Physical Sciences and Mathematics Commons^™

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 …

The Further Geometry Of Grain Boundaries In Hexagonal Close-Packed Metals, Fu-Rong Chen, Alexander H. King

Alexander H. King

A technique is given for finding partial DSC vectors appropriate to crystals with more than one atom per lattice site. The DSC lattice is made up of vectors that represent displacements of one crystal with respect to the other that leave the boundary structure shifted, but not complete. A new, rapid method for finding the step vectors associated with perfect DSC dislocations is described. Partial DSC vectors and step vectors for perfect DSC dislocations in hexagonal close-packed crystals are determined. The availability of reactions between lattice partial dislocations and grain boundaries in hexagonal close-packed crystals is also assessed.

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

Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell

All HMC Faculty Publications and Research

The dynamics of two‐dimensional Rayleigh–Bénard convection rolls are studied in a finite layer with no‐slip, fixed temperature upper and lower boundaries and no‐slip insulating side walls. The dominant mechanism controlling the number of rolls seen in the layer is an instability concentrated near the side walls. This mechanism significantly narrows the band of stable wavenumbers although it can take a time comparable to the long (horizontal) diffusion time scale to operate.

Designing The Optimal Placement Of Spaces In A Parking Lot, R. Bingle, D. Meindertsma, W. Oostendorp, Gene A. Klaasen

University Faculty Publications and Creative Works

We develop a method for determining the optimal size and placement of parking spaces and approach aisles for an automobile parking lot. In particular, our solution concerns a parking lot of size 100' x 200' located at the corner of an intersection of two streets in a New England town. We begin by arguing the superiority of driver operation over attendant operation of vehicles to be parked. Then a statistical analysis is performed on a sampling of 160 1987 model automobiles to determine upper bounds and ideal values for the length and width of a parking space and for the …

Deconvolution Techniques With Applications In Cardiovascular Systems Analysis, Lakshminarayan Rajaram

Theses

System characterization by means of Impulse and Frequency Response Functions are well known in classical linear systems analysis. Impulse Response Function is a time domain description of a linear system where as the Frequency Response Function represents the frequency domain counterpart. Linear systems are often characterized in frequency domain. In many biological research applications, it becomes necessary to examine the impulse response function in order to understand the behavior of the system under investigation. One such application is the arterial system in cardiovascular dynamics. It has been shown that although both representations are identical, some aspects of the arterial system …

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.

Sight - A Tool For Building Multi-Media Structured-Document Interactive Editing And Formatting Applications, Robert F. Gordon Ph.D., George B. Leeman Jr, Christian L. Cesar, Mark A. Martin

Faculty Works: MCS (1984-2023)

SIGHT is a tool for building applications that edit and format multi-media structured documents. The media supported include text, line graphics, handwriting, images and audio. These information media are maintained in a single integrated hierarchical database. The document architecture models documents as trees in which nodes can be shared, i.e., as directed acyclic graphs. For each document there is a logical (or abstract) represention tree and one or more physical (or layout) representation trees. A physical representation is the result of applying the formatter to a logical representation. Both trees are separate but share document content data. The physical representation …

Alphabetic Minimax Trees Of Degree At Most T*, D. Coppersmith, Maria M. Klawe, Nicholas Pippenger

All HMC Faculty Publications and Research

Problems in circuit fan-out reduction motivate the study of constructing various types of weighted trees that are optimal with respect to maximum weighted path length. An upper bound on the maximum weighted path length and an efficient construction algorithm will be presented for trees of degree at most t, along with their implications for circuit fan-out reduction.

Reliable Computation In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.

A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …

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 …

On Common Subgraphs, Hung Bin Zou

Dissertations

A greatest common (induced) subgraph of graphs G(,1) and G(,2) of equal size is a (an induced) common subgraph (without isolated vertices) of G(,1) and G(,2) having maximum size. For a given graph L, a graph G is locally L if the induced subgraph of the neighborhood of each vertex of G is isomorphic to L (L is called a common link). Several topics concerning these concepts are investigated in this dissertation. An historical background to these topics is given in Chapter I.

Chapter II is devoted to the topic on highly connected unique greatest common subgraphs of graphs. We …

Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be …

On Universal Tests For The Truth Of World Views: Their Existence And Identifiability, William Buttelmann, Paul Fienberg

ACMS Conference Proceedings 1985

In his book, Christian Apologetics, Norman Geisler proposes a universal test for the truth of world views. We examine this concept and find that it raises serious difficulties. This paper first presents some basic definitions for "world view" and "truth-value of a world view," then studies the concept of a universal test for the truth of world views in light of these definitions. Geisler has proposed what amounts to a universal decision procedure to determine the truth-value of world views. We show that, in the general case, no such universal decision procedure exists. Whether or not such universal tests for …

Selected Bibliography Of Donald Maccrimmon Mackay, Gene B. Chase

ACMS Conference Proceedings 1985

A selected bibliography of Donald MacCrimmon MacKay, including his written works and biographical sources.

Random Genetic Drift Diffusion Model And Deterministic And Stochastic Models Of Epidemics, Norman W. Loney

Theses

In the Random Genetic Drift Diffusion model two approaches are taken. First we examined a discrete model that represent a relatively idealised version of the phenomena. Hefurther make the assumption that the Population reproduces itself and then dies, thus maintaining a finite population size at all times. If at a given locus there are two possible allels A and B and if X(t) is the number of A type in the genetic pool of size 2N, then 2N-X(t) is the number of B type. We then proceed to obtain a probability density function of X( t) by an Exact method …

Introduction (1985), Robert Brabenec

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Table Of Contents (1985), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Application Interface Development Environment, Robert F. Gordon Ph.D., Barry E. Willner

Faculty Works: MCS (1984-2023)

RC 11160 (#50246)

The user of interactive systems must learn a different interface for each system he uses. Furthermore the designer of such systems has limited guidelines to create good user interfaces. We describe an application interface development environment, AIDE, in which one can create and select multiple interfaces easily for a given application, and conversely one can create multiple applications with a given interface. This benefits the end-user by providing the possibility of familiar, even identical, interfaces among wide ranges of products, and this helps the designer by supporting Human Factors testing of interfaces. We formulate a model of …

Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri

Mathematics and Statistics Faculty Publications

A Cramer type large deviation theorem is proved under alternatives as well as under hypothesis for the generalized linear rank statistic which includes as special cases (unsigned) linear rank statistics, signed linear rank statistics, linear combination of functions of order statistics, and a rank combinatorial statistic.

Some Graph-Colouring Theorems With Applications To Generalized Connection Networks, David G. Kirkpatrick, Maria M. Klawe, Nicholas Pippenger

All HMC Faculty Publications and Research

With the aid of a new graph-colouring theorem, we give a simple explicit construction for generalized n-connectors with 2k - 1 stages and O( n^{1 + 1 / k} (log n )^{( k - 1)/ 2} ) edges. This is asymptotically the best explicit construction known for generalized connectors.

On The Eigenvalue Problem For Toeplitz Matrices Generated By Rational Functions, William F. Trench

William F. Trench

We give formulas for the characteristic polynomial and eigenvectors of of $n\times n$ Toeplitz matrices generated by a formal Laurent series of a rational function $R(z)$. The formulas are in terms of a certain fixed polynomial with coefficients that are simple functions of $\lambda$ and the coefficients of $R(z)$. The complexity of the formulas is independent of $n$.

On The Eigenvalue Problem For Toeplitz Band Matrices, William F. Trench

William F. Trench

No abstract provided.

Concepts And Implications Of Interactive Recovery, Robert F. Gordon Ph.D., George B. Leeman Jr, Clayton H. Lewis

Faculty Works: MCS (1984-2023)

RC 10562 (#47293)

When working interactively on the computer, it is valuable to be able to undo a series of commands in order to return to a previous state. We identify contradictions and limitations in the basic concepts of undo. We introduce three types of undo functions with which we examine the characteristics of undo, explain these limitations, and determine the minimum requirements for a recovery facility. Then we discuss the implications of undo for user interfaces and suggest au.xiliary functions to display and simplify the resulting history structure and to view and recover prior states.

Optimal Stochastic Scheduling Of Power Generation Systems With Scheduling Delays And Large Cost Differentials, G. L. Blankenship, J.-L. Menaldi

Mathematics Faculty Research Publications

The optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law. We study the behavior of this optimality system in terms of two parameters: (i) a scheduling delay, e.g., the startup time of a generation unit; and (ii) the relative magnitudes of the costs (operating or starting) of different units. In the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay, and, as the delay approaches zero, that …

A Note On Irreducibility And Weak Covering Properties, Joe Mashburn

Mathematics Faculty Publications

A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N₁-compactness. …

It is shown in this paper that T₁ δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T₁ nor …

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …

Uniqueness Of Positive Solutions For A Class Of Elliptic Boundary Value Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.