Mathematics Commons^™

Pdp/Academic Excellence Workshops In Mathematics, M. Catharine Hudspeth

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics Appreciation: A Humanities Course, Thomas L. Bartlow

Humanistic Mathematics Network Journal

No abstract provided.

Introducing Undergraduates To Mathematics Information Resources, Sallie H. Barringer

Humanistic Mathematics Network Journal

No abstract provided.

Abstracts Of All Papers Presented At The Humanistic Mathematics Sessions In Phoenix 1989

Humanistic Mathematics Network Journal

No abstract provided.

Back Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball With Jumping Nonlinearities, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

Let p,φ :[0,T] → R be bounded functions with φ > 0. Let g:R → R be a locally Lipschitzian function satisfying the superlinear jumping condition:

(i) lim u → - ∞ (g(u)/u) ε R

(ii) lim u → ∞ (g(u)/(u^{1 + ρ} )) = ∞ for some ρ > 0, and

(iii) lim u → ∞ (u/g(u))^N/2(NG(κ u) - ((N - 2)/2)u · g(u)) = ∞ for some κ ε (0,1] where G is the primitive of g.

Here we prove that the number of solutions of the boundary value problem Δu + g(u) = p(|x|) + cφ …

Review: J.R. Porter And R.G. Woods, Extensions And Absolutes Of Hausdorff Spaces (New York, Berlin, Heidelberg, 1987), Melvin Henriksen

All HMC Faculty Publications and Research

Reviewed work: Jack R. Porter and R. Grant Woods. Extensions and absolutes of Hausdorff spaces. Springer-Verlag, New York, Berlin, Heidelberg, 1987, xiii + 856 pp., $89.00. ISBN 0-387-96212-3.

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.

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.

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 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.

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

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.

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.

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.

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.

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.

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 …

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

Humanistic Mathematics Network Journal

No abstract provided.

Readings In Mathematics Education, Harriet Edwards

Humanistic Mathematics Network Journal

No abstract provided.

Foundational Studies And Mathematics Teaching, Allan Muir

Humanistic Mathematics Network Journal

No abstract provided.

Excerpts From And Inserts Into My January 23 Talk At The Mathematics As A Humanistic Discipline Session, Anneli Lax

Humanistic Mathematics Network Journal

No abstract provided.

Cognitive Science Studies Of Mathematical Thought, Robert B. Davis

Humanistic Mathematics Network Journal

No abstract provided.