Applied Mathematics Commons^™

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

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 …

Maximal And Maximum Independent Sets In Graphs, Jiuqiang Liu

Dissertations

A maximal independent set of a graph G is an independent set which is not contained properly in any other independent set of G. An independent set is called maximum if it is of largest cardinality. Denote i(G) to be the number of maximal independent sets of G. These special sets and the parameter i(G) have interested many researchers leading to a number of properties and results. One of these is the determination of the maximum number of maximal independent sets among all graphs of order n, and the external graphs. In this investigation,we develop new properties for …

Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic

Aviation Department Publications

In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …

Existence, Uniqueness, And Numerical Analysis Of Solutions Of A Quasilinear Parabolic Problem, Dongming Wei

Mathematics Faculty Publications

A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are L² error estimates for the error between the extended fully discrete finite element solutions and the exact solution.

Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar

Mathematics Faculty Research Publications

A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.

A Center Of A Polytope: An Expository Review And A Parallel Implementation, S. K. Sen, Hongwei Du, Donald W. Fausett

Mathematics and System Engineering Faculty Publications

The solution space of the rectangular linear system Ax = b, subject to x ≥ 0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem. © 1993, Hindawi Publishing Corporation. All rights reserved.

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

Data On Four-Rewriteability In Finite Groups, Sharon A. Kineke

Mathematical Sciences Technical Reports (MSTR)

A four-tuple of elements, (x₁,x₂,x₃,x₄), from a finite group, G, is said to be

rewriteable (see [l], [2], [3]) by p where p is an element of the symmetric group on four symbols, if
x₁x₂x₃x₄ = x_p(l)x_p(2)x_p(3)x_p(4)

The entry at the intersection of the G-th row and j-th column of each table on the succeeding three pages is the number of four-tuples from G which are rewriteable by exactly j permutations in the symmetric group …

Tem Observations Of The Mechanism Of Delamination Of Chromium Films From Silicon Substrates, D. Goyal, Alexander H. King

Alexander H. King

We have observed the complete delamination of polycrystalline chromium films from single crystal silicon substrates during deposition due to the formation of high internal stresses. These intrinsic stresses can give rise to interfacial defects which assist in the separation of the film from the substrate. Stresses in the film are balanced by stresses in the substrate, which cause mechanical failure in the substrate near the interface. Extensive arrays of dislocations and cracking of the substrate have been observed. We find that the delamination of the films from the substrate is initiated by the formation of damage in the substrate, rather …

Automorphisms Of The Lattice Of Recursively Enumerable Sets: Promptly Simple Sets, Peter Cholak, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

We show that for every coinfinite r.e. set A there is a complete r.e. set B such that ℒ⋆(A)≈ ℒ⋆(B) and that every promptly simple set is automorphic (in f⋆) to a complete set.

A Note On The Connectedness Problem For Nest Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

It has been conjectured that a certain operator T belonging to the group ff of invertible elements of the algebra Alg Z of doubly infinite uppertriangular bounded matrices lies outside the connected component of the identity in W. In this note we show that T actually lies inside the connected component of the identity of & .

Combination Of Orthogonality And Simplex Method For Solving Linear Programming, G.R. Jahanshahloo, S. Abbasbandy

Saeid Abbasbandy

For obtaining an optimal solution in L.P. combination of orthogonality and simplex method is used. It seems that the number of iteration is reduced.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Yi Li

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

Generalized Two Point Boundary Value Problems. Existence And Uniqueness, K. N. Murty, Seenith Sivasundaram

Mathematics and System Engineering Faculty Publications

An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

Extremal Solutions To A Class Of Multivalued Integral Equations In Banach Space, Sergiu Aizicovici, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.

Lyapunov Stability Theory For Dynamic Systems On Time Scales, Billur Kaymakçalan

Mathematics and System Engineering Faculty Publications

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov’s second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

Existence Of A Solution Of A Fourier Nonlocal Quasilinear Parabolic Problem, Ludwik Byszewski

Mathematics and System Engineering Faculty Publications

The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder’s theorem is used. The paper is a continuation of papers [l]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …

On A Multilevel Controlled Bulk Queueing System Mx/Gr,R/1, Lev M. Abolnikov, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors introduce and study a class of bulk queueing systems with a compound Poisson input modulated by a semi-Markov process, multilevel control service time and a queue length dependent service delay discipline. According to this discipline, the server immediately starts the next service act if the queue length is not less than r; in this case all available units, or R (capacity of the server) of them, whichever is less, are taken for service. Otherwise, the server delays the service act until the number of units in the queue reaches or exceeds level r. The authors establish a necessary …

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Mathematics and Statistics Faculty Publications

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H^1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.

On A First Passage Problem In General Queueing Systems With Multiple Vacations, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled …

Existence Of Approximate Solution To Abstract Nonlocal Cauchy Problem, Ludwik Byszewski

Mathematics and System Engineering Faculty Publications

The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

Automorphisms Of The Lattice Of Recursively Enumerable Sets: Orbits, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

No abstract provided.

Rewriteability In Finite Groups, Judy Leavitt Walker, G. J. Sherman, Mark E. Walker

Department of Mathematics: Faculty Publications

What's the probability that two elements in a finite group commute? A formal answer,

Pr₂(G) = {(x, y) [element of] G² |xy = yx}| / |G|²

begs our next question. How many ordered pairs of elements of a finite group commute?