Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2007

Discipline
Institution
Keyword
Publication
Publication Type

Articles 91 - 120 of 150

Full-Text Articles in Applied Mathematics

Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr. Mar 2007

Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr.

Theses and Dissertations

This research focuses on numerically solving a class of computationally expensive optimization problems that possesses a unique characteristic: as the optimal solution is approached, the computational time required to compute an objective function value decreases. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration and comparison process. The goal is to find the parameters of a predetermined image by comparing the flow dynamics from the numerical simulation and the predetermined image through the image comparison process. The generalized pattern search and mesh adaptive direct search methods …

Go to article

Classifying Failing States, Nathan E. Nysether Mar 2007

Classifying Failing States, Nathan E. Nysether

Theses and Dissertations

The US is heavily involved in the first major war of the 21st Century -- The Global War on Terror (GWOT). As with any militant group, the foundation of the enemy's force is their people. There are two primary strategies for defeating the terrorists and achieving victory in the GWOT. First, we must root out terrorists where they live, train, plan, and recruit and attack them militarily. Second, we must suffocate them by cutting off the supply of new soldiers willing to choose aggression or even death over their current life. This thesis helps to achieve these objectives by applying …

Go to article

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06 Feb 2007

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06

All HMC Faculty Publications and Research

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots

Go to article

Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino Feb 2007

Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino

Articles and Preprints

We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.

Go to article

Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich Feb 2007

Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which~being certainly of independent interest are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang formulated via an appropriate subdifferential notion for …

Go to article

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang Feb 2007

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

Go to article

Application Of Chimera Grid To Modelling Cell Motion And Aggregation In A Narrow Tube, Bong Jae Chung, P. C. Johnson, A. S. Popel Jan 2007

Application Of Chimera Grid To Modelling Cell Motion And Aggregation In A Narrow Tube, Bong Jae Chung, P. C. Johnson, A. S. Popel

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A computational scheme using the Chimera grid method is presented for simulation of three-dimensional motion and aggregation of two red blood cells (RBCs) in a narrow tube. The cells are modelled as rigid ellipsoidal particles; the computational scheme is applicable to deformable fluid-filled particles. Attractive energy between two RBCs is modelled by a depletion interaction theory and used for simulating aggregation of two cells. Through the simulation, we show that the Chimera grid method is applicable to the simulation of three-dimensional motion and aggregation of multiple RBCs in a microvessel and microvascular network.

Go to article

Codes Generated By Matrix Expansions, Chris Meyer Jan 2007

Codes Generated By Matrix Expansions, Chris Meyer

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Go to article

On A Spatial Rock-Paper-Scissors Game, Robert D. Macmartin, Jan Rychtar Jan 2007

On A Spatial Rock-Paper-Scissors Game, Robert D. Macmartin, Jan Rychtar

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Go to article

Analysis Of A Modified Feedback Control Technique For Suppressing Electrical Alternans In Cardiac Tissue, Srinivasan V. Narayanan, John W. Cain Jan 2007

Analysis Of A Modified Feedback Control Technique For Suppressing Electrical Alternans In Cardiac Tissue, Srinivasan V. Narayanan, John W. Cain

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Go to article

Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich Jan 2007

Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich

Mathematics Research Reports

We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modi- fied one-sided Lipschitz condition imposed on the right-hand side (i.e., on the velocity sets) of the differential inclusion, which is a significant improvement of the conventional Lipschitz continuity. Our main attention is paid to establishing efficient conditions that ensure the strong approximation (in the W^1,p-norm as p greater than or equal to 1) of feasible trajectories for the one-sided Lipschitzian differential inclusions under. consideration by …

Go to article

A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler Jan 2007

A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler

Mathematics Faculty Publications

If a large number of educated people were asked, ``What was your most exciting class?'', odds are that very few of them would answer ``Trigonometry.'' The subject is generally presented in a less-than-exciting fashion, with the repeated caveat that ``you'll need this when you take calculus,'' or ``this has lots of applications'' without ever really seeing many of them. This manuscript addresses how the author is trying to change this tradition by exposing casual students from kindergarten to college to Joseph Fourier's secret, that nearly any function can be built out of sine and cosine curves. And music serves as …

Go to article

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley Jan 2007

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Journal 2007

From a Christian perspective, both modern and post-modern approaches to the philosophy of mathematics have significant shortcomings. This paper explores an alternative. It summarizes Augustine of Hippo’s views on the four classical themes of the philosophy of mathematics-the ontology of mathematical objects, their epistemology, the nature of truth in mathematics, and how we account for the effectiveness of mathematics in describing the natural world. It then traces what has happened to Augustine’s perspective in the roughly 1600 years since it was written concluding with a discussion of some spiritual and intellectual problems with the currently dominant secular perspective.

Go to article

A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia Jan 2007

A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝα with optimal state uĝαα and optimal adjoint state pĝαα are convergent as α → 1 …

Go to article

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson Jan 2007

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

Scholarship and Professional Work - LAS

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Go to article

Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge Jan 2007

Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge

Articles

This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based …

Go to article

Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen Jan 2007

Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider Turing patterns for reaction-diffusion systems on the surface of a growing sphere. In particular, we are interested in the effect of dynamic growth on the pattern formation. We consider exponential isotropic growth of the sphere and perform a linear stability analysis and compare the results with numerical simulations.

Go to article

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li Jan 2007

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Go to article

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li Jan 2007

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

Go to article

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis Jan 2007

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

Go to article

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty Jan 2007

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

Go to article

Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon Jan 2007

Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon

LSU Doctoral Dissertations

Let G be a quasi simply reducible group, and let V be a representation of G over the complex numbers $mathbb{C}$. In this thesis, we introduce the twisted 6j-symbols over G which have their origin to Wigner's 6j-symbols over the group SU(2) to study the structure constants of the subrepresentation semiring S_{G}(End(V)), and we study the representation theory of a quasi simply reducible group G laying emphasis on our new G-module objects. We also investigate properties of our twisted 6j-symbols by establishing the link between the twisted 6j-symbols and Wigner's 3j-symbols over the group G.

Go to article

Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov Jan 2007

Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov

Articles

Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this ontribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions …

Go to article

Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu Jan 2007

Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu

Articles

The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves.

Go to article

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang Jan 2007

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang

Scholarship

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

Go to article

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter Shiue, Leetsch Hsu Jan 2007

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter Shiue, Leetsch Hsu

Scholarship

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.

Go to article

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu Jan 2007

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu

Scholarship

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

Go to article

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He Jan 2007

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He

Scholarship

No abstract provided.

Go to article

Covering Properties And Cohen Forcing, Akira Iwasa Jan 2007

Covering Properties And Cohen Forcing, Akira Iwasa

Computer Science and Mathematics Faculty Publications

We will show that adding Cohen reals preserves the covering property that every open cover has a σ-P Q refinement and deduce that adding Cohen reals preserves covering properties such as paracompactness, subparacompactness and screenability.

Go to article

The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng Jan 2007

The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng

Department of Mathematics: Faculty Publications

Sexual reproduction in nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.

Go to article

First Prev Next Last