Physical Sciences and Mathematics Commons^™

Nonnegative Solutions For A Class Of Radially Symmetric Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the existence of radially symmetric non-negative solutions for the boundary value problem

\begin{displaymath}\begin{array}{*{20}{c}} { - \Delta u(x) = \lambda f(u(x))\qua... ...\\ {u(x) = 0\quad \left\Vert x \right\Vert = 1} \\ \end{array} \end{displaymath}

where $ \lambda > 0,f(0) < 0$ (non-positone), $ f' \geq 0$ and $ f$ is superlinear. We establish existence of non-negative solutions for $ \lambda $ small which extends some work of our previous paper on non-positone problems, where we considered the case $ N = 1$. Our work also proves a recent conjecture by Joel Smoller and Arthur Wasserman.

Γ To X Transport Of Photoexcited Electrons In Type Ii Gaas/Alas Multiple Quantum Well Structures, Peter N. Saeta, John F. Federici, R. J. Fischer, Benjamin I. Greene, L. Pfeiffer, R. C. Spitzer, B. A. Wilson

All HMC Faculty Publications and Research

We report novel femtosecond time‐resolved measurements performed on staggered type II GaAs/AlAs multiple quantum well structures. Photoexcited electrons were determined to transfer from the Γ valley of the GaAs layers to the X valleys of the AlAs in 100 and 400 fs for 8‐ and 11‐monolayer‐thick GaAs samples, respectively.

The Prey Of Common Barn Owls (Tyto Alba) In Dry Limestone Scrub Forest Of Southern Jamaica, Donald A. Mcfarlane, Kimball L. Garrett

WM Keck Science Faculty Papers

A collection of common barn-owl (Tyto alba Scopoli) pellets from caves on the Portland Ridge of Jamaica reveals that whereas introduced rodents constitute approximately 90% of the total prey, bats and birds are also frequent prey items. Of the bats, frugivorous species predominate with Ariteus flavescens Gray and Artibeus jamaicensis Leach accounting for the largest portion of the bat prey. Insectivorous bats are markedly under-represented with respect to the known diversity of insectivorous species in the habitat.

Viscous Cross-Waves: An Analytical Treatment, Andrew J. Bernoff, L. P. Kwok, Seth Lichter

All HMC Faculty Publications and Research

Viscous effects on the excitation of cross‐waves in a semi‐infinite box of finite depth and width are considered. A formalism using matched asymptotic expansions and an improved method of computing the solvability condition is used to derive the relative contributions of the free‐surface, sidewall, bottom, and wavemaker viscous boundary layers. This analysis yields an expression for the damping coefficient previously incorporated on heuristic grounds. In addition, three new contributions are found: a viscous detuning of the resonant frequency, a slow spatial variation in the coupling to the progressive wave, and a viscous correction to the wavemaker boundary condition. The wavemaker …

Continuum Model Of Thin-Film Deposition And Growth, Andrew J. Bernoff, Seth Lichter

All HMC Faculty Publications and Research

A continuum theory for the deposition and growth of solid films is presented. The theory is developed in a coordinate-independent manner and so incorporates the fully nonlinear physics. The evolution of the film is modeled in three steps. First, the adsorption of atoms in the incident beam is modeled as a ballistic process. Second, the random motion of the adatoms is treated as a diffusive process. Finally, sticking of adatoms to the film occurs as a Poisson process. The resulting system of differential equations is examined in several parameter limits. The diffusively dominated limit appears similar to zone 1 of …

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 …

A Theoretical Study Of Models For X2y2 Zintl Ions, Robert J. Cave, Ernest R. Davidson, Philippe Sautet, Enric Canadell, Odile Eisenstein

All HMC Faculty Publications and Research

Ab initio and extended Hückel calculations have been used to discuss the bonding scheme in X₂Y₂ neutral and ionic main group clusters. A qualitative analysis suggests that two different electron counts, 20 and 22, are possible for the butterfly structures of these systems. This results from two orbital crossings in the correlation diagram for the tetrahedral (T_d) -> butterfly (C_2v) -> square-planar (D_2h) transformation. Detailed ab initio computations substantiate this analysis and show that the 20-electron butterfly structure becomes increasingly favored over the tetrahedral one in X₂Y₂ clusters when the 2 atoms have increasing electronegativity difference. …

Nonnegative Solutions To A Semilinear Dirichlet Problem In A Ball Are Positive And Radially Symmetric, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We prove that nonnegative solutions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular, this answers a question in [3] where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the domain which ensures that nonnegative solutions are positive in the interior.

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.

Quasidegenerate Variational Perturbation Theory And The Calculation Of First‐Order Properties From Variational Perturbation Theory Wave Functions, Robert J. Cave, Ernest R. Davidson

All HMC Faculty Publications and Research

In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly more …

The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner

Pitzer Faculty Publications and Research

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.

Implementing Educational Software And Evaluating Its Academic Effectiveness: Part Ii, Karen Jolicoeur, Dale E. Berger

CGU Faculty Publications and Research

In Part I, published last month, we presented a successful classroom implementation plan for integrating educational software into elementary school classrooms. Implementing educational software successfully into classrooms is an essential prerequisite to achieving the second goal of the present research-evaluating how much students learned by using specific software programs. In Part II, we will measure how effective eight software programs were at teaching fifth grade students new fraction concepts and spelling words. In addition, we will examine the validity of teacher and student software ratings based on the effectiveness of each program.

The Space Of Minimal Prime Ideals Of C(X) Need Not Be Basically Disconnected, Alan Dow, Melvin Henriksen, Ralph Kopperman, J. Vermeer

All HMC Faculty Publications and Research

Problems posed twenty and twenty-five years ago by M. Henriksen and M. Jerison are solved by showing that the space of minimal prime ideals of the ring C(X) of continuous real-valued functions on a compact (Hausdorff) space need not be basically disconnected-or even an F-space.

Implementing Educational Software And Evaluating Its Academic Effectiveness: Part I, Karen Jolicoeur, Dale E. Berger

CGU Faculty Publications and Research

Two major obstacles are responsible for the delay in getting good educational software into schools. First, software implementation is a complex process that many schools are simply not prepared to undertake. Second, there is very little empirical research available on the specific factors that make educational software effective, leaving it extremely difficult to separate good from poor quality software. We will describe a basic plan for implementing educational software into classrooms, incorporating a research design that permits educational researchers to measure the effectiveness of the software. Part I of this series of two articles presents a basic plan for implementing …

Multiple Solutions For A Dirichlet Problem With Jumping Nonlinearities Ii, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article.

Locally Finite Families, Completely Separated Sets And Remote Points, Melvin Henriksen, Thomas J. Peters

All HMC Faculty Publications and Research

It is shown that if X is a nonpseudocompact space with a σ-locally finite π-base, then X has remote points. Within the class of spaces possessing a σ-locally finite π-base, this result extends the work of Chae and Smith, because their work utilized normality to achieve complete separation. It provides spaces which have remote points, where the spaces do not satisfy the conditions required in the previous works by Dow, by van Douwen, by van Mill, or by Peters.

The lemma: "Let X be a space and let {Cε: € < α} be a locally finite family of cozero sets of X. Let {Zε: € < α } be a family of zero sets of X such that for each € < α, Zε с Cε. Then ∪_ε<α Zε is completely separated from X/∪εCε", is a fundamental …

Hylleraas Variational Perturbation Theory: Application To Correlation Problems In Molecular Systems, Robert J. Cave, Ernest R. Davidson

All HMC Faculty Publications and Research

Hylleraas variational perturbation theory is applied through second order in energy to estimate the correlation energy in several molecular systems. The specific choices for H₀ and V which are made lead to equations nearly identical to the multireference linearized coupled‐cluster method of Laidig and Bartlett. The results obtained are in virtually exact agreement where comparisons have been made. Results from test calculations are presented for BeH₂, CH₂, and C₂H₄. In addition, the utility of perturbation theory for selecting correlating configurations is examined. This procedure is found to be quite accurate while …

Letter From The Editor, Issue 2, 1988, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

I'Ll Carry My Coals Where They're Needed, Professor Henriksen, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Please Carry Your Coals To Where They Are Needed, Professor Stein, Melvin Henriksen

Humanistic Mathematics Network Journal

No abstract provided.