Physical Sciences and Mathematics Commons^™

A Remark On Conservative Diffeomorphisms, Jairo Bochi, Bassam R. Fayad, Enrique Pujals

Publications and Research

Abstract:

We show that a stably ergodic diffeomorphism can be C¹ approximated by a diffeomorphism having stably non-zero Lyapunov exponents.

Résumé:

On montre qu'un difféomorphisme stablement ergodique peut être C¹ approché par un difféomorphisme ayant des exposants de Lyapunov stablement non-nuls.

Variational Analysis Of Evolution Inclusions, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such roblems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of Asplund (and hence any reflexive Banach) spaces. In this way we establish extended results on stability of discrete approximations (with the strong W^1,2-convergence of optimal solutions under consistent perturbations of …

Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko

Mathematics Faculty Publications and Presentations

The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.

Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Raymond J. Carroll

Jeffrey S. Morris

Increasingly, Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary formand the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the …

Abstract Second-Order Damped Mckean-Vlasov Stochastic Evolution Equations, N. I. Mahmudov, Mark A. Mckibben

Mathematics Faculty Publications

We establish results concerning the global existence, uniqueness, approximate and exact controllability of mild solutions for a class of abstract second-order stochastic evolution equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t. First-order equations of McKean-Vlasov type were first analyzed in the finite dimensional setting when studying diffusion processes, and then subsequently extended to the Hilbert space setting. The current manuscript provides a formulation of such …

A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang

Doctoral Dissertations

The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of …

An Interactive Relaxation Approach For Anomaly Detection And Preventive Measures In Computer Networks, Garrick A. Bell

Theses and Dissertations

It is proposed to develop a framework of detecting and analyzing small and widespread changes in specific dynamic characteristics of several nodes. The characteristics are locally measured at each node in a large network of computers and analyzed using a computational paradigm known as the Relaxation technique. The goal is to be able to detect the onset of a worm or virus as it originates, spreads-out, attacks and disables the entire network. Currently, selective disabling of one or more features across an entire subnet, e.g. firewalls, provides limited security and keeps us from designing high performance net-centric systems. The most …

Getting More Out Of Two Asset Portfolios, Tom Arnold, Terry D. Nixon

Finance Faculty Publications

Two-asset portfolio mathematics is a fixture in many introductory finance and investment courses. However, the actual development of the efficient frontier and capital market line are generally left to a heuristic discussion with diagrams. In this article, the mathematics for calculating these attributes of two-asset portfolios are introduced in a framework intended for the undergraduate classroom.

Nonlinear Evolution Of The Plasma Beat Wave: Compressing The Laser Beat Notes Via Electromagnetic Cascading, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

The near-resonant beat wave excitation of an electron plasma wave (EPW) can be employed for generating the trains of few-femtosecond electromagnetic (EM) pulses in rarefied plasmas. The EPW produces a comoving index grating that induces a laser phase modulation at the difference frequency. As a result, the cascade of sidebands red and blue shifted by integer multiples of the beat frequency is generated in the laser spectrum. The bandwidth of the phase-modulated laser is proportional to the product of the plasma length, laser wavelength, and amplitude of the electron density perturbation. When the beat frequency is lower than the electron …

Development Of An Unbiased Statistical Method For The Analysis Of Unigenic Evolution, Colleen D. Behrsin, Chris J. Brandl, David W. Litchfield, Brian H. Shilton, Lindi M. Wahl

Biochemistry Publications

Background: Unigenic evolution is a powerful genetic strategy involving random mutagenesis of a single gene product to delineate functionally important domains of a protein. This method involves selection of variants of the protein which retain function, followed by statistical analysis comparing expected and observed mutation frequencies of each residue. Resultant mutability indices for each residue are averaged across a specified window of codons to identify hypomutable regions of the protein. As originally described, the effect of changes to the length of this averaging window was not fully eludicated. In addition, it was unclear when sufficient functional variants had been examined …

Optimization And Equilibrium Problems With Equilibrium Constraints In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The …

Analysis Of Mass Spectrometry Data Using Bayesian Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Philip J. Brown, Keith A. Baggerly, Kevin R. Coombes

Jeffrey S. Morris

In this chapter, we demonstrate how to analyze MALDI-TOF/SELDITOF mass spectrometry data using the wavelet-based functional mixed model introduced by Morris and Carroll (2006), which generalizes the linear mixed models to the case of functional data. This approach models each spectrum as a function, and is very general, accommodating a broad class of experimental designs and allowing one to model nonparametric functional effects for various factors, which can be conditions of interest (e.g. cancer/normal) or experimental factors (blocking factors). Inference on these functional effects allows us to identify protein peaks related to various outcomes of interest, including dichotomous outcomes, categorical …

Existence Of Explosive Solutions To Non-Monotone Semilinear Elliptic Equations, Zachary H. Proano

Theses and Dissertations

We consider the semilinear elliptic equation Δu = p(x)f(u) on a domain ­ Ω ⊆ Rⁿ, n ≥ 3, where f is a nonnegative function which vanishes at the origin and satisfies g₁ ≤ f ≤ g₂ where g₁; g₂ are nonnegative, nondecreasing functions which also vanish at the origin, and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in ­ such that p is positive on its boundary. For Ω­ bounded, we show that a nonnegative solution u satisfying u(x) …

Doppler-Only Multistatic Radar, Dustin G. Mixon

Theses and Dissertations

In order to estimate the position and velocity of a target, most multistatic radar systems require multiple independent target measurements, such as angle-of-arrival, time-of-arrival, and Doppler information. Though inexpensive and reliable, Doppler-only systems have not been widely implemented due to the inherent nonlinear problem of determining a target’s position and velocity from their measurements. We solve this problem. In particular, we first establish the lack of observability in the Doppler-only bistatic system, thereby demonstrating the need for multiple transmitters and/or receivers. Next, for a multistatic system with a sufficient number of transmitter-receiver pairs, we invoke classical optimization techniques, such as …

Bifurcations And Competing Coherent Structures In The Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (Cw) Solutions, S.C. Mancas, S. Roy Choudhury

Publications

Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equa- tion (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes each of the possible quartic (the quartic fold and an unnamed form), cubic (the pitchfork and the winged cusp), and quadratic (four possible cases) normal forms for singularities of codimension up to three. Since the actual governing equations are …

Doppler Aliasing Reduction In Wide-Angle Synthetic Aperture Radar Using Phase Modulated Random Stepped-Frequency Waveforms, Andrew W. Hyatt

Theses and Dissertations

This research effort examines the theory, application and results of side-looking airborne radar operation in hot clutter. Hot clutter is an electronic counter-measure used to degrade the performance of airborne radar. Hot clutter occurs by illuminating the ground with an airborne jammer at some velocity, azimuth, elevation, and range from the airborne radar. When the received RCS scattered hot clutter waveform is perfectly coherent with the radar waveform, the radar believes the returns created by the hot clutter jammer resulted from the transmitting radar. Hot clutter degrades radar performance at locations in azimuth and Doppler. The effect of hot clutter …

Quantitative Object Reconstruction Using Abel Transform Tomography And Mixed Variable Optimization, Kevin R. O'Reilly

Theses and Dissertations

Researchers at the Los Alamos National Laboratory (LANL) are interested in quantitatively reconstructing an object using Abel transform x-ray tomography. Specifically, they obtain a radiograph by x-raying an object and attempt to quantitatively determine the number and types of materials and the thicknesses of each material layer. Their current methodologies either fail to provide a quantitative description of the object or are generally too slow to be useful in practice. As an alternative, the problem is modeled here as a mixed variable programming (MVP) problem, in which some variables are nonnumeric and for which no derivative information is available. The …

Fun With Fractals, Borbala Mazzag

Borbala Mazzag

No abstract provided.

Vectorial Lorentz Transformations, Jorge A. Franco

Jorge A Franco

We have noticed in relativistic literature that the derivation of Lorentz Transformations (LT) usually is presented by confining the moving system O’ to move along the X-axis, namely, as a particular case of a more general movement. When this movement is generalized different transformations are obtained (which is a contradiction by itself) and a hidden vectorial characteristic of time is revealed. LT have been generalized in order to solve some physical and mathematical inconsistencies, such as the dissimilar manners (transversal, longitudinal) the particle’s shape is influenced by its velocity and LT’s inconsistency with Maxwell equations when in its derivation the …

New Oscillating Reaction – Phenylacetylene Oxidative Carbonylation To Anhydride Of Phenylmaleic Acid (In Russian), Sergey N. Gorodsky, Olga V. Kasatkina, Lev G. Bruk, Oleg N. Temkin

Sergey N. Gorodsky

No abstract provided.

Sea Surface Temperature Patterns On The West Florida Shelf Using Growing Hierarchical Self-Organizing Maps, Yonggang Liu, Robert H. Wesiberg, Ruoying He

Yonggang Liu

Neural network analyses based on the self-organizing map (SOM) and the growing hierarchical self-organizing map (GHSOM) are used to examine patterns of the sea surface temperature (SST) variability on the West Florida Shelf from time series of daily SST maps from 1998 to 2002. Four characteristic SST patterns are extracted in the first-layer GHSOM array: winter and summer season patterns, and two transitional patterns. Three of them are further expanded in the second layer, yielding more detailed structures in these seasons. The winter pattern is one of low SST, with isotherms aligned approximately along isobaths. The summer pattern is one …

Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht

Publications

Systematic experimental work [S. Zhuang, G. Ravichandran, D. Grady, J. Mech. Phys. Solids 51 (2003) 245–265] on laminated composites subjected to high velocity impact loading exhibits the dispersed wave field and the oscillatory behavior of waves with respect to a mean value. Such a behavior is absent in homogeneous solids. An approximate solution to the plate impact in layered heterogeneous solids has been developed in [X. Chen, N. Chandra, A.M. Rajendran, Int. J. Solids Struct. 41 (2004) 4635–4659]. The influence of the particle velocity on many process characteristics was demonstrated. Based on earlier results [A. Berezovski, J. Engelbrecht, G.A. Maugin, …

Why Is The Number Of Dna Bases 4?, Bo Deng

Department of Mathematics: Faculty Publications

In this paper we construct a mathematical model for DNA replication based on Shannon’s mathematical theory for communication. We treatDNAreplication as a communication channel. We show that the mean replication rate is maximal with four nucleotide bases under the primary assumption that the pairing time of the G–C bases is between 1.65 and 3 times the pairing time of the A–T bases.

Decentralized Convex-Type Equilibrium In Nonconvex Models Of Welfare Economics Via Nonlinear Prices, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving nonconvex economies with infinite-dimensional commodity spaces. The main results relate to generalized/ extended second welfare theorems ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. The usage of nonlinear (vs. standard linear) prices allow us to decentralized price equilibria in fully nonconvex models similarly to linear prices …

Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa

Faculty Publications

We discuss when a subspace of ω_ω is paracompact in some forcing extension.

Approximation Of Fuzzy Functions By Distance Method, S. Abbasbandy, M. Amirfakhrian

Saeid Abbasbandy

Approximation of functions in a given space is an old problem in applied mathematics. In this paper the problem is considered for fuzzy data and fuzzy functions using the defuzzification function introduced by Fortemps and Roubens. We introduce a fuzzy polynomial approximation as D-approximation of a fuzzy function on a discrete set of points and we present a method to compute it.

Ranking Of Fuzzy Numbers By Min Distance, S. Abbasbandy, M. Otadi, M. Mosleh

Saeid Abbasbandy

Several different strategies have been proposed for ranking of fuzzy numbers. These include methods based on the coefficient of variation (CV index), distance between fuzzy sets, centroid point and original point, and weighted mean value. Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper we propose a ranking method for fuzzy numbers by min distance. The method for ranking fuzzy numbers suggested in this paper is based on comparison of distance from fuzzy numbers to fuzzy minimum where fuzzy minimum is a reference set and this method able to overcome the shortcomings …

New Interpretation Of Homotopy Perturbation Method, Ji-Huan He

Ji-Huan He

The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method

Some Asymptotic Methods For Strongly Nonlinear Equations, Ji-Huan He

Ji-Huan He

This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation …

Posterminaries: Plain Text, Alexander H. King

Alexander H. King

You just can’t win an argument with an English professor.