# Poster Session

Saturday, April 23, 2005 - 4:00pm - 5:30pm

Lind 400

**Pseudo almost periodic solutions to semilinear abstract differential equations**

Crepin Mahop (Howard University)

We study the existence and uniqueness of pseudo almost

periodic solutions to semilinear abstract differential equations of the form

u'(t)+ Au(t) = f(t,u(t)) (*)

where -A is the infintesimal generator of an analytic semigroup acting

on a (complex) Banach space X, and f: RxX ---> X is a jointly continuous

function. Under some additional assumptions on A and f, the existence

and uniqueness of pseucdo almost periodic (classical) solutions to (*)

is obtained by using both fractional powers of operators and the Banach

fixed-point principle.**Thermal criticality in a reactive viscous flow through channel filled with porous medium**

Oluwole Makinde (University of Limpopo)

This paper examines the steady-state solutions of strongly exothermic reaction of a viscous combustible material in a channel filled with saturated porous medium under Arrhenius kinetics, neglecting the consumption of the material. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.

Keywords: Porous medium flows, Arrhenius kinetics, Hermite-Padé approximants, Thermal criticality.**A decoupling technique and necessary conditions for the neutral problem of Bolza**

Norma Ortiz (Louisiana State University)

Our study uses Clarke's decoupling technique to obtain Euler-Lagrange and Hamiltonian necessary conditions for the problem of Bolza with Lipschitz continuously varying delay in both the state and velocity parameters.**Extention of the Cayley-Hamilton theorem and application to finding the inverse frame operator**

Alberto Teguia (East Tennessee State University)

We present an extension of the Cayley-Hamilton Theorem over a seperable Hilbert space . Applications of our results include expressions on the one-sided inverse and the resolvent of an elliptic operator, and some new insights into finding the inverse of a frame operator.**Comparison of bit allocation methods for compressing three-dimensional meterological data after applying KLT**

Aldo Lucero (University of Texas)

Joint work with Sergio Cabrera, Alberto Aguirre, Miguel Argaez, Eduardo Vidal Jr.

This poster present the latest results of an ongoing project to assess the impact of lossy compression applied to three-dimensional meteorological data. The main innovative outcomes presented are based on different bit allocation techniques used to compress Karhunen-Loeve transformed data. The transform is applied in the z-direction (between slices) as suggested in the JPEG2000 Part 2 standard. New results using these bit allocation techniques are presented on two data sets. The performance results are presented in terms of SNR, root-mean squared error (RMSE), and the maximum absolute error (MAE) for the entire cube of data.**On solving a nonzero residual nonlinear hyperboloid least-squares problem**

Leticia Velazquez (University of Texas)

Joint work with Brenda Bueno and Miguel Argaez

We study a nonlinear least squares problem that arises in a process of mapping selected atom positions of the beta sheets in proteins onto a hyperboloid. We use the TIM barrel data as a test case since it has a clear barrel structure, and it is expected for the mapped atoms to arrange themselves in a barrel shape around the calculated hyperboloid. Then, we investigate allosteric enzymes and describe the conformational changes of the beta sheets between the active (R) and the inactive (T) states.**A new primal-dual interior-point algorithm for linear programming**

Miguel Argaez (University of Texas)

We present a primal-dual interior-point algorithm for solving linear programming problems using the notion of the quasicentral path as a central region. We introduce a Newton direction associated to the quasicentral path that yields an implementation using only primal and complementarity variables. A semi-iterative solvers for obtaining this Newton direction is presented where only one matrix factorization is done in all the iterative procedure. A promising numerical experimentation using a predictor-corrector algorithm is performed on the set of NETLIB test problems.**Explicit exact solutions for the generalized non conservative ultrashort pulse propagation system**

Emmanuel Yomba

We consider the complex Ginzburg-Landau equation form

which describes the femtosecond pulses propagation in

optical system. Using the separation method, we

obtained under some specific constraint conditions the

existence of dark soliton. In the particular case of

degenearcy, a generalized method, which is generally

called the projective Riccati equation method is used

to construct new exact solutions of the above

mentioned equation based on a system of Riccati

equations. These new solutions include bright soliton,

dark soliton, new solitary wave solutions and periodic

solutions.**The set of hearing-impaired math PhDs is countably finite on the order of**

at least 18!

J. Tilak Ratnanather (Johns Hopkins University)

We discuss the paucity of hearing-impaired people with PhDs in mathematics

given the incidence of hearing loss in the general population to be one in

ten. We list the names and background of 18 such people including

Charlotte Agnas Scott who was a co-founder of the American Mathematical

Society and Kathleen Ollerenshaw who became the President of the UK-based

Institute of Mathematics and its Applications in the late 1970s. We

comment on the possibility that web-based mathematics could be the way to

attract people from all under-represented communities as well as those in

the mainstream.**Enterprise portfolio analysis using a finite state Markov decision process**

Robert Hampshire (Princeton University)

Managing a portfolio of computer and software resources in a sufficiently large business enterprise is a complicated and daunting task involving an analysis of a myriad of factors to include business capabilities, business value and business risk. A finite horizon discrete time Markov decision process (MDP) is developed to model enterprise portfolio transformation.**Determining robustness in drosophila melanogaster**

Jean Cadet (Stony Brook University)

Driever and Nusslein-Volhard showed that the bicoid gene protein determines position in the Drosophila embryo in a concentration-dependent manner. We combine our knowledge of this result with the gene circuit model which is based on 4 steps: formulate a theoretical model, acquire data, optimize using simulated annealing and learn new biology. Published versions of the gene circuit model yielded biologically inaccurate results. First, we modify the model to get biologically robust results. Then, we propose a manner to characterize statistically biological robustness despite changes in the bicoid dosage.**Exploring goodness-of-fit and spatial correlation using components of Tango's index of spatial clustering**

Monica Jackson (Emory University)

The ability to detect anomalies as clustering in data sets plays an important role in spatial data analysis. Tango (1995) developed a statistic that can be used to detect clusters in data sets. Rogerson (1999) observed that Tango's index may be decomposed into the summation of two distinct statistics, the first part a test of goodness-of-fit (GOF), and the second part an index of spatial autocorrelation (SA) similar to Moran's I. In this poster we investigate the effectiveness of Rogerson's expression of Tango's statistic in separating GOF from SA in data sets containing clusters. We simulate data under the null hypothesis of no clustering as well as two alternative hypotheses. The first alternative hypothesis induces a poor fit from the null hypothesis while maintaining independent observations and the second alternative hypothesis induces spatial autocorrelation while maintaining fit. Using Rogerson's decomposition and leukemia incidence data from New York, we show graphically one is unable to statistically distinguish poor fit from autocorrelation.**Oxygen distribution in multiple capillaries in skeletal muscles with axial diffusion**

Miranda Teboh-Ewungkem (Lafayette College)

A model to study the strength and effects of axial diffusion on many interacting capillaries in skeletal muscle is presented. The method consists of determining the oxygen concentration in a functional unit,consisting of a single capillary surrounded by a region of tissue, in which a flux is prescribed on the outer boundary of the region. This flux, which is a result of the interaction among all of the capillaries comprising the vascular bed, is found by matching the concentration along the common border between adjacent units.

Because capillary lengths are large compared to their spacing, diffusion in the tissue in the direction parallel to the capillaries (axial diffusion) is small compared to diffusion in the plane perpendicular to the capillaries. For this reason axial diffusion is often neglected in diffusion analyses. However, axial diffusion does have a significant effect on oxygen and substrate concentration within the tissue, and on how these substances are delivered to the tissue by the capillaries. Axial diffusion is included in the analysis by obtaining the solutions to the differential equation derived from the model with axial diffusion as a perturbation to the solution without axial diffusion. However, in the region near the arterial end axial diffusion is comparable to diffusion in the plane perpendicular to the capillaries. Hence singular perturbation techniques are used to study these regions and appropriately match these regions (inner regions) to the regions where axial diffusion is negligible (outer region) using the method of matched asymptotic expansion.**A trust region interior-point method for solving nonlinear programs**

Maria Cristina Villalobos (University of Texas Pan American)

Close to a solution of the nonlinear program, the Jacobian associated with

the Karush-Kuhn-Tucker (KKT) system is nonsingular. However, for points far

from a solution of the nonlinear program, the Jacobian may be singular. In this

paper, we propose a global method that obtains a least-squares solution to the

linearization of the perturbed KKT conditions subject to a limit on the step

size. In addition, we use the_{2}

norm of the KKT conditions as a merit function to solve the nonlinear program.

We implement trust-region and interior-point methods to solve the nonlinear

program.