Digital Commons Network^™

Turnpike Structures For Optimal Maneuvers, Arthur T. Benjamin

All HMC Faculty Publications and Research

This dissertation is concerned with problems of optimally maneuvering a collection of objects ("pieces") from one location to another, subject to various restrictions on the allowable movements. We illustrate and prove that when the "distance" from the origin to the destination is large, and the movement rules and environment satisfy certain "homogeneity" properties, there exist near-optimal trajectories with very special (turnpike) structure.

These results are obtained by representing the problem through a configuration graph. Here, we have a node for each configuration and an arc for every "different" legal move. Each arc is endowed with a scalar weight …

Random Sequential Absorption On Graphs, Nicholas Pippenger

All HMC Faculty Publications and Research

This paper analyzes a process whereby the vertices of a graph are considered in a random sequence,and each considered vertex is “occupied” unless it or an adjacent vertex has previously been occupied. The process continues until no more vertices can be occupied, at which point the “jamming limit” has been reached. The case in which the graph is regular (so that every vertex has degree $d\geqq 2$ and has “few short cycles” is treated. In particular, the results apply to infinite regular trees, to finite graphs obtained from them by forming quotient graphs, and to random regular graphs.

It is …

Augustine’S Mathematical Realism, Paul Zwier

ACMS Journal 2004

This paper begins by outlining an argument advanced against mathematical realism by Philip Kitcher. It then sketches the life and work of the great Christian philosopher and theologian, Augustine of Hippo. It discusses Augustine’s view that there exist eternal ideas in the mind of God that God used as templates in his creation of material objects. Among these are ideas about numbers and other mathematical objects. It also discusses Augustine’s understanding of how human beings have access to such ideas. It concludes with a discussion of some possible objections to Augustine’s perspective.

The Fourth Dimension And The Theology Of Edwin Abbott Abbott, Thomas Banchoff

ACMS Journal 2004

This paper is a brief biography of Edwin Abbott Abbott, author of Flatland, and a sketch of the main ideas in the book. It also incorporates some personal reflections.

Corrigendum, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Supercomputer Simulation Of Cracks And Fractures By Quasimolecular Dynamics, Donald Greenspan

Mathematics Technical Papers - Archive

The gross physical behavior of solids and liquids is the result of atomic or molecular reactions to external forces. Using molecular dynamics, we can study such reactions in the small, on the molecular level. In quasimolecular dynamics, molecules are aggregated into larger units, called quasimolecules, in order to simulate behavior in the large. Mass and energy conservation considerations are fundamental in this approach. In particular, we will simulate the generation of cracks in a slotted plate which, for illustrative purposes, is chosen to be of pure copper. CRAY X—MP/24 supercomputer examples are described and discussed.

Quantitative, Quasimolecular Modelling Of The Fall Of A Drop Into A Basin Of Water, Donald Greenspan, Mohsen Mahmoudi

Mathematics Technical Papers - Archive

The fall of a drop into a basin of water is simulated by a molecular aggregate approach. The dynamical equations are large systems of nonlinear, ordinary differential equations which are derived using conservation of mass and total energy. These equations have to be solved numerically. Supercomputer examples of backdrop and wave simulations are described and discussed.

Asymptotic Analysis Of Model Problems For A Coupled System, F. A. Howes, S. Shao

Mathematics and Statistics Faculty Publications

No abstract provided.

Neighborhoods Of Compacta In 4-Manifolds, Gerard A. Venema

University Faculty Publications and Creative Works

In this paper we investigate conditions under which a compact set in a piecewise linear 4-manifold has close neighborhoods with 1-dimensional spines. We prove that such neighborhoods exist in case the compactum satisfies the inessential loops condition and either has fundamental dimension 0 or has the shape of S1. Corollaries include two complement theorems and a weak flatness theorem for compacta in S4.

Quasimolecular Simulation Of Pendent Water Drops, Donald Greenspan

Mathematics Technical Papers - Archive

Pendent water drops are simulated by molecular aggregates, called quasimolecules. The quasimolecules interact in accordance with classical molecular type formulas. Supercomputer examples are described and discussed for both stationary and for falling drops.

Supercomputer Simulation Of Colliding Microdrops Of Water, Donald Greenspan

Mathematics Technical Papers - Archive

Microdrop collisions are important in fast kinetic, microwave, nucleation, and rainstorm studies. In this Paper a molecular model of colliding microdrops of water is simulated on a CRAY X-MP/24. A least squares fit of the force field allows relatively large time steps in the numerical procedure. Rotating "raindrop" modes, "dumbell" modes, and oscillatory oblateness modes are demonstrated, as are nonadhesive soft and hard collisions.

Dupin Submanifolds In Lie Sphere Geometry, Thomas E. Cecil, Shiing-Shen Chern

Mathematics and Computer Science Department Faculty Scholarship

No abstract provided.

Fixed Point Theorems For Compatible Multi-Valued And Single-Valued Mappings, Hideaki Kaneko, Salvatore Sessa

Mathematics & Statistics Faculty Publications

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued mapping.

On A Multi-Channel Queue With State Dependent Input Flow And Interruptions, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

This paper deals with a multi-channel queueing system with a finite waiting room but without losses. The latter is achieved by a temporary interruption of the input flow activity until the waiting room is ready to place a new customer. In addition, the input flow on its busy period is non-recurrent: It is state dependent and may be controlled over relevant times of decision making. A similar model without interruptions (i.e. with losses) was earlier studied by the author, where in particular, major probability characteristics of the queueing process in equilibrium were obtained. Now the author derives a simple explicit …

Mixed Modules In L, R. Gobel, Brendan Goldsmith

Articles

By assuming the set-theoretic hypothesis V = L we show that, for a large class of rings R, there exist, for any regular not weekly compact cardinals K, strongly k-cyclic mixed R-modules having endomorphism algebra isomorphic to the split extension of the R-algebra A by the ideal of bounded endomorphism provided A is free qua R-module and K./Az/

Partially Confluent Maps And N-Ods, Van C. Nall

Department of Math & Statistics Faculty Publications

Let f : X-->Y be a map between topological spaces. A Wf-set in Y is a continuum in Y which is the image under f of a continuum in X. The map f is partially confluent if each continuum in Y is the union of a finite number of Wf-sets, and n-partially confluent if each continuum in Y is the union of n Wf-sets. In this paper, it is shown that every partially confluent map onto an n-cell is weakly confluent. Also, the relationship between partially confluent maps and continua which …

Identifying Outliers In A Random Effects Model For Longitudinal Data, Tamarah Crouse Dishman

UNF Graduate Theses and Dissertations

Identifying non-tracking individuals in a population of longitudinal data has many applications as well as complications. The analysis of longitudinal data is a special study in itself. There are several accepted methods, of those we chose a two-stage random effects model coupled with the Estimation Maximization Algorithm (E-M Algorithm) . Our project consisted of first estimating population parameters using the previously mentioned methods. The Mahalanobis distance was then used to sequentially identify and eliminate non-trackers from the population. Computer simulations were run in order to measure the algorithm's effectiveness.

Our results show that the average specificity for the repetitions for …

A Theory Of Testability With Application To Fault Coverage Analysis, Sharad Seth, Vishwani Agrawal, Hassan Farhat

Mathematics Faculty Publications

When test vectors are applied to a circuit, the fault coverage increases. The rate of increase, however, could be circuit-dependent. In fact, the actual rise of fault coverage depends on the characteristics of vectors, as well as, on the circuit. The paper shows that the average fault coverage can be computed from circuit testability. A relationship between fault coverage and circuit testability is derived. The mathematical formulation allows computation of coverage for deterministic and random vectors. Applications of this analysis include: determination of circuit testability from fault simulation, coverage prediction from testability analysis, prediction of test length, and test generation …

Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn

Mathematics Faculty Publications

The techniques developed by Wage and Norden are used to show that the Pixley-Roy hyperspaces of any two ω-graphs are homeomorphic. The Pixley-Roy hyperspaces of several subsets of Rⁿ are also shown to be homeomorphic.

Optimal Intervals For Third Order Lipschitz Equations, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

For the third order differential equation (see PDF), subintervals of (a,b) of maximal length are characterized, in terms of the Lipschitz coefficients (see PDF) on which certain boundary value problems possess unique solutions. The techniques for determining best interval length involve applications of the Pontryagin Maximum Principle along with uniqueness implies existence arguments.

Maximal Order Abelian Subgroups Of Symmetric Groups, J. M. Burns, Brendan Goldsmith

Articles

No abstract available

On Almost-Free Modules Over Complete Discrete Valuation Rings, Brendan Goldsmith, R. Gobel

Articles

No abstract available

On The Existence And Symmetry Properties Of Finite Total Mass Solutions Of The Matukuma Equation, The Eddington Equation And Their Generalizations, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Minimal Convex Extensions And Intersections Of Primary I-Ideals In F-Rings, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Minimal Convex Extensions And Intersections Of Primary I-Ideals In F-Rings, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Efficient Multiple-Precision Evaluation Of Elementary Functions, David M. Smith

Mathematics, Statistics and Data Science Faculty Works

Let M(t) denote the time required to multiply two t-digit numbers using base b arithmetic. Methods are presented for computing the elementary functions in O(t^1/3 M(t)) time.

A Less-Polluted Future For Boston Harbor?: Assessing Selected Impacts Of A Citizen Information Program, Enid Carol Kumin

Marine Affairs Theses and Major Papers

The demand for good public information is a need which many environmental groups are now attempting to fill. Programs are generally designed around a particular environmental issue. One such effort is the Boston Harbor "Sewer Tour" Program run by 'Save the Harbor/Save the Bay' in Boston, Massachusetts. The Sewer Tour Program addresses matters of water pollution control in the Metropolitan Boston area. The present study examines the impact of the Sewer Tour Program on participants and spillover effects on their communities. A mailed survey is used to collect the data. A framework for data analysis is drawn from psychological research …

A Nonlinear Eigenvalue Problem In Astrophysical Magnetohydrodynamics: Some Properties Of The Spectrum, John A. Adam

Mathematics & Statistics Faculty Publications

The equations of ideal magnetohydrodynamics (MHD) with an external gravitational potential—a ‘‘magnetoatmosphere’’—are examined in detail as a singular nonlinear eigenvalue problem. Properties of the spectrum are discussed with specific emphasis on two systems relevant to solar magnetohydrodynamics. In the absence of a gravitational potential, the system reduces to that of importance in MHD and plasma physics, albeit in a different geometry. This further reduces to a form isomorphic to that derived in the study of plasma oscillations in a cold plasma, Alfvén wave propagation in an inhomogeneous medium, and MHD waves in a sheet pinch. In cylindrical geometry, the relevant …

Impedance Controlled Connector Interface, Stephen L. Clark

Mathematics and Statistics Faculty Research & Creative Works

A connector interface for electrically mating a multi-row connector with a printed circuit board is defined by a flex circuit in the form of laminated polyimide layers having conductive traces for each interconnect pair with connection fields at the opposite ends of the traces for electrical connection to the terminal pins on the connector and the conductive pads or pins on the circuit board. The conductive traces are all of equal length to provide equal resistance and impedance paths for each of the circuit interconnects.

The Strong Perfect Graph Conjecture For Pan-Free Graphs, Stephan Olariu

Computer Science Faculty Publications

A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the largest number ω(F) of pairwise adjacent vertices in F. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement G contains an odd chordless cycle of length at least five. Its resolution has eluded researchers for more than twenty years. We prove that the conjecture is true for a class of graphs which strictly contains the claw-free graphs.