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Mathematics & Statistics Faculty Publications

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Articles 211 - 226 of 226

Full-Text Articles in Physical Sciences and Mathematics

A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam Jan 1988

A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam

Mathematics & Statistics Faculty Publications

A diffusion model of the prevascular stage of tumor growth is presented. The basic feature of such a model is the diffusion of growth inhibitor, which is produced at a spatially non-uniform rate within the tissue. Regimes of limited and unlimited tissue growth are determined, and the consistency of this and simpler models is discussed in the light of observational results.

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Ignition Of A Combustible Solid With Reactant Consumption, D. Glenn Lasseigne, W. E. Olmstead Jan 1987

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

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Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman Jan 1987

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQn(x) = zn-1 exp[ -Hn(x)]Π dP(xj), where x = (x1,..., xn) ∈ Rn, where Hn is the Hamiltonian, zn is …

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On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke Jan 1986

On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …

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Large Deviation Local Limit Theorems For Arbitrary Sequences Of Random Varibles, Narasinga Rao Chaganty, J Sethuraman Jan 1985

Large Deviation Local Limit Theorems For Arbitrary Sequences Of Random Varibles, Narasinga Rao Chaganty, J Sethuraman

Mathematics & Statistics Faculty Publications

The results of W. Richter (Theory Prob. Appl. (1957) 2 206-219) on sums of independent, identically distributed random variables are generalized to arbitrary sequences of random variables Tn. Under simple conditions on the cumulant generating function of Tn, which imply that Tn/n converges to zero, it is shown, for arbitrary sequences {mn}, that kn (mn), the probability density function of Tn/n at mn, is asymptotic to an expression involving the large deviation rate of Tn/n. Analogous results for lattice …

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On The First Passage Time Distribution For A Class Of Markov Chains, Mark Brown, Narasinga Rao Chaganty Jan 1983

On The First Passage Time Distribution For A Class Of Markov Chains, Mark Brown, Narasinga Rao Chaganty

Mathematics & Statistics Faculty Publications

Consider a stochastically monotone chain with monotone paths on a partially ordered countable set S. Let C be an increasing subset of S with finite complement. Then the first passage-time from i ∈ S to C is shown to be IFRA (increasing failure rate on the,av;rage). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.

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Quantitative Estimates For Lp Approximation With Positive Linear Operators, J. J. Swetits, B. Wood Jan 1983

Quantitative Estimates For Lp Approximation With Positive Linear Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

Quantitative estimates for approximation with positive linear operators are derived. The results are in the same vein as recent results of Berens and DeVore. Two examples are provided.

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Local Lp-Saturation Of Positive Linear Convolution Operators, J. J. Swetits, B. Wood Jan 1982

Local Lp-Saturation Of Positive Linear Convolution Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

Local Lp-saturation of positive linear convolution operators is investigated. Results are obtained for two important classes of operators previously studied by Bojanic, DeVore, Korovkin and the authors.

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Unbounded Functions And Positive Linear-Operators, J. J. Swetits, B. Wood Jan 1982

Unbounded Functions And Positive Linear-Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

The approximation of unbounded functions by positive linear operators under multiplier enlargement is investigated. It is shown that a very wide class of positive linear operators can be used to approximate functions with arbitrary growth on the real line. Estimates are given in terms of the usual quantities which appear in the Shisha-Mond theorem. Examples are provided.

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Smallest Cubic And Quartic Graphs With A Given Number Of Cutpoints And Bridges, Gary Chartrand, Farrokh Saba, John K. Cooper Jr., Frank Harary, Curtiss E. Wall Jan 1982

Smallest Cubic And Quartic Graphs With A Given Number Of Cutpoints And Bridges, Gary Chartrand, Farrokh Saba, John K. Cooper Jr., Frank Harary, Curtiss E. Wall

Mathematics & Statistics Faculty Publications

For positive integers b and c, with c even, satisfying the inequalities b+1≤c≤2b, the minimum order of a connected cubic graph with b bridges and c cutpoints is computed. Furthermore, the structure of all such smallest cubic graphs is determined. For each positive integer c, the minimum order of a quartic graph with c cutpoints is calculated. Moreover, the structure and number of all such smallest quartic graphs are determined.

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A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood Jan 1980

A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

A saturation theorem and an asymptotic theorem are proved for an optimal, discrete, positive algebraic polynomial operator. The operator is based on the Gauss-Legendre quadrature formula.

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Note: On Summability And Positive Linear Operators, J. J. Swetits Jan 1979

Note: On Summability And Positive Linear Operators, J. J. Swetits

Mathematics & Statistics Faculty Publications

Quantitative estimates for approximation by positive linear operators are obtained with the use of a summability method which includes both convergence and almost convergence.

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Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke Jan 1979

Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by …

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Complementary Extremum Principles, J. Swetits, C. Rogers Jan 1978

Complementary Extremum Principles, J. Swetits, C. Rogers

Mathematics & Statistics Faculty Publications

Important complementary extremum principles are generated without recourse to general variational theory. The results are illustrated by an application to a class of boundary value problems in Magnetohydrodynamics.

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Approximation By Discrete Operators, J. J. Swetits, B. Wood Jan 1978

Approximation By Discrete Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained.

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Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam Jan 1977

Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam

Mathematics & Statistics Faculty Publications

The inhomogeneous wave equation for a special class of magnetoatmospheric waves is formally solved, and the principle of stationary phase used to provide information on the group velocity properties of such waves. General results are presented concerning the associated mechanical energy flux. The basic problem considered is relevant to waves initiated by sudden events in the solar atmosphere.

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