Applied Mathematics Commons^™

On Sources In Comparability Graphs, With Applications, Stephan Olariu

Computer Science Faculty Publications

We characterize sources in comparability graphs and show that our result provides a unifying look at two recent results about interval graphs.

A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu

Computer Science Faculty Publications

A graph G is P₄-sparse if no set of five vertices in G induces more than one chordless path of length three. P₄-sparse graphs generalize both the class of cographs and the class of P₄-reducible graphs. We give several characterizations for P₄-sparse graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P₄-sparse graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line, D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the incompressible, infinite swept attachment line flow is unstable to streamwise disturbances that originate in the boundary layer when the cross-flow exceeds a critical magnitude. Furthermore, a small degree of suction at the surface has a significant stabilizing influence while a small degree of blowing has a considerable destabilizing influence. This paper investigates the stabilizing and destabilizing effects of, respectively, cooling or heating the plate and the competing or enhancing effects of suction or blowing. A nonorthogonal flow with respect to the attachment line is also considered by adding a component of shear to the mean …

Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In the recent paper [7], it was shown that the solutions of weakly singular Hammerstein equations satisfy certain regularity properties. Using this result, the optimal convergence rate of a standard piecewise polynomial collocation method and that of the recently proposed collocationtype method of Kumar and Sloan [10] are obtained. Superconvergence of both of these methods are also presented. In the final section, we discuss briefly a standard productintegration method for weakly singular Hammerstein equations and indicate its superconvergence property. © 1992 Rocky Mountain Mathematics Consortium.

Solution Uniqueness And Stability Criteria For A Model Of Growth Factor Production, J. A. Adam

Mathematics & Statistics Faculty Publications

Uniqueness and stability criteria are established for the steady states of a nonlinear model of growth factor production. A specific expression for the nonlinearity is chosen, containing three parameters which can be adjusted to fit a specific biological context, but much of the analysis applies to a general class of source terms that exhibit the same qualitative behavior.

A Charming Class Of Perfectly Orderable Graphs, Chinh T. Hoang, Frederic Maffray, Stephan Olariu, Myriam Preissmann

Computer Science Faculty Publications

We investigate the following conjecture of Vašek Chvátal: any weakly triangulated graph containing no induced path on five vertices is perfectly orderable. In the process we define a new polynomially recognizable class of perfectly orderable graphs called charming. We show that every weakly triangulated graph not containing as an induced subgraph a path on five vertices or the complement of a path on six vertices is charming.

Some Aspects Of The Semi-Perfect Elimination, Stephan Olariu

Computer Science Faculty Publications

Several efficient algorithms have been proposed to construct a perfect elimination ordering of the vertices of a chordal graph. We study the behaviour of two of these algorithms in relation to a new concept, namely the semi-perfect elimination ordering, which provides a natural generalization of chordal graphs.

On A Unique Tree Representation For P4-Extendible Graphs, B. Jamison, S. Olariu

Computer Science Faculty Publications

Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P₄-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the …

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

Self-Activation And Inhibition: A Simple Nonlinear Model, J. A. Adam

Mathematics & Statistics Faculty Publications

Self-activation and self-inhibition of cell number density (or growth factor concentration) due to a spatially localized source are studied. Both the time-independent and time-dependent models are examined, and the linear stability of the resulting three steady states of the former is discussed.

A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll _∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ _∞ = inf { ∥ƒ - g∥_∞ : g ∈ K}.

Parametric Instability Of Supersonic Shear Layers Induced By Periodic Mach Waves, Fang Q. Hu, Christopher K. W. Tam

Mathematics & Statistics Faculty Publications

It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier-Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

Grid Generation And Flow Computation About A Martian Entry Vehicle, John Edward Stewart

Mechanical & Aerospace Engineering Theses & Dissertations

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results have been obtained for this vehicle in 1968. These results show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed here to verify the earlier results and to further describe the flight characteristics of this vehicle.

An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using an algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are …

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

The Truncated Cauchy Distribution: Estimation Of Parameters And Application To Stock Returns, Paul G. Staneski

Mathematics & Statistics Theses & Dissertations

The problem addressed in this dissertation is the existence and estimation of the parameters of a truncated Cauchy distribution. It is known that when a number of distributions with infinite support are truncated to a finite interval that the maximum likelihood estimator of the scale parameter fails to exist with positive probability. In particular, necessary and sufficient conditions which give rise to instances of non-existence have been found for the exponential (Deemer and Votaw (1955)), gamma (Broeder (1955), Hegde and Dahiya (1989)), Weibull (Mittal and Dahiya (1989)) and normal distribution (Barndorff-Nielsen (1978), Mittal and Dahiya (1987), Hegde and Dahiya (1989)). …

Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson

Mathematics & Statistics Theses & Dissertations

In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …

Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead

Mathematics & Statistics Faculty Publications

The system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects. The stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number. For highly elastic fluids, the bifurcated state is periodic with a shift in frequency.

Wings And Perfect Graphs, Stephan Olariu

Computer Science Faculty Publications

An edge uv of a graph G is called a wing if there exists a chordless path with vertices u, v, x, y and edges uv, vx, xy. The wing-graph W(G) of a graph G is a graph having the same vertex set as G; uv is an edge in W(G) if and only if uv is a wing in G. A graph G is saturated if G is isomorphic to W(G). A star-cutset in a graph G is a non-empty set of …

A Characterization Of The Solution Of A Fredholm Integral Equation With L∞ Forcing Term, Hideaki Kaneko, Richard Noren, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In this paper we investigate the regularity properties of the Fredholm equation (Formula Presented) . The kernel is the product of the smooth function k and the singular function gα (Formula Presented). The forcing function f is in L∞. We obtain a decomposition of the solution as the sum of two functions—one with a discontinuity reflecting that of the forcing function—and the other a regular function. Our results extend those of C. Schneider [6], who assumes a condition that is stronger than f ∈ C[a, b] ∩ C^m(a,b) (for some integer m). © 1990 …

Best Quasi-Convex Uniform Approximation, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

No abstract provided.

A Generalization Of Linear Multistep Methods, Leon Arriola

Mathematics & Statistics Theses & Dissertations

A generalization of the methods that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically, the class of linear multistep methods of the Adams and BDF type are discussed.

Synthesis Of An Efficient Band Mechanism For Robots And Prosthetic Devices, Run Chen Zhou

Mechanical & Aerospace Engineering Theses & Dissertations

A noncircular pulley has been applied to improve the system efficiency of an electrical-powered elbow prosthesis. The dynamics of the motor and the prosthetic arm have been incorporated into the kinematic synthesis relationships for determining the pulley profile that maximizes the efficiency of the elbow prosthesis.

The nonlinear dynamic equations have been solved by the code Differential Equation (DE) while determining the motor power and efficiency which are the criteria in the nonlinear programming problem. The optimal design variables for determining the pulley profile along with some simulation results have been obtained from an optimization program (based on the Generalized …

Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis

Mathematics & Statistics Theses & Dissertations

A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest.

The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption …

Weak Bipolarizable Graphs, Stephan Olariu

Computer Science Faculty Publications

We characterize a new class of perfectly orderable graphs and give a polynomial-time recognition algorithm, together with linear-time optimization algorithms for this class of graphs.

On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge

Mathematics & Statistics Theses & Dissertations

This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.

It is assumed that the sequence is generated from a linear matrix iteration x_i+ i = Gx_i + k where G is an n x n square matrix and x_I+1 , x_i,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …

Uniform L1 Behavior In Classes Of Integrodifferential Equations With Convex Kernels, Richard Noren

Mathematics & Statistics Faculty Publications

No abstract provided.

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

On A Moving Boundary Problem Of Transitional Ballistics, Jen-Ing G. Hwang

Mathematics & Statistics Theses & Dissertations

A major problem which arises in computer simulation of the firing of a gun weapon is the development of numerical schemes which effectively account for the physics of projectile motion. The chief difficulty is that away from the projectile the calculation is ordinarily accomplished on a fixed numerical grid, whereas due to projectile movement some cells of the grid near the projectile undergo volume changes as the calculation proceeds. A local finite volume scheme is developed which accounts for the expansion or compression of cells fore-and-aft of the projectile. Through the process of numerical experiment, the effectiveness of the scheme …

Ignition Of A Combustible Solid With Reactant Consumption, D. Glenn Lasseigne, W. E. Olmstead

Mathematics & Statistics Faculty Publications

The effects of excessive reactant consumption on the ignition of a combustible solid are introduced through a revised scaling of the heat release constant. Large activation energy asymptotics then yields a new one-parameter integral equation governing the temperature evolution near ignition. Analysis of the integral equation reveals a critical value of the parameter which distinguishes between the cases of ignition and nonignition. © 1987 Society for Industrial and Applied Mathematics