Applied Mathematics Commons^™

Improving Math Instruction In Schools That Serve The Poor, John, L. Jr. Sims

LSU Master's Theses

Public alarm concerning how well U.S. schools are performing in mathematics compared to other developed nations is increasing. Reports of inadequate teaching, poor curriculum design, and low performance on standardized test have been fueled by the media. These issues in American mathematics classrooms are far compounded in schools that serve the poorest in America. When comparing mathematical proficiency rates of U.S. schools with other countries, schools with less than 25% free and reduced lunch score competitively with counterparts in other countries. In contrast, schools with rates of free and reduced lunch higher than 50% score dismally in comparison. Conditions such …

A C0 Interior Penalty Method For The Von Kármán Equations, Armin Karl Reiser

LSU Doctoral Dissertations

In this dissertation we develop a C⁰ interior penalty method for the von Kármán equations for nonlinear elastic plates. We begin with a brief survey on frequently used finite element methods for the von Kármán equations. After addressing some topics from functional analysis in the preliminaries, we present existence, uniqueness and regularity results for the solutions of the von Kármán equations in Chapter 3. In the next chapter we review the C⁰ interior penalty method for the biharmonic problem. Motivated by these results, we propose a C⁰ interior penalty method for the linearized von Kármán equations in …

On Greenberg's Question: An Algebraic And Computational Approach, David H. Chapman

LSU Doctoral Dissertations

Greenberg asked whether arithmetically equivalent number fields share the same Iwasawa invariants. In this dissertation it is shown that the problem naturally breaks up into four cases, depending on properties of Galois groups. This analysis is then used to give a positive answer to Greenberg’s question in some nontrivial examples.

Analysis Of Hdg Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan, Ngoc Cuong Nguyen, Jaume Peraire, Francisco-Javier Sayas

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree $ k$ for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges. As a consequence, we prove that the approximations of the velocity gradient, the …

Paley-Wiener Theorems With Respect To The Spectral Parameter, Susanna Dann

LSU Doctoral Dissertations

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then harmonic analysis on M is closely related to the representations of G and the direct integral decomposition of L^2(M) into irreducible representations of G. R^n can be realized as the quotient R^n=E(n)/SO(n), where E(n) is the orientation preserving Euclidean motion group. The pair (E(n), SO(n)) is a Gelfand pair. Hence this realization of R^n comes with its own natural …

Symmetric Spaces, Se-Jong Kim

LSU Doctoral Dissertations

We first review the basic theory of a general class of symmetric spaces with canonical reflections, midpoints, and displacement groups. We introduce a notion of gyrogroups established by A. A. Ungar and define gyrovector spaces slightly different from Ungar's setting. We see the categorical equivalence of symmetric spaces and gyrovector spaces with respect to their corresponding operations. In a smooth manifold with spray we define weighted means using the exponential map and develop the Lie-Trotter formula with respect to midpoint operation. Via the idea that we associate a spray with a Loos symmetric space, we construct an analytic scalar multiplication …

Excluded-Minor Characterization Of Apex-Outerplanar Graphs, Stanislaw Dziobiak

LSU Doctoral Dissertations

It is well known that the class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: K_4 and K_{2,3}. The class of graphs that contain a vertex whose removal leaves an outerplanar graph is also minor-closed. We provide the complete list of 57 excluded minors for this class.

The Sir Model When S(T) Is A Multi-Exponential Function., Teshome Mogessie Balkew

Electronic Theses and Dissertations

The SIR can be expressed either as a system of nonlinear ordinary differential equations or as a nonlinear Volterra integral equation. In general, neither of these can be solved in closed form. In this thesis, it is shown that if we assume S(t) is a finite multi-exponential, i.e. function of the form S(t) = a+ ∑ⁿ_k=1 r_ke^-σ_kt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+e^wt, then …

A Sequel To “A Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa

Computer Science and Mathematics Faculty Publications

We consider a topological space ⟨𝑋, 𝜏 (ℱ)⟩, where 𝑋 = {𝑝 ∗} ∪ [𝜔 Å~ 𝜔] and ℱ ⊆ 𝜔𝜔. Each point in 𝜔 Å~ 𝜔 is isolated and a neighborhood of 𝑝∗ has the form {𝑝∗}∪{⟨𝑖, 𝑗⟩ : 𝑖 ≥ 𝑛, 𝑗 ≥ 𝑓(𝑖)} for some 𝑛 ∈ 𝜔 and 𝑓 ∈ ℱ. We show that there are subsets ℱ and 𝒢 of 𝜔𝜔 such that ℱ is not bounded, 𝒢 is bounded, yet ⟨𝑋, 𝜏 (ℱ)⟩ and ⟨𝑋, 𝜏 (𝒢)⟩ are homeomorphic. This answers a question of the second author posed in A space topologized by functions …

Quantitative Stability And Optimality Conditions In Convex Semi-Infinite And Infinite Programming, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T. Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is loo(T). Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this …

Solving A Generalized Heron Problem By Means Of Convex Analysis, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr

Mathematics Research Reports

The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of IR!, find a point such that the sum of the distances from that point to n given nonempty …

Explicit Level Lowering Of 2-Dimensional Modular Galois Representations, Rodney Keaton

All Theses

Let f be a normalized eigenform of level Npα for some positive integer α and some odd prime p satisfying gcd(p,N)=1. A construction of Deligne, Shimura, et. al., attaches a p-adic continuous two-dimensional Galois representation to f. The Refined Conjecture of Serre states that such a representation should in fact arise from a normalized eigenform of level prime to p.
In this presentation we present a proof of Ribet which allows us to 'strip' these powers of p from the level while still retaining the original Galois representation, i.e., the residual of our new representation arising from level N will …

Holomorphic Hardy Space Representations For Convex Domains In Cn, Jennifer West Paulk

Graduate Theses and Dissertations

This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are strongly convex with real boundary of class C^2. We obtain integral representations utilizing the Leray kernel for Hardy space (p=1) functions on such domains D. Next we define an operator to prove the non-tangential limits of a function in Hardy space (p between 1 and infinity, inclusive) of domain D …

A Mathematical Approach For Optimizing The Casino Slot Floor: A Linear Programming Application, Kasra Christopher Ghaharian

UNLV Theses, Dissertations, Professional Papers, and Capstones

Linear programming is a tool that has been successfully applied to various problems across many different industries and businesses. However, it appears that casino operators may have overlooked this useful and proven method. At most casino properties the bulk of gaming revenues are derived from slot machines. It is therefore imperative for casino operators to effectively manage and cultivate the performance of this department. A primary task for the casino operator is planning and deciding the mix of slot machines in order to maximize performance.

This paper presents the task of optimizing the casino slot floor as a linear programming …

On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.

Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation.

Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the differential transform method (DTM) will be applied to the generalized Burgers-Huxley equation, and some special cases of the equation, say, Huxley equation and Fitzhugh-Nagoma equation. The DTM produces an approximate solution for the equation, with few and easy computations. Numerical comparison between differential transform method, Adomian decomposition method and Variational iteration method for Burgers-Huxley, Huxley equation and Fitzhugh-Nagoma equation reveal that differential transform method is simple, accurate and efficient.

A New Method For Fuzzy Critical Path Analysis In Project Networks With A New Representation Of Triangular Fuzzy Numbers, Amit Kumar, Parmpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The method for finding fuzzy optimal solution of fully fuzzy critical path (FFCP) problems i.e., critical path problems in which all the parameters are represented by fuzzy numbers, is at best scant; possibly non-existent. In this paper, a method is proposed to find the fuzzy optimal solution of FFCP problems, together with a new representation of triangular fuzzy numbers. This paper will show the advantages of using, the proposed representation over the existing representations of triangular fuzzy numbers and will present with great clarity the proposed method and illustrate its application to FFCP problems occurring in real life situations.

Differential Transform Method For Nonlinear Parabolic-Hyperbolic Partial Differential Equations, J. Biazar, M. Eslami, M. R. Islam

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper an analytic solution of non-linear parabolic-hyperbolic equations is deduced with the help of the powerful differential transform method (DTM). To illustrate the capability and efficiency of the method four examples for different cases of the equation are solved. The method can easily be applied to many problems and is capable of reducing the size of computational work.

Exact Solutions For The Kdv6 And Mkdv6 Equations Via Tanh-Coth And Sech Methods, Alvaro H. Salas, Cesar. A. Gómez S

Applications and Applied Mathematics: An International Journal (AAM)

The tanh-coth method is used to seek solutions to obtain solutions to the new integrable sixthorder Korteweg-de Vries equation (KdV6). Following the analogy between the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (MKdV) we construct a new system equivalent to KdV6 from which exact solutions to original equation and derived, during the sech method.