Physical Sciences and Mathematics Commons^™

Editorial, Issue 4, 1989, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Front Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

Pumps, Filters, And Lenses; Humanistic Issues In Calculus Reform, Dan Kalman

Humanistic Mathematics Network Journal

No abstract provided.

Reflections On Attending Three Contributed Paper Sessions On Humanistic Mathematics In Phoenix 1989, Peter Flusser

Humanistic Mathematics Network Journal

No abstract provided.

The Visits Of Hassler Whitney To Brazil: Hassler Whitney, In Memoriam, Ubiratan D'Ambrosio

Humanistic Mathematics Network Journal

No abstract provided.

Hassler Whitney 1907-1989: Some Recollections, 1979·1989, Anneli Lax

Humanistic Mathematics Network Journal

No abstract provided.

Lessons From Cognitive Theory For Teaching Mathematical Modeling To Freshmen, Richard H. Elderkin

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

Education Is For The Students' Future, Hassler Whitney

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.

Tapping Creativity And Ingenuity Of Liberal Arts Majors In A Math Course, Helen Christensen

Humanistic Mathematics Network Journal

No abstract provided.

Back Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

An Empowering, Participatory Research Model For Humanistic Mathematics Pedagogy, Arthur B. Powell, Dawud A. Jeffries, Aleshia E. Selby

Humanistic Mathematics Network Journal

No abstract provided.

Prophet Inequalities For Parallel Processes, Theodore P. Hill, D. P. Kennedy

Research Scholars in Residence

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then E(sup X_i,j) ≤ (n + 1) max sup {E(X_i,t): t is a stop rule for X_i,1, X_i,2, ...} and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.

Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson

Faculty Publications

The study of ordinary differential equations has long been a staple in mathematics at both the undergraduate and graduate levels. Recently, instruction in the study of difference equations has widened, primarily due to the expanded role of the digital computer in mathematics. The two topics are inextricably linked at all levels, from elementary techniques through current research questions. Pursuing the analogies between these fields of study can only deepen the understanding of each. In particular, the study of many elementary topics in difference equations, requiring not even the use of calculus, can serve as a founda- tion for intuition and …

Mat 751 Algebraic Topology I - Fall '89, David Handel

Mathematics Faculty Research Publications

A collection of notes for the course Mat 751, Algebraic Topology I, prepared by Professor David Handel of the Wayne State University Mathematics Department. The notes include examples, exercises, and additional lecture notes on related concepts.

On Minimal Triangle-Free 5-Chromatic Graphs, Charles M. Grinstead, Matthew H. Katinsky , '87, David William Van Stone , '88

Mathematics & Statistics Faculty Works

No abstract provided.

Definitizable Extensions Of Positive Symmetric Operators In A Krein Space, Branko Ćurgus

Mathematics Faculty Publications

The Friedrichs extension and the Krein extension of a positive operator in a Krein space are characterized in terms of their spectral functions in a Krein space.

Optimal-Partitioning Inequalities In Classification And Multi-Hypotheses Testing, Theodore P. Hill, Y. L. Tong

Research Scholars in Residence

Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions. Bounds for general (including discontinuous) distributions are also obtained.

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 …

Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn

Mathematics and Statistics Faculty Publications

The number of spatial critical points is nonincreasing in time, for positive, analytic solutions of a scalar, nonlinear, parabolic partial differential equation in one space dimension. While proving this, we answer the question: What happens to a critical point which loses simplicity?

On The Dimension Of Bivariate Superspline Spaces, Tian-Xiao He

Scholarship

A bivariate piecewise polynomial function of total degree d on some grid partition △ that has rth order continuous partial derivatives everywhere may have higher-order partial derivatives at the vertices of the grid partition. In finite element considerations and in the construction of vertex splines, it happens that only those functions with continuous partial derivatives of order higher than r at the vertices are needed to give the same full approximation order as the entire space of piecewise polynomials. This is certainly the case for d > 4r + 1. Such piecewise polynomial functions are called supersplines. This paper is devoted …

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.

Best Approximation With Geometric Constraints, Yuesheng Xu

Mathematics & Statistics Theses & Dissertations

This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best L_p approximation to a function in L_p (0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.

On The Dimension Of Bivariate Superspline Spaces, Tian-Xiao He

Tian-Xiao He

A bivariate piecewise polynomial function of total degree d on some grid partition △ that has rth order continuous partial derivatives everywhere may have higher-order partial derivatives at the vertices of the grid partition. In finite element considerations and in the construction of vertex splines, it happens that only those functions with continuous partial derivatives of order higher than r at the vertices are needed to give the same full approximation order as the entire space of piecewise polynomials. This is certainly the case for d > 4r + 1. Such piecewise polynomial functions are called supersplines. This …

Contribution To The Theory Of Stochastic Games., Sagnik Sinha Dr.

Doctoral Theses

A mathematical theory of Games of Strategy was born in several stages between 1928 and 1941. John von Neumann is known as its father. The culmination of the pioneering work of von Neumann and Morgenstern was the publication of the Theory of Games and Economic Behavior (Ref.28] in 1944. Ik is snid of the book . posterity may regard this book as one of the major scientifie achievements of the first half of the twentieth century. Emphasizing a new approach to competetive behaviour through a mathematical reduction to suitable games of strategy, this giant work laid bare a host of …

Beauty In Mathematics: Some Theological Implications, David L. Neuhouser

ACMS Conference Proceedings 1989

It may come as a surprise to some that science or mathematics could be considered beautiful, but many prominent sciences and mathematicians from around the world have made such claims. Furthermore, the beauty of mathematics and order of the universe inspired some of the greatest developments in science and mathematics. This paper examines the beauty of mathematics and what scientists and other individuals have said about the subject.