Digital Commons Network^™

The Automorphism Groups Of The Hyperelliptic Surfaces, Curtis Bennett, Rick Miranda

Mathematics, Statistics and Data Science Faculty Works

In this paper, the automorphism groups of the seven classes of the so- called hyperelliptic surfaces are calculated. Writing these as (E×F)/G, where E and F are elliptic curves and G is a finite group of translations of E acting on F not only as translations, covering space theory is then used to calculate the automorphisms. Letting M be the centralizer of G in Aut(E)×Aut(F), it is then noted that in all cases M is generated by its E-translations, its F-translations, its E- automorphisms, and its F-automorphisms. Finally, two tables list the automorphism groups …

Density Continuity Versus Continuity, Krzysztof Ciesielski

Faculty & Staff Scholarship

Real-valued functions of a real variable which are continuous with respect to the density topology on both the domain and the range are called density continuous. A typical continuous function is nowhere density continuous. The same is true of a typical homeomorphism of the real line. A subset of the real line is the set of points of discontinuity of a density continuous function if and only if it is a nowhere dense F_\sigma set. The corresponding characterization for the approximately continuous functions is a first category F_\sigma set. An alternative proof of that result is given. Density …

The Linear Least Squares Problem Of Bundle Adjustment, Joseph Walker Woodard

UNF Graduate Theses and Dissertations

A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most …

An Extension Of Essentially Non-Oscillatory Shock-Capturing Schemes To Multi-Dimensional Systems Of Conservation Laws, Jay Casper

Mathematics & Statistics Theses & Dissertations

In recent years, a class of numerical schemes for solving hyperbolic partial differential equations has been developed which generalizes the first-order method of Godunov to arbitrary order of accuracy. High-order accuracy is obtained, wherever the solution is smooth, by an essentially non-oscillatory (ENO) piecewise polynomial reconstruction procedure, which yields high-order pointwise information from the cell averages of the solution at a given point in time. When applied to piecewise smooth initial data, this reconstruction enables a flux computation that provides a time update of the solution which is of high-order accuracy, wherever the function is smooth, and avoids a Gibbs …

Bivariate C1 Quadratic Finite Elements And Vertex Splines, Tian-Xiao He

Scholarship

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.

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.

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

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.

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.

Front Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

Editorial, Issue 4, 1989, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Education Is For The Students' Future, Hassler Whitney

Humanistic Mathematics Network Journal

No abstract provided.

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.

Local Molecular Temperature, Donald Greenspan

Mathematics Technical Papers - Archive

For the study of phase-transition by molecular dynamics, the concept of local temperature is desirable. Such a concept, defined and studied previously for atoms, is extended in this paper to molecules. The fundamental formula involves Planck's constant, not Boltzmann's. Related dynamical calculations are described for approximating, theoretically, the melting points of N2, 02, CO, NO, and CH4, and the results are compared with those available experimentally.

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.

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.

Local Atomic Temperature, Donald Greenspan

Mathematics Technical Papers - Archive

For the study of phase-transition by molecular dynamics, the concept of local temperature is desirable. Such a concept is defined and studied in this paper. From computer studies of tetrahedral arrangements of four atoms, the constant which results in the formulation is Planck's constant, not Boltzmann's. Related dynamical calculations reveal that the approach yields good approximations for the melting point of the Noble gases, copper and alpha-iron.

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.

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 …

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.

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?

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.