Physical Sciences and Mathematics Commons^™

Stochastic Intra-Cellular Modeling, Thomas E. Hopkins

Theses and Dissertations

Air Force personnel may sometimes come into contact with potentially harmful chemicals while performing their duties. Of course the Air Force desires to keep any potential health risks to its members to a minimum. To this end the Air Force would like to identify which chemicals are toxic, their level of toxicity, and the processes by which these chemicals disrupt normal biological activities at the cellular level. The development of mathematical models can be of great benefit to toxicity studies. Because real world systems involve randomness, that is noise, and the desire is to create mathematical models to represent those …

Feature Guided Image Registration Applied To Phase And Wavelet-Base Optic Flow, Kate R. Duffy

Theses and Dissertations

Optic Flow algorithms are useful in problems such as computers vision, navigational systems, and robotics. However, current algorithms are computationally expensive or lack the accuracy to be effective compared with traditionally navigation systems. Recently, lower accuracy inertial navigation systems (INS) based on Microelectromechanical systems (MEMS) technology have been proposed to replace more accurate traditional navigation systems.

The Cohomology Of The Steendrod Algebra And Representations Of The General Linear Groups, Nguyen H. V. Hu'ng

Mathematics Research Reports

Let Tr_k be the algebraic transfer that maps from the coinvariants of certain GL_k-representation to the cohomology of the Steenrod algebra. This transfer was defined by W. Singer as an algebraic version of the geometrical transfer tr_k : pi_*^S((B[doublestrike V]_k)_+) --> pi_*^S(S^0). It has been shown that the algebraic transfer is highly nontrivial, more precisely, that Tr_k is an isomorphism for k = 1, 2, 3 and that T_r = ⊕_k(Tr_k) is a homomorphism of algebras.

In this paper, we first recognize the phenomenon that if we start from any degree d, and apply Sq^0 repeatedly at most (k- 2) …

Checking Assumptions In Latent Class Regression Models Via A Markov Chain Monte Carlo Estimation Approach: An Application To Depression And Socio-Economic Status, Elizabeth Garrett, Richard Miech, Pamela Owens, William W. Eaton, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to …

Impulsive Differential Equations With Non-Local Conditions, Robert Knapik

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

A Cnf Analogue To Strengthening, Sean Weaver

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Integral Transforms Of Functionals In L2(C0[0, T]), Byoung Soo Kim, David Skough

Department of Mathematics: Faculty Publications

In this paper we give a necessary and sufficient condition that a functional F(x) in L₂(C₀[0, T]) has an integral transform F_α,βF(x) which also belongs to L₂(C₀[0, T]).

Approximation By Piecewise Constant Functions In A Bv Metric, Pavel Bělík, Mitchell Luskin

Faculty Authored Articles

Westudytheapproximationpropertiesofpiecewiseconstantfunc- tions with respect to triangular and rectangular finite elements in a metric defined on functions of bounded variation. We apply our results to a thin film model for martensitic crystals and to the approximation of deformations with microstructure.

Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo

Mathematics Faculty Publications

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.

Optimal Control Of Neutral Functional-Differential Inclusions, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper deals with optimal control problems for dynamical systems governed by constrained functional-differential inclusions of neutral type. Such control systems contain time-delays not only in state variables but also in velocity variables, which make them essentially more complicated than delay-differential (or differential-difference) inclusions. Our main goal is to derive necessary optimality conditions for general optimal control problems governed by neutral functional-differential inclusions with endpoint constraints. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of …

Nonlinear Equations And Wavelets, Andrei Ludu

Andrei Ludu

No abstract provided.

A New Method For Ranking Of Fuzzy Numbers Through Using Distance Method, S. Abbasbandy, C. Lucas, B. Asady

Saeid Abbasbandy

In this paper, by using a new approach on distance between two fuzzy numbers, we construct a new ranking system for fuzzy number which is very realistic and also matching our intuition as the crisp ranking system on R.

Fuzzy Interpolation, S. Abbasbandy

Saeid Abbasbandy

In this paper, we will consider the interpolation of fuzzy data by a continuous fuzzy-valued function. We will use Lagrange polynomials, natural splines and complete splines.

Fractional Bandwidth Reacquisition Algorithms For Vsw-Mcm, Ben Cook, Daniel Marthaler, Chad M. Topaz, Andrea L. Bertozzi, Mathieu Kemp

Chad M. Topaz

Autonomous underwater vehicles are gradually being recognized as key assets in future combat systems. Central to this attitude is the realization that teams of vehicles acting in concerted fashion can accomplish tasks that are either too costly or simply outside the range of capabilities of single vehicles. The VSW-MCM target reacquisition problem is the primary driver of underwater multi-agent research. Because of the VSW's inherent high vehicle attrition rate and unreliable communication, it is felt that vehicle coordination must be done off-site. In this paper, we suggest an alternative to this which permits on-site coordination despite loss of vehicles and …

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Yi Li

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Yi Li

No abstract provided.

Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We present new random fixed point theorems in spaces with two metrics. Our results extend recent results of Tan and Yuan [10] and Xu [11].

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Mathematics and Statistics Faculty Publications

No abstract provided.

An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

Advances In The Use Of Neurophysiologycally-Based Fusion For Visualization And Pattern Recognition Of Medical Imagery, Mario Aguilar, Joshua New, Erion Hasanbelliu

Research, Publications & Creative Work

The ever increasing number of image modalities available to doctors for diagnosis purposes has established an important need to develop techniques that support work-load reduction and information maximization. To this end, we have improved on an image fusion architecture first developed for night vision applications. This technique, presented at Fusion 2002, utilizes 3D operators to combine volumetric image sets while maximizing information content. In our approach, we have combined the use of image fusion and userdefined pattern recognition within a 3D human-computer interface. Here, we present our latest advances towards enhancing information visualization and supporting pattern recognition. We also report …

Homogeneous Weights And Exponential Sums, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

In this paper, we give a formula as an exponential sum for a homogeneous weight defined by Constantinescu and Heise [3] in the case of Galois rings (or equivalently, rings of Witt vectors) and use this formula to estimate the weight of codes obtained from algebraic geometric codes over rings.

Book Embeddings Of Graphs, Robin Leigh Blankenship

LSU Doctoral Dissertations

We use a structural theorem of Robertson and Seymour to show that for every minor-closed class of graphs, other than the class of all graphs, there is a number k such that every member of the class can be embedded in a book with k pages. Book embeddings of graphs with relation to surfaces, vertex extensions, clique-sums and r-rings are combined into a single book embedding of a graph in the minor-closed class. The effects of subdividing a complete graph and a complete bipartite graph with respect to book thickness are studied. We prove that if n ≥ 3, …

Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno

LSU Doctoral Dissertations

Let g be a class of graphs and ≤ be a graph containment relation. A splitter theorem for g under ≤ is a result that claims the existence of a set O of graph operations such that if G and H are in g and H≤G with G≠H, then there is a decreasing sequence of graphs from G to H, say G=G₀≥G₁≥G₂...G_t=H, all intermediate graphs are in g, and each G_i can be obtained from G_i-1 by applying a single …

Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand

LSU Master's Theses

This work presents Gauss' justification of the method of least squares, following the treatment given by Gauss himself in "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," where the main idea is to show that the least squares estimate is the unbiased linear estimate of minimum variance. (Actually, we present Gauss' argument both in his terminology and translated into matrix terminology.) We show how this contrasts with Gauss' earlier justfication in "Theoria Motus Corporum Coelestium" which was based on the assumption of a normal distribution of errors, and yielded the estimate of maximum likelihood. We present as a background the development from …

A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch

LSU Master's Theses

We present how blackjack is related to a discrete-time control problem, rather than a zero-sum game. Using the compiler Visual C++, we write a program for a strategy for blackjack, but instead of maximizing the expected value, we use a risk-averse approach. We briefly describe how this risk-averse strategy is solved by using a special type of dynamic programming called fractional dynamic programming.

The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We consider the Dirichlet problem Δu + λu + |u|^2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in R^N, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

The Mathematics Of Object Recognition In Machine And Human Vision, Sunyoung Kim

Theses Digitization Project

The purpose of this project was to see why projective geometry is related to the sort of sensors that machines and humans use for vision.

Finite Subsets Of The Plane Are 18-Reconstructible, L. Pebody, A. J. Radcliffe, A. D. Scott

Department of Mathematics: Faculty Publications

We prove that every finite subset of the plane is reconstructible from the multiset of its subsets of at most 18 points, each given up to rigid motion. We also give some results concerning the reconstructibility of infinite subsets of the plane.