Physical Sciences and Mathematics Commons^™

Quasilinearization For Some Nonlocal Problems, Yunfeng Yin

Mathematics and System Engineering Faculty Publications

The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation ut – Lu = f{t,x,u) with nonlocal boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is relaxed by requiring f(t,x,u) Muz to be convex for some M > 0. The quadratic convergence of monotone sequence is obtained.

Optimal Controllability Of Impulsive Control Systems, Farzana A. Mcrae

Mathematics and System Engineering Faculty Publications

The problem of optimal controllability of a nonlinear impulsive control system is studied using the method of vector Lyapunov functions and the generalized comparison principle.

A Bulk Queueing System Under N-Policy With Bilevel Service Delay Discipline And Start-Up Time, David C.R. Muh

Mathematics and System Engineering Faculty Publications

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r (≥ 1), the system, with server capacity Λ, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥ r). Two cases, with N ≦ R and N ≥ R, are studied. The author finds explicitly the probability generating function of the stationary distribution of …

On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions and periodic solutions is studied for a system of infinite delay integral equations having nonlinear perturbations. An equivalent system of equations is obtained in terms of the resolvent kernel. Then the existence results are shown for the equivalent equations. Contraction principle, Schauder’s fixed point theorem, and monotone method are used in the study.

On The Positive Solutions Of The Matukuma Equation, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Uniqueness Criterion For Solution Of Abstract Nonlocal Cauchy Problem, Ludwik Byszewski

Mathematics and System Engineering Faculty Publications

The aim of the paper is to prove an uniqueness criterion for a solution of an abstract nonlocal Cauchy problem. A dissipative operator in the nonlocal problem and an arbitrary functional in the nonlocal condition are considered. The paper is a continuation of papers [l]-[3] and generalizes some results from [4].

Induced Mach Wave-Flame Interactions In Laminar Supersonic Fuel Jets, F. Q. Hu, T. L. Jackson, D. G. Lasseigne, C. E. Grosch

Mathematics & Statistics Faculty Publications

A model problem is proposed to investigate the steady response of a reacting, compressible laminar jet to Mach waves generated by wavy walls in a channel of finite width. The model consists of a two-dimensional jet of fuel emerging into a stream of oxidizer which are allowed to mix and react in the presence of the Mach waves. The governing equations are taken to be the steady parabolized Navier-Stokes equations which are solved numerically. The kinetics is assumed to be a one-step, irreversible reaction of the Arrhenius type. Two important questions on the Mach wave-flame interactions are discussed: (i) how …

Erratum: "Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line" [Physics Of Fluids A 4, 2008 (1992)], D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

Erratum to:

Lasseigne, D. G., Jackson, T. L., & Hu, F. Q. (1992). Temperature and suction effects on the instability of an infinite swept attachment line. Physics of Fluids A: Fluid Dynamics, 4(9), 2008-2012. doi:10.1063/1.858370

A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL^-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …

Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91

All HMC Faculty Publications and Research

In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.

On The Construction Of A Potential From Cauchy Data, Lester Caudill, Bruce D. Lowe

Department of Math & Statistics Faculty Publications

We investigate the problem of recovering a potential q(y)in the differential equation:

-∆u+q(y)u = 0, (x, y) ∈ (0, 1) x (0, 1),
u(0, y) = u(1, y) = u(x, 0) = 0,
u(x, 1) = f(x), u_y(x, 1) = g(x).

The method of separation of variables reduces the recovery of q(y) to a nonstandard inverse Sturm-Liouville problem. An asymptotic formula is developed that suggests that under appropriate conditions on the Cauchy pair (f, g), q(y) is uniquely determined up to the mean. Moreover, the recovery of …

Quasi-Brittle Graphs, A New Class Of Perfectly Orderable Graphs, Stephan Olariu

Computer Science Faculty Publications

A graph G is quasi-brittle if every induced subgraph H of G contains a vertex which is incident to no edge extending symmetrically to a chordless path with three edges in either Hor its complement H¯. The quasi-brittle graphs turn out to be a natural generalization of the well-known class of brittle graphs. We propose to show that the quasi-brittle graphs are perfectly orderable in the sense of Chvátal: there exists a linear order < on their set of vertices such that no induced path with vertices a, b, c, d and edges ab, bc, cd has a < b and d < c.

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

A Numerical Study Of Wave Propagation In A Confined Mixing Layer By Eigenfunction Expansions, Fang Q. Hu

Mathematics & Statistics Faculty Publications

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance …

The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li

Mathematics & Statistics Faculty Publications

The purpose of this paper is to derive the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations. The Lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp.

The Dynamics Of Growth-Factor-Modified Immune-Response To Cancer Growth: One-Dimensional Models, J. A. Adam

Mathematics & Statistics Faculty Publications

By characterizing the effect of tumor growth factors as deviations from normal logistic-type growth rates, the spatio-temporal dynamics for a one-dimensional model of cancer growth incorporating immune response are studied. The growth rates considered are classified respectively as normal, activated, inhibited and delay activated. The homogeneous steady states are defined by relative extrema of a ''free energy'' function V(x) for each of the above four cases. This function is of particular importance in studying the coexistence of tumoral and cancer-free steady states, and in identifying the nature (progressive or regressive) of travelling wave solutions to the nonlinear partial differential equation …

Optimal Greedy Algorithms For Indifference Graphs, Peter J. Looges, Stephan Olariu

Computer Science Faculty Publications

A fundamental problem in social sciences and management is understanding and predicting decisions made by individuals, various groups, or the society as a whole. In this context, one important concept is the notion of indifference. We characterize the class of indifference graphs, that is, graphs which arise in the process of quantifying indifference relations. In particular, we show that these graphs are characterized by the existence of a special ordering of their vertices. As it turns out, this ordering leads naturally to optimal greedy algorithms for a number of computational problems, including coloring, finding a shortest path between two vertices, …

Scattering Parameters For An Epstein Profile In A Half-Space, J. A. Adam

Mathematics & Statistics Faculty Publications

The reflection of waves for a stratified medium in (-∞, ∞) can be studied by transforming the hypergeometric differential equation into a wave equation. In the context of an astrophysical problem [1], the corresponding analysis is carried out for an Epstein profile in (0, ∞). This profile represents a scattering potential in quantum mechanical terminology: its properties are briefly discussed.

The Scattering Potential For A Polytrope Of Degree-5, J. A. Adam

Mathematics & Statistics Faculty Publications

By regarding the study of radial and non-redial stellar oscillations as a problem in potential scattering theory, a standard form of the radial Schrödinger equation can be derived. After establishing some preliminary results of astrophysical interest, an analytic expression for the potential is derived for a truncated (i.e., finite radius) polytrope (or class of self-gravitating compressible spheres) of degree n = 5. Properties of the potential are discussed.

Temporal Model Of An Optically Pumped Co-Doped Solid State Laser, T. G. Wangler, J. J. Swetits, A. M. Buoncristiani

Mathematics & Statistics Faculty Publications

Currently, research is being conducted on the optical properties of materials associated with the development of solid-state lasers in the 2 micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are obtained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

Integrated Computer Controlled Sensor Monitor, Tariq Hafeez Malik

Theses : Honours

This research has developed an Integrated Computer Controlled Sensor Monitor (ICCSM) environment, to monitor and analyse alarm events associated with sensors, including an interface between a PC and a number of detectors. Such an environment will help the security industry analyse the factors causing false alarms at particular locations. The ICCSM environment monitors, and records, alarm data. Knowing exactly which sensor has been activated, and its location, is of paramount importance to the effective deployment of response forces and making the identification of causes of spurious alarms easier. The lCCSM environment is a combination of software and general purpose hardware, …

Decay Of The Relative Error In The Formation Of Acoustic Bullets, Harry E. Moses, Reese T. Prosser

Dartmouth Scholarship

In a previous paper, the authors showed how to construct certain solutions of the acoustic and electromagnetic wave equations in three dimensions, which are constrained asymptotically to a narrow conical sector of an outgoing spherical shell, i.e., which behave like “bullets.” In this paper, it is shownthat, in the acoustic case, the magnitude of the relative error between the true solution and its asymptotic form decays in time according to an inverse square root law.
Read More: https://epubs.siam.org/doi/10.1137/0153025

Construction Of Process Control Charts Using Asymmetric Data, Bruce Sivwright

Theses : Honours

As part of my undergraduate degree I studied various areas in quality control. Included in these areas of study was the concept of control charts, which are becoming increasingly more important in industry for effective manufacturing processes. The general form for constructing a control chart assumes that the outcomes of the process conform to a normal distribution. Data gathered at an industrial site in Western Australia illustrates that this is not always the case. The distribution of the data collected for a specific manufacturing process was found to be significantly different from the normal distribution, in that it was right …

A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

Sliding Mode Control Of The Systems With Uncertain Direction Of Control Vector, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

Vertex Coloring For Weighted Graphs With Application To Timetabling, Lynn Kiaer, Jay Yellen

Mathematical Sciences Technical Reports (MSTR)

This paper applies the methods of vertex coloring to timetabling problems

Theory And Implementation Of Wavelet Analyses In Rational Resolution Decompositions, Bruce P. Anderson

Theses and Dissertations

The multiresolution analysis (MRA) developed by Mallat and Meyer and further discussed by Daubechies is a useful tool in the analysis of sampled signals such as images and speech. This thesis develops the theory and implementation of a rational-resolution analysis (RRA) as an extension of the dyadic MRA for arbitrary rational dilation factors. We present a method to calculate families of compactly-supported scaling functions and wavelets based on arbitrary integer dilation factors and provide examples. The perfect- reconstruction properties of the RRA are discussed and it is demonstrated that the compactly-supported scaling functions and wavelets do not yield perfect- reconstruction. …

A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly Tucker Perry

Dissertations

The purpose of this dissertation was to explore the appropriateness of testing the equality of two means using either a t test, the Welch test, or the Mann-Whitney-Wilcoxon test for two independent samples based on the results of using two classes of preliminary tests. One class of preliminary tests determines whether the population variances differ, and the other class ascertains if the underlying distributions are symmetric or skewed. The F-ratio test and the Levene test (using the median) were compared as preliminary tests for variance homogeneity; and the DAgostino Sy and the Triples tests were also compared as preliminary tests …

Multivariate Quadrature On Mimd Machines With Shared Or Distributed Memory, Ignatios E. Vakalis

Dissertations

For a procedure as numerical integration, of high computational expense which is used extensively in large-scale computations, it is natural to aim at the design of algorithms which can be used on parallel computes. This work deeds with the design of efficient and portable parallel algorithms on MIMD (Multiple Instruction Multiple Data) architectures with shared memory, and on distributed memory systems.

A parallel global adaptive algorithm is presented for multivariate integration over simplex type regions. Process synchronization is achieved through the use of monitors. Macros were developed, for managing the task pool with a heap data structure. Layered over the …