Physical Sciences and Mathematics Commons^™

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

Mathematics Technical Papers

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.

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

Articles

No abstract available

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/

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.

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.

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.

Quasimolecular Simulation Of Pendent Water Drops, Donald Greenspan

Mathematics Technical Papers

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.

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

Articles

No abstract available

A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu

Computer Science Faculty Publications

H. Meyniel proved that in every minimal imperfect graph, every pair of vertices is joined by a chordless path containing an odd number of edges. We conjectured that in every minimal imperfect graph, every pair of vertices is joined by a path containing an even number of edges. We give an equivalent version of this new conjecture.

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.

Corrigendum, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Dilatations Des Commutants D'Opérateurs Pour Des Espaces De Krein De Fonctions Analytiques, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

Let K1 and K2 be two Krein spaces of functions analytic in the unit disk and invariant for the left shift operator R0(R0f(z)=(f(z)−f(0))/z), and let A be a linear continuous operator from K1 into K2 whose adjoint commutes with R0. We study dilations of A which preserve this commuting property and such that the Hermitian forms defined by I−AA∗ and I−BB∗ have the same number of negative squares. We thus obtain a version of the commutant lifting theorem in the framework of Krein spaces of analytic functions. To prove this result we suppose that the graph of the operator A∗, …

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.

Organizational Inducements And Social Motives: A Game Theoretic Analysis, Richard G. Davis

Dissertations and Theses

Game theory was used to analyze compensation systems based on individual and group incentives. Payoff formulas were developed for these incentives assuming different preferences for individual and social outcomes. Two levels of contributions were considered: (1) Defection. The minimum acceptable level of contributions, and (2) Cooperation. A level of discretionary contributions above the minimum. The discretionary contributions associated with cooperation were represented as a cost to the individual.

A classification scheme for uniform n-person games was developed using the approach of Rappaport and Guyer (1966) for 2 x 2 games. This classification scheme defines the natural outcome (cooperation or defection) …

Spectral Continuity In Complex Interpolation, Karen Saxe, D. Herrero

Karen Saxe

No abstract provided.

General Functional Differential Systems With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.

Existence Of Solutions Of Functional-Differential Systems With Prescribed Asymptotic Behavior, William F. Trench

William F. Trench

No abstract provided.

Letter From The Editor, Issue 3, 1988, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

A Humanistic Academic Environment For Learning Undergraduate Mathematics, Clarence F. Stephens

Humanistic Mathematics Network Journal

No abstract provided.

Letter From A Harvey Mudd College Student, Chris Jewell

Humanistic Mathematics Network Journal

No abstract provided.

Increasing Learning By Decreasing Math Anxiety, Gregg Turner

Humanistic Mathematics Network Journal

No abstract provided.

An Innovative Curriculum Idea For The First Two Years Of College Mathematics, Larry Copes

Humanistic Mathematics Network Journal

No abstract provided.

For Whom Nobel Tolls, William Dunham

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Metaphors From Advanced Placement Students, Dorothy Buerk

Humanistic Mathematics Network Journal

No abstract provided.

Transparadigm Mathematics Research Initiative, EleméR E. Rosinger

Humanistic Mathematics Network Journal

No abstract provided.

Report On Work At Brunel University, Anthony Briginshaw

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Its Application, Jack V. Wales Jr.

Humanistic Mathematics Network Journal

No abstract provided.

A Simple Test For The Nth Term Of A Series To Approach Zero, Jonathan W. Lewin, Myrtle Lewin

Faculty Articles

No abstract provided.

The Compensatory Bargaining Set Of A Cooperative N-Person Game With Side Payments, Irinel C. Dragan

Mathematics Technical Papers

The bargaining sets have been introduced as solution concepts for cooperative n-person games with side payments by R. J. Aumann and M. Maschler (1964). A further study on the relationships between various concepts of solution for such games is due to R. J. Aumann and J. Dreze (1975). The Aumann/Maschler definition of a bargaining set relies upon a stability principle imposed to the payoffs in this set: an admissible payoff belongs to a bargaining set if for every objection against this payoff there is a counter objection. Two modification of the stability principle have been discussed in earlier papers of …