Applied Mathematics Commons^™

On Circulant And Two-Circulant Weighing Matrices, K. T. Arasu, I. S. Kotsireast, C. Koukouvinos, Jennifer Seberry

Mathematics and Statistics Faculty Publications

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we con- struct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer “YES”, by constructing a circulant weighing matrix of order 142 with weight 100.

A Class Of Discontinuous Petrov–Galerkin Methods. Part Iv: The Optimal Test Norm And Time-Harmonic Wave Propagation In 1d., Jeffrey Zitelli, Leszek Demkowicz, Jay Gopalakrishnan, D. Pardo, V. M. Calo

Mathematics and Statistics Faculty Publications and Presentations

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test …

Coarser Connected Metrizable Topologies, Lynne Yengulalp

Mathematics Faculty Publications

We show that every metric space, X, with w(⩾) c has a coarser connected metrizable topology.

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Scholarship

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, Aychiluhim Habte, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia

Applications and Applied Mathematics: An International Journal (AAM)

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

Geometry, Greed, Games, And 'Roids, James Oxley

Dalrymple Lecture Series

A three-legged stool doesn’t wobble. But four-legged stools often teeter because the tips of their legs don’t lie in the same plane.

This phenomenon of dependent sets, first theorized 75 years ago, is the focus of the 16th Dalrymple Lecture in Mathematics, set for 5:30 p.m. Friday (May 21) at the University of Mississippi. James Oxley, who holds an alumni professorship at Louisiana State University, is to deliver the address, which is free and open to the public in the Student Union Ballroom.

“There is some beautiful and intriguing mathematics that arises from some natural problems in geometry and network …

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

Masters Theses & Specialist Projects

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …

On Directionally Dependent Subdifferentials, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

In this paper directionally contextual concepts of variational analysis, based on dual-space constructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulness, necessary and also sufficient optimality conditions in terms of directioual subdifferentials are established, and it is shown that they can be effective in the situations where known optimality conditions in terms of nondirectional subdifferentials fail.

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

Undergraduate Theses and Capstone Projects

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

A Non-Autonomous Second Order Boundary Value Problem On The Half-Line, Gregory S. Spradlin

Publications

By variational arguments, the existence of a solution to a nonautonomous second-order boundary problem on the half-line is proven. The corresponding autonomous problem has no solution, revealing significant differences between the autonomous and the non-autonomous case.

Codes From Riemann-Roch Spaces For Y2 = Xp - X Over Gf(P), Darren B. Glass, David Joyner, Amy Ksir

Math Faculty Publications

Let Χ denote the hyperelliptic curve y2 = xp - x over a field F of characteristic p. The automorphism group of Χ is G = PSL(2, p). Let D be a G-invariant divisor on Χ(F). We compute explicit F-bases for the Riemann-Roch space of D in many cases as well as G-module decompositions. AG codes with good parameters and large automorphism group are constructed as a result. Numerical examples using GAP and SAGE are also given.

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina

Mathematics Research Reports

Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

First-Order And Second-Order Optimality Conditions For Nonsmooth Constrained Problems Via Convolution Smoothing, Andrew C. Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials, and secondorder subdifferentials defined via coderivatives of first-order constructions.

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

Mathematics Faculty Publications

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …

Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty

Mathematics and Statistics Faculty Publications

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …

Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.

Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik

Mathematics Faculty Publications

A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have …