manifolds and Lagrangian coherent structures (LCS) in flows. LCS exist in natural fluid flows at various scales, and they are time-varying extensions of stable and unstable manifolds of time invariant dynamical systems. In this work, we present the first steps toward experimentally validating our previously proposed real-time manifold and LCS tracking strategy that relies solely on local measurements. Although we have validated the strategy in simulations using analytical flow models, experimental flow data, and actual ocean data, the strategy has never been implemented …

Transportation Of Perishable And Refrigerated Foods In Mylar Foil Bags And Insulated Containers: A Time-Temperature Study, Yanyan Li, John P. Schrade, Haiyan Su, John Specchio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Data are lacking on the temperature changes of food during transport without the use of refrigerated trucks. The purpose of this study was to evaluate the ability of several insulated and noninsulated containers with or without frozen gel packs to keep perishable and refrigerated foods within the temperature safe zone in relationship to duration of transport. The study was designed to duplicate the practices exhibited by customers purchasing perishable food products from a cash-and-carry business. Approximately 40 perishable food items were evaluated. Four types of containers were tested: a mylar foil bag, a commercial insulated bag, a generic insulated bag, …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith

College of Graduate Studies: Theses & Dissertations

Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.

A Linearised Singularly Perturbed Convection-Diffusion Problem With An Interior Layer, Eugene O'Riordan, Jason Quinn

Articles

A linear time dependent singularly perturbed convection-diffusion problem is examined. The convective coefficient contains an interior layer (with a hyperbolic tangent profile), which in turn induces an interior layer in the solution. A numerical method consisting of a monotone finite difference operator and a piecewise-uniform Shishkin mesh is constructed and analysed. Neglecting logarithmic factors, first order parameter uniform convergence is established.

Resilient Digital Image Watermarking For Document Authentication, Jonathan Blackledge, Oleksandr Iakovenko

Articles

Abstract—We consider the applications of the Discrete Cosine Transform (DCT) and then a Chirp coding method for producing a highly robust system for watermarking images using a block partitioning approach subject to a self-alignment strategy and bit error correction. The applications for the algorithms presented and the system developed include the copyright protection of images and Digital Right Management for image libraries, for example. However, the principal focus of the research reported in this paper is on the use of printscan and e-display-scan image authentication for use in e-tickets where QR code, for example, are embedded in a full colour …

Zakharov-Shabat System With Constant Boundary Conditions. Reflectionless Potentials And End Point Singularities, Tihomir Valchev, Rossen Ivanov, Vladimir Gerdjikov

Conference papers

We consider scalar defocusing nonlinear Schroedinger equation with constant boundary conditions. We aim here to provide a self contained pedagogical exposition of the most important facts regarding integrability of that classical evolution equation. It comprises the following topics: direct and inverse scattering problem and the dressing method.

A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn

Articles

A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small …

Area Based Fan Beam Projection Model For Computed Tomography, Phillip J. Stevens

Phi Kappa Phi Research Symposium (Archived)

Computed tomography (CT) is image reconstruction of objects using computer processed transmission or reflection data, usually referred to as projection data, from x-ray scanning. This projection data is often modeled using line integrals, but x-rays are of finite width in reality, so the accuracy of the projection data can be improved if an area based approach is used instead. In addition emitter beam shapes affect the reconstruction effectiveness and data collection efficiency, with the two main types of beam choice for 2-D scanning being fan beam and parallel beam. Fan beam scanning offers some advantages over parallel beam, such as …

The Geometry Of The Projective Joint Spectrum And The Commutativity Of Self-Adjoint Operators, Isaak Chagouel

Legacy Theses & Dissertations (2009 - 2024)

The theory of single operators is by now a very mature subject, with the notion of spectrum playing a key role in the theory. However, multivariate operator theory is only in its very early stages of development. There is not even wide agreement about how "the joint spectrum" of an n-tuple A = (A₁, · · · , A_n) of bounded linear operators on the same Hilbert space H should be defined.

Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo

Computer Science and Mathematics Faculty Publications

We say that a sequence of points converges to a set if every open set containing the set contains all but finitely many terms of the sequence. We investigate preservation of convergence of a sequence to a set in forcing extensions.

On The Infinitesimal Theory Of Chow Groups, Benjamin F. Dribus

LSU Doctoral Dissertations

The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. Except for the case p=1, which yields an algebraic group, the Chow groups remain mysterious. This thesis explores a "linearization" approach to this problem, focusing on the infinitesimal structure of the Chow groups near their identity elements. This method was adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others. A famous formula of Bloch expresses the Chow …

Matrix G-Strands, Darryl Holm, Rossen Ivanov

Articles

We discuss three examples in which one may extend integrable Euler–Poincare ordinary differential equations to integrable Euler–Poincare partial differential
equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained …

Hamiltonian Approach To The Modeling Of Internal Geophysical Waves With Vorticity, Alan Compelli

Articles

We examine a simplified model of internal geophysical waves in a rotational 2-dimensional water-wave system, under the influence of Coriolis forces and with gravitationally induced waves. The system consists of a lower medium, bound underneath by an impermeable flat bed, and an upper lid. The 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of its conjugate variables and perform a variable transformation to show that it has canonical Hamiltonian structure. We then linearize the system, …

Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi

Articles

We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.

A Posteriori Estimates Using Auxiliary Subspace Techniques, Harri Hakula, Michael Neilan, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show …

Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion, Mark A. Mckibben, Micah Webster

Mathematics Faculty Publications

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownianmotion in a real separable Hilbert space.Global existence results concerningmild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.

Communicative Universal Convertibility Matter-Energy-Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative-neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does not …

A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho

Theses and Dissertations--Mathematics

Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.

In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△_Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Mathematics Faculty Publications

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Mathematics Faculty Publications

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.

Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Laser ablation in an ambient environment is becoming increasingly important in science and technology. It is used in applications ranging from chemical analysis via mass spectroscopy, to pulsed laser deposition and nanoparticle manufacturing. We describe numerical schemes for a multiphase hydrodynamic model of nanosecond laser ablation expressing energy, momentum, and mass conservation in the target material, as well as in the expanding plasma plume, along with collisional and radiative processes for laser-induced breakdown (plasma formation). Numerical simulations for copper in a helium background gas are presented and the efficiency of various ODE integrators is compared.

Coloring Graphs Drawn With Crossings, Daniel Allen Guillot

LSU Doctoral Dissertations

This dissertation will examine various results for graph colorings. It begins by introducing some basic graph theory concepts, focusing on those ideas relevant to graph embeddings, and by introducing terminology to allow a formal discussion of drawings of graphs. Chapter 2 focuses on results for proper colorings of graphs with good drawings, using a previous result from Král and Stacho as inspiration. Chapter 3 expands on the ideas of Chapter 2 and focuses on cyclic colorings of embedded graphs. Chapters 5 and 6 examine results for total and list colorings, respectively, of drawings of graphs. Finally, Chapter 6 introduces generalized …

Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng

LSU Doctoral Dissertations

The celebrated Ito theory of stochastic integration deals with stochastic integrals of adapted stochastic processes. The Ito formula and Girsanov theorem in this theory are fundamental results which are used in many applied fields, in particular, the finance and the stock markets, e.g. the Black-Scholes model. In chapter 1 we will briefly review the Ito theory. In recent years, there have been several extension of the Ito integral to stochastic integrals of non-adapted stochastic processes. In this dissertation we will study an extension initiated by Ayed and Kuo in 2008. In Chapter 2 we review this new stochastic integral and …

Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …

Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli

Articles

We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.