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Full-Text Articles in Physical Sciences and Mathematics

Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn Aug 1989

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 Jul 1989

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 …


Nonnegative Solutions For A Class Of Radially Symmetric Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji Jul 1989

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.


Beauty In Mathematics: Some Theological Implications, David L. Neuhouser Jun 1989

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.


A Course On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke Jun 1989

A Course On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke

ACMS Conference Proceedings 1989

The January interim term at Calvin College provides an opportunity for developing and teaching courses outside a normal major program. As a result faculty members are frequently given the interim off to provide time for research and development of new courses. In 1987 we were given such a leave in order to pursue the questions of the relationship between mathematics and the Christian Faith. One result was our presentation at the 1987 Association of Christians in the Mathematical Sciences conference. Immediately thereafter we began to develop a specific interim course based on our studies. We offered the course during the …


The Mathematical Intelligencer, Dmitrii Egorov: Mathematics And Theology In Russia, Charles E. Ford Jun 1989

The Mathematical Intelligencer, Dmitrii Egorov: Mathematics And Theology In Russia, Charles E. Ford

ACMS Conference Proceedings 1989

This paper tells the story of Russian mathematician Dmitri Egorov, recounting his faith and contributions to the field of mathematics.


The Bisexual Galton-Watson Branching Process, David M. Hull Jun 1989

The Bisexual Galton-Watson Branching Process, David M. Hull

ACMS Conference Proceedings 1989

I would like to present the bisexual Galton-Watson branching process. The word "bisexual" indicates that we will be considering a population of two sexes--which will be designated as the usual male and female. Here is a brief overview of what I would like to cover.

  1. The bisexual process motivated: why is it needed?
  2. The standard Galton-Watson branching process.
  3. The state of affairs regarding two-sex models.
  4. The nuts and bolts of the bisexual Galton-Watson branching process (parameters defined and how it works).
  5. A review of published bisexual results to date.
  6. What is to come?


Newton And Saccheri: Case Studies In The Interplay Of Mathematics And Religion, Tommy Leavelle Jun 1989

Newton And Saccheri: Case Studies In The Interplay Of Mathematics And Religion, Tommy Leavelle

ACMS Conference Proceedings 1989

In the course of this paper I will try to present to you the basic facts and some of the subsequent assessments of the life and work of two mathematicians for whom the interplay of mathematics and religion was influential: Issac Newton and Girolamo Saccheri.


A Tutorial On Prolog, Russell C. Bjork Jun 1989

A Tutorial On Prolog, Russell C. Bjork

ACMS Conference Proceedings 1989

PROLOG is a programming language based on the use of mathematical logic—specifically the first order predicate calculus. The name is a contraction for “Programming in Logic”. PROLOG was developed in 1972 by Phillippe Roussel of the AI Group (Groupe d’Intelligence Artificielle) of the University of Marseille. Specifically, it is an outgrowth of research there on automatic theorem proving. PROLOG has been widely used by AI researchers in Europe and Japan. In fact, the Japanese have made it the basis for the software side of their “Fifth Generation” computer project. PROLOG is currently used in a wide variety of areas, not …


Agustine's Mathematical Realism, Paul J. Zwier Jun 1989

Agustine's Mathematical Realism, Paul J. Zwier

ACMS Conference Proceedings 1989

After a review of Philip Kitcher's argument against Mathematical Realism, this paper presents the case for Mathematical Realism by looking at the life and writings of Saint Augustine.


Simulated Annealing On Np-Complete Problems, Russell W. Howell Jun 1989

Simulated Annealing On Np-Complete Problems, Russell W. Howell

ACMS Conference Proceedings 1989

The Random House Dictionary defines anneal as " ... to free (glass, metals, etc.) from internal stress by heating and gradually cooling." In the physical world, impurities are annealed out of a substance by heating it to a high temperature. As it is cooled, its molecular structure gradually settles into a stable "low-energy" configuration. It is important to cool the substance slowly, especially at lower temperatures, so that impurities do not get "frozen" into place. With careful cooling, a low-energy state can eventually be reached. This state may not be the one with the lowest potential energy, where the spins …


Introduction (1989), Gene B. Chase Jun 1989

Introduction (1989), Gene B. Chase

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor


Schedule (1989), Association Of Christians In The Mathematical Sciences Jun 1989

Schedule (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor


Table Of Contents (1989), Association Of Christians In The Mathematical Sciences May 1989

Table Of Contents (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor


Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng May 1989

Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng

Department of Mathematics: Faculty Publications

A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.


Some Estimates For Finite Difference Approximations, José-Luis Menaldi May 1989

Some Estimates For Finite Difference Approximations, José-Luis Menaldi

Mathematics Faculty Research Publications

Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.


On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin Jan 1989

On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.


Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn Jan 1989

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.


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 Jan 1989

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.


Viscous Cross-Waves: An Analytical Treatment, Andrew J. Bernoff, L. P. Kwok, Seth Lichter Jan 1989

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 …


Turnpike Structures For Optimal Maneuvers, Arthur T. Benjamin Jan 1989

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 …


Nonnegative Solutions To A Semilinear Dirichlet Problem In A Ball Are Positive And Radially Symmetric, Alfonso Castro, Ratnasingham Shivaji Jan 1989

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.


Weak Bipolarizable Graphs, Stephan Olariu Jan 1989

Weak Bipolarizable Graphs, Stephan Olariu

Computer Science Faculty Publications

We characterize a new class of perfectly orderable graphs and give a polynomial-time recognition algorithm, together with linear-time optimization algorithms for this class of graphs.


Report On The Application Of An Evapotranspiration Equation To The Waca Dome, P R. Scott Jan 1989

Report On The Application Of An Evapotranspiration Equation To The Waca Dome, P R. Scott

Resource management technical reports

No abstract provided.